diff --git a/.gitattributes b/.gitattributes new file mode 100644 index 0000000..dfe0770 --- /dev/null +++ b/.gitattributes @@ -0,0 +1,2 @@ +# Auto detect text files and perform LF normalization +* text=auto diff --git a/.github/workflows/main.yml b/.github/workflows/main.yml new file mode 100644 index 0000000..6ac38c0 --- /dev/null +++ b/.github/workflows/main.yml @@ -0,0 +1,193 @@ +name: Build LaTeX document + +on: + push: + pull_request: + types: + - closed + branches: + - master + + + +jobs: + build_latex: + runs-on: ubuntu-latest + steps: + - name: Set up Git repository + uses: actions/checkout@v2 + + - name: Compile LaTeX document Introduction + uses: xu-cheng/latex-action@master + with: + root_file: main.tex + working_directory: Slides/Introduction/ + + - name: Compile LaTeX document Stability + uses: xu-cheng/latex-action@master + with: + root_file: main.tex + working_directory: Slides/Stability/ + + - name: Compile LaTeX document Laplace + uses: xu-cheng/latex-action@master + with: + root_file: main.tex + working_directory: Slides/Laplace/ + + - name: Compile LaTeX document Bode + uses: xu-cheng/latex-action@master + with: + root_file: main.tex + working_directory: Slides/Bode/ + + - name: Compile LaTeX document Control + uses: xu-cheng/latex-action@master + with: + root_file: main.tex + working_directory: Slides/Control/ + + - name: Compile LaTeX document Discrete + uses: xu-cheng/latex-action@master + with: + root_file: main.tex + working_directory: Slides/Discrete/ + + - name: Compile LaTeX document LyapunovTheory + uses: xu-cheng/latex-action@master + with: + root_file: main.tex + working_directory: Slides/LyapunovTheory/ + + - name: Compile LaTeX document HJB_LQR + uses: xu-cheng/latex-action@master + with: + root_file: main.tex + working_directory: Slides/HJB_LQR/ + + - name: Compile LaTeX document Observer + uses: xu-cheng/latex-action@master + with: + root_file: main.tex + working_directory: Slides/Observer/ + + - name: Compile LaTeX document ControllabilityObservability + uses: xu-cheng/latex-action@master + with: + root_file: main.tex + working_directory: Slides/ControllabilityObservability/ + + - name: Compile LaTeX document Kalman + uses: xu-cheng/latex-action@master + with: + root_file: main.tex + working_directory: Slides/Kalman/ + + - name: Compile LaTeX document Linearization + uses: xu-cheng/latex-action@master + with: + root_file: main.tex + working_directory: Slides/Linearization/ + + + + + + + - name: Save Introduction artifact + uses: actions/upload-artifact@v1 + with: + name: Introduction.pdf + path: Slides/Introduction/main.pdf + + - name: Save Stability artifact + uses: actions/upload-artifact@v1 + with: + name: Stability.pdf + path: Slides/Stability/main.pdf + + - name: Save Laplace artifact + uses: actions/upload-artifact@v1 + with: + name: Laplace.pdf + path: Slides/Laplace/main.pdf + + - name: Save Bode artifact + uses: actions/upload-artifact@v1 + with: + name: Bode.pdf + path: Slides/Bode/main.pdf + + - name: Save Control artifact + uses: actions/upload-artifact@v1 + with: + name: Control.pdf + path: Slides/Control/main.pdf + + - name: Save Discrete artifact + uses: actions/upload-artifact@v1 + with: + name: Discrete.pdf + path: Slides/Discrete/main.pdf + + - name: Save LyapunovTheory artifact + uses: actions/upload-artifact@v1 + with: + name: LyapunovTheory.pdf + path: Slides/LyapunovTheory/main.pdf + + - name: Save HJB_LQR artifact + uses: actions/upload-artifact@v1 + with: + name: HJB_LQR.pdf + path: Slides/HJB_LQR/main.pdf + + - name: Save Observer artifact + uses: actions/upload-artifact@v1 + with: + name: Observer.pdf + path: Slides/Observer/main.pdf + + - name: Save ControllabilityObservability artifact + uses: actions/upload-artifact@v1 + with: + name: ControllabilityObservability.pdf + path: Slides/ControllabilityObservability/main.pdf + + - name: Save Kalman artifact + uses: actions/upload-artifact@v1 + with: + name: Kalman.pdf + path: Slides/Kalman/main.pdf + + - name: Save Linearization artifact + uses: actions/upload-artifact@v1 + with: + name: Linearization.pdf + path: Slides/Linearization/main.pdf + + + + - name: Update compiled PDFs in git repository + if: github.event.pull_request.merged == true || github.event_name == 'push' + run: | + git config --global user.name 'CI PDF compiler' + git config --global user.email '<>' + git add Slides/Introduction/main.pdf + git add Slides/Stability/main.pdf + git add Slides/Laplace/main.pdf + git add Slides/Bode/main.pdf + git add Slides/Control/main.pdf + git add Slides/Discrete/main.pdf + git add Slides/LyapunovTheory/main.pdf + git add Slides/HJB_LQR/main.pdf + git add Slides/Observer/main.pdf + git add Slides/ControllabilityObservability/main.pdf + git add Slides/Kalman/main.pdf + git add Slides/Linearization/main.pdf + + + + + git commit -m "Update compiled PDFs" + git push diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..5780b4b --- /dev/null +++ b/.gitignore @@ -0,0 +1,8 @@ +*.gz +*.aux +*.log +*.out +*.nav +*.snm +*.toc +*.vrb diff --git a/Assignment/Assignment1.ipynb b/Assignment/Assignment1.ipynb new file mode 100644 index 0000000..cd33236 --- /dev/null +++ b/Assignment/Assignment1.ipynb @@ -0,0 +1,389 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "provenance": [] + }, + "kernelspec": { + "display_name": "Python 3", + "name": "python3" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "zVZdDu7VjMqg" + }, + "source": [ + "# From linear ODE to State Space\n", + "\n", + "Given an ODE:\n", + "\n", + "$$a_{k}y^{(k)} +a_{k-1}y^{(k-1)}+...+a_{2}\\ddot y+a_{1}\\dot y + a_0 y= b_0$$\n", + "\n", + "find its state space representation:\n", + "\n", + "$$\\dot x = Ax + b$$\n", + "\n", + "## Process\n", + "\n", + "The first step is to express higher derivatives\n", + "\n", + "Step 1.1:\n", + "\n", + "$$y^{(k)} + \n", + "\\frac{a_{k-1}}{a_{k}}y^{(k-1)}+\n", + "...+\n", + "\\frac{a_{2}}{a_{k}}\\ddot y+\n", + "\\frac{a_{1}}{a_{k}}\\dot y + \n", + "\\frac{a_{0}}{a_{k}} y = \n", + "\\frac{b_0}{a_{k}}$$\n", + "\n", + "Step 1.2:\n", + "\n", + "$$y^{(k)} = \n", + "-\\frac{a_{k-1}}{a_{k}}y^{(k-1)}-\n", + "...-\n", + "\\frac{a_{2}}{a_{k}}\\ddot y -\n", + "\\frac{a_{1}}{a_{k}}\\dot y - \n", + "\\frac{a_{0}}{a_{k}} y + \n", + "\\frac{b_0}{a_{k}}$$\n", + "\n", + "Second step s introduction of new variables $x$:\n", + "\n", + "Step 2.1:\n", + "\n", + "$$x_k = y^{(k-1)} \\\\\n", + " x_{k-1} = y^{(k-2)} \\\\\n", + " ... \\\\\n", + " x_1 = y$$\n", + "\n", + "Step 2.2:\n", + "$$\\dot x_1 = x_2 \\\\\n", + "\\dot x_2 = x_3 \\\\\n", + "... \\\\\n", + "\\dot x_k = \n", + "-\\frac{a_{k-1}}{a_{k}}x_k-\n", + "...-\n", + "\\frac{a_{2}}{a_{k}} x_3 -\n", + "\\frac{a_{1}}{a_{k}} x_2 - \n", + "\\frac{a_{0}}{a_{k}} x_1 + \n", + "\\frac{b_0}{a_{k}}$$\n", + "\n", + "Finally, we write it in a matrix form." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "sk9IEZJg2cS_" + }, + "source": [ + "# Tasks 1.1: ODE to State Space conversion\n", + "\n", + "Convert to State Space represantation and to a transfer function representation\n", + "\n", + "Variant 1:\n", + "* $10 y^{(4)} -7 y^{(3)} + 2 \\ddot y + 0.5 \\dot y + 4y = 15 u$\n", + "* $5 y^{(4)} -17 y^{(3)} - 3 \\ddot y + 1.5 \\dot y + 2y = 25 u$\n", + "\n", + "Variant 2:\n", + "* $5 y^{(4)} -17 y^{(3)} - 1.5 \\ddot y + 100 \\dot y + 1.1y= 45 u$\n", + "* $1.5y^{(4)} -23 y^{(3)} - 2.5 \\ddot y + 0.1 \\dot y + 100y= -10 u$\n", + "\n", + "# Task 1.2\n", + "\n", + "Convert the following to a second order ODE and to a transfer function representation:\n", + "\n", + "Variant 1:\n", + "$$\\dot x = \n", + "\\begin{pmatrix} 1 & 0 \\\\ -5 & -10\n", + "\\end{pmatrix}\n", + "x\n", + "+ \\begin{pmatrix} 0 \\\\ 1\n", + "\\end{pmatrix} u\n", + "$$\n", + "$$\\dot x = \n", + "\\begin{pmatrix} 0 & 8 \\\\ 1 & 3\n", + "\\end{pmatrix}\n", + "x\n", + "+ \\begin{pmatrix} 0 \\\\ 1\n", + "\\end{pmatrix} u\n", + "$$\n", + "\n", + "Variant 2:\n", + "$$\\dot x = \n", + "\\begin{pmatrix} 0 & 8 \\\\ 6 & 0\n", + "\\end{pmatrix}\n", + "x\n", + "+ \\begin{pmatrix} 0 \\\\ 1\n", + "\\end{pmatrix} u\n", + "$$\n", + "$$\\dot x = \n", + "\\begin{pmatrix} 0 & 1 \\\\ 6 & 3\n", + "\\end{pmatrix}\n", + "x\n", + "+ \\begin{pmatrix} 0 \\\\ 1\n", + "\\end{pmatrix} u\n", + "$$\n", + "\n", + "For all of the above, $$y = \\begin{pmatrix} 1 & 0 \\end{pmatrix} x$$ \n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "68FDuYjmAw_S" + }, + "source": [ + "# Solve ODE\n", + "\n", + "Below is an example of how one can solve and ODE in Python" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "7U4i-VI8jQsm" + }, + "source": [ + "import numpy as np\n", + "from scipy.integrate import odeint\n", + "\n", + "n = 4\n", + "A = np.array([[0, 1, 0], [0, 0, 1], [-10, -5, -2]])\n", + "\n", + "# x_dot from state space\n", + "def StateSpace(x, t):\n", + " return A.dot(x)# + B*np.sin(t)\n", + "\n", + "time = np.linspace(0, 1, 1000) \n", + "x0 = np.random.rand(n-1) # initial state\n", + "\n", + "solution = {\"SS\": odeint(StateSpace, x0, time)}\n", + "\n", + "import matplotlib.pyplot as plt\n", + "\n", + "plt.subplot(121)\n", + "plt.plot(time, solution[\"SS\"])\n", + "plt.xlabel('time')\n", + "plt.ylabel('x(t)')\n", + "\n", + "plt.show()" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "PYXA8KSmm9do" + }, + "source": [ + "## Task 1.3 Implement Euler Integration or Runge-Kutta Integration scheme, solve the equation from the Task 1 using it." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "ufR3L7_eC6x-" + }, + "source": [ + "# Task 2.1, convert to state space and simulate\n", + "\n", + "Variant 1:\n", + "* $10 y^{(5)} + 10 y^{(4)} -7 y^{(3)} + 2 \\ddot y + 0.5 \\dot y + 4y = 0$\n", + "* $1 y^{(5)} + 5 y^{(4)} -17 y^{(3)} - 3 \\ddot y + 1.5 \\dot y + 2y = \\sin(t)$\n", + "\n", + "Variant 2:\n", + "* $22 y^{(5)} + 5 y^{(4)} -17 y^{(3)} - 1.5 \\ddot y + 100 \\dot y + 1.1y= 0$\n", + "* $-10 y^{(5)} + 1.5y^{(4)} -23 y^{(3)} - 2.5 \\ddot y + 0.1 \\dot y + 100y= \\sin(t)$\n", + "\n", + "## Subtask 2.3 Mass-spring-damper system\n", + "\n", + "Find or derive equations for a mass-spring-damper system with mass 10kg, spring stiffness of 1000 N / m and damping coefficient 1 N s / m, write them in state-space and second order ODE forms, and simulate them." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "uMA0Cu1j9PHe" + }, + "source": [ + "# Task 3.1, Convert to transfer functions\n", + "\n", + "* \n", + "$\n", + "\\begin{cases}\n", + "\\ddot x + 0.5 \\dot x + 4y = u \\\\\n", + "y = 1.5 \\dot x + 6 x\n", + "\\end{cases}\n", + "$\n", + "\n", + "* \n", + "$\n", + "\\begin{cases}\n", + "10 \\ddot x + 1.5 \\dot x + 8y = 0.5u \\\\\n", + "y = 15 \\dot x + 16 x\n", + "\\end{cases}\n", + "$\n", + "\n", + "* \n", + "$\n", + "\\begin{cases}\n", + "\\ddot x + 2 \\dot x - 5y = u \\\\\n", + "y = 2.5 \\dot x - 7 x\n", + "\\end{cases}\n", + "$\n", + "\n", + "* \n", + "$\n", + "\\begin{cases}\n", + "\\ddot x + 22 \\dot x + 10y = 10u \\\\\n", + "y = 10.5 \\dot x + 11 x\n", + "\\end{cases}\n", + "$\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "wnJVPiHXtSDY" + }, + "source": [ + "# 4. Stability of an autonomous linear system\n", + "\n", + "Autonomous linear system is *stable*, iff the eigenvalues of its matrix have negative real parts. In other words, their should lie on the left half of the complex plane.\n", + "\n", + "Consider the system:\n", + "\n", + "$$\\dot x = \n", + "\\begin{pmatrix} -1 & 0.4 \\\\ -20 & -16\n", + "\\end{pmatrix}\n", + "x\n", + "$$\n", + "\n", + "Let us find its eigenvalues:" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "WDbYiXgBtQ4j", + "outputId": "c56a0d2b-6277-4930-e4f7-432b2752cbe4" + }, + "source": [ + "import numpy as np\n", + "from numpy.linalg import eig\n", + "\n", + "A = np.array([[-1, 0.4], [-20, -16]]) # state matrix\n", + "e, v = eig(A)\n", + "print(\"eigenvalues of A:\", e)" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "eigenvalues of A: [ -1.55377801 -15.44622199]\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "r0Ubzs_htXfw" + }, + "source": [ + "The eigenvalues are $\\lambda_1 = -1.55$ and $\\lambda_1 = -15.44$, both real and negative. Let us test those and show that the system's state converges:" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 279 + }, + "id": "o-al2c9ytdwB", + "outputId": "b5ce00f2-2e68-4e90-a911-ea100e03851a" + }, + "source": [ + "from scipy.integrate import odeint\n", + "import matplotlib.pyplot as plt\n", + "\n", + "def LTI(x, t):\n", + " return A.dot(x)\n", + "\n", + "time = np.linspace(0, 10, 1000) # interval from 0 to 10\n", + "x0 = np.random.rand(2) # initial state\n", + "\n", + "solution = odeint(LTI, x0, time)\n", + "\n", + "plt.plot(time, solution)\n", + "plt.xlabel('time')\n", + "plt.ylabel('x(t)')\n", + "plt.show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "cF2aes2Wtngd" + }, + "source": [ + "## Task 4.1. Find if the following autonomous linear systems are stable\n", + "\n", + "Variant 1:\n", + "$$\\dot x = \n", + "\\begin{pmatrix} 1 & 0 \\\\ -5 & -10\n", + "\\end{pmatrix}\n", + "x\n", + "$$\n", + "$$\\dot x = \n", + "\\begin{pmatrix} 0 & 8 \\\\ 1 & 3\n", + "\\end{pmatrix}\n", + "x\n", + "$$\n", + "\n", + "Variant 2:\n", + "$$\\dot x = \n", + "\\begin{pmatrix} 0 & 8 \\\\ 6 & 0\n", + "\\end{pmatrix}\n", + "x\n", + "$$\n", + "$$\\dot x = \n", + "\\begin{pmatrix} 0 & 1 \\\\ 6 & 3\n", + "\\end{pmatrix}\n", + "x\n", + "$$\n", + "\n", + "## Task 4.2 Simulate systems from 4.1, to show convergence.\n", + "## Task 4.3 Add a constant term to the equation and show via simulation how the point where the system converges changes (two examples are sufficient)." + ] + } + ] +} \ No newline at end of file diff --git a/Assignment/Assignment1.pdf b/Assignment/Assignment1.pdf new file mode 100644 index 0000000..8dbee78 Binary files /dev/null and b/Assignment/Assignment1.pdf differ diff --git a/Assignment/Assignment2.ipynb b/Assignment/Assignment2.ipynb new file mode 100644 index 0000000..eb23ee7 --- /dev/null +++ b/Assignment/Assignment2.ipynb @@ -0,0 +1,83 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "provenance": [] + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# Task\n", + "\n", + "Given a system:\n", + "\n", + "\n", + "\n", + "$$ \n", + "\\begin{cases}\n", + "\\dot x = \n", + "\\begin{bmatrix} \n", + "0 & 0 & 1 & 0 \\\\\n", + "0 & 0 & 0 & 1 \\\\\n", + " n & -2 & -10/n & -2 \\\\\n", + "-5 & -n/10 & 0 & -3\n", + "\\end{bmatrix}\n", + "x\n", + "+ \n", + "\\begin{bmatrix} \n", + "0 \\\\\n", + "0 \\\\\n", + "-1\\\\\n", + "1\n", + "\\end{bmatrix}\n", + "u \\\\\n", + "y = \\begin{bmatrix} \n", + "1 & 1 & 0 & 0\n", + "\\end{bmatrix} x\n", + "\\end{cases}\n", + "$$\n", + "\n", + "where $n$ is your number in your group list (ask your TA to give you your number if you don't have one).\n", + "\n", + "\n", + "\n", + "1. Find its transfer function representation ($y(s) / u(s) = W(s)$).\n", + "1. Propose an ODE representation of the system.\n", + "1. Propose a controller (control law $u = -Kx$) that makes the system stable. Do it via pole placement and as an LQR. For LQR show the cost function you chose.\n", + "1. Show stability of the closed-loop system via eigenvalue analysis.\n", + "1. Find stability margins by analysing Bode diagram for the system.\n", + "1. Simulate closed-loop system.\n", + "1. Modify the control law in such a way that the state of the system converges to $x_0 = \\begin{bmatrix} \n", + "2+0.1n \\\\\n", + "n-5 \\\\\n", + "0 \\\\\n", + "0 \n", + "\\end{bmatrix}$. Show resulting control law. Simulate the system and demostrate convergence via graphs of state dynamics and error dynamics.\n", + "1. Discretize the system with $\\Delta t = 0.01$. Write equations of the discrete dinamics.\n", + "1. Propose a control law for the discrete system via pole-placement and LQR (show cost function for the LQR).\n", + "1. Show eigenvalue analisys of the slosed-loop dynamics of the discrete system (with the proposed discrete control law. Demonstrate stability.\n", + "1. Simulate the discrete system. Show graphs.\n", + "\n", + "\n", + "\n" + ], + "metadata": { + "id": "jkpb8xiEzdwR" + } + } + ] +} \ No newline at end of file diff --git a/Assignment/Assignment2.pdf b/Assignment/Assignment2.pdf new file mode 100644 index 0000000..9f71f00 Binary files /dev/null and b/Assignment/Assignment2.pdf differ diff --git a/Assignment/Assignment3.ipynb b/Assignment/Assignment3.ipynb new file mode 100644 index 0000000..7a0ed0b --- /dev/null +++ b/Assignment/Assignment3.ipynb @@ -0,0 +1,576 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "Assignment3.ipynb", + "provenance": [], + "collapsed_sections": [], + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "_kVWFukOo2xf" + }, + "source": [ + "#**Stabilization of Cart Pole system**: \n", + "> Consider cart pole system:\n", + ">\n", + ">\n", + ">

\"mbk\"

\n", + ">\n", + ">\n", + "> Do the following:\n", + ">* 1) Design the linear feedback controller using linearization of the cart-pole dynamics.\n", + ">* 2) Simulate the response of your controller on the linearized and nonlinear system, compare the results.\n", + ">* 3) Taking into account that $y = Cx$ is measured, design observer and linear control that uses observer state. \n", + ">* 4) Simulate the nonlinear system with the observer and controller, show the difference between the actual motion of the nonlinear system and its estimate produced by teh observer.\n", + ">\n", + "> [Here is the great illustration of the hardware implemintation of the cart-pole](https://www.youtube.com/shorts/NJxBJ2LJY7w) \n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "WrEHbu0anIiU" + }, + "source": [ + "##**System Dynamics**: \n", + "\n", + "Recall the dynamics of cart-pole system:\n", + "\\begin{equation}\n", + "\\begin{cases} \n", + "\\left(M+m\\right){\\ddot {p}}-m L \\ddot{\\theta} \\cos \\theta +m L \\dot{\\theta }^{2}\\sin \\theta = u \\\\\n", + "L \\ddot{\\theta}- g\\sin \\theta =\\ddot{p} \\cos \\theta \\\\\n", + "\\end{cases}\n", + "\\end{equation}\n", + "\n", + "where $\\theta$ is angle of the pendulum measured from the upper equilibrium and $p$ is position of cart\n", + "\n", + "\n", + "Choosing the state to be $\\mathbf{x} = [\\theta, \\dot{\\theta}, p, \\dot{p}]^T$One may rewrite this dynamics in the state-space form as:\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{x}} = \n", + "\\begin{bmatrix}\n", + "\\dot{\\theta} \\\\ \n", + "\\ddot{\\theta} \\\\ \n", + "\\dot{p} \\\\ \n", + "\\ddot{p}\n", + "\\end{bmatrix} \n", + "= \n", + "\\begin{bmatrix}\n", + "\\dot{\\theta} \\\\ \n", + "\\frac{(M+m)g \\sin \\theta - mL \\dot{\\theta}^2 \\sin\\theta \\cos\\theta}{(M + m\\sin^2 \\theta)L} \\\\ \n", + "\\dot{x} \\\\ \n", + "\\frac{mg\\sin\\theta \\cos\\theta - mL\\dot{\\theta}^2 \\sin \\theta}{M + m\\sin^2 \\theta} \\\\ \n", + "\\end{bmatrix} \n", + "+\n", + "\\begin{bmatrix}\n", + "0 \\\\ \n", + "\\frac{\\cos\\theta}{(M + m\\sin^2 \\theta)L} \\\\ \n", + "0 \\\\ \n", + "\\frac{1}{M + m\\sin^2 \\theta} \\\\ \n", + "\\end{bmatrix} u\n", + "\\end{equation}\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "VAnL3N08Ur7h" + }, + "source": [ + "###**System parameters**: \n", + "Let us choose the following parameters:" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "M2NL56xAUrM3" + }, + "source": [ + "m = 0.5 # mass of pendulum bob\n", + "M = 2 # mass of cart\n", + "pendulumn_length = 0.3 # length of pendulum\n", + "g = 9.81 # gravitational acceleration \n" + ], + "execution_count": 7, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "7EaVQAp7MlhL" + }, + "source": [ + "####**Nonlinear dynamics**: \n", + "\n", + "First of all let us define the nonlinear system in form $\\dot{\\mathbf{x}} = \\mathbf{f}(\\mathbf{x}, \\mathbf{u})$ :" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "lMSbMWXnWwRC", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "164cba9d-6d27-4119-cfe0-61a469ae66fe" + }, + "source": [ + "import numpy as np\n", + "from math import cos, sin\n", + "\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# sin, cos = np.sin, np.cos\n", + "# Nnonlinear cart-pole dynamics\n", + "def f(x, u):\n", + " theta, dtheta, p, dp = x\n", + " u = u[0]\n", + "\n", + " denominator = M + m*(sin(theta)**2)\n", + " ddtheta = ((M + m)*g*sin(theta) - m* pendulumn_length * dtheta**2 *sin(theta) * cos(theta) + cos(theta)*u)/(denominator * pendulumn_length)\n", + " ddp = (m*g*sin(theta)*cos(theta) - m* pendulumn_length * dtheta**2 *sin(theta) + u)/denominator\n", + "\n", + " dx = np.array([dtheta, ddtheta, dp, ddp])\n", + " return dx\n", + "\n", + "x0 = np.array([1, # Initial pendulum angle\n", + " 0, # Initial pendulum angular speed\n", + " 1, # Initial cart position\n", + " 0]) # Initial cart speed\n", + "u0 = np.array([0])\n", + "print(f(x0, u0))" + ], + "execution_count": 8, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "[ 0. 29.22225161 0. 0.947331 ]\n" + ] + } + ] + }, + { + "cell_type": "code", + "source": [ + "" + ], + "metadata": { + "id": "7N8K9HjdKr0X" + }, + "execution_count": 8, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "D_Cvl8EyTVMG" + }, + "source": [ + "###**Linearized Dynamics**: \n", + "\n", + "Liniarization around the upper equilibrium $\\mathbf{x} = [0,0,0,0]$ yields:\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{x}} = \n", + "\\begin{bmatrix}\n", + "\\dot{\\theta} \\\\ \n", + "\\ddot{\\theta} \\\\ \n", + "\\dot{p} \\\\ \n", + "\\ddot{p}\n", + "\\end{bmatrix} \n", + "=\n", + "\\begin{bmatrix}\n", + "0 & 1 & 0 & 0\\\\\n", + "\\frac{(M+m)}{M}\\frac{g}{L} & 0 & 0 & 0 \\\\\n", + "0 & 0 & 0 & 1 \\\\\n", + "\\frac{m}{M}g & 0 & 0 & 0 \n", + "\\end{bmatrix} \n", + "\\begin{bmatrix}\n", + "\\theta \\\\ \n", + "\\dot{\\theta} \\\\ \n", + "p \\\\ \n", + "\\dot{p}\n", + "\\end{bmatrix} \n", + "+\n", + "\\begin{bmatrix}\n", + "0 \\\\\n", + "\\frac{1}{ML} \\\\\n", + "0 \\\\\n", + "\\frac{1}{M}\n", + "\\end{bmatrix}\n", + "u\n", + "\\end{equation}" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "i3y-TnTmTUf4" + }, + "source": [ + "# System matrix\n", + "A = np.array([[0, 1, 0, 0],\n", + " [(M + m)*g /(M*pendulumn_length), 0, 0, 0],\n", + " [0,0,0,1],\n", + " [m*g/M, 0, 0, 0]])\n", + "# Input matrix\n", + "B = np.array([[0],\n", + " [1/(M*pendulumn_length)],\n", + " [0], \n", + " [1/M]])\n", + "C = np.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0]])" + ], + "execution_count": 9, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "BwYSjfDTVTCF" + }, + "source": [ + "###**Controller Design**: \n", + "\n", + "Let us design the controller for linearized plant by placing poles (eigen values) on the left-hand side of complex plane:\n" + ] + }, + { + "cell_type": "markdown", + "source": [ + "Insert your control design / observer design code here.\n", + "\n", + "Check eigenvalues of the closed-loop system for 1) closed-loop for the case when full state information is availible and no observer is used, 2) when only measurement y = C*x is availible and an observer is used." + ], + "metadata": { + "id": "FMjO0AyEJ2bb" + } + }, + { + "cell_type": "markdown", + "metadata": { + "id": "uJTVJ1pCYdHV" + }, + "source": [ + "##**Simulation**:\n", + "We proceed with the simulation of designed controller, firstly we will define the simulation parameters: " + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "L473KDm6Y7GK" + }, + "source": [ + "# Time settings\n", + "t0 = 0 # Initial time \n", + "tf = 10 # Final time\n", + "N = 1000 # Numbers of points in time span\n", + "t = np.linspace(t0, tf, N) # Create time span\n", + "\n", + "# Define initial point \n", + "theta_0 = 0.4\n", + "p_0 = 0.1\n", + "\n", + "# Set initial state \n", + "x0 = np.array([theta_0, # Initial pendulum angle\n", + " 0, # Initial pendulum angular speed\n", + " p_0, # Initial cart position\n", + " 0]) # Initial cart speed" + ], + "execution_count": 10, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "zojvh_scXgvZ" + }, + "source": [ + "\n", + "####**Linearized dynamics**: \n", + "Now let us simulate the response of linear controller on the **linearized** system:" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "iGhlbLIxPJBV" + }, + "source": [ + "# import integrator routine\n", + "from scipy.integrate import odeint \n", + "\n", + "# Define the linear ODE to solve\n", + "def linear_ode(x, t, A, B, K):\n", + " # Linear controller\n", + " u = - np.dot(K,x) \n", + " # Linearized dynamics\n", + " dx = np.dot(A,x) + np.dot(B,u)\n", + " return dx\n", + "\n", + "# integrate system \"sys_ode\" from initial state $x0$\n", + "x_l = odeint(linear_ode, x0, t, args=(A, B, K,)) \n", + "theta_l, dtheta_l, p_l, dp_l = x_l[:,0], x_l[:,1], x_l[:,2], x_l[:,3] \n", + "# Plot the resulst\n", + "plt.plot(t, theta_l, 'b--', linewidth=2.0, label = r'$\\theta$ linear')\n", + "plt.plot(t, p_l, 'r--', linewidth=2.0, label = r'$p$ linear')\n", + "plt.grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "plt.grid(True)\n", + "plt.legend()\n", + "plt.xlim([t0, tf])\n", + "plt.ylabel(r'Coordinates $p,\\theta$')\n", + "plt.xlabel(r'Time $t$ (s)')\n", + "plt.show()" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "xf4RANelaCG3" + }, + "source": [ + "Now we will simulate similarly to linear case while using the same gains $\\mathbf{K}$:" + ] + }, + { + "cell_type": "code", + "source": [ + "def nonliear_ode(x, t, K):\n", + "\n", + " # Linear controller\n", + " u = - np.dot(K,x) \n", + "\n", + " # Nonlinear dynamics\n", + " dx = f(x, u)\n", + "\n", + " return dx\n", + "\n", + "# integrate system \"sys_ode\" from initial state $x0$\n", + "x_nl = odeint(nonliear_ode, x0, t, args=(K,)) \n", + "theta_nl, dtheta_nl, p_nl, dp_nl = x_nl[:,0], x_nl[:,1], x_nl[:,2], x_nl[:,3] \n", + "# Plot the resulst\n", + "plt.plot(t, theta_nl, 'b', linewidth=2.0, label = r'$\\theta$ nonlinear')\n", + "plt.plot(t, p_nl, 'r', linewidth=2.0, label = r'$p$ nonlinear')\n", + "plt.grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "plt.grid(True)\n", + "plt.legend()\n", + "plt.xlim([t0, tf])\n", + "plt.ylabel(r'Coordinates $p,\\theta$')\n", + "plt.xlabel(r'Time $t$ (s)')\n", + "plt.show()" + ], + "metadata": { + "id": "IPF4ezxF75Dj" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "source": [ + "### Simulation with observer\n", + "\n", + "Insert your code simulating the behaviour of the nonlinear system with an observer. Plot the results, compare state estimatio and actual state of the system." + ], + "metadata": { + "id": "XSU6vW6PKpUd" + } + }, + { + "cell_type": "markdown", + "metadata": { + "id": "I8K0gNMmaqrr" + }, + "source": [ + "\n", + "###**Comparison**: \n", + "One may compare the linear and nonlinear responses by plotting them together:" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "HMT9U1H7a2Wz" + }, + "source": [ + "# theta_l, p_l - values of theta and p for the linear system\n", + "# theta_nl, p_nl - values of theta and p for the nonlinear system\n", + "\n", + "plt.plot(t, theta_l, 'b--', linewidth=2.0, label = r'$\\theta$ linear')\n", + "plt.plot(t, p_l, 'r--', linewidth=2.0, label = r'$p$ linear')\n", + "plt.plot(t, theta_nl, 'b', linewidth=2.0, label = r'$\\theta$ nonlinear')\n", + "plt.plot(t, p_nl, 'r', linewidth=2.0, label = r'$p$ nonlinear')\n", + "plt.grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "plt.grid(True)\n", + "plt.legend()\n", + "plt.xlim([t0, tf])\n", + "plt.ylabel(r'Coordinates $p,\\theta$')\n", + "plt.xlabel(r'Time $t$ (s)')\n", + "plt.show()" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "source": [ + "# Animation" + ], + "metadata": { + "id": "zvwB54-6LjIR" + } + }, + { + "cell_type": "code", + "source": [ + "p = p_nl\n", + "theta = theta_nl\n", + "time = t" + ], + "metadata": { + "id": "Pa5FNEfQR2NJ" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "%matplotlib inline\n", + "\n", + "# create a figure and axes\n", + "fig = plt.figure(figsize=(12,5))\n", + "ax1 = plt.subplot(1,2,1) \n", + "ax2 = plt.subplot(1,2,2)\n", + "\n", + "# set up the subplots as needed\n", + "# ax1.set_xlim(( 0, 2)) \n", + "# ax1.set_ylim((-0.3, 0.3))\n", + "ax1.set_xlabel('Time')\n", + "ax1.set_ylabel('Magnitude')\n", + "\n", + "ax2.set_xlim((-0.5,0.5))\n", + "ax2.set_ylim((0,1))\n", + "ax2.set_xlabel('X')\n", + "ax2.set_ylabel('Y')\n", + "ax2.set_title('animation')\n", + "\n", + "# create objects that will change in the animation. These are\n", + "# initially empty, and will be given new values for each frame\n", + "# in the animation.\n", + "txt_title = ax1.set_title('plot')\n", + "line_x, = ax1.plot(time, p, 'b') # ax.plot returns a list of 2D line objects\n", + "line_theta, = ax1.plot(time, theta, 'r')\n", + "point_x, = ax1.plot([], [], 'g.', ms=20)\n", + "point_theta, = ax1.plot([], [], 'g.', ms=20)\n", + "\n", + "draw_cart, = ax2.plot([], [], 'b', lw=2)\n", + "draw_shaft, = ax2.plot([], [], 'r', lw=2)\n", + "\n", + "ax1.legend(['x','theta']);" + ], + "metadata": { + "id": "xCSCmInpRwj7" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "\n", + "shaft_l = 0.3\n", + "cart_l = 0.1\n", + "cart_x = np.array([-1, -1, 1, 1, -1])*cart_l\n", + "cart_y = np.array([ 0, 1, 1, 0, 0])*cart_l\n", + "\n", + "\n", + "# animation function. This is called sequentially\n", + "def drawframe(n):\n", + "\n", + " shaft_x = np.array([ p[n], p[n] + shaft_l*sin(theta[n] )])\n", + " shaft_y = np.array([ cart_l/2, cart_l/2 + shaft_l*cos(theta[n] )])\n", + "\n", + " line_x.set_data(time, p)\n", + " line_theta.set_data(time, theta)\n", + "\n", + " point_x.set_data(time[n], p[n])\n", + " point_theta.set_data(time[n], theta[n])\n", + "\n", + " draw_cart.set_data(cart_x+p[n], cart_y)\n", + " draw_shaft.set_data(shaft_x, shaft_y)\n", + " \n", + " txt_title.set_text('Frame = {0:4d}'.format(n))\n", + " return (draw_cart,draw_shaft)" + ], + "metadata": { + "id": "oE2hVzA0Q_7Y" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "source": [ + "from matplotlib import animation\n", + "\n", + "# blit=True re-draws only the parts that have changed.\n", + "anim = animation.FuncAnimation(fig, drawframe, frames=200, interval=20, blit=True)" + ], + "metadata": { + "id": "mje05MpaRCOz" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "source": [ + "## Here we try to make a video of the cart-pole as it moves" + ], + "metadata": { + "id": "8jQfAyiVL9hR" + } + }, + { + "cell_type": "code", + "source": [ + "from IPython.display import HTML\n", + "HTML(anim.to_html5_video())" + ], + "metadata": { + "id": "Ml0P9dt0RD22" + }, + "execution_count": null, + "outputs": [] + } + ] +} \ No newline at end of file diff --git a/Assignment/Assignment3.pdf b/Assignment/Assignment3.pdf new file mode 100644 index 0000000..22fa874 Binary files /dev/null and b/Assignment/Assignment3.pdf differ diff --git a/LICENSE b/LICENSE new file mode 100644 index 0000000..d7f7c5b --- /dev/null +++ b/LICENSE @@ -0,0 +1,21 @@ +MIT License + +Copyright (c) 2020 SergeiSa + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. diff --git a/README.md b/README.md new file mode 100644 index 0000000..a11d021 --- /dev/null +++ b/README.md @@ -0,0 +1,190 @@ +# How to use + +This repository contains regularly updated course materials. You can use lecture slides for self study (they are written as lecture notes). Lecture recordings from this and last year offerings are linked below. The links in the Self-study with Colab section are both for self-study and reviewing the practical sessions. Refer to the book and resourses suggestions at the bottom of the page. + +# Lecture slides + +* Lecture 1 - [Introduction](https://github.com/SergeiSa/Control-Theory-Slides-Spring-2023/blob/main/Slides/Introduction) +* Lecture 2 - [Stability](https://github.com/SergeiSa/Control-Theory-Slides-Spring-2023/blob/main/Slides/Stability) +* Lecture 3 - [Control](https://github.com/SergeiSa/Control-Theory-Slides-Spring-2023/blob/main/Slides/Control) +* Lecture 4 - [Laplace transform](https://github.com/SergeiSa/Control-Theory-Slides-Spring-2023/blob/main/Slides/Laplace) +* Lecture 5 - [Bode](https://github.com/SergeiSa/Control-Theory-Slides-Spring-2023/blob/main/Slides/Bode) +* Lecture 6 - [Discrete models](https://github.com/SergeiSa/Control-Theory-Slides-Spring-2023/blob/main/Slides/Discrete/main.pdf) +* Lecture 7 - [LQR, Riccati, Hamilton-Jacobi-Bellman](https://github.com/SergeiSa/Control-Theory-Slides-Spring-2023/blob/main/Slides/HJB_LQR) +* Lecture 8 - [State estimation, Observers](https://github.com/SergeiSa/Control-Theory-Slides-Spring-2023/tree/main/Slides/Observer) +* Lecture 9 - [Controllability, Observability](https://github.com/SergeiSa/Control-Theory-Slides-Spring-2023/tree/main/Slides/ControllabilityObservability) +* Lecture 10 - [Kalman](https://github.com/SergeiSa/Control-Theory-Slides-Spring-2023/tree/main/Slides/Kalman) + +* Lecture 11 - https://github.com/SergeiSa/Control-Theory-Slides-Spring-2023/tree/main/Slides/Linearization +* Lecture 12 - https://github.com/SergeiSa/Control-Theory-Slides-Spring-2023/tree/main/Slides/LyapunovTheory + +* Lecture - https://github.com/SergeiSa/Control-Theory-Slides-Spring-2023/tree/main/Slides/LMI + +# Lecture videos: + +([playlist](https://www.youtube.com/watch?v=yxns2JKQK0M&list=PLlxR_sEKjSpRACHIQZcKNm-KjNQWlAltM&ab_channel=SergeiS)) + +* Lecture 1 (State Space) - https://youtu.be/yxns2JKQK0M +* Lecture 2 (Stability) - https://youtu.be/XnNlYsVebkU +* Lecture 3 (Stabilizing control) - https://youtu.be/wV1iPkvXVV4 +* Lecture 4 (Laplace, Transfer functions) - https://youtu.be/8LMwvjSmt28 +* Lecture 5 (Bode) - https://youtu.be/d-R31Hmmrtk +* Lecture 6 (Discrete) - https://youtu.be/j0Gooh-2mT4 +* Lecture 7 (LQR, Riccati) - https://youtu.be/CcZ2RnvFS2A + +* Lecture 8 (Observers) - +* Lecture 9 (Controllability, Observability) - +* Lecture 10 (Kalman) - + + +# Tutorial slides + + + + + +# Assignments (labs) + +* Assignment / lab / submission / gradable item \# 1: +* * PDF: https://github.com/SergeiSa/Control-Theory-Slides-Spring-2022/blob/main/Assignment/Assignment1.pdf +* * Colab: https://github.com/SergeiSa/Control-Theory-Slides-Spring-2022/blob/main/Assignment/Assignment1.ipynb +* Assignment / lab / submission / gradable item \# 2: +* * PDF: https://github.com/SergeiSa/Control-Theory-Slides-Spring-2022/blob/main/Assignment/Assignment2.pdf +* * Colab: https://github.com/SergeiSa/Control-Theory-Slides-Spring-2022/blob/main/Assignment/Assignment2.ipynb +* Assignment / lab / submission / gradable item \# 3: +* * PDF: https://github.com/SergeiSa/Control-Theory-Slides-Spring-2022/blob/main/Assignment/Assignment3.pdf +* * Colab: https://github.com/SergeiSa/Control-Theory-Slides-Spring-2022/blob/main/Assignment/Assignment3.ipynb + +# Practice sessions with Colab + +* Practice 1 (State Space) - https://github.com/SergeiSa/Control-Theory-Slides-Spring-2022/blob/main/Practice/Practice_1_ODE_to_StateSpace.ipynb +* Practice 2 (Stability) - https://github.com/SergeiSa/Control-Theory-Slides-Spring-2022/blob/main/Practice/Practice_2_Stability.ipynb +* Practice 3 (Laplace, Transfer functions) - https://github.com/SergeiSa/Control-Theory-Slides-Spring-2022/blob/main/Practice/Practice_3_Laplace_TransferFunctions.ipynb +* Practice 4 (Bode) - https://github.com/SergeiSa/Control-Theory-Slides-Spring-2022/blob/main/Practice/Practice_4_Bode.ipynb +* Practice 5 (Feedback control) - https://github.com/SergeiSa/Control-Theory-Slides-Spring-2022/blob/main/Practice/Practice_5_FeedbackControl.ipynb +* Practice 6 (Trajectory tracking) - https://github.com/SergeiSa/Control-Theory-Slides-Spring-2022/blob/main/Practice/Practice_6_TrajectoryTracking.ipynb +* Practice 7 (Discrete) - https://github.com/SergeiSa/Control-Theory-Slides-Spring-2022/blob/main/Practice/Practice_7_Discrete.ipynb +* Practice 8 (Lyapunov) - https://github.com/SergeiSa/Control-Theory-Slides-Spring-2022/blob/main/Practice/Practice_8_Lyapunov.ipynb + +# For contributors + +Pull requests with suggestions and improvements, however small or big, are welcome! + +The changes in lecture slides are going through an automated check. + +The PDFs are compiled and updated automatically when PR is merged (thanks to k1rill-fedoseev from the 2020 Linear Control class!). You don't need to update them manually. They are also uploaded as workflow artifacts for every new commit pushed into this repository. You can use them to see your changes. + +Consider adding \*.pdf to the .git/info/exclude file on your local repo. Here is the ~~overy long but helpful~~ [description why it works](https://medium.com/@dave_lunny/exclude-files-from-git-without-committing-changes-to-gitignore-986fa712e78d) + +# Book suggestions + + +## Lecture 1. State-Space, ODE + +* Control Systems Engineering Norman S. Nise + * Chapter 3.3: The General State-Space Representation + * Chapter 3.4: Applying the State-Space Representation +* Systems of First Order Linear Differential Equations. [Download](http://www.personal.psu.edu/sxt104/class/Math251/Notes-LinearSystems.pdf) + + +## Lecture 2. Stability + +* Control System Design, An Introduction to State-Space Methods Bernard Friedland https://books.google.co.in/books/about/Control_System_Design.html?id=9WRKZlaCnF8C&redir_esc=y + * 4.4 STABILITY +* Control Systems Engineering Norman S. Nise (chapters 3.3, 3.4) +* Paul's Online Notes (systems of linear ODE, solutions for them): + * http://tutorial.math.lamar.edu/Classes/DE/SystemsDE.aspx + * http://tutorial.math.lamar.edu/Classes/DE/SolutionsToSystems.aspx +* Astolfi, A., 2006. Systems and Control Theory: An Introduction. Imperial College London lecture notes. - 2.3.1 Linear systems (on equilibrioum of linear systems): +http://www3.imperial.ac.uk/pls/portallive/docs/1/31851696.PDF +* Videos: + * State Space Stability (Linear Systems Theory EECS 221a, Berkeley) - https://youtu.be/7GarcEQ0uk8 + + +## Lecture 3. Stabilizing control +* Control theory by S. Simrock - sections 5, 6 (stability discussed in terms of TF): +https://cds.cern.ch/record/1100534/files/p73.pdf +* Module 9: State Feedback Control Design, Lecture Note 1: +https://nptel.ac.in/content/storage2/courses/108103008/PDF/module9/m9_lec1.pdf +* 16.31 Feedback Control Systems +https://ocw.mit.edu/courses/aeronautics-and-astronautics/16-30-feedback-control-systems-fall-2010/lecture-notes/MIT16_30F10_lec11.pdf +* Chapter 6 State Feedback - http://www.cds.caltech.edu/~murray/books/AM05/pdf/am06-statefbk_16Sep06.pdf + +## Lecture 4. Laplace Transform, Transfer functions + +* Control System Design, An Introduction to State-Space Methods Bernard Friedland https://books.google.co.in/books/about/Control_System_Design.html?id=9WRKZlaCnF8C&redir_esc=y + * 3.4 SOLUTION BY THE LAPLACE TRANSFORM: THE RESOLVENT + * 3.5 INPUT-OUTPUT RELATIONS: TRANSFER FUNCTIONS +* Control Systems Engineering, by Norman S. Nise + * chapter 2.2 Laplace Transform Review + * chapter 2.3 The Transfer Function (optional) +* Cho W. S. To, Introduction to Dynamics and Control in Mechanical Engineering Systems. + * 2 Review of Laplace Transforms + * 8.3 Transfer Functions +* Control theory by S. Simrock - sections 2, 3 and 4: https://cds.cern.ch/record/1100534/files/p73.pdf +* Videos: + * Control Systems Lectures - Transfer Functions, Brian Douglas: https://youtu.be/RJleGwXorUk + * The Laplace Transform - A Graphical Approach, Brian Douglas: https://youtu.be/ZGPtPkTft8g + +## Lecture 5. Frequency response, Bode plot + +* Control System Lectures - Bode Plots, Introduction, by Brian Douglas: +* Bode Plots by Hand, Real Constants, by Brian Douglas: https://youtu.be/CSAp9ooQRT0 + + +## Lecture 6. Discrete Systems +* Control System Design, An Introduction to State-Space Methods Bernard Friedland https://books.google.co.in/books/about/Control_System_Design.html?id=9WRKZlaCnF8C&redir_esc=y + * 3.1 DIFFERENTIAL EQUATIONS REVISITED + * 3.2 SOLUTION OF LINEAR DIFFERENTIAL EQUATIONS IN STATE-SPACE FORM +* MIT 2.14, State Space response https://web.mit.edu/2.14/www/Handouts/StateSpaceResponse.pdf + * 2 State-Variable Response of Linear Systems +* Astolfi, A., 2006. Systems and Control Theory: An Introduction. Imperial College London lecture notes: + * 1.2.9 Approximate discrete-time models; + * Proposition 2.3 (Trajectories of linear, discrete-time, systems) - on Controllability: +http://www3.imperial.ac.uk/pls/portallive/docs/1/31851696.PDF +* Dahleh, M., Dahleh, M.A. and Verghese, G., 2004. Lectures on dynamic systems and control. A+ A, 4(100), pp.1-100. (goes to z-transform, which is outside the scope of our course): +https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-241j-dynamic-systems-and-control-spring-2011/readings/MIT6_241JS11_chap10.pdf + +## Lecture 8 Lyapunov Theory +* 3.9 Liapunov’s direct method - https://folk.uib.no/nmagb/m2142002l3.pdf +* Universita degli studi di Padova Dipartimento di Ingegneria dell'Informazione, Nicoletta Bof, Ruggero Carli, Luca Schenato, Technical Report, Lyapunov Theory for Discrete Time Systems - https://arxiv.org/abs/1809.05289 + +## Lecture 9 LQR +* Linear Quadratic Regulators - http://underactuated.mit.edu/lqr.html +* Videos: + * Linear Quadratic Regulator (LQR) Control for the Inverted Pendulum on a Cart, Steve Brunton https://youtu.be/1_UobILf3cc + +## Lecture 10 Observers + +* Control System Design, An Introduction to State-Space Methods Bernard Friedland https://books.google.co.in/books/about/Control_System_Design.html?id=9WRKZlaCnF8C&redir_esc=y + * LINEAR OBSERVERS +* Videos: + * Motivation for Full-State Estimation, Steve Brunton https://youtu.be/LTNMf8X21cY + +## Lecture 11 Controllability, Observability + +* Control System Design, An Introduction to State-Space Methods Bernard Friedland https://books.google.co.in/books/about/Control_System_Design.html?id=9WRKZlaCnF8C&redir_esc=y + * 5.4 ALGEBRAIC CONDITIONS FOR CONTROLLABILITY AND OBSERVABILITY +* Invariant subspaces, Sylvester equation, PBH https://stanford.edu/class/ee363/sessions/s2notes.pdf +* EE363 Winter 2008-09 Lecture 6 Invariant subspaces https://web.stanford.edu/class/ee363/lectures/inv-sub.pdf +* Videos: + * Degrees of Controllability and Gramians, Steve Brunton - https://youtu.be/ZNHx62HbKNA + * Controllability and the PBH Test, Steve Brunton - https://youtu.be/0XJHgLrcPeA + +## Observer Design, Kalman Filter +* Control System Design, An Introduction to State-Space Methods Bernard Friedland https://books.google.co.in/books/about/Control_System_Design.html?id=9WRKZlaCnF8C&redir_esc=y + * RANDOM PROCESSES + * KALMAN FILTERS: OPTIMUM OBSERVERS + +## Other + +### MIMO, LTI, LTV + * Equilibrium Points of Linear Autonomous Systems. + [Link](https://www.math24.net/linear-autonomous-systems-equilibrium-points/) + +### Optimal Control of LTI systems + * Underactuated Robotics. Continuous dynamic programming. + [Link](http://underactuated.csail.mit.edu/dp.html#section3) + * Control theory by S. Simrock - section 8: +https://cds.cern.ch/record/1100534/files/p73.pdf + diff --git a/Slides/Bode/main.pdf b/Slides/Bode/main.pdf new file mode 100644 index 0000000..a1023de Binary files /dev/null and b/Slides/Bode/main.pdf differ diff --git a/Slides/Bode/main.tex b/Slides/Bode/main.tex new file mode 100644 index 0000000..f5a0655 --- /dev/null +++ b/Slides/Bode/main.tex @@ -0,0 +1,322 @@ +\documentclass{beamer} + +\input{settings.tex} + + +\title{Frequency response, Bode} +\subtitle{Control Theory, Lecture 5} +\author{by Sergei Savin} +\centering +\date{\mydate} + + + +\begin{document} +\maketitle + + +\begin{frame}{Content} + +\begin{itemize} +\item Laplace and Fourier transforms +\item Laplace and steady state solution +\item Bode plot +\item Bode plot - example +\item Stability margins +\item Code example +\end{itemize} + +\end{frame} + + + +\begin{frame}{Frequency response} + % \framesubtitle{O} + \begin{flushleft} + + \begin{block}{Frequency response} + Frequency response is a steady-state output of the system, given sinusoidal input. + \end{block} + + \bigskip + + Consider a system $Y(s) = G(s)U(s)$. Sinusoidal input $u(t) = \text{sin}(\omega t)$ in time domain translates to $U(s) = \frac{\omega}{\omega^2 + s^2}$ in Laplace domain. So, given a sinusoidal input, the system becomes: + + \begin{equation} + Y(s) = G(s)\frac{\omega}{\omega^2 + s^2} + \end{equation} + + \end{flushleft} +\end{frame} + + + +\begin{frame}{Fraction expansion} + % \framesubtitle{O} + \begin{flushleft} + + If a transfer function $G(s)$ is a rational fraction, it can be represented as: + + \begin{equation} + G(s) = \frac{n(s)}{(s + p_1)(s + p_2) \ ... \ (s + p_n)} + \end{equation} + + where $p_i$ are the roots on the denominator - called \emph{poles} of the transfer function. + + \bigskip + + In many cases (for example when $p_i$ are real and non-repeating), the fraction can be expanded: + + \begin{equation*} + G(s) = \frac{n(s)}{(s + p_1)(s + p_2) \ ... \ (s + p_n)} = \frac{r_1}{s + p_1} + \frac{r_2}{s + p_2} + ... + \frac{r_n}{s + p_n} + \end{equation*} + + + \end{flushleft} +\end{frame} + + + +\begin{frame}{Fraction expansion} + % \framesubtitle{O} + \begin{flushleft} + + We can expand the function $Y(s) = G(s)\frac{\omega}{\omega^2 + s^2}$ in a similar way: + + \begin{equation*} + Y(s) = \frac{r_1}{s + p_1} + \frac{r_2}{s + p_2} + ... + \frac{r_n}{s + p_n} + \frac{\alpha}{s + j\omega} + \frac{\beta}{s - j\omega} + \end{equation*} + + Laplace function of the form $\frac{r_i}{s + p_i}$ corresponds to the following time function: + + \begin{align} + y(t) = r_i e^{-p_i t} + \end{align} + + So, for a stable transfer function as time goes to infinity, $r_i e^{-p_i t}$ goes to zero. The only components of the function $Y(s)$ that do not disappear are the last two: $\frac{\alpha}{s + j\omega} + \frac{\beta}{s - j\omega}$. + + + \end{flushleft} +\end{frame} + + + +\begin{frame}{Fraction expansion} + % \framesubtitle{O} + \begin{flushleft} + + One can show that constants in the expansion $\frac{\alpha}{s + j\omega} + \frac{\beta}{s - j\omega}$ can be found in the form: + + \begin{align} + \alpha = -G(j\omega) g + \\ + \beta = G(-j\omega) g + \end{align} + + \bigskip + + In fact, the analysis of the frequency response will involve analyzing the transfer function $G(j\omega)$. + + \end{flushleft} +\end{frame} + + + + + + +\begin{frame}{Laplace and Fourier transforms} +% \framesubtitle{O} +\begin{flushleft} + +\begin{itemize} + \item \emph{Fourier series} can be seen as representing a periodic function as a sum of harmonics (sines and cosines). These sines and cosines can be thought of as forming a basis in a linear space. The coefficients of the series can be thought of as a discrete spectrum of the function. + + \item \emph{Fourier transform} gives a continuous spectrum of the function. The "basis" is still made of harmonic functions. + + \item \emph{Laplace transform} also gives a continuous spectrum of the function, but in a different basis: the basis is given by complex exponentials. I like to think of this basis as solutions of second order ODEs. +\end{itemize} + +\end{flushleft} +\end{frame} + + + + +\begin{frame}{Laplace and Fourier transforms} +% \framesubtitle{O} +\begin{flushleft} + +Let's compare. Fourier transform: + +\begin{equation} + F(\omega) = \int_{-\infty}^\infty f(t) e^{-2\pi j t \omega} dt, \ \ \omega \in \mathbb{R} +\end{equation} + +Laplace transform: + +\begin{equation} + F(s) = \int_0^\infty f(t) e^{-st}dt, \ \ s \in \mathbb{C} +\end{equation} + +We can see that Fourier looks like Laplace with purely imaginary number in the exponent. + +\end{flushleft} +\end{frame} + + + + + + + +\begin{frame}{Laplace and steady state solution} +% \framesubtitle{O} +\begin{flushleft} + +From analysing solutions of linear ODEs we know that, given harmonic input (sine, cosine, their combination) "after the transient process is over, the solution approaches a harmonic with the same frequency", but possibly different amplitude and phase. + +\bigskip + +Intuitively we can think of the imaginary part of $s$ as having to do with this frequency response. + +\bigskip +The kernel function of the Laplace transform is $e^{-st}$ with $s = \sigma + j \omega$ being a complex variable. If $\sigma = 0$, the kernel becomes $e^{-j \omega t} = \text{cos}(\omega t) - j \text{sin}(\omega t)$. You can see the similarity with Fourier transform kernel. + + +\end{flushleft} +\end{frame} + + + + + +\begin{frame}{Bode plot} +% \framesubtitle{O} +\begin{flushleft} + +The first key idea of a Bode plot is substitution of purely complex variable $j \omega$ in place of Laplace variable $s$, which can have non-zero real part. + +\bigskip + +Given a transfer function $W(s)$, $s = \sigma + j \omega$ we can analyse its behaviour when $\sigma = 0$. We can plot its amplitude $a(\omega) = \left| W(j \omega) \right|$ and its phase $\varphi(\omega) = \text{atan2}( \text{im}(W(j \omega)), \ \text{real}(W(j \omega)) )$. + +\bigskip + +Bode plot is actually two plots, 1) $20 \cdot \text{log}(a(\omega))$ and 2) $\frac{180}{\pi} \varphi(\omega)$. The 20 and log has to do with the vertical axis being in decibels. + +\end{flushleft} +\end{frame} + + + + +\begin{frame}{Bode plot - example} +% \framesubtitle{O} +\begin{flushleft} + +Consider $W(s) = \frac{1}{1 + s}$. Then $W(j \omega) = \frac{1}{1 + j \omega}$. We can transform it as: + +\begin{equation} + W(j \omega) = \frac{1 - j \omega}{(1 + j \omega)(1 - j \omega)} = + \frac{1 - j \omega}{1 + \omega^2} +\end{equation} + +Thus we have $\text{real}(W(j \omega)) = \frac{1}{1 + \omega^2}$ and $\text{im}(W(j \omega)) = - \frac{\omega}{1 + \omega^2}$. + +\bigskip + +Bode plot is then given as: + +\begin{equation} + a(\omega) = \sqrt{\frac{1 + \omega^2}{(1 + \omega^2)^2}} = + \frac{1}{\sqrt{(1 + \omega^2)}} +\end{equation} +\begin{equation} + \varphi(\omega) = \text{atan2} \left(-\frac{\omega}{1 + \omega^2}, \ \frac{1}{1 + \omega^2} \right) +\end{equation} + +\end{flushleft} +\end{frame} + + + + + +\begin{frame}{Bode plot - stability margins} +% \framesubtitle{O} +\begin{flushleft} + +Before we discuss the use of Bode plot, let us remember that closed-loop transfer function has form (when simple feedback is used): + +\begin{equation} + W(s) = \frac{G(s)}{1 + G(s)} +\end{equation} + +Substituting $s \longrightarrow j \omega$ we get: + +\begin{equation} + W(\omega) = \frac{G(j \omega)}{1 + G(j \omega)} +\end{equation} + +From this we can see that $W(\omega)$ becomes ill-defined if $G(j \omega) = -1$. Meaning, we want to avoid two things happening simultaneously: the amplitude of $G(j \omega)$ being equal to 1, and its phase (argument) being equal to $180\degree$ (remember, phase of $0\degree$ is pure positive real number, phase of $90\degree$ is pure positive imaginary number, $180\degree$ is pure negative real number, etc.). + +\end{flushleft} +\end{frame} + + + + + +\begin{frame}{Stability margins - graphical example} +% \framesubtitle{O} +\begin{flushleft} + +Let's check an illustration: + +\bigskip + +\centerline{\textcolor{black}{\qrcode[height=1.6in]{https://www.electrical4u.com/bode-plot-gain-margin-phase-margin/}}} + + +\end{flushleft} +\end{frame} + + + + +\begin{frame}{Code example} +% \framesubtitle{O} +\begin{flushleft} + +Check the colab notebook based on the example above for an illustration of how the Bode plot can be made by hand or via scipy signal library. + +\bigskip + +\centerline{\textcolor{black}{\qrcode[height=1.6in]{https://github.com/SergeiSa/Control-Theory-Slides-Spring-2022/blob/main/ColabNotebooks/lecture_Bode.ipynb}}} + + +\end{flushleft} +\end{frame} + + + + +\begin{frame}{Read more} + +\begin{itemize} +\item \bref{https://youtu.be/_eh1conN6YM}{Control System Lectures - Bode Plots, Introduction} + +\item \bref{https://global.oup.com/us/companion.websites/fdscontent/uscompanion/us/static/companion.websites/9780199339136/Appendices/Appendix_F.pdf}{Oxford University Press. s-Domain analysis: poles, zeros, and Bode plots} + + +\end{itemize} + +\end{frame} + + + + +\myqrframe + +\end{document} diff --git a/Slides/Bode/settings.tex b/Slides/Bode/settings.tex new file mode 100644 index 0000000..9f11cce --- /dev/null +++ b/Slides/Bode/settings.tex @@ -0,0 +1,186 @@ +\pdfmapfile{+sansmathaccent.map} + + +\mode +{ + \usetheme{Warsaw} % or try Darmstadt, Madrid, Warsaw, Rochester, CambridgeUS, ... + \usecolortheme{seahorse} % or try seahorse, beaver, 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Second one is not autonomous, and we won't know whether or not the solution converges to zero, until we know what $u$ is. + +\bigskip + +If we pick $u=0$, the result is an unstable equation. But we can also pick $u$ such that the resulting dynamics is stable, such as $u=-3x$: + +\begin{equation} + \dot{x} = 2 x + u = 2 x - 3x = -x +\end{equation} + +\begin{block}{ } +So, we can use \emph{control input} $u$ to change stability of the system! +\end{block} + + +\end{flushleft} +\end{frame} + + + + + +\begin{frame}{Stabilizing control} +% \framesubtitle{O} +\begin{flushleft} + +\begin{definition} +The problem of finding control law $\bo{u}$ that make a certain solution $\bo{x}^*$ of dynamical system $\dot{\bo{x}} = \bo{f}(\bo{x}, \bo{u})$ stable is called \emph{stabilizing control problem} +\end{definition} + +\bigskip + +This is true for both linear and non-linear systems. But for linear systems we can get a lot more details about this problem, if we restrict our choice of control law. + + + +\end{flushleft} +\end{frame} + + + +\begin{frame}{Linear control} +\framesubtitle{Closed-loop system} +\begin{flushleft} + +Consider an LTI system: + +\begin{equation} + \dot{\bo{x}} = \bo{A}\bo{x} + \bo{B}\bo{u} +\end{equation} + +and let us chose \emph{control as a linear function of the state} $x$: + +\begin{equation} + \bo{u} = -\bo{K}\bo{x} +\end{equation} + +We call matrix $\bo{K}$ \emph{control gain}. Thus, we know how the system is going to look when the control is applied: + +\begin{equation} + \dot{\bo{x}} = \bo{A}\bo{x} - \bo{B}\bo{K}\bo{x} +\end{equation} +\begin{equation} +\label{eq:closed_loop} + \dot{\bo{x}} = (\bo{A} - \bo{B}\bo{K})\bo{x} +\end{equation} + +Note that \eqref{eq:closed_loop} is an autonomous system. We call this a \emph{closed loop} system. + +\end{flushleft} +\end{frame} + + + +\begin{frame}{Linear control} +%\framesubtitle{Stability of the closed-loop system} +\begin{flushleft} + +Observing the system $\dot{\bo{x}} = (\bo{A} - \bo{B}\bo{K})\bo{x}$ we obtained, we can notice that we already have the tools to analyse its stability: + +\begin{block}{Stability condition for LTI closed-loop system} +The real parts of the eigenvalues of the matrix $(\bo{A} - \bo{B}\bo{K})$ should be negative for asymptotic stability, or non-positive for stability in the sense of Lyapunov. +\end{block} + +\begin{block}{Hurwitz matrix} + If square matrix $\bo{M}$ has eigenvalues with strictly negative real parts, it is called Hurwitz. We will denote it as $\bo{M} \in \mathcal{H}$. +\end{block} + +%\bigskip + +So, all you need to do is to find such $\bo{K}$ that $(\bo{A} - \bo{B}\bo{K})$ is Hurwitz, and you made a an asymptotically stable closed-loop system! + +\end{flushleft} +\end{frame} + + + + +\begin{frame}{Scalar case} + %\framesubtitle{Stability of the closed-loop system} + \begin{flushleft} + + Let us consider the following system: + + \begin{equation} + \dot x = a x + b u + \end{equation} + + we can choose the following linear control law: $u = - k x$. The close loop system for this example is: + + \begin{equation} + \dot x = (a- bk) x + \end{equation} + + The solution to the closed-loop system is: + + \begin{equation} + x(t) = x_0 e^{(a- bk)t} + \end{equation} + + As long as $a- bk < 0$, the solution is converging to zero. Since we can pick $k$, we can choose it so that $a- bk = -q$, where $q$ is a positive number. Then, we pick $k = \frac{q+a}{b}$, giving us stable system with eigenvalue $-q$. + + \end{flushleft} +\end{frame} + + + +\begin{frame}{Multivariable case} + %\framesubtitle{Stability of the closed-loop system} + \begin{flushleft} + + Let us consider the following system: + % + \begin{equation} + \begin{bmatrix} + \dot x_1 \\ \dot x_2 + \end{bmatrix} + = + \begin{bmatrix} + a_{11} & a_{12} \\ 0 & a_{22} + \end{bmatrix} + \begin{bmatrix} + x_1 \\ x_2 + \end{bmatrix} + + + \begin{bmatrix} + b \\ 0 + \end{bmatrix} + u + \end{equation} + + With control law: + % + \begin{equation} + u + = + - + \begin{bmatrix} + k_1 & k_2 + \end{bmatrix} + \begin{bmatrix} + x_1 \\ x_2 + \end{bmatrix} + \end{equation} + + Close-loop system is: + % + \begin{equation} + \begin{bmatrix} + \dot x_1 \\ \dot x_2 + \end{bmatrix} + = + \begin{bmatrix} + a_{11}-b k_1 & a_{12}-b k_2 \\ 0 & a_{22} + \end{bmatrix} + \begin{bmatrix} + x_1 \\ x_2 + \end{bmatrix} + \end{equation} + + The eigenvalues of the closed-loop system are $a_{11}-b k_1$ and $a_{22}$. The second eigenvalue cannot be influenced by the choice of control gains. If $a_{22} < 0$, we need to pick $k_1$, such as $a_{11}-b k_1 = -q$, where $q$ is a positive number: $k_1 = \frac{q + a_{11}}{b}$. + + \end{flushleft} +\end{frame} + + + + +\begin{frame}{Trajectory tracking (1)} + %\framesubtitle{Stability of the closed-loop system} + \begin{flushleft} + + Let the function $\bo{x}^* = \bo{x}^*(t)$ and control $\bo{u}^* = \bo{u}^*(t)$ be a solution to the system $\dot{\bo{x}} = \bo{A}\bo{x} + \bo{B}\bo{u}$, meaning: + % + \begin{equation} + \dot{\bo{x}}^* = \bo{A}\bo{x}^* + \bo{B}\bo{u}^* + \end{equation} + + We call $\bo{x}^*(t)$ a \emph{reference} or \emph{reference input} and $\bo{u}^*(t)$ a \emph{feed-forward control}. + + \bigskip + + We can try to find control law that would stabilize this reference trajectory. We begin by finding the difference between $\dot{\bo{x}}^*$ and $\dot{\bo{x}}$: + % + \begin{equation} + \dot{\bo{x}}^* - \dot{\bo{x}}= \bo{A}(\bo{x}^*-\bo{x}) + \bo{B}(\bo{u}^*-\bo{u}) + \end{equation} + + We define new variables: $\bo{e} = \bo{x}^* - \bo{x}$ and $\bo{v} = \bo{u}^* - \bo{u}$: + % + \begin{equation} + \dot{\bo{e}} = \bo{A}\bo{e} + \bo{B}\bo{v} + \end{equation} + + \end{flushleft} +\end{frame} + + + +\begin{frame}{Trajectory tracking (1)} + %\framesubtitle{Stability of the closed-loop system} + \begin{flushleft} + + We call $\bo{e}$ \emph{control error} and the equation $\dot{\bo{e}} = \bo{A}\bo{e} + \bo{B}\bo{v}$ is \emph{error dynamics}. + + With error dynamics we are back to the familiar problem - find control law $\bo{v} = -\bo{K}\bo{e}$ that makes closed-loop system stable: + % + \begin{equation} + \dot{\bo{e}} = (\bo{A} - \bo{B}\bo{K}) \bo{e} + \end{equation} + + In original variables it is: + % + \begin{equation} + \bo{u} = \bo{K}(\bo{x}^* - \bo{x}) + \bo{u}^* + \end{equation} + + \end{flushleft} +\end{frame} + + + + +\begin{frame}{Point-to-point control} + %\framesubtitle{Stability of the closed-loop system} + \begin{flushleft} + + Consider the system $\dot{\bo{x}} = \bo{A}\bo{x} + \bo{B}\bo{u}$ and the reference input $\bo{x}^* = \text{const}$ and feed-forward control $\bo{u}^*= \text{const}$. This implies: + + \begin{equation} + \bo{A}\bo{x}^* + \bo{B}\bo{u}^* = 0 + \end{equation} + + We can try to find control law that would stabilize this reference trajectory. The error dynamics and the stabilizing control law are the same as in the previous case. But this time, we can find $\bo{u}^*$ if it is not provided: + + \begin{equation} + \bo{u}^* = -\bo{B}^+\bo{A}\bo{x}^* + \end{equation} + + \end{flushleft} +\end{frame} + + + +\begin{frame}{New input} + %\framesubtitle{Stability of the closed-loop system} + \begin{flushleft} + + Consider the system $\dot{\bo{x}} = \bo{A}\bo{x} + \bo{B}\bo{u}$ and control law $\bo{u} = \bo{K}(\bo{x}^*(t) - \bo{x}) + \bo{u}^*(t)$. We can find the expression for the resulting system: + + \begin{align} + \dot{\bo{x}} = \bo{A}\bo{x} + \bo{B}\bo{K}(\bo{x}^*(t) - \bo{x}) + \bo{B}\bo{u}^*(t) \\ + \dot{\bo{x}} = (\bo{A}- \bo{B}\bo{K})\bo{x} +\bo{B}\bo{K}\bo{x}^*(t) + \bo{B}\bo{u}^*(t) + \end{align} + + Assuming that $\bo{u}^*(t) = 0$ gives us a simplified system: + + \begin{align} + \dot{\bo{x}} = (\bo{A}- \bo{B}\bo{K})\bo{x} +\bo{B}\bo{K}\bo{x}^*(t) + \end{align} + + Here we can see that $\bo{x}^*(t)$ acts as a new input, and it makes sense to discuss how the system reacts to various inputs. + + \end{flushleft} +\end{frame} + + +\begin{frame}{} + + \centering{\huge Extra material} + +\end{frame} + + +\begin{frame}{Input-output control (State-Space), 1} + %\framesubtitle{Stability of the closed-loop system} + \begin{flushleft} + + Given a system where we measure $\bo{y}$: + % + \begin{equation} + \begin{cases} + \dot{\bo{x}} = \bo{A}\bo{x} + \bo{B}\bo{u} \\ + \bo{y} = \bo{C}\bo{x} + \end{cases} + \end{equation} + % + it makes sense that the control law can use output $\bo{y}$, but not state $\bo{x}$: + % + \begin{equation} + \bo{u} = -\bo{K}\bo{y} + \end{equation} + + Closed loop system in this case becomes: + % + \begin{equation} + \dot{\bo{x}} = (\bo{A}- \bo{B}\bo{K}\bo{C})\bo{x} + \end{equation} + + The problem with this control method is that finding $\bo{K}$ such that $\bo{A}- \bo{B}\bo{K}\bo{C} \in \mathbb{H}$ is not always possible. + + \end{flushleft} +\end{frame} + + +\begin{frame}{Input-output control (State-Space), 2} + %\framesubtitle{Stability of the closed-loop system} + \begin{flushleft} + + \begin{example} + Let us consider a second order system: + + \begin{equation} + \begin{cases} + \begin{bmatrix} + \dot x_1 \\ \dot x_2 + \end{bmatrix} = + \begin{bmatrix} + 0 & 1 \\ + -1 & 2 + \end{bmatrix} + \begin{bmatrix} + x_1 \\ x_2 + \end{bmatrix} + + + \begin{bmatrix} + 0 \\ u + \end{bmatrix} + \\ + y = \begin{bmatrix} 1 & 0 \end{bmatrix} + \begin{bmatrix} + x_1 \\ x_2 + \end{bmatrix} + \end{cases} + \end{equation} + + Control law $u = -k y$ is equivalent to $u = -k x_1$. Closed loop system takes form: + + \begin{equation} + \begin{bmatrix} + \dot x_1 \\ \dot x_2 + \end{bmatrix} = + \begin{bmatrix} + 0 & 1 \\ + -(k+1) & 2 + \end{bmatrix} + \begin{bmatrix} + x_1 \\ x_2 + \end{bmatrix} + \end{equation} + + This system will not be stable under any choice of $k$. + \end{example} + + + \end{flushleft} +\end{frame} + + + + +\begin{frame}{Input-output control (State-Space), 3} + %\framesubtitle{Stability of the closed-loop system} + \begin{flushleft} + + Assuming that $\bo{C}\bo{B} = 0$, we can find $\dot{\bo{y}}$: + % + \begin{equation} + \dot{\bo{y}} = \bo{C}\dot{\bo{x}} = \bo{C}(\bo{A}\bo{x} + \bo{B}\bo{u}) = \bo{C}\bo{A}\bo{x} + \end{equation} + + With that, we could propose control law: + % + \begin{align} + \bo{u} = -\bo{K}_p \bo{y} - \bo{K}_d \dot{\bo{y}} \\ + \bo{u} = -(\bo{K}_p \bo{C} + \bo{K}_d \bo{C}\bo{A})\bo{x} + \end{align} + + This looks mysterious, so let us clarify this with an example. + + \end{flushleft} +\end{frame} + + +\begin{frame}{Input-output control (State-Space), 4} + %\framesubtitle{Stability of the closed-loop system} + \begin{flushleft} + + \begin{example} + Let us consider spring-damper system: + + \begin{equation} + \begin{cases} + \begin{bmatrix} + \dot x_1 \\ \dot x_2 + \end{bmatrix} = + \begin{bmatrix} + 0 & 1 \\ + -c & -\mu + \end{bmatrix} + \begin{bmatrix} + x_1 \\ x_2 + \end{bmatrix} + + + \begin{bmatrix} + 0 \\ u + \end{bmatrix} + \\ + y = \begin{bmatrix} 1 & 0 \end{bmatrix} + \begin{bmatrix} + x_1 \\ x_2 + \end{bmatrix} + \end{cases} + \end{equation} + + We can see that $y = x_1$ and $\dot y = x_2$, we can check that $\bo{C}\bo{B} = 0$. Control law $u = -k_p y - k_d \dot y$ is equivalent to $u = -k_p x_1 - k_d x_2$. Closed loop system takes form: + + \begin{equation} + \begin{bmatrix} + \dot x_1 \\ \dot x_2 + \end{bmatrix} = + \begin{bmatrix} + 0 & 1 \\ + -c-k_p & -\mu- k_d + \end{bmatrix} + \begin{bmatrix} + x_1 \\ x_2 + \end{bmatrix} + \end{equation} + + This can be achieved with regular state feedback. + \end{example} + + \end{flushleft} +\end{frame} + + + +\begin{frame}{Input-output control (State-Space), 5} + %\framesubtitle{Stability of the closed-loop system} + \begin{flushleft} + + Here is a counter-example: + + \begin{example} + + \begin{equation} + \begin{cases} + \dot x = 2x + u \\ + y = x + \end{cases} + \end{equation} + % + If we allow control law $u = -3 y +k \dot y = -3 x + k \dot x$. This gives us closed-loop system: + % + \begin{align} + \dot x = -x + k \dot x \\ + \dot x-k \dot x = -x + \end{align} + + If we choose $k = 0.9$ we get close-loop dynamics $0.1\dot x = -x$ with solution $x = C e^{-10t}$. + + If we choose $k = 0.99$ we get close-loop dynamics $0.01\dot x = -x$ with solution $x = C e^{-100t}$. + \end{example} + + \end{flushleft} +\end{frame} + + +\begin{frame}{Input-output control (State-Space), 6} + %\framesubtitle{Stability of the closed-loop system} + \begin{flushleft} + + We observed in the last example that small changes in control gain lead to vast changes in the closed-loop dynamics. This behavior is not physical. + + \bigskip + + The difference between this and the previous example is that here we have a \textcolor{red}{first order system with a first order controller} (not acceptable), while in the previous example we had a \textcolor{mydarkgreen}{second-order system with a first order controller}. + + \bigskip + + In general, one needs to be careful introducing derivatives in the control law. + + \end{flushleft} +\end{frame} + + +\begin{frame}{Input-output control (ODE)} + %\framesubtitle{Stability of the closed-loop system} + \begin{flushleft} + + With ODE representation, input-output control design is a little more clear. For example, consider a system: + + \begin{equation} + \ddot y + a \dot y + b y = u + \end{equation} + + We can propose a control law $u = -k_p y - k_d \dot y$. This is called \emph{proportional-derivative (PD) control}. + + \bigskip + + Closed-loop system in this case looks like: + + \begin{equation} + \ddot y + (a + k_d) \dot y + (b + k_p) y = 0 + \end{equation} + + \end{flushleft} +\end{frame} + + + +\begin{frame}{Read more} + +\begin{itemize} +\item Richard M. Murray Control and Dynamical Systems California Institute of Technology \bref{http://www.cds.caltech.edu/~murray/books/AM08/pdf/obc-trajgen_03Jan10.pdf}{Optimization-Based Control} +\item \bref{https://apmonitor.com/pdc/index.php/Main/ModelSimulation}{Dynamic Simulation in Python} +\end{itemize} +\end{frame} + + + + +\myqrframe + +\end{document} diff --git a/Slides/Control/settings.tex b/Slides/Control/settings.tex new file mode 100644 index 0000000..c9e906a --- /dev/null +++ b/Slides/Control/settings.tex @@ -0,0 +1,192 @@ +\pdfmapfile{+sansmathaccent.map} + + +\mode +{ + \usetheme{Warsaw} % or try Darmstadt, Madrid, Warsaw, Rochester, CambridgeUS, ... + \usecolortheme{seahorse} % or try seahorse, beaver, crane, wolverine, ... + \usefonttheme{serif} % or try serif, structurebold, ... + \setbeamertemplate{navigation symbols}{} + \setbeamertemplate{caption}[numbered] +} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% itemize settings + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% itemize settings + +\definecolor{mypaleblue}{RGB}{240, 240, 255} +\definecolor{mylightblue}{RGB}{120, 150, 255} +\definecolor{myblue}{RGB}{90, 90, 255} +\definecolor{mygblue}{RGB}{70, 110, 240} +\definecolor{mydarkblue}{RGB}{0, 0, 180} +\definecolor{myblackblue}{RGB}{40, 40, 120} + +\definecolor{mygreen}{RGB}{0, 200, 0} +\definecolor{mydarkgreen}{RGB}{0, 120, 0} +\definecolor{mygreen2}{RGB}{245, 255, 230} + +\definecolor{mygray}{gray}{0.8} +\definecolor{mygray2}{RGB}{130, 130, 130} +\definecolor{mydarkgray}{RGB}{80, 80, 160} +\definecolor{mylightgray}{RGB}{160, 160, 160} + +\definecolor{mydarkred}{RGB}{160, 30, 30} +\definecolor{mylightred}{RGB}{255, 150, 150} +\definecolor{myred}{RGB}{200, 110, 110} +\definecolor{myblackred}{RGB}{120, 40, 40} + +\definecolor{mypink}{RGB}{255, 30, 80} +\definecolor{myhotpink}{RGB}{255, 80, 200} +\definecolor{mywarmpink}{RGB}{255, 60, 160} +\definecolor{mylightpink}{RGB}{255, 80, 200} +\definecolor{mydarkpink}{RGB}{155, 25, 60} + +\definecolor{mydarkcolor}{RGB}{60, 25, 155} +\definecolor{mylightcolor}{RGB}{130, 180, 250} + +\setbeamertemplate{itemize items}[default] + +\setbeamertemplate{itemize item}{\color{myblackblue}$\blacksquare$} +\setbeamertemplate{itemize subitem}{\color{mygblue}$\blacktriangleright$} +\setbeamertemplate{itemize subsubitem}{\color{mygray}$\blacksquare$} + +\setbeamercolor{palette quaternary}{fg=white,bg=mydarkgray} +\setbeamercolor{titlelike}{parent=palette quaternary} + +\setbeamercolor{palette quaternary2}{fg=black,bg=mypaleblue} +\setbeamercolor{frametitle}{parent=palette quaternary2} + +\setbeamerfont{frametitle}{size=\Large,series=\scshape} +\setbeamerfont{framesubtitle}{size=\normalsize,series=\upshape} + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% block settings + +\setbeamercolor{block title}{bg=red!30,fg=black} + +\setbeamercolor*{block title example}{bg=mygreen!40!white,fg=black} + +\setbeamercolor*{block body example}{fg= black, bg= mygreen2} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% URL settings +\hypersetup{ + colorlinks=true, + linkcolor=blue, + filecolor=blue, + urlcolor=blue, +} + +%%%%%%%%%%%%%%%%%%%%%%%%%% + +\renewcommand{\familydefault}{\rmdefault} + +\usepackage{amsmath} +\usepackage{mathtools} + +\usepackage{subcaption} + +\usepackage{qrcode} + +\DeclareMathOperator*{\argmin}{arg\,min} +\newcommand{\bo}[1] {\mathbf{#1}} + +\newcommand{\R}{\mathbb{R}} +\newcommand{\T}{^\top} + +\newcommand{\dx}[1] {\dot{\mathbf{#1}}} +\newcommand{\ma}[4] {\begin{bmatrix} + #1 & #2 \\ #3 & #4 +\end{bmatrix}} +\newcommand{\myvec}[2] {\begin{bmatrix} + #1 \\ #2 +\end{bmatrix}} +\newcommand{\myvecT}[2] {\begin{bmatrix} + #1 & #2 +\end{bmatrix}} + + +\newcommand{\mydate}{Spring 2023} + +\newcommand{\mygit}{\textcolor{blue}{\href{https://github.com/SergeiSa/Control-Theory-Slides-Spring-2023}{github.com/SergeiSa/Control-Theory-Slides-Spring-2023}}} + +\newcommand{\myqr}{ \textcolor{black}{\qrcode[height=1.5in]{https://github.com/SergeiSa/Control-Theory-Slides-Spring-2023}} +} + +\newcommand{\myqrframe}{ + \begin{frame} + \centerline{Lecture slides are available via Github, links are on Moodle} + \bigskip + \centerline{You can help improve these slides at:} + \centerline{\mygit} + \bigskip + \myqr + \end{frame} +} + + +\newcommand{\bref}[2] {\textcolor{blue}{\href{#1}{#2}}} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% code settings + +\usepackage{listings} +\usepackage{color} +% \definecolor{mygreen}{rgb}{0,0.6,0} +% \definecolor{mygray}{rgb}{0.5,0.5,0.5} +\definecolor{mymauve}{rgb}{0.58,0,0.82} +\lstset{ + backgroundcolor=\color{white}, % choose the background color; 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If it's 1, each line will be numbered + stringstyle=\color{mymauve}, % string literal style + tabsize=2, % sets default tabsize to 2 spaces + title=\lstname % show the filename of files included with \lstinputlisting; also try caption instead of title +} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% URL settings +\hypersetup{ + colorlinks=false, + linkcolor=blue, + filecolor=blue, + urlcolor=blue, +} + +%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% tikz settings + +\usepackage{tikz} +\tikzset{every picture/.style={line width=0.75pt}} \ No newline at end of file diff --git a/Slides/ControllabilityObservability/main.pdf b/Slides/ControllabilityObservability/main.pdf new file mode 100644 index 0000000..b7044eb Binary files /dev/null and b/Slides/ControllabilityObservability/main.pdf differ diff --git a/Slides/ControllabilityObservability/main.tex b/Slides/ControllabilityObservability/main.tex new file mode 100644 index 0000000..c94948f --- /dev/null +++ b/Slides/ControllabilityObservability/main.tex @@ -0,0 +1,585 @@ +\documentclass{beamer} + +\input{settings.tex} + + +\title{Controllability, Observability} +\subtitle{Control Theory, Lecture 9} +\author{by Sergei Savin} +\centering +\date{\mydate} + + + +\begin{document} +\maketitle + + +\begin{frame}{Content} +\begin{itemize} +\item Cayley–Hamilton +\item Controllability of Discrete LTI +\begin{itemize} + \item Controllability matrix + \item Controllability criterion +\end{itemize} +\item Observability of Discrete LTI +\begin{itemize} + \item Dual system + \item Observability criterion +\end{itemize} +%\item Analytical solution to ODE +%\item Forced State Response +\item Controllability of Continuous-Time LTI +\end{itemize} +\end{frame} + + + + + +\begin{frame}{Cayley–Hamilton} + % \framesubtitle{Limited control} + \begin{flushleft} + + Equation $\text{det}(\bo{M} - \lambda\bo{I}) = 0$ is called \emph{characteristic equation} of matrix $\bo{M}$, its roots being eigenvalues of the matrix. + + \bigskip + + \begin{theorem}[Cayley–Hamilton] + A matrix $\bo{M} \in \R^{n, n}$ satisfies its own characteristic equation. + \end{theorem} + + A characteristic equation can be written as $\lambda^n + a_{n-1}\lambda^{n-1} + ... + a_0 = 0$, meaning that we can write: + + \begin{equation} + \bo{M}^n + a_{n-1}\bo{M}^{n-1} + ... + a_0\bo{I} = 0 + \end{equation} + + Meaning that \textcolor{mydarkblue}{$\bo{M}^n$ is a linear combination of $\bo{M}^{n-1}$, $\bo{M}^{n-2}$, ..., $\bo{I}$}. + + + \end{flushleft} +\end{frame} + + +\begin{frame}{Definitions} + % \framesubtitle{Limited control} + \begin{flushleft} + + \begin{definition}[Controllability] + A system is controllable on time interval $t_0 \leq t \leq t_f$, if it is possible to find control input $u(t)$ that would drive the system to a desired state $\bo{x}(t_f)$ from any initial state $\bo{x}(t_0)$. + \end{definition} + + \begin{definition}[Observability] + A system is observable on time interval $t_0 \leq t \leq t_f$, if using output $\bo{y}(t)$ on that time interval it is possible to estimate exactly the state of the system $\bo{x}(t_f)$, given any initial estimation error. + \end{definition} + + \begin{definition}[Observability, alternative] + A system is observable on time interval $t_0 \leq t \leq t_f$, if any initial state $\bo{x}(t_0)$ is uniquely determined by output $\bo{y}(t)$ on that interval. + \end{definition} + + \end{flushleft} +\end{frame} + + + + + +\begin{frame}{Controllability of Discrete LTI} +% \framesubtitle{Definitions} +\begin{flushleft} + +Consider discrete LTI: +\begin{equation} +\bo{x}_{i+1} = \bo{A} \bo{x}_i + \bo{B} \bo{u}_i +\end{equation} + +Assume the initial state is $\bo{x}_1$. Then we can deduce that: + +\begin{align*} +\bo{x}_2 &= \bo{A} \bo{x}_1 + \bo{B} \bo{u}_1 \\ +\bo{x}_3 &= \bo{A} \bo{x}_2 + \bo{B} \bo{u}_2 = \bo{A} (\bo{A} \bo{x}_1 + \bo{B} \bo{u}_1) + \bo{B} \bo{u}_2 \\ +\bo{x}_4 &= \bo{A} \bo{x}_3 + \bo{B} \bo{u}_3 = \bo{A} (\bo{A} (\bo{A} \bo{x}_1 + \bo{B} \bo{u}_1) + \bo{B} \bo{u}_2) + \bo{B} \bo{u}_3 \\ +... \\ +\bo{x}_{n+1} &= \bo{A}^n \bo{x}_1 + \bo{A}^{n-1} \bo{B} \bo{u}_1 + ... + +\bo{A}^{n - k} \bo{B} \bo{u}_{k} + ... + +\bo{B} \bo{u}_n +\end{align*} + +\end{flushleft} +\end{frame} + + + +\begin{frame}{Controllability matrix} +%\framesubtitle{Controllability matrix} +\begin{flushleft} + +Equation $\bo{x}_{n+1} = \bo{A}^n \bo{x}_1 + \bo{A}^{n-1} \bo{B} \bo{u}_1 + ... ++ \bo{A}^{n - k} \bo{B} \bo{u}_{k} + ... +\bo{B} \bo{u}_n$ can be re-written as: + +\begin{equation} + \bo{x}_{n+1} - \bo{A}^n \bo{x}_1 = + \begin{bmatrix} + \bo{B} & + \bo{A} \bo{B} & + \bo{A}^2 \bo{B} & ... & + \bo{A}^{n - 1} \bo{B} + \end{bmatrix} + \begin{bmatrix} + \bo{u}_{n} \\ + \bo{u}_{n-1} \\ + \bo{u}_{n-2} \\ ... \\ + \bo{u}_{1} + \end{bmatrix} +\end{equation} + +Notice that in order for the system to go from $\bo{x}_1$ to $\bo{x}_{n+1}$, vector $\bo{x}_{n+1} - \bo{A}^n \bo{x}_1$ needs be in the column space of $\mathcal{C} = \begin{bmatrix} + \bo{B} & + \bo{A} \bo{B} & ... & + \bo{A}^{n - 1} \bo{B} + \end{bmatrix}$. + +Since $\bo{x}_{n+1}$ can be anything, and $\bo{x}_1$ might be equal to zero (among other possibilities), we should require that all vectors in $\R^n$ are in the column space of $\mathcal{C}$, meaning $\mathcal{C}$ needs to be full row rank. + +\end{flushleft} +\end{frame} + + +\begin{frame}{Controllability criterion} +%\framesubtitle{Controllability criterion} +\begin{flushleft} + +\begin{block}{Controllability} +For a system $\bo{x}_{i+1} = \bo{A} \bo{x}_i + \bo{B} \bo{u}_i$, where $\bo{x} \in \R^n$, if the matrix $\mathcal{C} = \begin{bmatrix} + \bo{B} & + \bo{A} \bo{B} & ... & + \bo{A}^{n - 1} \bo{B} + \end{bmatrix}$ is full row rank (i.e. $\text{rank}(\mathcal{C}) = n$), any state can be reached, which means that \emph{the system is controllable}. +\end{block} + +\end{flushleft} +\end{frame} + + + + +\begin{frame}{Controllability matrix rank} + % \framesubtitle{Limited control} + \begin{flushleft} + + What happens if we add more columns to the controllability matrix, for example $\bo{A}^n \bo{B}$? Consider the matrix: + + \begin{equation} + \mathcal{C}_+ = \begin{bmatrix} + \bo{B} & + \bo{A} \bo{B} & ... & + \bo{A}^{n - 1} \bo{B} & + \bo{A}^n \bo{B} + \end{bmatrix} + \end{equation} + + But from Cayley–Hamilton we know that: + + \begin{align} + \bo{A}^n = -a_{n-1}\bo{A}^{n-1} - ... - a_0\bo{I} + \\ + \bo{A}^n\bo{B} = -a_{n-1}\bo{A}^{n-1}\bo{B} - ... - a_0\bo{B} + \end{align} + + Meaning that columns of $\bo{A}^n\bo{B}$ are expressed as linear combination of columns of $\mathcal{C}$, hence the matrix $\mathcal{C}_+$ has the same rank as $\mathcal{C}$. + + \end{flushleft} +\end{frame} + + +%\begin{frame}{Controllability matrix rank} +% % \framesubtitle{Limited control} +% \begin{flushleft} +% +% If you are interested why the controllability matrix for not include more columns, like $\bo{A}^n$, Consider the following: +% +% The controllability matrix can be written as +% +% \begin{equation} +% \mathcal{C} = \begin{bmatrix} +% \bo{I} & +% \bo{A} & ... & +% \bo{A}^{n - 1} +% \end{bmatrix} +% \begin{bmatrix} +% \bo{B} & \bo{0} & ... & \bo{0} \\ +% \bo{0} & \bo{B} & ... & \bo{0} \\ +% ... & ... & ... & ... \\ +% \bo{0} & \bo{0} & ... & \bo{B} +% \end{bmatrix} +% \end{equation} +% +% meaning that the rank of $\mathcal{C}$ depends only on matrix $\begin{bmatrix} +% \bo{I} & +% \bo{A} & ... & +% \bo{A}^{n - 1} +% \end{bmatrix}$. Adding to it columns $\bo{A}^n$ does not change the rank, as $\bo{A}^n$ is a linear combination of the other columns, as we proved in the previous slide. +% +% \end{flushleft} +%\end{frame} + + + + +\begin{frame}{Observability of Discrete LTI} +% \framesubtitle{Definitions} +\begin{flushleft} + +Consider discrete LTI: +\begin{equation} +\begin{cases} +\bo{x}_{i+1} = \bo{A} \bo{x}_i + \bo{B} \bo{u}_i \\ +\bo{y}_i = \bo{C} \bo{x}_i +\end{cases} +\end{equation} + +And an observer: + +\begin{equation} +\hat{\bo{x}}_{i+1} = \bo{A} \hat{\bo{x}}_i + \bo{B} \bo{u}_i + +\bo{L} (\bo{y}_i - \bo{C} \hat{\bo{x}}_i) +\end{equation} + +Remember that we can define observation error $\bo{e}_i = \hat{\bo{x}}_i - \bo{x}_i$ and write its dynamics: + +\begin{equation} +\bo{e}_{i+1} = \bo{A} \bo{e}_i - +\bo{L} \bo{C} \bo{e}_i +\end{equation} + +Dual system (which is stable if and only if the original is stable), has form: + +\begin{equation} +\varepsilon_{i+1} = \bo{A}^\top \varepsilon_i - +\bo{C}^\top \bo{L}^\top \varepsilon_i +\end{equation} + + +\end{flushleft} +\end{frame} + + + + +\begin{frame}{Observability of Discrete LTI} +\framesubtitle{Dual system} +\begin{flushleft} + +Dynamical system $\varepsilon_{i+1} = \bo{A}^\top \varepsilon_i - \bo{C}^\top \bo{L}^\top \varepsilon_i$, we can be represented as: + +\begin{equation} +\begin{cases} +\varepsilon_{i+1} = \bo{A}^\top \varepsilon_i + \bo{C}^\top \bo{v}_i \\ +\bo{v}_i = - \bo{L}^\top \varepsilon_i +\end{cases} +\end{equation} + +Controllability matrix of this system is: + +\begin{equation} +\mathcal{O}^\top = \begin{bmatrix} + \bo{C}^\top & + (\bo{A}^\top) \bo{C}^\top & ... & + (\bo{A}^\top)^{n - 1} \bo{C}^\top + \end{bmatrix} +\end{equation} + +It is easier to represent this matrix in its transposed form: + +\begin{equation} +\mathcal{O} = \begin{bmatrix} + \bo{C} \\ + \bo{C}\bo{A} \\ ... \\ + \bo{C}\bo{A}^{n - 1} + \end{bmatrix} +\end{equation} + +\end{flushleft} +\end{frame} + + +\begin{frame}{Observability criterion} +%\framesubtitle{Observability criterion} +\begin{flushleft} + +\begin{block}{Observability} +For a system $\bo{x}_{i+1} = \bo{A} \bo{x}_i + \bo{B} \bo{u}_i$ and $\bo{y}_i = \bo{C} \bo{x}_i$, where $\bo{x} \in \R^n$, if the matrix $\mathcal{O} = \begin{bmatrix} + \bo{C} \\ + \bo{C}\bo{A} \\ ... \\ + \bo{C}\bo{A}^{n - 1} + \end{bmatrix}$ is full column rank (i.e. $\text{rank}(\mathcal{O}) = n$), observation error can go to zero from any initial position, which means that \emph{the system is observable}. +\end{block} + +\end{flushleft} +\end{frame} + + + + +\begin{frame}{Controllability, continuous-time (1)} + % \framesubtitle{Limited control} + \begin{flushleft} + + Let us consider matrix exponential $e^{\bo{A}t}$ is defined as a series: + + \begin{equation} + e^{\bo{A}t} = \bo{I}+\bo{A}t+\frac{1}{2} \bo{A}\bo{A}t^2 + +\frac{1}{6} \bo{A}\bo{A}\bo{A}t^3 + ... + \end{equation} + + Using Cayley–Hamilton we can observe that any powers of $\bo{A}$ higher than $n$ can be represented as a linear combination of lower powers. This gives us the following expression: + % + \begin{equation} + e^{\bo{A}t} = \phi_0(t)\bo{I}+\phi_1(t)\bo{A}+\phi_2(t) \bo{A}^2 + ... + + \phi_{n-1}(t) \bo{A}^{n-1} + \end{equation} + + This allows us to re-write the forced state response: + + \begin{align*} + \bo{x}(t) &= e^{\bo{A}t} \bo{x}(0) + + \int_{0}^{t} e^{\bo{A}(t-\tau)} \bo{b} u(\tau) d\tau + \\ + \bo{x}(t) &= e^{\bo{A}t} \bo{x}(0) + + \int_{0}^{t} + ( \phi_0(t-\tau)\bo{I}+\phi_1(t-\tau)\bo{A}+ ... + \\ + &+ \phi_{n-1}(t-\tau) \bo{A}^{n-1} ) + \bo{b} u(\tau) \ d\tau + \end{align*} + + + \end{flushleft} +\end{frame} + + + +\begin{frame}{Controllability, continuous-time (2)} + % \framesubtitle{Limited control} + \begin{flushleft} + + \begin{align*} + \bo{x}(t) &= e^{\bo{A}t} \bo{x}(0) + + \int_{0}^{t} \phi_0(t-\tau)\bo{b} u(\tau) d\tau + \\ + &+ + \int_{0}^{t} \phi_1(t-\tau)\bo{A}\bo{b} u(\tau) d\tau+ ... + \int_{0}^{t} \phi_{n-1}(t-\tau) \bo{A}^{n-1} + \bo{b} u(\tau) d\tau + \end{align*} + % + \begin{align*} + \bo{x}(t) - e^{\bo{A}t} \bo{x}(0) = + \begin{bmatrix} + \bo{b} & \bo{A}\bo{b}& ... &\bo{A}^{n-1}\bo{b} + \end{bmatrix} + \begin{bmatrix} + \int_{0}^{t} \phi_0(t-\tau) u(\tau) d\tau \\ + \int_{0}^{t} \phi_1(t-\tau) u(\tau) d\tau \\ + ... \\ + \int_{0}^{t} \phi_{n-1}(t-\tau) u(\tau) d\tau \\ + \end{bmatrix} + \end{align*} + + This shows that if controllability matrix is rank-deficient, it would not be possible to achieve some state from some initial condition. + + \end{flushleft} +\end{frame} + + + + +\begin{frame}{PBH controllability criterion} + % \framesubtitle{Limited control} + \begin{flushleft} + + There is an alternative way to test if pair $(\bo{A}, \ \bo{B})$ is controllable: + + \begin{block}{PBH controllability criterion} + If for any $\lambda \in \mathbb{C}$, the the matrix $[ (\bo{A}-\lambda\bo{I}), \bo{B}]$ has full row rank, then the pair $(\bo{A}, \ \bo{B})$ is controllable. + \end{block} + + \begin{itemize} + \item If $\lambda$ is not an eigenvalue of $\bo{A}$, then $\text{det}(\bo{A}-\lambda\bo{I}) \neq 0$ and the matrix has full row rank. + + \item If $\text{det}(\bo{A}-\lambda\bo{I}) = 0$ and $\mathcal{V} = \text{null}(\bo{A}-\lambda\bo{I})$, $\text{dim}(\mathcal{V}) = 1$ and $\bo{v} \in \mathcal{V}$ , meaning $\lambda, \ \bo{v}$ are eigenvalue and eigenvector of $\bo{A}$, then in order for the criterion to hold the columns fo $\bo{B}$ should not all be orthogonal to $\bo{v}$: $\bo{v}\T \bo{B} \neq 0$. + + \item If eigenspace $\mathcal{V}$ is $k$-dimensional, the projection of $\bo{B}$ onto that eigenspace should also be $k$-dimensional. + + \end{itemize} + + \end{flushleft} +\end{frame} + + + + +\begin{frame}{Read more} + + \begin{itemize} + + \item Controllability and Observability (Rutgers University) \bref{https://www.ece.rutgers.edu/~gajic/psfiles/chap5.pdf}{https://www.ece.rutgers.edu/~gajic/psfiles/chap5.pdf} + + \end{itemize} + +\end{frame} + +\myqrframe + + +\begin{frame} + + \centering{\huge Appendix A: Analytical solution (recap)} + +\end{frame} + + + +\begin{frame}{Matrix exponential} + % \framesubtitle{Limited control} + \begin{flushleft} + + Exponential $e^a$ is defined as a series: + + \begin{equation} + e^a =1+a+\frac{1}{2} a^2 + +\frac{1}{6} a^3 + ... = \sum_{n=0}^{\infty} \frac{1}{n!} a^n + \end{equation} + + Matrix exponential $e^\bo{A}$ is defined as a series: + + \begin{equation} + e^\bo{A} = \bo{I}+\bo{A}+\frac{1}{2} \bo{A}\bo{A} + +\frac{1}{6} \bo{A}\bo{A}\bo{A} + ... = \sum_{n=0}^{\infty} \frac{1}{n!} \bo{A}^n + \end{equation} + + + \end{flushleft} +\end{frame} + + + + +\begin{frame}{Analytical solution to ODE} + % \framesubtitle{Limited control} + \begin{flushleft} + + An ODE of the form $\dot x = a x$ has analytical solution $x(t) = e^{at} x(0)$. + + \bigskip + + An ODE of the form $\dot{\bo{x}} = \bo{A} \bo{x}$ has analytical solution $\bo{x}(t) = e^{\bo{A}t} \bo{x}(0)$. + + \bigskip + + Let us check that this is a solution: + + \begin{align} + \bo{x}(t) &= \left( \bo{I}+\bo{A}t+\frac{1}{2} \bo{A}\bo{A}t^2 + +\frac{1}{6} \bo{A}\bo{A}\bo{A}t^3 + ... \right) \bo{x}(0) & + \\ + \dot{\bo{x}}(t) &= \left( \bo{A}+\bo{A}\bo{A}t + +\frac{1}{2}\bo{A}\bo{A}\bo{A}t^2 + ... \right) \bo{x}(0) & + \\ + \dot{\bo{x}}(t) &= \bo{A} \left(\bo{I} +\bo{A}t + +\frac{1}{2}\bo{A}\bo{A}t^2 + ... \right) \bo{x}(0) & + \\ + \dot{\bo{x}}(t) &= \bo{A} e^{\bo{A}t} \bo{x}(0) & + \\ + \dot{\bo{x}}(t) &= \bo{A} \bo{x}(t) &\ \ \qed + \end{align} + + + + \end{flushleft} +\end{frame} + + + +\begin{frame}{Forced State Response (LTI) (1)} + % \framesubtitle{Limited control} + \begin{flushleft} + + An ODE of the form $\dot x = a x + bu(t)$ also has analytical solution. To find it, we first find the following derivative: + % + \begin{equation} + \frac{d}{dt} \left( e^{-at} x(t) \right) = e^{-at} \dot x(t) - a e^{-at} x(t) + \end{equation} + + Multiplying $\dot x = a x + bu(t)$ by $e^{-at}$ we see: + + \begin{align} + e^{-at} \dot x = e^{-at} a x + e^{-at} bu(t) + \\ + e^{-at} \dot x - e^{-at} a x= e^{-at} bu(t) + \\ + \frac{d}{dt} \left( e^{-at} x(t) \right) = e^{-at} bu(t) + \\ + \int_{0}^{t} \frac{d}{d\tau} \left( e^{-a\tau} x(\tau) \right) d\tau = \int_{0}^{t} e^{-a\tau} bu(\tau) d\tau + \end{align} + + + + \end{flushleft} +\end{frame} + + + +\begin{frame}{Forced State Response (LTI) (2)} + % \framesubtitle{Limited control} + \begin{flushleft} + + Continuing the derivation: + + \begin{align} + \int_{0}^{t} \frac{d}{d\tau} \left( e^{-a\tau} x(\tau) \right) d\tau = \int_{0}^{t} e^{-a\tau} bu(\tau) d\tau + \\ + e^{-at} x(t) - x(0) = \int_{0}^{t} e^{-a\tau} bu(\tau) d\tau + \\ + x(t) = e^{at} x(0) + e^{at} \int_{0}^{t} e^{-a\tau} bu(\tau) d\tau + \\ + x(t) = e^{at} x(0) + \int_{0}^{t} e^{a(t-\tau)} bu(\tau) d\tau + \end{align} + + + + \end{flushleft} +\end{frame} + + + + +\begin{frame}{Forced State Response (LTI) (3)} + % \framesubtitle{Limited control} + \begin{flushleft} + + State-space equation $\dot{\bo{x}} = \bo{A} \bo{x} + \bo{B} \bo{u}(t)$ also has an analytical solution: + + \begin{equation} + \bo{x}(t) = e^{\bo{A}t} \bo{x}(0) + + \int_{0}^{t} e^{\bo{A}(t-\tau)} \bo{B} \bo{u}(\tau) d\tau + \end{equation} + + The same can be re-written as: + + \begin{equation} + \bo{x}(t) = e^{\bo{A}t} \bo{x}(0) + + e^{\bo{A}t} \int_{0}^{t} e^{-\bo{A}\tau} \bo{B} \bo{u}(\tau) d\tau + \end{equation} + + \end{flushleft} +\end{frame} + + + + + +\end{document} diff --git a/Slides/ControllabilityObservability/settings.tex b/Slides/ControllabilityObservability/settings.tex new file mode 100644 index 0000000..c9e906a --- /dev/null +++ b/Slides/ControllabilityObservability/settings.tex @@ -0,0 +1,192 @@ +\pdfmapfile{+sansmathaccent.map} + + +\mode +{ 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+ \item are easily simulated. +\end{itemize} + +\bigskip + +The affine control for this system can be given as: + +\begin{equation} + \bo{u}_i = -\bo{K}\bo{x}_i + \bo{u}_i^* +\end{equation} + +\end{flushleft} +\end{frame} + + + + +\begin{frame}{Stability of the Discrete Dynamics} + \framesubtitle{Real eigenvalues} + \begin{flushleft} + + Let us consider stability of the discrete dynamical system where matrix $\bo{A}$ has purely real eigenvalues: + + \begin{equation} + \bo{x}_{i+1} = \bo{A}\bo{x}_i + \end{equation} + + With eigendecomposition $\bo{A} = \bo{V}^{-1} \bo{D} \bo{V}$ (where $\bo{D}$ is a diagonal matrix with eigenvalues $\lambda_j$ of $\bo{A}$ on its diagonal) and introducing notation $\bo{z}_i = \bo{V}\bo{x}_i$ we get: + + \begin{equation} + \bo{x}_{i+1} = \bo{V}^{-1} \bo{D} \bo{V}\bo{x}_i + \end{equation} + \begin{equation} + \bo{z}_{i+1} = \bo{D} \bo{z}_i + \end{equation} + + Meaning that the dynamics became a system of independent scalar equations $z_{j, i+1} = \lambda_j z_{j, i}$. + + + \end{flushleft} +\end{frame} + + + + +\begin{frame}{Stability of the Discrete Dynamics} + \framesubtitle{Real eigenvalues} + \begin{flushleft} + + Thus, with $z_{j, i+1} = \lambda_j z_{j, i}$ we can find now the absolute value of the scalars $z_{j}$ will dwindle with time iff $|\lambda_j| < 1$: + + \begin{equation} + \left| \frac{z_{j, i+1}}{z_{j, i}} \right | = | \lambda_j | + \end{equation} + + + \end{flushleft} +\end{frame} + + + +\begin{frame}{Stability of the Discrete Dynamics} + \framesubtitle{2x2 system} + \begin{flushleft} + + Let us consider stability of the discrete dynamical system with a 2-by-2 matrix $\bo{A}$: + + \begin{equation} + \begin{bmatrix} + x_{1, i+1} \\ x_{2, i+1} + \end{bmatrix} + = + \begin{bmatrix} + \alpha & -\beta \\ \beta & \alpha + \end{bmatrix} + \begin{bmatrix} + x_{1, i} \\ x_{2, i} + \end{bmatrix} + \end{equation} + + Let us find norms of $\begin{bmatrix} + x_{1, i+1} \\ x_{2, i+1} + \end{bmatrix}$ and $\begin{bmatrix} + x_{1, i} \\ x_{2, i} + \end{bmatrix}$: + + + \begin{equation} + \left | \left| + \begin{bmatrix} + x_{1, i} \\ x_{2, i} + \end{bmatrix} + \right | \right|^2 + = + x_{1, i}^2 + x_{2, i}^2 + \end{equation} + + \begin{equation} + \left | \left| + \begin{bmatrix} + x_{1, i+1} \\ x_{2, i+1} + \end{bmatrix} + \right | \right|^2 + = + (\alpha^2 + \beta^2) (x_{1, i}^2 + x_{2, i}^2) + \end{equation} + + + \end{flushleft} +\end{frame} + + + +\begin{frame}{Stability of the Discrete Dynamics} + \framesubtitle{2x2 system} + \begin{flushleft} + + We can find the ratio of the norms of $\begin{bmatrix} + x_{1, i+1} \\ x_{2, i+1} + \end{bmatrix}$ and $\begin{bmatrix} + x_{1, i} \\ x_{2, i} + \end{bmatrix}$: + + + + \begin{equation} + \left | \left| + \begin{bmatrix} + x_{1, i+1} \\ x_{2, i+1} + \end{bmatrix} + \right | \right|^2 + / + \left | \left| + \begin{bmatrix} + x_{1, i} \\ x_{2, i} + \end{bmatrix} + \right | \right|^2 + = + \alpha^2 + \beta^2 + \end{equation} + + Remembering that eigenvalues of the system are $\lambda = \alpha \pm j\beta$, we can rewrite the expression above as: + + \begin{equation} + \left | \left| + \begin{bmatrix} + x_{1, i+1} \\ x_{2, i+1} + \end{bmatrix} + \right | \right|^2 + / + \left | \left| + \begin{bmatrix} + x_{1, i} \\ x_{2, i} + \end{bmatrix} + \right | \right|^2 + = + | \lambda |^2 + \end{equation} + + We can see that the norm of the variable $\bo{x}$ will dwindle with time iff $|\lambda| < 1$. + + \end{flushleft} +\end{frame} + + + + +\begin{frame}{Stability of the Discrete Dynamics} +\begin{flushleft} + +General stability criterion is given below: + +\bigskip + +\begin{block}{Stability criterion} +In general, discrete system $\bo{x}_{i+1} = \bo{A}\bo{x}_i$ is stable as long as the eigenvalues of $\bo{A}$ are smaller than 1 by absolute value: $|\lambda_i(\bo{A})| \leq 1, \; \forall i$. +\end{block} + +\end{flushleft} +\end{frame} + + + +\begin{frame} + + \centering{\huge CT-LTI: Analytical solution} + +\end{frame} + + + + + +\begin{frame}{Matrix exponential} + % \framesubtitle{Limited control} + \begin{flushleft} + + Exponential $e^a$ is defined as a series: + + \begin{equation} + e^a =1+a+\frac{1}{2} a^2 + +\frac{1}{6} a^3 + ... = \sum_{n=0}^{\infty} \frac{1}{n!} a^n + \end{equation} + + Matrix exponential $e^\bo{A}$ is defined as a series: + + \begin{equation} + e^\bo{A} = \bo{I}+\bo{A}+\frac{1}{2} \bo{A}\bo{A} + +\frac{1}{6} \bo{A}\bo{A}\bo{A} + ... = \sum_{n=0}^{\infty} \frac{1}{n!} \bo{A}^n + \end{equation} + + + \end{flushleft} +\end{frame} + + + + +\begin{frame}{Analytical solution to ODE} + % \framesubtitle{Limited control} + \begin{flushleft} + + An ODE of the form $\dot x = a x$ has analytical solution $x(t) = e^{at} x(0)$. + + \bigskip + + An ODE of the form $\dot{\bo{x}} = \bo{A} \bo{x}$ has analytical solution $\bo{x}(t) = e^{\bo{A}t} \bo{x}(0)$. + + \bigskip + + Let us check that this is a solution: + + \begin{align} + \bo{x}(t) &= \left( \bo{I}+\bo{A}t+\frac{1}{2} \bo{A}\bo{A}t^2 + +\frac{1}{6} \bo{A}\bo{A}\bo{A}t^3 + ... \right) \bo{x}(0) & + \\ + \dot{\bo{x}}(t) &= \left( \bo{A}+\bo{A}\bo{A}t + +\frac{1}{2}\bo{A}\bo{A}\bo{A}t^2 + ... \right) \bo{x}(0) & + \\ + \dot{\bo{x}}(t) &= \bo{A} \left(\bo{I} +\bo{A}t + +\frac{1}{2}\bo{A}\bo{A}t^2 + ... \right) \bo{x}(0) & + \\ + \dot{\bo{x}}(t) &= \bo{A} e^{\bo{A}t} \bo{x}(0) & + \\ + \dot{\bo{x}}(t) &= \bo{A} \bo{x}(t) &\ \ \qed + \end{align} + + + + \end{flushleft} +\end{frame} + + + +\begin{frame}{Forced State Response (LTI) (1)} + % \framesubtitle{Limited control} + \begin{flushleft} + + An ODE of the form $\dot x = a x + bu(t)$ also has analytical solution. To find it, we first find the following derivative: + % + \begin{equation} + \frac{d}{dt} \left( e^{-at} x(t) \right) = e^{-at} \dot x(t) - a e^{-at} x(t) + \end{equation} + + Multiplying $\dot x = a x + bu(t)$ by $e^{-at}$ we see: + + \begin{align} + e^{-at} \dot x = e^{-at} a x + e^{-at} bu(t) + \\ + e^{-at} \dot x - e^{-at} a x= e^{-at} bu(t) + \\ + \frac{d}{dt} \left( e^{-at} x(t) \right) = e^{-at} bu(t) + \\ + \int_{0}^{t} \frac{d}{d\tau} \left( e^{-a\tau} x(\tau) \right) d\tau = \int_{0}^{t} e^{-a\tau} bu(\tau) d\tau + \end{align} + + + + \end{flushleft} +\end{frame} + + + +\begin{frame}{Forced State Response (LTI) (2)} + % \framesubtitle{Limited control} + \begin{flushleft} + + Continuing the derivation: + + \begin{align} + \int_{0}^{t} \frac{d}{d\tau} \left( e^{-a\tau} x(\tau) \right) d\tau = \int_{0}^{t} e^{-a\tau} bu(\tau) d\tau + \\ + e^{-at} x(t) - x(0) = \int_{0}^{t} e^{-a\tau} bu(\tau) d\tau + \\ + x(t) = e^{at} x(0) + e^{at} \int_{0}^{t} e^{-a\tau} bu(\tau) d\tau + \\ + x(t) = e^{at} x(0) + \int_{0}^{t} e^{a(t-\tau)} bu(\tau) d\tau + \end{align} + + + + \end{flushleft} +\end{frame} + + + + +\begin{frame}{Forced State Response (LTI) (3)} + % \framesubtitle{Limited control} + \begin{flushleft} + + State-space equation $\dot{\bo{x}} = \bo{A} \bo{x} + \bo{B} \bo{u}(t)$ also has an analytical solution: + + \begin{equation} + \bo{x}(t) = e^{\bo{A}t} \bo{x}(0) + + \int_{0}^{t} e^{\bo{A}(t-\tau)} \bo{B} \bo{u}(\tau) d\tau + \end{equation} + + The same can be re-written as: + + \begin{equation} + \bo{x}(t) = e^{\bo{A}t} \bo{x}(0) + + e^{\bo{A}t} \int_{0}^{t} e^{-\bo{A}\tau} \bo{B} \bo{u}(\tau) d\tau + \end{equation} + + \end{flushleft} +\end{frame} + + + + + + +\begin{frame} + + \centering{\huge Discretization} + +\end{frame} + + + + + +\begin{frame}{From analytical solution to discrete dynamics} + % \framesubtitle{Limited control} + \begin{flushleft} + Given a solution to a state-space system we can consider how the system evolves from the point $t=0$ to the point $t=\Delta t$, assuming that $\bo{u}(t) = \bo{u}_0 = \text{const}, \ t \in [ 0, \ \Delta t ]$, and denoting $\bo{x}(0) = \bo{x}_0$ and $\bo{x}(\Delta t) = \bo{x}_1$: + + \begin{equation} + \bo{x}_1 = e^{\bo{A}\Delta t} \bo{x}_0 + + e^{\bo{A} \Delta t} \int_{0}^{\Delta t} e^{-\bo{A}\tau} \bo{B} \bo{u}_0 d\tau + \end{equation} + + Now we denote: + % + \begin{align} + \bar{\bo{A}} = e^{\bo{A}\Delta t}, \ \ \ + \bar{\bo{B}} = e^{\bo{A} \Delta t} \int_{0}^{\Delta t} e^{-\bo{A}\tau} \bo{B} d\tau + \end{align} + + We get: + % + \begin{equation} + \bo{x}_1 = \bar{\bo{A}} \bo{x}_0 + \bar{\bo{B}} \bo{u}_0 + \end{equation} + + \end{flushleft} +\end{frame} + + + + +\begin{frame}{Discretization via finite differences} +%\framesubtitle{Finite difference} +\begin{flushleft} + +Consider linear time-invariant autonomous system: + +\begin{equation} + \dot {\bo{x}} = \bo{A} \bo{x} +\end{equation} + + +The time derivative $\dot {\bo{x}}$ can be replaces with a finite difference: + +\begin{equation} +\dot {\bo{x}} \approx \frac{1}{\Delta t}(\bo{x}(t + \Delta t) - \bo{x}(t)) +\end{equation} + +Note that we could have also used other definitions of a finite difference: + +\begin{equation} +\dot {\bo{x}} \approx \frac{1}{\Delta t}(\bo{x}(t + 0.5\Delta t) - \bo{x}(t - 0.5\Delta t)) +\end{equation} + +or + +\begin{equation} +\dot {\bo{x}} \approx \frac{1}{\Delta t}(\bo{x}(t) - \bo{x}(t - \Delta t)) +\end{equation} + +\end{flushleft} +\end{frame} + + + + +\begin{frame}{Zero-order hold (1)} +%\framesubtitle{Finite difference notation} +\begin{flushleft} +We can introduce notation: + +\begin{equation} +\begin{cases} +\bo{x}_0 = \bo{x}(0) \\ +\bo{x}_1 = \bo{x}(\Delta t) \\ +\bo{x}_2 = \bo{x}(2\Delta t) \\ +... \\ +\bo{x}_n = \bo{x}(n\Delta t) +\end{cases} +\end{equation} + +We say that $\bo{x}_i$ is the value of $\bo{x}$ at the time step $i$. Then the finite difference can be written, for example, as follows: + +\begin{equation} +\dot {\bo{x}} \approx \frac{1}{\Delta t}(\bo{x}_{i+1} - \bo{x}_i) +\end{equation} + +\end{flushleft} +\end{frame} + + + +\begin{frame}{Zero-order hold (2)} +%\framesubtitle{Finite difference in an autonomous LTI} +\begin{flushleft} + +We can rewrite our original autonomous LTI as follows: + +\begin{equation} +\frac{1}{\Delta t}(\bo{x}_{i + 1} - \bo{x}_i) = \bo{A} \bo{x}_i +\end{equation} +Isolating $\bo{x}_{i + 1}$ on the left hand side, we get: +\begin{equation} +\bo{x}_{i + 1} = (\bo{A} \Delta t + \bo{I}) \bo{x}_i +\end{equation} + +\noindent\rule{11cm}{0.4pt} + +Or alternatively: + +\begin{equation} +\frac{1}{\Delta t}(\bo{x}_{i + 1} - \bo{x}_i) = \bo{A} \bo{x}_{i + 1} +\end{equation} +Isolating $\bo{x}_{i + 1}$ on the left hand side, we get: +\begin{equation} +\bo{x}_{i + 1} = (\bo{I} - \bo{A} \Delta t)^{-1} \bo{x}_i +\end{equation} + +\end{flushleft} +\end{frame} + + + + +\begin{frame}{Zero-order hold (3)} +%\framesubtitle{Zero order hold} +\begin{flushleft} + +Defining \emph{discrete state space matrix} $\bar{\bo{A}}$ and \emph{discrete control matrix} $\bar{\bo{B}}$ as follows: + +\begin{equation} +\bar{\bo{A}} = \bo{A} \Delta t + \bo{I} +\end{equation} +\begin{equation} +\bar{\bo{B}} = \bo{B} \Delta t +\end{equation} +% +We get discrete dynamics: + +\begin{equation} +\bo{x}_{i+1} = \bar{\bo{A}} \bo{x}_i + \bar{\bo{B}} \mathbf u_i +\end{equation} + +This way of defining discrete dynamics is called \emph{zero order hold (ZOH)}. + +\end{flushleft} +\end{frame} + + +\begin{frame}{Zero-order hold (4)} +%\framesubtitle{Zero order hold vs First order hold} +\begin{flushleft} + +Graphically, we can understand what zero order hold is, by comparing it to the first order hold: + +\begin{figure} [h!] +\begin{center} +\includegraphics[width=3.5in]{ZOH.PNG} +\end{center} +\caption{Different types of discretization} \label{F:ZOH} +\end{figure} + +\end{flushleft} +\end{frame} + + +%\begin{frame}{ZOH and other types of discretization} +%\framesubtitle{Exact discretization} +%\begin{flushleft} +% +%Let the discrete state $\bo{x}_i$ correspond to continuous state $\bo{x}$ at the moment of time $t_i$. Then, we can say that the discretization is \emph{exact} the following holds for any solution $\bo{x}(t)$ +% +%\begin{equation} +%\bo{x}_0 = \bo{x}(t_0) \rightarrow +%\bo{x}_i = \bo{x}(t_i), \ \forall i +%\end{equation} +% +%We can compute the exact discretization as follows: +% +%\begin{equation} +%\bar{\bo{A}} = e^{\bo{A} \Delta t} +%\end{equation} +%\begin{equation} +%\bar{\bo{B}} = \bo{B} \int_{t_0}^{t_0 + \Delta t} e^{\bo{A} s} ds +%\end{equation} +% +% +%\end{flushleft} +%\end{frame} + + + + + + + + + +\begin{frame}{Read more} + +\begin{itemize} +\item \bref{http://cse.lab.imtlucca.it/~bemporad/teaching/ac/pdf/04a-TD_sys.pdf}{Automatic Control 1 Discrete-time linear systems}, Prof. Alberto Bemporad, University of Trento + +\item \bref{https://web.mit.edu/2.14/www/Handouts/StateSpaceResponse.pdf}{MIT 2.14, State Space Response} + +\end{itemize} + +\end{frame} + + + +\myqrframe + +\end{document} diff --git a/Slides/Discrete/settings.tex b/Slides/Discrete/settings.tex new file mode 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If it's 1, each line will be numbered + stringstyle=\color{mymauve}, % string literal style + tabsize=2, % sets default tabsize to 2 spaces + title=\lstname % show the filename of files included with \lstinputlisting; also try caption instead of title +} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% URL settings +\hypersetup{ + colorlinks=false, + linkcolor=blue, + filecolor=blue, + urlcolor=blue, +} + +%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% tikz settings + +\usepackage{tikz} +\tikzset{every picture/.style={line width=0.75pt}} \ No newline at end of file diff --git a/Slides/HJB_LQR/main.pdf b/Slides/HJB_LQR/main.pdf new file mode 100644 index 0000000..6bf88f4 Binary files /dev/null and b/Slides/HJB_LQR/main.pdf differ diff --git a/Slides/HJB_LQR/main.tex b/Slides/HJB_LQR/main.tex new file mode 100644 index 0000000..9ca416c --- /dev/null +++ b/Slides/HJB_LQR/main.tex @@ -0,0 +1,362 @@ +\documentclass{beamer} + +\input{settings.tex} + + +\title{Hamilton-Jacobi-Bellman eq., Riccati eq., Linear Quadratic Regulator} +\subtitle{Control Theory, Lecture 7} +\author{by Sergei Savin} +\centering +\date{\mydate} + + + +\begin{document} +\maketitle + + +\begin{frame}{Content} +\begin{itemize} +\item Hamilton-Jacobi-Bellman equation +\begin{itemize} + \item Definitions + \item Cost, optimal cost + \item Differentiating optimal cost +\end{itemize} +\item Algebraic Riccati equation +\begin{itemize} + \item HJB for LTI + \item Linear Quadratic Regulator + \item Numerical methods +\end{itemize} +\end{itemize} +\end{frame} + +\begin{frame}{Hamilton-Jacobi-Bellman equation} +\framesubtitle{Definitions} +\begin{flushleft} + +Let us define dynamics: + +\begin{equation} + \dot {\bo{x}} = \bo{f} (\bo{x}, \bo{u}) +\end{equation} +% +with initial conditions $\bo{x}(0)$. + +\bigskip + +Additionally we define \emph{control policy} as: + +\begin{equation} + \bo{u} = \pi (\bo{x}, t) +\end{equation} + +To connect with the previous ways we talked about control, we can say that choosing different control gains and different feed-forward control amounts to choosing a different control policy. + +\end{flushleft} +\end{frame} + + + + +\begin{frame}{Hamilton-Jacobi-Bellman equation} +\framesubtitle{Cost, optimal cost} +\begin{flushleft} + +Let $J$ be an additive cost function: + +\begin{equation} +J (\bo{x}_0, \pi (\bo{x}, t)) = \int_0^\infty g(\bo{x}, \bo{u}) dt +\end{equation} +% +where $g(\bo{x}, \bo{u})$ is instantaneous cost and $\bo{x}_0 = \bo{x}(0)$ is the initial conditions. Notice that $J$ depends on $\bo{x}_0$ rather than $\bo{x}(t)$, since initial conditions and control policy completely define the trajectory of the system $\bo{x}(t)$. + + +\bigskip + +Let $J^*$ be the optimal (lowest possible) cost. In other words: + +\begin{equation} +J^*(\bo{x}_0) = \underset{\pi}{\inf{}} J(\bo{x}_0, \pi (\bo{x}, t)) +\end{equation} + +Optimal cost is attained when optimal policy is attained: $\pi = \pi^*(\bo{x}, t)$ + +\end{flushleft} +\end{frame} + + + + + +%\begin{frame}{Hamilton-Jacobi-Bellman equation} +%\framesubtitle{Differentiating optimal cost} +%\begin{flushleft} +% +% +%Since $J^*(\bo{x}_0)$ does not depend on $t$, its full derivative is zero: +% +%\begin{equation} +%\frac{d J^*(\bo{x}_0)}{dt} = 0 +%\end{equation} +% +%At the same time, we can expand the full derivative as follows: +% +%\begin{equation} +%\frac{d J^*}{dt } = +%\frac{\partial J^*}{\partial \bo{x}} \dot {\bo{x}} + +%\frac{\partial J^*}{\partial t} = 0 +%\end{equation} +% +%\bigskip +% +%Observe that $\frac{\partial J^*}{\partial t} = g(\bo{x}, \bo{u})$, and $\dot {\bo{x}} = \bo{f} (\bo{x}, \bo{u})$. Therefore: +% +%\begin{equation} +%\frac{\partial J^*}{\partial \bo{x}} \bo{f} (\bo{x}, \bo{u}) + +%g(\bo{x}, \bo{u}) = 0 +%\end{equation} +% +%\end{flushleft} +%\end{frame} + + + + +\begin{frame}{Hamilton-Jacobi-Bellman equation} +% \framesubtitle{HJB} +\begin{flushleft} + +With this, we can formulate \emph{Hamilton-Jacobi-Bellman equation} (HJB): + +\begin{equation} +\label{eq:HJB_0} +\underset{\bo{u}}{\min} \ +\left[ +g(\bo{x}, \bo{u}) + +\frac{\partial J^*}{\partial \bo{x}} \bo{f} (\bo{x}, \bo{u}) +\right] = 0 +\end{equation} + +This can be loosely interpreted as follows: the value in square brackets is $\dot J(\bo{x}_0, \pi)$, which is equal to 0 when $\pi = \pi^*(\bo{x}, t)$, and is positive otherwise (in the small vicinity of $\pi^*$), as $J(\bo{x}_0, \pi^*)$ is smaller than any $J(\bo{x}_0, \pi), \ \pi^* \neq \pi$. + +\bigskip + + +We can find control that delivers minimum to the function \eqref{eq:HJB_0}: + +\begin{equation} +u^* = \underset{\bo{u}}{\argmin} \ +\left[ +g(\bo{x}, \bo{u}) + +\frac{\partial J^*}{\partial \bo{x}} \bo{f} (\bo{x}, \bo{u}) \right] +\end{equation} + +\end{flushleft} +\end{frame} + + + + + +\begin{frame}{Algebraic Riccati} +\framesubtitle{HJB for LTI} +\begin{flushleft} + +For LTI, dynamics is: +\begin{equation} +\dot {\bo{x}} = \bo{A} \bo{x} + \bo{B} \bo{u} +\end{equation} + +We can choose quadratic cost: +\begin{equation} +g(\mathbf x, \mathbf u) = +\mathbf x^\top \bo{Q} \bo{x} + +\mathbf u^\top \bo{R} \bo{u} +\end{equation} + +Then HJB becomes: +\begin{equation} +\underset{\bo{u}}{\min} \ [ +\bo{x}^\top \bo{Q} \bo{x} + +\bo{u}^\top \bo{R} \bo{u} + +\frac{\partial J^*}{\partial \bo{x}} +(\bo{A} \bo{x} + \bo{B} \bo{u})] = 0 +\end{equation} +% +where $\bo{Q} = \bo{Q}^\top \geq 0 $ and $\bo{R} = \bo{R}^\top > 0$. + +\end{flushleft} +\end{frame} + + +\begin{frame}{Algebraic Riccati} +\framesubtitle{HJB for LTI, part 2} +\begin{flushleft} + +There is a theorem that says that for LTI with quadratic cost, $J^*$ has the form: + +\begin{equation} +J^* = \mathbf x^\top \bo{S} \bo{x} +\end{equation} +% +where $\bo{S} = \bo{S}^\top \geq 0$. + +\bigskip + +Then HJB becomes: + +\[ +\underset{\bo{u}}{\min} \ +\left [ +\mathbf x^\top \bo{Q} \bo{x} + +\mathbf u^\top \bo{R} \bo{u} ++ +\bo{x}^\top \bo{S} +(\bo{A} \bo{x} + \bo{B} \bo{u}) ++ +(\bo{A} \bo{x} + \bo{B} \bo{u})^\top +\bo{S} \bo{x} +\right ] = 0 +\] + +Simplifying, we get: + +\[ +\underset{\bo{u}}{\min} \ +\left [ +\bo{u}^\top \bo{R} \bo{u} ++ +\bo{x}^\top ( +\bo{Q} + \bo{S} \bo{A} + \bo{A}^\top \bo{S} +)\bo{x} ++ +\bo{x}^\top \bo{S} \bo{B} \bo{u} ++ \bo{u}^\top \bo{B}^\top \bo{S} \bo{x} +\right ] = 0 +\] + +\end{flushleft} +\end{frame} + + +\begin{frame}{Algebraic Riccati} +\framesubtitle{Linear Quadratic Regulator} +\begin{flushleft} + + +Finding partial derivative of the HJB with respect to $\bo{u}$ and setting it to zero (as it is an extreme point) we get: +\begin{equation} +2 \mathbf u^\top \bo{R} + +2 \bo{x}^\top \bo{S} \bo{B} = 0 +\end{equation} + +This expression can be transposed and $\mathbf u$ separated: + +\begin{equation} +\mathbf u = +-\bo{R}^{-1} \bo{B}^\top \bo{S} \bo{x} +\end{equation} + +This is the desired control law. We can see that it is \emph{proportional}. We can re-write it as: + +\begin{equation} +\mathbf u = -\mathbf K \bo{x} +\end{equation} + +where $\mathbf K = \bo{R}^{-1} \bo{B}^\top \bo{S}$ is the controller gain. This control law is called Linear Quadratic Regulator (LQR). + +\end{flushleft} +\end{frame} + + + + + +\begin{frame}{Algebraic Riccati} +% \framesubtitle{Algebraic Riccati} +\begin{flushleft} + +Substituting found control law into the HJB, we find: +\begin{equation} +\begin{split} +\underset{\bo{u}}{\min} \ +[ +\bo{x}^\top ( +\bo{Q} + \bo{S} \bo{A} + \bo{A}^\top \bo{S} +)\bo{x} ++ +\bo{x}^\top \bo{S} \bo{B} \bo{R}^{-1} \bo{R} \mathbf R^{-1} \bo{B}^\top \bo{S} \bo{x} +- \\ +- +\bo{x}^\top \bo{S} \bo{B} \bo{R}^{-1} \bo{B}^\top \bo{S} \bo{x} +- +\bo{x}^\top\bo{S} \bo{B} \bo{R}^{-1} \bo{B}^\top \bo{S} \bo{x} +] = 0 +\end{split} +\end{equation} + +Simplifying, we get: + +\begin{equation} +\bo{x}^\top (\bo{Q} + \bo{S} \bo{A} + \bo{A}^\top \bo{S} +- \bo{S} \bo{B} \bo{R}^{-1} \bo{B}^\top \bo{S}) \bo{x} = 0 +\end{equation} +% +which would hold for all $\bo{x}$ iff: +% + +\begin{equation} +\bo{Q} - \bo{S} \bo{B} \bo{R}^{-1} \bo{B}^\top \bo{S} + + \bo{S} \bo{A} + \bo{A}^\top \bo{S} = 0 +\end{equation} + +This is the \emph{Algebraic Riccati equation}. + +\end{flushleft} +\end{frame} + + + +\begin{frame}{Algebraic Riccati} +\framesubtitle{Numerical methods} +\begin{flushleft} + +There are a number of ways to solve LQR: + +\bigskip + +\begin{itemize} + \item In MATLAB there is a function \texttt{[K,S,P] = lqr(A,B,Q,R), where P=eig(A-B*K)} + \item In Python, there is \texttt{S = scipy.linalg.solve\_continuous\_are(A,B,Q,R)} + \item In Drake there is a function \texttt{(K,S) = LinearQuadraticRegulator(A,B,Q,R)} +\end{itemize} + +\end{flushleft} +\end{frame} + + + +\begin{frame}{LQR and pole placement} +% \framesubtitle{Numerical methods} + \begin{flushleft} + + \begin{itemize} + \item Pole placement \textcolor{mydarkgreen}{upsides}: allows to design exactly how fast the control error decays to zero; allows to design control error oscillations. + + \item Pole placement \textcolor{red}{downsides}: may require unreasonably high control gains. Easy to ask for "unreasonable" performance. + + \item LQR \textcolor{mydarkgreen}{upsides}: easy to produce "reasonable" control gains. + + \item LQR \textcolor{red}{downsides}: may produce very slow decaying control error with oscillations. + \end{itemize} + + + \end{flushleft} +\end{frame} + + +\myqrframe + +\end{document} diff --git a/Slides/HJB_LQR/settings.tex b/Slides/HJB_LQR/settings.tex new file mode 100644 index 0000000..c9e906a --- /dev/null +++ b/Slides/HJB_LQR/settings.tex @@ -0,0 +1,192 @@ +\pdfmapfile{+sansmathaccent.map} + + +\mode +{ + \usetheme{Warsaw} % or try Darmstadt, Madrid, Warsaw, Rochester, CambridgeUS, ... + \usecolortheme{seahorse} % or try seahorse, beaver, crane, wolverine, ... + \usefonttheme{serif} % or try serif, structurebold, ... + \setbeamertemplate{navigation symbols}{} + \setbeamertemplate{caption}[numbered] +} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% itemize settings + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% itemize settings + +\definecolor{mypaleblue}{RGB}{240, 240, 255} +\definecolor{mylightblue}{RGB}{120, 150, 255} +\definecolor{myblue}{RGB}{90, 90, 255} +\definecolor{mygblue}{RGB}{70, 110, 240} +\definecolor{mydarkblue}{RGB}{0, 0, 180} +\definecolor{myblackblue}{RGB}{40, 40, 120} + +\definecolor{mygreen}{RGB}{0, 200, 0} +\definecolor{mydarkgreen}{RGB}{0, 120, 0} +\definecolor{mygreen2}{RGB}{245, 255, 230} + +\definecolor{mygray}{gray}{0.8} +\definecolor{mygray2}{RGB}{130, 130, 130} +\definecolor{mydarkgray}{RGB}{80, 80, 160} +\definecolor{mylightgray}{RGB}{160, 160, 160} + +\definecolor{mydarkred}{RGB}{160, 30, 30} +\definecolor{mylightred}{RGB}{255, 150, 150} +\definecolor{myred}{RGB}{200, 110, 110} +\definecolor{myblackred}{RGB}{120, 40, 40} + +\definecolor{mypink}{RGB}{255, 30, 80} +\definecolor{myhotpink}{RGB}{255, 80, 200} +\definecolor{mywarmpink}{RGB}{255, 60, 160} +\definecolor{mylightpink}{RGB}{255, 80, 200} +\definecolor{mydarkpink}{RGB}{155, 25, 60} + +\definecolor{mydarkcolor}{RGB}{60, 25, 155} +\definecolor{mylightcolor}{RGB}{130, 180, 250} + +\setbeamertemplate{itemize items}[default] + +\setbeamertemplate{itemize item}{\color{myblackblue}$\blacksquare$} +\setbeamertemplate{itemize subitem}{\color{mygblue}$\blacktriangleright$} +\setbeamertemplate{itemize subsubitem}{\color{mygray}$\blacksquare$} + +\setbeamercolor{palette quaternary}{fg=white,bg=mydarkgray} +\setbeamercolor{titlelike}{parent=palette quaternary} + +\setbeamercolor{palette quaternary2}{fg=black,bg=mypaleblue} +\setbeamercolor{frametitle}{parent=palette quaternary2} + +\setbeamerfont{frametitle}{size=\Large,series=\scshape} +\setbeamerfont{framesubtitle}{size=\normalsize,series=\upshape} + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% block settings + +\setbeamercolor{block title}{bg=red!30,fg=black} + +\setbeamercolor*{block title example}{bg=mygreen!40!white,fg=black} + +\setbeamercolor*{block body example}{fg= black, bg= mygreen2} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% URL settings +\hypersetup{ + colorlinks=true, + linkcolor=blue, + filecolor=blue, + urlcolor=blue, +} + +%%%%%%%%%%%%%%%%%%%%%%%%%% + +\renewcommand{\familydefault}{\rmdefault} + +\usepackage{amsmath} +\usepackage{mathtools} + +\usepackage{subcaption} + +\usepackage{qrcode} + +\DeclareMathOperator*{\argmin}{arg\,min} +\newcommand{\bo}[1] {\mathbf{#1}} + +\newcommand{\R}{\mathbb{R}} +\newcommand{\T}{^\top} + +\newcommand{\dx}[1] {\dot{\mathbf{#1}}} +\newcommand{\ma}[4] {\begin{bmatrix} + #1 & #2 \\ #3 & #4 +\end{bmatrix}} +\newcommand{\myvec}[2] {\begin{bmatrix} + #1 \\ #2 +\end{bmatrix}} +\newcommand{\myvecT}[2] {\begin{bmatrix} + #1 & #2 +\end{bmatrix}} + + +\newcommand{\mydate}{Spring 2023} + +\newcommand{\mygit}{\textcolor{blue}{\href{https://github.com/SergeiSa/Control-Theory-Slides-Spring-2023}{github.com/SergeiSa/Control-Theory-Slides-Spring-2023}}} + +\newcommand{\myqr}{ \textcolor{black}{\qrcode[height=1.5in]{https://github.com/SergeiSa/Control-Theory-Slides-Spring-2023}} +} + +\newcommand{\myqrframe}{ + \begin{frame} + \centerline{Lecture slides are available via Github, links are on Moodle} + \bigskip + \centerline{You can help improve these slides at:} + \centerline{\mygit} + \bigskip + \myqr + \end{frame} +} + + +\newcommand{\bref}[2] {\textcolor{blue}{\href{#1}{#2}}} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% code settings + +\usepackage{listings} +\usepackage{color} +% \definecolor{mygreen}{rgb}{0,0.6,0} +% \definecolor{mygray}{rgb}{0.5,0.5,0.5} +\definecolor{mymauve}{rgb}{0.58,0,0.82} +\lstset{ + backgroundcolor=\color{white}, % choose the background color; 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Same as before, it is a \emph{dynamical system}, but this time we need more variables to describe the state of this system, for example we can use the set $\{ y, \ \dot{y} , ...\,,y^{(n-1)} \}$. + +\begin{example}[Pendulum] +\begin{equation} + \ddot{y} = - 0.1 \dot y - 7\sin(y) +\end{equation} +\end{example} + + +\begin{example}[DC motor under constant voltage] +\begin{equation} +\begin{cases} + \dot{y}_1 = - 100 \dot{y}_2 -2 y_1 + 10 \\ + \ddot{y}_2 = -0.1 \dot{y}_2 + 100 y_1 +\end{cases} +\end{equation} +\end{example} + +\end{flushleft} +\end{frame} + + + + +\begin{frame}{Linear ODE, 1st order} +\begin{flushleft} + +Linear ODEs of the first order have normal form: + +\begin{equation} + \dot{\bo{x}} = \bo{A} \bo{x} +\end{equation} + +\begin{example} +\begin{equation} +\begin{cases} + \dot{x}_1 = -20 x_1 + 7 x_2 \\ + \dot{x}_2 = 10.5 x_1 - 3 x_2 +\end{cases} +\end{equation} +\end{example} + +\begin{example} +\begin{equation} +\begin{bmatrix} +\dot{x}_1 \\ +\dot{x}_2 \\ +\dot{x}_3 +\end{bmatrix} += +\begin{bmatrix} +-8 & 5 & 2 \\ + 0.5 & -10 & -2 \\ + 1 & -1 & -20 +\end{bmatrix} +\begin{bmatrix} +x_1 \\ +x_2 \\ +x_3 +\end{bmatrix} +\end{equation} +\end{example} + +\end{flushleft} +\end{frame} + + + + +\begin{frame}{Linear differential equations, n-th order} +%\framesubtitle{n-th order} +\begin{flushleft} + +A single linear ODE of the n-th order are often written in the form: + +\begin{equation} + a_n y^{(n)} + + ... + + a_2 \ddot{y} + a_1 \dot{y} + + a_0 y = 0 +\end{equation} + +\begin{example} +\begin{equation} +12 \dddot{y} - + 3 \ddot{y} + 5.5 \dot{y} + + 2 y = 0 +\end{equation} +\end{example} + +\begin{example} +\begin{equation} + 5 \ddot{y} - 2 \dot{y} + + 10 y = 0 +\end{equation} +\end{example} + +\end{flushleft} +\end{frame} + + + + +\begin{frame}{ODEs with an input, 1} + %\framesubtitle{n-th order} + \begin{flushleft} + + Sometimes it is convenient to write an ODE in the form with an \emph{input}, for example: + + \begin{equation} + a_2 \ddot{y} + a_1 \dot{y} + + a_0 y = u(t) + \end{equation} + + In this equation $u(t)$ is a function of time. This form offers us many uses: + + \begin{itemize} + \item We can use $u(t)$ to model \emph{control input}, (e.g. voltage, motor torque) that we directly control. + + \item We can use $u(t)$ to model external forces acting on the system. + + \item We can substitute particular function instead of $u(t)$, e.g. sine wave or step function, to study how the system behaves with such an input. + \end{itemize} + + \end{flushleft} +\end{frame} + + + +\begin{frame}{ODEs with an input, 1} + \begin{flushleft} + + Some examples of linear ODEs with one input: + + + \begin{example} + \begin{equation} + \begin{cases} + \dot{y}_1 = -20 y_1 + 7 y_2 + u \\ + \dot{y}_2 = 10.5 y_1 - 3 y_2 + \end{cases} + \end{equation} + \end{example} + + \begin{example} + \begin{equation} + \begin{bmatrix} + \dot{x}_1 \\ + \dot{x}_2 \\ + \dot{x}_3 + \end{bmatrix} + = + \begin{bmatrix} + -8 & 5 & 2 \\ + 0.5 & -10 & -2 \\ + 1 & -1 & -20 + \end{bmatrix} + \begin{bmatrix} + x_1 \\ + x_2 \\ + x_3 + \end{bmatrix} + + + \begin{bmatrix} + 1 \\ + 0 \\ + 0 + \end{bmatrix} + u + \end{equation} + \end{example} + + \end{flushleft} +\end{frame} + + + +\begin{frame}{Equations with an input} + %\framesubtitle{n-th order} + \begin{flushleft} + + General form of an n-th order linear ODE with an input can be presented as follows: + % + \begin{equation} + a_n y^{(n)} + + ... + + a_2 \ddot{y} + a_1 \dot{y} + + a_0 y = u(t) + \end{equation} + + \bigskip + + State-space representation of a linear system with an input is: + % + \begin{equation} + \dot{\bo{x}} = \bo{A} \bo{x} + \bo{B} \bo{u} + \end{equation} + + Note that in latter, $\bo{u}$ can be either scalar or a vector. + + \end{flushleft} +\end{frame} + + + + + + + +\begin{frame}{Equations with an output} + %\framesubtitle{n-th order} + \begin{flushleft} + + Equations can also have an output. The meaning of what is an output of an equation depends on the particular use-case - it is not a mathematical issue, it is a question of interpretation. For example, an output can mean: + + \begin{itemize} + \item What we measure (position and orientation of a quadrotor, angular velocity of motor's rotor, etc.). + + \item What we care about and/or what we want to control (height of a quadrotor, velocity of a car, etc.) + + \item etc. + \end{itemize} + + We often denote output as $y$, and it depends on the state of the system: $y = g(\bo{x})$ + + \end{flushleft} +\end{frame} + + +\begin{frame}{Equations with an output} + %\framesubtitle{n-th order} + \begin{flushleft} + + State-space representation of a linear system with an input and an output is: + % + \begin{equation} + \begin{cases} + \dot{\bo{x}} = \bo{A} \bo{x} + \bo{B}\bo{u} \\ + \bo{y} = \bo{C}\bo{x} + \end{cases} + \end{equation} + + If $\bo{u} \in \R$ and $\bo{y} \in \R$ (i.e. if they are scalars) and you want to represent the system with an output as a single ODE, it is typical to treat the output as the ODE variable: + + \begin{equation} + a_n y^{(n)} + + ... + + a_2 \ddot{y} + a_1 \dot{y} + + a_0 y = u(t) + \end{equation} + + \end{flushleft} +\end{frame} + + + + + + +\begin{frame}{Linear differential equations} +%\framesubtitle{...are what we will study} +\begin{flushleft} + +In this course we will focus entirely on linear dynamical systems, expressed as ODEs: + +\begin{equation} + a_n y^{(n)} + + ... + + a_2 \ddot{y} + a_1 \dot{y} + + a_0 y = u(t) +\end{equation} + +or in state-space form: + +\begin{equation} + \begin{cases} + \dot{\bo{x}} = \bo{A} \bo{x} + \bo{B}\bo{u} \\ + \bo{y} = \bo{C}\bo{x} + \end{cases} +\end{equation} + +If $\bo{u}$ and $\bo{y}$ are scalars, the system is called \emph{single-input single-output (SISO)}, if they are vectors - \emph{multi-input multi-output (MIMO)}. + +\bigskip + +We can always express a SISO system in either form - ODE or state-space. + +\end{flushleft} +\end{frame} + + + + +\begin{frame}{ODE to State-Space conversion} +% \framesubtitle{...are what we will study} +\begin{flushleft} + +Consider eq. $\dddot{y} + a_2 \ddot{y} + a_1 \dot{y} + a_0 y =u$. + +\bigskip + +Make a substitution: $x_1 = y$, $x_2 = \dot{y}$, $x_3 = \ddot{y}$. We get: + +\begin{align} + \dot{x}_1 &= \dot{y} = x_2 \\ + \dot{x}_2 &= \ddot{y} = x_3 \\ + \dot{x}_3 &= u-a_2 \ddot{y} - a_1 \dot{y} - a_0 y = + u-a_2 x_3 - a_1 x_2 - a_0 x_1 +\end{align} + +Which can be directly put in the state-space form: + +\begin{equation} +\begin{bmatrix} +\dot{x}_1 \\ \dot{x}_2 \\ \dot{x}_3 +\end{bmatrix} += +\begin{bmatrix} +0 & 1 & 0 \\ +0 & 0 & 1 \\ +-a_0 & -a_1 & -a_2 +\end{bmatrix} +\begin{bmatrix} +x_1 \\ x_2 \\ x_3 +\end{bmatrix} ++ +\begin{bmatrix} +0 \\ 0 \\ u +\end{bmatrix} +\end{equation} + + +\end{flushleft} +\end{frame} + + + + +{ +\setbeamercolor{background canvas}{bg=mywhitepink} +\begin{frame}{State-Space to ODE conversion, 1} + % \framesubtitle{...are what we will study} + \begin{flushleft} + + Consider State-Space system: + % + \begin{equation} + \begin{cases} + \dot{\bo{x}} = \bo{A} \bo{x} \\ + y = \bo{C}\bo{x} + \end{cases} + \end{equation} + + We want to find an equivalent representation in the ODE form: + % + \begin{equation} + y^{(n)} = d_{n-1} y^{(n-1)} + ... + d_1 \dot y + d_0 y + \end{equation} + + Defining $\bo{d}\T = \begin{bmatrix} + d_0 & d_1 & ... & d_{n-1} + \end{bmatrix}$ and + $\bo{y} = \begin{bmatrix} + y & \dot y & ... & y^{(n-1)} + \end{bmatrix}\T$, we can re-write the ODE as: + % + \begin{equation} + y^{(n)} = \bo{d}\T \bo{y} + \end{equation} + + Thus, if we can find $\bo{d}$, we can solve the problem. + + + \end{flushleft} +\end{frame} +} + + + +{ + \setbeamercolor{background canvas}{bg=mywhitepink} +\begin{frame}{State-Space to ODE conversion, 2} + % \framesubtitle{...are what we will study} + \begin{flushleft} + + We can differentiate $y = \bo{C}\bo{x}$ n times: + % + \begin{align} + y &= \bo{C}\bo{x} \\ + \dot y &= \bo{C}\dot{\bo{x}} = \bo{C}\bo{A}\bo{x} \\ + ... \\ + y^{(n)} &= \bo{C}\bo{x}^{(n)} = \bo{C}\bo{A}^n\bo{x} + \end{align} + + This gives us relation between $\bo{y}$ and $\bo{x}$: + % + \begin{align} + \bo{y} = + \begin{bmatrix} + \bo{C} \\ + \bo{C} \bo{A} \\ + ... \\ + \bo{C}\bo{A}^{n-1} + \end{bmatrix} + \bo{x} = \mathcal{O}\bo{x} + \end{align} + % + where matrix $\mathcal{O}$ is called observability matrix. + + + \end{flushleft} +\end{frame} +} + + +{ + \setbeamercolor{background canvas}{bg=mywhitepink} +\begin{frame}{State-Space to ODE conversion, 3} + % \framesubtitle{...are what we will study} + \begin{flushleft} + + As long as the observability matrix $\mathcal{O}$ is full rank, we can express the state as: + % + \begin{align} + \bo{x}=\mathcal{O}^{-1}\bo{y} + \end{align} + + Then we re-write $y^{(n)} = \bo{C}\bo{A}^n\bo{x}$ as: + % + \begin{align} + y^{(n)} = \bo{C}\bo{A}^n\mathcal{O}^{-1}\bo{y} + \end{align} + + Thus, $\bo{d}\T = \bo{C}\bo{A}^n\mathcal{O}^{-1}$ and the ODE takes the form: + % + \begin{align} + y^{(n)} = \bo{C}\bo{A}^n\mathcal{O}^{-1} + \begin{bmatrix} + y \\ \dot y \\ ... \\ y^{(n-1)} + \end{bmatrix} + \end{align} + + You can see an example in the appendix A. + + + \end{flushleft} +\end{frame} +} + + +\begin{frame}{Read more} + +\begin{itemize} + +\item 2.14 Analysis and Design of Feedback Control Systems: + +\begin{itemize} + \item \bref{http://web.mit.edu/2.14/www/Handouts/StateSpace.pdf}{State-Space Representation of LTI Systems} + + \item \bref{http://web.mit.edu/2.14/www/Handouts/StateSpaceResponse.pdf}{Time-Domain Solution of LTI State Equations} +\end{itemize} + +\item \bref{https://lpsa.swarthmore.edu/}{Linear Physical Systems Analysis}: + +\begin{itemize} +\item State Space Representations of Linear Physical Systems \bref{https://lpsa.swarthmore.edu/Representations/SysRepSS.html}{lpsa.swarthmore.edu/Representations/SysRepSS.html} + +\item Transformation: Differential Equation to State Space \bref{https://lpsa.swarthmore.edu/Representations/SysRepTransformations/DE2SS.html}{lpsa.swarthmore.edu/.../DE2SS.html} +\end{itemize} + +\end{itemize} + +\end{frame} + + + +\myqrframe + + + +\begin{frame}{Appendix} + + \centerline{\huge Appendix A} + +\end{frame} + + + +\begin{frame}{State Space to ODE conversion, 1} + \framesubtitle{(extra)} + \begin{flushleft} + + Consider a system in state-space form: + + \begin{equation} + \label{eq:SS} + \begin{cases} + \begin{bmatrix} + \dot x_1 \\ + \dot x_2 + \end{bmatrix} + = + \begin{bmatrix} + a_{11} & a_{12} \\ + a_{21} & a_{22} + \end{bmatrix} + \begin{bmatrix} + x_1 \\ + x_2 + \end{bmatrix} + \\ + y = + \begin{bmatrix} + c_1 & + c_2 + \end{bmatrix} + \begin{bmatrix} + x_1 \\ + x_2 + \end{bmatrix} + \end{cases} + \Longleftrightarrow \ \ + \begin{cases} + \dx{x} = \bo{A} \bo{x} \\ + y = \bo{C} \bo{x} + \end{cases} + \end{equation} + + We want to rewrite it as a linear ODE: + + \begin{equation} + \label{eq:ODE} + \ddot{y} + b_2 \dot{y} + b_1 y = 0 + \end{equation} + + Note that initial conditions of both equation need to agree. + + + \end{flushleft} +\end{frame} + + + +\begin{frame}{State Space to ODE} + \begin{flushleft} + + Since $y = \bo{C} \bo{x}$, its derivative is $\dot y = \bo{C} \dot{\bo{x}}$: + + \begin{equation} + \dot y = \bo{C} \bo{A} \bo{x} + \end{equation} + % + \begin{equation} + \dot y = \myvecT{(a_{11}c_1 + a_{21}c_2)}{(a_{12}c_1 + a_{22}c_2)} + \myvec{x_1}{x_2} + \end{equation} + + Analogous for $\ddot y$: + + \begin{equation} + \ddot y = \bo{C} \bo{A} \bo{A} \bo{x} + \end{equation} + + \end{flushleft} +\end{frame} + + + + +\begin{frame}{State Space to ODE} + \begin{flushleft} + + Combining our results we find the linear transformation between the variables $x_1$, $x_2$ and $y$, $\dot y$: + + \begin{equation} + \myvec{y}{\dot y} = + \begin{bmatrix} + c_1 & c_2 \\ + (a_{11}c_1 + a_{21}c_2) & (a_{12}c_1 + a_{22}c_2) + \end{bmatrix} + \myvec{x_1}{x_2} + \end{equation} + + Resulting transformation matrix is: + + \begin{equation} + \bo{T} = + \begin{bmatrix} + c_1 & c_2 \\ + (a_{11}c_1 + a_{21}c_2) & (a_{12}c_1 + a_{22}c_2) + \end{bmatrix} + \end{equation} + \begin{equation} + \bo{x} + = + \bo{T}^{-1} + \begin{bmatrix} + y \\ + \dot y + \end{bmatrix} + \end{equation} + + \end{flushleft} +\end{frame} + + + +\begin{frame}{State Space to ODE} + \begin{flushleft} + + Remember that: + % + \begin{align} + \ddot y = \bo{C} \bo{A} \bo{A} \bo{x} + \\ + \ddot y = \bo{C} \bo{A} \bo{A} \bo{T}^{-1} + \begin{bmatrix} + y \\ + \dot y + \end{bmatrix} + \end{align} + + So, we obtained $\ddot y$ as a linear function of $y$, $\dot y$. From this it is clear how the same can be generalized to higher dimensions. + + \end{flushleft} +\end{frame} + + + +\begin{frame}{State Space to ODE} + %\framesubtitle{part 5} + \begin{flushleft} + + \textcolor{blue}{\href{https://github.com/SergeiSa/Control-Theory-Slides-Spring-2022/blob/main/ColabNotebooks/StateSpace2ODE.ipynb}{Check out the code implementation.}} + + \bigskip + + + \centerline{\textcolor{black}{\qrcode[height=2.1in]{https://github.com/SergeiSa/Control-Theory-Slides-Spring-2022/blob/main/ColabNotebooks/StateSpace2ODE.ipynb}}} + + + \end{flushleft} +\end{frame} + + +\end{document} diff --git a/Slides/Introduction/settings.tex b/Slides/Introduction/settings.tex new file mode 100644 index 0000000..834ffc6 --- /dev/null +++ b/Slides/Introduction/settings.tex @@ -0,0 +1,186 @@ +\pdfmapfile{+sansmathaccent.map} + + +\mode +{ + \usetheme{Warsaw} % or try Darmstadt, Madrid, Warsaw, Rochester, CambridgeUS, ... + \usecolortheme{seahorse} % or try seahorse, beaver, crane, wolverine, ... + \usefonttheme{serif} % or try serif, structurebold, ... + \setbeamertemplate{navigation symbols}{} + \setbeamertemplate{caption}[numbered] +} + + +\definecolor{mypaleblue}{RGB}{240, 240, 255} +\definecolor{mylightblue}{RGB}{120, 150, 255} +\definecolor{myblue}{RGB}{90, 90, 255} +\definecolor{mygblue}{RGB}{70, 110, 240} +\definecolor{mydarkblue}{RGB}{0, 0, 180} +\definecolor{myblackblue}{RGB}{40, 40, 120} + +\definecolor{mygreen}{RGB}{0, 200, 0} +\definecolor{mydarkgreen}{RGB}{0, 120, 0} +\definecolor{mygreen2}{RGB}{245, 255, 230} + +\definecolor{mygray}{gray}{0.8} +\definecolor{mygray2}{RGB}{130, 130, 130} +\definecolor{mydarkgray}{RGB}{80, 80, 160} +\definecolor{mylightgray}{RGB}{160, 160, 160} + +\definecolor{mydarkred}{RGB}{160, 30, 30} +\definecolor{mylightred}{RGB}{255, 150, 150} +\definecolor{myred}{RGB}{200, 110, 110} +\definecolor{myblackred}{RGB}{120, 40, 40} + +\definecolor{mypink}{RGB}{255, 30, 80} +\definecolor{myhotpink}{RGB}{255, 80, 200} +\definecolor{mywarmpink}{RGB}{255, 60, 160} +\definecolor{mylightpink}{RGB}{255, 80, 200} +\definecolor{mydarkpink}{RGB}{155, 25, 60} +\definecolor{mywhitepink}{RGB}{255, 240, 240} + +\definecolor{mydarkcolor}{RGB}{60, 25, 155} +\definecolor{mylightcolor}{RGB}{130, 180, 250} + +\setbeamertemplate{itemize items}[default] + +\setbeamertemplate{itemize item}{\color{myblackblue}$\blacksquare$} +\setbeamertemplate{itemize subitem}{\color{mygblue}$\blacktriangleright$} +\setbeamertemplate{itemize subsubitem}{\color{mygray}$\blacksquare$} + +\setbeamercolor{palette quaternary}{fg=white,bg=mydarkgray} +\setbeamercolor{titlelike}{parent=palette quaternary} + +\setbeamercolor{palette quaternary2}{fg=black,bg=mypaleblue} +\setbeamercolor{frametitle}{parent=palette quaternary2} + +\setbeamerfont{frametitle}{size=\Large,series=\scshape} +\setbeamerfont{framesubtitle}{size=\normalsize,series=\upshape} + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% block settings + +\setbeamercolor{block title}{bg=red!30,fg=black} + +\setbeamercolor*{block title example}{bg=mygreen!40!white,fg=black} + +\setbeamercolor*{block body example}{fg= black, bg= mygreen2} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% URL settings +\hypersetup{ + colorlinks=true, + linkcolor=blue, + filecolor=blue, + urlcolor=blue, +} + +%%%%%%%%%%%%%%%%%%%%%%%%%% + +\renewcommand{\familydefault}{\rmdefault} + +\usepackage{amsmath} +\usepackage{mathtools} + +\usepackage{subcaption} + +\usepackage{qrcode} + +\DeclareMathOperator*{\argmin}{arg\,min} +\newcommand{\bo}[1] {\mathbf{#1}} + +\newcommand{\R}{\mathbb{R}} +\newcommand{\T}{^\top} + +\newcommand{\dx}[1] {\dot{\mathbf{#1}}} +\newcommand{\ma}[4] {\begin{bmatrix} + #1 & #2 \\ #3 & #4 + \end{bmatrix}} +\newcommand{\myvec}[2] {\begin{bmatrix} + #1 \\ #2 + \end{bmatrix}} +\newcommand{\myvecT}[2] {\begin{bmatrix} + #1 & #2 + \end{bmatrix}} + + +\newcommand{\mydate}{Spring 2023} + +\newcommand{\mygit}{\textcolor{blue}{\href{https://github.com/SergeiSa/Control-Theory-Slides-Spring-2023}{github.com/SergeiSa/Control-Theory-Slides-Spring-2023}}} + +\newcommand{\myqr}{ \textcolor{black}{\qrcode[height=1.5in]{https://github.com/SergeiSa/Control-Theory-Slides-Spring-2023}} +} + +\newcommand{\myqrframe}{ + \begin{frame} + \centerline{Lecture slides are available via Github, links are on Moodle} + \bigskip + \centerline{You can help improve these slides at:} + \centerline{\mygit} + \bigskip + \myqr + \end{frame} +} + + +\newcommand{\bref}[2] {\textcolor{blue}{\href{#1}{#2}}} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% code settings + +\usepackage{listings} +\usepackage{color} +% \definecolor{mygreen}{rgb}{0,0.6,0} +% \definecolor{mygray}{rgb}{0.5,0.5,0.5} +\definecolor{mymauve}{rgb}{0.58,0,0.82} +\lstset{ + backgroundcolor=\color{white}, % choose the background color; 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If it's 1, each line will be numbered + stringstyle=\color{mymauve}, % string literal style + tabsize=2, % sets default tabsize to 2 spaces + title=\lstname % show the filename of files included with \lstinputlisting; also try caption instead of title +} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% URL settings +\hypersetup{ + colorlinks=false, + linkcolor=blue, + filecolor=blue, + urlcolor=blue, +} + +%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% tikz settings + +\usepackage{tikz} +\tikzset{every picture/.style={line width=0.75pt}} \ No newline at end of file diff --git a/Slides/Kalman/main.pdf b/Slides/Kalman/main.pdf new file mode 100644 index 0000000..8115194 Binary files /dev/null and b/Slides/Kalman/main.pdf differ diff --git a/Slides/Kalman/main.tex b/Slides/Kalman/main.tex new file mode 100644 index 0000000..1ba40de --- /dev/null +++ b/Slides/Kalman/main.tex @@ -0,0 +1,865 @@ +\documentclass{beamer} + +\input{settings.tex} + + +\title{Kalman Filter} +\subtitle{Control Theory, Lecture 10} +\author{by Sergei Savin} +\centering +\date{\mydate} + + + +\begin{document} +\maketitle + + + +\begin{frame}{Content} +\begin{itemize} +\item Random variables, mean, autocovariance +\item Models with uncertainty, observer +\begin{itemize} + \item Process noise, measurement noise + \item Open loop observer + \item Estimation error autocovariance propagation + \item Kalman filter +\end{itemize} +\item Kalman filter gain +\end{itemize} +\end{frame} + + + + +\begin{frame}{Random variable, 1} +%\framesubtitle{How do we know the state?} +\begin{flushleft} + +We can think of a \emph{random variable} $\bo{v}$ as a sequence of values $\bo{v}_1$, $\bo{v}_2$, $\bo{v}_3$, ... - sampled from a distribution. + +\bigskip + +Mean $\bar{\bo{v}}$ of a random variable $\bo{v}$ is denoted as: + +\begin{equation} + \bar{\bo{v}} = E[\bo{v}] +\end{equation} +%\begin{equation} +% \bar{\bo{v}} = \underset{N \rightarrow \infty}{\text{lim}} \left( \frac{1}{N} \sum_{i = 1}^{N} \bo{v}_i \right) +%\end{equation} + +Mean has a number of properties: + +\begin{align} + E[\bo{a}] &= \bo{a}, & \bo{a}= \text{const} \\ + E[\bo{x}+\bo{y}] &= E[\bo{x}] + E[\bo{y}] &\\ + E[\alpha \bo{x}] &= \alpha E[\bo{x}] & \alpha = \text{const}\\ + E[\bo{A} \bo{x}] &= \bo{A} E[\bo{x}] & \bo{A} = \text{const} +\end{align} + + +\end{flushleft} +\end{frame} + + + +\begin{frame}{Random variable, 2} + %\framesubtitle{How do we know the state?} + \begin{flushleft} + + Autocovariance $\bo{V} = \textbf{cov}(\bo{v}, \bo{v})$ of a random variable $\bo{v}$ is defined as: + + \begin{equation} + \textbf{cov}(\bo{v}, \bo{v}) = E[(\bo{v} - E[\bo{v}])(\bo{v} - E[\bo{v}])\T] + \end{equation} + + To simplify notation in the following sections, we define $\textbf{cov}(\bo{v}) = \textbf{cov}(\bo{v}, \bo{v})$. For zero-mean process $E[\bo{v}] = 0$ the formula simplifies: + + \begin{equation} + \textbf{cov}(\bo{v}) = E[\bo{v}\bo{v}\T] + \end{equation} + + Autocovariance has a number of properties: + + \begin{align} + \textbf{cov}(\bo{a}) &= \bo{0}, & \bo{a}= \text{const} + \\ + \textbf{cov}(\bo{x}+\bo{a}) &= \textbf{cov}(\bo{x}), & \bo{a}= \text{const} + \\ + \textbf{cov}(\alpha \bo{x}) &= \alpha^2 \ \textbf{cov}(\bo{x}) & + \end{align} + + + + \end{flushleft} +\end{frame} + + + + +\begin{frame}{Random variable, 3} + %\framesubtitle{How do we know the state?} + \begin{flushleft} + + A random variable $\bo{x}$ with Gaussian distribution can be fully described via its mean $\bar{\bo{x}}$ and covariance $\bo{X}$: + + \begin{equation} + \bo{x} \sim \mathcal{N} (\bar{\bo{x}}, \bo{X}) + \end{equation} + + + \end{flushleft} +\end{frame} + + + + +\begin{frame}{Mean of a linear transform} + %\framesubtitle{How do we know the state?} + \begin{flushleft} + + Let $\bo{x}$ be a random variable $\bo{x} \sim \mathcal{N} (\bar{\bo{x}}, \bo{X})$. Given a constant matrix $\bo{M}$ we can define an affine transformation of $\bo{x}$: + + \begin{equation} + \bo{y} = \bo{M}\bo{x} + \end{equation} + + We can find mean of $\bo{y}$: + % + \begin{align} + E[\bo{y}] = E[\bo{M}\bo{x}] \\ + E[\bo{y}] = \bo{M}E[\bo{x}] \\ + E[\bo{y}] = \bo{M}\bar{\bo{x}} + \end{align} + + If $\bar{\bo{x}} = E[\bo{x}] = 0$, then $\bar{\bo{y}} = E[\bo{y}] = 0$. + + \end{flushleft} +\end{frame} + + + +\begin{frame}{Autocovariance over linear transform} + %\framesubtitle{How do we know the state?} + \begin{flushleft} + + Assuming $\bar{\bo{x}} = E[\bo{x}] = 0$, we get $E[\bo{y}] = 0$; with that we can find autocovariance of $\bo{y}$: + % + \begin{align*} + \textbf{cov}(\bo{y}) &= E[(\bo{y} - E[\bo{y}])(\bo{y} - E[\bo{y}])\T] = + \\ + &=E[\bo{y}\bo{y}\T] = + \\ + &=E[(\bo{M}\bo{x})(\bo{M}\bo{x})\T]= + \\ + &=E[\bo{M}\bo{x}\bo{x}\T \bo{M}\T]= + \\ + &=\bo{M}\bo{X} \bo{M}\T + \end{align*} + + \end{flushleft} +\end{frame} + + + +%\begin{frame}{Autocovariance over linear transform} +% %\framesubtitle{How do we know the state?} +% \begin{flushleft} +% +% Without this assumption, the covariance of $\bo{y}$ is a little more complicated: +% % +% \begin{align*} +% \textbf{cov}(\bo{y}) = E[(\bo{y} - E[\bo{y}])(\bo{y} - E[\bo{y}])\T] = +% \\ +% = E[\bo{y}\bo{y}\T +% + E[\bo{y}]E[\bo{y}]\T +% - \bo{y}E[\bo{y}]\T +% - E[\bo{y}]\bo{y}\T] = +% \\ +% = +% E[\bo{y}\bo{y}\T +% + \bar{\bo{y}}\bar{\bo{y}}\T +% - \bo{y}\bar{\bo{y}}\T +% - \bar{\bo{y}}\bo{y}]\T]= +% \\ +% = +% E[\bo{y}\bo{y}\T] +% + \bar{\bo{y}}\bar{\bo{y}}\T +% - E[\bo{y}]\bar{\bo{y}}\T +% - \bar{\bo{y}}E[\bo{y}]\T= +% \\ +% = +% E[\bo{y}\bo{y}\T] +% + \bar{\bo{y}}\bar{\bo{y}}\T +% - \bar{\bo{y}}\bar{\bo{y}}\T +% - \bar{\bo{y}}\bar{\bo{y}}\T= +% \\ +% = +% E[(\bo{M}\bo{x})(\bo{M}\bo{x})\T] +% - (\bo{M}\bar{\bo{x}})(\bo{M}\bar{\bo{x}})\T +% \\ +% = +% E[\bo{M}\bo{x}\bo{x}\T \bo{M}\T] +% - (\bo{M}\bar{\bo{x}}\bar{\bo{x}}\T\bo{M}\T)= +% \\ +% = +% \bo{M}\bo{X} \bo{M}\T +% - (\bo{M}\bar{\bo{x}}\bar{\bo{x}}\T\bo{M}\T)= +% \\ +% = +% \bo{M}\bo{X} \bo{M}\T +% - \bo{M}\bar{\bo{x}}\bar{\bo{x}}\T\bo{M}\T +% \end{align*} +% +% \end{flushleft} +%\end{frame} + + + + + +\begin{frame}{State estimation error - dynamics} + %\framesubtitle{How do we know the state?} + \begin{flushleft} + + Assume the DT-LTI dynamics takes the form: + + \begin{equation} + \bo{x}_{i+1} = \bo{A} \bo{x}_i + \bo{B} \bo{u}_i + \bo{w}_i, + \end{equation} + + where $\bo{w} \sim \mathcal{N} (0, \bo{Q})$ is \emph{process noise} - random input with Gaussian distribution and $\bo{Q} \succeq 0$ (meaning that it is positive semidefinite). We can propose an open-loop observer: + + \begin{equation} + \bhat{x}_{i+1} = \bo{A} \bhat{x}_i + \bo{B} \bo{u}_i, + \end{equation} + + where $\bhat{x}$ is state estimate. We can find estimation error $\btil{x} = \bo{x}_i - \bhat{x}_i$ dynamic: + + \begin{equation} + \btil{x}_{i+1} = \bo{A} \btil{x}_i + \bo{w}_i + \end{equation} + + \end{flushleft} +\end{frame} + + + +\begin{frame}{State estimation error - mean} + %\framesubtitle{How do we know the state?} + \begin{flushleft} + + Assume you could pick your initial state estimate $\bhat{x}_0$ such that your initial state estimation error $\btil{x}_0$ behaves as a random variable sampled from a Gaussian distribution $\btil{x}_0 \sim \mathcal{N} (0, \bo{P}_0)$. + + \bigskip + + Knowing mean $E[\btil{x}_i]$ we can compute $E[\btil{x}_{i+1}]$: + + \begin{equation} + E[\btil{x}_{i+1}] = E[\bo{A} \btil{x}_i + \bo{w}_i] = + \bo{A} E[\btil{x}_i] + \end{equation} + + Since $E[\btil{x}_0] = 0$, we can conclude that $E[\btil{x}_i] = 0, \ \forall i$. + + + \end{flushleft} +\end{frame} + + + +\begin{frame}{State estimation error - covariance} + %\framesubtitle{How do we know the state?} + \begin{flushleft} + + Knowing autocovariance $\bo{P}_i$ we can compute $\bo{P}_{i+1}$: + + \begin{align*} + \bo{P}_{i+1} &= E[\btil{x}_{i+1}\btil{x}_{i+1}\T] = + E[(\bo{A} \btil{x}_i + \bo{w}_i) (\bo{A} \btil{x}_i + \bo{w}_i)\T] = + \\ + &= + E[\bo{A} \btil{x}_i \btil{x}_i\T \bo{A}\T + + \bo{A} \btil{x}_i \bo{w}_i\T + + \bo{w}_i \btil{x}_i\T \bo{A}\T + + \bo{w}_i \bo{w}_i\T] + \end{align*} + + We can assume that random process $\bo{w}$ is uncorrelated with $\btil{x}$, meaning that $E[\btil{x}_i \bo{w}_i\T] = E[\bo{w}_i \btil{x}_i\T] = 0$: + + \begin{align*} + \bo{P}_{i+1} + &= + E[\bo{A} \btil{x}_i \btil{x}_i\T \bo{A}\T + + \bo{w}_i \bo{w}_i\T] + = + \bo{A} \bo{P}_i \bo{A}\T + + \bo{Q} + \end{align*} + + + \end{flushleft} +\end{frame} + + + +\begin{frame}{Closed-loop observer, 1} + %\framesubtitle{How do we know the state?} + \begin{flushleft} + + Previously, we computed dynamics of mean and covariance of state estimation error for the case of open-loop observer. But, a stable observer with feedback is obviously preferable. We start by introducing a measurement model: + + \begin{equation} + \bo{y}_i = \bo{H} \bo{x}_i + \bo{v}_i + \end{equation} + + where $\bo{H}$ is a measurement matrix, $\bo{y}_i$ is measured output and $\bo{v}_i$ is a measurement noise sampled from a Gaussian distribution $\bo{v}_i \sim \mathcal{N} (0, \bo{R})$, where $\bo{R} \succ 0$. + + \end{flushleft} +\end{frame} + + +\begin{frame}{Closed-loop observer, 2} + %\framesubtitle{How do we know the state?} + \begin{flushleft} + + + We can propose the following modification to the observer: + + \begin{equation} + \label{eq:observer} + \begin{cases} + \bhat{x}_{i+1}^- = \bo{A} \bhat{x}_i + \bo{B} \bo{u}_i, \\ + \bhat{x}_{i+1} = \bhat{x}_{i+1}^- + \bo{L}_i (\bo{y}_i - \bo{H} \bhat{x}_{i+1}^-) + \end{cases} + \end{equation} + + where $\bhat{x}_{i+1}^-$ is an \emph{a priori} estimate. \textcolor{mygray2}{We can re-write the last equation as + $\bhat{x}_{i+1} = \bhat{x}_{i+1}^- + \bo{L}_i (\bo{H} \bo{x}_i - \bo{H} \bhat{x}_{i+1}^- + \bo{v}_i) $.} + + \bigskip + + We can re-write all this in terms of state estimation error, defining $\btil{x}_{i+1}^- = \bo{x}_{i+1} - \bhat{x}_{i+1}^-$. For the last eq. in \eqref{eq:observer}, we subtract $\bo{x}_{i+1}$ from both sides: + % + \begin{equation} + \bhat{x}_{i+1}-\bo{x}_{i+1} = \bhat{x}_{i+1}^- - \bo{x}_{i+1} + + \bo{L}_i (\bo{H} \bo{x}_i - \bo{H} \bhat{x}_{i+1}^- + \bo{v}_i) + \end{equation} + % + and flip the sign: + + \begin{equation} + \begin{cases} + \btil{x}_{i+1}^- = \bo{A} \btil{x}_i + \bo{w}_i, \\ + \btil{x}_{i+1} = (\bo{I} - \bo{L}_i \bo{H}) \btil{x}_{i+1}^- + \bo{L}_i\bo{v}_i + \end{cases} + \end{equation} + + + + \end{flushleft} +\end{frame} + + + +\begin{frame}{Closed-loop observer - mean dynamics} + %\framesubtitle{How do we know the state?} + \begin{flushleft} + + We can compute estimation error mean dynamics (\emph{propagation}): + % + \begin{align*} + E[\btil{x}_{i+1}^-] = + E[\bo{A} \btil{x}_i + \bo{w}_i] = + E[\bo{A} \btil{x}_i] + E[\bo{w}_i] = + \bo{A}E[\btil{x}_i]. + \end{align*} + % + \begin{align*} + E[\btil{x}_{i+1}] = + E[(\bo{I} - \bo{L}_i \bo{H}) \btil{x}_{i+1}^- + \bo{L}_i\bo{v}_i] =\\ + =E[(\bo{I} - \bo{L}_i \bo{H}) \btil{x}_{i+1}^-] + = + (\bo{I} - \bo{L}_i \bo{H}) E[\btil{x}_{i+1}^-] + \end{align*} + + So, we obtain the following mean dynamics: + + \begin{equation} + \begin{cases} + E[\btil{x}_{i+1}^-] = \bo{A} E[\btil{x}_i], \\ + E[\btil{x}_{i+1}] = (\bo{I} - \bo{L}_i \bo{H}) E[\btil{x}_{i+1}^-] + \end{cases} + \end{equation} + + Since $E[\btil{x}_0] = 0$, then $E[\btil{x}_1^-] = 0$, and then $E[\btil{x}_1] = 0$, and the same for $E[\btil{x}_i] = 0$, $E[\btil{x}_i^-] = 0$. + + \end{flushleft} +\end{frame} + + + +\begin{frame}{Closed-loop observer - covariance dynamics} + %\framesubtitle{How do we know the state?} + \begin{flushleft} + + We can compute autocovariance dynamics (propagation). Below is \emph{a priori} estimation error covariance: + % + \begin{align*} + \bo{P}_{i+1}^- + &= E[\btil{x}_{i+1}^- (\btil{x}_{i+1}^-)\T] = \\ + &= E[ (\bo{A} \btil{x}_i + \bo{w}_i) (\bo{A} \btil{x}_i + \bo{w}_i)\T] = \\ + &= \bo{A} \bo{P}_i \bo{A}\T +\bo{Q}. + \end{align*} + + \bigskip + + \textcolor{mydarkgray}{Reminder: $E[\bo{w}_i \bo{w}_i\T] = \bo{Q}$ since $\bo{w} \sim \mathcal{N} (0, \bo{Q})$, $E[\btil{x}_i \bo{w}_i\T] = 0$ since the two variables are independent, and $E[\btil{x}_i \btil{x}_i\T] = \bo{P}_i$ by definition.} + + + \end{flushleft} +\end{frame} + + + + + +\begin{frame}{Closed-loop observer - covariance dynamics} + %\framesubtitle{How do we know the state?} + \begin{flushleft} + + + With that, we can find \emph{a posteriori} estimation error covariance: + % + \begin{align*} + E[\btil{x}_{i+1} \btil{x}_{i+1}\T] + = + E[ (\bo{I} - \bo{L}_i \bo{H}) \btil{x}_{i+1}^- (\btil{x}_{i+1}^-)\T (\bo{I} - \bo{L}_i \bo{H})\T + \\ + +(\bo{I} - \bo{L}_i \bo{H}) \btil{x}_{i+1}^- \bo{v}_i\T + + \bo{v}_i (\btil{x}_{i+1}^-)\T (\bo{I} - \bo{L}_i \bo{H})\T + + \bo{L}_i \bo{v}_i \bo{v}_i\T \bo{L}_i\T] + \end{align*} + + Assuming that $\btil{x}_{i+1}^-$ and $\bo{v}_i$ are uncorrelated, we get $E[(\bo{I} - \bo{L}_i \bo{H}) \btil{x}_{i+1}^- \bo{v}_i\T] = 0$ and $E[\bo{v}_i (\btil{x}_{i+1}^-)\T (\bo{I} - \bo{L}_i \bo{H})\T] = 0$. With that we simplify: + % + \begin{align*} + E[\btil{x}_{i+1} \btil{x}_{i+1}\T] + &= + (\bo{I} - \bo{L}_i \bo{H}) \bo{P}_{i+1}^- (\bo{I} - \bo{L}_i \bo{H})\T +\bo{L}_i\bo{R}\bo{L}_i\T = \bo{P}_{i+1} + \end{align*} + + \end{flushleft} +\end{frame} + + + + + + +\begin{frame} + %\framesubtitle{How do we know the state?} + \begin{flushleft} + + \centering{\Huge Kalman filter gain} + + \end{flushleft} +\end{frame} + + +\begin{frame}{Preliminaries, 1} + %\framesubtitle{How do we know the state?} + \begin{flushleft} + + Before discussing how we can propose Kalman filter gain, we need two mathematical facts. First, inner and outer product: + + \begin{equation} + \bo{x}\T \bo{x} = \text{tr}(\bo{x}\bo{x}\T) + \end{equation} + % + where $\text{tr}(\cdot)$ is a trace operation. + + \bigskip + + Example: + % + \begin{align*} + \bo{x} = + \begin{bmatrix} + x_1 \\ x_2 \\ x_3 + \end{bmatrix},& + \ \ \ + \bo{x}\T \bo{x} = x_1^2+x_2^2+x_3^2, + \\ + \bo{x}\bo{x}\T = + \begin{bmatrix} + x_1^2 & x_1 x_2 & x_1 x_3 \\ + x_2 x_1 & x_2^2 & x_2 x_3 \\ + x_3 x_1 & x_3 x_2 & x_3^2 + \end{bmatrix},& + \ \ \ + \text{tr}(\bo{x}\bo{x}\T) = x_1^2+x_2^2+x_3^2. + \end{align*} + + \end{flushleft} +\end{frame} + + + +\begin{frame}{Preliminaries, 2} + %\framesubtitle{How do we know the state?} + \begin{flushleft} + + Second, derivatives of a trace: + % + \begin{align} + \frac{\partial ( \text{tr}(\bo{A} \bo{X}) )}{\partial \bo{X}} = + \frac{\partial ( \text{tr}(\bo{X}\bo{A}) )}{\partial \bo{X}} + &= + \bo{A} + \\ + \frac{\partial ( \text{tr}(\bo{A} \bo{X}\T) )}{\partial \bo{X}} = + \frac{\partial ( \text{tr}(\bo{X}\T\bo{A}) )}{\partial \bo{X}} + &= + \bo{A}\T + \\ + \frac{\partial ( \text{tr}(\bo{A} \bo{X}) )}{\partial \bo{X}\T} = + \frac{\partial ( \text{tr}(\bo{X}\bo{A}) )}{\partial \bo{X}\T} + &= + \bo{A}\T + \end{align} + + \begin{align} + \frac{\partial ( \text{tr}(\bo{X}\T \bo{A} \bo{X}) )}{\partial \bo{X}} + &= + \bo{X}\T (\bo{A} + \bo{A}\T) + \\ + \frac{\partial ( \text{tr}(\bo{X} \bo{A} \bo{X}\T) )}{\partial \bo{X}} + &= + (\bo{A} + \bo{A}\T) \bo{X}\T + \\ + \frac{\partial ( \text{tr}(\bo{X}\T \bo{A} \bo{X}) )}{\partial \bo{X}\T} + &= + (\bo{A} + \bo{A}\T) \bo{X} + \\ + \frac{\partial ( \text{tr}(\bo{X} \bo{A} \bo{X}\T) )}{\partial \bo{X}\T} + &= + \bo{X}(\bo{A} + \bo{A}\T) + \end{align} + + + + \end{flushleft} +\end{frame} + + +\begin{frame}{Kalman gain, 1} + %\framesubtitle{How do we know the state?} + \begin{flushleft} + + Here we will attempt to derive optimal Kalman gain $\bo{L}_i$ for the $i$-th step, such that the following cost function is minimized: + + \begin{equation} + J = E \left[ \sum \Tilde x_{i+1}^2 \right] + \end{equation} + % + meaning that we minimize mean value of the square of the estimation error. We also know that as long as estimation error on the $i+1$-th step has zero mean (as a random variable), covariance takes the following form: $\bo{P}_{i+1} = E [ \btil{x}_{i+1} \btil{x}_{i+1}\T ]$. Its trace gives us the cost function $J$: + + \begin{align*} + J = E \left[ \text{tr}(\bo{P}_{i+1}) \right] = + \text{tr} (E \left[ \bo{P}_{i+1} \right]) = \\ + = \text{tr}( + (\bo{I} - \bo{L}_i \bo{H}) \bo{P}_{i+1}^- (\bo{I} - \bo{L}_i \bo{H})\T +\bo{L}_i\bo{R}\bo{L}_i\T + ) = \\ + \text{tr}( + \bo{P}_{i+1}^- - \bo{L}_i \bo{H} \bo{P}_{i+1}^- + - \bo{P}_{i+1}^- \bo{H}\T \bo{L}_i\T + + \bo{L}_i (\bo{H}\bo{P}_{i+1}^- \bo{H}\T + \bo{R}) \bo{L}_i\T + ) + \end{align*} + + + \end{flushleft} +\end{frame} + + + +\begin{frame}{Kalman gain, 2} + %\framesubtitle{How do we know the state?} + \begin{flushleft} + + Next, we find derivative of $J$ with respect to $\bo{L}_i$ and set it to zero: + + \begin{align*} + \frac{\partial J}{\partial \bo{L}_i} + = + -\bo{H} \bo{P}_{i+1}^- -(\bo{P}_{i+1}^- \bo{H}\T)\T + + 2(\bo{H}\bo{P}_{i+1}^- \bo{H}\T + \bo{R}) \bo{L}_i\T = 0 + \\ + -2 \bo{H} \bo{P}_{i+1}^- + 2(\bo{H}\bo{P}_{i+1}^- \bo{H}\T + \bo{R}) \bo{L}_i\T = 0 + \\ + \bo{L}_i (\bo{H}\bo{P}_{i+1}^- \bo{H}\T + \bo{R}) = \bo{P}_{i+1}^- \bo{H}\T + \\ + \bo{L}_i = \bo{P}_{i+1}^- \bo{H}\T (\bo{H}\bo{P}_{i+1}^- \bo{H}\T + \bo{R})^{-1} + \end{align*} + + +So, the Kalman gain can be optimally chosen as $\bo{L}_i = \bo{P}_{i+1}^- \bo{H}\T (\bo{H}\bo{P}_{i+1}^- \bo{H}\T + \bo{R})^{-1}$. + + \end{flushleft} +\end{frame} + + + + + + +\begin{frame}{Kalman gain, 3} + %\framesubtitle{How do we know the state?} + \begin{flushleft} + + There are alternative but equivalent ways to pick $\bo{L}_i$. We can do it "the same way" as we did with LQR: + + \begin{equation} + \bo{L}_i = \bo{P}_{i+1} \bo{H}\T \bo{R}^{-1} + \end{equation} + + The equivalence of this formula to the earlier one will be shown in the Appendix B. + + + \end{flushleft} +\end{frame} + +\begin{frame}{Further reading} + %\framesubtitle{How do we know the state?} + \begin{flushleft} + + \begin{itemize} + \item Simon, D., 2006. Optimal state estimation: Kalman, H infinity, and nonlinear approaches. John Wiley \& Sons. + \end{itemize} + + \end{flushleft} +\end{frame} + + +\myqrframe + + + +\begin{frame} + %\framesubtitle{How do we know the state?} + \begin{flushleft} + + \centering{\Huge Appendix A} + + \end{flushleft} +\end{frame} + +\begin{frame}{Mean of an affine transform} + %\framesubtitle{How do we know the state?} + \begin{flushleft} + + Given a constant vector $\bo{c}$ and a constant matrix $\bo{M}$ we can define an affine transformation of $\bo{x}$: + + \begin{equation} + \bo{y} = \bo{M}\bo{x} + \bo{c} + \end{equation} + + We can find mean of $\bo{y}$: + % + \begin{align} + E[\bo{y}] = E[\bo{M}\bo{x} + \bo{c}] \\ + E[\bo{y}] = \bo{M}E[\bo{x}] + \bo{c} \\ + E[\bo{y}] = \bo{M}\bar{\bo{x}} + \bo{c} + \end{align} + + + \end{flushleft} +\end{frame} + + + +\begin{frame}{Autocovariance with zero mean} + %\framesubtitle{How do we know the state?} + \begin{flushleft} + + Assuming $E[\bo{x}] = 0$, we can find covariance of $\bo{y}$: + % + \begin{align*} + \textbf{cov}(\bo{y}) = E[(\bo{y} - E[\bo{y}])(\bo{y} - E[\bo{y}])\T] = + \\ + = E[\bo{y}\bo{y}\T + + E[\bo{y}]E[\bo{y}]\T + - \bo{y}E[\bo{y}]\T + - E[\bo{y}]\bo{y}\T] = + \\ + = + E[\bo{y}\bo{y}\T + + \bar{\bo{y}}\bar{\bo{y}}\T + - \bo{y}\bar{\bo{y}}\T + - \bar{\bo{y}}\bo{y}]\T]= + \\ + = + E[\bo{y}\bo{y}\T] + + \bar{\bo{y}}\bar{\bo{y}}\T + - E[\bo{y}]\bar{\bo{y}}\T + - \bar{\bo{y}}E[\bo{y}]\T= + \\ + = + E[\bo{y}\bo{y}\T] + + \bar{\bo{y}}\bar{\bo{y}}\T + - \bar{\bo{y}}\bar{\bo{y}}\T + - \bar{\bo{y}}\bar{\bo{y}}\T + \\ + = + E[(\bo{M}\bo{x} + \bo{c})(\bo{M}\bo{x} + \bo{c})\T] + - \bo{c}\bo{c}\T + \\ + = + E[\bo{M}\bo{x}\bo{x}\T \bo{M}\T+ + \bo{c}\bo{c}\T+ + \bo{M}\bo{x}\bo{c}\T+ + \bo{c}\bo{x}\T \bo{M}\T] + - \bo{c}\bo{c}\T= + \\ + = + \bo{M}\bo{X} \bo{M}\T+ + \bo{M}\bar{\bo{x}}\bo{c}\T+ + \bo{c}\bar{\bo{x}}\T \bo{M}\T= + \\ + = + \bo{M}\bo{X} \bo{M}\T + \end{align*} + + \end{flushleft} +\end{frame} + +\begin{frame}{Autocovariance over affine transform} + %\framesubtitle{How do we know the state?} + \begin{flushleft} + + Without this assumption, the covariance of $\bo{y}$ is a little more complicated: + % + \begin{align*} + \textbf{cov}(\bo{y}) = E[(\bo{y} - E[\bo{y}])(\bo{y} - E[\bo{y}])\T] = + \\ + = E[\bo{y}\bo{y}\T + + E[\bo{y}]E[\bo{y}]\T + - \bo{y}E[\bo{y}]\T + - E[\bo{y}]\bo{y}\T] = + \\ + = + E[\bo{y}\bo{y}\T + + \bar{\bo{y}}\bar{\bo{y}}\T + - \bo{y}\bar{\bo{y}}\T + - \bar{\bo{y}}\bo{y}]\T]= + \\ + = + E[\bo{y}\bo{y}\T] + + \bar{\bo{y}}\bar{\bo{y}}\T + - E[\bo{y}]\bar{\bo{y}}\T + - \bar{\bo{y}}E[\bo{y}]\T= + \\ + = + E[\bo{y}\bo{y}\T] + + \bar{\bo{y}}\bar{\bo{y}}\T + - \bar{\bo{y}}\bar{\bo{y}}\T + - \bar{\bo{y}}\bar{\bo{y}}\T + \\ + = + E[(\bo{M}\bo{x} + \bo{c})(\bo{M}\bo{x} + \bo{c})\T] + - (\bo{M}\bar{\bo{x}} + \bo{c})(\bo{M}\bar{\bo{x}} + \bo{c})\T + \\ + = + E[\bo{M}\bo{x}\bo{x}\T \bo{M}\T+ + \bo{c}\bo{c}\T+ + \bo{M}\bo{x}\bo{c}\T+ + \bo{c}\bo{x}\T \bo{M}\T] + -\\ + - (\bo{M}\bar{\bo{x}}\bar{\bo{x}}\T\bo{M}\T + + \bo{M}\bar{\bo{x}}\bo{c}\T+ + \bo{c}\bar{\bo{x}}\T\bo{M}\T+ + \bo{c}\bo{c}\T)= + \\ + = + \bo{M}\bo{X} \bo{M}\T+ + \bo{c}\bo{c}\T+ + \bo{M}\bar{\bo{x}}\bo{c}\T+ + \bo{c}\bar{\bo{x}}\T \bo{M}\T + -\\ + - (\bo{M}\bar{\bo{x}}\bar{\bo{x}}\T\bo{M}\T + + \bo{M}\bar{\bo{x}}\bo{c}\T+ + \bo{c}\bar{\bo{x}}\T\bo{M}\T+ + \bo{c}\bo{c}\T)= + \\ + = + \bo{M}\bo{X} \bo{M}\T + - \bo{M}\bar{\bo{x}}\bar{\bo{x}}\T\bo{M}\T + \end{align*} + + \end{flushleft} +\end{frame} + + +\begin{frame} + %\framesubtitle{How do we know the state?} + \begin{flushleft} + + \centering{\Huge Appendix B} + + \end{flushleft} +\end{frame} + +\begin{frame}{Observer Gain, 1} + %\framesubtitle{How do we know the state?} + \begin{flushleft} + + Given observer gain $\bo{L}_i = \bo{P}_{i+1} \bo{H}\T \bo{R}^{-1}$ and autocovariance propagation $ \bo{P}_{i+1} = (\bo{I} - \bo{L}_i \bo{H}) \bo{P}_{i+1}^- (\bo{I} - \bo{L}_i \bo{H})\T +\bo{L}_i\bo{R}\bo{L}_i\T$, we can derive expression for $\bo{L}_i$ as a function of $\bo{P}_{i+1}^-$: + % + \begin{align} + \bo{L}_i \bo{R} = \bo{P}_{i+1} \bo{H}\T + \\ + \bo{L}_i \bo{R}\bo{L}_i\T = \bo{P}_{i+1} \bo{H}\T \bo{L}_i\T + \\ + \bo{P}_{i+1} = (\bo{I} - \bo{L}_i \bo{H}) \bo{P}_{i+1}^- (\bo{I} - \bo{L}_i \bo{H})\T +\bo{P}_{i+1} \bo{H}\T \bo{L}_i\T + \\ + \bo{P}_{i+1}(\bo{I}- \bo{H}\T \bo{L}_i\T) = (\bo{I} - \bo{L}_i \bo{H}) \bo{P}_{i+1}^- (\bo{I} - \bo{L}_i \bo{H})\T + \end{align} + + Assuming that $\text{det}(\bo{I}- \bo{L}_i \bo{H} )\T \neq 0$, we can multiply on the right by $(\bo{I}- \bo{L}_i \bo{H} )^{-\top}$: + % + \begin{align} + \bo{P}_{i+1} = (\bo{I} - \bo{L}_i \bo{H}) \bo{P}_{i+1}^- + \end{align} + + \end{flushleft} +\end{frame} + + +\begin{frame}{Observer Gain, 2} + %\framesubtitle{How do we know the state?} + \begin{flushleft} + + \begin{align} + \bo{P}_{i+1} &= (\bo{I} - \bo{L}_i \bo{H}) \bo{P}_{i+1}^- + \\ + \bo{P}_{i+1}\bo{H}\T\bo{R}^{-1} &= (\bo{I} - \bo{L}_i \bo{H}) \bo{P}_{i+1}^- \bo{H}\T\bo{R}^{-1} + \\ + \bo{L}_i &= (\bo{I} - \bo{L}_i \bo{H}) \bo{P}_{i+1}^- \bo{H}\T\bo{R}^{-1} + \\ + \bo{L}_i\bo{R} &= (\bo{I} - \bo{L}_i \bo{H}) \bo{P}_{i+1}^- \bo{H}\T + \\ + \bo{L}_i\bo{R} + \bo{L}_i \bo{H}\bo{P}_{i+1}^- \bo{H}\T &= \bo{P}_{i+1}^- \bo{H}\T + \\ + \bo{L}_i (\bo{R} + \bo{H}\bo{P}_{i+1}^- \bo{H}\T) &= \bo{P}_{i+1}^- \bo{H}\T + \\ + \bo{L}_i &= \bo{P}_{i+1}^- \bo{H}\T (\bo{R} + \bo{H}\bo{P}_{i+1}^- \bo{H}\T)^{-1}. \ \ \ \qed + \end{align} + + \end{flushleft} +\end{frame} + + + +\end{document} diff --git a/Slides/Kalman/settings.tex b/Slides/Kalman/settings.tex new file mode 100644 index 0000000..ba0f0ae --- /dev/null +++ b/Slides/Kalman/settings.tex @@ -0,0 +1,187 @@ +\pdfmapfile{+sansmathaccent.map} + + +\mode +{ + \usetheme{Warsaw} % or try Darmstadt, Madrid, Warsaw, Rochester, CambridgeUS, ... + \usecolortheme{seahorse} % or try seahorse, beaver, crane, wolverine, ... + \usefonttheme{serif} % or try serif, structurebold, ... + \setbeamertemplate{navigation symbols}{} + \setbeamertemplate{caption}[numbered] +} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% itemize settings + + 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\textcolor{black}{\qrcode[height=1.5in]{https://github.com/SergeiSa/Control-Theory-Slides-Spring-2023}} +} + +\newcommand{\myqrframe}{ + \begin{frame} + \centerline{Lecture slides are available via Github, links are on Moodle} + \bigskip + \centerline{You can help improve these slides at:} + \centerline{\mygit} + \bigskip + \myqr + \end{frame} +} + + +\newcommand{\bref}[2] {\textcolor{blue}{\href{#1}{#2}}} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% code settings + +\usepackage{listings} +\usepackage{color} +% \definecolor{mygreen}{rgb}{0,0.6,0} +% \definecolor{mygray}{rgb}{0.5,0.5,0.5} +\definecolor{mymauve}{rgb}{0.58,0,0.82} +\lstset{ + backgroundcolor=\color{white}, % choose the background color; you must add \usepackage{color} or \usepackage{xcolor}; should come as last argument + basicstyle=\footnotesize, % the size of the fonts that are used for the code + breakatwhitespace=false, % sets if automatic breaks should only happen at whitespace + breaklines=true, % sets automatic line breaking 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If it's 1, each line will be numbered + stringstyle=\color{mymauve}, % string literal style + tabsize=2, % sets default tabsize to 2 spaces + title=\lstname % show the filename of files included with \lstinputlisting; also try caption instead of title +} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% URL settings +\hypersetup{ + colorlinks=false, + linkcolor=blue, + filecolor=blue, + urlcolor=blue, +} + +%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% tikz settings + +\usepackage{tikz} +\tikzset{every picture/.style={line width=0.75pt}} \ No newline at end of file diff --git a/Slides/LMI/main.pdf b/Slides/LMI/main.pdf new file mode 100644 index 0000000..49cc7a5 Binary files /dev/null and b/Slides/LMI/main.pdf differ diff --git a/Slides/LMI/main.tex b/Slides/LMI/main.tex new file mode 100644 index 0000000..f293627 --- /dev/null +++ b/Slides/LMI/main.tex @@ -0,0 +1,442 @@ +\documentclass{beamer} + +\input{settings.tex} + + +\title{LMI: Control design and robustness} +\subtitle{Control Theory, Lecture ??} +\author{by Sergei Savin} +\centering +\date{\mydate} + + + +\begin{document} + \maketitle + + + + \begin{frame}{Content} + \begin{itemize} + \item LMI + \item Control design + \item Robustness + \item S-procedure + \item Appendix A + \end{itemize} + \end{frame} + + + + + \begin{frame}{linear matrix inequalities (LMI)} + %\framesubtitle{How do we know the state?} + \begin{flushleft} + + A linear matrix inequality (LMI) is a semidefinite constraint placed on a matrix: + + \begin{equation} + \bo{S} \succ 0 + \end{equation} + + We assume (and this is true!) that there exist \emph{solvers} that can solve problems with such constraints. + + + \begin{example} + Given $\bo{A}$, find such $\bo{S}\succ 0$ that $\bo{A}^\top\bo{S} + \bo{S}\bo{A} \prec 0$. + \end{example} + + Notice that the last example is continious-time Lyapunov eq. for LTI system $\dot{\bo{x}} = \bo{A}\bo{x}$, and if such $\bo{S}$ exists the system is stable. + + \end{flushleft} + \end{frame} + + + + \begin{frame}{Control design, 1} + % \framesubtitle{Part 1} + \begin{flushleft} + + Consider a system $\dot{\bo{x}} = \bo{A}\bo{x} + \bo{B}\bo{u}$, control $\bo{u} = \bo{K}\bo{x}$ and a Lyapunov function $V = \bo{x}^\top\bo{S}\bo{x}$, $\bo{S} \succ 0$. + + \bigskip + + Closed-form of the system is $\dot{\bo{x}} = (\bo{A} + \bo{B}\bo{K})\bo{x}$, and full derivative of the Lyapunov function: + + \begin{equation} + \dot V = \bo{x}^\top (\bo{A} + \bo{B}\bo{K})^\top\bo{S}\bo{x} + \bo{x}^\top\bo{S} (\bo{A} + \bo{B}\bo{K}) \bo{x} \leq 0 + \end{equation} + + This can be re-written as an LMI: + + \begin{equation} + \label{eq:vdot} + (\bo{A} + \bo{B}\bo{K})^\top\bo{S} + \bo{S} (\bo{A} + \bo{B}\bo{K}) \prec 0 + \end{equation} + + This is \emph{not linear} in decision variables ($\bo{S}$ and $\bo{K}$), and can't be solved directly using popular solvers. + + \end{flushleft} + \end{frame} + + + + + \begin{frame}{Control design, 2} + % \framesubtitle{Part 2} + \begin{flushleft} + + Introducing new variable $\bo{P} = \bo{S}^{-1}$ and multiplying \eqref{eq:vdot} by $\bo{P}$ on both sides (we can do it, as both $\bo{P}$ and $\bo{S}$ are full rank, and thus it is a congruence transformation which preserves definiteness, see appendix) we get: + + \begin{equation} + \bo{P}(\bo{A} + \bo{B}\bo{K})^\top + (\bo{A} + \bo{B}\bo{K})\bo{P} \prec 0 + \end{equation} + + Now we introduce one more variable $\bo{L} = \bo{K}\bo{P}$ and get an LMI constraint: + + \begin{equation} + \label{control_design} + \bo{P}\bo{A}^\top + \bo{A}\bo{P} + \bo{L}^\top\bo{B}^\top + \bo{B}\bo{L} \prec 0 + \end{equation} + + Solving \eqref{control_design} gives us $\bo{P}$ and $\bo{L}$, from which we can compute $\bo{K} = \bo{L}\bo{P}^{-1}$ and $\bo{S} = \bo{P}^{-1}$, solving the original problem. + + \end{flushleft} + \end{frame} + + + + + \begin{frame}{Robustness, 1} + % \framesubtitle{Part 1} + \begin{flushleft} + + Consider a system $\dot{\bo{x}} = \bo{A}\bo{x}$, but when you don't know $\bo{A}$ exactly. In other words, you don't know the model exactly. This is not to say that we know nothing about the model, but there is an uncertainty in our knowledge. + + \bigskip + + A good way to model is luck of model knowledge, this \emph{uncertainty}, is this: + + \begin{equation} + \label{eq:uncertain} + \dot{\bo{x}} = (\bo{A} + \bo{F} \Delta \bo{E})\bo{x} + \end{equation} + % + where $\bo{F}$ and $\bo{E}$ are arbitrary matrices, and $\Delta$ is a \emph{norm-bounded} matrix: $||\Delta|| \leq 1$. + + \bigskip + + We can think of it this way: $\bo{A} + \bo{F} \Delta \bo{E}$ is the true but unknown model, and the range of all possible models we can expect is bounded by the possible values of $\Delta$. + + \end{flushleft} + \end{frame} + + + + \begin{frame}{Robustness, 2} + % \framesubtitle{Part 1} + \begin{flushleft} + + Lets write the Lyapunov equation for the system \eqref{eq:uncertain}: + + \begin{equation} + \dot V = \bo{x}^\top + (\bo{A} + \bo{F} \Delta \bo{E})^\top\bo{S}\bo{x} + \bo{x}^\top\bo{S} (\bo{A} + \bo{F} \Delta \bo{E}) \bo{x} \leq 0 + \end{equation} + + Let us introduce a new variable $\bo{w} = \Delta \bo{E}\bo{x}$: + + \begin{equation} + \label{eq:Lyapunov_xw} + \dot V = \bo{x}^\top + (\bo{A}^\top \bo{S} + \bo{S}\bo{A}) \bo{x} + + \bo{w}^\top \bo{F}^\top\bo{S} \bo{x} + + \bo{x}^\top \bo{S}\bo{F} \bo{w} \leq 0 + \end{equation} + + Let us consider $\bo{w}^\top \bo{w}$: + + \begin{equation} + \label{eq:Delta-inequality} + \bo{w}^\top \bo{w} = + \bo{x}^\top\bo{E}^\top \Delta \Delta \bo{E}\bo{x} + \leq + \bo{x}^\top\bo{E}^\top \bo{E}\bo{x} + \end{equation} + % + which is true because $|| \Delta ||\leq 1$. In fact, the only property of the norm that we need here is that the delta inequality \eqref{eq:Delta-inequality} holds. + + \end{flushleft} + \end{frame} + + + + \begin{frame}{Robustness, 3} + % \framesubtitle{Part 1} + \begin{flushleft} + + With $\bo{w}^\top \bo{w} + \leq + \bo{x}^\top\bo{E}^\top \bo{E}\bo{x}$ we can write: + + \begin{equation} + \bo{x}^\top\bo{E}^\top \bo{E}\bo{x} - \bo{w}^\top \bo{w} \geq 0 + \end{equation} + + Which is the same as: + + \begin{equation} + \label{eq:EEww} + \begin{bmatrix} + \bo{x} \\ \bo{w} + \end{bmatrix}^\top + \begin{bmatrix} + \bo{E}^\top \bo{E} & 0 \\ + 0 & -\bo{I} + \end{bmatrix} + \begin{bmatrix} + \bo{x} \\ \bo{w} + \end{bmatrix} + \geq 0 + \end{equation} + + The same way we can rewrite \eqref{eq:Lyapunov_xw}: + + \begin{equation} + \label{eq:xw_Lyapunov} + \begin{bmatrix} + \bo{x} \\ \bo{w} + \end{bmatrix}^\top + \begin{bmatrix} + \bo{A}^\top \bo{S} + \bo{S}\bo{A} & \bo{S}\bo{F} \\ + \bo{F}^\top\bo{S} & 0 + \end{bmatrix} + \begin{bmatrix} + \bo{x} \\ \bo{w} + \end{bmatrix} + \leq 0 + \end{equation} + % + which only need to hold while \eqref{eq:EEww} holds. + + \end{flushleft} + \end{frame} + + + + \begin{frame}{S-procedure} + % \framesubtitle{Part 1} + \begin{flushleft} + + There is a way to enforce constraint $\bo{z}^\top \bo{M}\bo{z} \leq 0$ for such $\bo{z}$ that $\bo{z}^\top \bo{N}\bo{z} \geq 0$. This is called \emph{s-procedure}. + + \begin{theorem} + If $\gamma > 0$ and $\bo{M} + \gamma \bo{N} \prec 0$ then $\bo{z}^\top \bo{N}\bo{z} \geq 0 \implies \bo{z}^\top \bo{M}\bo{z} \leq 0$ + \end{theorem} + + \end{flushleft} + \end{frame} + + + + \begin{frame}{Robustness, 4} + % \framesubtitle{Part 1} + \begin{flushleft} + + + Using s-procedure we enforce \eqref{eq:xw_Lyapunov} when \eqref{eq:EEww} holds: + + \begin{equation} + % \label{eq:EEww} + \begin{bmatrix} + \bo{x} \\ \bo{w} + \end{bmatrix}^\top + \begin{bmatrix} + \bo{A}^\top \bo{S} + \bo{S}\bo{A} + \gamma \bo{E}^\top \bo{E} & \bo{S}\bo{F} \\ + \bo{F}^\top\bo{S} & -\gamma\bo{I} + \end{bmatrix} + \begin{bmatrix} + \bo{x} \\ \bo{w} + \end{bmatrix} + \leq 0 + \end{equation} + + In LMI form this is: + + \begin{equation} + \begin{bmatrix} + \bo{A}^\top \bo{S} + \bo{S}\bo{A} + \gamma \bo{E}^\top \bo{E} & \bo{S}\bo{F} \\ + \bo{F}^\top\bo{S} & -\gamma\bo{I} + \end{bmatrix} + \prec 0 + \end{equation} + + + This is a condition that the system is stable for all values of $\Delta$. The decision variables are $\bo{S}$ and $\gamma$. + + \end{flushleft} + \end{frame} + + + + + + \begin{frame}{Quadratic stability, 1} + % \framesubtitle{Part 1} + \begin{flushleft} + + Let us consider the following system: + + \begin{equation} + \dot{\bo{x}} = \bo{A}\bo{x} + \end{equation} + % + where $\bo{A} = \sum\limits_{i=1}^{n} \alpha_i \bo{A}_i$, $\alpha_i \geq 0$, $\sum\limits_{i=1}^{n} \alpha_i = 1$ with known $\bo{A}_i$ but unknown coefficients $\alpha_i$. Is it stable for all possible values of $\alpha_i$? Note that we can't use eigenvalue analysis in this case. + + \bigskip + + Geometrically, this means $\bo{A}$ is in a polytope with vertices $\bo{A}_i$. + + \end{flushleft} + \end{frame} + + + + \begin{frame}{Quadratic stability, 2} + % \framesubtitle{Part 1} + \begin{flushleft} + + \begin{theorem}[Quadratic stability] + $\bo{A}_i^\top \bo{S} + \bo{S} \bo{A}_i \leq 0$ implies $\dot{\bo{x}} = \sum\limits_{i=1}^{n} \alpha_i \bo{A}_i \bo{x}$ is stable, where $\alpha_i \geq 0$, $\sum\limits_{i=1}^{n} \alpha_i = 1$ + \end{theorem} + + \bigskip + + Proof: $\dot V = \left(\sum\limits_{i=1}^{n} \alpha_i \bo{A}_i \right)^\top \bo{S} + \bo{S} + \left( \sum\limits_{i=1}^{n} \alpha_i \bo{A}_i \right) \leq 0$ can be re-written as: + $\dot V = \sum\limits_{i=1}^{n} \left( \alpha_i (\bo{A}_i^\top \bo{S} + \bo{S} \bo{A}_i) \right) $ and since $\bo{A}_i^\top \bo{S} + \bo{S} \bo{A}_i \leq 0$ and $\alpha_i \geq 0$, then $\dot V \leq 0$. \qed + + \end{flushleft} + \end{frame} + + + + + \begin{frame}{Quadratic stability - Control design, 1} + % \framesubtitle{Part 1} + \begin{flushleft} + + Let us consider the following system: + + \begin{equation} + \dot{\bo{x}} = \bo{A}\bo{x} + \bo{B}\bo{x} + \end{equation} + % + where $\bo{A} = \sum\limits_{i=1}^{n} \alpha_i \bo{A}_i$, $\alpha_i \geq 0$, $\sum\limits_{i=1}^{n} \alpha_i = 1$ with known $\bo{A}_i$ but unknown coefficients $\alpha_i$. How to design control law $\bo{u} = \bo{K}\bo{x}$ making the system stable for all possible values of $\alpha_i$? + + \bigskip + + The closed-loop form of the system is: + + \begin{equation} + \dot{\bo{x}} = (\sum\limits_{i=1}^{n} \alpha_i \bo{A}_i + \bo{B}\bo{K})\bo{x} + \end{equation} + + + \end{flushleft} + \end{frame} + + + + \begin{frame}{Quadratic stability - Control design, 2} + % \framesubtitle{Part 1} + \begin{flushleft} + + Let us write Lyapunov eq. for the system: + + \begin{equation} + \left( + \sum\limits_{i=1}^{n} \alpha_i (\bo{A}_i + \bo{B}\bo{K}) + \right)^\top \bo{S} + + + \bo{S} + \left( + \sum\limits_{i=1}^{n} \alpha_i (\bo{A}_i + \bo{B}\bo{K}) + \right) + \prec 0 + \end{equation} + + We can re-write it as: + + \begin{equation} + \sum\limits_{i=1}^{n} \alpha_i + \left( + (\bo{A}_i + \bo{B}\bo{K})^\top \bo{S} + + \bo{S} (\bo{A}_i + \bo{B}\bo{K}) + \right) + \prec 0 + \end{equation} + + Hence if $(\bo{A}_i + \bo{B}\bo{K})^\top \bo{S} + + \bo{S} (\bo{A}_i + \bo{B}\bo{K}) \prec 0$, the original system is stable. + + \end{flushleft} + \end{frame} + + + + \begin{frame}{Quadratic stability - Control design, 3} + % \framesubtitle{Part 1} + \begin{flushleft} + + From $(\bo{A}_i + \bo{B}\bo{K})^\top \bo{S} + + \bo{S} (\bo{A}_i + \bo{B}\bo{K}) \prec 0$, we can go on to do control design. Introducing $\bo{P} = \bo{S}^{-1}$, we use congruence transformation multiplying by $\bo{P}$ on both sides: + + \begin{equation} + \bo{P}(\bo{A}_i + \bo{B}\bo{K})^\top + + (\bo{A}_i + \bo{B}\bo{K})\bo{P} \prec 0 + \end{equation} + + Introducing new variable $\bo{L} = \bo{K} \bo{P}$ we get a problem linear in decision variables: + + \begin{equation} + \bo{P}\bo{A}_i^\top + \bo{A}_i \bo{P} + + \bo{L}^\top\bo{B}^\top + \bo{B}\bo{L} \prec 0 + \end{equation} + % + where the decision variables are $\bo{P}$ and $\bo{L}$. The control gain matrix is found as $\bo{K} = \bo{L} \bo{P}^{-1}$. + + \end{flushleft} + \end{frame} + + + +\myqrframe + + + + + \begin{frame}{Appendix A} + \framesubtitle{Congruence transformation and definiteness} + \begin{flushleft} + + Consider matrices $\bo{P} \succ 0$, and $\bo{V} \in \R^{n, n}$ is full rank. We can prove that: + + \begin{equation} + \bo{P} \succ 0 \implies \bo{V}^\top\bo{P}\bo{V} \succ 0 + \end{equation} + + Proof: $\bo{x}^\top\bo{V}^\top\bo{P}\bo{V}\bo{x} = \bo{z}^\top\bo{P}\bo{z}$, where $\bo{z} = \bo{V}\bo{x}$. Since $\bo{P} \succ 0$, $\bo{z}^\top\bo{P}\bo{z} \geq 0$, hence $\bo{x}^\top\bo{V}^\top\bo{P}\bo{V}\bo{x} \geq 0$. + + \begin{definition} + Congruence transformation preserves semi-definiteness: $\text{det}(\bo{V}) \neq 0, \ \bo{P} \succ 0 \implies \bo{V}^\top\bo{P}\bo{V} \succ 0$ + \end{definition} + + + \end{flushleft} + \end{frame} + + + + +\end{document} diff --git a/Slides/LMI/settings.tex b/Slides/LMI/settings.tex new file mode 100644 index 0000000..ba0f0ae --- /dev/null +++ b/Slides/LMI/settings.tex @@ -0,0 +1,187 @@ +\pdfmapfile{+sansmathaccent.map} + + +\mode +{ + \usetheme{Warsaw} % or try Darmstadt, Madrid, Warsaw, Rochester, CambridgeUS, ... + \usecolortheme{seahorse} % or try seahorse, beaver, crane, wolverine, ... + \usefonttheme{serif} % or try serif, structurebold, ... + \setbeamertemplate{navigation symbols}{} + \setbeamertemplate{caption}[numbered] +} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% itemize settings + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% itemize settings + +\definecolor{mypaleblue}{RGB}{240, 240, 255} +\definecolor{mylightblue}{RGB}{120, 150, 255} +\definecolor{myblue}{RGB}{90, 90, 255} +\definecolor{mygblue}{RGB}{70, 110, 240} +\definecolor{mydarkblue}{RGB}{0, 0, 180} +\definecolor{myblackblue}{RGB}{40, 40, 120} + +\definecolor{mygreen}{RGB}{0, 200, 0} +\definecolor{mydarkgreen}{RGB}{0, 120, 0} +\definecolor{mygreen2}{RGB}{245, 255, 230} + +\definecolor{mygray}{gray}{0.8} +\definecolor{mygray2}{RGB}{130, 130, 130} +\definecolor{mydarkgray}{RGB}{80, 80, 160} +\definecolor{mylightgray}{RGB}{160, 160, 160} + +\definecolor{mydarkred}{RGB}{160, 30, 30} +\definecolor{mylightred}{RGB}{255, 150, 150} +\definecolor{myred}{RGB}{200, 110, 110} +\definecolor{myblackred}{RGB}{120, 40, 40} + +\definecolor{mypink}{RGB}{255, 30, 80} +\definecolor{myhotpink}{RGB}{255, 80, 200} +\definecolor{mywarmpink}{RGB}{255, 60, 160} +\definecolor{mylightpink}{RGB}{255, 80, 200} +\definecolor{mydarkpink}{RGB}{155, 25, 60} + +\definecolor{mydarkcolor}{RGB}{60, 25, 155} +\definecolor{mylightcolor}{RGB}{130, 180, 250} + +\setbeamertemplate{itemize items}[default] + +\setbeamertemplate{itemize item}{\color{myblackblue}$\blacksquare$} +\setbeamertemplate{itemize subitem}{\color{mygblue}$\blacktriangleright$} +\setbeamertemplate{itemize subsubitem}{\color{mygray}$\blacksquare$} + +\setbeamercolor{palette quaternary}{fg=white,bg=mydarkgray} +\setbeamercolor{titlelike}{parent=palette quaternary} + +\setbeamercolor{palette quaternary2}{fg=black,bg=mypaleblue} +\setbeamercolor{frametitle}{parent=palette quaternary2} + +\setbeamerfont{frametitle}{size=\Large,series=\scshape} +\setbeamerfont{framesubtitle}{size=\normalsize,series=\upshape} + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% block settings + +\setbeamercolor{block title}{bg=red!30,fg=black} + +\setbeamercolor*{block title example}{bg=mygreen!40!white,fg=black} + +\setbeamercolor*{block body example}{fg= black, bg= mygreen2} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% URL settings +\hypersetup{ + colorlinks=true, + linkcolor=blue, + filecolor=blue, + urlcolor=blue, +} + +%%%%%%%%%%%%%%%%%%%%%%%%%% + +\renewcommand{\familydefault}{\rmdefault} + +\usepackage{amsmath} +\usepackage{mathtools} + +\usepackage{subcaption} + +\usepackage{qrcode} + +\DeclareMathOperator*{\argmin}{arg\,min} +\newcommand{\bo}[1] {\mathbf{#1}} + +\newcommand{\R}{\mathbb{R}} +\newcommand{\T}{^\top} + +\newcommand{\db}[1] {\dot{\mathbf{#1}}} +\newcommand{\bhat}[1] {\hat{\mathbf{#1}}} +\newcommand{\dhat}[1] {\dot{\hat{\mathbf{#1}}}} +\newcommand{\btil}[1] {\Tilde{\mathbf{#1}}} +\newcommand{\dtil}[1] {\dot{\Tilde{\mathbf{#1}}}} + + +\newcommand{\mydate}{Spring 2023} + +\newcommand{\mygit}{\textcolor{blue}{\href{https://github.com/SergeiSa/Control-Theory-Slides-Spring-2023}{github.com/SergeiSa/Control-Theory-Slides-Spring-2023}}} + +\newcommand{\myqr}{ \textcolor{black}{\qrcode[height=1.5in]{https://github.com/SergeiSa/Control-Theory-Slides-Spring-2023}} +} + +\newcommand{\myqrframe}{ + \begin{frame} + \centerline{Lecture slides are available via Github, links are on Moodle} + \bigskip + \centerline{You can help improve these slides at:} + \centerline{\mygit} + \bigskip + \myqr + \end{frame} +} + + +\newcommand{\bref}[2] {\textcolor{blue}{\href{#1}{#2}}} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% code settings + +\usepackage{listings} +\usepackage{color} +% \definecolor{mygreen}{rgb}{0,0.6,0} +% \definecolor{mygray}{rgb}{0.5,0.5,0.5} +\definecolor{mymauve}{rgb}{0.58,0,0.82} +\lstset{ + backgroundcolor=\color{white}, % choose the background color; 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However, we will consider transform of one case of interest - transform of a derivative. + +\end{flushleft} +\end{frame} + + + +\begin{frame}{Laplace Transform of a derivative} +% \framesubtitle{O} +\begin{flushleft} + +Consider a derivative $\frac{dx}{dt}$ and its transform: + +\begin{equation} + \mathcal{L}\left(\frac{dx}{dt}\right) = \int_0^\infty \frac{dx}{dt} e^{-st}dt +\end{equation} + +we will make use of the integration by parts formula: + +\begin{block}{Integration by parts} +\begin{equation} +\int v \frac{du}{dt} dt = vu - +\int \frac{dv}{dt} u dt +\end{equation} +\end{block} + +In our case, $\frac{du}{dt} = \frac{dx}{dt}$, $u = x$, $v = e^{-st}$, $\frac{dv}{dt} = -se^{-st}$: + +\begin{equation} +\mathcal{L}\left(\frac{dx}{dt}\right) = \left[x e^{-st} \right]_0^\infty - +\int_0^\infty -se^{-st} x dt +\end{equation} + +\begin{equation} +\mathcal{L}\left(\frac{dx}{dt}\right) = -x(0) + s\mathcal{L}(x) +\end{equation} + +\end{flushleft} +\end{frame} + + + + +\begin{frame}{Derivative operator} +% \framesubtitle{O} +\begin{flushleft} + +Thus, assuming that $x(0) = 0$ and denoting $\mathcal{L}\left( x \right) = X(s)$, we can obtain a \emph{derivative operator}: + +\begin{equation} +\label{eq:NoIC_laplace} +\mathcal{L}\left(\frac{dx}{dt}\right) = s \mathcal{L}\left(x\right) = s X(s) +\end{equation} + +\bigskip + +This form of a derivative operator is very simple to use in practice. + +\end{flushleft} +\end{frame} + + + +\begin{frame}{Transfer Function} +% \framesubtitle{O} +\begin{flushleft} + +Consider the following ODE, where $u$ is an input (function of time that influences the solution of the ODE): + +\begin{equation} +\ddot y + a \dot y + b y = u +\end{equation} + +We can rewrite it using the derivative operator: + +\begin{equation} +s^2 Y(s) + a s Y(s) + b Y(s) = U(s) +\end{equation} + +and then collect $Y(s)$ on the left-hand-side: + +\begin{equation} +Y(s) = \frac{1}{s^2 + a s + b} U(s) +\end{equation} + +This form is called a \emph{transfer function}. + +\end{flushleft} +\end{frame} + + +\begin{frame}{Transfer Function} +\framesubtitle{Examples} +\begin{flushleft} + +\begin{example} +Given ODE: $2 \dddot y + 5\dot y - 40 y = 10 u$ + +The transfer function for it looks: +$Y(s) = \frac{10}{2 s^3 + 5 s - 40} U(s)$ +\end{example} + + +\begin{example} +Given ODE: $2 \dot y - 4 y = u$ + +The transfer function for it looks: $Y(s) = \frac{1}{2 s - 4} U(s)$ +\end{example} + + +\begin{example} +Given ODE: $3 \dddot y + 4y = u$ + +The transfer function for it looks: $Y(s) = \frac{1}{2 s^3 + 4} U(s)$ +\end{example} + +\end{flushleft} +\end{frame} + + + + +\begin{frame}{Transfer Functions, 1} +%\framesubtitle{Interesting things done easy} +\begin{flushleft} + +Consider the following (strange) ODE: + +\begin{equation} +2 \ddot y + 3 \dot y + 2 y = 10 \dot u - u +\end{equation} + +Using the differential equation: + +\begin{equation} +2 s^2 Y(s) + 3s Y(s) + 2Y(s) = 10s U(s) - U(s) +\end{equation} + +...which is the same as: + +\begin{equation} +(2s^2 + 3s + 2) Y(s) = (10s - 1)U(s) +\end{equation} + +The transfer function for it looks: + +\begin{equation} +Y(s) = \frac{10s - 1}{2s^2 + 3s + 2} U(s) +\end{equation} + +\end{flushleft} +\end{frame} + + + + +\begin{frame}{Transfer Functions, 2} +% \framesubtitle{Interesting things done easy} + \begin{flushleft} + + Consider the control law: + + \begin{equation} + u = -k_p y - k_d \dot y + \end{equation} + + Transfer function representation of this control law is: + % + \begin{equation} + U(s) = -(k_d s + k_p) Y(s) + \end{equation} + + \end{flushleft} +\end{frame} + + + + +\begin{frame}{State-Space to Transfer Function conversion} +% \framesubtitle{O} +\begin{flushleft} + +Transfer functions are being used to study the relation between the input and the output of the dynamical system. + +\bigskip + +Consider standard form state-space dynamical system: + +\begin{equation} +\begin{cases} +\dot{\bo{x}} = \bo{A}\bo{x} + \bo{B}\bo{u} \\ + \bo{y} = \bo{C}\bo{x} + \bo{D}\bo{u} +\end{cases} +\end{equation} + +We can rewrite it using the derivative operator: + +\begin{equation} +\begin{cases} +s\bo{I}\bo{x} -\bo{A}\bo{x} = \bo{B}\bo{u} \\ +\bo{y} = \bo{C}\bo{x} + \bo{D}\bo{u} +\end{cases} +\end{equation} + +and then collect $\bo{x}$ on the left-hand-side: $\bo{x} = (s\bo{I} -\bo{A})^{-1} \bo{B}\bo{u}$ + +and finally, express $\bo{y}$ out: + +\begin{equation} +\bo{y} = \left( \bo{C}(s\bo{I} -\bo{A})^{-1} \bo{B} + \bo{D} \right) \bo{u} +\end{equation} + +\end{flushleft} +\end{frame} + + + + + +\begin{frame}{System - open-loop} + % \framesubtitle{Interesting things done easy} + \begin{flushleft} + + Consider a linear ODE, and its equivalent representations as a state space equation and as a transfer function: + + \begin{align} + &a_n y^n + ... + a_1 y = b_m u^m + ... + b_1 u + \\ + &\begin{cases} + \dot{\bo{x}} = \bo{A}\bo{x} + \bo{B}\bo{u} \\ + \bo{y} = \bo{C}\bo{x} + \bo{D}\bo{u} + \end{cases} + \\ + &Y(s) = G(s) U(s) + \end{align} + + We can call it a \emph{system} $\mathcal{G}$ to avoid referencing particular representation. + + \end{flushleft} +\end{frame} + + + +\begin{frame}{Closed-loop, 1} + % \framesubtitle{Interesting things done easy} + \begin{flushleft} + + Open-loop system representation is $Y(s) = G(s) U(s)$. Let us propose control law (in time domain): + + \begin{equation} + u(t) = k_p (v(t) - y(t)) + k_d (\dot v(t) - \dot y(t)) + \end{equation} + + where $v(t)$ is a control reference. Laplace transform of this control law takes form: + + \begin{equation} + U(s) = (k_p + k_d s) (V(s) - Y(s)) + \end{equation} + + Defining $H(s) = k_p + k_d s$ we find closed loop system takes form: + % + \begin{align} + Y(s) &= G(s) H(s) (V(s) - Y(s)) \\ + Y(s) &= -G(s) H(s) Y(s) + G(s) H(s)V(s) \\ + (1 + G(s) H(s)) Y(s) &= G(s) H(s)V(s) \\ + Y(s) &= \frac{G(s) H(s)}{1 + G(s) H(s)} V(s) + \end{align} + + + \end{flushleft} +\end{frame} + + + +\begin{frame}{Closed-loop, 2} + % \framesubtitle{Interesting things done easy} + \begin{flushleft} + + Alternatively, we can define a new reference signal $r(t)$: + % + \begin{equation} + r(t) = k_p v(t) + k_d \dot v(t) + \end{equation} + + Control law then takes form: + % + \begin{equation} + u(t) = -k_p y(t) - k_d \dot y(t) + r(t) + \end{equation} + + Laplace transform of the control law takes form: + % + \begin{equation} + U(s) = -H(s)Y(s) + R(s) + \end{equation} + + The closed loop system takes form: + % + \begin{align} + Y(s) &= -G(s) H(s)Y(s) + G(s)R(s) \\ + Y(s) + G(s) H(s)Y(s) &= G(s)R(s)\\ + Y(s) &= \frac{G(s)}{1 + G(s) H(s)} R(s) + \end{align} + + + \end{flushleft} +\end{frame} + +%\begin{frame}{Transfer Function and Control (1)} +% % \framesubtitle{O} +% \begin{flushleft} +% +% Let the dynamic system be described as a transfer function: +% +% \begin{equation} +% Y(s) = G(s) U(s) +% \end{equation} +% +% We can try to modify the input based on how the output looks. Since we always do it in a linear way, we can write it as: +% +% \begin{align} +% Y(s) = G(s) (U(s) - H(s) Y(s)) +% \end{align} +% +% where $H(s) y$ is called \emph{feedback}. +% +% \bigskip +% +% How would the transfer function from $U(s)$ to $Y(s) $ look like? +% +% \end{flushleft} +%\end{frame} + + +%\begin{frame}{Closed-loop, 3} +% % \framesubtitle{O} +% \begin{flushleft} +% +% From $Y(s) = G(s) (U(s) - H(s) Y(s) )$ we go: +% +% \begin{equation} +% Y(s) = G(s)U(s) - G(s)H(s) Y(s) +% \end{equation} +% \begin{equation} +% Y(s) + G(s)H(s) Y(s) = G(s)U(s) +% \end{equation} +% \begin{equation} +% Y(s) = \frac{G(s)}{1 + G(s)H(s)} U(s) +% \end{equation} +% +% Thus, we found \emph{closed-loop} transfer function: +% +% \begin{equation} +% W(s) = \frac{G(s)}{1 + G(s)H(s)} +% \end{equation} +% +% \end{flushleft} +%\end{frame} + + + + +\begin{frame}{Steady-State gain} + % \framesubtitle{Interesting things done easy} + \begin{flushleft} + + If a system $\mathcal{G}$ is stable and given constant input $u_0$ its output is approaching some constant value $y_0$, we can call this pair a \emph{steady-state solution}. The ratio between $y_0$ and $u_0$ is a \emph{steady-state gain} - how much does the system increase the input signal. + + Assume the system $\mathcal{G}$ represented as a transfer function: + + \begin{equation} + Y(s) = \frac{b_m s^m + ... + b_1}{a_n s^n + ... + a_1} U(s) + \end{equation} + + Then, as any element multiplied by the differential operator $s$ with power higher than 0 is a derivative of $u$ or $y$ and both are 0 at the steady-state solution, the steady-state gain can be found by setting those to zero: + + \begin{equation} + K = \frac{b_1}{a_1} + \end{equation} + + + + \end{flushleft} +\end{frame} + + +\begin{frame}{Read more} + +\begin{itemize} +\item \bref{https://www.cds.caltech.edu/~murray/courses/cds101/fa04/caltech/am04_ch6-3nov04.pdf}{Chapter 6 Transfer Functions} + +\item \bref{https://youtu.be/RJleGwXorUk}{Control Systems Lectures - Transfer Functions, by Brian Douglas} + +\item \bref{https://youtu.be/ZGPtPkTft8g}{The Laplace Transform - A Graphical Approach, by Brian Douglas} + +\end{itemize} + +\end{frame} + + + +\myqrframe + +\end{document} diff --git a/Slides/Laplace/settings.tex b/Slides/Laplace/settings.tex new file mode 100644 index 0000000..c9e906a --- /dev/null +++ b/Slides/Laplace/settings.tex @@ -0,0 +1,192 @@ +\pdfmapfile{+sansmathaccent.map} + + +\mode +{ + \usetheme{Warsaw} % or try Darmstadt, Madrid, Warsaw, Rochester, CambridgeUS, ... + \usecolortheme{seahorse} % or try seahorse, beaver, crane, wolverine, ... + \usefonttheme{serif} % or try serif, structurebold, ... + \setbeamertemplate{navigation symbols}{} + \setbeamertemplate{caption}[numbered] +} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% itemize settings + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% itemize settings + +\definecolor{mypaleblue}{RGB}{240, 240, 255} +\definecolor{mylightblue}{RGB}{120, 150, 255} +\definecolor{myblue}{RGB}{90, 90, 255} +\definecolor{mygblue}{RGB}{70, 110, 240} +\definecolor{mydarkblue}{RGB}{0, 0, 180} +\definecolor{myblackblue}{RGB}{40, 40, 120} + 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We define new variables $\bo{e}$ and $\bo{v}$ as distance from the expansion point: + % + \begin{align} + \bo{e} = \bo{x} - \bo{x}_0, &\ \ \ \dot{\bo{e}} = \dot{\bo{x}}, \\ + \bo{v} = \bo{u} - \bo{u}_0. &\\ + \end{align} + + + \end{flushleft} +\end{frame} + + +\begin{frame}{Taylor expansion around node, 2} + % \framesubtitle{Linearization, Taylor Expansion} + \begin{flushleft} + + With that we can re-write the Taylor expansion: + % + \begin{align} + \dot{\bo{e}} = \frac{\partial \bo{f}}{\partial \bo{x}} \bo{e} + + \frac{\partial \bo{f}}{\partial \bo{u}} \bo{v} + \text{H.O.T.} + \end{align} + + We can introduce notation: + + \begin{align} + \bo{A} = \frac{\partial \bo{f}}{\partial \bo{x}}, \ \ \ + \bo{B} = \frac{\partial \bo{f}}{\partial \bo{u}}. + \end{align} + + If we drop higher order terms from the Taylor expansion, we obtain \emph{linearization} of the system dynamics: + + \begin{align} + \dot{\bo{e}} = \bo{A} \bo{e} + \bo{B} \bo{v} + \end{align} + + In this context, $\bo{x}_0$ and $\bo{u}_0$ is the \emph{linearization point}. + + \end{flushleft} +\end{frame} + + + +\begin{frame}{Taylor expansion along a trajectory} + % \framesubtitle{Linearization, Taylor Expansion} + \begin{flushleft} + + Consider a non-linear dynamical system: + % + \begin{equation} + \dot{\bo{x}} = \bo{f}(\bo{x}, \bo{u}) + \end{equation} + + and a trajectory $\dot{\bo{x}}_0 = \bo{f}(\bo{x}_0, \bo{u}_0)$. We can consider a Taylor expansion along this trajectory: + + \begin{equation} + \bo{f}(\bo{x}, \bo{u}) \sim \bo{f}(\bo{x}_0, \bo{u}_0) + + \frac{\partial \bo{f}}{\partial \bo{x}} (\bo{x} - \bo{x}_0) + + \frac{\partial \bo{f}}{\partial \bo{u}} (\bo{u} - \bo{u}_0) + \text{H.O.T.} + \end{equation} + + Since $\dot{\bo{e}} = \dot{\bo{x}} - \dot{\bo{x}}_0$, we re-write: + % + \begin{align} + \dot{\bo{e}} \sim + \bo{A} \bo{e} + + \bo{B} \bo{v} + \text{H.O.T.} + \end{align} + + As before, we drop higher order terms and obtain linearization: + + \begin{align} + \dot{\bo{e}} = + \bo{A} \bo{e} + + \bo{B} \bo{v} + \end{align} + + \end{flushleft} +\end{frame} + + + + +\begin{frame}{Affine expansion} + % \framesubtitle{Linearization, Taylor Expansion} + \begin{flushleft} + + If we want to maintain our original variables, we can still use Taylor expansion: + + \begin{equation} + \bo{f}(\bo{x}, \bo{u}) \sim \bo{f}(\bo{x}_0, \bo{u}_0) + + \bo{A} (\bo{x} - \bo{x}_0) + + \bo{B} (\bo{u} - \bo{u}_0) + \end{equation} + + Denoting $ \bo{f}(\bo{x}_0, \bo{u}_0) - \bo{A}\bo{x}_0 - \bo{B} \bo{u}_0 = \bo{c}$ and dropping H.O.T. we approximate the system as affine: + + \begin{equation} + \dot{\bo{x}} = \bo{A} \bo{x} + + \bo{B} \bo{u} + \bo{c} + \end{equation} + + + \end{flushleft} +\end{frame} + + + +\begin{frame}{Manipulator equation linearization, 1} +%\framesubtitle{Idea} +\begin{flushleft} + +Consider Manipulator equation: + +\begin{equation} + \bo{H} \ddot{\bo{q}} + \bo{C} \dot{\bo{q}} + \bo{g} = \tau +\end{equation} + +We will attempt to linearize it. + +\bigskip + +We begin by proposing the following new variables: + +\begin{align} + \bo{x} = + \begin{bmatrix} + \bo{q} - \bo{q}_0 \\ + \dot{\bo{q}} - \dot{\bo{q}}_0 + \end{bmatrix},& +\ \ \ + \bo{u} = \tau - \tau_0 + \\ + \bo{q} = \bo{S}_q \bo{x},& + \ \ \ + \dot{\bo{q}} = \bo{S}_v \bo{x} +\end{align} + +where $\tau_0$ is chosen such that $\bo{C}(\dot{\bo{q}}_0, \bo{q}_0) \dot{\bo{q}}_0 + \bo{g}(\bo{q}_0) = \tau_0$, and $\bo{S}_q$ and $\bo{S}_v$ are choice matrices. + + +\end{flushleft} +\end{frame} + + + +\begin{frame}{Manipulator equation linearization, 2} +% \framesubtitle{Idea} + \begin{flushleft} + + Next, we introduce function $\phi(\dot{\bo{q}}, \bo{q}, \tau) = \ddot{\bo{q}}$, expressed as: + + \begin{equation} + \phi(\dot{\bo{q}}, \bo{q}, \tau) + = + \bo{H}^{-1} (\tau - \bo{C} \dot{\bo{q}} - \bo{g} ) + \end{equation} + + Next, we write our dynamics as a first order ODE: + + \begin{equation} + \frac{d}{dt} + \left( + \begin{bmatrix} + \bo{q} \\ \dot{\bo{q}} + \end{bmatrix} + \right) + = + \begin{bmatrix} + \dot{\bo{q}} \\ + \phi(\dot{\bo{q}}, \bo{q}, \tau) + \end{bmatrix} + \end{equation} + + \begin{equation} + \dot{\bo{x}} + = + \begin{bmatrix} + \bo{S}_v \bo{x} \\ + \phi(\bo{x}, \tau) + \end{bmatrix} +\end{equation} + + With that, we can find matrices $\bo{A}$ and $\bo{B}$. + + \end{flushleft} +\end{frame} + + + +\begin{frame}{Manipulator equation linearization, 3} +%\framesubtitle{State matrix} +\begin{flushleft} + +In this case, state matrices $\bo{A}$ and $\bo{B}$ become: + + +\begin{equation} + \bo{A} = + \begin{bmatrix} + \frac{\partial \dot{\bo{q}}}{\partial \bo{q}} & + \frac{\partial \dot{\bo{q}}}{\partial \dot{\bo{q}}} + \\ + \frac{\partial \phi}{\partial \bo{q}} & + \frac{\partial \phi}{\partial \dot{\bo{q}}} + \end{bmatrix} += + \begin{bmatrix} + 0 & \bo{I} + \\ + \frac{\partial \phi}{\partial \bo{q}} & + \frac{\partial \phi}{\partial \dot{\bo{q}}} +\end{bmatrix} +\end{equation} + + +\begin{equation} + \bo{B} = + \begin{bmatrix} + \frac{\partial \dot{\bo{q}}}{\partial \tau} + \\ + \frac{\partial \phi}{\partial \tau} + \end{bmatrix} + = + \begin{bmatrix} + 0 + \\ + \bo{H}^{-1} + \end{bmatrix} +\end{equation} + +Thus. our task is to find the following jacobians: $\frac{\partial \phi}{\partial \bo{q}}$ and $\frac{\partial \phi}{\partial \dot{\bo{q}}}$. + +\end{flushleft} +\end{frame} + + + +\begin{frame}{Manipulator equation linearization, 4} + %\framesubtitle{State matrix} + \begin{flushleft} + + Let us find $\frac{\partial \phi}{\partial \bo{q}}$: + + \begin{align} + \frac{\partial \phi}{\partial \bo{q}} + &= + \frac{\partial }{\partial \bo{q}} \left(\bo{H}^{-1} (\tau - \bo{C} \dot{\bo{q}} - \bo{g} ) \right) + = \\ + &= + \frac{\partial \bo{H}^{-1}}{\partial \bo{q}} (\tau - \bo{C} \dot{\bo{q}} - \bo{g} ) + + + \bo{H}^{-1} \frac{\partial }{\partial \bo{q}} \left( \tau - \bo{C} \dot{\bo{q}} - \bo{g} \right) + \end{align} + + If we evaluate $\frac{\partial \phi}{\partial \bo{q}}$ at the point $\bo{q} = \bo{q}_0$, $\dot{\bo{q}} = \dot{\bo{q}}_0$, $\tau = \tau_0$, we can use the fact that $\bo{C}(\dot{\bo{q}}_0, \bo{q}_0) \dot{\bo{q}}_0 + \bo{g}(\bo{q}_0) = \tau_0$ to avoid computing derivative $\frac{\partial \bo{H}^{-1}}{\partial \bo{q}}$: + + \begin{align} + \frac{\partial \phi}{\partial \bo{q}} + &= + \bo{H}^{-1} \left( \tau - \frac{\partial \bo{C}\dot{\bo{q}}}{\partial \bo{q}} - \frac{\partial \bo{g}}{\partial \bo{q}} \right) + \end{align} + + \end{flushleft} +\end{frame} + + + + +\begin{frame}{Manipulator equation linearization, 5} + %\framesubtitle{State matrix} + \begin{flushleft} + + Let us find $\frac{\partial \phi}{\partial \dot{\bo{q}}}$: + % + \begin{align} + \frac{\partial \phi}{\partial \dot{\bo{q}}} + &= + \frac{\partial }{\partial \dot{\bo{q}}} \left(\bo{H}^{-1} (\tau - \bo{C} \dot{\bo{q}} - \bo{g} ) \right) + = \\ + &= + -\bo{H}^{-1}\frac{\partial \bo{C} \dot{\bo{q}}}{\partial \dot{\bo{q}}} + \end{align} + + With that, we expressed all jacobians. The rest is the same as in the general case we studied in the first slides. + + \end{flushleft} +\end{frame} + + + +%\begin{equation} +% \bo{A} = +% \begin{bmatrix} +% 0 & \bo{I} \\ +% \frac{\partial (\bo{H}^{-1} (\bo{T}\bo{u} - \bo{C} \dot{\bo{q}} - \bo{g}) )}{\partial \bo{q}} +% & +% \frac{\partial (\bo{H}^{-1} (\bo{T}\bo{u} - \bo{C} \dot{\bo{q}} - \bo{g}) )}{\partial \dot{\bo{q}}} +% \end{bmatrix} +%\end{equation} +% +% +%\begin{equation*} +% \frac{\partial }{\partial \bo{q}} (\bo{H}^{-1} (\bo{T}\bo{u} - \bo{C} \dot{\bo{q}} - \bo{g}) ) +% = +% \frac{\partial \bo{H}^{-1}}{\partial \bo{q}} (\bo{T}\bo{u} - \bo{C} \dot{\bo{q}} - \bo{g}) +% + +% \bo{H}^{-1} +% \frac{\partial }{\partial \bo{q}} +% (\bo{T}\bo{u} - \bo{C} \dot{\bo{q}} - \bo{g}) ) +%\end{equation*} +% +%\begin{equation} +% \frac{\partial (\bo{H}^{-1} (\bo{T}\bo{u} - \bo{C} \dot{\bo{q}} - \bo{g}) )}{\partial \dot{\bo{q}}} +% = +% -\bo{H}^{-1}\bo{C} - \bo{H}^{-1} +% \frac{\partial \bo{C}}{\partial \dot{\bo{q}}} \dot{\bo{q}} +%\end{equation} +% +%\begin{equation} +% \frac{\partial \bo{H}^{-1}}{\partial \bo{q}} = +% - \bo{H}^{-1} \frac{\partial \bo{H}}{\partial \bo{q}} +% \bo{H}^{-1} +%\end{equation} + + + +%\begin{frame}{Linear control for nonlinear systems} +% \framesubtitle{Linearization around node} +% \begin{flushleft} +% +% In the general case it is: +% +% Let us make an assumption that our linearization point $\bo{q}_0$, $\dot{\bo{q}}_0$ and $\bo{u}_0$ is a node, meaning that $\ddot{\bo{q}}_0 = 0$, which implies: +% +% \begin{equation} +% \bo{C} \dot{\bo{q}} + \bo{g} = \bo{T}\bo{u} +% \end{equation} +% +%Then +% +% \begin{equation*} +% \frac{\partial }{\partial \bo{q}} (\bo{H}^{-1} (\bo{T}\bo{u} - \bo{C} \dot{\bo{q}} - \bo{g}) ) +% = +% \frac{\partial \bo{H}^{-1}}{\partial \bo{q}} 0 +% + +% \bo{H}^{-1} +% \frac{\partial }{\partial \bo{q}} +% (\bo{T}\bo{u} - \bo{C} \dot{\bo{q}} - \bo{g}) ) +% \end{equation*} +% +% +% +% \end{flushleft} +%\end{frame} + + +%\begin{frame}{Linear control for nonlinear systems} +%\framesubtitle{Control matrix} +%\begin{flushleft} +% +%Control matrix $\bo{B}$ becomes: +% +%\begin{equation} +% \bo{B} = +% \begin{bmatrix} +% 0\\ +% \frac{\partial (\bo{H}^{-1} (\bo{T}\bo{u} - \bo{C} \dot{\bo{q}} - \bo{g}) )}{\partial \bo{u}} +% \end{bmatrix} +% = +% \begin{bmatrix} +% 0\\ +% \bo{H}^{-1} \bo{T} +% \end{bmatrix} +%\end{equation} +% +%...and this does not look very clean and nice to use. Indeed, it is not easy or nice in practice. +% +%\end{flushleft} +%\end{frame} + + + +\myqrframe + +\end{document} diff --git a/Slides/Linearization/settings.tex b/Slides/Linearization/settings.tex new file mode 100644 index 0000000..31551c7 --- /dev/null +++ b/Slides/Linearization/settings.tex @@ -0,0 +1,193 @@ +\pdfmapfile{+sansmathaccent.map} + + +\mode +{ + \usetheme{Warsaw} % or try Darmstadt, Madrid, Warsaw, Rochester, CambridgeUS, ... + \usecolortheme{seahorse} % or try seahorse, beaver, crane, wolverine, ... + \usefonttheme{serif} % or try serif, structurebold, ... + \setbeamertemplate{navigation symbols}{} + \setbeamertemplate{caption}[numbered] +} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% itemize settings + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% itemize settings + +\definecolor{myhotpink}{RGB}{255, 80, 200} +\definecolor{mywarmpink}{RGB}{255, 60, 160} +\definecolor{mylightpink}{RGB}{255, 80, 200} +\definecolor{mypink}{RGB}{255, 30, 80} +\definecolor{mydarkpink}{RGB}{155, 25, 60} + +\definecolor{mypaleblue}{RGB}{240, 240, 255} +\definecolor{mylightblue}{RGB}{120, 150, 255} +\definecolor{myblue}{RGB}{90, 90, 255} +\definecolor{mygblue}{RGB}{70, 110, 240} +\definecolor{mydarkblue}{RGB}{0, 0, 180} +\definecolor{myblackblue}{RGB}{40, 40, 120} + +\definecolor{mygreen}{RGB}{0, 200, 0} +\definecolor{mydarkgreen}{RGB}{0, 120, 0} +\definecolor{mygreen2}{RGB}{245, 255, 230} + +\definecolor{mygray}{gray}{0.8} +\definecolor{mydarkgray}{RGB}{80, 80, 160} + +\definecolor{mydarkred}{RGB}{160, 30, 30} +\definecolor{mylightred}{RGB}{255, 150, 150} +\definecolor{myred}{RGB}{200, 110, 110} +\definecolor{myblackred}{RGB}{120, 40, 40} + +\definecolor{mygreen}{RGB}{0, 200, 0} +\definecolor{mygreen2}{RGB}{205, 255, 200} + +\definecolor{mydarkcolor}{RGB}{60, 25, 155} +\definecolor{mylightcolor}{RGB}{130, 180, 250} + +\setbeamertemplate{itemize items}[default] + +\setbeamertemplate{itemize item}{\color{myblackblue}$\blacksquare$} +\setbeamertemplate{itemize subitem}{\color{mygblue}$\blacktriangleright$} +\setbeamertemplate{itemize subsubitem}{\color{mygray}$\blacksquare$} + +\setbeamercolor{palette quaternary}{fg=white,bg=mydarkgray} +\setbeamercolor{titlelike}{parent=palette quaternary} + +\setbeamercolor{palette quaternary2}{fg=black,bg=mypaleblue} +\setbeamercolor{frametitle}{parent=palette quaternary2} + +\setbeamerfont{frametitle}{size=\Large,series=\scshape} +\setbeamerfont{framesubtitle}{size=\normalsize,series=\upshape} + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% block settings + +\setbeamercolor{block title}{bg=red!30,fg=black} + +\setbeamercolor*{block title example}{bg=mygreen!40!white,fg=black} + +\setbeamercolor*{block body example}{fg= black, bg= mygreen2} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% URL settings +\hypersetup{ + colorlinks=true, + linkcolor=blue, + filecolor=blue, + urlcolor=blue, +} + +%%%%%%%%%%%%%%%%%%%%%%%%%% + +\renewcommand{\familydefault}{\rmdefault} + +\usepackage{amsmath} +\usepackage{mathtools} + +\usepackage{subcaption} + +\usepackage{qrcode} + +\DeclareMathOperator*{\argmin}{arg\,min} +\newcommand{\bo}[1] {\mathbf{#1}} + +\newcommand{\R}{\mathbb{R}} +\newcommand{\T}{^\top} + +\newcommand{\dx}[1] {\dot{\mathbf{#1}}} +\newcommand{\ma}[4] {\begin{bmatrix} + #1 & #2 \\ #3 & #4 +\end{bmatrix}} +\newcommand{\myvec}[2] {\begin{bmatrix} + #1 \\ #2 +\end{bmatrix}} +\newcommand{\myvecT}[2] {\begin{bmatrix} + #1 & #2 +\end{bmatrix}} + + +\newcommand{\mydate}{Spring 2023} + +\newcommand{\mygit}{\textcolor{blue}{\href{https://github.com/SergeiSa/Control-Theory-Slides-Spring-2023}{github.com/SergeiSa/Control-Theory-Slides-Spring-2023}}} + +\newcommand{\myqr}{ \textcolor{black}{\qrcode[height=1.5in]{https://github.com/SergeiSa/Control-Theory-Slides-Spring-2023}} +} + +\newcommand{\myqrframe}{ + \begin{frame} + \centerline{Lecture slides are available via Github, links are on Moodle} + \bigskip + \centerline{You can help improve these slides at:} + \centerline{\mygit} + \bigskip + \myqr + \end{frame} +} + + +\newcommand{\bref}[2] {\textcolor{blue}{\href{#1}{#2}}} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% code settings + +\usepackage{listings} +\usepackage{color} +% \definecolor{mygreen}{rgb}{0,0.6,0} +% \definecolor{mygray}{rgb}{0.5,0.5,0.5} +\definecolor{mymauve}{rgb}{0.58,0,0.82} +\lstset{ + backgroundcolor=\color{white}, % choose the background color; 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If it's 1, each line will be numbered + stringstyle=\color{mymauve}, % string literal style + tabsize=2, % sets default tabsize to 2 spaces + title=\lstname % show the filename of files included with \lstinputlisting; also try caption instead of title +} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% URL settings +\hypersetup{ + colorlinks=false, + linkcolor=blue, + filecolor=blue, + urlcolor=blue, +} + +%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% tikz settings + +\usepackage{tikz} +\tikzset{every picture/.style={line width=0.75pt}} \ No newline at end of file diff --git a/Slides/LyapunovTheory/main.pdf b/Slides/LyapunovTheory/main.pdf new file mode 100644 index 0000000..32d8320 Binary files /dev/null and b/Slides/LyapunovTheory/main.pdf differ diff --git a/Slides/LyapunovTheory/main.tex b/Slides/LyapunovTheory/main.tex new file mode 100644 index 0000000..8775a4b --- /dev/null +++ b/Slides/LyapunovTheory/main.tex @@ -0,0 +1,322 @@ +\documentclass{beamer} + +\input{settings.tex} + + +\title{Lyapunov Theory, Lyapunov equations} +\subtitle{Control Theory, Lecture 12} +\author{by Sergei Savin} +\centering +\date{\mydate} + + +\begin{document} +\maketitle + + +\begin{frame}{Content} + +\begin{itemize} +\item Lyapunov method: stability criteria +\item Lyapunov method: examples +\item Linear case +\item Discrete case +\item Lyapunov equations +\item Read more +\end{itemize} + +\end{frame} + + + + + +\begin{frame}{Lyapunov method: stability criteria} +% \framesubtitle{Parameter estimation} +\begin{flushleft} + +\begin{block}{Asymptotic stability criteria} +Autonomous dynamic system $\dot{\bo{x}} = \bo{f}(\bo{x})$ is assymptotically stable, if there exists a scalar function $V = V(\bo{x}) > 0$, whose time derivative is negative $\dot V(\bo{x}) < 0$, except $V(\bo{0}) = 0$, $\dot V(\bo{0}) = 0$. +\end{block} + +\begin{block}{Marginal stability criteria} +$\dot{\bo{x}} = \bo{f}(\bo{x})$ is stable in the sense of Lyapunov, $\exists V(\bo{x}) > 0$, $\dot V(\bo{x}) \leq 0$. +\end{block} + +\begin{definition} +Function $V(\bo{x}) > 0$ in this case is called \emph{Lyapunov function}. +\end{definition} + +\bigskip + +This is not the only type of stability as you remember, you are invited to study criteria for other stability types on your own. + +\end{flushleft} +\end{frame} + + +\begin{frame}{Lyapunov method: Example 1} +%\framesubtitle{Example 1} +\begin{flushleft} + +Take dynamical system $\dot{x} = -x$. + +\bigskip + +We propose a \emph{Lyapunov function candidate} $V(x) = x^2 \geq 0$. Let's find its derivative: + +\begin{equation} + \dot V(x) = \frac{\partial V}{\partial x} (-x) = 2x (-x) = -x^2 \leq 0 +\end{equation} + +This satisfies the Lyapunov criteria, so the system is stable. It is in fact asymptotically stable, because $\dot V(x) \neq 0$ if $x \neq 0$. + +\end{flushleft} +\end{frame} + + + +\begin{frame}{Lyapunov method: Example 2} +% \framesubtitle{Example 3} + \begin{flushleft} + + Consider pendulum $\ddot{q} = f(q, \dot{q}) = -\dot{q} - \sin(q)$. + + \bigskip + + We propose a \emph{Lyapunov function candidate} $V(q, \dot{q}) = E(q, \dot{q}) = \frac{1}{2} \dot{q}^2 + 1 - \cos(q)\geq 0$, where $E(q, \dot{q})$ is total energy of the system. Let's find its derivative: + + \begin{equation} + \dot V(q, \dot{q}) = + \frac{\partial V}{\partial q} \dot{q} + + \frac{\partial V}{\partial \dot{q}} f(q, \dot{q}) = + \dot{q} \sin(q) + \dot{q}(-\dot{q} - \sin(q)) = + -\dot{q}^2 \leq 0 + \end{equation} + + + This satisfies the Lyapunov criteria, so the system is stable. It is not proven to be asymptotically stable, because $\dot V(q, \dot{q}) = 0$ for any $q$, as long as $\dot{q} = 0$. + + \end{flushleft} +\end{frame} + + +\begin{frame}{LaSalle's invariance principle, 1} + % \framesubtitle{Parameter estimation} + \begin{flushleft} + + \begin{block}{LaSalle's invariance principle} + Autonomous dynamic system $\dot{\bo{x}} = \bo{f}(\bo{x})$ is asymptotically stable, if there exists a scalar function $V = V(\bo{x}) > 0$, whose time derivative is negative $\dot V(\bo{x}) \leq 0$, except $V(\bo{0}) = 0$, where the set $\{\bo{x}: \ \dot V(\bo{x}) = 0 \}$ does not contain non-trivial trajectories. + \end{block} + + \bigskip + + A trivial trajectory is $\bo{x}(t) = 0$. Unlike Lyapunov condition, LaSalle's principle allows us to prove asymptotic stability even for systems with $\dot V(\bo{x}) = 0$. + + + \end{flushleft} +\end{frame} + + + + +\begin{frame}{LaSalle's invariance principle, 2} + % \framesubtitle{Parameter estimation} + \begin{flushleft} + + Local version of LaSalle's invariance principle has the following form: + + \begin{block}{Local LaSalle's invariance principle} + Autonomous dynamic system $\dot{\bo{x}} = \bo{f}(\bo{x})$ is asymptotically stable in the neighborhood $\mathcal D$ of the origin, if there exists a scalar function $V = V(\bo{x}) > 0$, whose time derivative is negative $\dot V(\bo{x}) \leq 0$, except $V(\bo{0}) = 0$, where the set $\mathcal M = \{\bo{x}: \ \dot V(\bo{x}) = 0 \} \cap \mathcal D$ does not contain non-trivial trajectories. + \end{block} + + + \end{flushleft} +\end{frame} + + + +\begin{frame}{LaSalle principle: Example 2} + % \framesubtitle{Example 3} + \begin{flushleft} + + In our previous example $\dot V(q, \dot{q}) = 0$ for any $q$, as long as $\dot{q} = 0$. But the set $\{(q, \dot{q}): \ \dot{q} = 0 \}$ contains no trajectories of the system $\ddot{q} = -\dot{q} - \sin(q)$ other than $q(t) = 0$ in the region $-\frac{\pi}{2} < q < \frac{\pi}{2}$. So, LaSalle principle proves local asymptotic stability. + + \end{flushleft} +\end{frame} + + + +\begin{frame}{LaSalle principle: Example 3} + %\framesubtitle{Example 2} + \begin{flushleft} + + Consider oscillator $\ddot{q} = f(q, \dot{q}) = -\dot{q}$. + + \bigskip + + We propose a \emph{Lyapunov function candidate} $V(q, \dot{q}) = T(q, \dot{q}) = \frac{1}{2} \dot{q}^2 \geq 0$, where $T(q, \dot{q})$ is kinetic energy of the system. Let's find its derivative: + + \begin{equation} + \dot V(q, \dot{q}) = + \frac{\partial V}{\partial q} \dot{q} + + \frac{\partial V}{\partial \dot{q}} f(q, \dot{q}) = + \dot{q} (-\dot{q}) = -\dot{q}^2 \leq 0 + \end{equation} + + + This satisfies the Lyapunov criteria, so the system is stable. Note that $\dot V(q, \dot{q}) = 0$ for any $q$ as long as $\dot{q} = 0$. But the set $\{(q, \dot{q}): \ \dot{q} = 0 \}$ contains infinitely many trajectories of the system $\ddot{q} = -\dot{q}$ other than $q(t) = 0$, for example $q(t) = 1$ or $q(t) = -2$. So, LaSalle principle does not prove asymptotic stability in this case. + + \end{flushleft} +\end{frame} + + +%\begin{frame}{LaSalle principle: Example 3} +% %\framesubtitle{Example 2} +% \begin{flushleft} +% +% In our previous example $\dot V(q, \dot{q}) = 0$ for any $q$ as long as $\dot{q} = 0$. But the set $\{(q, \dot{q}): \ \dot{q} = 0 \}$ contains infinitely many trajectories of the system $\ddot{q} = -\dot{q}$ other than $q(t) = 0$, for example $q(t) = 1$ or $q(t) = -2$. So, LaSalle principle does not prove assymptotic stability in this case. +% +% \end{flushleft} +%\end{frame} + + + + + + +\begin{frame}{Linear case} +\framesubtitle{Part 1} +\begin{flushleft} + +As you saw, Lyapunov method allows you to deal with nonlinear systems, as well as linear ones. But for linear ones there are additional properties we can use. + +\bigskip + +\begin{block}{Observation 1} +For a linear system $\dot{\bo{x}} = \bo{A}\bo{x}$ we can always pick Lyapunov function candidate in the form $V = \bo{x}^\top\bo{S}\bo{x} > 0$, where $\bo{S}$ is a positive definite matrix. +\end{block} + +\bigskip + +Next slides will shows where this leads us. + +\end{flushleft} +\end{frame} + + +\begin{frame}{Linear case} +\framesubtitle{Part 2} +\begin{flushleft} + +Given $\dot{\bo{x}} = \bo{A}\bo{x}$ and $V = \bo{x}^\top\bo{S}\bo{x} \geq 0$, let's find its derivative: + +\begin{equation} + \dot V(\bo{x}) = \dot{\bo{x}}^\top\bo{S}\bo{x} + + \bo{x}^\top\bo{S}\dot{\bo{x}} +\end{equation} + +\begin{equation} + \dot V(\bo{x}) = (\bo{A}\bo{x})^\top\bo{S}\bo{x} + + \bo{x}^\top\bo{S}\bo{A}\bo{x} = + \bo{x}^\top(\bo{A}^\top\bo{S} + \bo{S}\bo{A})\bo{x} +\end{equation} + +Notice that $\dot V(x)$ should be negative for all $\bo{x}$ for the system to be stable, meaning that $\bo{A}^\top\bo{S} + \bo{S}\bo{A}$ should be negative definite. A more strict form of this requirement is \emph{Lyapunov equation}: + +\begin{equation} + \bo{A}^\top\bo{S} + \bo{S}\bo{A} = -\bo{Q} +\end{equation} + +where $\bo{Q}$ is a positive-definite matrix. + +\end{flushleft} +\end{frame} + + + +\begin{frame}{Discrete case} +\framesubtitle{Part 1} +\begin{flushleft} + +\begin{block}{Asymptotic stability criteria, discrete case} +Given $\bo{x}_{i+1} = \bo{f}(\bo{x}_i)$, if $V(\bo{x}_i) > 0$, and $V(\bo{x}_{i+1}) - V(\bo{x}_i) < 0$, the system is stable. +\end{block} + +\bigskip + +Same as before, for linear systems we will be choosing \emph{positive-definite quadratic forms} as Lyapunov function candidates. + +\end{flushleft} +\end{frame} + + + +\begin{frame}{Discrete case} +\framesubtitle{Part 2} +\begin{flushleft} + +Consider dynamics $\bo{x}_{i+1} = \bo{A}\bo{x}_i$ and $V = \bo{x}_i^\top\bo{S}\bo{x}_i \geq 0$, let's find $V(\bo{x}_{i+1}) - V(\bo{x}_i)$: + +\begin{equation} + V(\bo{x}_{i+1}) - V(\bo{x}_i) = (\bo{A}\bo{x}_i)^\top\bo{S}\bo{A}\bo{x}_i - + \bo{x}_i^\top\bo{S}\bo{x}_i +\end{equation} +\begin{equation} + V(\bo{x}_{i+1}) - V(\bo{x}_i) = \bo{x}_i^\top(\bo{A}^\top\bo{S}\bo{A} - \bo{S})\bo{x}_i +\end{equation} + +Notice that $V(\bo{x}_{i+1}) - V(\bo{x}_i)$ should be negative for all $\bo{x}_i$ for the system to be stable, meaning that $\bo{A}^\top\bo{S}\bo{A} - \bo{S}$ should be negative definite, giving us \emph{Discrete Lyapunov equation}: + +\begin{equation} + \bo{A}^\top\bo{S}\bo{A} - \bo{S} = -\bo{Q} +\end{equation} + +where $\bo{Q}$ is a positive-definite matrix. + +\end{flushleft} +\end{frame} + + + + + + +\begin{frame}{Lyapunov equations} +% \framesubtitle{Local coordinates} +\begin{flushleft} + +In practice, you can easily use Lyapunov equations for stability verification. Python and MATLAB have built-in functionality to solve it: + +\begin{itemize} + \item scipy: \texttt{linalg.solve\_continuous\_lyapunov(A, Q)} + \item MATLAB: \texttt{lyap(A,Q)} +\end{itemize} + +\end{flushleft} +\end{frame} + + + + + + + +\begin{frame}{Read more} +% \framesubtitle{Local coordinates} +\begin{flushleft} + +\begin{itemize} + \item \bref{https://folk.uib.no/nmagb/m2142002l3.pdf}{3.9 Liapunov’s direct method} + \item \bref{https://arxiv.org/abs/1809.05289}{Universita degli studi di Padova Dipartimento di Ingegneria dell'Informazione, Nicoletta Bof, Ruggero Carli, Luca Schenato, Technical Report, Lyapunov Theory for Discrete Time Systems} +\end{itemize} + +\end{flushleft} +\end{frame} + + + + +\myqrframe + +\end{document} diff --git a/Slides/LyapunovTheory/settings.tex b/Slides/LyapunovTheory/settings.tex new file mode 100644 index 0000000..31551c7 --- /dev/null +++ b/Slides/LyapunovTheory/settings.tex @@ -0,0 +1,193 @@ +\pdfmapfile{+sansmathaccent.map} + + +\mode +{ + \usetheme{Warsaw} % or try Darmstadt, Madrid, Warsaw, Rochester, CambridgeUS, ... + \usecolortheme{seahorse} % or try seahorse, beaver, crane, wolverine, ... + \usefonttheme{serif} % or try serif, structurebold, ... + \setbeamertemplate{navigation symbols}{} + \setbeamertemplate{caption}[numbered] +} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% itemize settings + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% itemize settings + +\definecolor{myhotpink}{RGB}{255, 80, 200} +\definecolor{mywarmpink}{RGB}{255, 60, 160} +\definecolor{mylightpink}{RGB}{255, 80, 200} +\definecolor{mypink}{RGB}{255, 30, 80} +\definecolor{mydarkpink}{RGB}{155, 25, 60} + +\definecolor{mypaleblue}{RGB}{240, 240, 255} +\definecolor{mylightblue}{RGB}{120, 150, 255} +\definecolor{myblue}{RGB}{90, 90, 255} +\definecolor{mygblue}{RGB}{70, 110, 240} +\definecolor{mydarkblue}{RGB}{0, 0, 180} +\definecolor{myblackblue}{RGB}{40, 40, 120} + +\definecolor{mygreen}{RGB}{0, 200, 0} +\definecolor{mydarkgreen}{RGB}{0, 120, 0} +\definecolor{mygreen2}{RGB}{245, 255, 230} + +\definecolor{mygray}{gray}{0.8} +\definecolor{mydarkgray}{RGB}{80, 80, 160} + +\definecolor{mydarkred}{RGB}{160, 30, 30} +\definecolor{mylightred}{RGB}{255, 150, 150} +\definecolor{myred}{RGB}{200, 110, 110} +\definecolor{myblackred}{RGB}{120, 40, 40} + +\definecolor{mygreen}{RGB}{0, 200, 0} +\definecolor{mygreen2}{RGB}{205, 255, 200} + +\definecolor{mydarkcolor}{RGB}{60, 25, 155} +\definecolor{mylightcolor}{RGB}{130, 180, 250} + +\setbeamertemplate{itemize items}[default] + +\setbeamertemplate{itemize item}{\color{myblackblue}$\blacksquare$} +\setbeamertemplate{itemize subitem}{\color{mygblue}$\blacktriangleright$} +\setbeamertemplate{itemize subsubitem}{\color{mygray}$\blacksquare$} + +\setbeamercolor{palette quaternary}{fg=white,bg=mydarkgray} +\setbeamercolor{titlelike}{parent=palette quaternary} + +\setbeamercolor{palette quaternary2}{fg=black,bg=mypaleblue} +\setbeamercolor{frametitle}{parent=palette quaternary2} + +\setbeamerfont{frametitle}{size=\Large,series=\scshape} +\setbeamerfont{framesubtitle}{size=\normalsize,series=\upshape} + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% block settings + +\setbeamercolor{block title}{bg=red!30,fg=black} + +\setbeamercolor*{block title example}{bg=mygreen!40!white,fg=black} + +\setbeamercolor*{block body example}{fg= black, bg= mygreen2} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% URL settings +\hypersetup{ + colorlinks=true, + linkcolor=blue, + filecolor=blue, + urlcolor=blue, +} + +%%%%%%%%%%%%%%%%%%%%%%%%%% + +\renewcommand{\familydefault}{\rmdefault} + +\usepackage{amsmath} +\usepackage{mathtools} + +\usepackage{subcaption} + +\usepackage{qrcode} + +\DeclareMathOperator*{\argmin}{arg\,min} +\newcommand{\bo}[1] {\mathbf{#1}} + +\newcommand{\R}{\mathbb{R}} +\newcommand{\T}{^\top} + +\newcommand{\dx}[1] {\dot{\mathbf{#1}}} +\newcommand{\ma}[4] {\begin{bmatrix} + #1 & #2 \\ #3 & #4 +\end{bmatrix}} +\newcommand{\myvec}[2] {\begin{bmatrix} + #1 \\ #2 +\end{bmatrix}} +\newcommand{\myvecT}[2] {\begin{bmatrix} + #1 & #2 +\end{bmatrix}} + + +\newcommand{\mydate}{Spring 2023} + +\newcommand{\mygit}{\textcolor{blue}{\href{https://github.com/SergeiSa/Control-Theory-Slides-Spring-2023}{github.com/SergeiSa/Control-Theory-Slides-Spring-2023}}} + +\newcommand{\myqr}{ \textcolor{black}{\qrcode[height=1.5in]{https://github.com/SergeiSa/Control-Theory-Slides-Spring-2023}} +} + +\newcommand{\myqrframe}{ + \begin{frame} + \centerline{Lecture slides are available via Github, links are on Moodle} + \bigskip + \centerline{You can help improve these slides at:} + \centerline{\mygit} + \bigskip + \myqr + \end{frame} +} + + +\newcommand{\bref}[2] {\textcolor{blue}{\href{#1}{#2}}} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% code settings + +\usepackage{listings} +\usepackage{color} +% \definecolor{mygreen}{rgb}{0,0.6,0} +% \definecolor{mygray}{rgb}{0.5,0.5,0.5} +\definecolor{mymauve}{rgb}{0.58,0,0.82} +\lstset{ + backgroundcolor=\color{white}, % choose the background color; 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Here are some: + +\begin{itemize} +\item Digital measurements are done in discrete time intervals. +\item Unpredicted events (faults, collisions, etc.). +\item Un-modelled kinematics or dynamics (links bending, gear box backlash, friction, etc.) making the very definition of the state disconnected from reality. +\item Lack of sensors. +\item Imprecise, nonlinear and biased sensors. +\item Other physical effects. +\end{itemize} + +\end{flushleft} +\end{frame} + +\begin{frame}{Measurement and estimation} +%\framesubtitle{Definition} +\begin{flushleft} + +Let us introduce new notation. We have an LTI system of the following form: + +\begin{equation} +\begin{cases} +\dot {\bo{x}} = \bo{A} \bo{x} + \bo{B} \bo{u} \\ +\bo{y} = \bo{C} \bo{x} \\ +\hat{\bo{x}}(t) = \text{estimate} \ (\bo{y}(t)) \\ +\bo{u} = -\bo{K}\hat{\bo{x}} +\end{cases} +\end{equation} + +Then: + +\begin{itemize} +\item $\bo{x}$ and $\bo{y}$ are the state and output (actual or true) +\item $\hat{\bo{x}}$ and $\hat{\bo{y}} =\bo{C} \hat{\bo{x}}$ are the estimated (observed) state +and output. +\end{itemize} + +Notice that we never know true state $\bo{x}$, and therefore for the control purposes we have to use the estimated state $\hat{\bo{x}}$. + +\end{flushleft} +\end{frame} + + + + +\begin{frame}{Estimation error} + %\framesubtitle{Observer} + \begin{flushleft} + + How can we quantify the error in our estimation? We can do it directly as state estimation error: + + \begin{equation} + \varepsilon = \hat{\bo{x}} - \bo{x} + \end{equation} + + But this is impossible to compute, since we do not know $\bo{x}$. Alternatively, we can compare measured output $\bo{y}$ with estimated output $\hat{\bo{y}} =\bo{C} \hat{\bo{x}}$: + + \begin{equation} + \Tilde{\bo{y}} = \bo{C} \hat{\bo{x}} - \bo{y} + \end{equation} + + This can always be computed. + + \end{flushleft} +\end{frame} + + + +\begin{frame}{Estimation - dynamics} +%\framesubtitle{Using the knowledge about dynamics} +\begin{flushleft} + +Let us consider autonomous dynamical system +\begin{equation} +\label{eq:LTI} +\begin{cases} +\dot {\bo{x}} = \bo{A} \bo{x} + \bo{B} \bo{u} \\ +\bo{y} = \bo{C} \bo{x} +\end{cases} +\end{equation} +% +with measurements $\bo{y}$. We want to get as good an estimate of the state $\hat{\bo{x}}$ as we can. + +\bigskip + +First note: dynamics should also hold for our observed state: +\begin{equation} +\hat{\dot {\bo{x}}} = \bo{A} \hat{\bo{x}} + \bo{B} \bo{u} +\end{equation} +% +Therefore if we know the initial conditions of our system exactly, and we know our model exactly, we can find exact state of the system without using measurement $\bo{y}$. We can call it an open loop observation. Unfortunately, we know neither the model nor the initial conditions precisely. + + +\end{flushleft} +\end{frame} + + + + + +\begin{frame}{Estimation - observer} +%\framesubtitle{Observer} +\begin{flushleft} + +We propose \emph{observer} that takes into account measurements in a linear way; analogues with linear control $-\bo{K}\bo{x}$, here we propose a linear law $-\bo{L}\Tilde{\bo{y}}$. Remembering that $\Tilde{\bo{y}} = \bo{C} \hat{\bo{x}} - \bo{y}$ we get: + +\begin{equation} +\label{eq:Observer} +\hat{\dot {\bo{x}}} = \bo{A} \hat{\bo{x}} + \bo{B} \bo{u} + \bo{L}(\bo{y} - \bo{C} \hat{\bo{x}}) +\end{equation} +% +With this observer, we want to get as good estimate of the state $\hat{\bo{x}}$ as we can. + +\bigskip + +We can subtract \eqref{eq:LTI} from \eqref{eq:Observer}, to get \emph{observer error dynamics}: + +\begin{equation} +\hat{\dot {\bo{x}}} - \dot {\bo{x}}= +\bo{A} \hat{\bo{x}} - \bo{A} \bo{x} + +\bo{L}(\mathbf y - \bo{C} \hat{\bo{x}}) +\end{equation} +% +\begin{equation} +\dot {\varepsilon}= +(\bo{A} - \bo{L} \bo{C}) \varepsilon +\end{equation} + +\end{flushleft} +\end{frame} + + + +\begin{frame}{Observer gains} +%\framesubtitle{Observer gains} +\begin{flushleft} + +The observer $\dot {\varepsilon}= +(\bo{A} - \bo{L} \bo{C}) \varepsilon$ is \emph{stable} (i.e., the state estimation error tends to zero), as long as the following matrix has eigenvalues with negative real parts: + +\[ +\bo{A} - +\bo{L} \bo{C} \in \mathbb{H} +\] + +We need to find $\bo{L}$. Let us observe the key difference between observer design and controller design: + +\bigskip + +\begin{itemize} + \item Controller design: find such $\bo{K}$ that $\bo{A} - \bo{B} \bo{K} \in \mathbb{H}$. + \item Observer design: find such $\bo{L}$ that: $\bo{A} - \bo{L} \bo{C} \in \mathbb{H}$ +\end{itemize} + +\bigskip + +We have instruments for finding $\bo{K}$, what about $\bo{L}$? + +\end{flushleft} +\end{frame} + + +\begin{frame}{Observer Design} +\framesubtitle{General case: design via Riccati eq.} +\begin{flushleft} + +In general, we can observe that if $\bo{A} - \bo{L} \bo{C}\in \mathbb{H}$, then $(\bo{A} - +\bo{L} \bo{C})^{\top}\in \mathbb{H}$ (eigenvalues of a matrix and its transpose are the same, see Appendix). + +\bigskip + +Therefore, we can solve the following \emph{dual problem}: + +\begin{itemize} + \item find such $\bo{L}$ that $\bo{A}^{\top} - +\bo{C}^{\top} \bo{L}^{\top} \in \mathbb{H}$. +\end{itemize} + +\bigskip + +The dual problem is \emph{equivalent} to the control design problem. We can solve it by producing and solving algebraic Riccati equation, as in the LQR formulation. In pseudo-code it can be represented the following way: + +\bigskip + +$\bo{L}^{\top}$ \texttt{= lqr}($\bo{A}^{\top}$, $\bo{C}^{\top}$, $\mathbf Q$, $\mathbf R$). + +where $\mathbf Q$ and $\mathbf R$ are weight matrices, determining the "sensitivity" or "aggressiveness" of the observer. + + +\end{flushleft} +\end{frame} + + + + +\begin{frame}{Observation and Control} +%\framesubtitle{LTI} +\begin{flushleft} + +Thus we get dynamics+observer combination: + +\begin{equation} +\begin{cases} +\dot {\bo{x}} = \bo{A} \bo{x} + \bo{B} \bo{u} \\ +\hat{\dot {\bo{x}}} = \bo{A} \hat{\bo{x}} + \bo{B} \mathbf u + \bo{L}(\mathbf y - \bo{C} \hat{\bo{x}})\\ +\bo{y} = \bo{C} \bo{x} \\ +\bo{u} = -\bo{K} \hat{\bo{x}} +\end{cases} +\end{equation} + +\bigskip + +where $\bo{A} - \bo{B} \bo{K} \in \mathbb{H}$ and $\bo{A}^{\top} - +\bo{C}^{\top} \bo{L}^{\top} \in \mathbb{H}$. + + +\end{flushleft} +\end{frame} + + + + +\begin{frame}{Observation and Control} +\framesubtitle{Stability analysis} +\begin{flushleft} + +Let us re-write the dynamics + +\begin{equation} +\begin{cases} +\dot {\bo{x}} = \textcolor{mydarkblue}{\bo{A}} \bo{x} \textcolor{mydarkpink}{- \bo{B} \bo{K}} \hat{\bo{x}} +\\ +\hat{\dot {\bo{x}}} = \textcolor{mydarkgray}{\bo{A}} \hat{\bo{x}} \textcolor{mydarkgray}{- \bo{B} \bo{K}} \hat{\bo{x}} + \textcolor{mydarkgreen}{\bo{L}\bo{C}} \bo{x} \textcolor{mydarkgray}{- \bo{L}\bo{C}} \hat{\bo{x}} +\end{cases} +\end{equation} + +in a matrix form: + +\begin{equation} +\begin{bmatrix} +\dot {\bo{x}} \\ +\hat{\dot {\bo{x}}} +\end{bmatrix} += +\begin{bmatrix} +\textcolor{mydarkblue}{\bo{A}} & \textcolor{mydarkpink}{-\bo{B}\bo{K}}\\ +\textcolor{mydarkgreen}{\bo{L}\bo{C}} & (\textcolor{mydarkgray}{\bo{A} - \bo{B}\bo{K}-\bo{L}\bo{C}}) +\end{bmatrix} +\begin{bmatrix} +\bo{x} \\ +\hat{\bo{x}} +\end{bmatrix} +\end{equation} + +\bigskip + +We can't directly reason about eigenvalues of this matrix. Next slide will show a way to do it with a change of variables. + +\end{flushleft} +\end{frame} + + + + +\begin{frame}{Observation and Control} +\framesubtitle{Change of variables} +\begin{flushleft} + +Let us use the following substitution: $\bo{e} = \bo{x} - \hat{\bo{x}}$, which implies $\hat{\bo{x}} = \bo{x} - \bo{e}$: + +Our system had form: + +\begin{equation} +\begin{cases} +\dot {\bo{x}} = \textcolor{mydarkblue}{\bo{A} \bo{x} - \bo{B}\bo{K} \hat{\bo{x}}} \\ +\hat{\dot {\bo{x}}} = \textcolor{mydarkpink}{\bo{A} \hat{\bo{x}} - \bo{B}\bo{K} \hat{\bo{x}} + \bo{L}\bo{C} \bo{x} - \bo{L}\bo{C} \hat{\bo{x}}} +\end{cases} +\end{equation} + +Since $\dot{\bo{e}} = \textcolor{mydarkblue}{\dot{\bo{x}}} - \textcolor{mydarkpink}{\hat{\dot{\bo{x}}}}$, we get: +% +\[ +\dot{\bo{e}} = +\textcolor{mydarkblue}{\bo{A} \bo{x} - \bo{B}\bo{K} \hat{\bo{x}}} - +\textcolor{mydarkpink}{(\bo{A} \hat{\bo{x}} - \bo{B}\bo{K} \hat{\bo{x}} + \bo{L}\bo{C} \bo{x} - \bo{L}\bo{C} \hat{\bo{x}})} +\] +% +\[ +\dot{\bo{e}} = +\bo{A} (\bo{x} - \hat{\bo{x}}) - \bo{L}\bo{C}(\bo{x} - \hat{\bo{x}}) +\] +% +\[ +\dot{\bo{e}} = +(\bo{A} - \bo{L}\bo{C})\bo{e} +\] + +Equation $\dot {\bo{x}} = \bo{A} \bo{x} - \bo{B}\bo{K} \hat{\bo{x}}$ takes form: + +\[ +\dot {\bo{x}} = (\bo{A}-\bo{B}\bo{K}) \bo{x} + \bo{B}\bo{K}\bo{e} +\] + + +\end{flushleft} +\end{frame} + + + + +\begin{frame}{Observation and Control} +\framesubtitle{Upper triangular form} +\begin{flushleft} + +Collecting $\dot {\bo{x}}$ and $\dot{\bo{e}}$ we get: + +\begin{equation} +\begin{cases} +\dot {\bo{x}} = (\bo{A}-\bo{B}\bo{K}) \bo{x} + \bo{B}\bo{K}\bo{e} \\ +\dot{\bo{e}} = +(\bo{A} - \bo{L}\bo{C})\bo{e} +\end{cases} +\end{equation} + +In matrix form it becomes: + +\begin{equation} +\begin{bmatrix} +\dot {\bo{x}} \\ +\dot{\bo{e}} +\end{bmatrix} += +\begin{bmatrix} +(\bo{A}-\bo{B}\bo{K}) & \bo{B}\bo{K} \\ +0 & (\bo{A} - \bo{L}\bo{C}) +\end{bmatrix} +\begin{bmatrix} +\bo{x} \\ +\bo{e} +\end{bmatrix} +\end{equation} + +Eigenvalues of a upper block-triangular matrices equal to the union of the eigenvalues of the blocks on the main diagonal (see Appendix B). Hence here, the eigenvalues of the system are equal to the union of eigenvalues of $(\bo{A}-\bo{B}\bo{K})$ and $(\bo{A} - \bo{L}\bo{C})$. + +\end{flushleft} +\end{frame} + + + +\begin{frame}{Observation and Control} +\framesubtitle{Separation principle} +\begin{flushleft} + +Since the eigenvalues of the system are equal to the union of eigenvalues of $(\bo{A}-\bo{B}\bo{K})$ and $(\bo{A} - \bo{L}\bo{C})$, we can make the following observation: + +\bigskip + +\begin{alertblock}{Separation principle} +As long as the observer and the controller are stable independently, the overall system is stable too. This is called \emph{separation principle}. +\end{alertblock} + +\end{flushleft} +\end{frame} + + + + +% \begin{frame}{Observation and Control} +% \framesubtitle{Affine case} +% \begin{flushleft} + + +% Affine case is almost the same: + +% \begin{equation} +% \begin{cases} +% \dot {\bo{x}} = \bo{A} \bo{x} + \bo{B} \bo{u} + \bo{c}\\ +% \hat{\dot {\bo{x}}} = \bo{A} \hat{\bo{x}} + \bo{B} \mathbf u + \bo{L}(\mathbf y - \bo{C} \hat{\bo{x}}) + \bo{c} \\ +% \bo{y} = \bo{C} \bo{x} \\ +% \bo{u} = -\bo{K} (\hat{\bo{x}} - \bo{x}^*(t)) + \bo{u}^*(t) +% \end{cases} +% \end{equation} + +% \bigskip + +% where $\bo{A} - \bo{B} \bo{K} < 0$ and $\bo{A}^{\top} - +% \bo{c}^{\top} \bo{L}^{\top} < 0$. + + +% \end{flushleft} +% \end{frame} + + + +\myqrframe + + + +\begin{frame}{Appendix A. Eigenvalues of transpose} +% \framesubtitle{General case: design via Riccati eq.} + \begin{flushleft} + + Given matrix $\bo{M}$ and its eigenvalue $\lambda$ and eigenvector $\bo{v}$. we can prove that $\lambda$ is an eigenvector of $\bo{M}\T$: + + \begin{align} + \bo{M}\bo{v} = \lambda \bo{v} \\ + \text{det}\ (\bo{M}- \bo{I} \lambda) = 0 \\ + \text{det}\ (\bo{M}\T- \bo{I} \lambda) = 0 \\ + \bo{M}\T\bo{u} = \lambda \bo{u} + \end{align} + + We used the fact that determinant of a matrix is equal to the determinant of its transpose: $\text{det}\ (\bo{A}) = \text{det}\ (\bo{A}\T)$. + + \end{flushleft} +\end{frame} + + +\begin{frame}{Appendix B., 1} + \framesubtitle{Eig. values of block-diagonal matrices} + \begin{flushleft} + + Given matrix $\bo{M}$: + % + \begin{align} + \bo{M} = + \begin{bmatrix} + \bo{A} & \bo{B} \\ \bo{0} & \bo{C} + \end{bmatrix} + \end{align} + + Let $\lambda$, $\bo{v}$ be an eigenvalue and eigenvector of $\bo{A}$ and $\mu$, $\bo{u}$ be an eigenvalue and eigenvector of $\bo{C}$. We can prove that $\lambda$, $\bo{v}_M = \begin{bmatrix} + \bo{v} \\ 0 + \end{bmatrix}$ are eigenvalue and eigenvector of $\bo{M}$: + + \begin{align} + \begin{bmatrix} + \bo{A} & \bo{B} \\ \bo{0} & \bo{C} + \end{bmatrix} + \begin{bmatrix} + \bo{v} \\ \bo{0} + \end{bmatrix} + = + \begin{bmatrix} + \bo{A}\bo{v} \\ \bo{0} + \end{bmatrix} + = + \lambda + \begin{bmatrix} + \bo{v} \\ \bo{0} + \end{bmatrix}. + \end{align} + + \end{flushleft} +\end{frame} + + + +\begin{frame}{Appendix B., 2} + \framesubtitle{Eig. values of block-diagonal matrices} + \begin{flushleft} + + If $\mu$ is not an eigenvalue of $\bo{A}$, we can prove that $\mu$, $\bo{u}_M = \textcolor{mydarkpink}{\begin{bmatrix} + (\bo{I}\mu - \bo{A})^{-1} \bo{B} \bo{u} \\ \bo{u} + \end{bmatrix}}$ are eigenvalue and eigenvector of $\bo{M}$: + + \begin{align*} + \begin{bmatrix} + \bo{A} & \bo{B} \\ \bo{0} & \bo{C} + \end{bmatrix} +\begin{bmatrix} + (\bo{I}\mu - \bo{A})^{-1}\bo{B} \bo{u} \\ \bo{u} +\end{bmatrix} + = + \begin{bmatrix} + \bo{A}(\bo{I}\mu - \bo{A})^{-1}\bo{B} \bo{u} + \bo{B} \bo{u} + \\ + \bo{C}\bo{u} + \end{bmatrix} + = \\ + = + \begin{bmatrix} + (\bo{I}+\bo{A}(\bo{I}\mu - \bo{A})^{-1}) \bo{B} \bo{u} + \\ + \mu \bo{u} + \end{bmatrix} += + \begin{bmatrix} + (\bo{I}\mu - \bo{A}+\bo{A})(\bo{I}\mu - \bo{A})^{-1} \bo{B} \bo{u} + \\ + \mu \bo{u} + \end{bmatrix} += \\ += + \begin{bmatrix} + \mu(\bo{I}\mu - \bo{A})^{-1} \bo{B} \bo{u} + \\ + \mu \bo{u} + \end{bmatrix} += +\mu +\textcolor{mydarkpink}{ +\begin{bmatrix} +(\bo{I}\mu - \bo{A})^{-1} \bo{B} \bo{u} +\\ +\bo{u} +\end{bmatrix} +}. + \end{align*} + + + + Counting the number of eigenvalues we observe that eigenvalues of $\bo{M}$ include only eigenvalues of $\bo{A}$ and $\bo{B}$. + + \end{flushleft} +\end{frame} + + +\end{document} diff --git a/Slides/Observer/settings.tex b/Slides/Observer/settings.tex new file mode 100644 index 0000000..31551c7 --- /dev/null +++ b/Slides/Observer/settings.tex @@ -0,0 +1,193 @@ +\pdfmapfile{+sansmathaccent.map} + + +\mode 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This solution is stable, but not asymptotically stable (solution corresponding to $x(0) = 7+\delta$ do not diverge, but do not converge to $x = 7$ either). +\end{example} + +\begin{example} +Consider dynamical system $\dot{x} = -x$, and solution $x = 0$. This solution is stable and asymptotically stable (all solutions converge to $x = 0$). +\end{example} + +\begin{example} +Consider dynamical system $\dot{x} = x$, and solution $x = 0$. This solution is unstable (all other solutions diverge from $x = 0$). +\end{example} + +\end{flushleft} +\end{frame} + + + +\begin{frame}{Linear systems} +% \framesubtitle{O} +\begin{flushleft} + +Consider the following linear ODE: + +\begin{equation} + \dot{\bo{x}} = \bo{A} \bo{x} + \bo{B} \bo{u} +\end{equation} + +This is called a \emph{linear time-invariant system (LTI)}, indicating that $\bo{A}$ and $\bo{B}$ are constant. + +\bigskip + +Removing the input we find an even simpler equation: + +\begin{equation} + \dot{\bo{x}} = \bo{A} \bo{x} +\end{equation} + +This LTI is an \emph{autonomous system}, since its evolution depends only on the state of the system. + +\end{flushleft} +\end{frame} + + + + +\begin{frame}{Stability of autonomous LTI} + \framesubtitle{Real eigenvalues} + \begin{flushleft} + + Consider autonomous LTI: + + \begin{equation} + \dot{\bo{x}} = \bo{D} \bo{x} + \end{equation} + + where $\bo{D} = \text{diag}(d_1, \ ..., \ d_n)$ is a diagonal matrix. This is the same as a system of independent equations: + + \begin{equation} + \begin{cases} + \dot{x}_1 = d_1 x_1 \\ + ... \\ + \dot{x}_n = d_n x_n + \end{cases} + \end{equation} + + Each of these equations has an exact solution $ x_i = C_i e^{d_i t}$. It diverges from 0 if $d_i > 0$, it does not diverge if $d_i \leq 0$ and it converges to 0 if $d_i < 0$. + + \end{flushleft} +\end{frame} + + +\begin{frame}{Stability of autonomous LTI} +\framesubtitle{Real eigenvalues} +\begin{flushleft} + +Consider autonomous LTI: + +\begin{equation} + \dot{\bo{x}} = \bo{A} \bo{x} +\end{equation} + +where $\bo{A}$ can be decomposed via eigen-decomposition as $\bo{A} = \bo{V} \bo{D} \bo{V}^{-1}$, where $\bo{D}$ is a diagonal matrix. + +\bigskip + +\begin{equation} + \dot{\bo{x}} = \bo{V} \bo{D} \bo{V}^{-1} \bo{x} +\end{equation} + +Multiplying it by $\bo{V}^{-1}$ +we get: +$\bo{V}^{-1} \dot{\bo{x}} = \bo{V}^{-1} \bo{V} \bo{D} \bo{V}^{-1} \bo{x}$. + +Defining $\bo{z} = \bo{V}^{-1} \bo{x}$ we transform the equation: +$\dot{\bo{z}} = \bo{D} \bo{z}$. + +\bigskip + +Since elements of $\bo{D}$ are real, we can clearly see, that iff they are \emph{all negative} will the system be asymptotically stable. If they are non-positive, the system is stable. And those elements are eigenvalues of $\bo{A}$. + +\end{flushleft} +\end{frame} + + + + +\begin{frame}{Upper triangular matrices} +% \framesubtitle{Real eigenvalues} + \begin{flushleft} + + Examples of upper triangular matrices are: + + \begin{equation} + \begin{bmatrix} + 1 & 5 & -2 \\ + 0 & 3 & 1 \\ + 0 & 0 & -2 + \end{bmatrix}, + \ \ \ + \begin{bmatrix} + -2 & 0 & 8 \\ + 0 & -2 & 8 \\ + 0 & 0 & 7 + \end{bmatrix}, + \ \ \ + \begin{bmatrix} + 4 & 1 \\ + 0 & 3 + \end{bmatrix} + \end{equation} + + Eigenvalues of upper triangular matrices are the diagonal elements of these matrices. + + \end{flushleft} +\end{frame} + + +\begin{frame}{Upper triangular matrices} + % \framesubtitle{Real eigenvalues} + \begin{flushleft} + + Consider autonomous LTI: + + \begin{equation} + \dot{\bo{x}} = \bo{M} \bo{x} + \end{equation} + + where $ \bo{M}$ is an upper triangular matrices with negative eigenvalues $m_{1,1}$, ... $m_{n,n}$. + + \bigskip + + The last equation is $\dot x_n = m_{n,n} x_n$, and since $m_{n,n} < 0$ we can observe that $\underset{t \rightarrow \infty}{\text{lim}} x_n(t) = 0$. + + \bigskip + + The equation \# n-1 is $\dot x_{n-1} = m_{n-1,n-1} x_{n-1} + m_{n-1,n} x_n$, and since $m_{n-1,n-1} < 0$ and $\underset{t \rightarrow \infty}{\text{lim}} x_n(t) = 0$ we can observe that $\underset{t \rightarrow \infty}{\text{lim}} x_{n-1}(t) = 0$. + + This can be repeated for all equations, proving asymptotic stability for the system. + + \end{flushleft} +\end{frame} + + + + +\begin{frame}{Stability of autonomous LTI} +\framesubtitle{Complex eigenvalues, 2-dimensional case (1)} +\begin{flushleft} + +Let us consider the following system: + +\begin{equation} +\begin{bmatrix} + \dot{\bo{x}}_1 \\ \dot{\bo{x}}_2 +\end{bmatrix} + = +\begin{bmatrix} + \alpha & -\beta \\ \beta & \alpha +\end{bmatrix} +\begin{bmatrix} + \bo{x}_1 \\ \bo{x}_2 +\end{bmatrix} +\end{equation} + +The eigenvalues of the system are $\alpha \pm i \beta$. We denote $\begin{bmatrix} + \bo{x}_1 \\ \bo{x}_2 +\end{bmatrix} = \bo{x}$. + +\bigskip + +We start by claiming that the system will be stable iff the $\dot{\bo{x}}^\top \bo{x} < 0$. Indeed, vector $\dot{\bo{x}}$ can always be decomposed into two components, $\dot{\bo{x}}_{||}$ parallel to $\bo{x}$, and $\dot{\bo{x}}_{\perp}$ perpendicular to $\bo{x}$. By definition $\dot{\bo{x}}_{\perp}^\top \bo{x} = 0$, and is responsible for the change in orientation of $\bo{x}$. The value of $\dot{\bo{x}}_{||}$ is responsible for the change in the length of $\bo{x}$; the length would shrink iff $\dot{\bo{x}}_{||}$ is of opposite direction to $\bo{x}$, giving negative value of the dot product $\dot{\bo{x}}^\top \bo{x}$. + +\end{flushleft} +\end{frame} + + + +\begin{frame}{Stability of autonomous LTI} +\framesubtitle{Complex eigenvalues, 2-dimensional case (2)} +\begin{flushleft} + +Let us compute $\dot{\bo{x}}^\top \bo{x}$: + +\begin{equation} +\dot{\bo{x}}^\top \bo{x} = +\begin{bmatrix} + \bo{x}_1 & \bo{x}_2 +\end{bmatrix} +\begin{bmatrix} + \alpha & -\beta \\ \beta & \alpha +\end{bmatrix} +\begin{bmatrix} + \bo{x}_1 \\ \bo{x}_2 +\end{bmatrix} +\end{equation} + +\begin{equation} +\dot{\bo{x}}^\top \bo{x} = +\alpha (\bo{x}_1^2 + \bo{x}_2^2) +\end{equation} + +From this it is clear that the product $\dot{\bo{x}}^\top \bo{x} < 0$ is negative iff $\alpha < 0$. + +\begin{definition} +As long as the \emph{real parts of the eigenvalues} of the system are \emph{strictly negative}, the system is \emph{asymptotically stable}. If the real parts of the eigenvalues of the system are zero, the system is \emph{marginally stable}. +\end{definition} + +\end{flushleft} +\end{frame} + + + +\begin{frame}{Stability of autonomous LTI} +\framesubtitle{Complex eigenvalues, 2-dimensional case (3)} +\begin{flushleft} + +Vector field of +$\begin{bmatrix} + \dot{\bo{x}}_1 \\ \dot{\bo{x}}_2 +\end{bmatrix} += +\begin{bmatrix} + \alpha & -\beta \\ \beta & \alpha +\end{bmatrix} +\begin{bmatrix} + \bo{x}_1 \\ \bo{x}_2 +\end{bmatrix} $ +is shown below: +% +\begin{figure} + \centering + \includegraphics[width=7cm]{Figure_1.png}%, width=7cm + % \caption{Caption} + \label{fig:my_label} +\end{figure} + +\end{flushleft} +\end{frame} + + + +\begin{frame}{Stability of autonomous LTI} +\framesubtitle{General case (1)} +\begin{flushleft} + +Given $\dot{\bo{x}} = \bo{A} \bo{x}$, where $\bo{A}$ can be decomposed via eigen-decomposition as $\bo{A} = \bo{U} \bo{C} \bo{U}^{-1}$, where $\bo{C}$ is a complex-valued diagonal matrix and $\bo{U}$ is a complex-valued inevitable matrix. + +\bigskip + +We multiply both sides by $\bo{U}^{-1}$, then define $\bo{z} = \bo{U}^{-1} \bo{x}$ to arrive at: + +\begin{equation} + \dot{\bo{z}} = \bo{C} \bo{z} +\end{equation} + +which falls into a set of independent equations, with complex coefficients $c_j$: + +\begin{equation} + \dot{z}_j = c_j z_j +\end{equation} + +\end{flushleft} +\end{frame} + + + +\begin{frame}{Stability of autonomous LTI} +\framesubtitle{General case (2)} +\begin{flushleft} + +Expanding $c_j = \alpha + i \beta$, and $z_j = u + i v$ (we dismiss subscripts for clarity), we find that $\dot{z}_j = c_j z_j$ can be expanded as: + +\begin{equation} + \dot{u} + i \dot{v} = \dot{z}_j = c_j z_j = (\alpha + i \beta) (u + i v) +\end{equation} +% +\begin{equation} + \dot{u} + i \dot{v} = \alpha u + i \beta u + i \alpha v - \beta v +\end{equation} +% +\begin{equation} +\begin{bmatrix} + \dot{u} \\ \dot{v} +\end{bmatrix} + = +\begin{bmatrix} + \alpha & -\beta \\ \beta & \alpha +\end{bmatrix} +\begin{bmatrix} + u \\ v +\end{bmatrix} +\end{equation} + +As we can see, $\dot{z}_j = c_j z_j$ is asymptotically stable iff $\text{Re}(c_j) < 0$, and marginally stable if $\alpha = \text{Re}(c_j) = 0$. Same is true for $\dot{\bo{z}} = \bo{C} \bo{z}$ and hence, for $\dot{\bo{x}} = \bo{A} \bo{x}$, as $\bo{U}$ is invertible. + +\end{flushleft} +\end{frame} + + + + +\begin{frame}{Stability of autonomous LTI} +\framesubtitle{Condition} +\begin{flushleft} + +Consider an autonomous LTI: + +\begin{equation} +\label{eq:LTI} + \dot{\bo{x}} = \bo{A} \bo{x} +\end{equation} + +\begin{definition} +Eq. \eqref{eq:LTI} is stable iff real parts of eigenvalues of $\bo{A}$ are non-positive. +\end{definition} + +\begin{definition} +Eq. \eqref{eq:LTI} is asymptotically stable iff real parts of eigenvalues of $\bo{A}$ are negative. +\end{definition} + +\end{flushleft} +\end{frame} + + + + +\begin{frame}{Stability of autonomous LTI} +\framesubtitle{Illustration} +\begin{flushleft} + +Here is an illustration of \emph{phase portraits} of two-dimensional LTIs with different types of stability: + +\begin{figure} + \centering + \includegraphics[width=1.0\linewidth]{Stability.PNG} + \caption{phase portraits for different types of stability} + \label{fig:Stability} +\end{figure} + +\bigskip + +\scriptsize{Credit: \bref{http://staff.uz.zgora.pl/wpaszke/materialy/spc/Lec13.pdf}{staff.uz.zgora.pl/wpaszke/materialy/spc/Lec13.pdf}} + +\end{flushleft} +\end{frame} + + +\begin{frame} +\hspace*{-2.5cm} +\includegraphics[height=\textheight,width=1.4\textwidth,keepaspectratio]{Figure_2.png} +\end{frame} + + + +\begin{frame}{Read/Watch more} + +\begin{itemize} +\item Control Systems Design, by Julio H. Braslavsky \bref{http://staff.uz.zgora.pl/wpaszke/materialy/spc/Lec13.pdf}{staff.uz.zgora.pl/wpaszke/materialy/spc/Lec13.pdf} + +\item Stability and Eigenvalues, Steve Brunton \bref{https://youtu.be/h7nJ6ZL4Lf0 }{youtu.be/h7nJ6ZL4Lf0} + +\item MAE509 (LMIs in Control): Lecture 4, part A - Stability and Eigenvalues \bref{https://youtu.be/8zYOJbpiT38 }{youtu.be/8zYOJbpiT38} + +\end{itemize} + +\end{frame} + + + +\begin{frame}{Thank you!} +\centerline{Lecture slides are available via Moodle.} +\bigskip +\centerline{You can help improve these slides at:} +\centerline{\mygit} +\bigskip +\centerline{Check Moodle for additional links, videos, textbook suggestions.} +\bigskip + +\centerline{\textcolor{black}{\qrcode[height=1.6in]{https://github.com/SergeiSa/Control-Theory-Slides-Spring-2023}}} +\end{frame} + +\end{document} diff --git a/Slides/Stability/settings.tex b/Slides/Stability/settings.tex new file mode 100644 index 0000000..85e604a --- /dev/null +++ b/Slides/Stability/settings.tex @@ -0,0 +1,192 @@ +\pdfmapfile{+sansmathaccent.map} + + +\mode +{ + \usetheme{Warsaw} % or try Darmstadt, Madrid, Warsaw, Rochester, CambridgeUS, ... + \usecolortheme{seahorse} % or try seahorse, beaver, crane, wolverine, ... + \usefonttheme{serif} % or try serif, structurebold, ... + \setbeamertemplate{navigation symbols}{} + \setbeamertemplate{caption}[numbered] +} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% itemize settings + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% itemize settings + +\definecolor{myhotpink}{RGB}{255, 80, 200} +\definecolor{mywarmpink}{RGB}{255, 60, 160} +\definecolor{mylightpink}{RGB}{255, 80, 200} +\definecolor{mypink}{RGB}{255, 30, 80} +\definecolor{mydarkpink}{RGB}{155, 25, 60} + +\definecolor{mypaleblue}{RGB}{240, 240, 255} +\definecolor{mylightblue}{RGB}{120, 150, 255} +\definecolor{myblue}{RGB}{90, 90, 255} +\definecolor{mygblue}{RGB}{70, 110, 240} +\definecolor{mydarkblue}{RGB}{0, 0, 180} +\definecolor{myblackblue}{RGB}{40, 40, 120} + +\definecolor{mygreen}{RGB}{0, 200, 0} +\definecolor{mygreen2}{RGB}{245, 255, 230} + +\definecolor{mygray}{gray}{0.8} +\definecolor{mydarkgray}{RGB}{80, 80, 160} + +\definecolor{mydarkred}{RGB}{160, 30, 30} +\definecolor{mylightred}{RGB}{255, 150, 150} +\definecolor{myred}{RGB}{200, 110, 110} +\definecolor{myblackred}{RGB}{120, 40, 40} + +\definecolor{mygreen}{RGB}{0, 200, 0} +\definecolor{mygreen2}{RGB}{205, 255, 200} + +\definecolor{mydarkcolor}{RGB}{60, 25, 155} +\definecolor{mylightcolor}{RGB}{130, 180, 250} + +\setbeamertemplate{itemize items}[default] + +\setbeamertemplate{itemize item}{\color{myblackblue}$\blacksquare$} +\setbeamertemplate{itemize subitem}{\color{mygblue}$\blacktriangleright$} +\setbeamertemplate{itemize subsubitem}{\color{mygray}$\blacksquare$} + +\setbeamercolor{palette quaternary}{fg=white,bg=mydarkgray} +\setbeamercolor{titlelike}{parent=palette quaternary} + +\setbeamercolor{palette quaternary2}{fg=black,bg=mypaleblue} +\setbeamercolor{frametitle}{parent=palette quaternary2} + +\setbeamerfont{frametitle}{size=\Large,series=\scshape} +\setbeamerfont{framesubtitle}{size=\normalsize,series=\upshape} + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% block settings + +\setbeamercolor{block title}{bg=red!30,fg=black} + +\setbeamercolor*{block title example}{bg=mygreen!40!white,fg=black} + +\setbeamercolor*{block body example}{fg= black, bg= mygreen2} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% URL settings +\hypersetup{ + colorlinks=true, + linkcolor=blue, + filecolor=blue, + urlcolor=blue, +} + +%%%%%%%%%%%%%%%%%%%%%%%%%% + +\renewcommand{\familydefault}{\rmdefault} + +\usepackage{amsmath} +\usepackage{mathtools} + +\usepackage{subcaption} + +\usepackage{qrcode} + +\DeclareMathOperator*{\argmin}{arg\,min} +\newcommand{\bo}[1] {\mathbf{#1}} + +\newcommand{\R}{\mathbb{R}} +\newcommand{\T}{^\top} + +\newcommand{\dx}[1] {\dot{\mathbf{#1}}} +\newcommand{\ma}[4] {\begin{bmatrix} + #1 & #2 \\ #3 & #4 +\end{bmatrix}} +\newcommand{\myvec}[2] {\begin{bmatrix} + #1 \\ #2 +\end{bmatrix}} +\newcommand{\myvecT}[2] {\begin{bmatrix} + #1 & #2 +\end{bmatrix}} + + +\newcommand{\mydate}{Spring 2023} + +\newcommand{\mygit}{\textcolor{blue}{\href{https://github.com/SergeiSa/Control-Theory-Slides-Spring-2023}{github.com/SergeiSa/Control-Theory-Slides-Spring-2023}}} + +\newcommand{\myqr}{ \textcolor{black}{\qrcode[height=1.5in]{https://github.com/SergeiSa/Control-Theory-Slides-Spring-2023}} +} + +\newcommand{\myqrframe}{ + \begin{frame} + \centerline{Lecture slides are available via Github, links are on Moodle} + \bigskip + \centerline{You can help improve these slides at:} + \centerline{\mygit} + \bigskip + \myqr + \end{frame} +} + + +\newcommand{\bref}[2] {\textcolor{blue}{\href{#1}{#2}}} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% code settings + +\usepackage{listings} +\usepackage{color} +% \definecolor{mygreen}{rgb}{0,0.6,0} +% \definecolor{mygray}{rgb}{0.5,0.5,0.5} +\definecolor{mymauve}{rgb}{0.58,0,0.82} +\lstset{ + backgroundcolor=\color{white}, % choose the background color; you must add \usepackage{color} or \usepackage{xcolor}; should come as last argument + basicstyle=\footnotesize, % the size of the fonts that are used for the code + breakatwhitespace=false, % sets if automatic breaks should only happen at whitespace + breaklines=true, % sets automatic line breaking + captionpos=b, % sets the caption-position to bottom + commentstyle=\color{mygreen}, % comment style + deletekeywords={...}, % if you want to delete keywords from the given language + escapeinside={\%*}{*)}, % if you want to add LaTeX within your code + extendedchars=true, % lets you use non-ASCII characters; for 8-bits encodings only, does not work with UTF-8 + firstnumber=0000, % start line enumeration with line 0000 + frame=single, % adds a frame around the code + keepspaces=true, % keeps spaces in text, useful for keeping indentation of code (possibly needs columns=flexible) + keywordstyle=\color{blue}, % keyword style + language=Octave, % the language of the code + morekeywords={*,...}, % if you want to add more keywords to the set + numbers=left, % where to put the line-numbers; possible values are (none, left, right) + numbersep=5pt, % how far the line-numbers are from the code + numberstyle=\tiny\color{mygray}, % the style that is used for the line-numbers + rulecolor=\color{black}, % if not set, the frame-color may be changed on line-breaks within not-black text (e.g. comments (green here)) + showspaces=false, % show spaces everywhere adding particular underscores; it overrides 'showstringspaces' + showstringspaces=false, % underline spaces within strings only + showtabs=false, % show tabs within strings adding particular underscores + stepnumber=2, % the step between two line-numbers. If it's 1, each line will be numbered + stringstyle=\color{mymauve}, % string literal style + tabsize=2, % sets default tabsize to 2 spaces + title=\lstname % show the filename of files included with \lstinputlisting; also try caption instead of title +} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% URL settings +\hypersetup{ + colorlinks=false, + linkcolor=blue, + filecolor=blue, + urlcolor=blue, +} + +%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% tikz settings + +\usepackage{tikz} +\tikzset{every picture/.style={line width=0.75pt}} \ No newline at end of file diff --git a/Slides/Stability/test_1.py b/Slides/Stability/test_1.py new file mode 100644 index 0000000..f2c18ac --- /dev/null +++ b/Slides/Stability/test_1.py @@ -0,0 +1,48 @@ +import numpy as np +import scipy as sp +from scipy.integrate import solve_ivp + +import matplotlib.pyplot as pp + +alpha = np.random.randn() - 0.2 +beta = np.random.randn() + 1 + +A = np.array([[alpha, -beta], [beta, alpha]]) +h, _ = np.linalg.eig(A) + +print(h) +print(alpha, beta) + +lims = np.array([-1, 1]) +Count = 30 +qu_X = np.zeros((Count, Count)) +qu_Y = np.zeros((Count, Count)) +qu_U = np.zeros((Count, Count)) +qu_V = np.zeros((Count, Count)) +qu_C = np.zeros((Count, Count)) +v = np.zeros((2, )) +for i in range(Count): + for j in range(Count): + v[0] = lims[0] + i * (lims[1] - lims[0]) / Count + v[1] = lims[0] + j * (lims[1] - lims[0]) / Count + dvdt = A @ v + qu_X[i, j] = v[0] + qu_Y[i, j] = v[1] + qu_U[i, j] = dvdt[0] + qu_V[i, j] = dvdt[1] + qu_C[i, j] = np.linalg.norm(v) + +v0 = np.array((0.8, 0.8)) +def dvdt_fnc(t, v): + return A @ v +tf = 10 +times = np.linspace(0, tf, num=150) +vv = solve_ivp(dvdt_fnc, (0, tf), v0, t_eval=times) + +v = vv["y"] +t = vv["t"] + +pp.quiver(qu_X, qu_Y, qu_U, qu_V, qu_C) +pp.plot(v[0, :], v[1, :]) + +pp.show() \ No newline at end of file diff --git a/Slides/Stability/test_2.py b/Slides/Stability/test_2.py new file mode 100644 index 0000000..5928811 --- /dev/null +++ b/Slides/Stability/test_2.py @@ -0,0 +1,73 @@ +import numpy as np +import scipy as sp +from scipy.integrate import solve_ivp + +import matplotlib.pyplot as pp + + +A1 = np.array([[-0.1, -2], [2, -0.1]]) +h1, _ = np.linalg.eig(A1) +print(h1) + +A2 = np.array([[-0.1, -2], [-2, -0.1]]) +h2, _ = np.linalg.eig(A2) +print(h2) + +A3 = np.array([[-2.1, -1], [-1, -2.1]]) +h3, _ = np.linalg.eig(A3) +print(h3) + +A4 = np.array([[-2.0, -1], [-1, 0]]) +h4, _ = np.linalg.eig(A4) +print(h4) + + + +fig, ((ax1, ax2), (ax3, ax4)) = pp.subplots(nrows=2, ncols=2) + +def solve_and_plot(A, ax): + # h, _ = np.linalg.eig(A) + lims = np.array([-1, 1]) + Count = 30 + qu_X = np.zeros((Count, Count)) + qu_Y = np.zeros((Count, Count)) + qu_U = np.zeros((Count, Count)) + qu_V = np.zeros((Count, Count)) + qu_C = np.zeros((Count, Count)) + v = np.zeros((2, )) + for i in range(Count): + for j in range(Count): + v[0] = lims[0] + i * (lims[1] - lims[0]) / Count + v[1] = lims[0] + j * (lims[1] - lims[0]) / Count + dvdt = A @ v + qu_X[i, j] = v[0] + qu_Y[i, j] = v[1] + qu_U[i, j] = dvdt[0] + qu_V[i, j] = dvdt[1] + qu_C[i, j] = np.linalg.norm(v) + + ax.quiver(qu_X, qu_Y, qu_U, qu_V, qu_C) + + def dvdt_fnc(t, v): + return A @ v + v0 = np.array((0.8, 0.7)) + tf = 30 + Count2 = 500 + times = np.linspace(0, tf, num=Count2) + vv = solve_ivp(dvdt_fnc, (0, tf), v0, t_eval=times) + + v = vv["y"] + t = vv["t"] + # print(v.shape) + for i in range(Count2): + if (abs(v[0, i]) > 1) or (abs(v[1, i]) > 1): + v[0, i] = np.NaN + v[1, i] = np.NaN + print(v) + ax.plot(v[0, :], v[1, :]) + +solve_and_plot(A1, ax1) +solve_and_plot(A2, ax2) +solve_and_plot(A3, ax3) +solve_and_plot(A4, ax4) +pp.show() \ No newline at end of file diff --git a/legacy - ColabNotebooks/Practice_1_ODE_to_StateSpace.ipynb b/legacy - ColabNotebooks/Practice_1_ODE_to_StateSpace.ipynb new file mode 100644 index 0000000..0fce565 --- /dev/null +++ b/legacy - ColabNotebooks/Practice_1_ODE_to_StateSpace.ipynb @@ -0,0 +1,677 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "[Control theory] Practice 1.ipynb", + "provenance": [], + "collapsed_sections": [], + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "KRXDRXIJhfgg" + }, + "source": [ + "# **Control theory. Course introduction**" + ] + }, + { + "cell_type": "markdown", + "source": [ + ">**FEEDBACK** \\\n", + "Feedback form is available by the [link](https://forms.gle/CcqEwfg97aHQcZJi6)" + ], + "metadata": { + "id": "4t7qV5Wh0Fe_" + } + }, + { + "cell_type": "markdown", + "metadata": { + "id": "XkFkXyYInr9L" + }, + "source": [ + "## **Study load**\n", + "Course grade breakdown:\n", + "\n", + "* Midterm exam - 20%\n", + "* Final exam - 30%\n", + "* Practice attendance - 10%\n", + "* Labs - 40%\n", + "\n", + "> **LABS** \\\\\n", + "You will have 3 homework assignment during the course. All homeworks will be graded.\n", + "I **strongly** recomended to complete the tasks in HW right after the practice session. \\\n", + "**File name for lab submission:** `yourname_group.ipynb` (example: `IvanovIvan_B20-05.ipynb`)\n", + "\n", + "\n", + "> **BONUS** \\\\\n", + "Problems that will be graded separately and will give you bonus points on final exam" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "7l_xFIcpmBbz" + }, + "source": [ + "## **About me**\n", + "My name is Valeria Skvortsova. I'm master in Robotics and second year PhD student in IU. \\\\\n", + "\\\n", + "***Office hours:*** every Tuesday from 4:30 PM to 6 PM in room 105 (Technical Underground) \\\\\n", + "Please don't disturb me with messages at night and on weekends\n", + "\n", + ">**For contacts:** \\\\\n", + "*t-me:* @valeriaskvo \\\\\n", + "*e-mail:* v.skvortsova@innopolis.university \\\\\n", + "*instagram:* valeria_skv \\\\" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "TAUwwMDol5cT" + }, + "source": [ + "## **Prerequisites for practice**" + ] + }, + { + "cell_type": "markdown", + "source": [ + "### **Math**\n", + "During the course we will cover the following areas of mathematics:\n", + "\n", + "\n", + "* [Linear Algebra](https://laurentlessard.com/teaching/ece532/cheat_sheet.pdf)\n", + "* [Calculus](https://project.hupili.net/tutorial/hu2012-matrix-calculus/hu2012matrix-calculus.pdf)\n", + "* [Differential equations](http://people.uncw.edu/hermanr/mat361/ODEsheet.pdf)\n", + "* Dynamics (Mechanics and Physics)\n", + "\n" + ], + "metadata": { + "id": "vJhw3Pir0TeE" + } + }, + { + "cell_type": "markdown", + "source": [ + "### **Python programming**\n", + "In the labs and practice sessions we will use a [Python](http://www.datasciencefree.com/python.pdf) programming language and following libraries:\n", + "\n", + "* [NumPy](https://s3.amazonaws.com/dq-blog-files/numpy-cheat-sheet.pdf)\n", + "* [SciPy](https://s3.amazonaws.com/assets.datacamp.com/blog_assets/Python_SciPy_Cheat_Sheet_Linear_Algebra.pdf)\n", + "* [Matplotlib](https://s3.amazonaws.com/assets.datacamp.com/blog_assets/Python_Matplotlib_Cheat_Sheet.pdf)\n", + "\n" + ], + "metadata": { + "id": "0_3NT_9m34Rr" + } + }, + { + "cell_type": "markdown", + "metadata": { + "id": "qprFw87Jvc1j" + }, + "source": [ + "# **Practice 1: Linear system representations**\n", + "Content:\n", + "1. Ordinary differential equation\n", + "2. State space modeling\n", + "3. Simulations\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "WyWEVhq3LKdx" + }, + "source": [ + "## **Control systems**\n", + "\n", + "A control system is a system, which provides the desired response by controlling the output. The following figure shows the simple block diagram of a control system.\n", + "\n", + "![image.png](data:image/png;base64,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)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "kH4YCoUTx0jB" + }, + "source": [ + "## **Ordinary Differential Equations (ODE)**\n", + "The normal form of an $n$-th order differential equation is:\n", + "$$\\mathbf{x}^{(n)}=\\mathbf{f}(\\mathbf{x}^{(n-1)},\\mathbf{x}^{(n-2)},...,\\ddot{\\mathbf{x}},\\dot{\\mathbf{x}},\\mathbf{x},t)$$\n", + "where $\\mathbf{x} = \\mathbf{x}(t)$ is the solution of the equation. It is a **dynamical system**.\n", + "\n", + "The set $\\{ \\mathbf{x}, \\ \\dot{\\mathbf{x}} \\ ..., \\ \\mathbf{x}^{(n-1)} \\}$ is called the **state** of the dynamical system.\n", + "\n", + "In canonical form **linear ODE** as follows:\n", + "$$a_{n}z^{(n)} +a_{n-1}z^{(n-1)}+...+a_{2}\\ddot z+a_{1}\\dot z + a_0 z= b_0$$\n", + "\n", + "**A state-space representation** is a mathematical model of a physical system as a set of input $\\mathbf{u}$, output $\\mathbf{y}$ and state variables $\\mathbf{x}$ related by first-order differential equations (difference equations in discrete time). \n", + "\n", + "State variables $\\mathbf{x}$ are variables whose values evolve through time $t$ in a way that depends on the values they have at any given time and also depends on the externally imposed values of input variables $\\mathbf{u}$. Output $\\mathbf{y}$ depend on the values of the state variables $\\mathbf{x}$." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "RmYWR4GoO1dc" + }, + "source": [ + "## **Linear State Space**\n", + "In case if relationships between state, output and control is **linear**, we can formulate the model of system in following form:\n", + "\\begin{equation}\n", + "\\begin{cases} \n", + "\\mathbf{\\dot{x}} =\\mathbf{A}\\mathbf{x} + \\mathbf{B}\\mathbf{u} \\\\ \n", + "\\mathbf{y}=\\mathbf{C}\\mathbf{x} + \\mathbf{D}\\mathbf{u}\n", + "\\end{cases}\n", + "\\end{equation}\n", + "\n", + "where\n", + "* $\\mathbf{x} \\in \\mathbb{R}^n$ states of the system\n", + "* $\\mathbf{y} \\in \\mathbb{R}^l$ output vector\n", + "* $\\mathbf{u} \\in \\mathbb{R}^m$ control inputs\n", + "* $\\mathbf{A} \\in \\mathbb{R}^{n \\times n}$ state matrix\n", + "* $\\mathbf{B} \\in \\mathbb{R}^{n \\times m}$ input matrix\n", + "* $\\mathbf{C} \\in \\mathbb{R}^{l \\times n}$ output matrix\n", + "* $\\mathbf{D} \\in \\mathbb{R}^{l \\times m}$ feedforward matrix\n", + "\n", + ">Note: \n", + "If matrices $\\mathbf{A},\\mathbf{B},\\mathbf{C},\\mathbf{D}$ are time dependend, we call such systems **time-varient**. However, in practice we often deal with systems whose dynamics is time-invarient. In this case this matrices will be constant.\n", + "\n", + "Often we work with system when output is independent from control:\n", + "\n", + "\\begin{equation}\n", + "\\begin{cases} \n", + "\\mathbf{\\dot{x}}=\\mathbf{A}\\mathbf{x} + \\mathbf{B}\\mathbf{u} \\\\ \n", + "\\mathbf{y}=\\mathbf{C}\\mathbf{x}\n", + "\\end{cases}\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "PERj-Fr-O4Iy" + }, + "source": [ + "## **Unforced systems**\n", + "\n", + "Today we will consider uncontrolled systems as follows:\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{x}}=\\mathbf{A}\\mathbf{x} + \\mathbf{b}\n", + "\\end{equation}\n", + "where $\\mathbf{b} \\in \\mathbb{R}^n$ is a constant vector" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "g9Iq6PxHPBJL" + }, + "source": [ + "## **From the linear ODE to the State Space**\n", + "\n", + "A probleim is to, given an ODE in canonical form:\n", + "\n", + "$$a_{n}z^{(n)} +a_{n-1}z^{(n-1)}+...+a_{2}\\ddot z+a_{1}\\dot z + a_0 z= b_0$$\n", + "\n", + "find its state space representation:\n", + "\n", + "$$\\dot{ \\mathbf{x}} = \\mathbf{A}\\mathbf{x} + \\mathbf{b}$$\n", + "\n", + "### **Methodology**\n", + "\n", + "The first step is to express higher derivatives as follows:\n", + "\n", + "$$z^{(n)} = \n", + "-\\frac{a_{n-1}}{a_{n}}z^{(n-1)}-\n", + "...-\n", + "\\frac{a_{2}}{a_{n}}\\ddot z -\n", + "\\frac{a_{1}}{a_{n}}\\dot z - \n", + "\\frac{a_{0}}{a_{n}} z + \n", + "\\frac{b_0}{a_{n}}$$\n", + "\n", + "Now let us introduce new variables $\\mathbf{x}$ as follows:\n", + "$$\n", + "\\mathbf{x} = \n", + "\\begin{bmatrix}\n", + "x_1 \\\\ \n", + "x_{2} \\\\\n", + "... \\\\\n", + "x_n \\\\\n", + "\\end{bmatrix}\n", + "=\n", + "\\begin{bmatrix}\n", + "z \\\\\n", + "z^{(1)} \\\\\n", + " ... \\\\\n", + "z^{(n-1)} \\\\\n", + "\\end{bmatrix}\n", + "$$\n", + "\n", + "Thus original ODE may be written as:\n", + "$$\n", + "\\begin{bmatrix}\n", + "\\dot{x}_1 \\\\ \n", + "\\dot{x}_{2} \\\\\n", + "... \\\\\n", + "\\dot{x}_n \\\\\n", + "\\end{bmatrix}\n", + "=\n", + "\\begin{bmatrix}\n", + "x_2 \\\\ \n", + "x_3 \\\\\n", + "... \\\\\n", + "-\\frac{a_{k-1}}{a_{n}}x_n-\n", + "...-\n", + "\\frac{a_{2}}{a_{n}} x_3 -\n", + "\\frac{a_{1}}{a_{n}} x_2 - \n", + "\\frac{a_{0}}{a_{n}} x_1 + \n", + "\\frac{b_0}{a_{n}} \\\\\n", + "\\end{bmatrix}$$\n", + "\n", + "Finally, in a matrix form:\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{x}} = \\mathbf{A}\\mathbf{x} + \\mathbf{b}\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "53NPUbfjUXPh" + }, + "source": [ + "## **Exercises**\n", + "> Convert equations from canonical form to State Space represantation:\n", + "\n", + "1. $6\\ddot{z}-2\\dot{z}+1.5z=0$\n", + "2. $3\\ddot{z}+3\\dot{z}+5.5z=1$\n", + "3. $10 \\dddot{z} + 5\\ddot{z}-2\\dot{z}+20z-20=0$\n", + "\n", + "> Transform system of equations from canonical form to State Space representation:\n", + "\n", + "1. $$\n", + "\\begin{cases}\n", + "\\dot{z}+5z = 10\\\\\n", + "\\dddot{y}-2\\ddot{y} + 5\\dot{y} +100y-1=2\n", + "\\end{cases}\n", + "$$\n", + "\n", + "\n", + "2. $$\n", + "\\begin{cases}\n", + "5\\ddot{z}+\\dot{z}+5z = 10\\\\\n", + "-2\\dddot{y}-5\\ddot{y} + 15\\dot{y} +2y-10=0\n", + "\\end{cases}\n", + "$$\n", + "\n", + "\n", + "3. $$\n", + "\\begin{cases}\n", + "5\\ddot{z}+\\dot{z}+5z - y = 10\\\\\n", + "\\dddot{y}+3\\ddot{y} + 7.5\\dot{y} -2\\dot{z} +2y-z-10=0\n", + "\\end{cases}\n", + "$$\n", + "\n", + "\n", + "4. $$\n", + "\\begin{cases}\n", + "25\\ddot{z}+16\\dot{z}+27\\dot{y}+z+4y = -6\\\\\n", + "-2\\dddot{y}+2\\ddot{y} + \\dot{y} -\\dot{z} +12y-8z = 6\n", + "\\end{cases}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "XAglBzyXSpFy" + }, + "source": [ + "## **Intro to Simulation (solution of ODE)**\n", + "While studying ODE $\\dot{\\mathbf{x}} = \\boldsymbol{f}(\\mathbf{x}, \\mathbf{u}, t)$, one is often interested in its solution $\\mathbf{x}(t)$ (integral curve):\n", + "\\begin{equation}\n", + "\\mathbf{x} = \\int_{t_0}^{t_f} \\boldsymbol{f}(t,\\mathbf{x}(t),\\mathbf{u}(t))dt,\\quad \\text{s.t: } \\mathbf{x}(t_0) = \\mathbf{x}_0\n", + "\\end{equation}\n", + "\n", + "In most practical situations the integral above cannot be solved analyticaly and one should consider numerical integration instead." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Prjo8jWyTbE1" + }, + "source": [ + "### **Numerical integration in Python**" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "fQf4HoWCTVU_" + }, + "source": [ + "import numpy as np\n", + "from scipy.integrate import odeint\n", + "\n", + "# x_dot from state space\n", + "def StateSpace(x, t, A, B):\n", + " return np.dot(A,x)+B\n", + "\n", + "n = 5\n", + "A = np.array([[0, 1, 0, 0, 0],\n", + " [0, 0, 1, 0, 0],\n", + " [0, 0, 0, 1, 0],\n", + " [0, 0, 0, 0, 1],\n", + " [-5/4, -3, 0, -6, -2/4]])\n", + "\n", + "B = np.array([0, 0, 0, 0, 3/4])\n", + "\n", + "t0 = 0 # Initial time \n", + "tf = 10 # Final time\n", + "t = np.linspace(t0, tf, 1000) \n", + "\n", + "# x0 = np.array([0, 0, 0]) # initial state\n", + "x0 = np.random.rand(n) # random initial state\n", + "\n", + "solution = odeint(StateSpace, x0, t, args=(A,B))" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "6D9M1VSPTzP_" + }, + "source": [ + "### **Result visualization**" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 281 + }, + "id": "Q5zsv2MwTx0v", + "outputId": "c87b637d-27ff-4ab2-d8f6-bdf3de173f14" + }, + "source": [ + "from matplotlib.pyplot import *\n", + "\n", + "plot(t, solution, linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'State ${x}$')\n", + "xlabel(r'Time $t$')\n", + "show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "5EqjfSx7e6Sy" + }, + "source": [ + "## **Model design examples**\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "bZ1NTT4wmTYa" + }, + "source": [ + "### **Mass-spring-damper (mechanical systems example)**\n" + ] + }, + { + "cell_type": "markdown", + "source": [ + 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)" + ], + "metadata": { + "id": "A5KHkuB7JsQm" + } + }, + { + "cell_type": "markdown", + "source": [ + "ODE for this system is:\n", + "$$ m\\ddot{x}+b\\dot{x}+kx = mg$$" + ], + "metadata": { + "id": "z2pb2nT6J27d" + } + }, + { + "cell_type": "code", + "metadata": { + "id": "XZmJgTpbmPYh", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 281 + }, + "outputId": "b5f58b63-9fdc-4680-977c-349f667b08b3" + }, + "source": [ + "m = 1\n", + "k = 5\n", + "b = 2\n", + "g = 9.8\n", + "\n", + "n = 2\n", + "A = np.array([[0, 1],\n", + " [-k/m, -b/m]])\n", + "\n", + "B = np.array([0,\n", + " -g])\n", + "\n", + "x0 = np.array([5,\n", + " 0]) # initial state\n", + "\n", + "solution = odeint(StateSpace, x0, t, args=(A,B))\n", + "\n", + "subplot(2,1,1)\n", + "plot(t, solution[:,0], linewidth=2.0, color = 'red')\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'Position ${x}$')\n", + "\n", + "subplot(2,1,2)\n", + "plot(t, solution[:,1], linewidth=2.0, color = 'red')\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'Velocity ${\\dot{x}}$')\n", + "\n", + "xlabel(r'Time $t$')\n", + "show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "q8Ooj_p_fmMJ" + }, + "source": [ + "### **Model of Love by J.C. Sprott**\n", + "[Original model](https://docs.google.com/presentation/d/1IIpxxsNaPc6MA5b5Db5o-aZr-hRr3g_O/edit?usp=sharing&ouid=114023358498041511244&rtpof=true&sd=true) based on a system of linear differential equations:\n", + "\n", + "$$\n", + "\\begin{cases}\n", + "\\dot{R}=aR+bJ \\\\\n", + "\\dot{J}=cR+dJ\n", + "\\end{cases}\n", + "$$\n", + "\n", + "when $R$ and $J$ are time depended functions of Romeo's or Juliet's love (or hate if negative) and $a$, $b$, $c$ and $d$ is constants that determine the \"Romantic styles\". \n", + "\n", + "Assume that the Romantic styles can be following based on Romeo's equation:\n", + "$$\\dot{R}=aR+bJ$$\n", + "\n", + "\n", + "* $a=0$ - out of touch with own feelings\n", + "* $b=0$ - oblivious to other's feelings\n", + "* $a>0$, $b>0$ - relationship enthusiast\n", + "* $a>0$, $b<0$ - narcissistic nerd\n", + "* $a<0$, $b>0$ - cautious lover\n", + "* $a<0$, $b<0$ - hermit" + ] + }, + { + "cell_type": "code", + "source": [ + "#@title **Love model**\n", + "#@markdown Romeo's parameters\n", + "a = 0 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "b = 5 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "\n", + "#@markdown Juliet's parameters\n", + "c = -1 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "d = 0 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "\n", + "#@markdown How much did Romeo and Juliet like each other at first sight?\n", + "R_0 = 6 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "J_0 = 0 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "\n", + "A = np.array([[a, b],\n", + " [c, d]])\n", + "\n", + "B = np.array([0,\n", + " 0])\n", + "\n", + "x0 = np.array([R_0,\n", + " J_0]) # initial state\n", + "\n", + "t0 = 0 # Initial time \n", + "tf = 10 # Final time\n", + "t = np.linspace(t0, tf, 1000)\n", + "\n", + "love = odeint(StateSpace, x0, t, args=(A,B))\n", + "\n", + "plot(t, love[:,0], linewidth=2.0, color = 'b', label = \"Romeo\")\n", + "plot(t, love[:,1], linewidth=2.0, color = 'm', label = \"Juliet\")\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'Level of love ${X}$')\n", + "xlabel(r'Time $t$')\n", + "legend()\n", + "show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 281 + }, + "id": "M3LLDShRM2Tt", + "outputId": "d362479c-6f3e-460a-fd9e-90a2f9b4ae28" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "B36csPHVULs5" + }, + "source": [ + "## **Homework exercises** for self-study\n", + "> Solve equations using Python integrator and visualize results:\n", + "1. $\\dddot{z}+2\\ddot{z}+5\\dot{z}+10z=1$\n", + "2. $2\\dddot{z}+4\\dot{z}-6z=0$\n", + "3. $4z^{(5)}+2z^{(4)}-\\ddot{z}+5z=3$\n", + "4. $z^{(5)}-4\\dddot{z}-3\\ddot{z}+10\\dot{z}=0$\n", + "5. $4z^{(5)}+3z^{(4)}-2\\dddot{z}+3\\ddot{z}+5\\dot{z}-z=1$\n", + "\n", + "\n", + "## **Bonus Exercise**\n", + "> Implement your own integration routine that will take state-space function \n", + "$\\mathbf{f}$, free variable $t$, and initial state $\\mathbf{x}(0)$ as input and produce the solution $\\mathbf{x}^*(t)$ as output. Use [Runge-Kutta method](https://en.wikipedia.org/wiki/Runge–Kutta_methods) for solve this task." + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "Yac2ZnNFpyh_" + }, + "source": [ + "# Put your code here" + ], + "execution_count": null, + "outputs": [] + } + ] +} \ No newline at end of file diff --git a/legacy - ColabNotebooks/Practice_2_Stability.ipynb b/legacy - ColabNotebooks/Practice_2_Stability.ipynb new file mode 100644 index 0000000..1804180 --- /dev/null +++ b/legacy - ColabNotebooks/Practice_2_Stability.ipynb @@ -0,0 +1,750 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "[Control theory] Practice 2.ipynb", + "provenance": [], + "collapsed_sections": [], + "toc_visible": true, + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "markdown", + "source": [ + "# **Important information**\n", + "\n", + "> **LABS** \\\n", + "**Tasks for lab 1:** [Lab 1](https://colab.research.google.com/drive/1dLIgEAn5ksFEcVXAI_GifKkip1izppNm?usp=sharing)\\\n", + "**Deadline:** 15th of February\\\n", + "**File name for lab submission:** `yourname_group.ipynb` (example: `IvanovIvan_B20-05.ipynb`)\n", + "\n", + ">**FEEDBACK** \\\n", + "Feedback form is available by the [link](https://forms.gle/CcqEwfg97aHQcZJi6)" + ], + "metadata": { + "id": "apRhA2aASDp0" + } + }, + { + "cell_type": "markdown", + "metadata": { + "id": "D-dOD4xqsPiR" + }, + "source": [ + "# **Practice 2: On the Stability of Continues Linear Dynamical Systems**\n", + "## **Goals for today**\n", + "\n", + "---\n", + "\n", + "\n", + "\n", + "During today practice we will:\n", + "* Recall what the solution of ODE and study their stability\n", + "* Check stability criteria for particular cases of ODE\n", + "* Discuss why do we need for our system to be stable" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "RCityqOscrJV" + }, + "source": [ + "## **Solutions of ODE**\n", + "While studying ODE $\\dot{\\mathbf{x}} = \\boldsymbol{f}(\\mathbf{x}, \\mathbf{u}, t)$, one is often interested in its solution $\\mathbf{x}^*(t)$ (integral curve):\n", + "\\begin{equation}\n", + "\\mathbf{x}^*(t) = \\int_{t_0}^{t_f} \\boldsymbol{f}(t,\\mathbf{x}(t),\\mathbf{u}(t))dt,\\quad \\text{s.t: } \\mathbf{x}(t_0) = \\mathbf{x}_0\n", + "\\end{equation}\n", + "\n", + "\n", + "---\n", + "\n", + "\n", + "In most practical situations the integral above cannot be solved analyticaly and one should consider numerical integration instead, however when we deal with LTI systems like:\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{x}} (t)=\\mathbf{A}\\mathbf{x}(t)\n", + "\\end{equation}\n", + "An integral above can be calculated analytically:\n", + "\\begin{equation}\n", + "\\mathbf{x}^*(t)=e^{\\mathbf{A}t}\\mathbf{x}(0)\n", + "\\end{equation}\n", + "where matrix exponential is defined via power series:\n", + "\\begin{equation} \n", + " e^{\\mathbf{A}t}=\\sum _{k=0}^{\\infty }{1 \\over k!}\\mathbf{A}^{k}t^k\n", + " \\end{equation}\n", + "\n", + "\n", + "\n", + "\n", + "---\n", + "\n", + "\n", + "\n", + "> A natural questions to ask:\n", + "* How to calculate this matrix exponential without power series?\n", + "* Can we analyze the behaviour of solutions without explicitly solving ODE?\n", + "\n", + "Let us first consider the first question, assume for a while that we can do the following factorization:\n", + "\\begin{equation}\n", + "\\mathbf{A}=\\mathbf{Q}\\mathbf{\\Lambda}\\mathbf{Q}^{-1} \n", + "\\end{equation}\n", + "where: \n", + "\n", + "\n", + "* $\\mathbf{Q}\\in \\mathbb{R}^{n \\times n}$ containing normalized eigen vectors $\\mathbf{q}_i = \\frac{\\mathbf{v}_i}{\\|\\mathbf{v}_i\\|}$ as columns. \n", + "* $\\mathbf{\\Lambda}\\in \\mathbb{R}^{n \\times n}$ diagonal matrix whose diagonal elements are the corresponding eigenvalues $\\Lambda_{ii} = \\lambda_i$. \n", + "\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "h17SqNO1cb_q", + "outputId": "001b8b81-641f-42de-af56-ea2744124663" + }, + "source": [ + "# Note Eigen decomposition via Python\n", + "import numpy as np\n", + "\n", + "A = [[2., 5.],\n", + " [1., 3.]]\n", + "\n", + "A = np.array(A)\n", + "\n", + "print(f\"Original matrix:\\n{A}\\n\")\n", + "\n", + "Lambda, Q = np.linalg.eig(A)\n", + "print(f\"Eigen values:\\n{Lambda}, \\n\\n Eigen vectors:\\n{Q}\\n\")\n", + "\n", + "Qinv = np.linalg.inv(Q)\n", + "A_rec = (Q.dot(np.diag(Lambda))).dot(Qinv)\n", + "print(f\"Reconstructed matrix:\\n{A_rec}\")" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Original matrix:\n", + "[[2. 5.]\n", + " [1. 3.]]\n", + "\n", + "Eigen values:\n", + "[0.20871215 4.79128785], \n", + "\n", + " Eigen vectors:\n", + "[[-0.94140906 -0.87315384]\n", + " [ 0.33726692 -0.48744474]]\n", + "\n", + "Reconstructed matrix:\n", + "[[2. 5.]\n", + " [1. 3.]]\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "ejwnvf48c1-3" + }, + "source": [ + "Substitution to the system dynamics and multiplying by $\\mathbf{Q}^{-1}$ yields:\n", + "\\begin{equation}\n", + "\\mathbf{Q}^{-1}\\mathbf{\\dot{x}} =\\mathbf{Q}^{-1}\\mathbf{A}\\mathbf{x} =\\mathbf{Q}^{-1}\\mathbf{Q}\\mathbf{\\Lambda} \\mathbf{Q}^{-1}\\mathbf{x} = \\mathbf{\\Lambda} \\mathbf{Q}^{-1}\\mathbf{x}\n", + "\\end{equation}\n", + "\n", + "Thus defining new variables $\\mathbf{z} = \\mathbf{Q}^{-1}\\mathbf{x}$ yields:\n", + "\\begin{equation}\n", + "\\dot{\\mathbf{z}} = \\mathbf{\\Lambda}\\mathbf{z}\n", + "\\end{equation}\n", + "Which is in fact just a system of decoupled equations:\n", + "\\begin{equation}\n", + "\\dot{z}_i = \\lambda_i z_i,\\quad i = 1,2\\dots,n\n", + "\\end{equation}\n", + "with known solutions:\n", + "\\begin{equation}\n", + "z^*_i = e^{\\lambda_i t} z_i(0)\n", + "\\end{equation}\n", + "\n", + "\n", + "---\n", + "\n", + "\n", + ">**NOTE:** Another way to decompose our system is by applying following property of matrix exponential:\n", + "\\begin{equation}\n", + "e^{\\mathbf{Y}\\mathbf{X}\\mathbf{Y}^{-1}} = \\mathbf{Y}e^{\\mathbf{X}}\\mathbf{Y}^{-1}\n", + "\\end{equation}\n", + "where $\\mathbf{Y}$ is invertable" + ] + }, + { + "cell_type": "markdown", + "source": [ + "## **Homework exercises** for self-study\n", + "> Compare the solutions given by matrix exponential with one given by numerical integration for LTI system with diagonizable $\\mathbf{A}$." + ], + "metadata": { + "id": "IhbxUFACXmO5" + } + }, + { + "cell_type": "code", + "metadata": { + "id": "XhdOya2kDB3A" + }, + "source": [ + "# Put your code here" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "PqMQNNRchKZI" + }, + "source": [ + "##**Basics on the Eigenvalues and Eigenvectors**\n", + "\n", + "A (non-zero) vector v of dimension N is an eigenvector of a square N × N matrix A if it satisfies the linear equation\n", + "\n", + "\\begin{equation}\n", + "\\mathbf {v} =\\lambda \\mathbf {v}\n", + "\\end{equation}\n", + "\n", + "where $\\lambda$ is a scalar, termed the eigenvalue corresponding to $\\mathbf{v}$. \n", + "\n", + "This yields an equation for the eigenvalues\n", + "\n", + "\\begin{equation}\n", + "\\det \\left(\\mathbf {A} -\\lambda \\mathbf {I} \\right)=0\n", + "\\end{equation}\n", + "We call $\\Delta(\\lambda)$ the characteristic polynomial, and the equation, called the characteristic equation, is an $n$ - th order polynomial equation in the unknown $\\lambda$ with $N_\\lambda$ solutions$ \n", + "\n", + "We can factor $\\Delta(\\lambda)$ as\n", + "\\begin{equation}\n", + "\\Delta(\\lambda)=\\left(\\lambda -\\lambda _{1}\\right)^{k_{1}}\\left(\\lambda -\\lambda _{2}\\right)^{k_{2}}\\cdots \\left(\\lambda -\\lambda _{N_{\\lambda }}\\right)^{k_{N_{\\lambda }}}=0.\n", + "\\end{equation}\n", + "\n", + "The integer $k_i$ is termed the algebraic multiplicity of eigenvalue $\\lambda_i$. If the field of scalars is algebraically closed, the algebraic multiplicities sum to N:\n", + "\\begin{equation}\n", + " \\sum \\limits _{i=1}^{N_{\\lambda }}{k_{i}}=n\n", + "\\end{equation}\n", + "For each eigenvalue $\\lambda_i$ we have a specific equation:\n", + "\\begin{equation}\n", + "\\left(\\mathbf {A} -\\lambda _{i}\\mathbf {I} \\right)\\mathbf {v} =0\n", + "\\end{equation}\n", + "\n", + "There will be $1 ≤ m_i ≤ k_i$ linearly independent solutions to each eigenvalue equation. \n", + "The linear combinations of the $m_i$ solutions are the eigenvectors associated with the eigenvalue $\\lambda_i$. The integer $m_i$ is termed the geometric multiplicity of $\\lambda_i$. The total number of linearly independent eigenvectors $N_\\mathbf{v}$ can be calculated by summing the geometric multiplicities\n", + "\\begin{equation}\n", + "\\sum \\limits _{i=1}^{N_{\\lambda }}{m_{i}}=N_{\\mathbf {v}}\n", + "\\end{equation}\n", + "\n", + ">**QUESTION:** What are the relationship between $N_{\\mathbf {v}}$ and rank of $\\mathbf{Q}$\n", + "\n", + "\n", + "\n", + "---\n", + ">### **Exercises**\n", + ">\n", + "> Find eigen system (values and vectors) of following matrices by hand, compare your solution with result of numerical routine:\n", + ">$$\n", + "\\begin{bmatrix} 0 & 1 \\\\ -5 & -2\n", + "\\end{bmatrix},\\quad\n", + "\\begin{bmatrix} 0 & 8 \\\\ 1 & 3\n", + "\\end{bmatrix}\n", + ",\\quad\n", + "\\begin{bmatrix} 0 & 8 \\\\ 6 & 0\n", + "\\end{bmatrix}\n", + ",\\quad\n", + "\\begin{bmatrix} 0 & 1 \\\\ -3 & 0\n", + "\\end{bmatrix}\n", + "$$\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "yMj6ordwKi32", + "outputId": "b26038c3-877f-441a-8d7a-2fef228bba59" + }, + "source": [ + "A = [[0, 1],\n", + " [2, 0]]\n", + "\n", + "Lambda, Q = np.linalg.eig(A)\n", + "print(f\"Eigen values:\\n{Lambda}, \\n\\n Eigen vectors:\\n{Q}\")" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Eigen values:\n", + "[ 1.41421356 -1.41421356], \n", + "\n", + " Eigen vectors:\n", + "[[ 0.57735027 -0.57735027]\n", + " [ 0.81649658 0.81649658]]\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "S2xBjo0JC_4f" + }, + "source": [ + "## **Intro to Stability**\n", + "\n", + "Various types of stability may be discussed for the solutions of differential equations or difference equations describing dynamical systems. The one practically important type is that concerning the stability of solutions near to a point of equilibrium. This may be ,analyzed by the theory of **Aleksandr Lyapunov**. \n", + "\n", + "In simple terms, if the solutions that start out near an equilibrium point $\\mathbf{x}_{0}$ stay near $\\mathbf{x}_{0}$ forever, then $\\mathbf{x}_{0}$ is Lyapunov stable. More strongly, if $\\mathbf{x}_{0}$ is Lyapunov stable and all solutions that start out near $\\mathbf{x}_{0}$ converge to $\\mathbf{x}_0$, then $\\mathbf{x}_{0}$ is asymptotically stable. \n", + "\n", + "\n", + "\n", + "---\n", + "A strict deffenitions are as follows:\n", + "\n", + "Equilibrium $\\mathbf{x}_0$ is said to be:\n", + "\n", + "* **Lyapunov stable** if:\n", + "\\begin{equation}\n", + "\\forall \\epsilon>0,\\exists\\delta>0, \\|\\mathbf{x}(0) - \\mathbf{x}_0\\|<\\delta \\rightarrow \\|\\mathbf{x}(t) - \\mathbf{x}_0\\|<\\epsilon, \\quad \\forall t\n", + "\\end{equation}\n", + "* **Asymptotically stable** if it is Lyapunov stable and:\n", + "\\begin{equation}\n", + "\\exists \\delta >0, \\|\\mathbf{x}(0) - \\mathbf{x}_0\\|< \\delta, \\rightarrow \\lim_{t\\to\\infty} \\|\\mathbf{x}(t) - \\mathbf{x}_0\\| = 0, \\quad \\forall t\n", + "\\end{equation}\n", + "* **Exponentially stable** if it is asymptotically stable and:\n", + "\\begin{equation}\n", + "\\exists \\delta, \\alpha, \\beta >0, \\|\\mathbf{x}(0) - \\mathbf{x}_0\\|< \\delta, \\rightarrow \\|\\mathbf{x}(t) - \\mathbf{x}_0\\| \\leq\\alpha\\|\\mathbf{x}(0) - \\mathbf{x}_0\\|^{-{\\beta}t}, \\quad \\forall t \n", + "\\end{equation}\n", + "\n", + "Conceptually, the meanings of the above terms are the following:\n", + "\n", + "\n", + "* **Lyapunov stability** of an equilibrium means that solutions starting \"close enough\" to the equilibrium (within a distance $\\delta$ from it) remain \"close enough\" forever\n", + "* **Asymptotic stability** means that solutions that start close enough not only remain close enough but also eventually converge to the equilibrium.\n", + "* **Exponential** stability means that solutions not only converge, but in fact converge faster than or at least as fast as a particular known rate $\\alpha\\|\\mathbf{x}(0) - \\mathbf{x}_0\\|^{-{\\beta}t}$\n", + "\n", + "---\n", + "\n", + "\n", + "The solution $z_i = e^{\\lambda_i t}z_i(0)$ can be decomposed using Euler's identity:\n", + "\\begin{equation}\n", + " z_i = e^{\\lambda_i t}z_i(0) =\n", + " e^{(\\alpha_i + i \\beta_i) t}z_i(0) =\n", + " e^{\\alpha_i t} \n", + " e^{i \\beta_i t}z_i(0) = \n", + " e^{\\alpha_i t} \n", + " (\\cos(\\beta_i t) + i \\sin(\\beta_i t))z_i(0)\n", + "\\end{equation}\n", + "where $\\lambda_i = \\alpha_i + i \\beta_i, \\operatorname{Re}{\\lambda_i} = \\alpha_i, \\operatorname{Im}{\\lambda_i} = \\beta_i$\n", + "\n", + "\n", + "---\n", + "Since $\\| (\\cos(\\beta_i t) + i \\sin(\\beta_i t))\\| =1$ thus, norm of $z_i$:\n", + "\n", + "* Bounded if $\\operatorname{Re}{\\lambda_i} = \\alpha_i = 0$, hence the system is **Lyapunov stable**. \n", + "* Decreasing if $\\operatorname{Re}{\\lambda_i} = \\alpha_i < 0$, hence the system is **asymptotically** and moreover **exponentially** stable. \n", + "* Increasing if $\\operatorname{Re}{\\lambda_i} = \\alpha_i > 0$, hence the system is **unstable**. \n", + "---\n", + "\n", + "\n", + ">**QUESTION:** how norms $\\|\\mathbf{z}\\|$ and $\\|\\mathbf{x}\\|$ are related?" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 428 + }, + "id": "GIkpu55rMt96", + "outputId": "c53c5c86-f433-4520-8a6d-8e9dbba5372e" + }, + "source": [ + "from scipy.integrate import odeint\n", + "from matplotlib.pyplot import *\n", + "\n", + "A = [[0, 4],\n", + " [-1, -20]]\n", + "\n", + "A = np.array(A)\n", + "n = np.shape(A)[0]\n", + "\n", + "Lambda, Q = np.linalg.eig(A)\n", + "print(f\"Eigen values:\\n{Lambda}, \\n\\n Eigen vectors:\\n{Q}\\n\\n\")\n", + "\n", + "# x_dot from state space\n", + "def f(x, t):\n", + " return A.dot(x)\n", + "\n", + "t0 = 0 # Initial time \n", + "tf = 10 # Final time\n", + "t = np.linspace(t0, tf, 1000)\n", + "\n", + "x0 = np.random.rand(n) # initial state\n", + "\n", + "solution = odeint(f, x0, t)\n", + "\n", + "plot(t, solution, linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'State ${x}$')\n", + "xlabel(r'Time $t$')\n", + "show()\n" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Eigen values:\n", + "[ -0.20204103 -19.79795897], \n", + "\n", + " Eigen vectors:\n", + "[[ 0.99872679 -0.19803942]\n", + " [-0.05044595 0.98019406]]\n", + "\n", + "\n" + ] + }, + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "hG_fXxA-NGqE" + }, + "source": [ + " >### **Exercises**\n", + "> Check the stability of the following LTI systems $\\dot{ \\mathbf{x}} = \\mathbf{A} \\mathbf{x}$\n", + "\n", + "1. \\begin{equation}\n", + " \\dot{\\mathbf{x}} = \n", + "\t\\begin{bmatrix} \n", + " -11 & 0 \\\\\n", + " 5 & -50\n", + " \\end{bmatrix}\n", + " \\mathbf{x}\n", + "\\end{equation}\n", + "\n", + "2. \\begin{equation}\n", + " \\dot{\\mathbf{x}} = \n", + " \\begin{bmatrix} \n", + " 0 & 4 \\\\\n", + " -1 & -20\n", + " \\end{bmatrix}\n", + " \\mathbf{x}\n", + "\\end{equation}\n", + "\n", + "3. \\begin{equation}\n", + " \\dot{\\mathbf{x}} = \n", + "\t\\begin{bmatrix} \n", + " -12 & 10 \\\\\n", + " 1.5 & -7\n", + " \\end{bmatrix}\n", + " \\mathbf{x}\n", + "\\end{equation}\n", + "\n", + "\n", + "4. \\begin{equation}\n", + " \\dot{\\mathbf{x}} = \n", + " \\begin{bmatrix} \n", + " -50 & 0 & 2 \\\\\n", + " 0 & -30 & 20 \\\\\n", + " -1 & 0 & -30\n", + " \\end{bmatrix}\n", + " \\mathbf{x}\n", + "\\end{equation}\n", + "\n", + "\n", + "5. \\begin{equation}\n", + " \\dot{\\mathbf{x}} = \n", + " \\begin{bmatrix} \n", + " 20 & 1 & 5 \\\\\n", + " 5 & 14.5 & 7 \\\\\n", + " 5 & -2 & -12\n", + " \\end{bmatrix}\n", + " \\mathbf{x}\n", + "\\end{equation}\n", + "\n", + "6. \\begin{equation}\n", + " \\dot{\\mathbf{x}} = \n", + " \\begin{bmatrix} \n", + " -25 & 10 & 2 \\\\\n", + " 4 & -30 & -5 \\\\\n", + " -4 & 7 & -2\n", + " \\end{bmatrix}\n", + " \\mathbf{x}\n", + "\\end{equation}\n", + "\n", + "\n", + "> Check the stability of the following systems (numerically)\n", + "\n", + "1. \\begin{equation}\n", + " 2\\ddot{y} + 7\\dot{y} + 7 y = 0\n", + "\\end{equation}\n", + "\n", + "2. \\begin{equation}\n", + " -\\ddot{y} + 9\\dot{y} + 10 y = 10\n", + "\\end{equation}\n", + "\n", + "3. \\begin{equation}\n", + " \\ddot{y} -6\\dot{y} + 2y = 2\n", + "\\end{equation}\n", + "\n", + "4. \\begin{equation}\n", + " 2\\dddot{y}-\\ddot{y} + 4\\dot{y} +8 y = 2\n", + "\\end{equation}\n", + "\n", + "5. \\begin{equation}\n", + " 10\\dddot{y}+5\\ddot{y} + 2\\dot{y} + 30 y + 15 = 0\n", + "\\end{equation}\n", + "\n", + ">Consider the mass-spring-damper system:\n", + ">

\"mbk\"

\n", + ">\n", + "> with dynamics given by\n", + "> \\begin{equation}\n", + "m \\ddot y + b \\dot y + k y = 0 \n", + "\\end{equation} \n", + ">\n", + ">What are the conditions on the real $m, b, k$ for this system to be stable?\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "1QN4NjiJOZBt" + }, + "source": [ + "## **Basics of Phase Space Analysys**\n", + "\n", + "---\n", + "\n", + "In dynamical system theory, a **phase space** $\\mathcal{S}$ is a space in which all possible states $\\mathbf{x}$ of a system are represented, with each possible state corresponding to one unique point in the phase space. The concept of phase space was developed in the late 19th century by *Ludwig Boltzmann*, *Henri Poincaré*, and *Josiah Willard Gibbs*.\n", + "\n", + "Phase space is great tool to graphically analyze systems up to third order, without actually solving their related ODEs.\n", + "\n", + "One can build the phase portrait by plotting the vectors $\\dot{\\mathbf{x}}_i$:\n", + "\\begin{equation}\n", + "\\dot{\\mathbf{x}}_i = \\mathbf{f}(\\mathbf{x}_i)\n", + "\\end{equation}\n", + "\n", + "Thus for choosen points $\\mathbf{x}_i$ you may analyze the tendency of your states dynamics, via $\\dot{\\mathbf{x}}_i$\n", + "\n", + "---\n", + " ### **Example**\n", + "\n", + "Let us consider the example of \"love\" equations given in the first practice:\n", + "\n", + "$$\n", + "\\begin{cases}\n", + "\\dot{R}=aR+bJ \\\\\n", + "\\dot{J}=cR+dJ\n", + "\\end{cases}\n", + "$$\n", + "\n", + "when $R$ and $J$ are time depended functions of Romeo's or Juliet's love (or hate if negative) and $a$, $b$, $c$ and $d$ is constants that determine the \"Romantic styles\". " + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "7U4i-VI8jQsm", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 1000 + }, + "outputId": "8878a472-9dc3-42cb-c975-fb898811bd4a" + }, + "source": [ + "def StateSpace(x, t, A, B):\n", + " return np.dot(A,x)+B\n", + "\n", + "def f(x, t):\n", + " R, J = x[0], x[1]\n", + " \n", + " dR = a*R +b*J\n", + " dJ = c*R + d*J\n", + " return dJ, dR\n", + "\n", + "#@title **Love model**\n", + "#@markdown Romeo's parameters\n", + "a = 0 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "b = 5 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "\n", + "#@markdown Juliet's parameters\n", + "c = -1 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "d = 0 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "\n", + "#@markdown How much did Romeo and Juliet like each other at first sight?\n", + "R_0 = 6 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "J_0 = 3 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "\n", + "A = np.array([[a, b],\n", + " [c, d]])\n", + "\n", + "B = np.array([0,\n", + " 0])\n", + "\n", + "x0 = np.array([R_0,\n", + " J_0]) # initial state\n", + "\n", + "Lambda, Q = np.linalg.eig(A)\n", + "print(f\"Eigen values:\\n{Lambda}, \\n\\n Eigen vectors:\\n{Q}\\n\\n\")\n", + "\n", + "t0 = 0 # Initial time \n", + "tf = 10 # Final time\n", + "t = np.linspace(t0, tf, 1000)\n", + "\n", + "love = odeint(StateSpace, x0, t, args=(A,B))\n", + "R, J = love[:,0], love[:,1]\n", + "\n", + "plot(t, love, linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'Level of love ${X}$')\n", + "xlabel(r'Time $t$')\n", + "show()\n", + "\n", + "plot(J, R, linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlabel(r'Love of Juliet ${J}$')\n", + "ylabel(r'Love of Romeo ${R}$')\n", + "show()\n", + "\n", + "# Phase space with stream plot\n", + "J_e_max, R_e_max = 10, 10\n", + "J_e_span = np.arange(-J_e_max,J_e_max,0.1)\n", + "R_e_span = np.arange(-R_e_max,R_e_max,0.1)\n", + "J_e_grid, R_e_grid = np.meshgrid(J_e_span, R_e_span)\n", + "\n", + "figure(figsize=(7, 7))\n", + "title('Phase Plane')\n", + "# Varying color along a streamline\n", + "L = (J_e_grid**2 + R_e_grid**2)**0.5\n", + "lw = 3*L / L.max()\n", + "contourf(J_e_span, R_e_span, L, cmap='autumn', alpha = 0.25)\n", + "\n", + "dJ, dR = f([R_e_grid, J_e_grid],t)\n", + "\n", + "strm = streamplot(J_e_span, R_e_span, dJ, dR, density = 1,color=L, cmap='autumn', linewidth = lw)\n", + "\n", + "plot(J, R, 'r-', lw = 3.0)\n", + "plot(x0[1], x0[0], 'ro', lw = 10)\n", + "hlines(0, -J_e_max, J_e_max,color = 'red', linestyle = '--', alpha = 0.6)\n", + "vlines(0, -R_e_max, R_e_max,color = 'red', linestyle = '--', alpha = 0.6)\n", + "xlim([-0.9*J_e_max,0.9*J_e_max])\n", + "ylim([-0.9*R_e_max,0.9*R_e_max])\n", + "xlabel(r'Love of Juliet ${J}$')\n", + "ylabel(r'Love of Romeo ${R}$')\n", + "tight_layout()\n", + "show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Eigen values:\n", + "[0.+2.23606798j 0.-2.23606798j], \n", + "\n", + " Eigen vectors:\n", + "[[0.91287093+0.j 0.91287093-0.j ]\n", + " [0. +0.40824829j 0. -0.40824829j]]\n", + "\n", + "\n" + ] + }, + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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\n", 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\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + } + } + ] + } + ] +} \ No newline at end of file diff --git a/legacy - ColabNotebooks/Practice_3_Laplace_TransferFunctions.ipynb b/legacy - ColabNotebooks/Practice_3_Laplace_TransferFunctions.ipynb new file mode 100644 index 0000000..9614ae9 --- /dev/null +++ b/legacy - ColabNotebooks/Practice_3_Laplace_TransferFunctions.ipynb @@ -0,0 +1,1020 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "[Control theory] Practice 3.ipynb", + "provenance": [], + "collapsed_sections": [], + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "markdown", + "source": [ + "# **Important information**\n", + "\n", + "> **LABS** \\\n", + "**Tasks for lab 1:** [Lab 1](https://colab.research.google.com/drive/1dLIgEAn5ksFEcVXAI_GifKkip1izppNm?usp=sharing)\\\n", + "**Deadline:** 15th of February\\\n", + "**File name for lab submission:** `yourname_group.ipynb` (example: `IvanovIvan_B20-05.ipynb`)\n", + "\n", + ">**FEEDBACK** \\\n", + "Feedback form is available by the [link](https://forms.gle/CcqEwfg97aHQcZJi6)" + ], + "metadata": { + "id": "dLR9vEFEY-iE" + } + }, + { + "cell_type": "markdown", + "metadata": { + "id": "D-dOD4xqsPiR" + }, + "source": [ + "# **Practice 3: Laplace Transform and Transfer Functions**\n", + "## **Goals for today**\n", + "\n", + "---\n", + "\n", + "\n", + "\n", + "During today practice we will:\n", + "* Recall the Laplace transform\n", + "* Define the transfer functions\n", + "* Model particular systems with transfer functions \n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "RCityqOscrJV" + }, + "source": [ + "## **Laplace transform**\n", + "\n", + "In mathematics, the Laplace transform, named after its inventor Pierre-Simon Laplace, is an integral transform that converts a function of a real variable $t$ (time domain) to a function of a complex variable $s$ (frequency domain). The transform has many applications in science and engineering because it is a tool for solving differential equations. In particular, it transforms differential equations into algebraic equations.\n", + "\n", + "The Laplace transform of a function $f(t)$ is given as:\n", + "\\begin{equation}\n", + " F(s) = \\mathcal{L} \\{ x(t)\\} = \\int_0^\\infty f(t) e^{-st}dt\n", + "\\end{equation}\n", + "\n", + "where $F(s)$ is called an ***image*** of the function and $s=\\alpha +\\beta i $ is a complex frequency.\n", + "\n", + "Laplace transform is defined as transformation from the time domain $t$ to the frequency domain $s$.\n", + "\n", + "it is convinient to use the table of precalculated Laplace transforms:\n", + "

\"mbk\"

\n", + "\n", + "#### **Some Usefull properties**\n", + "Linear properties:\n", + "\\begin{equation}\n", + " {\\mathcal {L}}\\{f(t)+g(t)\\}={\\mathcal {L}}\\{f(t)\\}+{\\mathcal {L}}\\{g(t)\\}\n", + "\\end{equation}\n", + "\n", + "\\begin{equation}\n", + " {\\mathcal {L}}\\{af(t)\\}=a{\\mathcal {L}}\\{f(t)\\}\n", + "\\end{equation}\n", + "Final value theorem:\n", + "\\begin{equation}\n", + "f(\\infty )=\\lim _{s\\to 0}{sF(s)}\n", + "\\end{equation}\n", + "The final value theorem is useful because it gives the long-term behaviour for particular function. \n", + "\n", + "#### **Inverse Laplace Transform**\n", + "The inverse Laplace transform is going in other way, by transforming image of your function $F(s)$ from frequancy domain to time domain $x(t)$:\n", + "\\begin{equation}\n", + "{\\displaystyle f(t)={\\mathcal {L}}^{-1}\\{F\\}(t)={\\frac {1}{2\\pi i}}\\lim _{T\\to \\infty }\\int _{\\gamma -iT}^{\\gamma +iT}e^{st}F(s)\\,ds}\n", + "\\end{equation}\n", + "\n", + "However in poractice we mostly use precalculated laplace transforms and then trying to decompose the image $X(s)$ into known transforms of functions obtained from a table, and construct the inverse by inspection, or just use some symbolic routines:\n", + "\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "MKcM-1G4gaYW" + }, + "source": [ + "import sympy\n", + "sympy.init_printing()\n" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "0Qj3OoWjgikM" + }, + "source": [ + "t, s = sympy.symbols('t, s')\n", + "a = sympy.symbols('a', real=True, positive=True)" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 38 + }, + "id": "psiuazxSgkhO", + "outputId": "f0381b12-95d1-47af-e0a6-1a096a3a927c" + }, + "source": [ + "f = sympy.exp(a*t)\n", + "f" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "image/png": "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\n", + "text/latex": "$\\displaystyle e^{a t}$", + "text/plain": [ + " a⋅t\n", + "ℯ " + ] + }, + "metadata": {}, + "execution_count": 30 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 52 + }, + "id": "ntT8J1XIgzKW", + "outputId": "7df84586-6f7e-4dc7-f32e-94e7e54899ae" + }, + "source": [ + "F = sympy.laplace_transform(f, t, s, noconds=True)\n", + "F" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "image/png": "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\n", + "text/latex": "$\\displaystyle \\frac{1}{- a + s}$", + "text/plain": [ + " 1 \n", + "──────\n", + "-a + s" + ] + }, + "metadata": {}, + "execution_count": 31 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 38 + }, + "id": "ClrfANLng66x", + "outputId": "5eb323af-2802-4228-aea3-4fb22ec99051" + }, + "source": [ + "f = sympy.inverse_laplace_transform(F, s, t)\n", + "f" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "image/png": "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\n", + "text/latex": "$\\displaystyle e^{a t} \\theta\\left(t\\right)$", + "text/plain": [ + " a⋅t \n", + "ℯ ⋅θ(t)" + ] + }, + "metadata": {}, + "execution_count": 32 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "TdHXASZ6hJAq" + }, + "source": [ + "def L(f):\n", + " return sympy.laplace_transform(f, t, s, noconds=True)\n", + "\n", + "def invL(F):\n", + " return sympy.inverse_laplace_transform(F, s, t)" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 52 + }, + "id": "H0g7os87j51Y", + "outputId": "fdbe8faa-7811-41f0-f389-9ecaecfa416e" + }, + "source": [ + "L(sympy.exp(a*t))" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "image/png": "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\n", + "text/latex": "$\\displaystyle \\frac{1}{- a + s}$", + "text/plain": [ + " 1 \n", + "──────\n", + "-a + s" + ] + }, + "metadata": {}, + "execution_count": 34 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 38 + }, + "id": "Ma5asUr4j5db", + "outputId": "a91a04bc-5dcf-40b7-8ddc-87deca03c94e" + }, + "source": [ + "invL(F)" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "image/png": "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\n", + "text/latex": "$\\displaystyle e^{a t} \\theta\\left(t\\right)$", + "text/plain": [ + " a⋅t \n", + "ℯ ⋅θ(t)" + ] + }, + "metadata": {}, + "execution_count": 35 + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Bj7W6rQViF4J" + }, + "source": [ + "## **Homework exercises** for self-study\n", + "> Write the code that will reproduce the first 5 rows of the table above." + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "fY3HSwLsiAtM" + }, + "source": [ + "# Put your code here" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "o3Z6WvjdfnpO" + }, + "source": [ + "\n", + "\n", + "### **Laplace transform of a function's derivative**\n", + ">For us one of the most usefull properties of Laplace transform is that if we apply it to the derevetive of a given variable it will result with following:\n", + ">\n", + "> \\begin{equation}\n", + "\\mathcal{L}\\left\\{\\frac{dx(t)}{dt}\\right\\} = s \\mathcal{L}\\left(x\\right) = s X(s)\n", + "\\end{equation}\n", + "which is true for $x(0) = 0$\n", + ">\n", + ">Thus we can define a **derivative operator**:\n", + "\\begin{equation}\n", + "\\frac{dx}{dt} \\xrightarrow{\\mathcal{L}} s X(s)\n", + "\\end{equation}\n", + "\n", + "The proof is as follows, using defenition of Laplace transform:\n", + "\\begin{equation}\n", + " \\mathcal{L}\\left\\{\\frac{dx}{dt}\\right\\} = \\int_0^\\infty \\frac{dx}{dt} e^{-st}dt\n", + "\\end{equation}\n", + "Then using integration by parts:\n", + "\n", + "\\begin{equation}\n", + "\\int_0^\\infty \\frac{dx}{dt} e^{-st}dt = \\left[x e^{-st} \\right]_0^\\infty - \n", + "\\int_0^\\infty -se^{-st} x dt \n", + "\\end{equation}\n", + "which yields:\n", + "\\begin{equation}\n", + "\\left[x e^{-st} \\right]_0^\\infty + \n", + "s\\int_0^\\infty e^{-st} x dt = x(0) + s\\mathcal{L}\\{x(t)\\} = x(0) + sX(s)\n", + "\\end{equation}\n", + "\n", + "by induction it can be shown that:\n", + "\\begin{equation}\n", + "{\\mathcal {L}}\\left\\{\\frac{d^{n}x}{dt^{n}}(t)\\right\\}=s^{n}\\cdot {\\mathcal {L}}\\{x(t)\\}+s^{n-1}x(0)+\\cdots +x^{(n-1)}(0)\n", + "\\end{equation}\n", + "\n", + "\\begin{equation}\n", + " \\mathcal{L}\\left(\\frac{dx}{dt}\\right) = \\int_0^\\infty \\frac{dx}{dt} e^{-st}dt\n", + "\\end{equation}\n", + "\n", + "### **Applications to the linear ODEs**\n", + ">Let us consider the following ODE:\n", + "\\begin{equation}\n", + "a_{n}x^{(n)} +a_{n-1}x^{(n-1)}+...+a_{2}\\ddot x+a_{1}\\dot x + a_0 x= u_{m}b^{(m)} +b_{m-1}u^{(m-1)}+...+b_{2}\\ddot u+b_{1}\\dot u + b_0 u\n", + "\\end{equation}\n", + "Notice that we introduce a new variable that we call the input $u$ (control). \n", + "\n", + "Aplying the inverse laplace transform with zero initial conditions yields:\n", + "\\begin{equation}\n", + "a_{n}s^{(n)}X(s) +a_{n-1}s^{(n-1)}X(s)+...+a_{2} s^2 X(s)+a_{1}s X(s) + a_0 X(s) =\\\\\n", + "= b_{m}s^{(m)}U(s) +b_{m-1}s^{(m-1)}U(s)+...+b_{2}s^2 U(s)+b_{1}sU(s) + b_0 U(s)\n", + "\\end{equation}\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "RDrejDYJkiWH" + }, + "source": [ + "\n", + "## **Exercise**\n", + "> Apply Laplace transform to the following ODEs:\n", + "\n", + "1. $$\n", + " -\\ddot{y} - 10\\dot{y} + 1.5 y = u\n", + "$$\n", + "\n", + "2. $$\n", + " 2\\ddot{y} + 10\\dot{y} + 2 y = 5 u\n", + "$$\n", + "\n", + "3. $$\n", + " \\ddot{y} + 4.5 \\dot{y} - y = -u\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "xC0pbISDkw-g" + }, + "source": [ + "\n", + "## **Transfer Functions**\n", + "A transfer function is a mathematical function which theoretically models the device's output for each possible input. Transfer functions are commonly used in the analysis of systems such as single-input single-output filters in the fields of signal processing, communication theory, and control theory. The term is often used exclusively to refer to linear time-invariant (LTI) systems\n", + "\n", + "Thus, for continuous-time input signal $u(t)$ and output $x(t)$, the transfer function $H(s)$ is the linear mapping of the Laplace transform of the input, $U(s) = \\mathcal{L}\\left\\{u(t)\\right\\}$, to the Laplace transform of the output $X(s) = \\mathcal{L}\\left\\{x(t)\\right\\}$:\n", + "\\begin{equation}\n", + " X(s) = W(s)\\;U(s) \\rightarrow W(s) = \\frac{X(s)}{U(s)} = \\frac{ \\mathcal{L}\\left\\{x(t)\\right\\} }{ \\mathcal{L}\\left\\{u(t)\\right\\} }\n", + "\\end{equation}\n", + "\n", + "Considering this defenition we can evaluate tha transfer function for ODE given above as:\n", + "\\begin{equation}\n", + "W(s) = \\frac{X(s)}{U(s)} = \\frac{b_{m}s^{(m)} +b_{m-1}s^{(m-1)}+...+b_{2}s^2 +b_{1}s + b_0 }{a_{n}s^{(n)} +a_{n-1}s^{(n-1)}+...+a_{2} s^2 +a_{1}s + a_0 }\n", + "\\end{equation}\n", + "\n", + "A transfer function thus represent the ODE by its behaviour from input image $U(s)$ to output image $X(s)$.\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "source": [ + "## **From ODE to transfer function**\n", + "Let us consider the following ODE:\n", + "\\begin{equation}\n", + "a_{n}x^{(n)} +a_{n-1}x^{(n-1)}+...+a_{2}\\ddot x+a_{1}\\dot x + a_0 x= u_{m}b^{(m)} +b_{m-1}u^{(m-1)}+...+b_{2}\\ddot u+b_{1}\\dot u + b_0 u\n", + "\\end{equation}\n", + "\n", + "Aplying the inverse laplace transform with zero initial conditions yields:\n", + "\\begin{equation}\n", + "a_{n}s^{(n)}X(s) +a_{n-1}s^{(n-1)}X(s)+...+a_{2} s^2 X(s)+a_{1}s X(s) + a_0 X(s) =\\\\\n", + "= b_{m}s^{(m)}U(s) +b_{m-1}s^{(m-1)}U(s)+...+b_{2}s^2 U(s)+b_{1}sU(s) + b_0 U(s)\n", + "\\end{equation}\n", + "\n", + "Now lets rewrite this equation in the following form:\n", + "$$\n", + "\\begin{cases}\n", + "U(s)=\\frac{a_ns^n+a_{n-1}s^{(n-1)}+...+a_{1}s+a_0}{b_{m}s^{(m)}+b_{m-1}s^{(m-1)}+...+b_{1}s+b_0}X(s) \\\\\n", + "Y(s)=X(s)\n", + "\\end{cases}\n", + "$$\n", + "\n", + "This mean that our transfer function is equal to:\n", + "$$\n", + "\\mathbf{G}(s)=\\frac{Y(s)}{U(s)}=\\frac{b_{m}s^{(m)}+b_{m-1}s^{(m-1)}+...+b_{1}s+b_0}{a_ns^n+a_{n-1}s^{(n-1)}+...+a_{1}s+a_0}\n", + "$$" + ], + "metadata": { + "id": "vKH3G7tybGKs" + } + }, + { + "cell_type": "markdown", + "metadata": { + "id": "oV6h4Uok27gX" + }, + "source": [ + ">### **Example**\n", + ">Consider the mass-spring-damper system:\n", + ">

\"mbk\"

\n", + ">\n", + "> with dynamics given by\n", + "> \\begin{equation}\n", + "m \\ddot y + b \\dot y + k y = u\n", + "\\end{equation} \n", + ">\n", + ">where $u$ is force that applied to the mass, let's model this system by using transfer functions.\n", + "\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 279 + }, + "id": "3cPmD7N7tZow", + "outputId": "26c4f7c6-4706-4f68-c5df-07345ccfa1d2" + }, + "source": [ + "import numpy as np\n", + "from scipy import signal\n", + "import matplotlib.pyplot as plt\n", + "from scipy.integrate import odeint\n", + "\n", + "# Simulate m d^2y/dt^2 + b dy/dt + k y = u \n", + "# from u to y\n", + "# W(s) = 1/(m s^2 + bs + k)\n", + "\n", + "m = 2\n", + "b = 1\n", + "k = 5\n", + "\n", + "num = [1,0]\n", + "den = [m, b, k]\n", + "sys_tf = signal.TransferFunction(num,den)\n", + "t_tf,y_tf = signal.step(sys_tf)\n", + "\n", + "plt.figure(1)\n", + "plt.plot(t_tf,y_tf,'r',linewidth=2,label=r'$y$ response')\n", + "plt.xlabel(r'Time')\n", + "plt.ylabel(r'Response (y)')\n", + "plt.grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "plt.grid(True)\n", + "plt.xlim([t_tf[0], t_tf[-1]])\n", + "plt.legend(loc='best')\n", + "plt.show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "## **Homework exercises** for self-study\n", + "> 1. Find the transfer function of the ODEs given above\n", + ">\n", + "> 2. Modify the code above to represent the response from input force $u$ to output velocity $\\dot{y}$\n", + ">\n", + "> 3. Compare solutions with ones provided by `odeint` " + ], + "metadata": { + "id": "xEQAMgs9cq8Z" + } + }, + { + "cell_type": "code", + "source": [ + "# put your code here" + ], + "metadata": { + "id": "M6GnxAnrc60I" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "1qQ-mJEhs7L3" + }, + "source": [ + "## **Exercises**\n", + "> Calculate transfer function for the following systems:\n", + "\n", + "1. $$\n", + " \\dddot{y}+3\\ddot{y} + 2\\dot{y} + 8 y = 2 u\n", + "$$\n", + "\n", + "2. $$\n", + " 5\\dddot{y}-4\\ddot{y} - 5\\dot{y} - 3 y = u\n", + "$$\n", + "\n", + "3. $$\n", + "\\begin{cases}\n", + " 2\\dddot{y}+3\\ddot{y} + 7\\dot{y} + 12 y - u = 0 \\\\\n", + " \\dot{z}+5z = u\n", + "\\end{cases}\n", + "$$\n", + "\n", + "4. $$\n", + "\\begin{cases}\n", + " 3\\dddot{y}+9\\ddot{y} + 2\\dot{y} + 6 y = u + v \\\\\n", + " 5\\ddot{z}+\\dot{z}+5z = v\n", + "\\end{cases}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "f_jpmegAx_Pj" + }, + "source": [ + "### **From State Space to Transfer Functions**\n", + "\n", + "Consider standard form state-space dynamical system:\n", + "\n", + "\\begin{equation}\n", + "\\begin{cases}\n", + "\\dot{\\mathbf{x}} = \\mathbf{A}\\mathbf{x} + \\mathbf{B}\\mathbf{u} \\\\\n", + " \\mathbf{y} = \\mathbf{C}\\mathbf{x} + \\mathbf{D}\\mathbf{u}\n", + "\\end{cases}\n", + "\\end{equation}\n", + "\n", + "We can rewrite it using the derivative operator:\n", + "\n", + "\\begin{equation}\n", + "\\begin{cases}\n", + "s\\mathbf{I}\\mathbf{X}(s) -\\mathbf{A}\\mathbf{X}(s) = \\mathbf{B}\\mathbf{U}(s) \\\\\n", + "\\mathbf{Y}(s) = \\mathbf{C}\\mathbf{X}(s) + \\mathbf{D}\\mathbf{U}(s)\n", + "\\end{cases}\n", + "\\end{equation}\n", + "\n", + "and then collect $\\mathbf{X}(s)$ on the left-hand-side: $\\mathbf{X}(s) = (s\\mathbf{I} -\\mathbf{A})^{-1} \\mathbf{B}\\mathbf{U}(s)$\n", + "\n", + "and finally, express $\\mathbf{Y}(s)$ output:\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{Y}(s) = \\left( \\mathbf{C}(s\\mathbf{I} -\\mathbf{A})^{-1} \\mathbf{B} + \\mathbf{D} \\right) \\mathbf{U}(s)\n", + "\\end{equation}\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "bYjgqfd22d2b" + }, + "source": [ + ">### **Example**\n", + "> Let us recall the \"love equation\" between Romeo and Juliet:\n", + "$$\n", + "\\begin{cases}\n", + "\\dot{R}=aR+bJ \\\\\n", + "\\dot{J}=cR+dJ\n", + "\\end{cases}\n", + "$$\n", + "\n", + "But now lets consider the case when they can manipulate each other feelings with some control inputs $u_R$ and $u_J$:\n", + "\\begin{equation}\n", + "\\begin{bmatrix}\n", + "\\dot{R} \\\\\n", + "\\dot{J} \n", + "\\end{bmatrix} = \n", + "\\begin{bmatrix}\n", + "a R + bJ + e u_R + f u_J\\\\\n", + "c R + dJ + j u_R + h u_J\n", + "\\end{bmatrix}\n", + "\\end{equation}\n", + "State space representation of this system is given as:\n", + "\\begin{equation}\n", + "\\begin{bmatrix}\n", + "\\dot{R} \\\\\n", + "\\dot{J} \n", + "\\end{bmatrix} = \n", + "\\begin{bmatrix}\n", + "a & b \\\\\n", + "c & d \n", + "\\end{bmatrix}\n", + "\\begin{bmatrix}\n", + "R \\\\\n", + "J \n", + "\\end{bmatrix} +\n", + "\\begin{bmatrix}\n", + "e & f \\\\\n", + "j & h \n", + "\\end{bmatrix}\n", + "\\begin{bmatrix}\n", + "u_R \\\\\n", + "u_J \n", + "\\end{bmatrix}\n", + "\\end{equation}\n", + "\n", + "And our goal is to find the transfer functions form Romeo effort to Juliet love and vice versa. " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "RPWJbCSS-Les" + }, + "source": [ + "Lets first find the solution analytically:" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "5ip-SUMp-Qih" + }, + "source": [ + "a, b, c, d, e, f, g, h = sympy.symbols('a, b, c, d, e, f, g, h') \n", + "s = sympy.symbols('s')\n", + "\n", + "A = sympy.Matrix([[a, b], [c, d]])\n", + "B = sympy.Matrix([[e, f],[g, h]])" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 68 + }, + "id": "HLhxjSqiA8-S", + "outputId": "06527033-373c-43d4-9a19-77e53d44dbd4" + }, + "source": [ + "Xs = (s * sympy.eye(2) - A).inv()*B\n", + "Xs" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/latex": "$\\displaystyle \\left[\\begin{matrix}\\frac{b g}{a d - a s - b c - d s + s^{2}} + \\frac{e \\left(- d + s\\right)}{a d - a s - b c - d s + s^{2}} & \\frac{b h}{a d - a s - b c - d s + s^{2}} + \\frac{f \\left(- d + s\\right)}{a d - a s - b c - d s + s^{2}}\\\\\\frac{c e}{a d - a s - b c - d s + s^{2}} + \\frac{g \\left(- a + s\\right)}{a d - a s - b c - d s + s^{2}} & \\frac{c f}{a d - a s - b c - d s + s^{2}} + \\frac{h \\left(- a + s\\right)}{a d - a s - b c - d s + s^{2}}\\end{matrix}\\right]$", + "text/plain": [ + "⎡ b⋅g e⋅(-d + s) b⋅h \n", + "⎢────────────────────────── + ────────────────────────── ────────────────────\n", + "⎢ 2 2 \n", + "⎢a⋅d - a⋅s - b⋅c - d⋅s + s a⋅d - a⋅s - b⋅c - d⋅s + s a⋅d - a⋅s - b⋅c - d⋅\n", + "⎢ \n", + "⎢ c⋅e g⋅(-a + s) c⋅f \n", + "⎢────────────────────────── + ────────────────────────── ────────────────────\n", + "⎢ 2 2 \n", + "⎣a⋅d - a⋅s - b⋅c - d⋅s + s a⋅d - a⋅s - b⋅c - d⋅s + s a⋅d - a⋅s - b⋅c - d⋅\n", + "\n", + " f⋅(-d + s) ⎤\n", + "────── + ──────────────────────────⎥\n", + " 2 2⎥\n", + "s + s a⋅d - a⋅s - b⋅c - d⋅s + s ⎥\n", + " ⎥\n", + " h⋅(-a + s) ⎥\n", + "────── + ──────────────────────────⎥\n", + " 2 2⎥\n", + "s + s a⋅d - a⋅s - b⋅c - d⋅s + s ⎦" + ] + }, + "metadata": {}, + "execution_count": 37 + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "Let's add in our system the output equation:\n", + "\\begin{equation}\n", + "\\begin{cases}\n", + "\\dot{\\mathbf{x}} = \\mathbf{A}\\mathbf{x} + \\mathbf{B}\\mathbf{u} \\\\\n", + " \\mathbf{y} = \\mathbf{C}\\mathbf{x} + \\mathbf{D}\\mathbf{u}\n", + "\\end{cases}\n", + "\\end{equation}\n", + "\n", + "when $\\mathbf{x} = \\begin{bmatrix}\n", + "\\dot{R} \\\\\n", + "\\dot{J} \n", + "\\end{bmatrix}$, $\\mathbf{A} = \\begin{bmatrix}\n", + "a & b \\\\\n", + "c & d \n", + "\\end{bmatrix}$, $\\mathbf{B} = \\begin{bmatrix}\n", + "e & f \\\\\n", + "j & h \n", + "\\end{bmatrix}$, $\\mathbf{C} = \\begin{bmatrix}\n", + "1 \\\\\n", + "0 \n", + "\\end{bmatrix}$, $\\mathbf{D} = \\begin{bmatrix}\n", + "0 \\\\\n", + "0 \n", + "\\end{bmatrix}$" + ], + "metadata": { + "id": "tBqkI-rr6ihD" + } + }, + { + "cell_type": "code", + "metadata": { + "id": "4WMJSP2OBlCs" + }, + "source": [ + "# lets now denote output equations\n", + "C = sympy.Matrix([[1, 0]])\n", + "D = sympy.Matrix([[0,0]])" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 47 + }, + "id": "ptRHD0Lk_Tnh", + "outputId": "0122eda5-64c4-49c9-9300-dd47c14bde22" + }, + "source": [ + "Ys = C*(s * sympy.eye(2) - A).inv()*B +D\n", + "Ys" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/latex": "$\\displaystyle \\left[\\begin{matrix}\\frac{b g}{a d - a s - b c - d s + s^{2}} + \\frac{e \\left(- d + s\\right)}{a d - a s - b c - d s + s^{2}} & \\frac{b h}{a d - a s - b c - d s + s^{2}} + \\frac{f \\left(- d + s\\right)}{a d - a s - b c - d s + s^{2}}\\end{matrix}\\right]$", + "text/plain": [ + "⎡ b⋅g e⋅(-d + s) b⋅h \n", + "⎢────────────────────────── + ────────────────────────── ────────────────────\n", + "⎢ 2 2 \n", + "⎣a⋅d - a⋅s - b⋅c - d⋅s + s a⋅d - a⋅s - b⋅c - d⋅s + s a⋅d - a⋅s - b⋅c - d⋅\n", + "\n", + " f⋅(-d + s) ⎤\n", + "────── + ──────────────────────────⎥\n", + " 2 2⎥\n", + "s + s a⋅d - a⋅s - b⋅c - d⋅s + s ⎦" + ] + }, + "metadata": {}, + "execution_count": 39 + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "jhLtdz0a-RUF" + }, + "source": [ + "We can do the same numerically instead:" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "Azm-4SVl82nx", + "outputId": "1fb4b17c-1be3-41bc-96d4-5be8adaf9e85" + }, + "source": [ + "from scipy.signal import ss2tf\n", + "a, b, c, d, e, f, g, h = 1, 1, 1, 1, 1, 1, 1, 1\n", + "\n", + "A = [[a, b], [c, d]]\n", + "B = [[e, f],[g, h]]\n", + "C = [[1, 0]]\n", + "D = [[0,0]]\n", + "ss2tf(A, B, C, D)" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "(array([[0, 1, 0]]), array([ 1., -2., 0.]))" + ] + }, + "metadata": {}, + "execution_count": 26 + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "## **Exercises**\n", + "> Convert following state space models to transfer function\n", + "\n", + "1. $$\n", + "\\begin{cases}\n", + " \\dot{\\mathbf{x}} = \\begin{bmatrix} 0 & 1 \\\\ -7 & -5 \\end{bmatrix} \n", + " \\mathbf{x} + \n", + " \\begin{bmatrix} 1 \\\\ 1 \\end{bmatrix} u \\\\\n", + " y = \\begin{bmatrix} 1 & 1 \\end{bmatrix} \\mathbf{x}\n", + "\\end{cases}\n", + "$$\n", + "\n", + "2. $$\n", + "\\begin{cases}\n", + " \\dot{\\mathbf{x}} = \\begin{bmatrix} 2 & -1 \\\\ 3 & -4 \\end{bmatrix} \n", + " \\mathbf{x} + \n", + " \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix} u \\\\\n", + " y = \\begin{bmatrix} 1 & 0 \\end{bmatrix} \\mathbf{x}\n", + "\\end{cases}\n", + "$$\n", + "\n", + "\n", + "3. $$\n", + "\\begin{cases}\n", + " \\dot{\\mathbf{x}} = \\begin{bmatrix} 0 & 10 \\\\ -3 & 5 \\end{bmatrix}\n", + " \\mathbf{x} + \n", + " \\begin{bmatrix} 2 \\\\ -1 \\end{bmatrix} u \\\\\n", + " y = \\begin{bmatrix} -1 & -1 \\end{bmatrix} \\mathbf{x}\n", + "\\end{cases}\n", + "$$\n", + "\n", + "4. $$\n", + "\\begin{cases}\n", + " \\dot{\\mathbf{x}} = \n", + " \\begin{bmatrix} \n", + " 0 & 2 & 0 \\\\\n", + " 0 & 0 & 2 \\\\\n", + " 8 & -20 & -1\n", + " \\end{bmatrix}\n", + " \\mathbf{x} + \n", + " \\begin{bmatrix} 2 \\\\ -1 \\\\ -3 \\end{bmatrix} u \\\\\n", + " y = \\begin{bmatrix} 1 & -1 & 1 \\end{bmatrix} \\mathbf{x}\n", + "\\end{cases}\n", + "$$\n", + "\n", + "5. $$\n", + "\\begin{cases}\n", + " \\dot{\\mathbf{x}} = \n", + " \\begin{bmatrix} \n", + " 0 & 1 & 0 \\\\\n", + " 0 & 1 & 1 \\\\\n", + " 4 & 11 & -20\n", + " \\end{bmatrix}\n", + " \\mathbf{x} + \n", + " \\begin{bmatrix} -1 \\\\ -1 \\\\ 0 \\end{bmatrix} u \\\\\n", + " y = \\begin{bmatrix} 0 & 0 & 1 \\end{bmatrix} \\mathbf{x}\n", + "\\end{cases}\n", + "$$\n", + "\n", + "6. $$\n", + "\\begin{cases}\n", + " \\dot{\\mathbf{x}} = \n", + " \\begin{bmatrix} \n", + " 0 & 1 & 1 \\\\\n", + " 0 & 0 & 1 \\\\\n", + " -1 & 1 & 9\n", + " \\end{bmatrix}\n", + " \\mathbf{x} + \n", + " \\begin{bmatrix} 1 \\\\ 0 \\\\ 1 \\end{bmatrix} u \\\\\n", + " y = \\begin{bmatrix} 1 & -1 & 2 \\end{bmatrix} \\mathbf{x}\n", + "\\end{cases}\n", + "$$\n", + "\n", + "7. $$\n", + "\\begin{cases}\n", + " \\dot{\\mathbf{x}} = \n", + " \\begin{bmatrix} \n", + " 1 & 1 & 0 \\\\\n", + " 1 & 0 & 1 \\\\\n", + " -3 & 2 & 10\n", + " \\end{bmatrix}\n", + " \\mathbf{x} + \n", + " \\begin{bmatrix} 2 \\\\ 2 \\\\ -1 \\end{bmatrix} u \\\\\n", + " y = \\begin{bmatrix} 0 & -1 & 0 \\end{bmatrix} \\mathbf{x}\n", + "\\end{cases}\n", + "$$\n", + "\n", + "8. $$\n", + "\\begin{cases}\n", + " \\dot{\\mathbf{x}} = \n", + " \\begin{bmatrix} \n", + " 0 & 1 & 0 \\\\\n", + " 0 & 0 & 1 \\\\\n", + " 0 & 1 & 5\n", + " \\end{bmatrix}\n", + " \\mathbf{x} + \n", + " \\begin{bmatrix} 0 \\\\ 0 \\\\ 1 \\end{bmatrix} u \\\\\n", + " y = \\begin{bmatrix} -10 & -10 & 0 \\end{bmatrix} \\mathbf{x}\n", + "\\end{cases}\n", + "$$" + ], + "metadata": { + "id": "kyv_c59Sdfzg" + } + }, + { + "cell_type": "markdown", + "metadata": { + "id": "5hHBY9f_-VuS" + }, + "source": [ + "## **Homework exercises** for self-study\n", + "> 1. Simulate the response of \"love\" system using transfer functions and state space approaches compare results. (you may use [this as reference](https://apmonitor.com/pdc/index.php/Main/ModelSimulation) )\n", + "\n", + "> 2. Considering the following ODE:\n", + "> \\begin{equation}\n", + "a_{n}y^{(n)} +a_{n-1}y^{(n-1)}+...+a_{2}\\ddot y+a_{1}\\dot y + a_0 y= u_{m}b^{(m)} +b_{m-1}u^{(m-1)}+...+b_{2}\\ddot u+b_{1}\\dot u + b_0 u\n", + "\\end{equation}\n", + ">With related transfer function:\n", + "\\begin{equation}\n", + "W(s) = \\frac{Y(s)}{U(s)} = \\frac{b_{m}s^{(m)} +b_{m-1}s^{(m-1)}+...+b_{2}s^2 +b_{1}s + b_0 }{a_{n}s^{(n)} +a_{n-1}s^{(n-1)}+...+a_{2} s^2 +a_{1}s + a_0 }\n", + "\\end{equation}\n", + ">\n", + ">where $Y(s) = \\mathcal{}$ $m\\leq n$ suggest a method to represent it in the equalient state space representation:\n", + "\\begin{equation}\n", + "\\begin{cases}\n", + "\\dot{\\mathbf{x}} = \\mathbf{A}\\mathbf{x} + \\mathbf{B}\\mathbf{u} \\\\\n", + " \\mathbf{y} = \\mathbf{C}\\mathbf{x} + \\mathbf{D}\\mathbf{u}\n", + "\\end{cases}\n", + "\\end{equation}\n", + "and output $Y(s) = \\mathcal{L}\\{y\\} = \\mathcal{L}\\{\\mathbf{y}_1\\} =\\mathcal{L}\\{\\mathbf{x}_1\\}$ \n", + ">\n", + ">Use [this link as reference](https://lpsa.swarthmore.edu/Representations/SysRepTransformations/TF2SS.html)\n" + ] + } + ] +} \ No newline at end of file diff --git a/legacy - ColabNotebooks/Practice_4_Bode.ipynb b/legacy - ColabNotebooks/Practice_4_Bode.ipynb new file mode 100644 index 0000000..760003f --- /dev/null +++ b/legacy - ColabNotebooks/Practice_4_Bode.ipynb @@ -0,0 +1,697 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "[Control theory] Practice 4.ipynb", + "provenance": [], + "collapsed_sections": [], + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "markdown", + "source": [ + "\n", + "# **Important information**\n", + "\n", + "> **LABS** \\\n", + "**Tasks for lab 1:** [Lab 1](https://github.com/SergeiSa/Control-Theory-Slides-Spring-2022/blob/main/Assignment/Assignment1.ipynb)\\\n", + "**Deadline:** 15th of February\\\n", + "**Requirements for the submission:** upload a `.pdf`-file (printout of the Colab page / jupiter notebook with the results of the code run) plus the code itself `.ipynb`-file\\\n", + "**File name for lab submission:** `yourname_group.ipynb` (example: `IvanovIvan_B20-05.ipynb`)\n", + "\n", + ">**FEEDBACK** \\\n", + "Feedback form is available by the [link](https://forms.gle/CcqEwfg97aHQcZJi6)" + ], + "metadata": { + "id": "dLR9vEFEY-iE" + } + }, + { + "cell_type": "markdown", + "metadata": { + "id": "D-dOD4xqsPiR" + }, + "source": [ + "# **Practice 4: Bode plot**\n", + "## **Goals for today**\n", + "\n", + "---\n", + "\n", + "During today practice we will:\n", + "* Repeat State space representation\n", + "* Recall transformation between State space model and Transfer function\n", + "* Define frequency response\n", + "* Learn how to make a bode plot\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "source": [ + "## **State space representation**\n", + "\n", + "In control engineering, a *state-space representation* is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations or difference equations. State variables are variables whose values evolve over time in a way that depends on the values they have at any given time and on the externally imposed values of input variables. Output variables’ values depend on the values of the state variables.\n", + "\n", + "A control system is a system, which provides the desired response by controlling the output. The following figure shows the simple block diagram of a control system.\n", + "\n", + "![image.png](data:image/png;base64,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)" + ], + "metadata": { + "id": "vUFOXd73b2ef" + } + }, + { + "cell_type": "markdown", + "source": [ + "In case if relationships between state, output and control is **linear**, we can formulate the model of system in following form:\n", + "\\begin{equation}\n", + "\\begin{cases} \n", + "\\mathbf{\\dot{x}} =\\mathbf{A}\\mathbf{x} + \\mathbf{B}\\mathbf{u} \\\\ \n", + "\\mathbf{y}=\\mathbf{C}\\mathbf{x} + \\mathbf{D}\\mathbf{u}\n", + "\\end{cases}\n", + "\\end{equation}\n", + "\n", + "where\n", + "* $\\mathbf{x} \\in \\mathbb{R}^n$ states of the system\n", + "* $\\mathbf{y} \\in \\mathbb{R}^l$ output vector\n", + "* $\\mathbf{u} \\in \\mathbb{R}^m$ control inputs\n", + "* $\\mathbf{A} \\in \\mathbb{R}^{n \\times n}$ state matrix\n", + "* $\\mathbf{B} \\in \\mathbb{R}^{n \\times m}$ input matrix\n", + "* $\\mathbf{C} \\in \\mathbb{R}^{l \\times n}$ output matrix\n", + "* $\\mathbf{D} \\in \\mathbb{R}^{l \\times m}$ feedforward matrix\n", + "\n", + ">Note: \n", + "If matrices $\\mathbf{A},\\mathbf{B},\\mathbf{C},\\mathbf{D}$ are time dependend, we call such systems **time-varient**. However, in practice we often deal with systems whose dynamics is time-invarient. In this case this matrices will be constant." + ], + "metadata": { + "id": "ig0-m6LTffdS" + } + }, + { + "cell_type": "markdown", + "metadata": { + "id": "f_jpmegAx_Pj" + }, + "source": [ + "## **Transformation from State space representation to transfer function**\n" + ] + }, + { + "cell_type": "markdown", + "source": [ + "Consider standard form state-space dynamical system:\n", + "\n", + "\\begin{equation}\n", + "\\begin{cases}\n", + "\\dot{\\mathbf{x}} = \\mathbf{A}\\mathbf{x} + \\mathbf{B}\\mathbf{u} \\\\\n", + " \\mathbf{y} = \\mathbf{C}\\mathbf{x} + \\mathbf{D}\\mathbf{u}\n", + "\\end{cases}\n", + "\\end{equation}\n", + "\n", + "We can rewrite it using the derivative operator:\n", + "\n", + "\\begin{equation}\n", + "\\begin{cases}\n", + "s\\mathbf{I}\\mathbf{X}(s) -\\mathbf{A}\\mathbf{X}(s) = \\mathbf{B}\\mathbf{U}(s) \\\\\n", + "\\mathbf{Y}(s) = \\mathbf{C}\\mathbf{X}(s) + \\mathbf{D}\\mathbf{U}(s)\n", + "\\end{cases}\n", + "\\end{equation}\n", + "\n", + "and then collect $\\mathbf{X}(s)$ on the left-hand-side: $\\mathbf{X}(s) = (s\\mathbf{I} -\\mathbf{A})^{-1} \\mathbf{B}\\mathbf{U}(s)$\n", + "\n", + "and finally, express $\\mathbf{Y}(s)$ output:\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{Y}(s) = \\left( \\mathbf{C}(s\\mathbf{I} -\\mathbf{A})^{-1} \\mathbf{B} + \\mathbf{D} \\right) \\mathbf{U}(s)\n", + "\\end{equation}\n", + "\n", + "This mean that the transfer function can be calculated as:\n", + "$\\mathbf{G}(s) = \\mathbf{C}(s\\mathbf{I} -\\mathbf{A})^{-1} \\mathbf{B} + \\mathbf{D}$" + ], + "metadata": { + "id": "TW0lzJuzdwlT" + } + }, + { + "cell_type": "markdown", + "source": [ + ">***Note:***\n", + "To get an inverse matrix from a 2x2 matrix (for example $A = \\dot{\\mathbf{x}} = \\begin{bmatrix} a & b \\\\ c & d \\end{bmatrix}$, you can use the formula:\n", + ">\n", + ">$$\n", + "A^{-1} = \\frac{1}{ad-bc}\\begin{bmatrix} d & -b \\\\ -c & a \\end{bmatrix}\n", + "$$\\\n", + "When $ad-bc$ is determinant of $A$ and $\\begin{bmatrix} d & -b \\\\ -c & a \\end{bmatrix}$ is adjoint of $A$" + ], + "metadata": { + "id": "X60QF72XeHYe" + } + }, + { + "cell_type": "markdown", + "source": [ + "### **Exercises**\n", + "> Convert following state space models to transfer function\n", + "\n", + "1. $$\n", + "\\begin{cases}\n", + " \\dot{\\mathbf{x}} = \\begin{bmatrix} 0 & 1 \\\\ -7 & -7 \\end{bmatrix} \n", + " \\mathbf{x} + \n", + " \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix} u \\\\\n", + " y = \\begin{bmatrix} 1 & 0 \\end{bmatrix} \\mathbf{x}\n", + "\\end{cases}\n", + "$$\n", + "\n", + "2. $$\n", + "\\begin{cases}\n", + " \\dot{\\mathbf{x}} = \\begin{bmatrix} 0 & 1 \\\\ -200 & -2 \\end{bmatrix} \n", + " \\mathbf{x} + \n", + " \\begin{bmatrix} 10 \\\\ 0 \\end{bmatrix} u \\\\\n", + " y = \\begin{bmatrix} 1 & 0 \\end{bmatrix} \\mathbf{x}\n", + "\\end{cases}\n", + "$$\n", + "\n", + "3. $$\n", + "\\begin{cases}\n", + " \\dot{\\mathbf{x}} = \\begin{bmatrix} 0 & 1 \\\\ -1 & -1000 \\end{bmatrix}\n", + " \\mathbf{x} + \n", + " \\begin{bmatrix} 0 \\\\ -2 \\end{bmatrix} u \\\\\n", + " y = \\begin{bmatrix} 1 & 0 \\end{bmatrix} \\mathbf{x}\n", + "\\end{cases}\n", + "$$" + ], + "metadata": { + "id": "kyv_c59Sdfzg" + } + }, + { + "cell_type": "markdown", + "source": [ + "## **Frequency response**\n" + ], + "metadata": { + "id": "52GoHUsoN1oH" + } + }, + { + "cell_type": "markdown", + "source": [ + "Consider a linear, time-invariant system with transfer function $\\mathbf{G}(s)$. Assume that the system is subject to a sinusoidal input with frequency $\\omega$:\n", + "\n", + "$$\n", + "u(t) = \\sin{(wt)}\n", + "$$\n", + "\n", + "that is applied persistently, i.e. from a time $-\\infty$ to a time $t$. The response will be of the form\n", + "$$y(t) = y_0 \\sin (\\omega t + \\varphi)$$\n", + "\n", + "i.e., also a sinusoidal signal with amplitude $y_{0}$ shifted in phase with respect to the input by a phase $\\varphi$." + ], + "metadata": { + "id": "Mbd1ku4zoK4j" + } + }, + { + "cell_type": "markdown", + "source": [ + "## **Bode plot**" + ], + "metadata": { + "id": "FQh-XLrfpaZ7" + } + }, + { + "cell_type": "markdown", + "source": [ + "**Bode plot** is a graph of the frequency response of a system. It is usually a combination of a *Bode magnitude plot*, expressing the magnitude (usually in decibels) of the frequency response, and a *Bode phase plot*, expressing the phase shift.\n", + "\n", + "The ***Bode magnitude plot*** is the graph of the function $|\\mathbf{G}(s=j\\omega )|$ of frequency $\\omega$ (with $j$ being the imaginary unit). The $\\omega$-axis of the magnitude plot is logarithmic and the magnitude is given in decibels, i.e., a value for the magnitude $|\\mathbf{G}|$ is plotted on the axis at $20\\log _{10}|\\mathbf{G}|$.\n", + "\n", + "The ***Bode phase plot*** is the graph of the phase, commonly expressed in degrees, of the transfer function $\\arg \\left(\\mathbf{G}(s=j\\omega )\\right)$ as a function of $\\omega$ . The phase is plotted on the same logarithmic $\\omega$-axis as the magnitude plot, but the value for the phase is plotted on a linear vertical axis." + ], + "metadata": { + "id": "yCLXZ82aph-D" + } + }, + { + "cell_type": "markdown", + "source": [ + ">### **Examples**" + ], + "metadata": { + "id": "uKC4G4rq9jcn" + } + }, + { + "cell_type": "markdown", + "source": [ + "> **Mass-spring-damper system**\n", + ">\n", + ">Consider the mass-spring-damper system:\n", + ">

\"mbk\"

\n", + ">\n", + "> with dynamics given by\n", + "> \\begin{equation}\n", + "m \\ddot y + b \\dot y + k y = u\n", + "\\end{equation} \n", + ">\n", + ">where $u$ is force that applied to the mass" + ], + "metadata": { + "id": "JH4bvW3P-21Y" + } + }, + { + "cell_type": "code", + "source": [ + "import numpy as np\n", + "from matplotlib.pyplot import *\n", + "from scipy.integrate import odeint\n", + "\n", + "def Harmonic_control_signal(w,t):\n", + " u = np.sin(w*t)\n", + " return np.array([u])\n", + "\n", + "def StateSpace(x, t, A, B, w):\n", + " u = Harmonic_control_signal(w,t)\n", + " x = np.dot(A,x)+np.dot(B,u)\n", + " return x\n", + "\n", + "def Control_system(A, B, C, D, w):\n", + " x0 = np.array([0, 0])\n", + "\n", + " t0 = 0 # Initial time \n", + " tf = 1/w*30 # Final time\n", + " t = np.linspace(t0, tf, 1000) \n", + " solution = odeint(StateSpace, x0, t, args=(A,B,w))\n", + " u = Harmonic_control_signal(w,t)\n", + " y = np.dot(C,solution.T)+np.dot(D,u)\n", + " \n", + " return t, np.reshape(u,t.shape), np.reshape(y,t.shape), solution\n", + "\n", + "#@markdown Mass-spring-damper parameters\n", + "w = 0.01 #@param {type:\"slider\", min:0.01, max:10, step:0.01}\n", + "m = 1 #@param {type:\"slider\", min:0, max:10, step:1}\n", + "k = 5 #@param {type:\"slider\", min:0, max:5, step:0.1}\n", + "b = 3.17 #@param {type:\"slider\", min:0, max:5, step:0.01}\n", + "\n", + "n = 2\n", + "A = np.array([[0, 1],\n", + " [-k/m, -b/m]])\n", + "\n", + "B = np.array([[0], [1]])\n", + "\n", + "C = np.array([[1, 0]])\n", + "\n", + "D = np.array([[0]])\n", + "\n", + "t, u, y, x = Control_system(A, B, C, D, w)\n", + "\n", + "plot(t, u, color = \"red\", label = \"System input\")\n", + "plot(t, y, color = \"blue\", label = \"System output\")\n", + "legend()\n", + "grid(True, color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 265 + }, + "id": "haAi0fdSq68Z", + "outputId": "4e03f1b9-92b1-4c68-a191-a5d771313acb", + "cellView": "form" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "code", + "source": [ + "from scipy.signal.ltisys import TransferFunction\n", + "from scipy.signal import ss2tf\n", + "\n", + "G = ss2tf(A, B, C, D)\n", + "sys = TransferFunction(G[0], G[1])\n", + "\n", + "w, mag, phase = sys.bode()\n", + "\n", + "f, (ax1, ax2) = subplots(2, 1, sharex=True)\n", + "ax1.semilogx(w, mag, color=\"blue\") # Bode magnitude plot\n", + "ax1.grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "ax1.grid(True)\n", + "\n", + "ax2.semilogx(w, phase, color=\"blue\") # Bode phase plot\n", + "ax2.grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "ax2.grid(True)\n", + "show()\n", + "\n", + "plot(w, phase)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 573 + }, + "id": "VTi_ealq6_Sa", + "outputId": "63f0a8b7-7520-453f-cd5d-8df3c616078f" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "name": "stderr", + "text": [ + "/usr/local/lib/python3.7/dist-packages/scipy/signal/filter_design.py:1622: BadCoefficients: Badly conditioned filter coefficients (numerator): the results may be meaningless\n", + " \"results may be meaningless\", BadCoefficients)\n" + ] + }, + { + "output_type": "display_data", + "data": { + "image/png": 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0vvwrKQnmzoVZs2D+fMjKgq+/ju4xXMWXL5K/Ukq5IgJXXw1/+xssWQInnWQfCY11mvyVUioKfv1rWLgQ3n4bjjsOgvOyxCxfJP/CwkKvq6ASmMaXqvfLX9rn/zdvhmOPhddei3yfruLLF8k/LS3N6yqoBKbxpUKNHdt0Ypinn45sf67iyxfJP3S+TKWiTeNL/djw4bB0KQwdCqefDhUV4e/LVXz5IvkrpVRn23dfeP55e/vn/PPhllu8rlFTmvyVUsqRPfe0o4BOmgTTp8Mf/wi7dnldK8sXyT8jI8PrKqgEpvGlWtOzpx0DKNzOYK7iS4d3UEqpTmAM3HADXHMNZGTAww/D7ru7Pabvh3coKCjwugoqgWl8qfYQgZkz4d577dwAJ58Mn3/e9udcxZcvkv+6WO9toeKaxpfqiIsvhscegzfftJ3BPvig9e1dxZcvkr9SSsWSM86wz/9/8YV9GqgzZwar54vkn5yc7HUVVALT+FLhOO44Oy9A1662M9gzzzS/nav40gZfpZTy0Mcf21nBAgE7MuikSdHbt+8bfCsi6V6nVBs0vlQk9tvP/gIYPRrOPRd+PIKzq/hynvxFZLqIGBFJCb4XEblNRAIi8oaIHO26DpWVla4PoXxM40tFKjnZPgE0YQLk50NhoX00FNzFl9PkLyL7AacCH4UsPg0YFixTgTtc1kEppeJBr17w6KP2aaDrr4epU2HHDnfH6+pu1wDMAf4ELAxZNhG439jGhldEZE8RGWiM+dRxXZRSKqZ17Qr33AP77GNnB/vsM9i5s7uTYzn75i8iE4ENxphVP1o1CPg45P364DJn5syZ43L3yuc0vlQ0idhv/nPnQlUVfP75/7J1a/SPE9E3fxF5GtinmVUzgauxt3wi2f9U7K0hUlJSyMrKalhX/z/ctGnTGpZlZ2eTk5NDbm4udXV1AKSmppKfn09ZWRk1NTUN25aXlxMIBCgpKWlYlpeXR2ZmZpPjpKenU1RURHFxMcuXL29YXlVVRXV1dZP5NQsLC0lLS2syBGtGRgb5+fkUFBQ0dNZITk6mvLycioqKJvfzOnJOpaWlek4xck5bt27lkksuSahzSsR/p3g8p7VrX+Thhzdz3nl3IdLxc2qNk0c9ReRwYAnwbXDRYOATYAxwHfCsMaYyuO0a4Odt3faJ5FHPrKwsqqqqwvqsUm3R+FIuRRJfnf6opzHmTWPMXsaYIcaYIdhbO0cbY/4DLAKmBJ/6GQts0fv9SinVuVw3+DZnMXA6EMD+Mvi1B3VQSilfi5seviKyBXivlU32ALa0sC4F+CLqlXKvtXOK1eNEsq+Ofra927dnu7a20fiKnWOFuy9X8dWebb2KrwOMMQOaXWOMiYsC3B3uemCF1/V3cc6xeJxI9tXRz7Z3+/Zsp/EVP8cKd1+u4qs928ZifMXT8A5ttXgkYotbZ51TNI8Tyb46+tn2bt+e7TS+4udY4e7LVXy1Z9uYi6+4ue0TCRFZYVpo8VYqUhpfyiVX8RVP3/wjcbfXFVAJTeNLueQkvnzxzV8ppVRTfvnmr5RSKoQmf6WU8iFN/kop5UOa/JVSyoc0+SullA9p8ldKKR/S5K+UUj6kyV8ppXxIk79SSvmQJn+llPIhTf5KKeVDmvyVUsqHNPkrpZQPeZb8RSRTRNaISEBErvSqHkop5UeeDOksIknAWuAUYD2wHMg2xrzd0mdSUlLMkCFDwjpeXV0dycnJYX1WqbZofCmXIomvlStXfmFamMO3a0S1Ct8YIGCMeR9ARBYAE4EWk/+QIUNYsWJFWAfLysqiqioRZ+FTsUDjS7kUSXyJyIctrfPqts8g4OOQ9+uDy5RSSnUCr775t4uITAWmAqSkpJCVldWwbs6cOQBMmzatYVl2djY5OTnk5uZSV1cHwD77jOSHH/pw88138swzTyKyC4Dy8nICgQAlJSUNn8/LyyMzM7PJcdLT0ykqKqK4uJjly5c3LK+qqqK6upp58+Y1LCssLCQtLY3c3NyGZRkZGeTn51NQUMC6desASE5Opry8nIqKCiorKzt8TqmpqZSWllJWVkZNTU3DtnpO3pzTsmXLqKioSKhzSsR/p3g9p2XLljUcr6Pn1Bqv7vmPA/5sjMkIvr8KwBgzu6XPjB492oRz22f33WHr1sb3XbvCbrv9tPTq1fR1c6V378a/9WX33Rv/1pdu3TpcTRXH9J6/cimS+BKRlS1N/u7VN//lwDARGQpsACYDOS4OdOut8PbbH7L33gfw3Xfw/fe2fPfdT8u338KmTfZiUf9+61a7fUf06AF9+tgLQZ8+jaVvX1vqX++xhy2hr/fcs7H06OHiv4iKtkAgwJgxY7yuhkpQruLLswncReR0oBRIAv5mjJnV2vbhfvOHyBvkdu2yF4OtW2359lv45pvG9/Wvv/kGvv7a/q1//fXX8NVXTV9/9ZVd35aePaFfP3sh6NfPluTkxtK/f+Pf/v0hJcWWXr1AJOzTVR2kDb7KpQgbfGPumz/GmMXAYq+O3xFdujTe5omWnTvtBWDLlp+WzZvhyy/t6y+/bCyffAKrV0Ndnb2QtKRnT3sRGDCgsey1ly177934d5997Ovu3aN3Xkqp+BDTDb6JLCmp8VZPOLZvtxeETZsayxdfNP79/PPGsnat/Rva9hGqf38YONCWffdtWgYNgsGD7YUiKSn881VKxRZfJP+8vDyvqxB13bo1fptvr61b4bPPYONGW/7zn8a/n35qy7vv2r87djT9bFKSvTgMHgz7799YDjjAliFDwr+QxbtEjC8VO1zFl2f3/Dsqknv+qmN27bK/HjZsaCzr18PHHzeWjz6Cbduafq5fP3sRGDoUDjwQUlPt37Q0e6Ho6ouvGkrFjpi859+ZtEGuY7p0afxVMXJk89sYY39FfPihLf/+ty0ffABvvw1PPNH04tC1q70oHHRQYzn4YBg+3N5SiucGao0v5ZKr+PJF8lfRJ2IbjffeG5p7Cm3XLttA/f77EAjY8t57tjzzjH1iql7fvnDIIXDoobaMGAGHHWZvMcXzRUGpWKbJXznRpYtN3oMHwwknNF1njL2NtGaNbWN45x1bFi+Gv/+9cbs99oDDD4cjjoAjj4SjjrIXhV69OvdclEpEvkj+6enpXldBhRCB/fazZfz4puvq6uzjrKtXw5tv2vKPf8Dtt9v1XbrY20VHHw2jRsHo0fbWVDQfw+0ojS/lkqv40gZfFfOMse0JtbW2vPaaLZ98Ytd36WJ/EYwZA8ccA+PG2dtIXXSqIuVzrTX4+uJ/j+LiYq+roCIgYhuLzzwTrrsOqqrsE0iffGJfX3ON7ZPw6KPwm9/YC0G/fpCZCSUlP21jiDaNL+WSq/jyxW2f0JH2VOIYOBAmTLAF7C+EQABeftmWl16Ca6+1y7t1g/R0OPFEOOkkOO646LUdaHwpl1zFly+Sv/IHERg2zJYpU+yyL7+EpUvh+efhuefgr3+F2bPtkBbjxsEvfgEZGbb9QHswKz/R5K8SWr9+8Mtf2gJ2PKUXX4R//QuWLLG/DIqK7HannAKnnw6nndaxntNKxSNt8FW+9vnn9iJQU2PLp5/a5enpcMYZthx+uPY3UPHJ9w2+1dXVXldBxagBA2DyZNu/YMMG+xRRSYl9Uqiw0PYvOPBAmD7dtiHs2vXTfWh8KZdcxZcvkn/oNGpKtUTE9hm45hp45RX7K+Cee2yP47Iy+NnPbKe13//etiPUXwg0vpRLruLLF8lfqXDssw9ccgk8/rgdx2j+fNuP4K677NNCQ4bAlVfC11/v73VVleowTf5KtcMee0BODjz2mL0Q3H+/7U9w003w3HPzGDnSThn6xRde11Sp9vFF8i8sLPS6CiqB9O0LF15oxyL65BOYPv1DkpKgoMB2Nps0yTYeN9c+oFRHucpfvkj+aWlpXldBJai99oKrr+7DihXwxhuQn2/7E2Rm2nkMZs+2E+YoFS5X+csXyT83N9frKqgEVh9fhx8Ot9xiRyxdsMC2CVx9tZ3I5sIL4dVXva2nik+u8pez5C8ifxaRDSJSGyynh6y7SkQCIrJGRDJc1UEpL/ToAeedZzuSvfsuXHopLFwIY8fa8tBDP50mU6nO5vqb/xxjzFHBshhARA4FJgMjgEzgdhHRjvUqIQ0fDrfdZvsQzJ1rG4TPPdcOQTF3rtsB55RqjRe3fSYCC4wx24wxHwABoJm5oKInI0N/XCh32hNfffrY9oA1a+zoo/vuC7/7HRxwAFx/vR2DSKnmuMpfrsf2yReRKcAKYLox5ktgEPBKyDbrg8t+QkSmAlMBUlJSyMrKalg3Z84cAKZNm9awLDs7m5ycHHJzc6mrqwMgNTWV0tJSysrKqKmpadi2vLycQCBASUlJw7K8vDwyMzObHCc9PZ2ioiKKi4ubjK5XVVVFdXV1kw4YhYWFpKWlNblHl5GRQX5+PgUFBaxbtw6A5ORkysvLqaiooLKyUs8pAc4pOTm5Q+c0aFCAadMeIRCYRGFhOrNnb+cPf+jGsmXZdO/+TUycUyL+O8XjOdXU1DTUq6Pn1CpjTNgFeBpY3UyZCOwNJGF/XcwC/hb8TBlwQcg+7gMmtXWsUaNGmXD9/ve/D/uzSrUl0viqrTXm7LONAWP69DHmmmuM+fLLKFVOxb1I4gtYYVrIqRHd9jHGjDfGHNZMWWiM2WiM2WmM2QXcQ+OtnQ3AfiG7GRxc5kz91VQpFyKNryOPhIcftlNWZmba20BDh9rHRLdujVIlVdxylb9cPu0zMOTtmdhfBACLgMki0kNEhgLDgGWu6qFUvDjsMHjwQXj9dTuO0NVX274Cd92lTwep6HPZ4PtXEXlTRN4ATgKmARhj3gIeBN4GqoE8Y8xOh/UgOTnZ5e6Vz0U7vo46yk5PuXSpTf6XXWb7ECxcaGclU/7iKn/peP5KxTBj7IXgiitsn4GTT4Y5c+CII7yumYoHvh/Pv6KiwusqqATmMr5E7IQyb74J8+bBqlV22OlLL9VB5PzCVXz5IvmHPv6lVLR1Rnx17QqXXw7vvWf7B9x3Hxx0ENxxB+x0etNUec1VfPki+SuVKPr1s7d9Vq2ybQOXX26nnFymj0yoDtLkr1QcGjHCzj28YIEdNXTsWHsh2LzZ65qpeOGL5F/fK04pF7yKLxE7gNw779hbQXfdBQcfbB8XjZPnOFQ7uIovXyR/pRJZ375QWgrLl9s5hs87DyZOhI8/9rpmKpb5IvmHjoOhVLTFSnwdfbSdeP6mm+Dpp+2toTvv1BnF4p2r+PJF8lfKL7p2henT4a237GTzv/0tjB8POsKJ+jFN/koloKFD4amn4N57YeVK2yls7lz9FaAa+SL5Z2dne10FlcBiNb5E4OKL7a+AE0+0jcInnwzvv+91zVRHuIovHd5BKR8wBv7+d5g2zXYKu+km20tYxOuaKZd8P7yDTuCuXIqH+BKBiy6yw0SMG2fbAk47zU4vqWJb3E3gHkvqZ7dRyoV4iq/994eaGjtO0Asv2GGkdfST2OYqvnyR/JVSjbp0sb2Ba2vhkEMgJwcmT4Y4uoapKPBF8k9NTfW6CiqBxWt8DRsGzz8Ps2bBI4/YOQNCprBVMcJVfGmDr1KK11+HCy6At9+G/Hz4y1+gVy+va6Ui5fsG37KyMq+roBJYIsTXyJG2P0BBAZSV2d7C+l0rNriKL18k/xr9LascSpT46tnTDhf99NN24vhx46C4WOcP9pqr+PJF8ldKtd8vfgFvvAHnngvXXmsnk3/vPa9rpaItouQvIueIyFsisktERv9o3VUiEhCRNSKSEbI8M7gsICJXRnJ8pZQb/frB/Pl2voC1a+3EMbffrkNFJ5KIGnxF5BBgF3AXMMMYsyK4/FCgEhgD7As8DRwU/Nha4BRgPbAcyDbGvN3WsSJp8K2rqyM5OTmszyrVlkSPrw0b7DARNTWQkWGnkBw0yOta+Uck8eWswdcY844xZk0zqyYCC4wx24wxHwAB7IVgDBAwxrxvjPkBWBDc1qlAIOD6EMrHEj2+Bg2CJ5+03/zrO4bNn6+/AjqLq/jq6mSvMAh4JeT9+uAygI9/tPyYlnYiIlOBqQApKSlkZWU1rKuf3SZ0rOvs7GxycnLIzc1t6BWXmprKunXryMjIaNbK7scAAAtmSURBVNJwUl5eTiAQoKSkpGFZXl4emZmZTY6Tnp5OUVERxcXFLF++vGF5VVUV1dXVzJs3r2FZYWEhaWlpTbpjZ2RkkJ+fT0FBAeuC4+omJydTXl5ORUVFk8mZO3JOpaWllJWV6TnFwDktW7aMOXPmJNQ5tfTvNGnSMQQC13DBBTBjxlIOP/x2evTYEtfnFOv/TtOmTWPMmDFhnVOrjDGtFuwtm9XNlIkh2zwLjA55XwZcEPL+PmBSsNwbsvxCoKytOhhjGDVqlAnXhAkTwv6sUm3xW3zt2GHMX/9qTPfuxqSkGPPgg17XKLFFEl/ACtNCTm3zto8xZrwx5rBmysJWPrYB2C/k/eDgspaWK6XiRFIS/PGP8NprMGSIfSronHPgs8+8rpnqCFePei4CJotIDxEZCgwDlmEbeIeJyFAR6Q5MDm7rVF5enutDKB/za3yNGAEvvww33ACLFsGhh0JFhbYFRJur+Ir0aZ8zgbnAAGAzUGuMyQiumwlcBOwACowxTwaXnw6UAknA34wxs9pzLB3eQanY9dZb9omgV1+FX/4S7rgD9tuv7c8pt1w+7fOYMWawMaaHMWbv+sQfXDfLGJNqjBlen/iDyxcbYw4KrmtX4o9UaOOMUtGm8WV/Bbz0EtxyC/zrX/b9vHl24hgVGVfxpT18lVJRkZRkZwpbvRrGjrUDxB13nO0trGKPJn+lVFQdeKDtEPa//2vnCz76aJgxA77+2uuaqVC+SP7p6eleV0ElMI2vnxKB88+Hd96x00fefLOdOOahh7RBuKNcxZeO56+Ucu6VV+y8wbW1cPLJcOuttqewcsv34/kXFxd7XQWVwDS+2jZ2LCxfboeIqK21A8X9v/8HmzZ5XbPY5yq+fJH8Q7tcKxVtGl/t07Wr/fa/di1ceqm9EKSl2SeEtm3zunaxy1V8+SL5K6ViR//+9jHQVavsL4Lp0+2joQ88ALt2eV07/9Dkr5TyxGGH2dFCq6vtfMGTJ0N6Ovzzn9oo3Bm0wVcp5bmdO+3QEIWF8OGHcOKJUFICxx/vdc3im+8bfKurq72ugkpgGl+RS0qCCy+ENWvgttvs3xNOgFNOgRdf9Lp23nIVX75I/qHjaSsVbRpf0dOjh30KaN062zdg1Sr77f+kk2DJEn/eDnIVX75I/kqp+NKrF/zhD/DBBzBnjv0lMH68bSB+5BEdMygaNPkrpWJW795QUGCHibjjDqirg0mT4OCD7aOi33zjdQ3jly+Sf2FhoddVUAlM48u9nj3hssvg3Xfh4YchORny8uyw0X/6k20kTlSu4ssXyT8tLc3rKqgEpvHVeZKS4Oyz7XARS5fCqafaTmJDh8IZZ9jHRhOtr4Cr+PJF8g+dLFmpaNP46nwiMG6c7Rj2wQcwcyYsWwannWZ7Dc+aBZ984nUto8NVfPki+SulEtd++9k+AR99BJWV9lfANdfY5VlZ9jaRDh/xU5r8lVIJoXt320t4yRJ47z3bFvDaa3Zy+YED7bhCL76YeLeFwuWL5J+RkdH2RkqFSeMr9qSlwezZ9tdAdTVkZkJ5ue0zMHQoXHEFrFwZH/0GXMWXDu+glPKFb76B//s/mD/fjh+0c6eddWzSJDjrLDuuUJcE+zrsbHgHETlHRN4SkV0iMjpk+RAR+U5EaoPlzpB1o0TkTREJiMhtIiKR1KE9CgoKXB9C+ZjGV3zYfXe44AI7mNzGjXDvvTBsmH1aaOxY20Zw+eV2/fffe13bRq7iK9Lr3GrgLOD5ZtatM8YcFSyXhSy/A/gNMCxYMiOsQ5vWrVvn+hDKxzS+4k///nDxxfaW0GefwT/+YS8A5eVw+ul2/cSJcOed3vchcBVfXSP5sDHmHYD2fnkXkYFAX2PMK8H39wP/BTwZST2UUipc/frZXwQXXGC/8T/7LFRVwRNPwKJFdptDDrGDzJ1yih1xtE8fT6scFREl/zYMFZHXga+Aa4wxLwCDgPUh26wPLmuWiEwFpgKkpKSQlZXVsG7OnDkATJs2rWFZdnY2OTk55ObmUldXB0BqairJycmUlZVRU1PTsG15eTmBQICSkpKGZXl5eWRmZjY5Tnp6OkVFRRQXFzeZUaeqqorq6uomgy4VFhaSlpbW5LncjIwM8vPzKSgoaLiCJycnU15eTkVFBZWVlWGdU2lpqZ5TjJxTbW0tFRUVCXVOifjv1NFzWrmynCVL1nPddcv4/POjKSsbwW239aBrV+jT5x3693+T/v3fYPz43lx//VXOzqm2trbhv2FHz6k1bTb4isjTwD7NrJppjFkY3OZZYIYxZkXwfQ9gd2PMJhEZBfwfMAI4CLjRGDM+uN3xwBXGmAmtVgJt8FVKeev7722v4qefhmeesXMS79xpp6ccPdo+SfSzn8Gxx0JKite1tSJq8DXGjDfGHNZMWdjKZ7YZYzYFX68E1mET/wZgcMimg4PLnKqoqHB9COVjGl/+0LMnnHwy3HADvPwyfPklLF4MM2bYYSdKS207wYABMHw4/OpXdjC611+H7dvDP66r+HLyYJOIDBCRpODrA7ENu+8bYz4FvhKRscGnfKYALV5EoiX0p6BS0abx5U99+tjhJGbPtp3HtmyB55+HG2+0yX/xYvv00NFHQ9++djiK3/0O7r8fVq+GHTvadxxX8RXRPX8ROROYCwwAnhCRWmNMBnACUCwi24FdwGXGmLrgxy4H/gfYDdvQq429Sqm4t9tu9tZP/dSTxsC//20HoVu+3Jb77oO5cxu3P+IIOPJIOOoo+/rww+2FojNE+rTPY8BjzSx/BHikhc+sAA6L5LhKKRXrRGxv4qFDITvbLtu5005M89prtofxqlXw0ENw992NnzvgADu5/YgRtmzenIoxdn9RrZ8fevgGAgEddlc5o/GlImEMfPwxvPEGvPmmLatX24vEDz9Av347qatLCmvfrTX4unzUUymlVBtEYP/9bZkQ8tzjjh0QCMDKlf+hlSfiw5ZgI1k0L/SZWKWiTeNLudC1q52ucsGCy9reOAy+SP5KKaWa0uSvlFI+FDcNviKyBXivlU32ALa0sC4F+CLqlXKvtXOK1eNEsq+Ofra927dnu7a20fiKnWOFuy9X8dWebb2KrwOMMQOaXWOMiYsC3B3uemCF1/V3cc6xeJxI9tXRz7Z3+/Zsp/EVP8cKd1+u4qs928ZifMXTbZ+qCNfHo846p2geJ5J9dfSz7d2+PdtpfMXPscLdl6v4as+2MRdfcXPbJxIissK08KyrUpHS+FIuuYqvePrmH4m7295EqbBpfCmXnMSXL775K6WUasov3/yVUkqF0OSvlFI+pMlfKaV8yPfJX0QOFJH7RORhr+uiEoOI9BaRchG5R0TO97o+KrFEK2fFdfIXkb+JyGcisvpHyzNFZI2IBETkytb2YYx53xhzsduaqnjXwVg7C3jYGPMb4IxOr6yKOx2Jr2jlrLhO/tgZwTJDFwSnj5wHnAYcCmSLyKEicriIPP6jslfnV1nFqf+hnbGGnZv64+BmOzuxjip+/Q/tj6+oiOvx/I0xz4vIkB8tHgMEjDHvA4jIAmCiMWY2MAGlwtCRWAPWYy8AtcT/FyzVCToYX29H45iJGJiDaPzWBfZ/xBZnQhCR/iJyJzBSRK5yXTmVUFqKtUeBs0XkDhJzWAjVOZqNr2jlrLj+5h8NxphNgJvZEpQvGWO2Ar/2uh4qMUUrZyXiN/8NwH4h7wcHlykVbRpryiWn8ZWIyX85MExEhopId2AysMjjOqnEpLGmXHIaX3Gd/EWkEngZGC4i60XkYmPMDiAfqAHeAR40xrzlZT1V/NNYUy55EV86sJtSSvlQXH/zV0opFR5N/kop5UOa/JVSyoc0+SullA9p8ldKKR/S5K+UUj6kyV8ppXxIk79SSvmQJn+llPKh/w9YjqQ8wT851wAAAABJRU5ErkJggg==\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "source": [ + ">Let us recall the \"love equation\" between Romeo and Juliet:\n", + "$$\n", + "\\begin{cases}\n", + "\\dot{R}=aR+bJ \\\\\n", + "\\dot{J}=cR+dJ\n", + "\\end{cases}\n", + "$$\n", + ">\n", + ">But now lets consider the case when in our model of love there is an external control $u$ (psychologist, family or mistress of one of the partners) and this signal can affect the level of love between Romeo and Juliet with different coefficients:\n", + "\\begin{equation}\n", + "\\begin{bmatrix}\n", + "\\dot{R} \\\\\n", + "\\dot{J} \n", + "\\end{bmatrix} = \n", + "\\begin{bmatrix}\n", + "a R + bJ + e u\\\\\n", + "c R + dJ + f u\n", + "\\end{bmatrix}\n", + "\\end{equation}\n", + ">\n", + ">State space representation of this system is given as:\n", + "\\begin{equation}\n", + "\\begin{bmatrix}\n", + "\\dot{R} \\\\\n", + "\\dot{J} \n", + "\\end{bmatrix} = \n", + "\\begin{bmatrix}\n", + "a & b \\\\\n", + "c & d \n", + "\\end{bmatrix}\n", + "\\begin{bmatrix}\n", + "R \\\\\n", + "J \n", + "\\end{bmatrix} +\n", + "\\begin{bmatrix}\n", + "e \\\\f \n", + "\\end{bmatrix}\n", + "u\n", + "\\end{equation}\n", + ">\n", + ">Let us also imagine that we are Romeo's close friend, so we can trace all the output about their love only from him. Naturally, Romeo may downplay or exaggerate his feelings, so let's take his opinion with a coefficient $g$. We're a good friend, so we try not to influence his relationship with Juliette in any way, and we don't bring any additional input into the output. This mean that our dynamical system will have following form:\n", + "\\begin{equation}\n", + "\\begin{cases}\n", + "\\dot{\\mathbf{x}} = \\mathbf{A}\\mathbf{x} + \\mathbf{B}\\mathbf{u} \\\\\n", + " \\mathbf{y} = \\mathbf{C}\\mathbf{x} + \\mathbf{D}\\mathbf{u}\n", + "\\end{cases}\n", + "\\end{equation}\n", + "when $\\mathbf{x} = \\begin{bmatrix}\n", + "R \\\\\n", + "J \n", + "\\end{bmatrix}$, $\\mathbf{A} = \\begin{bmatrix}\n", + "a & b \\\\\n", + "c & d \n", + "\\end{bmatrix}$, $\\mathbf{B} = \\begin{bmatrix}\n", + "e \\\\f \n", + "\\end{bmatrix}$, $\\mathbf{C} = \\begin{bmatrix}\n", + "g & 0 \n", + "\\end{bmatrix}$ and $\\mathbf{D} = \\begin{bmatrix} 0 \\end{bmatrix}$\n" + ], + "metadata": { + "id": "Dzw6DMe7Otg3" + } + }, + { + "cell_type": "code", + "source": [ + "from scipy.signal import ss2tf\n", + "import numpy as np\n", + "#@title **Love model**\n", + "#@markdown Romeo's parameters\n", + "a = 0 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "b = 5 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "\n", + "#@markdown Juliet's parameters\n", + "c = -1 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "d = 0 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "\n", + "#@markdown Control parameters\n", + "e = 8 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "f = 4 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "\n", + "#@markdown Output parameter\n", + "g = 6 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "\n", + "\n", + "A = np.array([[a, b], [c, d]])\n", + "B = np.array([[e], [f]])\n", + "C = np.array([[g, 0]])\n", + "D = np.array([[0]])\n", + "G = ss2tf(A, B, C, D)\n", + "\n", + "sys = TransferFunction(G[0], G[1])\n", + "\n", + "w, mag, phase = sys.bode()\n", + "\n", + "f, (ax1, ax2) = subplots(2, 1, sharex=True)\n", + "ax1.semilogx(w, mag, color=\"blue\") # Bode magnitude plot\n", + "ax1.grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "ax1.grid(True)\n", + "\n", + "ax2.semilogx(w, phase, color=\"blue\") # Bode phase plot\n", + "ax2.grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "ax2.grid(True)\n", + "show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 325 + }, + "id": "k4oZD4ZEOH1v", + "outputId": "15dccdb3-9674-463e-901e-7e37524070d5" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "name": "stderr", + "text": [ + "/usr/local/lib/python3.7/dist-packages/scipy/signal/filter_design.py:1622: BadCoefficients: Badly conditioned filter coefficients (numerator): the results may be meaningless\n", + " \"results may be meaningless\", BadCoefficients)\n" + ] + }, + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "code", + "source": [ + "w_des = w[np.argmax(mag)]\n", + "\n", + "t, u, y, x = Control_system(A, B, C, D, w_des)\n", + "\n", + "plot(t, x[:,0], linewidth=2.0, color = 'b', label = \"Romeo\")\n", + "plot(t, x[:,1], linewidth=2.0, color = 'm', label = \"Juliet\")\n", + "grid(True, color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "ylabel(r'Level of love ${X}$')\n", + "xlabel(r'Time $t$')\n", + "legend()\n", + "show()\n", + "\n", + "plot(t, u, color = \"red\", label = \"System input\")\n", + "plot(t, y, color = \"blue\", label = \"System output\")\n", + "legend()\n", + "grid(True, color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 531 + }, + "id": "R0p73yXV_dXG", + "outputId": "62446c6f-dc60-430a-c861-fb3db64be105" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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ppWkk/IjqTZlomMfDxBcsXqzSYI8bp3oPFot6LyQEVq6EY8f8rdA4Dh9Ws6ZTUiAsrMqtbbWehGZkAo1z3khERkZSVFRkXhgbkVJSVFREZGSkv6WYnMPU1cHf/qaeP/kkCKGe9+wJv/qVuvMOoo6CU/bsUcv+/d3fNtCHmwIhBNardOvWjdzcXAoKChyuV1tbS3Ygz423gx7dkZGRdOvWzUuKXGOuNg4RZJi6XeOzz1Q21IEDzy6+M2MGvPsurFgBzz1nPxFeMB3rxqhU+vSBu+5yT7dpJPxMWFgYvXr1crpecXEx8fHxPlBkLMGqOy0tzd8SdGHqdo3//Ect77ijuRehcdFF0K2bGm7auBEuvLDtNoLpWGuJEFJT3dedkqKKEBUUQEUFOEkY7XPO+eEmV7GduBJMmLp9i6nbOXV1sErNEeOGG87+3GJRQ04A779vv51gOtZaTyI11X3dFosahgM4dMhYXUZgGgkTExND+fZb5bAeMAC7OYwmT1ZLm8nLQY1mJJwVGrKHNthhGgkTE5Nznk8/VcvrHaTkvPBCNaySleXanIlApqGh+eJuGolzGC0vT7Bh6vYtpm7nrF2rlo6mBoWHw+WXq+dfftn2OsFyrE+eVOGviYmqbKke3YFsJMS5FBo6atQoqZUANTEx8T1FRepiGRGhhpwcRVq/8grMmgV33gnvvOMziYbz/fcqgmvsWDVhUA///rfy01x3HXz8sbH6XEEIsUVKOaqtz8yeRCOzZs3ytwRdmLp9i6nbMd9+q5YXXujYQABcfLFabtjQ9ufBcqxtndagT3cg9yRMI9GIln432DB1+xZTt2PWrVNLbSjJEcOGqRKe+/apFB6tCZZj3dpprUe3ZiQOHlSpEAMJ00iYmJgYxg8/qOWllzpfNywMxoxRz390LydeQGE7R0IvHTsqf0ZlZdsG05+YRqKRYJyQBqZuX2Pqtk91NezYoeL+R7U5un02F12klm0NOQXLsW493KRHtxCBO+RkOq5NTEwM4ccf1UV/8GDXy3GuWqWctZdd1hwVFWwkJ6vZ0rm50LWr/nZuuAE++kilLPn1r43T5wqm49oFVqxY4W8JujB1+xZTt320qpzaEJIrjByplpmZZ4/FB8OxLi9XBiIyErp0Ue/p1a31JA4fNkabUZhGohHbGrHBhKnbt5i67ZORoZajR7u+TZcu6k68tPTsi2MwHGtNc8+ezYkK9eru3l0tAy2FumkkTExMDEHrSbhjJISAESPU823bjNfkbY4eVcsePTxvS0vMbBoJExOTc47SUhXKGh4OQ4a4t20wG4kjR9RS6wV4wnnnqaVpJAKUhQsX+luCLkzdvsXU3TZbt6rl8OHKULjD8OFq2dpIBMOx1noStkZCr27TSDhBCBEihNgmhPi08XUvIcRGIUSOEOI9IYSbp56JiYmv2L5dLbVegTsEc0+iLSOhl06dIDRUzZOorva8PaMIGCMBPATYllj7E7BQSpkGlAD/580vnz17tjeb9xqmbt+iR/dHH6m75fbt4Zpr/FPL2NvHWwt5dXeoCSAtTc28PnECSkqa3w+Gc6Qtn4Re3SEhzSG0x497KMxAAsJICCG6AdcCbza+FsAVwL8bV0kHHCQeNjEJTN5+W8W/b9+uwiX/+181lyAry9/KjMUTI2GxqNoTAMFWQdhInwQE5pBTQBgJYBHwGNDQ+DoBKJVS1je+zgU8mKZiYuJ7MjNh+nT1/Lnn1AXl2muhuBimTIHaWv/qMwqrFXbvVs/1GAlQtbAhuIxnXZ3q/Qjh2SQ6WwLRSPi9xrUQYiKQL6XcIoS4TMf204HpAImJiUyaNKnpM82BZNv9mzJlClOnTmXatGkUFxcDkJqaypQpU1iyZAlrbEplpaenk5OTw4IFC5remzFjBhMmTGjxPaNHj2bevHnMnz+fTVocILBq1SpWr17N0qVLm96bO3cuaWlpLUocjh8/npkzZzJr1qym5GDx8fGkp6ezYsWKFnHXrffp+PHjrFixos19WrRoUcDu0/Hjx5u+z53fyd/7NGXKFJd+p5deWsi0ad2wWiPp0eNTNmz4Kz16TOG996bSpUseO3Z0Yvjwdxg/frtP9un48eNkZGQYeu5pv9Po0VOprobIyELuuOM3un6nzZvTgWk899xHnDixg3nz5hEREdFiX33xf9L2yZVzr6oqiYaGt0lKOsONN97YtP3ARoun53fKzp4G3MTevVVMmtQ87drb++QQKaVfH8DzqJ7CYeAUUAUsBwqB0MZ1LgTWOGtr5MiR0sQkEPjwQylBypQUKU+fbvnZf/+rPktIOPuzYOSDD9T+TJigv42PPlJtjB9vnC5v8913SvMFFxjX5uLFqs177zWuTVcANks711W/DzdJKedIKbtJKXsCtwDfSClvBdYCNzWuNg3waimOYCq6boup27e4oltKeOYZ9fyJJyA2tuXn48crv0RRke+K7XjzeHvij9Boa7gp0M8RzR/ReiKdJ7oDcbjJ70bCAY8DDwshclA+ire8+WVaFyzYMHX7Fld0b9miHgkJcPfdZ38uBGgjAX/9q2/qB3jzeBthJHr1UtXsjh2D06fVe4F+jtgLf/VEdyDOug4oIyGlXCelnNj4/KCUcoyUMk1K+Ssp5Tni5jM513njDbW84w4V2tkWkydD587qzjmYaymAMUYiNBT69VPP9+zxXJMvMHKOhIbWk8jNNa5NTwkoI+FPUj2pGOJHTN2+xZnuykrQkoDec4/99cLCYOpU9fz99w0S5wBvHe/qasjJUTH+WhirXloPOQX6OWLPSHiiOylJ9ahKStS5FBDYc1YE48N0XJv4m/ffV47HsWOdr7thg1q3WzcprVbva/MGmZlqH/r187ytp59WbT3+uOdt+YKBA5XezExj201NVe1mZxvbriMIZMd1oOA0DCxAMXX7Fme6/904/fOmmxyuBsDYsWoMOjcXNm40QJwDvHW8taGh/v09b6tPH7Xcv18tA/kckdJ+T8JT3YHmvDaNRCO28dzBhKnbtzjSXVMDn32mntuEzdvFYmle72Ovxu5573hrKUY0f4IntDYSgXyOlJZCRQW0awdxcS0/81S3NjHvxAmPmjEM00iYmBjEV1+pC8f55zdXGXPG1Ver5RdfeE+XN9GMhBE9ibQ0tczJ8U3ElyfY9iKEMLbtlBS1NI2Eick5xurVamkz0dYpP/+5clRu2wb5+d7R5U204SYjehJxcZCYqJzhgXKBtIc2FKQNDRmJaSQClPT0dH9L0IWp27c40q2NMowf73p7UVHKUAB8+aUHwpzgjeMtpSo0BMYYCWg55BTI54gWoqrNa7DFU92mkQhQcnJy/C1BF6Zu32JP98GDapgkLs698p3QbFS8OeTkjeN94oQaXktIUA8jsDUSgXKOVB+s5tC8Q2RNzeLI80eoK6lrSuXdVmI/T3VrRuLkSY+aMQzTSDRim3QsmDB1+xZ7urUL/JVXqolh7nDFFWr5/fceCHOCN463kZFNGrZGIhDOkVP/OMWmQZs4suAI+SvzOfT7Q2T0y6B2WxnQtpHwVLfZkzAxOQfRjIQ7Q00aQ4ao/E6HDgVWsRlnGBnZpKEZiUDoROS/n8+eO/fQUNNA0s1J9HuzHx0u6UBdQR1Xrt5BTyoMSxFuS5cuanniRGA48J0aCSFEulk61MTEPg0NsHatej5unPvbh4bChReq5+vXG6fL23jDSGgRTloYrL+oOVLD3rv3goRez/Vi0HuD6PJ/XRi2dhhJNycRYbXyB7JISbAa/t1RUdCxo6pXUVRkePNu40pP4hjwoxCip+2bQoihQoi3vSHKH8yYMcPfEnRh6vYtbenetUvFzXfvDj176mv3kkvU8ocf9GtzhDeOtzeHm3Jy4P77/XOOSCnZe89erKetJF6fSPcnmmfLWUIt9H+7P7mWaHpSRcTHZ894M+JY2/Ym/I1TIyGl/H/AH4CvhBDXCiGuF0KsA94B1nlXnu+YMGGCvyXowtTtW9rSrfkSfvYz/e1620h443h7oyfRvj0kJ6uJiUOG+OccKfmyhJIvSwiNC6Xv3/oiWk2EqBUhvNigrFnhK0c5k3emxedGHOtA8ku46pP4DlgNrAJeB+ZJKUdKKf/hNWU+ZpI7we0BhKnbt7Sl2wgjMWaMGnbavr05VbaRGH28q6rUhLLQUOjd29Cmm3oTN9/8pLENu4CUkoNzDgLQ/YnuhCedPdJ+/DhspyPbohJoqG4g95WWKVuNONZBZSSEEH8BdgIVwADgG+C3QohoL2szMQl4pDTGSMTEwIgRyr+RkWGMNm+yf7/a99RUldHWSLQkqlVVnY1t2AVK15ZSsbWCsE5hdH2wba+0FlyQ0UcNQx1fepy60jpDdQSVkQC2A/2llE9IKfdKKacCPwI/CSH6eleeyblAeTksXw4LFsCyZer1ucLBg+qPnJDgeapsbX7Fli2e6/I2WvSRdtdvJFpKk6qqZOMbd0Luq6pX0PWBroREh7S5jmYk5IAOxF0Wh/W0lbxleYbqCKS5Ek4juqWUf23jvZeEENuAz4E0bwjzNaPdnQEVIAS67vffh/vuA9tiXR07wlVX3e4/UR7Q+njb9iI8zeEzapRaesNIGH2eaEYizQv/fs1IREUNNL5xB1QfqqbokyJEuCDl3hS762mzrbt2hZQbUyhdV8rJN07SdWZXhBCGHOtg60m0iZTyG+ByA7X4lXnz5vlbgi4CWfdf/gI336wMxIUXwqOPqmVJCbz33s0+q+9sJK2Pt+Zo9mSoSUMzEps3e95Wazw9T+qK6qjYUUFdiRpWOXBAve+NukBahFi7dh6UutPBib+eAAnJtyQT3sl+1L/tbOvEyYmEJYZRubOS8k2qi2zEf/KcMBIAUsoAyXjuOfPnz/e3BF0Equ6PPoKZM9Xzl19W8f8vvKCWzz+v3r/nHtiwwX8a9dD6eGt1ILR5Dp4wYICKkT90yPj4eL3nScWOCraP2876xPVsHraZ9Unr2f2r3RTsrgG825PYudN345KyQZK/XGVY7HJPF4fr2hoJS7iFTtM6AWp2NhjznzxnjIQRCCHOE0KsFUJkCSF2CyEeanw/XgjxpRBif+Oyozd1bNq0yZvNe41A1H38ONx1l3JsPvsszJ7dPBQjBDzxBPTu/SFWqyrhWVXlX73uYHu8q6pUqc2QEBg+3PO2Q0OV8xqMH3LSc54UfFjA1rFbKfmqBEukhegBKlal4N8F3PXTZvpz2is9ia5dlTO8oiKW6mrj22+L0m9Lqc2tJbJnJB0u7uBw3dZ5mzpNUUai8INCpFUa8p/s3OizP3lSBTP4E5eNhFDcJoSY1/i6uxBijAEa6oFHpJQDgQuAGUKIgcATwNdSyj7A142vTYKA++9XQ0pXXw1z5rS9Tv/+6QwfDkeOqB5GMJKZqf7AgwapHoAReHPIyR2Kvywm69dZNNQ00Pmuzlx44kLGZI3hwiMX0mFcR2Ib6vkTO0g+Y7yFDwlprvZ2+LDhzbdJ3j+V4zn51uSz5kW0prWRaHd+OyJ7R3Lm1BnKfigzRE9EhEqbbrVCQYEhTerGnZ7EX4ALgSmNr8uBpZ4KkFKelFJubXxeDmQDXYHJgJZzNx243tPvMvE+X30Fq1apXERvvmnfmWuxWFm8WD3/05+anYHBhHYh1y7sRuBN57Wr1B6vJeuWLGSdpNusbvR7sx9hHVWca0TXCCJfGsIGEmhPPfum7qbhjPG3utqQ06FDhjd9FtYaKwX/VlfiTrd2cryutTniSBsSEkKQ9KskQOV7MopAmXXtjpEYK6WcAdQASClLAENzOjWm/hgBbAQ6SSm1ALBTgONfz0NWrVrlzea9RiDptlrhkUfU89//vvlP1BarVq3ikktULeiaGnjpJd9o9BTb461dyL1hJIzuSbh6nkgp2fObPdQX1xM/IZ7Ul1LPurM+eNTCMwygJCqSyh2VHHnuiLFi8a2RKP2mFOtpKzHDYogZEONw3fx8dZ4nJqq7fY3km1W4bsG/C/jk408M0RUofgl3khrXCSFCAAkghEgCDLuFEEK0Az4AZkkpT9uemFJKKYRoMx+iEGI6MB0gMTGxxWzHhQsXAjB79uym96ZMmcLUqVOZNm0axY1xmampqUyYMIGcnJwW9WnT03YqY/oAACAASURBVNPJyclpkfp3xowZTJgwocX3jB49mnnz5jF//vwW45GrVq1i9erVLF3a3OGaO3cuaWlpTJs2rem98ePHM3PmTGbNmsWBxrCR+Ph40tPTWbFiBStXrrS7T/n5+Tz00ENt7tOiRYtYsmSJz/bpyivfZseO3xEVlU94+AfA/Xb36ZVXXiE5OZmysl7Aq/z1rw1kZd1OePhph7+Tr/ep9e+UlpbG6tWrOXDgAOvWLQW6M3IkTn8nV/dJSgshIe9y9GgUX3yxlcWL/2DIPuXn57N48WKn517fE32ZtHUSoQmhZE3K4snJzbOetX16/PFvqGY6r7cvZU51JEefO8qLO17kaN1Rw36nXr1UhNDLL/+H1avfcft3cuf/VPKPEgC+rP6S+ZPmO/ydFi78F3AzZ84cZNKkh5r3af4C7o66mw55HXjlgVeY9fosj8+9rKwtwDjmzFnMoUNC9zUCnJ97DpFSuvQAbgU+AXKBZ4G9wK9c3d5J22HAGuBhm/f2Al0an3cB9jprZ+TIkVIvEydO1L2tPwkU3VarlIMHSwlSvvGG8/VtdV9zjdrumWe8KNAgNN3l5VIKIWVoqJTV1cZ+x9ix6nh8841xbbpyntRX1csNPTbItayVx18/bne9Bx9U+v78Zymzbs+Sa1krd0/dbZxYKeWKFeo7brzR0GbPosHaIH/o9INcy1pZnlnudP2PPlK6rr327M/23r9XrmWtfLbvs4Zo+/3v1XfNn29Icw4BNks711WXh5uklMuBx4DngZPA9VLK913d3h5CdRneArKllC/bfPQJoN0eTAM+9vS7TLzHZ5+pbKgpKXC7m/PkfvtbtXzzTf9HcrhKZqaK3hoyBCIjjW176FC13LHD2HadcXzJcWqP1BIzNIYud9sPA7WdI9FrQS9EuCB/RT4VuyoM0+Kr4abTG09Tl1dHZM9IYoY6HmqCs53WtsRfHQ9Az/yehmjTIpxOnTKkOd24E930MFAupVwqpVwipcw2SMPFwO3AFUKIzMbHNcAfgXFCiP3ALxpfmwQoWoTSI4+0HKt1hXHjoEcPFcnizTrPRqL5DEaONL5tfxgJa7WVYy+paU+9/9QbEWI/wkczEmlpENkjsmlewbEXjZs25SsjUfhRIQCJ1yc6jWqClrOtW9Pxio6IcEGX0i6cKThz9gpuEnRGAogFvhBCfC+EmCmEMMSRLKX8QUoppJRDpZTDGx+fSymLpJRXSin7SCl/IaUsdt6afubOnevN5r1GIOjesUPNPI6NVRPkXMFWt8XSvN1fz0oCE1hour3htNbQjMTOnca16ew8OfXOKery6mh3fjvix8fbXc9qVfmqoDn763kPnwcWyF+RT+3xWkP0JidDZKSVkhIoMyaqtE0KP242Eq7gqCcREhNC3KVxCATFazy/XAWdkZBSPi2lHATMQPkIvhVCfOU1ZT4mzRtTR31AIOh+/XW1vOMOZShcobXu3/xGGYtPP1VzLAKFhtoG8t/PZ+89e9kxcQcRiyI49Y9TbM9QFcm80ZMY0piNYtcudVE2AkfnSUNdA8f+rHoB3ed0d3hHnZurKqZ16aIy1wJE9Y4i6cYkZJ0kd7ExscxCQI8eKlbFW72JmmM1VO+tJiQ2hPYXt3dpG0dGAiD+GmVgi//7P2gkbMhHhaQWAb5P0+glbKMjggl/6y4vV5ldQSXyc5XWulNS4PLL1QXoww8NFOgBRZ8VsbHfRrJuzuLkmycp/qyYkpUl7Jm2h7n7NvKzkMKmC7qRdOwI550H1dXNQzue4ug8KfiggJrDNUT1iyLphiSH7WiJ/VrPtO72cDcATr11yrB5EyUl2wDvGYmSr9XdSNxlcVhCXbsUOjUSE5SRKPmyRAvA0Y2tkfBnrWt3fBIPNFak+xpIAO6RUg71ljCT4GDFCqioUJXVBg/2rK1bblHLd9/1XJcnSCk5NO8QOyfupPZILdEDo+n9594M/ngw3wz6BtJiSOIM8627OPnnwx5fDNrCl36JE6+rQPxuD3Vz6IsA+4n92o9tT8yQGOoK6yj8pNAQXdHR6hbaW7OuS78uBaDjL1zP+OPMSET3i6Y8opy6gjoqd1d6pK9dO4iOVulfKoyLCXAbd3oS56HmMAySUj4lpczyliiT4EDK5qGm++/3vL1f/lLlL/rmGzVpyR9IKTnw8AGOLDgCFuXEHbV9FN1/153E6xLZ1msbW+8dxev0RgKH5x7myHzjJ5P5ykhUZldS9m0ZIe1C6HSbczejrdPaFiFEU0TUyTeNKYIQFaVmQR89akhzLZBSUvKV6kl0vNI1I1Ferh6Rkaq31xZCCI4lqqG70rWlHmkUIjCGnNzxScwBZKPTeqYQYpgXdfmc8ePH+1uCLvype8cOFQoaHw833ujetm3pjo+H8ePVOPx//mOQSDc5+vxRchflIsIEgz8eTPfHurcYihg/fjybtwreozunpg8ECxx+6jCnlhn7LzbaSNg7T078VfUikm9NJjTW+dxae8NNAJ1u64SIEJR8UULN0RrdWjUuuEBNOT5ivA2mKruKM6fOEN45nOiBrhXZtO1FOAqE6nCpShDoqZGAIDMSQojfAstRfohk4J9CiAe9JczXzNTyWgcZ/tT9z3+q5S23uB/2ak/3L3+plp8Yk9nALYrXFHPoyUMgYMCKASROPDviZebMmU2RTf3vS6bPq6o0277791G1z7hkd5qvwygj0dbxtlZZyUtXie0cFdmxxV5PAiAsPozEyYkgIX+l513B6dMnAN7pSWi9iLgr41wKfQXnQ00av1ygTuLSb0uRDcb5JfyFO8NNd6PyN82TUs5DZWx1MeAx8Jk1a5a/JejCX7qtVuWPALjtNve3t6f72mvVXdo330ClZ0O6blGTW0P2bWrqT8/5PUm+qe2YjPvvf4J9+yA8XGV/TXkgheQpyTRUNpA1NYuGOmOctn37qu84dAhOn/a8vbaOd8H7BdSX1hM7JpbYEc7D0qR0XmwoeYo6bvnvem4k3npLpebwRk9Cc1q7OtQEzUaiWzfH6815ZQ4R3SOoL66nYodnzoRgMxICsA3Isza+d05wwKgwEh/jL91r16rEY717wwUXuL+9Pd2dOsHYsVBb67uJdVJK9ty5h7rCOjpe1ZEev+9hd93MTPWXGTZMXcSFEPR9rS8RPSKo2FLB8SXHDdEUFtZcM3v3bs/ba+t4a+mxHc2utiU/XzlQ4+LU0GBbJFydQEiHECoyK6jc45mVP3kyk/BwKCw0tuZIQ30DpesandY6jISznsSBgweIuzwO8HzISTMSecaW0HYLd4zEO8BGIcRTQoingJ9Q6TRM/gfRhppuu83z2s6t0fKi+WrI6VT6KUq/LiUsMYwBywYgLPZ3qKxMjbPYTqIL7RBK36V9ATj8h8PUnjBmQtmgQWqZbVRuAxtqT9ZS8k0JIlyQdJPjsFcNR0NNGpYIC0m/bEyb7eGQkxCS885Tz48ZWAOzfHM51tNWovpEEdnd9ZwqrhoJgI6XK+PjqZHo1BhLEBQ9ica8SncBxY2P30gpF3lLmK+Jt3drFOD4Q3dVFXzwgXquZ6gJHOvWjMRnn3k/l9OZ/DMceERd/VIXphKe7Dj7fXX1QODsSXQJ1yaQcF0C1nIrB584aIi2geqryDIgjrD18c5/Lx8aIOGahKZaEc5w5LS2JfmW5iEnT8KD4+Pjm4oPGTnkpCf0FRyn5LAlPj6+uSfxXSnSqv8YBNtwE1LKLVLKVxsf27wlyh+kp6c7X8lDamuhtBTOeJ7WpQlf6JZSUnOshvIt5VTsqGDVsjNUVKhhoT599LXpSPfgwSqXU34+ZGToFO0iOQ/nUF9cT8fxHZ0WnAEICVFja22l40hbmIYIE+T9M8/jGHkw1ki0Pt5aPefkW12fD+tKTwIg7oo4wpLCqN5XTeVO/cchPT29yUgY6bx2N/RVw9WeRHp6OpHdI4noEYG1zOrRuRAURkIIUS6EON3Go1wIYYBLLTBYoXlhDeTMGfjoI7j1VpWwTIuvjoxUjsnf/tbz8WZv6AZVGL54TTG7b9nNhuQN/NT9J7aM2sLmYZvpdN8GlrGR30XnUJWjb7DYkW4h4Jpr1PMvvtDVvEuczjhN/vJ8LJEW+r7W12mUS0mJulBGRjZfwG2J6h2lkt1JODTX82nCRhoJ2+Ndta+K8s3lhMSGkHBtgsttOHNaa1hCLSRcp9rVciPpYcWKFfRodA8Z1ZOwVlkp21AGgqa7fVdx1Uhox1qrlV22Xn/yqaAwElLKWCll+zYesVJK1xKeBAG2RTs8paYGXnlF/ZluuEFFAR0+rCaKtW+vLoL798Pixequ+bbb9E8eM1I3qF5D4ceFbBq0iR0TdlDwXgF1hXWEJYYRMyyGiH7RVBFCN6pJXJtLRt8M9k7fy5lC97pHznSPG6eW3nJeSyk58Ji66nWb1Y2oXs6LVG/dqpbDhinHclv0+H89sERZKPywkNObPLuHSk1V33PkiOczbm2Pd94K5QVNujGJkKgQl9twdbgJmhPmaVlW9bBy5UrDexJlP5Qhz0jand+OsHjXhtkA6uuV81iI5rKi9tCOdYdLPDcSmk8iL89/afT15G4yccD338Pw4TBrlhrDHDBA1XDeuVPl4ikrU0bkxx/hgQfUXeny5equcd06/2qvOVbDjvE72HX9Lqr2VBHRPYJez/RizL4xXJR/EaMzR7N5xhgmcTErLxpB5zs7I0IEJ984yaZBmyj5xrjMfJdfDiEh6jgZEQLamqLPiij7tozQhFC6P9HdpW1cqWkd0SWCrg+qW80jz3p2+xsaCv36qed79njUVBNSSvJXuD/UBK4PN4Ea77fEWKjYWuHRxDqtJ2GUkWgKfXXTH3HqlLpIJyfbv0FoTVNP4gf9RiIiQo0+1NdDsVfzYNvHNBIGcfq0uuj//Oewdy/076+GmnbtgsceUz2G0MYJrWFhKmx06VL1+ZVXQlGRunv+xz/8oz9vRR6bhmyi5MsSQhNCSVucxticsfR4sgfRfaKbhmKWLYMGLFzx2w70f6c/o3aOosOlHajLr2P7uO3kLjEmC2hcHIwZo+ZjGG08G+obOPiYci73nNuT0A6uVfHVJtE5y/x63sPnISIERR8XUZntmW/CyCEnUJE91furCe8c3hSB4wplZSoUNSrK+Z00QEhkCAlXez7kZLTj2tv+CFtiBsUQ0j6E2iO1HqVQ9/eQk2kkGtHqwurh009VuOJrrylDMHcubNsGkyer9NeOSE2FNWvgd79Tdwt33ql6Fr7QDSCtkgOPHiD71mysZVYSJicwJmsM3WZ2wxLWUvzevbBpk0oHrkUgxfSPYfjXw+n+ZHdogJwHczj8tPOkd67ovuoqtTR6yOnUO6eoyq4isnckKfe7NtMYXOtJAIR3CqfLXY2FeF7wLHbTKCOhHe+85WqoKfmWZKfJ/GzRehG9e7se8uzpkNPChQubQmBzcz1Pm15XVEfFtgpEhGgaCnIVd4yEdqxFiKDDRcHvl3DFcb2scfmQ9+UEF/n5MGWKumDm5qo7361bYf5890pahoTAn/8MzzyjZrVOmwZf+aBSR315Pbuu38WxF48hQgV9XuvD4A8H2w0D1YzXjTeq7JQaIkTQ+5ne9HuzX1MuI0+HWqDZL2Gk89paaeXwvMMA9H6uN5Zw1+6TiorU7OfIyIamSW6OOO93qhBP3vI8anL1D7cY2ZOQVtk0Ezp5qveGmjTir4lHhApKvy2lrqjOre/TiIpSQzx1dZ5fJEvWloCEDhd1cMsXA/p6EkBTnQpPhpwC3kgAI4UQKcBdQoiOQoh424e3BfqK2bNnu7yulJCervwN776rLpgLF8KGDXhUX+DJJ+GJJ9Qd0803NzsKjdJtS/XharZdtI2iT4sIjQ9l6JdD6XpfV7sRPlK2nEDXFl3+rwsDVw4EobKjasnj9OoeM0Y5+vftM2644djLxzhz6gyxo2NJutm1SWTQ7LSOitrbNGzoiKjeUST9qrEQzyL9Q3BGGYnZs2dT8k0JdXl1RPWJInaUi9WhGnE1ssmWsI5hxF0WB1blA3IX7RwxynndND/CzaEmUNkFwDUjYXtunwsRTq4YiddRNST6A1taPTZ7T1pgsns3XHqpGhYqLlZDIrt2KUd1iHs3J23y7LNw3XUq3HLyZGPTEWiUrS9j65itVO6qJLp/NOdvPJ+Olzn+42zYoO6ku3aFyy6zv17yzcn0fU3NPt73wD4KV+kfjw4LUw5sMGbI6Uzemabhn9Q/p7qc2A2ah5o6dHDBcjfS/VF1dTv55knqK+pdF2pDnz7qvDp0SAU+eEKTw3pqslv7DvqMBNgMOXlQY8Io57VepzV40JMY0x4RKqjIrKC+XN85EPBGonHi3ADgbSllbyllL5tHb28LFEJMEELsFULkCCGe8Pb32eP4cZgxQ0Uuff89JCUpJ/Pq1c1F243AYlF37P37q7vHRx81rm2AU8tOkXlFJnUFKk/RiB9HEJ3mPFWyVn1u6lTnxjDl3hR6Pt0TGiD71myPcvgY6Zc4PP8w1gorCZMSiLvUvRh5zUjExe13eZvYkbG0v6g91jJrU54kdwkPV4aioUH1qPQSag2l4ANVn6HTVPfL07sT/mpLwiTlvC5eXYy1Rp9TwQjndc3RGqr3VxPSPoR2I9u5vb1eIxESE0K7Ee2gAU5v1BemF/BGQkNKeb8QYphNPQmvV6UTQoQAS4GrgYHAFCFEG9OYPGfKlClnvSelmvF7zz1qLPYvf1FDQffdp5y4t99ufN4iUI7hlSvVnfRf/qIc4+7obgvZIDk45yB77tiDPCPpOrMrQz4bQlic83i+2lr417/U89tvd+nr6DG3B0m/SsJabmXX9buoL2t5F+Wq7l/8Qi2/+cazOPGqvVVq+MsCvf/o/r2NFtk0ZUo/t7bTwmGPLz6uO0WFEUNOt/e5HWu5ldhRsUT3da1+gi16exKR3SNpN7wdDZXNSfVcRTtHjOhJNJUqvdz1UqW2aEYixYU4h9bntjbkdHp9cBoJ12L/aKonMR3QysEsF0L8TUq52CvKFGOAHCnlwUYN7wKTAUOr4lUWW/n54BvJ+rqakrwGDu9t4MDWOvZlnKEu/wwdqWMWZ+jXuY60TvWEr6sne2A99afVhU+ECESYICwxjPDO4UR0iyBmSAzthrcjdmQs4UmO8wG1xfDh8Nxzqicxfbq6QMS1cfM7depUp23Vn64n+7ZsilYVQQj0ebUPXR9w/Zbo88/V8NewYa77XIQQ9Hu7H1V7qqjcWUn2HdkM/mhw0zCHK7pB3UV366YCA3buVBr0cPD3B8EKXe7pQszAGLe2LSxUd7HR0fDII9e6tW3SjUkc6HKAqqwqSr8p1TUePnCgKsLkiZHoe7QvhRS6PTcC1E1Cbq7qQfawnyDXLgnXJVCRWUHRJ0UkTHB9hrd2jhjRk9Ab+qrhTk+i9bnd4ZIO5C7K1e289reRCPR6El0B2xjC3Mb3DGXFRTnkDPuR/F9spO7WTXSdv4Wff7qDu/P3cD8HuYVjjCePnqeKqd9+mqo9qqpVQ1UDDVUNWMut1BfXU72vmrLvyshfkc+hOYfYefVONiRvYPOIzRx4/AClP7hXhOThh+Gii+DkSZgzp+11HBW4B6jKqWLrhVspWqUc1MO+GOaWgYDmoSZ3k/mFtgtl8EeDCY0LpeiTInJfaXbgOtOtIYSaRwLw9dfufb9G2foyCv9TiCXaQs+nerq9vdaLOP98uOsu13RrWMIsTWG2uYv1ObA97UnUldSR90keWCD51+4biUOHVK+6e3fXJ5LZog05Fa0qcqs3pZ0jnjqupZQe+SNOn1Yz3qOi2r5Ra03rc1uLcDr902ka6t3vDvvbSLjckyBA60kIIaajejgkJiYySQvgpzle2TbaYMqUKUydOpVp06ZR3DiFcUTpbBIJp84iqEVSH1JPTVgNfcd2ITy5nHXb11IZUUl1eDXX3HwNl1x9CXc/dDe1YWqCzMgRI3l09qO8+vSrHNxykA5VHUg6ncTl511O6cZSKjIrqMis4NgLxxCdBIk3J/Jy5svkt88HoUpLzpw5k1mzZjXl/Y+Pjyc9PZ3Jkz/jxx+v4vXXw9ix4zHS06e32KeMjAxWrFhx1j6lpqYyZ/Qcdt29i5CaEArbFfLRsI94dfirZGRksGDBgqZjMmPGDCZMmNDi2I0ePZp58+bxxBMv8PHHswELa9bcxe9+l87q1atZunRp07pz584lLS2txZ9D26c5r85BpAomb5nMvkf20eGSDny671NWr17d9H3OfqcdO4YBD7N48W4efngQS5YsYc2aNU3rpqenk5OT0/Y+TZzElPVTSCGFQ6MP8fOUnzN//nw2bdrUtO6qVasc7tP+/TcDtxMamklxcXGbv9OKFStapL6w3afo2mjusdxD4SeFVB+q5r6n7mvxOy1atMjhPp0+3RNYzKZNFUC7Nn8nR/s05OgQrmq4CssYC5URldw06aazfidH+5SXNwr4AykpVeTknHD6fzprnyRMj5gOubDxnxt59l/Pnv07tbFPP/30E5MmTeLMmfbAco4exa1zT9unhNMJ3Jl3J+Fdwvl468esfKzt38nePlVUdANeo2tXWLrU+bmX35hjx3afHuj4AFElUSx8cCHrcte1+TvZ2ycpLVgsH1JUZOHBBx/h8OF9bf5O7uxT69/JIVJKlx7Aw8B24KnGRyYwy9Xt9TyAC4E1Nq/nAHPsrT9y5Eipl4kTJ+re1hH1VfWy6Isiuf/h/XLDeRvkWtY2PTYO2iiP/OmIrMmtcdjG//t/UoKUAwdKWVvrXHdtQa3Mui2r6Xt23rhT1pXV6dL/+uvqu8eN07V5E3tn7JVrWSt/TP1R1pXVuXW8jx9XGmJizt5/Z5xaeUquZa1c33m9rCvXdwyuv159/7Jl+s8T7ffI+V2O29tWVUlpsUgZEuL+/ksp5dZLt8q1rJUn3jnh/sZSyldeUft/3326NpdSSrnn3j1yLWvloacOubyNdqwbGqSMilIaysrc/+5ji47JtayVWbdnub+xlPKrr9R3X3qpa+u3dY5k3a5+/2OLj+nS0KWL0nBM3+ZOATZLO9dVd+tJ/Abf1pPYBPQRQvQSQoQDtwBeKUWT6q5HzkVCokKIHxdP2ktpXHD4Akb8MIKUGSmEJYZRtbuKg48f5MfzfmT7uO2c+sepNkMln3xSjc1nZcHLL9vX3VDXwPHXjpPRN4O8f+ZhibbQ942+DHp/EKHt3ek0NqN3qKk1qS+m0m54O2oO1LDv3n2k9nb9eKekqGivykr3Uodba5prO/Rc0JPQdvqOgTbcNGqU/vOk62/VEN/JN09irXQvyicqSs10tlrdj3CqOVpD2bdlWEOsTcWA3EWv09qWxOvcD4XVjrUQnjmvjfJHuOK0hrbPkWB2XrtbT2Kr9GE9CSllPTATWANkA/+SUhpQzPFsFi3yfv0kYRF0uLgDfZf05cITFzL4k8Ek3ZSECBOUfFXCnml72NBpA9m3Z1P8ZXFTsZLISBXlBGo2t60Db9GiRdQV1ZG7RGVk3f/AfupL6uk4riOjto0i5e4Ut2PiNfbsgfXrISYGfvlLz/Y9JDKEge8NxBJjIf/dfB4f+rhb2+vxSxx/9Ti1R2qJGRJDl9+4VqKzNXl5qipau3Yqvbve86T96Pa0v6A99aX1Takx3EGb5e1ulTqtOlznGzvrvlHQG/5qS9wVcViiGxP+uTgD3fZY63VeN9Q3UPqtiqqKu9K9sGcNd8Nf2zpHmmZe65xUFzRGwh9IKT+XUvaVUqZKKZ91voU+nI7LGYwlzELipEQGvT+Ii05dRN+/9qXDJR1oqGog75957LhqB+uT1rPj2h0cfuYwQwrzeOiKMs6rLuf528so+KCAwwsO8+mAT9nQZQM5D+ZQc7iGqH5RDHx/IEPXDNUV6mjLG2+o5ZQp6iLpKdF9o5sm2mXfn03FTtfzX7trJGpP1DalBkl9MdWtPEW2aMP8I0eqOSyenCdaOGzuq7luh8PqdV5r8zM2x+mf92pETyIkMoT48SpBQ9Gnrs2+tj3WensS5ZvKsZZbieoXRWQ3N3Ll2OCukWjrHIkZGENoXCi1x2qpOeZ+mhbTSAQAts4oXxPWMYyU6SmM+H4EYw+MpefTPYlKi6K+pJ7iz4s5PPcw2VOyuf6bbfyVLdzy/TZ237Sbw/MO025PO6RV0nF8Rwa+P5Axu8eQfJP7M2pbU1urUo+ACsE1is63d6bznZ2x1FnYfePupjBiZ1x2mbpI//STGnZyRs7sHKyn1cS5+Kv0Z4/RJtGNHq2WnpwnSTclEd45nKrdVW7XPtZjJCp2VFC5q5LQ+FD+k/sf5xu0gdWqoptADXl5QlOU0yeuGQnbY623J+HpUBO4l5ID2j5HhEXQ/kL9vQl/1ro2jUSAEdU7ip7zejJ2/1guOHIBA5YPoNvsbiT+MpHYMbFUdWvHHmLZFpVApxndWHX+Ki46eRHDVg9TxkHnHXNrPvpIJbUbNsx51lN36bO0DwWxBVTvr2bv3Xtduqvu2FGFoNbVqRnvjihaXUTBvwqwRFvos1hnfdVGtJ6EZiQ8wRJuEw77qnvhsJqRcGe4SetFJN+cTINF30zE48dVhcVOnTzvTSZcmwBCTWxzN02J3jDYki8bjcQ4/UZC72zr1nhSXyKgexKtypeW27w+p8qXBiKR3SPpNLUTaS+nMfiDwYzcOJKrDo3itaEjebh6CCs6prEvZZ/drK2e8Le/qeU99xg/qzwkOoRVI1cREhtCwfsFHF983KXttNnXjoac6ivq2f+ASp3R8+meRPbQN8QAam6AZiSMMpQp96YgwgRFnxRRfcj1ZEz9+6vl3r0qpbwzpFU2+SM63eZ+Gg4NPdlf7RGeHE77C9sjz0hKvnCvQJWeMqb15fWc/vE0hOBW7YzWuOu4tkfTfAkdzuuANhKyZfnSWJvX51T50taF4gOV0NBmJ/YLA7wBUwAAIABJREFUL8DcucsM/47sbJUGIypK1ef2Bos+WES/t1WKiwOPHHCpC+6KXyJnVg41h2qIGRZDt4e6eaTx6FEoKICEhOb8XJ6eJ+GdwtWENgnHl7pmHEHdxXfvru7qDx50vn7xF8XU5tYS2TuS9he1163bCH+ELe5EOdlq1tOTKF1XiqyXtB/b3uXCUq2xWpsvzK4aCXvHuinZ3w73k/1pRuLkSbc2MwSXh5uE4jYhxNzG1+cJIcZ4T5pvyXElL3eAcPHFcNdd6oLx4IMCnSmB7KLVA5o2zbUZpnrIyckh+aZkus3qhqyXqmRqjuOUtxdfrMo5ZmaqobDWFHxQwKm3TiEiBAP+OeCsoknuYtuL0HpTRpwnWjjsqbdOuRUO645f4uSb6mrS5f+6IITQrdtoI5FwXWPCv8+ao/fsYau5WzflkzpxQg05uoLWW/FkqCkvTxmKpCSVbNEV7B3rkGibZH8/udeb0IxEnr48kR7hzr/oL6jJbVpikgpU8r1zAtsZk8HAn/4E8fGQkdGB9983rt38/OYSqrNmGddua7Tj3fvPvYm/Op66wjp2Xr2TM4Vn7G4TFaXSlEgJa9e2/KxqbxV7/k8Vgk59MZV2gz0Px2rttLbV7QktwmHdyA7rql/iTN4Z5RwOgc53qquLXt1GhL/aEt0/mqi0KOoK65xeKG01h4WpO/mGBpVHyhWKv1Qziz0JXHDXaQ2Oj7Xe+hJaydiAHG6yYayUcgZQAyClLAGMHww3cYnERHj+efV89mwoLzem3ddeU5FNkyZBP/cSnurCEmph4HsDaTe8HdU51ewYt8OhoWhryKmuqI6dE3diLbOSeEMiXWcYk97LSKd1a7TehDvhsK72JE6ln0LWSxKuTSAiJcITmYb3JIQQTVFO7taYcGfIqeZoDdV7VWrw2DHuFViyxSintYZev0RsrLpJqqw07r/uKu4YibrG1N0SQAiRBHiQvNnEU+6+G+Li9nLiBDz1lOftnT4Nixtz+j78sOftuUpobChDPhtCVJ8oKjIr2H75dmpPtF04XjMSWnnXMwVnyLwik+qcatqNaMeAZQM8Dv8Fdcfqak1rPSTdmER4l3CqsqpcduJqE+ocGQkpZfNQ0z36JhA2t2W8kYDmISdXQ2E13HFeN0U1XdFRV2pwDaOc1hpNM6/dTPYnhP+c1+4cvVeBD4FkIcSzwA/Ac15R5QdmzJjhbwluY7HAggVFWCzwyisqlbYnvPKKGuu/+GJVfc+btD7eESkRDP92ONEDoqncVcnm8zdTsu7si+eoUaqkaU4O5HxVybafbaNyRyVRfaMY8ukQQmIMKA8I7N+vjGZKSssLhFHniSXc0tSbOPKcayE7trOu7dXWKPmqhOr91YSnhBM/oXmYRY/uoiJ1DGJjVc/VKDpc3IHQjqFU7amiar99P1Rrze4YieIv1FCTJ/4I0NeTcHSsI7pEENkrEmuFlcqd7hXjCngjIaVcDjwGPA+cBK6XUho4Gu5fJkyY4G8Jupg58yIeeEA51+6/X39hnpISePFF9fyZZ7xTTMmWto53RBdlKOIuj6Mur47tl28n+45sKrOb/0yhoTDhgjNM4xBHr91C9d5qYobEMPzb4R4Prdhib6jJyPOk6wNdCY0Lpey7Mkp/cD65rmNHNTZdXW3/Qpn7shqw7zqza4s7aD26bXsRRp4PljAL8dc0zr5eZb830Vqzq8NN0iqbJ9H5wUg4O9ae+iV8HeHkTnTTw0C5lHKplHKJlNLNLDKBjW1a32Bi0qRJLFigJjutX988S9pd/vAHddd45ZWOa1gbhb3jHZ4UztAvhtLjDz0Q4YK8ZXlsGriJjX02kvmLTDaP3Mx9X/3InRzBcqaBTtM6cf6P5xPR2TgDAWpmN8CYVvF7Rp4noe1Dm1J1HH3WtdhOR87ryt2VFK8uxhJtIeXeluMjenQbOUeiNa6EwrbW7GpPouzHMuqL64lKiyIqLcojnXqMhLNjrdcvEfA9CSAW+EII8X1j+VL9M3RMDCUuDl56ST1/6CH3M4Vu2QJLl6rKY62zzPoDS6iFXk/1YkzWGLrc04WQdiFU51RT+nUpFVsrEEh+Ip6n4ofT/50Bhg0x2bJhg1pefLHhTbeg20PdsMRYKF5dzOnNzi8ajpzXuYtUL6LznZ0Ji9dRHagV3vBHaMSPj0eECcp+KKOuyLWYVleNhNY7SZiU4LF/Sk90kzM6XKKvJxHwRkJK+bSUchAwA+gCfCuE+MprykzcYupU+NWvVOTDjTe6lt8IVCTT9OlqmGrWLBjq9crlrhOVGkW/v/Xj4uKLGbltJEO/GMqIH0ZwcdElLOo0lG+L49zOiuoKFRWwfbsymt6IbLIlLCGsqVLgwccOOo10sue8rjlaw6l/nAKBx5MINfarieteMRKhHUKJuzQOrFD0X9cc2LbDTY4Ok62R8BSjo5tAf7K/gDcSNuQDp4AiwP1aiAHKaG9fDbyEplsIeOstlb5h1y6VudWVSUePPgpbt0LPnsZESLmKO8fbEmYhdngs8ePi6XBxB8LiQj0uaeqIjAxlNEeMUHWtbfHGedJ9TndCO4ZSuraU4s+LHa5rrydxeP5h5BlJ8i3JbWb/1aNb65F6KxTaWZRTa82xscovU1OjZsK3RfWBaqqyqwjpENJ0x66XykooK1MTOOPdmGrh7FjrTfbnL5+EO1XiHgDWAbtRlekGurqtrx6eVKY7V8jKkjI+XlWxuvlmx5XMXn5ZrRcWJmVGhu80GsFbbyntkycb3/aCBart3/7W+LbtcfSlo6pa4YCN0lpntbtefr7SFhurKrZJKWXl3kq5NmStXBuyVlbuqzRET0ODlHFx6rtOnjSkybOoOlQl17JWfhf7nbTW2t9nW4YPV5rsna9aFbpdv97lsb69e9V39erlcVNncfiZw3Ita+W+mftc3mbTJqVn+HDj9WBEZTrgPFS50kFSyqeklDrLsgcm8+fP97cEXbTWPWAArF6t7rr+9S+44ormsWWN+nqYM6d5LsQbb3h/WKU1nh5vrSexbp1rCe/cQfNHXHTR2Z956zzpOqMrkb0iqcquIvcl+1OKk5JUOGp5uRovl1KSMzsHrMoXEd2n7Roi7uouKoLSUnUedfKS9zGqZxQxQ2OwllspXXd2dFdbmp2lDNcc4YmTPI/Z1TvU5Mqx1lOEKBiGm54EBtvkbup+LuVusi0iH0y0pXv0aJW2omtXFfE0aJBK1PfqqzBvnhqy+OMf1Zj766+rHE2BoNsdevRQY+VlZWq4zCgaGuDHH9XztoyEt84TS4SlqSDToT8conKPfaeS7ZBT4X8KKf68mJAOIfR6ppfdbdzVrQ019e3r3XDoxOvVxTz/vfyzPmtLs6PiQ2fyzlC6rhQRJppCbD1Br9PalWPdfkx7RJigIrOCuhLXHPeasc7PVyHvvsIdI7GUlrmbyjmHcjeda4wcqaKW7rhDOadXrFCRTwsWKIdkaqoaz7/3Xn8r1Y83/BJ79qg76G7d4LzzjGvXFeLHx9P5rs7IWkn21GysVW1fCTTn9f4NNey7T13Nez/b29AwYFsj4U063aqufAXvF9jdX1scRTgV/KcAGqDjVR0J6+h5dJc3nNYaIdEhyi8haSqv6oywMNWLbGiw75PxBmbupnOYTp3UvIkDB9REufvvV47qTz5RcfbenlXtbVqn6DCCb79Vy7Z6Eb4g9aVUIlMjqdhWwZ7f7GkzU+rAgRCJlaTXsqgrrKPjVR2bihkZhbed1hrRfaOJHROLtdxK4cfOczk5MhJabyT518bE0xidkqM1WrW80m9cr1LojyEnv+ZuEkL8WQixRwixQwjxoRAizuazOUKIHCHEXiHEeE++xxVWrVrl7a/wCq7o7t0bHnlE1aF44QWVvC/M8xstjzDieF9+uVquX69mIRuBll1Wa7s13j5PwuLCGPLxEELahVDwrwKypmadlU58YPc6nmEnSXmniegWofJVWRyPCbmr21c9CYDOd6grX94/WmbEbUuzvVnXtSdrKfuuDBEumibqecqxY2rpbo/S1WMdd4W63JV87XoBpkA3Et7I3fQlMFhKORTYB8wBEEIMBG4BBgETgL80GiivsXr1am827zX+l3UnJanyqrW1zc5mT5BSOcLBvpHwxfGOGRTD0NVDVeW+fxWwadgmjr9+nNLvSsldnEvkjM2MpJQSEcbQr4a5VJnQXd2+NBJJv05ChApVKOlkc2LHtjTb60nkLc8DCfFXx+suMNQavUbC1WP9/9s79/goqmzff1cI4SnBEF6CiPJGEBSioOJzlBwV0aOjgh7joNcZhdHw0evo8aAO9+rxnHEGrgZl7szRyflcA75HUSeAIziOAhEQRUAgQUZ5vwQEDBCy7x+7OumEflS/qrrD+n4+/dnVVdVVv9pV3av3Y63V7tx2ZLXO4tDqQxzeFjqgZWP8CBmeUOwmIKHeOmPMPGNMYG7KYiDgBTQWmG2MOWyM+QaoBFI6SD5jRmYOr5zoupM5LrFqle3r7do1/I+jV/Wde0EuZ39yNm0Gt6G6qpr196xnxcUrqLyvkpoth6nMastEcw4HTw49m6kxseiura13pOuTWIpwV+Tk59Dhmg5QC1v/q94JIJTmTp2s38KePdbpERpFvp2QWOTbYOI1Em7rOisni9xR1pdj7wJ3XU5+ZKiLyZnOGPO1aRi7KZkBpScAf3GWuwHfBW3bRIIGSWmaJNNIBLciUh3g0A1tB7dl2NJh9C/tT/4N+bQ7vx0db+rIgFkDeLFgGFtp5SpLXaxs2mQd1rp0sRF3veCUibbjf8sLW6g9Gr4XW+T4Lqd9f9/Hj2t/JKdrTlJmNYFtnW7fbmcAdk2e3TmOWMcl/OhuSrRdFvWr5ITu6BJi06PGmLedfR4FaoCXYxYgcjdwN0B+fn6D4FrTnDyckydPrls3btw4xo8fT1FREXv2WO/WXk7cgZKSEubOnVu3b2lpKZWVlQ0yTU2cOJHCwsIG5ykoKOCxxx5j6tSpDaa/zZkzh/Ly8gb/LKZMmULv3r0pCpp3Onr0aCZNmkRxcTFVjlNDXl4epaWllJWVMWvWrLDXVFFRQVlZWchrmj59etpeU0VFRd35YrlPja+ppqYl2dmvsnQpFBaOo3nzg3Ff05NPtgPO56uvnqOi4ryQ1wTEdZ9iuaaw92lK/TVt2vJL4EqeeeZ9Lrnkqqj3qaKigoqKClf3qbp6FPAQ7dtvZ8yYu1J7Tc59KppexB1t76DDlg7MvHUm9756L+vWrWtw/wLX9P33nYGz+dnPnuC5564ip8R2t/2tzd/49+v/PaHvU+CaRoywkzibN9/JdddNiOmaduywA+hunr2yJ8oAWFO2hge3PQhE/j7Nm/ffwO289trH7N37x6Q9exEJ52Xn5gV8m8jnnWPcASwCWgetewR4JOj9XGBktGMl4nG9ZMmSuD/rJ6rbmFGjrCfqK6/Ef4wjR4xp184eZ8OG8PulS30/84zVOmmSu/1j0V1SYo99111xiouTTSWbzAIWmGUjlpna2tqwmu+80+p74QVjqjdVm4XNF5oFssAcqjqUNC0LF9pznH9+7J+Npa5ra2rNx3kfmwUsMAfXRveW//BDq2vUqNh1RYJEPK5F5AcR2R/i9QOQ0OQwESnEjnNca4wJzj7yDnCLiLQQkdOBPkBFIueKRu9UxEP2ANUN111nyzfeiP8Yn35qQ6X37w+nh/dJS5v6dpvKNEAsur0ctA6mc1Fnsjtks3/xfr6f/31YzcFe15umb8IcNXS8sSOtzkgsLHgwgfGI7nHESoylrqWZ1CWH2v1e9ECHaTm7yRhzkjGmXYjXScaYRLurSrAhyOeLyAoRmemccxXwKrAaKAcmGmNS6mNY5IfbcRJQ3fDP/2zL996Lfyrse+/Z8uqrI++XLvXtJpVpMLHoXrvWll4biey22Zz6oB0l3vj4RopuD605MMNp59ojbJlp3aJ7/KpHUrXEO2gNsT8jHa5xAh1GSMAUIC2NRCoxxvQ2xpxqjBnqvH4RtO1JY0wvY0w/Y8xfIh1HObHp2dN6mB88CEHdxTHx/vu2jGYk0oUePWyE2m3b7EyfZLJqlS0DrRUv6TapG807Nmf/4v0M2Dwg5D4BI9Hv0284duAYHa7pwEnDTkqqjk1O+CwvvO7zCvOgGez7eB9H90YO0dG+vZ3d9cMP7tMBJIqvRkJRksWNN9oyni6nf/zD/jCedFLqkwwli6wsGDTILn/5ZfKOu3+//YFs0cI6YXpNdttszvhPe+JLVl/CkZ1HjtunRw8YwD6Gbd+KZAu9nkl+wotEWhKx0vzk5uRemIupMXw/L7JjnYj3rQk1Eg6BmSuZhuq23HCDLd95x07fjIW33rLllVdCThS/tHSq7yFDbPnFF9H3das70H3Vv7+d/ukHXYq6kHtxLq2PtGb1TauPmxLbueUR/o01ZAGn3N+d1v3c+YrEQiJGIp5npK7L6d3Yu5xqj9ay7p517JqzK2rSqnhQI+EwadIkvyXEheq29OljkwTt3w9vvx3bZ2fPtuVNN0XfN53qO2AkVqyIvq9b3YGupjPPjFNUEhARBpYNJKdLDnsX7mXVT1fVRUr9ceOPrLn6S06hmnW0Jft/RJhlkACJGIl4npHgcYnaw5GjHTU2Ens/2suWmVvY8NCGhNO1hkKNhENxcbHfEuJCddczYYItX3zR/We++QaWLIE2bdyNR6RTfcfSknCrO9CS8NNIALQ4pQXzLp5Hdvtsdr+9m8WnLWZZwTIq+lZwYMUBdrdoySMM5tttyf8JO3TI5tNo3tx6eMdKPM9Im/5taHNWG2r21rCnPPIgU2MjsesNJ4fGDcmJWdUYNRIOVY0z82QIqrue8eNtX/r8+eGT0jQm4IN07bXWUEQjneo7kI981aroqWrd6vZz0Loxyw4u45zF59D+0vYc++EYPyz9AXPMpmidc9Uw9tAiZF6JRAkMWnfvbsd+YiXeZyQQNn172faI+wWnMa09WsvO123c8I43dozrvNFQI6E0GfLy4PrrbaA+N62JY8dsVj6A225LrbZU0K6dHVw+cqR+2mqipEtLIkDrfq0Z+uFQRmwcwdCPhzJy00gGzhpIl742jLHbPwOx4OWgdTCdbrHNlt3v7KZmf/h0i8EtiT3lezi66yitz2xN2yFtU6JLjYRDXiyZztMI1d2QXziTqGfMiD5FsLwcNm60znNuxxrTrb7ddjm50b1/v/2B9GtmU2OCNbc8rSXtL2xPi642sVKkvBKJkqiRiPcZadmjJbkX5VJbXcvO18JnFQo2EoHw6l1u75KS8QhQI1FHaWmp3xLiQnU35KKL4NxzbZ9ytNbEs8/a8he/cD+TJ93q262RcKM7HWY2BRNJc7Rc14mQqJFI5BnpeqftS9pcsjnsTKWAkTjw3RGb01vqu6pSgRoJh7KyMr8lxIXqbogIPPywXX7qKfvvOBSffgrz5kHbtnDnne6Pn2717dZIuNGdbl1NkTQHQqd8803yz5uokUjkGel0cyead2zOgRUH2PfJvpD7BMYkBm/YjDli6HBNB1p0S17q2saokXAIjqKYSaju4xk7Fs47zzbHg4Jz1nHsmM3UB1BcDB06uD92utW3WyPhRvfKlbZMh0FriKw5YCQ2brT3M5kkaiQSeUayWmRxys9tSLxvnwo9Kt+5M+RwjMsP2JAkpz6Q2sETNRJKkyMrC0pKbKti2rT6lKQBfvtbWLzY5i5+8EF/NCaLnj3tAPb27faVCJ9/bsuzz05YVspp1crev5qa+tlIyWLjRlv27Jnc47ql233daHZSM/b8ZQ/fLzzeA7tFC7i11Wbac5SWQ9qSe1FuSvWokVCaJMOHw69+Zf9lXn+9DeB37Jg1HoHuqJkzITe136+UI1Lfmli2LP7jGFPvlJcJRgLqB9eTOSvZGP+NRE7HHE59yLYOKosrj3Ouq95UzU8P28GY5veckbIB6zrCxRDPxFci+STWr18f92f9RHWHp6bGmBtvtPH3wZicnPrlp5+O75jpWN8PPGCv6fHHw+8TTXdVlT1Gp07G1NYmV1+8RNN8++1W8x/+kLxzbt1qj9mhQ/zHSMYzUnOgxiw6Y5FZwAKz9p61pta5KTWHaszyUcvNAhaY/82XZu7chE9ljEkwn4SiZCrNmtmQG08/DR07Wn+C00+HV16xrYymwrlO9veKBDKuBHc1pUPqVjcEWhIbNiTvmH63IgI0a9OMAS8PQJoLW17YwuqbV7PjlR188ZMv2PfxPg62yuEZ+nkS5E+NhENwqr9MQnVHplkzaxC2b7cznaqq3MVoCkc61vd559myosK2k0IRTXc6djVF05wKIxGYLZWIkUjWM5I7Ipcz3ziTrFZZ7HxtJ6tvWc3+T/eT0zWHip8OYS85aiQUJVmI2FDgmfIvORZ69LAxhnbvjv8HM5MGrQM4qelT0pKIlJ3QS/LH5FOwuoBu93ejw7UdOO3x0yhYWUDbQTaGzNatqdeQaGY5RVF8RsR2Ob37rm1N9IojvUImGolUDFynS3dTMK16tqLP9D4N1gV8JbQl4SHjxo3zW0JcqG5vSVfdgS6nJUtCb4+ke+tW2LLFtrTiMTCpIlpdd+5sp8Lu2QN79ybnnMnobvLiGQl4XXvRkhCTgiQVfjF8+HCzdOlSv2UoiufMm2fjT40cab3JY+HNN23Spssvhw8+SI2+VDFokI1cu3x5clpBffvC+vX2mOniVBiKNWusvt69rd5EEZFlxpjhobalRUtCRB4QESMi+c57EZFnRaRSRL4UkXNSrSFdEtzHiur2lnTVXVBgy+XL7SyuxkTSvXixLUeOTIGwBHBT18kcvK6trY8FFQggGA9ePCPdutly8+bwkxWShe9GQkROBa4Egn3Q/wno47zuBl5ItY49yc4m7xGq21vSVffJJ9t/locPh54KG0n3okW2HDEiReLixE1dJ3PweutWa2A7dnSXWyQcXjwj7drZuGM//pi8rrZw+G4kgGnAQ0CwPRwL/Lfj57EYaC8iXX1RpygZwqWX2rJxGJJIHDkCgR7adDMSbkjm4HU6DlpHIrg1kUp8NRIiMhbYbIxpHJ6sG/Bd0PtNzrqU0SudRuxiQHV7SzrrjmQkwun+4guorrZ98bEEOvQCN3WdzO6mwKB1otNfvXpGvDISKZ8CKyIfAF1CbHoU+FdsV1Mix78b2yVFfn4+Y8aMqds2bdo0oKFzy7hx4xg/fjxFRUV1zcJevXoxffp0SkpKmDt3bt2+paWlVFZW8r+CQolOnDiRwsLCBucpKCjgscceY+rUqXz22Wd16+fMmUN5eTkzZsyoWzdlyhR69+7doN9y9OjRTJo0ieLi4rrUh3l5eZSWllJWVtYgqmSoayorK8u4a6qqqqo7Xybdp+nTp8d9n1J9TZ98shZ4mY8+OkJ1dQ4LFza8poqKiuOuKSvrEeB8mjdfxJgxT6XVNeXl5TVYH+o+3Xbbk8BZfPLJVsaMubvuPsXzfVq//ibgXzh0aDUwMKFrAlL+fdq48WHgAt54YzElJU8mdJ8iEi5eR6pfwGBgB7DRedVgxyW6AL8HxgXtuxboGu2YicRueu655+L+rJ+obm9Jd91nnWVjDy1Y0HB9ON1XXGH3LytLvbZYcVPX1dXGZGXZV3V1YucrKrJ1MXNmYsfx6hl5+GGrd+rUxI9FOsZuMsasNMZ0Msb0NMb0xHYpnWOM2Qa8A9zuzHIaAewzxqR0RnDwv4NMQnV7S7rrvuQSW374YcP1oXQfPgx//7tdvuyy1OqKBzd13aKFHUOorU18XCIwlbRPn8j7RcOrZyTQ3ZTsUOmNSYeB61C8D2wAKoE/APf6K0dRMoNAru53342+76JFdnbM4MHWMS1T6dfPlmvXJnacZBkJrzghBq6DcVoUu5xlY4yZaIzpZYwZbIxRDzlFccFll9npm59/Dt+GTmxWR3m5LS+/PPW6Ukn//rZMxEjs2wc7d0LLlvU/vulO9+62PGGMhN+kW4J7t6hub0l33S1bQmGhXX777fr1jXUbA2+9ZZevvdYjcTHitq4DLYmvv47/XIFWRO/eNrNhInj1jJxwLQm/qays9FtCXKhub8kE3WPH2vLNN+vXNda9Zg2sW2envY4a5aG4GHBb18nobkpmV5NXz0jnzjYU/s6ddnwpVaiRcAiewpZJqG5vyQTdY8bYFsXChfUOYo11l5XZcuxYyE7TWNBu6zrYSMQboiKZRsKrZ6RZM28C/amRUJQmRvv2NmAfwEsvHb+9pqZ+/R13eCYrZXTpYiPYfv897NoV3zEybdA6gBddTmokFKUJctddtnz+eTh4sOG2P//Zhgbv2xcuvNB7bclGJPEuJzUS4VEj4RDwksw0VLe3ZIruiy+2iYh27YIZM+p119bCE0/Yfe6/P70z9cVS14nOcEqmkfDyGVEj4SGFgSkhGYbq9pZM0S0Cv/61XX7iCTjjDKt7+nSbK6FHD7jzTv/0uSGWuk5khtPu3TZxUZs29RnfEsHLZ0SNhIcEx1nJJFS3t2SS7sJCuPVW6zA3ZMguJkyABx+025591norpzOx1HUiRmLVKlsOGJCclpWXz4gaCUVREuL55+GCC6C6Op+XXrKzf556qn6abFNh0CBbfvVV7J9dvdqWZ56ZPD1e4YWRSNPJb4qiJIN27exU2HPP/Q033PA/ueIKO1bR1OjTx7aMNm603tO5ue4/G2hJZKKRCHhdpzJ+k7YkHAoC+R8zDNXtLZmoOzsbrrvuRx59NLMMRCx1nZ1d/yO/cmVs50m2kfDyGQk2ErW1qTmHmFQnSPWQ4cOHm6VLNcyTopyITJhg/T9mzIB7YwgJ2rkz7NhhWyGJ5Lb2i44d7Sy2LVviH3gXkWXGmOGhtmlLwmHq1Kl+S4gL1e0tqts7YtV81lm2/KJxnssI7NplDUTbtnbGVzLwuq4DuqMFdIwXNRIOwdmiMgnV7S2q2zti1RwwEl89jvzeAAAKc0lEQVR+6f4zga6mgQOT5zPidV0HjMR330XeL17USCiK0iQIGImVK933zy9fbsshQ1KjyQu0JaEoiuKC/Hw45RQbhmTDBnefWbbMlsOGpU5Xqkm1kdCBa0VRmgxXXw3vvw+zZ8PNN0fff8AA64D32WcwPOSwbfrz2mtw001w/fUNw8PHgg5cu6A8kKYrw1Dd3qK6vSMezSNG2HLRouj7HjhgYz1lZ9sUrsnC67rW7iaPmDFjht8S4kJ1e4vq9o54NI8cacvFi6Pvu2KF9UAfNCi5IUq8ruu+feE//gOmTEnN8X03EiLySxH5WkRWich/Bq1/REQqRWStiIz2U6OiKJlBQYGdpfT559GztTWF8QiAk0+Ghx5KXagVX42EiFwKjAWGGGPOBJ5x1g8EbgHOBAqB50WkmW9CFUXJCHJz7XTWI0esoYjEJ5/Y8rzzUq8rk/G7JXEP8LQx5jCAMWaHs34sMNsYc9gY8w1QCaQ0oMCUVLXVUozq9hbV7R3xag6MSwSMQCiMgY8/tssXXRTXacKSiXUdCb+NRF9glIgsEZGPRCQQ9KQbEOwasslZlzJ69+6dysOnDNXtLarbO+LVfMkltpw/P/w+lZWwbRt06mT79JNJJtZ1JFIeBVZEPgC6hNj0qHP+PGAEUAC8KiJnxHj8u4G7AfLz8xvEcp82bRoAkydPrls3btw4xo8fT1FREXv27AGgV69eVFVVMXr0aObOnVu3b2lpKZWVlQ0Sm0+cOJHCwsIG5ykoKOCxxx5j6tSpDbwt58yZQ3l5eYOBrClTptC7d2+Kiorq1o0ePZpJkyZRXFxMVVUVAHl5eZSWllJWVsasWbPCXlNFRQXTpk0LeU3Tp0+npKQkLa9p8uTJnOtEm4vlPvl9TXPnzq17XmK5T35fU0VFBXPmzEnqs5fqaxo5ciR9g37B3d6nkSOvA+7kgw+OcNVVt9Cs2dHjrunbb68EfsnQoQeoqtqW1GvasWMHS5YsSZvfCDfXFBFjjG8voBy4NOh9FdAReAR4JGj9XGBktOMNGzbMxMs111wT92f9RHV7i+r2jkQ0Dx1qDBgzf37o7ddfb7e/8ELcpwhLJtY1sNSE+V31u7vpz8ClACLSF8gBdgHvALeISAsROR3oA1T4plJRlIxitDMfMpTLwuHD9V1RV13lnaZMxW8j8SJwhoh8BcwGihzDtgp4FViNbW1MNMYcS6WQ0aMzc5at6vYW1e0diWgO/Pi//vrxcZwWLLCOdIMHJy/yazCZWNeR0LAciqI0OWproWdPGxn1o48azmAaN86G7XjiCXj8cb8UphcalsMFxcXFfkuIC9XtLarbOxLRnJUFt95ql3//+/r1e/bAW29Zh7uf/SxBgWHIxLqOhBoJh8CMgUxDdXuL6vaORDX//Oc2LtPs2TZGE8DvfmfHJEaPTk1XE2RmXUdCjYSiKE2Snj1ta6G21pavvAK/+Y3d1sT83VKKGgmHvLw8vyXEher2FtXtHcnQ/OST0K2bjQp7yy02XMe998L55ydBYBgysa4joQPXiqI0aaqq4L77bJfTzTfDr39tu6GUenTg2gVlZWV+S4gL1e0tqts7kqW5Vy947z0biuPJJ1NvIDKxriOhRsIh2K09k1Dd3qK6vSMTNUPm6g6HGglFURQlLGokFEVRlLDowLVDZWVlRob4Vd3eorq9IxM1Q2bq1oFrRVEUJS7USDgEx17PJFS3t6hu78hEzZC5usOhRkJRFEUJixoJRVEUJSxNauBaRHYC/4jz4/nYhEeZhur2FtXtHZmoGTJT92nGmI6hNjQpI5EIIrI03Oh+OqO6vUV1e0cmaobM1R0O7W5SFEVRwqJGQlEURQmLGol6/q/fAuJEdXuL6vaOTNQMmas7JDomoSiKooRFWxKKoihKWNRIACJSKCJrRaRSRB72W48bRORUEVkgIqtFZJWI3O+3JreISDMR+VxE3vVbi1tEpL2IvC4iX4vIGhEZ6bcmN4jIZOf5+EpEZolIS781hUJEXhSRHSLyVdC6PBGZLyLrnfJkPzWGIozu3zjPyZci8paItPdTY6Kc8EZCRJoBM4B/AgYC40RkoL+qXFEDPGCMGQiMACZmiG6A+4E1fouIkf8DlBtj+gNDyAD9ItINuA8YbowZBDQDbvFXVVj+BBQ2Wvcw8FdjTB/gr877dONPHK97PjDIGHMWsA54xGtRyeSENxLAuUClMWaDMeYIMBsY67OmqBhjthpjljvLP2B/tLr5qyo6ItIduBr4o99a3CIiucBFwH8BGGOOGGP2+qvKNdlAKxHJBloDW3zWExJjzN+APY1WjwVKneVS4DpPRbkglG5jzDxjTI3zdjHQ3XNhSUSNhP1h/S7o/SYy4Mc2GBHpCZwNLPFXiSumAw8BtX4LiYHTgZ3AS0432R9FpI3foqJhjNkMPAN8C2wF9hlj5vmrKiY6G2O2OsvbgM5+iomTCcBf/BaRCGokMhwRaQu8ARQbY/b7rScSInINsMMYs8xvLTGSDZwDvGCMORs4SHp2fTTA6cMfizVypwBtROQ2f1XFh7HTMDNqKqaIPIrtFn7Zby2JoEYCNgOnBr3v7qxLe0SkOdZAvGyMedNvPS64ALhWRDZiu/UuE5H/568kV2wCNhljAi2117FGI935CfCNMWanMeYo8CZwvs+aYmG7iHQFcModPutxjYjcAVwD3Goy3M9AjQR8BvQRkdNFJAc7sPeOz5qiIiKC7SNfY4z5nd963GCMecQY090Y0xNbzx8aY9L+n60xZhvwnYj0c1ZdDqz2UZJbvgVGiEhr53m5nAwYcA/iHaDIWS4C3vZRi2tEpBDbpXqtMeaQ33oS5YQ3Es4A0yRgLvYL9KoxZpW/qlxxAfAv2H/jK5zXVX6LasL8EnhZRL4EhgJP+awnKk7L53VgObAS+31PS29gEZkFLAL6icgmEbkTeBq4QkTWY1tFT/upMRRhdJcAJwHzne/lTF9FJoh6XCuKoihhOeFbEoqiKEp41EgoiqIoYVEjoSiKooRFjYSiKIoSFjUSiqIoSljUSCiKoihhUSOhKIqihEWNhKJEQUQ6BDksbhORzUHvc0Tk0xSdt7uI3JyKYyuKW9SZTlFiQESeAA4YY57x4FxFwEBjzK9SfS5FCYe2JBQlQUTkgIj0dLKR/UlE1onIyyLyExH5xMmsdm7Q/reJSIXTEvm9k/iq8TEvBH4H3Ojsd4aX16QoAdRIKEry6A38FujvvMYDFwIPAv8KICIDgJuBC4wxQ4FjwK2ND2SM+Ts2+ORYY8xQY8wGT65AURqR7bcARWlCfGOMWQkgIquwqTeNiKwEejr7XA4MAz6zgVlpRfgQ2P2Ar1OqWFGioEZCUZLH4aDl2qD3tdR/1wQoNcZEzHssIvnYTHI1kfZTlFSj3U2K4i1/xY4zdAIQkTwROS3Efj1J03zUyomFGglF8RBjzGrg34B5Tm6K+UDXELt+DeSLyFcikknZ5JQmhk6BVRRFUcKiLQlFURQlLGokFEVRlLCokVAURVHCokZCURRFCYsaCUVRFCUsaiQURVGUsKiRUBRFUcKiRkJRFEUJy/8Hy52xc/moCucAAAAASUVORK5CYII=\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "**Resonance** describes the phenomenon of increased amplitude that occurs when the frequency of a periodically applied force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillating force is applied at a resonant frequency of a dynamic system, the system will oscillate at a higher amplitude than when the same force is applied at other, non-resonant frequencies.\n", + "Resonance examples you can see by the following links:\n", + "* [How swing works](https://www.youtube.com/watch?v=UXo6WvHRs_I)\n", + "* [Tacoma Bridge Collapse](https://www.youtube.com/watch?v=3mclp9QmCGs)" + ], + "metadata": { + "id": "-uICgi0nEmeR" + } + }, + { + "cell_type": "markdown", + "source": [ + "## **Exercises**\n", + "> Plot Bode diagrams for the following systems:\n", + "\n", + "1. $$\n", + "\\begin{cases}\n", + " \\dot{\\mathbf{x}} = \\begin{bmatrix} 0 & 1 \\\\ -7 & -7 \\end{bmatrix} \n", + " \\mathbf{x} + \n", + " \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix} u \\\\\n", + " y = \\begin{bmatrix} 1 & 0 \\end{bmatrix} \\mathbf{x}\n", + "\\end{cases}\n", + "$$\n", + "\n", + "2. $$\n", + "\\begin{cases}\n", + " \\dot{\\mathbf{x}} = \\begin{bmatrix} 0 & 1 \\\\ -200 & -2 \\end{bmatrix} \n", + " \\mathbf{x} + \n", + " \\begin{bmatrix} 10 \\\\ 0 \\end{bmatrix} u \\\\\n", + " y = \\begin{bmatrix} 1 & 0 \\end{bmatrix} \\mathbf{x}\n", + "\\end{cases}\n", + "$$\n", + "\n", + "3. $$\n", + "\\begin{cases}\n", + " \\dot{\\mathbf{x}} = \\begin{bmatrix} 0 & 1 \\\\ -1 & -1000 \\end{bmatrix}\n", + " \\mathbf{x} + \n", + " \\begin{bmatrix} 0 \\\\ -2 \\end{bmatrix} u \\\\\n", + " y = \\begin{bmatrix} 1 & 0 \\end{bmatrix} \\mathbf{x}\n", + "\\end{cases}\n", + "$$" + ], + "metadata": { + "id": "hT0bEjnNNpLj" + } + }, + { + "cell_type": "code", + "source": [ + "# Put your code here" + ], + "metadata": { + "id": "6nrTtGv7GfRe" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "5hHBY9f_-VuS" + }, + "source": [ + "## **Homework exercises** for self-study\n", + "\n", + ">Redo the code to build Bode diagrams without calculating the Transfer function, based only on the State space model. Use [this link as reference](https://docs.scipy.org/doc/scipy-0.17.0/reference/generated/scipy.signal.StateSpace.bode.html)\n" + ] + } + ] +} \ No newline at end of file diff --git a/legacy - ColabNotebooks/Practice_5_FeedbackControl.ipynb b/legacy - ColabNotebooks/Practice_5_FeedbackControl.ipynb new file mode 100644 index 0000000..38030ed --- /dev/null +++ b/legacy - ColabNotebooks/Practice_5_FeedbackControl.ipynb @@ -0,0 +1,880 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "[Control theory] Practice 5.ipynb", + "provenance": [], + "collapsed_sections": [], + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "zPmrTNlSBW-R" + }, + "source": [ + "# **Practice 5: Basics Of Feedback Control**\n", + "## **Goals for today**\n", + "\n", + "---\n", + "\n", + "\n", + "\n", + "During today practice we will:\n", + "* Consider a linear state feedback\n", + "* Learn the pole placement method\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "kgF8BN0GTBfP" + }, + "source": [ + "## **Idea of Control and Feedback**" + ] + }, + { + "cell_type": "markdown", + "source": [ + 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)\n", + "\n", + "**Control Systems** can be classified as **open loop control systems** and **closed loop control systems** based on the feedback path.\n", + "\n", + "In **open loop control systems**, output is not fed-back to the input. So, the control action is independent of the desired output.\n", + "\n", + "![image.png](data:image/png;base64,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)\n", + "\n", + "Here, an input is applied to a controller and it produces an actuating signal or controlling signal. This signal is given as an input to a plant or process which is to be controlled. So, the plant produces an output, which is controlled.\n", + "\n", + "In **closed loop control systems**, output is fed-back to the input. So, the control action is dependent on the desired output.\n", + "\n", + "![image.png](data:image/png;base64,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)" + ], + "metadata": { + "id": "d9YRQjvf8Ii6" + } + }, + { + "cell_type": "markdown", + "source": [ + "In this course we will consider two type of tasks:\n", + "* **Stabilization** (regulation) a control system (stabilizer, or regulator) is to be designed so that the state of the closed-loop system will be stabilized around a **static point**.\n", + "* **Tracking** (servo) the design objective is to construct a controller (tracker) so that the system output tracks a given time-varying trajectory.\n", + "\n", + "A really nice visualization of control tasks are available [here](https://www.matthewpeterkelly.com/tutorials/pdControl/index.html)\n", + "\n", + "\n", + "One of the most widely used approaches supporting the solution of the problems above is the so-called **feedback control**" + ], + "metadata": { + "id": "HZzDdWf78uXK" + } + }, + { + "cell_type": "markdown", + "metadata": { + "id": "VMv9_G55JAVR" + }, + "source": [ + "## **Linear State Feedback**\n", + "\n", + "Recall the linear system in state space form:\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{x}}=\\mathbf{A}\\mathbf{x} + \\mathbf{B}\\mathbf{u}\n", + "\\end{equation}\n", + "\n", + "The general form of feedback that may stabilize our system is know to be linear:\n", + "\\begin{equation}\n", + "\\mathbf{u}=-\\mathbf{K}\\mathbf{x}\n", + "\\end{equation}\n", + "\n", + "Substitution to the system dynamics yields:\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{x}}=(\\mathbf{A} - \\mathbf{B}\\mathbf{K})\\mathbf{x} = \\mathbf{A}_c\\mathbf{x}\n", + "\\end{equation}\n", + "Thus the stability of the controlled system is completely determined by the eigen values of $\\mathbf{A}_c$ and consequantially by the matrix $\\mathbf{K}$\n" + ] + }, + { + "cell_type": "markdown", + "source": [ + ">### **Examples**" + ], + "metadata": { + "id": "ucdVrprh9opb" + } + }, + { + "cell_type": "markdown", + "source": [ + "> **Model of Love**\\\n", + ">Let us consider the example of \"love\" equations given in the first practice:\n", + "$$\n", + "\\begin{cases}\n", + "\\dot{R}=aR+bJ \\\\\n", + "\\dot{J}=cR+dJ\n", + "\\end{cases}\n", + "$$\n", + ">\n", + ">when $R$ and $J$ are time depended functions of Romeo's or Juliet's love (or hate if negative) and $a$, $b$, $c$ and $d$ is constants that determine the \"Romantic styles\". " + ], + "metadata": { + "id": "vjNqUXItX26g" + } + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 613 + }, + "id": "dMQ68HJ4H4zp", + "outputId": "c49239d4-0189-46ae-91d9-20dafb8ab7e8" + }, + "source": [ + "import numpy as np\n", + "from scipy.integrate import odeint\n", + "from matplotlib.pyplot import *\n", + "\n", + "def StateSpace_without_control(x, t, A):\n", + " return np.dot(A,x)\n", + "\n", + "def f(x, t, control=False):\n", + " R, J = x[0], x[1]\n", + " \n", + " dR = a*R +b*J\n", + " dJ = c*R + d*J\n", + "\n", + " if control:\n", + " dR+= -k_1*e*R -k_2*e*J\n", + "\n", + " return dJ, dR\n", + "\n", + "def draw_phase_plane(R, J, x0, plot_title, control = False):\n", + " # Phase space with stream plot\n", + " J_e_max, R_e_max = 10, 10\n", + " J_e_span = np.arange(-J_e_max,J_e_max,0.1)\n", + " R_e_span = np.arange(-R_e_max,R_e_max,0.1)\n", + " J_e_grid, R_e_grid = np.meshgrid(J_e_span, R_e_span)\n", + "\n", + " figure()\n", + " title(\"System dynamics \"+plot_title)\n", + " plot(t, R, linewidth=2.0, color = 'b', label = \"Romeo\")\n", + " plot(t, J, linewidth=2.0, color = 'm', label = \"Juliet\")\n", + " grid(True, color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + " ylabel(r'Level of love ${X}$')\n", + " xlabel(r'Time $t$')\n", + " legend()\n", + " show()\n", + "\n", + " figure()\n", + " title(\"Phase Plane \"+plot_title)\n", + " # Varying color along a streamline\n", + " L = (J_e_grid**2 + R_e_grid**2)**0.5\n", + " lw = 3*L / L.max()\n", + " contourf(J_e_span, R_e_span, L, cmap='autumn', alpha = 0.25)\n", + "\n", + " dJ, dR = f([R_e_grid, J_e_grid],t, control=control)\n", + "\n", + " strm = streamplot(J_e_span, R_e_span, dJ, dR, density = 1,color=L, cmap='autumn', linewidth = lw)\n", + "\n", + " plot(J, R, 'r-', lw = 3.0)\n", + " plot(x0[1], x0[0], 'ro', lw = 10)\n", + " hlines(0, -J_e_max, J_e_max,color = 'red', linestyle = '--', alpha = 0.6)\n", + " vlines(0, -R_e_max, R_e_max,color = 'red', linestyle = '--', alpha = 0.6)\n", + " xlim([-0.9*J_e_max,0.9*J_e_max])\n", + " ylim([-0.9*R_e_max,0.9*R_e_max])\n", + " xlabel(r'Love of Juliet ${J}$')\n", + " ylabel(r'Love of Romeo ${R}$')\n", + " tight_layout()\n", + " show()\n", + " return\n", + "\n", + "#@markdown Romeo's parameters\n", + "a = 0 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "b = 5 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "\n", + "#@markdown Juliet's parameters\n", + "c = 3 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "d = 0 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "\n", + "#@markdown How much did Romeo and Juliet like each other at first sight?\n", + "R_0 = 1 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "J_0 = 1 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "\n", + "A = np.array([[a, b],\n", + " [c, d]])\n", + "\n", + "x0 = np.array([R_0,\n", + " J_0]) # initial state\n", + "\n", + "Lambda, Q = np.linalg.eig(A)\n", + "print(f\"Eigen values:\\n{Lambda}\")\n", + "\n", + "t0 = 0 # Initial time \n", + "tf = 10 # Final time\n", + "t = np.linspace(t0, tf, 1000)\n", + "\n", + "love = odeint(StateSpace_without_control, x0, t, args=(A,))\n", + "R, J = love[:,0], love[:,1]\n", + "\n", + "draw_phase_plane(R, J, x0, \"without control\")" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Eigen values:\n", + "[ 3.87298335 -3.87298335]\n" + ] + }, + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "source": [ + ">Suppose we can control Romeo's feelings with the coefficient $e$. So our control system will have following form:\n", + "\\begin{equation}\n", + "\\begin{bmatrix}\n", + "\\dot{R} \\\\\n", + "\\dot{J} \n", + "\\end{bmatrix} = \n", + "\\begin{bmatrix}\n", + "a & b \\\\\n", + "c & d \n", + "\\end{bmatrix}\n", + "\\begin{bmatrix}\n", + "R \\\\\n", + "J \n", + "\\end{bmatrix} +\n", + "\\begin{bmatrix}\n", + "e \\\\0 \n", + "\\end{bmatrix}\n", + "u\n", + "\\end{equation}\n", + ">\n", + ">Let's set the control signal to the following form:\n", + "$u = -\\begin{bmatrix}\n", + "k_1 & k_2 \n", + "\\end{bmatrix}\\begin{bmatrix}\n", + "R \\\\\n", + "J \n", + "\\end{bmatrix}$\n", + ">\n", + ">After these changes, the dynamics of our system will have the following form:\n", + "\\begin{equation}\n", + "\\begin{bmatrix}\n", + "\\dot{R} \\\\\n", + "\\dot{J} \n", + "\\end{bmatrix} = \n", + "\\left(\\begin{bmatrix}\n", + "a & b \\\\\n", + "c & d \n", + "\\end{bmatrix}-\\begin{bmatrix}\n", + "e \\\\0 \n", + "\\end{bmatrix}\\begin{bmatrix}\n", + "k_1 & k_2 \n", + "\\end{bmatrix} \\right)\n", + "\\begin{bmatrix}\n", + "R \\\\\n", + "J \n", + "\\end{bmatrix} = \\begin{bmatrix}\n", + "a - ek_1 & b - ek_2 \\\\\n", + "c & d \n", + "\\end{bmatrix}\\begin{bmatrix}\n", + "R \\\\\n", + "J \n", + "\\end{bmatrix}\n", + "\\end{equation}" + ], + "metadata": { + "id": "dIL_3yjEAy6T" + } + }, + { + "cell_type": "code", + "source": [ + "def StateSpace_with_control(x, t, A, B, K):\n", + " u = - np.dot(K,x) \n", + " dx = np.dot(A,x) + np.dot(B,u)\n", + " return dx\n", + "\n", + "#@markdown Control parameters\n", + "e = 1 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "\n", + "#@markdown Gain parameters\n", + "# k_1 = 3 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "# k_2 = 1 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "\n", + "k_1 = 3\n", + "k_2 = 17/3\n", + "\n", + "B = np.array([[e],\n", + " [0]])\n", + "\n", + "K = np.array([[k_1,k_2]]) \n", + "\n", + "Lambda, Q = np.linalg.eig(A-np.dot(B, K))\n", + "print(f\"Eigen values:\\n{Lambda}\")\n", + "\n", + "love = odeint(StateSpace_with_control, x0, t, args=(A, B, K,))\n", + "R, J = love[:,0], love[:,1]\n", + "\n", + "draw_phase_plane(R, J, x0, \"with control\", control=True)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 613 + }, + "id": "CS89vIl4AyUu", + "outputId": "3a2e667c-1357-4eda-f93e-4ee60b3a07d5" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Eigen values:\n", + "[-2. -1.]\n" + ] + }, + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "LFhTSmgYWaDW" + }, + "source": [ + "> **Mass-spring-damper system**\n", + ">\n", + ">Consider a following unforced system:\n", + ">\n", + ">

\"mbk\"

\n", + ">\n", + ">Dynamics of this system desribed by following ODE:\n", + "\\begin{equation}\n", + "m\\ddot{y} + b \\dot{y} + k y = u\n", + "\\end{equation}\n", + ">\n", + ">And one can formulate this system in state space as:\n", + "\\begin{equation}\n", + "\\dot{\\mathbf{x}}\n", + " = \\mathbf{A}\\mathbf{x} + \\mathbf{B}\\mathbf{u} =\n", + "\\begin{bmatrix}\n", + "\\dot{y}\\\\\n", + "\\ddot{y}\n", + "\\end{bmatrix}\n", + "=\n", + "\\begin{bmatrix}\n", + "0 & 1\\\\\n", + "-\\frac{k}{m} & -\\frac{b}{m}\n", + "\\end{bmatrix}\n", + " \\begin{bmatrix}\n", + "y\\\\\n", + "\\dot{y}\n", + "\\end{bmatrix}+\n", + "\\begin{bmatrix}\n", + "0\\\\\n", + "\\frac{1}{m}\n", + "\\end{bmatrix}\n", + "u\n", + "\\end{equation}\n", + ">\n", + ">Let us simulate the response of the system with different parameters:" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "xx6wTlUAWZT8", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 293 + }, + "outputId": "1c34162e-3c41-4f55-db3a-cd7e2aba073f" + }, + "source": [ + "#@markdown Mass-spring-damper parameters\n", + "\n", + "m = 1 #@param {type:\"slider\", min:0, max:10, step:1}\n", + "k = 5 #@param {type:\"slider\", min:0, max:5, step:0.1}\n", + "b = 2 #@param {type:\"slider\", min:0, max:5, step:0.1}\n", + "\n", + "#@markdown Initial state\n", + "x_0 = 7 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "dx_0 = 0 #@param {type:\"slider\", min:-2, max:2, step:0.1}\n", + "\n", + "#@markdown Gain parameters\n", + "k_1 = -7 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "k_2 = -2 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "\n", + "x0 = [x_0, dx_0] # Set initial state \n", + "\n", + "A = [[0,1],\n", + " [-k/m, -b/m]]\n", + "\n", + "B = [[0],\n", + " [1/m]]\n", + "\n", + "K = [[k_1, k_2]] \n", + "\n", + "x_sol = odeint(StateSpace_with_control, x0, t, args=(A, B, K,)) # integrate system \"sys_ode\" from initial state $x0$\n", + "y, dy = x_sol[:,0], x_sol[:,1] # set theta, dtheta to be a respective solution of system states\n", + "\n", + "plot(t, y, 'r', linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'Position ${y}$ (m)')\n", + "xlabel(r'Time $t$ (s)')\n", + "show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "orDzncSidhQk" + }, + "source": [ + "**NOTE**\n", + "\n", + "> It is often the case (especially in fully actuated mechanical systems) that one can analyze system response and stability without actually transforming the system to state-space form, for instance, one may directly substitute control law to the system dynamics to analyze closed-loop response.\n", + "\n", + "For instance consider the mass-spring damper above:\n", + "\n", + "\\begin{equation}\n", + "m\\ddot{y} + b \\dot{y} + k y = -k_1 y - k_2 \\dot{y}\n", + "\\end{equation}\n", + "\n", + "which yields:\n", + "\n", + "\\begin{equation}\n", + "m\\ddot{y} + (b + k_2) \\dot{y} + (k + k_1) y = 0 \n", + "\\end{equation}\n", + "\n", + "It is obvious now which gains make this system stable\n", + "\n", + "In case of mechanical systems (system of second order equations), the matrix $\\mathbf{K}$ represent the so called proportinal-derivative (PD) controller $\\mathbf{K} = [\\mathbf{k}_p,\\mathbf{k}_d]^T$.\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "cWMGBtXBpNQS" + }, + "source": [ + ">### **Exercise** \n", + "\n", + "Find the gains $k_1, k_2$ that will stabilize the following system:\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{x}}\n", + "=\n", + "\\begin{bmatrix}\n", + "3 & 1\\\\\n", + "1 & 3\n", + "\\end{bmatrix}\n", + "\\mathbf{x}\n", + "+\n", + "\\begin{bmatrix}\n", + "0\\\\\n", + "1 \n", + "\\end{bmatrix}\n", + "\\mathbf{u}\n", + "\\end{equation}\n", + "simulate the response. \n" + ] + }, + { + "cell_type": "code", + "source": [ + "# Put your code here" + ], + "metadata": { + "id": "sHEZuPz4WBCN" + }, + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "source": [ + "## **Pole placement method** or Full state feedback" + ], + "metadata": { + "id": "soOefnN0XuoS" + } + }, + { + "cell_type": "markdown", + "source": [ + "**Pole placement**, is a method employed in feedback control system theory to place the closed-loop poles of a plant in pre-determined locations in the s-plane.\n", + "\n", + "Placing poles is desirable because the location of the poles corresponds directly to the eigenvalues of the system, which control the characteristics of the response of the system. The system must be considered controllable in order to implement this method." + ], + "metadata": { + "id": "juaNMpntYU6R" + } + }, + { + "cell_type": "markdown", + "source": [ + "Let's consider the following dynamical system:\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{x}}=\\begin{bmatrix}\n", + "1 & 1\\\\\n", + "1 & 1\n", + "\\end{bmatrix}\\mathbf{x} + \\begin{bmatrix}\n", + "1\\\\\n", + "0\n", + "\\end{bmatrix}\\mathbf{u}\n", + "\\end{equation}\n", + "\n", + "Let's build a regulator based on a linear model of feedback control:\n", + "\\begin{equation}\n", + "\\mathbf{u}=-\\mathbf{K}\\mathbf{x}=-\\begin{bmatrix}\n", + "k_1 & k_2\n", + "\\end{bmatrix}\\mathbf{x}\n", + "\\end{equation}\n", + "\n", + "And now we have a following system:\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{x}}=(\\mathbf{A} - \\mathbf{B}\\mathbf{K})\\mathbf{x} = \\mathbf{A}_c\\mathbf{x}=\\begin{bmatrix}\n", + "1-k_1 & 1-k_2\\\\\n", + "1 & 1\n", + "\\end{bmatrix}\n", + "\\end{equation}\n", + "\n", + "Let's put this matrix into equation for eigenvalues:\n", + "\\begin{equation}\n", + "\\det \\left(\\begin{bmatrix}\n", + "1-k_1 & 1-k_2\\\\\n", + "1 & 1\n", + "\\end{bmatrix} - \\begin{bmatrix} \\lambda & 0 \\\\ 0 & \\lambda\n", + "\\end{bmatrix} \\right)=0\n", + "\\end{equation}\n", + "\n", + "Now we get the following equation:\n", + "$$ \\lambda^2 + (k_1 - 2)\\lambda - k_1 + k_2=0$$\n", + "With roots:\n", + "$$\\lambda_{1,2}=\\frac{-k_1 \\pm \\sqrt{k_1^2-4k_2+4}}{2} $$\n", + "\n", + "The system will be stable if $\\operatorname{Re}{\\lambda_i} < 0$. Let's assume that $\\lambda_1=-1$ and $\\lambda_2=-2$ which we will call poles.\n", + "\n", + "Now that we have fixed the poles we can calculate $k_1$ and $k_2$:\n", + "$$\n", + "\\begin{equation}\n", + "\\begin{cases}\n", + "\\frac{-k_1 \\pm \\sqrt{k_1^2-4k_2+4}}{2} = -1\\\\\n", + "\\frac{-k_1 \\pm \\sqrt{k_1^2-4k_2+4}}{2} = -2\n", + "\\end{cases}\n", + "\\end{equation}\n", + "$$\n", + "So we can express $k_1$ and $k_2$ and find their values. For this system solution will be following: $k_1 = 5$ and $k_2 = 7$" + ], + "metadata": { + "id": "f6cazawiZoQ7" + } + }, + { + "cell_type": "code", + "source": [ + "from scipy.signal import place_poles\n", + "\n", + "A = [[3,1],\n", + " [1,3]]\n", + "\n", + "B = [[0],\n", + " [1]]\n", + "\n", + "P = [-1, -2]\n", + "\n", + "Lambda, Q = np.linalg.eig(A)\n", + "print(f\"Eigen values of original system:\\n{Lambda}\\n\")\n", + "\n", + "pp =place_poles(np.array(A), np.array(B), np.array(P))\n", + "\n", + "K = pp.gain_matrix\n", + "print(f\"Calculated gains:\\n{K}\\n\")\n", + "\n", + "Lambda, Q = np.linalg.eig(A-np.dot(B, K))\n", + "print(f\"Eigen values:\\n{Lambda}\")" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "IahBqiCxaNI1", + "outputId": "927be270-9807-4860-8d43-1b6bdf08073e" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Eigen values of original system:\n", + "[4. 2.]\n", + "\n", + "Calculated gains:\n", + "[[21. 9.]]\n", + "\n", + "Eigen values:\n", + "[-1. -2.]\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "source": [ + ">### **Exercises**\n", + "\n", + "Find the gains $k_1, k_2$ that will stabilize the following system:\n", + "1. $$\\dot{\\mathbf{x}} = \n", + "\\begin{bmatrix} 0 & 1\\\\\n", + " -7 & -7 \\end{bmatrix} \n", + " \\mathbf{x} + \n", + " \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix} \\mathbf{u}\n", + " $$\n", + "\n", + "2. $$\\mathbf{\\dot{x}}=\\begin{bmatrix}\n", + "10 & 5\\\\\n", + "-5 & -10\n", + "\\end{bmatrix}\\mathbf{x} + \\begin{bmatrix}\n", + "-1\\\\\n", + "2\n", + "\\end{bmatrix}\\mathbf{u}\n", + " $$\n", + "\n", + "3. $$\\mathbf{\\dot{x}}=\\begin{bmatrix}-8 & 1 \\\\ -2 & 2\n", + "\\end{bmatrix}\\mathbf{x} + \\begin{bmatrix}\n", + "2\\\\\n", + "0\n", + "\\end{bmatrix}\\mathbf{u}\n", + " $$" + ], + "metadata": { + "id": "779h___-evRr" + } + }, + { + "cell_type": "markdown", + "source": [ + ">### **Example**" + ], + "metadata": { + "id": "3mKcjuoUhce5" + } + }, + { + "cell_type": "markdown", + "metadata": { + "id": "2Ea3TESnkBmu" + }, + "source": [ + ">**Higher Order Systems. DC-motor dynamic model**\n", + ">\n", + ">Stabilization of the fully actuated second-order systems is a trivial task, however, in practice, you will face systems with higher dimensions, where defining the feedback gain may not be trivial. Thus one may use so-called pole-placement or LQR techniques\n", + ">\n", + ">Consider the DC motor equations:\n", + ">\n", + ">\\begin{equation}\n", + "\\begin{bmatrix}\n", + "\\dot{\\theta} \\\\\n", + "\\ddot{\\theta} \\\\\n", + "\\dot{i}\n", + "\\end{bmatrix} \n", + "=\n", + "\\begin{bmatrix}\n", + "0 & 1 & 0 \\\\\n", + "0 & -\\frac{b}{J} & \\frac{K_m}{J} \\\\\n", + "0 & -\\frac{K_v}{L} & -\\frac{R}{L}\n", + "\\end{bmatrix} \n", + "\\begin{bmatrix}\n", + "\\theta \\\\\n", + "\\dot{\\theta} \\\\\n", + "i\n", + "\\end{bmatrix}\n", + "+\n", + "\\begin{bmatrix}\n", + "0 \\\\\n", + "0 \\\\\n", + "\\frac{1}{L}\n", + "\\end{bmatrix}\n", + "V\n", + "\\end{equation}\n", + "\n", + "![image.png](data:image/png;base64,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)\n", + "\n", + "we will assume that full-state is given (measured).\n", + "\n", + "Let us now try to assign stable poles in order to control DC motor" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "97QxmcR0A8Iq", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 300 + }, + "outputId": "2b3b56fe-cfbb-4cda-d7a2-1c32323ebf45" + }, + "source": [ + "k_m = 0.0274\n", + "k_e = k_m\n", + "J = 3.2284E-6\n", + "b = 3.5077E-6\n", + "L = 2.75E-6\n", + "R = 4\n", + "\n", + "A = [[0, 1, 0],\n", + " [0, -b/J, k_m/J],\n", + " [0, -k_e/L, -R/L]]\n", + "\n", + "B = [[0], \n", + " [0], \n", + " [1/L]];\n", + "\n", + "P = [-100, -500, - 2000]\n", + "\n", + "pp =place_poles(np.array(A), np.array(B), np.array(P)) \n", + "\n", + "K = pp.gain_matrix\n", + "print(K)\n", + "\n", + "tf = 0.2 # Final time\n", + "N = int(2E3) # Numbers of points in time span\n", + "t = np.linspace(t0, tf, N) # Create time span\n", + "x0 = [10, 0, 10] # Set initial state \n", + "\n", + "x_sol = odeint(StateSpace_with_control, x0, t, args=(A, B, K,)) # integrate system \"sys_ode\" from initial state $x0$\n", + "theta, dtheta, i = x_sol[:,0], x_sol[:,1], x_sol[:,2] # set theta, dtheta to be a respective solution of system states\n", + "\n", + "plot(t, theta, 'r', linewidth=2.0, label = r\"$\\theta$\")\n", + "plot(t, dtheta, 'b', linewidth=2.0, label = r\"$\\dot{\\theta}$\")\n", + "plot(t, i, 'g', linewidth=2.0,label = r\"$i$\")\n", + "legend()\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'Motor state')\n", + "xlabel(r'Time $t$ (s)')\n", + "show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "[[ 0.03240182 -0.02699589 -3.99285299]]\n" + ] + }, + { + "output_type": "display_data", + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + } + } + ] + } + ] +} \ No newline at end of file diff --git a/legacy - ColabNotebooks/Practice_6_TrajectoryTracking.ipynb b/legacy - ColabNotebooks/Practice_6_TrajectoryTracking.ipynb new file mode 100644 index 0000000..354e48e --- /dev/null +++ b/legacy - ColabNotebooks/Practice_6_TrajectoryTracking.ipynb @@ -0,0 +1,764 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "[Control theory] Practice 6.ipynb", + "provenance": [], + "collapsed_sections": [], + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "zPmrTNlSBW-R" + }, + "source": [ + "# **Practice 6: Control design regulation and tracing**\n", + "## **Goals for today**\n", + "\n", + "---\n", + "\n", + "During today practice we will:\n", + "* Recall the pole placement and root locus techniques\n", + "* Learn control strategy for affine systems\n", + "* Consider an error dynamics\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "source": [ + "## **Pole Placement**\n", + "\n", + "There is a technique for finding suitable $\\mathbf{K}$ matrix that would produced desired eigenvalues of the $\\mathbf{A}_c$ system. It is called pole placement.\n", + "\n", + "Watch the intoduction to pole placement for self-study: [link](https://www.youtube.com/watch?v=FXSpHy8LvmY&ab_channel=MATLAB). Notice the difference between the approach to \"steady state\" control design show there, and in the lecture." + ], + "metadata": { + "id": "tkGHwuEoaBJJ" + } + }, + { + "cell_type": "code", + "source": [ + "from scipy.signal import place_poles\n", + "import numpy as np\n", + "\n", + "A = [[3,1],\n", + " [1,3]]\n", + "\n", + "B = [[0],\n", + " [1]]\n", + "\n", + "P = [-1, -2]\n", + "\n", + "Lambda, Q = np.linalg.eig(A)\n", + "print(f\"Eigen values of original system:\\n{Lambda}\\n\")\n", + "\n", + "pp =place_poles(np.array(A), np.array(B), np.array(P))\n", + "\n", + "K = pp.gain_matrix\n", + "print(f\"Calculated gains:\\n{K}\\n\")\n", + "\n", + "Lambda, Q = np.linalg.eig(A-np.dot(B, K))\n", + "print(f\"Eigen values:\\n{Lambda}\")" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "czE-FrBka28o", + "outputId": "7842c830-3006-4ef1-81cd-6bf174da300f" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Eigen values of original system:\n", + "[4. 2.]\n", + "\n", + "Calculated gains:\n", + "[[21. 9.]]\n", + "\n", + "Eigen values:\n", + "[-1. -2.]\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "## **Root Locus**\n", + "\n", + "Consider the following question: given system $\\dot{\\mathbf{x}} = \\mathbf{A}\\mathbf{x}+\\mathbf{B}\\mathbf{u}$ and control $\\mathbf{u} = \n", + "-\\mathbf{K} \\mathbf{x}$, how does the change in $\\mathbf{K}$ changes the eigenvalues of theresulting matrix $\\mathbf{A} - \\mathbf{B}\\mathbf{K}$?\n", + "\n", + "Root locus method is drawing the graph of eigenvalues of the matrix $\\mathbf{A} - \\mathbf{B}\\mathbf{K}$ for a given change of matrix $\\mathbf{K}$ . We only vary a single component of $\\mathbf{K}$ , so the result is a line." + ], + "metadata": { + "id": "5n28vcZtZwLU" + } + }, + { + "cell_type": "code", + "source": [ + "from matplotlib.pyplot import *\n", + "\n", + "\n", + "A = np.array([[1, -7],\n", + " [2, -10]])\n", + "\n", + "B = np.array([[1],\n", + " [0]])\n", + "\n", + "K0 = np.array([[1., 1.]])\n", + "\n", + "k_min = -10;\n", + "k_max = 10;\n", + "k_step = 0.01;\n", + "\n", + "Count = int(np.floor((k_max-k_min)/k_step))\n", + "\n", + "k_range = np.linspace(k_min, k_max, Count)\n", + "E = np.zeros((Count, 4))\n", + "\n", + "for i in range(Count):\n", + " K0[0, 0] = k_range[i]\n", + " ei, v = np.linalg.eig((A - B.dot(K0)))\n", + "\n", + " E[i, 0] = np.real(ei[0])\n", + " E[i, 1] = np.imag(ei[0])\n", + " E[i, 2] = np.real(ei[1])\n", + " E[i, 3] = np.imag(ei[1])\n", + "\n", + " #print(\"eigenvalues of A - B*K:\", ei)\n", + "\n", + "\n", + "plot(E[:, 0], E[:, 1], color = 'r')\n", + "plot(E[:, 2], E[:, 3], color = 'b')\n", + "xlabel(r'Re')\n", + "ylabel(r'Im')\n", + "ylim()\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 278 + }, + "id": "J4XojEi3b14h", + "outputId": "d8c57d55-4276-4eaf-d03d-b74e53ce1e48" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "## **Affine control systems**\n", + "Affine system can be writing by the following way:\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{x}}=\\mathbf{A}\\mathbf{x}+\\mathbf{B}\\mathbf{u}+\\mathbf{c}\n", + "\\end{equation}\n", + "when $\\mathbf{c}$ is a constant term." + ], + "metadata": { + "id": "bjz7Cah0cYlt" + } + }, + { + "cell_type": "markdown", + "source": [ + ">### **Example**" + ], + "metadata": { + "id": "TATHLnKiujcd" + } + }, + { + "cell_type": "markdown", + "metadata": { + "id": "LFhTSmgYWaDW" + }, + "source": [ + "> **Mass-spring-damper system**\n", + ">\n", + ">You can imagine this system like a mass-spring-damper with gravity\n", + ">\n", + ">

\"mbk\"

\n", + ">\n", + ">ODE for this system is:\n", + "\\begin{equation}\n", + "m\\ddot{y}+b\\dot{y}+ky=F-mg\n", + "\\end{equation}\n", + "We can rewrite this equation in terms of affine control systems:\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{x}}=\\begin{bmatrix} 0 & 1 \\\\ -\\frac{k}{m} & -\\frac{b}{m}\n", + "\\end{bmatrix}\\mathbf{x} + \\begin{bmatrix} 0 \\\\ \\frac{1}{m}\n", + "\\end{bmatrix}\\mathbf{u}+\\begin{bmatrix} 0 \\\\ -g\n", + "\\end{bmatrix}\n", + "\\end{equation}\n", + ">\n", + ">when $\\mathbf{x}=\\begin{bmatrix} y \\\\ \\dot{y}\n", + "\\end{bmatrix}$ and $\\mathbf{u}=F$\n", + ">\n", + ">Let's simulate this system without control part." + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "xx6wTlUAWZT8", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 552 + }, + "outputId": "cf22ab23-0893-460b-999b-03f9ec938ead" + }, + "source": [ + "from scipy.integrate import odeint\n", + "\n", + "def StateSpace_affine_without_control(x, t, A, c):\n", + " return np.dot(A,x)+c\n", + "\n", + "m = 1\n", + "b = 2\n", + "k = 5\n", + "g = 9.8\n", + "\n", + "t0 = 0\n", + "tf = 10\n", + "t = np.linspace(t0, tf, 1000)\n", + "\n", + "A = np.array([[0, 1],\n", + " [-k/m, -b/m]])\n", + "\n", + "B = np.array([[0],\n", + " [1/m]])\n", + "\n", + "c = np.array([0,\n", + " -g])\n", + "\n", + "x0 = np.array([-4, 0])\n", + "\n", + "x_sol = odeint(StateSpace_affine_without_control, x0, t, args=(A,c))\n", + "\n", + "y, dy = x_sol[:,0], x_sol[:,1]\n", + "\n", + "plot(t, y, 'r', linewidth=2.0, label = r'Position $y$ (m)')\n", + "plot(t, dy, 'b', linewidth=2.0, label = r'Velocity $\\dot{y}$ (m/s)')\n", + "legend()\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'System state')\n", + "xlabel(r'Time $t$ (s)')\n", + "show()\n", + "\n", + "plot(y, dy, 'r', linewidth = 2.)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "ylabel(r'Velocity $\\dot{y}$ (m/s)')\n", + "xlabel(r'Position $y$ (m)')\n", + "xlim([-10, 10])\n", + "ylim([-10, 10])\n", + "show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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8jSqoTpqkeuGFqq+9lt8yenpUFywIlgGqxx+v+sQTBYkbh5L/zmNmOeMFrNUJ/j2P3IhAVZ9U1XZVrQNOB+4HPg48OKEKmIfwB683Ateq6k1ZMg6o6ivh49uAqSJyULHymQLZvTu4fnPjjcFptHvugW99K7i+k48TT4Rbb2XZvHnwznfC738PJ5wAXV0FiW2MGV/kAiQiJ4rIzSLyMEHRuRj4gE70ECz65wvBb482qOoPx5jnkHA+RGQewfo9X4x8poAuughuvjm4vnP33XDqqRNa3O8rK2HdOjjvvKAF3Sc/CRdeGBwXGWOKJp+eEDYStHpbD+wemq6qzxYm2h6ffwpw36jP/2fg/4Q5LheRZuB8ghZzrwFfVdX/Hm+51ggh4e6+G+bPh0mTgtZuZ50V37JVoaMjaNCwe3fQQOHyy4PPMsaMK45GCPlce7l/ouf7kng78sgjo5zudO722293HSGSWHP++c+qRx0VXK+56KLYFrtHxltvVd1nn+BzvvQl1TfeiO2zJqIkv/MCspzxopjXgIALReRKEWkQkXOGbhOqfgnQ19fnOkIkmS1ekizWnO3tsGkTzJkDX/96bIvdI+OCBbB6dXBN6ac/hW98I7bPmoiS/M4LyHImTz4F6LPAXIIfo9aHt8i/tzEmLzt2wPe/Hzy+7DKYVuBen844A375S5gyBS65BK6+urCfZ4zJqyeEGlV9V8GSGJPpyivh+efhpJOC4lAMtbXw4x/DkiXwpS/BMcfAyScX57ONKUVRz9UB/w4cM9Fzfkm7HX300W/h7GfxPfjgg64jRBJLzt2737z2c/PNE1/eKDkz/t3fBZ99xBGqL70U++dHVVLfeRFYznhR5GtAJwPrRGSjiDwqIutF5NFCFMViKisrcx0hkupqP0Y+jyXn2rXBtZ+DD4aF8Z/lzZnxkktg7lx4+mlobo7986Mqqe+8CCxn8uRTgOqAI4GzePP6j/cDV/T29rqOEElmFxtJFkvOa68N7hctCq7JxCxnxrIyWLUK9t0XfvazoPm3AyX1nReB5UyenAVo6IedqvpstlvmPMbEYvXq4H7RIncZjj4a2sKRPC64IPjBqjEmVlGOgO4RkQtE5P9kThSRaSJyuoh0AqVTsk1h9fYGp75mzADX3dJ/5StBQ4TNm+EHP3CbxZi9UJQCVEcwGuoqEXlORJ4QkaeBp4AGYIWqXlPAjAU1ffp01xEiqa2tdR0hkgnnvOee4P6002Dy5AnnySZyxqlT4V//NXh86aXw4osFyTOWkvnOi8RyJk/krnhguDPQg4DXVLW4/xoLxLriSZgvfAGuuir4EWpLi+s0gdNPDwrjhRcGnaAaY2LpiievTq9U9XVV3b63FB+ALVu2uI4QSUtS/hjnMOGc69cH98cfP/EwY8g740UXBfeXXQavvhp/oDGUzHdeJJYzeUq+18XBwUHXESIZGlAq6SaUc/duGBp0793vjidQFnlnfP/7gx/EvvgiXHddYUJlURLfeRFZzuQp+QJkEuTZZ4MueGbOhAMPdJ1mpPPPD+4vv9xtDmP2IvmMB3SniLynkGFcmFKA35kUQkVFhesIkUwo57PhyB5VVfGEGcNbyviJT8Db3w49PfDMM/GHyqIkvvMispzJk894QCcAPwB6gX9W1e0FzFU01gghQVatgsWL4eMfhxtucJ1mT+eeG+T64Q+htdV1GmOcKmgjBBG5P/O5qj6sqh8Efg10i8iFIrLvRD48Cfr7+11HiKTLk2GjJ5TzueeC+5kz4wkzhrec8aMfDe6HfihbYCXxnReR5UyeMQuQqp4yelrY48FG4CfABcBTIvLpwsUrPF8K0KpVq1xHiGRCObeHB9UFLkBvOePppwf3qRTs2hVfoDGUxHdeRJYzefK5BvRbYBvQDhwGfAY4DZgnIlcUIpwpMa+8EtzPmOE2x1gqK+GII4KGEkOt9Ywxb1k+reCWAIep6pmqulRVf62qaVW9AHh/gfKNICJ1YW/caRHZY4hMESkTkevD1x8UkdnFyGViMtTf2j77uM3R1wevv579tfeE7XA2bixeHmP2UpELkKo+rmO3WPjrmPKMSUQmAyuBDwHHAA0icsyo2T4PvKCq1QRHahfnWu6sWbPijloQ7e3triNEMqGcQwVo38JeWhw3Y1tbMAzEUUdlb+02tL8U4QfMJfGdF5HlTJ5Yfgekqk/HsZwc5gFpVX1aVXcC1wFnj5rnbKAzfPwLYL711O0R10dAqm8OA97bCw0Ne85z0EHB/QsvFC2WMXsrP34EEzgMyPxv51bgpLHmUdVdIvIScCDwp8yZRGQJwSlFpk6dSn39m8MaDf3vozWjmW1DQwOLFy+msbFxuNFCVVUVK1asoKOjgzVr1gzP29nZSTqdZvny5cPTmpqaqKurG/E5NTU1LFu2jLa2Nnp6eoanr169mu7ublauXDk8benSpSxdupRp06YNT6utraW5uZmWlpbhX05XVFTQ2dlJV1fXiAuZxVynnp6e4ftc61RdXT1i7JOOzZv5C+Dya67h1quuKtg6pVIpNmzYsOc6nX8+dRnDLux+8EG+3dY24ns6d9MmPhW+HmWdJvI9pVIp2tvbne97udYplUpRV1fnfN/LtU6pVIp58+bF/j3FvU5DOeP+nuJep1hEHTqVoNXbARMdgvWt3oCPAVdmPP800DFqnseAwzOebwYOGm+5M2bMGG/U2cRYuHCh6wiRTCjnK6+o9vWpvvZafIGyGDfjCScEw3HX1Kju2LHn60PDdV9ySeEChkriOy8iyxkvijwk98FAj4jcEDYGKPaprW1A5gWbw8NpWecRkSnADOD5oqQzE1deDu94h9tGCJmn3bIN1z7UWeqRRxYnjzF7sXwaIfwLwZDcVxE0wX5KRL4rIoXtN+VNPcCRIvJOEZkGLAJuGTXPLbw5ON7HgLvDSj0mX7q9aMh2PSKBfMg5bsbzzw9+h9TTA//yL8F1oSFbt8J99wXjFJ16qtucCWI54+VLzjjkNR4QQNgf3GcJBqq7BzgZuFNV/zH+eHt89gJgBTAZuFpVvyMibQSHgreIyD7Az4DjgX5gkeZoIGFd8Zg93HUXnHVW0Dv3Zz4TjAM0dSqcdx7cfXdyuwoypoji6Ionn2swXwEeAtYAHwemhtMnAZsnei7Q1e3AAw/M99SnE+edd57rCJH4kDNSxuuuU502Lbjek3mrrFR95pmCZ1T1Y1uqWs64+ZKTIl8DqgDOUdVaVf25qr4eFrDdwMIJVUGHdhWhS5U4+NJlkA85I2U891xYty64339/eNvb4MMfhvvvh9mzC54R/NiWYDnj5kvOOOTTDHsfVX02c4KIXKyq/6SqG2LOZYx7c+YUdQA6Y0pNPkdAZ2aZ9qG4grhSlq2lUwJVFXiMnLj4kNOHjGA542Y5kydnIwQROR/4W+AIgt/VDNkP+K2qfirrGz1hjRCMMSZ/BR0PKEMXUE/QxLk+4/Ze34sPQF9fn+sIkcT2y+MC8yGnDxnBcsbNciZPzgKkqi+paq+qNqjqsxm3veJK2cDAgOsIkWR25ZFkPuT0ISNYzrhZzuTJ2QhBRO5X1VNE5GUg83ydAKqq0wuWzhhjzF4rZwHScGRUVd2v8HGMMcaUirx7QtjbzJ07V9etW+c6Rk79/f1edBvkQ04fMoLljJvljFexGiEMfViniOyf8fwAEbl6Ih+eBIODg64jRJJOp11HiMSHnD5kBMsZN8uZPPn8Duj/quqLQ09U9QWCPte8tn37dtcRIskcOyTJfMjpQ0awnHGznMmTTwGaJCIHDD0RkQr8GtDOGGNMguRTQH4A/E5Efk7QAu5jwHcKksoYY8xeL3IBUtX/EJG1wOkEzbHPUdUnCpasSCorK11HiKSpqcl1hEh8yOlDRrCccbOcyZNXK7hwLKBTCQrQfar6SKGCFYt1xWOMMfkrdiu4rwDXAgcBlcB/isgFE/nwJPClxUl9fb3rCJH4kNOHjGA542Y5kyefa0CfB05S1R0QDMUA/A7410IEM8YYs3fLpxWcAG9kPH8jnGaMMcbkLZ8joH8HHhSRm8PnHwGuij/SnkTkUoIeuHcSDAnx2czfJGXM1wu8TFAcd0U5P1leXh5v2AKpqalxHSESH3L6kBEsZ9wsZ/Lk2wjhvcBfhU/vU9XfFyTVnp97FnC3qu4KT/2hqv+UZb5e4ERV/VPUZVsjBGOMyV9RGyEAqOpDqvqj8FaU4hN+7h2quit8+gBweFzL9qUnhLa2NtcRIvEhpw8ZwXLGzXImT5ThGDKHYZDRjx0Mx/A54PoxXlPgDhFR4KeqekW2mURkCbAEYOrUqSNanbS3twPQ2to6PK2hoYHFixfT2NhIf38wDFJVVRUrVqygo6NjxPgdnZ2dpNPpEd1pNDU1UVdXN+JzampqWLZsGW1tbfT09AxPX716Nd3d3axcuXJ42tKlS/ntb3874v21tbU0NzfT0tLC5s3BQLUVFRV0dnbS1dXFqlWrnKxTT09P5HWqrq6msbGx6OuUSqVobm4uyPcU5zqlUimqq6ud73u51imVSrF582bn+16udUqlUvT09Djd96Ks01BOl/telHWKhaom4gb8Bngsy+3sjHm+CdxMeOowyzIOC+8rgUeAU3N97owZM9QHCxcudB0hEh9y+pBR1XLGzXLGC1irE/y7H7kRgogI8Engnaq6XERmATNVNRVTITwjx+d/BlgIzA9XPtsytoX3fWFjiXnAvXHkM8YYE6/IjRBE5CfAbuB0VZ0Tdkx6h6oWvMmGiNQBPwQ+oKr/O8Y85cAkVX05fHwn0Kaq3eMt2xohGGNM/ordCOEkVW0C/gzDwzFMm8iH56ED2A+4U0TWicjlACJyqIjcFs5zMHC/iDwCpIBbcxUfgIGBgUJljlV3d85VSQQfcvqQESxn3Cxn8uRTgF4XkcmEjRBE5B0ER0QFp6rVqjpLVeeGty+H059T1QXh46dV9T3h7VhVjdRTd19fXyGjxybzgmOS+ZDTh4xgOeNmOZMnnwL0I4IGAJUi8h3gfuC7BUlljDFmrxelGfZKoEtVrxWRh4D5BE2wP6KqGwod0BhjzN4pZyOEsBfsRcBM4AZglRbxR6iFNmfOHN2wIfl1NJVKMW/ePNcxcvIhpw8ZwXLGzXLGqyiNEFT1MlV9H/AB4HngahF5UkQuFJGjJvLhSVBWVuY6QiTV1dWuI0TiQ04fMoLljJvlTJ7I14BU9VlVvVhVjwcaCDojTf6hQw69vb2uI0SS+QvnJPMhpw8ZwXLGzXImTz4D0k0RkXoRuRa4HdgInFOwZMYYY/ZqURohnElwxLOA4Pc11wFLNByYzhhjjHkronTF8w2gC/j78Mene5Xp04vdl+pbU1tb6zpCJD7k9CEjWM64Wc7kyWs8oL2RdcVjjDH5K/p4QHujLVu2uI4QSUtLi+sIkfiQ04eMYDnjZjmTp+QL0ODgoOsIkQyN55F0PuT0ISNYzrhZzuQp+QJkjDHGjZIvQFOmRB4SyamKigrXESLxIacPGcFyxs1yJo81QrBGCMYYkzdrhBCDobHOk66rq8t1hEh8yOlDRrCccbOcyWMFyJMCtGrVKtcRIvEhpw8ZwXLGzXImT8kXIGOMMW5YATLGGOOEF40QRORbwBeB/w0n/bOq3pZlvjrgMmAycKWqfi/Xso877jhdv359jGkLI51Oe9FNuw85fcgIljNuljNecTRC8KMNcqBdVb8/1osiMhlYCZwJbAV6ROQWVX2iWAGNMcZEtzedgpsHpFX1aVXdSdBr99m53uRLVzytra2uI0TiQ04fMoLljJvlTB6fjoCaReQ8YC3Ze+Y+DMisJluBk7ItSESWAEsApk6dSn19/fBr7e3twMidoKGhgcWLF9PY2Djcaq6qqooVK1bQ0dHBmjVrhuft7OwknU6zfPny4WlNTU3U1dWN+JyamhqWLVtGW1sbPT09w9NXr15Nd3c3K1euHJ62dOlSdu7cOeL9tbW1NDc309LSMtx1R0VFBZ2dnXR1dY1oSVPMdQIir1N1dfWIwbeKtU6pVIr+/v6CfE9xrlMqlaKrq8v5vpdrnVKpFI2Njc73vVzrlEqlqK+vd7rvRVmnoZwu970o6xQLVU3EDfgN8FiW29nAwQTXdSYB306W/JIAAA9kSURBVAGuzvL+jxFc9xl6/mmgI9fnzpgxQ32wcOFC1xEi8SGnDxlVLWfcLGe8gLU6wb/7iTkCUtUzoswnIv8G/DrLS9uAWRnPDw+njcuXbi8aGhpcR4jEh5w+ZATLGTfLmTy+tIKbqarbw8etwEmqumjUPFOATcB8gsLTAyxW1cfHW7Z1xWOMMfkrpa54LhGR9SLyKPBBoBVARA4VkdsAVHUX0AysATYAN+QqPgC9vb0FCx2nzHO7SeZDTh8yguWMm+VMnsScghuPqn56jOnPAQsynt8G7PH7oPHs2rVrYuGKxJcug3zI6UNGsJxxs5zJ48sRkDHGmL1MyRegsrIy1xEiqaqqch0hEh9y+pARLGfcLGfyeNEIoZCsEYIxxuSvlBohFExfX5/rCJHE9sOvAvMhpw8ZwXLGzXImT8kXoIGBAdcRIsn8JXWS+ZDTh4xgOeNmOZOn5AuQMcYYN6wAGWOMcaLkGyHMnTtX161b5zpGTv39/V50G+RDTh8yguWMm+WMlzVCiMHg4KDrCJGk02nXESLxIacPGcFyxs1yJk/JF6Dt27e7jhBJZtftSeZDTh8yguWMm+VMnpIvQMYYY9ywAmSMMcaJki9AlZWVriNE0tTU5DpCJD7k9CEjWM64Wc7kKflWcNYVjzHG5M9awcXAlxYn9fX1riNE4kNOHzKC5Yyb5Uyeki9Axhhj3LACZIwxxomSL0Dl5eWuI0RSU1PjOkIkPuT0ISNYzrhZzuTxohGCiFwPvCt8uj/woqrOzTJfL/Ay8AawK8oFMmuEYIwx+SuZRgiqeq6qzg2Lzo3ATePM/sFw3kgbxpeeENra2lxHiMSHnD5kBMsZN8uZPFNcB8iHiAjwCeD0uJa5Y8eOuBZVUD09Pa4jROJDTh8yguWMm+VMHi+OgDK8H/ijqj41xusK3CEiD4nIkiLmMsYYk6fEHAGJyG+AQ7K89E1V/VX4uAFYNc5iTlHVbSJSCdwpIk+q6r1ZPmsJsARg6tSpI9rdt7e3A9Da2jo8raGhgcWLF9PY2Eh/fz8AVVVVrFixgo6OjhEjGHZ2dpJOp0d0KNjU1ERdXd2Iz6mpqWHZsmW0tbWN+B/P6tWr6e7uZuXKlcPTli5dys6dO0e8v7a2lubmZlpaWti8eTMAFRUVdHZ20tXVxapVb26mYq4TEHmdqquraWxsLPo6pVIp+vv7C/I9xblOqVSKrq4u5/ternVKpVI0NjY63/dyrVMqlaK+vt7pvhdlnYZyutz3oqxTHLxohAAgIlOAbcB7VXVrhPm/Bbyiqt8fbz5rhGCMMfkrmUYIoTOAJ8cqPiJSLiL7DT0GzgIey7XQgYGBWEMWSnd3t+sIkfiQ04eMYDnjZjmTx6cCtIhRp99E5FARuS18ejBwv4g8AqSAW1U15zfZ19cXe9BCyDzcTjIfcvqQESxn3Cxn8iTmGlAuqvqZLNOeAxaEj58G3lPkWMYYY94in46AjDHG7EW8aYRQKHPmzNENGza4jpFTKpVi3rx5rmPk5ENOHzKC5Yyb5YxXqTVCKIiysjLXESKprq52HSESH3L6kBEsZ9wsZ/KUfAHq7e11HSGSzPb9SeZDTh8yguWMm+VMnpIvQMYYY9ywAmSMMcaJki9A06dPdx0hktraWtcRIvEhpw8ZwXLGzXImT8m3grOueIwxJn/WCi4GW7ZscR0hkpaWFtcRIvEhpw8ZwXLGzXImT8kXoMHBQdcRIhnqzTbpfMjpQ0awnHGznMlT8gXIGGOMGyVfgKZM8aM7vIqKCtcRIvEhpw8ZwXLGzXImjzVCsEYIxhiTN2uEEIOhkf6Srqury3WESHzI6UNGsJxxs5zJYwXIkwKUOXxukvmQ04eMYDnjZjmTp+QLkDHGGDesABljjHGi5BshHHfccbp+/XrXMXJKp9NedNPuQ04fMoLljJvljJc1QjDGGOOtxBQgEfm4iDwuIrtF5MRRr31DRNIislFEsvbUJyLvFJEHw/muF5FpUT7Xl654WltbXUeIxIecPmQEyxk3y5k8iSlAwGPAOcC9mRNF5BhgEXAsUAf8WEQmZ3n/xUC7qlYDLwCfL2xcY4wxE5GYAqSqG1R1Y5aXzgauU9VBVX0GSAMjBkwXEQFOB34RTuoEPlLIvMYYYybGh35oDgMeyHi+NZyW6UDgRVXdNc48w0RkCbAkfDooIo/FlLWQDhKRP7kOEYEPOX3ICJYzbpYzXu+a6AKKWoBE5DfAIVle+qaq/qpYOVT1CuCKMNPaibbkKAbLGR8fMoLljJvljJeITLgPs6IWIFU94y28bRswK+P54eG0TM8D+4vIlPAoKNs8xhhjEiQx14DGcQuwSETKROSdwJFAKnMGDX7MdA/wsXBSI1C0IypjjDH5S0wBEpGPishW4H3ArSKyBkBVHwduAJ4AuoEmVX0jfM9tInJouIh/Ar4qImmCa0JXRfzoK2JcjUKynPHxISNYzrhZznhNOGfJ94RgjDHGjcQcARljjCktVoCMMcY4URIFyFU3PxPMfL2IrAtvvSKyboz5ekVkfThf0Yd2FZFvici2jKwLxpivLtzGaRH5epEzXioiT4rIoyJys4jsP8Z8TrZlrm0TNsC5Pnz9QRGZXaxsGRlmicg9IvJE+G/pK1nmOU1EXsrYF5YVO2eYY9zvUQI/CrfnoyJygoOM78rYTutEZEBEWkbN42R7isjVItKX+ftIEakQkTtF5Knw/oAx3tsYzvOUiDTm/DBV3etvwByCH039F3BixvRjgEeAMuCdwGZgcpb33wAsCh9fDpxf5Pw/AJaN8VovcJDDbfst4B9yzDM53LZHANPCbX5METOeBUwJH18MXJyUbRll2wB/C1wePl4EXO/ge54JnBA+3g/YlCXnacCvi50t3+8RWADcDghwMvCg47yTgT8Af5GE7QmcCpwAPJYx7RLg6+Hjr2f7NwRUAE+H9weEjw8Y77NK4ghIPe7mJ/z8TwA+D5M4D0ir6tOquhO4jmDbF4Wq3qFv9pLxAMHvxJIiyrY5m2C/g2A/nB/uF0WjqttV9eHw8cvABsbpbSThzgb+QwMPEPyGcKbDPPOBzar6rMMMw1T1XmD0UNGZ++BYfwNrgTtVtV9VXwDuJOi/c0wlUYDGcRiQ2R32hLv5KYD3A39U1afGeF2BO0TkIQm6GHKhOTyVcfUYh+ZRtnOxfI7gf7/ZuNiWUbbN8DzhfvgSwX7pRHgK8HjgwSwvv09EHhGR20Xk2KIGe1Ou7zFJ+yMER7Vj/QczCdsT4GBV3R4+/gNwcJZ58t6uPvQFF4kkpJuffETM3MD4Rz+nqOo2EakE7hSRJ8P/wRQlJ/ATYDnBP/rlBKcLPxfn50cRZVuKyDeBXcC1Yyym4NvSdyLyduBGoEVVB0a9/DDBaaRXwmuBvyT44XixefM9hteTPwx8I8vLSdmeI6iqikgsv9/ZawqQetjNT67MIjKFYIiK946zjG3hfZ+I3ExwSifWf2xRt62I/Bvw6ywvRdnOExJhW34GWAjM1/CEdZZlFHxbZhFl2wzNszXcJ2YQ7JdFJSJTCYrPtap60+jXMwuSqt4mIj8WkYNUtagda0b4Hgu+P+bhQ8DDqvrH0S8kZXuG/igiM1V1e3i6si/LPNsIrlsNOZzguvuYSv0UXNK7+TkDeFJVt2Z7UUTKRWS/occEF9uL2rP3qHPnHx3j83uAIyVoTTiN4JTDLcXIB0ErM+AfgQ+r6qtjzONqW0bZNrcQ7HcQ7Id3j1VECyW85nQVsEFVfzjGPIcMXZsSkXkEf1+KWigjfo+3AOeFreFOBl7KOL1UbGOe4UjC9syQuQ+O9TdwDXCWiBwQnoo/K5w2tmK3sHBxI/jDuBUYBP4IrMl47ZsErZA2Ah/KmH4bcGj4+AiCwpQGfg6UFSn3NcCXR007FLgtI9cj4e1xgtNNxd62PwPWA4+GO+nM0TnD5wsIWk5tLnbO8HvbAqwLb5ePzuhyW2bbNkAbQcEE2Cfc79LhfniEg+/5FILTrI9mbMcFwJeH9lGgOdx2jxA09vhLBzmzfo+jcgqwMtze68loGVvkrOUEBWVGxjTn25OgIG4HXg//bn6e4JrjXcBTwG+AinDeE4ErM977uXA/TQOfzfVZ1hWPMcYYJ0r9FJwxxhhHrAAZY4xxwgqQMcYYJ6wAGWOMccIKkDHGGCesABljjHHCCpAxxhgnrAAZk4WIvBGOwfKYiPxcRN72Fpbx3+H9/iLyt9leKwYR2VdE/p+ITM7jPdNE5N6w6x9jCsIKkDHZvaaqc1X13cBOgl+o50VV/zJ8uD/BmD7ZXiuGzwE3qeobUd+gwdAQdwHnFiyVKXlWgIzJ7T6gGkBEvhoeFT02NIJl2P/YrWG3+Y+JyLnh9FfC938PqAqPqC7NfG2M5c0WkQ0i8m8SjD56h4jsOzqUiLw780hKRE4Qkbuy5P8kYd9d4bKfFJFrRGSTiFwrImeIyG8lGMUyczysX4bvNaYgrCseY7IQkVdU9e3hKagbgW6CftiuIRhFUwjGw/kUQf9jdar6xfC9M1T1pYxlzCYY2fLdmcsHPjDG8l4g6EvrRFVdJyI3ALeo6n+OyjgJeA44TFXfEJH/Ar6q4cBx4TzTgP9R1UPC57PDZR9P0M9YD0FfY58nGBbgs6r6kXDeycAfVPUdE9qYxozBjoCMyW5fEVkHrAX+h6An6FOAm1V1h6q+AtxEMGDgeuBMEblYRN6vqi9F/IyxlgfwjKquCx8/BMwe/WZV3U1QRI4Vkb8Bns0sPqGDgBdHTXtGVddnvP8uDf4nuj7zc8JTdjuHepc2Jm52gdGY7F5T1bmZE2SMUbBVdZOInEDQO/S3ReQuVW2b4OcPZjx+A9jjFFzoAeCvCK4xZRv++DWC3rTHWvbujOe72fNvQhnw5wh5jcmbHQEZE919wEdE5G3hWDMfBe4TkUOBV8NTZJcCJ4x638tAtqOIrMvLM9MDwLcJjqT2GFRNVV8AJovI6CKUk4gcCPxJVV/P973GRGFHQMZEpKoPi8g1vDlo4ZWq+nsRqQUuFZHdBGOonD/qfc+HF/kfA25X1a/lWN7sPGI9SXAEc/E489xBcLrvN3ksF+CDwK15vseYyKwRgjEeE5EOoEdVO8eZ5wSgVVU/neeybwK+rqqbJhjTmKzsFJwxHhKRKhF5Eth3vOIDwZEWcE++P0QFfmnFxxSSHQEZY4xxwo6AjDHGOGEFyBhjjBNWgIwxxjhhBcgYY4wTVoCMMcY4YQXIGGOME1aAjDHGOPH/AWpzEwWG0CeiAAAAAElFTkSuQmCC\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "source": [ + ">As you can see when we add a constant term we obtain that convergence point is not zero for this system. Let's imagine a task when we should to design the control input to stabilize this system at point $\\mathbf{x^*}(t)=0$.\n", + ">\n", + ">So, we can design our controller by the following law:\n", + "\\begin{equation}\n", + "\\mathbf{u}=-\\mathbf{K}\\mathbf{x}+\\mathbf{u^*}\n", + "\\end{equation}\n", + "where $\\mathbf{u^*}$ will compensate the constant term in this system.\n", + "When we put this control law into affine control equation we get:\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{x}}=\\mathbf{Ax}-\\mathbf{BK}\\mathbf{x}+\\mathbf{Bu^*}+\\mathbf{c}\n", + "\\end{equation}\n", + ">\n", + ">To compensate the constant term we can choose $$\\mathbf{u^*}=-\\mathbf{B^+c}$$\n", + ">\n", + ">When $\\mathbf{B^+}$ is Moore-Penrose inverse operator (or pseudoinverse). In case when each elements of matrix $\\mathbf{B}$ is real and rows linearly independent we can $\\mathbf{B^+}$ can be computed as:\n", + "$$ \\mathbf{B^+}=\\mathbf{B}^T\\left(\\mathbf{BB}^T\\right)^{-1}$$\n", + "This is right inverse as $\\mathbf{BB^+}=I$.\n", + ">\n", + ">More information about this operator is available [here](https://en.wikipedia.org/wiki/Moore–Penrose_inverse).\n", + ">\n", + ">In the result we get the following control law:\n", + "\\begin{equation}\n", + "\\mathbf{u}=-\\mathbf{K}\\mathbf{x}-\\mathbf{B^+c}\n", + "\\end{equation}\n", + "When $-\\mathbf{K}\\mathbf{x}$ is feedback part and $\\mathbf{B^+c}$ is feedforward part." + ], + "metadata": { + "id": "4QpmAzWXgfmb" + } + }, + { + "cell_type": "code", + "source": [ + "def StateSpace_affine(x, t, A, B, c, K):\n", + " u_fb = -np.dot(K,x)\n", + " u_ff = -np.linalg.pinv(B).dot(c)\n", + " u = u_fb+u_ff\n", + " return np.dot(A,x)+np.dot(B,u)+c\n", + "\n", + "K = np.array([[0,0]])\n", + "\n", + "x_sol = odeint(StateSpace_affine, x0, t, args=(A,B,c,K))\n", + "\n", + "y, dy = x_sol[:,0], x_sol[:,1]\n", + "\n", + "plot(t, y, 'r', linewidth=2.0, label = r'Position $y$ (m)')\n", + "plot(t, dy, 'b', linewidth=2.0, label = r'Velocity $\\dot{y}$ (m/s)')\n", + "legend()\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'System state')\n", + "xlabel(r'Time $t$ (s)')\n", + "show()\n", + "\n", + "plot(y, dy, 'r', linewidth = 2.)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "ylabel(r'Velocity $\\dot{y}$ (m/s)')\n", + "xlabel(r'Position $y$ (m)')\n", + "xlim([-10, 10])\n", + "ylim([-10, 10])\n", + "show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 552 + }, + "id": "HzBftzNogkA_", + "outputId": "f99ef7df-f96e-4e36-84ae-b25c3967c1e7" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "source": [ + ">### **Exercises**\n", + "> Compute the control law $\\mathbf{u}$ to stabilize (this mean $\\mathbf{x^*}(t)=0$) the following systems:\n", + "1. $\n", + "\\mathbf{\\dot{x}}=\\begin{bmatrix}\n", + "1 & 1\\\\\n", + "-6 & -2\n", + "\\end{bmatrix}\\mathbf{x} + \\begin{bmatrix}\n", + "3 & 1\\\\\n", + "1 & 0\n", + "\\end{bmatrix}\\mathbf{u} +\\begin{bmatrix}\n", + "0\\\\\n", + "20\n", + "\\end{bmatrix}\n", + "$\n", + ">\n", + ">2. $\n", + "\\mathbf{\\dot{x}}=\\begin{bmatrix}\n", + "0 &2\\\\\n", + "-1 & -5\n", + "\\end{bmatrix}\\mathbf{x} + \\begin{bmatrix}\n", + "2 & 2\\\\\n", + "0 & 5\n", + "\\end{bmatrix}\\mathbf{u} +\\begin{bmatrix}\n", + "1\\\\\n", + "5\n", + "\\end{bmatrix}\n", + "$" + ], + "metadata": { + "id": "3gK8AgxNue4J" + } + }, + { + "cell_type": "code", + "source": [ + "B = np.array([[0, 0],\n", + " [0, 1]])\n", + "c = np.array([0, 1])\n", + "\n", + "u_star = -np.linalg.pinv(B).dot(c)\n", + "\n", + "print(\"B+ = \",np.linalg.pinv(B))\n", + "print(\"u* = \",u_star)" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "rCLvbUlkuaSW", + "outputId": "f0623834-eaa5-47c9-dc4c-f898724d3d33" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "B+ = [[0. 0.]\n", + " [0. 1.]]\n", + "u* = [-0. -1.]\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "## **Error dynamics**\n", + "\n", + "Consider the following system:\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{x}}=\\mathbf{A}\\mathbf{x}+\\mathbf{B}\\mathbf{u}\n", + "\\end{equation}\n", + "with some trajectory $\\mathbf{x^*}=\\mathbf{x^*}(t)$, this mean that this solution is satisfies this equation:\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{x}^*}=\\mathbf{A}\\mathbf{x^*}+\\mathbf{B}\\mathbf{u^*}\n", + "\\end{equation}\n", + "When $\\mathbf{u^*}$ is control law when this trajectory exist. This law can be calculated by the following way:\n", + "$$\\mathbf{u^*}=\\mathbf{B^+}\\left(\\mathbf{\\dot{x}^*}-\\mathbf{Ax^*} \\right)$$\n", + "\n", + "After this we can change our system into the error control concept:\n", + "$$ \\mathbf{e}=\\mathbf{x}-\\mathbf{x^*} $$\n", + "and now e can get the following form of our system:\n", + "$$\n", + "\\mathbf{\\dot{e}}=\\mathbf{Ae}+\\mathbf{Bv}\n", + "$$\n", + "where $\\mathbf{v}=\\mathbf{u}-\\mathbf{u^*}$.\n", + "Assyme that for this system we can choose the linear control rule:\n", + "$$\\mathbf{v}=-\\mathbf{Ke}$$\n", + "This mean that the final control law for original system is:\n", + "$$\\mathbf{u}=-\\mathbf{K}(\\mathbf{x}-\\mathbf{x^*})+\\mathbf{u^*} $$" + ], + "metadata": { + "id": "EeJE9Hq6vL6F" + } + }, + { + "cell_type": "markdown", + "source": [ + ">### **Example**\n", + ">\n", + "> **Mass-spring-damper system**\n", + ">\n", + "> The equation for the unforced system:\n", + "\\begin{equation}\n", + "m\\ddot{y}+b\\dot{y}+ky=F\n", + "\\end{equation}\n", + "Consider the situation when we want to bring the system to the position $y^* = 3$ and hold it there. This mean that $\\dot{y}^* = 0$ and $\\ddot{y}^* = 0$. If we will substitude this solution into original ODE we will consider needed force for this position is $F^* = ky^*$ and this is equivelent solution as $\\mathbf{u^*}=\\mathbf{B^+}\\left(\\mathbf{\\dot{x}^*}-\\mathbf{Ax^*} \\right)$" + ], + "metadata": { + "id": "olHrzHN9-Iyx" + } + }, + { + "cell_type": "code", + "source": [ + "def StateSpace(x, t, A, B, K, x_des, dx_des):\n", + " u_ff = np.linalg.pinv(B) @ (dx_des - A @ x_des)\n", + " u_fb = - K @ (x-x_des) \n", + " u = u_fb + u_ff\n", + " return A @ x + B @ u\n", + "\n", + "A = np.array([[0, 1],\n", + " [-k/m, -b/m]])\n", + "\n", + "B = np.array([[0],\n", + " [1/m]])\n", + "\n", + "K = np.array([[3,4]])\n", + "\n", + "x_des = np.array([3, 0])\n", + "dx_des = np.array([0, 0])\n", + "x0 = np.array([-4, 0])\n", + "\n", + "StateSpace(x0, t, A, B, K, x_des, dx_des)\n", + "\n", + "x_sol = odeint(StateSpace, x0, t, args=(A, B, K, x_des, dx_des))\n", + "\n", + "y, dy = x_sol[:,0], x_sol[:,1]\n", + "\n", + "plot(t, y, 'r', linewidth=2.0, label = r'Position $y$ (m)')\n", + "plot(t, dy, 'b', linewidth=2.0, label = r'Velocity $\\dot{y}$ (m/s)')\n", + "legend()\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'System state')\n", + "xlabel(r'Time $t$ (s)')\n", + "show()\n", + "\n", + "plot(y, dy, 'r', linewidth = 2.)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "ylabel(r'Velocity $\\dot{y}$ (m/s)')\n", + "xlabel(r'Position $y$ (m)')\n", + "xlim([-10, 10])\n", + "ylim([-10, 10])\n", + "show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 552 + }, + "id": "OO7jrnbl9BSl", + "outputId": "19de9bad-4ae1-4c98-b69f-f47833b48747" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "source": [ + ">The same idea with trajectory following. Let our mass spring damper describe the trajectory $y^* = \\sin{t}$. Then $\\dot{y}^* = \\cos{t}$ and $\\ddot{y}^* = -\\sin{t}$. Then our force should be $F = -m\\sin{t} + b\\cos{t}+ k \\sin{t}$. " + ], + "metadata": { + "id": "fGylirBPGAfi" + } + }, + { + "cell_type": "code", + "source": [ + "def trajectory(t):\n", + " x_des = np.array([np.sin(t),np.cos(t)])\n", + " dx_des = np.array([np.cos(t),-np.sin(t)])\n", + " return x_des, dx_des\n", + "\n", + "\n", + "def StateSpace_trajectory(x, t, A, B, K):\n", + " x_des, dx_des = trajectory(t)\n", + " u_ff = np.linalg.pinv(B) @ (dx_des - A @ x_des)\n", + " u_fb = - K @ (x-x_des) \n", + " u = u_fb + u_ff\n", + " return A @ x + B @ u\n", + "\n", + "A = np.array([[0, 1],\n", + " [-k/m, -b/m]])\n", + "\n", + "B = np.array([[0],\n", + " [1/m]])\n", + "\n", + "K = np.array([[3,4]])\n", + "\n", + "x_des = np.array([3, 0])\n", + "dx_des = np.array([0, 0])\n", + "x0 = np.array([-4, 0])\n", + "\n", + "StateSpace(x0, t, A, B, K, x_des, dx_des)\n", + "\n", + "x_sol = odeint(StateSpace_trajectory, x0, t, args=(A, B, K))\n", + "\n", + "y, dy = x_sol[:,0], x_sol[:,1]\n", + "\n", + "plot(t, y, 'r', linewidth=2.0, label = r'Position $y$ (m)')\n", + "plot(t, dy, 'b', linewidth=2.0, label = r'Velocity $\\dot{y}$ (m/s)')\n", + "legend()\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'System state')\n", + "xlabel(r'Time $t$ (s)')\n", + "show()\n", + "\n", + "plot(y, dy, 'r', linewidth = 2.)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "ylabel(r'Velocity $\\dot{y}$ (m/s)')\n", + "xlabel(r'Position $y$ (m)')\n", + "xlim([-10, 10])\n", + "ylim([-10, 10])\n", + "show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 552 + }, + "id": "SU_aYbA8H56D", + "outputId": "761bf342-abd5-452e-fd90-480c8061b1fd" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "source": [ + ">### **Exercises**\n", + ">1. Compute the control law $\\mathbf{u}$ for following systems:\n", + ">* $\\dot x = \\begin{bmatrix}-8 & 1 \\\\ -2 & 2\n", + "\\end{bmatrix}x+\n", + "\\begin{bmatrix} 2 \\\\ 0\\end{bmatrix}u\n", + "\\quad \\quad \\quad x_d = \\begin{bmatrix} 10 \\\\ 10\\end{bmatrix}$\n", + ">\n", + ">\n", + ">* $\\dot x = \\begin{bmatrix}-3 & 7 \\\\ -1 & -10\n", + "\\end{bmatrix}x+\n", + "\\begin{bmatrix} 3 \\\\ 1\\end{bmatrix}u\n", + "\\quad \\quad \\quad x_d = \\begin{bmatrix} 3 \\\\ 0\\end{bmatrix}$\n", + ">\n", + ">\n", + ">* $\\dot x = \\begin{bmatrix}0 & -1 \\\\ -1 & 3\n", + "\\end{bmatrix}x+\n", + "\\begin{bmatrix} 1 \\\\ -4\\end{bmatrix}u\n", + "\\quad \\quad \\quad x_d = \\begin{bmatrix} 5 \\\\ -5\\end{bmatrix}$\n", + ">\n", + ">\n", + "> 2. Compute control law for $\\mathbf{u}$ for mass spring dampher with trajectory $y = A \\cos (wt)$. Take gravity into account.\n", + ">\n", + ">\n", + "> 3. Calculate the position control for a motor in which you can only control the current. A simplified model of the motor dynamics for this situation:\n", + "> $$J\\ddot{\\theta}+b\\dot{\\theta} = K_m I$$\n", + "> when $J$ - motor rotor moment of inertia, $b$ - coefficient of viscous friction, $K_m$ - motor torque constant" + ], + "metadata": { + "id": "PovhbNduEl9O" + } + } + ] +} \ No newline at end of file diff --git a/legacy - ColabNotebooks/Practice_7_Discrete.ipynb b/legacy - ColabNotebooks/Practice_7_Discrete.ipynb new file mode 100644 index 0000000..ad3ccd2 --- /dev/null +++ b/legacy - ColabNotebooks/Practice_7_Discrete.ipynb @@ -0,0 +1,619 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "[Control theory] Practice 7.ipynb", + "provenance": [], + "collapsed_sections": [], + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "zPmrTNlSBW-R" + }, + "source": [ + "# **Practice 7: Discrete systems**\n", + "## **Goals for today**\n", + "\n", + "---\n", + "\n", + "During today practice we will:\n", + "* Discrete-time state space model\n", + "* Stability theory for discrete case\n", + "* Feedback control for discrete systems\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "source": [ + "## **Discrete-time state space model**" + ], + "metadata": { + "id": "ocrd609UpN5_" + } + }, + { + "cell_type": "markdown", + "source": [ + "**Discrete-time systems** are either inherently discrete (e.g. models of bank accounts, national economy growth models, population growth models, digital words) or they are obtained as a result of sampling (discretization) of continuous-time systems. In such kinds of systems, inputs, state space variables, and outputs have the discrete form and the system models can be represented in the form of transition tables.\n", + "\n", + "The mathematical model of a discrete-time system can be written in terms of a recursive formula by using linear matrix **difference equations** as:\n", + "\n", + "\\begin{equation}\n", + "\\begin{cases} \n", + "\\mathbf{x} [(k+1)T] = \\mathbf{A_dx} [kT] + \\mathbf{B_du} [kT]\\\\\n", + "\\mathbf{y} [kT] = \\mathbf{C_dx} [kT] + \\mathbf{D_du} [kT]\n", + "\\end{cases} \n", + "\\end{equation}\n", + "\n", + "where\n", + "* $\\mathbf{x} [(k+1)T]$ - system state vector in the future\n", + "* $\\mathbf{x} [kT]$ - current system state vector\n", + "* $\\mathbf{y} [kT]$ - current output vector\n", + "* $\\mathbf{u} [kT]$ - control inputs\n", + "* $\\mathbf{A_d}$ - discrete state matrix\n", + "* $\\mathbf{B_d}$ - discrete input matrix\n", + "* $\\mathbf{C_d}$ - discrete output matrix\n", + "* $\\mathbf{D_d}$ - discrete feedforward matrix\n", + "\n", + "Note that $\\mathbf{A_d}$ and $\\mathbf{B_d}$ are obtained for the time interval from to $0$ to $T$. It can easily be shown that due to system time invariance the same expressions for $\\mathbf{A_d}$ and $\\mathbf{B_d}$ are obtained for any time interval.\n" + ], + "metadata": { + "id": "qdckblFdo3ZV" + } + }, + { + "cell_type": "markdown", + "source": [ + "## **Approximations**\n", + "Real physical dynamic systems are continuous in nature, but since computers are discrete in idea, let's look at an example of transformation from continuous systems to discrete.\n", + "\n", + "Let's compare discrete model with continuous-time state space:\n", + "\\begin{equation}\n", + "\\begin{cases} \n", + "\\mathbf{\\dot{x}} =\\mathbf{A}\\mathbf{x} + \\mathbf{B}\\mathbf{u} \\\\ \n", + "\\mathbf{y}=\\mathbf{C}\\mathbf{x} + \\mathbf{D}\\mathbf{u}\n", + "\\end{cases}\n", + "\\end{equation}\n", + "\n", + "Let's apply the **Euler method** for the first equation. It is based on the approximation of the first derivative at $t = kT$:\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{x}} = \\frac{d\\mathbf{x}}{dt} \\approx \\frac{1}{T}\\left(\\mathbf{x} [(k+1)T] - \\mathbf{x}[kT]\\right)\n", + "\\end{equation}\n", + "\n", + "Applying this approximative formula to the state space system equation, we have:\n", + "\n", + "\\begin{equation}\n", + "\\frac{1}{T}\\left(\\mathbf{x} [(k+1)T] - \\mathbf{x}[kT]\\right) \\approx \\mathbf{A}\\mathbf{x}[kT] + \\mathbf{B}\\mathbf{u}[kT]\n", + "\\end{equation}\n", + "\n", + "So, after the little changes we obtain:\n", + "\\begin{equation}\n", + "\\mathbf{x} [(k+1)T] \\approx (I+T\\mathbf{A})\\mathbf{x}[kT] + T\\mathbf{B}\\mathbf{u}[kT]\n", + "\\end{equation}\n", + "\n", + "Then we can conclude that $\\mathbf{A_d} = (I+T\\mathbf{A})$ and $\\mathbf{B_d} = T\\mathbf{B}$" + ], + "metadata": { + "id": "k96lffmSvVCK" + } + }, + { + "cell_type": "markdown", + "source": [ + "### **Example**" + ], + "metadata": { + "id": "CQ0eWRRDy3WW" + } + }, + { + "cell_type": "markdown", + "source": [ + "> **Mass-spring-damper system**\n", + ">\n", + ">Consider a following unforced system:\n", + ">\n", + ">

\"mbk\"

\n", + ">\n", + ">Dynamics of this system desribed by following ODE:\n", + "\\begin{equation}\n", + "m\\ddot{y} + b \\dot{y} + k y = u\n", + "\\end{equation}\n", + ">\n", + ">And one can formulate this system in state space as:\n", + "\\begin{equation}\n", + "\\dot{\\mathbf{x}}\n", + " = \\mathbf{A}\\mathbf{x} + \\mathbf{B}\\mathbf{u} =\n", + "\\begin{bmatrix}\n", + "\\dot{y}\\\\\n", + "\\ddot{y}\n", + "\\end{bmatrix}\n", + "=\n", + "\\begin{bmatrix}\n", + "0 & 1\\\\\n", + "-\\frac{k}{m} & -\\frac{b}{m}\n", + "\\end{bmatrix}\n", + " \\begin{bmatrix}\n", + "y\\\\\n", + "\\dot{y}\n", + "\\end{bmatrix}+\n", + "\\begin{bmatrix}\n", + "0\\\\\n", + "\\frac{1}{m}\n", + "\\end{bmatrix}\n", + "u\n", + "\\end{equation}\n", + ">\n", + "> In discrete space this model will have a following form:\n", + "> \\begin{equation}\n", + "\\mathbf{x}[(k+1)T]\n", + " = \\mathbf{A_d}\\mathbf{x}[kT] + \\mathbf{B_d}\\mathbf{u}[kT] =\n", + "\\begin{bmatrix}\n", + "y[(k+1)T]\\\\\n", + "y[(k+2)T]\n", + "\\end{bmatrix}\n", + "=\n", + "\\begin{bmatrix}\n", + "1 & 1\\\\\n", + "-\\frac{k}{m}T & 1-\\frac{b}{m}T\n", + "\\end{bmatrix}\n", + " \\begin{bmatrix}\n", + "y[kT]\\\\\n", + "y[(k+1)T]\n", + "\\end{bmatrix}+\n", + "\\begin{bmatrix}\n", + "0\\\\\n", + "\\frac{1}{m}T\n", + "\\end{bmatrix}\n", + "u[kT]\n", + "\\end{equation}" + ], + "metadata": { + "id": "_Vta3AHcyZIk" + } + }, + { + "cell_type": "markdown", + "source": [ + ">### **Exercise**\n", + ">Find the exact and approximate descretization of the following systems. \n", + "* $\\dot x = \n", + "\\begin{bmatrix} 10 & 0 \\\\ -5 & 10\n", + "\\end{bmatrix}\n", + "x\n", + "+\n", + "\\begin{bmatrix} \n", + "2 \\\\ 0\n", + "\\end{bmatrix}\n", + "u\n", + "$\\\n", + ">\\\n", + ">when $T=0.1$ sec\n", + ">\n", + ">* $\\dot x = \n", + "\\begin{bmatrix} 2 & 2 \\\\ -6 & 10\n", + "\\end{bmatrix}\n", + "x\n", + "+\n", + "\\begin{bmatrix} \n", + "0 & -1 \\\\ 5 & -1\n", + "\\end{bmatrix}\n", + "u\n", + "$\\\n", + ">\\\n", + ">when $T = 0.5$ sec" + ], + "metadata": { + "id": "TDjeTBuG9nVe" + } + }, + { + "cell_type": "markdown", + "source": [ + "## **Solution of the Discrete-Time state equation**\n", + "\n", + "We find the solution of the difference state equation for the given initial state $\\mathbf{x}[0]$ and the input signal $\\mathbf{u}[kT]$. From the state equation:\n", + "$$\n", + "\\mathbf{x} [(k+1)T] = \\mathbf{A_dx} [kT] + \\mathbf{B_du} [kT]\\\n", + "$$\n", + "for $k = 1, 2 ...$ it follows:\n", + "$$\n", + "\\mathbf{x}[T] = \\mathbf{A_dx} [0] + \\mathbf{B_du} [0]\\\\\n", + "\\mathbf{x}[2T] = \\mathbf{A_dx} [T] + \\mathbf{B_du} [T] = \\mathbf{A_d}^2\\mathbf{x} [0] + \\mathbf{A_d}\\mathbf{B_du} [0] + \\mathbf{B_du} [T] \\\\\n", + "\\mathbf{x}[3T] = \\mathbf{A_dx} [2T] + \\mathbf{B_du} [2T] = \\mathbf{A_d}^3\\mathbf{x} [0] + \\mathbf{A_d}^2\\mathbf{B_du} [0] + \\mathbf{A_d}\\mathbf{B_du} [T]+\\mathbf{B_du} [2T] \\\\\n", + "\\vdots \\\\\n", + "\\mathbf{x}[kT] = \\mathbf{A_dx} [(k-1)T] + \\mathbf{B_du} [(k-1)T] = \\mathbf{A_d}^k\\mathbf{x} [0] + \\sum^{k-1}_{i=0} \\mathbf{A_d}^{k-i-1}\\mathbf{B_du} [i]\n", + "$$\n", + "\n" + ], + "metadata": { + "id": "xNFwQZs_0dK2" + } + }, + { + "cell_type": "markdown", + "source": [ + "## **Stability**\n", + "\n", + "The concepts of stability is fairly general and can be applied to the descrete time systems, however, in this case solutions may be analized directly, and stability criterias are the following:\n", + "\n", + "\n", + "* Asymptotically stable $|\\lambda_i| = \\sqrt{\\operatorname{Re}(\\lambda_i)^2 + \\operatorname{Im}(\\lambda_i)^2} < 1,\\forall i$ \n", + "* Lyapunov stable: $ |\\lambda_i|\\leq 1,\\forall i$\n", + "* Unstable: $\\exists\\lambda_i, |\\lambda_i|>1 $" + ], + "metadata": { + "id": "-vkIPnsh_tfU" + } + }, + { + "cell_type": "code", + "source": [ + "import numpy as np\n", + "from matplotlib.pyplot import *\n", + "from scipy.integrate import odeint\n", + "\n", + "def StateSpace_without_control(x, t, A):\n", + " return np.dot(A,x)\n", + "\n", + "#@markdown Mass-spring-damper parameters\n", + "\n", + "m = 1 #@param {type:\"slider\", min:0, max:10, step:1}\n", + "k = 5 #@param {type:\"slider\", min:0, max:5, step:0.1}\n", + "b = 2 #@param {type:\"slider\", min:0, max:5, step:0.1}\n", + "T = 0.515 #@param {type:\"slider\", min:0.001, max:1, step:0.001}\n", + "\n", + "t0 = 0\n", + "tf = 10\n", + "t = np.arange(t0, tf, T)\n", + "\n", + "A = np.array([[0, 1],\n", + " [-k/m, -b/m]])\n", + "\n", + "B = np.array([[0],\n", + " [1/m]])\n", + "\n", + "x0 = np.array([-4, 0])\n", + "\n", + "x_d = x0\n", + "x_disc = x0\n", + "\n", + "A_d = np.eye(2) + T*A\n", + "\n", + "# Simulation for discrete time model\n", + "for time in t:\n", + " x_d = A_d @ x_d\n", + " x_disc = np.vstack((x_disc, x_d))\n", + "\n", + "y_disc, dy_disc = x_disc[:,0], x_disc[:,1] \n", + "t_disc = np.insert(t, 0, 0)\n", + "\n", + "# Simulation for continuous time model\n", + "x_sol = odeint(StateSpace_without_control, x0, t, args=(A,))\n", + "\n", + "y_cont, dy_cont = x_sol[:,0], x_sol[:,1]\n", + "\n", + "plot(t, y_cont, 'r', linewidth=2.0, label = r'Position $y_c$ (m)', alpha = 0.5)\n", + "step(t_disc, y_disc, 'r', linewidth=2.0, label = r'Position $y_d$ (m)')\n", + "plot(t, dy_cont, 'b', linewidth=2.0, label = r'Velocity $\\dot{y_c}$ (m/s)', alpha = 0.5)\n", + "step(t_disc, dy_disc, 'b', linewidth=2.0, label = r'Velocity $\\dot{y_d}$ (m/s)')\n", + "legend()\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'System state')\n", + "xlabel(r'Time $t$ (s)')\n", + "show()\n", + "\n", + "plot(y_cont, dy_cont, 'r', linewidth = 2., alpha = 0.5, label = 'Continuous model')\n", + "step(y_disc, dy_disc, 'r', linewidth = 2., label = 'Discrete model')\n", + "legend()\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "ylabel(r'Velocity $\\dot{y}$ (m/s)')\n", + "xlabel(r'Position $y$ (m)')\n", + "xlim([-10, 10])\n", + "ylim([-10, 10])\n", + "show()" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 552 + }, + "id": "eY5Id0j4AGLo", + "outputId": "3a5eab5b-a7a3-468b-af30-900628ff55ce" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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7zcvLY+XKlTz88MP1OgwITfkaDvFM93pme9oypoWDaREZXhkI/zqwOuj9HBH5FrAeuFtVPz3zBBG5HbgdoH379iGJVZYsWcKpU6dCEhJ1796dtLQ0du/eHRiQ7dixI/369aO8vJwjR44Ejh04cCBVVVUhcZx69uxJt27dQupMSUmhT58+HDhwICR8x6BBgzhy5EjIrK4+ffrQsWPHkC/1bt260bNnTz788EOqqqoAaNeuHQMHDqSiooLDhw8Hjr3wwgsB2Lt3b6NtqhtfCLdN6enpgXnrO3fubFGbJkyYwK5du8Ju05e+9CV27twZdpsauk+1tbWUlJSwePHiQNns2bOZMmUKubm5lJSUkJubS3Z2NgsXLmTRokUhISQKCwspKioKGeBfsGABGRkZIV8sOTk5zJkzh7lz51JWVhaws6CggFWrVrF6tfPRXbJkCQDz5s0LlOXl5TFz5kzy8/MD9zQ9PZ2lS5eybNkyiouLA8cWFBRQWlraYJvqaG6bqqurQ85PhDa19D6VlJQE1kud2SaYCTiJmlrSpjpaw2evJbjePSUiHYADwAhV/UhEegGfAAosBnqraqOJqFNTU7WysjKkrK12T+3cuZNBgwa5bUZcaOoe5+bm2kIuP6aFQ2NaWPdU03ihe+oqYKOqfgSgqh+pao2q1gK/A8Y2VYHlCHewHOEOOTk5bpvgGUwLB9MiMrzgNPII6poSkeCpUDOALU1V0LNnzxiY1ToxLRzmzJnjtgmewbRwMC0iw1WnISIpwNeA/w0q/pmIbBaRd4FJwLx6Tw4iuE+8rfPhhx+6bYJnmDt3rtsmeAbTwsG0iAxXB8JV9RiQdkbZN5tbT92Aq2FaBFM3cGiYFsGYFpHhhe4pwzAMo5WQEE6jJYvZEpVoauF2gqdIscVsDqaFg2kRGa5PuY0Gl1xyia5fvz6krK1OuW1L2D02oo1NuW2ahHjSCF4E5yUmTZoUsiAIYOnSpdx1110NnlOXVKklXHbZZVRUVNSb4S9WNDfdazB33nknb7zxxlnl0UoJu2rVqojOTyRMCwfTIjLMacSQvLw81qxZE1K2Zs0a/8rT6PPmm29y+PDhuDqN5qZ7Deatt95i3LhxZ5VHKyVs8GrZto5p4WBaREZCOA2vcsMNN/D8889TXV0N+GJkHThwgAkTJvDEE08wduxYMjMzueOOO+r9pV5fSliA3//+93zxi19k9OjRfPObzmSzhtLCLly4MOT8++67j1/+8pch12ppyteWpHsFX9fS4MGDOXnyZL0pbuOVEtYwjGbS3FR/Xty6det2VhrDplKBxoupU6fq2rVrVVX1gQce0Lvvvlu3bdum06ZN0+rqalVVveuuu7SgoEBVndSuDaWE3bJliw4aNEg//vhjVVWtqKgIXCslJUXff//9s9LC7t69W7OyslTVl9r1oosu0k8++STEzpakfG1puldV1QcffFBXrFjRYIrbcFLCNnWPp02b1uj+toRp4dCYFpbutektIaYd1QW+a4gf/Sg21w2n3rouqunTp7NmzRpWrFjByy+/zIYNG8jOzgZ84wJnruQOTuEKBFK4igg33ngjPXr0AM6eCXLhhRdy6NChkLIBAwaQlpbGpk2b+Oijj8jKyiItLWR5TEjK1507d9ab8vVMGkv3CjSY7hV86WMfe+wxPv/8c+6++27uuecepk2bFkgeFZwStkuXLo3a0RB1AdwM0yIY0yIyEsJpeJnp06czb948Nm7cyPHjx7n44ot58803yc/P54EHHoibHbfddhsrV67k0KFDzJpVf/zH+lK+1tTUMH/+fESE/v37893vfjdwfEvTvR4/fpzKykr69OkD0GCKW0sJaxgepLmPJl7cvNw9pap600036ejRo3XhwoWqqrp161bNyMjQjz76SFV9XUx79uxRVad7asOGDTpq1Cg9duyYfv755zpixIiQ7qm67qX6uqc++eQT7devX4gNVVVVOnjwYB04cGCgC+pMnn32We3evbsuWLAgUPbrX/9a//a3vzXYtr59++qJEydUVc/qFsvPz9c//elPZ+177rnn9J577lFV1f379wfOLywsDHRhffLJJzpkyJAGr6tq3VPNwbRwsO4pB9pq95TXycvLY8aMGYGZVMOHD+fHP/4xV155JbW1tbRv357ly5fTv3//wDkNpYQF30D2xIkTSU5OJisri5UrV4Zcr760sB06dGDSpEmkpqY2ONOpvpSvGzZs4M4772ywbS1J9/riiy9yww03ALB58+Z6U9zGKyWsYXiWqVPhhUYzXYePRnHRSHO9jBc3rz9pxJP333+/3vKamhodPXp0g/tVVWfPnq0rV64MKVu7dq3OmjVL77777pCnmjo2bNigN998c7NszMrKCkwCaIgZM2boe++91+gx9qQRPqaFQ6t50qirKBpbg5do/pNGQky5tbAADvVpsW3bNjIyMpg8eXK9CZoaS/k6ffp0VqxYwS9+8Yt6625uulfwjWG0b9++wf3RSgkbq/UwrRHTwiFeWohEuKFM5bnouI1otkujXKEbWBiRtondYyPaRCMESDR7lSK1pSnabBiR4KmcbZ3gHORtnTOfmtoypoVDrLV4/nnPPRxElYRwGpHGKEokTAsHr4aXcQPTwsG0iIyEcBqGYRhGfEgIpxG8oKytY1o4pKenu22CZzAtHEyLyHB9IFxE9gBHgRrgtKpeIiLdgT8AA4A9wE2q+mlDddhAeNvE7rERbbyUCyMetrTmgfBJqpoZZPy9wMuqOgh42f++QcrLy2NtX6vBtHBYtmyZ2yZ4BtPCwbSIDK84jTOZDhT4XxcA1zZ28GeffRZzg1oLR44ccdsEz3BmAqy2jGnhYFpEhhfCiCjwkogo8N+q+lugl6oe9O8/BPQ68yQRuR24HaB9+/bk5uYG9i1ZsoRTp06xc+fOQFn37t1JS0tj9+7dgRlGHTt2pF+/fpSXl4d82Q4cOJCqqioOHDgQKOvZsyfdunULqTMlJYU+ffpw4MABjh07FigfNGgQR44cCfnV36dPHzp27BgyJbZbt2707NmTDz/8kKqqKsCX43vgwIFUVFSEzPKoi+S7d+/eRttUF0AwkdrU0H2qra2lpKSExYsXB8pmz57NlClTyM3NpaSkhNzcXLKzs1m4cCGLFi1i3bp1gWMLCwspKipi+fLlgbIFCxaQkZERMi0zJyeHOXPmMHfuXMrKygJ2FhQUsGrVqpCkPnURVOfNmxcoy8vLY+bMmeTn5wfan56eztKlS1m2bFnIl1hBQQGlpaUNtqmO5rapuro65PxEaFNL71NJSQmlpaX1tglmAgTscrdNhYF9sbpPLaK5S8ijvQEX+P/2BP4JfAWoPOOYTxurw8KIODQWJqQlfOlLX4pqfdHEwoiEj2nhEOswItEiHrbQGsOIqOp+/99y4BlgLPCRiPQG8P9ttKN+wIABMbay9TBw4MCo1vfmm29Gtb54UlBQ0PRBbQTTwsG0iAxXnYaIpIhIl7rXwJXAFuBZoO4ZLR/4c2P11HWDeI1Jkyad1X+6dOlS7rrrrgbPqUvZ2hIuu+wyqqqq4pojHHxJpCZOnNis+FMAd955J2+88Ua9+6qrq/nKV74S0WLFui4Iw7QIxrSIDLefNHoBr4vIP4ES4HlVLQJ+CnxNRHYCV/jfN8jBgwcb2+0adVn7glmzZk3MAqa9+eabHDhwIO5O49FHH+W6665rMOR6Q7z11luMGzeu3n0dOnRg8uTJgZzhLSG4vznRmDq1ecHvLr10bL3lbTH6fCJ/LuKBq05DVXep6mj/NkJV/9NfXqGqk1V1kKpeoaqtct3/DTfcwPPPP091dTXgi5F14MABJkyYwBNPPMHYsWPJzMzkjjvuqPdX+kMPPcTIkSMZOXIkS5cuDZT//ve/54tf/CKjR4/mm9/8ZqC87inl3nvvpaysjMzMTObPn8/ChQtDzr/vvvv45S9/GXKtLVu2cNlllwXeb9y4kcmTJ4fVzieffJLp06ezZ88ehg4dyi233MLgwYP5xje+wV//+lfGjx/PoEGDKCkpCZyzfft2Bg8eTHJyMseOHWPq1KmMHj2akSNHBhzFtddey5NPPhmWDW2NaAXEi2ZgPaON0NxBEC9uTQ2ERzMsfRgh6kOYOnWqrl27VlVVH3jgAb377rt127ZtOm3atEBOibvuuksLCgpU1cnct379eh05cqR+/vnnevToUR0+fHhI5r6PP/5YVevP3HdmBr3du3drVlaWqvryalx00UWBzH911NTUaK9evQJZ/SZOnKgbNmxosn1VVVXaq1evwHWSk5P13Xff1ZqaGh0zZozeeuutWltbq2vXrg1k5VNVffDBB3XFihWqqvrUU0/pbbfdFthXWVmpqqqnT5/WHj16NHjttjwQ3txB0vq08NKgbzyxgfDga7TRzH09e/Z024QGqeuimj59OmvWrGHFihW8/PLLbNiwgezsbMA3JnBmG15//XVmzJhBSkoKANdddx2vvfYaIsKNN95Ijx49gLPzZ/Ts2ZNPPw1dPD9gwADS0tLYtGkTH330EVlZWaSlpYUck5SUxIgRI9i6dSs7d+6kf//+jBkzJuSY4uJiysvLQ55uPvnkE1JTUwPvBw4cyKhRowAYMWIEkydPRkQYNWpUSDTi4uJiHnvsMQBGjRrF3XffzT333MO0adOYMGECAMnJyXTo0IGjR4/SpUuXMNQOZfbs2c0+J1ExLRxMi8hICKfRtWvXRveriyEBpk+fzrx589i4cSPHjx/n4osv5s033yQ/P58HHngg6tfr1q3bWU4DfOliV65cyaFDh5g1a1a9544bN4433niDhx9+mKKiIsA3IP3973+frl278vbbb4fMKwc455xzAmtDIDT2VVJSUuB9UlJSYFD7+PHjVFZW0qdPHwAGDx7Mxo0beeGFF7j//vuZPHkyCxcuBHyTHDp16tQiLaZMmdKi8xIR08LBtIgMtwfCo4KXZ0Oce+65TJo0iVmzZgUGwCdPnsxTTz0VWCh3+PBhPvjgg5DzJkyYwNq1azl+/DjHjh3jmWeeYcKECXz1q1/lT3/6ExUVFYFzg9m5cyddunTh6NGjIeUzZsygqKiIdevWkZOTU6+t48aN4/7772fGjBlccMEFADzyyCPk5+fzk5/8hKqqKoYMGRJyznnnnUdNTU2I42iKV155hUmTJgXeHzhwgM6dO3PzzTczf/58Nm7cCEBFRQU9evRoNMtfYwQvsmrrmBYOpkVkJMSThtfJy8tjxowZgZlUw4cP58c//jFXXnkltbW1tG/fnuXLl9O/f//AOWPGjOGWW25h7NixgO9JISsrC/ANZE+cOJHk5GSysrJYuXJlyPXS0tIYP348I0eO5KqrruLnP/85HTp0YNKkSaSmpjY4y2no0KF07NiRe+65J1C2adMm7rjjDo4ePUqPHj2QuihqQVx55ZW8/vrrZGRkhKXHiy++yA033BB4v3nzZubPn09SUhLt27fnkUceAXzOZWoCTu+JdmY3w4grTQ164JsWuwJ40f9+OPDt5g6exHKzFeEODa0Ir6mp0dGjRze6Ynz27Nm6cuXKkLJVq1Zpfn6+3nXXXTp//vx6z9uwYYPefPPNYduYlZUVmATQGDNmzND33nuvwf2tdSA8WhMxrr46/GvaQLiDDYQHXyM2A+ErgceA+/zv38cXtnxFlP1Xi6kbLDbq12Lbtm1MmzaNGTNmMGjQoLP2l5WVMXXqVMaPH39WKsy8vLwm15WMGTOGSZMmUVNTE9Zajbrup8aorq7m2muvZfDgwU0e2xB1Ew28SjzH2ryuRTwxLSKjyXwaIrJOVbNFZJOqZvnL3lHVzLhYGAaWT6Nt0lrvsVdyNnjFDi/hJU1acz6NYyKShi8aLSIyDvBU/G2vrgh3g+Aotm2dRYsWuW2CZzAtHEyLyAine+r7+GJBpYvIG8AXgBtjalUzCQ7h3dYxLRyCQ1G3dUwLB9MiMsJxGluBicAQQID3SJCpuoZhGEbzCOfL/x+qelpVt6rqFlU9Bfwj1oZFg6bGa4zWi91bw3CHBp80ROR84ALgHBHJwveUAdAV6BwH28KmvvUBnTp1oqKigrS0tHrXFiQq9c2OSjRUlYqKiiZXihcWFja6vy3RFvDw2UkAACAASURBVLQIf/1LIW3oKyHqNNY9lQPcAvQFHgoqPwr8ewxtajb15Qjv27cv+/bt4+OPP3bBIvc4ceIE55xzjttmxJxOnTrRt2/fRo8pKiqykBF+2oIW0VowefXV0aknUQlnyu31qvp0nOxpEampqVpZWem2GZ4gNze3TfyqDAevauHGtM76tPDS9NJoEG57vPq5OBOvTrltciBcVZ8WkanACKBTULnNWzMMwziTqMWJ8aY3b3IgXER+A/wL8B184xo3Av0bPckwDKOtkuCBxcKZPXWZqn4L+FRV/wP4EtDy2A4xoHfv3m6b4BkWLFjgtgmewbRwMC0c4qZFpOHFPEo4TuOE/+9xEekDnAIi/pYWkQtF5BUR2SYiW0Xke/7yH4nIfhF5x781OSwVnMOhrRNupNm2gGnhYFo4mBaREY7TeE5EUoGfAxuBPcDqKFz7NHC3qg4HxgGzRWS4f98SVc30b00+6wVnhGvrnBlwsC1jWjg0qoVIZFsrC19vn4vICGdF+M9UtQp4WkSewzcYHn7GnQZQ1YPAQf/royKyHd+6EMMwWhMJ3odvhBKO0/gHMAbA7zyqRGRjXVk0EJEBQBbwNjAemCMi3wLW43saOSt/qYjcDtwO0L59+5BsXEuWLAFg3rx5gbK8vDxmzpxJfn5+INtdeno6S5cuZdmyZRQXFweOLSgooLS0lMWLFwfKZs+ezZQpU0Kuk52dzcKFC1m0aFFIPJvCwkKKiopCUqMuWLCAjIyMkF85OTk5zJkzh7lz51JWVgb4cn4XFBSwatUqVq92HujCbdPWrVsBotKm5cuvorw88jDSF1zwDvv2Zba4TS29TyUlJeTm5nrwPjnTPeP12auurg4535e9cQ4AudOmtbhNdfNCc3NzXf9/qtO1qftUUlISyPYZi89eHZF/9pzPSTS/I4Lb1CIaSrQBnA9cDGzH94U+xr9dDuxobuKORq5zLrABuE6dpE/J+LrO/hN4tKk6LrzwwhYnIUk0fv3rX0etrmglC3IrqU00tYgmbmhSnxZRscNDWYvCNSXmn4soaeLVJEwNLu4TkXx8K8IvAdbhhBE5CqxU1f9tmZsKuUZ74DmgWFUfqmf/AOA5VR3ZWD315dMwIicai4sSbQFZNPCKJlGxwyuNwUOmRMkQry7ua3AgXFULVHUScIuqflVVJ/m3a6LkMARf9r/twQ5DRIJnZs0AtjRV1969eyM1J2GYO3eu2yZ4BtPCIeZaRDqYHscBdftcREY4s6f6ikhX8fE/IrJRRK6MwrXHA98EvnrG9NqfichmEXkXmATMa7QWoKqqKgrmJAZ1/Z6GaRFMzLSIZqCmOA2o2+ciMsIZCJ+lqr8UkRwgDd8X/ePAS5FcWFVfx+nyCsamYhhGa+H556NTj4WdbTWE86RRdzevBn6vqlup/8veNdq1C8f3tQ26d+/utgmewbRwMC0cTIvICCfK7WP41k8MBEbjm9n0N1W9OPbmhYcNhMcGGwiPDV7RxCt2AFExxjPtaasD4UF8G7gXyFbV40AH4NYW2Bcz6uYfG7Bq1Sq3TfAMpoWDaeFgWkRGk05DVWtVdaOqVvrfV6jqu7E3LXzMaTgEL/Zp65gWDqaFg2kRGeE8aRiGYRgGYE7DMAzDaAZNDoQDiMh5wIUETdFV1Y0xtKtZjBo1Sjdv3uy2GZ6gtLQ0aqGfPTMQHq1MaFdfHb0pohHgxoBtfZ8LzwwcQ1wHwqP5PxKRIfGppolrxCDdq4gsxhdOpAwn/6ACX22ugYbRIqK16MuisRpGxITTPXUTkK6qlweFEvGUw7AwIg7BES4TjmbGScydNs3zWdDiRUJ/LpqJaREZ4TiNLUBqrA2JhCNHLBNXMFOnRicUUDSJyBaUqTwXXYMMw2gR4TiNB4BNIlIsIs/WbbE2rLm0onhpMSeavTCRhhaKVmiiF0iQm2MYrZxw4m8UAP8FbAZqY2uOuyRCl3deXh7P+X+Ue6FXJhrjzi196snLy4v84gmCaeFgWkRGOGFE1qlq5OnbYojIJaoaWRgRT80kiRBPtSUKM5/EP//C8j4kph2AhRGJXTVNXCM2YUReE5EHRORLIjKmbmuhjUaMCU1/6QFcfHzznBYuYlo4mBaREU73VJb/77igssSdchvpCLDLawE8G1IlosUeLTvNs1q4gGnhYFpERpNOw5+9LyE5fRrKymDbNqdsNV8nlcqztk6cDO+7KxEGRgzDMBognMV9vYCfAH1U9SoRGQ58SVVXxNy6GFBdDTt3wvbt8P77vvfBvPfD+oOZdewIqakNb506gST53YqLTyvp6emRXTuBMC0cTAsH0yIywhkIfxF4DLhPVUeLSDtgk6qOioeB4dDUQPjJkz4HsW0blJb6njDq6NMHhg2Dr3zF937rVqisPHs707mcSceOkPrkcr6w9RXO5xC9Ocj5HCKF4y1rVCIMCIJ3Bjg9JIpXTPGKHYB3PifRIMEHwsOePSUim1Q1y1/2jqpmRmBrVKnPaRw/Djt2+J4odu2Cmhpn34UX+hzFsGFw3nl1dfj+1ieHKpw4Ub8zacqpdO0KvXvD+ef7/vbu7Str8GEkwk/KsmXL+M535kRSRXRx8ctg2bJlzJkzJ7SSaBDhuJVX4nFFZVZatIjj5yTkcxELEtxphDMQfkxE0vDHnRKRccCRFtjXLERkCvBLfJkC/0dVf9rECRzlXLYzjO0MYw8DUP8ohKAM4AOGs42h7KArR+upoOE7IwKdO/u2Pn3qOdPvVD79FMrL4eBBOHTIt332mW977z3n+M6dHSdyfs9aenevIq1LNXIqyPPs3w/JyZCU5Pt75uu690lJIV+IxcXFQAz/IVoRxcXFzpfD1VcnVgwrL9jQSgn5XBjNJhyn8X3gWSBdRN4AvgDcGEujRCQZWA58DdgHrBORZ1V1W0PnrGAW++gbcBRJ1JJOGcPYzlB2tLybKBx7q6voXFlB508Pc8HpE2R1rYJO1dT2quLwYThUnsTB8mQOVnTgUEV7jp8QdtXUsKumBmp96yU7JNfQK+VzenMVPfiEc378Zzq3P8U57U/7/rY7RYfkmvp/MAc5lBllZU7AjeXLoV0735ac7LwOdzvTMYk4r4P+KkKNJnHqtHCqNtn3tyaJ6tNJnOIiakim9h+fUluj1Nbi+6tCzWn/+7qtRqlVqK3xPRnWlUMPAIoe/xhUA7+QQ/6eVa6wdxD/t/JD3/sbH0Zu9B0TMB9FxPeJqQtXEhy6RASSREPLb7rBd42n3wu14YzhrJC/ImccNxSAnYU7Qg8+64PlKz/rl6YIMMj3+rnnz9qvZ0zZUIVFixaxcOHCkDKm+15ve7a0wXPrIza/fEf4NPpzadOHNogvnNDWJuo491Bak8dE9mA6zPfn2UjaAoH2PFsWUS3J7ZMYetXACG1xCMdpbAUmAkPwTX58j9jn4RgLlKrqLgARWYPvI96g09j7wxW0awfp6TB8OAweDOec04wrNvUhOXUKDh+GigrfVvf68GH4/PN6T0nC93XXAxh5DtAX9AL4rKojhz4/l4Ofd+Hg5104dKIbR051Zu/pLuxlrO/kfZf6vjHrAu7V1pJMDee0O8U5ydV0blft/G13KuBgDh/vF7j+/rKT1GgSNbUS9t9adV6frk3yOYEa5291TfJZZadqk6nVhgT8pu/Pv/0z/HtxFpcD8NaKrc06q8Pegfx95a4Irlsf1/v+/PpgBHX4nMaTDx6KoI6Zvj8/3x/W0dW7svnDg/vOKPV9Kf3xoTPL3cDnjFkSiS2+9vypiTqqd13c5DGRcZPvT8S6+tvzUGQBWc85h7g7jX+o6hh8zgMAEdkIxHKB3wVAsFL7gEuDDxCR24Hbfe8u5pVXZpOScoC33z7NkiVL2L8/NJplXl4eM2fOJD8/PzBPOz09naVLl7Js2TLqunS+ceWVLF+0iANbtvDUb39Ll+pqupw6xeVZWWRkZITkF77ggguYOHEir7z2GjvKy/msQweqkpNZ+OMf8/Y77/CnZ5/ldFISp0S44zvfod+gQXz3Bz/gVFISp5OSmJSTw//3vXzmzpvH++/v4+TJ81jMNipJ5aWLJvP3v6+jpqYjNTUdmTJlBqdOCUVFRYHrjxo1ilGDR7L2mWc4eeIEAnQ97y74wLd/yp97kqS+345TvvY1Kj/9lPUlJYGykcOGceEFF/CXl14iSWsR4AvduzNqxAi2bN7MpxUVvl/hwPjLLuPQx4fYVVYW8K9DBw8mJSWFTRs3kkQNyXKaC85PY9jggWx+Zx0nj33KFXxAO06TNGAcu3eVsXt3GUlSC6J8+bJxiCj/ePN1oJYkahk6dBDDhw2h+KUiqk4eR6ilzmmkdXiFXbt2oQgqwrTcXD79tJLXXnsd9f2k5+LsS0hPH8SaNWtI61bLof3/pHcf3336299fY/+Bg6C+X9T/8vWvs7N0F+vXb/A7PeGy8V8m9bzuPPfc84BQizBwwEDGXHwJf/nry3yVLQA8/zFcffVVbN22gx3bt1P3q2PiRJ+tf3v174H7NHjIUIYOGUpxcTEnT1YF2pMxujP//Oe7fPCB/4apcmXOlRyprKSkpCRw/he/+EUG9O/Ps4WFgbJr2I2gvH3yPMo/KnfKr5nGnj0f8O67vozMgjL20kv52oAM/v5qMXXdsP379w/YsfND32eqU8eO5OTksGPHDt57//1AnZdPnHBWm4YOGczQoUMpKirmZFUVAKndunH55ZfzzjvvsKeuTcCUnBwqKyt56+23A2WZo0czYMAA1v75zwBci9+5Z13JW2+9xaGPPgoce+306ezZs4d3/un88Bh36aWkpqZSVFyMg6895Uf+wZEjvh70Tp06kZNzJTt2vMd7/j7i9l1q6TPQ94X86quvBs4eMmQIQ4cOobj4JU6ePAlAt27duPzyibzzzj+d+wTk+Nv0dlCbRo8ezYAB/eFV32/bP394kl69ejFu3KW89dbbfBTUpunTr2HPng/4Z1CbLvW3qTjQJl97hmd14G9/e7XRNgFMnDix3jYNyRzeyPde82lwIFxEzsf35f0Evp81dd8VXYHfqOrQFl0xHKNEbgCmqOpt/vffBC5V1Xo7Ii8R0fVNPTOrwrFjcOSIM9AQtMmsW32H/fBH9Z+fnOwbNe/eHdLSfFvd60ZHtptJI6Nfp0/7xk6OH2/47+bNpSxc6PuH+O//Dh0CacnWvn3o1qHD2WXt2/uObW57oiBJo5SUlDB27NgWXzeqxkS3imZXUp8WnpltBHHVNSafi5YYEp9qmrhGdAfCc/AlX+oLPIjjNI4C/94SA5vBfnyZAuvo6y9rmKNHfQ6gAafAZ58Fxg8a5bzzznYKaWnQrZuvI9xF2rWDLl18W0OsWDEP8P0ivf32+NjlVRYvXkxh0K/ztoxp4WBaREaDTkNVC4ACEbleVZ+Oo00A64BBIjIQn7P4OoFO3AZ48MGma+3c2fdU0K2b72/w9h++Q2Tu9yIyPGpRRFr45FJIi6NunE200qwahpEwhDOm0VdEuuJ7wvgdvrGMe1X1pVgZpaqnRWQOUIxvyu2jqtr4KGhKiuMA6nMKXbr4+lEaIFozMiOuI5pTQyMlWnZEK6mGB5jKc77cHlFc9mEYrYlwnMYsVf2liOQAafimwzwOxMxpAKjqC0BY31qfZWTA/PkRXc/NvA8hRGhIUVERXBUFO4LxRKd385k9e3bU64xWMqh4+9FYaNFaMS0iI5wV4e+q6hdF5JfA31T1meDV4V7gkksu0fXrI8unEQ28MrAYNTs80iCPmAF4yBavDMhHi0RqT4IPhIczsrtBRF4CrgaKRaQLHsvgV1oa6SKaxCE3N9dtEzyDaeHQmBZtLU2yfS4iIxyn8W3gXiBbVY8DHYBbY2qVYRgxJ2r52z0yBGfEh3Ccxp+A3sBnAKpaoarvxtQqIzpE+hPSSGief94JONDSzWh7hOM0HsE33XWniPxURIbE2KZmk5KS4rYJniE7O8rp3FvxzKeoa9GKMS0cTIvIaHIgPHCgSDcgD7gPX4iP3wFPqOqp2JkXHok0EB7NpRGJ8kvQMwOceMgWjxjipUkXHpHEBsL9FafhWx1+G7AJX8jyMcBfmmljTDh4MJLgcd7ClkZEj0WLFrltgmdoNVrEoTu11WjhUZp0GiLyDPAa0BnIVdVrVPUPqvod4NxYGxgOx44dc9uEqNPSPuZp03JRjdKq9FbOunXr3DbBM3heizj+yvG8Fh4nnMV9v1LVV+rb0dzHGsMwjHqJyurayKswmqbBJw0RyRaR8+schoh8S0T+LCK/EpHu8TPRMAzD8AqNhUbfCFyhqodF5CvAGuA7QCYwTFVviJ+ZjZNIA+GeGczzEF7SJGBLpD9rI41s6RFRPGIG4CFb2vBAeLKqHva//hfgt6r6tKouoC6llEf47LPP3DYhBDeXRgQnaWrreFqLOK+I87QWcca0iIxGnYaI1I15TAb+L2hfOGMhcaO8vLzpg+JAtMbyIqln+fLl0TEiAYipFq1sRZx9LhxMi8ho7Mt/NfCqiHwCnMA3gwoRyQCOxMG2VofNWDKaha26N1ohDT5pqOp/AncDK4EvqzP4kYRvbMMwjJbghUdSw2ghYa8I9zLDhg3T7du3u22GJ4h5/mMX8FKOcM8MtjaTWH0uvKSH5QhvyTVitCLc63Ts2NFtEzxDRoan5ii4imnhYFo4mBaRkRBOY8+ePW6b4Bny8/PdNiFmNHcmWlpa91ad9yGaJPLnormYFpHhitMQkZ+LyA4ReVdEnhGRVH/5ABE5ISLv+LffuGGf4S0s74MRN6ZOtZQCTeDWk8ZfgJGq+kXgfeDfgvaVqWqmf7vTHfMML9HSvA91cbi80N9utBIsYmiTuLLeQlVfCnr7FhDR6vKuXbtGZlACkZOT47YJnsG0cDAtHMLSwn5pNIgXFunNAv4Q9H6giGzClynwflV9rb6TROR24HaAHj16hOT9XbJkCQDz5s0LlOXl5TFz5kzy8/M5fNi30D09PZ2lS5eybNkyiouLA8cWFBRQWlrK4sWLA2WzZ89mypQpIdfJzs5m4cKFLFq0KCRyZmFhIUVFRSGLiBYsWEBGRkZIf2pOTg5z5sxh7ty5lJWVAdC9e3cKCgpYtWoVq1evblGbgIRrU0vvU3FxsT/pzkIgND90S9oESwFfv7hbbYLm36eZM2eGnB+t+1RHbm6u6/9PUAgQVpumTJlSf5uC2gNuf0cUBvbF6v+pRahqTDbgr8CWerbpQcfcBzyDM/W3I5Dmf30xvmRPXZu6Vs+ePdXw8b3vfc9tEzxDsBZ1nVaREq164k2sPhde0iNcWxrVwkMNiocpwHpt5nd7zJ40VPWKxvaLyC3ANGCy33hUtQqo8r/eICJlwGCg0WiEVVVV0TA5Iaj7NWKYFsGYFg6mRWS4NXtqCvD/gGtU9XhQ+RdEJNn/+iJgELDLDRsNwzCMs3FrTGMZvq6ov4hvitpb6psp9RVgkYicAmqBO9WJtNsg7dp5YWjGG3TvbqlO6jAtHEwLB9MiMhIijIhX8mkY3iVaIRm8FDbDC3hJj6jY4qEGWRiRGFI3K8CAVatWuW2CZzAtHEwLB9MiMsxpJBjBU/DaOqaFg2nhYFpERkI4DcMwDCM+mNMwDMMwwiYhBsJHjRqlmzdvdtsMT1BaWmqhn/0EaxHtOHKt7d8mVp8LD40bh21Lo1p4qEE2EG4YLhLN+HEJHIvOMJokIZzG3r173TbBMwTHnWnrBGvR0ki59W2tMRe8fS4cTIvISAinYRiGYcQHcxqGYRhG2CSE07CwAA55eXlum+AZTAsH08LBtIiMhJg9ZWFEDMMdPDTZyLGFKEyV80CDbPZUDNmzZ4/bJniG0KQ0bRvTwsG0aAY2Pa5REsJpnD592m0TPIOFVHEwLRzalBZNTH/LnTYt8abHxZGEcBqGYRhGfEgIp9GxY0e3TfAMdTnCDdMiGNPCwbSIDBsINwyjxXhyINwDtkQDGwiPIeXl5W6b4BmWLVvmtgmewbRwMC0cTIvISAin8dlnn7ltgmcoLi522wTPYFo4mBYOpkVkuOI0RORHIrJfRN7xb1cH7fs3ESkVkfdEJMcN+wzDMIz6aefitZeo6i+CC0RkOPB1YATQB/iriAxW1Ro3DDQMwzBC8Vr31HRgjapWqepuoBQY29RJAwYMiLVdrYaCggK3TfAMpoWDaeFgWkSGm08ac0TkW8B64G5V/RS4AHgr6Jh9/rKzEJHbgdsBunXrRm5ubmDfkiVLgNAQyHl5ecycOZP8/PzAQqf09HSWLl3KsmXLQvo5CwoKKC0tZfHixYGy2bNnM2XKlJDrZGdns3DhQhYtWsS6desC5YWFhRQVFbF8+fJA2YIFC8jIyAhZmZuTk8OcOXOYO3cuZWVlgC+OVkFBAatWrQrJZRxum1JSUlizZk1Ctaml96myspLU1NSEalNL79ORI0f41a9+FfU21ZGbm+v6/xMUAjTZpsrKSh577LEG2+Sd74jCwL5YffZaQsym3IrIX4Hz69l1Hz7H8AmgwGKgt6rOEpFlwFuq+oS/jhXAi6r6VGPXSk1N1crKyqja31rJzc2lsLCw6QPbAKaFQ6y08NI013BtaS2fC69OuY3Zk4aqXhHOcSLyO+A5/9v9wIVBu/v6ywzDMAwP4Nbsqd5Bb2cAW/yvnwW+LiIdRWQgMAgoibd9hmEYRv24NabxMxHJxNc9tQe4A0BVt4rIH4FtwGlgdjgzp3r27BlDU1sXs2fPdtsEz2BaOHhdi6lT4YUX4nMtr2vhdSyMiGEYLSZa/e4ShRQY4ItqnihBar06puG1KbctorS01G0TPEPwzI22jmnh0Fq0aCKqeZNbOA6jtWjhVRLCaRiGYRjxwZyGYRiGETYJ4TRSUlLcNsEzZGdnu22CZzAtHEwLB9MiMmwg3DCMFhPtgfAE+DqKGjYQHkMOHjzotgmeYdGiRW6b4BlMCwfTwsG0iIyEcBrHjh1z2wTPEBzfpq1jWjiYFg6mRWQkhNMwDMMw4oM5DcMwDCNsbCDcMIwWYwPhscMGwmOI5Qh3KCoqctsEz2BaOJgWDqZFZCSE0ygvL3fbBM8QnNSlrWNaOMRaC5HItnhin4vISAinYRiGO1x9tTfrMmKHm+leDcNo5SRKRFkjfBLiSaN3795NH9RGWLBggdsmeAbTwsG0cDAtIiMhnEbHjh3dNsEzZGRkuG2CZzAtHEwLB9MiMhLCaezZs8dtEzxDfn6+2yZ4BtPCwbRwMC0iIyGchmEYhhEfXBkIF5E/AEP8b1OBSlXNFJEBwHbgPf++t1T1zvhbaBiGYdSHK05DVf+l7rWIPAgcCdpdpqqZzamva9eu0TKt1ZOTk+O2CZ7BtHAwLRxMi8hwNYyIiAjwIfBVVd3pf9J4TlVHNqceCyNiGEaiYWFE6mcC8JGq7gwqGygim0TkVRGZEE4le/fujY11rZC5c+e6bYJnMC0cTAsH0yIyYtY9JSJ/Bc6vZ9d9qvpn/+s8YHXQvoNAP1WtEJGLgbUiMkJVzwouJSK3A7cDtG/fntzc3MC+JUuWADBv3rxAWV5eHjNnziQ/P5/Dhw8DkJ6eztKlS1m2bBnFxcWBYwsKCigtLWXx4sWBstmzZzNlypSQ62RnZ7Nw4UIWLVoUEqO/sLCQoqKikHAFCxYsICMjI2TmRk5ODnPmzGHu3LmUlZUB0L17dwoKCli1ahWrVzvShNumrVu3JlybWnqfSkpKKCsrS6g2tfQ+bd++PeT8RGhTS+9TSUkJc+bMaQVtKgzsi9V9agmudU+JSDtgP3Cxqu5r4Ji/AT9Q1Ub7nlJTU7WysjL6RrZCcnNzKSwsbPrANoBp4WBaOLQWLbzaPeVmGJErgB3BDkNEvgAcVtUaEbkIGATsaqqidu0sGkod3bt3d9sEz2BaOJgWDq1Ni2gEdIym43HzSWMlvim1vwkqux5YBJwCaoEfqmqTPwlsINwwjERj6lR44YXo1NXQ13yrGghX1VuCHYa/7GlVHaGqmao6JhyHAQT66gxYtWqV2yZ4BtPCwbRwaC1aPP+878s+Gls0cXv2VFQwp+EQPDDW1jEtHEwLB9MiMhLCaRiGYRjxwZyGYRiGETaurgiPFqNGjdLNmze7bYYnKC0ttdDPfkwLB9PCwbRwaFUD4YZhGEbrIyGchoURcQheDdrWMS0cTAsH0yIyEsJpGIZhGPHBnIZhGIYRNgkxEC4iR3ESN7V1egCfuG2ERzAtHEwLB9PCYYiqdmnOCYkStOm95s4ASFREZL1p4cO0cDAtHEwLBxFpdvwl654yDMMwwsachmEYhhE2ieI0fuu2AR7CtHAwLRxMCwfTwqHZWiTEQLhhGIYRHxLlScMwDMOIA+Y0DMMwjLBp9U5DRKaIyHsiUioi97ptj1uIyIUi8oqIbBORrSLyPbdtchsRSRaRTSLynNu2uImIpIrIUyKyQ0S2i8iX3LbJLURknv//Y4uIrBaRTm7bFC9E5FERKReRLUFl3UXkLyKy0//3vKbqadVOQ0SSgeXAVcBwIE9EhrtrlWucBu5W1eHAOGB2G9aiju8B2902wgP8EihS1aHAaNqoJiJyAfBd4BJVHQkkA19316q4shKYckbZvcDLqjoIeNn/vlFatdMAxgKlqrpLVauBNcB0l21yBVU9qKob/a+P4vtiuMBdq9xDRPoCU4H/cdsWNxGRbsBXgBUAqlqtqpXuWuUq7YBzRKQd0Bk44LI9cUNV/w6cmeZ0OlDgf10AXNtUPa3daVwABIe43Ucb/qKsQ0QGAFnA2+5a4ipLgf8H1LptiMsMBD4GHvN31f2PiKS4bZQbqOp+4BfAh8BB4IiqvuSuVa7TS1UP+l8fAno1dUJrdxrGGYjIucDTwFxV/cxte9xARKYB5aq6wW1bPEA7YAzwiKpmAccIowsiEfH310/H50j7ACkicrO7VnkH9a2/aHINRmt3GvuBC4Pe9/WX1PPMQgAAA6JJREFUtUlEpD0+h/Gkqv6v2/a4yHjgGhHZg6/L8qsi8oS7JrnGPmCfqtY9dT6Fz4m0Ra4Adqvqx6p6Cvhf4DKXbXKbj0SkN4D/b3lTJ7R2p7EOGCQiA0WkA75BrWddtskVRETw9VtvV9WH3LbHTVT131S1r6oOwPeZ+D9VbZO/KFX1ELBXRIb4iyYD21w0yU0+BMaJSGf//8tk2uikgCCeBfL9r/OBPzd1QquOcquqp0VkDlCMbybEo6q61WWz3GI88E1gs4i84y/7d1V9wUWbDG/wHeBJ/w+rXcCtLtvjCqr6tog8BWzEN9twE20opIiIrAYuB3qIyD7gh8BPgT+KyLeBD4CbmqzHwogYhmEY4dLau6cMwzCMOGJOwzAMwwgbcxqGYRhG2JjTMAzDMMLGnIZhGIYRNuY0DMMwjLAxp2EYhmGEjTkNo00jImki8o5/OyQi+4PedxCRN2N03b4i8i8N7DtHRF71h/6vb38HEfm7P1KrYcQVcxpGm0ZVK1Q1U1Uzgd8AS+re+8OIxyo20WQajgE1C/hfVa1pwOZqfLkP6nU6hhFLzGkYRiOIyOciMsCf9W6liLwvIk+KyBUi8oY/49nYoONvFpES/5PKf9f3tCAiXwYeAm7wH3fRGYd8A38MIBFJEZHnReSf/mxzdY5irf84w4gr5jQMIzwygAeBof5tJvBl4AfAvwOIyDB8v/7H+59caqjni11VX8cXbHO6/4lmV90+f3yoi1R1j79oCnBAVUf7s80V+cu3ANnRbqRhNIU5DcMIj92qullVa4Gt+FJkKrAZGOA/ZjJwMbDOHzRyMnDmU0QdQ4Ad9ZT3AIIz620GviYi/yUiE1T1CIC/66paRLpE2C7DaBY2kGYY4VEV9Lo26H0tzv+RAAWq+m+NVSQiPfBljTtdz+4TQKe6N6r6voiMAa4GfiwiL6vqIv/ujsDJZrfEMCLAnjQMI3q8jG+coieAiHQXkf71HDeABnJTq+qnQLKIdPLX0Qc4rqpPAD/HP3guImnAJ/5kQoYRN8xpGEaUUNVtwP3ASyLyLvAXoHc9h+7Al9Ngi4jUNzvrJXzjJQCjgBJ/d9cPgR/7yycBz0fTfsMIB8unYRgew98dNU9Vv9nIMf8L3Kuq78fPMsOwJw3D8ByquhF4pbHFfcBacxiGG9iThmEYhhE29qRhGIZhhI05DcMwDCNszGkYhmEYYWNOwzAMwwgbcxqGYRhG2JjTMAzDMMLm/wfgo4NY+Ah3hAAAAABJRU5ErkJggg==\n", 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\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "source": [ + "## **Descrete Feedback**\n", + "\n", + "The general form of feedback that may stabilize our system is linear as well as for continues time system:\n", + "\\begin{equation}\n", + "\\mathbf{u}[kT]=-\\mathbf{K}\\mathbf{x}[kT]\n", + "\\end{equation}\n", + "\n", + "## **Pole Placement for descrete systems**\n", + "\n", + "Previously we have designed a stable poles for continues time systems by placing them on the left hand side of comple plane. In case of descrete time systems we should place them inside of **unit circle**\n" + ], + "metadata": { + "id": "IKKfgjO8Iuif" + } + }, + { + "cell_type": "markdown", + "source": [ + ">### **Example**" + ], + "metadata": { + "id": "OJd5A1FgJcGU" + } + }, + { + "cell_type": "markdown", + "source": [ + "> **Model of Love**\\\n", + ">Let us consider the example of \"love\" equations given in the first practice:\n", + "$$\n", + "\\begin{cases}\n", + "\\dot{R}=aR+bJ \\\\\n", + "\\dot{J}=cR+dJ\n", + "\\end{cases}\n", + "$$\n", + ">\n", + ">when $R$ and $J$ are time depended functions of Romeo's or Juliet's love (or hate if negative) and $a$, $b$, $c$ and $d$ is constants that determine the \"Romantic styles\". \n", + ">Suppose we can control Romeo's feelings with the coefficient $e$. So our control system will have following form:\n", + "\\begin{equation}\n", + "\\begin{bmatrix}\n", + "\\dot{R} \\\\\n", + "\\dot{J} \n", + "\\end{bmatrix} = \n", + "\\begin{bmatrix}\n", + "a & b \\\\\n", + "c & d \n", + "\\end{bmatrix}\n", + "\\begin{bmatrix}\n", + "R \\\\\n", + "J \n", + "\\end{bmatrix} +\n", + "\\begin{bmatrix}\n", + "e \\\\0 \n", + "\\end{bmatrix}\n", + "u\n", + "\\end{equation}\n", + ">\n", + ">Let's set the control signal to the following form:\n", + "$u = -\\begin{bmatrix}\n", + "k_1 & k_2 \n", + "\\end{bmatrix}\\begin{bmatrix}\n", + "R \\\\\n", + "J \n", + "\\end{bmatrix}$\n", + ">\n", + "> Also consider that we may meet with Romeo every few days, the difference in our meetings we denote as $T$, thus after all of our changes we get following descrete system:\n", + "\\begin{equation}\n", + "\\begin{bmatrix}\n", + "R[(k+1)T] \\\\\n", + "J[(k+1)T] \n", + "\\end{bmatrix} = \n", + "\\left(\\begin{bmatrix}\n", + "1+aT & bT \\\\\n", + "cT & 1+dT \n", + "\\end{bmatrix}-\\begin{bmatrix}\n", + "eT \\\\0 \n", + "\\end{bmatrix}\\begin{bmatrix}\n", + "k_1 & k_2 \n", + "\\end{bmatrix} \\right)\n", + "\\begin{bmatrix}\n", + "R [kT]\\\\\n", + "J [kT]\n", + "\\end{bmatrix}\n", + "\\end{equation}" + ], + "metadata": { + "id": "qAiXYCpaJXmp" + } + }, + { + "cell_type": "code", + "source": [ + "from scipy.signal import place_poles\n", + "\n", + "#@markdown Romeo's parameters\n", + "a = 0 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "b = 5 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "\n", + "#@markdown Juliet's parameters\n", + "c = 3 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "d = 0 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "\n", + "#@markdown How much did Romeo and Juliet like each other at first sight?\n", + "R_0 = 1 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "J_0 = 1 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "\n", + "#@markdown Control parameters\n", + "e = 1 #@param {type:\"slider\", min:-10, max:10, step:1}\n", + "\n", + "#@markdown Discretization time\n", + "T = 0.5 #@param {type:\"slider\", min:0.01, max:0.5, step:0.01}\n", + "\n", + "#@markdown Poles parameters\n", + "p1 = 0.4 #@param {type:\"slider\", min:-2, max:2, step:0.1}\n", + "p2 = 0.3 #@param {type:\"slider\", min:-2, max:2, step:0.1}\n", + "\n", + "A = np.array([[a, b],\n", + " [c, d]])\n", + "\n", + "B = np.array([[e],\n", + " [0]])\n", + "\n", + "x0 = np.array([R_0,\n", + " J_0]) # initial state\n", + "\n", + "t = np.arange(t0, tf, T)\n", + "\n", + "A_d = np.eye(2) + T*A\n", + "B_d = T*B\n", + "\n", + "P = np.array([p1, p2])\n", + "pp = place_poles(A_d, B_d, P)\n", + "K = pp.gain_matrix\n", + "\n", + "x_d = x0\n", + "love = x0\n", + "\n", + "for time in t:\n", + " u_d = - np.dot(K,x_d) \n", + " x_d = np.dot(A_d,x_d) + np.dot(B_d,u_d)\n", + " love = np.vstack((love, x_d))\n", + "\n", + "y_disc, dy_disc = x_disc[:,0], x_disc[:,1] \n", + "t_disc = np.insert(t, 0, 0)\n", + "\n", + "R, J = love[:,0], love[:,1]\n", + "\n", + "step(t_disc, R, linewidth=2.0, color = 'b', label = \"Romeo\")\n", + "step(t_disc, J, linewidth=2.0, color = 'm', label = \"Juliet\")\n", + "grid(True, color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "ylabel(r'Level of love ${X}$')\n", + "xlabel(r'Time $t$')\n", + "legend()\n", + "show()\n", + "\n", + "Lambda, Q = np.linalg.eig(A_d)\n", + "print(f\"Eigen values of original system:\\n{Lambda}\\n\")\n", + "\n", + "Lambda, Q = np.linalg.eig(A_d-np.dot(B_d, K))\n", + "print(f\"Eigen values for system with control:\\n{Lambda}\")" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 372 + }, + "id": "2KLURuAcJQpk", + "outputId": "93e868ac-87cc-4b6f-ca4c-8e009f455292" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + } + }, + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Eigen values of original system:\n", + "[ 2.93649167 -0.93649167]\n", + "\n", + "Eigen values for system with control:\n", + "[0.3 0.4]\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "source": [ + ">### **Exercises**\n", + ">\n", + ">1. Find the gains $k_1, k_2$ that will stabilize the following system:\n", + "> * $\\dot{\\mathbf{x}} = \n", + "\\begin{bmatrix} 0 & 1\\\\\n", + " -7 & -7 \\end{bmatrix} \n", + " \\mathbf{x} + \n", + " \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix} \\mathbf{u}\n", + " $\\\n", + " >\\\n", + " >with $T = 0.1$ sec\n", + ">\n", + ">* $\\mathbf{\\dot{x}}=\\begin{bmatrix}\n", + "10 & 5\\\\\n", + "-5 & -10\n", + "\\end{bmatrix}\\mathbf{x} + \\begin{bmatrix}\n", + "-1\\\\\n", + "2\n", + "\\end{bmatrix}\\mathbf{u}\n", + " $\\\n", + " >\\\n", + " with $T = 0.6$ sec\n", + ">\n", + ">* $\\mathbf{\\dot{x}}=\\begin{bmatrix}-8 & 1 \\\\ -2 & 2\n", + "\\end{bmatrix}\\mathbf{x} + \\begin{bmatrix}\n", + "2\\\\\n", + "0\n", + "\\end{bmatrix}\\mathbf{u}\n", + " $\\\n", + " >\\\n", + " with $T = 0.2$ sec\n", + ">\n", + "> 2. At what time step will the motor stop being stable? A simplified model of the motor dynamics for this situation:\n", + "> $$I\\ddot{\\theta}+b\\dot{\\theta} = K_m I$$\n", + "> when $I$ - motor rotor moment of inertia, $b$ - coefficient of viscous friction, $K_m$ - motor torque constant. \n", + "> 3. Create a motor position control model with discretization time of $T = 0.1$ sec" + ], + "metadata": { + "id": "CAifcIjCO6vr" + } + } + ] +} \ No newline at end of file diff --git a/legacy - ColabNotebooks/Practice_8_Lyapunov.ipynb b/legacy - ColabNotebooks/Practice_8_Lyapunov.ipynb new file mode 100644 index 0000000..1ddd451 --- /dev/null +++ b/legacy - ColabNotebooks/Practice_8_Lyapunov.ipynb @@ -0,0 +1,996 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "[Control theory] Practice 8.ipynb", + "provenance": [], + "collapsed_sections": [], + "toc_visible": true, + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "zPmrTNlSBW-R" + }, + "source": [ + "# **Practice 8: Lyapunov Functions and Stability**\n", + "## **Goals for today**\n", + "\n", + "---\n", + "\n", + "During today practice we will:\n", + "* Recall stability of the Linear Systems\n", + "* Linearization of Nonlinear Systems\n", + "* Lyapunov Direct method" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "DEdCnYFHUUSS" + }, + "source": [ + "## **Stability of the Linear Systems**\n", + "A linear system in form:\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{x}} (t)=\\mathbf{A}\\mathbf{x}(t)\n", + "\\end{equation}\n", + "\n", + "Is said to be **assymptotically** stable (internally) if following holds:\n", + "\\begin{equation}\n", + "\\Re(\\lambda_i) < 0, \\forall i \n", + "\\end{equation}\n", + "\n", + "\n", + "\n", + "One can easialy proof the fact above by directly solving ODE above, which may be done fairly easy by applying spectral decomposition:\n", + "\\begin{equation}\n", + "\\mathbf{x}(t) = e^{\\mathbf{A}t}\\mathbf{x}(0)=\\mathbf{Q}e^{\\mathbf{\\Lambda}t}\\mathbf{Q}^{-1} \\mathbf{x}(0) \n", + "\\end{equation}\n", + "\n", + "Linear system is said to be stable in the sense of Lyapunov (marginally stable) if: \n", + "\\begin{equation}\n", + "\\Re(\\lambda_i) \\leq 0, \\forall i \n", + "\\end{equation}\n", + "Note that additionally algebraic and geometric multiplicity of the zero eigenvalues should coincide. \n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "7anwqUrRZmMW" + }, + "source": [ + "### **Example:**\n", + "\n", + "Recall the mass spring damper system with state space representattion given as:\n", + "\n", + "\\begin{equation}\n", + "\\dot{\\mathbf{x}}\n", + " = \\mathbf{A}\\mathbf{x} =\n", + "\\begin{bmatrix}\n", + "\\dot{y}\\\\\n", + "\\ddot{y}\n", + "\\end{bmatrix}\n", + "=\n", + "\\begin{bmatrix}\n", + "0 & 1\\\\\n", + "-\\frac{k}{m} & -\\frac{b}{m}\n", + "\\end{bmatrix}\n", + " \\begin{bmatrix}\n", + "y\\\\\n", + "\\dot{y}\n", + "\\end{bmatrix}\n", + "\\end{equation}\n", + "\n", + "Let us numerically find the eigen values of this matrix in order to analyze stability of the system:" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "Nrez8QSYanPJ", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "5f98d38a-3ff4-41e8-b9d7-1aeff77f9373" + }, + "source": [ + "from numpy.linalg import eig\n", + "from numpy import real\n", + "\n", + "m = 1\n", + "b = 2\n", + "k = 5\n", + "\n", + "A = [[0,1],\n", + " [-k/m, -b/m]]\n", + "\n", + "# One may find eigen system using following command \n", + "lambdas, Q = eig(A) # lambdas - is the array of eigen values and Q is the matrix with eigen vector on its columns v = Q[:,i]\n", + "print(f'Eigen values:\\n {lambdas}')\n", + "print(f'Real parts:\\n {real(lambdas)}')\n" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Eigen values:\n", + " [-1.+2.j -1.-2.j]\n", + "Real parts:\n", + " [-1. -1.]\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "XA5UTk7Ji181" + }, + "source": [ + "\n", + "We can obtain response by integrating the system " + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "Q5rqRbMCiyeH", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 862 + }, + "outputId": "8f4f99b6-59f7-4521-af0e-ab5e3001cd30" + }, + "source": [ + "from numpy import dot, linspace\n", + "from scipy.integrate import odeint # import integrator routine\n", + "\n", + "def mbk_ode(x, t, A):\n", + " dx = dot(A,x)\n", + " return dx\n", + "\n", + "\n", + "t0 = 0 # Initial time \n", + "tf = 15 # Final time\n", + "N = int(2E3) # Numbers of points in time span\n", + "t = linspace(t0, tf, N) # Create time span\n", + "\n", + "x0 = [1,1]\n", + "x_sol = odeint(mbk_ode, x0, t, args=(A,)) # integrate system \"sys_ode\" from initial state $x0$\n", + "y, dy = x_sol[:,0], x_sol[:,1] # set theta, dtheta to be a respective solution of system states\n", + "\n", + "from matplotlib.pyplot import *\n", + "\n", + "title(r'Position response')\n", + "plot(t, y, 'r', linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'Position ${y}$ (m)')\n", + "xlabel(r'Time $t$ (s)')\n", + "show()\n", + "\n", + "title(r'Velocity response')\n", + "plot(t, dy, 'r', linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'Velocity $\\dot{y}$ (m/s)')\n", + "xlabel(r'Time $t$ (s)')\n", + "show()\n", + "\n", + "title(r'Phase portrait')\n", + "plot(y, dy, 'r', linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "ylabel(r'Position ${y}$ (m)')\n", + "xlabel(r'Velocity $\\dot{y}$ (m/s)')\n", + "show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "exj4xtx_Q9zJ" + }, + "source": [ + "## **Linearized systems**\n", + "\n", + "An approach above may be used to analyze the stability of the nonlinear systems in form:\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{x}} (t)=\\boldsymbol{f}\\big(\\mathbf{x}(t)\\big) \n", + "\\end{equation}\n", + "\n", + "To do so once may find the liniarized representation of the nonlinear system nearby equalibrium of interest as follows:\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{\\tilde{x}}} (t) = \\frac{\\partial \\boldsymbol{f}}{\\partial \\mathbf{x}}\\mid_{\\mathbf{x}_e} \\tilde{x} =\\mathcal{J}(\\mathbf{x}_e)\\tilde{x}=\\mathbf{A}\\tilde{x}\n", + "\\end{equation}\n", + "where $\\tilde{x}= \\mathbf{x}_e - \\mathbf{x}(t)$ is the deviation from the equalibrium point.\n", + "\n", + "### **Example:**\n", + "\n", + "Consider the following system:\n", + "\n", + "\\begin{equation}\n", + "\\begin{cases}\n", + "\\dot{x}_1 = x_1 - x_1^3 + 2 x_1 x_2\\\\\n", + "\\dot{x}_2 = -x_2 + \\frac{1}{2}x_1 x_2\n", + "\\end{cases}\n", + "\\end{equation}\n", + "\n", + "Analyze the system stability in the following equalibrias:\n", + "\n", + "\\begin{equation}\n", + "x_{e_1} = \n", + "\\begin{bmatrix}\n", + "0 \\\\ \n", + "0\n", + "\\end{bmatrix},\n", + "\\quad\n", + "x_{e_2} = \n", + "\\begin{bmatrix}\n", + "1 \\\\ \n", + "0\n", + "\\end{bmatrix},\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "k2GgUHahkCL0" + }, + "source": [ + "\n", + "Sometimes finding jacobians of the state space equations is envolving, and one may use a symbolic routines instead.\n", + "\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "br09lunYkCn4", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "f9ee1945-cb68-4166-8090-fb1f10db9f86" + }, + "source": [ + "from sympy import Matrix, symbols\n", + "from sympy.utilities.lambdify import lambdify\n", + "from numpy.random import randn\n", + "\n", + "# Define vector for states \n", + "x = symbols('x1, x2') \n", + "\n", + "# Define state vector field: f(x)\n", + "f_symb = Matrix([x[0]- x[0]**3 + 2*x[0]*x[1],\n", + " -x[1] + x[0]*x[1]/2]) \n", + "\n", + "# Find analytical expression of jacobian\n", + "J_symb = Matrix([f_symb]).jacobian(x)\n", + "print(f'System Jacobian:\\n{J_symb}')" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "System Jacobian:\n", + "Matrix([[-3*x1**2 + 2*x2 + 1, 2*x1], [x2/2, x1/2 - 1]])\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "P3g3co5Jx7LF" + }, + "source": [ + "Now we can create a numerical function from the obtained system Jacobian:" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "RFzmo4xgx6Gh", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "bbf2cf99-ddcd-4421-b092-76d163bf6f66" + }, + "source": [ + "J_num = lambdify([x], J_symb)\n", + "\n", + "x_e = 1.0, 0.0 \n", + "A = J_num(x_e)\n", + "lambdas, Q = eig(A) \n", + "print(f'Eigen values:\\n {lambdas}')" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Eigen values:\n", + " [-2. -0.5]\n" + ] + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "NJgwK5GWxPkj", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 297 + }, + "outputId": "9eb1b1a6-8e0b-451a-b9ac-1f1aaad223bf" + }, + "source": [ + "from scipy.integrate import odeint # import integrator routine\n", + "\n", + "f_num = lambdify([x], f_symb)\n", + "\n", + "def sys_ode(x, t):\n", + " dx = f_num(x)[:,0]\n", + " return dx\n", + "\n", + "t0 = 0 # Initial time \n", + "tf = 100 # Final time\n", + "N = int(2E3) # Numbers of points in time span\n", + "t = linspace(t0, tf, N) # Create time span\n", + "\n", + "x0 = x_e + 0.1*randn(2)\n", + "x_sol = odeint(sys_ode, x0, t) # integrate system \"sys_ode\" from initial state $x0$\n", + "x_1, x_2 = x_sol[:,0], x_sol[:,1] # set theta, dtheta to be a respective solution of system states\n", + "\n", + "\n", + "title(r'Phase portrait')\n", + "plot(x_e[0], x_e[1], 'r', markersize=10, marker='o')\n", + "plot(x_1[0], x_2[0], 'r', markersize=10, marker=\"s\")\n", + "plot(x_1, x_2, 'r', linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlabel(r'${x_1}$')\n", + "ylabel(r'${x_2}$')\n", + "show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "zX3mPQQHzL6M" + }, + "source": [ + "### **Exercise**: \n", + "* Repeat the analysis above for stability points of nonlinear pendulum whose dynamics given by:\n", + "\\begin{equation}\n", + "\\dot{\\mathbf{x}} = \n", + "\\begin{bmatrix}\n", + "\\dot{\\theta} \\\\\n", + "\\ddot{\\theta} \n", + "\\end{bmatrix} \n", + "=\n", + "\\begin{bmatrix}\n", + "\\dot{\\theta} \\\\\n", + "-\\frac{1}{m l^2}( mgl \\sin \\theta+b \\dot{\\theta})\n", + "\\end{bmatrix} \n", + "\\end{equation}\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "gMG8-wjxeF3x" + }, + "source": [ + "## **Lyapunov Direct Method**\n", + "In the Lyapunov Direct Method, we are trying to prove stability of an equilibrium for a given dynamical system ${\\dot{\\mathbf{x}}=\\boldsymbol{f}(\\mathbf{x})}$ by looking for **candidate Lyapunov function** $V(\\mathbf{x}):\\mathbb{R}^{n}\\rightarrow \\mathbb{R} $ that satisfies the following conditions:\n", + "\n", + "\n", + "\n", + ">* $V(\\mathbf{x})=0$ if and only if $\\mathbf{x}=\\mathbf{0}$\n", + ">* $V(\\mathbf{x})>0$ if and only if $\\mathbf{x}\\neq\\mathbf{0}$\n", + ">* $\\dot{V}(\\mathbf{x}) \\leq 0$ if and only if $\\mathbf{x}\\neq\\mathbf{0}$ \n", + "\n", + "This is known as the criteria of **asymptotic stability** of the equilibrium of ${\\dot{\\mathbf{x}}=\\boldsymbol{f}(\\mathbf{x})}$\n", + " \n", + "In two dimensions $\\mathbf{x}\\in\\mathbb{R}^2$ one can interpret the stability criteria above geometrically by thinking of a projection of system dynamics vector $\\boldsymbol{f}$ onto the gradient of $V$. \n", + "\n", + "\n", + "### **Example:**\n", + "\n", + "Consider the following system:\n", + "\\begin{equation}\n", + "\\begin{cases}\n", + "\\dot{x}_1 = -x_1 + x_2 \\\\ \n", + "\\dot{x}_2 = -x_1 - x_2^3\n", + "\\end{cases}\n", + "\\end{equation}\n", + "\n", + "with following Lyapunov candidate:\n", + "\\begin{equation}\n", + "V(\\mathbf{x}) = x_1^2 + x_2^2 \n", + "\\end{equation}\n", + "\n", + "One may use a chain rule in order to find $\\dot{V}$ as follows:\n", + "\\begin{equation}\n", + "\\dot{V} = \\sum_{i=1}^n\\frac{\\partial V}{\\partial \\mathbf{x}_i}\\mathbf{\\dot{x}}_i = \\sum_{i=1}^n\\frac{\\partial V}{\\partial \\mathbf{x}_i}\\boldsymbol{f}_i = \\nabla V \\cdot \\boldsymbol{f}\n", + "\\end{equation}\n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "zngMQVsWh-Ee" + }, + "source": [ + "Let's use symbolical tools in order to find the derevitive of Lyapunov function:" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "gBuo-G-Dh5AA", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "3c87093d-0663-4e01-fefc-5a8c290953df" + }, + "source": [ + " from sympy import simplify\n", + " x = symbols('x_1, x_2')\n", + " V_symb = x[0]**2 + x[1]**2\n", + "\n", + " grad_V = Matrix([V_symb]).jacobian(x)\n", + " print(f'Gradient of Lyapunov candidate:\\n {grad_V}')\n", + " \n", + " f_symb = Matrix([-x[0] + x[1],\n", + " -x[0] - x[1]**3])\n", + " \n", + " dV = simplify(grad_V*f_symb) \n", + " print(f'Time derevitive of Lyapunov candidate:\\n {dV}')\n", + " " + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Gradient of Lyapunov candidate:\n", + " Matrix([[2*x_1, 2*x_2]])\n", + "Time derevitive of Lyapunov candidate:\n", + " Matrix([[-2*x_1**2 - 2*x_2**4]])\n" + ] + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "DFf9gVuPLH6r", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "cae15424-1542-4aaf-d1bf-8023e15d1ad3" + }, + "source": [ + " from sympy import simplify\n", + " x = symbols('x_1, x_2')\n", + " V_symb = 4*x[0]**2 + 2*x[1]**2 + 4*x[0]**4 \n", + "\n", + " grad_V = Matrix([V_symb]).jacobian(x)\n", + " print(f'Gradient of Lyapunov candidate:\\n {grad_V}')\n", + " \n", + " f_symb = Matrix([x[1] - x[0],\n", + " -2*x[0] - 2*x[1] - 4*x[0]**3])\n", + " \n", + " dV = simplify(grad_V*f_symb) \n", + " print(f'Time derevitive of Lyapunov candidate:\\n {dV}')\n", + " " + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Gradient of Lyapunov candidate:\n", + " Matrix([[16*x_1**3 + 8*x_1, 4*x_2]])\n", + "Time derevitive of Lyapunov candidate:\n", + " Matrix([[-16*x_1**4 - 8*x_1**2 - 8*x_2**2]])\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "iEHIN_gajGgE" + }, + "source": [ + "Clearly with choosen Lyapunov candidate the system is stable (in fact globally asymptotically stable)\n", + "\n", + "Let us now visualyse response of the system:\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "wswnRpqalnAl", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 297 + }, + "outputId": "f0f272a0-7671-467e-fc65-7053e922b2d1" + }, + "source": [ + "# Create a numerical function from symbolic one\n", + "f_num = lambdify([x], f_symb)\n", + "\n", + "def sys_ode(x, t):\n", + " dx = f_num(x)[:,0]\n", + " return dx\n", + "\n", + "t0 = 0 # Initial time \n", + "tf = 100 # Final time\n", + "N = int(2E3) # Numbers of points in time span\n", + "t = linspace(t0, tf, N) # Create time span\n", + "\n", + "x_e = 0, 0 \n", + "x0 = randn(2)\n", + "x_sol = odeint(sys_ode, x0, t) # integrate system \"sys_ode\" from initial state $x0$\n", + "x_1, x_2 = x_sol[:,0], x_sol[:,1] # set theta, dtheta to be a respective solution of system states\n", + "\n", + "\n", + "title(r'Phase portrait')\n", + "plot(x_e[0], x_e[1], 'r', markersize=10, marker='o')\n", + "plot(x_1[0], x_2[0], 'r', markersize=10, marker=\"s\")\n", + "plot(x_1, x_2, 'r', linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlabel(r'${x_1}$')\n", + "ylabel(r'${x_2}$')\n", + "show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Ugayq1mvlRlC" + }, + "source": [ + "Lets plot response of the system together with our choosen Lyapunov candidate:" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "CiyUp-W4eEra", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 575 + }, + "outputId": "07ca8622-f801-4cec-9e79-928c9e57d6aa" + }, + "source": [ + "V_num = lambdify([x], V_symb)\n", + "\n", + "N = 1000\n", + "x_max = max(abs(x_1[0]),abs(x_2[0]))\n", + "\n", + "x1 = linspace(-x_max, x_max, N)\n", + "x2 = linspace(-x_max, x_max, N)\n", + "X_1, X_2 = np.meshgrid(x1, x2)\n", + "\n", + "\n", + "V_gen = X_1**2 + X_2**2\n", + "# V_gen = V_num([X_1, X_2])\n", + "# V with solution x(t)\n", + "V_sol = np.zeros((len(x_1),), dtype = float)\n", + "for i in range (len(x_1)):\n", + " V_sol[i] = x_1[i]**2 + x_2[i]**2 \n", + "\n", + "fig = figure(figsize=(10,10))\n", + "ax = fig.gca(projection='3d')\n", + "surf = ax.plot_surface(X_1, X_2, V_gen, cmap = cm.coolwarm, alpha = 0.3)\n", + "ax.plot(x_1, x_2, V_sol, 'r', label=r'solution $\\mathbf{x}(t)$')\n", + "title(r'Lyapunov candidate $V(x)$ with the solution $\\mathbf{x}(t)$')\n", + "fig.colorbar(surf, shrink=1, aspect=10)\n", + "ax.legend(loc = 'lower right')\n", + "show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Qx8-P6NGtTmK" + }, + "source": [ + "## **Linear Systems, Lyapunov Equations**\n", + "It may be shown that for linear system:\n", + "\n", + "\\begin{equation}\n", + "\\dot{\\mathbf{x}} = \\mathbf{A}\\mathbf{x}\n", + "\\end{equation}\n", + "\n", + "if one would choose Lyapunov candidate as:\n", + "\n", + "\\begin{equation}\n", + "V(\\mathbf{x}) = \\mathbf{x}^T\\mathbf{S}\\mathbf{x}\n", + "\\end{equation}\n", + "\n", + "with derevitive given by:\n", + "\\begin{equation}\n", + " \\dot V(\\mathbf{x}) = (\\mathbf{A}\\mathbf{x})^T\\mathbf{S}\\mathbf{x} + \n", + " \\mathbf{x}^T\\mathbf{S}\\mathbf{A}\\mathbf{x} = \n", + " \\mathbf{x}^T(\\mathbf{A}^\\top\\mathbf{S} + \\mathbf{S}\\mathbf{A})\\mathbf{x}\n", + "\\end{equation}\n", + "\n", + "thus system should be stable provided the solution of the following equation exist:\n", + "\n", + "\\begin{equation}\n", + " \\mathbf{A}^\\top\\mathbf{S} + \\mathbf{S}\\mathbf{A} = -\\mathbf{Q}\n", + "\\end{equation}\n", + "\n", + "The matrix $\\mathbf{S}$ and $\\mathbf{Q}$ should be a **positive-definite matrices**. \n" + ] + }, + { + "cell_type": "markdown", + "source": [ + "### **Positive definite matix**\n", + "In mathematics, a **symmetric matrix** $\\mathbf{M}$ with real entries is positive-definite if the real number $z^T\\mathbf{M}z$ is positive for every nonzero real column vector $z$.\n", + "\n", + "A matrix $\\mathbf{M}$ is positive-definite if and only if it satisfies any of the following equivalent conditions:\n", + "\n", + "* $\\mathbf{M}$ is congruent with a diagonal matrix with positive real entries.\n", + "* $\\mathbf{M}$ is symmetric or Hermitian, and all its eigenvalues are real and positive .\n", + "* $\\mathbf{M}$ is symmetric or Hermitian, and all its leading principal minors are positive." + ], + "metadata": { + "id": "OrKzmm6XXaA8" + } + }, + { + "cell_type": "markdown", + "source": [ + "### **Examples:**\n", + "Let's consider the following system:\n", + "$$\\dot{\\mathbf{x}} = \n", + "\\begin{bmatrix} -1 & 1 \\\\ -5 & -1\n", + "\\end{bmatrix}\n", + "\\mathbf{x}\n", + "$$\n", + "\n", + "Assume that: $\\mathbf{S} = \\begin{bmatrix} s_1 & s_2 \\\\ s_3 & s_4\n", + "\\end{bmatrix}$ and $\\mathbf{Q} = \\begin{bmatrix} 1 & 0 \\\\ 0 & 1\n", + "\\end{bmatrix}$\n", + "\n", + "Then we can substitude this values into the equation:\n", + "$\\mathbf{A}^\\top\\mathbf{S} + \\mathbf{S}\\mathbf{A} = -\\mathbf{Q}$. And we get:\n", + "\n", + "$$\n", + "\\begin{bmatrix} -1 & -5 \\\\ 1 & -1\n", + "\\end{bmatrix}\n", + "\\begin{bmatrix} s_1 & s_2 \\\\ s_3 & s_4\n", + "\\end{bmatrix}\n", + "+\n", + "\\begin{bmatrix} s_1 & s_2 \\\\ s_3 & s_4\n", + "\\end{bmatrix}\n", + "\\begin{bmatrix} -1 & 1 \\\\ -5 & -1\n", + "\\end{bmatrix}\n", + "=\n", + "-\\begin{bmatrix} 1 & 0 \\\\ 0 & 1\n", + "\\end{bmatrix}\n", + "$$\n", + "\n", + "After multiplying the matrices we get:\n", + "\n", + "$$\n", + "\\begin{bmatrix} -s_1-5s_3 & -s_2-5s_4 \\\\ s_1-s_3 & s_2-s_4\n", + "\\end{bmatrix}+\n", + "\\begin{bmatrix} -s_1-5s_2 & s_1-s_2 \\\\ -s_3-5s_4 & s_3-s_4\n", + "\\end{bmatrix}\n", + "= \\begin{bmatrix} -1 & 0 \\\\ 0 & -1\n", + "\\end{bmatrix}\n", + "$$\n", + "\n", + "Finally we should to solve following equation:\n", + "\n", + "$$\n", + "\\begin{bmatrix} -2s_1-5s_2-5s_3 & s_1 - 2s_2 - 5s_4 \\\\ s_1-2s_3-5s_4 & s_2 + s_3 - 2s_4\n", + "\\end{bmatrix}\n", + "=\n", + "\\begin{bmatrix} -1 & 0 \\\\ 0 & -1\n", + "\\end{bmatrix}\n", + "$$\n", + "\n", + "Which we can rewrite into the form:\n", + "\n", + "$$\n", + "\\begin{cases}\n", + "-2s_1-5s_2-5s_3 = -1\\\\\n", + "s_1 - 2s_2 - 5s_4 = 0\\\\\n", + "s_1-2s_3-5s_4 = 0\\\\\n", + "s_2 + s_3 - 2s_4 = -1\n", + "\\end{cases}\n", + "$$\n", + "\n", + "The solution for this system is: $s_1 = \\frac{1}{3}$, $s_2 = -\\frac{1}{6}$, $s_3 = -\\frac{1}{6}$, $s_4 = \\frac{4}{3}$" + ], + "metadata": { + "id": "RqdP4xb-bgOn" + } + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "dguJXY3qvRJF", + "outputId": "605522d7-17a2-4a9f-a13b-3bbeb5ce9280" + }, + "source": [ + "from scipy.linalg import solve_continuous_lyapunov as lyap\n", + "from numpy import eye\n", + "A = [[-1,1],\n", + " [-5,-1]]\n", + "\n", + "Q = -eye(2)\n", + "\n", + "lambdas, _ = eig(A) \n", + "\n", + "S = lyap(A, Q)\n", + "lambdas, _ = eig(S)\n", + "print(\"S:\",S)\n", + "print(\"Eigen values for S-matrix:\",lambdas)" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "S: [[ 0.33333333 -0.16666667]\n", + " [-0.16666667 1.33333333]]\n", + "Eigen values for S-matrix: [0.30628706 1.36037961]\n" + ] + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "lT5s7G82vVdD" + }, + "source": [ + "**Mass-spring-damper system**\n", + "\n", + "Consider again the mass spring damper:" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 858 + }, + "id": "Czx0qK_gvYu_", + "outputId": "d90a8065-81d5-4247-cec5-25e84d1da64c" + }, + "source": [ + "m = 1\n", + "b = 0.5\n", + "k = 2\n", + "\n", + "A = [[0,1],\n", + " [-k/m, -b/m]]\n", + " \n", + "t0 = 0 # Initial time \n", + "tf = 15 # Final time\n", + "N = int(2E3) # Numbers of points in time span\n", + "t = linspace(t0, tf, N) # Create time span\n", + "\n", + "x0 = [0.3,0]\n", + "x_sol = odeint(mbk_ode, x0, t, args=(A,)) # integrate system \"sys_ode\" from initial state $x0$\n", + "x_1, x_2 = x_sol[:,0], x_sol[:,1] # set theta, dtheta to be a respective solution of system states\n", + "\n", + "N = 1000\n", + "x_max = max(abs(x_1[0]),abs(x_2[0]))\n", + "\n", + "x1 = linspace(-x_max, x_max, N)\n", + "x2 = linspace(-x_max, x_max, N)\n", + "X_1, X_2 = np.meshgrid(x1, x2)\n", + "\n", + "X = [X_1, X_2]\n", + "\n", + "# V_gen = \n", + "V_gen = X_1**2 + X_2**2\n", + "\n", + "V_sol = np.zeros((len(x_1),), dtype = float)\n", + "for i in range (len(x_1)):\n", + " V_sol[i] = x_1[i]**2 + x_2[i]**2 \n", + "\n", + "fig = figure(figsize=(10,10))\n", + "ax = fig.gca(projection='3d')\n", + "surf = ax.plot_surface(X_1, X_2, V_gen, cmap = cm.coolwarm, alpha = 0.3)\n", + "ax.plot(x_1, x_2, V_sol, 'r', label=r'solution $\\mathbf{x}(t)$')\n", + "title(r'Lyapunov candidate $V(x)$ with the solution $\\mathbf{x}(t)$')\n", + "fig.colorbar(surf, shrink=1, aspect=10)\n", + "ax.legend(loc = 'lower right')\n", + "show()\n", + "\n", + "title(r'Phase portrait')\n", + "plot(x_1, x_2, 'r', linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "ylabel(r'Position ${y}$ (m)')\n", + "xlabel(r'Velocity $\\dot{y}$ (m/s)')\n", + "show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + } + } + ] + } + ] +} \ No newline at end of file diff --git a/legacy - ColabNotebooks/README.md b/legacy - ColabNotebooks/README.md new file mode 100644 index 0000000..2541641 --- /dev/null +++ b/legacy - ColabNotebooks/README.md @@ -0,0 +1 @@ +Commit colab notebooks here \ No newline at end of file diff --git a/legacy - ColabNotebooks/StateSpace2ODE.ipynb b/legacy - ColabNotebooks/StateSpace2ODE.ipynb new file mode 100644 index 0000000..04f0aff --- /dev/null +++ b/legacy - ColabNotebooks/StateSpace2ODE.ipynb @@ -0,0 +1,247 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "StateSpace2ODE.ipynb", + "provenance": [], + "authorship_tag": "ABX9TyNKm58vwUKdTGNQl/dRaF3J", + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 383 + }, + "id": "JdcpMyrG7H3S", + "outputId": "cbf8f91b-2f7a-453e-9aca-761dda811eff" + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "[-10.77200187 -2.22799813]\n", + "[ 0.37812495 -7.27596935]\n", + "[[-24. -13.]]\n", + "(array([0.09810489, 0.03269944]), array([-0.09304505, 1.11851616]))\n" + ] + }, + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "[,\n", + " ]" + ] + }, + "metadata": {}, + "execution_count": 2 + }, + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + } + } + ], + "source": [ + "import numpy as np\n", + "from numpy.linalg import pinv\n", + "from scipy.integrate import odeint\n", + "from matplotlib import pyplot as pp\n", + "\n", + "# we work with a system dx/dt = A*x\n", + "A = np.array([[-10, 3], [2, -3]])\n", + "# l, _ = np.linalg.eig(A) \n", + "# print( l )\n", + "\n", + "w = np.random.randn(1, 2)\n", + "\n", + "#map from x to y, dy/dt\n", + "T = np.concatenate((w, w @ A), axis=0)\n", + "l, _ = np.linalg.eig(T) #check eigenvalues to see if the matrix is degenerate\n", + "print(l)\n", + "\n", + "# coefficients of the ODE to be found\n", + "b = w @ A @ A @ pinv(T)\n", + "print(b)\n", + "\n", + "#collable functions for simulation with odeint\n", + "def mySS(x, t):\n", + " return A @ x\n", + "\n", + "def myODE(x, t):\n", + " # y = x[0]\n", + " # dy = x[1]\n", + " # ddy = b1*y + b2*dy\n", + " dx = np.zeros((2, ))\n", + " dx[0] = x[1]\n", + " dx[1] = b @ x\n", + " return dx\n", + "\n", + "#initial conditions for simulation with odeint\n", + "x0_SS = np.random.randn(2, )\n", + "x0_ODE = T @ x0_SS\n", + "# print((x0_SS, x0_ODE))\n", + "\n", + "#simulation\n", + "time = np.linspace(0, 2, num=200)\n", + "solution_1 = odeint(mySS, x0_SS, time)\n", + "solution_2 = odeint(myODE, x0_ODE, time)\n", + "\n", + "#mapping back to the same coordinates\n", + "solution_2_mapped = pinv(T) @ solution_2.transpose()\n", + "solution_2_mapped = solution_2_mapped.transpose()\n", + "\n", + "#plotting\n", + "fig, axs = pp.subplots(nrows=1, ncols=3)\n", + "axs[0].plot(time, solution_1)\n", + "axs[1].plot(time, solution_2_mapped)\n", + "axs[2].plot(time, solution_1 - solution_2_mapped)\n" + ] + }, + { + "cell_type": "code", + "source": [ + "import numpy as np\n", + "from numpy.linalg import pinv\n", + "from scipy.integrate import odeint\n", + "from matplotlib import pyplot as pp\n", + "\n", + "n = 4;\n", + "A = np.random.randn(n, n) - np.eye(n)*2\n", + "l, _ = np.linalg.eig(A) #checking the eigenvalues to see what behaviour we can expect\n", + "print( l )\n", + "\n", + "w = np.random.randn(1, n)\n", + "\n", + "#map from x to y, dy/dt, ...\n", + "T = np.zeros((n, n))\n", + "h = w\n", + "T[0, :] = h\n", + "for i in range(n-1):\n", + " h = h @ A\n", + " T[i+1, :] = h\n", + "\n", + "# T = np.concatenate((w, w @ A, w @ A @ A), axis=0) #the n = 3 case\n", + "l, _ = np.linalg.eig(T) #check eigenvalues to see if the matrix is degenerate\n", + "print(l)\n", + "\n", + "# coefficients of the ODE to be found\n", + "b = h @ A @ pinv(T)\n", + "# b = w @ A @ A @ A @ pinv(T) #the n = 3 case\n", + "print(b)\n", + "\n", + "#collable functions for simulation with odeint\n", + "def mySS(x, t):\n", + " return A @ x\n", + "\n", + "def myODE(x, t):\n", + " dx = np.zeros((n, ))\n", + "\n", + " for i in range(n-1):\n", + " dx[i] = x[i+1]\n", + " # dx[0] = x[1] #the n = 3 case\n", + " # dx[1] = x[2] #the n = 3 case\n", + " dx[n-1] = b @ x\n", + " return dx\n", + "\n", + "#initial conditions for simulation with odeint\n", + "x0_SS = np.random.randn(n, )\n", + "x0_ODE = T @ x0_SS\n", + "# print((x0_SS, x0_ODE))\n", + "\n", + "#simulation\n", + "time = np.linspace(0, 2, num=200)\n", + "solution_1 = odeint(mySS, x0_SS, time)\n", + "solution_2 = odeint(myODE, x0_ODE, time)\n", + "\n", + "#mapping back to the same coordinates\n", + "solution_2_mapped = pinv(T) @ solution_2.transpose()\n", + "solution_2_mapped = solution_2_mapped.transpose()\n", + "\n", + "#plotting\n", + "fig, axs = pp.subplots(nrows=1, ncols=3)\n", + "axs[0].plot(time, solution_1)\n", + "axs[1].plot(time, solution_2_mapped)\n", + "axs[2].plot(time, solution_1 - solution_2_mapped)\n" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 437 + }, + "id": "U_SY6vsWazAu", + "outputId": "7e05c993-71ff-439c-ec41-e5747a90024b" + }, + "execution_count": 15, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "[-3.92810937+2.2805071j -3.92810937-2.2805071j -2.54336951+0.j\n", + " -1.76815324+0.j ]\n", + "[-36.44816834 8.65893429 8.01861546 -0.19437355]\n", + "[[ -92.77789218 -124.27991553 -59.00008869 -12.16774149]]\n", + "(array([ 0.56296019, 0.13010345, -1.47539038, -0.71385999]), array([ -1.93269822, 2.2061749 , 15.21707476, -144.6538674 ]))\n" + ] + }, + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "[,\n", + " ,\n", + " ,\n", + " ]" + ] + }, + "metadata": {}, + "execution_count": 15 + }, + { + "output_type": "display_data", + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + } + } + ] + } + ] +} \ No newline at end of file diff --git a/legacy - ColabNotebooks/lecture8_LyapunovEq.ipynb b/legacy - ColabNotebooks/lecture8_LyapunovEq.ipynb new file mode 100644 index 0000000..ff44839 --- /dev/null +++ b/legacy - ColabNotebooks/lecture8_LyapunovEq.ipynb @@ -0,0 +1,365 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "LyapunovEq.ipynb", + "provenance": [], + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "3ncmZERaeTOW" + }, + "source": [ + "# Lyapunov equations\n", + "\n", + "Lyapunov equations for continious systems has form:\n", + "\n", + "$AP + PA^{\\top} =-Q$\n", + "\n", + "and for discrete systems it is \n", + "\n", + "$A P A^{\\top} - P = -Q$\n", + "\n", + "As long as there exists such positive definite $P$ that Lyapunov equations holds for a positive definite $Q$, the system is stable.\n", + "\n", + "Let's see it in code:" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "fIlKWi1heNiV", + "outputId": "47c52c5d-ac5b-4e5f-eeee-c9547cb90fd0" + }, + "source": [ + "import numpy as np\n", + "from scipy.linalg import solve_continuous_lyapunov\n", + "from scipy.linalg import solve_discrete_lyapunov\n", + "from scipy.linalg import eig\n", + "\n", + "\n", + "Q = np.array([[-1, 0], [0, -1]])\n", + "\n", + "A = np.array([[-10, 5], [-5, -10]])\n", + "e, v = eig(A)\n", + "print(\"eig(A):\\n\", e)\n", + "\n", + "P = solve_continuous_lyapunov(A, Q)\n", + "print(\"P\", P)\n", + "e, v = eig((A.transpose().dot(P) + P.dot(A)))\n", + "print(\"eig(A'P + P*A):\\n\", e)\n", + "print(\" \")\n", + "print(\" \")\n", + "\n", + "\n", + "A = np.array([[0.9, 0.5], [-0.2, -0.8]])\n", + "e, v = eig(A)\n", + "print(\"eig(A)\", e)\n", + "\n", + "P = solve_discrete_lyapunov(A, Q)\n", + "print(\"P\", P)\n", + "print(\"(A'PA - P + Q ):\")\n", + "print(((A.dot(P)).dot(A.transpose()) - P + Q))\n" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "eig(A) [-10.+5.j -10.-5.j]\n", + "P [[ 5.00000000e-02 7.34706413e-20]\n", + " [-1.24900090e-18 5.00000000e-02]]\n", + "eig(A'P + P*A) [-1.+0.j -1.+0.j]\n", + " \n", + " \n", + "eig(A) [ 0.83898669+0.j -0.73898669+0.j]\n", + "P [[-4.03347296 0.9268445 ]\n", + " [ 0.9268445 -2.40207966]]\n", + "(A'PA - P + Q ):\n", + "[[0.00000000e+00 3.33066907e-16]\n", + " [1.11022302e-16 4.44089210e-16]]\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "FdmioTfehF-z" + }, + "source": [ + "Test the following systems' stability:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "W0mjs9LugtlN" + }, + "source": [ + "\n", + "$$x_{i+1} = \n", + "\\begin{pmatrix} 1.5 & 0.2 \\\\ -0.15 & 0.23\n", + "\\end{pmatrix}\n", + "x_i\n", + "$$\n", + "\n", + "\n", + "$$x_{i+1} = \n", + "\\begin{pmatrix} -1 & -1 \\\\ -2 & 0.1\n", + "\\end{pmatrix}\n", + "x_i\n", + "$$\n", + "\n", + "\n", + "$$x_{i+1} = \n", + "\\begin{pmatrix} -3 & -1 \\\\ -1.5 & -10.3\n", + "\\end{pmatrix}\n", + "x_i\n", + "$$\n", + "\n", + "\n", + "$$x_{i+1} = \n", + "\\begin{pmatrix} -0.2 & -1 \\\\ 1.7 & 1.1\n", + "\\end{pmatrix}\n", + "x_i\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "XIJZDiUmhvWv" + }, + "source": [ + "Test stability of continious systems with the same state matrices:\n", + "\n", + "\n", + "$$\\dot x = \n", + "\\begin{pmatrix} 1.5 & 0.2 \\\\ -0.15 & 0.23\n", + "\\end{pmatrix}\n", + "x\n", + "$$\n", + "\n", + "\n", + "$$\\dot x = \n", + "\\begin{pmatrix} -1 & -1 \\\\ -2 & 0.1\n", + "\\end{pmatrix}\n", + "x\n", + "$$\n", + "\n", + "\n", + "$$\\dot x = \n", + "\\begin{pmatrix} -3 & -1 \\\\ -1.5 & -10.3\n", + "\\end{pmatrix}\n", + "x\n", + "$$\n", + "\n", + "\n", + "$$\\dot x = \n", + "\\begin{pmatrix} -0.2 & -1 \\\\ 1.7 & 1.1\n", + "\\end{pmatrix}\n", + "x\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "ARtI-McEi9n5" + }, + "source": [ + "Consider the following matrices:\n", + "\n", + "$$\\dot x = \n", + "\\begin{pmatrix} -10.05 & -0.021 & -0.02 \\\\ \n", + "0 & 0 & 0 \\\\ \n", + "-0.022 & 0.0032 & -10.055\n", + "\\end{pmatrix}\n", + "x\n", + "$$\n", + "\n", + "$$\\dot x = \n", + "\\begin{pmatrix} -2.009 & 0 & 0.0012 \\\\ \n", + "0.05 & 0 & -0.041 \\\\ \n", + "-0.042 & 0 & -4.055\n", + "\\end{pmatrix}\n", + "x\n", + "$$\n", + "\n", + "Can you reason about assymptotic stability of the system without computations?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "fBgQ4jhckZq_" + }, + "source": [ + "**Answer:**\n", + "\n", + "First system is Lyapunov stable, but not assymptotically stable. You can see that its eigenvalues are not going to have negative eigenvalues, but also you see that the matrix has a non-trivial null space.\n", + "\n", + "You can also directly notice that the second component of $x$ is not going to change, rulling out assymptotic stability.\n", + "\n", + "Second sistem has a non-trivial null space too, meaning some of its eigenvalues are going to be 0. " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "9ajNVPtmna3c" + }, + "source": [ + "Consider the following system again:\n", + "\n", + "$$\\dot x = \n", + "\\begin{pmatrix} -10.05 & -0.021 & -0.02 \\\\ \n", + "0 & 0 & 0 \\\\ \n", + "-0.022 & 0.0032 & -10.055\n", + "\\end{pmatrix}\n", + "x\n", + "$$\n", + "\n", + "You know that $x_2$ is a constant. Let's denote the value of $x_2$ as $c$. Can you rewrite the system in terms of remaining variables $x_1$ and $x_3$ and prove its stability using the Lyapuniv eq?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "kBR3IQ6sn0to" + }, + "source": [ + "## Solution\n", + "\n", + "### Way 1\n", + "\n", + "Denote:\n", + "\n", + "$$y = \n", + "\\begin{pmatrix} \n", + "x_1 \\\\ \n", + "x_3\n", + "\\end{pmatrix}\n", + "$$\n", + "\n", + "And rewrite:\n", + "\n", + "$$\\dot y = \n", + "\\begin{pmatrix} -10.05 & -0.02 \\\\ \n", + "-0.022 & -10.055\n", + "\\end{pmatrix}\n", + "y\n", + "+\n", + "\\begin{pmatrix} -0.021 \\\\ \n", + "0.0032\n", + "\\end{pmatrix}\n", + "c\n", + "$$\n", + "\n", + "The rest you know how to do.\n", + "\n", + "### Way 2\n", + "\n", + "Orthonormal basis in the column space of the state matrix in this case is:\n", + "\n", + "$$\n", + "C =\n", + "\\begin{pmatrix} \n", + "1 & 0 \\\\ \n", + "0 & 0 \\\\ \n", + "0 & 1\n", + "\\end{pmatrix}\n", + "$$\n", + "\n", + "Motion of the system takes place in that column space. Let's denote $y = C^{\\top}x$, and as long as $x$ is in this column space, it is true that $x = Cy$. But if $x$ is not in the column space, it is $x = Cy + x^*$\n", + "\n", + "Notice that $x^*$ is in the left null space of the state matrix, as long as $y = C^{\\top}x$, because: \n", + "\n", + "$$Cy = CC^{\\top}x$$\n", + "$$x-x^* = CC^{\\top}x$$\n", + "$$x^* = (I-CC^{\\top})x$$\n", + "\n", + "where the last expression is a projection of $x$ onto the left null space of the state matrix. Orthonormal basis in the left null space of the state matrix is:\n", + "\n", + "$$\n", + "L =\n", + "\\begin{pmatrix} \n", + "0 \\\\ \n", + "1 \\\\ \n", + "0\n", + "\\end{pmatrix}\n", + "$$\n", + "\n", + "And we know that $x_2 = c$, so $x^* = Lc$.\n", + "\n", + "Variable $y$ is the new coordinates in the column space basis.\n", + "\n", + "Let's project teh dynamics into the column space. First we multiply it by $C^{\\top}$:\n", + "\n", + "$$C^{\\top} \\dot x = \n", + "C^{\\top}\n", + "\\begin{pmatrix} -10.05 & -0.021 & -0.02 \\\\ \n", + "0 & 0 & 0 \\\\ \n", + "-0.022 & 0.0032 & -10.055\n", + "\\end{pmatrix}\n", + "x\n", + "$$\n", + "\n", + "$$\\dot y = \n", + "\\begin{pmatrix} -10.05 & -0.021 & -0.02 \\\\ \n", + "-0.022 & 0.0032 & -10.055\n", + "\\end{pmatrix}\n", + "x\n", + "$$\n", + "\n", + "Then, since $x = Cy + Lc$ on teh system trajectory, we get:\n", + "\n", + "$$\\dot y = \n", + "\\begin{pmatrix} -10.05 & -0.021 & -0.02 \\\\ \n", + "-0.022 & 0.0032 & -10.055\n", + "\\end{pmatrix}\n", + "(Cy + Lc)\n", + "$$\n", + "\n", + "$$\\dot y = \n", + "\\begin{pmatrix} -10.05 & -0.02 \\\\ \n", + "-0.022 & -10.055\n", + "\\end{pmatrix}\n", + "y\n", + "+\n", + "\\begin{pmatrix} \n", + "-0.021 \\\\ \n", + "0.0032\n", + "\\end{pmatrix}\n", + "c\n", + "$$\n", + "\n", + "From here you apply Lyapunov eq. directly." + ] + } + ] +} \ No newline at end of file diff --git a/legacy - ColabNotebooks/lecture_Bode.ipynb b/legacy - ColabNotebooks/lecture_Bode.ipynb new file mode 100644 index 0000000..b6bd46d --- /dev/null +++ b/legacy - ColabNotebooks/lecture_Bode.ipynb @@ -0,0 +1,145 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "lecture_Bode.ipynb", + "provenance": [], + "authorship_tag": "ABX9TyNiFyYhRZgL2vzRqUzl15sc", + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + }, + "language_info": { + "name": "python" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 521 + }, + "id": "5KVGlAIvHPxa", + "outputId": "622f7640-eda5-44a7-a727-0d24a9c38509" + }, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + } + } + ], + "source": [ + "import numpy as np\n", + "from scipy import signal\n", + "import matplotlib.pyplot as plt\n", + "\n", + "sys = signal.TransferFunction([1], [1, 1])\n", + "array_w, mag, phase = signal.bode(sys)\n", + "\n", + "plt.figure()\n", + "plt.semilogx(array_w, mag) # Bode magnitude plot\n", + "plt.figure()\n", + "plt.semilogx(array_w, phase) # Bode phase plot\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "source": [ + "from math import atan2, pi\n", + "\n", + "def my_tf_w(w):\n", + " re = 1 / (1 + w*w)\n", + " im = -w / (1 + w*w)\n", + " return re, im \n", + "\n", + "Count = array_w.shape[0]\n", + "array_amp = np.zeros((Count, ))\n", + "array_arg = np.zeros((Count, ))\n", + "\n", + "for i in range(Count):\n", + " w = array_w[i]\n", + " re, im = my_tf_w(w)\n", + " array_amp[i] = 20*np.log10( np.sqrt(re*re + im*im) ) \n", + " array_arg[i] = atan2(im, re) * 180 / pi\n", + "\n", + "plt.figure()\n", + "plt.semilogx(array_w, array_amp) # Bode magnitude plot\n", + "plt.figure()\n", + "plt.semilogx(array_w, array_arg) # Bode phase plot\n", + "plt.show()\n" + ], + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 521 + }, + "id": "45esPvQrRqbO", + "outputId": "cf969231-1760-43f5-a6ee-f811ddd52a2a" + }, + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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5jU6rlKOmkBcJEoO7JXPzGU3TEr+4otDrciRIKORFgsiMib05oVcad7+6jp37K70uR4KAQl4kiPgijPsuHEGjc9z6/GrNVimtUsiLBJnctHh+evZglmzZy5+XbPO6HAlwCnmRIHTx2Fy+PjCTexdsoGBPhdflSABTyIsEITPj3vOGERft4+bnV1Hf0Oh1SRKgFPIiQSozOZafTR3Kqh2lPP6ebgIuLVPIiwSxbw7vypShWfx+4SY27dYkZvJVCnmRIGZm/PzcoSTGRnKLhm2kBe0S8mZ2s5k5M0tv/t3MbJaZFZjZajMb3R7HEZGvSk+M4edTh7J6ZxmP6t6w8iVtDnkzywXOAD4/ZPEUoF/zYybwSFuPIyKHd9bwrpw1vCsPvrVZc8/Lf2iPnvzvgduAQ6/KmArMcU2WAqlm1rUdjiUih/Gzc4aQHBvFrS9o2Eb+rU0hb2ZTgULn3KovrcoGdhzy+87mZSLiJ50TY7h76hBW7yzT2TbyL5GtbWBmi4CsFlbdCfyYpqGa42ZmM2ka0qF79+5t2ZVI2DtrWFdeG7KL3y/axDcGZ9I3M8nrksRjrfbknXOTnHNDv/wAtgC9gFVmtg3IAVaYWRZQCOQespuc5mUt7X+2cy7POZeXkZHR1r9HJKz982yb+Ggftzy/mgbNbRP2jnu4xjm3xjmX6Zzr6ZzrSdOQzGjnXBHwKnB581k244Ey59yu9ilZRI4kIymGu88ZwsodpfzvBxq2CXf+Ok/+dZp6+gXA48C1fjqOiLTgnBHdmDQok/v+sZFtJQe9Lkc81G4h39yjL2l+7pxz1znn+jjnhjnn8tvrOCLSOjPjF+cOIyoigttf1JTE4UxXvIqEqKyUWH5y9iCWbd3HMx993voLJCQp5EVC2EV5uZzcN517Xv+UwtIqr8sRDyjkRUKYmXHPecNwwI9f0g3Aw5FCXiTE5abFc9uZA3h3UzEv6QbgYUchLxIGLj+xJ3k9OvGz19azp7za63KkAynkRcJARITx6wuGU1XXwP/MX+d1OdKBFPIiYaJPRiI/nNSPBWuLWLBG1yaGC4W8SBiZObE3Q7OT+en8dZRW1npdjnQAhbxIGIn0RfDr84dTWlnLz15b73U50gEU8iJhZki3FK45tQ8vrSjk7Y17vC5H/EwhLxKGbji9L30zE7nzpTWUV9d5XY74kUJeJAzFRPr49fnD2XWgml+/scHrcsSPFPIiYWpMj05cdVIv/rL0c5Zu2et1OeInCnmRMHbLGQPonhbP7S+upqq2wetyxA8U8iJhLC7ax73nD2P73kruX7jR63LEDxTyImFuQp90Lj2hO0++v5UVn+/3uhxpZwp5EeGOKQPJSo7l1udXUV2nYZtQopAXEZJio7jn/OF8VnyQB9/a7HU50o4U8iICwKn9M7goL4fH3v2MVTtKvS5H2olCXkT+5c6zBpOZFMutL6yipl7DNqFAIS8i/5ISF8U95w1j0+4KZmnYJiQo5EXkP3xtYCYXjMnh0Xe3aNgmBCjkReQrfnr2YDISY7hFZ9sEPYW8iHxFSlwU954/jM17KnhgkYZtgplCXkRadNqATKaNzWX24s90kVQQU8iLyGHdedYguqbEcctzqzS3TZBSyIvIYSXFRvHbC4azpeSgpiQOUgp5ETmiCX3T+c6Enjz14TY+KCjxuhw5Rgp5EWnV7ZMH0js9gVufX8UB3UkqqCjkRaRVcdE+fnfRCIoOVHPXq+u8LkeOgUJeRI7KqO6duP5rfXlpRSGvr9nldTlylBTyInLUbji9HyNyUvjxy2soKqv2uhw5Cgp5ETlqUb4Ifn/xSGrqGrn1hVU0NjqvS5JWKORF5Jj0zkjkzrMG8d7mEp76cJvX5UgrFPIicsymn9Cd0wdmcu+CDXy664DX5cgRKORF5JiZGb+5YDgp8VHc+Ownuho2gCnkReS4dE6M4f6LRrB5TwW/fH291+XIYSjkReS4TeyXwcxTevOXpZ/z5roir8uRFrQ55M3sBjPbYGbrzOw3hyy/w8wKzGyjmZ3Z1uOISGC65YwBDMtO4bYXVlNYWuV1OfIlbQp5M/saMBUY4ZwbAtzXvHwwMA0YAkwGHjYzXxtrFZEAFB0ZwR8uGUVDo+PGZz+hrqHR65LkEG3tyX8fuNc5VwPgnNvTvHwqMM85V+Oc2woUAOPaeCwRCVA90xO457xhLN++n/sXbvK6HDlEW0O+PzDRzJaZ2btmNrZ5eTaw45DtdjYvE5EQ9c0R3bj0hO488s5nvLNxT+svkA7Rasib2SIzW9vCYyoQCaQB44FbgefMzI6lADObaWb5ZpZfXFx8XH+EiASG/z57MAOzkrjprys1Ph8gWg1559wk59zQFh7zaeqhv+SafAQ0AulAIZB7yG5ympe1tP/Zzrk851xeRkZG2/8iEfFMbJSPh6ePpq7Bcd3TK6it1/i819o6XPMK8DUAM+sPRAMlwKvANDOLMbNeQD/gozYeS0SCQO+MRO67cDgrd5Tyy7/r/HmvtTXk/wT0NrO1wDzgiuZe/TrgOWA98AZwnXNOl8SJhInJQ7ty9cm9+POS7cxf2eKHeOkgkW15sXOuFrjsMOt+CfyyLfsXkeB1+5SBrNxRyo9eXEP/LkkM6prsdUlhSVe8iohfRPkieHj6aJLjIpk5N5/SylqvSwpLCnkR8ZvM5FgeuWwMu8tquOHZT2jQ/PMdTiEvIn41unsnfjZ1CO9tLuE3b2zwupyw06YxeRGRozFtXHfWFJbx2OIt9O+SxPljcrwuKWyoJy8iHeKuc4Ywvncad7y0huXb93ldTthQyItIh4jyRfDI9DF0S41l5pzl7Nxf6XVJYUEhLyIdplNCNE9cMZbahkau/nM+5dV1XpcU8hTyItKh+mYm8vD00RTsqeDap1doamI/U8iLSIeb2C+DX503jPc2l3Dny2twTqdW+ovOrhERT1yUl8vO/VXMemszOZ3iufH0fl6XFJIU8iLimZsm9WPn/kruX7iJzKQYpo3r7nVJIUchLyKeMTN+ff5w9h2s5ccvryE1PprJQ7O8LiukaExeRDz1zzluRuamcuO8T1jy2V6vSwopCnkR8Vx8dCR/+s5YeqTFM2NOPqt2lHpdUshQyItIQEiNj2bud08gLSGay//0Eeu/OOB1SSFBIS8iASMrJZanrz6B+Ggf335yGZt3l3tdUtBTyItIQMlNi+eZGeOJiDCmP7GMz4orvC4pqCnkRSTg9EpP4OmrT6DROabNXkrBHvXoj5dCXkQCUv8uSTw7YzzOwbTZy9ikoZvjopAXkYDVr0sS82aOJ8LgktlLWfdFmdclBR2FvIgEtL6ZicybOZ6YyAimzV5K/jbNRX8sFPIiEvB6ZyTy/PcnkJEYw2VPLuOdjXu8LiloKORFJChkp8bx3DUn0js9kRlz8pm/stDrkoKCQl5EgkZ6YgzPzhzP6O6d+MG8lTz67meaprgVCnkRCSopcVHM+e44vjmiG/cu2MD/vLqOhkYF/eFoFkoRCToxkT4evHgk3VJieWzxFnbsq2TWJaNIio3yurSAo568iASliAjjjv8axC/OHcrizSWc/8iHfL5XNwf/MoW8iAS1y8b3YO5V49h9oIapD73Ph5+VeF1SQFHIi0jQm9A3nVeuO4m0hGi+/eRHzF6sL2T/SSEvIiGhV3oC868/mTMGd+FXr2/g+mc+oaKm3uuyPKeQF5GQkRgTycPTR/OjKQNZsHYX5/zh/bCfCkEhLyIhxcy45tQ+PDNjPAdr6/nWwx8yd8m2sB2+UciLSEga37szr984kZP6dOan89cxc+5ySipqvC6rwynkRSRkdU6M4ckrxvKTswbx7qZiJj+wmEXrd3tdVodSyItISIuIMK6e2Ju/XX8yGUmxXD0nn9teWEVZVZ3XpXUIhbyIhIUBWUm8ct0Erj2tDy+uKOQb97/LP9YVeV2W3ynkRSRsxET6uG3yQF65tumc+plzl3Pd0ysoKqv2ujS/UciLSNgZlpPCq9efzM3f6M/CT3cz6f53efL9rdQ3NHpdWrtTyItIWIqOjOCG0/ux8KZTGNOjEz9/bT1n/yH0pkVoU8ib2UgzW2pmK80s38zGNS83M5tlZgVmttrMRrdPuSIi7atH5wSeunIsj0wfTXl1PZc+vozvzc0PmcnO2tqT/w1wt3NuJPDfzb8DTAH6NT9mAo+08TgiIn5jZkwZ1pW3bj6VW87oz3ubSzj9/ne469V17A3yc+vbGvIOSG5+ngJ80fx8KjDHNVkKpJpZ1zYeS0TEr2KjfFz/9X68fctpXDAmhzlLtnHqb9/hwUWbKa8OzlMurS2X+prZIOBNwGj6D2OCc267mb0G3Ouce795u7eA251z+S3sYyZNvX26d+8+Zvv27cddj4hIeyrYU8F9b27kjXVFpMRFMWNiL66Y0DPgbk5iZsudc3ktrmst5M1sEZDVwqo7gdOBd51zL5rZRcBM59ykYwn5Q+Xl5bn8/CNuIiLS4dYWlvHAok0s+nQPKXFRXDGhJ9+Z0JO0hGivSwPaGPKt7LgMSHXOOTMzoMw5l2xmjwHvOOeebd5uI3Cac27XkfankBeRQLZ6Zyl/+P8FLFy/m7goH9PG5XLVSb3ITYv3tK4jhXxbx+S/AE5tfv51YHPz81eBy5vPshlPU/gfMeBFRALd8JxUHr88j4U3ncKUYVnMXbKdU3/7NtfMXc7H2/YF5EyXbe3Jnww8SNMNwauBa51zy5t79X8EJgOVwJWtDdWAevIiElx2lVUxZ8l2nln2OWVVdQzqmsxl47tz7shsEmIiO6wOvw3XtDeFvIgEo8rael7+pJC/LP2cT3cdIDEmkm+O6MbFY3MZkZNCU7/XfxTyIiIdwDnHis9LeXrZdl5fs4vqukYGdEnivNHZTB2ZTVZKrF+Oq5AXEelgB6rreG3VLp7L38HKHaWYwYQ+nTlnRDfOHJJFanz7nZmjkBcR8dDWkoO88kkhr6wsZPveSiIjjJP6pjNlaBaTBnchPTGmTft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" + ] + }, + "metadata": { + "needs_background": "light" + } + } + ] + } + ] +} \ No newline at end of file diff --git a/legacy - ColabNotebooks/practice_01_StateSpace_transformation_simulation.ipynb b/legacy - ColabNotebooks/practice_01_StateSpace_transformation_simulation.ipynb new file mode 100644 index 0000000..a30fd5a --- /dev/null +++ b/legacy - ColabNotebooks/practice_01_StateSpace_transformation_simulation.ipynb @@ -0,0 +1,441 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "[CT21] lab01_state_space.ipynb", + "provenance": [], + "collapsed_sections": [], + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "zVZdDu7VjMqg" + }, + "source": [ + "# **Introduction**\r\n", + "\r\n", + "---\r\n", + "\r\n", + "## **Practice Instructor**\r\n", + "Name: Simeon Nedelchev\r\n", + "\r\n", + "Background:\r\n", + "* **MSTU STANKIN** (Bachelor/Master in Robotics 2018) \r\n", + "* **Korea University of Technology And Education** (KoreaTech) (Master ME 2019), Research fellow 'BioRobotics' lab\r\n", + "* **Innopolis University** (PhD), Research fellow 'MCP' lab\r\n", + "\r\n", + "\r\n", + "Research interests:\r\n", + "\r\n", + "\r\n", + "* **Control**: Nonlinear, Robust, Adaptive, Energy based, Noncolocated and Underactuated, with focus on discrete-time and physically inspired numerical methods.\r\n", + "* **Online Identification and Estimation**: Moving Horizon Estimators, Sliding Mode Observers.\r\n", + "* **Analytical Mechanics and Dynamical Systems**:\r\n", + "Dynamical Modeling, Limit Cycles, Constrained Dynamics (UK), Computational mechanics.\r\n", + "* **Applied Optimization**:\r\n", + "Linear, Quadratic, and Nonlinear programming, Dynamical programming, Optimal Control, Optimal Mechanical Design. \r\n", + "\r\n", + "\r\n", + "Feel free to contact me in person (in basement lab/office 105) or via [telegram](https://t.me/simkasimka) and [mail](https://t.me/simkasimka) if you face any problems with the course or would like to do research and work on hardware\r\n", + "## **Prerequisites for practice**\r\n", + "There are no strong prerequisites for this class, however:\r\n", + "* **Linear Algebra**, **Calculus**, **Differential Equations**, and **Dynamics** (Mechanics, Physics) courses will be really helpfull\r\n", + "* We will use a bit of **Python** in this class\r\n", + "* We will often use [mathematical quantifiers](https://en.wikipedia.org/wiki/Quantifier_(logic)). Revise them by going over [exercises](https://www.whitman.edu/mathematics/higher_math_online/section01.02.html) if you forgot some.\r\n", + "\r\n", + "## **Notation**\r\n", + "We will use the following notation in \"notebooks\":\r\n", + "> A key points or equations looks like this \r\n", + "\r\n", + ">**QUESTION**: \r\n", + "Questions related to the subject, pay attention to them, they may enhance your understanding of the topic\r\n", + "\r\n", + ">**EXERCISE**: \r\n", + "These exercises we will do during the practice sessions, remaining you may treat as your HW\r\n", + "\r\n", + ">**BONUS EXERCISE** Problems that will be graded separately and will give you bonus points on final exam\r\n", + "\r\n", + "## **Literature**\r\n", + "I personally suggest a following books on the subject:\r\n", + "\r\n", + "\r\n", + "* C.T. Chen, **Linear System Theory and Design**\r\n", + "\r\n", + "* Vladimir I. Arnold, **Ordinary Differential Equations**\r\n", + "\r\n", + "* Steven H. Strogatz, **Nonlinear Dynamics and Chaos**\r\n", + "\r\n", + "\r\n", + "\r\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "D-dOD4xqsPiR" + }, + "source": [ + "# **Practice 1: State Space modeling, Transformations and Simulation**\n", + "## **Goals for today**\n", + "\n", + "---\n", + "\n", + "\n", + "\n", + "During today practice we will:\n", + "* Recall the notion of ODE, transform \n", + "* Write mathematical models in state space form.\n", + "* Obtain solution of state space equations with `odeint`.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "RCityqOscrJV" + }, + "source": [ + "## **State Space and Ordinary Differential Equations**\n", + "A state-space representation is a mathematical model of a physical system as a set of input $\\mathbf{u}$, output $\\mathbf{y}$ and state variables $\\mathbf{x}$ related by first-order differential equations (difference equations in discrete time). \n", + "\n", + "State variables $\\mathbf{x}$ are variables whose values evolve through time $t$ in a way that depends on the values they have at any given time and also depends on the externally imposed values of input variables $\\mathbf{u}$. Output $\\mathbf{y}$ depend on the values of the state variables $\\mathbf{x}$.\n", + "\n", + "### **Ordinary Differential Equations**\n", + "\n", + "Given $\\mathcal{F}$, a function of $t$, $z$, and derivatives of $z$ . Then an equation of the form\n", + "\n", + "$$\n", + "\\mathcal{F} \\left(t,z,\\dot{z},\\ldots ,z^{(n-1)}\\right)=z^{(n)}\n", + "$$\n", + "\n", + "is called an explicit **ordinary differential equation** of order n.\n", + "\n", + "### **Nonlinear State Space**\n", + "\n", + "General form of a state-space model can be written as system of two functions:\n", + "\\begin{equation}\n", + "\\begin{cases} \n", + "\\mathbf{\\dot{x}} (t)=\\boldsymbol{f}(t,\\mathbf{x}(t),\\mathbf{u}(t)) \\\\ \n", + "\\mathbf{y}(t)=\\boldsymbol{h}(t,\\mathbf{x}(t),\\mathbf{u}(t))\n", + "\\end{cases}\n", + "\\end{equation}\n", + "\n", + "\n", + "In this class we consider a simplest case of equations above, namely **linear** ones.\n", + "\n", + "\n", + "### **Linear State Space**\n", + "if relationships between state, output and control is **linear**, we can formulate the model of system in following form:\n", + "\\begin{equation}\n", + "\\begin{cases} \n", + "\\mathbf{\\dot{x}} (t)=\\mathbf{A}(t)\\mathbf{x}(t) + \\mathbf{B}(t)\\mathbf{u}(t) \\\\ \n", + "\\mathbf{y}(t)=\\mathbf{C}(t)\\mathbf{x}(t) + \\mathbf{D}(t)\\mathbf{u}(t)\n", + "\\end{cases}\n", + "\\end{equation}\n", + "\n", + "where\n", + "* $\\mathbf{x} \\in \\mathbb{R}^n$ states of the system\n", + "* $\\mathbf{y} \\in \\mathbb{R}^l$ output vector\n", + "* $\\mathbf{u} \\in \\mathbb{R}^m$ control inputs\n", + "* $\\mathbf{A} \\in \\mathbb{R}^{n \\times n}$ state matrix\n", + "* $\\mathbf{B} \\in \\mathbb{R}^{n \\times m}$ input matrix\n", + "* $\\mathbf{C} \\in \\mathbb{R}^{l \\times n}$ output matrix\n", + "* $\\mathbf{D} \\in \\mathbb{R}^{l \\times m}$ feedforward matrix\n", + "\n", + "Note that matrices $\\mathbf{A},\\mathbf{B},\\mathbf{C},\\mathbf{D}$ are time dependend, we call such systems **time-varient**.\n", + "\n", + "However, in practice we often deal with systems whose dynamics is time-invarient and output is independent from control, such that we can rewrite the model as:\n", + "\\begin{equation}\n", + "\\begin{cases} \n", + "\\mathbf{\\dot{x}} (t)=\\mathbf{A}\\mathbf{x}(t) + \\mathbf{B}\\mathbf{u}(t) \\\\ \n", + "\\mathbf{y}(t)=\\mathbf{C}\\mathbf{x}(t)\n", + "\\end{cases}\n", + "\\end{equation}\n", + "\n", + "### **Unforced systems**\n", + "\n", + "During today practice however we will consider a unforced (uncontrolled systems)as follows:\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{x}} (t)=\\mathbf{A}\\mathbf{x}(t) + \\mathbf{b}\n", + "\\end{equation}\n", + "where $\\mathbf{b} \\in \\mathbb{R}^n$ is a constant vector\n", + "\n", + ">**QUESTION:** Can we rewrite system above in the following form?\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{x}}_n (t)=\\mathbf{A}_n\\mathbf{x}_n(t)\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "N-krnoYnbvmu" + }, + "source": [ + "\n", + "\n", + "\n", + "## **From the linear ODE to the State Space**\n", + "\n", + "\n", + "A probleim is to, given an ODE in canonical form:\n", + "\n", + "$$a_{n}z^{(n)} +a_{n-1}z^{(n-1)}+...+a_{2}\\ddot z+a_{1}\\dot z + a_0 z= b_0$$\n", + "\n", + "find its state space representation:\n", + "\n", + "$$\\dot{ \\mathbf{x}} = \\mathbf{A}\\mathbf{x} + \\mathbf{b}$$\n", + "\n", + "### **Methodology**\n", + "\n", + "The first step is to express higher derivatives as follows:\n", + "\n", + "$$z^{(n)} = \n", + "-\\frac{a_{n-1}}{a_{n}}z^{(n-1)}-\n", + "...-\n", + "\\frac{a_{2}}{a_{n}}\\ddot z -\n", + "\\frac{a_{1}}{a_{n}}\\dot z - \n", + "\\frac{a_{0}}{a_{n}} z + \n", + "\\frac{b_0}{a_{n}}$$\n", + "\n", + "Now let us introduce new variables $\\mathbf{x}$ as follows:\n", + "$$\n", + "\\mathbf{x} = \n", + "\\begin{bmatrix}\n", + "x_1 \\\\ \n", + "x_{2} \\\\\n", + "... \\\\\n", + "x_n \\\\\n", + "\\end{bmatrix}\n", + "=\n", + "\\begin{bmatrix}\n", + "z \\\\\n", + "z^{(1)} \\\\\n", + " ... \\\\\n", + "z^{(n-1)} \\\\\n", + "\\end{bmatrix}\n", + "$$\n", + "\n", + "Thus original ODE may be written as:\n", + "$$\n", + "\\begin{bmatrix}\n", + "\\dot{x}_1 \\\\ \n", + "\\dot{x}_{2} \\\\\n", + "... \\\\\n", + "\\dot{x}_n \\\\\n", + "\\end{bmatrix}\n", + "=\n", + "\\begin{bmatrix}\n", + "x_2 \\\\ \n", + "x_3 \\\\\n", + "... \\\\\n", + "-\\frac{a_{k-1}}{a_{n}}x_n-\n", + "...-\n", + "\\frac{a_{2}}{a_{n}} x_3 -\n", + "\\frac{a_{1}}{a_{n}} x_2 - \n", + "\\frac{a_{0}}{a_{n}} x_1 + \n", + "\\frac{b_0}{a_{n}} \\\\\n", + "\\end{bmatrix}$$\n", + "\n", + "Finally, in a matrix form:\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{x}} (t) = \\mathbf{A}\\mathbf{x}(t) + \\mathbf{b}\n", + "\\end{equation}\n", + "\n", + ">**QUESTION:** How matrix $\\mathbf{A}$ and vector $\\mathbf{b}$ will look like?\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "sk9IEZJg2cS_" + }, + "source": [ + " >### **Exercises**\r\n", + ">\r\n", + "> 1) Convert to State Space represantation\r\n", + ">\r\n", + ">* $10 z^{(4)} -7 z^{(3)} + 2 \\ddot z + 0.5 \\dot z + 4z = 15$\r\n", + "* $5 z^{(4)} -17 z^{(3)} - 3 \\ddot z + 1.5 \\dot z + 2z = 25$\r\n", + "* $-3 z^{(4)} + 22 z^{(3)} + 4 \\ddot z + 1.5 \\dot z + 1z = 15$\r\n", + "* $5 z^{(4)} -17 z^{(3)} - 1.5 \\ddot z + 100 \\dot z + 1.1z= 45$\r\n", + "* $1.5 z^{(4)} -23 z^{(3)} - 2.5 \\ddot z + 0.1 \\dot z + 100z= -10$\r\n", + ">\r\n", + "> 2) Do the same in the oposit way, in order to convert the following to a second order ODE:\r\n", + ">\r\n", + ">$$\\dot{\\mathbf{x}} = \\mathbf{A}\\mathbf{x}\r\n", + "$$\r\n", + ">\r\n", + ">with wollowing matrices $\\mathbf{A}$:\r\n", + ">$$\r\n", + "\\begin{bmatrix} 1 & 0 \\\\ -5 & -10\r\n", + "\\end{bmatrix},\\quad\r\n", + "\\begin{bmatrix} 0 & 8 \\\\ 1 & 3\r\n", + "\\end{bmatrix}\r\n", + ",\\quad\r\n", + "\\begin{bmatrix} 0 & 8 \\\\ 6 & 0\r\n", + "\\end{bmatrix}\r\n", + ",\\quad\r\n", + "\\begin{bmatrix} 0 & 1 \\\\ 6 & 3\r\n", + "\\end{bmatrix}\r\n", + "$$\r\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "HKH0Tk6Rl7ec" + }, + "source": [ + "## **Intro to Simulation (solution of ODE)**\n", + "While studying ODE $\\dot{\\mathbf{x}} = \\boldsymbol{f}(\\mathbf{x}, \\mathbf{u}, t)$, one is often interested in its solution $\\mathbf{x}(t)$ (integral curve):\n", + "\\begin{equation}\n", + "\\mathbf{x} = \\int_{t_0}^{t_f} \\boldsymbol{f}(t,\\mathbf{x}(t),\\mathbf{u}(t))dt,\\quad \\text{s.t: } \\mathbf{x}(t_0) = \\mathbf{x}_0\n", + "\\end{equation}\n", + "\n", + "In most practical situations the integral above cannot be solved analyticaly and one should consider numerical integration instead.\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "7U4i-VI8jQsm" + }, + "source": [ + "import numpy as np\r\n", + "from scipy.integrate import odeint\r\n", + "\r\n", + "n = 3\r\n", + "A = np.array([[0, 1, 0], \r\n", + " [0, 0, 1], \r\n", + " [-10, -5, -2]])\r\n", + "\r\n", + "# x_dot from state space\r\n", + "def f(x, t):\r\n", + " return A.dot(x)\r\n", + "\r\n", + "t0 = 0 # Initial time \r\n", + "tf = 10 # Final time\r\n", + "t = np.linspace(t0, tf, 1000)\r\n", + "\r\n", + "x0 = np.random.rand(n) # initial state\r\n", + "\r\n", + "solution = {\"ss\": odeint(f, x0, t, args = (1,2,3,4))}" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "TIRdklAZCxBc" + }, + "source": [ + "Let us plot the result of simulation:" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 281 + }, + "id": "m96wVXsfCd7V", + "outputId": "c261ec17-dbfc-41ad-f5c4-c0922455fad2" + }, + "source": [ + "\r\n", + "from matplotlib.pyplot import *\r\n", + "\r\n", + "plot(t, solution['ss'], linewidth=2.0)\r\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\r\n", + "grid(True)\r\n", + "xlim([t0, tf])\r\n", + "ylabel(r'State ${x}$')\r\n", + "xlabel(r'Time $t$')\r\n", + "show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "E3hMR9WiBCA5" + }, + "source": [ + ">**QUESTION:** How would you find analytical solution for linear state space equations:\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{x}} (t)=\\mathbf{A}\\mathbf{x}(t)\n", + "\\end{equation}\n", + ">**TIP:** recall the solution of the equation $\\dot{x} = a x$, and try to generilize it to the $n$-dimensional case. " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "ufR3L7_eC6x-" + }, + "source": [ + "\r\n", + ">### **Exercises**\r\n", + ">\r\n", + "> 1) Convert the following ODE to state space and simulate them from random initial conditions. If solution diverges, try to change parameters so it will converge\r\n", + ">\r\n", + ">* $10 z^{(5)} + 10 z^{(4)} -7 z^{(3)} + 2 \\ddot z + 0.5 \\dot z + 4z = 0$\r\n", + "* $1 z^{(5)} + 5 z^{(4)} -17 z^{(3)} - 3 \\ddot z + 1.5 \\dot z + 2z = 0$\r\n", + "* $6 z^{(5)} -3 z^{(4)} 22 z^{(3)} + 4 \\ddot z + 1.5 \\dot z + 1z = 0$\r\n", + "* $22 z^{(5)} + 5 z^{(4)} -17 z^{(3)} - 1.5 \\ddot z + 100 \\dot z + 1.1z = 0$\r\n", + "* $-10 z^{(5)} + 1.5z^{(4)} -23 z^{(3)} - 2.5 \\ddot z + 0.1 \\dot z + 100z = 0$\r\n", + ">\r\n", + "> 2) Solve the same but without converting it to state space.\r\n", + ">\r\n", + "> 3) Find or derive equations for a mass-spring-damper system (shown on figure below), write them in state-space and second order ODE forms, integrate them from different initial conditions, play with coefficients and investigate how they affect the solution.\r\n", + "\r\n", + "

\"mbk\"

\r\n", + "\r\n", + "\r\n", + ">### **Bonus Exercises**\r\n", + ">\r\n", + ">* Implement your own integration routine that will take state-space function \r\n", + "$\\mathbf{f}$, free variable $t$, and initial state $\\mathbf{x}(0)$ as input and produce the solution $\\mathbf{x}^*(t)$ as output. You may use [Runge–Kutta method](https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods) \r\n", + ">\r\n", + ">* Suppose Romeo is in love with Juliet, but in our version of the story, Juliet is a fickle lover. The more Romeo loves her, the more she wants to run away and hide, such that the rate of her love is decreasing proportional to love of Romeo with constant $b$. But when he takes the hint and backs off, she begins to find him strangely attractive and her love raise again with same rate. He, on the other hand, tends to echo her: he warms up when she loves him and cools down when she hates him, but with rate proportional to constant $a$. Write differential equation that will model how their love evolve in time. Solve them and plot the result.\r\n" + ] + } + ] +} \ No newline at end of file diff --git a/legacy - ColabNotebooks/practice_02_LTI_Stability.ipynb b/legacy - ColabNotebooks/practice_02_LTI_Stability.ipynb new file mode 100644 index 0000000..3bc517a --- /dev/null +++ b/legacy - ColabNotebooks/practice_02_LTI_Stability.ipynb @@ -0,0 +1,658 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "[CT21] lab02_lti_stability.ipynb", + "provenance": [], + "collapsed_sections": [], + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "D-dOD4xqsPiR" + }, + "source": [ + "# **Practice 2: On the Stability of Continuous Linear Dynamical Systems**\n", + "## **Goals for today**\n", + "\n", + "---\n", + "\n", + "\n", + "\n", + "During today practice we will:\n", + "* Recall what the solution of ODE and study their stability\n", + "* Check stability criteria for particular cases of ODE\n", + "* Discuss why do we need for our system to be stable" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "RCityqOscrJV" + }, + "source": [ + "## **Solutions of ODE**\n", + "While studying ODE $\\dot{\\mathbf{x}} = \\boldsymbol{f}(\\mathbf{x}, \\mathbf{u}, t)$, one is often interested in its solution $\\mathbf{x}^*(t)$ (integral curve):\n", + "\\begin{equation}\n", + "\\mathbf{x}^*(t) = \\int_{t_0}^{t_f} \\boldsymbol{f}(t,\\mathbf{x}(t),\\mathbf{u}(t))dt,\\quad \\text{s.t: } \\mathbf{x}(t_0) = \\mathbf{x}_0\n", + "\\end{equation}\n", + "\n", + "\n", + "---\n", + "\n", + "\n", + "In most practical situations the integral above cannot be solved analyticaly and one should consider numerical integration instead, however when we deal with LTI systems like:\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{x}} (t)=\\mathbf{A}\\mathbf{x}(t)\n", + "\\end{equation}\n", + "An integral above can be calculated analytically:\n", + "\\begin{equation}\n", + "\\mathbf{x}^*(t)=e^{\\mathbf{A}t}\\mathbf{x}(0)\n", + "\\end{equation}\n", + "where matrix exponential is defined via power series:\n", + "\\begin{equation} \n", + " e^{\\mathbf{A}t}=\\sum _{k=0}^{\\infty }{1 \\over k!}\\mathbf{A}^{k}t^k\n", + " \\end{equation}\n", + "\n", + "\n", + "\n", + "\n", + "---\n", + "\n", + "\n", + "\n", + "> A natural questions to ask:\n", + "* How to calculate this matrix exponential without power series?\n", + "* Can we analyze the behaviour of solutions without explicitly solving ODE?\n", + "\n", + "Let us first consider the first question, assume for a while that we can do the following factorization:\n", + "\\begin{equation}\n", + "\\mathbf{A}=\\mathbf{Q}\\mathbf{\\Lambda}\\mathbf{Q}^{-1} \n", + "\\end{equation}\n", + "where: \n", + "\n", + "\n", + "* $\\mathbf{Q}\\in \\mathbb{R}^{n \\times n}$ containing normalized eigen vectors $\\mathbf{q}_i = \\frac{\\mathbf{v}_i}{\\|\\mathbf{v}_i\\|}$ as columns. \n", + "* $\\mathbf{\\Lambda}\\in \\mathbb{R}^{n \\times n}$ diagonal matrix whose diagonal elements are the corresponding eigenvalues $\\Lambda_{ii} = \\lambda_i$. \n", + "\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "h17SqNO1cb_q", + "outputId": "22cf505f-8c91-4e06-e990-b5634999b9de" + }, + "source": [ + "# Note Eigen decomposition via Python\n", + "import numpy as np\n", + "\n", + "A = [[2., 5.],\n", + " [1., 3.]]\n", + "\n", + "A = np.array(A)\n", + "\n", + "print(f\"Original matrix:\\n{A}\\n\")\n", + "\n", + "Lambda, Q = np.linalg.eig(A)\n", + "print(f\"Eigen values:\\n{Lambda}, \\n\\n Eigen vectors:\\n{Q}\\n\")\n", + "\n", + "Qinv = np.linalg.inv(Q)\n", + "A_rec = (Q.dot(np.diag(Lambda))).dot(Qinv)\n", + "print(f\"Reconstructed matrix:\\n{A_rec}\")" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Original matrix:\n", + "[[2. 5.]\n", + " [1. 3.]]\n", + "\n", + "Eigen values:\n", + "[0.20871215 4.79128785], \n", + "\n", + " Eigen vectors:\n", + "[[-0.94140906 -0.87315384]\n", + " [ 0.33726692 -0.48744474]]\n", + "\n", + "Reconstructed matrix:\n", + "[[2. 5.]\n", + " [1. 3.]]\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "ejwnvf48c1-3" + }, + "source": [ + "Substitution to the system dynamics and multiplying by $\\mathbf{Q}^{-1}$ yields:\n", + "\\begin{equation}\n", + "\\mathbf{Q}^{-1}\\mathbf{\\dot{x}} =\\mathbf{Q}^{-1}\\mathbf{A}\\mathbf{x} =\\mathbf{Q}^{-1}\\mathbf{Q}\\mathbf{\\Lambda} \\mathbf{Q}^{-1}\\mathbf{x} = \\mathbf{\\Lambda} \\mathbf{Q}^{-1}\\mathbf{x}\n", + "\\end{equation}\n", + "\n", + "Thus defining new variables $\\mathbf{z} = \\mathbf{Q}^{-1}\\mathbf{x}$ yields:\n", + "\\begin{equation}\n", + "\\dot{\\mathbf{z}} = \\mathbf{\\Lambda}\\mathbf{z}\n", + "\\end{equation}\n", + "Which is in fact just a system of decoupled equations:\n", + "\\begin{equation}\n", + "\\dot{z}_i = \\lambda_i z_i,\\quad i = 1,2\\dots,n\n", + "\\end{equation}\n", + "with known solutions:\n", + "\\begin{equation}\n", + "z^*_i = e^{\\lambda_i t} z_i(0)\n", + "\\end{equation}\n", + "\n", + "\n", + "---\n", + "\n", + "\n", + ">**NOTE:** Another way to decompose our system is by applying following property of matrix exponential:\n", + "\\begin{equation}\n", + "e^{\\mathbf{Y}\\mathbf{X}\\mathbf{Y}^{-1}} = \\mathbf{Y}e^{\\mathbf{X}}\\mathbf{Y}^{-1}\n", + "\\end{equation}\n", + "where $\\mathbf{Y}$ is invertable\n", + "\n", + "\n", + "---\n", + "\n", + ">### **Bonus Exercise**\n", + "> Compare the solutions given by matrix exponential with one given by numerical integration for LTI system with diagonizable $\\mathbf{A}$.\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "XhdOya2kDB3A" + }, + "source": [ + "# Put your code here" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "PqMQNNRchKZI" + }, + "source": [ + "##**Basics on the Eigenvalues and Eigenvectors**\n", + "\n", + "A (non-zero) vector v of dimension N is an eigenvector of a square N × N matrix A if it satisfies the linear equation\n", + "\n", + "\\begin{equation}\n", + "\\mathbf {v} =\\lambda \\mathbf {v}\n", + "\\end{equation}\n", + "\n", + "where $\\lambda$ is a scalar, termed the eigenvalue corresponding to $\\mathbf{v}$. \n", + "\n", + "This yields an equation for the eigenvalues\n", + "\n", + "\\begin{equation}\n", + "\\det \\left(\\mathbf {A} -\\lambda \\mathbf {I} \\right)=0\n", + "\\end{equation}\n", + "We call $\\Delta(\\lambda)$ the characteristic polynomial, and the equation, called the characteristic equation, is an $n$ - th order polynomial equation in the unknown $\\lambda$ with $N_\\lambda$ solutions$ \n", + "\n", + "We can factor $\\Delta(\\lambda)$ as\n", + "\\begin{equation}\n", + "\\Delta(\\lambda)=\\left(\\lambda -\\lambda _{1}\\right)^{k_{1}}\\left(\\lambda -\\lambda _{2}\\right)^{k_{2}}\\cdots \\left(\\lambda -\\lambda _{N_{\\lambda }}\\right)^{k_{N_{\\lambda }}}=0.\n", + "\\end{equation}\n", + "\n", + "The integer $k_i$ is termed the algebraic multiplicity of eigenvalue $\\lambda_i$. If the field of scalars is algebraically closed, the algebraic multiplicities sum to N:\n", + "\\begin{equation}\n", + " \\sum \\limits _{i=1}^{N_{\\lambda }}{k_{i}}=n\n", + "\\end{equation}\n", + "For each eigenvalue $\\lambda_i$ we have a specific equation:\n", + "\\begin{equation}\n", + "\\left(\\mathbf {A} -\\lambda _{i}\\mathbf {I} \\right)\\mathbf {v} =0\n", + "\\end{equation}\n", + "\n", + "There will be $1 ≤ m_i ≤ k_i$ linearly independent solutions to each eigenvalue equation. \n", + "The linear combinations of the $m_i$ solutions are the eigenvectors associated with the eigenvalue $\\lambda_i$. The integer $m_i$ is termed the geometric multiplicity of $\\lambda_i$. The total number of linearly independent eigenvectors $N_\\mathbf{v}$ can be calculated by summing the geometric multiplicities\n", + "\\begin{equation}\n", + "\\sum \\limits _{i=1}^{N_{\\lambda }}{m_{i}}=N_{\\mathbf {v}}\n", + "\\end{equation}\n", + "\n", + ">**QUESTION:** What are the relationship between $N_{\\mathbf {v}}$ and rank of $\\mathbf{Q}$\n", + "\n", + "\n", + "\n", + "---\n", + ">### **Exercises**\n", + ">\n", + "> Find eigen system (values and vectors) of following matrices by hand, compare your solution with result of numerical routine:\n", + ">$$\n", + "\\begin{bmatrix} 0 & 1 \\\\ -5 & -2\n", + "\\end{bmatrix},\\quad\n", + "\\begin{bmatrix} 0 & 8 \\\\ 1 & 3\n", + "\\end{bmatrix}\n", + ",\\quad\n", + "\\begin{bmatrix} 0 & 8 \\\\ 6 & 0\n", + "\\end{bmatrix}\n", + ",\\quad\n", + "\\begin{bmatrix} 0 & 1 \\\\ -3 & 0\n", + "\\end{bmatrix}\n", + "$$\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "yMj6ordwKi32", + "outputId": "e9eadef3-f31a-4ef0-ab2c-60b035a18b9e" + }, + "source": [ + "A = [[0, 1],\n", + " [-5, -2]]\n", + "\n", + "Lambda, Q = np.linalg.eig(A)\n", + "print(f\"Eigen values:\\n{Lambda}, \\n\\n Eigen vectors:\\n{Q}\")" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Eigen values:\n", + "[-1.+2.j -1.-2.j], \n", + "\n", + " Eigen vectors:\n", + "[[-0.18257419-0.36514837j -0.18257419+0.36514837j]\n", + " [ 0.91287093+0.j 0.91287093-0.j ]]\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "S2xBjo0JC_4f" + }, + "source": [ + "## **Intro to Stability**\n", + "\n", + "Various types of stability may be discussed for the solutions of differential equations or difference equations describing dynamical systems. The one practically important type is that concerning the stability of solutions near to a point of equilibrium. This may be ,analyzed by the theory of **Aleksandr Lyapunov**. \n", + "\n", + "In simple terms, if the solutions that start out near an equilibrium point $\\mathbf{x}_{0}$ stay near $\\mathbf{x}_{0}$ forever, then $\\mathbf{x}_{0}$ is Lyapunov stable. More strongly, if $\\mathbf{x}_{0}$ is Lyapunov stable and all solutions that start out near $\\mathbf{x}_{0}$ converge to $\\mathbf{x}_0$, then $\\mathbf{x}_{0}$ is asymptotically stable. \n", + "\n", + "\n", + "\n", + "---\n", + "A strict deffenitions are as follows:\n", + "\n", + "Equilibrium $\\mathbf{x}_0$ is said to be:\n", + "\n", + "* **Lyapunov stable** if:\n", + "\\begin{equation}\n", + "\\forall \\epsilon>0,\\exists\\delta>0, \\|\\mathbf{x}(0) - \\mathbf{x}_0\\|<\\delta \\rightarrow \\|\\mathbf{x}(t) - \\mathbf{x}_0\\|<\\epsilon, \\quad \\forall t\n", + "\\end{equation}\n", + "* **Asymptotically stable** if it is Lyapunov stable and:\n", + "\\begin{equation}\n", + "\\exists \\delta >0, \\|\\mathbf{x}(0) - \\mathbf{x}_0\\|< \\delta, \\rightarrow \\lim_{t\\to\\infty} \\|\\mathbf{x}(t) - \\mathbf{x}_0\\| = 0, \\quad \\forall t\n", + "\\end{equation}\n", + "* **Exponentially stable** if it is asymptotically stable and:\n", + "\\begin{equation}\n", + "\\exists \\delta, \\alpha, \\beta >0, \\|\\mathbf{x}(0) - \\mathbf{x}_0\\|< \\delta, \\rightarrow \\|\\mathbf{x}(t) - \\mathbf{x}_0\\| \\leq\\alpha\\|\\mathbf{x}(0) - \\mathbf{x}_0\\|^{-{\\beta}t}, \\quad \\forall t \n", + "\\end{equation}\n", + "\n", + "Conceptually, the meanings of the above terms are the following:\n", + "\n", + "\n", + "* **Lyapunov stability** of an equilibrium means that solutions starting \"close enough\" to the equilibrium (within a distance $\\delta$ from it) remain \"close enough\" forever\n", + "* **Asymptotic stability** means that solutions that start close enough not only remain close enough but also eventually converge to the equilibrium.\n", + "* **Exponential** stability means that solutions not only converge, but in fact converge faster than or at least as fast as a particular known rate $\\alpha\\|\\mathbf{x}(0) - \\mathbf{x}_0\\|^{-{\\beta}t}$\n", + "\n", + "---\n", + "\n", + "\n", + "The solution $z_i = e^{\\lambda_i t}z_i(0)$ can be decomposed using Euler's identity:\n", + "\\begin{equation}\n", + " z_i = e^{\\lambda_i t}z_i(0) =\n", + " e^{(\\alpha_i + i \\beta_i) t}z_i(0) =\n", + " e^{\\alpha_i t} \n", + " e^{i \\beta_i t}z_i(0) = \n", + " e^{\\alpha_i t} \n", + " (\\cos(\\beta_i t) + i \\sin(\\beta_i t))z_i(0)\n", + "\\end{equation}\n", + "where $\\lambda_i = \\alpha_i + i \\beta_i, \\operatorname{Re}{\\lambda_i} = \\alpha_i, \\operatorname{Im}{\\lambda_i} = \\beta_i$\n", + "\n", + "\n", + "---\n", + "Since $\\| (\\cos(\\beta_i t) + i \\sin(\\beta_i t))\\| =1$ thus, norm of $z_i$:\n", + "\n", + "* Bounded if $\\operatorname{Re}{\\lambda_i} = \\alpha_i = 0$, hence the system is **Lyapunov stable**. \n", + "* Decreasing if $\\operatorname{Re}{\\lambda_i} = \\alpha_i < 0$, hence the system is **asymptotically** and moreover **exponentially** stable. \n", + "* Increasing if $\\operatorname{Re}{\\lambda_i} = \\alpha_i > 0$, hence the system is **unstable**. \n", + "---\n", + "\n", + "\n", + ">**QUESTION:** how norms $\\|\\mathbf{z}\\|$ and $\\|\\mathbf{x}\\|$ are related?" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 426 + }, + "id": "GIkpu55rMt96", + "outputId": "7905a3a0-d9ac-4b8f-f78c-b39f545c3b19" + }, + "source": [ + "from scipy.integrate import odeint\n", + "from matplotlib.pyplot import *\n", + "\n", + "A = [[0, 1],\n", + " [-7, 0]]\n", + "\n", + "A = np.array(A)\n", + "n = np.shape(A)[0]\n", + "\n", + "Lambda, Q = np.linalg.eig(A)\n", + "print(f\"Eigen values:\\n{Lambda}, \\n\\n Eigen vectors:\\n{Q}\\n\\n\")\n", + "\n", + "# x_dot from state space\n", + "def f(x, t):\n", + " return A.dot(x)\n", + "\n", + "t0 = 0 # Initial time \n", + "tf = 10 # Final time\n", + "t = np.linspace(t0, tf, 1000)\n", + "\n", + "x0 = np.random.rand(n) # initial state\n", + "\n", + "solution = {\"ss\": odeint(f, x0, t)}\n", + "\n", + "plot(t, solution['ss'], linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'State ${x}$')\n", + "xlabel(r'Time $t$')\n", + "show()\n" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Eigen values:\n", + "[0.+2.64575131j 0.-2.64575131j], \n", + "\n", + " Eigen vectors:\n", + "[[0. -0.35355339j 0. +0.35355339j]\n", + " [0.93541435+0.j 0.93541435-0.j ]]\n", + "\n", + "\n" + ], + "name": "stdout" + }, + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "hG_fXxA-NGqE" + }, + "source": [ + " >### **Exercises**\n", + "> 1) Conclude the stability of the LTI systems $\\dot{ \\mathbf{x}} = \\mathbf{A} \\mathbf{x}$ with matrices $\\mathbf{A}$ given in previous exercise.\n", + ">\n", + "> 2) Check the stability of the following systems (numerically)\n", + ">\n", + ">* $3 z^{(2)} -7 z = 0$\n", + ">* $ z^{(3)} - 3 \\ddot z + 2z = 0$\n", + ">* $10 z^{(4)} -7 z^{(3)} + 2 \\ddot z + 0.5 \\dot z + 4z = 0$\n", + ">\n", + ">3) Consider the mass-spring-damper system:\n", + ">

\"mbk\"

\n", + ">\n", + "> with dynamics given by\n", + "> \\begin{equation}\n", + "m \\ddot y + b \\dot y + k y = 0 \n", + "\\end{equation} \n", + ">\n", + ">What are the conditions on the real $m, b, k$ for this system to be stable?\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "1QN4NjiJOZBt" + }, + "source": [ + "## **Basics of Phase Space Analysys**\n", + "\n", + "---\n", + "\n", + "In dynamical system theory, a **phase space** $\\mathcal{S}$ is a space in which all possible states $\\mathbf{x}$ of a system are represented, with each possible state corresponding to one unique point in the phase space. The concept of phase space was developed in the late 19th century by *Ludwig Boltzmann*, *Henri Poincaré*, and *Josiah Willard Gibbs*.\n", + "\n", + "Phase space is great tool to graphically analyze systems up to third order, without actually solving their related ODEs.\n", + "\n", + "One can build the phase portrait by plotting the vectors $\\dot{\\mathbf{x}}_i$:\n", + "\\begin{equation}\n", + "\\dot{\\mathbf{x}}_i = \\mathbf{f}(\\mathbf{x}_i)\n", + "\\end{equation}\n", + "\n", + "Thus for choosen points $\\mathbf{x}_i$ you may analyze the tendency of your states dynamics, via $\\dot{\\mathbf{x}}_i$\n", + "\n", + "---\n", + " ### **Example**\n", + "\n", + "Let us consider the example of \"love\" equations given in the first practice:\n", + "\\begin{equation}\n", + "\\begin{bmatrix}\n", + "\\dot{J} \\\\\n", + "\\dot{R} \n", + "\\end{bmatrix} = \n", + "\\begin{bmatrix}\n", + "-b R \\\\\n", + "a J\n", + "\\end{bmatrix} \\rightarrow \\dot{\\mathbf{x}} = \\mathbf{A} \\mathbf{x}\n", + "\\end{equation}\n", + "with $a, b >0$\n", + "\n", + "Let us plot the solution of this equation in phase plane:" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "Hq9ycBH9ELV3", + "outputId": "ac2091c1-8c2a-4a0a-a893-55faeee98bf1" + }, + "source": [ + "A = [[1, -1],\r\n", + " [1, -1]]\r\n", + "\r\n", + "A = np.array(A)\r\n", + "n = np.shape(A)[0]\r\n", + "\r\n", + "Lambda, Q = np.linalg.eig(A)\r\n", + "print(f\"Eigen values:\\n{Lambda}, \\n\\n Eigen vectors:\\n{Q}\\n\\n\")\r\n" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Eigen values:\n", + "[3.25176795e-17+1.57009246e-16j 3.25176795e-17-1.57009246e-16j], \n", + "\n", + " Eigen vectors:\n", + "[[0.70710678+1.11022302e-16j 0.70710678-1.11022302e-16j]\n", + " [0.70710678+0.00000000e+00j 0.70710678-0.00000000e+00j]]\n", + "\n", + "\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "7U4i-VI8jQsm", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 1000 + }, + "outputId": "e296e382-0526-42ff-aaef-0ff358e79f91" + }, + "source": [ + "a, b, c, d = 1, 1, 0, 2\r\n", + "\r\n", + "def f(x, t):\r\n", + " J, R = x[0], x[1]\r\n", + " \r\n", + " dJ = -b*R +c*J\r\n", + " dR = a*J - d*R\r\n", + " return dJ, dR\r\n", + "\r\n", + "t0 = 0 # Initial time \r\n", + "tf = 10 # Final time\r\n", + "t = np.linspace(t0, tf, 1000)\r\n", + "\r\n", + "x0 = 0.1,0.5 # initial state\r\n", + "\r\n", + "solution = {\"ss\": odeint(f, x0, t)}\r\n", + "J, R = solution['ss'][:,0], solution['ss'][:,1]\r\n", + "plot(t, solution['ss'], linewidth=2.0)\r\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\r\n", + "grid(True)\r\n", + "xlim([t0, tf])\r\n", + "ylabel(r'Love ${x}$')\r\n", + "xlabel(r'Time $t$')\r\n", + "show()\r\n", + "\r\n", + "plot(J, R, linewidth=2.0)\r\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\r\n", + "grid(True)\r\n", + "xlabel(r'Love of Juliet ${J}$')\r\n", + "ylabel(r'Love of Romeo ${R}$')\r\n", + "show()\r\n", + "\r\n", + "J_e_max, R_e_max = 1.5, 1.5\r\n", + "J_e_span = np.arange(-J_e_max,J_e_max,0.1)\r\n", + "R_e_span = np.arange(-R_e_max,R_e_max,0.1)\r\n", + "J_e_grid, R_e_grid = np.meshgrid(J_e_span, R_e_span)\r\n", + "\r\n", + "figure(figsize=(7, 7))\r\n", + "title('Phase Plane')\r\n", + "# Varying color along a streamline\r\n", + "L = (J_e_grid**2 + R_e_grid**2)**0.5\r\n", + "lw = 3*L / L.max()\r\n", + "contourf(J_e_span, R_e_span, L, cmap='autumn', alpha = 0.25)\r\n", + "\r\n", + "dJ, dR = f([J_e_grid, R_e_grid],t)\r\n", + "\r\n", + "strm = streamplot(J_e_span, R_e_span, dJ, dR, density = 1,color=L, cmap='autumn', linewidth = lw)\r\n", + "seed_points = np.array([x0[0], x0[1]])\r\n", + "\r\n", + "plot(J, R, 'r-', lw = 3.0)\r\n", + "plot(seed_points[0], seed_points[1], 'ro', lw = 10)\r\n", + "hlines(0, -J_e_max, J_e_max,color = 'red', linestyle = '--', alpha = 0.6)\r\n", + "vlines(0, -R_e_max, R_e_max,color = 'red', linestyle = '--', alpha = 0.6)\r\n", + "xlim([-0.9*J_e_max,0.9*J_e_max])\r\n", + "ylim([-0.9*R_e_max,0.9*R_e_max])\r\n", + "xlabel(r'Love of Juliet ${J}$')\r\n", + "ylabel(r'Love of Romeo ${R}$')\r\n", + "tight_layout()\r\n", + "show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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\n", 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" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + } + ] +} \ No newline at end of file diff --git a/legacy - ColabNotebooks/practice_03_transfer_functions.ipynb b/legacy - ColabNotebooks/practice_03_transfer_functions.ipynb new file mode 100644 index 0000000..6234abf --- /dev/null +++ b/legacy - ColabNotebooks/practice_03_transfer_functions.ipynb @@ -0,0 +1,796 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "[CT21] lab03_transfer_functions.ipynb", + "provenance": [], + "collapsed_sections": [], + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "D-dOD4xqsPiR" + }, + "source": [ + "# **Practice 3: Laplace Transform and Transfer Functions**\n", + "## **Goals for today**\n", + "\n", + "---\n", + "\n", + "\n", + "\n", + "During today practice we will:\n", + "* Recall the Laplace transform\n", + "* Define the transfer functions\n", + "* Model particular systems with transfer functions \n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "RCityqOscrJV" + }, + "source": [ + "## **Laplace transform**\n", + "\n", + "In mathematics, the Laplace transform, named after its inventor Pierre-Simon Laplace, is an integral transform that converts a function of a real variable $t$ (time domain) to a function of a complex variable $s$ (frequency domain). The transform has many applications in science and engineering because it is a tool for solving differential equations. In particular, it transforms differential equations into algebraic equations.\n", + "\n", + "The Laplace transform of a function $f(t)$ is given as:\n", + "\\begin{equation}\n", + " F(s) = \\mathcal{L} \\{ x(t)\\} = \\int_0^\\infty f(t) e^{-st}dt\n", + "\\end{equation}\n", + "\n", + "where $F(s)$ is called an ***image*** of the function and $s=\\alpha +\\beta i $ is a complex frequency.\n", + "\n", + "Laplace transform is defined as transformation from the time domain $t$ to the frequency domain $s$.\n", + "\n", + "it is convinient to use the table of precalculated Laplace transforms:\n", + "

\"mbk\"

\n", + "\n", + "#### **Some Usefull properties**\n", + "Linear properties:\n", + "\\begin{equation}\n", + " {\\mathcal {L}}\\{f(t)+g(t)\\}={\\mathcal {L}}\\{f(t)\\}+{\\mathcal {L}}\\{g(t)\\}\n", + "\\end{equation}\n", + "\n", + "\\begin{equation}\n", + " {\\mathcal {L}}\\{af(t)\\}=a{\\mathcal {L}}\\{f(t)\\}\n", + "\\end{equation}\n", + "Final value theorem:\n", + "\\begin{equation}\n", + "f(\\infty )=\\lim _{s\\to 0}{sF(s)}\n", + "\\end{equation}\n", + "The final value theorem is useful because it gives the long-term behaviour for particular function. \n", + "\n", + "#### **Inverse Laplace Transform**\n", + "The inverse Laplace transform is going in other way, by transforming image of your function $F(s)$ from frequancy domain to time domain $x(t)$:\n", + "\\begin{equation}\n", + "{\\displaystyle f(t)={\\mathcal {L}}^{-1}\\{F\\}(t)={\\frac {1}{2\\pi i}}\\lim _{T\\to \\infty }\\int _{\\gamma -iT}^{\\gamma +iT}e^{st}F(s)\\,ds}\n", + "\\end{equation}\n", + "\n", + "However in poractice we mostly use precalculated laplace transforms and then trying to decompose the image $X(s)$ into known transforms of functions obtained from a table, and construct the inverse by inspection, or just use some symbolic routines:\n", + "\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "MKcM-1G4gaYW" + }, + "source": [ + "import sympy\n", + "sympy.init_printing()\n" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "id": "0Qj3OoWjgikM" + }, + "source": [ + "t, s = sympy.symbols('t, s')\n", + "a = sympy.symbols('a', real=True, positive=True)" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 38 + }, + "id": "psiuazxSgkhO", + "outputId": "b26ec563-1f02-4f55-d04f-52f98f450600" + }, + "source": [ + "f = sympy.exp(a*t)\n", + "f" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "image/png": "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\n", + "text/latex": "$$e^{a t}$$", + "text/plain": [ + " a⋅t\n", + "ℯ " + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 19 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 39 + }, + "id": "ntT8J1XIgzKW", + "outputId": "020ea8c7-51df-4311-f257-90e6ee5aa3f0" + }, + "source": [ + "F = sympy.laplace_transform(f, t, s, noconds=True)\n", + "F" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "image/png": "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\n", + "text/latex": "$$\\frac{1}{- a + s}$$", + "text/plain": [ + " 1 \n", + "──────\n", + "-a + s" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 20 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 38 + }, + "id": "ClrfANLng66x", + "outputId": "41c64eaa-c256-4150-f126-023c75ca22fb" + }, + "source": [ + "f = sympy.inverse_laplace_transform(F, s, t)\n", + "f" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEAAAAAYCAYAAABKtPtEAAAABHNCSVQICAgIfAhkiAAAA9pJREFUWIXt11uMXlMUB/Bfb2PGjJRMxS3UAx2ZuJS2o9HiQTsJ9YIIrUhDpA+YB8JDG6Qv7hUiBJMQEg1FQiLRqAfiFreUmNQlCEOr1VZLielNPw9rn86ZM+f06+iYRjL/5GSfs9Zea+2199prrcMo/nPcj9cP9iKqMHYEbHTgoxGwc9BwGz7Hn9iEp9GEBuxELfd8USJ/KO7AV9iOn3AXJuzD5jPYiOb9XOO0ZP+6/Zw/JCzFLEzGHKzDYhFdmeEOHI0jCrLHYI3YqBW4N33X8ESFvRnYg5tLeDcl2QUlvJexHi375dUBoFucEFyMbRhTMq8Bn4jImZWjt6AXf4tNK2IVfhNRVsSzYgPaSngdibekrgdDwPF4GD3YIpzZhTsT/3a8UyG7JC3ohhLeQ4l3eYE+RZx+d4XOL/GH8g3P+L1yua8qCV6GldgswvObtOBxuTmt+Fic0i04F9PFPf4szZmKT0v0N+FWEZJlzvyaxmIEXCucW1Gg3yM27BQRQXv0552rc/OexwmYmxHGFxSNE2F0Jb7Fi9iBC8WptmFhmjsPjbgiGZJ4Lfo34AyxkUVcgsPxpIiYIhrTuLNAnyOuxgcF+mpx7RbifbyR472Ve38vjXNVlOZHhDN3G7g5E5JwDe2JNg+7kzMnoUucaP7O/4BlOFY4nGF50vWcSKLF58PEvygn05zs9ZQtHIuSzKIKPkxMc0rL8tkidF6pY+Ca9D0GjwqHN4pcsAzv5mSuwtqk97EcvdfA8lj1nJiTmZJoqyrW93jiT6/gZ+jDhuwjf8pdyam/xCkUcWoas7yRJbCyJJZheXryaBb3cE1OZx6HiRywQURQhtY0bq2wdZa4TlURkmELjso+8hvQmcb5dRT01uHXw3FpXFfB7xRX7rUCvS+NjQZjPE4TjdaOOvabcrr2bkAjjsTbOL+OggNFQxqrFppdsacK9I1pbDUY7cKH1XVsjxW56Ps8gf6kNamOguFAdv/KmpyZIvGtNDhRrRetdlmTMzWNZSU3jzbha1al9m5An+jn23FphfBsA/uAf4vNoiGZhtNz9MmiKvyO60vkaiJCJ4mqk0cWFdvq2J6ZxjfLmJ0iidREHX0AD+IFfIcf6ygfChYkO5uSjW7R3m7FOfuQm6+8ezwv0deK3++lBneRxAbvFh1sKWbgJRGmu8Rp9Ygfkwv26dLQsVBUgu1i4d36E2QVGvCL6BOKuBFfJ301/e14hoki0qvK/P8Gi4WDZw5RrivJzR72FY0wGkUpfnUIMk34WUT3AAxHUhtp7Bbl7hDxO132L1HEyaLs3idyzShGMYrAP5TL7ueF0LOgAAAAAElFTkSuQmCC\n", + "text/latex": "$$e^{a t} \\theta\\left(t\\right)$$", + "text/plain": [ + " a⋅t \n", + "ℯ ⋅Heaviside(t)" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 21 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "TdHXASZ6hJAq" + }, + "source": [ + "def L(f):\n", + " return sympy.laplace_transform(f, t, s, noconds=True)\n", + "\n", + "def invL(F):\n", + " return sympy.inverse_laplace_transform(F, s, t)\n", + "\n" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 39 + }, + "id": "H0g7os87j51Y", + "outputId": "9757fb16-958f-4139-d797-c698427b2d1d" + }, + "source": [ + "L(sympy.exp(a*t))" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "image/png": "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\n", + "text/latex": "$$\\frac{1}{- a + s}$$", + "text/plain": [ + " 1 \n", + "──────\n", + "-a + s" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 23 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 38 + }, + "id": "Ma5asUr4j5db", + "outputId": "89227400-769f-464a-ca66-e06b5baec9be" + }, + "source": [ + "invL(F)" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "image/png": "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\n", + "text/latex": "$$e^{a t} \\theta\\left(t\\right)$$", + "text/plain": [ + " a⋅t \n", + "ℯ ⋅Heaviside(t)" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 24 + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Bj7W6rQViF4J" + }, + "source": [ + "\n", + ">### **Exercise**\n", + "> Write the code that will reproduce the first 5 rows of the table above." + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "fY3HSwLsiAtM" + }, + "source": [ + "# Put your code here" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "o3Z6WvjdfnpO" + }, + "source": [ + "\n", + "\n", + "### **Laplace transform of a function's derivative**\n", + ">For us one of the most usefull properties of Laplace transform is that if we apply it to the derevetive of a given variable it will result with following:\n", + ">\n", + "> \\begin{equation}\n", + "\\mathcal{L}\\left\\{\\frac{dx(t)}{dt}\\right\\} = s \\mathcal{L}\\left(x\\right) = s X(s)\n", + "\\end{equation}\n", + "which is true for $x(0) = 0$\n", + ">\n", + ">Thus we can define a **derivative operator**:\n", + "\\begin{equation}\n", + "\\frac{dx}{dt} \\xrightarrow{\\mathcal{L}} s X(s)\n", + "\\end{equation}\n", + "\n", + "The proof is as follows, using defenition of Laplace transform:\n", + "\\begin{equation}\n", + " \\mathcal{L}\\left\\{\\frac{dx}{dt}\\right\\} = \\int_0^\\infty \\frac{dx}{dt} e^{-st}dt\n", + "\\end{equation}\n", + "Then using integration by parts:\n", + "\n", + "\\begin{equation}\n", + "\\int_0^\\infty \\frac{dx}{dt} e^{-st}dt = \\left[x e^{-st} \\right]_0^\\infty - \n", + "\\int_0^\\infty -se^{-st} x dt \n", + "\\end{equation}\n", + "which yields:\n", + "\\begin{equation}\n", + "\\left[x e^{-st} \\right]_0^\\infty + \n", + "s\\int_0^\\infty e^{-st} x dt = x(0) + s\\mathcal{L}\\{x(t)\\} = x(0) + sX(s)\n", + "\\end{equation}\n", + "\n", + "by induction it can be shown that:\n", + "\\begin{equation}\n", + "{\\mathcal {L}}\\left\\{\\frac{d^{n}x}{dt^{n}}(t)\\right\\}=s^{n}\\cdot {\\mathcal {L}}\\{x(t)\\}+s^{n-1}x(0)+\\cdots +x^{(n-1)}(0)\n", + "\\end{equation}\n", + "\n", + "\\begin{equation}\n", + " \\mathcal{L}\\left(\\frac{dx}{dt}\\right) = \\int_0^\\infty \\frac{dx}{dt} e^{-st}dt\n", + "\\end{equation}\n", + "\n", + "### **Applications to the linear ODEs**\n", + ">Let us consider the following ODE:\n", + "\\begin{equation}\n", + "a_{n}x^{(n)} +a_{n-1}x^{(n-1)}+...+a_{2}\\ddot x+a_{1}\\dot x + a_0 x= u_{m}b^{(m)} +b_{m-1}u^{(m-1)}+...+b_{2}\\ddot u+b_{1}\\dot u + b_0 u\n", + "\\end{equation}\n", + "Notice that we introduce a new variable that we call the input $u$ (control). \n", + "\n", + "Aplying the inverse laplace transform with zero initial conditions yields:\n", + "\\begin{equation}\n", + "a_{n}s^{(n)}X(s) +a_{n-1}s^{(n-1)}X(s)+...+a_{2} s^2 X(s)+a_{1}s X(s) + a_0 X(s) =\\\\\n", + "= b_{m}s^{(m)}U(s) +b_{m-1}s^{(m-1)}U(s)+...+b_{2}s^2 U(s)+b_{1}sU(s) + b_0 U(s)\n", + "\\end{equation}\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "RDrejDYJkiWH" + }, + "source": [ + "\n", + ">### **Exercise**\n", + "> Apply Laplace transform to the following ODEs:\n", + ">* $2 \\ddot{x} -7 x = u $\n", + ">* $ x^{(3)} - 2 \\ddot x + 2x = u + 3\\dot{u}$\n", + ">* $10 x^{(4)} -7 x^{(3)} + 2 \\ddot x + 0.5 \\dot x + 4x = u + 3\\dot{u} -2 {\\ddot{u}}$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "xC0pbISDkw-g" + }, + "source": [ + "\n", + "## **Transfer Functions**\n", + "A transfer function is a mathematical function which theoretically models the device's output for each possible input. Transfer functions are commonly used in the analysis of systems such as single-input single-output filters in the fields of signal processing, communication theory, and control theory. The term is often used exclusively to refer to linear time-invariant (LTI) systems\n", + "\n", + "Thus, for continuous-time input signal $u(t)$ and output $x(t)$, the transfer function $H(s)$ is the linear mapping of the Laplace transform of the input, $U(s) = \\mathcal{L}\\left\\{u(t)\\right\\}$, to the Laplace transform of the output $X(s) = \\mathcal{L}\\left\\{x(t)\\right\\}$:\n", + "\\begin{equation}\n", + " X(s) = W(s)\\;U(s) \\rightarrow W(s) = \\frac{X(s)}{U(s)} = \\frac{ \\mathcal{L}\\left\\{x(t)\\right\\} }{ \\mathcal{L}\\left\\{u(t)\\right\\} }\n", + "\\end{equation}\n", + "\n", + "Considering this defenition we can evaluate tha transfer function for ODE given above as:\n", + "\\begin{equation}\n", + "W(s) = \\frac{X(s)}{U(s)} = \\frac{b_{m}s^{(m)} +b_{m-1}s^{(m-1)}+...+b_{2}s^2 +b_{1}s + b_0 }{a_{n}s^{(n)} +a_{n-1}s^{(n-1)}+...+a_{2} s^2 +a_{1}s + a_0 }\n", + "\\end{equation}\n", + "\n", + "A transfer function thus represent the ODE by its behaviour from input image $U(s)$ to output image $X(s)$.\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "oV6h4Uok27gX" + }, + "source": [ + ">### **Example**\r\n", + ">Consider the mass-spring-damper system:\r\n", + ">

\"mbk\"

\r\n", + ">\r\n", + "> with dynamics given by\r\n", + "> \\begin{equation}\r\n", + "m \\ddot y + b \\dot y + k y = u\r\n", + "\\end{equation} \r\n", + ">\r\n", + ">where $u$ is force that applied to the mass, let's model this system by using transfer functions.\r\n", + "\r\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 279 + }, + "id": "3cPmD7N7tZow", + "outputId": "8695b5eb-434b-4181-b9c4-70e331e23a07" + }, + "source": [ + "import numpy as np\r\n", + "from scipy import signal\r\n", + "import matplotlib.pyplot as plt\r\n", + "from scipy.integrate import odeint\r\n", + "\r\n", + "# Simulate m d^2y/dt^2 + b dy/dt + k y = u \r\n", + "# from u to y\r\n", + "# W(s) = 1/(m s^2 + bs + k)\r\n", + "\r\n", + "m = 2\r\n", + "b = 1\r\n", + "k = 5\r\n", + "\r\n", + "num = [1,0]\r\n", + "den = [m, b, k]\r\n", + "sys_tf = signal.TransferFunction(num,den)\r\n", + "t_tf,y_tf = signal.step(sys_tf)\r\n", + "\r\n", + "plt.figure(1)\r\n", + "plt.plot(t_tf,y_tf,'r',linewidth=2,label=r'$y$ response')\r\n", + "plt.xlabel(r'Time')\r\n", + "plt.ylabel(r'Response (y)')\r\n", + "plt.grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\r\n", + "plt.grid(True)\r\n", + "plt.xlim([t_tf[0], t_tf[-1]])\r\n", + "plt.legend(loc='best')\r\n", + "plt.show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "1qQ-mJEhs7L3" + }, + "source": [ + " >### **Exercises**\r\n", + "> 1) Find the transfer function of the ODEs given above\r\n", + ">\r\n", + "> 2) Modify the code above to represent the response from input force $u$ to output velocity $\\dot{y}$\r\n", + ">\r\n", + "> 2) Compare solutions with ones provided by `odeint` \r\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "f_jpmegAx_Pj" + }, + "source": [ + "### **From State Space to Transfer Functions**\n", + "\n", + "Consider standard form state-space dynamical system:\n", + "\n", + "\\begin{equation}\n", + "\\begin{cases}\n", + "\\dot{\\mathbf{x}} = \\mathbf{A}\\mathbf{x} + \\mathbf{B}\\mathbf{u} \\\\\n", + " \\mathbf{y} = \\mathbf{C}\\mathbf{x} + \\mathbf{D}\\mathbf{u}\n", + "\\end{cases}\n", + "\\end{equation}\n", + "\n", + "We can rewrite it using the derivative operator:\n", + "\n", + "\\begin{equation}\n", + "\\begin{cases}\n", + "s\\mathbf{I}\\mathbf{X}(s) -\\mathbf{A}\\mathbf{X}(s) = \\mathbf{B}\\mathbf{U}(s) \\\\\n", + "\\mathbf{Y}(s) = \\mathbf{C}\\mathbf{X}(s) + \\mathbf{D}\\mathbf{U}(s)\n", + "\\end{cases}\n", + "\\end{equation}\n", + "\n", + "and then collect $\\mathbf{X}(s)$ on the left-hand-side: $\\mathbf{X}(s) = (s\\mathbf{I} -\\mathbf{A})^{-1} \\mathbf{B}\\mathbf{U}(s)$\n", + "\n", + "and finally, express $\\mathbf{Y}(s)$ output:\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{Y}(s) = \\left( \\mathbf{C}(s\\mathbf{I} -\\mathbf{A})^{-1} \\mathbf{B} + \\mathbf{D} \\right) \\mathbf{U}(s)\n", + "\\end{equation}\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "bYjgqfd22d2b" + }, + "source": [ + ">### **Example**\r\n", + "> Let us recall the \"love equation\" between Romeo and Juliet:\r\n", + "\\begin{equation}\r\n", + "\\begin{bmatrix}\r\n", + "\\dot{J} \\\\\r\n", + "\\dot{R} \r\n", + "\\end{bmatrix} = \r\n", + "\\begin{bmatrix}\r\n", + "-b R \\\\\r\n", + "a J\r\n", + "\\end{bmatrix}\r\n", + "\\end{equation}\r\n", + "\r\n", + "But now lets consider the case when they can manipulate each other feelings with some control inputs $u_R$ and $u_J$, however suppose Romeo now really love to manipulate Juliet feelings but hold down a bit when notice Juliet manipulation thus:\r\n", + "\\begin{equation}\r\n", + "\\begin{bmatrix}\r\n", + "\\dot{J} \\\\\r\n", + "\\dot{R} \r\n", + "\\end{bmatrix} = \r\n", + "\\begin{bmatrix}\r\n", + "-b R + c u_R - d u_J\\\\\r\n", + "a J + e u_R\r\n", + "\\end{bmatrix}\r\n", + "\\end{equation}\r\n", + "State space representation of this system is given as:\r\n", + "\\begin{equation}\r\n", + "\\begin{bmatrix}\r\n", + "\\dot{J} \\\\\r\n", + "\\dot{R} \r\n", + "\\end{bmatrix} = \r\n", + "\\begin{bmatrix}\r\n", + "0 & -b \\\\\r\n", + "a & 0 \r\n", + "\\end{bmatrix}\r\n", + "\\begin{bmatrix}\r\n", + "J \\\\\r\n", + "R \r\n", + "\\end{bmatrix} +\r\n", + "\\begin{bmatrix}\r\n", + "-d & c \\\\\r\n", + "0 & e \r\n", + "\\end{bmatrix}\r\n", + "\\begin{bmatrix}\r\n", + "u_J \\\\\r\n", + "u_R \r\n", + "\\end{bmatrix}\r\n", + "\\end{equation}\r\n", + "\r\n", + "And our goal is to find the transfer functions form Romeo effort to Juliet love and vice versa. " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "RPWJbCSS-Les" + }, + "source": [ + "Lets first find the solution analytically:" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "5ip-SUMp-Qih" + }, + "source": [ + "a, b, c, d, e = sympy.symbols('a, b, c, d, e') \r\n", + "s = sympy.symbols('s')\r\n", + "\r\n", + "A = sympy.Matrix([[0, -b], [a, 0]])\r\n", + "B = sympy.Matrix([[-d, c],[0, e]])\r\n" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 61 + }, + "id": "HLhxjSqiA8-S", + "outputId": "72050bb4-18f2-4a76-967c-d10898a70e99" + }, + "source": [ + "Xs = (s * sympy.eye(2) - A).inv()*B\r\n", + "Xs" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/latex": "$$\\left[\\begin{matrix}- \\frac{d s}{a b + s^{2}} & - \\frac{b e}{a b + s^{2}} + \\frac{c s}{a b + s^{2}}\\\\- \\frac{a d}{a b + s^{2}} & \\frac{a c}{a b + s^{2}} + \\frac{e s}{a b + s^{2}}\\end{matrix}\\right]$$", + "text/plain": [ + "⎡ -d⋅s b⋅e c⋅s ⎤\n", + "⎢──────── - ──────── + ────────⎥\n", + "⎢ 2 2 2⎥\n", + "⎢a⋅b + s a⋅b + s a⋅b + s ⎥\n", + "⎢ ⎥\n", + "⎢ -a⋅d a⋅c e⋅s ⎥\n", + "⎢──────── ──────── + ──────── ⎥\n", + "⎢ 2 2 2 ⎥\n", + "⎣a⋅b + s a⋅b + s a⋅b + s ⎦" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 28 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "4WMJSP2OBlCs" + }, + "source": [ + "# lets now denote output equations\r\n", + "C = sympy.Matrix([[1, 0]])\r\n", + "D = sympy.Matrix([[0,0]])" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 39 + }, + "id": "ptRHD0Lk_Tnh", + "outputId": "3c31a2b6-6a76-41a4-c3eb-73e6ee56a4f4" + }, + "source": [ + "Ys = C*(s * sympy.eye(2) - A).inv()*B +D\r\n", + "Ys" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/latex": "$$\\left[\\begin{matrix}- \\frac{d s}{a b + s^{2}} & - \\frac{b e}{a b + s^{2}} + \\frac{c s}{a b + s^{2}}\\end{matrix}\\right]$$", + "text/plain": [ + "⎡ -d⋅s b⋅e c⋅s ⎤\n", + "⎢──────── - ──────── + ────────⎥\n", + "⎢ 2 2 2⎥\n", + "⎣a⋅b + s a⋅b + s a⋅b + s ⎦" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 30 + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "jhLtdz0a-RUF" + }, + "source": [ + "We can do the same numerically instead:" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "Azm-4SVl82nx", + "outputId": "9111818d-4a07-4f89-ebdd-e99f9485963f" + }, + "source": [ + "from scipy.signal import ss2tf\r\n", + "a, b, c, d, e = 1, 1, 1, 1, 1\r\n", + "\r\n", + "A = [[0, -b], [a, 0]]\r\n", + "B = [[-d, c],[0, e]]\r\n", + "C = [[1, 0],[0, 1]]\r\n", + "D = [[0,0],[0,0]]\r\n", + "ss2tf(A, B, C, D)" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "(array([[ 0, -1, 0],\n", + " [ 0, 0, -1]]), array([1., 0., 1.]))" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 31 + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "5hHBY9f_-VuS" + }, + "source": [ + ">### **Exercises**\r\n", + "> Simulate the response of \"love\" system using transfer functions and state space approaches compare results. (you may use [this as reference](https://apmonitor.com/pdc/index.php/Main/ModelSimulation) )\r\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "B_UjtGnvCXGf" + }, + "source": [ + ">### **Bonus Exercise**\r\n", + "> Considering the following ODE:\r\n", + "> \\begin{equation}\r\n", + "a_{n}y^{(n)} +a_{n-1}y^{(n-1)}+...+a_{2}\\ddot y+a_{1}\\dot y + a_0 y= u_{m}b^{(m)} +b_{m-1}u^{(m-1)}+...+b_{2}\\ddot u+b_{1}\\dot u + b_0 u\r\n", + "\\end{equation}\r\n", + ">With related transfer function:\r\n", + "\\begin{equation}\r\n", + "W(s) = \\frac{Y(s)}{U(s)} = \\frac{b_{m}s^{(m)} +b_{m-1}s^{(m-1)}+...+b_{2}s^2 +b_{1}s + b_0 }{a_{n}s^{(n)} +a_{n-1}s^{(n-1)}+...+a_{2} s^2 +a_{1}s + a_0 }\r\n", + "\\end{equation}\r\n", + ">\r\n", + ">where $Y(s) = \\mathcal{}$ $m\\leq n$ suggest a method to represent it in the equalient state space representation:\r\n", + "\\begin{equation}\r\n", + "\\begin{cases}\r\n", + "\\dot{\\mathbf{x}} = \\mathbf{A}\\mathbf{x} + \\mathbf{B}\\mathbf{u} \\\\\r\n", + " \\mathbf{y} = \\mathbf{C}\\mathbf{x} + \\mathbf{D}\\mathbf{u}\r\n", + "\\end{cases}\r\n", + "\\end{equation}\r\n", + "and output $Y(s) = \\mathcal{L}\\{y\\} = \\mathcal{L}\\{\\mathbf{y}_1\\} =\\mathcal{L}\\{\\mathbf{x}_1\\}$ \r\n", + ">\r\n", + ">Use [this link as reference](https://lpsa.swarthmore.edu/Representations/SysRepTransformations/TF2SS.html)" + ] + } + ] +} \ No newline at end of file diff --git a/legacy - ColabNotebooks/practice_04_basics_of_control.ipynb b/legacy - ColabNotebooks/practice_04_basics_of_control.ipynb new file mode 100644 index 0000000..d047803 --- /dev/null +++ b/legacy - ColabNotebooks/practice_04_basics_of_control.ipynb @@ -0,0 +1,547 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "[CT21] lab04_basics_of_control.ipynb", + "provenance": [], + "collapsed_sections": [], + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "zPmrTNlSBW-R" + }, + "source": [ + "# **Practice 4: Basics Of Feedback Control**\n", + "## **Goals for today**\n", + "\n", + "---\n", + "\n", + "\n", + "\n", + "During today practice we will:\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "kgF8BN0GTBfP" + }, + "source": [ + "## **Idea of Control and Feedback**\n", + "So far we have discussed the methods allowing us to check the stability of the unforced (uncontolled) dynamical systems. Today we will answer a more practical question, namely: **How to make the given dynamical system display desired behavior?** this is one of the questions of concern in the field of **control** theory.\n", + "\n", + "In this class we will mainly consider two sets of problems:\n", + "* **Stabilization** (regulation) a control system (stabilizer, or regulator) is to be designed so that the state of the closed-loop system will be stabilized around a **static point**.\n", + "* **Tracking** (servo) the design objective is to construct a controller (tracker) so that the system output tracks a given time-varying trajectory.\n", + "\n", + "One of the most widely used approaches supporting the solution of the problems above is the so-called **feedback control**\n", + "\n", + "\n", + "Recall the autonomous system written in state space:\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{x}}=\\boldsymbol{f}(\\mathbf{x},\\mathbf{u})\n", + "\\end{equation} \n", + "\n", + "Let us now assume that one have designed feedback law as follows:\n", + "\\begin{equation}\n", + "u = \\boldsymbol{\\varphi}(\\mathbf{x})\n", + "\\end{equation} \n", + "\n", + "

\"ff_fb\"

\n", + "\n", + "One may substitute control law and obtain the equations of the **closed loop** system:\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{x}}=\\boldsymbol{f}(\\mathbf{x},\\boldsymbol{\\varphi}(\\mathbf{x})) = \\boldsymbol{f}_c(\\mathbf{x})\n", + "\\end{equation} \n", + "now one can use stability tools to study the behaviour of the controlled system.\n", + "\n", + "Let us begin with the simplest case, namely linear systems. \n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "VMv9_G55JAVR" + }, + "source": [ + "### **Linear State Feedback**\n", + "\n", + "Recall the linear system in state space form:\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{x}}=\\mathbf{A}\\mathbf{x} + \\mathbf{B}\\mathbf{u}\n", + "\\end{equation}\n", + "\n", + "The general form of feedback that may stabilize our system is know to be linear:\n", + "\\begin{equation}\n", + "\\mathbf{u}=-\\mathbf{K}\\mathbf{x}\n", + "\\end{equation}\n", + "\n", + "Substitution to the system dynamics yields:\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{x}}=(\\mathbf{A} - \\mathbf{B}\\mathbf{K})\\mathbf{x} = \\mathbf{A}_c\\mathbf{x}\n", + "\\end{equation}\n", + "Thus the stability of the controlled system is completely determined by the eigen values of $\\mathbf{A}_c$ and consequantially by the matrix $\\mathbf{K}$\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 282 + }, + "id": "dMQ68HJ4H4zp", + "outputId": "eee6f610-c9f2-4628-dc84-28a84869d6e5" + }, + "source": [ + "import numpy as np\n", + "from scipy.integrate import odeint\n", + "\n", + "def system_ode(x, t, A, B, K):\n", + " u = - np.dot(K,x) \n", + " dx = np.dot(A,x) + np.dot(B,u)\n", + " return dx\n", + "\n", + "\n", + "t0 = 0 # Initial time \n", + "tf = 10 # Final time\n", + "N = int(2E3) # Numbers of points in time span\n", + "t = np.linspace(t0, tf, N) # Create time span\n", + "\n", + "x0 = [1, 1] # Set initial state \n", + "\n", + "A = [[-1,0],\n", + " [7, 1]]\n", + "\n", + "B = [[0],\n", + " [1]]\n", + "\n", + "K = [[0,1]] \n", + "\n", + "x_sol = odeint(system_ode, x0, t, args=(A, B, K,)) # integrate system \"sys_ode\" from initial state $x0$\n", + "x1, x2 = x_sol[:,0], x_sol[:,1] # set theta, dtheta to be a respective solution of system states\n", + "\n", + "from matplotlib.pyplot import *\n", + "\n", + "plot(t, x1, 'r', linewidth=2.0)\n", + "plot(t, x2, 'b', linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'States ${x}$')\n", + "xlabel(r'Time $t$ (s)')\n", + "show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "LFhTSmgYWaDW" + }, + "source": [ + "### **Example: Stabilization of Linear System**\n", + "\n", + "Consider a following unforced system:\n", + "\n", + "

\"mbk\"

\n", + "\n", + "Dynamics of this system desribed by following ODE:\n", + "\\begin{equation}\n", + "m\\ddot{y} + b \\dot{y} + k y = u\n", + "\\end{equation}\n", + "\n", + "And one can formulate this system in state space as:\n", + "\\begin{equation}\n", + "\\dot{\\mathbf{x}}\n", + " = \\mathbf{A}\\mathbf{x} + \\mathbf{B}\\mathbf{u} =\n", + "\\begin{bmatrix}\n", + "\\dot{y}\\\\\n", + "\\ddot{y}\n", + "\\end{bmatrix}\n", + "=\n", + "\\begin{bmatrix}\n", + "0 & 1\\\\\n", + "-\\frac{k}{m} & -\\frac{b}{m}\n", + "\\end{bmatrix}\n", + " \\begin{bmatrix}\n", + "y\\\\\n", + "\\dot{y}\n", + "\\end{bmatrix}+\n", + "\\begin{bmatrix}\n", + "0\\\\\n", + "\\frac{1}{m}\n", + "\\end{bmatrix}\n", + "u\n", + "\\end{equation}\n", + "\n", + "Let us simulate the response of the system with different parameters:" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "xx6wTlUAWZT8", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 282 + }, + "outputId": "a553da95-b802-459b-a424-a00df2891ff8" + }, + "source": [ + "import numpy as np\n", + "from scipy.integrate import odeint\n", + "\n", + "def system_ode(x, t, A, B, K):\n", + " u = - np.dot(K,x) \n", + " dx = np.dot(A,x) + np.dot(B,u)\n", + " return dx\n", + "\n", + "\n", + "t0 = 0 # Initial time \n", + "tf = 10 # Final time\n", + "N = int(2E3) # Numbers of points in time span\n", + "t = np.linspace(t0, tf, N) # Create time span\n", + "y_0 = 0.5\n", + "x0 = [y_0, 0] # Set initial state \n", + "\n", + "m = 1\n", + "b = -0.5\n", + "k = 2\n", + "\n", + "A = [[0,1],\n", + " [-k/m, -b/m]]\n", + "\n", + "B = [[0],\n", + " [1/m]]\n", + "\n", + "K = [[0,0.5]] \n", + "\n", + "x_sol = odeint(system_ode, x0, t, args=(A, B, K,)) # integrate system \"sys_ode\" from initial state $x0$\n", + "y, dy = x_sol[:,0], x_sol[:,1] # set theta, dtheta to be a respective solution of system states\n", + "\n", + "from matplotlib.pyplot import *\n", + "\n", + "plot(t, y, 'r', linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'Position ${y}$ (m)')\n", + "xlabel(r'Time $t$ (s)')\n", + "show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "cWMGBtXBpNQS" + }, + "source": [ + ">**EXERCISE**: \n", + "* Find the gains $k_1, k_2$ that will stabilize the following system:\n", + "> \\begin{equation}\n", + "\\mathbf{\\dot{x}}\n", + "=\n", + "\\begin{bmatrix}\n", + "3 & 1\\\\\n", + "1 & 3\n", + "\\end{bmatrix}\n", + "\\mathbf{x}\n", + "+\n", + "\\begin{bmatrix}\n", + "0\\\\\n", + "1 \n", + "\\end{bmatrix}\n", + "\\mathbf{u}\n", + "\\end{equation}\n", + "> simulate the response. \n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "orDzncSidhQk" + }, + "source": [ + "**NOTE**\n", + "\n", + "> It is often the case (especially in fully actuated mechanical systems) that one can analyze system response and stability without actually transforming the system to state-space form, for instance, one may directly substitute control law to the system dynamics to analyze closed-loop response.\n", + "\n", + "For instance consider the mass-spring damper above:\n", + "\n", + "\\begin{equation}\n", + "m\\ddot{y} + b \\dot{y} + k y = -k_1 y - k_2 \\dot{y}\n", + "\\end{equation}\n", + "\n", + "which yields:\n", + "\n", + "\\begin{equation}\n", + "m\\ddot{y} + (b + k_2) \\dot{y} + (k + k_1) y = 0 \n", + "\\end{equation}\n", + "\n", + "It is obvious now which gains make this system stable\n", + "\n", + "In case of mechanical systems (system of second order equations), the matrix $\\mathbf{K}$ represent the so called proportinal-derivative (PD) controller $\\mathbf{K} = [\\mathbf{k}_p,\\mathbf{k}_d]^T$.\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "2Ea3TESnkBmu" + }, + "source": [ + "### **Higher Order Systems**\n", + "\n", + "Stabilization of the fully actuated second-order systems is a trivial task, however, in practice, you will face systems with higher dimensions, where defining the feedback gain may not be trivial. Thus one may use so-called pole-placement or LQR techniques\n", + "\n", + "For instnaceRecall the DC motor equations:\n", + "\n", + "\\begin{equation}\n", + "\\begin{bmatrix}\n", + "\\dot{\\theta} \\\\\n", + "\\ddot{\\theta} \\\\\n", + "\\dot{i}\n", + "\\end{bmatrix} \n", + "=\n", + "\\begin{bmatrix}\n", + "0 & 1 & 0 \\\\\n", + "0 & -\\frac{b}{J} & \\frac{K_m}{J} \\\\\n", + "0 & -\\frac{K_e}{L} & -\\frac{R}{L}\n", + "\\end{bmatrix} \n", + "\\begin{bmatrix}\n", + "\\theta \\\\\n", + "\\dot{\\theta} \\\\\n", + "i\n", + "\\end{bmatrix}\n", + "+\n", + "\\begin{bmatrix}\n", + "0 \\\\\n", + "0 \\\\\n", + "\\frac{1}{L}\n", + "\\end{bmatrix}\n", + "V\n", + "\\end{equation}\n", + "\n", + "we will assume that full-state is given (measured).\n", + "\n", + "Let us now try to assign stable poles in order to control DC motor" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "97QxmcR0A8Iq", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 318 + }, + "outputId": "28394a93-4f32-4b01-cf35-ba59ae439be5" + }, + "source": [ + "\n", + "\n", + "k_m = 0.0274\n", + "k_e = k_m\n", + "J = 3.2284E-6\n", + "b = 3.5077E-6\n", + "L = 2.75E-6\n", + "R = 4\n", + "\n", + "A = [[0, 1, 0],\n", + " [0, -b/J, k_m/J],\n", + " [0, -k_e/L, -R/L]]\n", + "\n", + "B = [[0], \n", + " [0], \n", + " [1/L]];\n", + "\n", + "P = [-100, -500, - 2000]\n", + "\n", + "from scipy.signal import place_poles\n", + "pp =place_poles(np.array(A), np.array(B), np.array(P)) \n", + "print(pp.computed_poles)\n", + "K = pp.gain_matrix\n", + "print(K)\n", + "tf = 1.5 # Final time\n", + "N = int(2E3) # Numbers of points in time span\n", + "t = np.linspace(t0, tf, N) # Create time span\n", + "x0 = [1, 10, 1] # Set initial state \n", + "\n", + "x_sol = odeint(system_ode, x0, t, args=(A, B, K,)) # integrate system \"sys_ode\" from initial state $x0$\n", + "theta, dtheta, i = x_sol[:,0], x_sol[:,1], x_sol[:,2] # set theta, dtheta to be a respective solution of system states\n", + "\n", + "from matplotlib.pyplot import *\n", + "\n", + "plot(t, theta, 'r', linewidth=2.0)\n", + "plot(t, dtheta, 'b', linewidth=2.0)\n", + "plot(t, i, 'g', linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'Motor Angle ${\\theta}$ (rad)')\n", + "xlabel(r'Time $t$ (s)')\n", + "show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "[-2000. -500. -100.]\n", + "[[ 0.03240182 -0.02699589 -3.99285299]]\n" + ], + "name": "stdout" + }, + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "XCseemxbf4Wm" + }, + "source": [ + "### **Regulation**\n", + "\n", + "In some practical problems we are always want to move our system not to the some equalibrium but to the **desired point** $\\mathbf{x}_d$, and stay there ($\\mathbf{\\dot{x}}_d = \\mathbf{0}$). To do so one may consider the change of variables: \n", + "\\begin{equation}\n", + "\\mathbf{\\tilde{x}} = \\mathbf{x}_d - \\mathbf{x} \n", + "\\end{equation}\n", + "\n", + "\n", + "

\"ff_fb\"

\n", + "\n", + "For instance applying the full state feedback in the new variables yields:\n", + "\\begin{equation}\n", + "\\mathbf{u} = \\mathbf{K}\\mathbf{\\tilde{x}} \n", + "\\end{equation}\n", + "\n", + "Thus transforming problem back to the stabilization of new variables $\\mathbf{\\tilde{x}}$ (control error):\n", + "\\begin{equation}\n", + "\\dot{\\tilde{\\mathbf{x}}}=(\\mathbf{A} - \\mathbf{B}\\mathbf{K})\\tilde{\\mathbf{x}}\n", + "\\end{equation}\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "k20MK1tj87wC", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 282 + }, + "outputId": "1ede8159-e9e2-43a6-9abc-de9fd7e76370" + }, + "source": [ + "import numpy as np \n", + "from scipy.integrate import odeint # import integrator routine\n", + "\n", + "def system_ode(x, t, A, B, K, x_d):\n", + " x_e = x_d - x \n", + " u = np.dot(K,x_e) \n", + " dx = np.dot(A,x) + np.dot(B,u)\n", + " return dx\n", + "\n", + "x_d = [3, 0, 0]\n", + "\n", + "x_sol = odeint(system_ode, x0, t, args=(A, B, K,x_d,)) # integrate system \"sys_ode\" from initial state $x0$\n", + "theta, dtheta, i = x_sol[:,0], x_sol[:,1], x_sol[:,2] # set theta, dtheta, i to be a respective solution of system states\n", + "\n", + "from matplotlib.pyplot import *\n", + "\n", + "hlines(x_d[0], min(t), max(t), color = 'black', linestyles='--', linewidth=2.0)\n", + "plot(t, theta, 'r', linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'Motor Angle ${\\theta}$ (rad)')\n", + "xlabel(r'Time $t$ (s)')\n", + "show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + } + ] +} \ No newline at end of file diff --git a/legacy - ColabNotebooks/practice_05_reg_tracking.ipynb b/legacy - ColabNotebooks/practice_05_reg_tracking.ipynb new file mode 100644 index 0000000..9f02d0a --- /dev/null +++ b/legacy - ColabNotebooks/practice_05_reg_tracking.ipynb @@ -0,0 +1,426 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "[CT21] lab05_reg_tracking.ipynb", + "provenance": [], + "collapsed_sections": [], + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "zPmrTNlSBW-R" + }, + "source": [ + "# **Practice 5: Regulation and Tracking**\n", + "## **Goals for today**\n", + "\n", + "---\n", + "\n", + "\n", + "\n", + "During today practice we will:\n", + "- Recall the pole placement and root locus techniques\n", + "- Solve the regulation and tracking problems\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "VMv9_G55JAVR" + }, + "source": [ + "### **Linear State Feedback**\n", + "\n", + "Recall the linear system in state space form:\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{x}}=\\mathbf{A}\\mathbf{x} + \\mathbf{B}\\mathbf{u}\n", + "\\end{equation}\n", + "\n", + "The general form of feedback that may stabilize our system is know to be linear:\n", + "\\begin{equation}\n", + "\\mathbf{u}=-\\mathbf{K}\\mathbf{x}\n", + "\\end{equation}\n", + "\n", + "Substitution to the system dynamics yields:\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{x}}=(\\mathbf{A} - \\mathbf{B}\\mathbf{K})\\mathbf{x} = \\mathbf{A}_c\\mathbf{x}\n", + "\\end{equation}\n", + "Thus the stability of the controlled system is completely determined by the eigen values of $\\mathbf{A}_c$ and consequantially by the matrix $\\mathbf{K}$\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Oy2uWXakaWXW" + }, + "source": [ + "### **Pole Placement**\n", + "\n", + "There is a technique for finding suitable $\\mathbf{K}$ matrix that would produced desired eigenvalues of the $\\mathbf{A}_c$ system. It is called pole placement.\n", + "\n", + "Watch the intoduction to pole placement for self-study: [link](https://www.youtube.com/watch?v=FXSpHy8LvmY&ab_channel=MATLAB). Notice the difference between the approach to \"steady state\" control design show there, and in the lecture." + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "UoGq0eulafoH", + "outputId": "53343852-583c-41df-fc6e-e94948411192" + }, + "source": [ + "import numpy as np\n", + "from numpy.linalg import eig\n", + "from scipy.signal import place_poles\n", + "\n", + "A = np.array([[0, 0], \n", + " [0, -1]])\n", + "\n", + "B = np.array([[1], \n", + " [1]])\n", + "\n", + "#desired eigenvalues\n", + "poles = np.array([-10-1j, -10+1j])\n", + "place_obj = place_poles(A, B, poles)\n", + "\n", + "#found control gains\n", + "K = place_obj.gain_matrix\n", + "print(\"K:\", K)\n", + "\n", + "#test that eigenvalues of the closed loop system are what they are supposed to be \n", + "e, v = eig((A - B.dot(K)))\n", + "print(\"eigenvalues of A - B*K:\", e)" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "K: [[101. -82.]]\n", + "eigenvalues of A - B*K: [-10.+1.j -10.-1.j]\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "MQ3fceFLKoH_" + }, + "source": [ + "### **Exercise:**\n", + "Make the follwing systems Lyapunov and asymptotically stable. \n", + "$$\\dot x = \n", + "\\begin{bmatrix} 10 & 0 \\\\ -5 & 10\n", + "\\end{bmatrix}\n", + "x\n", + "+\n", + "\\begin{bmatrix} \n", + "2 \\\\ 0\n", + "\\end{bmatrix}\n", + "u\n", + "$$\n", + "\n", + "$$\\dot x = \n", + "\\begin{bmatrix} 2 & 2 \\\\ -6 & 10\n", + "\\end{bmatrix}\n", + "x\n", + "+\n", + "\\begin{bmatrix} \n", + "0 & -1 \\\\ 5 & -1\n", + "\\end{bmatrix}\n", + "u\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "C5KyZ1TVbCd2" + }, + "source": [ + "Give example of an unstable system of the form $\\mathbf{\\dot{x}}=\\mathbf{A}\\mathbf{x} + \\mathbf{B}\\mathbf{u}$ that can't be stabilized\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "_Vxzvsu5bFu4" + }, + "source": [ + "### **Root Locus**\n", + "\n", + "Consider the following question: given system $\\dot{\\mathbf{x}} = \\mathbf{A}\\mathbf{x}+\\mathbf{B}\\mathbf{u}$ and control $\\mathbf{u} = \n", + "-\\mathbf{K} \\mathbf{x}$, how does the change in $\\mathbf{K}$ changes the eigenvalues of theresulting matrix $\\mathbf{A} - \\mathbf{B}\\mathbf{K}$?\n", + "\n", + "Root locus method is drawing the graph of eigenvalues of the matrix $\\mathbf{A} - \\mathbf{B}\\mathbf{K}$ for a given change of matrix $\\mathbf{K}$ . We only vary a single component of $\\mathbf{K}$ , so the result is a line." + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 279 + }, + "id": "ZcilfRflbHjx", + "outputId": "d930eee2-e528-4c9f-a205-3bc93600eae5" + }, + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "A = np.array([[1, -7], [2, -10]])\n", + "B = np.array([[1], [0]])\n", + "K0 = np.array([[1., 1.]])\n", + "\n", + "k_min = -10;\n", + "k_max = 10;\n", + "k_step = 0.01;\n", + "\n", + "Count = int(np.floor((k_max-k_min)/k_step))\n", + "\n", + "k_range = np.linspace(k_min, k_max, Count)\n", + "E = np.zeros((Count, 4))\n", + "\n", + "for i in range(Count):\n", + " K0[0, 0] = k_range[i]\n", + " ei, v = eig((A - B.dot(K0)))\n", + "\n", + " E[i, 0] = np.real(ei[0])\n", + " E[i, 1] = np.imag(ei[0])\n", + " E[i, 2] = np.real(ei[1])\n", + " E[i, 3] = np.imag(ei[1])\n", + "\n", + " #print(\"eigenvalues of A - B*K:\", ei)\n", + "\n", + "\n", + "plt.plot(E[:, 0], E[:, 1], color = 'r')\n", + "plt.plot(E[:, 2], E[:, 3], color = 'b')\n", + "plt.xlabel(r'Re')\n", + "plt.ylabel(r'Im')\n", + "plt.ylim()\n", + "plt.grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "plt.grid(True)\n", + "plt.show()\n" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "XCseemxbf4Wm" + }, + "source": [ + "## **Regulation**\n", + "\n", + "In some practical problems we are always want to move our system not to the some equalibrium but to the **desired point** $\\mathbf{x}_d$, and stay there ($\\mathbf{\\dot{x}}_d = \\mathbf{0}$). To do so one may consider the change of variables: \n", + "\\begin{equation}\n", + "\\mathbf{\\tilde{x}} = \\mathbf{x}_d - \\mathbf{x} \n", + "\\end{equation}\n", + "\n", + "\n", + "

\"ff_fb\"

\n", + "\n", + "For instance applying the full state feedback in the new variables yields:\n", + "\\begin{equation}\n", + "\\mathbf{u} = \\mathbf{K}\\mathbf{\\tilde{x}} + \\mathbf{u}_d\n", + "\\end{equation}\n", + "\n", + "where following holds $\\mathbf{A}\\mathbf{x}_d + \\mathbf{B}\\mathbf{u}_d=\\mathbf{0}$\n", + "\n", + "Thus transforming problem back to the stabilization of new variables $\\mathbf{\\tilde{x}}$ (control error):\n", + "\\begin{equation}\n", + "\\dot{\\tilde{\\mathbf{x}}}=(\\mathbf{A} - \\mathbf{B}\\mathbf{K})\\tilde{\\mathbf{x}}\n", + "\\end{equation}\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "_rwz15m6esAC" + }, + "source": [ + "### **Example:**\n", + "\n", + "Given system:\n", + "\n", + "$$\\dot x = \n", + "\\begin{bmatrix} 10 & 5 \\\\ -5 & -10\n", + "\\end{bmatrix}\n", + "x\n", + "+\n", + "\\begin{bmatrix} \n", + "-1 \\\\ 2\n", + "\\end{bmatrix}\n", + "u\n", + "$$\n", + "\n", + "let us drive it towards the point $x_d = \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix}$\n", + "\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 282 + }, + "id": "dMQ68HJ4H4zp", + "outputId": "708d34ce-d97c-426d-a192-ea72c60ce44f" + }, + "source": [ + "import numpy as np\n", + "from scipy.integrate import odeint\n", + "\n", + "def system_ode(x, t, A, B, K, x_d, u_d):\n", + " x_e = x_d - x \n", + " u = np.dot(K,x_e) + u_d\n", + " dx = np.dot(A,x) + np.dot(B,u)\n", + " return dx\n", + "\n", + "\n", + "t0 = 0 # Initial time \n", + "tf = 10 # Final time\n", + "N = int(2E3) # Numbers of points in time span\n", + "t = np.linspace(t0, tf, N) # Create time span\n", + "y_0 = 0.5\n", + "x0 = [0, 0] # Set initial state \n", + "\n", + "A = [[10, 5], \n", + " [-5, -10]]\n", + "\n", + "B = [[-1], \n", + " [2]]\n", + "\n", + "c = 10\n", + "x_d = [0, c]\n", + "u_d = 5*c\n", + "K = [[-13.26666667, -5.13333333]]\n", + "\n", + "\n", + "\n", + "x_sol = odeint(system_ode, x0, t, args=(A, B, K,x_d, u_d )) # integrate system \"sys_ode\" from initial state $x0$\n", + "\n", + "from matplotlib.pyplot import *\n", + "\n", + "plot(t, x_sol[:,0], 'r', linewidth=2.0)\n", + "plot(t, x_sol[:,1], 'b', linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'Position ${y}$ (m)')\n", + "xlabel(r'Time $t$ (s)')\n", + "show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "-Nl7EaBShXzu" + }, + "source": [ + "## **Tracking**\n", + "In case of tracking a desired signal is given by function of time $\\mathbf{x}_d(t)$, thus $\\dot{\\mathbf{x}}_d \\neq \\mathbf{0}$ and in order to calculate feedforward one should be able to solve:\n", + "\\begin{equation}\n", + "\\dot{\\mathbf{x}}_d = \\mathbf{A}\\mathbf{x}_d + \\mathbf{B}\\mathbf{u}_d\n", + "\\end{equation}\n", + "\n", + "Then applying control law:\n", + "\\begin{equation}\n", + "\\mathbf{u} = \\mathbf{K}\\mathbf{\\tilde{x}} + \\mathbf{u}_d\n", + "\\end{equation}\n", + "\n", + "yields:\n", + "\\begin{equation}\n", + "\\dot{\\tilde{\\mathbf{x}}}=(\\mathbf{A} - \\mathbf{B}\\mathbf{K})\\tilde{\\mathbf{x}}\n", + "\\end{equation}" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "7V1pKvTldWDP" + }, + "source": [ + "# CODE FOR TRACKING PROBLEM" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "LFhTSmgYWaDW" + }, + "source": [ + "### **Bonus: Frequency responce**\n", + "\n", + "\n", + "Simulate the equations of DC motor for a sinusoidal input voltage $V = A \\sin\\omega t$ and analyze responce in angle $\\theta$.\n", + "\n", + "How does the choice of $\\omega$ affects the result?\n", + "\n", + "Watch [video](https://youtu.be/bU7y051Ejgw) on \"frequency responce\" and find how you could use the proposed method to analyse the effect of $\\omega$ in your problem.\n", + "\n", + "**Note:** To plot the frequancy rersponce it is convinient to use ```scipy.signal.ss2tf``` and ```scipy.signal.freqz```\n", + "\n" + ] + } + ] +} \ No newline at end of file diff --git a/legacy - ColabNotebooks/practice_06_discrete_systems.ipynb b/legacy - ColabNotebooks/practice_06_discrete_systems.ipynb new file mode 100644 index 0000000..50c02b2 --- /dev/null +++ b/legacy - ColabNotebooks/practice_06_discrete_systems.ipynb @@ -0,0 +1,487 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "[CT21] lab06_discrete_systems.ipynb", + "provenance": [], + "collapsed_sections": [], + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "zPmrTNlSBW-R" + }, + "source": [ + "# **Practice 6: Discrete Systems**\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "vE2ZtaIMguPd" + }, + "source": [ + "\n", + "### **Discrete Time State Space**\n", + "The state space representation of such models are given by:\n", + "\\begin{equation}\n", + "{\\mathbf {x}}[k+1]={\\mathbf A}_{d}{\\mathbf {x}}[k]+{\\mathbf B}_{d}{\\mathbf {u}}[k]\n", + "\\end{equation}\n", + "\n", + "where $\\mathbf{x}[k],\\mathbf{u}[k]$ are descrete **sequences** " + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 283 + }, + "id": "UXqCEwzXhIkz", + "outputId": "cf90cc08-6d40-42ce-e942-af033d9ef7e2" + }, + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "A_d = np.array([[0.6, 0.5], \n", + " [-0.8, 0.5]])\n", + "N = 40\n", + "x = np.array([1,-1])\n", + "X = x\n", + "for k in range(N):\n", + " x = A_d.dot(x)\n", + " X = np.vstack((X, x))\n", + "\n", + "plt.step(range(N+1),X)\n", + "plt.xlim([-0.2, N])\n", + "plt.grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "plt.grid(True)\n", + "plt.ylabel(r'State $\\mathbf{x}[k]$')\n", + "plt.xlabel(r'Sample $k$')\n", + "plt.show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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VNVfevOTU1NSknRCJhc7JkyennRC6A8KNtz3MsWPHyhsRtqPGrp/kLyUGnYurrwWuLE9fgiz8XIKNTguNcUVZQ7kLuBy4CbgMmANsBH5TRLaoamJH+ROROuDvyO81druqfmHQ/ZOArwHzgZeAG1X12SiP3djYaGJ3PQudO3bswMLbFnfs2AH8UvwHiLqreLEdNUK+/mj3z9iae4G/2T4/fiMjfF9RRBZ+LsFGp4XGuKJsQ3kAeKDvuoiMBy4iP8hcBSQyoIjIOKAN+CDwPLBRRNaq6raCyT4J7FfVGhH5OPBF4MYknt+5NxnhruJhe7MtO7qMueN3sfylPy6Z8dPJ7y26C3US7ysKFeXoCFH4KQvGvGG/U15VjwFdweXrCbZcCeRU9RkAEfkmsAgoHFAWAZ8PPr8HWC0ioqqaYIdzbxjBruJhe7M9ccYHmbjnn7liTomdEPZ0cfFbHmPJTSuGvPvG2x4O3TkhdA0mbE1s10+4tMRZFfYePMyLrx4pPgFw8dEu2PUTtn7vqyWnK6XUwNrnmTkfKbos3n/oPhaNe4gZU08e8v4o85GElsteY+ut15T9edIQZRvKY6p6xUiniWAW8FzB9efJrwENOY2qHhORV4AzgRcH9SwBlgBMmzaN+vp6nn32Werr61m5ciUAy5Yt65/+1StvZvr06TQ2Nva/sbC6uppVq1axevVqNmzYwK1vz5/fY1ZPD7lcjhUr3vgFb2pqoq6ubsCpPWtra1m+fDmtra1s3LiRZ+Z8JLjnatavX09bW1v/tC0tLdTU1NDY2NjfuXDhQpYuXUpzczM7d+4E4K/nbueiCy+io6ODNWvW9H/9UPPU0NDA4sWL3zRPXHQj3d3dA1rb29ujz9O5oKoDbl+3bl3JeerTN0+5nTkO9x6mvv5WqqqqaG9vHzBPt769i7lVxzn6pfeR2/nGZrrp06czY/oMtu/YzrFjx/hRz3Ryp18z4PvUZ2Ldn3B0ylu5+H/8Y/9tZ599NlVVVf2ng37LK0+zsObUAd+nwnnq6emh+4VubgnmtdQ8FX6f+uZp3759nHhpH4ceXTvk92kd8NCZ7+KuL95V9Gfvl1/sghe7uKW+fsjv02XX/z7MPGPAKa6nTp3K7Nmz2bVrF3tOTOWR/+zhr76+gUsuuYSenh5eeOGN9zrNnj2bvz5yO+cdybHj+NkATBg/gYmTJtLb28uJEyeA81n72mU8PfP32LdvH/v27ev/+urqap7Y0wvAKa+90P99mj59Ojt27OjfjtVw6iaun7qVo0eO8vqx1/u/fsqUKZw4foLDR97YUXTSxEmMnzCe1157rf+2Kyc8w8VHu1iwfz3Hjr+xbeyUU07h2OvHOHI0PxCcOPUEU/ZO4aRxJ3Ho0KH+6SaMn8A75UkAOveeD4CIMGXKFF4/+jpHXz/KiXH5XdVPmZA/Zm7v4d7+r584YSITJk7g0KFD9P3/etJJJzF58uRhz9OJEyd47bXXGD9uPJNOnsSRw0dKzhPAyZNOHnKeBn6f3jxPfSafPHnY8xSHhP1zLyK9QKk3RwhwuqqOaJ1bRG4A6lT15uD6bwFXqerSgmm2BNM8H1zfGUzz4lCPCbBgwQLdtGlTyefu+4+m5C69fav7Mf9bjfQcYUbYkEhHhIawN3H2/ddetCHK3lMh2y9G3ACh85rIc4S580MjOqxPlP+657z+DM9OOJ/WM/9PrOeAUdiOE+VnIkSUQ/qMxvYoK0TkUVVdMJyvifKSV/EXgd9wfDhPWkQ3cG7B9XOC24aa5vlgW87p5DfOh2pubmbVqlUJZJaXhc7czhyl9lMJe6ln7szTSu/2u+Cm8NfaQ17PX3zVeXSu+duiy/IrK1t490s/LP2el5A/5COeTyJ8v0d4OJ8ZU08u+hLPG97JxZfewN0Lig98qf9cRvmZoHTnDPIvWyxJtmzYUl+WZRRlo/wuABGZoKqvF94nIqep6oGEWjYCF4jI28gPHB8HFg+aZi3QCDwM3AA8EHX7Sd/LEVmXemeEPZt6e4vf3WfE/5knoNSyfHfvDzn36E627q4u8Qjn8dOXr+D+Iq/JJ7EGEvr9jviHtNxS/7mMyEKnhca4hrNR/jER+W1VfRxARK4FvsLAtYrYgm0iS4EN5HcbvkNVt4pIK7BJVdcCXwX+KXhzZQ/5QcclKcKeTT96aq+J3YZLmXbqJJ57tXpEL/NEWQNxrpIMZ0A5E3hERL4IzAR+B3gyyRhVvQ+4b9Btyws+Pwz8epzHrqoa0fFxR00mOkP2bNr4YGPR+7Kk1LLseyno7pvSXYvKxPc7Au9MjoXGuIYzoFwI3A7cElxvA/4o8aIyaW9vTzshEgudFhrBRqeFRvDOJFlojGs4A8rHyb/p8DVgEnA98APg3jJ0Ja6jo4PFiwdvkskeC52ZaSxxki6Avfv2MmP6jOJfm4HTFGdmWYbwzuRYaIzrpGFM+2XyG84vIf/+kBeBfylHVDkUvm8jy0ajs++NcENdtu5+hb0HSx88OhPL8tIbQgeEwvdLvElGTlOciWUZgXcmx0JjXMNZQ2lS1X8IPv+5iCwAxu5hM8eosI3Ih44e58VXj1Dk//rsiLD30y319az7m7F5zCTnsijygFIwmPRdPwb8r8SLXFmFHaV3663jRrHGOTeWDOclL9P6DnuRdRY6LTSCjU4LjeCdSbLQGNewDw7pKlvHIz/nmw//nMmTf1F0mrBTHTvnxqbIayiS95sisjy4fp6IZP/MQIHCAydmWdY7793czZbul0tOk5U3/GV9WYKNRvDOJFlojGs4ayhfAk4A7wNagYPAt4HaMnS5YkJ2lR2Nc05MPvwSd3/qV8v6HM45e4YzoFylqleIyOMAqrpfRCaWqcsNJWw31z35Q+xn4dhPzrnKM5wB5fXgrIoKICJvJb/GYkJDQ0PaCZGU7AzbVXakZ9QLHDp6vOhJirbtPsD06dMTeZ5ys/A9t9AI3pkkC41xDWdA+X/AvwLTReSvyB/t18z7UKy8MzXtzmmnTip5/oz89pGLRrEovrSXZRQWGsE7k2ShMa7IG+VV9RvAnwD/G9gNfFRVv1WusKQVnmUvy9LunDH1ZC6eeTp3f+rqopcNX7Lxf0TayzIKC43gnUmy0BhX5DUUEfmiqv4psGOI2zKv7/SqWWeh00Ij2Oi00AjemSQLjXEN542NHxzitmuTCnHOOWdb6BqKiPw+8GngfBF5ouCuqcBD5QpLWnV1qTPzZYeFTguNYKPTQiN4Z5IsNMYlYWfQFZHTgTPIbzv5bMFdB1U18+tuCxYs0E2bNpWcpm+PppKncu3bg6rEiadG/BwjFaUxwil+w06w5Zwb+0TkUVVdMJyvCX3JS1VfUdVnVbUBOADMAGYDl4jIe+Kljr7Vq1ennRBJ2Tv7TvFbTITDuvuyTI6FRvDOJFlojGs4h165Gfgx+XO+/0Xw8fPlyUrehg0b0k6IZFQ6+9ZAil1C3hjpyzI5FhrBO5NkoTGu4WyU/wz5w6zsUtX3Au8ESh/UyTnnXMUYzoByWFUPA4jIJFXdAbyjPFnOOeesGc475Z8XkbcA/wZ8X0T2A7vKk5W89vb2tBMisdBpoRFsdFpoBO9MkoXGuIbzTvnrVfVlVf08+UOufBVYVK6wpOVyubQTIrHQaaERbHRaaATvTJKFxriGs1H+i32fq+qPVHUt8JdlqSqDFStWpJ0QiYVOC41go9NCI3hnkiw0xjWcl7w+CAw+zMq1Q9zm0hR2vpS+95k451zC4r5TXoBTgZ+Wsc0NV9j5UiDS+0yccy6OKGsoHcB3MfpO+T5NTU1lffyOR37OvZu7i94f9TzrI+oMO19KQsq9LJNiodNCI3hnkiw0xhXl0Cu1wHOquie4/tvAr5Hfw+vzWR9URuvQKzfe9nDooLFo3iwWX3Ve6WDnnMuAshx6BbgNOBo8wXuALwBfA14BvjLcyLTU19eX/Tnmzjyt5HlEogwmo9E5UhYawUanhUbwziRZaIwrykte4wrWQm4EvqKq3wa+LSKby5fmnHPOkihrKONEpG/geT/wQMF9w9lLzDnn3BgWZUBYA/xIRF4EeoH/DyAiNeRf9jKhtrY27YRILHRaaAQbnRYawTuTZKExrtCN8gAi8i5gJvA9VX0tuO3twKmq+lh5E0dmNDfKhz6Gc84ZUa6N8qjqf6jqv/YNJsFtT2V9MCnU2tqadkIkFjotNIKNTguN4J1JstAY13CONlw2IlIlIt8XkaeDj2cUme64iGwOLmuH8xwbN25MJrbMLHRaaAQbnRYawTuTZKExrkwMKOTfMHm/ql4A3M/AN1AW6lXVecHlI6OX55xzLkxWBpRFQN8xnduBj6bY4pxzLoas7PY7Q1V3B5/vIX/e+qGcLCKbgGPAF1T134aaSESWAEsApk2b1v9Govr6elauXAnAsmXL+qd/9cqbmT59Oo2NjfT05N9yU11dzapVq1i9ejUbNmzg1rfnz8M+q6eHXC434Iih+UMpnM6WLVuor78VyO/JsXz5clpbWwes4q5bt47169fT1tbWf1tLSws1NTU0Njb2dy5cuJClS5fS3NzMzp07AaiqqqK9vZ2Ojg7WrFnT//VDzVNDQwOLFy8uOU992tvbh5ynurq6AW/C6pun2traAbdHmSdg1OeppaVlQGepeYrzfUpqnoCyfJ+Snicg9Z+9KPPU2dmZ+s9e2DzV19dn4mev1DzFoqqjcgF+AGwZ4rIIeHnQtPuLPMas4OP5wLNAddjzzp8/X1VVv/vd72oxH/vyQ/qxLz9U9H5VVb3juvxlJI8RQanOrLDQqGqj00KjqncmyUKjqiqwSYf5d37UXvJS1Q+o6iVDXO4F9orITIDg474ij9EdfHwGeJD8ee0jKRzts8xCp4VGsNFpoRG8M0kWGuPKyjaUtUDfulwjcO/gCUTkDBGZFHw+DXg3sG3UCp1zzpWUlQHlC8AHReRp4APBdURkgYjcHkxzEbBJRH4G/JD8NhQfUJxzLiMysVFeVV8if5ywwbdvAm4OPn8IiH2qwZaWlth9o8lCp4VGsNFpoRG8M0kWGuPKyhpK2dXU1KSdEImFTguNYKPTQiN4Z5IsNMZVMQNK4e52Q9m2+wA33vZw0cvW3a+w9+Dh1DuzwEIj2Oi00AjemSQLjXFl4iWvtC2aNyt0mkNHj/Piq0eKvkHGOecqnQ8owOKrzgs9m+LWW8eNUo1zztlUMS95LVy4MO2ESCx0WmgEG50WGsE7k2ShMa5I50OxLMr5UKLYeus1AFx8y0+GvN/Ph+KcG0vKdj6UsaC5uTnthEgsdFpoBBudFhrBO5NkoTGuihlQ+g6elnUWOi00go1OC43gnUmy0BhXxQwozjnnyqtiBpS+w29nnYVOC41go9NCI3hnkiw0xuUb5SPyjfLOuUriG+VL6OjoSDshEgudFhrBRqeFRvDOJFlojKtiBpTCs5fFdejo8aKHZtm2+0AClcl0lpuFRrDRaaERvDNJFhrj8nfKA2y6E7ruKTnJBSee5emJc4reP3fmaZEO4eKcc2OVDyiQH0z2dMFZxY+OP3HW5Vx86Q3cvcC3kTjn3FAqZqN8LpcrftjoOz+U/3jTv49eWBElOzPCQiPY6LTQCN6ZJAuN4BvlnXPOpahiBpRly5alnRCJhU4LjWCj00IjeGeSLDTGVTEDinPOufLyAcU551wiKmZAaWhoSDshEgudFhrBRqeFRvDOJFlojKti9vIqKUN7eTnnXBb4Xl4lNDY2pp0QiYVOC41go9NCI3hnkiw0xlUxA0pPT0/aCZFY6LTQCDY6LTSCdybJQmNcFTOgOOecK6+KGVCqq6vTTojEQqeFRrDRaaERvDNJFhrj8o3y4BvlnXNuEN8oX8Lq1avTTojEQqeFRrDRaaERvDNJFhrjqpgBZcOGDWknRGKh00Ij2Oi00AjemSQLjXFVzIDinHOuvHxAcc45l4iK2Sjf09NDVVXV0BNlaKN8yc6MsNAINjotNIJ3JslCI/hG+ZJyuVzaCZFY6LTQCDY6LTSCdybJQmNcFTOgrFixIu2ESCx0WmgEG50WGsE7k2ShMa5MDCgi8usislVETohI0VUsEakTkSdFJCcinx3NRuecc6VlYkABtgC/Cvy42AQiMg5oA0uHMQcAAAtKSURBVK4F5gINIjJ3dPKcc86FGZ92AICqbgcQkVKTXQnkVPWZYNpvAouAbaFP8N3P8vcfOmXkoaOgqakp7YRQFhrBRqeFRvDOJFlojCsTA0pEs4DnCq4/D1w11IQisgRYAjBt2jS6ftABQH19PStXrgQGntf59mv2MmP6DBobG/uPBFpdXc2qVatYvXr1gDcitbe3k8vlBrwO2tTURF1dHfX19f231dbWsnz5clpbW9m4cWP/7evWrWP9+vW0tbX139bS0kJNTU3/Ya3b2tpYuHAhS5cupbm5mZ07dwJQVVVFe3s7HR0drFmzpv/rh5qnhoYGFi9eXJZ56uzsHNAfZZ6AUZ+nqqqqAf1Jf5+SmicgMz97peaprq4u9Z+9KPNUVVWV+s9e2Dy1tbVl4mev1DzFoqqjcgF+QP6lrcGXRQXTPAgsKPL1NwC3F1z/LWB12PPOnz9f9Y7r9Ik/PFeLuuO6/CUDPvzhD6edEMpCo6qNTguNqt6ZJAuNqqrAJh3m3/lRW0NR1Q+M8CG6gXMLrp8T3Oaccy4DsrJRPoqNwAUi8jYRmQh8HFibcpNzzrlAJgYUEbleRJ4Hrgb+XUQ2BLefLSL3AajqMWApsAHYDnxLVbdGfY6pU6cmH14GtbW1aSeEstAINjotNIJ3JslCY1yVceiVphn5K8UOrZKhQ68451wW+KFXSnh217NpJ0TS2tqadkIoC41go9NCI3hnkiw0xlUxA8rBgwfTToikcPfBrLLQCDY6LTSCdybJQmNcFTOgOOecKy8fUJxzziXCN8qDb5R3zrlBfKN8CX2HFsi69evXp50QykIj2Oi00AjemSQLjXFVzIDS/YKNN9UXHr8nqyw0go1OC43gnUmy0BhXxQwozjnnyssHFOecc4momAFl9uzZaSdE0tLSknZCKAuNYKPTQiN4Z5IsNMZVMQPK5MmT006IpKamJu2EUBYawUanhUbwziRZaIyrYgaUHTt2pJ0QSeEJdLLKQiPY6LTQCN6ZJAuNcVXMgOKcc668fEBxzjmXiIoZUKrOqEo7IZKFCxemnRDKQiPY6LTQCN6ZJAuNcfmhV8APveKcc4P4oVdKyO3MpZ0QSXNzc9oJoSw0go1OC43gnUmy0BhXxQwovb29aSdEsnPnzrQTQlloBBudFhrBO5NkoTGuihlQnHPOldf4tANGy/lTXntjW8lge7rgrEtHN6iIqqrs7zxgoRFsdFpoBO9MkoXGuCpjo/yXm6DrntITXnoDLLhpdKKccy7jfKN8MQtuomPSb+T34ip2ychg0tHRkXZCKAuNYKPTQiN4Z5IsNMZVGQMKsGbNmrQTIrHQaaERbHRaaATvTJKFxrgqZkBxzjlXXj6gOOecS0RlbJTftIlcLmfisNEWOi00go1OC43gnUmy0Ai+Ud4551yKKmZAWbZsWdoJkVjotNAINjotNIJ3JslCY1wVM6A455wrLx9QnHPOJWLMb5QXkV8Au4BpwIsp50RhodNCI9jotNAI3pkkC40A71DVqcP5gjF/LC9VfSuAiGwa7h4LabDQaaERbHRaaATvTJKFRsh3Dvdr/CUv55xzifABxTnnXCIqaUD5StoBEVnotNAINjotNIJ3JslCI8ToHPMb5Z1zzo2OSlpDcc45V0Y+oDjnnEvEmB9QRKRORJ4UkZyIfDbtnmJE5FkR6RKRzXF21ysXEblDRPaJyJaC26pE5Psi8nTw8Yw0G4OmoTo/LyLdwTLdLCLXpdx4roj8UES2ichWEflMcHumlmeJzswsTxE5WUQ6ReRnQeNfBLe/TUQeCX7f7xaRiWk1hnTeJSL/WbAs56XZGTSNE5HHReQ7wfVhL8sxPaCIyDigDbgWmAs0iMjcdKtKeq+qzsvYPup3AXWDbvsscL+qXgDcH1xP2128uRNgZbBM56nqfaPcNNgx4H+q6lzgXUBT8POYteVZrBOyszyPAO9T1cuBeUCdiLwL+GLQWAPsBz6ZYiMU7wT444JluTm9xH6fAbYXXB/2shzTAwpwJZBT1WdU9SjwTWBRyk2mqOqPgZ5BNy8C2oPP24GPjmrUEIp0Zoqq7lbVx4LPD5L/5Z1FxpZnic7M0LxXg6sTgosC7wPuCW7PwrIs1pkpInIO8CHg9uC6EGNZjvUBZRbwXMH158nYL0YBBb4nIo+KyJK0Y0LMUNXdwed7gBlpxoRYKiJPBC+Jpf7SXB8RmQO8E3iEDC/PQZ2QoeUZvESzGdgHfB/YCbysqseCSTLx+z64U1X7luVfBctypYhMSjERYBXwJ8CJ4PqZxFiWY31AseQaVb2C/MtzTSLynrSDotD8fueZ+48r8A9ANfmXGnYDf5NuTp6InAp8G2hW1QOF92VpeQ7RmanlqarHVXUecA75VyMuTLOnmMGdInIJ8DnyvbVAFfCnafWJyIeBfar66Egfa6wPKN3AuQXXzwluyxxV7Q4+7gP+lfwvSFbtFZGZAMHHfSn3DElV9wa/zCeAfyQDy1REJpD/I/0NVf2X4ObMLc+hOrO4PAFU9WXgh8DVwFtEpO8YhZn6fS/orAteVlRVPQLcSbrL8t3AR0TkWfKbBd4H/B0xluVYH1A2AhcEeytMBD4OrE256U1E5BQRmdr3OfDfgS2lvypVa4HG4PNG4N4UW4rq+yMduJ6Ul2nwuvRXge2q+rcFd2VqeRbrzNLyFJG3ishbgs8nAx8kv63nh8ANwWRZWJZDde4o+AdCyG+bSG1ZqurnVPUcVZ1D/m/kA6r6G8RZlqo6pi/AdcBT5F9f/bO0e4o0ng/8LLhszVInsIb8yxuvk38d9ZPkX1+9H3ga+AFQldHOfwK6gCfI/9GemXLjNeRfznoC2Bxcrsva8izRmZnlCVwGPB60bAGWB7efD3QCOeCfgUkpL8tinQ8Ey3IL8HXg1DQ7C3p/BfhO3GXph15xzjmXiLH+kpdzzrlR4gOKc865RPiA4pxzLhE+oDjnnEuEDyjOOecS4QOKc865RPiA4pxzLhE+oDgXQkT+LDiXxRPBuSuuKvPzvRo+1YDp3y8i/1SuHueiGh8+iXOVS0SuBj4MXKGqR0RkGpDqSZuGcDn5d2M7lypfQ3GutJnAi5o/iB+q+qKqvgAgIv8WnG5ga98pB0RkjojsCM7I95SIfENEPiAiPw3OyHjloOm+ISLbReQeEZky+MlF5DeDM/5tFpHbgpPGDXY58LiITAqe99bgGFHOjSofUJwr7XvAucHg8CUR+eWC+35HVecDC4A/EJEzg9tryB/a/cLgspj88bH+CLil4OvfAXxJVS8CDgCfLnxiEbkIuBF4t+YPf34c+I0hGi8jf4TiDcAPVPUW9WMquRT4gOJcCZo/2958YAnwC+BuEflEcPcfiMjPgP8gf5qEC4Lb/1NVuzR/mPet5E/vq+QPBjin4OGfU9WfBp9/nfygU+j9wXNvDE7Q9H7yB+zrFxxm/nzyB8f8nKp+fWRz7Fx8vg3FuRCqehx4EHhQRLqAxuDcER8ArlbVQyLyIHBy8CVHCr78RMH1Ewz8nRu8FjH4ugDtqvq5EnkXkT9NQxX5NRjnUuNrKM6VICLvEJELCm6aB+wCTgf2B4PJhcC7Yjz8ecFGf8i/LPaTQfffD9wgItODlioRmT1omsuBh8ifx+JOEcnM6YNd5fEBxbnSTgXaRWSbiDwBzAU+D6wHxovIduAL5F/2Gq4nyZ/ueTtwBvlT7PZT1W3AnwPfC577++R3Eih0ObBFVZ8ifxrZbwUvgzk36vx8KM6lQETmkD+R0SUppziXGF9Dcc45lwhfQ3HOOZcIX0NxzjmXCB9QnHPOJcIHFOecc4nwAcU551wifEBxzjmXCB9QnHPOJcIHFOecc4n4L2d4Pe2ooE8ZAAAAAElFTkSuQmCC\n", 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" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "VMv9_G55JAVR" + }, + "source": [ + "### **Discretization**\n", + "\n", + "Recall the linear system in state space form:\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{x}}(t)=\\mathbf{A}\\mathbf{x}(t) + \\mathbf{B}\\mathbf{u}(t)\n", + "\\end{equation}\n", + "\n", + "This equations may be represented in the descrete form via so called **discretization**. Discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical evaluation and implementation on digital computers.\n", + "\n", + "\n", + "\n", + "\n", + "In order to descretize system exactly, one just need to solve it on time interval $T$ (sampling time):\n", + "\n", + "\\begin{equation}\n", + "{\\mathbf A}_{d}=e^{{{\\mathbf A}T}}={\\mathcal {L}}^{{-1}}\\{(s{\\mathbf I}-{\\mathbf A})^{{-1}}\\}_{{t=T}}\n", + "\\\\\n", + "{\\mathbf B}_{d}=\\left(\\int _{{\\tau =0}}^{{T}}e^{{{\\mathbf A}\\tau }}d\\tau \\right){\\mathbf B}={\\mathbf A}^{{-1}}({\\mathbf A}_{d}-I){\\mathbf B}\n", + "\\end{equation}\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "DsFdX0WDewf7", + "outputId": "1a9398be-f58a-474c-9f6f-30a58b17160f" + }, + "source": [ + "import numpy as np\n", + "from scipy.integrate import odeint\n", + "from scipy import signal\n", + "\n", + "def system_ode(x, t, A):\n", + " dx = np.dot(A,x)\n", + " return dx\n", + "\n", + "A = np.array([[0, 1], \n", + " [-10, -5]])\n", + "\n", + "B = np.array([[0], \n", + " [1]])\n", + "\n", + "C = np.array([[1, 0]])\n", + "D = np.array([[0]])\n", + "\n", + "T = 0.1\n", + "\n", + "A_d, B_d, C_d, D_d, _ = signal.cont2discrete((A,B,C,D), T)\n", + "print(A_d, B_d, C_d, D_d)\n" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "[[ 0.95772944 0.07739424]\n", + " [-0.7739424 0.57075825]] [[0.00422706]\n", + " [0.07739424]] [[1 0]] [[0]]\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "W0MN40s6gh-7" + }, + "source": [ + "Lets compare solutions of descrete system and it's continues original:" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 283 + }, + "id": "9l-WQQd1ghi1", + "outputId": "71438748-57a4-4abd-b094-161b75a0af4a" + }, + "source": [ + "N = 30\n", + "tf = N*T # Final time\n", + "t = np.linspace(0, tf, N) # Create time span\n", + "x0 = [1, 0] # Set initial state \n", + "\n", + "x_sol = odeint(system_ode, x0, t, args=(A, )) \n", + "x = x0\n", + "x_d = x0\n", + "for k in range(N):\n", + " x = A_d.dot(x)\n", + " x_d = np.vstack((x_d, x))\n", + "\n", + "plt.step(range(N+1), x_d)\n", + "plt.plot(x_sol)\n", + "plt.grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "plt.grid(True)\n", + "plt.ylabel(r'State $\\mathbf{x}[k]$')\n", + "plt.xlabel(r'Sample $k$')\n", + "plt.show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "vBBWZU9fOtf7" + }, + "source": [ + "### **Approximations**\n", + "\n", + " Exact discretization may sometimes be intractable due to the heavy matrix exponential and integral operations involved. It is much easier to calculate an approximate discrete model, based on that for small timesteps $e^{{{\\mathbf A}T}}\\approx {\\mathbf I}+{\\mathbf A}T$. The approximate solution then becomes:\n", + "\n", + "\n", + "\\begin{equation}\n", + "{\\mathbf x}[k+1]\\approx ({\\mathbf I}+{\\mathbf A}T){\\mathbf x}[k]+T{\\mathbf B}{\\mathbf u}[k]\n", + "\\end{equation}\n", + "Another method is to use so called bilinear transform, or Tustin transform. \n", + "\\begin{equation}\n", + "\\mathbf{A}_d = e^{{{\\mathbf A}T}}\\approx \\left({\\mathbf I}+{\\frac {1}{2}}{\\mathbf A}T\\right)\\left({\\mathbf I}-{\\frac {1}{2}}{\\mathbf A}T\\right)^{{-1}}\n", + "\\end{equation}\n", + "\n", + "Each of these approximations has different stability properties. The bilinear transform preserves the instability of the continuous-time system." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "MQ3fceFLKoH_" + }, + "source": [ + "### **Exercise:**\n", + "Find the exact and approximate descretization of the following systems. \n", + "$$\\dot x = \n", + "\\begin{bmatrix} 10 & 0 \\\\ -5 & 10\n", + "\\end{bmatrix}\n", + "x\n", + "+\n", + "\\begin{bmatrix} \n", + "2 \\\\ 0\n", + "\\end{bmatrix}\n", + "u\n", + "$$\n", + "\n", + "$$\\dot x = \n", + "\\begin{bmatrix} 2 & 2 \\\\ -6 & 10\n", + "\\end{bmatrix}\n", + "x\n", + "+\n", + "\\begin{bmatrix} \n", + "0 & -1 \\\\ 5 & -1\n", + "\\end{bmatrix}\n", + "u\n", + "$$" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "LHBJaMF7ndeG", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "b92fa638-1674-4d6b-ee10-13466e842ff7" + }, + "source": [ + "A = np.array([[0, 1], \n", + " [-10, -5]])\n", + "\n", + "B = np.array([[0], \n", + " [1]])\n", + "\n", + "C = np.array([[1, 0]])\n", + "\n", + "D = np.array([[0]])\n", + "\n", + "T = 0.001\n", + "\n", + "A_d, B_d, C_d, D_d, _ = signal.cont2discrete((A,B,C,D), T)\n", + "\n", + "print(f\"Exact discretization:\\n {A_d, B_d}\")\n", + "\n", + "A_d_approx = np.eye(2) + T*A \n", + "B_d_approx = T*B\n", + "\n", + "print(f\"\\nApproximate discretization:\\n {A_d_approx, B_d_approx}\")" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Exact discretization:\n", + " (array([[ 9.99995008e-01, 9.97502499e-04],\n", + " [-9.97502499e-03, 9.95007496e-01]]), array([[4.99167291e-07],\n", + " [9.97502499e-04]]))\n", + "\n", + "Approximate discretization:\n", + " (array([[ 1. , 0.001],\n", + " [-0.01 , 0.995]]), array([[0. ],\n", + " [0.001]]))\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "POx7WJ1aRBh8" + }, + "source": [ + "### **Stability**\n", + "\n", + "the concepts of stability is fairly general and can be applied to the descrete time systems, however, in this case solutions may be analized directly, and stability criterias are the following:\n", + "\n", + "\n", + "* Asymptotically stable $|\\lambda_i| = \\sqrt{\\operatorname{Re}(\\lambda_i)^2 + \\operatorname{Im}(\\lambda_i)^2} < 1,\\forall i$ \n", + "* Lyapunov stable: $ |\\lambda_i|\\leq 1,\\forall i$\n", + "* Unstable: $\\exists\\lambda_i, |\\lambda_i|>1 $\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "W7PpZtoyo_pw" + }, + "source": [ + "### **Exercise:**\n", + "Check the stability properties for system defined above. " + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "aVilPFmQRA_g", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "1b70f100-ffda-42a0-8f8f-a7fca288f988" + }, + "source": [ + "from numpy.linalg import eig\n", + "e, v = eig(A_d)\n", + "print(\"Eigenvalues of A:\\n\", abs(e))" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Eigenvalues of A:\n", + " [0.99750312 0.99750312]\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "BV2VxRCyUUCP" + }, + "source": [ + "### **Descrete Feedback**\n", + "\n", + "The general form of feedback that may stabilize our system is linear as well as for continues time system:\n", + "\\begin{equation}\n", + "\\mathbf{u}[k]=-\\mathbf{K}\\mathbf{x}[k]\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Oy2uWXakaWXW" + }, + "source": [ + "### **Pole Placement**\n", + "\n", + "Previously we have designed a stable poles for continues time systems by placing them on the left hand side of comple plane. In case of descrete time systems we should place them inside of **unit circle**\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "UoGq0eulafoH", + "outputId": "91a302ff-8c6a-4564-b8dc-bbb91f169bef" + }, + "source": [ + "A = np.array([[3, 1], \n", + " [0, 2]])\n", + "\n", + "B = np.array([[1], \n", + " [1]])\n", + "\n", + "C = np.array([[1, 0]])\n", + "D = np.array([[0]])\n", + "\n", + "T = 0.1\n", + "\n", + "A_d, B_d, C_d, D_d, _ = signal.cont2discrete((A,B,C,D), T)\n", + "\n", + "e, v = eig(A_d)\n", + "print(\"Original eigenvalues of A:\\n\", e)\n", + "\n", + "#desired eigenvalues\n", + "poles = np.array([0.5+0.2j, 0.5-0.2j])\n", + "place_obj = signal.place_poles(A_d, B_d, poles)\n", + "\n", + "#found control gains\n", + "K = place_obj.gain_matrix\n", + "print(\"\\nGain matrix K:\\n\", K)\n", + "\n", + "#test that eigenvalues of the closed loop system are what they are supposed to be \n", + "e, v = eig((A_d - B_d.dot(K)))\n", + "print(\"\\nPlaced eigenvalues of A - B*K:\\n\", abs(e))" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Original eigenvalues of A:\n", + " [1.34985881 1.22140276]\n", + "\n", + "Gain matrix K:\n", + " [[ 25.44175186 -13.96834808]]\n", + "\n", + "Placed eigenvalues of A - B*K:\n", + " [0.53851648 0.53851648]\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "7V1pKvTldWDP" + }, + "source": [ + "# Implement the stabilization problem" + ], + "execution_count": null, + "outputs": [] + } + ] +} \ No newline at end of file diff --git a/legacy - ColabNotebooks/practice_07_ffs_svd.ipynb b/legacy - ColabNotebooks/practice_07_ffs_svd.ipynb new file mode 100644 index 0000000..8c8a64e --- /dev/null +++ b/legacy - ColabNotebooks/practice_07_ffs_svd.ipynb @@ -0,0 +1,551 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "[CT21] lab07_ffs_svd.ipynb", + "provenance": [], + "collapsed_sections": [], + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "zPmrTNlSBW-R" + }, + "source": [ + "# **Practice 7: Fundamental Subspaces and SVD**\n", + "## **Goals for today**\n", + "\n", + "---\n", + "\n", + "During today practice we will:\n", + "* Exploit a structure of linear mapping between inputs and outputs.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "kgF8BN0GTBfP" + }, + "source": [ + "## **Four Fundamental Subspaces. Recall**\n", + "---\n", + ">As we have studied on the lectures there are four fundamental subspaces accompanying any linear operator (matrix) $\\mathbf{A}^{m \\times n}$, namely:\n", + ">* **Column** space (range, image): $\\mathcal{C}(\\mathbf{A}) \\in \\mathbb{R}^m$ \n", + ">* **Null** space (kernel): $\\mathcal{N}(\\mathbf{A}) \\in \\mathbb{R}^n$\n", + ">* **Row** space: $\\mathcal{R}(\\mathbf{A}) = \\mathcal{C}(\\mathbf{A}^T) \\in \\mathbb{R}^n$\n", + ">* **Left null** space: $\\mathcal{N}(\\mathbf{A}^T) \\in \\mathbb{R}^m$\n", + "---\n", + "\n", + "## **Linear Mapping**\n", + "\n", + ">Let us consider following equation kinematic relationship:\n", + ">\\begin{equation}\n", + " \\mathbf{y} = \\mathbf{A}\\mathbf{x}\n", + "\\end{equation}\n", + ">where\n", + ">\n", + ">* $\\mathbf{A} \\in \\mathbb{R}^{m \\times n}$ is linear operator (matrix)\n", + "* $\\mathbf{x} \\in \\mathbb{R}^n$ are inputs of operator $\\mathbf{A}$\n", + "* $\\mathbf{y} \\in \\mathbb{R}^m$ are outputs of operator $\\mathbf{A}$\n", + "\n", + "This equations can be characterized in terms of the columns space $\\mathcal{C}(\\mathbf{A})$ (range) and null space $\\mathcal{N}(\\mathbf{A})$ of the mapping $\\mathbf{A}$\n", + "\n", + "* The column space of $\\mathbf{A}$ is the subspace $\\mathcal{C}(\\mathbf{A}) \\in \\mathbb{R}^m$ of outputs $\\mathbf{y}$ that can be produced by inputs $\\mathbf{x}$\n", + "* The null space of $\\mathbf{A}$ is the subspace $\\mathcal{N}(\\mathbf{A}) \\in \\mathbb{R}^n$ of inputs $\\mathbf{x}$ that produce zero output $\\mathbf{y}$.\n", + "\n", + "

\"linear

\n", + "\n", + "If the matrix $\\mathbf{A}$ have full rank, one has $\\text{dim}\\{\\mathcal{C}(\\mathbf{A})\\} = m,\\text{dim}\\{\\mathcal{N}(\\mathbf{A})\\} = n - m $. \n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "PTlAj8zrNvtB", + "outputId": "99af42fa-668c-4fd5-8bd4-2a2fb3984e9e" + }, + "source": [ + "from scipy.linalg import null_space, orth\n", + "A = [[0, 0], \n", + " [0, -1]]\n", + "\n", + "print(f\"Null space:\\n {null_space(A)}\\n\")\n", + "\n", + "print(f\"Column space:\\n {orth(A)}\\n\")" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Null space:\n", + " [[1.]\n", + " [0.]]\n", + "\n", + "Column space:\n", + " [[0.]\n", + " [1.]]\n", + "\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "4mkxyZoho9n2" + }, + "source": [ + "## **Singular Value Decomposition**\n", + "The singular value decomposition of an $m\\times n$ real or complex matrix $\\mathbf{A}$ is a factorization of the form $\\mathbf{U S V^{*}}$, where $\\mathbf {U}$ is an $m\\times m$ real or complex unitary matrix, $\\mathbf{S}$ is an ${m\\times n}$ rectangular diagonal matrix with non-negative real numbers on the diagonal, and $\\mathbf {V}$ is an $n\\times n$ real or complex unitary matrix. \n", + "\n", + "The diagonal entries $\\sigma_{i}=\\mathbf{S}_{ii}$ are known as the singular values of $\\mathbf{A}$. The number of non-zero singular values is equal to the rank of $\\mathbf{A}$. . Let us for now stick in to a real domain where SVD can be written as:\n", + "\n", + "---\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{A} = \\mathbf{U}\\mathbf{S}\\mathbf{V}^T\n", + "\\end{equation}\n", + "\n", + "---\n", + "\n", + "with matrices $\\mathbf{U},\\mathbf{S},\\mathbf{V}$ above obeing following usefull properties:\n", + "* Rank $r$ of matrix $\\mathbf{A}$ is number of non zero singular values $\\sigma_i$ ($\\text{dim}\\{\\mathbf{S}_r\\}$)\n", + "* Singular values $\\sigma$ of $\\mathbf{A}$ and eigenvalues $\\lambda$ of $\\mathbf{A^TA}$ (or $\\mathbf{AA^T}$) are related as $\\sigma_i = \\lambda_i^2$ \n", + "* The columns of $\\mathbf{V}$ are eigenvectors of $A^TA$ called right singular vectors of $\\mathbf{A}$.\n", + "* The columns of $\\mathbf{U}$ are eigenvectors of $AA^T$ called left singular vecotrs of $\\mathbf{A}$.\n", + "* Determinant is equal to product of eigenvalues $\\det\\{\\mathbf{A}\\} = \\prod_{i=1}^r\\sigma_i$\n", + "\n", + ">**HW EXERCISE**: \n", + "* Proof the statements above\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "-hiCl_SzZlZi" + }, + "source": [ + "\n", + "### **SVD $\\rightarrow$Four Fundamental Subspaces**\n", + "Outstanding is that SVD directly provides all **four fundamental subspaces** at once. \n", + "\n", + "---\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{A} = \\mathbf{U}\\mathbf{S}\\mathbf{V}^T = \\begin{bmatrix}\\underset{m \\times r}{\\mathbf{U}_r} & \\underset{m \\times m - r}{\\mathbf{U}_n}\n", + "\\end{bmatrix}\n", + "\\begin{bmatrix}\n", + "\\underset{r \\times r}{\\mathbf{S}_r} & \\underset{r \\times n - r}{\\mathbf{0}} \\\\ \n", + "\\underset{m - r \\times r}{\\mathbf{0}} & \n", + "\\underset{m - r \\times n - r}{\\mathbf{0}}\n", + "\\end{bmatrix}\n", + "\\begin{bmatrix}\\underset{n \\times r}{\\mathbf{V}_r} & \\underset{n \\times n -r}{\\mathbf{V}_n}\n", + "\\end{bmatrix}^T\n", + "= \\mathbf{U}_r \\mathbf{S}_r \\mathbf{V}^T_r\n", + "\\end{equation}\n", + "\n", + "---\n", + "\n", + "* **Column space** $\\mathcal{C}(\\mathbf{A})$is spanned by first $r$ vectors in $\\mathbf{U}_r$\n", + "* **Left null space** $\\mathcal{N}(\\mathbf{A}^T)$ is spanned by $m-r$ vectors in $\\mathbf{U}_n$\n", + "* **Row space** $\\mathcal{R}(\\mathbf{A}^T)$is spanned by first $r$ right singular vectors in $\\mathbf{V}_r$\n", + "* **Null space** $\\mathcal{N}(\\mathbf{A})$ is spanned by $n-r$ vectors in $\\mathbf{V}_n$\n", + "\n", + "\n", + "\n", + "\n", + "---" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "mhW8S54gocc5" + }, + "source": [ + "## **Geometrical Representation**\n", + "A Singular Value Decomposition allow the intuitive geometrical interpretation. \n", + "\n", + "

\"ff_fb\"

" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "VKwy8-iwhSfb" + }, + "source": [ + "## **Example: Unit norm ellipsoids**\n", + "\n", + "Consider case of input bounded by unit circle (euclidean norm): \n", + "\\begin{equation}\n", + "\\|\\mathbf{x}\\|_2^2 = \\mathbf{x}^T \\mathbf{x} \\leq 1\n", + "\\end{equation}\n", + "Now think about output constraints defined by linear mapping which is nothing but transformation from the sphere in $\\mathbb{R}^n$ to the ellipsoid in $\\mathbb{R}^m$.\n", + "\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "-IEVsRS4yVQL", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 390 + }, + "outputId": "57cf51a7-f5b2-408a-b4e4-859abfa3ff95" + }, + "source": [ + "from matplotlib.pyplot import *\n", + "from numpy import linspace\n", + "# Define a circle in inputs\n", + "n = 100\n", + "phi = linspace(0, 1,n)\n", + "x_circle = cos(2*pi*phi), sin(2*pi*phi)\n", + " \n", + "# transform a circle by A in the particular posture\n", + "A = [[1,0],\n", + " [0.5,2]]\n", + " \n", + "y = dot(A,x_circle)\n", + "figure(figsize=(6,6))\n", + "plot(x_circle[0], x_circle[1], color = 'blue')\n", + "plot(y[0], y[1], color = 'red')\n", + "ylim([-2.5,2.5])\n", + "xlim([-2.5,2.5])\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "ylabel(r'$x_1$')\n", + "xlabel(r'$x_2$')\n", + "show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "obaS10Cb6YNI" + }, + "source": [ + "Now we can use SVD to characterize such transformation:" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "XCn_ojr52CBo", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 681 + }, + "outputId": "a9e2e119-2fff-4c2a-cd83-3e458214c9f5" + }, + "source": [ + "from numpy.linalg import svd\n", + "from numpy import transpose\n", + "from numpy import diag\n", + "U,S,VT = svd(A)\n", + "\n", + "print(f' Left singular vectors U:\\n {U}\\n\\n Singular values S:\\n {S}\\n\\n Right singular vectors V:\\n {VT.transpose()}\\n\\n ')\n", + "\n", + "figure(figsize=(6,6))\n", + "plot([0, S[0]*U[0,0]], [0, S[0]*U[0,1]], color = 'red', marker = 'o')\n", + "plot([0, S[1]*U[1,0]], [0, S[1]*U[1,1]], color = 'red', marker = 'o')\n", + "plot(x_circle[0], x_circle[1], color = 'blue')\n", + "plot(y[0], y[1], color = 'red')\n", + "ylim([-2.5,2.5])\n", + "xlim([-2.5,2.5])\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "ylabel(r'$x_1$')\n", + "xlabel(r'$x_2$')\n", + "show()\n", + "\n", + "print(f' Elipsoid semi-axes U*S:\\n {dot(U,diag(S))}\\n')\n" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + " Left singular vectors U:\n", + " [[ 0.14869598 0.98888296]\n", + " [ 0.98888296 -0.14869598]]\n", + "\n", + " Singular values S:\n", + " [2.07970763 0.96167364]\n", + "\n", + " Right singular vectors V:\n", + " [[ 0.30924417 0.95098267]\n", + " [ 0.95098267 -0.30924417]]\n", + "\n", + " \n" + ], + "name": "stdout" + }, + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + }, + { + "output_type": "stream", + "text": [ + " Elipsoid semi-axes U*S:\n", + " [[ 0.30924417 0.95098267]\n", + " [ 2.05658743 -0.14299701]]\n", + "\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "vNBZOcUl8sws" + }, + "source": [ + ">**QUESTION**: \n", + "What will happen in case of singular matrix $\\mathbf{A}$? How you can interpret corresponding SVD geometrically?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "L9p7kWFh-Xew" + }, + "source": [ + "## **Condition Number**\n", + "In order to characterize anisotropy of resulting transformation one can denote the following criteria: \n", + "\\begin{equation}\n", + "\\kappa (\\mathbf{A})={\\frac {\\sigma _{\\text{max}}(\\mathbf{A})}{\\sigma _{\\text{min}}(\\mathbf{A})}}\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Xh1yoCZaBF_j" + }, + "source": [ + "In general a condition number allow you to characterize how much the output value of the function can change for a small change in the input argument, namely sensativity. A definition above is valid for $\\ell^2$ norm:\n", + "\\begin{equation}\n", + "\\kappa (\\mathbf{A})= {\\frac {\\left\\|A^{-1}\\tilde{\\mathbf{y}}\\right\\|}{\\left\\|A^{-1}\\mathbf{y}\\right\\|}}/{\\frac {\\| \\mathbf{y} \\|}{\\| \\tilde{\\mathbf{y}} \\|}}\n", + "\\end{equation}" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "6e3t_R5NDj2m", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 426 + }, + "outputId": "07ed8bad-fc1a-4073-817c-7f7c72ec42f0" + }, + "source": [ + "from numpy.linalg import cond\n", + "\n", + "A1 = [[1.5,0.2],[0,1]]\n", + "A2 = [[2,1],[1,2]]\n", + "figure(figsize=(6,6))\n", + "plot(x_circle[0], x_circle[1], color = 'blue')\n", + "for matrix in A1, A2:\n", + " y = dot(matrix,x_circle)\n", + " plot(y[0], y[1])\n", + " ylim([-2.5,2.5])\n", + " xlim([-2.5,2.5])\n", + " print(f'Condition number c {cond(matrix)}')\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "ylabel(r'$x_1$')\n", + "xlabel(r'$x_2$')\n", + "show()\n", + "\n", + " " + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Condition number c 1.5468641541960593\n", + "Condition number c 2.999999999999999\n" + ], + "name": "stdout" + }, + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "RprUob8IDS-Q" + }, + "source": [ + "## **Applications to the LTI Systems**" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Uk0dtOIBByUT" + }, + "source": [ + "### **Equilibrium Points and Feedforward**\n", + "\n", + "Given LTI system $\\dot{\\mathbf{x}} = \\mathbf{A} \\mathbf{x} + \\mathbf{B} \\mathbf{u}$, where $\\mathbf{x} \\in \\mathbb{R}^n$, $\\mathbf{u} \\in \\mathbb{R}^m$, find all states that can be made into fixed points with a constant control law.\n", + "\n", + "\n", + "Let us find null space of the matrix $\\begin{bmatrix} \\mathbf{A} & \\mathbf{B} \\end{bmatrix}$ as $\\mathbf{N} = \\text{null} (\\begin{bmatrix} \\mathbf{A} & \\mathbf{B} \\end{bmatrix})$. \n", + "\n", + "We can find all $\\mathbf{x}$, $\\mathbf{u}$ pairs that produce equilibrium points as follows: $\\begin{bmatrix} \\mathbf{x} \\\\ \\mathbf{u} \\end{bmatrix} = \\mathbf{N} \\mathbf{z}$, $\\forall \\mathbf{z}$\n", + "\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "3bC4nO4oByAI", + "outputId": "0101d144-eae8-44a8-934b-ae2f91ce787e" + }, + "source": [ + "from numpy import hstack\n", + "A = [[0, 1],\n", + " [-2,-3]]\n", + "B = [[0], [1]]\n", + "\n", + "M = hstack((A,B))\n", + "\n", + "print(f'Stacked matrix:\\n {M}')\n", + "\n", + "U,S,VT = svd(M, full_matrices=True)\n", + "print(f'Left singular vectors:\\n {U}')\n", + "print(f'Singular values:\\n {S}')\n", + "print(f'Right singular vectors:\\n {VT.T}')" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Stacked matrix:\n", + " [[ 0 1 0]\n", + " [-2 -3 1]]\n", + "Left singular vectors:\n", + " [[-0.21452344 0.97671884]\n", + " [ 0.97671884 0.21452344]]\n", + "Singular values:\n", + " [3.82869567 0.58402865]\n", + "Right singular vectors:\n", + " [[-0.5102097 -0.73463328 0.4472136 ]\n", + " [-0.82134498 0.57043179 0. ]\n", + " [ 0.25510485 0.36731664 0.89442719]]\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "FfRXE6WnC35G" + }, + "source": [ + "\n", + "\n", + "\n", + "Given LTI system $\\dot{\\mathbf{x}} = \\mathbf{A} \\mathbf{x} + \\mathbf{B} \\mathbf{u}$, where $\\mathbf{x} \\in \\mathbb{R}^n$, $\\mathbf{u} \\in \\mathbb{R}^m$, \n", + "\n", + "1. check if $\\mathbf{x}_d$ can be transformed into a equilibrium point\n", + "2. find control constant $\\mathbf{u}_d$ that does it, given control law $\\mathbf{u} = \\mathbf{K}\\mathbf{x} + \\mathbf{u}_d$.\n", + "\n", + "\n", + " We can check that $(\\mathbf{A}-\\mathbf{B}\\mathbf{K}) \\mathbf{x}_d + \\mathbf{B} \\mathbf{u}_d = \\mathbf{0}$ has a solution, in other words that $-(\\mathbf{A}-\\mathbf{B}\\mathbf{K}) \\mathbf{x}^* \\in \\mathcal{C}(\\mathbf{B})$. Resulting condition is given via projection into the left null space of $\\mathbf{B}$: \n", + " $(\\mathbf{I} - \\mathbf{B}\\mathbf{B}^+)(\\mathbf{A}-\\mathbf{B}\\mathbf{K})\\mathbf{x}_d = \\mathbf{0}$\n", + "\n", + "This means finding such $\\mathbf{u}_d$ that $(\\mathbf{A}-\\mathbf{B}\\mathbf{K}) \\mathbf{x}_d + \\mathbf{B}\\mathbf{u}_d= \\mathbf{0}$. This is done via pseudo-inverse, which provides exact solution, as long as it exists: $\\mathbf{u}_d= -\\mathbf{B}^+(\\mathbf{A}-\\mathbf{B}\\mathbf{K}) \\mathbf{x}_d$.\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "CUzadWFLEs2I" + }, + "source": [ + "# ADD YOUR CODE HERE" + ], + "execution_count": null, + "outputs": [] + } + ] +} \ No newline at end of file diff --git a/legacy - ColabNotebooks/practice_08_la_applications.ipynb b/legacy - ColabNotebooks/practice_08_la_applications.ipynb new file mode 100644 index 0000000..00755d7 --- /dev/null +++ b/legacy - ColabNotebooks/practice_08_la_applications.ipynb @@ -0,0 +1,325 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "[CT21] lab08_la_applications.ipynb", + "provenance": [], + "collapsed_sections": [], + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "zPmrTNlSBW-R" + }, + "source": [ + "# **Practice 8: Fundamental Subspaces with application to LTI Systems**\n", + "## **Goals for today**\n", + "\n", + "---\n", + "\n", + "During today practice we will:\n", + "* Exploit a structure of linear mapping between inputs and outputs.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "kgF8BN0GTBfP" + }, + "source": [ + "## **Four Fundamental Subspaces. Recall**\n", + "---\n", + ">As we have studied on the lectures there are four fundamental subspaces accompanying any linear operator (matrix) $\\mathbf{A}^{m \\times n}$, namely:\n", + ">* **Column** space (range, image): $\\mathcal{C}(\\mathbf{A}) \\in \\mathbb{R}^m$ \n", + ">* **Null** space (kernel): $\\mathcal{N}(\\mathbf{A}) \\in \\mathbb{R}^n$\n", + ">* **Row** space: $\\mathcal{R}(\\mathbf{A}) = \\mathcal{C}(\\mathbf{A}^T) \\in \\mathbb{R}^n$\n", + ">* **Left null** space: $\\mathcal{N}(\\mathbf{A}^T) \\in \\mathbb{R}^m$\n", + "---\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "-hiCl_SzZlZi" + }, + "source": [ + "\n", + "### **SVD $\\rightarrow$Four Fundamental Subspaces**\n", + "Outstanding is that SVD directly provides all **four fundamental subspaces** at once. \n", + "\n", + "---\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{A} = \\mathbf{U}\\mathbf{S}\\mathbf{V}^T = \\begin{bmatrix}\\underset{m \\times r}{\\mathbf{U}_r} & \\underset{m \\times m - r}{\\mathbf{U}_n}\n", + "\\end{bmatrix}\n", + "\\begin{bmatrix}\n", + "\\underset{r \\times r}{\\mathbf{S}_r} & \\underset{r \\times n - r}{\\mathbf{0}} \\\\ \n", + "\\underset{m - r \\times r}{\\mathbf{0}} & \n", + "\\underset{m - r \\times n - r}{\\mathbf{0}}\n", + "\\end{bmatrix}\n", + "\\begin{bmatrix}\\underset{n \\times r}{\\mathbf{V}_r} & \\underset{n \\times n -r}{\\mathbf{V}_n}\n", + "\\end{bmatrix}^T\n", + "= \\mathbf{U}_r \\mathbf{S}_r \\mathbf{V}^T_r\n", + "\\end{equation}\n", + "\n", + "---\n", + "\n", + "* **Column space** $\\mathcal{C}(\\mathbf{A})$is spanned by first $r$ vectors in $\\mathbf{U}_r$\n", + "* **Left null space** $\\mathcal{N}(\\mathbf{A}^T)$ is spanned by $m-r$ vectors in $\\mathbf{U}_n$\n", + "* **Row space** $\\mathcal{R}(\\mathbf{A}^T)$is spanned by first $r$ right singular vectors in $\\mathbf{V}_r$\n", + "* **Null space** $\\mathcal{N}(\\mathbf{A})$ is spanned by $n-r$ vectors in $\\mathbf{V}_n$\n", + "\n", + "\n", + "\n", + "\n", + "---" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "PTlAj8zrNvtB", + "outputId": "c3ee790c-c7a5-4405-cfe9-2073cc3b6a1f" + }, + "source": [ + "# from numpy import array\n", + "import numpy as np\n", + "from numpy.linalg import svd\n", + "\n", + "A = [[0, 0], \n", + " [0, -1]]\n", + "A = np.array(A)\n", + "\n", + "U, S, VT = svd(A, full_matrices=True)\n", + "\n", + "# Let's print out the SVD matrices:\n", + "print(f\"Left Singular Vectors:\\n {U}\\n\")\n", + "print(f\"Singular Values:\\n {S}\\n\")\n", + "print(f\"Right Singular Vectors:\\n {VT.T}\\n\")\n" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Left Singular Vectors:\n", + " [[0. 1.]\n", + " [1. 0.]]\n", + "\n", + "Singular Values:\n", + " [1. 0.]\n", + "\n", + "Right Singular Vectors:\n", + " [[-0. 1.]\n", + " [-1. 0.]]\n", + "\n", + "[1. 0.]\n", + "[0. 0.]\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "4Pq23jm9pcdf" + }, + "source": [ + "# Fundamental subspaces are given by slicing resulting matrices" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "RprUob8IDS-Q" + }, + "source": [ + "## **Applications to the LTI Systems**" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "jBksZ-2LmF-_" + }, + "source": [ + "### **Equilibrium Points of Uncontrolled System**\n", + "\n", + "Given LTI system $\\dot{\\mathbf{x}} = \\mathbf{A}\\mathbf{x}$, where $\\mathbf{x} \\in \\mathbb{R}^n$, $\\mathbf{u} \\in \\mathbb{R}^m$, find all equalibrium states, namely:\n", + "\\begin{equation}\n", + "\\dot{\\mathbf{x}} = \\mathbf{A}\\mathbf{x} = 0\n", + "\\end{equation}\n", + "\n", + "The all posible equalibrium points thus given by $\\mathbf{x}_e = \\mathbf{N}\\mathbf{z}$, $\\forall \\mathbf{z}$\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "K_q0BPN1nehA", + "outputId": "1587b1f4-983f-4f96-8436-1f50efd7ea0f" + }, + "source": [ + "from numpy import hstack\n", + "A = [[0, 1],\n", + " [-2,-3]]\n", + "B = [[0], [1]]\n", + "\n", + "M = hstack((A,B))\n", + "\n", + "print(f'Stacked matrix:\\n {M}')\n", + "\n", + "U,S,VT = svd(M, full_matrices=True)\n", + "print(f'Left singular vectors:\\n {U}')\n", + "print(f'Singular values:\\n {S}')\n", + "print(f'Right singular vectors:\\n {VT.T}')" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Stacked matrix:\n", + " [[ 0 1 0]\n", + " [-2 -3 1]]\n", + "Left singular vectors:\n", + " [[-0.21452344 0.97671884]\n", + " [ 0.97671884 0.21452344]]\n", + "Singular values:\n", + " [3.82869567 0.58402865]\n", + "Right singular vectors:\n", + " [[-0.5102097 -0.73463328 0.4472136 ]\n", + " [-0.82134498 0.57043179 0. ]\n", + " [ 0.25510485 0.36731664 0.89442719]]\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Uk0dtOIBByUT" + }, + "source": [ + "### **Equilibrium Points and Feedforward**\n", + "\n", + "Given LTI system $\\dot{\\mathbf{x}} = \\mathbf{A} \\mathbf{x} + \\mathbf{B} \\mathbf{u}$, where $\\mathbf{x} \\in \\mathbb{R}^n$, $\\mathbf{u} \\in \\mathbb{R}^m$, find all states that can be made into fixed points with a constant control law.\n", + "\n", + "\n", + "Let us find null space of the matrix $\\begin{bmatrix} \\mathbf{A} & \\mathbf{B} \\end{bmatrix}$ as $\\mathbf{N} = \\text{null} (\\begin{bmatrix} \\mathbf{A} & \\mathbf{B} \\end{bmatrix})$. \n", + "\n", + "We can find all $\\mathbf{x}$, $\\mathbf{u}$ pairs that produce equilibrium points as follows: $\\begin{bmatrix} \\mathbf{x} \\\\ \\mathbf{u} \\end{bmatrix} = \\mathbf{N} \\mathbf{z}$, $\\forall \\mathbf{z}$\n", + "\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "3bC4nO4oByAI", + "outputId": "5d278b0d-dfeb-4cd6-9067-fd53e393a661" + }, + "source": [ + "from numpy import hstack\n", + "A = [[0, 1],\n", + " [-2,-3]]\n", + "B = [[0], [1]]\n", + "\n", + "M = hstack((A,B))\n", + "\n", + "print(f'Stacked matrix:\\n {M}')\n", + "\n", + "U,S,VT = svd(M, full_matrices=True)\n", + "print(f'Left singular vectors:\\n {U}')\n", + "print(f'Singular values:\\n {S}')\n", + "print(f'Right singular vectors:\\n {VT.T}')" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Stacked matrix:\n", + " [[ 0 1 0]\n", + " [-2 -3 1]]\n", + "Left singular vectors:\n", + " [[-0.21452344 0.97671884]\n", + " [ 0.97671884 0.21452344]]\n", + "Singular values:\n", + " [3.82869567 0.58402865]\n", + "Right singular vectors:\n", + " [[-0.5102097 -0.73463328 0.4472136 ]\n", + " [-0.82134498 0.57043179 0. ]\n", + " [ 0.25510485 0.36731664 0.89442719]]\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "FfRXE6WnC35G" + }, + "source": [ + "\n", + "\n", + "\n", + "Given LTI system $\\dot{\\mathbf{x}} = \\mathbf{A} \\mathbf{x} + \\mathbf{B} \\mathbf{u}$, where $\\mathbf{x} \\in \\mathbb{R}^n$, $\\mathbf{u} \\in \\mathbb{R}^m$, \n", + "\n", + "1. check if $\\mathbf{x}_d$ can be transformed into a equilibrium point\n", + "2. find control constant $\\mathbf{u}_d$ that does it, given control law $\\mathbf{u} = \\mathbf{K}\\mathbf{x} + \\mathbf{u}_d$.\n", + "\n", + "\n", + " We can check that $(\\mathbf{A}-\\mathbf{B}\\mathbf{K}) \\mathbf{x}_d + \\mathbf{B} \\mathbf{u}_d = \\mathbf{0}$ has a solution, in other words that $-(\\mathbf{A}-\\mathbf{B}\\mathbf{K}) \\mathbf{x}^* \\in \\mathcal{C}(\\mathbf{B})$. Resulting condition is given via projection into the left null space of $\\mathbf{B}$: \n", + " $(\\mathbf{I} - \\mathbf{B}\\mathbf{B}^+)(\\mathbf{A}-\\mathbf{B}\\mathbf{K})\\mathbf{x}_d = \\mathbf{0}$\n", + "\n", + "This means finding such $\\mathbf{u}_d$ that $(\\mathbf{A}-\\mathbf{B}\\mathbf{K}) \\mathbf{x}_d + \\mathbf{B}\\mathbf{u}_d= \\mathbf{0}$. This is done via pseudo-inverse, which provides exact solution, as long as it exists: $\\mathbf{u}_d= -\\mathbf{B}^+(\\mathbf{A}-\\mathbf{B}\\mathbf{K}) \\mathbf{x}_d$.\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "CUzadWFLEs2I" + }, + "source": [ + "# ADD YOUR CODE HERE" + ], + "execution_count": null, + "outputs": [] + } + ] +} \ No newline at end of file diff --git a/legacy - ColabNotebooks/practice_09_lyapunov_functions.ipynb b/legacy - ColabNotebooks/practice_09_lyapunov_functions.ipynb new file mode 100644 index 0000000..90c110e --- /dev/null +++ b/legacy - ColabNotebooks/practice_09_lyapunov_functions.ipynb @@ -0,0 +1,917 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "[CT21] lab09_lyapunov_functions.ipynb", + "provenance": [], + "collapsed_sections": [], + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "zPmrTNlSBW-R" + }, + "source": [ + "# **Practice 9: Lyapunov Functions and Stability**\n", + "\n", + "---" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "DEdCnYFHUUSS" + }, + "source": [ + "## **Stability of the Linear Systems**\n", + "A linear system in form:\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{x}} (t)=\\mathbf{A}\\mathbf{x}(t)\n", + "\\end{equation}\n", + "\n", + "Is said to be **assymptotically** stable (internally) if following holds:\n", + "\\begin{equation}\n", + "\\Re(\\lambda_i) < 0, \\forall i \n", + "\\end{equation}\n", + "\n", + "\n", + "\n", + "One can easialy proof the fact above by directly solving ODE above, which may be done fairly easy by applying spectral decomposition:\n", + "\\begin{equation}\n", + "\\mathbf{x}(t) = e^{\\mathbf{A}t}\\mathbf{x}(0)=\\mathbf{Q}e^{\\mathbf{\\Lambda}t}\\mathbf{Q}^{-1} \\mathbf{x}(0) \n", + "\\end{equation}\n", + "\n", + "Linear system is said to be stable in the sense of Lyapunov (marginally stable) if: \n", + "\\begin{equation}\n", + "\\Re(\\lambda_i) \\leq 0, \\forall i \n", + "\\end{equation}\n", + "Note that additionally algebraic and geometric multiplicity of the zero eigenvalues should coincide. \n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "7anwqUrRZmMW" + }, + "source": [ + "### **Example:**\n", + "\n", + "Recall the mass spring damper system with state space representattion given as:\n", + "\n", + "\\begin{equation}\n", + "\\dot{\\mathbf{x}}\n", + " = \\mathbf{A}\\mathbf{x} =\n", + "\\begin{bmatrix}\n", + "\\dot{y}\\\\\n", + "\\ddot{y}\n", + "\\end{bmatrix}\n", + "=\n", + "\\begin{bmatrix}\n", + "0 & 1\\\\\n", + "-\\frac{k}{m} & -\\frac{b}{m}\n", + "\\end{bmatrix}\n", + " \\begin{bmatrix}\n", + "y\\\\\n", + "\\dot{y}\n", + "\\end{bmatrix}\n", + "\\end{equation}\n", + "\n", + "Let us numerically find the igen values of this matrix in order to analyze stability of the system:" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "Nrez8QSYanPJ", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "a51fc20a-89a3-444a-ad2d-7219254f930b" + }, + "source": [ + "from numpy.linalg import eig\n", + "from numpy import real\n", + "\n", + "m = 1\n", + "b = 2\n", + "k = 5\n", + "\n", + "A = [[0,1],\n", + " [-k/m, -b/m]]\n", + "\n", + "# One may find eigen system using following command \n", + "lambdas, Q = eig(A) # lambdas - is the array of eigen values and Q is the matrix with eigen vector on its columns v = Q[:,i]\n", + "print(f'Eigen values:\\n {lambdas}')\n", + "print(f'Real parts:\\n {real(lambdas)}')\n" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Eigen values:\n", + " [-1.+2.j -1.-2.j]\n", + "Real parts:\n", + " [-1. -1.]\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "XA5UTk7Ji181" + }, + "source": [ + "\n", + "We can obtain response by integrating the system " + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "Q5rqRbMCiyeH", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 861 + }, + "outputId": "578d5786-d827-4159-acf7-6444c8a504fc" + }, + "source": [ + "from numpy import dot, linspace\n", + "from scipy.integrate import odeint # import integrator routine\n", + "\n", + "def mbk_ode(x, t, A):\n", + " dx = dot(A,x)\n", + " return dx\n", + "\n", + "\n", + "t0 = 0 # Initial time \n", + "tf = 15 # Final time\n", + "N = int(2E3) # Numbers of points in time span\n", + "t = linspace(t0, tf, N) # Create time span\n", + "\n", + "x0 = [1,1]\n", + "x_sol = odeint(mbk_ode, x0, t, args=(A,)) # integrate system \"sys_ode\" from initial state $x0$\n", + "y, dy = x_sol[:,0], x_sol[:,1] # set theta, dtheta to be a respective solution of system states\n", + "\n", + "from matplotlib.pyplot import *\n", + "\n", + "title(r'Position response')\n", + "plot(t, y, 'r', linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'Position ${y}$ (m)')\n", + "xlabel(r'Time $t$ (s)')\n", + "show()\n", + "\n", + "title(r'Velocity response')\n", + "plot(t, dy, 'r', linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'Velocity $\\dot{y}$ (m/s)')\n", + "xlabel(r'Time $t$ (s)')\n", + "show()\n", + "\n", + "title(r'Phase portrait')\n", + "plot(y, dy, 'r', linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "ylabel(r'Position ${y}$ (m)')\n", + "xlabel(r'Velocity $t$ (s)')\n", + "show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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3yO7aOS0sc/jSlhcscxTiyJu47klClaLisY+XXoLbb4fXXnP78clPwoUXQs+ecSczxhQgKx5Jt3MnXHUV/P73Deffdhtccw1cdx184xuQuZrMGGMiUDAN5sOHD9dlvXvDY4/Bww/DmWfGHalZ1dXVFB1wAHzhC/DQQ9CpE3zta/DpT0N1tTsKefppt/C557pi0rVr/JmLimLN4FfaMqctL1jmKISZt+AbzGtqalJ15FFVVQXf+Y4rHL17wz//CbNmwZe+5I40nnoK/vY3OPBAuOceKC2F99+PP3PKpC1z2vKCZY5CHHl9Fw8R6S4i7cMIE6aNGzfuLR4puNpq0YQJcNNN7ojjoYdgZKMBE0VcIXn2WejXD/7xD/j8591prphkj9WcFmnLnLa8YJmjEEfeFouHiLQTkfEi8oCIbAJeBTaKyCsi8isRKQ4/ZkAyl+om/cjjww/5xssvu+kbboBR+xwx7nXcce70Vb9+7mjkootgz55ochpjClY+Rx5PAINwAzAdpqoDVLUPcArwHPALEbkoxIzBSctpqxkzOGTnThg+3J26asnAge7o5MAD4e67YerUFj9ijDFtkc/VVmeo6u7GM1W1GrgbuFtEOgaeLGB9+vRJR/HYvh1++Us3/atfQfs8zxAOG+baPs48E66/HkaPhrFjw8uZw4QJEyLdXhDSljltecEyRyGOvC0eeWQKh4hcICI9vOkpInKPiIzIXibJevbsmY7iMWcObNkCJ50EZ5zh77OnneZOcwFcfLG7JyRCY8aMiXR7QUhb5rTlBcschTjy+mkwn6Kq20TkFOB04GbgD+HECl5VVVXyi8eePXDjjQD8vKamdeu4+mo4/3zYtg3OOy/SiwPKysoi21ZQ0pY5bXnBMkchjrx+ikemFfZzwJ9U9QGgU/CRQpT0q60efRSqqmDgQJ477LDWrUMEbrkFhgyB5cvhW99KRS/Cxph08VM81ovITcCXgQdFpLPPz8cv6Ucet97qni+9dO/4I63RowfcdZe7afDWW10xMcaYAPn55f8lYBFQqqpbgCLgu6GkCkH37t2Tfanutm0wf76bvugiSkpK2ra+44+HP3hnFSdOhBdfbNv68tDmzDFIW+a05QXLHIU48rbYPYmIfAJ4TlPej8moUaN0yW9/CyefDCee6G6uS5I5c+C//st1ePjUU8Gt92tfg5tvhuJiWLLEXc5rjDF5akv3JF8FnheRO0TkEhFp5cn4eDW4wzyJRx533+2ev/IVAKZNmxbMen/3O/jYx1xbymWXhdr+EVjmCKUtc9rygmWOQhx587lU95uqOgL4KXAQMEdEnhWR60XkU2npqmTHjh3JLR47drjGcqi/N2Px4sXBrLtrV/jf/3XtIHffDb/9bTDrzSGwzBFKW+a05QXLHIU48ubd5qGqr6rqdFUdA5wGPA1cAPwrrHCBS+rVVo8+6vqkOuEEaO1VVs0ZPBj+8hc3ffXV8NxzwW/DGFNQ8i4eIjJKROaLyFJcwfgF8Olc58ISK6lHHvfd557DvFb7vPPgyiuhttZ1qPjee+Ftyxiz38t7PA8ReQ13ddVLQF1mvqq+GU60YI0aNUqXLF7suvtQdb9E8+36I0x1ddC3L2zaBP/+t+tmJCy7drnxQJ57Ds4+G+6/H9ql62prY0y0ghjP411VvU9V31DVNzOPADOGauvWre4Guszlukk5dfXii65wHHGEu7zWs3DhwuC31amTGwOkqMh1pPjznwe6+lAyhyxtmdOWFyxzFOLI66d4/EREZovIOBE5N/MILVnANm3a5CaSdurqscfc8xlnNBhKdtasWeFs74gj3KiD4HrfDfCHLrTMIUpb5rTlBcschTjy+ike/wUMB8YAZd7jnDBChSppjeaPP+6eTzstum2efTZMmeJOmZ13nhul0BhjfMinS/aMElUdElqSLCIyBrgRaA/MVtUbGr3fGbgVGAm8B3xZVdfktfIkHXns3r33hsBTT4122//937BunbsK63OfgyefdPeDGGNMHvwUj3+KyFBVfSW0NIB338gs4ExgHbBYRO5rtN3LgP+oarGIXIi78uvLza23b9++biJTPLZtCzq6f5WV7gjouOPg8MMbvDVlypRwty0Cf/oT/Oc/cO+98JnPwIMPwic+0epVBp75ww9h9WpYtco9Nm6EzZvd47334IMP3EUAmQe4dp3sR7du0LNnw0ePHvXTv/nUp9yl0j16uJ+NAw7YO90pef1+hv5zEQLLHL448vopHicCy0TkDaAGEEBV9aMBZxoNVKnqagARuQMYC2QXj7G4mxYB7gJmiog014VK586d3USPHu45CcWjmVNWxcURjO7boQPccQdceKErIGec4RrUz2nd2cg2Zd6xw10F9vzz7rF0qbsrPmTHNPdmp04NC0rnztCxY+5Hp07uyjXV/B91dQ0fueY1mj9i1y63naaWb24dre1dwG8nnY2WH1VX1/JVfa3pCDTEz4zMzpywbLk+MzKf77gt28nBT/GIarSRfsDarNfrgBOaWkZVa0XkfeBgYHP2QiJyBXAFQMeOHSkrK+O7L77Ip4C3X3+d7VVVTJ48uX75cePGMX78eMrLy6murgZg0KBBzJgxg5kzZ7Jo0aL6ZSsqKqiqqmow8PyECRMYM2ZMg771S0pKmDp1KtOmTWtwF+iCBQvYfO+99AZuePZZnikrY8qUKRQXF1NeXk5lZSWjR4+mtLSUiRMnMmnSJFatWgVAUVERFRUVzJ07l3nz5tWvc/r06QC+96ldXR3f6d+f09etg7Iy7hg8mHnHHEOdiK99ynwH2Y132fuUUVpaysRvfpP/+cpXOGTZMoa/+y7HbdlCh7q6BuuqFaHuiCPYfcQRPPnWW2zu2pWtnTrxsdNP51Nf/CJTf/EL3tu2jdp27eg3cCBTp07ltr/8hWf/7//oqEqHujqmXn01b7/+OvfPnUvX2lq61dbyyY9+lKN79+aJv/+dmnffpW+PHvTu0oV+PXvy/oYNtP/gA7rW1tJ+1y6ornaPhPDzHzYp0ngxeAIu4vcljrz5dIzY7F/0+S6TdyCR84Exqvo17/XFwAmqOjFrmZe9ZdZ5r1d5y2zOtU6AXr166ZYtW+Dyy2H2bLjpJrjiiiAit05dHRx0EGzdCuvX73PaqqysjAULFkSb55e/hB/9yE2PHu2+o+HD815Fi5lXrYJHHnGPxx93IyZmtGsHI0a4u+xHjICRI2HoUPdXfYiazKwKNTWubWz7dnekWlPj2qlyPXbt2vuXvUjLj3btGj5yzcsxf/JVVzF9xoy8lt1nfmv+4vT73zrH8pdccglz5swJbhsRfObSSy/llltuSWS2XJ+5/PLL+fOf/xz8dlSRY47JeZ9HPn/IPCEidwN/V9W3MjNFpBNwClAOPAHM8ZeqSeuBAVmv+3vzci2zTkQ6AAfiGs5b1rOne966tY0x2+iVV1yGI47Yp3DEol07uOYaVzQuvti1x4wa5Tpq/P733S9yv955B554whWKRx+FN95o+P7RR7sx18880526O+igYPYlCCLQpYt79O4dd5p6Vb16ucKaIu917Qr9+8cdw5d3u3WDI4+MO0be3u7eHQYNinSb+RSPMcClwDwROQrYAnTBHSk9DMxQ1RcCzLQYGOxtaz1wITC+0TL34YrWs8D5wOMtHfn0zBSNzHPcbR6ZLuFPOinn26WlpRGGyXLaabBihbuUd9YsN5jUrbe6onLuua5L++OPd127Z/6SrauDd96hfPBg+P3v4YUXXPvFyy83XPdBB8Hpp7ticcYZrnjELLbvuZXSlhcscxRiyauqeT+AjkBfoJefz/l9AJ8FVgKrgB9586YBn/emuwD/C1QBlcDRLa1z5MiRqqqqv/mNazqcNEljdcklLseNN8abozmrVql+/euq3bvv29zbpYtq796qvXqpduyYu0m4a1fVs85SveEG1cpK1drauPfIGOMTsERz/E711ZalqrtVdaO6kQRDo6oPquoxqjpIVa/z5k1V1fu86Z2qeoGqFqvqaPWuzGrO2rVeG3xSTltlbsxr4shj0qRJEYZpwtFHwx//6LpPufNO+PrXXRvIAQe4XoA3b3btFrt3Q+/erD3kEPjqV2HGDPjHP9xlwIsWudNeJSXJ6EuskUR8zz6kLS9Y5ijEkTeNF2+0Sk1NjZtIwqW6mzfDypVurI0mbszLXFmVCN26wQUXuEfGtm2ugLRv797v0oVvlZWxoKIivpytkKjvOQ9pywuWOQpx5C2Y4lEvCUcelZXuedSo0K8mCk2PHnsLsTGm4PgZz+MREUlt/xUdOnh1MgkN5kuXuudRTQ+FUlRUFFGY4Fjm8KUtL1jmKMSR1894HiOA3wBrgB+q6sYQcwVu1KhRumTJEjdmxsc+5q4YeumleMKcey7Mnw9//StcdFE8GYwxJg++x/MQkaezX6vqUlU9FbgfWCgiPxGRrsFHDUfm7upEnLbKHHk0c73+3LlzIwoTHMscvrTlBcschTjyNlk8VPWUxvNERIDXgD8A3wZe9+4AT7x9ikdcp63eew/efNM1Mh/TdM9K2d2OpIVlDl/a8oJljkIcef20eTyDu2lvOq5vqUuAzwCjReRPYYQLRaaRd+vW1ncU1xaZo47hwxN56aoxxuTDz9VWVwCv6L6NJN8WkRUBZgpXx46uy4mdO12X3926Rbv9TPEYMSLa7RpjTIDyPvJQ1eU5CkfG5wLKE5oBA7K6y4rz1FWexSPTQ26aWObwpS0vWOYoxJE3kN6S87nDO1GyT11FLY/GcmOMSbo0drXfKvXdk0B8V1y9/74b4KhzZzd6YDOyx+RIC8scvrTlBcschTjy+mkw/7aIJKjP7DaIq4uSZcvc87Bh6b2z3Bhj8HfkcShuPPE7RWSMd9luOsV15JG5KbGJ/qyMMSYt/DSY/xgYDNyMu0z3dRG5XkSiHYGklRrcvh938Rg2rMVFx40bF3KY4Fnm8KUtL1jmKMSRN+/uSeo/4Pq3+i/cIFFPACcCj6jq94KPF5z67kkAvvENN8Tq738P3/xmdCFOPtl1xf7oo25QJGOMSTjf3ZPkWMGVIvI88EvgGWCYqn4TGAmcF1jSkKxZs2bviziOPFT3jqyXx5FHeXl5yIGCZ5nDl7a8YJmjEEdePzcJFgHnquqb2TNVtU5Ezgk2VvBqa2v3voijeKxd67Z3yCHQp0+Li9d3p5Iiljl8acsLljkKceT102DepXHhEJFfAKhqeu4wh3iutvLR3mGMMUnnp3icmWPe2UEFCVvnzp33vojjyCNzyur44/NafNCgVFyH0IBlDl/a8oJljkIceVtsMBeRbwLfAo4Gssc67AE8o6qpGJCiQYP53XfD+ee7cTXuvjuaABddBLffDn/6E1x+eTTbNMaYNmpLg/lcoAy4z3vOPEampXAAbNq0ae+LzGmr99+PLoCPxnKAmTNnhhgmHJY5fGnLC5Y5CnHkbbF4qOr7qrpGVcep6ptZj1S1KG3NPkV14IGZmdFsfPduWOE1C33kI3l9ZNGiRSEGCodlDl/a8oJljkIceVu82kpEnlbVU0RkG5B9jksAVdWeoaULS69e7nnLlmi2V1UFu3bBwIF7j3qMMSbFWiwemREFVXX/+a0XdfHIXGmVZ2O5McYkne87zNNq+PDhuizTMeHOndC1q+ucsKYGwu6ma+pUuPZa+MEP4Prr8/pIdXV1wy5VUsAyhy9tecEyRyHMvEHcYV4hIr2yXh8kIrcEFTBsNTU1e1906eIeu3e70QTDtny5ex46NO+PVFVVhRQmPJY5fGnLC5Y5CnHk9XOfx0dVtf48j6r+B/h48JHCsXHjxoYzojx19dpr7rmFMTyyXXvttSGFCY9lDl/a8oJljkIcef0Uj3bZ43mISBH+ujdJlqiKR20tvP66mx4yJNxtGWNMRPz88v8N8KyI/C/uSqvzgetCSRWFqIrHmjXuSqt+/eCAA8LdljHGRCTv4qGqt4rIEuA03CW756rqK6ElC1ifxp0RRlU8Mqesjj3W18cmTJgQQphwWebwpS0vWOYoxJHX72mnjrijjsx0avTs2eh2lKiKx6uvumefxWPMmDEhhAmXZQ5f2vKCZY5CHHl9jecB3A70BvoAt4nIt8MKFrR9rkZIeNsbNf0AABXpSURBVPEoKysLIUy4LHP40pYXLHMU4sjr58jjMuAEVd0B9d2xPwv8LqgwXiP834CBwBrgS95VXY2X2wN4d97xlqp+3vfGoj5tZY3lxpj9iJ+rrQTYk/V6D3tPYQXlGuAxVR0MPOa9zuVDVR3uPfwXDkj8kYcxxiSZnyOPvwD/EpH53usvADcHnGcs8BlvugJ4Evh+ECvu3r17wxlRFI/qanj3Xeje3V1t5UNJSUlIocJjmcOXtrxgmaMQR15f3ZOIyEjgZO/lP1T1hUDDiGxR1V7etAD/ybxutFwtsAyoBW5Q1XtbWneD8TwA/vY3uPBCuOACuPPOoHahoWefhZNOgo9/HJYuDWcbxhgToqa6J/F1tZWqPg8838YgjwKH5XjrR422pSLSVGU7UlXXi8jRwOMi8pKqrmq8kIhcAVwB0LVr1waNSjedey6HAy888QRTvfnjxo1j/PjxlJeX148JPGjQIGbMmMHMmTMbdHtcUVFBVVVVgzs7J0yYwJgxY+q3c/ratUwCOPZYpk2bxuLFi+uXXbBgAQsXLmTWrFn186ZMmUJxcTHl5eWsXLmSY445htLSUiZOnMikSZNYtcrtYlFRERUVFcydO5d58+bVf3769OkATJ48uX5e0PsE7q+cqVOn7rNPJSUljB49usl9ykjSPmW+56b2qaV/p6j3aeXKlTz77LNt+neKep+GDx/OgAED2vTvFPU+rVy5kgceeKDV/05R71N1dTXV1dWh/Ow1SVWbfQDbgK3eY5/plj7v5wG8BvT1pvsCr+XxmTnA+S0td+CBB2oDzz2nCqolJRqa733PbeO//9v3R88555wQAoXLMocvbXlVLXMUwswLLNEcv1PzGQyqh6r29B77TLf0eZ/uAzIltRz4e+MFvA4ZO3vTvXGn0fzfrBhFm4ddaWWM2U/5uc9DROQiEZnivR4gIqMDznMDcKaIvA6c4b1GREaJyGxvmeOAJSLyIvAErs0jmcXDrrQyxuyn8m4wF5E/AHXAaap6nNdJ4sOqmorLEvZpMA97TI/du6FbN9izB7Zvd9PGGJMybR7PA3eD4ARgJ9R3yd4poHyh29p4vPKwx/RYvdr1qHvkka0qHAsXLgw+U8gsc/jSlhcscxTiyOuneOwWkfZ445iLyCG4I5FU2LRp074zwzx1lTll1cr2juwrLNLCMocvbXnBMkchjrx+isdvgflAHxG5DngayG9M1aSKonhYe4cxZj/U4n0eIjILmKuqt4vI88DpuG5JvqCqK8IOGKowi0cru2I3xpg0yOcmwZXAr0WkL3AnME8DvrM8Cn379t13ZqZ4eDfGBKqNp62mTJkSYJhoWObwpS0vWOYoxJE3n/s8blTVTwCfBt4DbhGRV0XkJyJyTOgJA9K5c+d9Zx58sHt+771gN6ba5tNWxcXFAQaKhmUOX9rygmWOQhx5827zUNU3VfUXqvpxYByuY8TUnLZas2bNvjPDKh6bN8N//gM9e8JhuXpiaVl29wNpYZnDl7a8YJmjEEdePzcJdhCRMhG5HXgI15XIuaEli0JYxSP7lFXQ948YY0wC5NNgfibuSOOzQCVwB3CFeoNCpVrYxcMay40x+6l8Gsx/AMwFrtIco/qlxT5jmEN4xSOAK61KS0sDChMdyxy+tOUFyxyFOPL6Gs8jzfbpngTgkUfgrLPg1FPh8ceD29g558ADD8Bdd8F55wW3XmOMiVgQ3ZOk2tq1a/edmeDTVpMmTQooTHQsc/jSlhcscxTiyFswxaOmpmbfmb17u+cgi0dNDbzxBrRrB224fC4zqEuaWObwpS0vWOYoxJG3YIpHTmEceVRVQV0dHH005Lq3xBhj9gMFUzw6dMhxbUC3bu4X/M6d8MEHwWyojXeWZxQVFQUQJlqWOXxpywuWOQpx5C3sBnOAfv1gwwZ480044oi2b+i66+DHP4arroJf/7rt6zPGmBgVfIN5dVP9VwV96iqgDhHnzp0bQJhoWebwpS0vWOYoxJHXikfQxSOg01bz5s0LIEy0LHP40pYXLHMU4shbMMWjSUEWjwA6RDTGmDSw4hFk8di4EbZtg6KivZcBG2PMfqhgiseAAQNyvxFk8chu72hjh4jTp09ve56IWebwpS0vWOYoxJG3YIpHk4IsHnbKyhhTIAqmeOTsngT2nl569922byTA4jF58uQ2ryNqljl8acsLljkKceQtmOLRpEMPdc/vvNP2ddmRhzGmQFjxyBSPTZvavi4rHsaYAlEwxaPJ2/eDOvLYsQPeegs6doSjjmrbuoBx48a1eR1Rs8zhS1tesMxRiCOvdU+yezd06uR6wd21C9q3b90GXngBRoyAoUNh+fK2hTXGmIQo+O5J1qxZk/uNjh3dFVd1dbB5c+s3EPApqzgGtG8ryxy+tOUFyxyFOPIWTPGora1t+s0gTl0F1C1JRpPdqSSYZQ5f2vKCZY5CHHkLpng0K8jiYY3lxpgCUDDFo3NzAzMFUTwC6k03Y9CgQYGsJ0qWOXxpywuWOQpx5LUGc4BJk+DGG+E3v4H/9//8r7yuDrp3d4NKbdkCBx7YtrDGGJMQBd9gvqm5+zjaeuTx1luucPTtG1jhmDlzZiDriZJlDl/a8oJljkIceRNVPETkAhFZLiJ1IrJPpctaboyIvCYiVSJyTT7r3rp1a9Nv9unjnltbPEJo71i0aFFg64qKZQ5f2vKCZY5CHHkTVTyAl4FzgaeaWkBE2gOzgLOBocA4ERnapq229cjDGsuNMQWmQ9wBsqnqCgBpvjvz0UCVqq72lr0DGAu80uoN9+3rnjdubN3nMzcFHndcqyMYY0yaJKp45KkfkN1F7jrghFwLisgVwBXguicpKyurfy/T//3kyZPpVVPDX4Gdq1fTBXfDTea66UGDBjFjxgxmzpzZ4NCwoqKCqqoqrr32Wn719NMcC1R+8AGjocF2SkpKmDp1KtOmTWPx4sX18xcsWMDChQuZNWtW/bwpU6ZQXFxMeXk5u3fvpqysjNLSUiZOnMikSZNYtWoVmX2pqKhg7ty5DYafzN6njHHjxjF+/Hjf+5QxYcIExowZk9c+VVRUNLtPGUnap8z33Np/p6j3affu3VRXV7fp3ynqferevXt9rrB+9oLep927d1NVVdXqf6eo96mioiK0n70mqWqkD+BR3Ompxo+xWcs8CYxq4vPnA7OzXl8MzGxpu8cee6w2ac8e1Y4dVUH1ww+bXi6XujrVHj3cZzdt8vfZZvzrX/8KbF1RsczhS1teVcschTDzAks0x+/UyNs8VPUMVT0+x+Pvea5iPZA9LGB/b16zNjZ3SqpdO+jXz1t7i6tqaO1aN/TsIYe4R0Cy/1pJC8scvrTlBcschTjyJq3BPB+LgcEicpSIdAIuBO5r81r793fP69b5+9zLL7vn449vcwRjjEmLRBUPEfmiiKwDPgE8ICKLvPmHi8iDAKpaC0wEFgErgDtVte3d2La2eGQay614GGMKSKIazFV1PjA/x/wNwGezXj8IPOhn3X0y93I0pa1HHh/5iL/PtWDChAmBri8Kljl8acsLljkKceS17kkybrzRdVMycSL87nf5r3jkSFi6FJ5+Gk4+ue1BjTEmQQq+e5LMZXdNas2Rx549sGKFmw74yCP7Ur60sMzhS1tesMxRiCNvwRSPFmWKx9q1zS+X7Y034MMP3ZVavXqFk8sYYxLIikdGa4rHSy+554CPOowxJukKpnh07969+QUOO8wNSbtpE3zwQX4rfeEF9zx8eNvC5VBSUhL4OsNmmcOXtrxgmaMQR15rMM92zDHw+uvuCqp8jibKyuD+++GOO+DLXw4mqDHGJEjBN5g3e4d5RmY0Lq9/mBYtXeqeR4xoXahmTJs2LfB1hs0yhy9tecEyRyGOvAVTPHbs2NHyQn6KxzvvwIYN0KPH3s8FKLuDtLSwzOFLW16wzFGII2/BFI+8+Cke2e0d7exrNMYUFvutl81P8QjxlJUxxiSdNZhne/llGDYMBg+GlSubX/aCC+Cuu2DOHMjqW98YY/YnBd9g3uwY5hlHHw0i7ua/XbuaXzZzjjGkI4+FCxeGst4wWebwpS0vWOYoxJG3YIrHpk2bWl6oWzdXQGprmz/y2LAB3nwTevaEoW0bPr0p2aOHpYVlDl/a8oJljkIceQumeORt2DD3nLl7PJd//tM9n3gitG8ffiZjjEkYKx6NZcblyHS1nsszz7jnk04KP48xxiRQwRSPvn375regnyOPELtgnzJlSmjrDotlDl/a8oJljkIceQumeHTu3Dm/BTNHHk0Vj+3b3WW67drBCScEEy6H4uLi0NYdFsscvrTlBcschTjyFkzxWLNmTX4LHnOMazhfswbefXff95980jWojx7t7i4PSXkKL/+1zOFLW16wzFGII2/BFI+8dejgCgPsPT2VbdEi93zWWdFlMsaYhLHikUumITzTMJ4tUzxKS6PLY4wxCVMwxaNnz575L5xpCH/qqYbzly93Xbb36rX36CQkpSksTpY5fGnLC5Y5CnHkte5Jctm+HXr3hpoad0Ng5kqtKVPgZz+Dyy6D2bPDC2uMMQlR8N2TrPUzvOwBB+xt07j3Xve8Zw/cdpubvvDCYMPlMGnSpNC3ETTLHL605QXLHIU48hZM8aipqfH3gfPOc8+zZ4Oq6wRxzRrX8+6ppwaer7FV+Q5IlSCWOXxpywuWOQpx5C2Y4uHbl74Effq4ezquvx6++103/+qrrUsSY0zBK5ji0aFDB38f6NoVMkM7/vjHsHYtlJTA5ZcHHy6HoqKiSLYTJMscvrTlBcschTjyWoN5c1Thl790p66OPx7++Ec49NBwAhpjTAIVfIN5dXW1/w+JwPe/7y7PnT8/0sIxd+7cyLYVFMscvrTlBcschTjyWvFIqHnz5sUdwTfLHL605QXLHIU48hZM8TDGGBMcKx7GGGN8K5gG82HDhulLzY3RkTBVVVWp6xbaMocvbXnBMkchzLyJbzAXkQtEZLmI1InIPkGzllsjIi+JyDIR8Xn5lDHGmCAkpngALwPnAk+1tCBwqqoOz1UNm+Kre5IEmDx5ctwRfLPM4UtbXrDMUYgjr88758KjqisARCTuKMYYY1qQpCOPfCnwsIg8LyJXxB3GGGMKUaRHHiLyKHBYjrd+pKp/z3M1p6jqehHpAzwiIq+qas5TXV5xyRSYGhF52X/q2PQWkc1xh/DJMocvbXnBMkchzLxH5pqZuKutRORJ4GpVbbExXER+CmxX1V/nsewSP20kcUtbXrDMUUhbXrDMUYgjb6pOW4lIdxHpkZkGzsI1tBtjjIlQYoqHiHxRRNYBnwAeEJFF3vzDReRBb7FDgadF5EWgEnhAVRfGk9gYYwpXkq62mg/MzzF/A/BZb3o18LFWbuJPrU8Xi7TlBcschbTlBcschcjzJq7NwxhjTPIl5rSVMcaY9LDiYYwxxrf9vniIyBgReU1EqkTkmrjztEREBojIEyLyitfX15VxZ8qHiLQXkRdE5P64s+RDRHqJyF0i8qqIrBCRT8SdqSUiMtn7mXhZROaJSJe4MzUmIreIyKbse6pEpEhEHhGR173ng+LMmK2JvL/yfi7+LSLzRaRXnBkby5U5672rRERFpHfYOfbr4iEi7YFZwNnAUGCciAyNN1WLaoGrVHUocCIwIQWZAa4EVsQdwocbgYWqeizuIoxEZxeRfsB3gFGqejzQHrgw3lQ5zQHGNJp3DfCYqg4GHvNeJ8Uc9s37CHC8qn4UWAn8IOpQLZjDvpkRkQG42xfeiiLEfl08gNFAlaquVtVdwB3A2JgzNUtVN6rqUm96G+6XWr94UzVPRPoDnwNmx50lHyJyIPAp4GYAVd2lqlviTZWXDkBXEekAdAM2xJxnH15vD42H7RwLVHjTFcAXIg3VjFx5VfVhVa31Xj4H9I88WDOa+I4BpgPfw3XhFLr9vXj0A7K7011Hwn8RZxORgcDHgX/Fm6RFM3A/tHVxB8nTUcC7wF+8U22zvZtOE0tV1wO/xv1VuRF4X1UfjjdV3g5V1Y3e9Nu4+7XS4lLgobhDtERExgLrVfXFqLa5vxeP1BKRA4C7gUmqujXuPE0RkXOATar6fNxZfOgAjAD+oKofB3aQrFMp+/DaCcbiCt/hQHcRuSjeVP6puzcgFfcHiMiPcKeRb487S3NEpBvwQ2BqlNvd34vHemBA1uv+3rxEE5GOuMJxu6reE3eeFpwMfF5E1uBOC54mIrfFG6lF64B1qpo5orsLV0yS7AzgDVV9V1V3A/cAJ8WcKV/viEhfAO95U8x5WiQilwDnAF/R5N8MNwj3R8WL3v/D/sBSEcnVCW1g9vfisRgYLCJHiUgnXAPjfTFnapa4AU1uBlao6v/EnaclqvoDVe2vqgNx3+/jqprov4hV9W1grYgM8WadDrwSY6R8vAWcKCLdvJ+R00l4I3+W+4Byb7ocyLcH7ViIyBjcadjPq+oHcedpiaq+pKp9VHWg9/9wHTDC+zkPzX5dPLxGr4nAItx/tDtVdXm8qVp0MnAx7i/4Zd7js3GH2g99G7hdRP4NDAeujzlPs7yjpLuApcBLuP+7ietCQ0TmAc8CQ0RknYhcBtwAnCkir+OOoG6IM2O2JvLOBHrghnxYJiJ/jDVkI01kjj5H8o/IjDHGJM1+feRhjDEmHFY8jDHG+GbFwxhjjG9WPIwxxvhmxcMYY4xvVjyMMcb4ZsXDGGOMb1Y8jGmGiBycdbPm2yKyPut1JxH5Z0jb7S8iX27iva4i8n/ekAO53u8kIk95ve8aEworHsY0Q1XfU9Xhqjoc+CMwPfPa68o9rP6lTqfp/rYuBe5R1T1NZN6FGzcjZ/ExJghWPIxpAxHZLiIDvZHn5ojIShG5XUTOEJFnvNHzRmctf5GIVHpHLjflOnoQkVOA/wHO95Y7utEiX8HrH0pEuovIAyLyojfCYKZg3OstZ0worHgYE4xi4DfAsd5jPHAKcDWuu2xE5Djc0cDJ3pHMHnL8glfVp3Gdeo71jnBWZ97zOvg8WlXXeLPGABtU9WPeCIMLvfkvAyVB76QxGVY8jAnGG17vpnXActywq4rrxHCgt8zpwEhgsYgs8143PqrIGAK8mmN+byB71MOXcJ0O/kJEPqmq7wN4p7R2iUiPNu6XMTlZg5oxwajJmq7Lel3H3v9nAlSoarNjYotIb9xIgbU53v4Q6JJ5oaorRWQE8FngZyLymKpO897uDOz0vSfG5MGOPIyJzmO4dow+ACJSJCJH5lhuIE2MT66q/wHai0gXbx2HAx+o6m3Ar/Aa2UXkYGCzN3CUMYGz4mFMRFT1FeDHwMPeOCKPAH1zLPoq0NtrAM91NdfDuPYUgGFApXca7CfAz7z5pwIPBJnfmGw2nocxKeOdppqsqhc3s8w9wDWqujK6ZKaQ2JGHMSmjqkuBJ5q7SRC41wqHCZMdeRhjjPHNjjyMMcb4ZsXDGGOMb1Y8jDHG+GbFwxhjjG9WPIwxxvhmxcMYY4xv/x9KhCl8WZAt3QAAAABJRU5ErkJggg==\n", 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\n", 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" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "QhkWybKleiJr" + }, + "source": [ + ">**HW EXERCISE**: \n", + "* Implement the Python routine that concludes a stability property of given linear system, test your routine on the randomly generated matrices $\\mathbf{A}$\n", + "\n", + ">**BONUS**: \n", + "* Compare the solutions given by numerical integration with one obtained 'analytically' by applying spectral decomposition" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "exj4xtx_Q9zJ" + }, + "source": [ + "## **Linearized systems**\n", + "\n", + "An approach above may be used to analyze the stability of the nonlinear systems in form:\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{x}} (t)=\\boldsymbol{f}\\big(\\mathbf{x}(t)\\big) \n", + "\\end{equation}\n", + "\n", + "To do so once may find the liniarized representation of the nonlinear system nearby equalibrium of interest as follows:\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{\\dot{\\tilde{x}}} (t) = \\frac{\\partial \\boldsymbol{f}}{\\partial \\mathbf{x}}\\mid_{\\mathbf{x}_e} \\tilde{x} =\\mathcal{J}(\\mathbf{x}_e)\\tilde{x}=\\mathbf{A}\\tilde{x}\n", + "\\end{equation}\n", + "where $\\tilde{x}= \\mathbf{x}_e - \\mathbf{x}(t)$ is the deviation from the equalibrium point.\n", + "\n", + "### **Example:**\n", + "\n", + "Consider the following system:\n", + "\n", + "\\begin{equation}\n", + "\\begin{cases}\n", + "\\dot{x}_1 = x_1 - x_1^3 + 2 x_1 x_2\\\\\n", + "\\dot{x}_2 = -x_2 + \\frac{1}{2}x_1 x_2\n", + "\\end{cases}\n", + "\\end{equation}\n", + "\n", + "Analyze the system stability in the following equalibrias:\n", + "\n", + "\\begin{equation}\n", + "x_{e_1} = \n", + "\\begin{bmatrix}\n", + "0 \\\\ \n", + "0\n", + "\\end{bmatrix},\n", + "\\quad\n", + "x_{e_2} = \n", + "\\begin{bmatrix}\n", + "1 \\\\ \n", + "0\n", + "\\end{bmatrix},\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "k2GgUHahkCL0" + }, + "source": [ + "\n", + "Sometimes finding jacobians of the state space equations is envolving, and one may use a symbolic routines instead.\n", + "\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "br09lunYkCn4", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "6a443918-c4d9-4a4c-a685-f30e73386196" + }, + "source": [ + "from sympy import Matrix, symbols\n", + "from sympy.utilities.lambdify import lambdify\n", + "from numpy.random import randn\n", + "\n", + "# Define vector for states \n", + "x = symbols('x1, x2') \n", + "\n", + "# Define state vector field: f(x)\n", + "f_symb = Matrix([x[0]- x[0]**3 + 2*x[0]*x[1],\n", + " -x[1] + x[0]*x[1]/2]) \n", + "\n", + "# Find analytical expression of jacobian\n", + "J_symb = Matrix([f_symb]).jacobian(x)\n", + "print(f'System Jacobian:\\n{J_symb}')" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "System Jacobian:\n", + "Matrix([[-3*x1**2 + 2*x2 + 1, 2*x1], [x2/2, x1/2 - 1]])\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "P3g3co5Jx7LF" + }, + "source": [ + "Now we can create a numerical function from the obtained system Jacobian:" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "RFzmo4xgx6Gh", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "bd542d22-bd64-456e-fe97-583905ceaa9f" + }, + "source": [ + "J_num = lambdify([x], J_symb)\n", + "\n", + "x_e = 1.0, 0.0 \n", + "A = J_num(x_e)\n", + "lambdas, Q = eig(A) \n", + "print(f'Eigen values:\\n {lambdas}')" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Eigen values:\n", + " [-2. -0.5]\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "NJgwK5GWxPkj", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 297 + }, + "outputId": "d73e493d-7879-4193-d94e-5e41e4816616" + }, + "source": [ + "from scipy.integrate import odeint # import integrator routine\n", + "\n", + "f_num = lambdify([x], f_symb)\n", + "\n", + "def sys_ode(x, t):\n", + " dx = f_num(x)[:,0]\n", + " return dx\n", + "\n", + "t0 = 0 # Initial time \n", + "tf = 100 # Final time\n", + "N = int(2E3) # Numbers of points in time span\n", + "t = linspace(t0, tf, N) # Create time span\n", + "\n", + "x0 = x_e + 0.1*randn(2)\n", + "x_sol = odeint(sys_ode, x0, t) # integrate system \"sys_ode\" from initial state $x0$\n", + "x_1, x_2 = x_sol[:,0], x_sol[:,1] # set theta, dtheta to be a respective solution of system states\n", + "\n", + "\n", + "title(r'Phase portrait')\n", + "plot(x_e[0], x_e[1], 'r', markersize=10, marker='o')\n", + "plot(x_1[0], x_2[0], 'r', markersize=10, marker=\"s\")\n", + "plot(x_1, x_2, 'r', linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlabel(r'${x_1}$')\n", + "ylabel(r'${x_2}$')\n", + "show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "zX3mPQQHzL6M" + }, + "source": [ + ">**HW EXERCISE**: \n", + "* Repeat the analysis above for stability points of nonlinear pendulum whose dynamics given by:\n", + "\\begin{equation}\n", + "\\dot{\\mathbf{x}} = \n", + "\\begin{bmatrix}\n", + "\\dot{\\theta} \\\\\n", + "\\ddot{\\theta} \n", + "\\end{bmatrix} \n", + "=\n", + "\\begin{bmatrix}\n", + "\\dot{\\theta} \\\\\n", + "-\\frac{1}{m L^2 + I}( mgL \\sin \\theta+b \\dot{\\theta})\n", + "\\end{bmatrix} \n", + "\\end{equation}\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "gMG8-wjxeF3x" + }, + "source": [ + "## **Lyapunov Direct Method**\n", + "In the Lyapunov Direct Method, we are trying to prove stability of an equilibrium for a given dynamical system ${\\dot{\\mathbf{x}}=\\boldsymbol{f}(\\mathbf{x})}$ by looking for **candidate Lyapunov function** $V(\\mathbf{x}):\\mathbb{R}^{n}\\rightarrow \\mathbb{R} $ that satisfies the following conditions:\n", + "\n", + "\n", + "\n", + ">* $V(\\mathbf{x})=0$ if and only if $\\mathbf{x}=\\mathbf{0}$\n", + ">* $V(\\mathbf{x})>0$ if and only if $\\mathbf{x}\\neq\\mathbf{0}$\n", + ">* $\\dot{V}(\\mathbf{x}) \\leq 0$ if and only if $\\mathbf{x}\\neq\\mathbf{0}$ \n", + "\n", + "This is known as the criteria of **asymptotic stability** of the equilibrium of ${\\dot{\\mathbf{x}}=\\boldsymbol{f}(\\mathbf{x})}$\n", + " \n", + "In two dimensions $\\mathbf{x}\\in\\mathbb{R}^2$ one can interpret the stability criteria above geometrically by thinking of a projection of system dynamics vector $\\boldsymbol{f}$ onto the gradient of $V$. \n", + "\n", + "\n", + "### **Example:**\n", + "\n", + "Consider the following system:\n", + "\\begin{equation}\n", + "\\begin{cases}\n", + "\\dot{x}_1 = -x_1 + x_2 \\\\ \n", + "\\dot{x}_2 = -x_1 - x_2^3\n", + "\\end{cases}\n", + "\\end{equation}\n", + "\n", + "with following Lyapunov candidate:\n", + "\\begin{equation}\n", + "V(\\mathbf{x}) = x_1^2 + x_2^2 \n", + "\\end{equation}\n", + "\n", + "One may use a chain rule in order to find $\\dot{V}$ as follows:\n", + "\\begin{equation}\n", + "\\dot{V} = \\sum_{i=1}^n\\frac{\\partial V}{\\partial \\mathbf{x}_i}\\mathbf{\\dot{x}}_i = \\sum_{i=1}^n\\frac{\\partial V}{\\partial \\mathbf{x}_i}\\boldsymbol{f}_i = \\nabla V \\cdot \\boldsymbol{f}\n", + "\\end{equation}\n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "zngMQVsWh-Ee" + }, + "source": [ + "Let's use symbolical tools in order to find the derevitive of Lyapunov function:" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "gBuo-G-Dh5AA", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "94a848ac-fccf-409f-da3a-e3c64e7f253f" + }, + "source": [ + " from sympy import simplify\n", + " x = symbols('x_1, x_2')\n", + " V_symb = x[0]**2 + x[1]**2\n", + "\n", + " grad_V = Matrix([V_symb]).jacobian(x)\n", + " print(f'Gradient of Lyapunov candidate:\\n {grad_V}')\n", + " \n", + " f_symb = Matrix([-x[0] + x[1],\n", + " -x[0] - x[1]**3])\n", + " \n", + " dV = simplify(grad_V*f_symb) \n", + " print(f'Time derevitive of Lyapunov candidate:\\n {dV}')\n", + " " + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Gradient of Lyapunov candidate:\n", + " Matrix([[2*x_1, 2*x_2]])\n", + "Time derevitive of Lyapunov candidate:\n", + " Matrix([[-2*x_1**2 - 2*x_2**4]])\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "DFf9gVuPLH6r", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "e13f4733-1822-49fc-b9bc-d35b0c5320e0" + }, + "source": [ + " from sympy import simplify\n", + " x = symbols('x_1, x_2')\n", + " V_symb = 4*x[0]**2 + 2*x[1]**2 + 4*x[0]**4 \n", + "\n", + " grad_V = Matrix([V_symb]).jacobian(x)\n", + " print(f'Gradient of Lyapunov candidate:\\n {grad_V}')\n", + " \n", + " f_symb = Matrix([x[1] - x[0],\n", + " -2*x[0] - 2*x[1] - 4*x[0]**3])\n", + " \n", + " dV = simplify(grad_V*f_symb) \n", + " print(f'Time derevitive of Lyapunov candidate:\\n {dV}')\n", + " " + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Gradient of Lyapunov candidate:\n", + " Matrix([[16*x_1**3 + 8*x_1, 4*x_2]])\n", + "Time derevitive of Lyapunov candidate:\n", + " Matrix([[-16*x_1**4 - 8*x_1**2 - 8*x_2**2]])\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "iEHIN_gajGgE" + }, + "source": [ + "Clearly with choosen Lyapunov candidate the system is stable (in fact globally asymptotically stable)\n", + "\n", + "Let us now visualyse response of the system:\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "wswnRpqalnAl", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 297 + }, + "outputId": "3897e18e-7418-46bb-bc1f-4674268a8936" + }, + "source": [ + "# Create a numerical function from symbolic one\n", + "f_num = lambdify([x], f_symb)\n", + "\n", + "def sys_ode(x, t):\n", + " dx = f_num(x)[:,0]\n", + " return dx\n", + "\n", + "t0 = 0 # Initial time \n", + "tf = 100 # Final time\n", + "N = int(2E3) # Numbers of points in time span\n", + "t = linspace(t0, tf, N) # Create time span\n", + "\n", + "x_e = 0, 0 \n", + "x0 = randn(2)\n", + "x_sol = odeint(sys_ode, x0, t) # integrate system \"sys_ode\" from initial state $x0$\n", + "x_1, x_2 = x_sol[:,0], x_sol[:,1] # set theta, dtheta to be a respective solution of system states\n", + "\n", + "\n", + "title(r'Phase portrait')\n", + "plot(x_e[0], x_e[1], 'r', markersize=10, marker='o')\n", + "plot(x_1[0], x_2[0], 'r', markersize=10, marker=\"s\")\n", + "plot(x_1, x_2, 'r', linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlabel(r'${x_1}$')\n", + "ylabel(r'${x_2}$')\n", + "show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Ugayq1mvlRlC" + }, + "source": [ + "Lets plot response of the system together with our choosen Lyapunov candidate:" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "CiyUp-W4eEra", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 575 + }, + "outputId": "2b0bde26-5d93-45e9-bbda-6a0ad111227c" + }, + "source": [ + "V_num = lambdify([x], V_symb)\n", + "\n", + "N = 1000\n", + "x_max = max(abs(x_1[0]),abs(x_2[0]))\n", + "\n", + "x1 = linspace(-x_max, x_max, N)\n", + "x2 = linspace(-x_max, x_max, N)\n", + "X_1, X_2 = np.meshgrid(x1, x2)\n", + "\n", + "\n", + "V_gen = X_1**2 + X_2**2\n", + "# V_gen = V_num([X_1, X_2])\n", + "# V with solution x(t)\n", + "V_sol = np.zeros((len(x_1),), dtype = float)\n", + "for i in range (len(x_1)):\n", + " V_sol[i] = x_1[i]**2 + x_2[i]**2 \n", + "\n", + "fig = figure(figsize=(10,10))\n", + "ax = fig.gca(projection='3d')\n", + "surf = ax.plot_surface(X_1, X_2, V_gen, cmap = cm.coolwarm, alpha = 0.3)\n", + "ax.plot(x_1, x_2, V_sol, 'r', label=r'solution $\\mathbf{x}(t)$')\n", + "title(r'Lyapunov candidate $V(x)$ with the solution $\\mathbf{x}(t)$')\n", + "fig.colorbar(surf, shrink=1, aspect=10)\n", + "ax.legend(loc = 'lower right')\n", + "show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Qx8-P6NGtTmK" + }, + "source": [ + "## **Linear Systems, Lyapunov Equations**\n", + "It may be shown that for linear system:\n", + "\n", + "\\begin{equation}\n", + "\\dot{\\mathbf{x}} = \\mathbf{A}\\mathbf{x}\n", + "\\end{equation}\n", + "\n", + "if one would choose Lyapunov candidate as:\n", + "\n", + "\\begin{equation}\n", + "V(\\mathbf{x}) = \\mathbf{x}^T\\mathbf{S}\\mathbf{x}\n", + "\\end{equation}\n", + "\n", + "with derevitive given by:\n", + "\\begin{equation}\n", + " \\dot V(\\mathbf{x}) = (\\mathbf{A}\\mathbf{x})^T\\mathbf{S}\\mathbf{x} + \n", + " \\mathbf{x}^T\\mathbf{S}\\mathbf{A}\\mathbf{x} = \n", + " \\mathbf{x}^T(\\mathbf{A}^\\top\\mathbf{S} + \\mathbf{S}\\mathbf{A})\\mathbf{x}\n", + "\\end{equation}\n", + "\n", + "thus system should be stable provided the solution of the following equation exist:\n", + "\n", + "\\begin{equation}\n", + " \\mathbf{A}^\\top\\mathbf{S} + \\mathbf{S}\\mathbf{A} = -\\mathbf{Q}\n", + "\\end{equation}\n", + "\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "dguJXY3qvRJF", + "outputId": "4b48720b-7568-4e95-8676-08dec56a999f" + }, + "source": [ + "from scipy.linalg import solve_continuous_lyapunov as lyap\n", + "from numpy import eye\n", + "A = [[1,1],\n", + " [-1,-2]]\n", + "\n", + "Q = eye(2)\n", + "\n", + "print(lyap(A, Q))" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "[[ 2. -1.5]\n", + " [-1.5 0.5]]\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "lT5s7G82vVdD" + }, + "source": [ + "\n", + "### **Example:**\n", + "\n", + "Consider again the mass spring damper:" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 857 + }, + "id": "Czx0qK_gvYu_", + "outputId": "a50b852f-7d25-4e67-b7cf-36a9887337f1" + }, + "source": [ + "m = 1\n", + "b = 0.5\n", + "k = 2\n", + "\n", + "A = [[0,1],\n", + " [-k/m, -b/m]]\n", + " \n", + "t0 = 0 # Initial time \n", + "tf = 15 # Final time\n", + "N = int(2E3) # Numbers of points in time span\n", + "t = linspace(t0, tf, N) # Create time span\n", + "\n", + "x0 = [0.3,0]\n", + "x_sol = odeint(mbk_ode, x0, t, args=(A,)) # integrate system \"sys_ode\" from initial state $x0$\n", + "x_1, x_2 = x_sol[:,0], x_sol[:,1] # set theta, dtheta to be a respective solution of system states\n", + "\n", + "N = 1000\n", + "x_max = max(abs(x_1[0]),abs(x_2[0]))\n", + "\n", + "x1 = linspace(-x_max, x_max, N)\n", + "x2 = linspace(-x_max, x_max, N)\n", + "X_1, X_2 = np.meshgrid(x1, x2)\n", + "\n", + "X = [X_1, X_2]\n", + "\n", + "# V_gen = \n", + "V_gen = X_1**2 + X_2**2\n", + "\n", + "V_sol = np.zeros((len(x_1),), dtype = float)\n", + "for i in range (len(x_1)):\n", + " V_sol[i] = x_1[i]**2 + x_2[i]**2 \n", + "\n", + "fig = figure(figsize=(10,10))\n", + "ax = fig.gca(projection='3d')\n", + "surf = ax.plot_surface(X_1, X_2, V_gen, cmap = cm.coolwarm, alpha = 0.3)\n", + "ax.plot(x_1, x_2, V_sol, 'r', label=r'solution $\\mathbf{x}(t)$')\n", + "title(r'Lyapunov candidate $V(x)$ with the solution $\\mathbf{x}(t)$')\n", + "fig.colorbar(surf, shrink=1, aspect=10)\n", + "ax.legend(loc = 'lower right')\n", + "show()\n", + "\n", + "title(r'Phase portrait')\n", + "plot(x_1, x_2, 'r', linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "ylabel(r'Position ${y}$ (m)')\n", + "xlabel(r'Velocity $t$ (s)')\n", + "show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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\n", 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" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + } + ] +} \ No newline at end of file diff --git a/legacy - ColabNotebooks/practice_10_observers.ipynb b/legacy - ColabNotebooks/practice_10_observers.ipynb new file mode 100644 index 0000000..6db4e87 --- /dev/null +++ b/legacy - ColabNotebooks/practice_10_observers.ipynb @@ -0,0 +1,1061 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "[CT21] 10_observers.ipynb", + "provenance": [], + "collapsed_sections": [], + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "zPmrTNlSBW-R" + }, + "source": [ + "# **Practice 10: State Observers**\n", + "\n", + "---" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "DEdCnYFHUUSS" + }, + "source": [ + "## **Motivation**\n", + "\n", + "Recall the structure of the all previously derived controllers:\n", + "\\begin{equation}\n", + "\\begin{cases}\n", + "\\dot {\\mathbf{x}} = \\mathbf{A} \\mathbf{x} + \\mathbf{B} \\mathbf{u}\\\\\n", + "\\mathbf{u} = \\mathbf{K} \\mathbf{x}\n", + "\\end{cases}\n", + "\\end{equation}\n", + "\n", + "You may see that control is function of system state $\\mathbf{x}$, we call such controllers **full-state** feedback.\n", + "\n", + "However, in most practical cases, the physical state of the system cannot be determined by direct observation. Instead, indirect effects of the internal state are observed by way of the system outputs. \n", + "\n", + "A simple example is that of vehicles in a tunnel: the rates and velocities at which vehicles enter and leave the tunnel can be observed directly, but the exact state inside the tunnel can only be estimated. If a system is observable, it is possible to fully reconstruct the system state from its output measurements using the state observer.\n", + "\n", + "In many cases the outputs $\\mathbf{y} \\in \\mathbb{R}^{q}$ are given as linear function of states:\n", + "\\begin{equation}\n", + " \\mathbf{y} = \\mathbf{C}\\mathbf{x}\n", + "\\end{equation}\n", + "\n", + "where $\\mathbf{C}\\in \\mathbb{R}^{q \\times n}$ is so called output matrix. \n", + "\n", + "Thus the overall system from input $\\mathbf{u}$ to output $\\mathbf{y}$ is represented as follows:\n", + "\\begin{equation}\n", + "\\begin{cases}\n", + "\\dot {\\mathbf{x}} = \\mathbf{A} \\mathbf{x} + \\mathbf{B} \\mathbf{u}\n", + "\\\\\n", + "\\mathbf{y} = \\mathbf{C}\\mathbf{x}\n", + "\\end{cases}\n", + "\\end{equation}\n", + "\n", + "\n", + "And our goal is to deduce the internal **state** $\\mathbf{x}$ by means of **estimates** $\\hat{\\mathbf{x}}$ using the measurements of **output** $\\mathbf{y}$ and knowledge of the system dynamics. To do so we introduce the new system, namely **observer**, which provides the estimate of **states** based on the system output \n", + "\n", + "\n", + "\n", + "

\"mbk\"

\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "u8MGmtB_u5Li" + }, + "source": [ + "### **Open Loop Observer**\n", + "\n", + "Suppose that somehow you manage to get the initial conditions of the system $\\mathbf{x}(0)$, a most straighforward idea is just use the system dynamics in order to advance the state forward in time by solving:\n", + "\\begin{equation}\n", + "\\dot{\\hat{\\mathbf{x}}} = \\mathbf{A} \\hat{\\mathbf{x}} + \\mathbf{B} \\mathbf{u} \n", + "\\end{equation}\n", + "starting from $\\hat{\\mathbf{x}}(0) = \\mathbf{x}(0)$, \n", + "\n", + "Let us simulate this naive aproach. \n", + "As banchmark we will use the cart-pole (inverted pendulum). " + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 439 + }, + "id": "PDK3AB3og9Q3", + "outputId": "d0a40ac5-8813-4ca5-9b30-fbed8cdd2f28" + }, + "source": [ + "import numpy as np\n", + "from scipy.integrate import odeint\n", + "\n", + "def system_ode(x, t, A, B):\n", + " u = [np.sin(t)]\n", + " dx = np.dot(A,x) + np.dot(B, u)\n", + " return dx\n", + "\n", + "t0 = 0 # Initial time \n", + "tf = 15 # Final time\n", + "N = int(2E3) # Numbers of points in time span\n", + "t = np.linspace(t0, tf, N) # Create time span\n", + "\n", + "x_real_0 = [0.3, 0] # Set initial state \n", + "x_hat_0 = [0.31, 0] # \n", + "\n", + "A = [[0, 1], \n", + " [-2, -0.1]]\n", + "A = np.array(A)\n", + "\n", + "B = [[0], \n", + " [1]]\n", + "B = np.array(B)\n", + "\n", + "A_obsv = A\n", + "\n", + "x_real = odeint(system_ode, x_real_0, t, args=(A,B,))\n", + "x_hat = odeint(system_ode, x_hat_0, t, args=(A_obsv,B,))\n", + "\n", + "\n", + "from matplotlib.pyplot import *\n", + "y, dy = x_real[:, 0], x_real[:, 1]\n", + "y_hat, dy_hat = x_hat[:, 0], x_hat[:, 1]\n", + "\n", + "figure(figsize=(9, 3))\n", + "plot(t, y, 'b--', linewidth=2.0)\n", + "plot(t, y_hat, 'b', linewidth=2.0)\n", + "plot(t, dy, 'r--', linewidth=2.0)\n", + "plot(t, dy_hat, 'r', linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'State ${x}$ (m)')\n", + "xlabel(r'Time $t$ (s)')\n", + "show()\n", + "\n", + "figure(figsize=(9, 3))\n", + "plot(t, y - y_hat, 'b', linewidth=2.0)\n", + "plot(t, dy - dy_hat, 'r', linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'Estimates Error ${x}$ (m)')\n", + "xlabel(r'Time $t$ (s)')\n", + "show()\n", + "\n", + "\n" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "J7WaZNTXkpbK" + }, + "source": [ + "### **Closed Loop - Luenberger Observer**\n", + "The open loop observer defined amathbfve did not use the knowledge of output $\\mathbf{y} = \\mathbf{C} \\mathbf{x}$. Thus the estimates $\\hat{\\mathbf{x}}$ may dyverge from the actual state of system $\\mathbf{x}$, especially in case when system is unstable, subject to noise, or poorly modeled. instead one may introdece the **correction term** $\\mathbf{L}(\\mathbf y - \\hat{\\mathbf y })$ that will compensate for following effects:\n", + "\\begin{equation}\n", + "\\hat{\\dot {\\mathbf{x}}} = \n", + "\\mathbf{A} \\hat{\\mathbf{x}} + \\mathbf{B} \\mathbf u + \n", + "\\mathbf{L}(\\mathbf y - \\mathbf{C}\\hat{\\mathbf x })\n", + "\\end{equation}\n", + "This is so called **Luenberger observer**.\n", + "\n", + "If one will introduce the **estimation error** as $\\mathbf{e} = \\hat{\\mathbf{x}} - \\mathbf{x}$ it is easy to show that it will satisfy the following:\n", + "\\begin{equation}\n", + "\\dot{\\mathbf{e}}= \n", + "(\\mathbf{A} - \\mathbf{L} \\mathbf{C}) \n", + "\\mathbf{e}\n", + "\\end{equation}\n", + "\n", + "Thus if all eigenvalues of matrix $\\mathbf{A} - \\mathbf{L} \\mathbf{C}$ have negative real parts, the estimation error will converge to zero. \n", + "\\begin{equation}\n", + "\\Re\\big[\\lambda_i(\\mathbf{A} - \\mathbf{L} \\mathbf{C})\n", + "\\big] < 0, \\forall i \n", + "\\end{equation}\n", + "\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "nv6sRQHrglm-" + }, + "source": [ + "import numpy as np\n", + "from scipy.integrate import odeint\n", + "from scipy.signal import place_poles\n", + "\n", + "\n", + "\n", + "def observer_ode(state, t, system_param, observer_params):\n", + " x, x_hat = np.split(state,2)\n", + " \n", + " A = system_param['A']\n", + " B = system_param['B']\n", + "\n", + " C = observer_params['C']\n", + " L = observer_params['L']\n", + " A_obs = observer_params['A']\n", + "\n", + " # \n", + " u = [np.sin(t)]\n", + " # \n", + " dx = np.dot(A,x) + np.dot(B, u)\n", + "\n", + " y = np.dot(C, x)\n", + " \n", + " # \n", + " y_hat = np.dot(C, x_hat)\n", + " e = y - y_hat\n", + " \n", + " dx_hat = np.dot(A_obs,x_hat) + np.dot(B, u) + np.dot(L, e)\n", + " # print(dx_hat)\n", + "\n", + " #\n", + " dstate = np.hstack((dx, dx_hat))\n", + " # dstate = dx, dx_hat\n", + " return dstate\n" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 439 + }, + "id": "BcT-s2uLlpPD", + "outputId": "49defb21-2ee8-4027-de80-25a1d5f3eb3a" + }, + "source": [ + "system_params = {'A':A,'B':B}\n", + "\n", + "A_obs = A \n", + "B_obs = B\n", + "\n", + "C = [[1, 0]]\n", + "\n", + "L = [[4], [10]]\n", + "Cov = [0.01]\n", + "Cov = np.array(Cov)\n", + "observer_params = {'A':A_obs,'C':C, 'L':L}\n", + "x_real_0 = [0.3, 0] # Set initial state \n", + "x_hat_0 = [1, 0] # \n", + "\n", + "state_0 = np.hstack((x_real_0, x_hat_0))\n", + "\n", + "state_sol = odeint(observer_ode, state_0, t, args=(system_params, observer_params, )) # integrate system \"sys_ode\" from initial state $x0$\n", + "\n", + "y, dy, y_hat, dy_hat = np.split(state_sol, 4, axis = 1)\n", + "\n", + "figure(figsize=(9, 3))\n", + "plot(t, y, 'b--', linewidth=2.0)\n", + "plot(t, y_hat, 'b', linewidth=2.0)\n", + "plot(t, dy, 'r--', linewidth=2.0)\n", + "plot(t, dy_hat, 'r', linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'State ${x}$')\n", + "xlabel(r'Time $t$ (s)')\n", + "show()\n", + "\n", + "figure(figsize=(9, 3))\n", + "plot(t, y - y_hat, 'b', linewidth=2.0)\n", + "plot(t, dy - dy_hat, 'r', linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'Estimation Error ${x}$')\n", + "xlabel(r'Time $t$ (s)')\n", + "show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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/91RpDKUYgiAMAS9FwdOzZqa05bNmzQIAjLJIbRsSEoK+ffsiNDQUSUk8ORQQEIDZs2dj7ty5iI2NNR8bFRWF+Ph4TJkyxfzZ8OHDERwcnKmehg0bIiIiApGRkZkCDUVHRyMmJibT2uOkSZNQpUoVhIaGmj9r164dwsLCEB4ejrNnzwIA/P39ERUVheXLl2OFRaI9W9tUtmxZNGrUKFe1yZHfKSIiAl5eXrmqTfb+Tu8dPIjWAO7UrAmqXBmhFudrsU1Fi/bCgQP9ARBSU2eiS5cdUpvi4nCrZEn0u3MHe3r3hmHdOod+p7S0NHh5eSnapjJltuHq1Rcxe7YRPj4zMWPGWE32va1bt2aS363uES1a4F7r1iiSno7DxYphSWAgZgMO971atWqhUaNGzrVp82bce+YZFHn0CKbgYHzyyisYHxur6XuEtTaJ14ja94gssTbCUWND9jMzCwCEWLw/BaBMzmUG0e3bco4J3ZdOnTqpLYImyPN6OH2ayGAg8vSkN9q0UVsamyhdmh9sq1XL4oCEBH7qFQSHZ2dc0S9SUlhMgKh9e8Wrcxi3vUbu3iVq2JAV/MorRGlpThcpmy4SEoh8fVk2T0+3mRG1RCv9AlnMzLiLUck6AAMyvJqaALhLRDYlXvrrL2UF09FxKz7+mI02QkNxo0ABtaXJkS+/BK5f5/2VK7M4qGRJ9sgi4iitGsXHB4iI4P1Nm/JUWh/X8MIL7HZdrhzby3hqaOGhZEmO41SwIHveNWvGtjQ6sqGJwYwgCCsA7AbwnCAIVwRBGCQIwtuCILydcchGAOcAxAP4DoDNdyyNu8br6LiOAwcko0gZYrMoTXq65KT00ktA3brZHDxuHL+eOAGcPq24bI4yfnyG8TKkGDQ6MjBsmDQ6nDaNI/FqjWee4XxOPj5AaiqnTcglbttaQBODGSIKIaIyRORFROWIaDERzSei+RnfExENJ6IAIqpNRDaH9Y2J0ayTg0tp166d2iJogjyth+HD+bVsWeC55zSvi/ff55hjBoPkYZslnTtLowQHZmdcqYtFi/j15ElOB6Q1tN4vnmL3bo5KCLA79oABshUtuy4CAjjWjacnd+62bXnU7gZovV/k6nQGXl4NyGjcj2PH2ENORyfPcu2alH9m8WJoMqGRBWlpvFqQmMj/Tz/9ZMNJn38OfPghj37u3gUKFVJcTkd54w3OT2hz23SsYzTyIPbOHaBMGeDKFfdIIRAbC7z2Gg9owsKAr756Ormlk6SlAQcPciiDY8f4FvDoEX8uhgcoWBCoWJFj+5UsyZdNq1Ys2rPPyiqObGSVzkB1w18lt3z5qhNANHOmI2ZGuYt3331XbRE0QZ7VQ7dubHxYpIj5Iy3r4rvvWNzKlYkePrTxpPR0ycJ25Ei76nO1Li5cIPL2ZpvlXbtcWnWOaLlfPEWXLvx7CwLRiROyF6+oLnbs4E4g45/UuXNEw4axgXmBAly0o1uBAkRNmhB9+SUbr2ulX8DNDYAdQhDuA2Bju7zOWS3OZ6tAntRDSgoQHc37FkswWtXF48dAZCTvT50K2GynbDBwgDSApz3swNW6qFAB6NWL/zZEkbWCVvvFU/z5pxRSecIETpYqM4rqokULqZ+OHs1tcAAi4LvveCalcmUOjL1pE8/CPPcc0Lw50KUL8NFHvFz7999se3z4MM/YHDwI/P47J0KtXp1nawA+f88e4L33OAPEmjUdsWuXhs02rI1wcstWpIg/CQIPfu/fl2dU6K5oxa1ObfKkHkaO5EctL69M7qpa1UWfPixurVo82WIX//0nRac7cMDm09TQxdGj0lPwwoUurz5LtNovMmEyEb34IivvuecUq8YlumjfXuoI0dF2nfrZZ0SFCmWeUfH3J5o4kej6dcdFunGDaNo0Dlbp5ZW5/Bo1iIYOJbpyxfHynQF5cWbGy0tAo0ZsOL5li9rSqIu/v7/aImiCPKcHImD1at7v2TOTu6oWdZGYCPzyC+937+6A+cMzzwBDh/L+d9/ZfJoauqhVi72JASlVgxbQYr94ih9/BLZtA4oXB3buVKwal+hi/Xo2WgHYWOXixRxPOXyYTYU+/BB48IDNbZo25Yzyt24BU6YApUo5LlLx4ux5t38/T+xu3gwEBm5EmTI8q7NgAdu0NWjAsmgCayOc3LIFBQVRZCSPJgcNkmdUqKPjVmzdKj2u3bqltjQ50qEDi1uwoAOzMiLHjkmF3L0rq3xyc/689MQ7e7ba0rgJp09zfwaIfvwx5+PdgYQEonz5uE0lShA9fmz1sEePiMaN47h7Yr955RWia9dcI2ZqKtEnn7DpneVsTe3anEXCFSAvzswkJSWZ16PXrXMbDzhFWC7GF8nj5Dk9fPEFv44cCTzxlKk1XSQmSvZt48Y54ZRSsya7ZDx8KCXUzAG1dFGxIidVBtimQQtorV88RYcOnI26bl3g9dcVrcpluihZEvjjD55iuXEDaN36qUOWLmUbmBkz+L9s4EAOqRQby5nklWb58uXw8uJZxLt3WR7RQfLoUZ4ZatCAZ4ZUwdoIJ7dsvr6+ZDIRBQTw6HHHDnlGhu6IW6yDu4A8pYetW8lsNJaQ8NTXWtOF6Jji1KyMyPvvc2He3jYVpqYuLl6UnnC/+ko1McxorV9k4vvvJWX98Yfi1blcF59/LrVv+nQi4u776qvSx4GB6njAZaWLtWuJnn1Wks/Pj5uRnKyMHMiLMzMAD3S7deN9V2eB19FRlffe4/tLtWr85KdhkpLYdADgYHlOhwqJjORCUlOBOXOclk9Jnn0WaNmS9xcuVFcWTWMy8QwjADRuDLz8srryKMHo0Ww3AwDTpyPx71MoXx5Yu5Y/ql2bTYSaNlVPxCfp1o3NfJYvZ8+pO3c4wHjlymx3I8a0UZpcP5gBJNfHtWs17FamoyMnCQnAP//wvhjqX8OEhfFNL39+mZZbChRg11cAmD1bhgKV5ccfgcKF2VV29261pdEo777L1q4Gg2TUnhtZvZpzXTx4gButuuPO1YcAeJxz5Ajg56eyfFkQEgLs2MFLxTVrcpC+GTN4CWzbNhcIYG26JrdstWrVIiIio5GoZEmeAjt8WIZ5LjfkzJkzipWdmsrGX8uWEc2bx1PlixcTxcYSXb7MXpRaQUk9aIq+fbnDFy6c5SFa0cXjx0TlyrG4H30kY8G7dklz36dOZXuoFnQxfjxpIqO2FnTxFDduEHl4sIJCQ11WrVq6+GXRPTqB6kQAHUJdit3k7Lqr89iji8ePiXr0oExGwq1bE92+7bwcyGKZSUNpRZXDwwPo2pU9NdeuBerUUVsi9yUhgaPhHzrERminTgHx8RzoLCv8/Nges1Ej3ho35qdQHYUwmYA1a3g/NFRdWWzgxx85Cn3NmlJWaVlo2pR9TG/eZKtFca5eo7z3Hq+IbdrEKQ4Utm11L3r14htO/vy5fi1u505g4IjCqI6fsB8NUReHgeUDgeAf1RbNZry9gVWreCapWzfg/Hlg61Z2F58zB3j77ZzLsBtrI5zcsvn6+ppHczExZI6vpKWZAlfhjCHbjh1EnToR+fpmHmlbbh4eHEm+UCGeDMifP7P74JNblSpEX3/t+t9C08aNcjFrFivZYMg2WqQWdJGcTFSxIou7fLkCFYwezYX7+GRrCKwFXRARvfACi1umjHoyaEUXZq5fl9yWXey/7mpd/PmnlIageXOix28MlW6ay5a5VJYncUYXc+ZImRsAonfeIXrwwLGykFcNgEVeeoltIE+d4vDNOtlz/TonWS5UiI0T169ndzyAzRGCgoCoKA6qdO8e53tLSQHu3+f3YkKz5GTg+HF24xs2DChShMuIjwdGjOCywsKyn9nRsZPPP+fXFi00nWwRAEaNAi5cAIoV44dv2fnoI8DLizuYGxijiMmfr12TIvXneaZP55tLp05sN5NLmTYN6NiR752hoTyT4f39fClNQ2ioTQH1tMjIkRx6oVkzNnn69ls2Zv7rL/nq0MRgRhCEYEEQTgmCEC8Iwlgr3w8UBOGGIAiHMrbB9tbh6Qn07s37y5Y5L3NuJD0dWLmSL6hy5TjHx0O2PUP58twhz5/nz/bvBwYM4EFNdktG+fIBgYE8ZT5vHlu6r1/PKwCCwPeoefMAX1/gk09c085czZUrPBIFNG/4mp4OLFnC+50783Kw7BQqBISH876d+ZrUoE4djgwMSGLnac6dA+bP55vFtGlqS6MYs2cDEyey811oKPD99xbBunft4uU1oxFo0sR17kEy4+sL/O9//N9Rty7/l7Rty2O1//6ToQJr0zWu3AB4ADgLoDIAbwCHAQQ+ccxAAHPtLbtSpUqZpqf27uUprtKl2Sg4L7EsmynKe/eIwsJ4aUicBvT0JOralejdd4kSE5WR6c4dov79Jbs+gKh3b06voxTZ6SFXMHEiK7JnzxwPVVsXH38srYbdu6dgRSdPkjmATRYVqa0LS/7+W7oe/v7b9fVrSRdUtSoromtXVap3hS5++EH6vQMDs1gN3b5dyjnWsaPiMllDTl2kpkq3KvH/Zt48285FFstMWhjMNAUQa/F+HIBxTxzj0GAmKCgokxJMJrbVcFG8Jc1z5QoPHiwHE4JANHWqcgMYa9y9y5bv4lpxkSIcdCkv2jY5RUqK5La3fbva0uSIaIPlkntzo0Zc2ZAhLqjMeUQ7orp11ZZERdatk25MmzerLY0iREdLY5Rnn+U/+SwR3d0MBnVGuQrw22+ZH6KbNMn5wSarwYwWvJnKArhs8f4KgMZWjusuCEJLAKcBjCKiy1aOgSAIQwAMAQAfHx907tzZ/N2sWbPQvr0/vv7aH2+8sRXPP/8lQkJC0LdvX4SGhiIpKQkAEBAQgNmzZ2Pu3LmIjY01nx8VFYX4+HhMmTLF/Nnw4cMRHBycqZ6GDRsiIiICkZGRiIuLM38eHR2NmJgYzJs3z/zZpEmTUKVKFYRaeJ20a9cOYWFhCA8PN6eg9/f3R1RUFJYvX44VK1ZkahMAjBo1yvyZtTadPXsWJ06cwNy5c7Fy5SmcODEIt27VBSBk6C0dpUv/D7VqLURQUH+UKOG6Nq1fvxwpKSvQpEkJHD8+FAkJjfHBB0BExHU0a/YB8uW7I9vvVL58edSrV0+zv5Mzfe+tY8fQJTERCAxE5NatiBNtZ7Jok8lkwtKlS1Vp06VLbXD37igAhOTkgejcOclqm2T7nerVA/btQ/Lixeh19epTbTp06BDq1avnkt/Jljb5+/+DCxfG4fBhwsqVR9C2bXmX/U6NGzdGSYsgi2rd95b8+SeKA0CNGliekIAVT9zLXfE7Xb58GYcOHVLkHjFjxgaMHx8MwAPe3newbt1NXLyYfZverlABHS9eBHr3xuKwMPy2a5fLfifxGpG777VqlQ+HD3+Ka9cqY88ewM/vMZ5//nOUKbPXapuyxNoIx5UbgB4AFlm8748nZmEAFAPgk7E/FMAWW8q29GYSOX+eR8I+Phy6IK/QsWMn2rSJqG1baRQsRnt/+23t5OMzmXhpS5TPx4ct/OVCc54acmEySVNbb7xh0ylq6kKMK9OokYsqvHFD6lSrVz/1tRb7hTg7M3Gia+vVhC6WL5d+r7g41cRQShd37/KqJ8AeoDdv2nhiaiq7OQFEzZplmZBSCZTuF/PnSx6wgkA0c6b1JTdo2JvpPwDlLd6Xy/jMDBHdIiLR32URgCBHK6tYEWjfnp0b3MAe0HYeP+YMX5cusQHo3buA0YjHjzkuzJYti9C+PadyL1gQaNiQQ2/cusWW5aKXkdoIAhvDrV/PsQoePwZeeQX4+mu1JdM4ixaxG4QgADNnqi1Nthw/znbKABt/u4TixTmQDeA2hqRRUfz6zTcc+DZPISYIrV+fsxfmIkwmYPBgdqTw9AT27GFvPpvw8gJ++YWtaXfuzFUpHYYOBS5fZocRIu4CL71kuwOXFgYzcQCqCoJQSRAEbwB9AGRyShQEoYzF2y4A/rWlYB8fH6ufiwF7FixwQ8NwoxHYuxeYNYtDXjdoABQtym5DxYsDFSoAZcoAfn4gb2/cyl8WNQa/gG+TP8SH+b9G1Nu7cflsKvbtY+8hrXruduzIjgwlS3LHHjmS3XidJSAgwPlCtIj4B92o0VPZsbNCLV1kzDyjXz8X/8naYc8AACAASURBVE+NzXCUPHToqdGBFvtFixbs9ZeU5No4carrYu1a4OpV3l+8WFVRlNDFRx9xQLkiRYB9+6Qxts088wwwYQLv79jBrusuwBX9onRpftiJjuZ7/7ZtQNWqHNYjR6xN17h6A9ABbAtzFsCEjM8iAXTJ2J8B4DjY02krgOq2lPukAbCI0UhUvjxPZ8XE2DMRphImE9G2bUSDBxMVK5Z5ncjSHLxoUUotXY7u5C9Fd1GYjDBYP9bLiy0Lx44lunZN7dZly+PHRHXqSKJ/8YXaEmmQw4clBf3vf2pLky1Xr/LSpiAQnT7t4srT03ndEuC+7wb8/LN0eT98qLY0LiIoiBtdu7bakshORASZg4w6/d/Tpo20JrNnjyzyaYnERKKmTaVbW4UKRBcuZL3MpPpARsmtfPnyWSpqxgxufevW9inYpaSn89px3bqZByNVqhANGsQJkHbvJtP1BNrx6w36qu4i2oD29Ds68wWDNGrgf5aMBg+yOqgRjWbefJPo4EG1W5sl6emZbX2+/trxsr525mSt0ro1ORI2Vg1dvPYai/raay6vmunUiczxGSzQar9ITZUipw4d6po6VdXFv//yn7OXF9H+/erJkYGcuoiNle5hsoyl09Kkh9tChRQf7arRL9LTiQYMkPTGnrd5cDBjzQBY5M4ddgEGOEmi5ti1i6hhQ+lXLFmSaMIEoqNHzT7LyY9MtGHMdvrDtzulQsod8BD5qWLZVFq0KMM+bOVK+qR+faK1a4mWLmUXvxde4AvAcmATGMg3+7Nn1W17FnzxhSSqo1HNNWHcKCcPHrCrJsD+7Hbgal0kJkpuqN9959KqJY4cYSE8PIgSEswfa7lfDBzIOsuXzzXxsVTVRf/+pCUXerl0kZAgTQqWK5dtZg37OHlSiq1Rv75MhVpHzX4RGyv5Nzg9mAEwB4Bg6/Fa2LIbzBARjRvHGujSxS69KsvjxyyYeNcvU4Zo4UKOIZLBtWtE8wftoyMe0oxNGjwoPuBlujHjO1r99VVKS8tcbJYd8eRJolGjLHsKb717a9Ld66uvJBHDwuw/X8t/Wg6xahUrw9fX7n86V+uiZ08WtWBBlWMIibMzs2ZZfKTdfnH3rjRejYxUvj7VdLFlCzfU05PdTjWAHLpIT5c807y9FQgKumCBdFOcP1/mwiXUvkYePuS/KjkGM1MBRAMomPG+HYCdtp6vxgYEkbc33+cDAohatOD/6Pff5wR3CQlS/jIVvf8krl0jatyYBTIYiMaMyZQo8J9/+MHF05PoWVygx/Ci6yhJ070i6O6/2V8hOXbEmzeJhg3LnB0yf36ib7/VXPS69u0lESdPtu9ctS9I2XnxRVbEnDl2n+pKXaSkSF3r/fddVq11Vq9mQSwi0mm9X3TowCL7+Slfl2q6EKP91qunTv1WkEMXfftK96vff5dBKGuEhHAFRYoQnTmjSBVauUZkWWYC0BfsfbQTQCyAFvac7+oNCLJqJlKokPT//MEHZH6wfe89Tkz6778yTgPayrFjHAJSDAWZEeHRaOTVoR51T9NnGE0C0s3taGXYQf17pdg0ELt165Ztcly5wqHDLRXWsiWRree7AJMp8wrcDz/Yfq7NenAHjhwh81THnTt2n+5KXYixgzw9M00yqkNKirTE+vPPRKT9fnHxotTflyxRti5VdPHPP1IDNRSe3Vld/Pab1Kzhw2USyhomk2SQVrcu0aNHslehlWtEjpmZlzI8ibYBOAXgOVvPVWurXr06JSfz//CpU0RbtxL99BPRokWSYm7denqwIw54mjcn+vVX55WfI0ePEhUvzhU3aUKUkECJiUQffUQUWPEhRWIipYCtAEOxhCpWJPr0U/sckfbu3WufTFu2SDIJgnNWtwpgNBJVrkzmSaydO207z249aJkaNVgBffs6dLqrdGEZz69PH5dUmTO1arFAzz9PRO7RL8QBfGCgsvWoootmzbhxZcu6vu5scEYXycnS82nVqjIKlRV37kj5emrWlL14rVwjcgxmtgBonrFfG8AhAG1sPV+NLSebGSK+0U6ZQuYZug4dJLdtgO1lRaKi2Fuwf382Rv3zT3YVc8oo79QpMmXk00kICqYPRzwy198C2ykelc3C7KkxkPZGJzi06uPQFOG9e/zvIypj8GBFRvyO8uABUdGiZDaOtGUtWitTpU4THy/9Lhs3OlSEq3Qxc6Y0JrY50qnSiNn9BIHowQO36Bf//MNOPoLApm5K4XJd3Lgh2Qh+841r684BZ3QhzkY++yyHJHAJli5Tb70la9FauUZk92YCUAbALkfPd8Vmy2CGiD3cxKce0Yg+MZHjAFy/Lh0XFib1E8vNy4v94S2ZPZvtdn/4gQdEK1bwYGjuXKLjxzMOunWL7pTgkXQsXiYfJLOpCh7SLLxL6eAL3FS7ttPxQ5zqiEuWSKb4pUsThYdrxo7m3DnWP8Ch8XNaHtTKBek0ohFrsWJOFOEaXYgP3e3auaQ627CMOTN+vNv0i8GDFfmfyoTLdSHaexQsqML6fvY4qgsxR6anJ9G+fTILlROWvsy//CJbsVq5RhRxzQaQ35nzld5sHcwQscmK+Ke4apX1Yx484NhE8+dzPqNmzdjZCGC7XRGjUfI+sLYtXEhEqalkbMVBjw6iHhXEfQLYy25OwGwyv5k0SZb8G053xAMHeCAjNuL11zVz49m8WXKzz8kgWCsXpFOkpkrWtE4k7nGFLvbvZzELFya6fVvx6uxDtKotU8Zt+sXJk1IYFvNDkcy4VBdpadKNd+RI19VrI47o4tgxyVv6k08UECon0tPZ40X8D5FpGk8r10iejDNT1c6FylmzyPyAcOSI7ec9fMh2syIpKUSjR3MsugED2KShd2+ifv2I3nmHaOVKos1NJxIBdA2lqBwuUZky7HaZkED8Z9Wvn6xBozZt2uR8IVeuSD6GAPu0P+kDrhIxMXyTFwR+KsoKWfSgNmIYUU9Ppwa6rtCFuEqpugeTNQ4eNPfl7QsWqC2NzVSrxmK3aKFM+S69Rtau5cZ4e7ORicawVxfp6dIzn5+firfHW7ekTJZ+frIE1NPKvTNPDmaySmeQFSYTjyEyHtbo1Cm7Ts+x7O3b2eD8RWEbpUOgdAj0do1ttOHTo5Te9pVMQbw0y+3bmSMSd+mimRmaqVPJbBC8fbva0iiIGPWzQwe1JcmWffvI/HB46ZLa0mRBiRIspGohie1n7lwym/u4wy0jW8SQ/HYGfNQqQ4dKt0bVg7HGxUlLBBZhCNwdOQyABQCvA4jIeP8sgEa2nq/GZs8yk8ijR5mjwztrwH3zJtGXX7IHAkBUEPfpAtjE/UroeP5SXLt/5x3nKssGWacIk5OleDjikpMGbGiMRqJSpVikAgU42NiTaGWq1GH+/lvSu5PxJJTWhWiHVq6cotU4R0bkzHOFC6stic2YTJJneffu8pfvsmvk0CEyu45qbg2SsUcXBw9KdsxvvKGgUPbw3XeSUAsXOlWUVu6dWQ1m7Mma/Q2ApgBCMt7fBzDPjvPdgvz5OWNn69bAtWucufazz4DUVNvLePwYWL8eCAnhBKfvvQecOAGUKgXENvkYFXAJqF0bZS/t5i8fPwbeeosrcgfy5eN0pkFB/H7FCuDgQVVFAgAPD2DPHsDTE3j0iH+7XMfq1fzaujVQpYq6smTDpUtAXBzviwm9NUlEBODri0r37wNHj6otjU0IgpRF+LffgORkdeVxmNdf59d+/QA/P3VlcRKTCWjfnp8ySpQAFi1SW6IMBg+WhBk+HNi5U115FMSewUxjIhoOIAUAiOg2AG9FpFKZggWBmBhgxAgexIwZA9SoAcycCZw9yx3WkvR04NQp4LvveABTogTQuTPw889AWhp38l9/BS6vP4xmcbP5bnT+PLB1Kx/8++/AwoVAoULqNNgR8uUD/v4beP55VkDPnsD162pLhYoVpWv3yBFg3DhVxZGXBw+AJUt4/4sv1JUlB8Q/Wz8/YMAAdWXJlnz5gD59eD8qSl1Z7GDKFMDLiy+9Dz9UWxoHOHQIOHaM90X9uzHDhgEJCby/cSNgsOefVWnefBMID+c/ow4dgB071JZIGaxN11jbAOwF4AHgYMb7EgD+sfX8HMoOBgfiiwcw1sr3PgB+yfh+L4CKtpT7zDPPOD2lFRNDVL26NLMPEPn7E9Wpw/G2qlWTstpabvXqsQ3HhQsZBZlMmfOZA+xea+n7rSCT7Y37byv37xM1aMDtqV+f6MQJZeqxEzGIsSBktqNWTA+uQEz13qyZLMUppYv796WlerdQ944dZI6xoKE4Sjnx+ussdv788iagdMk10rw5Cy/DPVpJbNHFlSvSst+gQS4QyhHS0jiQnmhsHR9vdxFauXdCBpuZfgDWAbgCYFrG4KOXrednU64HgLMAKoNneg4DCHzimGEA5mfs9wHwiy1l22sAnBVpaewh0727ZHv55Fa2LFGPHpwI0aopg5gQsHRpog8/5ORgGrAzkYWEBMkV0NOTIxqrjNEoBTD293dNtmFFSU+XRs2Opgx3EW+9xWL6+LiJ3i11O2mS2tLYzO3bkgvw2rVqS2MHt25Jdhzz5qktjVOYTEQdO5LZHl8jvhDWuXxZSkZYpIhm7ZRywunBDJeB6gCGAwgDUMOec7MpsymAWIv34wCMe+KYWABNM/Y9AdyEDRm8axQoILsiTSaO5njgAG/Hj3P8mSy5do3o1Vd5tANw4kYVUHxUfeqUZMhcpIgmcjkdOSKFY5k+nT/TytOF3Xz+OZldtbLtcLajhC7S0yWPUM0+pVrhjBgGXmPh9HPis89Y7JYt5StT8WtEdBnVYJC8J8lJF2LCaj8/BbJhK8G+fdK0afnydvmOa+XemdVgxtPW5ShBED4lojEATlr5zBnKArhs8f4KgMZZHUNERkEQ7gIoBh7UPCnnEABDACAIwPqKFfF9YCDSPDwwa9YsAMCoUaPMx4eEhKBv374IDQ1FUlISACAgIACzZ8/G3LlzERsbaz42KioK8fHxmDJlivmz4cOHIzAwGJ07dzZ/1rBhQ0SMH49NXbuixZ9/olBaGn9RpQpiy5XDXItjJ02ahCpVqiA0NNT8Wbt27RAWFobw8HCcPXsWAODv74+oqCgsX74cK1asMB9ra5uOHz+OiIgIm9sUHGylTRERiIyMRJxo2QkgOjoaMTExmDdvHmo9/zym7dkDw717MDZvjtcqVwYJgmJtsuV3ql//eezbF4mICBM6dDBg3rx5ZvltaZOrf6es2vR7XBwMAA4XLYqJGTYGjv5OIrdv30ZYWJisbape/X08fPgivL0f4MqVN9C5c4rd15MzbXL0d0q5eRN/AMB//+Hi5s0YMWeOQ7+Tq9t07twYeHpOwo4dhdChQyQ2boxwuu+tXLkyk0xytslgMmH1pk3wApASEoKeXbva9Ts52iZHf6fTp09n2abvv9+OoUNbADCgbNlvceVKEPLlU+8eYWub+vfogV4rVwKXL+NU8eIYneEpkVPf27dvH+Li4lRvU5ZYG+FY25BhK/PEZ0dsPT+bcnsAWGTxvj+AuU8ccwxAOYv3ZwEUz6nsIHENqHZt18aU3rxZWp8U59sBc4ZeNXCZW52YiEdDj+bDh7M4lSsTvfJKT7XFsZ///U/S6eHDshWrRJ9o1YrFnDlT9qIVpVOnTtIack/36iOjR7PYNWrIU56i9woxGJSHhyyB3JQmO12ItpRFirjJcqol06dL95QuXWw6xe1dswVBeEcQhKMAnhME4YjFdh6AHL6M/wEob/G+XMZnVo8RBMETgC+AWzkVnGowAAEB7HLZuDEwciRw964MImfBf/8BwcFA27bA8eNApUrAO++w63WdOuzxk9t5/33gtdd4f/Fi4Kef1JUHwKefAv7+wLlzwL59k9UWx37ee49fK1TgfqRR1q8Htm8HihThSANuR0hG1IkNG9SVw07Ey+3ff9nBUNNs3cqvISFAgQLqyuIE33wDnMxYo1i2jMNCuBXjxvF/EwCsWwfMywVRVqyNcCw38MChIoAVACpYbP45nWvLBraBOQegEiQD4JpPHDMcmQ2AV9pSdpC3N9sXfPihZClXrJi8hk+WRrzJyWydX6gQj3wfPJBSsq9YIV+dWictTTIILlyY8zuozPz50oPIokVqS2MHiYmSseTixWpLky1itvdXX1VbEge5dUvqJL/9prY0dlGpEout6UCvhw9LtjJuanxKRHTvnmQvrlRKCZchhpMGOCuyGwCZDICLAmgEoKW42XN+NuV2AHAavHw0IeOzSABdMvbzAVgFds3eB6CyLeUGAdJg49AhngPv21fSitHIF5i9XkUmE2cTmzyZQ/vevCl9t2uX9F70YKpUSfUcRi7Pq3HjBlHRotz+8HDX1p0FjRqR2TNRA/bJtjFhgvQHIDNy9omtW6V7osuzBMuAWRctW3IjRo9WVyA7WblS0v/p086Vpdi9QvQlHzFCmfIVwJou2rYlsyd/UpIKQsnNF1+QOY5FNvfqXJObCcBg8LLSbQBbASQD2GLr+WpsQUDmJwCTKXMciQ0bWAUVKnAa7O+/ZxelhITMgw+TiQcpixezHUjVqtKdAyD6+uunNW4yEQUF8ffffGPDT6Qsqqx37tkjuRP9+qvr63+C27eJDIZUAvin0TwmE9t7AZwFVWbk7BOimAEBshXpUsy62LmTG1KmjOoPIPYihiJo08a5chS5V4izMoC8Se8U5kldbN4sNSOXpJNiQkOlhmWRVkfrNjP2DGaOZsyQHMp4Xx3Ar7aer8YWBBD9+2/WWlmwgKhkycwDE3ErUkQ6zmSS/E3FrVgxTou9aZN16y/xpliihCYCcanWEb/8kszTISoaQIvUrful+SecP19taXLgjz+kP1YFlurk6hMnT0qXhVvFO7HArAuTSXpY2bhRXaHsRLS9F4TMk8X2osi9okULqS+7EZa6MJmIXn7ZvQftWZKeLv1GAFH//k8dovXBjD1Bl1OIKAUABEHwIaKTAJ6z43x1EGNMW2PIEE7AtHcvMGMG0Ls3EBgIFCvGaQZEBIHzE/TuzWHkd+/m0P2LF7PBrzXrr2++4dfBgznhU14lPByoWZPzQvTvr3rKg/Llt6BpU95/7z0gJUVVcbJn9Gh+HTEC8PFRV5ZsGDqUX0uUALp1U1cWpxEEoGNH3hcNJN2EUaPYppaIfR00Q1IS8L//8f748erK4gSrVwN//gn4+ubCjAAGAzeqXTt+v3SpZFnuLlgb4VjbAKwF4AfgYwA7APwOYKOt56uxBTnjDu1MdN6EBJ6JMBgs8hmoy15n0387g6gPgPM/qBj5eO/evXTnDkcFBojGj1dNlOxZu1Z6Srp2TZEq5OgT169L9slffSWDUCqRSRd79ki6P3tWPaEcYNIkFrtsWaLHjx0rQ/Z7Rf/+LFSBApoPkvckoi4uXODg7W4xo+ssr70m9f8XXjCvPKj6H2IB5DAANp8EtALQBYCXI+e7agtSK/S7mEPHRv99V3BLbYtXSwvFDz5QTQxRDzt38p+whwfRP/+oJk7WVKtG5hhJCiFHn5g4kcUsVMi9s3M8pQtxtNunjzoCOUh6OvskAERRUY6VIeu9wjJVxLBh8pXrIkRdiCuPtWu73XjMMQYOlO7X3bsTJSer/x+SgdODGQCf2vKZlrYggGjcOLl0aBtGIxsUA5ylUiNoYr2zWzcyL+ofOqSKCJZ6GDGCzE+xmorfdfSodCP54w/FqnG2T6SkSFk6fvlFJqFU4ildDBtGSnmRKc2SJSx6jRqO/fHKeq+YMoWFMRg0dpHZRqdOnWjOHOly3LBBbYlcyNSpkq1os2bU95VX1JaIiLIezNhjM/Oylc/aO7S25UpcbaMRGwtcvMjB+l62prI8zMqVHL2OiHWTnq6qONOnsznTf/8BXbqoKkpmRozg11KlNN2HfvqJdVerFtCjh9rSyMzkjOCKDx9yNEA3om9foHBhDqL31VcqC/PDD/zarp1bBslLS8uPDz7g/VatgA4d1JXHpUyYAOzaBZQrB+zciYVbtgBRUWpLlSWORgA+mhEB+IjyIjpJdgbASiD+2IMGsVGVjoSXF7BxIxtZ3rgBLFmiqjiFCgGRkbz/118cCFN1bt7kMLoAMHasurJkQ1qaZJ88blwu7OrFiwPPZfg3TJ2qrix24u0N1K/P+9OnqyjIsWPA2bP8xCA6RLgZ+/ePR2oq37p+/11taVSgTh1gzx6galUUNBqBgQN5tGwyqS3ZU9hyC1oOoDOAdRmvnQF0AhBERK8rKJs8uHJm5vZt7vGCwJ47GqKdaKWuNo0bs0cYwO5E58+7tPon9TB6NFC9Ou/368dOV6oSFsYzVwULKu6S4kyfGDMGuHMH8PQEuneXUSiVsKoLUf9xcTx6cyO+/ZZfb9wA1qyx71zZ7hUZSQYxaBBQsaI8ZbqQzZuBW7fqAmBnV19flQVSi7JlgQMHcLNMGX6/YgX/nmfOqCrWU1hbe7LcADQEUNri/QCwJ9NXkCmlgVJbkGgQ4SrEmPlt27quTnfEZJIs5l94QfV0Bxcu8JI+wGY9qmE0EpUrR1qKmmyN9HSifPnIHe1j7SM9XUo+GRurtjR2U6sWi165sgqVHz3KIXIFgejMGRUEcI70dMkGXBX9aRXRlky0g/roI5eLACdsZhYASAUAQRBaAvgEwI8A7gJYKPvoSm4SElw3JSYuMQ0Y4Jr67CA8PFxtESQEAVi4kKfyd+0COnVyWdXW9FChghT+4rffgC1bXCZOZtasAa5c4aeezz5TvDpH+0RkJMfnMRikGQB3x6ouDAbg3Xd5X7T9cCNEe5lz53ilwFZkuVeEhfFsVqVKQJUqzpfnYtas4fA4gmBCdLTa0miD8PBwTki5dStnkzWZ2LasVSuO16YytgxmPIgoKWO/N4CFRLSGiCYB0HQvNQkCYDRyr1Sa06c5mF6hQpoMNnT27Fm1RchMsWKS0cXmzcDy5S6pNis9REbyoAbgWIo8CelCiCQDhzFjeJFeYRzpEyaTtErYoQPg5yezUCqRpS7EB5O1a4Fbt1wnkAy0bg2UL8/7b79t+3lO3yuSkqSoclp6iLKRu3elMWzNmt8iMFBdebSCuV+8+CKvX3bqxA+mO3awfdmXX6q6Tm/TYEYQBM+M/ZcAWD63elo5XjMYBYF3rlxRvrIff+TXHj3Y3kEnZ8aMAWrX5v0332QjDJUQBCAmhh0uzp7lZWGXMnUqcPgwh9EdONDFldvOzJnAgwesr+++U1saF1ChAkewTkmR/uHcCHHgefSoCx+eR43iwXn+/MDw4S6qVD5GjWJdNWkCVKgQq7Y42sTbG4iOBk6e5Oj49+8D77/PbnRDhqgSWt2WwcwKANsFQfgdnFzybwAQBKEKeKlJs6SLaQaUHswQSTMLGlxiAgB/f3+1RbDOli08C/H4MdC2reLVZaeH6tWBr7/m/ZEj+eHDJRDxKAEAGjUC8uVzSbX29gnLyaOXXwZKl1ZAKJXIVhfNm/OrG7qz9OwJtGnDM2pi384Jp+4VJhPwyy+8P3Cg27m5LVjATpYGA+8XK1ZUbZE0g9V+Ua0au4GuX88PYqmp/JTj6wu88YZrVkVErBnSPLkBaALgVQAFLT6rBqC+LednU64/gD8BnMl4LZrFcekADmVs62wtP0hMI/vtt7IbIWVi/36up3Rp60kndbJn8WLJqEyB7ND2YDIRvfQSi/Lccy6K9vn111L7r1xxQYWO8eefLGK+fJoWU34SE6Xfx82STxIR7d7Novv6Et29q3BlU6dKxqH37ytcmbw8eEDk48PiN22qtjRuSHIy0VtvEXl6SteLIBA1aUL011+yVQM50xnItQH4DMDYjP2xyCKiMIAHjpQf6OdHLknAM3YsaT1c97Jly9QWIXvEjK0eHkT//adYNbbo4eRJKd+QS35S0WOmVSsXVCZhT58wmdjxDCCaPl1BoVQiR12I8ezd9F+uZUsWv2fPnI916l4h9uV27RwvQyXat2fRPT2lrOOav2+6EJt18fAhD2oKFJAGNQBRw4ZEX37pdL4zrQ5mTgEok7FfBsCpLI5zaDBTPn9+buKAAU4pL1tMJqIqVbierVuVq8dJNJHOIDsePiQqXJj12K+fYtXYqofQUDI/WBw9qpg4kju/CkkN7ekTv/zCIhYrRnTvnoJCqUSOuhBnzwwGfgJ1M8QUBwDR+fPZH+vwveLwYemiiY93rAyV2L5d0o/lYF3z900XYrcu0tOJFixg33YxloO4eXlxoqsRI3jWxo4p8KwGMwJ/pw6CINwhIr+MfQHAbfH9E8cZwUtMRgCfENFv2ZQ5BMAQAPD39Ay6ZTTicLFimNi0KWZlBHEaNWqU+fiQkBD07dsXoaGhSMpY3wsICMDs2bMxd+5cxMZKBmBRUVGIj4/HlClTzJ+NDQ5Gs7Aw3PH2RujLL8MkCGjYsCEiIiIQGRmJuLg487HR0dGIiYnBvHnzzJ9NmjQJVapUQWhoqPmzdu3aISwsDOHh4WYLcn9/f0RFRWH58uVYYWGdamubjh8/jnPnztnUpuHDhyM4OBidO3c2f+aKNpV58ABf/f038qWn4/rs2Xhr82bZfiexTaVKlUKjRo1ybNP69TF47bVmSEsrjHz5bmDbtvOoWlWB32nECCApCSeKFsWYZs0capOjv9Pt27exbt26HNvk5+eP336LwoMHQOXKaxEY+H32bZLhd3J139u3bx8aNWqUdZv69IHRywueJhN+rlIFezp21HybRMQ21ahRCkZjYfj7H8HXXx/L8neqVasWKlWqZHebJl+9ivoHD2Jfw4aYUqqUS9okR98zmYA///wJaWm+qFABqF1batPp06dx6tQpTd3L1bqexGvEkTaNGTkSDRMS0PzaNTS9cQMeRiMsIQBCkSJIKlAAG3x9cb1AAdz19saYIUNwiQifrViBRx4eSPH0xPqNGw8QUQM8ibURjpwbgM0AjlnZugK488Sxt7MoneGdLgAAIABJREFUo2zGa2UAFwAE2FJ3iUKFeBRYtarNoz67mTCB6xg6VLk6ZMBtnjDEmQpfX6Jjx2Qv3h49bNsmPUiMHSu7KEQrVqg2K0Nkuy4mT5YeuK9dU1golbBJFx07kjkzqRtiaZp17lzWxzl0r0hIYIMTQSA6fdpxIVUgPFzSy5Ejmb9zm/umC5BNF8nJPGPTpg1RyZJSxFIbN7jzMtMT5/wAoIct5deqUYObmD8/LwfJjclEVK0a1/Hnn/KXLyNn3CUKp8lE9PzzrNMyZWS3wLVXD6++SubVBVnHGyYT28gARL17y1iw7diii7Q0vnwAotx8X7epX/z7LxtUGAxEly4pL5QCFC3Kv2Xz5lkf49C9IjiYC+7QwXHhVODWLcnMx9rqttvcN12AYrpITyfat4/o00+JRo4k+uADNu5q2ZKXp54Y7GQ1mFHbb24dAHFOLhScJiETgiAUFQTBJ2O/OIBmAE7YVLqHB0cqTE5WxkXs+HEOllesGAcS0nEeQQDmzuX9a9c4ZoGKrFjBcRBNJpiz58rCli2cULJoUfYB1SijR/PlYzC4ZRBcealenQNimkzA99+rLY1DzJjBr//7H2fVloWkJEBc7ggOlqlQ1zBmDMdCbNFC0wmhczcGA9CwIfDhh8CcORz9fOVKvj8mJwPp6dJQ5onlqUxYG+G4agNQDMBfYNfszcjI9QSgAYBFGfsvADgK4HDG6yBby/f19SWqWZPVcOiQ/CPKiAgue/Bg+cuWGbebLh00SBqN79ghW7GO6GHdOn44MBiI4uJkEMJoJBJnDVV0DcpJFw8fsp2ewjbZmsDmfrF5M5mXmh4/VlYohShRgpsQFGT9e7uvkb59ucACBVwUy0Ae1qwhsy3qiRPWj3G7+6aCaEUX0OLMDBHdIqKXiKgqEbWljLQJRLSfiAZn7O8iotpEVDfjdbFdlZQrx6+XL8ssPYDVq/m1Rw/5y87rLFwIiFlaO3fmoHoq0bkzR2U3mTgBsNMJlMeM4cdib29gxAhZZFQCsa1eXnkk2q8ttG7NORz++0+a5nAzxJxNx4/LEE/UaARWreL9QYPcJkjenTtAnz68P2IEUKOGuvLoOI979DxnEBPuXLggb7knTvBWtCiH2NSRF4OBczYJAidL6dlTVXEiI4HKlYEjR4BmzZwo6OFD6d/ktdd4DUuD3L8PbNzI+yNHcmR6HXC/bNKE9+fPV1cWB+nTh5+/UlKAiAgnC/voIx7xeni4JDmqXHTsyGJ7e8ugAx1NkKsHM/7+/kBAAL85d07ewsVZmW7dXJIU0FlCQkLUFsF+AgOBsWN5Pzoa2LbN6SId1UPBgtKDeFycZNZjN6Gh0nSHynYX2eniiy+Ae/d4KduN/qMcxq5+ISrk+nXg4EFlBFKYGTMAT0+2g/r778zf2aUL0Y23UyeXpeFwlhUrgF27eH/WLI68nxVued9UCM3rwtraU27ZgoKCiFat4oXRrl0dX6SzRu3aXO6GDfKWq5MZk4nDYQNEAQGqh0hv2pTMUUITEuw8+fx5KbSwIr7e8nD5shS8c/t2taXRKGXLsoLatlVbEofp3ZubULKkgwUsXSrZtV2+LKtsSvHokeSdV7eu2tLoOAK0aDOjNBcuXOC1AYBTIcvFqVOchtbX1yXJEeXAMpCTWyEIPCNTpw7/hu+/71Rxzuph40bAx4dNBV55xc6TX3uNb/2+vsC0aU7JIQdZ6aJNG+DRI6BLF6BlSxcLpRJ294thw/h161ZOrueGTJzIr4mJUnZtwA5drF/Pr23bSraJGqdLF3aQ8fQEYmJyPt5t75sKoHVd5OrBjNFolAYz587xH4kcrFnDr1278qKrG5DkyuylcuPjA/z0E+t64UKnDC+d1YOfH7A4wwT98GGepraJ338H/vmH9+fP14ShpDVdLFgAnDnD+06OG90Ku/vFhx/yP2J6OjB1qjJCKUytWtKz2MSJkmG7Tbq4eJGX2j09VV8utZV169gMD+BnCVuyvrv1fVNmtK4L9e+oSuPnB/j786NmYqI8ZYrW+7oXk+uoXVsyAp44UcYgGfbTrx/QqhXvf/ghh8PJFiLp0bdePcmNQmOkpgJiJPVmzfLOrIxDeHoC7drx/rJl6sriBD//zLa7KSnA4MF2nPjFFzyQ69ULKF9eMfnkIi0NmDyZ92vV4utWJ3eRqwczPj4+vCPnUlN8PHDoEFC4sAPrDOoRIBpCuzPff89BEE0mjnKVXQClLJBLDxs2sIeP0SgNALJk6VK2sixRgoPlaYQndREaylPwHh7A2rUqCaUSDvWLr79mo9dz53jp2Q0pVkxaMVu6lCdcctTF+fOSBfy77yoroEx8+inbaleoIBn/2kKuuG/KhOZ1Yc2QJrdsQWJUqF692OJr6VLnrY8++YTyRBQxrbJ3r2RE26aNqqJs3kzk7c2irFuXxUFnzkjx0qOiXCqfPRw9Kql19Gi1pXEj3nqLlTZihNqSOEx6OlGRItyMevVsOOGll/jgokUVl00Ofv6ZDfbdIOuMjg0gLxoAJ4rLSnK6Z7tpoLy5DvsSa4xGjTjoC8CzHOK+jciph5deksx3Bg7MYuWrbVuOl16nDtC/v2x1y4GlLjp35tWwYsX4KTav4XC/CAvj18WLOZCeG2IwsCkawHZg48atyPrgxERpdlG0INYwN2/yZWc0AiEh9vtr5Jr7pgxoXRe5ejBz79493hEHM6dPO1fghQvA/v0c6ExcL3cTLFPFuz0TJ0qBCj/+2K6lG7n1EB7Oq41JSTzOevTI4stx43jeHmBLYUGQtW5nEXWxdq0UU3L1ak3YJrsch/tFnTpsSfrokQ3rjdqld29ebiICFi6snbWvxNChfFChQtz5NU6rVmwv4+MDfPON/efnqvumk2hdF3njthUYyK/HjztXjmj427GjHhJVbWJjgVKl+Mb69tscJVgFDAY2nfDwAB484Gj3ALiviVMc3btrNkr0vXsc4RfgpJJ6vlQH6NuXX3//nY1i3ZRp09isKymplvXgxvfusUsQwLYyGh/1jh3LQdoBTiLp56euPDrKou3eKBfiYObkSeduNuJgplcv52XScQ5PTw7F+9xz7Evcs6cMSZMco1o1KUPBvn3AxxONPKoh4jvoimym7VVm9GjOz9OoEfDJJ2pL46ZMncqj2dRUtw6X7OcnOd0NHy5FEjAzYgQb3/v48Iyohtm3T/opunXjmSedXI41Q5rcstW1DPFYrhxbgJ0545jV0blzfH7BghxG0s24deuW2iIow7lzHMIUIAoO5ojB2aCkHoKDWYxodOQdQSDatUux+pzlgw8emrMGHzmitjTq4nS/ePll/s2LF5dHIJVITycqXjydAKJnnrG4nIxGIj8/buOwYarKmBOPHhEVLsyilijBojtKrr1vOoBWdAEtGgALgtBTEITjgiCYBEFokM1xwYIgnBIEIV4QhLG2lv/YMtOys0tN4qxM585uucQUHx+vtgjKUKkST317eHBIz86dsz1cST2sXw+8XnQDOmIDAOBu2ASgaVPF6nOGQ4eAmTO5H7drx2F88jJO9wvROPLmTSmophtiMAAzZrAl+9WrFp7Xq1dzquny5TOHC9YgAwdyolSDAdi+nW8NjpJr75sOoHldWBvhuGoDUAPAcwC2AWiQxTEeAM4CqAzAG8BhAIG2lO/r6ysN50aN4qH6tGmODQcbNODzf/3VsfNVplOnTmqLoCwjR5I5T8wbb2R5mKJ6uHCBjCVLEwG0Hc2pcmXnngqVIjWVyN+fVeXvT5SWprZE6iNLv6hTh5VaubLzZalIp06dqF8/aXJx/750olq1+IMFC9QWL1vWrGExPTyIvvnG+fJy/X3TDrSiC2hxZoaI/iWinKJNNQIQT0TniCgVwM8AutpdWc2a/OrIzMy5c5IXU3Cw/efrKM+cObw4DgBLlgDvvOPa+u/cATp1gkfiddyu1xodfbbg3DlgzBjXimELwcHsfQWY8NdfbH6kIwPi7MyFC8Dly6qK4ixRUUDx4vx0sLVlBHDsGM/KaDg/z6lTwBtv8P7nn7v+FqCjLu5gAFwWgOWd4UrGZ/YhDmaOHbNfAjG2jJsuMeUZfv0VePll3p8/n72cXMGtW+z+f+wYUL06im5Zg+gYL3h68oz8nDmuEcMWLD3Zn3tuGerVU1Wc3EWLFuwcYDIBs2erLY1TeHgAf/0FeCEVI1I+5w87dWLjXw1y/jxQty47XHXv7hZe4zoyo/gzmSAImwFYS+k1gYh+V6C+IQCGAECRIkXQOcOGwsdoxCqDATh+HD06dEBqxkJqSEgI+vbti9DQUHMirYCAAMyePRtz585FbGwsZu/YgQAA99u3x7/79mHKlCnm+oYPH47g4GBzPQDQsGFDREREIDIyEnFxcebPo6OjERMTg3nz5pk/mzRpEqpUqZIpI2m7du0QFhaG8PBwnM1IweDv74+oqCgsX74cKyy8Y2ZlZDocZRHjwlqbPDLaK7ZJJCoqCvHx8W7Zpid/JwCAtzd+bdECXn//DSxYgC3r12NWvXoYHhaG4OBgJCYmmtslS5v698eDcuVQKCUFJgDjq1XDJ0WL4urV5ahZMxGHD4cjPBzYv/8OPvropmNtkul3+uyzPZg8uTEAAcWKHcI77yQhKSlJnd9JpjbJ1ffEfuFsm3567z34rlyJR3Pm4M3jx/HQy8vtrqfy5cubZf2hSDJ87qUiDZ5od9CAghmfa6lNRqM3/vprCdLSiiB/fsDTcyi6dLma7e9ka9/zy/Dn1uLv5OrrSbxG1G5Tllhbe3L1huxtZpoCiLV4Pw7AOFvKNaczEKldmxdU7fEwOXqUz/H1JUpOtv08HXXp1EmyoRk2jA1F5ObSJQ7pLhoX/P77U4f07i2J8dFH8otgK9euEVWqxHKUK8deKzoK0aoVK7prV7UlcY7kZHZ1A+g7vEnlyhFdv662UJlJTyeqVk26BHfuVFsiHaWBFm1mbCQOQFVBECoJguANoA+Adbac+JT1daNG/Lpvn+21L13Kr717c1I5N6VzDl4+uY7oaOCnnwBvbw792bIlcOiQfHrYvZsDzNy+zW4Tq1YBXbo8ddiKFUDDhrw/eTIwaZI81dvDvXtAhw48Fd+wIQcSMxjyYJ/IBll10aEDv65bZ0NKde1h1sU77wBpaSAvLyxvOg9XrgDNmwMPH6ornyVt2kiB3b/7DnjhBXnL168RCa3rQm3X7FcFQbgCnn3ZIAhCbMbnzwiCsBEAiMgIIAxALIB/AawkIsf8q+0dzKSn8x8iAAwY4FCVOirSrx+wbRtQtiywZw9Qvz4GnjjBEyXOMGUK0KwZkJLCg6UtW3ih3gqCwFWLtilTpwLvv+9c9fZw/TpQpQoHQKtShbN9Fy7suvrzJKNHs5KJJItUd+PePfO9Txg8GMt/zYcCBYD4eKB+fTYLUptevdj1GuDMIYMGqSuPjrqo7c20lojKEZEPEZUionYZn18log4Wx20kompEFEBE0xyuUBzM2JoD/q+/ONhCQID8Q34d19C0Kc+iFC0KEKH7uXOcS2edTZN7mblyBXj9dSAigv+oihfnaY5WrbI9zWAADhwAGmREUvryS9fkKT1/HqhaFbhxA/Dy4jA8JUooX2+ex2Dgf1cA+OMPvoe4G6GhnJ3RxweYPRulS0u5jU6f5iSrajJnjhT6q39/YPp0deXRUR93WGZymIIFC2b+oHZt/lO7cMG2DNqLF/PrgAGaSxJoLw3FtY68SPnyQEIC0KsXCODMv1278ozNp59yGPqsMJk4CFr9+rystGwZ3+DHjOElBDGJaQ4YDMDevdKfwJo15ll8RdizB6hRg/NFeXgAGzc+LWqe7hNPILsuxoyRZmfefFPeshWmRa1aPKMJAOPH8+wjeHwzNiNk6bZt6qUI+PZbyVupa1fgxx+Vq0u/RiQ0rwtrhjS5ZXvKAJiIqHt3sin405UrHHnJw4Po8uXsj9VxHw4fJqpZU7LKBdiIt2tXogkTiAYMIOrXj6h9e6KAALMBpHnr2ZNTKDjBBx8Q+fhwcU2aOJ5hIytmzWJjSIDI25to9255y9exkU8+kSxTr1xRWxrbef99lrt1a6vpQfr3ly6H3r1dJ5bJRDR6tFT3zJmuq1tHOyALA2DVBxxKbs8888zTmpg/n5vdo0f2Gps0ybbj3ITJkyerLYImMOvhwAH2OvH1zTxYsbYJAlFgIFF0tGxy7NlDVLYsF28w8J/C48fOlZmSQtSypSR2sWJEZ89mfbzeJyQU0UV6upQkqEMH+ctXgv37Kc3Dg2U+cCDLw7p1k/pZ//7Ki5WSIjmjAkTz5ilfJ5F+jViiFV1kNZjJ1ctMD62Z3YtB1WJjgeRk6yempAALFvD+iBHKCOdiLOMJ5GXMeqhf///t3XuQVOWZx/Hv4yAiqCAOKBcjIkRQuQre15RiBBXjpdysEA1WNFYiKmgoo6i4ksRo0CBGyrhhVTBcsuWiiUvJgOguwXUFvCAiF1FQLl5QBKIgCDz7x3uGM2CPDDDT7+nu36dqij6nz3Q/55kzzTPveS+hrfzzz8Mtx3HjwlCjDh3CStzdu4d29D/9KVwnCxaEScNqycknw5tvpp0p//KXsGrxb36z550r3eGZZ8Jd1Jkzw77TT4dVq6Bt2+q/T9dEqk5ysd9+4TYmhGutEEY2XXIJ9bZtg3PPDRdnNZ5+Or3N9OST4WOyrm6ZLlwILVrA/Plh+4Yb4Lrr6ua9dqXfkVTWc1HUxUxObdvCiSeGlcimTMl9zKOPhn4VXbuGWT2leJmFxSqvvBKGDw+fnIsWhR67kybBNdfU2aynTZvCnDlhdFNZWaiZ7rgjrJrRr1/oW/xtFi8Ox7VsCZdcAu+8E+qwJ5+EWbMyO1lrafn5z0PHjo0bw/TLWfbAA7BiRehXVoNYJ00Kyx7Urx9Wcvje98L1XJt+9zs44YTwN4cZjB4NDz1Uu+8hxaH0ihkIQ3YhHXZd1Zdfwm9/Gx7ffXfBd/yVbNtvP7j//vBH+3nnhe1Nm8J/FMcfD926hdG9gweHNZXOPDP0Q27YMDQiTZoUhl83bw5/+EP46/WKK2KflezkvvtCtTpmTGgRzqIvvgidfYE3ystrvNr7j38chke3bBkGDZ58Mlx77b4P3V6+PHRg/+Uvw2sdckjoQJ+vFhkpQLnuPRXLV84OwO7uq1e716sXOissWbLzc7feGm7K9uyZs/ObSF1au9b9Zz9zb9YsXKK7685z2GFhguP162NHLt+qT5/wA2vWLJufK+efH+Lbf/+9upiWLQunVnldHnSQ+6hRe36qn3/ufs897k2apK/Vq5cmX5cUpdhnZsOGDbmfaNEijDPcvj2U/p5MojZrVlhu1SxMZFBErTJTp06NHUImZD0Phx4ahp5+8klYiHvWrLD905+GaZLOPDPcWho1Kow2//TT0PR+yCF7/l5Zz0U+1Xku7r8//LtmTToHTVa88koYuw9w111Mrek8XFW0aRNaCK+5JnxsfvEFDBoUbplefnm4c1udDRvC7aQOHcIsCkOHhmu/a9cwHdTzz8ebfF2/I6nM5yJXhVMsX40bN66+vHv//XSkwZAh7uPGpevsDBmyZ6ViAejbt2/sEDJBeUgpF6m85OKyy8LnS1lZWCwrC7Ztcy8vD3G1auXu+56LVavCqO7K6QEqv44+OjRQHX98WE+pVSv3hg2/2drYq5f7tGnZaMDS70gqK7mgmpaZOl81O7O+850wUqV///SvJoCLL077zIiI1Jbx40MLyMaNYR2vPVkjrq48/nho3qucWbEWtGwZVvhYty60ssyYEfqELVsWvnJp0CAMnho6FC64oFbCkBJTusUMhLGFzZqF+eXXrw/b110XemGKiNSmykVPr7oqDPuZODHcM4xlxQq4+ebweOxY6Ny5Vl++SZN0CYStW8Pou3ffDbeONm8Oo/mOPTasy9mmTa2+tZQg88r+IkWoY8eOvnDhwthhZMLs2bM5qXJtqhKmPKSUi1Rec9GlS5hk6MAD4bPPwr/5tnVrmIxo9uzQGj158o4+grouUspFKiu5MLNX3b3HrvuLugniAE20sUO7du1ih5AJykNKuUjlNRfTp4d1mzZtChM1xnDeeaGQadQo9DCvMthB10VKuUhlPRdRixkz+2czW2Bm283sG5VWleOWm9l8M3vDzObW9PWXL19eK3EWgwEDBsQOIROUh5RykcprLpo3D0N0ysrCLe4XXsjfe0MYCvf88+HxbbeFVeSr0HWRUi5SWc9F7JaZt4BLgZk1OPYsd++aq3lJRKSgnHRSaJVxDzME56sz8Jw5aT+Z006D22/Pz/uK1LGoxYy7L3T3xTFjEBGJ4o47oH37MCnL2WeHQQh16aOPwpoD27dD48ZhmJFIkYjdMlNTDkwzs1fN7NqaftMhezOTWJHq3bt37BAyQXlIKRepKLkoKwvrw5WVhWVUOncOHXPrwsaNYRa6TZtg//1DC001M9HpukgpF6ms56LOh2ab2fPAETmeut3d/1rDlznD3VeZWXNgupktcvect6aSYudagPLyci688MIdz40cORKAm266ace+fv360b9/fwYMGMDatWsBOOaYY3jwwQd5+OGHqaiylsrYsWNZunQpv/rVr3bsGzhwIH369NnpfXr27MmwYcMYPnz4TiuNPvvss0ydOpXRo0fv2HfnnXfSrl27ne5H9u7dm+uvv57Bgwfz7rvvAtC0aVPGjh3LhAkTmDhx4l6dE1B057SnP6eKioodxxbLOe3Lz2nt2rVFd057+3OqqKjI/zlNnMgBnTtzy+uvYx98AN27M/Xeexn9yCO1ck4AI0eM4IiBAzno449xYFi3bnScM4f+7dvnPCdgp1iz9nOC/F57QNGd097+nCoqKqKfU7VyzaSX7y/gv4EeNTz2X4EhNTm2efPm+zzbYLEYNGhQ7BAyQXlIKRep6Ll44IF0CtwePcLMvLVhyxb3fv18x4JJjz2222+JnosMUS5SWckFhbo2k5k1MrODKx8D5xI6Du/W5s2b6zK0glJZQZc65SGlXKSi5+Lmm+GWW8LjuXPD8tNff71vr/n+++HW1cSJYZGkadPCEuy7ET0XGaJcpLKei9hDsy8xs5XAqcAUM6tI9rc0s8q5tQ8HZpnZPGA2MMXdM77ilYjIHrrvPrj77jDny9y5cNZZsGrV3r3WuHGhc/GiRWEV0hdegFNPrd14RTIk6nIG7v408HSO/auB85PH7wFd9ub169Ur7dUaqmratGnsEDJBeUgpF6nM5GLYMDjnHPjhD+Gll6BTJ+jbF8aMCcsh7M7KleF7X345bDdoEDoZJ30/aiIzucgA5SKV9VwU9XIGPXr08LlzazzHnohINqxZAwMGwHPPhe369eHSS2H48NDisquXXgqrNP7976HnDYTRSy++GBZJEikSJbmcQWVPaYEJEybEDiETlIeUcpHKXC6aNQstKkOGhKHbW7bApEnw3e+GtZxatYJTTgmtNm3bwhlnwMyZoZA5+ODQkvP663tVyGQuFxEpF6ms50LFTImoOlyulCkPKeUilclcmMGIEbBhA9x4Y1hmGuCrr2D1anjllVDwLFsWJsE76ih46CFYtw6uvnqv3zaTuYhEuUhlPRfqVCIikmUNG4b1lEaNCrP4TpkC8+aF4qZLF2jXDjp2BPURlBKmq19EpFAcccQ+tbqIFKui7gDcqVMnnz9/fuwwMmHp0qWZX8I9H5SHlHKRUi5SykVKuUhlJRcl2QFYREREil9RFzMrVqyIHUJmVF0bo5QpDynlIqVcpJSLlHKRynouirqYERERkeKnYkZEREQKWlF3ADazfwCLY8eREeXAp7GDyADlIaVcpJSLlHKRUi5SWcnFUe7ebNedxT40e3GuXs+lyMzmKhfKQ1XKRUq5SCkXKeUilfVc6DaTiIiIFDQVMyIiIlLQir2Y+bfYAWSIchEoDynlIqVcpJSLlHKRynQuiroDsIiIiBS/Ym+ZERERkSJXlMWMmfUxs8VmttTMbo0dTyxmdqSZvWhmb5vZAjMbFDum2MyszMxeN7P/ih1LTGbWxMyeMrNFZrbQzE6NHVMsZnZT8vvxlplNNLMGsWPKFzN7zMw+MbO3quxrambTzeyd5N9DY8aYL9XkYkTyO/KmmT1tZk1ixpgvuXJR5blfmJmbWXmM2KpTdMWMmZUBo4HzgOOAfmZ2XNyootkK/MLdjwNOAQaWcC4qDQIWxg4iA0YBU929A9CFEs2JmbUCbgR6uPsJQBlwedyo8uoJoM8u+24FZrh7e2BGsl0KnuCbuZgOnODunYElwG35DiqSJ/hmLjCzI4FzgQ/yHdDuFF0xA5wELHX399x9CzAJuChyTFG4+4fu/lry+B+E/7BaxY0qHjNrDVwAjIkdS0xm1hg4E/h3AHff4u7r4kYVVT3gQDOrBzQEVkeOJ2/cfSawdpfdFwFjk8djgYvzGlQkuXLh7tPcfWuy+X9A67wHFkE11wXASOAWIHOdbYuxmGkFVF1hciUl/B94JTNrA3QDXokbSVQPEn4Rt8cOJLKjgTXA48kttzFm1ih2UDG4+yrgfsJfmh8C6919Wtyoojvc3T9MHn8EHB4zmAz5CfBc7CBiMbOLgFXuPi92LLkUYzEjuzCzg4D/BAa7+4bY8cRgZn2BT9z91dixZEA9oDvwiLt3A76kdG4l7CTpD3IRocBrCTQysyviRpUdHoa7Zu6v8Hwzs9sJt+3Hx44lBjNrCAwFhsWOpTrFWMysAo6sst062VeSzGx/QiEz3t0nx44notOBH5jZcsKtx7PN7M9xQ4pmJbDS3Stb6Z4iFDel6BxgmbuvcfevgcnAaZFjiu1jM2sBkPz7SeR4ojKzq4C+wI+8dOcyOYZQ8M9LPkNbA6+Z2RFRo6qiGIuZOUB7MzvazOoTOvP9LXJMUZiZEfpFLHT338eOJyZ3v83dW7t7G8I18YK7l+Rf4O7+EbDCzI5NdvW7hLmcAAADWUlEQVQC3o4YUkwfAKeYWcPk96UXJdoZuoq/AQOSxwOAv0aMJSoz60O4Nf0Dd98YO55Y3H2+uzd39zbJZ+hKoHvyWZIJRVfMJJ21rgcqCB9K/+HuC+JGFc3pwJWEVog3kq/zYwclmXADMN7M3gS6AvdEjieKpHXqKeA1YD7hMzHTM53WJjObCLwMHGtmK83sauBe4Ptm9g6h5eremDHmSzW5eBg4GJiefH7+MWqQeVJNLjJNMwCLiIhIQSu6lhkREREpLSpmREREpKCpmBEREZGCpmJGRERECpqKGRERESloKmZERESkoKmYERERkYKmYkZE6pSZHVZl0saPzGxVle36Zva/dfS+rc3sX6p57kAz+x8zK6vm+fpmNjNZSVtEMk7FjIjUKXf/zN27untX4I/AyMptd9/i7nW1FlIvql9z6ifAZHffVk3MW4AZQM5iSESyRcWMiERlZl+YWRszW2RmT5jZEjMbb2bnmNlLZvaOmZ1U5fgrzGx20rLzaK7WFTM7A/g9cFlyXNtdDvkRyZpDZtbIzKaY2Twze6tKa84zyXEiknEqZkQkK9oBDwAdkq/+wBnAEGAogJl1JLSWnJ609GwjR8Hh7rMIi85elLQAvVf5XLIAbVt3X57s6gOsdvcu7n4CMDXZ/xbQs7ZPUkRqn4oZEcmKZcnqvNuBBcAMD4vHzQfaJMf0Ak4E5pjZG8n2rq0ulY4FFuXYXw6sq7I9n7Cw4n1m9k/uvh4guQW1xcwO3sfzEpE6ps5tIpIVm6s83l5lezvpZ5UBY939tm97ITMrB9a7+9YcT28CGlRuuPsSM+sOnA/82sxmuPvw5OkDgK/2+ExEJK/UMiMihWQGoR9McwAza2pmR+U4rg2wOtcLuPvnQJmZNUheoyWw0d3/DIwg6TRsZocBn7r717V+FiJSq1TMiEjBcPe3gTuAaWb2JjAdaJHj0EVAedKhN9doqWmE/jgAnYDZyW2ru4BfJ/vPAqbUZvwiUjcs3JIWESkdyW2lm9z9ym85ZjJwq7svyV9kIrI31DIjIiXH3V8DXvy2SfOAZ1TIiBQGtcyIiIhIQVPLjIiIiBQ0FTMiIiJS0FTMiIiISEFTMSMiIiIFTcWMiIiIFDQVMyIiIlLQVMyIiIhIQft/wtmm4n9IM70AAAAASUVORK5CYII=\n", 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5Zy7Ljlx2GfzqV/CTn8D3v5/79xcREZEmuZgAPBZ43MxWmdlyM1thZstzUNta4OC054NT25q4+9vuvjX19Drg2NbedP369fk9zAQFMwm4qqoq7hISQ1kEyiJQFoGyCJRFkPQssmlmxgGHAKcBFcCZqfv2WgIcamYfMbMewLnAXek7mNmgtKdnAc+29qYbNmzouGYm4ZOA04fuOjtlESiLQFkEyiJQFkHSs2i1mTGz/wBw95eBMe7+cuMN+Hp7C3D3BmAKsICoSfmTu9ea2UwzOyu127fNrNbMngK+DVyQ0Zvnu5k59FDo2xdeey26iYiISIfLZGTm3LTH39vttfG5KMLd73H3f3H3Ye7+k9S2Ge5+V+rx99x9pLsf6e6nuvtzGb1xvpuZLl2gPHXoLuGHmkRERIpVJs2MtfC4ueeJMXTo0NDM9OuXvw8qgOvNVFdXx11CYiiLQFkEyiJQFoGyCJKeRSbNjLfwuLnnibF169b8j8xAQUwCbjzlVJRFOmURKItAWQTKIkh6Fpk0M0ea2QYz2wgckXrc+DyxazWtW7cO3n03etJRzUyGp7l3tPTz9Ds7ZREoi0BZBMoiUBZB0rNo9aJ57t61IwrJi44YmTnoIBg0CNatg7q6aFKwiIiIdJhsTs0uPB3RzJgVxKEmERGRYlW0zczA/fbrmGYGQjOzaFF+P6eN9nYJ6M5GWQTKIlAWgbIIlEWQ9CwyXs6g0JQfc4zXPPlktBjkli35/bCHH4ZTT4WjjoInn8zvZ4mIiHRSuVjOoKCsbpx53RGrWY8dCz16wFNPQQKXSU9faKyzUxaBsgiURaAsAmURJD2LjFbNBjCzEuBzwND0n3P3mbkvq/26NI44dUQz06sXHHccPPII/OMfMHFi/j9TREREgOxGZu4EJgINwKa0WyJ17chmBuDkk6P7v/+9Yz5PREREgCxGZoDB7p6T5Qs6Qq+SEti0Kb9X/013yikwa1Y0fyZhRjdOUBZlkUZZBMoiUBaBsgiSnkXGE4DN7Frg1+6+Ir8l5Ub5IYd4zUsvwXnnwc035/8DN2+ORoG2b4e33+64ESEREZFOIhcTgE8ElprZSjNbbmYrzGx57krMrfcaJ+L26dMxH9i7d7ROkzssXNgxn5mhmTMTOa0pFsoiUBaBsgiURaAsgqRnkc1hpgl5qyIPGrZujR707dtxH3rKKVEj89BDkKCZ30t0Mb8myiJQFoGyCJRFoCyCpGeR8ciMu78M9AMqUrd+qW2J1HQ2U0eNzACcfnp0v2BBx32miIhIJ5dxM2NmlwE3AwNTt5vM7NJ8FdZesTQzH/847LMPPPMMvPJKx32uiIhIJ5bNBODlwPHuvin1vBR4zN2PyGN9bVa+775eU18P1dXwla903AeffTb8+c9w7bXwta913OeKiIgUuVxMADZgR9rzHaltibS9cc5MR47MAIxPnb0+f37Hfu5ezE9QLXFTFoGyCJRFoCwCZREkPYtsmpnfA4vM7Eoz+xGwCLghP2W1X8MHH0QPcjQB+J134NZb4aqr4Je/hDvuiM7A3sO4cdH9/fdHp2knwJw5c+IuITGURaAsAmURKItAWQRJzyLjs5nc/Zdm9jBwQmpTpbsvy0tVOZCrOTNvvAEzZsANN0BDw66vmUVzfqdOhQkToEsXYOhQ+OhH4bnn4LHH4KST2vX5IiIisnetNjNmttDdTzSzjYCTdmjJzNzdO/g4Tmaahpza0cwsWhRNgVm3LmpUTj0VjjwSdu6Ep5+OzsK+//7oNmYMzJ4Nxx8PfPrTUTNz551qZkRERPIs4wnAhebYbt186Y4d8PrrsP/+Wf/8kiVR87JpU9SP/O530YBLunfegeuvjw47rVsXbbvoIrjmC/+kdNyJMGQIvPRSNIQTo8WLFzNmzJhYa0gKZREoi0BZBMoiUBZBUrJo9wRgM/t5JtuSwnbujB60YWTm1VfhM5+JGpnzz49GXnZvZCBaseC734Xnn4cf/ABKSqLm5rCLjmdr2SB4+WV44ol2fpP2Gz58eNwlJIayCJRFoCwCZREoiyDpWWQzAfiTzWxL7lWB3aFbN+jZM6sf27kTLrwQ3nwTzjgDfv976N597z+zzz7RGpNPPAGjR8Mra7pwXf3ZAGy/5ba2foOcqaysjLuExFAWgbIIlEWgLAJlESQ9i1abGTP7ppmtAEak1mRqvL0EJHZtJiA6kynLQzzXXw8PPAADBsBNN7XeyKQ77DB49FH48Y/hzq6fA2DNNbexZHFxHsoTERFJgkxGZuYSLV9wF2EpgwrgWHf/Uh5ra78sDzFt3BgdLgL49a/bNNWGbt3giivg54+dRH3XAXxk+/N88/hlXHllYs7UFhERKSqtNjPu/p67r3b3Se7+ctqtviMKbJcsm5lf/ALWr4/OSPriF9v30UeP7kafr50LwJd3VvOjH8EJJ8DKle1737YY13jtG1EWaZRFoCwCZREoiyDpWWR1NpOZ9QcOBZomorj7I3moq93KzbzmE5+ARzIrb+NGOPhgeO89+Mc/4MQTc1DE0qVQXs62vgM4rM9aVr3ag1694L/+C771rdR1aURERCQjuTib6WLgEWAB8KPU/ZW5KjAvshiZue66qJH5xCdy1MgAHHMMjBpFj/fe4qn//CuVlbBlC1x6aXS6d01Njj6nFVOnTu2YDyoAyiJQFoGyCJRFoCyCpGeRzdjAZcBo4GV3PxU4Gng3F0WY2XgzW2lmdWZ2eTOvl5jZH1OvLzKzoRm9cYZLGezYEV3wDqJTrXPGDC64AIDSm37HjTfCbbfBwIHwz39GF9q78MLoDO58WrVqVX4/oIAoi0BZBMoiUBaBsgiSnkU2zcwH7v4BRM2Fuz8HjGhvAWbWFZhDdJr3YcAkMztst90uAt5x9+HA1UBm17fJcGTmgQfglVfgkEPgzDMzrTxDF1wAvXvDggXwzDN89rPRdWm++91osvCNN8Lw4VFT88wzOf7sXNq5M5rBXKQXWRQRkcKV8dpMwBoz6wf8GbjPzN4BcjGmMAaoc/cXAczsFmAikP5P+0TCIa1bgSpLraWw13fOsJm58cbo/oIL8jCPpawMKivhN7+Jhn+uvZa+faPJxpdcAj/6EcybF9Vw443R5OOvfhUmToT99stVCWUtv7h2LTz5JLzwQnRbvRreeiu6vf02bN0aNTGNFyEEvEcPKCnBS3riPUrwnr3wXqXs7NV7r/feqzfeuzS69eqNl5ZCahu9ezdtp7QUK+kBZpiFs+tz8bhPnwPYsqXt71FM9vrfRSejLAJlESiLIOlZtGk5AzM7GegDzHf3dp1wbGbnAOPd/eLU8y8DY919Sto+T6f2WZN6viq1z1stvW+5mdf8+MfRedJ78e67MGhQ9G/2Sy9FKxDk3MqV0SWEe/aMPuSAA3Z5edUq+O//hptvjiYiQ/QP55gxcNpp0YX4jj02mqDc1n9Q3aP5Ohuee42dd/2F7o/czz4rHqPXW2syfo/tdKM7Da3vmAM76MImStlOdxzL+AZghP+mGx/vfl+I21rbX0Sk2PWgodkJwBmPzJhZOXAFMCT1cwb8BDgiV0W2l5ldAlwCcCzwu3nz+MvjjwNw9dVXAzBt2rSm/SdNmsT775/HBx/AgAHLmDJlOsOGDWP27NlUVVWxYMGCpn2rq6upq6tj1qxZTdsmT57M+PHjqaioaNo2evRoZsyYwcyZM1myZEnT9rvPPhvuuIO/HHccvxs1CoDp06czfPhwpk6Nrqx4wgklDBjwDd588wzuv7+BRYu6sWhR+H7duzfQo8fr9Or1Ft26beb44w+nd++dLFy4EPeuuHfhIx8ZzoABw3j00Vq2bOlBQ0Nv+m97n/N33s05O26hnKW7ZPYufamhnJWM4AUO5UUO4Q325y0GUE8ZH9CT7XRnB10Bw9hJCZvp1eV99uvThR4734Mt79CbzZSyiQG9YZ8uH+Dvr6e3b6a3baZft230674D21JPz52b6O2bKbUt9OnWQM+GjZTs3EQpjds/oLdvogfb6cPGdvzXICIinUXGIzNmthL4d2AF0HTMwd3bdajJzI4HrnT3cann30u970/T9lmQ2ucxM+sGvA7st7fDTP379vV33nwTevTY6+ePGwf33gs33BDNW8mb2lo44ojoONbKldEEnb3YtAkefBAeeyw66+mJJ6KjPplzTuFhLuXXVHB304jKFnrx6D6fpGbgZ3hp8CfYNHgEfft3oX9/drn16xfd9+0bDSiVlIRb165tjyFj27fD5s2wbVuYp+Pe+q25Y0Jp2yorK6n+wx+afa21be7hfpfHtP6zOdvW2v5Z+NznPsdtt8W/3EYSKItAWQTKIkhKFj1Ke7RvZAZ4093vymFNjZYAh5rZR4C1wLnAebvtcxdQCTwGnAM82Np8GTdrtZF5992oYejSBc46q63lZ2jkSPjKV6KJMf/+79FpTXtRWgoVFdGt0YYN0UTltWujw1Hvvx/dIGowunaFbl2dQ155iCNvv5L+T/8DgB1m7JhQQdeLL6TX+PGc3qsXp+fpa+ZM9+4Zn42WjfpeveDAA9v0s7bbfaHzbk733lms11HElEWgLAJlESQ9i2yamR+a2XXAA8DWxo3ufnt7CnD3BjObQnTdmq7ADe5ea2YzgZpUA3U98L9mVgfUEzU87XbPPdDQAKecAvvum4t3bMXMmXDrrXD77XDHHXD22Vn9eJ8+cPjh0W0P7vDQQ3DlldFV/yAaWpk6lQv/8Q/+8Nd89KEiIiLxy+Yw003AR4FawmEmd/ev5qm2dhk1apSvWLFir/t8/vNRb3HNNfDtb3dQYVVV0VXz9tsvOnY0eHD73s89Gl668kpYuDDa1r8/fOc70ef06UNdXV3il2/vKMoiUBaBsgiURaAsgqRk0dIVgLMZmRnt7u2+rkxSbN0Kf/tb9HjixA784G99C+68E+6/H845J2pEevfO/n0yaGJEREQ6g2yuqvJoMxezS6xXX311r68/9lg0yXbkyDydjt2SLl2iC8t8+MOwaFE0KWbTpsx/3j06PnbiiXDGGVEjU1YGP/lJdI2YK67Yo5FJP4Ors1MWgbIIlEWgLAJlESQ9i2xGZo4DlpnZS0RzZozoMFNiTs3Oxn33Rfef/GQMHz5gQHRF4FNOiUZXxo6FuXOjs51asnlzdEzsl7+Ep56KtpWVRSMxU6ZoJEZERDqtbJqZ8XmrIgb33x/dx9LMQHQRvb//PTrGVVsLRx8dHXb6whdg1Cjo1QvefBNWrIiKveuu6HQmiC66953vwNe/Dh/6UExfQEREJBkybmbaez2Zjra3Sy+/80507Zbu3eHkkzuwqN2NGAFLlkSHhn7zG/jTn6JbS8aOhYsvhi99Kbr4S4YmTZqUg2KLg7IIlEWgLAJlESiLIOlZtHo2k5ktdPcTzWwj7HLt9MbDTIk8vlFeXu41NTXNvnbbbdEgyMknw8MPd2xdLXr55Wg9g4cfjtZI2rYtmtD7L/8CJ50E48dHozkiIiKdVEtnM7U6AdjdT0zdf8jd+6TdPpTURgZg9erVLb720EPR/elJunLckCHw/e9HlyN+6aXoynhPPx1dk2bq1HY1MpWVlTkstLApi0BZBMoiUBaBsgiSnkXGZzOZ2c8z2ZYUDQ0tL4j4z39G9yed1EHFxKy+vj7uEhJDWQTKIlAWgbIIlEWQ9CyyOTW7uamyE3JVSEfZsAGWL4du3aLVqEVERKSwtToB2My+CXwLGGZmy9Ne+hDwaL4Ka6+SkpJmtz/+OOzcGTUybblWXSEaNmxY3CUkhrIIlEWgLAJlESiLIOlZZDIBuC/QH/gpcHnaSxvdPbHjTi1NAP7hD6Mlkv7t3+Cqq2IoTERERNqkPROA33P31cDtQH3qFO0vA9eZ2dE5rzRH1q9f3+z2xiv/n3hiBxYTs6qqqrhLSAxlESiLQFkEyiJQFkHSs8hmzsx0d99oZicCZxCtZP3b/JTVfhsaLzCXZvv2aAUBgI9/vIMLitGCBQviLiExlEWgLAJlESiLQFkESc8im2ZmR+r+M8C17v5XoEfuS8qf5cujZZAOPRT23z/uakRERCQXsmlm1prZ74AvAveYWUmWPx+7xYuj++OOi7cOERERyZ1WJwA37WjWm2h9phXu/oKZDQJGuZ7TWZwAAA1dSURBVPu9+SywrY466ihftmzZLtsuughuuAGuuQa+/e2YCotBfX39Xpd36EyURaAsAmURKItAWQRJyaLNE4DN7D8A3H0z0NXdX0g9XweckuM6c2br1q17bFu6NLov3yOG4lZXVxd3CYmhLAJlESiLQFkEyiJIehaZHCY6N+3x93Z7LbEraa9bt26X51u2RKsDdOkCRx0VU1ExmTVrVtwlJIayCJRFoCwCZREoiyDpWWTSzFgLj5t7nlhPPQU7dsDIkZ3nYnkiIiKdQSbNjLfwuLnnidV4/bzOdohJRESk2LW6nAFwpJltIBqF6ZV6TOp5z7xV1k4DBw7c5XlnbmYmT54cdwmJoSwCZREoi0BZBMoiSHoWGZ/NVGh2X87g8MOhtjZam2ns2BgLExERkTZp89lMhSp95vXmzfDss9C1KxxxRIxFxaSioiLuEhJDWQTKIlAWgbIIlEWQ9CyKtplJV1sbrZT9sY9Br15xVyMiIiK51CmameXLo/vOOCojIiJS7Iq2mSktLW163NmbmdGjR8ddQmIoi0BZBMoiUBaBsgiSnkWnmAB86qnw8MNwzz0wYUK8dYmIiEjbdLoJwI1XAHbXyMzMmTPjLiExlEWgLAJlESiLQFkESc+iaJuZTZs2AfDaa1BfD2VlcOCBMRcVkyVLlsRdQmIoi0BZBMoiUBaBsgiSnkXRNjON0kdlrGAWXxAREZFMxdrMmFmZmd1nZi+k7vu3sN8OM1uWut2VzWc0NjOjRrW/XhEREUmeWCcAm9l/AfXu/jMzuxzo7+7/r5n93nf3fbJ578YJwOefD3Pnwv/8D1x8ca4qFxERkY6W1AnAE4Hq1ONq4F9z9cYbNkRLSHX2yb8A8+fPj7uExFAWgbIIlEWgLAJlESQ9i7ibmf3dfV3q8evA/i3s19PMaszscTPLqOFZv34927bBc89Fc2VGjsxJvQVpzpw5cZeQGMoiUBaBsgiURaAsgqRnkcmq2e1iZvcDBzTz0hXpT9zdzaylY15D3H2tmR0CPGhmK9x9VTOfdQlwCUD37t351Kcm09Awh96917FuXXR207Rp05r2nzRpEueddx6VlZXU19cDMGzYMGbPnk1VVRULFixo2re6upq6ujpmzZrVtG3y5MmMHz9+lzUrRo8ezYwZM5g5c+Yus7/vvvtu5s+fv8t/ENOnT2f48OFUVlY2bRs3bhxTpkxh6tSprFoVfcWysjKqq6uZO3cu8+bNa9r36quvzug71dbWAhTVd2rr72nx4sVUVFQU1Xdq6+9p27Ztu/x8MXyntv6eFi9e3LSeW7F8p7b+nhr/jBTTd2rr7wkouu/U1t/T4sWLqaqqiv07tcjdY7sBK4FBqceDgJUZ/MyNwDmt7de3b1//v/9zB/czz/RO7czOHkAaZREoi0BZBMoiUBZBUrIAaryZf/PjPsx0F9DYylYCd+6+g5n1N7OS1OMBwAnAM6298aBBg3j22ejxxz6Wo2oL1PTp0+MuITGURaAsAmURKItAWQRJzyLuZuZnwCfN7AXgjNRzzKzczK5L7fMxoMbMngIeAn7m7q02MyUlJTyT2quzNzPDhw+Pu4TEUBaBsgiURaAsAmURJD2LWJsZd3/b3U9390Pd/Qx3r09tr3H3i1OPH3X3Ue5+ZOr++kzee/Xq1RqZSUk/jtvZKYtAWQTKIlAWgbIIkp5F3CMzebVyZXTf2ZsZERGRYla0zczOnd354INoPaa+feOuRkRERPKlaJuZkpJ+gEZlIDpFUCLKIlAWgbIIlEWgLIKkZxHrcgb5NHhwua9dW8Oll8KvfhV3NSIiItJeSV3OIG/efju6SJ5GZmDq1Klxl5AYyiJQFoGyCJRFoCyCpGdRtM3M9u1dATUzQNOVGkVZpFMWgbIIlEWgLIKkZ1G0zcyOHT0ANTMiIiLFrmibGehCWRkMHBh3HfErKyuLu4TEUBaBsgiURaAsAmURJD2Lop0AbFbuJ5xQw8KFcVciIiIiudDpJgCDDjE1mjt3btwlJIayCJRFoCwCZREoiyDpWaiZ6QTSl2Xv7JRFoCwCZREoi0BZBEnPomibmZ493yTh1/gRERGRHCjaZqak5D1Gjoy7ChEREcm3op0APGrUKF+xYkXcZSRCXV1d4pdv7yjKIlAWgbIIlEWgLIKkZNEpJwCLiIhI8SvaZubVV1+Nu4TEmDZtWtwlJIayCJRFoCwCZREoiyDpWRRtMyMiIiKdg5oZERERKWhFOwHYzDYCK+OuIyEGAG/FXURCKItAWQTKIlAWgbIIkpLFEHffb/eN3eKopIOsbG7Gc2dkZjXKIqIsAmURKItAWQTKIkh6FjrMJCIiIgVNzYyIiIgUtGJuZq6Nu4AEURaBsgiURaAsAmURKIsg0VkU7QRgERER6RyKeWRGREREOoGibGbMbLyZrTSzOjO7PO564mJmB5vZQ2b2jJnVmtllcdcUNzPramZPmtlf4q4lTmbWz8xuNbPnzOxZMzs+7priYmbTUn8+njazeWbWM+6aOoqZ3WBm683s6bRtZWZ2n5m9kLrvH2eNHaWFLH6R+jOy3MzuMLN+cdbYUZrLIu2175iZm9mAOGprSdE1M2bWFZgDTAAOAyaZ2WHxVhWbBuA77n4YcBwwuRNn0egy4Nm4i0iAa4D57v5R4Eg6aSZmdhDwbaDc3Q8HugLnxltVh7oRGL/btsuBB9z9UOCB1PPO4Eb2zOI+4HB3PwJ4HvheRxcVkxvZMwvM7GDgU8ArHV1Qa4qumQHGAHXu/qK7bwNuASbGXFMs3H2duz+ReryR6B+sg+KtKj5mNhj4DHBd3LXEycz6AicB1wO4+zZ3fzfeqmLVDehlZt2A3sBrMdfTYdz9EaB+t80TgerU42rgXzu0qJg0l4W73+vuDamnjwODO7ywGLTw3wXA1cB/AImbbFuMzcxBQPoqk2voxP+ANzKzocDRwKJ4K4nVbKI/iDvjLiRmHwHeBH6fOuR2nZmVxl1UHNx9LfDfRP+nuQ54z93vjbeq2O3v7utSj18H9o+zmAT5KvC3uIuIi5lNBNa6+1Nx19KcYmxmZDdmtg9wGzDV3TfEXU8czOxMYL27L427lgToBhwD/MbdjwY20XkOJewiNR9kIlGDdyBQamZfireq5PDodNfE/V94RzOzK4gO298cdy1xMLPewPeBGXHX0pJibGbWAgenPR+c2tYpmVl3okbmZne/Pe56YnQCcJaZrSY69Hiamd0Ub0mxWQOscffGUbpbiZqbzugM4CV3f9PdtwO3Ax+Puaa4vWFmgwBS9+tjridWZnYBcCZwvnfea5kMI2r4n0r9HToYeMLMDoi1qjTF2MwsAQ41s4+YWQ+iyXx3xVxTLMzMiOZFPOvuv4y7nji5+/fcfbC7DyX6b+JBd++U/wfu7q8Dr5rZiNSm04FnYiwpTq8Ax5lZ79Sfl9PppJOh09wFVKYeVwJ3xlhLrMxsPNGh6bPcfXPc9cTF3Ve4+0B3H5r6O3QNcEzq75JEKLpmJjVZawqwgOgvpT+5e228VcXmBODLRKMQy1K3T8ddlCTCpcDNZrYcOAr4z5jriUVqdOpW4AlgBdHfiYm+0mkumdk84DFghJmtMbOLgJ8BnzSzF4hGrn4WZ40dpYUsqoAPAfel/v78baxFdpAWskg0XQFYREREClrRjcyIiIhI56JmRkRERAqamhkREREpaGpmREREpKCpmREREZGCpmZGRERECpqaGRERESloamZEJK/MbN+0iza+bmZr0573MLNH8/S5g83siy281svM/m5mXVt4vYeZPZJaSVtEEk7NjIjklbu/7e5HuftRwG+Bqxufu/s2d8/XWkin0/KaU18Fbnf3HS3UvA14AGi2GRKRZFEzIyKxMrP3zWyomT1nZjea2fNmdrOZnWFm/zSzF8xsTNr+XzKzxamRnd81N7piZicCvwTOSe13yG67nE9qzSEzKzWzv5rZU2b2dNpozp9T+4lIwqmZEZGkGA5cBXw0dTsPOBH4LvB9ADP7GNFoyQmpkZ4dNNNwuPtCokVnJ6ZGgF5sfC21AO0h7r46tWk88Jq7H+nuhwPzU9ufBkbn+kuKSO6pmRGRpHgptTrvTqAWeMCjxeNWAENT+5wOHAssMbNlqee7j7o0GgE818z2AcC7ac9XEC2s+HMz+4S7vweQOgS1zcw+1M7vJSJ5psltIpIUW9Me70x7vpPwd5UB1e7+vb29kZkNAN5z94ZmXt4C9Gx84u7Pm9kxwKeBH5vZA+4+M/VyCfBB1t9ERDqURmZEpJA8QDQPZiCAmZWZ2ZBm9hsKvNbcG7j7O0BXM+uZeo8Dgc3ufhPwC1KThs1sX+Atd9+e828hIjmlZkZECoa7PwP8ALjXzJYD9wGDmtn1OWBAakJvc2dL3Us0HwdgFLA4ddjqh8CPU9tPBf6ay/pFJD8sOiQtItJ5pA4rTXP3L+9ln9uBy939+Y6rTETaQiMzItLpuPsTwEN7u2ge8Gc1MiKFQSMzIiIiUtA0MiMiIiIFTc2MiIiIFDQ1MyIiIlLQ1MyIiIhIQVMzIyIiIgVNzYyIiIgUNDUzIiIiUtD+P+tfDpdp4B49AAAAAElFTkSuQmCC\n", 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" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "zIh9ymNNxWai" + }, + "source": [ + "### **Placing Observer Poles**\n", + "\n", + "\n", + "Recall that we facing the similar problem while designing the stable feedback controllers: \n", + "\\begin{equation}\n", + "\\dot{\\mathbf{x}}= \n", + "(\\mathbf{A} - \\mathbf{B} \\mathbf{K}) \n", + "\\mathbf{x}\n", + "\\end{equation}\n", + "\n", + "Thus, using the fact that characteristical polynomial does not changes when we transpose the matrix we arrive to:\n", + "\\begin{equation}\n", + "\\lambda_i(\\mathbf{A} - \\mathbf{L} \\mathbf{C}) = \\lambda_i(\\mathbf{A}^T - \\mathbf{C}^T \\mathbf{L}^T)\n", + "\\end{equation}\n", + "\n", + "and we can use the same techniques that was used for controller design, \n", + "\n", + "\n", + "let us begin with pole placement for the inverted pendulum in downwoard position\n", + "\n", + "The linear feedback on the nonlinear system with state $\\mathbf{x}=[\\theta, \\dot{\\theta}, x, \\dot{x}]^T$ and dynamics given by:\n", + "\n", + "\\begin{equation}\n", + "\\begin{cases} \n", + "\\left(M+m\\right){\\ddot {x}}-m L \\ddot{\\theta} \\cos \\theta +m L \\dot{\\theta }^{2}\\sin \\theta = u \\\\\n", + "mL^2 \\ddot{\\theta}- mLg\\sin \\theta - m L \\cos \\theta \\ddot{x} = 0\\\\\n", + "\\end{cases}\n", + "\\end{equation}\n", + "\n", + "The linearized version nearby the downoward position is given by LTI system with following matrices:\n", + "\\begin{equation}\n", + "\\mathbf{A} = \n", + "\\begin{bmatrix}\n", + " 0 & 1& 0 & 0 \\\\\n", + " -\\frac{g}{L} \\frac{(M+m)}{M} & -\\frac{b}{ML}& 0 & 0 \\\\\n", + " 0 & 0& 0 & 1 \\\\\n", + " - g \\frac{m}{M} & -\\frac{b}{M} & 0 & 0 \\\\\n", + "\\end{bmatrix}, \\quad\n", + "\\mathbf{B} = \n", + "\\begin{bmatrix}\n", + " 0 \\\\\n", + " -\\frac{1}{ML} \\\\\n", + " 0 \\\\\n", + " \\frac{1}{M} \\\\\n", + "\\end{bmatrix}\n", + "\\end{equation}\n", + "\n", + "with state defined as $\\mathbf{x} = [ \\theta, \\dot{\\theta}, x, \\dot{x} ]^T$\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "Vr2KjV93Zd9H" + }, + "source": [ + "M, m, l, b, g = 2, .2, 0.2, 0.1, 9.81\n", + "\n", + "A = [[0, 1, 0, 0], \n", + " [-g*(M+m)/(M*l), 0 , 0, 0],\n", + " [0,0,0,1],\n", + " [-m*g/M, 0, 0,0]]\n", + "\n", + "A = np.array(A)\n", + "\n", + "B = [[0], \n", + " [-1/(M*l)], \n", + " [0], \n", + " [1/M]]\n", + "\n", + "B = np.array(B)\n", + "\n", + "system_params = {'A':A,'B':B}\n" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 650 + }, + "id": "fPqarlqQluwP", + "outputId": "4f06b160-00b4-4d50-b764-9e36b3828ea3" + }, + "source": [ + "\n", + "from scipy.signal import place_poles\n", + "\n", + "\n", + "A_obs = A \n", + "\n", + "C = [[1, 0, 0, 0],\n", + " [0, 0, 1, 0]]\n", + "\n", + "C = np.array(C)\n", + "\n", + "poles = [-0.5, -2, -0.2, -1]\n", + "pole_placement = place_poles(A.T, C.T, poles)\n", + "L = pole_placement.gain_matrix.T\n", + "# print(L)\n", + "observer_params = {'A':A_obs,'C':C, 'L':L}\n", + "\n", + "x_real_0 = [0.1, 0, 0, 0] # Set initial state \n", + "x_hat_0 = [0.15, 0, 0.05, 0]\n", + "\n", + "state_0 = np.hstack((x_real_0, x_hat_0))\n", + "\n", + "state_sol = odeint(observer_ode, state_0, t, args=(system_params, observer_params, )) # integrate system \"sys_ode\" from initial state $x0$\n", + "\n", + "x_real, x_hat =np.split(state_sol, 2, axis = 1)\n", + "\n", + "theta, dtheta, x, dx = np.split(x_real, 4, axis = 1)\n", + "\n", + "theta_hat, dtheta_hat, x_hat, dx_hat = np.split(x_hat, 4, axis = 1)\n", + "\n", + "figure(figsize=(9, 3))\n", + "plot(t, theta, 'b--', linewidth=2.0)\n", + "plot(t, theta_hat, 'b', linewidth=2.0)\n", + "plot(t, dtheta, 'r--', linewidth=2.0)\n", + "plot(t, dtheta_hat, 'r', linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'State ${x}$')\n", + "xlabel(r'Time $t$ (s)')\n", + "show()\n", + "\n", + "figure(figsize=(9, 3))\n", + "plot(t, x, 'b--', linewidth=2.0)\n", + "plot(t, x_hat, 'b', linewidth=2.0)\n", + "plot(t, dx, 'r--', linewidth=2.0)\n", + "plot(t, dx_hat, 'r', linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'State ${x}$')\n", + "xlabel(r'Time $t$ (s)')\n", + "show()\n", + "\n", + "figure(figsize=(9, 3))\n", + "plot(t, theta - theta_hat, 'b', linewidth=2.0)\n", + "plot(t, dtheta - dtheta_hat, 'r', linewidth=2.0)\n", + "plot(t, x - x_hat, 'b', linewidth=2.0)\n", + "plot(t, dx - dx_hat, 'r', linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'Estimation Error ${x}$')\n", + "xlabel(r'Time $t$ (s)')\n", + "show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "atQu2GNdZWu4" + }, + "source": [ + "### **Closed Loop - Linear Qudratic Estimator**\n", + "\n", + "As soon as one can place the poles of observer at any desired location designing the observer gain can be designed with help of LQR routines, we call such observers Linear Quadratic Estimator (LQE)." + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "qSkcb8_1dFoZ" + }, + "source": [ + "from scipy.linalg import solve_continuous_are as are\n", + "\n", + "def lqr(A, B, Q, R):\n", + " # Solve the ARE\n", + " S = are(A, B, Q, R)\n", + " R_inv = np.linalg.inv(R)\n", + " K = R_inv.dot((B.T).dot(S))\n", + " Ac = A - B.dot(K)\n", + " E = np.linalg.eigvals(Ac)\n", + " return S, K, E\n", + "\n", + "Q_o = 15*np.diag([1,1,1,1])\n", + "\n", + "R_o = np.diag([1,1])\n", + "\n", + "S, LT, E = lqr(A.T, C.T, Q_o, R_o)\n", + "L = LT.T\n", + "\n", + "observer_params = {'A':A_obs,'C':C, 'L':L}" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 650 + }, + "id": "HzryqKJqJ3U_", + "outputId": "9a66bd14-4eed-4f54-af94-d81063c0ad15" + }, + "source": [ + "\n", + "x_real_0 = [0.1, 0, 0, 0] # Set initial state \n", + "x_hat_0 = [0.15, 0, 0.05, 0]\n", + "\n", + "state_0 = np.hstack((x_real_0, x_hat_0))\n", + "\n", + "state_sol = odeint(observer_ode, state_0, t, args=(system_params, observer_params, )) # integrate system \"sys_ode\" from initial state $x0$\n", + "\n", + "x_real, x_hat =np.split(state_sol, 2, axis = 1)\n", + "\n", + "theta, dtheta, x, dx = np.split(x_real, 4, axis = 1)\n", + "\n", + "theta_hat, dtheta_hat, x_hat, dx_hat = np.split(x_hat, 4, axis = 1)\n", + "\n", + "figure(figsize=(9, 3))\n", + "plot(t, theta, 'b--', linewidth=2.0)\n", + "plot(t, theta_hat, 'b', linewidth=2.0)\n", + "plot(t, dtheta, 'r--', linewidth=2.0)\n", + "plot(t, dtheta_hat, 'r', linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'State ${x}$')\n", + "xlabel(r'Time $t$ (s)')\n", + "show()\n", + "\n", + "figure(figsize=(9, 3))\n", + "plot(t, x, 'b--', linewidth=2.0)\n", + "plot(t, x_hat, 'b', linewidth=2.0)\n", + "plot(t, dx, 'r--', linewidth=2.0)\n", + "plot(t, dx_hat, 'r', linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'State ${x}$')\n", + "xlabel(r'Time $t$ (s)')\n", + "show()\n", + "\n", + "figure(figsize=(9, 3))\n", + "plot(t, theta - theta_hat, 'b', linewidth=2.0)\n", + "plot(t, dtheta - dtheta_hat, 'r', linewidth=2.0)\n", + "plot(t, x - x_hat, 'b', linewidth=2.0)\n", + "plot(t, dx - dx_hat, 'r', linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'Estimation Error ${x}$')\n", + "xlabel(r'Time $t$ (s)')\n", + "show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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jWXiiJYucHLjmGuje3StAzjlHF5m79tqKFSDRkkV1sCw8Qc/CekKMMcZHs2dD//6wb59eb94cpk2zQaemZghkT4gxxkS7XbvgttvgjDO0AImN1XEgmZlWgJiaI5A9IUGfZjachg4d6ncTAsFy8FgWnkjM4sAB+M1vYPp02LYNYmJ0qvV77z26ReYiMYtQsSw8Qc8ikGfH2LTtxpho9NprMHy49oKAznb61FNw6qn+tsuYUIuoadvXrFnjdxMCIzU11e8mBILl4LEsPJGSxaZN0Lu3rveya5cONL35Zvjqq+orQCIli3CwLDxBzyKQRUh+fr7fTQgMm8JeWQ4ey8IT9CwKCnTcR9u2MG+ebuvWDVau1B6Q6lzrJehZhJNl4Ql6FoEsQowxJtKtWgUXXwyTJmkxUr8+PP88LFoEHTr43TpjgiGQA1Nr167tdxMCo1OnTn43IRAsB49l4QliFllZutjcww/D/v1Qrx5ceqlOOhYfH7rfG8Qs/GJZeIKehQ1MNcaYajJ+PDz4IBQdUf7Vr7QYadnS33YZ47eIGpiamZnpdxMCY8qUKX43IRAsB49l4QlKFp99Bq1awcSJWoDUrQsffqiHX8JVgAQliyCwLDxBzyKQRciuovPXDLNmzfK7CYFgOXgsC4/fWWzZAmefrVOsb96s2y69VOf/OO+88LbF7yyCxLLwBD2LChchzrnHnLMllIwxRgSefVYnF/v8c93Wvj3Mn6+TkNWt62vzjIkYlekJ2Q286ZyrD+CcG+ic+zI0zTLGmGCaM0d7P379a539tG5dmDoVVq+2SceMqaxKDUx1zg0DxgK5wB7gfhH5vLob1aNHD1mwYEF1P2xEysrKsmnssRxKsiw84czi2291RduVK/V68+Zwxx0wejTUqhWWJhyW7Rcey8ITlCyOemCqc24A8GtgL9AcuDUUBQhATk5OKB42ImVkZPjdhECwHDyWhSccWfz0E/TtC6efrgVITIwWHxkZ8L//G4wCBGy/KMmy8AQ9i8ocjrkHGCci5wJXAv9xzoVk6NWmTZtC8bARaeLEiX43IRAsB49l4QllFjt3wuWX68Ri33yj29q1gw8+gD//GRo3DtmvrhLbLzyWhSfoWVS4CBGR80Tki8L/LwIuAu4PVcOMMcYP+flw993QrJkOMhWBRo10IOratdC/v98tNCZ6VPkUXRHZBAyoxrYYY4xvCgrgv//VtV0efFAHndauDffcA9u3w003+d1CY6LPUU3bLiLZ1dWQkhITE0PxsBFp5MiRfjchECwHj2XhqY4sCgpg3Dg9w2XnTt3WsSPccAP84Q/BGfNxJLZfeCwLT9CzsGnbjTE1UlHxMXky7Nun2xIS4IEH4MYbQ7vOizE1TXWcHeOcc9c558YXXj/WOdenOhtZJOijecMpJSXF7yYEguXgsSw8VckiL0/PamnQQAuOffv0jJfLLtMzXm6+OTILENsvPJaFJ+hZVGZMyJNAX2Bo4fXdwNSK3tk5F+uc+84591YlfqcxxlSL/Hx44QVo2hQeeQSys7X4uPRSyMyE117TnxljwqcyY0JOE5GezrnvAERku3OuMkdLRwM/AI0q00BjjDkaP/0EaWl6dsu6dbotNhauuAKeesoKD2P8VJkiJM85FwsIgHOuBVBQkTs659oCvwD+D7jtSLevX79+JZoV3ZKTk/1uQiBYDh7LwnO4LGbN0knFvv/e29alC9x+u858Wq9eGBoYRrZfeCwLT9CzqEwR8jgwHUh0zv0fOmHZuAredzJwB9CwvBs450YAIwCaN29e6jjWpEmTABg7dmzxtqFDhzJs2DBSU1PJysoCoFOnTkyePJkpU6aUWjkwLS2NjIyMUpO2jBw5kkGDBpX6PcnJyYwfP54JEyYwZ86c4u0zZsxg5syZTJ3qHX0aN24cSUlJpKamFm8bOHAgo0aNYsyYMawsnNs5ISGBtLQ00tPTmTZtWpWeExB1z6myr9OcOXOKn1e0PKejeZ2ysrKi7jlV9XVKSUkpfk633noHy5cPZe3ageTleZ2utWrt4JRTJtO3705+/etJgX9OVXmdEhISSrU1Gp7T0bxOQNQ9p6q+TikpKb4/p3KJSIUvQFdgJDAKOKGC9xkMPFn4/3OBt450nzZt2ohR9913n99NCATLwWNZeIqyWL5c5JJLRGJiRHR6Mb0cf7zIyy/73Mgwsf3CY1l4gpIFMFfK+Htf4Z4Q59yfReQPwI9lbDucM4FLnHMXA3WARs65F0TkuvLusHfv3oo2K+qVrHhrMsvBY1moBQvg3//uyttvw+zZ3vZateCii+Cvf4XCjsQawfYLj2XhCXoWlTk75oIytl10pDuJyF0i0lZE2gPXAB8drgAxxpjyfPMNXHmlrtty6qmQkXE1s2dD/fo6udjTT+tZL6+/XrMKEGMi1RF7QpxzvwV+B3R0zpUY4kVD4KtQNcwYYw4cgJdfhiefhLlztcAoqXbtbTz/fDMGD46+gabG1ARHnDHVOdcYaAo8CNxZ4ke7RSQrFI2yGVONqZlE4PPPtcdjwQJdsXbLltK3adNG5/a46y5o29afdhpjKqfKM6aKyE4RWSMiQ4FdQEvgOKCbc+7s6m8q7Nq1KxQPG5FmzpzpdxMCwXLwRFMW+fnw5ptw/fW6Xkt8PJxzjq7ZMm2aFiBt20L37nDvvbqQ3IYNus5L27bRlcXRsiw8loUn6FlUZtr2/wE+A2YB9xX+e28oGpWZmRmKh41IJU+7qsksB0+kZpGXB8uXw/TpcPfd0K6dFh1DhsC//w2rV+vhF+cgKQmmTIElS2DtWp3r409/giZNSj9mpGYRCpaFx7LwBD2LyswTMhpIBr4Rkf7Oua7AA6FpljEmEuXmwsKFMH++Hk758UctLjIzDx3PUSQ2Flq3htNOg1/+Ug+1ROLaLcaYyqtMEbJfRPY753DO1RaRH51zXULWMmNM2BTNrJGbC3v2wLZteqprdrZeX7hQi4lt2/SQSFaWXnbt0iKiQQM9dLJpkx5iKU+zZtC7N/TsCe3b6xkuvXtr74cxpuapTBGy3jnXBHgdeN85tx34KRSNat26dSgeNiKNG1fRSWmjW7TkkJOjf8S3boWNG+H992HzZv2DvnMn7N4Ne/fq7YoOV+zfDz//rBcRKCh4o7inQET/gDdvXvQz2LFDD2uUNeY8NlYvBQV6OXCg+p9jTAzUqaMFR9u2OlV6375w/vk67qM6Rct+UR0sC49l4Ql6FhUuQkTkssL/3uuc+xhoDLwbikbVrl07FA8bkZKSkvxuQiBEQg4HDuj4hbffhm+/hVWrtHDYsUN7E/Lyyi4MylO02NqhDh3K9fPPFXvM/PzD91QUcQ5attQxGA0bag/I3r1Qt66eCtukCSQkQGKizsdxwQXQooXep27dirWlOkTCfhEuloXHsvAEPYsjnqJbfMMyZket4IypldakSRPZsWNHdT9sREpJSWHGjBl+N8N3QcpBBObN07M6vvwSVqzQwxGrV2uvxZG0aKE9F82bQ0aG3rdRI/1j36SJTsTVsCGccor+ga9TR4uYnTuhdm2YOHE8Dzwwgbg47dWIi4PjjtMeCOe0Z6WgQP9ftC0mRi+NGmnx4JwWRdu26WPWq6fFQ6SNxQjSfuE3y8JjWXiCkkV5p+hW5nDMBcDBBcdFZWwzJqrk5cFHH8Fjj8F33+kgy4Jy1o9u00aLiNxcPRTRvr2e6XHCCXDSSfr/uMq868rwzDPfcf755f+8ZcuKPU7t2loAGWOMX6o6Y6oDGgBfhrBtxvgiLw/S0+HDD7VX4YsvYN++0rdxTouNTp10kOWll8JZZ2lPgzHGmIqpyHeydHTsR9hmTG1kn+TFBg4c6HcTAiHUOaxaBZMm6XiONWsOHbtxwgm6PknPnrp2yXnn6aEQP9g+4bEsPJaFx7LwBD2LikzbngysE5GfC69fD1yBnhlzbygKEZu23YTD+vXw8MPw/PM6eLSk2Fjo3Fln7hw0CFq18qeNxhgTDao8bTvwNJBb+CBnAw8BzwM7gWeqs5FF1pV/WkCNM2bMGL+bEAjVlcN33+maI/366Smwjz/uFSBNm8Ill8Bbb+mYjh9+0JVZg1aA2D7hsSw8loXHsvAEPYuKHI6JLdHb8UvgGRF5FXjVObcgFI3KyckJxcNGpJUrV/rdhEA4mhw2b4bx43U11u3bve116sBFF8Exx8Btt0GHDtXQ0DCwfcJjWXgsC49l4Ql6FhUqQpxzcSKSDwwARlTy/saEXUEB/OMferhlxYrSP2vTBh56SAeTNmzoT/uMMcZUrIiYBnzqnNsKZAOfAzjnktBDMtXfqKM9hzGKJCQk+N2EQKhoDnv36mJo99+vq60WadhQD7Xcf7+eNhvJbJ/wWBYey8JjWXiCnkWFJitzzp0OtAbeE5G9hduOBxqIyPzqbpQNTDWV9cUXenbLRx95YzxiYiA5WZeAHzTI1+YZY0yNdjQDUxGRb0RkelEBUrhteSgKEICsrJCc+RuR0tPT/W5CIJSXw4sv6gDTfv3gtde0AOnbF6ZN07k9vvkm+goQ2yc8loXHsvBYFp6gZ1GhIiTcrAjxTJs2ze8mBELJHERg8mSd9vy66/RUW9DF0d5/H776Cq65RmcEjUa2T3gsC49l4bEsPEHPwgZfmIghAv/9L/z617rabJFeveBvf9NDL8YYYyKHFSEmImzd2p0zztDDK6DTpp97Lvz97zp1ujHGmMhT4VV0w6l79+6yaNEiv5sRCBkZGYFfijmU/vEPnbV02za93rw5XH893H67nmpbE9X0faIky8JjWXgsC09QsqiOVXSNCZvp0+G3v9WJxgDi44Xx4x2jR9vcHsYYEy0COTDVpm33jB071u8mhNVXX+ly95df7hUgffvCWWf9D3/8oxUgUPP2icOxLDyWhcey8AQ9i0AWIabm2bEDLr4YzjwTimYZ7t4dvv9eC5P69TP9baAxxphqZ0WI8VVeHkyZor0f776r2447Ticd+/57LUSMMcZEp0COCQn6NLPhNHToUL+bEBIFBbqa7dNPw87Cyf/PPlsXkhsy5NDbR2sOVWFZeCwLj2XhsSw8Qc8ikGfH2LTt0W36dLjpJm9F22OO0d6QIUP01FtjjDHR5aimbQ+3NWvW+N2EwEhNTfW7CdVm3To49VQddLp9uxYcV10Fy5friraHK0CiKYejZVl4LAuPZeGxLDxBzyKQRUh+fr7fTQiMaJjCvqAAbrlFV69dsEC3desGy5bpDKj16h35MaIhh+piWXgsC49l4bEsPEHPIuRFiHOunXPuY+fcUufcEufc6FD/ThMcCxfCWWfp4ZaCAmjQANLTYdEi6NzZ79YZY4zxUzgGpuYDt4vIfOdcQ2Cec+59EVla3h1qR+vKY1XQKULnJM/M1FlN09O1+GjZElJS4MknIT6+8o8XqTmEgmXhsSw8loXHsvAEPYuwD0x1zr0BTBGR98u7jQ1MjVwicOed8Ne/woEDEBOjh2Luuw8aN/a7dcYYY/wQiGnbnXPtgVOBb8v42QhgBED9+vVJSUkp/tmkSZOA0jO/DR06lGHDhpGamlp8zKtTp05MnjyZKVOmMGvWrOLbpqWlkZGRwcSJE4u3jRw5kkGDBpX6PcnJyYwfP54JEyYwZ86c4u0zZsxg5syZTJ06tXjbuHHjSEpKKjXoZ+DAgYwaNYoxY8awsnDGrYSEBNLS0khPTy+1pHJFn9OePXv4+OOPI+I5XX313xgzphVZWbpbxcTkMHr0Nzz66DlH/Tp1796d9u3bB/Z1Cue+16VLF+6+++6oek5VfZ3WrFlD+/bto+o5VfV1uuqqq9i/f39UPaeqvk4FBQW8/fbbUfWcqvo6Fb1H/H5O5RKRsFyABsA84PIj3bZx48Zi1ODBg/1uwhFlZYmce66I9oPo5aqrRPbvr77fEQk5hItl4bEsPJaFx7LwBCULYK6U8fc+LD0hzrl44FXgRRF5LRy/04THW2/B1VdDdrZe79AB3njDZjo1xhhzZOE4O8YB/wB+EJFHQ/37THj89JPO7ZGSogVI7drw2GOwapUVIMYYYyom5ANTnXNnAZ8Di4CCws13i8g75d2nR48esqBoQokaLisrK1DT2O/dC1deCR98APn5uqrthAnwm1zb4CoAAB01SURBVN9AnTqh+71By8FPloXHsvBYFh7LwhOULHybMVVEvhARJyIni0iPwku5BQhATk5OqJsVMTIyMvxuQrFHH4WEBJg5UwuQwYPhxx9hzJjQFiAQrBz8Zll4LAuPZeGxLDxBzyKQM6Zu2rTJ7yYERoVGF4fYggU62+ntt0Nurs7z8cADMGMGtGkTnjYEIYegsCw8loXHsvBYFp6gZxHIVXRNMOTlwS9/qQvOFRkwAF591eb8MMYYc/QC2RNi/PfFF9C7t1eAJCbCp5/qWBArQIwxxlSHQBYhiYmJfjchMEaOHBnW37dwIQwZAv36wfffQ7t2cM89sHkznH12WJtSSrhzCDLLwmNZeCwLj2XhCXoWYZ+2vSJs2vbw27cPhg3TOT5AT7m98074wx+gbl1/22aMMSay+XZ2TFUEfTRvOJWctjdUJk/Ws16KCpCWLeGrr+Dee4NTgIQjh0hhWXgsC49l4bEsPEHPIpBFiAmPOXPguONg7FjIyYG4OBg/HjZtgp49/W6dMcaYaGdnx9RA2dnw8MPa01F0NO688/SslyZNfG2aMcaYGiSQRUj9+vX9bkJgJCcnV9tjFRTAf/+rYz1++km3HXMMTJumA1GDrDpziHSWhcey8FgWHsvCE/QsbGBqDZGWBrfcArt36/WTT4ZJk7QHpNIOHNDulJgYiI3V2cti7MieMcaYspU3MDWQPSE2Y6pnwoQJjB8/vsr3nztXJxxbtUqvx8bCE0/AiBH6/2IisGULLF6sc7FnZGh3ye7d2l2ycaNeli7VLpWDxcToiNYePfS83oYNYdcu6NVLz+3t2hWcq/LzONocooll4QlMFgUFek77u+/qqO5ly3S2vxYtYNs2Pf0sM9M7/hkTo4Ow4uP1VLQuXfSbQbNmWuRv3QqtW0Pbtvp+6thRl6iuVavcJgQmiwCwLDxBzyKQRcjevXv9bkJgzJkzp0r3y8zU4uOTT4SmZNGPxaQc+z2/OW8FDd9dA0uOhf37tbD47jv4+eeja2hBgY5oPbiA/Pvf9V/noH59aNUKOnWC1FQ46SRISoJ69Y748FXNIRpZFh5fstizB5Ys0aLj5Zd1hPfOnV6BUdKaNWU/xoEDesnJ0cf76iu9HIlzWow0b64Fy8aNuq1pU07PyNCR5hddpLML1mD2HvEEPYtAFiGmirKzyV+xmncfXMCal77mNV6gIbuIK1q8eC3w3BEeIzZWz8tt1EjP223TBq6+Wv9t3Vq/ubVrp7eJjdUP0u3bYf16XWJ3+3ZYtw4+/1w/VIu+BYroh21Ghl5mzfJ+Z9262nPSti2ccAL06aO9JyeeeNhvfsaE1P798N578OGHMG8erFypPRT5+eXfp2FDfX90766X887TYqFBA71vTIwW7FlZ+k1h61a9NGum99+2TRdrWrBA3y/79mmhcuCAvodEtFuzqGuzhAsBbrhBr8TF6e8fMQLOOkvfS3bI1Phh8WJ4p/w1a60IiWT79sF//gP/+hcyfz5kZxNXUECZZ4XHxGiPQ+PG2kV82ml6Hm6bNtC0qRYYxx130DGaCoiJ0W9dB3/zKjlLX1FX9ccf6/Ghdev0NJzly/XDNDtbL5mZMH8+vPiid982beC88xiyapXuyD16hG/VPFMzFBTo4ZOffoJFi7RncPp0LULKEhurvXjdu2vPXoMGMHCgvqcO94f+aPfb3FxtY1ERs22bHv5Zvx62biVz/nwSRbRoyc/X5/Hb3+p9mzTRy6BBcOutWuwbEwqbNsHTT+sKp0uXlv8+KmQDUyPN+vU6qOO11/Sb2UGv32ras7xeD5r1P4VT+9Yhtk8vXQSmaVOfGnwEubn6QfrFF1qoZGToHPGHOyTXoIEeP7/iCvjNbyp0OMeYYmvXwr/+pYshLV2qY6HKGucE2qPQrJkeQuzVS1dwvOCCYO9z+/bB22/DihX6LfTzz/Vzo6T69fX5DBumh0br1PGnrSby/fyzFryff67vqbIOK7ZogduypcyBqYhI4C6dO3cWo959+22RDRtEXn1VZPhwkUaNijplRUAOECM/0EX+j7vk+PiVMnmyyP79fre6GuTmiixYIPLeeyJPPSVrL7pIpG3bUs9dQMQ5kQ4dRO64Q2TvXr9bHRbvvvuu300IjAplkZcn8sknItdcI9KgwaH7UNF+1K+fyKhRIk8/LZKeLrJuXeifQDUqN4uCApFZs0SGDBFJSDj0ucfEiFx+uchTT4msWhXeRoeIvUc81Z7FokUit90mcvLJInXrlv1+ql9f5MwzRSZNEtm5U0REgLlSxt973wuOsi6NGzeu3tAizaZNIn/9q0hysuQ6px8SJV7gvPi68lncuTKMF6QO+wRE+vcX2bjR74aHzuDBg/U/69eL/OlPIr16idSqVXrHr1tX5NJLRdLSRNas8bW9oVSchSk/i5wckUcf1T+uLVoc+iHZsKHuQ7fcIvLBByIHDoS34SFQ4f1i82Z9D3XvLhIff2g28fEi3bqJ/P73IhkZIW1zqNh7xHNUWRQUiKxYIfLAAyKdO5e9v4AWJP/7vyJvvimydWuZD1VeEWJjQoLi3XfhySe1Kysrq3hzPIAIcsYZrOk2mFtnDeatn7oBerrrGWfAc89B585+NNoHxxyjU73ee69enzULHntMx5esXAmvv64X0G70QYN0drZu3fxqsQmX3Fw9Fv3MM4eeSp6UpPtCs2Y6WLMmjytKTCz9HvrxR/jsMx2EO3OmHgpdvFgvjzyiA8dPOglSUnSsV9EgWhOd5s6FKVP0PbRuXdlnTiYkwCmnwODBcP31erZWFVkR4ocDB+Drr7XYmDMH3n8fZs8uPb4jLg66deNf+3IpGP4Jz0xvwexnvB/366eHtTt1Cn/zA2XgQL0AbNigBcjUqfDDDzpw78UX9dK4sZ6pcMcdcPrp/rbZVJsYEfjHP+Dxx/WPZsnCIy5OX+snntAPzKOYpyaqde2qlxEjdBDh88/r1Mrz5sGOHTpofO5cvUycqGevDRighd0ll9haD5GuoEBPcHjiCR3bcfBA0hYt9A+OCAwZAlddVb1josrqHvH70rVr16p3HwXVypUi48drt1Vc3KHdWbGxIu3a6biPTz+V1SvyZPBgkZiYguKbNGumDxFhh6qrxbffflu5O/z4o8gNN4gkJpbddXjbbSJvvy2yZUtoGhxClc4i2uTkiLzzjsjIkZLTrFnp1zYuTuT000VeeCEqDrFURkj2i23bRP7yF5EzzhBp3vyQQ8MCOs7kwgtF3nij+n9/FdX490gJ5WaxbJnI1VcfelgbRFq2FBk2TG9TUFAt7SCSxoSccsop1fKkfbdzp45RaNy47ONorVuLjB4t8tZbIrt3S0GByHPPiXTpUvpmtWqJ/PnPNWbcZZm2bdtW9Tv/9JMOODzmmLILwEaNRM49V+TJJyMi5KPKIlItXSry29+KdOyog0hLvn5t24okJ4s8/3yNKzxKCst+sWOHyIwZIjffLFKnzqHvpdq1RQYMEPnss9C35TBq5HukHKWy+OYbkT/8QaRnz9Kvm3MiJ50k8uCDItu3h6QdEVWEROzA1OxskZdfFnnpJZHLLtM35MHVRHKyyMMP6wDLQvv2iTz00KEDjRMSRJKS0iUvz8fnFBDVNtAsO1vkww9F7r5b5MQTyy4OW7YUueIKka+/rrZvAdWpRgy627dP5Ikn9Bt4vXqHvkb16onceaeMPuusQL5GfvBlv1i8WGTMGB20eHBxeOqp+u1pxYqwN6tGvEcqaMS554oMHXrImZXSqJHIddeJ3H+/vt9CzIqQUNm/X+SVV0TOOefQb9nO6Qj0X/9a/6CV+Ja2f7/I3/8ucuONOlC/5F169dLeZhF7MxUJWQ5r1ojceae+TmV1S7ZtK3LTTdpLkpUVmjZUUlTuEzt3ijz+uJ5qfc45Zb8WzZqJXHKJyOuvF7+XojKLKvI9i9279aybLl1Kf6gVnY105ZV6emcY+J6F3xYv1kP7LVpIwcHvo+OO0ykfsrPD2iQrQqpTfr4e/zz//LJPWeraVU8PLNHbIaKfmy+8oD1hBx9a7dNH378H94TV+DdTobDl8M03+ubt2rXsUzvbtdPTOg96bcMpavaJWbNEBg8ue+4K50SSkrQinzix3LE7UZNFNQhUFtnZItOna+Fx8GvbtKlIampIT/8NVBbhkJ0t8umn2qtx+umleqUKQD/Lbr7Z1wGFEVWEtGvXLlQ5VF1enlYRn30mMnLkoVVEq1Y62PGgN1Zensi//qX7xcH1Sny8yIgROoayPE888URon1eE8CWHAwd0wrS77y57Up7ERC1YwtzdHLH7RF6eflCedlrZPR21a+sAx9de0wGRFRCxWYRAYLPYtEnHZLVseehrfsIJIvfdpz3F+fnV9isDm0V12bJFJwI777yyi/hatXQg8dCh8u+77/a7tSJSfhFi07aXR0TXaXjnHUhP11NpExJKnzOdkKCLu40apefRF9q/X8+4fecdeOklfZgizumUFWPG6GzJlV2qxfjo88/hr3/VNXB27fK2x8To6b+XX65zKbRt618bg2bjRpg8Wd8377yjp00XcU7XK0pJgZtvLvUeMlFq9WqYMAHefLPUfEgA1K6tSzJ066ZT4193ne4fRj9vvvwSHn5Y/xbt2XPobRo21KXTBw/WU6gbNAh/Ow/DORc507YnJiaGphQ7kqwskdtv129qZQ2GA5H27XVmuNmziwfE5ebqeNSUFD1sfXAnSa1aOuTgkUcqfxhu9OjRIXiikSdwOSxcqKewtWihp1cffPx7wACRqVP1OHk1C1wWB/v4Y52ptKxvaElJIlddJTJ5crUckw58FmEUcVls3Kjje373O5FOncr+vK1VS3/2m9+IzJunH7YVEHFZHGzFCpG77tJj96ecUvap0XXr6nQDY8eKfPdduQ8VlCyIpBlTc3JyQvfgeXk6kdX8+VpR7twJZ57pXV+48ND7tGmj39Zuugl69yYv3/HWW/C3e/TmW7boXlFS587wi1/o3C79+lW9x2PlypVVu2OUCVwOJ5/srfablaXf7F55RRcO271bl3//8EOdYbJpUzj+eJ3Y6cordZKno1hWPXBZbNkCH3wAf/mLvrcOfv82bAjXXgujR0OXLtU6aVjgsvBRxGXRurV+QA4ZotfnzNGu408/1VWN9+zRWXBXrtTLU0/pQnsnnqi3P+ssnTjrjDMOeT9FXBaLF8M//6nvoxUrDp0wLC5OJ4k7/nidofKGG+DYYyv00EHPIixFiHNuEPAYEAs8KyIPheP3FvvoI/j3v3WW0owMnbG0pJJLxzunRUdyMtkXDuHLehfw3pJjmDsX8m/Xvy9Ll+p7o6SYGO05HDhQV88++eTQPy0TEAkJ+qFwww26jPWjj+r01ytW6B/k7dvh22/1cs89Og12YqLuRG3b6h/mHj20Wu3VK7jH6Nav11k0v/1WjzeuXavvl+XLD71tu3ZahY8Zo8/PmCNJTtZLkV274NVX9TDe3r362b1ihX5hBP338cd1H0xM1A/dgQP1y2KQFRTo7LPLlunq4Z98UvZ7qHFjfU6pqXDNNbrycRQKeRHinIsFpgIXAOuBOc65N0VkaXn3iYmphUglvzBt2waLFum0s99+C6edpi/2/PlaXWZmHnIXcY7sxOPYc+rZ/NymJxmNejLlix4sWNmQ3W9B/uvl/7qOHXXm2n799DBcv35H9eW2XAkJCdX/oBEoYnJo3VqP2z78sF5fvNgrgOPi9IN03TpvoNCmTfoN8IUXvMeoX1//gHfpot984uL0217hN5+QZLFhg753lizRN15OjrZz7lytug/XO1m3rk6PnpCgvYo33xy2pe4jZr8Ig6jLolEjGD5cL0WysnSK8Zdf1vfW1q3aDb15sy5/8f77cMcdPNmokU5DX7u2jtcaMEAfL9x27NBC4+OP9W/RsmXa1pLLC4D+8WjSBE49VXuGfvWrapsOP+j7RcgHpjrn+gL3isjAwut3AYjIg+Xdp5E7XjrGTadB8zo0aFabpo0O0KR2Ng3r5JFwTneaNNF9K+mp2zh27ZckZi2jbu7Ow7bjALGsienIN+50vi44nTnSi0V0J5vDf1jGxuq+0L499O0LQ4dC9+7aw2xMlezcqd9+PvpI/+ivWaNF8p49hx7XKykmRguU5s21ByUpCc4/H3r21J20USMtCJzTx8nN1WJnzRr94GvaVIuN9ev1g3zbNq/Lu6Li43Xn79BBe2+GD9dvr7VqHWUoxlRBQYG+l159Vf/Yb96s+3V+/qG3jYvT3oVmzbyCuWtX3ac3b9YvBAUF+n7IydF/c3P1fderlx7Kz8vT9+3evfqzvDzv3/x8aNVK32eZmfq+K2sAKeh7dOBA6N8fzj5b38NR/h4qb2BqOIqQK4FBIvI/hdd/BZwmIqPKu09v56Ssc2PyieVNLqElm2nJZjqyihgObX8ecSzlRL7iDObTk3n0YgknkUvtQ24bF6dfODt21AVaY2J0P+rdWztT/C4i09PTGTZsmL+NCIAak8OqVXrIIztbu2gXL9aVgg8+RhwK8fFa5Jx0kh5vb9dOP1BjYvRD8ijHsoRCjdkvKsCyKJSdzXsPPcSFzsGzz2qBUVZREi5xcfqHpH177em47DI9+ydM76Wg7BeBL0KccyOAEQC9oFdFT9DdQjN+dMezwJ3MorhTWN30LBbntyKPjTRsuJbY2P1cfvkvWLZsD0uXfkTdulupW3czv/vdAK699lwuuyyl+LGSk5MZP348EyZMYM6cOcXbZ8yYwcyZM5k6dWrxtnHjxpGUlERqamrxtoEDBzJq1CjGjBlTPBgoISGBtLQ00tPTmTZtWvFtJ02aBMDYsWOLtw0dOpRhw4aRmppKVuHpa0uWLGHVqlVMmTKFWbNmFd82LS2NjIwMJk6cWLxt5MiRDBo0iJSUYD+nTp06MXny5Eo9p5YtW9KnT5+oek6VeZ3+9sQTHL99O1127KD1tm1c2LEj2xYuZF98PLUOHCAhJoZ6+/YdOt7JOQpiYsgBliYksK1OHXpfeikxWVnMmDOHdQ0asLJxYwbceCPDrrsurM+pOl6n2bNn06dPn8C8Tn7ue926daNDhw5R9Zyq+jotX76cZcuWFT+nOvn5nLRtG/decAEbv/6azYsWsa1OHQqco2e3bjTeto2dCxeCcxxwjtr169OkWTM2bdnC7gMHWNKsGXH16pFy+eWsnzGDjRs2kBsTQ15sLD379kXq1OGjr75iU716/Fy/Pn0vuYSLhw9n+B13sHXHjmp5TlV9nYreI36/Tm+99ZZvRUilD8c0adJEdixfrt1ZWVl6yc/XYyO1aukgpFatdABplB8XSUlJYcaMGX43w3eWg6fcLES0xyQuTt8rAeu1CAXbLzyWhcey8AQli/J6QsJxdswcoLNzrgOwAbgGOHLfUGKiXowxFeOcjgkxxpgIEZYZU51zFwOT0VN0/yki/3e423fv3l0WLVoU8nZFgoyMDJKSkvxuhu8sB49l4bEsPJaFx7LwBCULP3tCEJF3gHfC8buMMcYYExkCedB43bp1fjchMEoODKrJLAePZeGxLDyWhcey8AQ9i0AWIcYYY4yJflaEGGOMMcYXYRmYWlnOud3AMr/bERDNga1+NyIALAePZeGxLDyWhcey8AQli+NEpMXBGwO5ii6wrKxRtDWRc26uZWE5lGRZeCwLj2XhsSw8Qc/CDscYY4wxxhdWhBhjjDHGF0EtQp7xuwEBYlkoy8FjWXgsC49l4bEsPIHOIpADU40xxhgT/YLaE2KMMcaYKBeoIsQ5N8g5t8w5l+Gcu9Pv9vjFOdfOOfexc26pc26Jc260323ym3Mu1jn3nXPuLb/b4ifnXBPn3CvOuR+dcz8UrlJdIznnxha+PxY756Y55+r43aZwcc790zmX6ZxbXGJbgnPufefcisJ/m/rZxnApJ4uHC98j3zvnpjvnmvjZxnApK4sSP7vdOSfOueZ+tK08gSlCnHOxwFTgIuBEYKhz7kR/W+WbfOB2ETkROB0YWYOzKDIa+MHvRgTAY8BMEekKnEINzcQ5dwxwK9BbRLqhi2Ne42+rwuo5YNBB2+4EPhSRzsCHhddrguc4NIv3gW4icjKwHLgr3I3yyXMcmgXOuXbAhcDacDfoSAJThAB9gAwRWSUiucBLwBCf2+QLEdkkIvML/78b/UNzjL+t8o9zri3wC+BZv9viJ+dcY+Bs4B8AIpIrIjv8bZWv4oC6zrk4oB6w0ef2hI2IfAZkHbR5CJBW+P804NKwNsonZWUhIu+JSH7h1W+AtmFvmA/K2S8AJgF3AIEbBBqkIuQYoOTKdeupwX94izjn2gOnAt/62xJfTUbfQAV+N8RnHYAtwL8KD00965yr73ej/CAiG4BH0G92m4CdIvKev63yXUsR2VT4/5+Bln42JkBuBN71uxF+cc4NATaIyEK/21KWIBUh5iDOuQbAq8AYEdnld3v84JwbDGSKyDy/2xIAcUBP4G8iciqwl5rT5V5K4XiHIWhh1gao75y7zt9WBYfoaY+B+9Ybbs65e9DD2y/63RY/OOfqAXcD4/1uS3mCVIRsANqVuN62cFuN5JyLRwuQF0XkNb/b46MzgUucc2vQQ3TnOede8LdJvlkPrBeRol6xV9CipCY6H1gtIltEJA94DTjD5zb5bbNzrjVA4b+ZPrfHV865G4DBwLVSc+ei6IQW6gsLP0PbAvOdc618bVUJQSpC5gCdnXMdnHO10EFmb/rcJl845xx63P8HEXnU7/b4SUTuEpG2ItIe3Sc+EpEa+Y1XRH4G1jnnuhRuGgAs9bFJfloLnO6cq1f4fhlADR2kW8KbQGrh/1OBN3xsi6+cc4PQQ7iXiMg+v9vjFxFZJCKJItK+8DN0PdCz8LMkEAJThBQOIhoFzEI/TP4rIkv8bZVvzgR+hX7rX1B4udjvRplAuAV40Tn3PdADeMDn9viisDfoFWA+sAj9LAv0zJDVyTk3Dfga6OKcW++cuwl4CLjAObcC7Sl6yM82hks5WUwBGgLvF35+PuVrI8OknCwCzWZMNcYYY4wvAtMTYowxxpiaxYoQY4wxxvjCihBjjDHG+MKKEGOMMcb4wooQY4wxxvjCihBjjDHG+MKKEGOMMcb4wooQY0yZnHPNSkyW97NzbkOJ67Wcc1+F6Pe2dc79spyf1XXOfeqciy3n57Wcc58VrqxrjAk4K0KMMWUSkW0i0kNEegBPAZOKrotIroiEaq2WAZS/Js6NwGsicqCcNucCHwJlFjHGmGCxIsQYUyXOuT3OufbOuR+dc88555Y75150zp3vnPvSObfCOdenxO2vc87NLuxJebqs3gzn3FnAo8CVhbfreNBNrqVwTRTnXH3n3NvOuYXOucUlek9eL7ydMSbgrAgxxhytJOCvQNfCyzDgLOD36DLiOOdOQHsnzizsWTlAGYWCiHyBLmY5pLDHZVXRzwoXtuwoImsKNw0CNorIKSLSDZhZuH0xkFzdT9IYU/2sCDHGHK3Vhat1FgBLgA8Ll05fBLQvvM0AoBcwxzm3oPD6wb0cRboAP5axvTmwo8T1ReiCbX92zvUTkZ0AhYdqcp1zDY/yeRljQswGbxljjlZOif8XlLhegPcZ44A0EbnrcA/knGsO7CxcVftg2UCdoisistw51xO4GLjfOfehiEwo/HFtYH+ln4kxJqysJ8QYEw4fouM8EgGccwnOuePKuF17YGNZDyAi24FY51ydwsdoA+wTkReAhykczOqcawZsFZG8an8WxphqZUWIMSbkRGQp8EfgPefc98D7QOsybvoj0LxwoGlZZ9+8h443AegOzC48vPMn4P7C7f2Bt6uz/caY0HB66NYYY4Kv8PDLWBH51WFu8xpwp4gsD1/LjDFVYT0hxpiIISLzgY8PN1kZ8LoVIMZEBusJMcYYY4wvrCfEGGOMMb6wIsQYY4wxvrAixBhjjDG+sCLEGGOMMb6wIsQYY4wxvrAixBhjjDG+sCLEGGOMMb74f050QMxgxvpaAAAAAElFTkSuQmCC\n", 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Sd2rt7wkouO/U2t/T/PnzmTVrVuLfqUnunugNOB2YV+f5jcCNTez7K+DiXN734N693cH9zDO9WfPmhX3POaf5fTuh888/P+kSUkNZRMoiUhaRsoiURZSWLICF3sjf+S25zkx7WQAcaWaHm1l3wtlTc9r6pgP69QsPcpkzU+CHmfbbzXYxyiJSFpGyiJRFpCyitGeR83IG7VqE2bnArUAxcJe7f9/MphM6sDlmNgb4PTAA2AW84+7H7e89R48Y4QuXL4fPfhYeeGD/BbzxRljG4IgjwrIGIiIikjr5WM6g3bj7n9z9KHcf4e7fz2yb5u5zMo8XuPswd+/t7gc218gArFu7Njzo2bP5ArIjMwV6NlPdY6ZdnbKIlEWkLCJlESmLKO1Z5LRqNoCZlQKfBQ6r+3PuPj3/ZbVd7QVwevRofue6zUxNTbhqsIiIiHQKLflb+w+E679UAzvq3FLJsofPchmZ6dYN+vQJjcz27e1bmIiIiORVziMzwDB3z8vyBR2htFs32LUrt5EZCKMz27eHScDZycMFInuKoSiLupRFpCwiZREpiyjtWeQ8AdjM7gB+5u5L2rek/Bh9yCG+cO1amDYNbr65+R8YNQqWLIEXXoCTTmr/AkVERKRF8jEBeCzwXGZByMVmtsTMFuevxPzavm1beNCSkRkoyEnA06enclpTIpRFpCwiZREpi0hZRGnPoiWHmT7VblW0g+qqqvAglzkzENdnKsBrzdS90mNXpywiZREpi0hZRMoiSnsWOY/MuPtKoD9Qnrn1z2xLpdovluvITIEvNikiIlKocm5mzOxa4B5gcOZ2t5l9rb0Ka6vas5laepipAEdmRERECllLJgAvBk539x2Z572Bv7r7qHasr9VGl5X5wk2b4Le/hUsuaf4Hbr4Zvvtd+M53IOWrg4qIiHRF+ZgAbMDeOs/3UufadGlTvXt3eKAJwMydOzfpElJDWUTKIlIWkbKIlEWU9ixa0sz8Evi7mX3XzG4G/g7c1T5ltV2VJgDXqruse1enLCJlESmLSFlEyiJKexY5n83k7j81s6eAj2Q2TXL3Re1SVR4UtXTOjCYAi4iIdErNNjNm9oy7jzWzbYBT59CSmbm7p/JyubVF5joyownAIiIinVKzzYy7j83c923/cvKnW3Ex7N3b8pGZAmxmpk6dmnQJqaEsImURKYtIWUTKIkp7Fi05NfuHuWxLi9ov1tKRmQI8zDRy5MikS0gNZREpi0hZRMoiUhZR2rNoyQTgTzayLbVXBa7esyc8SMPIzJYtsGwZ5HgafL5NmjQpkc9NI2URKYtIWUTKIlIWUdqzaLaZMbOvmtkS4OjMmkzZ25tAatdmavHITK9ekF1pe9eu/BXym9/AkCEwciSMHQvr1+fvvUVERCSnkZnZhOUL5hCXMigHPuzul7VjbW3S4isAm+X/UNP8+fClL8H774c6nn0WPvMZqK7Oz/uLiIhI882Mu29x9xXuPsHdV9a5beyIAlur9mymXJsZyP+hpm9/OzQuX/86LF8OQ4fCX/4Ct9+en/fP0bhx4zr089JMWUTKIlIWkbKIlEWU9ixyXs4AwMwGAEcCtR2Cuz/dDnW12WgzX9itG2QvnpeLU08NoynPPgunn962Ap57DkaPDqM9b74Z7h96CD79aTjwQHjrrXBoS0RERHLS5uUMzOxK4GlgHnBz5v67+SqwXeQ6XyYrnyMzv/51uP/CF+LhqwsvhFNOgffeg1/+su2fkaMpU6Z02GelnbKIlEWkLCJlESmLKO1ZtORspmuBMcBKdz8LOBlI93nM+zvE9M47cNdd8M//DF/+MlxzDaxdG1575ZVwjZrWqqmB++4Ljy+/PG43g299KzyeOTPs1wGWLVvWIZ/TGSiLSFlEyiJSFpGyiNKeRc7LGQC73H2XmWFmpe7+qpkd3W6V5UNjIzPvvgs33RQamaYaluuvh2nT4Pjj4cQT423UKOiXwwWPFy+GdevCHJkPf7j+axddBMOHh1O1n34azjyzxV9LREREopY0M6vNrD/wEPCYmW0CVrZPWXnScGRm0SIoL4fVq6GoCM49N5wuPXBgOOPo7rthwYLQsGzdGubPzJ9f/z0OPxyOPTbcH3ZYuGUfDxgQRl/mzQv7jhsXntdVXAxXXAEzZoSGqgOambKysnb/jM5CWUTKIlIWkbKIlEWU9ixaNAG49ofMPg70A+a6+568V5UHo8184UknwQsvhA1Ll8LHPgYbN8IZZ4RG4uijcYdHHoE//xnOW/ojPvbIt8OhpxtvDCMsL74Y75cuhd27m/7Qvn1DY/P227BhQ5gvc8klcNppUPc/hOXLYcSIMHK0di0ccED7hiEiIlIA8jEBeLSZ/d7Mngd+Bvwb8Fwea8y/7MjM9u3w2c+GRub88+HJJ+Hoo9m9O2wuL4cf/Qh+80iYALxi0aZwxtFZZ8GUKaHxee658D4vvQQPPgg//Wk45bq8HE44Afr0gW3bQuOzYUP43F//Gs47L7zXccfB1VeHi+iVlIT3fv99+O1v2z2G2bNnt/tndBbKIlIWkbKIlEWkLKLUZ+HuOd2A14ALgMOBQ7O3XH++o28fBvczz3R3d7/ySndwP+449x07POvqq8Pm/v3db7zR/Xsn3e8O/n/4tN9/v7dMTY37hg3ud98d3nTgQPfJk93HjnUvLQ3b6t4GDgz3I0e6L18efr6dnH/++e323p2NsoiURaQsImURKYsoLVkAC72Rv/NbMmfmXXefk/duqj317AkLF8Kdd0L37uEMo8y1XebNgzvuCJsffxw+9CHws/rDP0B/NnPe5XDooTBmTI6fZRZGYLZtC8/HjYNZs8Lj3bvh+efDBfOefjrcsqM3lZVwxBFhUvDHPx7m0Hz84+EwVMP5NiIiIrKPljQz/2pmdwKPA7UTR9z9wbxXlS+lpeEwEYT7444DwtDIDTeEzdOnh0YGwMrCYaaRB25i13swcWKYctOnTws+8+9/D/ennFK/jtNPD7frrw9nUS1eHA47LVwYDoetWhUmIN99d/iZQw4Jk5OPPz7UffzxocEpLm5lGCIiIoUp5wnAZnY3cAywFMheIMXd/UvtVFubjDbzhZ/4BDzxRDhbadmy2tOqsxfiHTo0DIzUnvS0bBmMHIkfehgnHfBmbb/RotUHjjsOXn4Z/va3cEXh/Xn8cTjnnDAE9NBDYcTmf/6n/shNXaWlYYJx9uypuo8PPTR8z0ZGcyorK1O/fHtHURaRsoiURaQsImURpSWLpiYAt2RkZoy7p/u6Mg299lq4v/baeteHue22cP/NbzY4eztzBWDbvIm7Hw6rEdxxB1xwQZjH26ytW8MF97p1C9elac5ZZ4XDSytXhsNTX/96uNXUhPdZsCCcQfXSS+F+1Sp49dVwa0xpKQwbts+td0kJbNkSng8aFE5LFxERKRAtGZn5JfBjd3+5fUvKj9FmvhDCHJm33grzWQjLJB1xRGhi1q6NKw0A4fBPSaa/q67mJ7cWc/31cNBBoZ8YOLCZD332WfjIR+Dkk8McmVz8y7/AD34QrkJ8553733frVlixInyJN9+s/3jVqtxW++7WLQxJDRsWGqlhw8LzwYPDF6x7a+lyEJ1AeXk5Dz/8cNJlpIKyiJRFpCwiZRGlJYt8jMycBiwyszcJc2aMcJhpVB6KGw/8O1AM3OnutzR4vRT4NfBh4D3gEndfkdObf+ELtY0MhLOsAS6+uEEjA2E+SvaCeVu3MmXKAP7wh3ANmn/6p3AW9ebNoTd6661wJGjLlrBt82bY8cKBVPNL9mw8kupLYM+eMMhSUhJ6iOwNwke8/z703PENTsLo/mun+Mgq+g/qTo8eNHHrR8++o+hxyih6fCxsKy3NDLTU1IQL8d1yC+za1XQee/aEJmhFDvH16hWamgMPDLnkcuvTB3r3Dj9b96a5PiIi0k5a0syMb48CzKwYuA34JLAaWGBmcxqMAH0Z2OTuI83sUuCHwCU5fcAXv1jvafayLl9qaqbPgAGh09i0iXXvD6C8HP76V7j/fvjjH0MD0rSjw20lLbg28kAe4PuwB7gh15+pr3t3p0fN+/So/kd6cAU9+pTQc1AfevTvQY/uzppXXuC4/qX0WLOMfns3cjDrGNx7B4MP78OBA40Bu9bSZ9cGer+/gZ47N9Bj+wZKt22geOfO2Lm1kZeWYtnGprFmp3fv0Jl17x5vDZ83t724OHSOJSXxcYNtg3buDFeAbuS12vuiIp1JJiLSibTqCsB5LcDsdOC77j4u8/xGAHf/QZ195mX2+auZlQDvAIN8P8WPNvOFgwaFNZIyfzG9/jocfXS4GO/69Y0PFmw4/kwqln6Y3xw1gxdf77XP6717h/m2w4eHw0/9+8db77t+Rrclz9Ht61+l5IxTa0dhnnkmnKT07rvZ7wNDhoQ6iovhkLcX8sF3/4fXOJpHOL/e55WWhgsL9+wZ/q6tqQlneu/aFW/tw+nDdgaygQN5j75sox9bm731ZRu92LnPrYhk/ztrqWqK2UsxNRRTg+EYTlG9xw6Ze2uw3XAzarKPG/xMDUWQ+ZlwH/er3WZhXlN238DxzGNn32Yrbsvu0/RrADUOZla7X/33rP859X97mW22by37qyuX2ht7rSO4O5ZDA5uv6tL8pyHXLHJ6rxwSS/M/G2q8hiLLzjFs/LeW1H+zHa3GoSgF/8g7e+9jrTvMZGbPuPtYM9tG/d9m9jBTDisv7tdQYFWd56uBhqcB1e7j7tVmtgU4EKh3yo+ZXQ1cDeF41HwzZlxwAQAzZ86kouIAYBA9ejzFRRf9hAkTJjBx4kQmTZrE2rU1vPHG51izYh57KIXXobh4FwceuJiysqX07HkZL7zQjZKS1/jAB26iuHg3l146mfHjx1NeXg7A7cue4BB2wlXXM/3B6Tz55GqWLv1H3n03nPs9dOgOBgyo4JBDnqF7921MnTqVkSNH8rUJN3HLY49R5M73r/oveh31FX7+85dYvfpQdu/uu88KCkVFVRQVVdG3Tw9+vucrTNx7N28zhH/gUSo5qtnAjb2cwBLO4FkG8y676MEOerGcEazhELbQn130wDF20YN3GcRW+vEugyihmmpK2Jv5yz77uJoSquhe+7yGotr7aorpzp7axqY3O/Zpdnqzg1J2052qRm9NvVZ3ezF7Kcm0IY3d5/paEU4JeymhDSunt/Vvq4762y7Nf6uKiOQoDSMzFwPj3f3KzPPLgVPd/Zo6+7yU2Wd15vmyzD6NnL8cHFNa6q/Om1dvIcdzzglnQ99zT7iGDIRrztxxR7j8y/bt4d/J5/Inrrr+AMbN+Gjt2U7r1oUlllasCAtf33dfOLJRa/fu2gvy7dywk1tmlvLDH0JVVRi1+cEP4Kqr9jN15JJL4He/C6dY/ehHQBiFefnlMGfnz38Ol6ZZtSocBQP4Lv/KvzKdnfTk030fZ/lBp3PQQdTeBg8O9/fd9zO+972vMXhwOIpW92Qmf/av9Pj5T+n96INYTU0jhdVXY0VsKhvJhoOPY+OQ49l0yHFsHnoc2w85iqIe3enWLR6tMYtHa6x6DyU7NlO8Ldy679hM8fbNdNu+meIdWyjesQXbsyeMhFgYDamhmL0l3dlb1J3q4m7UFHVnb1E3qovD/d6ibuy1buwtzjwu6s7eohJqrBivyV7dOvyOccdr4Nlnn+W0007PbMxsdzA8Pva92N4azKspqtkL7hSxF/aGcRWrCeMo4KEZ8BosfEgYX3EPYyihCMy99v3NQ8bmNZnPqvNzNXszr4XajJraOmtrrCv7GmDZr9PgtfA+ceyldpvDipUrOOzQQxvsE3+27njLPu/ljbxnY/s32K/+v+scsH32ScKqVW8xfPgH9r9T3spLdwe5atVqhg8f1iGflfBfP81avXo1w4Y1ncU+fyYL2JrVqxm6nyw6yv9aOr3RkZmWLGfww1y2tfQGnA7Mq/P8RuDGBvvMA07PPC4hjMjY/t73gAMOqHcJ5K1b3bt1cy8qcn/vvbBtyxb388+PKwycf777ks9ND09mzdrnMsovvxyWPgD3s85yX7OmzotLlriDbz1opB96aHzPK65wX7dun7fa1/z54Qf69nXfvHm/u+7Y4b79J//pDl5TVOR7H5qz3/1zugz12+wY5jcAABJ2SURBVG+733ef+ze/6f75z7ufe677pz/t/sUvus+Y4T57tvuiRe7vv5/Dl0mvtFySOw2URaQsImURKYsoLVmQh+UMPgl8u8G2TzWyraUWAEea2eHAGuBSYGKDfeYAk4C/AhcDT2S+VM4eeyycyPORj4S5KmvWwKc+BUuWhNGKn/8cLr0UmFoVfqCRi9Z98INhZOe888JalUcdBZ/5TJiHM/jpV7kKeGrdMawkXGZm1qxwEd+cjBkTrjvz5JNhEcubb25y116PPgTfnAyA3X47dmF5S6Jo3JAh8LnPhZuIiEgn0uzV08zsq2a2BDjGzBbXub0JLGlrAe5eDVxDGH15Bfiduy81s+lmdkFmt18AB5pZJfANcjjvp7S0tN7zRx4J9+edFyb/nnNOaGSOPjqsKHDppZkdsxeTaewKvISlDxYsCIeaduwIi2B/5zuw8tFwIbt1/Y/hjjvCIts5NzJZ06eH+x//OFxIrzFPPQUTJoRjUNOnw5VXNvu2I0aMaGEhhUtZRMoiUhaRsoiURZT2LJqdM2NmBwADgB9Qv4nY5u4b27G2Nhk9erQvXLgQCH/vDx0K77wTVhn4p38K17Q74YQwEFLnMjRhQs1ll4Xu5t579/sZr74aFqxcuxYuf/QyjnvhHmr++xcUXdmGFR4uvTRMyBk7NhRXUmfw7JlnYPz40EX94z+G4aQUzC4XERHpCE1dNK/ZkRl33+LhAnUPAhvdfSVwOXCnmZ2c90rzZP369bWPX3ghNDJDh4a//59/PqzZ+OijDRoZCJf7h3ge9X4cc0xYKeGWW+A4ewWAomOPaVvh//Ef4ZDPM8+EEZhNm8Is4v/4Dzj77NDIfOELYU2GHBuZWdnVu0VZ1KEsImURKYtIWURpz6Ili/RMdfdtZjYWOIdw6Oe/2qesttuaPeWHeIjpyCPh178OJx099BAcfHAjP9jMYaZG1dTE9ZKObuPyVYMHw4MPhqvpPvBAOB1pwIDQNVVVwVe/Cr/4RYvWV5o3b17baiogyiJSFpGyiJRFpCyitGfRkmYme9GN84A73P0RoPt+9k+NbDOzYEG4//nP4fjjm9i5Nc3MmjWwc2cY1dlnqKcVTjstXHb4nHOgujq896hR8Pvfh+JLWjJvW0REpLC15G/FNWZ2O+Gsph9m1ktK/fLL69eHJqaoKByhOffccJSmSXWbGffcDuVkR2U++ME211vr2GPDKVjbtoWGJrOit4iIiNTXklWzexHWZ1ri7m+Y2RDgBHd/tD0LbK2TTjrJFy1aREUFXHFF2Na7d7gI3QeauTYWvXqFRZi2bQsLJzbnZz+Dr38drr4abr+9raXn3caNGykrK0u6jFRQFpGyiJRFpCwiZRGlJYtWTwA2s28BuPtOoNjd38g8Xwucmec682Z3Zg2A7CEmCBfXbbaRgRZNAgbglTD5l2PaOPm3nVRWViZdQmooi0hZRMoiUhaRsojSnkUuh4kurfP4xgavtctK2vmwdu1a9uyJzUxZGXzjGzn+cEvnzWQPM6W0mZkxY0bSJaSGsoiURaQsImURKYso7Vnk0szsu5Ru089T5dlnw9xZgKlTw+rTOWltM5PPOTMiIiKSk1yaGW/icWPPU+U//zPc9+gRFnnMWUuamS1bwlXzevTI8RiWiIiI5FMuZzOdaGZbCaMwPTOPyTzv0W6VtdGgQYP54x/D44svDpN/W/DD4T6XZqbu9WVacO2XjjR58uSkS0gNZREpi0hZRMoiUhZR2rNotplx9+KOKCTfior6sWNHePz977fwh7MjM3WuItykTnCIafz41E5t6nDKIlIWkbKIlEWkLKK0Z5HOoYQ8WL48TJY59NBWHP056KBw/847ze+b8sm/AOXleVhVu0Aoi0hZRMoiUhaRsojSnkXBNjPV1T2BZi6Q15QhQ8J9gTQzIiIihaxgmxkwiorgxoYnk+ci28ysXdv8vim/xoyIiEihK+BmBk4+GXr2bMUP5trM7NkDy5aFJQ+OOqoVH9QxxowZk3QJqaEsImURKYtIWUTKIkp7FjkvZ9DZdO8+2mfPXsjFF7fih6uroXtmDc2qqqYXdnz11TDx9/DDYfnyVtcqIiIizWv1cgad1aBBa1vXyEBoXgYPDgtNrlvX9H6dZL7M9OnTky4hNZRFpCwiZREpi0hZRGnPomCbmR3Z87Jb6+CDw/3+DjV1kvkyCxYsSLqE1FAWkbKIlEWkLCJlEaU9i4JtZtoslzOaOsE1ZkRERAqdmpmm5DIJuJMcZhIRESlkBTsBePTo0b5w4cLWv8FNN8G//RvcfDNMm7bv6+7Qvz9s3RquFJxdAkFERETaRZebALx169bmd9qfYcPC/apVjb++enVoZAYOTH0jM3fu3KRLSA1lESmLSFlEyiJSFlHasyjYZmZ9Lusq7c9hh4X7FSsaf33p0nB/3HFt+5wOcNtttyVdQmooi0hZRMoiUhaRsojSnkXBNjNtVkDNjIiISCFTM9OUbDOzciXs3bvv62pmREREUqFgm5kh2bORWqtnz7B69p49jZ/R1ImamalTpyZdQmooi0hZRMoiUhaRsojSnkXBNjOlpaVtf5OmDjW5w8svh8edoJkZOXJk0iWkhrKIlEWkLCJlESmLKO1ZFGwzs6KpuS4t0VQz89ZbsH17WPJg4MC2f047mzRpUtIlpIayiJRFpCwiZREpiyjtWRRsM5MX2WbmzTfrb3/hhXA/alSHliMiIiL7UjOzP0ceGe5fe63+9uwaFSlfEl1ERKQrKNhmpl+/fm1/k+OPD/cvvVR/e/bKwqP3uQhhKo0bNy7pElJDWUTKIlIWkbKIlEWU9iwSXc7AzMqA+4DDgBXA59x9UyP7zQVOA55x9/Nzee82L2cAsG0b9OsH3bvDjh1QUhIm/w4cCBs3htO2P/CBtn2GiIiI5CStyxncADzu7kcCj2eeN+bHwOUteeNVTS1D0BJ9+4Z5M1VVUFkZti1fHhqZwYNh+PC2f0YHmDJlStIlpIayiJRFpCwiZREpiyjtWSTdzFwIVGQeVwAXNbaTuz8ObGvJG+/evbttlWWdcEK4z47yPPFEuD/jDDDLz2e0s2XLliVdQmooi0hZRMoiUhaRsojSnkXSzcxB7p69It07wEFJFtOoj3403D/1VLh/7LFw/8lPJlKOiIiI1FfS3h9gZv8POLiRl26q+8Td3czaNIHHzK4GroZw0bzy8vLa12bOnAnAddddV7ttwoQJTJw4kUmTJrFx40YARowYwa233sqsWbOYN28eR27ezE+BvU88wfN/+QvHPPQQfYGr77+fzxxxBOPHj6/3OWPGjGHatGlMnz6dBdmznoCHH36YuXPn1lusa+rUqYwcObLe+fvjxo3jmmuuYcqUKbWdcFlZGRUVFcyePZt77723xd8p+z7Z75RVUVFBZWUlM2bMqN02efLkTvGdGv6ecv1OixYtory8vKC+U2t/T717967384XwnVr7e1q0aBGVmUPJhfKdWvt7yv4ZKaTv1NrfU1lZWcF9p9b+nhYtWsSsWbMS/05NSXoC8GvAme6+1syGAE+5+9FN7HsmcH2HTgAGqK6GQYNg82aYOhVmzAhnOS1e3GkOM4mIiBSCtE4AngNkW9lJwB/y9cbZrq/NSkrgssvC42yHeNVVnaqRmT17dtIlpIayiJRFpCwiZREpiyjtWSTdzNwCfNLM3gDOyTzHzEab2Z3Znczsz8D9wNlmttrMmj3hPW/NDMANN8RlC048Eb7ylfy9dweoO/TX1SmLSFlEyiJSFpGyiNKeRbvPmdkfd38POLuR7QuBK+s8/2hH1rWPoUPhuefgb3+Dc8+FfCxiKSIiInmRaDPTqXzgA7pAnoiISAolOgG4PZ1wwgm+ZMmSpMtIhcrKytQv395RlEWkLCJlESmLSFlEackirROARURERNqkYJuZvCxnUCDqnuff1SmLSFlEyiJSFpGyiNKeRcE2MyIiItI1qJkRERGRTq1gJwCb2TbgtaTrSImBwIaki0gJZREpi0hZRMoiUhZRWrI41N0HNdxYyKdmv9bYjOeuyMwWKotAWUTKIlIWkbKIlEWU9ix0mElEREQ6NTUzIiIi0qkVcjNzR9IFpIiyiJRFpCwiZREpi0hZRKnOomAnAIuIiEjXUMgjMyIiItIFFGQzY2bjzew1M6s0sxuSricpZjbczJ40s5fNbKmZXZt0TUkzs2Ize8HM/ph0LUkys/5m9oCZvWpmr5jZ6UnXlBQzuy7z5+MlM7vXzHokXVNHMbO7zGy9mb1UZ1uZmT1mZm9k7gckWWNHaSKLH2f+jCw2s9+bWf8ka+wojWVR57V/NjM3s4FJ1NaUgmtmzKwYuA34FHAsMMHMjk22qsRUA//s7scCpwGTu3AWWdcCryRdRAr8OzDX3Y8BTqSLZmJmQ4GvA6Pd/XigGLg02ao61K+A8Q223QA87u5HAo9nnncFv2LfLB4Djnf3UcDrwI0dXVRCfsW+WWBmw4F/AN7q6IKaU3DNDHAKUOnuy929CvgtcGHCNSXC3de6+/OZx9sIf2ENTbaq5JjZMOA84M6ka0mSmR0AfAz4BYC7V7n75mSrSlQJ0NPMSoBewNsJ19Nh3P1pYGODzRcCFZnHFcBFHVpUQhrLwt0fdffqzNO/AcM6vLAENPHfBcBM4FtA6ibbFmIzMxSou8rkarrwX+BZZnYYcDLw92QrSdSthD+INUkXkrDDgXeBX2YOud1pZr2TLioJ7r4G+N+Ef2muBba4+6PJVpW4g9x9bebxO8BBSRaTIl8C/m/SRSTFzC4E1rj7i0nX0phCbGakATPrA/wfYIq7b026niSY2fnAend/LulaUqAE+BDwn+5+MrCDrnMooZ7MfJALCQ3eIUBvM7ss2arSw8Pprqn7V3hHM7ObCIft70m6liSYWS/gX4BpSdfSlEJsZtYAw+s8H5bZ1iWZWTdCI3OPuz+YdD0J+ghwgZmtIBx6/ISZ3Z1sSYlZDax29+wo3QOE5qYrOgd4093fdfc9wIPAGQnXlLR1ZjYEIHO/PuF6EmVmVwDnA5/3rnstkxGEhv/FzP9DhwHPm9nBiVZVRyE2MwuAI83scDPrTpjMNyfhmhJhZkaYF/GKu/806XqS5O43uvswdz+M8N/EE+7eJf8F7u7vAKvM7OjMprOBlxMsKUlvAaeZWa/Mn5ez6aKToeuYA0zKPJ4E/CHBWhJlZuMJh6YvcPedSdeTFHdf4u6D3f2wzP9DVwMfyvy/JBUKrpnJTNa6BphH+J/S79x9abJVJeYjwOWEUYhFmdu5SRclqfA14B4zWwycBPxbwvUkIjM69QDwPLCE8P/EVF/pNJ/M7F7gr8DRZrbazL4M3AJ80szeIIxc3ZJkjR2liSxmAX2BxzL///yvRIvsIE1kkWq6ArCIiIh0agU3MiMiIiJdi5oZERER6dTUzIiIiEinpmZGREREOjU1MyIiItKpqZkRERGRTk3NjIiIiHRqamZEpF2Z2YF1Ltr4jpmtqfO8u5k9206fO8zMLmnitZ5m9j9mVtzE693N7OnMStoiknJqZkSkXbn7e+5+krufBPwXMDP73N2r3L291kI6m6bXnPoS8KC7722i5irgcaDRZkhE0kXNjIgkysy2m9lhZvaqmf3KzF43s3vM7Bwz+4uZvWFmp9TZ/zIzm58Z2bm9sdEVMxsL/BS4OLPfEQ12+TyZNYfMrLeZPWJmL5rZS3VGcx7K7CciKadmRkTSYiTwE+CYzG0iMBa4HvgXADP7IGG05COZkZ69NNJwuPszhEVnL8yMAC3PvpZZgPYId1+R2TQeeNvdT3T344G5me0vAWPy/SVFJP/UzIhIWryZWZ23BlgKPO5h8bglwGGZfc4GPgwsMLNFmecNR12yjgZebWT7QGBznedLCAsr/tDMPuruWwAyh6CqzKxvG7+XiLQzTW4TkbTYXedxTZ3nNcT/VxlQ4e437u+NzGwgsMXdqxt5+X2gR/aJu79uZh8CzgW+Z2aPu/v0zMulwK4WfxMR6VAamRGRzuRxwjyYwQBmVmZmhzay32HA2429gbtvAorNrEfmPQ4Bdrr73cCPyUwaNrMDgQ3uvifv30JE8krNjIh0Gu7+MvAd4FEzWww8BgxpZNdXgYGZCb2NnS31KGE+DsAJwPzMYat/Bb6X2X4W8Eg+6xeR9mHhkLSISNeROax0nbtfvp99HgRucPfXO64yEWkNjcyISJfj7s8DT+7vonnAQ2pkRDoHjcyIiIhIp6aRGREREenU1MyIiIhIp6ZmRkRERDo1NTMiIiLSqamZERERkU5NzYyIiIh0ampmREREpFP7//dUqvgqbwRvAAAAAElFTkSuQmCC\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "JQWk0NRNdGBx" + }, + "source": [ + "### **Observer Based Control - Separation Principle**\n", + "Even though state estimation is interesting problem on it's own the main goal is to use the estimated state inside control loop:\n", + "\\begin{equation}\n", + "\\begin{cases}\n", + "\\dot {\\mathbf{x}} = \\mathbf{A} \\mathbf{x} + \\mathbf{B} \\mathbf{u} \\\\\n", + "\\dot{\\hat {\\mathbf{x}}} = \\mathbf{A} \\hat{\\mathbf{x}} + \\mathbf{B} \\mathbf u + \\mathbf{L}(\\mathbf y - \\mathbf{C} \\hat{\\mathbf{x}})\\\\\n", + "\\mathbf{y} = \\mathbf{C} \\mathbf{x} \\\\\n", + "\\mathbf{u} = -\\mathbf{K} \\hat{\\mathbf{x}}\n", + "\\end{cases}\n", + "\\end{equation}\n", + "\n", + "One can graphically represented observer-controller connection as follows:\n", + "\n", + "

\"mbk\"

\n", + "\n", + "\n", + "Collecting $\\dot {\\mathbf{x}}$ and $\\dot{\\mathbf{e}}$ we get:\n", + "\n", + "\\begin{equation}\n", + "\\begin{cases}\n", + "\\dot {\\mathbf{x}} = (\\mathbf{A}-\\mathbf{B}\\mathbf{K}) \\mathbf{x} + \\mathbf{B}\\mathbf{K}\\mathbf{e} \\\\\n", + "\\dot{\\mathbf{e}} = \n", + "(\\mathbf{A} - \\mathbf{L}\\mathbf{C})\\mathbf{e}\n", + "\\end{cases}\n", + "\\end{equation}\n", + "\n", + "In matrix form it becomes:\n", + "\n", + "\\begin{equation}\n", + "\\begin{bmatrix}\n", + "\\dot {\\mathbf{x}} \\\\\n", + "\\dot{\\mathbf{e}}\n", + "\\end{bmatrix}\n", + "=\n", + "\\begin{bmatrix}\n", + "(\\mathbf{A}-\\mathbf{B}\\mathbf{K}) & \\mathbf{B}\\mathbf{K} \\\\\n", + "0 & (\\mathbf{A} - \\mathbf{L}\\mathbf{C})\n", + "\\end{bmatrix}\n", + "\\begin{bmatrix}\n", + "\\mathbf{x} \\\\\n", + "\\mathbf{e}\n", + "\\end{bmatrix}\n", + "\\end{equation}\n", + "\n", + "Eigenvalues of a upper block-triangular matrices equal to the union of the eigenvalues of the blocks on the main diagonal. Hence here, the eigenvalues of the system are equal to the union of eigenvalues of $(\\mathbf{A}-\\mathbf{B}\\mathbf{K})$ and $(\\mathbf{A} - \\mathbf{L}\\mathbf{C})$. \n" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "c-YnaOM0SnmB" + }, + "source": [ + "def observer_controller(state, t, system_param, observer_params):\n", + " x, x_hat = np.split(state,2)\n", + " \n", + " A = system_param['A']\n", + " B = system_param['B']\n", + " K = system_param['K']\n", + "\n", + " C = observer_params['C']\n", + " L = observer_params['L']\n", + " A_obs = observer_params['A']\n", + "\n", + " # \n", + " u = -np.dot(K,x_hat)\n", + "\n", + " dx = np.dot(A,x) + np.dot(B, u)\n", + "\n", + " y = np.dot(C, x)\n", + " \n", + " # \n", + " y_hat = np.dot(C, x_hat)\n", + " e = y - y_hat\n", + " \n", + " dx_hat = np.dot(A_obs,x_hat) + np.dot(B, u) + np.dot(L, e)\n", + " # print(dx_hat)\n", + "\n", + " #\n", + " dstate = np.hstack((dx, dx_hat))\n", + " # dstate = dx, dx_hat\n", + " return dstate" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 650 + }, + "id": "lEfbSRp-UZnz", + "outputId": "e2825ba0-d727-4289-ddb8-003ac59628c5" + }, + "source": [ + "A = [[0, 1, 0, 0], \n", + " [g*(M+m)/(M*l), 0 , 0, 0],\n", + " [0,0,0,1],\n", + " [-m*g/M, 0, 0,0]]\n", + "\n", + "A = np.array(A)\n", + "A_o = A\n", + "Q_c = np.diag([1,1,1,1])\n", + "R_c = np.diag([1])\n", + "\n", + "_, K, _ = lqr(A, B, Q_c, R_c)\n", + "system_params = {'A':A,'B':B,'K':K}\n", + "\n", + "Q_o = 10*np.diag([1,1,1,1])\n", + "R_o = np.diag([1,1])\n", + "_, LT, _ = lqr(A_o.T, C.T, Q_o, R_o)\n", + "L = LT.T\n", + "observer_params = {'A':A_o,'C':C, 'L':L}\n", + "\n", + "state_sol = odeint(observer_controller, state_0, t, args=(system_params, observer_params, )) # integrate system \"sys_ode\" from initial state $x0$\n", + "\n", + "\n", + "x_real, x_hat =np.split(state_sol, 2, axis = 1)\n", + "\n", + "theta, dtheta, x, dx = np.split(x_real, 4, axis = 1)\n", + "\n", + "theta_hat, dtheta_hat, x_hat, dx_hat = np.split(x_hat, 4, axis = 1)\n", + "\n", + "figure(figsize=(9, 3))\n", + "plot(t, theta, 'b--', linewidth=2.0)\n", + "plot(t, theta_hat, 'b', linewidth=2.0)\n", + "plot(t, dtheta, 'r--', linewidth=2.0)\n", + "plot(t, dtheta_hat, 'r', linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'Pendulum $\\theta,\\dot{\\theta}$')\n", + "xlabel(r'Time $t$ (s)')\n", + "show()\n", + "\n", + "figure(figsize=(9, 3))\n", + "plot(t, x, 'b--', linewidth=2.0)\n", + "plot(t, x_hat, 'b', linewidth=2.0)\n", + "plot(t, dx, 'r--', linewidth=2.0)\n", + "plot(t, dx_hat, 'r', linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'Cart $x,\\dot{x}$')\n", + "xlabel(r'Time $t$ (s)')\n", + "show()\n", + "\n", + "figure(figsize=(9, 3))\n", + "plot(t, theta - theta_hat, 'b', linewidth=2.0)\n", + "plot(t, dtheta - dtheta_hat, 'r', linewidth=2.0)\n", + "plot(t, x - x_hat, 'b', linewidth=2.0)\n", + "plot(t, dx - dx_hat, 'r', linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'Estimation Error ${x}$')\n", + "xlabel(r'Time $t$ (s)')\n", + "show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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\n", 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gtLQ0pY6pp7/TVVdd1erzqXBMPf2dGhoaiMViKXVMPf2d4v+OpNIx9fR3WrBgQcodU09/p4aGBiorK0M9ps505y6wy3Bjgd0TrPoCcKOqXpvUDjre74nA91W1OFi+EkBVf5ywTU2wzb9EJAvYDBwQP6MjIguAN1X1Rx18xwVAkarO6qyW40eM0JXbtsFdd8EXv9jxhqefDkuXwt13w1lndeNo9x+xWIzCwsKwy4gEy8KzLDzLwrMsPMvCi0IWfXUX2EXACao6T1XnAR/GNYh6awVwhIgcJiI5wLnAkjbbLAHizeSzgb8lNH4ygC+R0P9HRLJEZEwwnw2cBjxPF3bu2OFmOrsEBmnRETqxBZ7uLAvPsvAsC8+y8CwLL+pZdOcSmABNCctNJPQb7qmgT88soAbIBG5W1TUiUgHUquoS4LfA70QkBtTjGklxHwdei3eiDuQCNUHjJxP4K/CbrmpJqhM0pEUDyBhjjEll3WkA3QI8JSL3Bstn4homvaaq9wP3t1k3L2F+F9DuNSlVfRR3NipxXQMwpbt1tHSC7uw5QACHHeZeX321u19hjDHGmAhIqgEkIgL8AXgUOClYfaGqPtNPdYUiOysLmpq6PgMUv6b5yiv9X1RIysrKwi4hMiwLz7LwLAvPsvAsCy/qWdhQGAmKhgzR2p07obYWpnRyAum992DYMHemaMcOyMwcuCKNMcYYk5TID4URFXv37HEzXZ0BGjoUDjoI9uyBjRv7v7AQJN6ame4sC8+y8CwLz7LwLAsv6lmEPhRGpCTzIMS4+GWw4DkgqSb+vAVjWSSyLDzLwrMsPMvCi3oW3ekDNANI6dueku4EDa4B9MQTrgF08sn9W5gxxhhj+lRSDSBVVRFZlOp9gFpOh9kZIAoKCsIuITIsC8+y8CwLz7LwLAsv6ll0pxN0FVCpqiu63Hg/VZSVpbVNTW6Mr1GjOt/4zjvh3HPhC1+Ae+7pfFtjjDHGDLi+6gR9AvBkKvcB0uZmN2NngKisrAy7hMiwLDzLwrMsPMvCsyy8qGfRnQZQMXA4cDJQihteorTTT+xnutUHKH5qLxbznadTSOIAc+nOsvAsC8+y8CwLz7Lwop5Flw0gEfk2gKquB6ap6vr4BFzc3wUOuIwMyEqia9TIkTB6NOzcCa+/3v91GWOMMabPJHMGKHHcrSvbvFfSh7VEQzKXv+KOOsq9vvhi/9RijDHGmH6RTANIOphvb3n/150G0KRJ7vWFF/qnlhBVVVWFXUJkWBaeZeFZFp5l4VkWXtSzSKYBpB3Mt7fcIyJSIiIviUhMRK5o5/1cEbkzeP8pEZkYrJ8oIjtFZFUwXZ/wmSlBR+2YiPwqeJZR15Lp/xOXwg2gWIp27u4Jy8KzLDzLwrMsPMvCi3oWyTSAjhORbSKyHTg2mI8v9/q5QCKSCSwCPgtMAspEZFKbzS4C3lHVQmAB8JOE9+pUdXIwXZKw/tfAfwFHBFNyl+vsDBAA8+fPD7uEyLAsPMvCsyw8y8KzLLyoZ9FlA0hVM1V1uKoOU9WsYD6+nN0HNUwDYqq6VlX3AHcAZ7TZ5gwgfi7tj8ApnZ3REZFxwHBVfVLdg45uA85MqpqeNIDWrEnJO8GMMcaYVNWd2+D7y3jgtYTlDcG6drdR1UZgKzA6eO8wEXlGRB4TkY8lbL+hi322rzuXwMaPd6PCv/02vPlm8p8zxhhjTKiSGgojwjYB71PVt0VkCvAnETm6OzsQkRm4cc6YAtRt2MDsUvd4owULFgAwZ86clu3LysqYPn065eXl1NfX87PMTI4CeOEFKu+6q9VzD6qqqojFYq1OA86cOZOSkhJKS/0jlKZOncq8efOoqKhgxQr/oO2lS5eybNkyFi1a1LJu7ty5FBYWthplt7i4mFmzZjF79mzq6uoAyM/Pp6qqiurqahYvXtyybTLHBJCZmQm4B1mlyjEVFBSwcOHCbh/Tli1bKC0tTalj6unvdP7557f6fCocU09/py1btrT0cUiVY+rp7xT/dySVjqmnv9PMmTNT7ph6+jtt2bKFysrKUI+pM0kPhdFfRORE4PuqWhwsXwmgqj9O2KYm2OZfIpIFbAYO0DbFi8ijwOXARuARVT0qWF8GfFJVO31uUZGI1hYVwYpujPZx0UVw882waBFcemnynzPGGGNMv+qroTD6ywrgCBE5TERycM8dWtJmmyVAvJl8NvC3YIDWA4JO1IjI4bjOzmtVdROwTUQ+HPQVOh/4c1LVZHezW1NiP6AUkvh/AOnOsvAsC8+y8CwLz7Lwop5F0pfARCQX+H/AxMTPqWpFbwpQ1UYRmQXUAJnAzaq6RkQqgFpVXQL8FvidiMSAevzDGT8OVIjIXqAZuERV64P3LgVuBQYDDwRT17rbADrmGPf6XEoNi2aMMcaktO70AfozrvPx08DuvixCVe8H7m+zbl7C/C7gi+187m7g7g72WQsc0+1ikhkGI9GHPuRen3kGmpvdUBrGGGOMibTu/LWfoKqpN/RFW909AzR2LEyYABs2wCuvwJFH9k9dA2zq1KlhlxAZloVnWXiWhWdZeJaFF/Usku4ELSI3Ateq6ur+LSk8RSJa+/nPw333de+DZ5wBS5ZAdTWUlfVPccYYY4zplr7qBH0S8HQwZMVzwTATqdfxpbtngKD1ZbAUUVHRq65dKcWy8CwLz7LwLAvPsvCinkV3LoF9tt+qiJKeNICOP969rlzZt7WEaEV3HgWQ4iwLz7LwLAvPsvAsCy/qWSR9BkhV1wMjgdJgGhmsSy3d7QQNvgFUW+s6QhtjjDEm0pJuAInIZcDtwNhg+r2IfKO/CgtNT84ATZjgpq1b4d//7vuajDHGGNOnutMJ+jngRFVtCJbzgH+p6rH9WN+AKhLR2osugptu6v6Hzz0X7rwTbrgBZszo++KMMcYY0y191QlagKaE5aZgXWrpySUwgI9+1L3+4x99V0uIli1bFnYJkWFZeJaFZ1l4loVnWXhRz6I7DaBbgKdE5Psi8gPgKeDm/ikrRD25BAYp1wBKHOAu3VkWnmXhWRaeZeFZFl7Us0j6dIeq/iIYbDT4S0+5qq7ql6rC1NMG0LHHQl4e1NXB5s1w0EF9W5cxxhhj+kyXDSAReUJVTxKR7YCScNlLRFRVh/dngQOuJ5fANm2CpUth2DBoaHDPBRoxAkaNgsMOg6OPdmeIpk2DIUP6vmZjjDHGdEuXf+1V9aTgdVj/lxMB3TkDtG4dfPe7cNdd0Njo12/e7CaAJ5/063NzobgYzjoLTj/dNZAiau7cuWGXEBmWhWdZeJaFZ1l4loUX9Sy6cxv8T5JZ1xMiUhI8YTomIle0836uiNwZvP+UiEwM1n9aRJ4Onkr9tIicnPCZR4N9rgqmsUkVk8wZIFW47jp3Zqe62j375/TTXWMI4IADYM0aeOwxuOUWmDULJk+G3bvdkBkXXADjxsGXvwyPPBLJZwcVFhaGXUJkWBaeZeFZFp5l4VkWXuSzUNWkJmBlO+ueS/bznew3E6gDDgdygGeBSW22uRS4Ppg/F7gzmP8QcHAwfwywMeEzjwJF3allCqjOn6+damxUveQSVdcMUj3nHNV169x7zc2q48a59atX7/vZjRtVr7tO9eSTVUX8PgoKVH/xC9V33+38uwfQaaedFnYJkWFZeJaFZ1l4loVnWXhRyAKo1Q7+5nd5BkhEvi4iq4EjgzHA4tOrQF+MBTYNiKnqWlXdA9wBnNFmmzOAqmD+j8Ap4jogPaOqrwfr1wCDRSS3V9V0dglM1Z3Nuf56GDTInf254w449FD3vgh85jNu/i9/2ffzBx8MX/86PPwwrF0L8+a5ByjW1cG3vgWHHAKzZ7tlY4wxxvSbLh+EKCIjgFHAj4HEy1PbVbW+1wWInA2UqOrXguXzgBNUdVbCNs8H22wIluuCbd5qs59LVPXUYPlRYDTueUV3A1drOwcrIjOAGQBTYMrXP/AB/lRQAMCCBQsAmDNnDgBfeuUVznvpJcjN5cef+AT/zMkBoKCggIULF1JZWcnWqiq+W1vLyyNGMGbtWmKxGPPnz2/5vpkzZ1JSUkJpaSkAGaqUDR/OuZs2waOPAtAMPHXggZx4550s27GDRddd1/L5uXPnUlhYSHl5ecu64uJiZs2axezZs6kLGk/5+flUVVVRXV3N4sWLW7Zte0wAZWVlTJ8+nfLycurr3U+6Zs0a1q5dS2VlJTU1NS3bVlVVdXlMAFOnTmXevHlUVFS0Gg9m6dKlLFu2rNXtkQN1TIm/U3eOafny5UybNi2ljqmnv9PcuXPJCf65T5Vj6unvtHz5cv4RPPYiVY6pp7/T/PnzmTZtWkodU09/pxUrVrS8psox9fR3Wr58OXPnzg31mO67774OH4TYq8tXfTEBZwM3JSyfB1S22eZ5YELCch0wJmH56GBdQcK68cHrMOBB4PyuapkCqr/8Zfvn0R57TDUjw126+tOfOj7ftmOHal6eu7T16qsdb9eeZ55RLS9Xzcnxl8cmT1a99VbVXbu6t69euvbaawf0+6LMsvAsC8+y8CwLz7LwopAFnVwCS3ooDAARGQUcAQxKaEA9nvQO2t/nicD3VbU4WL4y2O+PE7apCbb5l4hkAZuBA1RVRWQC8DfgQlVt9ymEInIBrj/QrPbejysS0drrrnOXqRJt3QrHHAMbNsCVV8KPftT5QcWHxfjZz+Dyyzvftj2bN7vLbNddB2++6daNHevquuQSe8aQMcYYk4Q+GQpDRL4GPA7UAD8IXr/fB/WtAI4QkcNEJAfXyXlJm22WAPHzhGcDfwsaPyOBvwBXJDZ+RCRLRMYE89nAabizSF1r7y6wq65yjZ9p0+AHP+h6H1/8onv93e/ceZzuOugg+P734T//cXeRTZ4MW7a4737f+6C8HFau7P5+u2H27Nn9uv/9iWXhWRaeZeFZFp5l4UU9i+4MhXEZMBVYr6qfwt2B9W5vC1DVRmAWrkH1b+AuVV0jIhUicnqw2W+B0SISA76F74s0CygE5rW53T0XqAkGcF0FbAR+k1RBbTtBr14NlZWQkeEGOk3mOUGnnQZjxsBzz8Hy5Ul9bbsGDXK3zK9c6foHnXmme97QbbfBlCnw8Y/D3Xe3fgZRH6mzjtgtLAvPsvAsC8+y8CwLL+pZdOexx7tUdZeIICK5qvqiiBzZF0Wo6v3A/W3WzUuY3wV8sZ3PXQ1c3cFup/SomLYNnG9/G5qaYOZMdyYmGbm5ruHyf/8HN94IJ5zQo1JaiMAnPuGmtWtdg+y3v4W//91N48bBhRfCV78KQQduY4wxxnSsO2eANgSXnP4EPCQifwbW909ZIUq8BPbUU7BsGQwd6i5Jdcd//Zd7ra6GN97os/I4/HD4xS/cJblf/QqOPNINxfGjH0FhIZxyivvOXbt69TX5+fl9VPD+z7LwLAvPsvAsC8+y8KKeRbc6Qbd8SOQTwHBgmaru7fOqQlIkorV33+2GqgD43OfggQeS6/jcnjPOcE9+/s534Jpr+rbYOFU3Av1vfgN/+APs3OnWjxwJZ5/tOmR/8pOQmdk/32+MMcZEVF91gi4SkXtFZCVwLfAj4Ok+qjE64meAVq1yjZ+hQ91DCnvie99zr4sWwVtvdb5tT4nASSdBVRW8/rq7c+z44+Hdd+Gmm+DUU93DFi+7zI1LlmSDt7q6un/q3Q9ZFp5l4VkWnmXhWRZe1LPoziWw24FbgP8HlOLurCrt9BP7o3gfoGuvda8XXeQ6NPfE1KnuLNJ778H//m/f1NeZkSPdrfJPPw3PP+/GJisocLfV/+pXcOKJ7i6ySy91l/Y6uUyW+HCqdGdZeJaFZ1l4loVnWXhRz6I7DaA3VXWJqr6qquvjU79VFpbsbHj7bdePBlzn5974+c/dWaWbbnJ9igbK0UfD1VfDK6+4O9G+9S0YP971Hfr1r+Gzn3UNu7POcrfab9gwcLUZY4wxIetOA+gqEblJRMpE5Kz41G+VhSUry91htWuXayQccUTv9nfUUa7xoepGf9++vW/qTJaIOxP185+75wqtWOHGIJs8GRoa4N573d1jhxziOlRfeincfTfD9uwZ2DqNMcaYAZR0J2gR+T1wFG7Q0eZgtarqV/uptgFXJKK1jz8O558P69a5AU0/93FAON0AABzFSURBVLne73jXLvjwh+HZZ90Zl7vuikan5P/8B+67z/V1euyxVo0zFUGOOcZdNotP73+/a1ClmVgsRmFhYdhlRIJl4VkWnmXhWRZeFLLorBN0d54DNFVV++S5P5G2Zo1r/LzvfVBS0jf7HDTIDY1xwglwzz3ustp117mHK4Yp3h/o0kth716orXUj1T/8sLuzbPVqN914o9s+P9815KZOdWeQjjsOJk5My0aRMcaY/Vt3/gL/U0Qm9VslUbFsmXv9ylf2aaCounZCjxx5JPz5z5CT454ofc45sGNH72rtS9nZ7izP974HjzzC2aee6h6y+NOfurNW48ZBfT3cf78bkuMLX3DPJBo1yj2R+hvfcLfi//3vbtiOngwBElGJIxOnO8vCsyw8y8KzLLyoZ9GdM0AfBlaJyKvAbkBwl8CO7ZfKwvLXv7rX885rWbV+PfzP/7i//Q0NrrvMpz/t2gWf+Uxyo2MA7knO998PZ53F1j8+yLNPzWDt+d9nXVYhr78O27a5cVffe8+1H+InVjIyIC8Phg1z09Ch7nXUKDjgANeXOXEaOrT3J2X2ZGa62+tPOsmtUHWXzP71L3jmGfeYgFWrXGMn/kTqRCNHuktmRx7ppiOOgEMPdWeMxo61s0bGGGNC1Z0GUB9dD4q4hgY36OlRRwFQV+eu+sQf4yMCr70GN9/sptGj3fMGp093bYWOrmrt3OnaVkuWnMITo9/gxW2D4DXgh31/CDk5rRtEiY2k9uZHj3ajd3RKxDVgDj3UPVwxbvNm17dp1Sp36/1LL7np3Xfd3WftjYU2aJC7/DZxot/nwQe7s0wHHeSmAw6IRj8pY4wxKSnpBlB/3vIuIiXAL4FM4CZVvabN+7nAbbjxvd4GzlHVdcF7VwIXAU3AN1W1Jpl9dur88wFobnZ/6996C04+GW691f2dfv55WLoU7rjDdRm64QY3TZgAZWWuMXTcca7N8MIL7jmIt93mzuw4g8jJUY4bvZH3b/k7E5vqGM9GRh44iBEfPYahJ0xyHZCHDUPVDUXW0OA+v327e922Dd55x9XWdmpocM9EfP315H+DYcNaN462b/8ll1/ul0eOdNOIEa2nQfEGS3Gx35mqG/4j3hh66SU3htn69W6qr4eXX3ZTRzIy3JmieKNo7FjXUsvP3/c1Pp+X1y9nlsrKyvp8n/sry8KzLDzLwrMsvKhn0eVdYCLyhKqeJCLbgcSN45fAhveqAJFM4GXg08AGYAVQpqovJGxzKXCsql4iIucCX1DVc4I+SYuBacDBwF+B9wcf63Sf7SkS0dqsLDe21pgx3HmnawCNH+8aOiNG7PuZ1avdI4Oqq90VorjDD3d/w2Mxv27KFDc6RnGx60Ock4NrKCxc6FpIbVss48fDpElw2GH+DMmBB7pChg93U/y62KBBLaefdu50jzJ6803fKOpqvqmp05+pQzk5+zaKRoxwl+Hy8mDIEPeaOD8iYzuj31vPqG3rGfHOOvLeWs+gdzeTU7+ZzDc3kbllM/J2D56cHS8mnkl8SswpcV1eHgwe3PWUkK0xxpj9R2d3gfVoLLC+JCInAt9X1eJg+UoAVf1xwjY1wTb/EpEsYDNwAHBF4rbx7YKPdbrP9hSJaG1xcUtH6I98xHV5uf56uPjizo+judlte/vtri3T0LDvNgce6BpGY8e2vvw0ZAgMyW3ifa8+xoQX/8rYNX9j2NpnydzTvQFNNSsLzcl1U3YO5OSiuW2Ws7Lcs44y3atmZaGZWWzV4bzVOIq3mkbyduMInvz3m4w8dApv7xnGW7uHs3XvELbuHcy2PYPZtmcQ2/YMYuuuXPY2989lqmz2cJC8wfuyXueQzE0cmLGFAzLeZrTUk089+VrPSK1nZHM9w5veYXhjPYOad/ZLLQBNWbk0ZefSlD2YpuxcNDOb5qxsNCsbzcxGs918c1aOW5ft1pOd7bLPCl6zs4LlLCQrC8nKdJf6MjOC130nzchEMjPQDLeNZGbt+5mMYNvMTCT+HoJkCIggmcGrCJrh1ou4dcS3yRCQDLeNCBmZGS2fj29z9Q9/yNx589zn4++JgIBkZkBGBhmZ0uq7VRK2SxRfFnGzHb0fn21Zln3eb+8zbb+j1Xd1tX18vpPv+PrXv8711/+6688k+R3+8Hp/FrMvT4Qms68LL7yQW265pU/2lazQuxF2UMAFF1zArbfeOrC1RFQUssjMyep9A0hEfqKq3+lqXXeJyNlAiap+LVg+DzhBVWclbPN8sM2GYLkOOAHX2HlSVX8frP8t8EDwsU732Z4iEa29+Wa48EJiMddvNy/PnaTJy+v6WOrr3c1d8X7UH/qQO3FTV+euAHXn2YIZNHEYrzKJF5jABg7mdcaxibFsYTjbGMZ2hrOtZX4wvRv9vScU2MUgtjJin+k9hrKDITSQRwN5LfPtrYvP72Qwu8ltmZrpXuNqEDtb8ohPbZcT1+fRwGB2JjENfLbGGGN6T6BPngP0aaBtY+ez7azbr4jIDGAGuA5GX6muZus991BX9wXgq5xyynbOPXd6y/ZlZWVMnz6d8vJy6uvrASgoKOAb31jIRz7yDlu2jCIn512OPfZaampmEovFmD9/PgUFGezaNZrPfOZiCgpO4Ac/WMSePcPYu3cY+fmHcPTRRdTWruGtt96jqSmH5uYcDjzqaF5+ewyPb34TEFQzGDv2IDIzc9iwYXPLusGDhzBs6HC21b9Bxt4d5LKbQdLEQaPyaNzxDk07tpHLHnLZzfC8PDK1kV0NW8nSRrJoZEhOJoOzM9mzYyuZ2kimNpLRvJfheYNp3rMDadpNFk1kaiNDcjPJaNoLjTvdOhrJzYRcaaJp724yaCYDJVOaGZnRwMjmd0GbWtZnZwhoE9LcSAZKBs1kZiiZKNK8N9iumQxRlAwaVWgii71k0UQWTWSzl0wag3XuCHLYSzaNbm80kRlsm0kTGTSS2bK+gTy2Mpwm3he877dtbGdZERTIDr4pmz3Bu80te3bfmvgtTcF8Y1Dpvt+SRSPuPEmzP+YgDzfFv6Mp2H8zErz695qDI9z3NYPmoHJ3BO67tMOJhG26+mxG8BzU9vbT2Wdb/XvXx8v9sc8wvqO97zTRY7/T/iGjq99JVTudgK8Dq4EdwHMJ06vA7V19Pon9nwjUJCxfCVzZZpsa4MRgPgt4C3cevNW28e2S2Wd707jRo1Wbm1VVtaREFVRvv127FIupjhvntj/uONXXXuv6M1F32WWXhV1CZFgWnmXhWRaeZeFZFl4UsgBqtYO/+cl0gh4BjAJ+TNDnJrBdVes7b151LejT8zJwCrAR12F5uqquSdhmJvBB9Z2gz1LVL4nI0UA1vhP0w8ARuMZRp/tsT1FRkdbW1rJnj7uxKH431bhxHX9mwwb42Mfcw6M/+UlYssT1sTXGGGNMuDrrBN3lrS2qulXdLef3APXqboc/D7hJRD7U2+JUtRGYhTt782/gLlVdIyIVInJ6sNlvgdEiEgO+he/8vAa4C3gBWAbMVNWmjvbZVS1btmwB3GNtGhrc8/s6a/zs2gVnnukaPyeckFqNn8rKyrBLiAzLwrMsPMvCsyw8y8KLehbdubd3rqpuF5GTgFNxjZLr+6IIVb1fVd+vqgWq+sNg3TxVXRLM71LVL6pqoapOU9W1CZ/9YfC5I1X1gc722ZVt27YB7pl+AEXtthm9b3wDnn7a3dl1//2p0/gBqKmpCbuEyLAsPMvCsyw8y8KzLLyoZ9GdBlD8STGfB25U1b8AOX1fUvieeca9Tp7c8TaLF8NNN7lHxNx9t7tkZowxxpj9Q3caQBtF5AbgHOD+4OnMKfl0uPgZoI4aQFu2uLM/AL/8ZecNJWOMMcZET3eeAzQENx7YalV9RUTG4TomP9ifBQ6kyZMn6zPPrGLECDfkxJYt7oGFbU2f7s4AnXoqPPhgBB7I1Q/q6+vJt9NagGWRyLLwLAvPsvAsCy8KWfSqE7SIfBtAVXcAmar6SrC8CfhkH9YZut27d/Pmm67xM3Kke1JzW//8p2v8DB4MN96Ymo0fgFjiGB5pzrLwLAvPsvAsC8+y8KKeRTKXsBKG/ubKNu+l1AjxmzZtahm7q7Bw38aNKvz3f7v5yy93Q3Slqvnz54ddQmRYFp5l4VkWnmXhWRZe1LNIpgEkHcy3t7zfS2wAtXXvvfDkk25Mr//5n4GtyxhjjDF9J5kGkHYw397yfq+jBpAqXH21m587N7VueTfGGGPSTTJjgR0nIttwZ3sGB/MEy4P6rbIQjB07lro6N19Q0Pq9mhp3e/yBB8JXvzrwtQ20mTNnhl1CZFgWnmXhWRaeZeFZFl7Us0j6LrB0UFRUpEOG1PL3v8PDD8PJJ/v3PvEJePxx+OlP7fKXMcYYsz/o1V1g6SQWi7Fxo5sfP96vX73aNX6GDYOLLw6ntoFWWloadgmRYVl4loVnWXiWhWdZeFHPwhpAbbTXAPr1r93r+efD8OEDX5Mxxhhj+pY1gBKoZrJ7N4wYAUOHunXbt8PvfufmL7kkvNqMMcYY03dCbQCJSL6IPCQirwSvozrYrjzY5hURKQ/WDRGRv4jIiyKyRkSuSdj+AhF5U0RWBdPXkqknN9e1ehLP/tx5J7z3Hpx0EhxzTC8Odj8zderUsEuIDMvCsyw8y8KzLDzLwot6FqF2ghaRnwL1qnqNiFwBjFLV77TZJh+oBYpwt90/DUwBdgMnqOojIpIDPAz8SFUfEJELgCJVndWdeo44okhjsVo+/Wk3xAXApz4Fjz4KN98MF17Ym6M1xhhjzECKcifoM4CqYL4KOLOdbYqBh1S1XlXfAR4CSlR1h6o+AqCqe4CVwITeFPPmm1sBfwZowwZ47DHIzYWzzurNnvc/FRUVYZcQGZaFZ1l4loVnWXiWhRf1LMJuAB0YjCkGsBk4sJ1txgOvJSxvCNa1EJGRQCnuLFDc/xOR50TkjyJySDLF7NrV6IoKqrjjDvcAxNNOc/2C0smKFSvCLiEyLAvPsvAsC8+y8CwLL+pZJPMgxF4Rkb8CB7Xz1ncTF1RVRaTb1+NEJAtYDPxKVdcGq5cCi1V1t4hcjDu7dHIHn58BzADIyDgUgCVLfsuaNX9i7do/AINYt+6HlJY+CUBZWRnTp0+nvLyc+vp6AAoKCli4cCGVlZXU1NS07LuqqopYLNZqPJSZM2dSUlLS6vbAqVOnMm/ePCoqKlr9A7N06VKWLVvGokWLWtbNnTuXwsJCysvLW9YVFxcza9YsZs+eTV3wJMf8/Hyqqqqorq5m8eLFLdsuWLAAgDlz5rSsa++Y1qxZA5BSx9TT32n58uWUlpam1DH19Hfas2dPq8+nwjH19Hdavnx5y2CPqXJMPf2d4v+OpNIx9fR3AlLumHr6Oy1fvpzKyspQj6lTqhraBLwEjAvmxwEvtbNNGXBDwvINQFnC8s24xk9H35EJbE2mnuzs9yuo3nqr6quvqoLq0KGqO3dq2jnttNPCLiEyLAvPsvAsC8+y8CwLLwpZALXawd/8sDtB/wx4W30n6HxV/XabbfJxHZ+PD1atBKaoar2IXA18APiiqjYnfGacBpfWROQLwHdU9cNd1TNiRJFu21bLX/4CdXXwzW/C2WfDH/7QJ4drjDHGmAEU5U7Q1wCfFpFXgFODZUSkSERuAlDVemA+sCKYKoLGzwTcZbRJwMo2t7t/M7g1/lngm8AFyRSze3cTAGPGwJIlbt3pp/fBUe6Hli1bFnYJkWFZeJaFZ1l4loVnWXhRz8LGAkuQkTFZVVexahUUFbkO0G+8AaNHh13ZwCstLWXp0qVhlxEJloVnWXiWhWdZeJaFF4UsonwGKFJUMwFYtQoaG93DD9Ox8WOMMcakOmsAtSLk5rqBTwE++9lwqzHGGGNM/7BLYAlEinT8+FqysmD9eqithSlTwq4qHMuXL2fatGlhlxEJloVnWXiWhWdZeJaFF4Us7BJYNwwd6ho/+fkweXLY1YSnsLAw7BIiw7LwLAvPsvAsC8+y8KKehTWA2mgObqb/1KcgMzPcWsKU+HCudGdZeJaFZ1l4loVnWXhRz8IaQG00NLjXU04Jtw5jjDHG9B9rALXx9tvu9dRTw63DGGOMMf3HGkBt7N4NhxwCEb902e+Ki4vDLiEyLAvPsvAsC8+y8CwLL+pZ2F1gCUSKFGopK4Pq6rCrMcYYY0xv2F1g3fSRj4RdQfhmz54ddgmRYVl4loVnWXiWhWdZeFHPwhpA7TjxxLArCF9dXV3YJUSGZeFZFp5l4VkWnmXhRT0LawC1kZsLxx4bdhXGGGOM6U+hNoBEJF9EHhKRV4LXUR1sVx5s84qIlCesf1REXgpGgl8lImOD9bkicqeIxETkKRGZmGxNH/gAZGf39sj2f/n5+WGXEBmWhWdZeJaFZ1l4loUX9SxC7QQtIj8F6lX1GhG5Ahilqt9ps00+UAsUAQo8DUxR1XdE5FHgclWtbfOZS4FjVfUSETkX+IKqntN1PUV64YW13HxznxyeMcYYY0IU5U7QZwBVwXwVcGY72xQDD6lqvaq+AzwElHRjv38EThERSaYg6wDtVNttcC0sC8+y8CwLz7LwLAsv6llkhfz9B6rqpmB+M3BgO9uMB15LWN4QrIu7RUSagLuBq9Wd0mr5jKo2ishWYDTwVtudi8gMYIZbmsLtt8/gz392JS1YsACAOXPmtGxfVlbG9OnTKS8vp76+HoCCggIWLlxIZWUlNTU1LdtWVVURi8WYP39+y7qZM2dSUlJCaWlpy7qpU6cyb948KioqWLFiRcv6pUuXsmzZMhYtWtSybu7cuRQWFrZ6xHhxcTGzZs1i9uzZLZ3O8vPzqaqqorq6msWLF7dsm+wxrVmzhunTp6fUMfX0d1q+fDmLFy9OqWPq6e9UVVXVqs5UOKae/k6JAz2myjH19HeaP39+yz5S5Zh6+jutWLGCWCyWUsfU099p+fLl1NfXh3pMnen3S2Ai8lfgoHbe+i5QpaojE7Z9R1Vb9QMSkcuBQap6dbA8F9ipqv8nIuNVdaOIDMM1gH6vqreJyPNAiapuCD5TB5ygqvs0gBJlZx+lu3a9mNZjgMWVlpaydOnSsMuIBMvCsyw8y8KzLDzLwotCFp1dAuv3M0Cq2uGgEiLyhoiMU9VNIjIO2NLOZhuBTyYsTwAeDfa9MXjdLiLVwDTgtuAzhwAbRCQLGAG83VWteXmbrfFjjDHGpIGwO0H/DHg7oRN0vqp+u802+biOz8cHq1YCU4BtwEhVfUtEsoHFwF9V9XoRmQl8MKET9Fmq+qWu6vngBz+oq1ev7rsD3I/FYjEK0308kIBl4VkWnmXhWRaeZeFFIYtQzwB14RrgLhG5CFgPfAlARIqAS1T1a6paLyLzgfjFx4pgXR5QEzR+MoG/Ar8Jtvkt8DsRiQH1wLkDd0jGGGOMiTobCyzByJEj9d133w27jEiIwrXbqLAsPMvCsyw8y8KzLLwoZBHl2+CNMcYYYwacNYCMMcYYk3bsElgCEdkOvBR2HRExhnaem5SmLAvPsvAsC8+y8CwLLwpZHKqqB7T3RtidoKPmpY6uFaYbEam1LBzLwrMsPMvCsyw8y8KLehZ2CcwYY4wxaccaQMYYY4xJO9YAau3GsAuIEMvCsyw8y8KzLDzLwrMsvEhnYZ2gjTHGGJN27AyQMcYYY9KONYACIlIiIi+JSCwYlywticghIvKIiLwgImtE5LKwawqTiGSKyDMicl/YtYRNREaKyB9F5EUR+beInBh2TWEQkTnBvxvPi8hiERkUdk0DSURuFpEtIvJ8wrp8EXlIRF4JXkeFWeNA6SCLnwX/jjwnIveKyMgwaxwo7WWR8N5/i4iKyJgwauuINYBwf+SARcBngUlAmYhMCreq0DQC/62qk4APAzPTOAuAy4B/h11ERPwSWKaqRwHHkYa5iMh44JtAkaoegxuHMN3GGrwVKGmz7grgYVU9Ang4WE4Ht7JvFg8Bx6jqscDLwJUDXVRIbmXfLBCRQ4DPAP8Z6IK6Yg0gZxoQU9W1qroHuAM4I+SaQqGqm1R1ZTC/HfdHbny4VYVDRCYAnwduCruWsInICODjuIGGUdU9qpquA+dlAYNFJAsYArwecj0DSlUfxw0ynegMoCqYrwLOHNCiQtJeFqr6oKo2BotPAhMGvLAQdPDPBcAC4NtA5DocWwPIGQ+8lrC8gTT9o59IRCYCHwKeCreS0CzE/YvbHHYhEXAY8CZwS3BJ8CYRyQu7qIGmqhuB/8P93+wmYKuqPhhuVZFwoKpuCuY3AweGWUyEfBV4IOwiwiIiZwAbVfXZsGtpjzWATLtEZChwNzBbVbeFXc9AE5HTgC2q+nTYtUREFnA88GtV/RDQQPpc5mgR9G05A9cgPBjIE5GvhFtVtKi7tThy/7c/0ETku7guBbeHXUsYRGQI8L/AvLBr6Yg1gJyNwCEJyxOCdWlJRLJxjZ/bVfWesOsJyUeB00VkHe6S6Mki8vtwSwrVBmCDqsbPBv4R1yBKN6cCr6rqm6q6F7gH+EjINUXBGyIyDiB43RJyPaESkQuA04Ava/o+a6YA9z8Kzwb/HZ0ArBSRg0KtKoE1gJwVwBEicpiI5OA6NS4JuaZQiIjg+nn8W1V/EXY9YVHVK1V1gqpOxP3z8DdVTdv/01fVzcBrInJksOoU4IUQSwrLf4APi8iQ4N+VU0jDzuDtWAKUB/PlwJ9DrCVUIlKCu3R+uqruCLuesKjqalUdq6oTg/+ObgCOD/5bEgnWAAKCDmuzgBrcf8zuUtU14VYVmo8C5+HOeKwKps+FXZSJhG8At4vIc8Bk4Ech1zPggjNgfwRWAqtx/w2N9NNu+5qILAb+BRwpIhtE5CLgGuDTIvIK7izZNWHWOFA6yKISGAY8FPz38/pQixwgHWQRafYkaGOMMcakHTsDZIwxxpi0Yw0gY4wxxqQdawAZY4wxJu1YA8gYY4wxaccaQMYYY4xJO9YAMsYYY0zasQaQMcYYY9KONYCMMZEjIqMTHsS5WUQ2JizniMg/++l7J4jIOR28N1hEHhORzA7ezxGRx4NR4o0xEWcNIGNM5Kjq26o6WVUnA9cDC+LLqrpHVftr/K1T6HiMs68C96hqUwc17wEeBtptQBljosUaQMaY/Y6IvCciE0XkRRG5VUReFpHbReRUEfmHiLwiItMStv+KiCwPziDd0N5ZHBE5CfgFcHaw3eFtNvkywRhXIpInIn8RkWdF5PmEs0Z/CrYzxkScNYCMMfuzQuDnwFHBNB04Cbgc+F8AEfkA7qzMR4MzSk2000hR1SdwAyOfEZxpWht/Lxgk+XBVXResKgFeV9XjVPUYYFmw/nlgal8fpDGm71kDyBizP3s1GHW6GVgDPKxugMPVwMRgm1OAKcAKEVkVLLc9uxN3JPBiO+vHAO8mLK/GDf75ExH5mKpuBQguj+0RkWG9PC5jTD+zznrGmP3Z7oT55oTlZvx/3wSoUtUrO9uRiIwBtqpqYztv7wQGxRdU9WUROR74HHC1iDysqhXB27nArm4fiTFmQNkZIGNMqnsY169nLICI5IvIoe1sNxF4vb0dqOo7QKaIDAr2cTCwQ1V/D/yMoOO0iIwG3lLVvX1+FMaYPmUNIGNMSlPVF4DvAQ+KyHPAQ8C4djZ9ERgTdGpu7y6zB3H9iwA+CCwPLqldBVwdrP8U8Je+rN8Y0z/EXS43xhjTmeCS1xxVPa+Tbe4BrlDVlweuMmNMT9gZIGOMSYKqrgQe6exBiMCfrPFjzP7BzgAZY4wxJu3YGSBjjDHGpB1rABljjDEm7VgDyBhjjDFpxxpAxhhjjEk71gAyxhhjTNqxBpAxxhhj0o41gIwxxhiTdv4/GbDizb+yBccAAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "KzS4ALVSZehP" + }, + "source": [ + "## **Descrete Time Case**\n", + "\n", + "The design of the observer in the descrete time case is similar to the continues, consider the discrete-time linear system described by:\n", + "\n", + "\n", + "\\begin{equation}\n", + "\\begin{cases}\n", + "\\mathbf{x}_{k+1}=\\mathbf{A} \\mathbf{x}_{k}+\\mathbf{B}\\mathbf{u}_{k}\n", + "\\\\\n", + "\\mathbf{y}_k = \\mathbf{C}\\mathbf{x}_k\n", + "\\end{cases}\n", + "\\end{equation}\n", + "\n", + "With the observer given as:\n", + "\\begin{equation}\n", + "\\hat{{\\mathbf{x}}}_{k+1} = \n", + "\\mathbf{A} \\hat{\\mathbf{x}}_{k} + \\mathbf{B} \\mathbf u_{k} + \n", + "\\mathbf{L}(\\mathbf y_{k} - \\mathbf{C}\\hat{\\mathbf x }_{k})\n", + "\\end{equation}\n", + "\n", + "It is easy to show that the dynamicsof the estimation error is given by:\n", + "\\begin{equation}\n", + "\\mathbf{e}_{k+1} = \n", + "(\\mathbf{A} - \\mathbf{L}\\mathbf{C})\\mathbf{e}_k\n", + "\\end{equation}\n", + "which can be transformed to stable system through placing poles inside the unit circle." + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 495 + }, + "id": "OxjrkmThZyxo", + "outputId": "49308f8d-ff38-4102-e99f-9204d91b7a39" + }, + "source": [ + "from scipy.signal import cont2discrete as c2d\n", + "\n", + "T = 0.05\n", + "tf = 10\n", + "N = int(tf/T)\n", + "\n", + "A = np.array([[0, 1], \n", + " [-1, -0.1]])\n", + "\n", + "B = np.array([[0], \n", + " [1]])\n", + "\n", + "C = np.array([[1, 0]])\n", + "D = np.array([[0]])\n", + "\n", + "A_d, B_d, C, D, _ = c2d((A,B,C,D), T)\n", + "x = np.array([1., 0])\n", + "X = x\n", + "\n", + "poles = [0.9, 0.95]\n", + "pole_placement = place_poles(A_d.T, C.T, poles)\n", + "L = pole_placement.gain_matrix.T\n", + "\n", + "x_hat = np.array([0.0, 0])\n", + "X_hat = x_hat\n", + "U = []\n", + "\n", + "for k in range(N):\n", + " y = C.dot(x)+ 0.1*np.random.randn(1)\n", + " y_hat = C.dot(x_hat) \n", + " e = y - y_hat \n", + "\n", + " x_hat = A_d.dot(x_hat) + B_d.dot(u) + L.dot(e)\n", + "\n", + " u = [-np.sin(20*k/N)/10]\n", + " x = A_d.dot(x) + B_d.dot(u)\n", + " U.append(u)\n", + "\n", + " X = np.vstack((X, x))\n", + " X_hat = np.vstack((X_hat, x_hat))\n", + "\n", + "\n", + "theta_d, dtheta_d = np.split(X, 2, axis = 1)\n", + "theta_e, dtheta_e = np.split(X_hat, 2, axis = 1)\n", + "\n", + "\n", + "figure(figsize=(9, 3))\n", + "step(T*np.arange(N+1),theta_d, 'r--')\n", + "step(T*np.arange(N+1),theta_e, 'r')\n", + "step(T*np.arange(N+1),dtheta_d, 'b--')\n", + "step(T*np.arange(N+1),dtheta_e, 'b')\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "ylabel(r'State $\\mathbf{x}[k]$')\n", + "xlabel(r'Sample $k$')\n", + "xlim([-0.1, tf])\n", + "show()\n", + "\n", + "step(T*np.arange(N),U, 'r')\n", + "# plot(T*np.arange(N+1), U, 'r--', linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([-0.1, tf])\n", + "ylabel(r'Control $\\mathbf{u}[k]$')\n", + "xlabel(r'Sample $k$')\n", + "show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + } + ] +} \ No newline at end of file diff --git a/legacy - ColabNotebooks/practice_11_controllability_observability.ipynb b/legacy - ColabNotebooks/practice_11_controllability_observability.ipynb new file mode 100644 index 0000000..0181f37 --- /dev/null +++ b/legacy - ColabNotebooks/practice_11_controllability_observability.ipynb @@ -0,0 +1,861 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "[CT21] 11_controllability_observability.ipynb", + "provenance": [], + "collapsed_sections": [], + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "zPmrTNlSBW-R" + }, + "source": [ + "# **Practice 11: Controllability**\n", + "\n", + "---" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "DEdCnYFHUUSS" + }, + "source": [ + "## **Motivation**\n", + "\n", + "**Controllability** is an important property of a control system, and the controllability property plays a crucial role in many control problems, such as stabilization of unstable systems by feedback, or optimal control.\n", + "\n", + "Roughly, the concept of controllability denotes the **ability to move a system around in its entire configuration space using only certain admissible manipulations**. The exact definition varies slightly within the framework or the type of models applied.\n", + "\n", + "We can informally define controllability as follows: \n", + "\n", + "If for some initial state $\\mathbf {x_{0}}$ and some final state $\\mathbf {x_{f}}$ there exists an input sequence to transfer the system state from $\\mathbf {x_{0}}$ to $\\mathbf {x_{f}}$ in a finite time interval, then the system modeled by the state-space representation is controllable.\n", + "\n", + "For the controllable system we can **place the poles at arbitary desired location** on the complex plane\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "u8MGmtB_u5Li" + }, + "source": [ + "### **Full State Controlability (Kalman)**\n", + "Consider the descrete or continues time systems:\n", + "\\begin{equation}\n", + "\\dot{\\mathbf{x}}\n", + "=\n", + "\\mathbf{A}\\mathbf{x}\n", + "+ \n", + "\\mathbf{B}\\mathbf{u}\n", + "\\\\\n", + "\\mathbf{x}_{k+1}\n", + "=\n", + "\\mathbf{A}_d\\mathbf{x}_k\n", + "+ \n", + "\\mathbf{B}_d\\mathbf{u}_k\n", + "\\end{equation}\n", + "The $n\\times nm$ controllability matrix is given by\n", + "\n", + "\\begin{equation}\n", + "\\mathcal{\\mathbf{R}}=\n", + "{\\begin{bmatrix}\n", + "\\mathbf{B}&\n", + "\\mathbf{AB}&\n", + "\\mathbf{A^{{2}}B}&\n", + "...&\n", + "\\mathbf{A^{{n-1}}B}\n", + "\\end{bmatrix}}\n", + "\\end{equation}\n", + "The system is **full state controllable** iff the controllability matrix has full row rank:\n", + "\\begin{equation}\n", + "\\text{rank}\\{\\mathcal{\\mathbf{R}}\\}\n", + "=n\n", + "\\end{equation}\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "ex834kChHu-K", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "e71fb79f-d8bd-4e21-8864-2086add75dd3" + }, + "source": [ + "import numpy as np\n", + "\n", + "def ctrb(A, B):\n", + " R = B\n", + " n = np.shape(A)[0]\n", + " # print(n)\n", + " for i in range(1,n):\n", + " A_pwr_n = np.linalg.matrix_power(A, i) \n", + " R = np.hstack((R,A_pwr_n.dot(B)))\n", + " rank_R = np.linalg.matrix_rank(R)\n", + " \n", + " if rank_R == n:\n", + " test = 'controllable'\n", + " else:\n", + " test = 'uncontrollable'\n", + " return R, rank_R, test\n", + "\n", + "A = [[0,1],\n", + " [-2,-3]]\n", + "A = np.array(A)\n", + "\n", + "B = [[0],\n", + " [1]]\n", + " \n", + "B = np.array(B)\n", + "\n", + "R, rank, test = ctrb(A, B)\n", + "print(f'Contralability matrix:\\n{R}\\n\\nRank of the controlability matrix: {rank},\\nsystem is {test}' )" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Contralability matrix:\n", + "[[ 0 1]\n", + " [ 1 -3]]\n", + "\n", + "Rank of the controlability matrix: 2,\n", + "system is controllable\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "lCzoAU3HTIXD", + "outputId": "66da87d1-e184-4270-c3c7-5fa180d3e303" + }, + "source": [ + "M, m, l, b, g = 2, .2, 0.2, 0.1, 9.81\n", + "\n", + "A = [[0, 1, 0, 0], \n", + " [g*(M+m)/(M*l), 0 , 0, 0],\n", + " [0,0,0,1],\n", + " [-m*g/M, 0, 0,0]]\n", + " \n", + "A = np.array(A)\n", + "\n", + "B = [[0], \n", + " [-1/(M*l)], \n", + " [0], \n", + " [1/M]]\n", + "\n", + "B = np.array(B)\n", + "\n", + "R, rank, test = ctrb(A, B)\n", + "print(f'Contralability matrix:\\n{R}\\n\\nRank of the controlability matrix: {rank},\\nsystem is {test}' )" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Contralability matrix:\n", + "[[ 0. -2.5 0. -134.8875]\n", + " [ -2.5 0. -134.8875 0. ]\n", + " [ 0. 0.5 0. 2.4525]\n", + " [ 0.5 0. 2.4525 0. ]]\n", + "\n", + "Rank of the controlability matrix: 4,\n", + "system is controllable\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "RWyfe7kEnIel" + }, + "source": [ + "### **Popov-Belevitch-Hautus test**\n", + "\n", + "The pair $\\{ \\mathbf{A}, \\mathbf{B}\\}$is said to be controllable iff:\n", + "\n", + "\\begin{equation}\n", + "\\text{rank}\\{ \n", + "\\begin{bmatrix}\n", + "\\mathbf{A} - \\zeta \\mathbf{I}\n", + "&\n", + "\\mathbf{B}\n", + "\\end{bmatrix}\n", + " \\} =n, \\quad\n", + " \\forall \\zeta \\in \n", + " \\mathbb{C}\n", + "\\end{equation}\n", + "\n", + "However the only way for $\\mathbf{A} - \\lambda\\mathbf{I}$ to lose the rank is for $\\lambda$ to be the eigenvalue of $\\mathbf{A}$, thus instead of checking the entire complex plane we may consider just the eigenvalues:\n", + "\n", + "\\begin{equation}\n", + "\\text{rank}\\{ \n", + "\\begin{bmatrix}\n", + "\\mathbf{A} - \\lambda_i \\mathbf{I}\n", + "&\n", + "\\mathbf{B}\n", + "\\end{bmatrix}\n", + " \\} =n, \\quad\n", + " \\forall i \\in \n", + " \\{1, 2,\\dots, n\\}\n", + "\\end{equation}\n", + "\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "J2BApExN4-rw", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "5189208c-72b1-4a71-c692-94736b7ad249" + }, + "source": [ + "def pbh(A, B):\n", + " lambdas, v = np.linalg.eig(A)\n", + " n = np.shape(A)[0]\n", + " ranks = n*[0]\n", + " test = 'controllable'\n", + " for i in range(n):\n", + " A_e = A - lambdas[i]*np.eye(n)\n", + " M = np.hstack((A_e, B))\n", + " ranks[i] = np.linalg.matrix_rank(M)\n", + " if ranks[i] != n:\n", + " test = 'uncontrollable'\n", + " return lambdas, ranks , test\n", + "\n", + "\n", + "eigs, ranks, test = pbh(A,B)\n", + "print(f'Eigen values of PBH matrices:\\n{eigs}\\n\\nRanks of the PBH matrices: {ranks},\\nsystem is {test}' )\n" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Eigen values of PBH matrices:\n", + "[ 0. 0. 7.34540673 -7.34540673]\n", + "\n", + "Ranks of the PBH matrices: [4, 4, 4, 4],\n", + "system is controllable\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "O-oqxaH24_Jy" + }, + "source": [ + "\n", + "it is interesting to see that:\n", + "\\begin{equation}\n", + "\\mathbf{B}\n", + "\\notin\n", + "\\mathcal{C}(\\mathbf{A} - \\lambda_i \\mathbf{I})\n", + "\\quad\n", + "\\forall i \\in \n", + "\\{1, 2,\\dots, n\\}\n", + "\\end{equation}\n", + "\n", + "The matrix $\\mathbf{B}$ better to not be aligned with **some of the eigenvectors** " + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "IAqnf6lz_oN2", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "ce81cd1b-118f-4e3c-e4a6-29edbaeba8b4" + }, + "source": [ + "from scipy.linalg import null_space, orth\n", + "# scipy.linalg.orth(A)\n", + "A = [[1,2,3],\n", + " [2,1,0],\n", + " [0,2,4]]\n", + "\n", + "A = np.array(A)\n", + "lambdas, v = np.linalg.eig(A)\n", + "print(v)\n", + "B = [v[:,0]+v[:,1]]\n", + "B = [[0],[0],[1]]\n", + "B = np.array(B)\n", + "\n", + "R, rank, test = ctrb(A, B)\n", + "print(f'Contralability matrix:\\n{R}\\n\\nRank of the controlability matrix: {rank},\\nsystem is {test}' )\n", + "\n", + "eigs, ranks, test = pbh(A,B)\n", + "print(f'Eigen values of PBH matrices:\\n{eigs}\\n\\nRanks of the PBH matrices: {ranks},\\nsystem is {test}' )\n" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "[[ 4.08248290e-01 -8.46641303e-16 6.66666667e-01]\n", + " [-8.16496581e-01 8.32050294e-01 3.33333333e-01]\n", + " [ 4.08248290e-01 -5.54700196e-01 6.66666667e-01]]\n", + "Contralability matrix:\n", + "[[ 0 3 15]\n", + " [ 0 0 6]\n", + " [ 1 4 16]]\n", + "\n", + "Rank of the controlability matrix: 3,\n", + "system is controllable\n", + "Eigen values of PBH matrices:\n", + "[4.4408921e-16 1.0000000e+00 5.0000000e+00]\n", + "\n", + "Ranks of the PBH matrices: [3, 3, 3],\n", + "system is controllable\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "GsfxAs8lE1oA" + }, + "source": [ + "Moreover condition above provide the insight on the **minimal number of the control channels** that we need for sytem to be controllable and is directly related to the multiplicity of the eigenvalues\n", + "\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "mLwbtlaQFBFR", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "38e35f78-fc3b-467c-b264-9e19fd894c73" + }, + "source": [ + "m = 1\n", + "k1 = 3\n", + "k2 = 3\n", + "A = [[0,1,0,0],\n", + " [-k1/m,0,0,0],\n", + " [0,0,0, 1],\n", + " [0,0,-k2/m,0]]\n", + "A = np.array(A)\n", + "B = [[0],[1/m],[0],[1/m]]\n", + "\n", + "B = [[0,0],[1/m,0],[0,0],[0,1/m]]\n", + "B = np.array(B)\n", + "lambdas, v = np.linalg.eig(A)\n", + "\n", + "eigs, ranks, test = pbh(A,B)\n", + "print(f'Eigen values of PBH matrices:\\n{eigs}\\n\\nRanks of the PBH matrices: {ranks},\\nsystem is {test}' )\n", + "\n", + "\n", + "print(lambdas)" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Eigen values of PBH matrices:\n", + "[0.+1.73205081j 0.-1.73205081j 0.+1.73205081j 0.-1.73205081j]\n", + "\n", + "Ranks of the PBH matrices: [4, 4, 4, 4],\n", + "system is controllable\n", + "[0.+1.73205081j 0.-1.73205081j 0.+1.73205081j 0.-1.73205081j]\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Vvc-lUC7EFsf" + }, + "source": [ + "It is clear that **multiplicity $\\gamma$ of the eigenvalues** is 2." + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "NCKWp4NFDmk2", + "outputId": "4d88a287-9b98-4c65-db38-3046b148e0c9" + }, + "source": [ + " n = len(lambdas)\n", + "\n", + " for i in range(n):\n", + " A_e = A - lambdas[i]*np.eye(n)\n", + " print(f'Eigenvalue s: {lambdas[i]}')\n", + " print(f'Rank of A - sI: {np.linalg.matrix_rank(A_e)}')\n", + " print(f'Rank difficiency: {n - np.linalg.matrix_rank(A_e)}\\n')" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Eigenvalue s: 1.7320508075688772j\n", + "Rank of A - sI: 2\n", + "Rank difficiency: 2\n", + "\n", + "Eigenvalue s: -1.7320508075688772j\n", + "Rank of A - sI: 2\n", + "Rank difficiency: 2\n", + "\n", + "Eigenvalue s: 1.7320508075688772j\n", + "Rank of A - sI: 2\n", + "Rank difficiency: 2\n", + "\n", + "Eigenvalue s: -1.7320508075688772j\n", + "Rank of A - sI: 2\n", + "Rank difficiency: 2\n", + "\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "6O2QcV6fE-VK" + }, + "source": [ + "thus we need at least $m = n - \\gamma$ control channels to control the system" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "9JUQyODTFSI9", + "outputId": "bd8138c6-f4eb-4112-bc72-aaded06a93b3" + }, + "source": [ + "A = [[0,1,0,0],\n", + " [0,0,1,0],\n", + " [0,0,0,1],\n", + " [-2,1,-3,4]]\n", + "A = np.array(A)\n", + "\n", + "lambdas, v = np.linalg.eig(A)\n", + "\n", + "n = len(lambdas)\n", + "for i in range(n):\n", + " A_e = A - lambdas[i]*np.eye(n)\n", + " print(f'Eigenvalue s: {lambdas[i]}')\n", + " print(f'Rank of A - sI: {np.linalg.matrix_rank(A_e)}')\n", + " print(f'Rank difficiency: {n - np.linalg.matrix_rank(A_e)}\\n')\n", + "\n", + "B = [[0],[0],[0],[1]]\n", + "B = np.array(B)\n", + "eigs, ranks, test = pbh(A,B)\n", + "print(f'Eigen values of PBH matrices:\\n{eigs}\\n\\nRanks of the PBH matrices: {ranks},\\nsystem is {test}' )\n" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Eigenvalue s: (3.0550069569440637+0j)\n", + "Rank of A - sI: 3\n", + "Rank difficiency: 1\n", + "\n", + "Eigenvalue s: (1.2648353428932393+0j)\n", + "Rank of A - sI: 3\n", + "Rank difficiency: 1\n", + "\n", + "Eigenvalue s: (-0.15992114991865097+0.7014362052215042j)\n", + "Rank of A - sI: 3\n", + "Rank difficiency: 1\n", + "\n", + "Eigenvalue s: (-0.15992114991865097-0.7014362052215042j)\n", + "Rank of A - sI: 3\n", + "Rank difficiency: 1\n", + "\n", + "Eigen values of PBH matrices:\n", + "[ 3.05500696+0.j 1.26483534+0.j -0.15992115+0.70143621j\n", + " -0.15992115-0.70143621j]\n", + "\n", + "Ranks of the PBH matrices: [4, 4, 4, 4],\n", + "system is controllable\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "xSxhOkVbk9n_" + }, + "source": [ + "### **Degrees of Controlability**\n", + "\n", + "A Kalman test given above is indeed usefull while providing the binary answer to the question does the system is controllable or not. However it may be the case that system is barely controllable, so system may pass controlability test but in practice may not be controllable or designed controller **provide poor performance/not implemntable gains**." + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "MZDxcbXkk9D0", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "dca8c521-0880-4907-931d-0f9abb753752" + }, + "source": [ + "from scipy.signal import place_poles\n", + "m = 1\n", + "k1 = 3\n", + "k2 = 3\n", + "A = [[0,1,0,0],\n", + " [-k1/m,0,0,0],\n", + " [0,0,0, 1],\n", + " [0,0,-k2/m,0]]\n", + "A = np.array(A)\n", + "\n", + "B = [[0, 0 ],\n", + " [1/m, 0 ], \n", + " [0, 0], \n", + " [ 0,1/m]]\n", + "\n", + "B = np.array(B)\n", + "\n", + "eigs, ranks, test = pbh(A,B)\n", + "print(f'Eigen values of PBH matrices:\\n{eigs}\\n\\nRanks of the PBH matrices: {ranks},\\nsystem is {test}' )\n", + "\n", + "P = np.array([-1,-2,-3,-4])\n", + "pp = place_poles(A, B, P)\n", + "K = pp.gain_matrix\n", + "print(K)" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Eigen values of PBH matrices:\n", + "[0.+1.73205081j 0.-1.73205081j 0.+1.73205081j 0.-1.73205081j]\n", + "\n", + "Ranks of the PBH matrices: [4, 4, 4, 4],\n", + "system is controllable\n", + "[[4.72093174 5.88837381 1.14781568 0.45912492]\n", + " [1.14779945 0.45911681 0.27906826 4.11162619]]\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "VIle3GpMna9W" + }, + "source": [ + "### **Stabilizability**\n", + "\n", + "A slightly weaker notion than controllability is that of stabilizability. A system is said to be stabilizable when all uncontrollable state variables can be made to have stable dynamics. Thus, even though some of the state variables **cannot be controlled** (as determined by the controllability test above) all the state variables will still remain **bounded during** the system's behavior.\n", + "\n", + "**Stabilizable** systems should be controllable only for the unstable eigenvalues i.e:\n", + "\n", + "\\begin{equation}\n", + "\\text{rank}\\{ \n", + "\\begin{bmatrix}\n", + "\\mathbf{A} - \\lambda_i \\mathbf{I}\n", + "&\n", + "\\mathbf{B}\n", + "\\end{bmatrix}\n", + " \\} =n, \\quad\n", + " \\forall \\lambda \\in \\{c: \\text{Re}(c)\\geq0\\}\n", + "\\end{equation}" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "nN0SPS6yHkoX", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 581 + }, + "outputId": "3db7e947-6ba7-4d4d-b13f-15418af10758" + }, + "source": [ + "from scipy.integrate import odeint \n", + "from matplotlib.pyplot import *\n", + "\n", + "\n", + "A = [[1,1],\n", + " [0,-1]]\n", + "A = np.array(A)\n", + "\n", + "B = [[1],\n", + " [0]]\n", + "B = np.array(B)\n", + "\n", + "def f(x, t, A, B):\n", + " x_1, x_2 = x\n", + " \n", + " u = -2*x_1 +2*x_2\n", + " # u = 0\n", + " dx_1 = A[0,0]*x_1 + A[0,1]*x_2 + B[0,0]*u\n", + " dx_2 = A[1,0]*x_1 + A[1,1]*x_2 + B[1,0]*u\n", + "\n", + " return dx_1, dx_2\n", + "\n", + "t0 = 0 # Initial time \n", + "tf = 8 # Final time\n", + "t = np.linspace(t0, tf, 1000)\n", + "\n", + "x0 = [0.5,0.5] # initial state\n", + "\n", + "solution = {\"ss\": odeint(f, x0, t, args = (A, B))}\n", + "x1, x2 = solution['ss'][:,0], solution['ss'][:,1]\n", + "\n", + "\n", + "\n", + "\n", + "figure(figsize=(9, 3))\n", + "plot(t, solution['ss'], linewidth=2.0)\n", + "grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "grid(True)\n", + "xlim([t0, tf])\n", + "ylabel(r'State space ${x}$')\n", + "xlabel(r'Time $t$')\n", + "show()\n", + "\n", + "\n", + "x1_max, x2_max = 1.5, 1.5\n", + "x1_span = np.arange(-x1_max,x2_max,0.1)\n", + "x2_span = np.arange(-x1_max,x2_max,0.1)\n", + "x1_grid, x2_grid = np.meshgrid(x1_span, x2_span)\n", + "\n", + "figure(figsize=(5, 5))\n", + "title('Phase Plane')\n", + "# Varying color along a streamline\n", + "L = (x1_grid**2 + x2_grid**2)**0.5\n", + "lw = 3*L / L.max()\n", + "contourf(x1_span, x2_span, L, cmap='autumn', alpha = 0.25)\n", + "\n", + "dx1, dx2 = f([x1_grid, x2_grid],t, A, B)\n", + "\n", + "strm = streamplot(x1_span, x2_span, dx1, dx2, density = 1,color=L, cmap='autumn', linewidth = lw)\n", + "seed_points = np.array([x0[0], x0[1]])\n", + "\n", + "\n", + "plot(x1, x2, 'r-', lw = 3.0)\n", + "plot(seed_points[0], seed_points[1], 'ro', lw = 10)\n", + "hlines(0, -x1_max, x2_max,color = 'red', linestyle = '--', alpha = 0.6)\n", + "vlines(0, -x1_max, x2_max,color = 'red', linestyle = '--', alpha = 0.6)\n", + "xlim([-0.9*x1_max,0.9*x2_max])\n", + "ylim([-0.9*x2_max,0.9*x2_max])\n", + "xlabel(r'State ${x}_1$')\n", + "ylabel(r'State ${x}_2$')\n", + "tight_layout()\n", + "show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "gTkCPrb60K05", + "outputId": "b069ee76-c363-4008-d70f-d48713b3311d" + }, + "source": [ + "\n", + "R, rank, test = ctrb(A, B)\n", + "print(f'Contralability matrix:\\n{R}\\n\\nRank of the controlability matrix: {rank},\\nsystem is {test}' )\n" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Contralability matrix:\n", + "[[1 1]\n", + " [0 0]]\n", + "\n", + "Rank of the controlability matrix: 1,\n", + "system is uncontrollable\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "XcjByvZ3rvIu" + }, + "source": [ + "Let's run the slightly modifed PBH test on this system:" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "xzvBrjgyruwN", + "outputId": "1c697231-89bb-423d-e07a-634815320277" + }, + "source": [ + "def pbh(A, B):\n", + " lambdas, v = np.linalg.eig(A)\n", + " n = np.shape(A)[0]\n", + " ranks = n*[0]\n", + " # M = n*[0]\n", + " test = 'controllable'\n", + " for i in range(n):\n", + " M = np.hstack((A - lambdas[i]*np.eye(n), B))\n", + " ranks[i] = np.linalg.matrix_rank(M)\n", + " if ranks[i] != n:\n", + " test = 'uncontrollable'\n", + " if np.real(lambdas[i])<0:\n", + " test += ' but stabilizable'\n", + " return ranks, lambdas, test\n", + "\n", + "\n", + "eigs, ranks, test = pbh(A,B)\n", + "print(f'Eigen values of PBH matrices:\\n{eigs}\\n\\nRanks of the PBH matrices: {ranks},\\nsystem is {test}' )\n" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Eigen values of PBH matrices:\n", + "[2, 1]\n", + "\n", + "Ranks of the PBH matrices: [ 1. -1.],\n", + "system is uncontrollable but stabilizable\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "H608E584MQst" + }, + "source": [ + "### **HW Problem:**\n", + "\n", + "Consider a satellite described by the following equations:\n", + "\\begin{equation}\n", + "\\left\\{\\begin{matrix}\n", + "m\\ddot{r}=m r\\dot{\\theta}^2 -G\\cfrac{m M}{r^2} + u_1\n", + "\\\\ \n", + "mr\\ddot{\\theta}=-2 m \\dot{r}\\dot{\\theta}+ u_2\n", + "\\end{matrix}\\right.\n", + "\\end{equation}\n", + "\n", + "try to answer if it is possible to stabilize the satelite nearby the desired orbit with constant radius $r_d = \\text{const}$ by only one control input (either $u_1$ or $u_2$)\n", + "\n", + "***Hint:*** Obtain the desired trajectory $\\mathbf{x}_d$ by substituting $r_d$ to the dynamics above and find the linearized version ($\\mathbf{A,B}$), then use techniques that you have studied in this class. \n", + "\n", + "#### **Bonus:**\n", + "Check if it is possible to use either only $r$ or $\\theta$ to design controller, if it's so design the observer to estimate the full state. " + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "nZV5wFi2ONap" + }, + "source": [ + "# Parametres\n", + "re=\t1737.10e+3\n", + "r0 = re + 50.0e+4;\n", + "\n", + "m = 100;\n", + "G = 6.67408e-11;\n", + "M = 7.3477e+22 \n", + "k = G*M;\n" + ], + "execution_count": null, + "outputs": [] + } + ] +} \ No newline at end of file diff --git a/legacy - ColabNotebooks/practice_12_design_example.ipynb b/legacy - ColabNotebooks/practice_12_design_example.ipynb new file mode 100644 index 0000000..5eac4d9 --- /dev/null +++ b/legacy - ColabNotebooks/practice_12_design_example.ipynb @@ -0,0 +1,1359 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "[CT21] 12_design_example.ipynb", + "provenance": [], + "collapsed_sections": [], + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "zPmrTNlSBW-R" + }, + "source": [ + "# **Practice 12: Design Example, Orbital maneuver**\n", + "\n", + "---" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "H608E584MQst" + }, + "source": [ + "### **Problem Definition:**\n", + "\n", + "Consider a satellite described by the following equations:\n", + "\\begin{equation}\n", + "\\left\\{\\begin{matrix}\n", + "m\\ddot{r}=m r\\dot{\\theta}^2 -G\\cfrac{m M}{r^2} + u_r\n", + "\\\\ \n", + "mr\\ddot{\\theta}=-2 m \\dot{r}\\dot{\\theta}+ u_\\theta\n", + "\\end{matrix}\\right.\n", + "\\end{equation}\n", + "\n", + "A problem is to **stabilize** the satellite on the desired orbit of constant radius $r_d = \\text{const}$ with minimal control effort. \n", + "\n", + "\n", + "\n", + "\n", + "

\"linear

\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "qEPSCPZ5SyZo" + }, + "source": [ + "\n", + "\n", + "The overall workflow to design the controller is summarized as follows:\n", + "\n", + "\n", + "1. Modeling, **State space representation** of system dynamics ( [Practice 1](https://colab.research.google.com/drive/1OE18rhr8Mhq3H5FS5yci037CQ52ag4yq))\n", + "2. Deducing **feasible trajectory** \n", + "3. **Linearizing** system dynamics nearby desired trajectory, **linear state space** ( [Practice 8](https://colab.research.google.com/drive/15l9Pyv-ol33NrwM3v48r9jjZLP_Vgimt)) \n", + "4. **Discretization** of linearized system ( [Practice 6](https://colab.research.google.com/drive/1FLxfvWfwhNvjlYz-9oQJviwlj9M0URUh))\n", + "5. **Controllability** analysis ( [Practice 11](https://colab.research.google.com/drive/1Rs_RygP56Fea_Y_QDGIl8vAy4Ht_wkSM))\n", + "6. **Сontroller** design ( [Practice 9](https://colab.research.google.com/drive/1_MjEdyWbJ2In3NZRfdrmKUPdR0IobKH-))\n", + "\n", + "\n", + "\n", + "In order to check the designed controller we will implement the following simulations:\n", + "1. Full state feedback on the **linearized** system \n", + "2. Full state feedback on the **original** system \n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "b2CcXs6tcpbP" + }, + "source": [ + "\n", + "### **State Space Representation**\n", + "\n", + "Let us first introduce the following constant $k = gM$ and rewrite system dynamics in normal form: \n", + "\\begin{equation}\n", + "\\left\\{\\begin{matrix}\n", + "\\ddot{r}= r\\dot{\\theta}^2 -\\cfrac{k}{r^2} + \\cfrac{u_r}{m}\n", + "\\\\ \n", + "\\ddot{\\theta}=-2 \\cfrac{\\dot{r}\\dot{\\theta}}{r}+ \\cfrac{u_\\theta}{mr}\n", + "\\end{matrix}\\right.\n", + "\\end{equation}\n", + "\n", + "Thus introducing the state variables as $\\mathbf{x} = [r, \\dot{r}, \\theta, \\dot{\\theta}]^T$ we may rewrite the equiations above in state space form:\n", + "\n", + "\\begin{equation}\n", + "\\begin{bmatrix}\n", + "\\dot{\\mathbf{x}}_1 \n", + "\\\\\n", + "\\dot{\\mathbf{x}}_2\n", + "\\\\\n", + "\\dot{\\mathbf{x}}_3\n", + "\\\\ \n", + "\\dot{\\mathbf{x}}_4\n", + "\\end{bmatrix}\n", + "=\n", + "\\begin{bmatrix}\n", + "\\mathbf{x}_2 \n", + "\\\\\n", + "\\mathbf{x}_1 \\mathbf{x}_4^2\n", + "\\\\\n", + "\\mathbf{x}_4\n", + "\\\\ \n", + "-2 \\cfrac{\\mathbf{x}_2\\mathbf{x}_4}{\\mathbf{x}_1}\n", + "\\end{bmatrix}\n", + "+\n", + "\\begin{bmatrix}\n", + " 0 & 0 \\\\\n", + " -\\frac{1}{m} & 0 \\\\\n", + " 0 & 0 \\\\\n", + " 0 & \\frac{1}{m \\mathbf{x}_1}\\\\\n", + "\\end{bmatrix}\n", + "\\begin{bmatrix}\n", + "u_r\n", + "\\\\\n", + "u_\\theta\n", + "\\end{bmatrix}\n", + "\\end{equation}\n", + "\n", + "Which may be written in general state space form as:\n", + "\n", + "\n", + "\\begin{equation}\n", + "\\dot{\\mathbf{x}}\n", + "= \n", + "\\mathbf{f}(\\mathbf{x}, \\mathbf{u})\n", + "\\end{equation}\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 105 + }, + "id": "_avHXMUccpJo", + "outputId": "21cb759f-ed3d-4178-c386-bf547ca5f3b7" + }, + "source": [ + "def f(x, u, params):\n", + " k, m = params\n", + " r, dr, theta, dtheta = x\n", + " u_r, u_theta = u\n", + " ddr = r*dtheta**2 -k/(r**2) + u_r/m \n", + " ddtheta = -2*dr*dtheta/r + u_theta/(r*m)\n", + " return dr, ddr, dtheta, ddtheta\n", + "\n", + "import sympy as sym\n", + "\n", + "sym.init_printing()\n", + "\n", + "x_sym = sym.symbols(r'r \\dot{r} \\theta \\dot{\\theta}') \n", + "u_sym = sym.symbols(r'u_r u_\\theta') \n", + "params_sym = sym.symbols(r'k m')\n", + "f_sym = sym.Matrix([f(x_sym, u_sym, params_sym)]).T\n", + "\n", + "f_sym\n" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/latex": "$\\displaystyle \\left[\\begin{matrix}\\dot{r}\\\\\\dot{\\theta}^{2} r - \\frac{k}{r^{2}} + \\frac{u_{r}}{m}\\\\\\dot{\\theta}\\\\- \\frac{2 \\dot{\\theta} \\dot{r}}{r} + \\frac{u_{\\theta}}{m r}\\end{matrix}\\right]$", + "text/plain": [ + "⎡ \\dot{r} ⎤\n", + "⎢ ⎥\n", + "⎢ 2 k uᵣ ⎥\n", + "⎢ \\dot{\\theta} ⋅r - ── + ── ⎥\n", + "⎢ 2 m ⎥\n", + "⎢ r ⎥\n", + "⎢ ⎥\n", + "⎢ \\dot{\\theta} ⎥\n", + "⎢ ⎥\n", + "⎢ 2⋅\\dot{\\theta}⋅\\dot{r} u_\\theta⎥\n", + "⎢- ────────────────────── + ────────⎥\n", + "⎣ r m⋅r ⎦" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 1 + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "MT3odtf5q5e1" + }, + "source": [ + "### **Feasible trajectory: Equatorial orbit**\n", + "Once model is given by the state space representation above we may obtain trajectory that is consistent with dynamics by direct substitution of the constant $r_d = \\text{const}$:\n", + "\\begin{equation}\n", + "\\left\\{\\begin{matrix}\n", + "0= r_d\\dot{\\theta}_d^2 -\\cfrac{k}{r_d^2} + \\cfrac{u_{r_d}}{m}\n", + "\\\\ \n", + "\\ddot{\\theta}_d= \\cfrac{u_{\\theta_d}}{mr_d}\n", + "\\end{matrix}\\right.\n", + "\\end{equation}\n", + "\n", + "Moreover if one will consider effortless ($u_{r_d}, u_{\\theta_d}$) trajectories the equations above represent the following: \n", + "\n", + "\\begin{equation}\n", + "r^3_d \\dot{\\theta}_d^2 = k \\rightarrow \\dot{\\theta}_d = \\omega = \\sqrt{\\frac{k}{r^3_d}}{}\n", + "\\end{equation}\n", + " Thus the desired trajectory is given by following state/control pair:\n", + "\\begin{equation}\n", + "\\mathbf{x}_d = \n", + "\\begin{bmatrix}\n", + "r_d & 0 & \\omega t & \\omega\n", + "\\end{bmatrix}^T\n", + "\\\\\n", + "\\mathbf{u}_d = \n", + "\\begin{bmatrix}\n", + "u_{\\theta_d} & u_{r_d}\n", + "\\end{bmatrix}^T\n", + "=\n", + "\\begin{bmatrix}\n", + "0 & 0\n", + "\\end{bmatrix}^T\n", + "\\end{equation}\n", + "Thus the solution is flies along the line of the Earth's equator with constant speed and represent so called equatorial orbit. \n", + "\n", + "***Note***\n", + "\n", + "To get into equatorial orbit, a satellite must be launched from a place on Earth close to the equator. NASA often launches satellites aboard an Ariane rocket into equatorial orbit from French Guyana. Special case of equatorial orbit is a geosynchronous (sometimes abbreviated GSO) is an orbit around Earth of a satellite with an orbital period that matches Earth's rotation on its axis, which takes one sidereal day (23 hours, 56 minutes, and 4 seconds) " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "t8qOnyoxuj7t" + }, + "source": [ + "### **Linearization**\n", + "System above is nonlinear, in order to implement the techniques that we studied in this class we need to first obtain the linear state space model. A convinient way to do so is to linearize system dynamics nearby equilibrium point or desired trajectory:\n", + "\n", + "\\begin{equation}\n", + "\\dot{\\mathbf{x}}\n", + "= \\mathbf{f}(\\mathbf{x}_d,\\mathbf{u}_d)+ \n", + "\\frac{\\partial\\mathbf{f}}{\\partial\\mathbf{x}}\\Bigr\\rvert_{\\mathbf{x}_d,\\mathbf{u}_d} \n", + "(\\mathbf{x} - \\mathbf{x}_d) + \n", + "\\frac{\\partial\\mathbf{u}}{\\partial\\mathbf{x}}\\Bigr\\rvert_{\\mathbf{x}_d,\\mathbf{u}_d} \n", + "(\\mathbf{u} - \\mathbf{u}_d) + \\text{H.O.T}\n", + "\\end{equation}\n", + "\n", + "Introducing the tracking error $\\tilde{\\mathbf{x}}$ we may rewrite the equation above in linear form as follows:\n", + "\n", + "\\begin{equation}\n", + "\\dot{\\tilde{\\mathbf{x}}} = \\mathbf{A}\\tilde{\\mathbf{x}} + \\mathbf{B}\\tilde{\\mathbf{u}} \n", + "\\end{equation}\n", + "where: $\\tilde{\\mathbf{x}}$ is tracking error, $\\tilde{\\mathbf{u}}$ is the new control input $\\mathbf{A} = \\frac{\\partial\\mathbf{f}}{\\partial\\mathbf{x}}\\Bigr\\rvert_{\\mathbf{x}_d,\\mathbf{u}_d}$ - state evaluation matrix, $\\mathbf{B} = \\frac{\\partial\\mathbf{f}}{\\partial\\mathbf{u}}\\Bigr\\rvert_{\\mathbf{x}_d,\\mathbf{u}_d}$\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Kr4TMd-_D7iZ" + }, + "source": [ + "Let us first calculate system jacobian with respect to state: $\\frac{\\partial\\mathbf{f}}{\\partial\\mathbf{x}}$\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 104 + }, + "id": "iEybo_f3ujQ-", + "outputId": "065d204a-4467-4856-a08d-ed9e68c221ba" + }, + "source": [ + "# Calculate the jacobian with respect to x\n", + "Jx_sym = f_sym.jacobian(x_sym)\n", + "Jx_sym\n" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/latex": "$\\displaystyle \\left[\\begin{matrix}0 & 1 & 0 & 0\\\\\\dot{\\theta}^{2} + \\frac{2 k}{r^{3}} & 0 & 0 & 2 \\dot{\\theta} r\\\\0 & 0 & 0 & 1\\\\\\frac{2 \\dot{\\theta} \\dot{r}}{r^{2}} - \\frac{u_{\\theta}}{m r^{2}} & - \\frac{2 \\dot{\\theta}}{r} & 0 & - \\frac{2 \\dot{r}}{r}\\end{matrix}\\right]$", + "text/plain": [ + "⎡ 0 1 0 0 ⎤\n", + "⎢ ⎥\n", + "⎢ 2 2⋅k ⎥\n", + "⎢ \\dot{\\theta} + ─── 0 0 2⋅\\dot{\\theta}⋅r⎥\n", + "⎢ 3 ⎥\n", + "⎢ r ⎥\n", + "⎢ ⎥\n", + "⎢ 0 0 0 1 ⎥\n", + "⎢ ⎥\n", + "⎢2⋅\\dot{\\theta}⋅\\dot{r} u_\\theta -2⋅\\dot{\\theta} -2⋅\\dot{r} ⎥\n", + "⎢────────────────────── - ──────── ──────────────── 0 ─────────── ⎥\n", + "⎢ 2 2 r r ⎥\n", + "⎣ r m⋅r ⎦" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 2 + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "O4KOaVZwG_lw" + }, + "source": [ + "\n", + "Now we can evaluate the jacobian nearby desired trajectory $\\mathbf{A} = \\frac{\\partial\\mathbf{f}}{\\partial\\mathbf{x}}\\Bigr\\rvert_{\\mathbf{x}_d,\\mathbf{u}_d}$\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 105 + }, + "id": "aoOae3bUgED1", + "outputId": "28f3fb46-49fb-4560-d3a5-7ec1d8bdcadb" + }, + "source": [ + "# Evaluate J_x nearby desired trajectory\n", + "n = len(x_sym)\n", + "A_sym = Jx_sym\n", + "\n", + "\n", + "A_sym = A_sym.subs({x_sym[0]: 'r_d'})\n", + "A_sym = A_sym.subs({x_sym[1]: 0})\n", + "A_sym = A_sym.subs({x_sym[3]: sym.symbols(r'\\omega')})\n", + "A_sym = A_sym.subs({u_sym[1]: 0})\n", + "\n", + "A_sym.simplify()\n", + "A_sym" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/latex": "$\\displaystyle \\left[\\begin{matrix}0 & 1 & 0 & 0\\\\\\omega^{2} + \\frac{2 k}{r_{d}^{3}} & 0 & 0 & 2 \\omega r_{d}\\\\0 & 0 & 0 & 1\\\\0 & - \\frac{2 \\omega}{r_{d}} & 0 & 0\\end{matrix}\\right]$", + "text/plain": [ + "⎡ 0 1 0 0 ⎤\n", + "⎢ ⎥\n", + "⎢ 2 2⋅k ⎥\n", + "⎢\\omega + ──── 0 0 2⋅\\omega⋅r_d⎥\n", + "⎢ 3 ⎥\n", + "⎢ r_d ⎥\n", + "⎢ ⎥\n", + "⎢ 0 0 0 1 ⎥\n", + "⎢ ⎥\n", + "⎢ -2⋅\\omega ⎥\n", + "⎢ 0 ────────── 0 0 ⎥\n", + "⎣ r_d ⎦" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 3 + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "aBuMq5GPHb4v" + }, + "source": [ + "System jacobian with respect to control: $\\frac{\\partial\\mathbf{f}}{\\partial\\mathbf{u}}$\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 98 + }, + "id": "YD6RTM42cqke", + "outputId": "6bb324c8-fa2f-404a-c15f-615673e148a0" + }, + "source": [ + "# calculate the jacobian with respect to u\n", + "Ju_sym = f_sym.jacobian(u_sym)\n", + "Ju_sym" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/latex": "$\\displaystyle \\left[\\begin{matrix}0 & 0\\\\\\frac{1}{m} & 0\\\\0 & 0\\\\0 & \\frac{1}{m r}\\end{matrix}\\right]$", + "text/plain": [ + "⎡0 0 ⎤\n", + "⎢ ⎥\n", + "⎢1 ⎥\n", + "⎢─ 0 ⎥\n", + "⎢m ⎥\n", + "⎢ ⎥\n", + "⎢0 0 ⎥\n", + "⎢ ⎥\n", + "⎢ 1 ⎥\n", + "⎢0 ───⎥\n", + "⎣ m⋅r⎦" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 4 + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "D1ytkCOgHhHA" + }, + "source": [ + "Now we may substitude the desired trajectory $\\mathbf{B} = \\frac{\\partial\\mathbf{f}}{\\partial\\mathbf{u}}\\Bigr\\rvert_{\\mathbf{x}_d,\\mathbf{u}_d}$\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 100 + }, + "id": "EQr0s1_GpLHm", + "outputId": "1821a6de-226e-41a0-86a0-7736abafcdef" + }, + "source": [ + "B_sym = Ju_sym.subs(x_sym[0], 'r_d')\n", + "B_sym" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/latex": "$\\displaystyle \\left[\\begin{matrix}0 & 0\\\\\\frac{1}{m} & 0\\\\0 & 0\\\\0 & \\frac{1}{m r_{d}}\\end{matrix}\\right]$", + "text/plain": [ + "⎡0 0 ⎤\n", + "⎢ ⎥\n", + "⎢1 ⎥\n", + "⎢─ 0 ⎥\n", + "⎢m ⎥\n", + "⎢ ⎥\n", + "⎢0 0 ⎥\n", + "⎢ ⎥\n", + "⎢ 1 ⎥\n", + "⎢0 ─────⎥\n", + "⎣ m⋅r_d⎦" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 5 + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "pzSpd1RGqMFj" + }, + "source": [ + "### **Similarity Transformation**\n", + "\n", + "There are situations when system matrices are not well defined in several directions, it may happen for instance when the variables to control represent a physical quantities that are highly different in their magnitudes, thus resulting system (matrices $\\mathbf{A}, \\mathbf{B}$) will be barely controllable. To tackle this one may appropriately scale the state variables with some matrix $\\mathbf{T}$ as follows:\n", + "\\begin{equation}\n", + "\\mathbf{x}^* = \\mathbf{T}\\mathbf{x}\n", + "\\end{equation}\n", + "\n", + "Thus the state transition may be calculated by substitution of the $\\mathbf{x} = \\mathbf{T}^{-1}\\mathbf{x}^*$ to the system dynamics:\n", + "\\begin{equation}\n", + "\\dot{\\mathbf{x}}^* = \\mathbf{A}^*\\mathbf{x}^* + \\mathbf{B}^*\\mathbf{u}\n", + "\\end{equation}\n", + "\\begin{equation}\n", + "\\mathbf{y}^* = \\mathbf{C}^*\\mathbf{x}^*\n", + "\\end{equation}\n", + "\n", + "where matrices $\\mathbf{A}^* = \\mathbf{T}\\mathbf{A}\\mathbf{T}^{-1}, \\mathbf{B}^* = \\mathbf{T}\\mathbf{B}, \\mathbf{C}^* = \\mathbf{C}\\mathbf{T}^{-1}$\n", + "\n", + "Note that the control input do not changed, thus we can design the controller in terms of new state $\\mathbf{x}^*$ and then apply the resulting controller directly to the original variables $\\mathbf{x}$\n", + "\n", + "Let us choose the following transformation:\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 98 + }, + "id": "Lr2hgPZ8qLmI", + "outputId": "b0fbde35-e040-432f-829e-0d8418f6a535" + }, + "source": [ + "T_sym = sym.matrices.zeros(4)\n", + "T_sym = T_sym.diag([1, 1, 'r_d', 'r_d'])\n", + "T_sym" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/latex": "$\\displaystyle \\left[\\begin{matrix}1 & 0 & 0 & 0\\\\0 & 1 & 0 & 0\\\\0 & 0 & r_{d} & 0\\\\0 & 0 & 0 & r_{d}\\end{matrix}\\right]$", + "text/plain": [ + "⎡1 0 0 0 ⎤\n", + "⎢ ⎥\n", + "⎢0 1 0 0 ⎥\n", + "⎢ ⎥\n", + "⎢0 0 r_d 0 ⎥\n", + "⎢ ⎥\n", + "⎣0 0 0 r_d⎦" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 6 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 104 + }, + "id": "wjge2Mzr2uT7", + "outputId": "ba3e4a1f-a7a4-4580-d7b6-07a3d99b02a1" + }, + "source": [ + "As_sym = T_sym*A_sym*T_sym.inv()\n", + "As_sym" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/latex": "$\\displaystyle \\left[\\begin{matrix}0 & 1 & 0 & 0\\\\\\omega^{2} + \\frac{2 k}{r_{d}^{3}} & 0 & 0 & 2 \\omega\\\\0 & 0 & 0 & 1\\\\0 & - 2 \\omega & 0 & 0\\end{matrix}\\right]$", + "text/plain": [ + "⎡ 0 1 0 0 ⎤\n", + "⎢ ⎥\n", + "⎢ 2 2⋅k ⎥\n", + "⎢\\omega + ──── 0 0 2⋅\\omega⎥\n", + "⎢ 3 ⎥\n", + "⎢ r_d ⎥\n", + "⎢ ⎥\n", + "⎢ 0 0 0 1 ⎥\n", + "⎢ ⎥\n", + "⎣ 0 -2⋅\\omega 0 0 ⎦" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 7 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 98 + }, + "id": "TjPwCpFR2tmZ", + "outputId": "f8a7019d-3de8-4c5d-b46a-636f041ad5ff" + }, + "source": [ + "Bs_sym = T_sym*B_sym\n", + "Bs_sym" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/latex": "$\\displaystyle \\left[\\begin{matrix}0 & 0\\\\\\frac{1}{m} & 0\\\\0 & 0\\\\0 & \\frac{1}{m}\\end{matrix}\\right]$", + "text/plain": [ + "⎡0 0⎤\n", + "⎢ ⎥\n", + "⎢1 ⎥\n", + "⎢─ 0⎥\n", + "⎢m ⎥\n", + "⎢ ⎥\n", + "⎢0 0⎥\n", + "⎢ ⎥\n", + "⎢ 1⎥\n", + "⎢0 ─⎥\n", + "⎣ m⎦" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 8 + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "cb-SYu1m36x1" + }, + "source": [ + "Let's now create the numerical representation of system matrices as follows:" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "zzR-yC6l4OQ4", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "e823ed61-ec48-4dc2-e359-fb61d6ba09eb" + }, + "source": [ + "import numpy as np\n", + "\n", + "re =\t6371e+3\n", + "r_d = re + 35e6\n", + "\n", + "m = 200\n", + "G = 6.67408e-11\n", + "M = 5.972e+24\n", + "k = G*M\n", + "omega = np.sqrt(k/r_d**3)\n", + "\n", + "A = np.array(As_sym.subs({'r_d':r_d, 'k':k, '\\omega':omega}), dtype = 'double')\n", + "B = np.array(Bs_sym.subs({'m':m}), dtype = 'double')\n", + "print(A)\n" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "[[ 0.00000000e+00 1.00000000e+00 0.00000000e+00 0.00000000e+00]\n", + " [ 1.68866852e-08 0.00000000e+00 0.00000000e+00 1.50051925e-04]\n", + " [ 0.00000000e+00 0.00000000e+00 0.00000000e+00 1.00000000e+00]\n", + " [ 0.00000000e+00 -1.50051925e-04 0.00000000e+00 0.00000000e+00]]\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "8unZC2cW8XHx" + }, + "source": [ + "### **Discretization**\n", + "In practice the control is implemented in digital fashion, thus in order to design the control, system dynamics must be discretized and be presented in the form:\n", + "\n", + "\\begin{equation}\n", + "{\\mathbf {x}}[k+1]={\\mathbf A}_{d}{\\mathbf {x}}[k]+{\\mathbf B}_{d}{\\mathbf {u}}[k]\n", + "\\end{equation}\n", + "\n", + "In order to descretize system exactly, one just need to solve it on time interval $T$ (sampling time):\n", + "\n", + "\\begin{equation}\n", + "{\\mathbf A}_{d}=e^{{{\\mathbf A}T}}={\\mathcal {L}}^{{-1}}\\{(s{\\mathbf I}-{\\mathbf A})^{{-1}}\\}_{{t=T}}\n", + "\\\\\n", + "{\\mathbf B}_{d}=\\left(\\int _{{\\tau =0}}^{{T}}e^{{{\\mathbf A}\\tau }}d\\tau \\right){\\mathbf B}={\\mathbf A}^{{-1}}({\\mathbf A}_{d}-I){\\mathbf B}\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "LSR2lugPHYoT" + }, + "source": [ + "Let us find the discrete representation of system dynamics with samplng time $T = 10$ s" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "cURZN5-q8W0N", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "5b87f01d-63fe-4ed8-8f34-86fb49633d00" + }, + "source": [ + "from scipy.signal import cont2discrete\n", + "\n", + "C = np.array([[1, 0, 0 ,0]])\n", + "D = np.array([[0, 0]])\n", + "\n", + "dT = 10\n", + "\n", + "B_r = np.array([B[:,0]]).T\n", + "B_theta = np.array([B[:,1]]).T\n", + "\n", + "A_d, B_d, C_d, D_d, _ = cont2discrete((A,B,C,D), dT)\n", + "_, B_theta_d, _, _, _ = cont2discrete((A,B_theta,C,D), dT)\n", + "_, B_r_d, _, _, _ = cont2discrete((A,B_r,C,D), dT)\n", + "\n", + "print(f\"Exact discretization:\\n {A_d, B_d}\")" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Exact discretization:\n", + " (array([[ 1.00000084e+00, 9.99999906e+00, 0.00000000e+00,\n", + " 7.50259590e-03],\n", + " [ 1.68866836e-07, 9.99999719e-01, 0.00000000e+00,\n", + " 1.50051911e-03],\n", + " [-4.22313257e-10, -7.50259590e-03, 1.00000000e+00,\n", + " 9.99999625e+00],\n", + " [-1.26693975e-10, -1.50051911e-03, 0.00000000e+00,\n", + " 9.99998874e-01]]), array([[ 2.49999988e-01, 1.25043267e-04],\n", + " [ 4.99999953e-02, 3.75129795e-05],\n", + " [-1.25043267e-04, 2.49999953e-01],\n", + " [-3.75129795e-05, 4.99999812e-02]]))\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "gvR4vEgw8BNj" + }, + "source": [ + "### **Controlability**\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "QkcaT1Qb-4_E" + }, + "source": [ + "def ctrb(A, B):\n", + " R = B\n", + " n = np.shape(A)[0]\n", + " for i in range(1,n):\n", + " A_pwr_n = np.linalg.matrix_power(A, i)\n", + " R = np.hstack((R,A_pwr_n.dot(B)))\n", + " rank_R = np.linalg.matrix_rank(R)\n", + " \n", + " if rank_R == n:\n", + " test = 'controllable'\n", + " else:\n", + " test = 'uncontrollable'\n", + " return R, rank_R, test" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "8nb_DTT-IUKZ" + }, + "source": [ + "Let us check the contrallability condition using both of the control channels \n", + "$u_r, u_\\theta$ and each of them separately:\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "tko_eOv-Brkm", + "outputId": "a30a3641-d125-43a7-b708-dc3d4ddf3daa" + }, + "source": [ + "for B_matrix in B_r_d, B_theta_d, B_d:\n", + " R, rank, test = ctrb(A_d, B_matrix)\n", + " print(f'\\nRank of the controlability matrix: {rank},\\nsystem is {test}' )" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "\n", + "Rank of the controlability matrix: 3,\n", + "system is uncontrollable\n", + "\n", + "Rank of the controlability matrix: 4,\n", + "system is controllable\n", + "\n", + "Rank of the controlability matrix: 4,\n", + "system is controllable\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "FMXgCn1jCreO" + }, + "source": [ + "Thus the system is controllable just with the one input, physically it represent the thrust vector pointing in tangent line: $u_\\theta$ " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "TUjoxX4vIsM_" + }, + "source": [ + "Recall that one can use the Popov-Belevitch-Hautus test to do the same. " + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "2ETkN4m0AQ3d", + "outputId": "2edbbff8-d6e3-439e-8a4d-424df6cb585a" + }, + "source": [ + "def pbh(A, B):\n", + " lambdas, v = np.linalg.eig(A)\n", + " n = np.shape(A)[0]\n", + " ranks = n*[0]\n", + " # M = n*[0]\n", + " test = 'controllable'\n", + " for i in range(n):\n", + " M = np.hstack((A - lambdas[i]*np.eye(n), B))\n", + " ranks[i] = np.linalg.matrix_rank(M)\n", + " if ranks[i] != n:\n", + " test = 'uncontrollable'\n", + " if np.real(lambdas[i])<0:\n", + " test += ' but stabilizable'\n", + " return ranks, lambdas, test\n", + "\n", + "\n", + "\n", + "eigs, ranks, test = pbh(A_d,B_r_d)\n", + "print(f'Eigen values of PBH matrices:\\n{eigs}\\n\\nRanks of the PBH matrices: {ranks},\\nsystem is {test}' )\n", + "\n", + "eigs, ranks, test = pbh(A_d,B_theta_d)\n", + "print(f'Eigen values of PBH matrices:\\n{eigs}\\n\\nRanks of the PBH matrices: {ranks},\\nsystem is {test}' )" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Eigen values of PBH matrices:\n", + "[3, 4, 4, 3]\n", + "\n", + "Ranks of the PBH matrices: [1. +0.j 0.99999972+0.00075026j 0.99999972-0.00075026j\n", + " 1. +0.j ],\n", + "system is uncontrollable\n", + "Eigen values of PBH matrices:\n", + "[4, 4, 4, 4]\n", + "\n", + "Ranks of the PBH matrices: [1. +0.j 0.99999972+0.00075026j 0.99999972-0.00075026j\n", + " 1. +0.j ],\n", + "system is controllable\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "tJafbrmEJfuG" + }, + "source": [ + "The number of necesarry control channels may be deduced by analyzing the rank of \"PBH matrices\"" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "4G1VL35LI6bA", + "outputId": "d55541ab-20a1-465b-a44a-903a6a611310" + }, + "source": [ + "lambdas, v = np.linalg.eig(A_d)\n", + "n = len(lambdas)\n", + "\n", + "for i in range(n):\n", + " A_e = A_d - lambdas[i]*np.eye(n)\n", + " print(f'Eigenvalue s: {lambdas[i]}')\n", + " print(f'Rank of A - sI: {np.linalg.matrix_rank(A_e)}')\n", + " print(f'Rank difficiency: {n - np.linalg.matrix_rank(A_e)}\\n')" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Eigenvalue s: (1+0j)\n", + "Rank of A - sI: 3\n", + "Rank difficiency: 1\n", + "\n", + "Eigenvalue s: (0.9999997185552608+0.0007502595547439014j)\n", + "Rank of A - sI: 3\n", + "Rank difficiency: 1\n", + "\n", + "Eigenvalue s: (0.9999997185552608-0.0007502595547439014j)\n", + "Rank of A - sI: 3\n", + "Rank difficiency: 1\n", + "\n", + "Eigenvalue s: (1.0000000000000002+0j)\n", + "Rank of A - sI: 3\n", + "Rank difficiency: 1\n", + "\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "fk4AlkpvJvB8" + }, + "source": [ + "Since the matrices are of rank 3 - we need the only one actuator to control this system. However, for this practice lets use both of them. " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "dKpvMqZgKOT6" + }, + "source": [ + "### **Discrete Time LQR**\n", + "For a discrete-time linear system described by:\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{x}_{k+1}=\\mathbf{A} \\mathbf{x}_{k}+\\mathbf{B}\\mathbf{u}_{k}\n", + "\\end{equation}\n", + "with a performance index defined as:\n", + "\\begin{equation}\n", + "J_c=\\sum \\limits _{{k=0}}^{{\\infty }}\\left(\\mathbf{x}_{k}^{T}\\mathbf{Q}\\mathbf{x}_{k}+\\mathbf{u}_{k}^{T}\\mathbf{R}\\mathbf{u}_{k}\\right)\n", + "\\end{equation}\n", + "\n", + "the optimal control sequence minimizing the performance index is given by:\n", + "\\begin{equation}\n", + "\\mathbf{u}_{k}=-\\mathbf{K} \\mathbf{x}_{k}\n", + "\\end{equation}\n", + "\n", + "where:\n", + "\\begin{equation}\n", + "\\mathbf{K}=(\\mathbf{R}+\\mathbf{B}^{T}\\mathbf{S}\\mathbf{B})^{{-1}}\\mathbf{B}^{T}\\mathbf{S}\\mathbf{A}\n", + "\\end{equation}\n", + "\n", + "and $\\mathbf{S}$ is the unique positive definite solution to the discrete time algebraic Riccati equation (DARE):\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{S}=\\mathbf{A}^{T}\\mathbf{S}\\mathbf{A}-(\\mathbf{A}^{T}\\mathbf{S}\\mathbf{B})\\left(\\mathbf{R}+\\mathbf{B}^{T}\\mathbf{S}\\mathbf{B}\\right)^{{-1}}(\\mathbf{B}^{T}\\mathbf{S}\\mathbf{A})+\\mathbf{Q}\n", + "\\end{equation}" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "OeQE3qRGFQZ1" + }, + "source": [ + "from scipy.linalg import solve_discrete_are as dare\n", + "\n", + "def dlqr(A, B, Q, R):\n", + " # Solve the DARE\n", + " S = dare(A, B, Q, R)\n", + " R_inv = np.linalg.inv(R + B.T @ S @ B )\n", + " K = R_inv @ (B.T @ S @ A)\n", + " Ac = A - B.dot(K)\n", + " E = np.linalg.eigvals(Ac)\n", + " return S, K, E\n" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "oEL_UfFcLE_v" + }, + "source": [ + "Let us find the descrete LQR gain that minimize the cost above while highly penelazing the thrust vector: " + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "bshxqqS4RT8K" + }, + "source": [ + "Q = np.diag([0.1,0.1,0.00001,0.01])\n", + "\n", + "R = np.diag([10000000, 1000000])\n", + "\n", + "S, Kd, E = dlqr(A_d, B_d, Q, R)" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "6hGVYCStRMAq" + }, + "source": [ + " ### **Simulation**\n", + "\n", + "As for now we find the controller to be:\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{u}_{k}=-\\mathbf{K} \\mathbf{x}_{k}\n", + "\\end{equation}\n", + "\n", + "Let us simulate the controller on two systems:\n", + "\n", + "1. Linear discrete system:\n", + "\\begin{equation}\n", + "\\mathbf{x}_{k+1}=\\mathbf{A} \\mathbf{x}_{k}+\\mathbf{B}\\mathbf{u}_{k}\n", + "\\end{equation}\n", + "\n", + "2. Nonlinear continues system, solved on discrete time instances (discrete control, continues dynamics):\n", + "\\begin{equation}\n", + "\\mathbf{x}_{k+1}=\\int_{t_k}^{t_k + dT} \\mathbf{f}(\\mathbf{x}(\\tau),\\mathbf{u}_k) d\\tau \n", + "\\end{equation}\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "KZknGLITR6O7" + }, + "source": [ + " #### **Linear Case**\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "SIN0KpNaU8JJ" + }, + "source": [ + "We will assume that the initial orbit is $5000$ km above desired one:" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "_DrG3UFZxi7W" + }, + "source": [ + "r_0 = r_d + 5e6" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "UaKk1FXCVRqP" + }, + "source": [ + "Let us first choose the initial orbit that $5000$ km far from the desired one:" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 450 + }, + "id": "QzW4yRKL_WZ7", + "outputId": "a2d89ba8-d70b-4680-b0a5-b1fe1c3674bd" + }, + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "N = 1600\n", + "x = np.array([ r_0 - r_d,0, 0, 0])\n", + "X = x\n", + "U = -Kd@x\n", + "\n", + "for k in range(N):\n", + " u = -Kd@x \n", + " x = A_d @ x + B_d @ u\n", + " X = np.vstack((X, x))\n", + " U = np.vstack((U, u))\n", + "\n", + "e_r_d, e_dr_d, e_theta_d, e_dtheta_d = np.split(X, 4, axis = 1)\n", + "\n", + "\n", + "t = np.array(range(N+1))*dT/60\n", + "\n", + "plt.figure(figsize=(9, 3))\n", + "plt.step(t,e_r_d)\n", + "plt.grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "plt.grid(True)\n", + "plt.ylabel(r'Error $\\tilde{r}$')\n", + "plt.xlabel(r'Time $T$ (min)')\n", + "plt.show()\n", + "\n", + "plt.figure(figsize=(9, 3))\n", + "plt.step(t,U)\n", + "plt.grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "plt.grid(True)\n", + "plt.ylabel(r'Control $\\mathbf{u}[k]$')\n", + "plt.xlabel(r'Time $T$ (min)')\n", + "plt.show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "I5tEr-YtRHph" + }, + "source": [ + " #### **Nonlinear Case**\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 450 + }, + "id": "9BmwnW7AUF9d", + "outputId": "5deddf80-7f87-4cec-9115-1d09a8fb0d9b" + }, + "source": [ + "from scipy.integrate import odeint\n", + "\n", + "params = k, m\n", + "\n", + "func = lambda x, t, u, params : f(x, u, params)\n", + "\n", + "x0 = np.array([r_0, 0, 0, 0])\n", + "T_span = np.linspace(0, dT, 5)\n", + "X = x0\n", + "\n", + "x_d = np.array([r_d, 0, 0, omega])\n", + "e = x0 - x_d \n", + "E = e\n", + "U = -Kd@e\n", + "\n", + "for k in range(N):\n", + " t = k*dT\n", + " x_d = np.array([r_d, 0, omega*t, omega])\n", + " e = x0 - x_d \n", + " u = -Kd@e\n", + " x_sol = odeint(func, x0, T_span, args=(u, params,))\n", + " x0 = x_sol[-1]\n", + "\n", + " X = np.vstack((X, x0))\n", + " E = np.vstack((E, e))\n", + " U = np.vstack((U, u))\n", + "\n", + "r, dr, theta, dtheta = np.split(X, 4, axis = 1)\n", + "e_r, e_dr, e_theta, e_dtheta = np.split(E, 4, axis = 1)\n", + "t = np.array(range(N+1))*dT/60\n", + "\n", + "plt.figure(figsize=(9, 3))\n", + "plt.step(t,e_r)\n", + "plt.grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "plt.grid(True)\n", + "plt.ylabel(r'Error $\\tilde{r}$')\n", + "plt.xlabel(r'Time $t$ (min)')\n", + "plt.show()\n", + "\n", + "plt.figure(figsize=(9, 3))\n", + "plt.step(t,U)\n", + "plt.grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "plt.grid(True)\n", + "plt.ylabel(r'Control $\\mathbf{u}[k]$')\n", + "plt.xlabel(r'Time $t$ (min)')\n", + "plt.show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "ywH2-r8rOXTf" + }, + "source": [ + "We can compare the response:" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 239 + }, + "id": "CbNcim53Oitl", + "outputId": "10569e98-12c7-4bef-bc15-98b2897723fd" + }, + "source": [ + "plt.figure(figsize=(9, 3))\n", + "plt.step(t,e_r)\n", + "plt.step(t,e_r_d)\n", + "plt.grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "plt.grid(True)\n", + "plt.ylabel(r'State $\\mathbf{x}[k]$')\n", + "plt.xlabel(r'Time $t$ (min)')\n", + "plt.show()\n" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Il8RG8NGQdtw" + }, + "source": [ + "### **HW Problem:**\n", + "\n", + "Check if it is possible to use either $r$ or $\\theta$ to design controller, if it's so design the observer to estimate the full state $\\mathbf{\\hat{x}}$ and then use the estimated state for full state feedback $\\mathbf{u}_k = -\\mathbf{K}\\mathbf{\\hat{x}}_k$. Simulate the designed controller both on linear and nonlinear systems.\n" + ] + } + ] +} \ No newline at end of file diff --git a/legacy - ColabNotebooks/practice_13_design_example.ipynb b/legacy - ColabNotebooks/practice_13_design_example.ipynb new file mode 100644 index 0000000..49628ae --- /dev/null +++ b/legacy - ColabNotebooks/practice_13_design_example.ipynb @@ -0,0 +1,1359 @@ +{ + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { + "colab": { + "name": "[CT21] lab13_design_example.ipynb", + "provenance": [], + "collapsed_sections": [], + "include_colab_link": true + }, + "kernelspec": { + "name": "python3", + "display_name": "Python 3" + } + }, + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "zPmrTNlSBW-R" + }, + "source": [ + "# **Practice 13: Design Example, Orbital maneuver**\n", + "\n", + "---" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "H608E584MQst" + }, + "source": [ + "### **Problem Definition:**\n", + "\n", + "Consider a satellite described by the following equations:\n", + "\\begin{equation}\n", + "\\left\\{\\begin{matrix}\n", + "m\\ddot{r}=m r\\dot{\\theta}^2 -G\\cfrac{m M}{r^2} + u_r\n", + "\\\\ \n", + "mr\\ddot{\\theta}=-2 m \\dot{r}\\dot{\\theta}+ u_\\theta\n", + "\\end{matrix}\\right.\n", + "\\end{equation}\n", + "\n", + "A problem is to **stabilize** the satellite on the desired orbit of constant radius $r_d = \\text{const}$ with minimal control effort. \n", + "\n", + "\n", + "\n", + "\n", + "

\"linear

\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "qEPSCPZ5SyZo" + }, + "source": [ + "\n", + "\n", + "The overall workflow to design the controller is summarized as follows:\n", + "\n", + "\n", + "1. Modeling, **State space representation** of system dynamics ( [Practice 1](https://colab.research.google.com/drive/1OE18rhr8Mhq3H5FS5yci037CQ52ag4yq))\n", + "2. Deducing **feasible trajectory** \n", + "3. **Linearizing** system dynamics nearby desired trajectory, **linear state space** ( [Practice 8](https://colab.research.google.com/drive/15l9Pyv-ol33NrwM3v48r9jjZLP_Vgimt)) \n", + "4. **Discretization** of linearized system ( [Practice 6](https://colab.research.google.com/drive/1FLxfvWfwhNvjlYz-9oQJviwlj9M0URUh))\n", + "5. **Controllability** analysis ( [Practice 11](https://colab.research.google.com/drive/1Rs_RygP56Fea_Y_QDGIl8vAy4Ht_wkSM))\n", + "6. **Сontroller** design ( [Practice 9](https://colab.research.google.com/drive/1_MjEdyWbJ2In3NZRfdrmKUPdR0IobKH-))\n", + "\n", + "\n", + "\n", + "In order to check the designed controller we will implement the following simulations:\n", + "1. Full state feedback on the **linearized** system \n", + "2. Full state feedback on the **original** system \n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "b2CcXs6tcpbP" + }, + "source": [ + "\n", + "### **State Space Representation**\n", + "\n", + "Let us first introduce the following constant $k = gM$ and rewrite system dynamics in normal form: \n", + "\\begin{equation}\n", + "\\left\\{\\begin{matrix}\n", + "\\ddot{r}= r\\dot{\\theta}^2 -\\cfrac{k}{r^2} + \\cfrac{u_r}{m}\n", + "\\\\ \n", + "\\ddot{\\theta}=-2 \\cfrac{\\dot{r}\\dot{\\theta}}{r}+ \\cfrac{u_\\theta}{mr}\n", + "\\end{matrix}\\right.\n", + "\\end{equation}\n", + "\n", + "Thus introducing the state variables as $\\mathbf{x} = [r, \\dot{r}, \\theta, \\dot{\\theta}]^T$ we may rewrite the equiations above in state space form:\n", + "\n", + "\\begin{equation}\n", + "\\begin{bmatrix}\n", + "\\dot{\\mathbf{x}}_1 \n", + "\\\\\n", + "\\dot{\\mathbf{x}}_2\n", + "\\\\\n", + "\\dot{\\mathbf{x}}_3\n", + "\\\\ \n", + "\\dot{\\mathbf{x}}_4\n", + "\\end{bmatrix}\n", + "=\n", + "\\begin{bmatrix}\n", + "\\mathbf{x}_2 \n", + "\\\\\n", + "\\mathbf{x}_1 \\mathbf{x}_4^2\n", + "\\\\\n", + "\\mathbf{x}_4\n", + "\\\\ \n", + "-2 \\cfrac{\\mathbf{x}_2\\mathbf{x}_4}{\\mathbf{x}_1}\n", + "\\end{bmatrix}\n", + "+\n", + "\\begin{bmatrix}\n", + " 0 & 0 \\\\\n", + " -\\frac{1}{m} & 0 \\\\\n", + " 0 & 0 \\\\\n", + " 0 & \\frac{1}{m \\mathbf{x}_1}\\\\\n", + "\\end{bmatrix}\n", + "\\begin{bmatrix}\n", + "u_r\n", + "\\\\\n", + "u_\\theta\n", + "\\end{bmatrix}\n", + "\\end{equation}\n", + "\n", + "Which may be written in general state space form as:\n", + "\n", + "\n", + "\\begin{equation}\n", + "\\dot{\\mathbf{x}}\n", + "= \n", + "\\mathbf{f}(\\mathbf{x}, \\mathbf{u})\n", + "\\end{equation}\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 105 + }, + "id": "_avHXMUccpJo", + "outputId": "21cb759f-ed3d-4178-c386-bf547ca5f3b7" + }, + "source": [ + "def f(x, u, params):\n", + " k, m = params\n", + " r, dr, theta, dtheta = x\n", + " u_r, u_theta = u\n", + " ddr = r*dtheta**2 -k/(r**2) + u_r/m \n", + " ddtheta = -2*dr*dtheta/r + u_theta/(r*m)\n", + " return dr, ddr, dtheta, ddtheta\n", + "\n", + "import sympy as sym\n", + "\n", + "sym.init_printing()\n", + "\n", + "x_sym = sym.symbols(r'r \\dot{r} \\theta \\dot{\\theta}') \n", + "u_sym = sym.symbols(r'u_r u_\\theta') \n", + "params_sym = sym.symbols(r'k m')\n", + "f_sym = sym.Matrix([f(x_sym, u_sym, params_sym)]).T\n", + "\n", + "f_sym\n" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/latex": "$\\displaystyle \\left[\\begin{matrix}\\dot{r}\\\\\\dot{\\theta}^{2} r - \\frac{k}{r^{2}} + \\frac{u_{r}}{m}\\\\\\dot{\\theta}\\\\- \\frac{2 \\dot{\\theta} \\dot{r}}{r} + \\frac{u_{\\theta}}{m r}\\end{matrix}\\right]$", + "text/plain": [ + "⎡ \\dot{r} ⎤\n", + "⎢ ⎥\n", + "⎢ 2 k uᵣ ⎥\n", + "⎢ \\dot{\\theta} ⋅r - ── + ── ⎥\n", + "⎢ 2 m ⎥\n", + "⎢ r ⎥\n", + "⎢ ⎥\n", + "⎢ \\dot{\\theta} ⎥\n", + "⎢ ⎥\n", + "⎢ 2⋅\\dot{\\theta}⋅\\dot{r} u_\\theta⎥\n", + "⎢- ────────────────────── + ────────⎥\n", + "⎣ r m⋅r ⎦" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 1 + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "MT3odtf5q5e1" + }, + "source": [ + "### **Feasible trajectory: Equatorial orbit**\n", + "Once model is given by the state space representation above we may obtain trajectory that is consistent with dynamics by direct substitution of the constant $r_d = \\text{const}$:\n", + "\\begin{equation}\n", + "\\left\\{\\begin{matrix}\n", + "0= r_d\\dot{\\theta}_d^2 -\\cfrac{k}{r_d^2} + \\cfrac{u_{r_d}}{m}\n", + "\\\\ \n", + "\\ddot{\\theta}_d= \\cfrac{u_{\\theta_d}}{mr_d}\n", + "\\end{matrix}\\right.\n", + "\\end{equation}\n", + "\n", + "Moreover if one will consider effortless ($u_{r_d}, u_{\\theta_d}$) trajectories the equations above represent the following: \n", + "\n", + "\\begin{equation}\n", + "r^3_d \\dot{\\theta}_d^2 = k \\rightarrow \\dot{\\theta}_d = \\omega = \\sqrt{\\frac{k}{r^3_d}}{}\n", + "\\end{equation}\n", + " Thus the desired trajectory is given by following state/control pair:\n", + "\\begin{equation}\n", + "\\mathbf{x}_d = \n", + "\\begin{bmatrix}\n", + "r_d & 0 & \\omega t & \\omega\n", + "\\end{bmatrix}^T\n", + "\\\\\n", + "\\mathbf{u}_d = \n", + "\\begin{bmatrix}\n", + "u_{\\theta_d} & u_{r_d}\n", + "\\end{bmatrix}^T\n", + "=\n", + "\\begin{bmatrix}\n", + "0 & 0\n", + "\\end{bmatrix}^T\n", + "\\end{equation}\n", + "Thus the solution is flies along the line of the Earth's equator with constant speed and represent so called equatorial orbit. \n", + "\n", + "***Note***\n", + "\n", + "To get into equatorial orbit, a satellite must be launched from a place on Earth close to the equator. NASA often launches satellites aboard an Ariane rocket into equatorial orbit from French Guyana. Special case of equatorial orbit is a geosynchronous (sometimes abbreviated GSO) is an orbit around Earth of a satellite with an orbital period that matches Earth's rotation on its axis, which takes one sidereal day (23 hours, 56 minutes, and 4 seconds) " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "t8qOnyoxuj7t" + }, + "source": [ + "### **Linearization**\n", + "System above is nonlinear, in order to implement the techniques that we studied in this class we need to first obtain the linear state space model. A convinient way to do so is to linearize system dynamics nearby equilibrium point or desired trajectory:\n", + "\n", + "\\begin{equation}\n", + "\\dot{\\mathbf{x}}\n", + "= \\mathbf{f}(\\mathbf{x}_d,\\mathbf{u}_d)+ \n", + "\\frac{\\partial\\mathbf{f}}{\\partial\\mathbf{x}}\\Bigr\\rvert_{\\mathbf{x}_d,\\mathbf{u}_d} \n", + "(\\mathbf{x} - \\mathbf{x}_d) + \n", + "\\frac{\\partial\\mathbf{u}}{\\partial\\mathbf{x}}\\Bigr\\rvert_{\\mathbf{x}_d,\\mathbf{u}_d} \n", + "(\\mathbf{u} - \\mathbf{u}_d) + \\text{H.O.T}\n", + "\\end{equation}\n", + "\n", + "Introducing the tracking error $\\tilde{\\mathbf{x}}$ we may rewrite the equation above in linear form as follows:\n", + "\n", + "\\begin{equation}\n", + "\\dot{\\tilde{\\mathbf{x}}} = \\mathbf{A}\\tilde{\\mathbf{x}} + \\mathbf{B}\\tilde{\\mathbf{u}} \n", + "\\end{equation}\n", + "where: $\\tilde{\\mathbf{x}}$ is tracking error, $\\tilde{\\mathbf{u}}$ is the new control input $\\mathbf{A} = \\frac{\\partial\\mathbf{f}}{\\partial\\mathbf{x}}\\Bigr\\rvert_{\\mathbf{x}_d,\\mathbf{u}_d}$ - state evaluation matrix, $\\mathbf{B} = \\frac{\\partial\\mathbf{f}}{\\partial\\mathbf{u}}\\Bigr\\rvert_{\\mathbf{x}_d,\\mathbf{u}_d}$\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Kr4TMd-_D7iZ" + }, + "source": [ + "Let us first calculate system jacobian with respect to state: $\\frac{\\partial\\mathbf{f}}{\\partial\\mathbf{x}}$\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 104 + }, + "id": "iEybo_f3ujQ-", + "outputId": "065d204a-4467-4856-a08d-ed9e68c221ba" + }, + "source": [ + "# Calculate the jacobian with respect to x\n", + "Jx_sym = f_sym.jacobian(x_sym)\n", + "Jx_sym\n" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/latex": "$\\displaystyle \\left[\\begin{matrix}0 & 1 & 0 & 0\\\\\\dot{\\theta}^{2} + \\frac{2 k}{r^{3}} & 0 & 0 & 2 \\dot{\\theta} r\\\\0 & 0 & 0 & 1\\\\\\frac{2 \\dot{\\theta} \\dot{r}}{r^{2}} - \\frac{u_{\\theta}}{m r^{2}} & - \\frac{2 \\dot{\\theta}}{r} & 0 & - \\frac{2 \\dot{r}}{r}\\end{matrix}\\right]$", + "text/plain": [ + "⎡ 0 1 0 0 ⎤\n", + "⎢ ⎥\n", + "⎢ 2 2⋅k ⎥\n", + "⎢ \\dot{\\theta} + ─── 0 0 2⋅\\dot{\\theta}⋅r⎥\n", + "⎢ 3 ⎥\n", + "⎢ r ⎥\n", + "⎢ ⎥\n", + "⎢ 0 0 0 1 ⎥\n", + "⎢ ⎥\n", + "⎢2⋅\\dot{\\theta}⋅\\dot{r} u_\\theta -2⋅\\dot{\\theta} -2⋅\\dot{r} ⎥\n", + "⎢────────────────────── - ──────── ──────────────── 0 ─────────── ⎥\n", + "⎢ 2 2 r r ⎥\n", + "⎣ r m⋅r ⎦" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 2 + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "O4KOaVZwG_lw" + }, + "source": [ + "\n", + "Now we can evaluate the jacobian nearby desired trajectory $\\mathbf{A} = \\frac{\\partial\\mathbf{f}}{\\partial\\mathbf{x}}\\Bigr\\rvert_{\\mathbf{x}_d,\\mathbf{u}_d}$\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 105 + }, + "id": "aoOae3bUgED1", + "outputId": "28f3fb46-49fb-4560-d3a5-7ec1d8bdcadb" + }, + "source": [ + "# Evaluate J_x nearby desired trajectory\n", + "n = len(x_sym)\n", + "A_sym = Jx_sym\n", + "\n", + "\n", + "A_sym = A_sym.subs({x_sym[0]: 'r_d'})\n", + "A_sym = A_sym.subs({x_sym[1]: 0})\n", + "A_sym = A_sym.subs({x_sym[3]: sym.symbols(r'\\omega')})\n", + "A_sym = A_sym.subs({u_sym[1]: 0})\n", + "\n", + "A_sym.simplify()\n", + "A_sym" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/latex": "$\\displaystyle \\left[\\begin{matrix}0 & 1 & 0 & 0\\\\\\omega^{2} + \\frac{2 k}{r_{d}^{3}} & 0 & 0 & 2 \\omega r_{d}\\\\0 & 0 & 0 & 1\\\\0 & - \\frac{2 \\omega}{r_{d}} & 0 & 0\\end{matrix}\\right]$", + "text/plain": [ + "⎡ 0 1 0 0 ⎤\n", + "⎢ ⎥\n", + "⎢ 2 2⋅k ⎥\n", + "⎢\\omega + ──── 0 0 2⋅\\omega⋅r_d⎥\n", + "⎢ 3 ⎥\n", + "⎢ r_d ⎥\n", + "⎢ ⎥\n", + "⎢ 0 0 0 1 ⎥\n", + "⎢ ⎥\n", + "⎢ -2⋅\\omega ⎥\n", + "⎢ 0 ────────── 0 0 ⎥\n", + "⎣ r_d ⎦" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 3 + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "aBuMq5GPHb4v" + }, + "source": [ + "System jacobian with respect to control: $\\frac{\\partial\\mathbf{f}}{\\partial\\mathbf{u}}$\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 98 + }, + "id": "YD6RTM42cqke", + "outputId": "6bb324c8-fa2f-404a-c15f-615673e148a0" + }, + "source": [ + "# calculate the jacobian with respect to u\n", + "Ju_sym = f_sym.jacobian(u_sym)\n", + "Ju_sym" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/latex": "$\\displaystyle \\left[\\begin{matrix}0 & 0\\\\\\frac{1}{m} & 0\\\\0 & 0\\\\0 & \\frac{1}{m r}\\end{matrix}\\right]$", + "text/plain": [ + "⎡0 0 ⎤\n", + "⎢ ⎥\n", + "⎢1 ⎥\n", + "⎢─ 0 ⎥\n", + "⎢m ⎥\n", + "⎢ ⎥\n", + "⎢0 0 ⎥\n", + "⎢ ⎥\n", + "⎢ 1 ⎥\n", + "⎢0 ───⎥\n", + "⎣ m⋅r⎦" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 4 + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "D1ytkCOgHhHA" + }, + "source": [ + "Now we may substitude the desired trajectory $\\mathbf{B} = \\frac{\\partial\\mathbf{f}}{\\partial\\mathbf{u}}\\Bigr\\rvert_{\\mathbf{x}_d,\\mathbf{u}_d}$\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 100 + }, + "id": "EQr0s1_GpLHm", + "outputId": "1821a6de-226e-41a0-86a0-7736abafcdef" + }, + "source": [ + "B_sym = Ju_sym.subs(x_sym[0], 'r_d')\n", + "B_sym" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/latex": "$\\displaystyle \\left[\\begin{matrix}0 & 0\\\\\\frac{1}{m} & 0\\\\0 & 0\\\\0 & \\frac{1}{m r_{d}}\\end{matrix}\\right]$", + "text/plain": [ + "⎡0 0 ⎤\n", + "⎢ ⎥\n", + "⎢1 ⎥\n", + "⎢─ 0 ⎥\n", + "⎢m ⎥\n", + "⎢ ⎥\n", + "⎢0 0 ⎥\n", + "⎢ ⎥\n", + "⎢ 1 ⎥\n", + "⎢0 ─────⎥\n", + "⎣ m⋅r_d⎦" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 5 + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "pzSpd1RGqMFj" + }, + "source": [ + "### **Similarity Transformation**\n", + "\n", + "There are situations when system matrices are not well defined in several directions, it may happen for instance when the variables to control represent a physical quantities that are highly different in their magnitudes, thus resulting system (matrices $\\mathbf{A}, \\mathbf{B}$) will be barely controllable. To tackle this one may appropriately scale the state variables with some matrix $\\mathbf{T}$ as follows:\n", + "\\begin{equation}\n", + "\\mathbf{x}^* = \\mathbf{T}\\mathbf{x}\n", + "\\end{equation}\n", + "\n", + "Thus the state transition may be calculated by substitution of the $\\mathbf{x} = \\mathbf{T}^{-1}\\mathbf{x}^*$ to the system dynamics:\n", + "\\begin{equation}\n", + "\\dot{\\mathbf{x}}^* = \\mathbf{A}^*\\mathbf{x}^* + \\mathbf{B}^*\\mathbf{u}\n", + "\\end{equation}\n", + "\\begin{equation}\n", + "\\mathbf{y}^* = \\mathbf{C}^*\\mathbf{x}^*\n", + "\\end{equation}\n", + "\n", + "where matrices $\\mathbf{A}^* = \\mathbf{T}\\mathbf{A}\\mathbf{T}^{-1}, \\mathbf{B}^* = \\mathbf{T}\\mathbf{B}, \\mathbf{C}^* = \\mathbf{C}\\mathbf{T}^{-1}$\n", + "\n", + "Note that the control input do not changed, thus we can design the controller in terms of new state $\\mathbf{x}^*$ and then apply the resulting controller directly to the original variables $\\mathbf{x}$\n", + "\n", + "Let us choose the following transformation:\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 98 + }, + "id": "Lr2hgPZ8qLmI", + "outputId": "b0fbde35-e040-432f-829e-0d8418f6a535" + }, + "source": [ + "T_sym = sym.matrices.zeros(4)\n", + "T_sym = T_sym.diag([1, 1, 'r_d', 'r_d'])\n", + "T_sym" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/latex": "$\\displaystyle \\left[\\begin{matrix}1 & 0 & 0 & 0\\\\0 & 1 & 0 & 0\\\\0 & 0 & r_{d} & 0\\\\0 & 0 & 0 & r_{d}\\end{matrix}\\right]$", + "text/plain": [ + "⎡1 0 0 0 ⎤\n", + "⎢ ⎥\n", + "⎢0 1 0 0 ⎥\n", + "⎢ ⎥\n", + "⎢0 0 r_d 0 ⎥\n", + "⎢ ⎥\n", + "⎣0 0 0 r_d⎦" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 6 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 104 + }, + "id": "wjge2Mzr2uT7", + "outputId": "ba3e4a1f-a7a4-4580-d7b6-07a3d99b02a1" + }, + "source": [ + "As_sym = T_sym*A_sym*T_sym.inv()\n", + "As_sym" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/latex": "$\\displaystyle \\left[\\begin{matrix}0 & 1 & 0 & 0\\\\\\omega^{2} + \\frac{2 k}{r_{d}^{3}} & 0 & 0 & 2 \\omega\\\\0 & 0 & 0 & 1\\\\0 & - 2 \\omega & 0 & 0\\end{matrix}\\right]$", + "text/plain": [ + "⎡ 0 1 0 0 ⎤\n", + "⎢ ⎥\n", + "⎢ 2 2⋅k ⎥\n", + "⎢\\omega + ──── 0 0 2⋅\\omega⎥\n", + "⎢ 3 ⎥\n", + "⎢ r_d ⎥\n", + "⎢ ⎥\n", + "⎢ 0 0 0 1 ⎥\n", + "⎢ ⎥\n", + "⎣ 0 -2⋅\\omega 0 0 ⎦" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 7 + } + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 98 + }, + "id": "TjPwCpFR2tmZ", + "outputId": "f8a7019d-3de8-4c5d-b46a-636f041ad5ff" + }, + "source": [ + "Bs_sym = T_sym*B_sym\n", + "Bs_sym" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/latex": "$\\displaystyle \\left[\\begin{matrix}0 & 0\\\\\\frac{1}{m} & 0\\\\0 & 0\\\\0 & \\frac{1}{m}\\end{matrix}\\right]$", + "text/plain": [ + "⎡0 0⎤\n", + "⎢ ⎥\n", + "⎢1 ⎥\n", + "⎢─ 0⎥\n", + "⎢m ⎥\n", + "⎢ ⎥\n", + "⎢0 0⎥\n", + "⎢ ⎥\n", + "⎢ 1⎥\n", + "⎢0 ─⎥\n", + "⎣ m⎦" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 8 + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "cb-SYu1m36x1" + }, + "source": [ + "Let's now create the numerical representation of system matrices as follows:" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "zzR-yC6l4OQ4", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "e823ed61-ec48-4dc2-e359-fb61d6ba09eb" + }, + "source": [ + "import numpy as np\n", + "\n", + "re =\t6371e+3\n", + "r_d = re + 35e6\n", + "\n", + "m = 200\n", + "G = 6.67408e-11\n", + "M = 5.972e+24\n", + "k = G*M\n", + "omega = np.sqrt(k/r_d**3)\n", + "\n", + "A = np.array(As_sym.subs({'r_d':r_d, 'k':k, '\\omega':omega}), dtype = 'double')\n", + "B = np.array(Bs_sym.subs({'m':m}), dtype = 'double')\n", + "print(A)\n" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "[[ 0.00000000e+00 1.00000000e+00 0.00000000e+00 0.00000000e+00]\n", + " [ 1.68866852e-08 0.00000000e+00 0.00000000e+00 1.50051925e-04]\n", + " [ 0.00000000e+00 0.00000000e+00 0.00000000e+00 1.00000000e+00]\n", + " [ 0.00000000e+00 -1.50051925e-04 0.00000000e+00 0.00000000e+00]]\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "8unZC2cW8XHx" + }, + "source": [ + "### **Discretization**\n", + "In practice the control is implemented in digital fashion, thus in order to design the control, system dynamics must be discretized and be presented in the form:\n", + "\n", + "\\begin{equation}\n", + "{\\mathbf {x}}[k+1]={\\mathbf A}_{d}{\\mathbf {x}}[k]+{\\mathbf B}_{d}{\\mathbf {u}}[k]\n", + "\\end{equation}\n", + "\n", + "In order to descretize system exactly, one just need to solve it on time interval $T$ (sampling time):\n", + "\n", + "\\begin{equation}\n", + "{\\mathbf A}_{d}=e^{{{\\mathbf A}T}}={\\mathcal {L}}^{{-1}}\\{(s{\\mathbf I}-{\\mathbf A})^{{-1}}\\}_{{t=T}}\n", + "\\\\\n", + "{\\mathbf B}_{d}=\\left(\\int _{{\\tau =0}}^{{T}}e^{{{\\mathbf A}\\tau }}d\\tau \\right){\\mathbf B}={\\mathbf A}^{{-1}}({\\mathbf A}_{d}-I){\\mathbf B}\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "LSR2lugPHYoT" + }, + "source": [ + "Let us find the discrete representation of system dynamics with samplng time $T = 10$ s" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "cURZN5-q8W0N", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "outputId": "5b87f01d-63fe-4ed8-8f34-86fb49633d00" + }, + "source": [ + "from scipy.signal import cont2discrete\n", + "\n", + "C = np.array([[1, 0, 0 ,0]])\n", + "D = np.array([[0, 0]])\n", + "\n", + "dT = 10\n", + "\n", + "B_r = np.array([B[:,0]]).T\n", + "B_theta = np.array([B[:,1]]).T\n", + "\n", + "A_d, B_d, C_d, D_d, _ = cont2discrete((A,B,C,D), dT)\n", + "_, B_theta_d, _, _, _ = cont2discrete((A,B_theta,C,D), dT)\n", + "_, B_r_d, _, _, _ = cont2discrete((A,B_r,C,D), dT)\n", + "\n", + "print(f\"Exact discretization:\\n {A_d, B_d}\")" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Exact discretization:\n", + " (array([[ 1.00000084e+00, 9.99999906e+00, 0.00000000e+00,\n", + " 7.50259590e-03],\n", + " [ 1.68866836e-07, 9.99999719e-01, 0.00000000e+00,\n", + " 1.50051911e-03],\n", + " [-4.22313257e-10, -7.50259590e-03, 1.00000000e+00,\n", + " 9.99999625e+00],\n", + " [-1.26693975e-10, -1.50051911e-03, 0.00000000e+00,\n", + " 9.99998874e-01]]), array([[ 2.49999988e-01, 1.25043267e-04],\n", + " [ 4.99999953e-02, 3.75129795e-05],\n", + " [-1.25043267e-04, 2.49999953e-01],\n", + " [-3.75129795e-05, 4.99999812e-02]]))\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "gvR4vEgw8BNj" + }, + "source": [ + "### **Controlability**\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "QkcaT1Qb-4_E" + }, + "source": [ + "def ctrb(A, B):\n", + " R = B\n", + " n = np.shape(A)[0]\n", + " for i in range(1,n):\n", + " A_pwr_n = np.linalg.matrix_power(A, i)\n", + " R = np.hstack((R,A_pwr_n.dot(B)))\n", + " rank_R = np.linalg.matrix_rank(R)\n", + " \n", + " if rank_R == n:\n", + " test = 'controllable'\n", + " else:\n", + " test = 'uncontrollable'\n", + " return R, rank_R, test" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "8nb_DTT-IUKZ" + }, + "source": [ + "Let us check the contrallability condition using both of the control channels \n", + "$u_r, u_\\theta$ and each of them separately:\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "tko_eOv-Brkm", + "outputId": "a30a3641-d125-43a7-b708-dc3d4ddf3daa" + }, + "source": [ + "for B_matrix in B_r_d, B_theta_d, B_d:\n", + " R, rank, test = ctrb(A_d, B_matrix)\n", + " print(f'\\nRank of the controlability matrix: {rank},\\nsystem is {test}' )" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "\n", + "Rank of the controlability matrix: 3,\n", + "system is uncontrollable\n", + "\n", + "Rank of the controlability matrix: 4,\n", + "system is controllable\n", + "\n", + "Rank of the controlability matrix: 4,\n", + "system is controllable\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "FMXgCn1jCreO" + }, + "source": [ + "Thus the system is controllable just with the one input, physically it represent the thrust vector pointing in tangent line: $u_\\theta$ " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "TUjoxX4vIsM_" + }, + "source": [ + "Recall that one can use the Popov-Belevitch-Hautus test to do the same. " + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "2ETkN4m0AQ3d", + "outputId": "2edbbff8-d6e3-439e-8a4d-424df6cb585a" + }, + "source": [ + "def pbh(A, B):\n", + " lambdas, v = np.linalg.eig(A)\n", + " n = np.shape(A)[0]\n", + " ranks = n*[0]\n", + " # M = n*[0]\n", + " test = 'controllable'\n", + " for i in range(n):\n", + " M = np.hstack((A - lambdas[i]*np.eye(n), B))\n", + " ranks[i] = np.linalg.matrix_rank(M)\n", + " if ranks[i] != n:\n", + " test = 'uncontrollable'\n", + " if np.real(lambdas[i])<0:\n", + " test += ' but stabilizable'\n", + " return ranks, lambdas, test\n", + "\n", + "\n", + "\n", + "eigs, ranks, test = pbh(A_d,B_r_d)\n", + "print(f'Eigen values of PBH matrices:\\n{eigs}\\n\\nRanks of the PBH matrices: {ranks},\\nsystem is {test}' )\n", + "\n", + "eigs, ranks, test = pbh(A_d,B_theta_d)\n", + "print(f'Eigen values of PBH matrices:\\n{eigs}\\n\\nRanks of the PBH matrices: {ranks},\\nsystem is {test}' )" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Eigen values of PBH matrices:\n", + "[3, 4, 4, 3]\n", + "\n", + "Ranks of the PBH matrices: [1. +0.j 0.99999972+0.00075026j 0.99999972-0.00075026j\n", + " 1. +0.j ],\n", + "system is uncontrollable\n", + "Eigen values of PBH matrices:\n", + "[4, 4, 4, 4]\n", + "\n", + "Ranks of the PBH matrices: [1. +0.j 0.99999972+0.00075026j 0.99999972-0.00075026j\n", + " 1. +0.j ],\n", + "system is controllable\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "tJafbrmEJfuG" + }, + "source": [ + "The number of necesarry control channels may be deduced by analyzing the rank of \"PBH matrices\"" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "4G1VL35LI6bA", + "outputId": "d55541ab-20a1-465b-a44a-903a6a611310" + }, + "source": [ + "lambdas, v = np.linalg.eig(A_d)\n", + "n = len(lambdas)\n", + "\n", + "for i in range(n):\n", + " A_e = A_d - lambdas[i]*np.eye(n)\n", + " print(f'Eigenvalue s: {lambdas[i]}')\n", + " print(f'Rank of A - sI: {np.linalg.matrix_rank(A_e)}')\n", + " print(f'Rank difficiency: {n - np.linalg.matrix_rank(A_e)}\\n')" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Eigenvalue s: (1+0j)\n", + "Rank of A - sI: 3\n", + "Rank difficiency: 1\n", + "\n", + "Eigenvalue s: (0.9999997185552608+0.0007502595547439014j)\n", + "Rank of A - sI: 3\n", + "Rank difficiency: 1\n", + "\n", + "Eigenvalue s: (0.9999997185552608-0.0007502595547439014j)\n", + "Rank of A - sI: 3\n", + "Rank difficiency: 1\n", + "\n", + "Eigenvalue s: (1.0000000000000002+0j)\n", + "Rank of A - sI: 3\n", + "Rank difficiency: 1\n", + "\n" + ], + "name": "stdout" + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "fk4AlkpvJvB8" + }, + "source": [ + "Since the matrices are of rank 3 - we need the only one actuator to control this system. However, for this practice lets use both of them. " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "dKpvMqZgKOT6" + }, + "source": [ + "### **Discrete Time LQR**\n", + "For a discrete-time linear system described by:\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{x}_{k+1}=\\mathbf{A} \\mathbf{x}_{k}+\\mathbf{B}\\mathbf{u}_{k}\n", + "\\end{equation}\n", + "with a performance index defined as:\n", + "\\begin{equation}\n", + "J_c=\\sum \\limits _{{k=0}}^{{\\infty }}\\left(\\mathbf{x}_{k}^{T}\\mathbf{Q}\\mathbf{x}_{k}+\\mathbf{u}_{k}^{T}\\mathbf{R}\\mathbf{u}_{k}\\right)\n", + "\\end{equation}\n", + "\n", + "the optimal control sequence minimizing the performance index is given by:\n", + "\\begin{equation}\n", + "\\mathbf{u}_{k}=-\\mathbf{K} \\mathbf{x}_{k}\n", + "\\end{equation}\n", + "\n", + "where:\n", + "\\begin{equation}\n", + "\\mathbf{K}=(\\mathbf{R}+\\mathbf{B}^{T}\\mathbf{S}\\mathbf{B})^{{-1}}\\mathbf{B}^{T}\\mathbf{S}\\mathbf{A}\n", + "\\end{equation}\n", + "\n", + "and $\\mathbf{S}$ is the unique positive definite solution to the discrete time algebraic Riccati equation (DARE):\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{S}=\\mathbf{A}^{T}\\mathbf{S}\\mathbf{A}-(\\mathbf{A}^{T}\\mathbf{S}\\mathbf{B})\\left(\\mathbf{R}+\\mathbf{B}^{T}\\mathbf{S}\\mathbf{B}\\right)^{{-1}}(\\mathbf{B}^{T}\\mathbf{S}\\mathbf{A})+\\mathbf{Q}\n", + "\\end{equation}" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "OeQE3qRGFQZ1" + }, + "source": [ + "from scipy.linalg import solve_discrete_are as dare\n", + "\n", + "def dlqr(A, B, Q, R):\n", + " # Solve the DARE\n", + " S = dare(A, B, Q, R)\n", + " R_inv = np.linalg.inv(R + B.T @ S @ B )\n", + " K = R_inv @ (B.T @ S @ A)\n", + " Ac = A - B.dot(K)\n", + " E = np.linalg.eigvals(Ac)\n", + " return S, K, E\n" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "oEL_UfFcLE_v" + }, + "source": [ + "Let us find the descrete LQR gain that minimize the cost above while highly penelazing the thrust vector: " + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "bshxqqS4RT8K" + }, + "source": [ + "Q = np.diag([0.1,0.1,0.00001,0.01])\n", + "\n", + "R = np.diag([10000000, 1000000])\n", + "\n", + "S, Kd, E = dlqr(A_d, B_d, Q, R)" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "6hGVYCStRMAq" + }, + "source": [ + " ### **Simulation**\n", + "\n", + "As for now we find the controller to be:\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{u}_{k}=-\\mathbf{K} \\mathbf{x}_{k}\n", + "\\end{equation}\n", + "\n", + "Let us simulate the controller on two systems:\n", + "\n", + "1. Linear discrete system:\n", + "\\begin{equation}\n", + "\\mathbf{x}_{k+1}=\\mathbf{A} \\mathbf{x}_{k}+\\mathbf{B}\\mathbf{u}_{k}\n", + "\\end{equation}\n", + "\n", + "2. Nonlinear continues system, solved on discrete time instances (discrete control, continues dynamics):\n", + "\\begin{equation}\n", + "\\mathbf{x}_{k+1}=\\int_{t_k}^{t_k + dT} \\mathbf{f}(\\mathbf{x}(\\tau),\\mathbf{u}_k) d\\tau \n", + "\\end{equation}\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "KZknGLITR6O7" + }, + "source": [ + " #### **Linear Case**\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "SIN0KpNaU8JJ" + }, + "source": [ + "We will assume that the initial orbit is $5000$ km above desired one:" + ] + }, + { + "cell_type": "code", + "metadata": { + "id": "_DrG3UFZxi7W" + }, + "source": [ + "r_0 = r_d + 5e6" + ], + "execution_count": null, + "outputs": [] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "UaKk1FXCVRqP" + }, + "source": [ + "Let us first choose the initial orbit that $5000$ km far from the desired one:" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 450 + }, + "id": "QzW4yRKL_WZ7", + "outputId": "a2d89ba8-d70b-4680-b0a5-b1fe1c3674bd" + }, + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "N = 1600\n", + "x = np.array([ r_0 - r_d,0, 0, 0])\n", + "X = x\n", + "U = -Kd@x\n", + "\n", + "for k in range(N):\n", + " u = -Kd@x \n", + " x = A_d @ x + B_d @ u\n", + " X = np.vstack((X, x))\n", + " U = np.vstack((U, u))\n", + "\n", + "e_r_d, e_dr_d, e_theta_d, e_dtheta_d = np.split(X, 4, axis = 1)\n", + "\n", + "\n", + "t = np.array(range(N+1))*dT/60\n", + "\n", + "plt.figure(figsize=(9, 3))\n", + "plt.step(t,e_r_d)\n", + "plt.grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "plt.grid(True)\n", + "plt.ylabel(r'Error $\\tilde{r}$')\n", + "plt.xlabel(r'Time $T$ (min)')\n", + "plt.show()\n", + "\n", + "plt.figure(figsize=(9, 3))\n", + "plt.step(t,U)\n", + "plt.grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "plt.grid(True)\n", + "plt.ylabel(r'Control $\\mathbf{u}[k]$')\n", + "plt.xlabel(r'Time $T$ (min)')\n", + "plt.show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "I5tEr-YtRHph" + }, + "source": [ + " #### **Nonlinear Case**\n" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 450 + }, + "id": "9BmwnW7AUF9d", + "outputId": "5deddf80-7f87-4cec-9115-1d09a8fb0d9b" + }, + "source": [ + "from scipy.integrate import odeint\n", + "\n", + "params = k, m\n", + "\n", + "func = lambda x, t, u, params : f(x, u, params)\n", + "\n", + "x0 = np.array([r_0, 0, 0, 0])\n", + "T_span = np.linspace(0, dT, 5)\n", + "X = x0\n", + "\n", + "x_d = np.array([r_d, 0, 0, omega])\n", + "e = x0 - x_d \n", + "E = e\n", + "U = -Kd@e\n", + "\n", + "for k in range(N):\n", + " t = k*dT\n", + " x_d = np.array([r_d, 0, omega*t, omega])\n", + " e = x0 - x_d \n", + " u = -Kd@e\n", + " x_sol = odeint(func, x0, T_span, args=(u, params,))\n", + " x0 = x_sol[-1]\n", + "\n", + " X = np.vstack((X, x0))\n", + " E = np.vstack((E, e))\n", + " U = np.vstack((U, u))\n", + "\n", + "r, dr, theta, dtheta = np.split(X, 4, axis = 1)\n", + "e_r, e_dr, e_theta, e_dtheta = np.split(E, 4, axis = 1)\n", + "t = np.array(range(N+1))*dT/60\n", + "\n", + "plt.figure(figsize=(9, 3))\n", + "plt.step(t,e_r)\n", + "plt.grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "plt.grid(True)\n", + "plt.ylabel(r'Error $\\tilde{r}$')\n", + "plt.xlabel(r'Time $t$ (min)')\n", + "plt.show()\n", + "\n", + "plt.figure(figsize=(9, 3))\n", + "plt.step(t,U)\n", + "plt.grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "plt.grid(True)\n", + "plt.ylabel(r'Control $\\mathbf{u}[k]$')\n", + "plt.xlabel(r'Time $t$ (min)')\n", + "plt.show()" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "ywH2-r8rOXTf" + }, + "source": [ + "We can compare the response:" + ] + }, + { + "cell_type": "code", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 239 + }, + "id": "CbNcim53Oitl", + "outputId": "10569e98-12c7-4bef-bc15-98b2897723fd" + }, + "source": [ + "plt.figure(figsize=(9, 3))\n", + "plt.step(t,e_r)\n", + "plt.step(t,e_r_d)\n", + "plt.grid(color='black', linestyle='--', linewidth=1.0, alpha = 0.7)\n", + "plt.grid(True)\n", + "plt.ylabel(r'State $\\mathbf{x}[k]$')\n", + "plt.xlabel(r'Time $t$ (min)')\n", + "plt.show()\n" + ], + "execution_count": null, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "tags": [], + "needs_background": "light" + } + } + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Il8RG8NGQdtw" + }, + "source": [ + "### **HW Problem:**\n", + "\n", + "Check if it is possible to use either $r$ or $\\theta$ to design controller, if it's so design the observer to estimate the full state $\\mathbf{\\hat{x}}$ and then use the estimated state for full state feedback $\\mathbf{u}_k = -\\mathbf{K}\\mathbf{\\hat{x}}_k$. Simulate the designed controller both on linear and nonlinear systems.\n" + ] + } + ] +} \ No newline at end of file