31_32_Sensitivity and Complementary Sensitivity-Video.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Goals of feedback"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "\n",
    "1.Stablity(design)\n",
    "2.Uncertainity(compensation)\n",
    "3.Disturbance(Rejection)\n",
    "4.Noise(Attenuation)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "d11b5571-a344-4ecf-ac59-f0108365e052"
    }
   },
   "source": [
    "# System flow"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "503aecb6-d4c3-4ac9-ac00-2138cd780668"
    }
   },
   "source": [
    "![loop.JPG](attachment:loop.JPG)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "01c045eb-8830-46c3-afe5-272c45577372"
    }
   },
   "source": [
    "Loop transfer function =combination of controller K and System P. L=PK                      \n",
    "\n",
    "Our Equation becomes,\n",
    "\n",
    "Y=Pd d+ PK(ε)= Pd d+ PK(r-ym)\n",
    "Y=Pd d+PK(r-y-n)-----------(1)\n",
    "In these equations we will consider it as matrix equation. So  equn (1) becomes\n",
    "I Y=Pd d+PK(r-y-n)----------(2)\n",
    "I Y=Pd d+PK r-PK y-PK n\n",
    "(I+PK) y=PK r+Pd d-PK n\n",
    "Ym=〖(𝐼+𝑃𝐾)〗^(−1)  (PK r)  +〖(𝐼+𝑃𝐾)〗^(−1)Pd d- 〖(𝐼+𝑃𝐾)〗^(−1)PK n--------(3)\n",
    "Where 〖(𝐼+𝑃𝐾)〗^(−1)=sensitivity,s and\n",
    "〖(𝐼+𝑃𝐾)〗^(−1)PK=complementary sensitivity\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So ,PK=L\n",
    "So S=〖(𝐼+𝐿)〗^(−1)\n",
    "T=〖(𝐼+𝐿)〗^(−1)L\n",
    "Now,its easy to show S+T=I-------- for all frequencies"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "5e55b130-fe2d-4866-bf11-4d6c7362e756"
    }
   },
   "source": [
    "Design K,so that S and T have beneficiary properties to attenuate noise,reduce disturbances and increase stability.\n",
    "ε = r-Ym\n",
    "=r- 〖(𝐼+𝑃𝐾)〗^(−1) PK r +〖(𝐼+𝑃𝐾)〗^(−1) Pd d – 〖(𝐼+𝑃𝐾)〗^(−1) PK n--------(4)\n",
    "We know 〖(𝐼+𝑃𝐾)〗^(−1) PK=T\n",
    "Equn (4) becomes\n",
    "=r- Tr - 〖(𝐼+𝑃𝐾)〗^(−1)Pd d + 〖(𝐼+𝑃𝐾)〗^(−1)PK n\n",
    "= r(I-T) - 〖(𝐼+𝑃𝐾)〗^(−1)Pd d + 〖(𝐼+𝑃𝐾)〗^(−1)PK n\n",
    "We know S+T=I\n",
    "Then \n",
    "Ε =r S- S Pd d +T n-------------(5)\n",
    "For control system, its difficult to control for a fast changing system .only when it is slow moving, it will be possible to track.\n",
    "\n"
   ]
  },
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    }
   },
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "e29767b5-810b-4237-ac87-a7a86f34e0a8"
    }
   },
   "source": [
    "\n",
    "\n",
    "![bode.JPG](attachment:bode.JPG)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Attaching the videos\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/hTu36q5yx20\" frameborder=\"0\" allowfullscreen></iframe>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import HTML\n",
    "HTML('<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/hTu36q5yx20\" frameborder=\"0\" allowfullscreen></iframe>')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/hEQdr1G5H2w\" frameborder=\"0\" allowfullscreen></iframe>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import HTML\n",
    "HTML('<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/hEQdr1G5H2w\" frameborder=\"0\" allowfullscreen></iframe>')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
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   },
   "themes": {
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    "theme": {
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        "id": "backgroundColor"
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 },
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