pid2_tclab_widget.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import odeint\n",
    "import ipywidgets as wg\n",
    "from IPython.display import display"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x504 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "n = 601 # time points to plot\n",
    "tf = 600.0 # final time\n",
    "\n",
    "# TCLab FOPDT\n",
    "Kp = 1.1\n",
    "Kd = 0.65\n",
    "taup = 190.0\n",
    "thetap = 25.0\n",
    "T1_0 = 21.3\n",
    "T2_0 = 21.3\n",
    "y0 = [T1_0,T2_0]\n",
    "Kff = -Kd/Kp\n",
    "\n",
    "def process(y,t,u1,u2):\n",
    "    y1,y2 = y\n",
    "    dy1dt = (1.0/taup) * (-(y1-y0[0]) + Kp * u1 + Kd * (y2-y1))\n",
    "    dy2dt = (1.0/taup) * (-(y2-y0[1]) + (Kp/2.0) * u2 + Kd * (y1-y2))\n",
    "    return [dy1dt,dy2dt]\n",
    "\n",
    "def pidPlot(Kc,tauI,tauD,Kff):\n",
    "    y0 = [23.0,23.0]\n",
    "    t = np.linspace(0,tf,n) # create time vector\n",
    "    P1 = np.zeros(n)         # initialize proportional term\n",
    "    I1 = np.zeros(n)         # initialize integral term\n",
    "    D1 = np.zeros(n)         # initialize derivative term\n",
    "    FF1 = np.zeros(n)        # initialize feedforward term\n",
    "    e1 = np.zeros(n)         # initialize error\n",
    "    P2 = np.zeros(n)         # initialize proportional term\n",
    "    I2 = np.zeros(n)         # initialize integral term\n",
    "    D2 = np.zeros(n)         # initialize derivative term\n",
    "    FF2 = np.zeros(n)        # initialize feedforward term\n",
    "    e2 = np.zeros(n)         # initialize error\n",
    "    OP1 = np.zeros(n)       # initialize controller output\n",
    "    OP2 = np.zeros(n)       # initialize disturbance\n",
    "    PV1 = np.ones(n)*y0[0]  # initialize process variable\n",
    "    PV2 = np.ones(n)*y0[1]  # initialize process variable\n",
    "    SP1 = np.ones(n)*y0[0]  # initialize setpoint\n",
    "    SP2 = np.ones(n)*y0[1]  # initialize setpoint\n",
    "    SP1[10:] = 60.0         # step up\n",
    "    SP1[400:] = 40.0         # step up\n",
    "    SP2[150:] = 50.0        # step down\n",
    "    SP2[350:] = 35.0        # step down\n",
    "    Kc1 = Kc\n",
    "    Kc2 = Kc*2.0\n",
    "    Kff1 = Kff\n",
    "    Kff2 = Kff*2.0\n",
    "    iae = 0.0\n",
    "    # loop through all time steps\n",
    "    for i in range(1,n):\n",
    "        # simulate process for one time step\n",
    "        ts = [t[i-1],t[i]]         # time interval\n",
    "        heaters = (OP1[max(0,i-int(thetap))],OP2[max(0,i-int(thetap))])\n",
    "        y = odeint(process,y0,ts,args=heaters)\n",
    "        y0 = y[1]                  # record new initial condition\n",
    "        # calculate new OP with PID\n",
    "        PV1[i] = y[1][0]              # record T1 PV\n",
    "        PV2[i] = y[1][1]              # record T2 PV\n",
    "        iae += np.abs(SP1[i]-PV1[i]) + np.abs(SP2[i]-PV2[i])\n",
    "        dt = t[i] - t[i-1]         # calculate time step\n",
    "\n",
    "        # PID for loop 1\n",
    "        e1[i] = SP1[i] - PV1[i]       # calculate error = SP - PV\n",
    "        P1[i] = Kc1 * e1[i]           # calculate proportional term\n",
    "        I1[i] = I1[i-1] + (Kc1/tauI) * e1[i] * dt  # calculate integral term\n",
    "        D1[i] = -Kc * tauD * (PV1[i]-PV1[i-1])/dt # calculate derivative\n",
    "        FF1[i] = Kff1 * (PV2[i]-PV1[i])\n",
    "        OP1[i] = P1[i] + I1[i] + D1[i] + FF1[i] # calculate new output\n",
    "        if OP1[i]>=100:\n",
    "            OP1[i] = 100.0\n",
    "            I1[i] = I1[i-1] # reset integral\n",
    "        if OP1[i]<=0:\n",
    "            OP1[i] = 0.0\n",
    "            I1[i] = I1[i-1] # reset integral            \n",
    "\n",
    "        # PID for loop 2\n",
    "        e2[i] = SP2[i] - PV2[i]       # calculate error = SP - PV\n",
    "        P2[i] = Kc2 * e2[i]           # calculate proportional term\n",
    "        I2[i] = I2[i-1] + (Kc2/tauI) * e2[i] * dt  # calculate integral term\n",
    "        D2[i] = -Kc2 * tauD * (PV2[i]-PV2[i-1])/dt # calculate derivative\n",
    "        FF2[i] = Kff2 * (PV1[i]-PV2[i])\n",
    "        OP2[i] = P2[i] + I2[i] + D2[i] + FF2[i] # calculate new output\n",
    "        if OP2[i]>=100:\n",
    "            OP2[i] = 100.0\n",
    "            I2[i] = I2[i-1] # reset integral\n",
    "        if OP2[i]<=0:\n",
    "            OP2[i] = 0.0\n",
    "            I2[i] = I2[i-1] # reset integral            \n",
    "\n",
    "    # plot PID response\n",
    "    plt.figure(1,figsize=(15,7))\n",
    "    plt.subplot(2,2,1)\n",
    "    plt.plot(t,SP1,'k-',linewidth=2,label='Setpoint 1 (SP)')\n",
    "    plt.plot(t,PV1,'r:',linewidth=2,label='Temperature 1 (PV)')\n",
    "    plt.ylabel(r'T $(^oC)$')\n",
    "    plt.text(100,35,'Integral Abs Error: ' + str(np.round(iae,2)))\n",
    "    plt.text(400,35,r'$K_{c1}$: ' + str(np.round(Kc,1)))  \n",
    "    plt.text(400,30,r'$\\tau_I$: ' + str(np.round(tauI,0)) + ' sec')  \n",
    "    plt.text(400,25,r'$\\tau_D$: ' + str(np.round(tauD,0)) + ' sec')  \n",
    "    plt.text(400,20,r'$K_{ff}$: ' + str(np.round(Kff1,2)))  \n",
    "    plt.ylim([15,70])\n",
    "    plt.legend(loc=1)\n",
    "    plt.subplot(2,2,2)\n",
    "    plt.plot(t,SP2,'k-',linewidth=2,label='Setpoint 2 (SP)')\n",
    "    plt.plot(t,PV2,'r:',linewidth=2,label='Temperature 2 (PV)')\n",
    "    plt.ylabel(r'T $(^oC)$')\n",
    "    plt.text(20,65,r'$K_{c2}$: ' + str(np.round(Kc*2,1)))  \n",
    "    plt.text(20,60,r'$\\tau_I$: ' + str(np.round(tauI,0)) + ' sec')  \n",
    "    plt.text(20,55,r'$\\tau_D$: ' + str(np.round(tauD,0)) + ' sec')  \n",
    "    plt.text(20,50,r'$K_{ff}$: ' + str(np.round(Kff2,2)))\n",
    "    plt.ylim([15,70])\n",
    "    plt.legend(loc=1)\n",
    "    plt.subplot(2,2,3)\n",
    "    plt.plot(t,OP1,'b--',linewidth=2,label='Heater 1 (OP)')\n",
    "    plt.legend(loc='best')\n",
    "    plt.xlabel('time (sec)')\n",
    "    plt.subplot(2,2,4)\n",
    "    plt.plot(t,OP2,'b--',linewidth=2,label='Heater 2 (OP)')\n",
    "    plt.legend(loc='best')\n",
    "    plt.xlabel('time (sec)')\n",
    "\n",
    "print('PID with Feedforward Simulator: Adjust Kc, tauI, tauD, and Kff ' + \\\n",
    "      'to achieve lowest Integral Abs Error')\n",
    "\n",
    "# ITAE Setpoint Tracking PI Tuning\n",
    "Kc = (0.586/Kp)*(thetap/taup)**(-0.916); tauI = taup/(1.03-0.165*(thetap/taup))\n",
    "print(f'ITAE Recommended: Kc={Kc:4.2f}, tauI={tauI:5.1f}, tauD=0, Kff={Kff:4.2f}')\n",
    "\n",
    "# IMC Aggressive PID Tuning\n",
    "tauc = max(0.1*taup,0.8*thetap); Kc = (1/Kp)*(taup+0.5*taup)/(tauc+0.5*thetap)\n",
    "tauI = taup+0.5*thetap; tauD = taup*thetap/(2*taup+thetap); Kff=-Kd/Kp\n",
    "print(f'IMC Recommended: Kc={Kc:4.2f}, tauI={tauI:5.1f}, tauD={tauD:4.2f}, Kff={Kff:4.2f}')\n",
    "\n",
    "Kc_slide = wg.FloatSlider(value=Kc,min=0.0,max=50.0,step=1.0)\n",
    "tauI_slide = wg.FloatSlider(value=tauI,min=20.0,max=250.0,step=1.0)\n",
    "tauD_slide = wg.FloatSlider(value=tauD,min=0.0,max=20.0,step=1.0)\n",
    "Kff_slide = wg.FloatSlider(value=Kff,min=-0.5,max=0.5,step=0.1)\n",
    "wg.interact(pidPlot, Kc=Kc_slide, tauI=tauI_slide, tauD=tauD_slide,Kff=Kff_slide)\n",
    "print('')"
   ]
  }
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