{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "*This notebook contains course material from [CBE30338](https://jckantor.github.io/CBE30338)\n", "by Jeffrey Kantor (jeff at nd.edu); the content is available [on Github](https://github.com/jckantor/CBE30338.git).\n", "The text is released under the [CC-BY-NC-ND-4.0 license](https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode),\n", "and code is released under the [MIT license](https://opensource.org/licenses/MIT).*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "< [Controller Tuning Rules in Frequency Domain](http://nbviewer.jupyter.org/github/jckantor/CBE30338/blob/master/notebooks/05.04-Controller-Tuning-Rules-in-Frequency-Domain.ipynb) | [Contents](toc.ipynb) | [Optimization](http://nbviewer.jupyter.org/github/jckantor/CBE30338/blob/master/notebooks/06.00-Optimization.ipynb) >

\"Open

\"Download\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Baroreflex as a Linear Control System\n", "\n", "The [baroreflex](https://en.wikipedia.org/wiki/Baroreceptor) is one of several mechanisms in the body for maintaining arterial blood pressure (AP) at near constant levels. Specialized neurons, known as [baroreceptors](https://en.wikipedia.org/wiki/Baroreceptor), sense pressure through the stretching of the walls in key blood vessels. The signals are processed in the brainstem which, in turn, produces a compensating change in sympathetic and parasympathetic nervous system causing a response by the heart. (Figure from Victor, 2015).\n", "\n", "![baroreflex system](figures/nrcardio.2015.96-f2.jpg)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook presents a linear control analysis of the closed-loop system consisting of a 'peripheral arc' from the sympathetic efferents connected to the heart tissue that cause the blood pressure to increase, and a corresponding 'neural arc' from the carotid baroreceptors sensing blood pressure to the sympathetic nervous response. Together these arcs comprise a closed-loop for the short-term control of blood pressure in the body (McLoone, 2014). \n", "\n", "This is diagrammed below in the form a closed loop control system\n", "\n", "![baroreflex control diagram](figures/baroreflex.png)\n", "\n", "where $AP$ refers to arterial blood pressure, and $SNA$ is the activity of the sympathetic nervous system correlated with response of the heart, $G_p$ represents the transfer function of the peripheral arc, and $G_c$ represents the transfer function of the neural (or control) arc. The signal $p$ is placeholder for the influence of exogenous influences on blood pressure, such as a change in body body position. " ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import numpy as np\n", "import seaborn as sns\n", "import matplotlib.pyplot as plt\n", "import control.matlab as control\n", "\n", "sns.set_context('talk')\n", "\n", "# needed to avoid a deprecation warning in the control library \n", "import warnings\n", "warnings.filterwarnings(\"ignore\", category=UserWarning) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Peripheral Arc\n", "\n", "Transfer function models for the 'peripheral arc', denoted $G_p(s)$ in the closed-loop diagram, have been measured for various animal models. For anesthesized rats, for example, Chapius et al., 2004, found\n", "\n", "$$G_p(jf) = \\left(\\frac{K}{1 + 2\\lambda(f/f_n) + (j(f/f_n))^2}\\right)\\exp\\left(-2\\pi Tjf\\right)$$\n", "\n", "where $j$ is the imaginary operator $\\sqrt{-1}$, and $f$ is frequency in units of Hertz. Reported values for the parameters are given in the following table.\n", "\n", "| Parameter | Description | $\\qquad\\qquad$ Value $\\qquad\\qquad$ | Conversion |\n", "| :--: | :- | :-: | :-: |\n", "| $K$ | static gain | $1.16 \\pm 0.21$ mmHg/% SNA | $K_p \\approx 1.16$ mmHg/% SNA|\n", "| $f_n$ | natural frequency | $0.089\\pm 0.007$ Hz | $\\tau \\approx 1.79$ sec |\n", "| $\\lambda$ | damping coefficient | $1.23\\pm 0.14$ | $\\zeta \\approx 1.23$\n", "| $T$ | fixed time delay | $0.476\\pm 0.020$ sec | $t_d \\approx 0.476$ |\n", "\n", "Using the indicated conversions of values and parameters, the literature model is recast into standard transfer function notation\n", "\n", "$$G_p(s) = \\left(\\frac{K_p}{\\tau^2 s^2 + 2\\zeta\\tau s + 1}\\right)\\exp\\left(-t_d s\\right)$$\n", "\n", "The following cell implements this transfer function using the [Python Control Systems Library](https://pypi.python.org/pypi/control/0.7.0)." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Without Time Delay -->\n", " \n", " 1.16\n", "-----------------------\n", "3.198 s^2 + 4.399 s + 1\n", "\n", "\n", "With a 3rd order Pade approximation for Time Delay -->\n", " \n", " -1.16 s^3 + 29.24 s^2 - 307.2 s + 1291\n", "------------------------------------------------------------\n", "3.198 s^5 + 85.02 s^4 + 958.7 s^3 + 4748 s^2 + 5160 s + 1113\n", "\n" ] } ], "source": [ "Kp = 1.16 # mmHg/%SNA\n", "tau = 1.0/(2*0.089*np.pi) # sec\n", "zeta = 1.23\n", "td = 0.476\n", "\n", "Gp_ = control.tf([Kp],[tau**2,2*zeta*tau,1])\n", "print('\\nWithout Time Delay -->\\n', Gp_)\n", "\n", "num,den = control.pade(td,3)\n", "Gp = Gp_ * control.tf(num,den)\n", "print('\\nWith a 3rd order Pade approximation for Time Delay -->\\n', Gp)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following cell demonstrates the step response of the peripheral arc to a 1% change in $SNA$." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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r1XW7J1yORGDquFLOOGYMNqqIvGx9xIpI96NPJhGREKpqG3lj0WZeXriJDdv2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\n2bad7PymN9Ou4UXERLJp6YeL/+9rNPDvZP8CnEV2CGhxcbq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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = np.linspace(0,20,1000)\n", "y,t = control.step(Gp,t)\n", "plt.plot(t,y)\n", "plt.xlabel('Time [sec]')\n", "plt.ylabel('arterial pressure [mmHg]')\n", "plt.title('Response of the Peripheral Arc to a 1% change in SNA');" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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X0O9006qZLJ9bzfef3c2OQ21s3duCaWrnnhvncfUlda5edZxs+atz78jG8hjB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\nOr2hmY0D3qnm1CrgHOAJYAQwHPi3u+eG1z0K7HD3GyrV9RHwFLALuMH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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "w = np.logspace(-2,1,300)\n", "mag,phase,w = control.bode(Gp,w)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## P, PI, PD, and PID Control\n", "\n", "Let's now consider how the baroreflex would behave if a controller were designed without regard to the underlying physiology. For this purpose we'll consider the design of a PID control using tuning rules typical of practice in process control.\n", "\n", "For coding convenience, we implement a utiity function that creates a transfer function for P, PI, PD, or PID control in standard form. The general expression is given by\n", "\n", "$$ G_c^{PID}(s) = K_c\\left[1 + \\frac{1}{\\tau_I s} + \\frac{\\tau_D s}{\\alpha \\tau_D s + 1}\\right] $$\n", "\n", "where the third term provides realizable derivative action. Parameter $\\alpha \\approx 0.1$ provides high-frequency roll-off of the derivative action. When specialized and expressed over a common denominator, the specific forms of the controller become\n", "\n", "\\begin{align*}\n", "G_c^{P} & = K_c \\\\\n", "G_c^{PI} & = K_c \\frac{\\tau_Is + 1}{\\tau_I s} \\\\\n", "G_c^{PD} & = K_c \\frac{(1+\\alpha)\\tau_D s + 1}{\\alpha\\tau_Ds + 1} \\\\\n", "G_c^{PID} & = K_c\\frac{(1+\\alpha) \\tau_I \\tau_D s^2 + (\\tau_I+\\alpha\\tau_D) s + 1}{\\alpha \\tau_I \\tau_D s^2 + \\tau_I s}\n", "\\end{align*}" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\n", "1.1 s^2 + 1.1 s + 1\n", "-------------------\n", " 0.1 s^2 + s" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def PID(Kc=1,tauI=0,tauD=0):\n", " alpha = 0.1\n", " Gc = control.tf([1],[1])\n", " if tauI != 0:\n", " Gc += control.tf([1],[1,0])\n", " if tauD != 0:\n", " Gc += control.tf([tauD,0],[alpha*tauD,1])\n", " return Kc*Gc\n", "\n", "def P(Kc=1):\n", " return PID(Kc,0,0)\n", "\n", "def PI(Kc=1,tauI=0):\n", " return PID(Kc,tauI,0)\n", "\n", "def PD(Kc=1,tauD=0):\n", " return PID(Kc,0,tauD)\n", "\n", "PID(1,1,1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Ziegler-Nichols Tuning\n", "\n", "[Ziegler-Nichols tuning](https://en.wikipedia.org/wiki/Ziegler%E2%80%93Nichols_method) is a well known and widely used methods for determining an intial tuning of P, PI, PD, and PID controllers. The methods requires values of $K_{cu}$ (the proportional-only control gain at which a sustained oscillation is observed) and $P_u$ (the period of the observed oscillation). \n", "\n", "| Control Type | $K_p$ | $\\tau_I$ | $\\tau_D$ |\n", "| :- | :-: | :-: | :-: |\n", "| P | $0.5 K_u$ | - | - |\n", "| PI | $0.45 K_u$ | $P_u$/$1.2$ | - |\n", "| PD | $0.8 K_u$ | - | $P_u$/$8$ |\n", "| classic PID | $0.6 K_u$ | $P_u$/$2$ | $P_u$/$8$ |\n", "| Pessen Integral Rule | $0.7 K_u$ | $P_u$/$2.5$ | $3 P_u$/$20$ |\n", "| some overshoot | $0.33 K_u$ | $P_u$/$2$ | $P_u$/$3$ |\n", "| no overshoot | $0.2 K_u$ | $P_u$/$2$ | $P_u$/$3$ |\n", "\n", "In the following cell, these values are obtained using the `margin` function from the Python Control Library, then verified by plotting a closed-loop step response using a proportional-only controller." ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Ultimate Gain = 8.80991289154\n", "Ultimate Period = 3.88965615063\n" ] }, { "data": { "image/png": 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zZ+e7vnzzEhZkp8/ZuS/bVEbhggwCts39Eps9L/D5A9zvOBHOXbOQZaUL5uzc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pjKMw+sR6xLf9cm5QP3l9HSM8H33miiqWucU3X9dA1O89kPblWSTC/+ZrJ3A7VSSs8tzzuAaill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\n+dDhcuUoEgXkZSby4E69k+fLp9tDWuTdMzTNsYt6Q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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gm,pm,Wcg,Wcp = control.margin(Gp)\n", "Kcu = gm\n", "Pu = 2*np.pi/Wcp\n", "\n", "print('Ultimate Gain = ', Kcu)\n", "print('Ultimate Period = ', Pu)\n", "\n", "def stepResponse(Gp,Gc,t):\n", " y,t = control.step(1/(1+Gp*Gc),t)\n", " u,t = control.step(-Gc/(1+Gp*Gc),t)\n", " plt.subplot(2,1,1)\n", " plt.plot(t,y,[0,0,max(t)],[0,1,1],'r--')\n", " plt.xlabel('Time [sec]')\n", " plt.ylabel('Arterial Pressure [mmHg]')\n", " plt.title('Baroreflex Disturbance Response')\n", " plt.legend(['Arterial Pressure','Disturbance'],loc='lower left')\n", " plt.subplot(2,1,2)\n", " plt.plot(t,u)\n", " plt.ylim(-10,10)\n", " plt.ylabel('Sympathetic Neural Activity [%]')\n", " plt.tight_layout()\n", " \n", "t = np.linspace(0,15,1000)\n", "stepResponse(Gp,PID(Kcu,0,0),t)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Proportional-Derivative Control\n", "\n", "Proportional-derivative control is generally associated with the suppression of peak overshoot in the disturbance response. The following shows the baroreflex response subject to PD control using a standard process control tuning rules." ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "image/png": 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ppZSaTKK9LuXTwIpEBjIVBefMpfXtWtixg+CcuUndd0lBNmWFdvTRph0dSd23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\nx+NPPsmm2hr+/Fku55x+BjPfmEZ9fX2Lx8vL68+dd97PE0/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+tdZu2Xkja+2iMMUTERER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QcuBWYDw7o/7+5fCnvOoaq1rZ0Va+sAOPnQKTz+wgesr93O/GeXceZRM3j69TUAHLjvaIoK1X9c\nREREJBtFUbJyH3Ao8CSwPYLr54wP1tfT3hF0UDly7kSSSXjshZX8/uVVbNzSxIcbGwA4+uOT4lym\niIiIiGQgioD8KOB4d38+gmvnlJXrgux4RXkRVSOKOfXTU3lt8QbWbmrk1cUbAJi3z2imV1fEuUwR\nERERyUAUbQ/fBxIRXDfnbNzaBMD4kaUAFBbkc9lp+zN2ZAkQHAR0/gkzY1ufiIiIiGQuigz5JcAd\nZnY7sBzo6Pqku/8+gjmHpE2pgHxURXHn2KSx5dxwySE0NLVRXlIY19JEREREJCRRlazMAX7ew3NJ\nQHcf9tOmbUFAXjWieKfxRCKhYFxERERkiIgiIP828B3gX91dN3VmIJ0hH11R3McrRURERCRbRVFD\n3g48qGA8M23tHWxtaAGgasRHukeKiIiIyBARRUB+PfB9M6uM4No5o357a+fjijIF5CIiIiJDVRQl\nK2cC84AzzawWaO36pLtXRzDnkFPfuGPbVC8uIiIiMnRFEZD/WwTXzDl127sG5FH8zyQiIiIig0EU\nkd5W4DF3b+3zlbJLDamAfFhhPoUFakwjIiIiMlRFUUN+G1BjZr8wsyMiuH5OSGfIVa4iIiIiMrRF\nkSGfCBwDnA08ZGYNwK+B+9z99QjmG5LqFZCLiIiI5ITQA3J37wCeBJ40s0uB44FTgefMbCXwK+Bu\nd18b9txDSfqmzvJSBeQiIiIiQ1kUJSsAmFkC+AxwCnAysB14FvgksNjMLopq7qEgnSEvK9YNnSIi\nIiJDWejRnpkdDpwFfAEYDjwKfA1Y4O5tqdd8C/gpcGfY8w8VTS1tAJQOU0AuIiIiMpRFEe09DTwF\nfBv4jbvX9fCal4H7M53IzH4GtLr7lV3GjgVuAqYBrwEXufviTOfa05pa2gEoVkAuIiIiMqRFEe1N\ncvd1vb3A3Z8BntndCcxsFHAjcF7qe3p8HPAb4MvAE8B3CG4s3d/dk7s7Xxy2NwcZ8uIitTwUERER\nGcpCC8jNrBg4kSAQTo9dDhwHbABucve3Q5ruOeB54MFu42cAb7j7o6n5fwD8f+Bg4KWQ5t4jOjPk\nRcqQi4iIiAxloUR7ZjYZ+BMwAdgfeN/M/gn4JvBIap7nzOwYd3+lH9crAMp7eKrD3bcBx7j7h2Z2\nT7fnZwLvpX9w93YzW5oa7zMgTyQS5EV2m2vP8vISO31PSwfkpcUF5OcnPvJ7ssOu9lD6T3uYOe1h\nZrR/mdMeZk57mBnt3+4LK/36fcCBA9y9zsxGA1cAD7n7FwDM7OrU607ox/WOJGid2N1KYKq7f7iL\n3ysDtnUbawRK+zEno0eXx/YvqLKybKef/+O6z8a0kuzVfQ9l4LSHmdMeZkb7lzntYea0h5nR/g1c\nWAH58cCpXW7g/CyQD9zb5TW/I6jp7pO7/wHYneC4ESjpNlYK1O/GtUREREREIhdWgUYl0PVGzqOA\nNuCPXca2EQTpUVoIWPoHM8sHZtCljEVEREREZDAJKyBfSSoQTgXBJwDPuntDl9ccCSwPab5deQg4\nyMzOMLMi4LvAauD1iOcVEREREdktYQXk9wI3m9mZwG3A+NR3oPOwoB8C/xXSfD1KtVs8DbgW2AQc\nC5yRbS0PRURERCR3JJLJzGPVVFb8BuBCoAP4Z3f/Ueq5m4HLCfqDn+PurRlPKCIiIiIyRIQSkPfG\nzOYA+e7+RqQTiYiIiIhkocgDchERERER2bU9fAyOiIiIiIh0pXPZY2Rm84Dbgf2AJcCl7v6XeFeV\nXczsMOBGgtNYNwI/cffb411V9jGzccDbwIXu/tu415NNzGwS8G/AZwjau/7E3W+Od1XZxcwOBW4G\n9gXWAte5+33xrio7mNkngPnuXp36eSRwF3A0sJVgL++McYmDXg97OAm4BTgcaAUeAK509+b4Vjm4\ndd/DLuN5wFPAq+5+ZSyLyxLKkMfEzIqBR4G7Cfq43ww8YmblsS4si6TeeB4BfgaMBL4I3GBmx8a6\nsOx0JzAq7kVkGzNLAPMJzkAYRXBI2j+mAkzph1RTgPnAj9x9BHAxcK+ZTY11YYOcmSXM7ELg90BR\nl6d+QXAY3jjgC8BPzOyQGJY46PWyh78iaJk8EZgLHAxcs+dXOPj1sodp3yJIVkgfFJDH5yigw91v\nc/dWd78LqAFOjHld2WQK8Ji73+fuHe7+GvA0oGBoAMzsUqABWBX3WrLQJ4Fq4OrU/4/fBT4FeLzL\nyiqVwBigIPUBpwNoAdpjXdXg93fAFQQthQFIJXROB6519yZ3fwm4Dzg3niUOej3tYRHBfw9/kNrD\ndcB/oveVXfnIHqaZ2QHABQRnxEgfFJDHZyYfPUHUU+PSD+7+hrt/Jf1zKmN+OPBmfKvKLma2L0EG\n47K415KlDgTeJchCrjOzxcAh7r4p5nVljdRe3QrcT1Ae8CxwubvrA2Lv7iLI3r7cZWwfoNXdl3UZ\n0/vKrn1kD929xd1PSgXiaaeg95Vd6enfIWY2DPgl8FWCv9hIHxSQx6cMaOw21giUxrCWrGdmFQQl\nQK+mvksfzKwA+A/gr919c9zryVJVBH/t2ghMBs4H/jV1GJr0Q6rGtJGg5KyUIPi5ycw+FuvCBjl3\nX9vDoXdlwPZuY3pf2YVd7GGnVDnGzQQfaG7YcyvLHr3s4Q3AE+7+/J5eU7bSTZ3xaQRKuo2Vok+S\nA2Zm04DfAkuBs9y9I+YlZYtrgDfcfUHcC8lizcBmd0+/Wf/ZzB4kODH42fiWlVXOAD7p7lelfn7M\nzH5LUGbxrfiWlZUageJuY3pf2Q1mVkKQsJgDHOHu62NeUtYws6MJbir+RNxrySbKkMdnIWDdxoyP\nlrFIL8zsQOBF4AngdHfvnh2SXTsLONvMtpjZFoIM76/N7OqY15VNnKD2Ob/LWD6QiGk92WgyMKzb\nWFvqSwZmCVBkZpO7jOl9ZYDMrAr4E8FfwD7l7stjXlK2ORuYDqxPvbd8Cbg89UFbdkEZ8vj8ERhm\nZt8gaJn2FYK74p+IdVVZJNWq73fAje7+47jXk23cfae6UjNbQVC7q/9o9t+TBFnJa83sewQZoc8B\nfxXrqrLLkwTdkS4A7iHoyPA5ggybDIC715nZwwT7+VWClrpfQs0C+i11Y/FvgHXA5929NeYlZR13\nvwS4JP2zmd0DbFTbw94pQx6TVD/TE4BzgM3AN4BT3b0h1oVll4sIujNcY2b1Xb4+cre3SBRSf5E5\nkiAQX0/Q0eKvdZ5A/7n72wTt+a4g6Jv9c+A8d38l1oVlr68ChQRt+x4ErnL3F+NdUlb5FHAEwYfq\n2i7vK8/EvC4Z4hLJ5C7vZxARERERkYgpQy4iIiIiEiMF5CIiIiIiMVJALiIiIiISIwXkIiIiIiIx\nUkAuIiIiIhIjBeQiIiIiIjFSQC4iIiIiEiMF5CIiIiIiMVJALiIiIiISo/8DHlDnBVcvJqIAAAAA\nSUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Gc = PID(0.8*Kcu,0,Pu/8)\n", "stepResponse(Gp,Gc,t)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Internal Model Control Tuning\n", "\n", "Case J" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "image/png": 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4BpIScG65Cwp6xzukNjvhwKFMs6spq6zjv+/8xNgzRuHr6MvSi4iIiHRxkfZk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\ns4Mt5kxhy82mssWmU9ls5mQ2nTGZOTMmMX3K+JbOJS5JkjTaDFpkR8S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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tauC = 2\n", "Kc = (2*zeta*tau)/(tauC + td)/Kp\n", "tauI = 2*zeta*tau\n", "tauD = tau/(2*zeta)\n", "\n", "GcIMC = PID(Kc,0,tauD)\n", "t = np.linspace(0,15,1000)\n", "stepResponse(Gp,GcIMC,t)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Measured Physiological Response of Neural Arc\n", "\n", "Petiot, et. al. (2001) (from the same laboratory cited above) provided laboratory measurements of the transfer function for the 'neural (or central) arc' for anesthesized rats. The results were given in the form\n", "\n", "$$G_c^{Phys}(jf) = K\\left(\\frac{1+j(f/f_c)}{1 + 2\\lambda j(f/fn)-(f/f_n)^2}\\right)\\exp\\left(-2\\pi jTf\\right)$$\n", "\n", "where $f$ is frequency in units of Hz. \n", "\n", "In the standard form for control engineering, the transfer function is written as\n", "\n", "$$G_c^{Phys}(s) = K_c \\frac{\\tau_c s + 1}{\\tau_n^2 s^2 + 2\\lambda\\tau_n s + 1} e^{-sT}$$\n", "\n", "where $\\tau = \\frac{1}{2\\pi f}$ and $s = 2\\pi f$ are the conversions from frequency in Hz to time constant and Laplace variable $s$, respectively.\n", "\n", "| Parameter | Description | $\\qquad\\qquad$ Value $\\qquad\\qquad$ | Conversion |\n", "| :--: | :- | :-: | :-: |\n", "| $K$ | static gain | 1.04 %SNA/mmHg | $K_c \\approx$ 1.04 %SNA/mmHg|\n", "| $f_c$ | corner frequency | 0.157 Hz | $\\tau_c \\approx$ 1.01 sec |\n", "| $f_n$ | natural frequency | 1.12 Hz | $\\tau_n \\approx$ 0.142 sec |\n", "| $\\lambda$ | damping coefficient | 1.71 | $\\zeta \\approx$ 1.71 |\n", "| $T$ | fixed time delay | 0.101 sec | $t_d \\approx$ 0.101 sec|" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.0137257521776772 0.14210262776062083\n" ] }, { "data": { "image/png": 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SQxTmpHL5SWO5/ZlZVFQ3cNdzX3PVaePpm9t6pkYRERGRniPS4SJP4V518Q50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\nvNJYPT1l5i9awZz5y5gzfxmPzF/OnPlLmbtgOfMXraR7CJ9gx43pZMq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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fc = 0.157\n", "fn = 1.12\n", "K = 1.04\n", "zetac = 1.71\n", "tdelay = 1.01\n", "\n", "tauc = 1/(2*np.pi*fc)\n", "taun = 1/(2*np.pi*fn)\n", "\n", "print(tauc,taun)\n", "\n", "num,den = control.pade(tdelay,3)\n", "\n", "GcPhys = K*control.tf([tauc,1],[taun**2,2*zetac*taun,1])\n", "stepResponse(Gp,GcPhys,t)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Comparison of ZN Tuned PD Control to the Observed Physiological Response of the Neural arc\n", "\n", "We observe a very different physiological behavior than what we naively predicted using a PD controller tuned using the Ziegler-Nichols rules. To highlight these differences, the next cell compares the step responses of the two control laws" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "image/png": 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yynxc7dp1SE1NZerU5znwwIMA2LFjBxkZm6latSoNGjRg3bq1hdtXVKLzxRef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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "u,t = control.step(Gc,t)\n", "uPhys,t = control.step(GcPhys,t)\n", "plt.plot(t,u,t,uPhys)\n", "plt.xlabel('Time [sec]')\n", "plt.ylabel('%SNA')\n", "plt.title('Step Responses for ZN tuning and Physiological controllers')\n", "plt.legend(['ZN Tuned PD Control','Measured Physiological Neural Arc']);" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "image/png": 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ZBkenGBidYjD1MzCSej82RTTDtLrXY9HWXMXGlmo2rq1mQ0s17WurWbemGm8J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VAAAH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\n5i6cpUcAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "control.bode(GcPhys);\n", "control.bode(Gc);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Modifications to the PD Controller\n", "\n", "Matching the Proportional-Derivative control law to the observed physiological response of the neural arc requires several modifications of the PD controller. The first step is to introduce a second-order filter to suppress the 'derivative kick' \n", "\n", "$$ G_c^{mod}(s) = K_c\\left[1 + \\frac{\\tau_D s}{\\alpha \\tau_D s + 1}\\right]\\left[\\frac{1}{\\tau_n s + 1}\\right]^2 $$\n", "\n", "The second is to substantially reduce the control gain, and to slightly reduce the derivative time constant for a corresponding tuning $K_c = 0.12 K_{cu}$ and $\\tau_D = P_u/6$. The following cells compares the computed baroreflex response with these modifications in place." ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "image/png": 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NJBJjx1hNM7Rtn6+0DSXXQSLLOvdqkyRJcyCWoW2s0rZp+7TBWKUtSmRJ1Pda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\nTyVJkmZa7EJbuTltc7kQoZw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V2orDo1baJElSlYlXaIuc0yZJkqpTvEJbyWMrbZIkqZrE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\nrkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Gc = PID(0.12*Kcu,0,Pu/6)\n", "Gcf = Gc*(control.tf([1],[1*taun,1]))**2\n", "uf,t = control.step(Gcf,t)\n", "\n", "uPhys,t = control.step(GcPhys,t)\n", "\n", "plt.plot(t,uf,t,uPhys)\n", "plt.legend(['Modified PD Controller','Neural Arc']);" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "image/png": 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LTXSIIiIiIgddtAMpNgM7Y9mxtbYaOBm4ECgCrgHOsNaWG2NmGGNmeE3/DNwL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\nZZt6s2IjrNi4m6feC3D0mD4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sBPoAf41XcCIiIiIiHVFUPdnW2s+BQcCT1tpdwCTgYeBy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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "stepResponse(Gp,Gcf,t)\n", "stepResponse(Gp,GcPhys,t)\n", "plt.legend(['Modified PD Control','Observed Neural Arc']);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conclusions\n", "\n", "To create a control response resembling the physiological response inferred from the cited papers, it was necessary to:\n", "\n", "1. Introduce a filter to significantly reduce the 'derivative kick' associated with a standard PID control implementation.\n", "2. Reduce the proportional gain by a factor of about 5 from a value that would be typically used in industrial process control.\n", "3. There was no integral response observed in the physiologically consistent control." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### References\n", "\n", "\n", "Chapuis, Bruno et al. “Linear Modelling Analysis of Baroreflex Control of Arterial Pressure Variability in Rats.” The Journal of Physiology 559.Pt 2 (2004): 639–649. PMC. Web. 29 Mar. 2017. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1665118/\n", "\n", "Kamiya, Atsunori et al. “Closed-Loop Spontaneous Baroreflex Transfer Function Is Inappropriate for System Identification of Neural Arc but Partly Accurate for Peripheral Arc: Predictability Analysis.” The Journal of Physiology 589.Pt 7 (2011): 1769–1790. PMC. Web. 28 Mar. 2017. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3099029/\n", "\n", "Roy Kanbar, Valérie Oréa, Bruno Chapuis, Christian Barrès, Claude Julien\n", "American Journal of Physiology - Regulatory, Integrative and Comparative Physiology Nov 2007, 293 (5) R1938-R1946; DOI: 10.1152/ajpregu.00374.2007 http://ajpregu.physiology.org/content/293/5/R1938.short\n", "\n", "McLoone, Violeta. \"Modelling of Long and Short Term Blood Pressure Control Systems.\" PhD Thesis, NUI Maynooth, 2014. http://eprints.maynoothuniversity.ie/5611/1/Thesis_V_McLoone-Final_Version.pdf\n", "\n", "Petiot, Emmanuelle et al. “Frequency Response of Renal Sympathetic Nervous Activity to Aortic Depressor Nerve Stimulation in the Anaesthetized Rat.” The Journal of Physiology 537.Pt 3 (2001): 949–959. PMC. Web. 29 Mar. 2017. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2278997/\n", "\n", "Victor, Ronald G. \"Carotid baroreflex activation therapy for resistant hypertension.\" Nature Reviews Cardiology 12, 451–463 (2015) doi:10.1038/nrcardio.2015.96 http://www.nature.com/nrcardio/journal/v12/n8/full/nrcardio.2015.96.html\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "< [Controller Tuning Rules in Frequency Domain](http://nbviewer.jupyter.org/github/jckantor/CBE30338/blob/master/notebooks/05.04-Controller-Tuning-Rules-in-Frequency-Domain.ipynb) | [Contents](toc.ipynb) | [Optimization](http://nbviewer.jupyter.org/github/jckantor/CBE30338/blob/master/notebooks/06.00-Optimization.ipynb) >

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