{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Bode Plots" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import control\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "plt.rcParams['figure.figsize'] = (5, 5)\n", "s = control.tf([1, 0], [0, 1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Derivative Terms\n", "\n", "$ G(s) = s$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$|G(j \\omega) |$ evaluated at $\\omega = 1$ \n", "\n", "$G(j \\omega) = j \\omega$\n", "\n", "$ evaluated at $\\omega = 1$\n", "\n", "G(j) = j\n", "\n", "|j| = 1 = 0 dB\n", "\n", "angel(j) = 90 deg" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\frac{s}{1}$$" ], "text/plain": [ "TransferFunction(array([1, 0]), array([1]))" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "G_D = s\n", "control.bode(G_D, dB=True);\n", "G_D" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "log10(|G(j omega)) = 1\n", "\n", "10**log10(|G(j omega)) = 10**1\n", "|G(j omega) = 10" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Integral Terms\n", "\n", "$ G(s) = \\dfrac{1}{s}$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\frac{1}{s}$$" ], "text/plain": [ "TransferFunction(array([1]), array([1, 0]))" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "G_I = 1/s\n", "control.bode(G_I, dB=True);\n", "G_I" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## First Order Zeros\n", "\n", "$ G(s) = \\dfrac{s + \\omega}{\\omega}$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\frac{s + 1}{1}$$" ], "text/plain": [ "TransferFunction(array([1, 1]), array([1]))" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "G_FZ = (s+1)/1\n", "control.bode(G_FZ, dB=True);\n", "G_FZ" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## First Order Poles\n", "\n", "$ G(s) = \\dfrac{\\omega}{s + \\omega}$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\frac{1}{s + 1}$$" ], "text/plain": [ "TransferFunction(array([1]), array([1, 1]))" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "G_FP = 1/(s+1)\n", "control.bode(G_FP, dB=True);\n", "G_FP" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Second Order Poles: Case 1, Real Poles\n", "\n", "$G(s) = \\dfrac{\\omega}{s^2 + 2 \\zeta \\omega s + \\omega_n^2}$\n", "\n", "$\\zeta >= 1$\n", "\n", "Factor into two first order poles." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "roots [-19.94987437 -0.05012563]\n" ] }, { "data": { "text/latex": [ "$$\\frac{1}{s^2 + 20 s + 1}$$" ], "text/plain": [ "TransferFunction(array([1]), array([ 1, 20, 1]))" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "zeta = 10\n", "wn = 1\n", "\n", "G_SR = 1/(s**2 + 2*zeta*wn*s + wn**2)\n", "control.bode(G_SR, dB=True);\n", "print('roots', np.roots([1, 2*zeta*wn, wn**2]))\n", "G_SR" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Second Order Poles: Case 2, Imaginary Poles\n", "\n", "$G(s) = \\dfrac{\\omega_n}{s^2 + 2 \\zeta \\omega_n s + \\omega_n^2}$\n", "\n", "$\\zeta < 1$" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\frac{1}{s^2 + 0.2 s + 1}$$" ], "text/plain": [ "TransferFunction(array([1]), array([1. , 0.2, 1. ]))" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "zeta = 0.1\n", "wn = 1\n", "\n", "G_SR = 1/(s**2 + 2*zeta*wn*s + wn**2)\n", "G_damp = [1/(s**2 + 2*zeta*wn*s + wn**2) for zeta in np.arange(0.01, 0.9, 0.2)]\n", "control.bode(G_damp, dB=True, omega=np.logspace(-2, 2, 1000));\n", "G_SR" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "20 *log10(mag) = 30" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "31.622776601683793" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "10**(30/20)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-40.0" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "20 *np.log10(1/100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Unstable Poles and Zeros\n", "\n", "* Same magnitude\n", "* Oppositive slope\n", "\n", "$G(s) = \\dfrac{1}{s + 1}$\n", "\n", "vs. \n", "\n", "$G(s) = \\dfrac{1}{s - 1}$" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "control.bode([1/(s+1), 1/(s-1)], dB=True);\n", "ax = plt.gca()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$G(s) = s + 1$\n", "\n", "vs. \n", "\n", "$G(s) = s - 1$" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "control.bode([(s+1), (s-1)], dB=True);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Leading Negative\n", "\n", "* Add 180 deg phase.\n", "\n", "$G(s) = -\\dfrac{1}{s + 1}$" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "control.bode([1/(s+1), -1/(s+1)], dB=True);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## **Bode Plot Rules Summary**\n", "\n", "1. Find $|G(0)|$, where your magnitude plot starts and $|G(\\infty)|$, where it ends.\n", "1. Find $\\angle G(0)$, where your phase plot starts and $\\angle G(\\infty)$, where it ends.\n", "1. Make table of slope and phase contribution for each factor. If you have a second order pole or zero if it has real roots, treat as two first order sytems. If it has complex roots, find the natural frequency and the damping ratio. The damping ratio determines the size of the resonant peak, and the natural frequency is the corner frequency.\n", "1. Draw asymptotes using $|G(0)|$ to start the magnitude plot and $\\angle G(0)$ to start the phase plot.\n", "1. Interpolate between asymptotes for magnitude and phase.\n", "\n", "Zeros:\n", "\n", "| factor | corner freq. (rad/s) | phase (deg) | slope (dB/dec) |\n", "|- -|- -|- -|- -|\n", "|$s$|0 | +90 | +20|\n", "|$(s+\\omega)$|$\\omega$| +90 | +20|\n", "|$(s-\\omega)$|$\\omega$| -90 | +20|\n", "|$(s^2 + 2\\zeta \\omega_n s + \\omega_n^2)$|$\\omega_n$| +180 | +40|\n", "\n", "Poles:\n", "\n", "| factor | corner freq. (rad/s) | phase (deg) | slope (dB/dec) |\n", "|- -|- -|- -|- -|\n", "|$1/s$| 0 | -90 |-20|\n", "|$1/(s+\\omega)$|$\\omega$| -90 | -20|\n", "|$1/(s-\\omega)$|$\\omega$| +90 | -20|\n", "|$1/(s^2 + 2\\zeta \\omega_n s + \\omega_n^2)$|$\\omega_n$| -180 | -40|\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Combining Factors\n", "\n", "$G(s) = \\dfrac{-1}{(s-1)(s-2)}$\n", "\n", "$|G(0)| = |-1/2| = 1/2 \\approx -6 dB$\n", "\n", "$\\angle G(0) = \\angle -1/2 = -180 deg$\n", "\n", "| factor | corner freq. (rad/s) | phase (deg) | slope (dB/dec) |\n", "|- -|- -|- -|- -|\n", "|$1/(s-1)$|1|+90|-20|\n", "|$1/(s-2)$|2|+90|-20|\n", "\n", "Notice phase contribution of the pole is now positive, since it is an unstable pole.\n" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import control\n", "s = control.tf([1, 0], [0, 1])\n", "control.bode(-1/((s-1)*(s-2)), dB=True);" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.12" } }, "nbformat": 4, "nbformat_minor": 4 }