{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "

Bode Plot Basics

\n", "

MCHE 474: Control Systems

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Dr. Joshua Vaughan
\n", "joshua.vaughan@louisiana.edu
\n", "http://www.ucs.louisiana.edu/~jev9637/

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "\t\"A
\n", " Figure 1: A Mass-Spring-Damper System \n", "

\n", "\n", "This notebook examines the frequency response of a mass-spring-damper system like the one shown in Figure 1 using the [Bode Plot](https://en.wikipedia.org/wiki/Bode_plot). We'll use some of the core functionality of the [Control System Library](http://python-control.readthedocs.io/en/latest/index.html) to do so. \n", "\n", "The equation of motion for the system is:\n", "\n", "\n", "$ \\quad m \\ddot{x} + c \\dot{x} + kx = f $\n", "\n", "We could also write this equation in terms of the damping ratio, $\\zeta$, and natural frequency, $\\omega_n$.\n", "\n", "$ \\quad \\ddot{x} + 2\\zeta\\omega_n \\dot{x} + \\omega_n^2x = \\frac{f}{m}$\n", "\n", "Using this form, we can write the Laplace Transform of the equation of motion:\n", "\n", "$ \\quad \\left(s^2 + 2\\zeta\\omega_n s + \\omega_n^2\\right)X = \\frac{1}{m}F $\n", "\n", "Then, we can use that to generate the transfer function for this system:\n", "\n", "$ \\quad \\frac{X}{F} = \\frac{1/m}{s^2 + 2\\zeta\\omega_n s + \\omega_n^2} $" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np # Grab all of the NumPy functions with namespace np" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# We want our plots to be displayed inline, not in a separate window\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Import the plotting functions \n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# import the Control Systems Library \n", "import control" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Define the System Parameters\n", "m = 1.0 # kg\n", "k = (2.0 * np.pi)**2 # N/m (Selected to give an undamped natrual frequency of 1Hz)\n", "wn = np.sqrt(k / m) # Natural Frequency (rad/s)\n", "\n", "z = 0.1 # Define a desired damping ratio\n", "c = 2 * z * wn * m # calculate the damping coeff. to create it (N/(m/s))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, we can define the system to examine with the Bode plot. We define the numerator and denominator of the transfer function, then using `control.tf()` to create the system." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "num = [1/m]\n", "den = [1, 2 * z * wn, wn**2]\n", "\n", "sys = control.tf(num, den)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "magnitude, phase, frequency = control.bode(sys, omega=np.linspace(0,100,10001), Plot=False) # we use Plot=False because we'll plot it prettier outselve)\n", "\n", "# We want the magnitude plotted in dB to match Bode Plot standards\n", "mag_dB = 20 * np.log10(magnitude)\n", "\n", "# We want the frequency plotted in Hz\n", "frequency_Hz = frequency / (2 * np.pi)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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WADcjPipY2MDv9+suQShSV1enuwShgORqrunIljweFF79VQBA33f/HRyNKv9M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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Let's plot the magnitude and phase as subplots, to make it easier to compare\n", "\n", "# Make the figure pretty, then plot the results\n", "# \"pretty\" parameters selected based on pdf output, not screen output\n", "# Many of these setting could also be made default by the .matplotlibrc file\n", "fig, (ax1, ax2) = plt.subplots(2, 1, sharex = True, figsize=(8,8))\n", "\n", "plt.subplots_adjust(bottom=0.12,left=0.17,top=0.96,right=0.96)\n", "plt.setp(ax1.get_ymajorticklabels(),family='serif',fontsize=18)\n", "plt.setp(ax1.get_xmajorticklabels(),family='serif',fontsize=18)\n", "\n", "ax1.spines['right'].set_color('none')\n", "ax1.spines['top'].set_color('none')\n", "ax1.xaxis.set_ticks_position('bottom')\n", "ax1.yaxis.set_ticks_position('left')\n", "ax1.grid(True,linestyle=':',color='0.75')\n", "ax1.set_axisbelow(True)\n", "\n", "ax2.spines['right'].set_color('none')\n", "ax2.spines['top'].set_color('none')\n", "ax2.xaxis.set_ticks_position('bottom')\n", "ax2.yaxis.set_ticks_position('left')\n", "ax2.grid(True,linestyle=':',color='0.75')\n", "ax2.set_axisbelow(True)\n", "\n", "plt.xlabel(r'Frequency (Hz)',family='serif',fontsize=22,weight='bold',labelpad=5)\n", "# plt.xticks([0,1],['0','$\\Omega = 1$'])\n", "\n", "# Magnitude plot - format each magnitude as 20 * log(mag)\n", "ax1.set_ylabel(r'Magnitude (dB)',family='serif',fontsize=22,weight='bold',labelpad=40)\n", "ax1.semilogx(frequency_Hz, mag_dB, linewidth=2, label=r'$\\zeta$ = 0.1')\n", "# ax1.set_ylim(0.0,7.0)\n", "# ax1.set_yticks([0,1,2,3,4,5],['0', '1'])\n", "\n", "# ax1.leg = ax1.legend(loc='upper right', fancybox=True)\n", "# ltext = ax1.leg.get_texts()\n", "# plt.setp(ltext,family='Serif',fontsize=16)\n", "\n", "# Phase plot \n", "ax2.set_ylabel('Phase (deg)',family='serif',fontsize=22,weight='bold',labelpad=10)\n", "# ax2.semilogx(wnorm,TFnorm_phase*180/np.pi,linewidth=2)\n", "ax2.semilogx(frequency_Hz, phase, linewidth=2, label=r'$\\zeta$ = 0.0')\n", "ax2.set_ylim(-200.0,20.0,)\n", "ax2.set_yticks([0, -90, -180])\n", "\n", "# Uncomment below to place a legend on the lower subplot too\n", "# ax2.leg = ax2.legend(loc='upper right', fancybox=True)\n", "# ltext = ax2.leg.get_texts()\n", "# plt.setp(ltext,family='Serif',fontsize=16)\n", "\n", "# Adjust the page layout filling the page using the new tight_layout command\n", "plt.tight_layout(pad=0.5)\n", "\n", "# If you want to save the figure, uncomment the commands below. \n", "# The figure will be saved in the same directory as your IPython notebook.\n", "# Save the figure as a high-res pdf in the current folder\n", "# plt.savefig('MassSpring_SeismicTF.pdf',dpi=300)\n", "\n", "fig.set_size_inches(9,9) # Resize the figure for better display in the notebook" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Analysis for Different Damping Ratios\n", "We can repeat this for a variety of damping ratios to compare the Bode Plots. We'll write this an array/list of tranfer functions and use indices to access the particular responses that we want." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "damping_ratios = [0.01, 0.1, 0.2, 0.4]\n", "\n", "# Now define some arrays, filled with zeros for now, to hold the various system information\n", "num = np.zeros_like(damping_ratios)\n", "den = np.zeros_like(damping_ratios)\n", "sys = []\n", "\n", "freq_range = np.linspace(0,100,10001)\n", "magnitude = np.empty((len(freq_range), len(damping_ratios)))\n", "phase = np.empty((len(freq_range), len(damping_ratios)))\n", "frequency = np.empty((len(freq_range), len(damping_ratios)))\n", "mag_dB = np.empty((len(freq_range), len(damping_ratios)))\n", "frequency_Hz = np.empty((len(freq_range), len(damping_ratios)))\n", "\n", "for index, z in enumerate(damping_ratios):\n", " num = [1/m]\n", " den = [1, 2 * z * wn, wn**2]\n", "\n", " sys.append(control.tf(num, den))\n", " \n", " magnitude[:,index], phase[:,index], frequency[:,index] = control.bode(sys[index], omega=freq_range, Plot=False) # we use Plot=False because we'll plot it prettier outselve)\n", "\n", " # We want the magnitude plotted in dB to match Bode Plot standards\n", " mag_dB[:,index] = 20 * np.log10(magnitude[:, index])\n", "\n", " # We want the frequency plotted in Hz\n", " frequency_Hz[:,index] = frequency[:,index] / (2 * np.pi)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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DyWPxRdHU1ERdXd34IIUdO3ZMOcITmHb06XS/WJWUlLB///7xJascDgcHDhy4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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Let's plot the magnitude (normlized by k G(Omega))\n", "\n", "# Make the figure pretty, then plot the results\n", "# \"pretty\" parameters selected based on pdf output, not screen output\n", "# Many of these setting could also be made default by the .matplotlibrc file\n", "fig = plt.figure(figsize=(6,4))\n", "ax = plt.gca()\n", "plt.subplots_adjust(bottom=0.17,left=0.17,top=0.96,right=0.96)\n", "plt.setp(ax.get_ymajorticklabels(),family='Serif',fontsize=18)\n", "plt.setp(ax.get_xmajorticklabels(),family='Serif',fontsize=18)\n", "ax.spines['right'].set_color('none')\n", "ax.spines['top'].set_color('none')\n", "ax.xaxis.set_ticks_position('bottom')\n", "ax.yaxis.set_ticks_position('left')\n", "ax.grid(True,linestyle=':',color='0.75')\n", "ax.set_axisbelow(True)\n", "\n", "plt.xlabel(r'Frequency (Hz)',family='Serif',fontsize=22,weight='bold',labelpad=5)\n", "plt.ylabel(r'Magnitude (dB)',family='Serif',fontsize=22,weight='bold',labelpad=35)\n", "\n", "plt.semilogx(frequency_Hz[:,0], mag_dB[:,0], linewidth=2, label=r'$\\zeta$ = 0.01')\n", "plt.semilogx(frequency_Hz[:,1], mag_dB[:,1], linewidth=2, linestyle = '-.', label=r'$\\zeta$ = 0.1')\n", "plt.semilogx(frequency_Hz[:,2], mag_dB[:,2], linewidth=2, linestyle = ':', label=r'$\\zeta$ = 0.2')\n", "plt.semilogx(frequency_Hz[:,3], mag_dB[:,3], linewidth=2, linestyle = '--',label=r'$\\zeta$ = 0.4')\n", "\n", "# plt.xlim(0,5)\n", "# plt.ylim(0,7)\n", "\n", "leg = plt.legend(loc='upper right', fancybox=True)\n", "ltext = leg.get_texts()\n", "plt.setp(ltext,family='Serif',fontsize=16)\n", "\n", "# save the figure as a high-res pdf in the current folder\n", "# plt.savefig('Forced_Freq_Resp_mag.pdf',dpi=300)\n", "\n", "fig.set_size_inches(9,6) # Resize the figure for better display in the notebook" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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qL426vq54PR2OcxzrOUavuxejzsixnqNsf+bLAGSZs/jSqi+zIi+Q7uNyQ3Ei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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Now let's plot the phase\n", "\n", "# Make the figure pretty, then plot the results\n", "# \"pretty\" parameters selected based on pdf output, not screen output\n", "# Many of these setting could also be made default by the .matplotlibrc file\n", "fig = plt.figure(figsize=(6,4))\n", "ax = plt.gca()\n", "plt.subplots_adjust(bottom=0.17,left=0.17,top=0.96,right=0.96)\n", "plt.setp(ax.get_ymajorticklabels(),family='Serif',fontsize=18)\n", "plt.setp(ax.get_xmajorticklabels(),family='Serif',fontsize=18)\n", "ax.spines['right'].set_color('none')\n", "ax.spines['top'].set_color('none')\n", "ax.xaxis.set_ticks_position('bottom')\n", "ax.yaxis.set_ticks_position('left')\n", "ax.grid(True,linestyle=':',color='0.75')\n", "ax.set_axisbelow(True)\n", "\n", "plt.xlabel(r'Frequency (Hz)',family='Serif',fontsize=22,weight='bold',labelpad=5)\n", "plt.ylabel(r'Phase (deg)',family='Serif',fontsize=22,weight='bold',labelpad=35)\n", "\n", "plt.semilogx(frequency_Hz[:,0], phase[:,0], linewidth=2, label=r'$\\zeta$ = 0.01')\n", "plt.semilogx(frequency_Hz[:,1], phase[:,1], linewidth=2, linestyle = '-.', label=r'$\\zeta$ = 0.1')\n", "plt.semilogx(frequency_Hz[:,2], phase[:,2], linewidth=2, linestyle = ':', label=r'$\\zeta$ = 0.2')\n", "plt.semilogx(frequency_Hz[:,3], phase[:,3], linewidth=2, linestyle = '--',label=r'$\\zeta$ = 0.4')\n", "\n", "plt.ylim(-200.0, 20.0)\n", "plt.yticks([0, -90, -180])\n", "\n", "leg = plt.legend(loc='upper right', fancybox=True)\n", "ltext = leg.get_texts()\n", "plt.setp(ltext,family='Serif',fontsize=16)\n", "\n", "# save the figure as a high-res pdf in the current folder\n", "# plt.savefig('Forced_Freq_Resp_Phase.pdf',dpi=300)\n", "\n", "fig.set_size_inches(9,6) # Resize the figure for better display in the notebook" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's plot the magnitude and phase as subplots, to make it easier to compare" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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cxmq1zrmPQCCA1WolFAphNpuRUk7Zh8ViIRgMYrPZ8Pv9U/bh8/mw2+1X7GM8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\n2mFdOFpHHSxFURKTACGEELLXmff1++MEiAgZcG7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RIa8t3fk8UKG1vnU0+5w3b55esybx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DjWOTBmWZeREb/B7tCKSovZzS7tVTp+QswCDoc0RSuSvBpj7pIszvmbVQC8/G9v0V439TIvrQMt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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Make the figure pretty, then plot the results\n", "# \"pretty\" parameters selected based on pdf output, not screen output\n", "# Many of these setting could also be made default by the .matplotlibrc file\n", "fig, (ax1, ax2) = plt.subplots(2, 1, sharex = True, figsize=(8,8))\n", "\n", "plt.subplots_adjust(bottom=0.12,left=0.17,top=0.96,right=0.96)\n", "plt.setp(ax.get_ymajorticklabels(),family='serif',fontsize=18)\n", "plt.setp(ax.get_xmajorticklabels(),family='serif',fontsize=18)\n", "\n", "ax1.spines['right'].set_color('none')\n", "ax1.spines['top'].set_color('none')\n", "ax1.xaxis.set_ticks_position('bottom')\n", "ax1.yaxis.set_ticks_position('left')\n", "ax1.grid(True,linestyle=':',color='0.75')\n", "ax1.set_axisbelow(True)\n", "\n", "ax2.spines['right'].set_color('none')\n", "ax2.spines['top'].set_color('none')\n", "ax2.xaxis.set_ticks_position('bottom')\n", "ax2.yaxis.set_ticks_position('left')\n", "ax2.grid(True,linestyle=':',color='0.75')\n", "ax2.set_axisbelow(True)\n", "\n", "plt.xlabel(r'Frequency (Hz)',family='Serif',fontsize=22,weight='bold',labelpad=5)\n", "\n", "# Magnitude plot\n", "ax1.set_ylabel(r'Magnitude (dB)',family='Serif',fontsize=22,weight='bold',labelpad=35)\n", "ax1.semilogx(frequency_Hz[:,0], mag_dB[:,0], linewidth=2, label=r'$\\zeta$ = 0.01')\n", "ax1.semilogx(frequency_Hz[:,1], mag_dB[:,1], linewidth=2, linestyle = '-.', label=r'$\\zeta$ = 0.1')\n", "ax1.semilogx(frequency_Hz[:,2], mag_dB[:,2], linewidth=2, linestyle = ':', label=r'$\\zeta$ = 0.2')\n", "ax1.semilogx(frequency_Hz[:,3], mag_dB[:,3], linewidth=2, linestyle = '--',label=r'$\\zeta$ = 0.4')\n", "\n", "ax1.leg = ax1.legend(loc='upper right', fancybox=True)\n", "ltext = ax1.leg.get_texts()\n", "plt.setp(ltext,family='Serif',fontsize=16)\n", "\n", "# Phase plot \n", "ax2.set_ylabel(r'Phase (deg)',family='Serif',fontsize=22,weight='bold',labelpad=35)\n", "\n", "ax2.semilogx(frequency_Hz[:,0], phase[:,0], linewidth=2, label=r'$\\zeta$ = 0.01')\n", "ax2.semilogx(frequency_Hz[:,1], phase[:,1], linewidth=2, linestyle = '-.', label=r'$\\zeta$ = 0.1')\n", "ax2.semilogx(frequency_Hz[:,2], phase[:,2], linewidth=2, linestyle = ':', label=r'$\\zeta$ = 0.2')\n", "ax2.semilogx(frequency_Hz[:,3], phase[:,3], linewidth=2, linestyle = '--',label=r'$\\zeta$ = 0.4')\n", "\n", "ax2.set_ylim(-200.0, 20.0)\n", "ax2.set_yticks([0, -90, -180])\n", "\n", "# Uncomment below to place a legend on the lower subplot too\n", "# ax2.leg = ax2.legend(loc='upper right', fancybox=True)\n", "# ltext = ax2.leg.get_texts()\n", "# plt.setp(ltext,family='Serif',fontsize=16)\n", "\n", "# Adjust the page layout filling the page using the new tight_layout command\n", "plt.tight_layout(pad=0.5)\n", "\n", "# If you want to save the figure, uncomment the commands below. \n", "# The figure will be saved in the same directory as your IPython notebook.\n", "# Save the figure as a high-res pdf in the current folder\n", "# plt.savefig('MassSpring_SeismicTF.pdf',dpi=300)\n", "\n", "fig.set_size_inches(9,9) # Resize the figure for better display in the notebook" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Licenses\n", "Code is licensed under a 3-clause BSD style license. See the licenses/LICENSE.md file.\n", "\n", "Other content is provided under a [Creative Commons Attribution-NonCommercial 4.0 International License](http://creativecommons.org/licenses/by-nc/4.0/), CC-BY-NC 4.0." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# This cell will just improve the styling of the notebook\n", "# You can ignore it, if you are okay with the default sytling\n", "from IPython.core.display import HTML\n", "import urllib.request\n", "response = urllib.request.urlopen(\"https://cl.ly/1B1y452Z1d35\")\n", "HTML(response.read().decode(\"utf-8\"))" ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "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": "3.6.2" } }, "nbformat": 4, "nbformat_minor": 1 }