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

Frequency Response to Direct-Force Inputs

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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 to a harmonic, direct-force input.\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}$" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np # Grab all of the NumPy functions with namespace np" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# We want our plots to be displayed inline, not in a separate window\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# Import the plotting functions \n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# Define the System Parameters\n", "m = 1.0 # kg\n", "k = (2.0 * np.pi)**2 # N/m (Selected to give an undamped natrual frequency of 1Hz)\n", "wn = np.sqrt(k / m) # Natural Frequency (rad/s)\n", "\n", "z = 0.25 # Define a desired damping ratio\n", "c = 2 * z * wn * m # calculate the damping coeff. to create it (N/(m/s))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's use the closed-form, steady-state solution we developed in lecture:\n", "\n", "Assume:\n", "\n", "$ \\quad f(t) = \\bar{f} \\sin{\\omega t} $\n", "\n", "Then, the solution $x(t)$ should have the form:\n", "\n", "$ \\quad x(t) = | x | \\sin{\\left( \\omega t + \\phi \\right) } $\n", "\n", "Substituting this assumed solution into the equation of motion and solving for $ \\bar{x} $ and $ \\phi $: \n", "\n", "$ \\quad | \\bar{x} | = \\frac{\\bar{f}}{m} \\left( \\frac{1}{\\sqrt{\\left(\\omega_n^2 - \\omega^2\\right)^2 + \\left(2 \\zeta \\omega_n \\right)^2}} \\right) $\n", "\n", "and\n", "\n", "$ \\quad \\phi = \\tan^{-1}\\left({\\frac{2 \\zeta \\omega_n \\omega}{\\omega_n^2 - \\omega^2}}\\right) $\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Transfer Function Form\n", "$ \\quad \\left| G(\\omega) \\right| = \\frac{1}{m \\sqrt{\\left(\\omega_n^2 - \\omega^2\\right)^2 + \\left(2 \\zeta \\omega_n \\right)^2}} $\n", "\n", "### Normalization\n", "We can also nondimensionalize/normalize this by defining $ \\Omega = \\frac{\\omega}{\\omega_n} $.\n", "\n", "$ \\quad \\left| G(\\Omega) \\right| = \\frac{1}{k \\sqrt{\\left(1 - \\Omega^2\\right)^2 + \\left(2 \\zeta \\Omega \\right)^2}} $\n", "\n", "and\n", "\n", "$ \\quad \\phi = \\tan^{-1}\\left({\\frac{2 \\zeta \\Omega}{1 - \\Omega^2}}\\right) $\n", "\n", "Let's plot the normalized versions." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# Set up input parameters\n", "wun = np.linspace(0, 10, 1000) # Frequency range for freq response plot, 0-10 Omega with 1000 points in-between\n", "w = np.linspace(0, 10, 1000) # Frequency range for freq response plot, 0-10 Omega with 1000 points in-between\n", "\n", "# Let's examine a few different damping ratios\n", "z = 0.0\n", "mag_normal_un = 1/(k*np.sqrt((1 - w**2)**2 + (2*z*w)**2))\n", "phase_un = -np.arctan2((2*z*w),(1 - w**2)) * 180/np.pi\n", "\n", "# Let's mask the phase discontinuity, so it isn't plotted\n", "pos = np.where(np.abs(k*mag_normal_un) >= 25)\n", "phase_un[pos] = np.nan\n", "wun[pos] = np.nan\n", "\n", "\n", "z = 0.1\n", "mag_normal_0p1 = 1/(k*np.sqrt((1 - w**2)**2 + (2*z*w)**2))\n", "phase_0p1 = -np.arctan2((2*z*w),(1 - w**2)) * 180/np.pi\n", "\n", "\n", "z = 0.2\n", "mag_normal_0p2 = 1/(k*np.sqrt((1 - w**2)**2 + (2*z*w)**2))\n", "phase_0p2 = -np.arctan2((2*z*w),(1 - w**2)) * 180/np.pi\n", "\n", "\n", "z = 0.4\n", "mag_normal_0p4 = 1/(k*np.sqrt((1 - w**2)**2 + (2*z*w)**2))\n", "phase_0p4 = -np.arctan2((2*z*w),(1 - w**2)) * 180/np.pi" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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SLSv29vYmlY0YGRlBX19fyvHHjh0D5zz+tbCwsOl4vk0WQBGtTXDOs1qsNRjI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RhKt5GUa7C0g+0bDSOx53TXjzx3WTD4s6+GwikoqqreFHP+PyI2Rb5P4b+V4+RcPkAottrpxh2u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\nJQiCIAiCkCDE0RIEQRAEQUgQ/x+rCS5K4Gf/bwAAAABJRU5ErkJggg==\n", "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'Normalized Frequency ($\\Omega$)',family='Serif',fontsize=22,weight='bold',labelpad=5)\n", "plt.ylabel(r'$k |G(\\Omega)|$',family='Serif',fontsize=22,weight='bold',labelpad=35)\n", "\n", "plt.plot(wun, k*mag_normal_un, linewidth=2, label=r'$\\zeta$ = 0.0')\n", "plt.plot(w, k*mag_normal_0p1, linewidth=2, linestyle = '-.', label=r'$\\zeta$ = 0.1')\n", "plt.plot(w, k*mag_normal_0p2, linewidth=2, linestyle = ':', label=r'$\\zeta$ = 0.2')\n", "plt.plot(w, k*mag_normal_0p4, 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": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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iXMREuYhLyVv7GI3GkQ7RcKdISsXFxRPOm5WVhZ07dzo9fnjka/y/d7PZ7Nal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FPPmZD62PPMhdhvj1uIOGba2bZgtlVcNye/rfOU+bxU5fqumuu2YOqe889Zp7+LdTPn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\nqm/a2uMAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Now let's plot the phase\n", "\n", "\n", "# Plot the Phase Response\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'Normalized Frequency ($\\Omega$)',family='Serif',fontsize=22,weight='bold',labelpad=5)\n", "plt.ylabel(r'Phase (deg.)',family='Serif',fontsize=22,weight='bold',labelpad=8)\n", "\n", "plt.plot(wun, phase_un, linewidth=2, label=r'$\\zeta$ = 0.0')\n", "plt.plot(w, phase_0p1, linewidth=2, linestyle = '-.', label=r'$\\zeta$ = 0.1')\n", "plt.plot(w, phase_0p2, linewidth=2, linestyle = ':', label=r'$\\zeta$ = 0.2')\n", "plt.plot(w, phase_0p4, linewidth=2, linestyle = '--', label=r'$\\zeta$ = 0.4')\n", "\n", "plt.xlim(0,5)\n", "plt.ylim(-190,10)\n", "plt.yticks([-180,-90,0])\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": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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EqlTh/ygwCSQiomTEJFBhQoh4h0C4atu4KBeGaDTh10gFdwyx2yGlXHxwREREKwCTQIVx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\nyQI2M3jYbptv/jydTu+ZZAZK9v/+zXJnpDZN3fDNfnX2ZuBG2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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(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'Normalized Frequency $\\left(\\Omega = \\frac{\\omega}{\\omega_n}\\right)$',family='serif',fontsize=22,weight='bold',labelpad=5)\n", "plt.xticks([0,1],['0','$\\Omega = 1$'])\n", "plt.xlim(0, 5)\n", "\n", "# Magnitude plot\n", "ax1.set_ylabel(r'$ k|G(\\Omega)| $',family='serif',fontsize=22,weight='bold',labelpad=40)\n", "ax1.plot(wun, k*mag_normal_un, linewidth=2, label=r'$\\zeta$ = 0.0')\n", "ax1.plot(w, k*mag_normal_0p1, linewidth=2, linestyle = '-.', label=r'$\\zeta$ = 0.1')\n", "ax1.plot(w, k*mag_normal_0p2, linewidth=2, linestyle = ':', label=r'$\\zeta$ = 0.2')\n", "ax1.plot(w, k*mag_normal_0p4, linewidth=2, linestyle = '--',label=r'$\\zeta$ = 0.4')\n", "ax1.set_ylim(0.0, 7.0)\n", "ax1.set_yticks([0,1,2,3,4,5,6,7])\n", "ax1.set_yticklabels(['$0$','$1$','','','','','',''])\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(r'$ \\phi $ (deg)',family='serif',fontsize=22,weight='bold',labelpad=10)\n", "# ax2.plot(wnorm,TFnorm_phase*180/np.pi,linewidth=2)\n", "ax2.plot(wun, phase_un, linewidth=2, label=r'$\\zeta$ = 0.0')\n", "ax2.plot(w, phase_0p1, linewidth=2, linestyle = '-.', label=r'$\\zeta$ = 0.1')\n", "ax2.plot(w, phase_0p2, linewidth=2, linestyle = ':', label=r'$\\zeta$ = 0.2')\n", "ax2.plot(w, phase_0p4, linewidth=2, linestyle = '--', label=r'$\\zeta$ = 0.4')\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": [ "## Bode Plots\n", "We can take these frequency responses and put them into [Bode plot](https://en.wikipedia.org/wiki/Bode_plot) form by plotting `20 * log(magnitude)` for the `magnitude` representing the magnitude desired response on a semi-log horizontal (frequency) axis." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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3OJiaw4/v+AYfd/by0XVTb/vX2tfK2+1v0TXk4tIFReSn5ANT5959N6/kCxuW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\nu/+b6oe62vBPhbzJ+1alXVHeVwkRdEQ/h6xLXCKU/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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(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'Normalized Frequency $\\left(\\Omega = \\frac{\\omega}{\\omega_n}\\right)$',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(wun, 20*np.log10(k*mag_normal_un), linewidth=2, label=r'$\\zeta$ = 0.0')\n", "ax1.semilogx(w, 20*np.log10(k*mag_normal_0p1), linewidth=2, linestyle = '-.', label=r'$\\zeta$ = 0.1')\n", "ax1.semilogx(w, 20*np.log10(k*mag_normal_0p2), linewidth=2, linestyle = ':', label=r'$\\zeta$ = 0.2')\n", "ax1.semilogx(w, 20*np.log10(k*mag_normal_0p4), linewidth=2, linestyle = '--',label=r'$\\zeta$ = 0.4')\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(r'$ \\phi $ (deg)',family='serif',fontsize=22,weight='bold',labelpad=10)\n", "# ax2.semilogx(wnorm,TFnorm_phase*180/np.pi,linewidth=2)\n", "ax2.semilogx(wun, phase_un, linewidth=2, label=r'$\\zeta$ = 0.0')\n", "ax2.semilogx(w, phase_0p1, linewidth=2, linestyle = '-.', label=r'$\\zeta$ = 0.1')\n", "ax2.semilogx(w, phase_0p2, linewidth=2, linestyle = ':', label=r'$\\zeta$ = 0.2')\n", "ax2.semilogx(w, phase_0p4, linewidth=2, linestyle = '--', label=r'$\\zeta$ = 0.4')\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": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 10, "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 }