{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1 style=\"text-align:center\">Step Response of a Mass-Spring-Damper System</h1>\n",
    "<h3 style=\"text-align:center\"> MCHE 485: Mechanical Vibrations</h3>\n",
    "<p style=\"text-align:center\">Dr. Joshua Vaughan <br>\n",
    "<a href=\"mailto:joshua.vaughan@louisiana.edu\">joshua.vaughan@louisiana.edu</a><br>\n",
    "http://www.ucs.louisiana.edu/~jev9637/   </p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"text-align:center\">\n",
    "\t<img src=\"http://shared.crawlab.org/MassSpringDamper_Seismic_Horiz.png\" alt=\"A Mass-Spring-Damper System\" width=50%/></a><br>\n",
    "    <strong> Figure 1: A Mass-Spring-Damper System </strong>\n",
    "</p>\n",
    "\n",
    "This notebook simluates a step response of a simple mass-spring-damper system like the one shown in Figure 1. We will also be using some functions from the [Python Control Systems Toolbox](https://www.cds.caltech.edu/~murray/wiki/Control_Systems_Library_for_Python).\n",
    "\n",
    "The equation of motion for the system is:\n",
    "\n",
    "$ \\quad m \\ddot{x} + c \\dot{x} + kx = c \\dot{y} + ky $\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 = 2\\zeta\\omega_n \\dot{y} + \\omega_n^2 y$\n",
    "\n",
    "For information on how to obtain this equation, you can see the lectures at the [class website](http://www.ucs.louisiana.edu/~jev9637/MCHE485.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll start by using the solution to the differential equation that we developed in class to plot the response. The solution for the underdamped case is:\n",
    "\n",
    "$ \\quad x(t) = c + e^{-\\zeta\\omega_nt}\\left(-c \\cos{\\omega_d t} - \\frac{\\zeta c}{\\sqrt{1-\\zeta^2}} \\sin{\\omega_d t}\\right) $\n",
    "\n",
    "where $c$ is the desired step size, and $\\omega_d = \\omega_n \\sqrt{1 - \\zeta^2}$ is the damped natural frequency."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np              # Grab all of the NumPy functions with nickname 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\n",
    "\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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 = 0.2                 # Define a desired damping ratio\n",
    "c = 2*z*wn*m            # calculate the damping coeff. to create it (N/(m/s))\n",
    "\n",
    "wd = wn*np.sqrt(1-z**2) # Damped natural frequency (rad/s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Define the time array\n",
    "t = np.linspace(0, 3, 301) # 0-3s with 301 points in between\n",
    "\n",
    "# Define the step input (We're using y_step, because we've already defined c as our damping coeff.)\n",
    "y_step = 1.0\n",
    "\n",
    "# Define x(t)\n",
    "# In this case, we're specifying that the step input occurs at t = 0\n",
    "x = y_step + np.exp(-z*wn*t)*(-y_step*np.cos(wd*t) + (z*y_step)/(np.sqrt(1-z**2)) * np.sin(wd*t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmgAAAGVCAYAAABKCw0TAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRETkmf8Pp3xcGu3qY3AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115970ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Set the plot size - 3x2 aspect ratio is best\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",
    "\n",
    "# Change the axis units to serif\n",
    "plt.setp(ax.get_ymajorticklabels(), family='serif', fontsize=18)\n",
    "plt.setp(ax.get_xmajorticklabels(), family='serif', fontsize=18)\n",
    "\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['top'].set_color('none')\n",
    "\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "\n",
    "# Turn on the plot grid and set appropriate linestyle and color\n",
    "ax.grid(True,linestyle=':', color='0.75')\n",
    "ax.set_axisbelow(True)\n",
    "\n",
    "# Define the X and Y axis labels\n",
    "plt.xlabel('Time (s)', family='serif', fontsize=22, weight='bold', labelpad=5)\n",
    "plt.ylabel('Position (m)', family='serif', fontsize=22, weight='bold', labelpad=10)\n",
    "\n",
    "plt.plot([t[0], t[-1]], [y_step, y_step], linewidth=2, linestyle='--', label=r'Step Input')\n",
    "plt.plot(t, x, linewidth=2, linestyle='-', label=r'Response')\n",
    "\n",
    "# uncomment below and set limits if needed\n",
    "# plt.xlim(0, 5)\n",
    "# plt.ylim(0, 10)\n",
    "\n",
    "# Create the legend, then fix the fontsize\n",
    "leg = plt.legend(loc='upper right', ncol = 1, fancybox=True)\n",
    "ltext  = leg.get_texts()\n",
    "plt.setp(ltext, family='serif', fontsize=20)\n",
    "\n",
    "# Adjust the page layout filling the page using the new tight_layout command\n",
    "plt.tight_layout(pad=0.5)\n",
    "\n",
    "# Uncommetn to save the figure as a high-res pdf in the current folder\n",
    "# It's saved at the original 6x4 size\n",
    "plt.savefig('Step_Response.pdf')\n",
    "\n",
    "fig.set_size_inches(9, 6) # Resize the figure for better display in the notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using the Control System Toolbox\n",
    "We can also simluate responses using the [Python Control Systems Library](http://www.cds.caltech.edu/~murray/wiki/Control_Systems_Library_for_Python). To do so, we'll use the transfer function form of the equations of motion. If you've had controls, you probably spent a lot of time working with transfer functions. If not, we'll learn more about them later. For now, just think of a transfer function as an experssion of how the input is \"transferred\" to the output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# import the control system toolbox\n",
    "import control"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Define the system to use in simulation - in transfer function form here\n",
    "num = [2.0*z*wn, wn**2]\n",
    "den = [1.0, 2.0*z*wn, wn**2]\n",
    "\n",
    "sys = control.tf(num,den)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Form the step input in desired position, yd, starting the step at t=0.0s\n",
    "yd = np.ones_like(t)              # This is an array of all ones, with the same size as t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Define the initial conditions x_dot(0) = 0, x(0) = 0\n",
    "x0 = [0.,0.]\n",
    "\n",
    "# run the simulation - utilize the built-in initial condition response function\n",
    "[T, yout, x_out] = control.forced_response(sys, t, yd, x0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's plot this version of the solution. It should look the same as the function-based version."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmgAAAGVCAYAAABKCw0TAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYFigEREREQXm/wO6VWhDQ2mufAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11dfcb4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Set the plot size - 3x2 aspect ratio is best\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",
    "\n",
    "# Change the axis units to serif\n",
    "plt.setp(ax.get_ymajorticklabels(), family='serif', fontsize=18)\n",
    "plt.setp(ax.get_xmajorticklabels(), family='serif', fontsize=18)\n",
    "\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['top'].set_color('none')\n",
    "\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "\n",
    "# Turn on the plot grid and set appropriate linestyle and color\n",
    "ax.grid(True,linestyle=':', color='0.75')\n",
    "ax.set_axisbelow(True)\n",
    "\n",
    "# Define the X and Y axis labels\n",
    "plt.xlabel('Time (s)', family='serif', fontsize=22, weight='bold', labelpad=5)\n",
    "plt.ylabel('Position (m)', family='serif', fontsize=22, weight='bold', labelpad=10)\n",
    "\n",
    "plt.plot(t, yd, linewidth=2, linestyle='--', label=r'Step Input')\n",
    "plt.plot(t, yout, linewidth=2, linestyle='-', label=r'Response')\n",
    "\n",
    "# uncomment below and set limits if needed\n",
    "# plt.xlim(0, 5)\n",
    "# plt.ylim(0, 10)\n",
    "\n",
    "# Create the legend, then fix the fontsize\n",
    "leg = plt.legend(loc='upper right', ncol = 1, fancybox=True)\n",
    "ltext  = leg.get_texts()\n",
    "plt.setp(ltext, family='serif', fontsize=20)\n",
    "\n",
    "# Adjust the page layout filling the page using the new tight_layout command\n",
    "plt.tight_layout(pad=0.5)\n",
    "\n",
    "# Uncommetn to save the figure as a high-res pdf in the current folder\n",
    "# It's saved at the original 6x4 size\n",
    "# plt.savefig('plot_filename.pdf')\n",
    "\n",
    "fig.set_size_inches(9, 6) # Resize the figure for better display in the notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr style=\"border: 0px;\n",
    "        height: 1px;\n",
    "        text-align: center;\n",
    "        background: #333;\n",
    "        background-image: -webkit-linear-gradient(left, #ccc, #333, #ccc); \n",
    "        background-image:    -moz-linear-gradient(left, #ccc, #333, #ccc); \n",
    "        background-image:     -ms-linear-gradient(left, #ccc, #333, #ccc); \n",
    "        background-image:      -o-linear-gradient(left, #ccc, #333, #ccc);\">"
   ]
  },
  {
   "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": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<script>\n",
       "    MathJax.Hub.Config({\n",
       "                        TeX: {\n",
       "                           extensions: [\"AMSmath.js\"]\n",
       "                           },\n",
       "                tex2jax: {\n",
       "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
       "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
       "                },\n",
       "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
       "                \"HTML-CSS\": {\n",
       "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
       "                }\n",
       "        });\n",
       "</script>\n",
       "\n",
       "<style>\n",
       "    @font-face {\n",
       "        font-family: \"Computer Modern\";\n",
       "        src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunss.otf');\n",
       "    }\n",
       "    @font-face {\n",
       "        font-family: \"Computer Modern\";\n",
       "        src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunsx.otf');\n",
       "        font-weight: bold;\n",
       "    }\n",
       "    @font-face {\n",
       "        font-family: \"Computer Modern\";\n",
       "        src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunsi.otf');\n",
       "        font-style: oblique;\n",
       "    }\n",
       "    @font-face {\n",
       "        font-family: \"Computer Modern\";\n",
       "        src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunso.otf');\n",
       "        font-weight: bold;\n",
       "        font-style: oblique;\n",
       "    }\n",
       "\n",
       "    div.cell {\n",
       "        max-width: 1100px;\n",
       "    }\n",
       "    \n",
       "    h1 {\n",
       "        font-family: Computer Modern;\n",
       "    }\n",
       "    \n",
       "    h4 {\n",
       "        margin-top: 12px;\n",
       "        margin-bottom: 3px;\n",
       "    }\n",
       "\n",
       "    div.text_cell_render {\n",
       "        font-family: Computer Modern, \"Helvetica Neue\", Arial, Helvetica, Geneva, sans-serif;\n",
       "        line-height: 145%;\n",
       "        font-size: 130%;\n",
       "        width: 100%;\n",
       "        max-width: 1100px;\n",
       "    }\n",
       "    \n",
       "    .CodeMirror {\n",
       "        font-family: \"Source Code Pro\", source-code-pro, Consolas, monospace;\n",
       "    }\n",
       "    \n",
       "    .warning {\n",
       "        color: rgb( 240, 20, 20 )\n",
       "    }  \n",
       "  \n",
       "   \n",
       "    hr.style-end {\n",
       "        border: 0px !important;\n",
       "        height: 1px !important;\n",
       "        text-align: center !important;\n",
       "        background: #333 !important;\n",
       "        background-image: -webkit-linear-gradient(left, #ccc, #333, #ccc) !important; \n",
       "        background-image:    -moz-linear-gradient(left, #ccc, #333, #ccc) !important; \n",
       "        background-image:     -ms-linear-gradient(left, #ccc, #333, #ccc) !important; \n",
       "        background-image:      -o-linear-gradient(left, #ccc, #333, #ccc) !important; \n",
       "    }\n",
       "\n",
       "    hr.style-end:after {\n",
       "        content: &#x269C !important;\n",
       "        left: 50% !important;\n",
       "        position: absolute !important;\n",
       "        /* Controls the whitespace around the symbol */\n",
       "        padding: 0px !important;\n",
       "        background: #fff !important;\n",
       "    }\n",
       "    \n",
       "/*  Center figures, etc\n",
       "    .ui-wrapper {\n",
       "        margin-left: auto !important;\n",
       "        margin-right: auto !important;\n",
       "    }\n",
       "*/\n",
       "    \n",
       "</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 11,
     "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
}