{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1 style=\"text-align:center\">Simluation of a Simple Mass-Spring-Damper System <br> with a Disturbance Force</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_SeismicWithDisturbance_Horiz.png\" alt=\"A Mass-Spring-Damper System with a Disturbance Force\" width=50%/></a><br>\n",
    "    <strong> Figure 1: A Mass-Spring-Damper System with a Disturbance Force</strong>\n",
    "</p>\n",
    "\n",
    "This notebook simluates a the simple mass-spring-damper model like the one shown in Figure 1. The system has both a position input $y(t)$ and a force input, $f(t)$. This system could also be used to model the position control of a mass via a Proportional Derivative (PD) controller.\n",
    "\n",
    "The equationof motion for this system is:\n",
    "\n",
    "$ \\quad m\\ddot{x} + c \\dot{x} + k x = c \\dot{y} + k y - f $\n",
    "\n",
    "We can also rewrie this in terms of damping ratio, $\\zeta$, and natural frequency, $\\omega_n$:\n",
    "\n",
    "$ \\quad \\ddot{x} + 2 \\zeta \\omega_n \\dot{x} + \\omega_n^2 x = \\zeta \\omega_n \\dot{y} + \\omega_n^2 y - \\frac{f}{m} $\n",
    "\n",
    "However, as we'll see below, we often will collect terms so that our ''motion'' variable are all on the left-hand side, like:\n",
    "\n",
    "$ \\quad \\ddot{x} = \\frac{k}{m}\\left( y - x \\right) + \\frac{c}{m} \\left(\\dot{y} - \\dot{x} \\right) - \\frac{f}{m} $\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "# Import the plotting functions \n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Import the ODE solver\n",
    "from scipy.integrate import odeint"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Functions defining the equations of motion and inputs\n",
    "We will first define the functions that define the equations of motion and the inputs. One \"trick\" that we will use is to define $y(t)$ and $\\dot{y}(t)$ as states. This allows us to specifiy an acceleration input $\\ddot{y}(t)$, which gets propogated to the $y(t)$ and $\\dot{y}(t)$ via the equations of motion (or state-transition matrix if we were solving in \"true\" matrix-based state-space form).\n",
    "\n",
    "So, we can then define our states as vector $ \\bar{w} = \\left[x \\ \\dot{x} \\  y \\ \\dot{y}\\right]^T $ and the inputs as $\\bar{u} = \\left[\\ddot{y} \\ f \\right]$.\n",
    "\n",
    "Then the system of first-order ODEs we have to solve is:\n",
    "\n",
    "$ \\quad \\dot{\\bar{w}} = g(\\bar{w}, \\bar{u}, t) $\n",
    "\n",
    "Writing these out, we have:\n",
    "\n",
    "$ \\quad \\dot{\\bar{w}}  = \\left[\\dot{x} \\right.$\n",
    "\n",
    "$\\phantom{\\quad \\dot{\\bar{w}}  = \\left[\\right.} \\frac{k}{m}(y - x) + \\frac{c}{m}\\left(\\dot{y} - \\dot{x}\\right) - \\frac{f}{m} $\n",
    "\n",
    "$\\phantom{\\quad \\dot{\\bar{w}}  = \\left[\\right.} \\dot{y}$\n",
    "\n",
    "$\\phantom{\\quad \\dot{\\bar{w}}  = \\left[\\right.} \\left.\\ddot{y}\\right]$\n",
    "\n",
    "Notice that the $\\ddot{y}$ in the last line is what we get to specify to generate the position input. In addition to allowing us to only specify one input that gets propograted to y and $\\dot{y}$, describing inputs in the acceleration domain is often preferrable. This is because representing a realistic input in this domain is often easier than in the position or velocity domain."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def eq_of_motion(w, t, p):\n",
    "    \"\"\"\n",
    "    Defines the differential equations for the coupled spring-mass system.\n",
    "\n",
    "    Arguments:\n",
    "        w :  vector of the state variables:\n",
    "        t :  time\n",
    "        p :  vector of the parameters:\n",
    "    \"\"\"\n",
    "    x, x_dot, y, y_dot = w\n",
    "    m, k, c, Distance, StartTime, Amax, Vmax, DistStart, F_amp = p\n",
    "\n",
    "    # Create sysODE = (x', x_dot', y', y_dot')\n",
    "    sysODE = [x_dot,\n",
    "             k/m * (y - x) + c/m * (y_dot - x_dot) - f(t, p)/m,\n",
    "             y_dot,\n",
    "             y_ddot(t, p)]\n",
    "    return sysODE\n",
    "\n",
    "\n",
    "def f(t, p):\n",
    "    \"\"\"\n",
    "    defines the disturbance force input to the system\n",
    "    \"\"\"\n",
    "    m, k, c, Distance, StartTime, Amax, Vmax, DistStart, F_amp = p\n",
    "    \n",
    "    # Select one of the two inputs below\n",
    "    # Be sure to comment out the one you're not using\n",
    "    \n",
    "    # Input Option 1: \n",
    "    #    Just a step in force beginning at t=DistStart\n",
    "    # f = F_amp * (t >= DistStart)\n",
    "    \n",
    "    # Input Option 2:\n",
    "    #    A pulse in force beginning at t=DistStart and ending at t=(DistStart+0.1)\n",
    "    f = F_amp * (t >= DistStart) * (t <= DistStart + 0.1)\n",
    "    \n",
    "    return f\n",
    "\n",
    "\n",
    "def y_ddot(t, p):\n",
    "    \"\"\"\n",
    "    Defines the accel input to the system.\n",
    "    \n",
    "    Depending on the desired move distance, max accel, and max velocity, the input is either\n",
    "    bang-bang or bang-coast-bang\n",
    "    \"\"\"\n",
    "    m, k, c, Distance, StartTime, Amax, Vmax, DistStart, F_amp = p\n",
    "    \n",
    "    # These are the times for a bang-coast-bang input \n",
    "    t1 = StartTime\n",
    "    t2 = (Vmax/Amax) + t1\n",
    "    t3 = (Distance/Vmax) + t1\n",
    "    t4 = (t2 + t3) - t1\n",
    "    \n",
    "    if t3 <= t2: # command should be bang-bang, not bang-coast-bang\n",
    "        t2 = np.sqrt(Distance/Amax)+t1\n",
    "        t3 = 2*np.sqrt(Distance/Amax)+t1\n",
    "        \n",
    "        accel = Amax*(t > t1) - 2*Amax*(t > t2) + Amax*(t > t3)\n",
    "    \n",
    "    else: # command is bang-coast-bang\n",
    "        accel = Amax*(t > t1) - Amax*(t > t2) - Amax*(t > t3) + Amax*(t > t4)\n",
    "\n",
    "    return accel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Define the parameters for simluation\n",
    "m = 1.0                      # mass (kg)\n",
    "k = (1.0*2*np.pi)**2             # spring constant (N/m)\n",
    "\n",
    "wn = np.sqrt(k/m)            # natural frequency (rad/s)\n",
    "\n",
    "# Select damping ratio and use it to choose an appropriate c\n",
    "zeta = 0.05                   # damping ratio\n",
    "c = 2*zeta*wn*m              # damping coeff.\n",
    "\n",
    "# ODE solver parameters\n",
    "abserr = 1.0e-9\n",
    "relerr = 1.0e-9\n",
    "max_step = 0.01\n",
    "stoptime = 10.0\n",
    "numpoints = 10001\n",
    "\n",
    "# Create the time samples for the output of the ODE solver\n",
    "t = np.linspace(0.,stoptime,numpoints)\n",
    "\n",
    "# Initial conditions\n",
    "x_init = 0.0                        # initial position\n",
    "x_dot_init = 0.0                    # initial velocity\n",
    "y_init = 0.0\n",
    "y_dot_init = 0.0\n",
    "\n",
    "# Set up the parameters for the input function\n",
    "Distance = 1.0               # Desired move distance (m)\n",
    "Amax = 20.0                   # acceleration limit (m/s^2)\n",
    "Vmax = 2.0                   # velocity limit (m/s)\n",
    "StartTime = 0.5              # Time the y(t) input will begin\n",
    "DistStart = 4.5              # Time the disturbance input will begin\n",
    "F_amp = 100.0                 # Amplitude of Disturbance force (N)\n",
    "\n",
    "# Pack the parameters and initial conditions into arrays \n",
    "p = [m, k, c, Distance, StartTime, Amax, Vmax, DistStart, F_amp]\n",
    "x0 = [x_init, x_dot_init, y_init, y_dot_init]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Call the ODE solver.\n",
    "resp = odeint(eq_of_motion, x0, t, args=(p,), atol=abserr, rtol=relerr,  hmax=max_step)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
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JhC58Uuq6qMvNNTUFnc9jTmKhkUS7OInxixcx/Hufwflbb8PEd5+02hyVUp8r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\nhBz+P883O7LM2hZpAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11caab1d0>"
      ]
     },
     "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 = 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('Time (s)',family='serif',fontsize=22,weight='bold',labelpad=5)\n",
    "plt.ylabel('Position (m)',family='serif',fontsize=22,weight='bold',labelpad=10)\n",
    "# plt.ylim(-1.,1.)\n",
    "\n",
    "# plot the response\n",
    "plt.plot(t,resp[:,0], linewidth=2, linestyle = '-', label=r'$x$')\n",
    "plt.plot(t,resp[:,2], linewidth=2, linestyle = '--', label=r'$y$')\n",
    "\n",
    "# If there is a non-zero force disturbance show where it began via an annotation\n",
    "if F_amp > 0:\n",
    "    plt.annotate(r'Force Disturbance Begins',\n",
    "         xy=(DistStart,resp[-1,2]), xycoords='data',\n",
    "         ha='center',\n",
    "         xytext=(DistStart, 1.05*np.max(resp[:,0])), textcoords='data', fontsize=16,\n",
    "         arrowprops=dict(arrowstyle=\"simple, head_width = 0.35, tail_width=0.05\", connectionstyle=\"arc3\", color=\"black\"),color = \"black\")\n",
    "    \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",
    "# 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('MassSpringDamper_Disturbance_Resp.pdf')\n",
    "\n",
    "fig.set_size_inches(9, 6) # Resize the figure for better display in the notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Forces\n",
    "We can also easily take a look at the forces acting on the system.\n",
    "\n",
    "The forces resulting from the position input are just the force from the spring, $F_{sp}$, and the force from damper, $F_{d}$:\n",
    "\n",
    "$ \\quad F_{pos} = F_{sp} + F_{d} = k \\left(y - x\\right) + c \\left(\\dot{y} - \\dot{x}\\right) $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Fsp = k * (resp[:,2] - resp[:,0])       # Spring Force (N)\n",
    "Fd =  c * (resp[:,3] - resp[:,1])       # Damping Force (N)\n",
    "\n",
    "F_pos = Fsp + Fd\n",
    "\n",
    "# Calculate the disturbance force over time by calling the disturbance force function\n",
    "F_dist = np.zeros_like(t)\n",
    "\n",
    "for ii in range(len(t)):\n",
    "    F_dist[ii] = -f(t[ii],p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Hh+axoSEgEoGptBQkP3/O601LlwIAoseP621a2vh/fT8QjaLgYx9FybduR94l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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f4d2048>"
      ]
     },
     "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 = 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('Time (s)',family='serif',fontsize=22,weight='bold',labelpad=5)\n",
    "plt.ylabel('Force (N)',family='serif',fontsize=22,weight='bold',labelpad=10)\n",
    "\n",
    "# You may need to reset these limits based on the forces in your simulation\n",
    "ymax = 1.1 * np.max([np.max(np.abs(F_pos)), np.max(np.abs(F_dist))])\n",
    "plt.ylim(-ymax, ymax)\n",
    "\n",
    "# plot the response\n",
    "plt.plot(t,F_pos, linewidth=2, linestyle = '-', label=r'Spring-Damper')\n",
    "plt.plot(t,F_dist, linewidth=2, linestyle = '--', label=r'Disturbance')\n",
    "\n",
    "leg = plt.legend(loc='best', fancybox=True)\n",
    "ltext  = 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('MassSpringDamper_Disturbance_Forces.pdf')\n",
    "\n",
    "fig.set_size_inches(9, 6) \n",
    "# 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": 10,
   "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": 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
}