Velocity_Control.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Automotive Velocity Control\n",
    "\n",
    "A self-driving car company has requested a speed controller for their new model of electric autonomous vehicles. Unlike standard cruise control systems, this speed controller must manage transitions between all velocities ranging from 0 to 25 m/s (56 mph or 90 km/hr).\n",
    "\n",
    "![title](https://apmonitor.com/pdc/uploads/Main/auto_schematic.png)\n",
    "\n",
    "\n",
    "The speed controller changes a gas pedal (%) input that adjusts electrical current to the motor, creates a torque on the drive train, applies forward thrust from wheel contact on the road, and changes the velocity of the vehicle. Regenerative braking is part of this application by allowing the gas pedal to go from -50% to 100%. Decreases in velocity are also due to resistive forces. Negative velocities (backwards driving) is highly undesirable.\n",
    "\n",
    "See [PDC Course Website](https://apmonitor.com/pdc/index.php/Main/SpeedControl) for full problem statement and [solution video](https://youtu.be/k46nCvOBllA). Below is an open-loop step test for changing the gas pedal from 0 to 50%."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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SJXDvve4xUEICjBjhxty3bRuZ2IwJFz+J/6iq/irskVSAVmCBcuN/BFQs+/e/XcIvOnCqZk244QaYONEmSDOxy89cPYtEZKyIpIpIo7wt7JGVISkpiZ07d1oSKydVZefOnSTF6aodX34Jgwa5eXICk36NGvA//wPr18Pzz1vSN7HNzxn/td7jpIAyBU4PfTj+NWvWjOzsbHbs2BHJMKJSUlJS/g1f8SI7G377WzdZWuDc9wkJ7gz/3nvdhGrGxIMyE7+qtqyKQMqrZs2atGxZLUMz1cju3fDYY24WzMBlDEXgmmvch0Hr1pGKzpjIKLWrR0SC3vMvIvVEpF3oQzKm8o4ehb/8xXXZTJ5cOOkPGADLl7sFUSzpm3gU7Ix/uLfs4jzc3bo7cJO2nQn0BVoA/xv2CI0pp48+gjvugNWrC5d37gyPPw4XXRSZuIypLoIttn6HiDQErsQtt5iKW3d3DfCcqn5SNSGGz549e8jNzS3xa7Vq1aKed1vmsWPH2LVrV6nvU69ePWrVqgXA/v37S51yOSEhgUaNCq6LB7s4XadOHerUqQPA4cOHg0690KhRIxISEuK+TWvXHuP223cxb17hfZo3h7vvhhtvrEdSUnS1KRZ/TtYm/206ePBgmXf4V0hJU3ZWt62kaZlD4ZJLLil1euYhQ4bk77dx48agUzn/4x//yN/37rvvLnW/5s2bFzp+kyZNSt33oYceyt9v1qxZQY+fNwV0vLZp/37Vu+9WrVkzdtoUiz8na1P52/Tkk09qZVCRaZljXb169WjcuHGJX0tJScl/npCQUOp+4C4056lTp06p+zZs2LDQ60aNGpV6hhL4KV+rVq2gxw+8lyHe2rR7dwrnnOMWQ3GXrNx+J5wAdeq4UTvR1qZY/DlZmyrWpnANuy5zrp7qoKS5eiqqV69e5OTk8M4779CiRYuQvKepet98A7fdBu+/X7i8e3d45hno1i0ycRlTnVRmrp6YsnLlSvbu3ZvfN2eiy5Ej8OST8NBDhUfqNG7shm3+7GeFz/KNMcX5mY8/Q0TGeRd6o9q+ffvYu3cvSUlJNGjQINLhmHL6/HPo0sVdqM1L+iLujtu1a92qV5b0jSmbnz+Ta4BTgKUiMl1EBkiUTpCzdetWAE455RSb4yeK5OS4bp0ePQoP0ezc2c2589e/ujN+Y4w/ZSZ+VV2vqncDZwGvAy8Cm0TkgeowZ095bNmyBcD3Grgm8v7xDzjnHPjjHyHvclSdOvD737v/AM6N21Wfjak4X/8Yi0gH4PfAE8BM3Nj+vbjpmqPG5s2bAXfGb6q3XbvcCleXX+7m2clzySVuorVf/cqWOTSmosr80xGRTGA38AIwUVXzFmP5XER6BqnXHHgFOBk3j/9UVX3a+y/hTSAN2AD8VFV3VaINvuWd8Vvir97eew/GjgWvZw6Apk3h6afd/DrWS2dM5fg5479KVS9S1dfzkr6ItARQ1WFB6h0F/ldV2wDdgXEicg4wEVigqq2ABd7rKtG9e3cmTZrExRdfXFWHNOWwa5ebKfOKKwon/REj4Kuv3KMlfWMqz8+au8tUtXORskxV7VKuA4m8AzzrbX1UdauIpAKLVTXoVFmhHMdvqqcPPoCbbgLvnzIATjrJTbQ2dGjk4jImmpV7HL+InA20BeqLSOCZfT3cZG3lOXga0An4HDhJVbcCeMn/xFLqjAXGApx22mnlOZyJIgcOwJ13wp/+VLj82mvdjVg2WseY0AvWx98aGAg0AK4IKM8Bxvg9gIgk4y4I366qe/0Oo1TVqcBUcGf8fo8XzOzZs6lXrx69evXKnzDJRM7SpXDddfD11wVlTZvC1KkwZEjEwjIm5gWbnfMd4B0R6aGqn1XkzUWkJi7pv6aqs7zibSKSGtDVs70i711eqsp1113HgQMH2Lt3ryX+CDp6FB59FB58EI4dKygfPNgl/RNL/B/QGBMqwbp67lTVx4FrRWRE0a+r6m3B3ti7yesFYI2qPhXwpXeBG4HJ3uM7FQm8vPbu3cuBAwdITk4uNLmSqVobN8LIkfCvfxWUJSe7ETs/+5ldvDWmKgTr6lnjPVb0qmpP4HpglYhkeWV34RL+WyIyGtiEm+s/7GwoZ+S99ZYbprlnT0HZBRfAK6+AraJpTNUJ1tUz13t8uSJvrG6hltLO36p8DSRL/JGzb5+bcuGllwrKEhPhgQdg4kT33BhTdfxM0vahiDQIeN1QRD4Ia1RhYIk/MrKy3MRqgUm/ZUv45BM32ZolfWOqnp8buJqq6u68F95dtlF3+c0Sf9VShT//2c2PHzhqZ+RI92HQvXvEQjMm7vmZ7eSYiJymqpsARKQFbpmwqBI4M6cJrz174OabYcaMgrLkZPdBcP31kYvLGOP4uXP3Etx4+n96Rb2BsapaZd09obhzV1XZuXMnNWvWpH79+iGKzBSVkQFXX+1WyMrTsaO7sHvWWZGLy5h4VOEVuFR1noh0xs23A3CHqv4Q6gDDTURo0qRJpMOIWXldO3fcAbm5BeW/+AU89RSEaelQY0wF+J3Y9nzcmX6e98IQi4lS+/a5YZpvvFFQlpICzz8PP/1p5OIyxpTMz6ieycB44CtvGy8ivwt3YKGkqnTr1o3LL7+co0ePRjqcmLJmjVsMJTDpd+oEy5db0jemuvJzxn8ZkK6qxwFE5GVgOTApnIGF0s6dO8nIyKB+/frUsNU7QuaNN2DMGNi/v6BszBg3uZp17RhTffldmrpBwPOouzJqQzlDKzcXxo93M2jmJf3atWHaNDfXjiV9Y6o3P6e/vwOWi8gi3J24vYmis30oGMp56qmnRjiS6Pf9964L5+OPC8patXJDNzt0iFxcxhj//IzqeUNEFgPdcIl/gqp+H+7AQsnO+EPjs8/gyisLL5YydKg7069XL2JhGWPKKdjsnJ2LFOUteX2KiJyiqsvCF1ZoWeKvHFX4619d907eUM2EBHjkEZgwwWbUNCbaBDvj/32QrynQL8SxhI0l/oo7dAjGjYMXXywoa9QIpk+H/v0jF5cxpuKCzc7ZtyoDCafu3buTk5NDenp6pEOJKlu2wLBh8PnnBWWdOsGsWZCWFrGwjDGV5GfKhjrAr4DTVHWsiLQCWqtqld3EZYutV73PPnNJ//uAqzk33OC6fGrXjlxcxhj/Spuywc9wzpeAI7i7d8H19T8cwthMNfP883DhhQVJPzERpkxxF3Et6RsT/fwk/jO8JRhzAVT1IKUvsFLtHD9+nEWLFrF27dpIh1Lt5ea6/vwxYwou4jZuDPPnuwu7dhHXmNjgZxz/ERGpjTcVs4icARwOa1QhtGPHDvr160eTJk3YsWNHpMOptn74Aa66ChYvLijr2BFmz7ZlEY2JNX4S//3APKC5iLyGW0t3VBhjCikb0VO21ath0CD49tuCsp/+1I3kqVs3cnEZY8Ij2Dj+Z4HXVXW+iGTipmUWYHw0TctsiT+4d96B665zM2zmefhhuOsu69oxJlYFO+NfB/xeRFKBN4E3VDWrSqIKIUv8JVOFRx+Fe+4pKEtOhldfhcGDIxeXMSb8Sr24q6pPq2oP4ELgR+AlEVkjIveJSNSspWSJv7iDB93at4FJv2VLN4TTkr4xsa/MUT2qulFVH1PVTsC1wFBgTdgjCxFL/IVt3Qp9+hSeP79PH1i6FNq1i1RUxpiq5GchlpoicoV3Yff/gK+B4WGPLEQs8RdYtgy6dYMvvigo+/nP3XDNxo0jF5cxpmoFu7jbHxgBXA58AUzHLbK+v7Q61dG0adPIzs6mRYsWkQ4lombOhOuvd908UHBT1rhxdhHXmHgT7OLuXcDrwK9V9ccqiifkGjduTOM4Pp1VdbNo3ntvQVn9+vD22zbJmjHxKi4maYtXhw7B6NHw+usFZa1awdy50Lp15OIyxkSW36UXo9K2bdsYOHAgEyZMiHQoVW7bNujbt3DS79cP/v1vS/rGxLuYXnl806ZNvP/++/lLL8aLlSvhiitg06aCsrFj4dlnoWbNyMVljKkeYvqMPx5H9Lz3HvTsWZD0ExLgD39w0ylb0jfGQIyf8W/evBmIj8Sv6hL8r3/tngOkpLiVsi67LLKxGWOql5hO/PFyxp+bC7fcAlOnFpS1aOHO/u2mLGNMURHp6hGRS0RkrYisF5GJ4TpOPCT+XbvgkksKJ/3zz3c3aVnSN8aUpMrP+EUkEfgT0B+3mtdSEXlXVb8K5XE++ghmznSJ//HHT+G550L57tXH5s2Fl0ccOdKtoJWUFLmYjDHVWyS6es4F1qvqNwAiMh0YDIQ08e/aBXv3dgWOsn59fKwk8tBDcPfddieuMSa4SCT+U4HvAl5nA+cV3UlExgJjAU477bQKHio+lgZOSYEXXnAraBljTFkikfhLOh/VYgWqU4GpAF27di329bJcdJGbcTIetGljK2UZY/yLROLPBpoHvG4GbAn1QRo1cpsxxpjCIjGqZynQSkRaikgt4Brg3QjEYYwxcUlUy92LUvmDilwGTAESgRdV9ZEy9t8BbKzg4ZoAUbNGsA+x1J5YagtYe6qzWGoL+G9PC1VtWrQwIom/KolIhqp2jXQcoRJL7YmltoC1pzqLpbZA5dsT03P1GGOMKc4SvzHGxJl4SPxTy94lqsRSe2KpLWDtqc5iqS1QyfbEfB+/McaYwuLhjN8YY0wAS/zGGBNnYjrxV9X0z+EiIi+KyHYRWR1Q1khEPhSRdd5jw0jG6JeINBeRRSKyRkS+FJHxXnnUtUdEkkTkCxFZ4bXlAa886toSSEQSRWS5iLznvY7a9ojIBhFZJSJZIpLhlUVle0SkgYjMEJH/eH8/PSrblphN/AHTP18KnAOMEJFzIhtVuU0DLilSNhFYoKqtgAXe62hwFPhfVW0DdAfGeT+PaGzPYaCfqnYE0oFLRKQ70dmWQOOBNQGvo709fVU1PWC8e7S252lgnqqeDXTE/Ywq1xZVjckN6AF8EPB6EjAp0nFVoB1pwOqA12uBVO95KrA20jFWsF3v4NZkiOr2AHWAZbgZZqO2Lbg5sxYA/YD3vLJobs8GoEmRsqhrD1AP+BZvIE6o2hKzZ/yUPP3zqRGKJZROUtWtAN7jiRGOp9xEJA3oBHxOlLbH6xbJArYDH6pq1LbFMwW4EzgeUBbN7VFgvohkelO8Q3S253RgB/CS1w33vIjUpZJtieXE72v6Z1O1RCQZmAncrqp7Ix1PRanqMVVNx50pnysiUbvQpYgMBLaramakYwmhnqraGdfVO05Eekc6oAqqAXQG/qKqnYD9hKCLKpYTf5VM/xwB20QkFcB73B7heHwTkZq4pP+aqs7yiqO2PQCquhtYjLsWE61t6QkMEpENwHSgn4i8SvS2B1Xd4j1uB2bjVv6LxvZkA9nef5QAM3AfBJVqSywn/lid/vld4Ebv+Y24vvJqT0QEeAFYo6pPBXwp6tojIk1FpIH3vDbwE+A/RGFbAFR1kqo2U9U03N/JQlW9jihtj4jUFZGUvOfAxcBqorA9qvo98J2ItPaKLsItU1u5tkT64kWYL4xcBnwN/Be4O9LxVCD+N4CtQC7uk3800Bh3EW6d99go0nH6bMsFuK62lUCWt10Wje0BOgDLvbasBu7zyqOuLSW0rQ8FF3ejsj24fvEV3vZl3t9+FLcnHcjwft/mAA0r2xabssEYY+JMLHf1GGOMKYElfmOMiTOW+I0xJs7UiHQAfjRp0kTT0tIiHYYxxkSVzMzMH7SENXejIvGnpaWRkZER6TCMMSaqiMjGksqjIvEbHw4fhqNH/e1bsybUqlW47NAhOHbMX/1atdx7BDp4EI4fL3n/ok44AWoU+dU7cAD8jjBLSoLExMJl+/f7qwtQuzYkBPRyqrrj+1WnDkjAjeHHj7v2+1W3buHXR4+6n58fIu74gXJz4cgRf/UTE933L9CRI+49/KhRw/38Atnvnr+6UP7fvZK+X6EQ6TGqfrYuXbqoKcMtt6i6X6Oyt4kTi9cfPtx//WeeKV6/Rw//9d9+u3j9tDT/9f/1r+L1a9XyX/+bbwrX/eEH/3VB9dChwvVXrfJft1Gj4rF/8IH/+m3bFq8/bZr/+v37F6//6KP+699wQ/H69rsXvt+9CROKH68cgAzV4jnVLu4aY0ycsa6eWFGrVvEugNIU/VcZ3L/AfusX/VcZ3L/AfusX/VcZ3L/AfusnlHC+UqdOyXGVREqYv8/vsUt7P7/1S9ovMdF//dq1i5fVqOG/ftFuGnC/D0Hq5zZoQPZdd3Ho9NMhJQXWrCm8w4gRMHCgv+PXq1e8/vjxMGaMv/oNGxav/+ij/rvKmjQpXv/55/13VdWpU7z+3Lnu/NyPffsK1z92DObNK33/kr5fJUhKSqJZs2bULOlvuwRRcedu165d1S7uGhMZ3377LSkpKTRu3Bgp6UPTRJSqsnPnTnJycmjZsmWhr4lIphYsRJPPzvij2cKF7qJc/frQvn3xi4bGhMChQ4dIS0uzpF9NiQiNGzdmx44dvutY4o9m48fDam853qws6NgxouGY2GVJv3or78/HLu5Gsz17Cp7Xrx+5OIwxUcUSfzTbG7CAlSV+E8O2bdvGtddey+mnn06XLl3o0aMHs2fPrvT79unTh9atW9OxY0d69uzJ2rVrfde9//77efLJJyu8z5QpU3jllVcAmDBhAh06dOCGG27I//rf//53nn766fzXq1atYtSoUb7jC8YSf7Q6frxw4k9JiVwsxoSRqjJkyBB69+7NN998Q2ZmJtOnTyc7Ozsk7//aa6+xYsUKbrzxRn7zm9+E5D3LcvToUV588UWuvfZa9uzZw6effsrKlSs5duwYq1at4uDBg0ybNo1f/vKX+XXat29PdnY2mzZtqvTxLfFHq337CoaQ1a3rfyijMZV1//1uCKufbezY4vXHji28z/33Bz3cwoULqVWrFj//+c/zy1q0aMGtt94KwIYNG+jVqxedO3emc+fOfPrppwBs3bqV3r17k56eTrt27fj444+DHqd3796sX78egCeeeIJu3brRoUMHfvvb3+bv88gjj9C6dWt+8pOfFPrv4G9/+xvdunWjY8eODB8+nANl3Am+cOFCOnfuTI0aNUhISODIkSOoKgcPHqRmzZo88cQT3HbbbcWGZ15xxRVMnz496Hv7YYk/Wlk3j4kTX375JZ07dy716yeeeCIffvghy5Yt48033+S2224D4PXXX2fAgAFkZWWxYsUK0tPTgx5n7ty5tG/fnvnz57Nu3Tq++OILsrKyyMzMZMmSJfn/aSxfvpxZs2axdOnS/LrDhg1j6dKlrFixgjZt2vDCCy8EPda//vUvunTpAkBKSgrDhw+nU6dOtGzZkvr167N06VIGDx5crF7Xrl3L/ADzw04To1Xghd169SIXhzFVbNy4cXzyySfUqlWLpUuXkpubyy233EJWVhaJiYl8/fXXAHTr1o2bbrqJ3NxchgwZUmriHzlyJLVr1yYtLY0//vGPPP3008yfP59OnToBsG/fPtatW0dOTg5Dhw6ljnez26BBg/LfY/Xq1dxzzz3s3r2bffv2MWDAgKBt2Lp1K23atMl/feedd3LnnXcCcPPNN/Pggw/y/PPPM3/+fDp06MA999wDuA+5LVu2VOwbF8DO+KOVjegxkXL//f5nNpo6tXj9qVML71NGV0/btm1ZtmxZ/us//elPLFiwIH/c+h/+8AdOOukkVqxYQUZGBke8Cet69+7NkiVLOPXUU7n++uvzL6QW9dprr5GVlcWcOXNo3rw5qsqkSZPIysoiKyuL9evXM3r0aKD0YZOjRo3i2WefZdWqVfz2t7/l0KFDQdtUu3btEvdZvnw5AGeddRavvPIKb731FqtXr2bdunWAu6eidkl3b5eTJf5oZV09Jk7069ePQ4cO8Ze//CW/LLAPfc+ePaSmppKQkMDf//53jnkzfW7cuJETTzyRMWPGMHr06EIfHsEMGDCAF198kX379gGwefNmtm/fTu/evZk9ezYHDx4kJyeHuXPn5tfJyckhNTWV3NxcXnvttTKP0aZNm/zrCYHuvfdeHnzwQXJzc/PbkZCQkN/er7/+mnbt2vlqRzDW1ROtrKvHxAkRYc6cOdxxxx08/vjjNG3alLp16/LYY48B8Mtf/pLhw4fz9ttv07dvX+p6d7AvXryYJ554gpo1a5KcnFzqGX9RF198MWvWrKFHjx4AJCcn8+qrr9K5c2euvvpq0tPTadGiBb169cqv89BDD3HeeefRokUL2rdvT05OTtBjXHrppVx//fWFyubMmUO3bt045ZRTAOjRowft27enQ4cOdPRuzly0aBGXX365r3YEY3P1RKt//AMeeMB9AAwcCGWMJzamotasWVOoP9qExtChQ3n88cdp1aqVr/0PHz7MhRdeyCeffEKNEkbxlfRzithcPSKSCGQAm1V1oIg0At4E0oANwE9VdVe444g5l13mNmNMVJo8eTJbt271nfg3bdrE5MmTS0z65VUVffzjgcB5RScCC1S1FbDAe22MMXGldevW9O7d2/f+rVq1ok+fPiE5dlgTv4g0Ay4Hng8oHgy87D1/GRgSzhiMMZUXDV3C8ay8P59wn/FPAe4EAhfEPElVtwJ4jyeWVFFExopIhohklGe6UWNMaCUlJbFz505L/tVU3nz8SUXXUg4ibH38IjIQ2K6qmSLSp7z1VXUqMBXcxd3QRhcDZs2CbdvciJ5+/SA1NdIRmRjVrFkzsrOzyzXfu6laeStw+RXOi7s9gUEichmQBNQTkVeBbSKSqqpbRSQV2B7GGGLXs8/CokXu+YcfWuI3YVOzZs1iKzuZ6Ba2rh5VnaSqzVQ1DbgGWKiq1wHvAjd6u90IvBOuGGKa3blrjKmgSNy5OxnoLyLrgP7ea1NedgOXMaaCSu3qEZFfBauoqk/5PYiqLgYWe893Ahf5rWtKYVM2GGMqKFgfv63sUZ1ZV48xpoJKTfyq+kBVBmLK4dAh8GYgpGZNKMcwLmOMKXNUj4gkAaOBtrjROQCo6k1hjMsEE9jNU6+eW8XIGGN88nNx9+/AycAA4J9AMyD41HMmvKybxxhTCX4S/5mqei+wX1Vfxk3B0D68YZmgLPEbYyrBT+LP9R53i0g7oD5uZk0TKTaU0xhTCX7u3J0qIg2Be3E3XyUD94U1KhNc48ZwzTXuA6BDh0hHY4yJMrYQizHGxKhyL8QSyhu4jDHGVB9+buBqDXTDdfMAXAEsCWdQxhhjwqfMG7hEZD7QWVVzvNf3A29XSXTGGGNCzs/F3dOAIwGvj2CjeiLr1VdhxQo3lHPIEGjXLtIRGWOiiJ/E/3fgCxGZDSgwFHglrFGZ4ObOhbfecs/PPNMSvzGmXMpM/Kr6iIj8H9DLK/qZqi4Pb1gmKBvHb4ypBL/z8dcB9qrq00C2iNhyPJFkUzIbYyqhzMQvIr8FJgCTvKKawKvhDMqUwaZsMMZUgp8z/qHAIGA/gKpuwebqjyzr6jHGVIKfxH9E3e29CiAidcMbkimTnfEbYyrBT+J/S0SeAxqIyBjgI+Bv4Q3LlOrYMdi3r+B1cnLkYjHGRCU/o3qeFJH+wF7cXbz3qeqHYY/MlCwnYCmElBRITIxcLMaYqBRsrp5WwJPAGcAq4NequrmqAjOlsG4eY0wlBevqeRF4DxgOZAJ/rJKITHBFl100xphyCjpJm6rm9eWvFZFlVRGQKUPDhjBpkvsAaNo00tEYY6JQsMSfJCKdgLyVvGsHvlZV+yCIhGbN4NFHIx2FMSaKBUv8W4HAOfe/D3itQL9wBWWMMSZ8gk3L3LcqAzHGGFM1/M7VY4wxJkaELfGLSHMRWSQia0TkSxEZ75U3EpEPRWSd99gwXDHEpJdegiuvhNGj4UO7ncIYU37hPOM/CvyvqrYBugPjROQcYCKwQFVbAQu818avjAyYORNefBH+859IR2OMiUJ+ZufsmTc/j4hcJyJPiUiLsuqp6ta8kT/eso1rgFOBwcDL3m4vA0MqGHt8snH8xphK8nPG/xfggIh0BO4ENlLOFbhEJA3oBHwOnKSqW8F9OAAnllJnrIhkiEjGjh07ynO42GZ37hpjKslP4j/qzc45GHjaW4zF97TMIpIMzARuV9W9Ze2fR1WnqmpXVe3a1G5UKmCJ3xhTSX4Sf46ITAKuA94XkUTcYixlEpGauKT/mqrO8oq3iUiq9/VUYHv5w45j1tVjjKkkP4n/auAwMFpVv8f10z9RViUREeAFYI2qBt4I9i5wo/f8RuCdckUc7+yM3xhTSX6mZQ68YxdV3YS/Pv6ewPXAKhHJ8sruAibj5vgfDWwCripnzPHN1ts1xlRSmYlfRLrjZuZsA9QCEoF9qho066jqJxTM81PUReWM0wCo2rKLxphK89PV8ywwAlgH1AZuBv4UzqBMKQ4ehKNH3fMTTnCbMcaUU5ln/ACqul5EElX1GPCSiHwa5rhMSaybxxgTAn4S/wERqQVkicjjuFk7bcH1SKhbF/72N9fdY0suGmMqyE/ivx7XJXQLcAfQHLcql6lqKSlw882RjsIYE+X8jOrZ6D09BDwQ3nCMMcaEW6kXd0VksIiMC3j9uYh8421XVk14xhhjQi3YqJ47cTdb5TkB6Ab0AX4RxpiMMcaEUbDEX0tVvwt4/Ymq7vRu4LKLu5EwbRp06QJ9+8Lzz0c6GmNMlArWx19ogRRVvSXgpc2aFgkbNsAyb437Xr0iGooxJnoFO+P/XETGFC0Ukf8BvghfSKZUNkGbMSYEgp3x3wHMEZFrAe80ky64vv4hYY7LlMQmaDPGhECpiV9VtwPni0g/oK1X/L6qLqySyExxlviNMSHgZxz/QsCSfXVgE7QZY0IgnIutm1CzuXqMMSFgiT+aWFePMSYELPFHE+vqMcaEgCX+aGJdPcaYELDEHy1yc+HAAfc8IQGSkyMbjzEmavlaiMVUAwkJsGCB6+45cACktFUtjTEmOEv80SIxEfr1i3QUxpgYYF09xhgTZyzxG2NMnLHEb4wxccYSf7R4/XVo0ABatIAJEyIdjTEmitnF3Wixa5cb0ZO3GWNMBdkZf7Swm7eMMSFiiT9a2Dw9xpgQiUjiF5FLRGStiKwXkYmRiCHqWOI3xoRIlffxi0gi8CegP5ANLBWRd1X1q7AccM0aOHTI375nnFF88rOVK+HYMX/1zz4batcueH38OKxY4a8uQPv2UCPgR3L4MHzlfVs2biwotwnajDGVEImLu+cC61X1GwARmQ4MBsKT+K+8siB5lmX+fOjfv3DZhRfC7t3+6q9eDW3bFrw+cgQ6d/ZXF+DHH6FhwBr3mzeXXN/O+I0xlRCJrp5Tge8CXmd7ZYWIyFgRyRCRjB07dlRZcFGhZctIR2CMiWKROOMvaXYxLVagOhWYCtC1a9diX/ft7LOhVi1/+6akFC9r3x5ycvzVT0oq/FoE0tP91QU3H0+gWrUK109MhOHDXUzGGFNBkUj82UDzgNfNgC1hO9rMmZWrv2RJxeuecAIsX17x+s2aVa6+McaUIBJdPUuBViLSUkRqAdcA70YgDmOMiUtVfsavqkdF5BbgAyAReFFVv6zqOIwxJl6JasW7z6uKiOwANpa5Y8maAD+EMJxIi6X2xFJbwNpTncVSW8B/e1qoatOihVGR+CtDRDJUtWuk4wiVWGpPLLUFrD3VWSy1BSrfHpuywRhj4owlfmOMiTPxkPinRjqAEIul9sRSW8DaU53FUlugku2J+T5+Y4wxhcXDGb8xxpgAlviNMSbOxHTij/Z5/0XkRRHZLiKrA8oaiciHIrLOe2wY7D2qCxFpLiKLRGSNiHwpIuO98qhrj4gkicgXIrLCa8sDXnnUtSWQiCSKyHIRec97HbXtEZENIrJKRLJEJMMri8r2iEgDEZkhIv/x/n56VLYtMZv4A+b9vxQ4BxghIudENqpymwZcUqRsIrBAVVsBC7zX0eAo8L+q2gboDozzfh7R2J7DQD9V7QikA5eISHeisy2BxgNrAl5He3v6qmp6wHj3aG3P08A8VT0b6Ij7GVWuLaoakxvQA/gg4PUkYFKk46pAO9KA1QGv1wKp3vNUYG2kY6xgu97BLcYT1e0B6gDLgPOiuS24yRIXAP2A97yyaG7PBqBJkbKoaw9QD/gWbyBOqNoSs2f8+Jz3PwqdpKpbAbzHEyMcT7mJSBrQCficKG2P1y2SBWwHPlTVqG2LZwpwJ3A8oCya26PAfBHJFJGxXlk0tud0YAfwktcN97yI1KWSbYnlxO9r3n9TtUQkGZgJ3K6qeyMdT0Wp6jFVTcedKZ8rIu0iHFKFichAYLuqZkY6lhDqqaqdcV2940Skd6QDqqAaQGfgL6raCdhPCLqoYjnxV+28/1Vnm4ikAniP2yMcj28iUhOX9F9T1VlecdS2B0BVdwOLcddiorUtPYFBIrIBmA70E5FXid72oKpbvMftwGzckq/R2J5sINv7jxJgBu6DoFJtieXEH6vz/r8L3Og9vxHXV17tiYgALwBrVPWpgC9FXXtEpKmINPCe1wZ+AvyHKGwLgKpOUtVmqpqG+ztZqKrXEaXtEZG6IpKS9xy4GFhNFLZHVb8HvhOR1l7RRbj1ySvXlkhfvAjzhZHLgK+B/wJ3RzqeCsT/BrAVyMV98o8GGuMuwq3zHhtFOk6fbbkA19W2EsjytsuisT1AB2C515bVwH1eedS1pYS29aHg4m5UtgfXL77C277M+9uP4vakAxne79scoGFl22JTNhhjTJyJ5a4eY4wxJbDEb4wxccYSvzHGxBlL/MYYE2cs8RtjTJyxxG9ikog09mZmzBKR70Vks/d8n4j8OUzHvF1Ebgjh+00XkVahej9j8thwThPzROR+YJ+qPhnGY9TATdbWWVWPhug9LwSuU9UxoXg/Y/LYGb+JKyLSJ2C++ftF5GURme/N3z5MRB735nGf500xgYh0EZF/ehN+fZB3q3wR/YBleUlfRG4Tka9EZKWITPfK6opbY2GpN+HWYK88UUSe9I67UkRu9d7zY+An3oeKMSFjv1Am3p0B9MWt2fAZMFxV7xSR2cDlIvI+8EdgsKruEJGrgUeAm4q8T08gcJKziUBLVT2cN70DcDduOoSbvLIvROQj4AagJdBJVY+KSCMAVT0uIutxc7DH0gRqJsIs8Zt493+qmisiq4BEYJ5Xvgq3FkJroB3woZtuiETcNBpFpVJ4EZOVwGsiMgd3mz24OWMGicivvddJwGm4uX7+mvffgqr+GPA+24FTsMRvQsgSv4l3hyH/7DpXCy56Hcf9fQjwpar2KON9DuISeZ7Lgd7AIOBeEWnrvddwVV0bWNGbwK60i21J3nsbEzLWx29McGuBpiLSA9zU0l4SL2oNcKa3TwLQXFUX4RY3aQAkAx8At3qJHhHp5NWdD/w8ry8/r6vHcxZuojFjQsYSvzFBqOoR4ErgMRFZgZtV9PwSdv0/3Bk+uO6gV73uo+XAH9TN2/8QUBNYKSKrvdcAzwObvPIVwLUAInIScFC9lZaMCRUbzmlMiHgXhO9U1XUher87gL2q+kIo3s+YPHbGb0zoTMRd5A2V3cDLIXw/YwA74zfGmLhjZ/zGGBNnLPEbY0ycscRvjDFxxhK/McbEGUv8xhgTZ/4fYAUXWor1qHwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import odeint\n",
    "from IPython import display\n",
    "\n",
    "# animate plots?\n",
    "animate=True # True / False\n",
    "\n",
    "# define model\n",
    "def vehicle(v,t,u,load):\n",
    "    # inputs\n",
    "    #  v    = vehicle velocity (m/s)\n",
    "    #  t    = time (sec)\n",
    "    #  u    = gas pedal position (-50% to 100%)\n",
    "    #  load = passenger load + cargo (kg)\n",
    "    Cd = 0.24    # drag coefficient\n",
    "    rho = 1.225  # air density (kg/m^3)\n",
    "    A = 5.0      # cross-sectional area (m^2)\n",
    "    Fp = 30      # thrust parameter (N/%pedal)\n",
    "    m = 500      # vehicle mass (kg)\n",
    "    # calculate derivative of the velocity\n",
    "    dv_dt = (1.0/(m+load)) * (Fp*u - 0.5*rho*Cd*A*v**2)\n",
    "    return dv_dt\n",
    "\n",
    "tf = 60.0                 # final time for simulation\n",
    "nsteps = 61               # number of time steps\n",
    "delta_t = tf/(nsteps-1)   # how long is each time step?\n",
    "ts = np.linspace(0,tf,nsteps) # linearly spaced time vector\n",
    "\n",
    "# simulate step test operation\n",
    "step = np.zeros(nsteps) # u = valve % open\n",
    "step[11:] = 50.0       # step up pedal position\n",
    "# passenger(s) + cargo load\n",
    "load = 200.0 # kg\n",
    "# velocity initial condition\n",
    "v0 = 0.0\n",
    "# set point\n",
    "sp = 25.0\n",
    "# for storing the results\n",
    "vs = np.zeros(nsteps)\n",
    "sps = np.zeros(nsteps)\n",
    "\n",
    "plt.figure(1,figsize=(5,4))\n",
    "if animate:\n",
    "    plt.ion()\n",
    "    plt.show()\n",
    "\n",
    "# simulate with ODEINT\n",
    "for i in range(nsteps-1):\n",
    "    u = step[i]\n",
    "    # clip inputs to -50% to 100%\n",
    "    if u >= 100.0:\n",
    "        u = 100.0\n",
    "    if u <= -50.0:\n",
    "        u = -50.0\n",
    "    v = odeint(vehicle,v0,[0,delta_t],args=(u,load))\n",
    "    v0 = v[-1]   # take the last value\n",
    "    vs[i+1] = v0 # store the velocity for plotting\n",
    "    sps[i+1] = sp\n",
    "\n",
    "    # plot results\n",
    "    if animate:\n",
    "        display.clear_output(wait=True)\n",
    "        plt.clf()\n",
    "        plt.subplot(2,1,1)\n",
    "        plt.plot(ts[0:i+1],vs[0:i+1],'b-',linewidth=3)\n",
    "        plt.plot(ts[0:i+1],sps[0:i+1],'k--',linewidth=2)\n",
    "        plt.ylabel('Velocity (m/s)')\n",
    "        plt.legend(['Velocity','Set Point'],loc=2)\n",
    "        plt.subplot(2,1,2)\n",
    "        plt.plot(ts[0:i+1],step[0:i+1],'r--',linewidth=3)\n",
    "        plt.ylabel('Gas Pedal')    \n",
    "        plt.legend(['Gas Pedal (%)'])\n",
    "        plt.xlabel('Time (sec)')\n",
    "        plt.pause(0.1)    \n",
    "\n",
    "if not animate:\n",
    "    # plot results\n",
    "    plt.subplot(2,1,1)\n",
    "    plt.plot(ts,vs,'b-',linewidth=3)\n",
    "    plt.plot(ts,sps,'k--',linewidth=2)\n",
    "    plt.ylabel('Velocity (m/s)')\n",
    "    plt.legend(['Velocity','Set Point'],loc=2)\n",
    "    plt.subplot(2,1,2)\n",
    "    plt.plot(ts,step,'r--',linewidth=3)\n",
    "    plt.ylabel('Gas Pedal')    \n",
    "    plt.legend(['Gas Pedal (%)'])\n",
    "    plt.xlabel('Time (sec)')\n",
    "    plt.show()"
   ]
  }
 ],
 "metadata": {
  "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}