state-space.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Open-loop poles = [1.         1.         0.46195118 0.87279415]\n",
      "Open-loop zeroes = [-0.77390768+0.j -0.95566712+0.j]\n",
      "Closed-loop poles = [0.07939405 0.58859207 0.85019422 0.84361883]\n",
      "Closed-loop zeroes = [-0.77390768+0.j -0.95566712+0.j]\n",
      "Observer poles = [6.57215245e-01 4.21323851e-01 3.99997056e-06 3.99997069e-06]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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cV155hfr6embOnMmSJUsAuP/++3nmmWdISkpi6NChjBs3rlVP4dVXX2XJkiU4nU5iYmLYuHEjZ599NnV1dSQnJ5OVlcWwYcO44447cLvdhIWF8dRTTzFs2LBW6TIzM/nJT35CTk4OjY2N3HvvvcyYMaPV+9q1a1erv6WIbFfV8a0St6DdnoKqPtqiwInAJcAA/3kFe2Pzls4CBoOhE9w1FZQXHqSqKI+6sjwaKw6j1YW4agsIa15UVUq43bL352tlH8/h8PM4EJYEUYNwRg8mNCGZqMSUZmU/1NH1vbSWvPEfdh7uWR+SkUOi+fX153eYpq6ujtGjRzefZ2VlMXXqVNauXcvu3bsRESoqKoiNjWX69OnNRqAtUlNTyc7O5s4772TevHl89NFHuN1u0tPTmT9/PqGhoaxdu5bo6GhKSkq4+OKLmT59OsuWLSMnJ6e5x7JhwwZyc3PZunUrqsr06dPZvHkzERERvPTSS2RnZ+PxeBg7dizjxo1rJcfSpUt59913SU5OpqKiguDgYJYuXcq2bdt45JFHAKiqquLDDz/E5XKxceNGFi1axJo1a1qlW7RoEZdffjmrV6+moqKCiy66iKlTpxIR0XLZXfcJZE7h91h7vYYBP8LqdU4CPreTVAFt/1UMhtMQ99FKygsOUmW37BvLD0NNAa6jhYTVFxPVaLXsI3AzGBjsl7dOgyl1xFPpSqAg7BwO2itoHdGDCItPIWpACnEDU4mNje+Wsu/vtDV85PF4CA0N5ZZbbiEzM5PMzMyAypo+fToAo0aNoqamhqioKKKioggJCaGiooKIiAgWLVrE5s2bcTgc5OfnU1hY2KqcDRs2sGHDBsaMGQNATU0Nubm5VFdXM3PmTMLDw4+pryWTJk1i3rx53Hjjjcya1Xbgh8rKSubOnUtubi4iQmNjY5vpNmzYwPr163nggQcAy4344MGDPdrDC8T76CpVvdtel7AJ+CPwfItVzQbDKU99bSVlBYeoKj5IbWm+NUFbfQTX0SJCbWUf7yvtUNlXOS1lfyh8AL7IpmGcZCITU4gfdAYxMfGkOB2k9NVD2nTWoj+RuFwutm7dyvvvv89rr73GI488wgcffNBpvpCQEAAcDkfzcdO5x+Ph+eefp7i4mO3btxMUFERaWlqbq7lVlaysLG6//fZjrj/00EMByb9q1Sq2bNnCW2+9xbhx49i+fXurNIsXL2bKlCmsXbuW/fv3c9lll7VZlqqyZs0azj23wx0GjotAjEJTmt8AdwG/BdJEZL1/IlVt20waDP2c+toqyxun+BB1pfk0VBxupezjfGVEUtdK2bs1iFKJp9KVSGHY2RwKuwSNGoQrejAh8cnWmH3SUGLjEklxnnot+xNBTU0NtbW1TJs2jUmTJnHmmdbOv1FRUVRXV3e73MrKSpKSkggKCmLTpk0cOHCgzXKvvvpqFi9ezJw5c4iMjCQ/P5+goCAmT57MvHnzyMrKwuPx8MYbb7QyHAB79+5lwoQJTJgwgbfffptDhw61qqOyspLk5GQAnn766ebrbcmycuVKVq5ciYjw2WefNfdgeopAjMKbfmGu3weCgbOAB3tUEoOhh6mvraKs8BBVRbbrZeURtOoIrqOFXVD2CRSGnU1eWBK+yIG4YoYQGj+EiMShxA9MJTYukWSng+S+eshTjJZzCtdccw133HEHM2bMwO12o6r84Q/WkqjZs2dz6623smLFCl577bUu1zVnzhyuv/56Ro0axfjx4znvvPMASEhIYNKkSaSnp3PttdeyfPlydu3axcSJEwFrMvy5555j7Nix3HTTTWRkZJCUlMSFF17YZj0LFiwgNzcXVeWKK64gIyOD1NRUli1bxujRo8nKyuLuu+9m7ty53HfffVx33XXNeadMmXJMusWLF/Ozn/2MCy64AJ/Px7Bhw3jzzTe7/Owd0ZH30RBVPWwfxwOVquq1o5xGqWqBiMQBQ1X18zYL6QWM95Hha2XvP0FbgPOo5XoZ2VhKnK+UqDZCctVrECViTdDWhgygPiwJIgfhjLFb9gkpxA1KJTZuAI7TrGXflseK4eSkV7yPgP+1jcHfgHeAf9jX3wKm2/e2A0Ui8pGq/rztYgyGwGioq6G0eRjHWlSl1UdwHi0k1N3UsreUfcuWfb26mlv2xWHDyA+7GI0chDNmECFxyUQlDiV24FDi4pNMy95g6ICOXFKniUgocBkwE3hARA4CZwKxWAvY/qyqvxaRE9ZTMJx8NLprKCs4RGXRIWrL8mgs/7plH2q37ON9pURR266yr3LFW8o+dILtZz+YkNghRA4YStzAVOLikxjidLRy3TQYDF2jwzkFVXVj9RLeARCRYVg9hieBi4HjW09uOKnxuI9SXniIiuJD1Jbm01CeD1VHcNQWEeouIqqhhFhfGdEcZSDHbsDdoM7mln1JaBqHwy6ylH201bKPHDCU2KShxCcMNMreYDiBdCUgXjRQCfwKywvpJVX9RETOBHJ7ST5DH+BtcFNeeJDKojyOlubRUJ6Pr+oIrtpCguuKiWwsJs5bRgw1DAAG+OW1lH0cla5EikPPID/sQtv1cjChcdYEbezAocQnDGKw03FMr8BgMPQ9gSxeux1YghUAr2lWWlX1dvtgH2DWLJwE+BrrKS/Ko6LoEEdLD9FQdhhflTVmH+IuIqKhhDhvKbFUkwgk+uVtbFL2znjKQoZyJHQc3iZlHzuEyMShxAyyWvaDXS6j7A2Gk5RAegp3AemqWgIgIinAShEpsu9/CNyhqnm9JKOhE3yNDVSW5FNeeIijpXnUl+fjqzyC82gBwXXFRDQUE+stJZ4qEoAEv7wedVAqsVQ4EygPHkxBWAa+iEE47DH7iMQUq2U/YAiDXC4G9dVDGgyGE0IgRmEvUOt3/hTwAvBt+/y79rUre1Y0g3obqSw5QnnRQY4W5+Euz0erjiA1BQTXWS37WE8pcVpJnChxfnm9KpRJLOXOBCqCB1IUmo43YhCO6MEExyUTkZhMTFIqCQOGMDA46JjxfoOhr2gKne3xeBg2bBjPPvsssbGxHeZZsWIFjz/+OGPHjuX5558/QZKeugRiFLKAj0VkC1APjAZ2qepT9v2nReRnxyOEiFwDPIwVWO9/VXXZ8ZTX31Gvh+rSAsqLDlFdcoj6sny8VUdw1BQQXFtEeEOxrewriBXF/yfhU6FMoil3JFAVPICiyJH4IpKQaKtlH544lJiBQ0lIGsKA4JBjxvsNhv6Of+yjuXPn8uijj/LLX/6ywzyPPfYYGzduJCUlsOAgHo8Hl6s7OxGfHgTyZv4EfAD8G/ABVwDBItIUGfVmoLS7AtjlPIrV08gDPhGR9aq6s7tl9hXq81JTXkh54UGqi/NwNyn76gKC6woJqy8hxltKvK+caPER3SJ/KTGUO+KpCU6kJOJcPJEDcUQNIjg2mfDEZGKTUokfmEJiSMgx4/0Gw6nIxIkT+fzzr73d2wpfPX/+fPbt28e1117LD37wA2677bY2Q0s//fTT/OUvf6Gmpgav18vf//73Nsvbv38/1157LZdeeikff/wxycnJvP7664SFhbFnzx7mz59PcXExTqeTV199lbPOOqvdsNonK4EYhSD/hWki8jdgJVBgX/oI+P5xyHARsMeesEZEXgJmAH1uFNTno76uhqPVFdRVlXG07DB15QU0VhXiqynGUVtMsLuUsIZSYjwlxPvKiRIvUS3KKdMoyp0J1AQlUBZxFrkRAyFqMMGxgwlPSCEmaSgJA4eSEBZ2zHi/wdBnvL0QCv7ds2UOGgXXBjYI4PV6ef/997nllluA9sNXr1q1infeeYdNmzaRmJjYbmhpgE8//ZTPP/+c+Pj4dstLTU0lNzeXF198kSeffJIbb7yRNWvW8N3vfpc5c+awcOFCZs6cidvtxufztVvO5MmTe/bdnUACMQpvi8htwBtYw0fVwDxVLeshGZKBQ37necCEHiq7mf989Bb8/XcIPkS9ONSH4MOhXvvbh8M+D6aBMK0jQmsJFSW0jfK8KpRLNFWOWKpdCZRHjWOPreyDYocQnpBMzACrZR8fEUF8Tz+QwXAK0hT7KD8/nxEjRnDlldZUZXvhq1sq3/ZCSwNceeWVxMfHd1heamoqw4YNa46/NG7cOPbv3091dTX5+fnMnDkTgNDQ0C7JdTIRiFG42f7O8ssTLyK1WC6q/wTubGrp9wa2UboNrI0zuoPiw6kefOLA5wi2dqAVJyoOfOIEcaBiXfM6QvAGR6HBkRAchSMsCkdoDMExg4iIH0zMgCHExg8kMTjIDOMYTk0CbNH3NE1zCrW1tVx99dU8+uij/PSnP203fHVL2gstvWXLlmM2ommvvP379x8TZtvpdFJX1zqGVmflnMx0ahRUdZj/uYj8C1gEvGhfmm0fd7d1nw8M9TtPsa/5y/AE8IRdf7GIHOhmXYlASTfznsqY99I+p827ee+990Z5vV5PIGm9Xq/L6XQGlLYr+Hy+8JycnFqAn/zkJ4477rgjZPLkyXXDhw93rly5Mmj06NHuiIgICgoKJCgoSBMSEmhoaAjbuXNnXXx8PKNHjw6655575Fe/+lWDiLBz507HyJEjfQcPHnQVFxc7cnJyGgDaK6+urk7q6upCc3Jy6gAOHz7sqq2tlQMHDjTGxcWFPvTQQ41Tp0711tfX4/P5WpVz+PBhV0hIiCchoW8HggsKClwjR45sOf53RiB52zUKInKpqv6jjVvhqvqsvcI5VVWfE5EFXZC3JZ8Aw+0QGvlYRuY77SVW1W471IjItkCiBJ5umPfSPqfTu9mxY8f+9PT0gAxgTk7OiPT09F29IMaYpnLT09NZtWrV2R999FHZj370o7Li4uKk733ve4kA4eHhvueff/6r888/v15ERg0fPjx38ODBnocfflhuu+221G9961sRPp9Phg4dWr9p06Y9H3zwQUJISEhEenr6waay2yrP5XKpw+EY3iRDZGTkQMCZnp5++IUXXgi59dZbz3jsscdcQUFB+uqrr+6dP39+g385oaGhrhdffPHL888/v/WG2ScQr9eb2N3/245CZ/8Rq/X/DlY01GIgFFgIDAIasbbpHAHEAcsBujPXICLTgIewXFJXq+r9XS0jwHpOmx94VzDvpX1Op3ezY8eO/RkZGX1tFE5q+st72bFjR2JGRkZad/J2FCX1Tjs89rewFqoNBuqAS7AWs9UDK/yyzMaaYzizq0Ko6l+Bv3Y1n8FgMBh6ls6ipJZhRUR9sqsFi8hQ4M9YwTEVeEJVH26R5jLgdeAr+9JfVHVpV+vqAk/0YtknM+a9tI95N22QmJhY3Ncy9EdOhffSm8v6PMAvVPVTEYkCtovIe20sSvtQVTN7UY5m7AlrQwvMe2mf0+zd+Hw+nzgcjrbHlP0YNGjQaTH53lX6w3vx+XyCtdC4W/TafoOqekRVP7WPq4FdYDa8Mhj6MTnFxcUxtlIxnIT4fD4pLi6OAXK6W8YJCQAiImnAGGBLG7cnisgO4DBwl6r+p6OyEhMTNS0tradF7D6quKtL8bmrEfV8HVycThtbrYvC/BZ7npP4nfZr0fu1cD2C/y840KdVBEIiCYuKx+Hs0/hKZ9FCCW3fvr0kEO/NQPZT2A6sBl5Q1XIReV9Vr2iRptU1v3uRwBrgZ6pa1eL2p8AZqlpjeyCtA4a3UcYxi9e2bdvWmdgnhH3/eJXo9/+HRC2nQiMocabgxYmI9S/UlZ+NdMOIdLWOY+lufd3LF2jetlJ09xnFz7OuK1L39jP2JF2tryn1cT1jOx6LvUX3fxvt5+usxO7WGaZ1xFNJOT52p/+Ci2fdgTh6bUCmSwS6vqtdl1S/gs7Gim00G9iBFSV1HF//VqOBd1T1vDbyBgFvAu+q6h8CEHo/ML5p74a2GD9+vPa5UVAl58Vfkv7lo3wpaRRetIgLr5hFaHBQ38plMBj6FPX5yP3sb3jf/TUjGj7n45jruPDHzxAU1Pe6QUS2B+Je3akJU9U9qvpLrCB4k4BhWGsW9gKfYXkPPdKGAAL8H1aY7TYNgogMstMhIhfZ8nQ74uqJYteLC0n/8lE+DJ/KwJ9/xDeuvckYBIPBgDgcnDPucs69exPbhn6fSyrfYtvD38Hn7fa87wknoH6NiFwATAUqgM244CtMAAAgAElEQVRYxuE+oFxVM1S1lVGw03wPuFxEsu3PNBGZLyLz7TQ3ADn2nMIKYLZ21nXpY758bzUjvlzFpvCruejOl4iJiuxrkQwGQz/D4XIx/paH2D5sPhNrNrD56Y73hOhPBDJ8tB3LGJwJnAf8U1XH2vf+oqqzel1KP/py+Kh8/+eEPX0FXziHc+bPNxIVEd4ncpyMNDY2kpeXh9vt7mtRDMdBaGgoKSkp/WI45GRAfT4+X3EDo8o/4NMpzzL+suv7TJZAh48CMQpnquo+EXkPa37mQqywF/5bdKKq049D3oDpK6OgXg/7fj+JeHc+JXP/zvAzzzrhMpzMfPXVV0RFRZGQkNA8EW84uVBVSktLqa6uZtiwYZ1nMABQX1tF6QMX4fP5iLhjC3FxcZ1n6gV6bE4BeM3+vg64Byti5FDgwRafU5rdbzzIWfW7+ez8LGMQuoHb7TYG4SRHREhISDC9vS4SEh5Nw3UrGaJFfP7c3X0tTqd0FCX1POB8IEZE/IeIVgDzgU9UtbbNzKcYdZWlJGc/zDbXWCbPmt95BkObGINw8mP+ht0jbdyVZP/reiYWreHLnT/inJGj+1qkdumop3AukAnEAtf7fb4BhAO7AUQkQ0Qe62U5+wx30T7KnrieSK0l+Nrf4HI5O89k6Jc4nU5Gjx7d/Fm2rP2NZNatW8fOnV9HZLnnnnvYuHHjcctQUVHBY491/edy7733Nu8m1hnZ2dn89a+dx5cMNJ2hZzjrpt/SKEFUvJ5Ff/an6ShK6uvA6yIyUVX/CSAiocC/gQ+AWSLyZ6zl1FeeCGH7guDHxpKM8nH4ZVwy7tK+FsdwHDTt6hUI69atIzMzk5EjRwKwdGnPxGlsMgo//OEPe6S8tsjOzmbbtm1MmzatR9IZeoaoxBQ+O/sHXLTnMXZs20zGhd/sa5HapN2egog0DX59R0RWiMgW4CAwBCuGUSnwClbguyQRec92XT1lqC46gMNe2RiR2StbPBj6AQsXLmTkyJFccMEF3HXXXXz88cesX7+eBQsWMHr0aPbu3cu8efN47TVrei0tLY2srCxGjx7N+PHj+fTTT7n66qs566yzWLVqFWDt1XvFFVcwduxYRo0axeuvv95c1969exk9ejQLFlh7Uy1fvpwLL7yQCy64gF//+tfNct1///2cc845XHrppXzxxRdtyv7qq6+Snp5ORkYGkydPpqGhgXvuuYeXX36Z0aNH8/LLL7N161YmTpzImDFjuOSSS/jiiy/aTHf06FF+8IMfcNFFFzFmzJhmmQ09x4gZC6ghHPf7y/talHbpKMxF00YRTa4+HuAx4MdYu6UlAe9iuam+DfwU6N4Gyv2Ufe8+TgawbcYmxp+f3tfinDIseeM/7DzcMuLJ8TFySDS/vv78DtM0bQrfRFZWFlOnTmXt2rXs3r0bEaGiooLY2FimT59OZmYmN9xwQ5tlpaamkp2dzZ133sm8efP46KOPcLvdpKenM3/+fEJDQ1m7di3R0dGUlJRw8cUXM336dJYtW0ZOTk5zj2XDhg3k5uaydetWVJXp06ezefNmIiIieOmll8jOzsbj8TB27FjGjRvXSo6lS5fy7rvvkpycTEVFBcHBwSxdupRt27bxyCPW8qGqqio+/PBDXC4XGzduZNGiRaxZs6ZVukWLFnH55ZezevVqKioquOiii5g6deoxexsbjo/QqHiy027mwq9Wk7PjE9IzLuxrkVrR0fDRG/b3M/7XReQt4GGs3kI+sAH4ob33QlHviXpiUW8jQ/a9yqdBYxg3ekxfi2PoAdoaPvJ4PISGhnLLLbeQmZlJZmZgUdynT7c8sEeNGkVNTQ1RUVFERUUREhJCRUUFERERLFq0iM2bN+NwOMjPz6ewsLBVORs2bGDDhg2MGWP9j9XU1JCbm0t1dTUzZ84kPDz8mPpaMmnSJObNm8eNN97IrFltLxmqrKxk7ty55ObmIiI0Nja2mW7Dhg2sX7++ee7C7XZz8OBBRowYEdA7MQTGOTPupv7hZyl/7wHIeLmvxWlFIAHx3gO+raoV9qVRWKub8+38GVjzCkN6S8i+YO/H6zhbS9g96pfG46KH6axFfyJxuVxs3bqV999/n9dee41HHnmEDz74oNN8ISEhADgcjubjpnOPx8Pzzz9PcXEx27dvJygoiLS0tDZdOVWVrKwsbr/99mOuP/TQQwHJv2rVKrZs2cJbb73FuHHj2L59e6s0ixcvZsqUKaxdu5b9+/dz2WWXtVmWqrJmzRrOPffcgOo2dI/wuEFkD7yOCwveJP/IYZIH9y/VGcg6hQF+BgFgFVCDtU3n9VgeSv13Kr2bNGz5X4o1lrFTb+5rUQy9SE1NDZWVlUybNo0//vGP7NixA4CoqCiqq6u7XW5lZSVJSUkEBQWxadMmDhw40Ga5V199NatXr6ampgaA/Px8ioqKmDx5MuvWraOuro7q6mreeOONNuvZu3cvEyZMYOnSpQwYMIBDhw61qqOyspLkZGsrk6effrr5eluyrFy5stkz5rPPPuv28xs6ZvDUHxMqjXzxzp/6WpRWBGIUvCLiP1dQBVSq6leqekBVD3Acu/z0R0r2ZjOy5l/kDJ5FRHhYX4tj6CGa5hSaPgsXLqS6uprMzEwuuOACLr30Uv7wByt24+zZs1m+fDljxoxh7969Xa5rzpw5bNu2jVGjRvHnP/+Z886zgggnJCQwadIk0tPTWbBgAVdddRXf+c53mDhxIqNGjeKGG26gurqasWPHctNNN5GRkcG1117LhRe2Pfa8YMECRo0aRXp6OpdccgkZGRlMmTKFnTt3Nk8g33333WRlZTFmzBg8Hk9z3pbpFi9eTGNjIxdccAHnn38+ixcv7sZbNgTCwOHj2RNyPmcdeJn6dobz+opAwlxcg7VP7d+xwmVfibUPwp+BejvZnwLZvKEnOBFhLnasvJlzSjZSdtunJCcP7dW6Thd27dplxqZPEczfsmfY/e6TnPfPu/h40mouufJbvV5fT4bOfgcYizVcNAuIB64CngFeAl4GEo5L2n5EZcFXjCx5l63x1xuDYDAYeo1zpnyXasJxf/Is5Ucb+lqcZgLdEugSLHfUx4BCVXWqarD9CVLV/rG1UA/w1br7EZTkaXf1tSgGg+EUxhEcxr6kq7m8YROfLLsGn69/TM12qsxFZBlwB7DT/oiIPNHbgvUFpQd2cv6Rv/Bx7HWcPXxkX4tjMBhOcRIvnQvAVc7t/GtT/1gsGEgLfxpwpaquVtXVWBPN/y0iX4jI5yLybxH5vHfFPDEc/stCGnAx7Fu/6WtRDAbDaUDyqMvIv+iX+BASPlqCu6HvJ50DHfaJ9Tu+CfgCa16hySW173aO6CFyP/oLoyr/zidDvsfQVBMr3mAwnABESJ52N19e8gDn+vax+ZXA1qf0JoEYhd8Cn4nIcyLyDNaezPc2uaP6uaUiIifl3pTumgqiNy7gK0lh/Hd7JvCZwWAwBMp5U3/AnrAMJuY+SG7u7j6VJRDvoxeBi7FWMscAdwJvNt0XkTNF5BYReRe4prcE7TVU+fJ/f0Cir5TyKx4k0sR5OWVpCp2dnp7O9ddfT0VFRad5VqxYwYgRI5gzZ84JkNBw2uJwkDDnSZyi1Lx0CzW1dX0nSns3RGRs0wcYDHwfeB+4DcgVkUoRKQWeAwYBc1X1tfbK6698+tISLqh4nw9T/z/GXnry2TRD4DTFPsrJySE+Pp5HH3200zyPPfYY7733Hs8//3xAdfgvDjMYukJcyrkcnnQfY7w5fPL4rTR6vH0iR0c9hZbbbT6ItU4hDNitqjGqmqCql6jq/apa0LIAEbnGnpDeIyIL27gfIiIv2/e3iEhaTzxUoHz62u8Z+8Uf2Ro+mW/MM6GxTycmTpxIfn5+83lb4avnz5/Pvn37uPbaa/njH//Ybmjpp59+munTp3P55ZdzxRVXtFve/v37GTFiBLfeeivnn38+V111FXV1Votwz549TJ06lYyMDMaOHdu8irq9sNqGU5Ozr7yVnLR5TKl+g78/Or9PVjt3FCV1yvEULCJO4FGsFdB5wCcisl5Vd/oluwUoV9WzRWQ28DusiexepbK8mNznfs740vV8Gnoxo37yCk7nKbPUov/z9kIo+HfPljloFFzb/k5q/ni9Xt5//31uueUWoP3w1atWreKdd95h06ZNJCYmthtaGuDTTz/l888/Jz4+vt3yUlNTyc3N5cUXX+TJJ5/kxhtvZM2aNXz3u99lzpw5LFy4kJkzZ+J2u/H5fO2WM3ny5J59d4Z+Rfp//ZGc1XVMzXuZfy0/SMJNjzD8rOEnrP5AoqSGAz8HUlX1NhEZDpyrqm92kvUiYI+q7rPLeQmYgbXWoYkZwL328WvAIyIi2gt71R34IpvD/3yJoLI9nFv1D8aom48GfY+L/vsPBAUF93R1hn5IU+yj/Px8RowYwZVXWhsGthe+uqXybS+0NMCVV15JfHx8h+WlpqYybNiw5j0dxo0bx/79+6muriY/P5+ZM2cCEBoa2iW5DKcYDgfpt/yJXWuHMebzB+HPE/lX2ATc8SOIG/FNMr7Ru86enRoF4ClgO9aqZrBCZr+K32RzOyQDh/zO84AJ7aVRVY+IVGKFzCjxTyQit2HNZZCa2r19fEr3/5uJ+x+nlBh2x0wm9oqfM+mCi7tVluE4CbBF39M0zSnU1tZy9dVX8+ijj/LTn/603fDVLWkvtPSWLVuO2YimvfL2799/TJhtp9PZPHzUXn2ByGU4BRFhxKwsqibM5Ks3lzOsYDMDD/+DLdIIvWwUAhkzOUtVfw80AqhqLdaq5iEiktr06U0hVfUJVR2vquMHDOhe3L3zv/kt3Hfnk3DvQS688xWGG4Nw2hIeHs6KFSt48MEH8Xg87YavbkmgoaUDLa+JqKgoUlJSWLduHQD19fXNhqsr5RhOPaKTzyPj9v9j4K9z0V8VMfa/er9BFUhPoUFEwrD3TBCRJcBI4D2+DpmtQMv9mfMB/4hyKfa1ttLkiYgLy+W1tCNhtm/fXiIiBwKQuy0SadELMQAn4L289957o7xeb5+65vh8vvCcnJxagKCgIM4444yQ3/3ud54ZM2Z4v/nNb7pGjx4dBBAeHq7Lli2rT01N1YaGhvCdO3fWxsfHM2vWLH77298GDx8+3KmqDBkyxPf444/XHzx40FVcXOzIyclpABgyZAhtledwOKirqwvNycmpAzh8+LCrtrZWcnJyGn/1q1/JkiVLQhYsWCAul0sffPDB+tTUVG1Prr55gxYFBQWukSNHHsH8ltqiP+uYMwJJFEjo7KuAX2IZgg3AjcC3VHV9J/lcwJfAFVjK/xPgO6r6H780PwJGqep8e6J5lqreGIjg3UFEtgUSOvZ040S8lx07duzPyMjorz+WdsnJyRmRnp6+q/OUpw87duxIHD16dIn5LbXmVNAxnfYUVHWDiGzHWsAmWNbmrwHk84jIj4F3ASewWlX/IyJLgW22Ufk/4FkR2QOUAbO7/ygGg8FgOF4C8T56A3gBWK+qR0VkJvA3EXmLrzfZQVX/0DKvqv6VFgZEVe/xO3YD3+6++AaDwWDoSQKZaH4A+AawU0ReAyKBTUAwEOX36RAR2W9HVM0WkW32tXgReU9Ecu3vuG4/SWCckiG/ewDzXtohMTGxuK9l6KeY/5m2OenfS6dzCs0JrcVolwO3YsU4GgKgqjUB5t8PjFfVEr9rvwfKVHWZveI5TlX/p0tPYDgp2LFjx75Ro0aVOxyO/rGTiKFb+Hw++fe//x2XkZFxZl/LYugdAjIKtvfR9VirjScAIUCtfbsE+C//CeR2ythPa6PwBXCZqh4RkcHA31T13PbKAEhMTNS0tLROZTYYDIZ+h/rweBpRnxefz4f6vKj9DQqqlpunKrbDp31s4QyJIDQiultVb9++vURVO/XpD2RO4RWs1cnvAI9gBcf7papusu9fBjzJ14vb2kOBDSKiwJ9U9QlgoKoese8XAAPbkeGYxWvbtm3rTGyDwWA4YXgb3JQXHqSy6BBHS/NpKM/HV3UEZ20RoXVFRDaWEOstJYaABlba5Z+DZzHx9pXdyhuoK38g6xT+D7hZVb12wRFNBgFAVf8mIoHEm75UVfNFJAl4T0SOCRquqmobjFbYBuQJgPHjx5vhB4PBcEJoVvbFeRwtyaOh4rCl7I8WEuIuIrKhhDhb2SdiLVJoolGdlEocFc4ESoJTyA8biy9yIM7IAbjConCGRhEUGkVQeBTBYRG4goJxOIJwOJ04nC6cThfidOF0OhG7zIzQsF5/5kBcUt9tcWmfiCwGnrXPvwvsC6CcfPu7SETWYvU+CkVksN/wkVmuaTAYeh1vg5vy4kNUFh6itjSP+vImZV9EiLuQyIYSYr1lxFLdgbKPpzQ4hcNhY/FFJOGIGUJI3BAiElKIGziU+AGDGeRyMaivHrKbBNJTaMkPgCXAX+zzD+1r7WL3JByqWm0fXwUsBdYDc4Fl9nf/2LnaYDCclHgb6ykvalL2h6gvP9KqZR/rLW1T2XvUQYndsi8NTuZw2Bh8EQNxRg8iOC6ZiMShxCalED9gCIOCTj5lHygBex8dVyUiZwJr7VMX8IKq3i8iCcArQCpwALhRVcs6Kmv8+PFq5hQMhp6nsbGRvLw83G53X4vSClXF5/Xg83lRnwf1ekG94PMi6sOhPhx4cTRH3vHLi+DDgQ8HKk5UHKjDiYgTcToRhzVc43A4EZE2aj+5CA0NJSUlhaCgoGOui8j2QFZbd9hTEJEUrDUJO7G8jr7EUuBxwN/906rq9PbKscNnZ7RxvRQrDIbBYOhj8vLyiIqKIi0t7YQpR/X58Hoa8Xoa8HoaUE8jeBvB14j4GnGqBydeXPjvQuYCXKiCR+y74kIdQeBwgTMIcQXjcAXhdAXjcgXhcJwe+6WoKqWlpeTl5TFs2LBuldGuURCRP2MFsQsHHsNq0X8FfAtrrcKZwJ+Az7tVs8Fg6Fe43e4eMwhdUfaWivfL66fsPRJEoyMMHEFtKvsgh4Og9oQ4DREREhISKC7u/prLjnoK+VgrmROBx6F5AjwYWITlDZSqqntE5A5a9BwMBsPJR2cGoWNl77GVvQenenFJF5S9MwiHKxhnkFH2x8vxGvWOjMKnqpolIj9V1RV2ZXHAR6r6iJ1mj/09D3j4uCQxGAx9hq+xAZ/XQ31t9XEpe6+4aHSEdlvZO51ORo0a1Xw+e/ZsFi5stb07AOvWreOcc85h5MiRANxzzz1Mnjy5eYvU7lJRUcELL7zAD3/4wy7lu/fee4mMjOSuu+7qNG12djaHDx9m2rRpPZKuJ+nIKGRh7bB2v4g8jRUyewUQLCJ7gaYVzFFYEU4NBkM/w+dppLI4n/LCg82LqryVR3AcLSSkroiIxmJiPGXEaSWOa14mpOLrLS96UtkHStPueIGwbt06MjMzm43C0qVLe0ACyyg89thjXTYKXSE7O5tt27YFZBQCSdeTtOt9JCLvYa1Cvhwr0ulZWAYgEivMRZOU1cDnqnpCNlAx3kcGg6XsK0oOU1l0kJrir/3sHTUFBLuLiGgoIdZTain7FmtCfSqUSgwVjnhqggfgDk3CF5FExJgbGT58uKXsXcG4gk78BG1kZGTzTnP+LFy4kPXr1+NyubjqqquYNWsWmZmZxMTEEBMTw5o1a/jNb35DZmYmN9xwA2lpadx88828/fbbuFwunnjiCbKystizZw8LFixg/vz51NTUMGPGDMrLy2lsbOS+++5jxowZzJ49m9dff51zzz2XK6+8kuXLl7N8+XJeeeUV6uvrmTlzJkuWLAHg/vvv55lnniEpKYmhQ4cybty4Vj2FV199lSVLluB0OomJiWHjxo2cffbZ1NXVkZycTFZWFsOGDeOOO+7A7XYTFhbGU089xbBhw1qly8zM5Cc/+Qk5OTk0NjZy7733MmPGjFbva9euXYwYMeKYaz3hfXQdMBb4JtY+zYuwhoi+wNobwcwhGAw9jHobqSg5QkXhAWpKbGVfeQQ5WkhIXSERDaXEeEqJ1wriRYn3y+tToUyiKXckUB2cSHHkCLwRA3FEWX724YnJxAwYSvzAFAaEhNAyCM6uXbuIiEkAYMkb/2Hn4aoefbaRQ6L59fXnd5imrq6O0aNHN59nZWUxdepU1q5dy+7duxERKioqiI2NZfr06c1GoC1SU1PJzs7mzjvvZN68eXz00Ue43W7S09OZP38+oaGhrF27lujoaEpKSrj44ouZPn06y5YtIycnp7nHsmHDBnJzc9m6dSuqyvTp09m8eTMRERG89NJLZGdn4/F4GDt2LOPGjWslx9KlS3n33XdJTk6moqKC4OBgli5dyrZt23jkEWskvqqqig8//BCXy8XGjRtZtGgRa9asaZVu0aJFXH755axevZqKigouuugipk6deswe4cdLu0ZBVRuAf4nID7EWqw1Q1SdEpAYIEZGm/xixkmv3ojQZDKcB6vVQUXKYisKDHC3Jw+3fsq+zWvYxnlLitII4UfxjyPtUKJdoyh3xVAcPoDjyXFvZDyYobggRCcnEJKUSn5RMYmjoMQuyTjbaGj7yeDyEhoZyyy23kJmZSWZmZkBlTZ9uecmPGjWKmpoaoqKiiIqKIiQkhIqKCiIiIli0aBGbN2/G4XCQn59PYWFhq3I2bNjAhg0bGDNmDAA1NTXk5uZSXV3NzJkzCQ8PP6a+lkyaNIl58+Zx4403MmvWrDbTVFZWMnfuXHJzcxERGhsb20y3YcMG1q9fzwMPPABYHmMHDx5s1Ss4HjpySb0Za/vNnXa6JiknAberau8NuBkMJwnq9VBZcpjyokNWy74sH19VAVJTQEhdIeHNwzitlT1AKTG2sk9sVvbS1LJPSCbWbtknhIaScAKfq7MW/YnE5XKxdetW3n//fV577TUeeeQRPvjgg07zhYSEAOBwOJqPm849Hg/PP/88xcXFbN++naCgINLS0tpcuKeqZGVlcfvttx9z/aGHHgpI/lWrVrFlyxbeeustxo0bx/bt21ulWbx4MVOmTGHt2rXs37+fyy67rM2yVJU1a9Zw7rkdBpM+LjoaPkrFmmgeD/wvcJ1Yvk41WENKTRFSLwD+rKoVvSalwXCCsZT9EcqL7JZ9mdWyl+aWvTVBG6/lxIoS2yJ/GV8P45RGnIMnYiASPZjgWL+WfR8o+5ORmpoaamtrmTZtGpMmTeLMM62tHKKioqiuru52uZWVlSQlJREUFMSmTZs4cOBAm+VeffXVLF68mDlz5hAZGUl+fj5BQUFMnjyZefPmkZWVhcfj4Y033mhlOAD27t3LhAkTmDBhAm+//TaHDh1qVUdlZSXJyckAPP30083X25Jl5cqVrFy5EhHhs88+a+7B9BQdDR/9DvidiHyCFd/ov4BPgTSgWkQmYK1VeB1ru84TNz1uMHSTJmVfUZxHTfEh3GX5eO1hnJC6IsL9hnFixdeOso+nJshS9l/6tewjEoYQPSCVhEEpxIeGHTPebwiMlnMK11xzDXfccQczZszA7XajqvzhD9bOv7Nnz+bWW29lxYoVvPbaa12ua86cOVx//fWMGjWK8ePHc9555wGQkJDApEmTSE9P59prr2X58uXs2rWLiRMnAtZk+HPPPcfYsWO56aabyMjIICkpiQsvvLDNehYsWEBubi6qyhVXXEFGRgapqaksW7aM0aNHk5WVxd13383cuXO57777uO6665rzTpky5Zh0ixcv5mc/+xkXXHABPp+PYcOG8eabb3b52Tui09hH9hacf8DaS2ECcAg4grXS+RFVXSkin6lqz5qrdjDeR4a2UJ+XqtIjlBdawzjusny8lYdxHC0iuK6QiPpiou2WvUtax8cpI4pyRwI1QQm4Q5Pw2BO0QbFDCE9MIWbAUBIGDSX0BIQu7iva8lgxnJz0lvdRE/OBZ7DCWpRgTSx/jDWE1GSizOJDQ6/QpOwrivKoPqZlX0hQXRER9cXNLfsY8RLTIn85UdaYfVAipRFnkRsxEIkaTHDsYMIThhKdlELCwFTiw0zL3mCAwIzC77F2RHsd8AExWPGP7lTVr0RkGF/vrWAwBIT6vFSXFlJu+9m7y/PxVB7GUVNIcF0R4fXFRHtLifd1rOxrghIpiziTPeEDIdpW9vEpRCcNJWHgUOLCw1tN7hoMhvYJxChcrKoj/S+IyEHg3yKSDnxhzz8YDKjPS01FEeUFB60x+/LDeCqPIDVHCKottidoS4jzVRAtXlr6MVdoJGVOaxinPHwYeyMGIU3DOAkpRA9IIX5QCnHhkUbZGwy9QCBG4Z8iMlJVd0Kzx9EQ4FGsoaShIjJXVTf3npiGPkfVUvaFB6kuzqO+LA9P5WGotoZxwuublH05UeIlqkX2Co2k3GkN45RFpbEnYiBEDSIoNpnw+CFEJ1kTtLHhka0mdw0Gw4kjEKPwZyzDUADUA8OxFqs1uaWeA7wItF7KZ+j/qFJbVUJZwSGqiw/iLjuMpzIfqgsIqi0izB6zj/eVESkeIltkr9AIKpzxVLkSKY8ax57wJCRqEK7YIYTFpxCTlEL8oFRiI4yyNxhOBjpavFaNFfsoEnBj9Q7ACp3d7LKkql+KiJlo7m+oUlddTlnhQaqLD1FXloen4ghUH8FlK/voxhISfGWESyPhLbJXaThl9gTtwcgM9oY3tewHE5aQQlSi5Y0TExlF7CmwW5XBYLDoaJ1CFICI/FNVJzZdF5HVgM8eRgKYAxgf0ROFKu6jFZQXHqKq6BC1pfnNLXtXbRFh7iKiGkuI1zLCaCC5RfYaDaPUYbXs8yLT+SrMUvau2CGExycTNSCFuIGpREfHEG2UveEE0xQ62+PxMGzYMJ599lliYzvuY65YsYLHH3+csWPH/v/tnXl8VNXZx79PFrJAWJKwhxBE1uwEEGQNgggqiiKiiPpqpbxatK3SglvRt622VkUqS9W61FJFQcCtyCKKLCoEAoYAQjBCwkZ7bekAACAASURBVBZAIIEkJJnn/eNOQoiTZEhmMhNyvp/P/WTunXPOfebM5D733POc38OCBQvqyNJLF2ceH20Vkf8AH2E9PloOjAIetL//FVZmNkMtKTx7ip8OH+BUzgHyj2dRdPIg5B7G98xRggrtF3vbcYIppC3QtlzdsxrAMfvF/mDjnvwY1Aote4zTnibhHQht3YFmzVvQxFzsDV5Kee2ju+66izlz5vDYY49VWWfu3LmsWrWKiIgIp85RXFyMn58zl76GiTM9E4TlDK4ud0ywRPJsWNFH52pjhIhcg6XA6gu8pqrP1qY9b6OoII8Th/dzqvTO/mQ2evowvmcPE1hwjJCiHFrYTtCEfNoAbcrVzddGHJdQTvmHcSi4Kz8GtYYmrfFt1o6gsPaEtOxA81aRtGjegsgGkofW0DDo378/27efz/brSL56ypQp7Nu3j1GjRnHPPfcwefJkh9LSb775Jh988AF5eXmUlJTw5ZdfOmwvMzOTUaNGMXDgQDZs2ED79u1ZtmwZQUFB7N27lylTppCTk4Ovry/vv/8+nTt3rlRWu75SrVNQ1f8pvy8i1wLzseQuBOgkIr9U1f/WxAAR8cWKZBoBZAGbROTD0mgnr0WVgjOnOHnsELnHsjh7LItzJw/C6UP4njlCQGEOIeeO0cJ2nBDO0hprsUcpBepvXez9wjgSdDkHglpha9IGv2ZtCSy9s28TSfPmYUT4+uDcPZDB4CL+Ox0Of+faNtvEwijn7vdKSkpYvXo19957L1C5fPX8+fNZvnw5a9asITw8vFJpaYAtW7awfft2QkNDK20vMjKSPXv28M477/Dqq68yfvx4Fi9ezB133MHEiROZPn06Y8eOpaCgAJvNVmk7gwcPdm3f1SFVTTQ/DsxV1YpZ1Z4HkrEE84KBncAnQI2cAtAX2Kuq++znfRe4AUud1WWc+ukYOft3o7YSbCXF1l9bCVpSgtrK7dtK0KJ8SvJzseWfQgtzoTAXn3OnCSg4RtC5nwgpOUEz2ymC5NzP7uwL1c9+sQ/laGAUWcFXYGts3dkHhrajSVgELdp0pEVoS9r7+vzsmb/B0JAp1T7Kzs6mR48ejBgxAqhcvrrixbcyaWmAESNGEBoaWmV7kZGRdOrUqUx/KSkpiczMTHJzc8nOzmbs2LEABAYGXpRd9YmqRgrfAR+JSAGWEF4OEAiEA0uAVcCfsaQvai5VCO2x9JRKycLSWHIpezcuI+nb39ao7lkN4IwEc8qnOWf8Q/kpuCPFgWHQpBW+IS3xb9aWJuEdaNG6A6HhbWjn61MWqmUw1EucvKN3NaVzCmfPnmXkyJHMmTOHBx98sFL56opUJi39zTffXJCIprL2MjMzL5DZ9vX1JT8/v8rzOWNXfaKq6KNlwDIR6YKVQ6EtcBr42l5vG5Yy6i1Yj3xustf7wNVGishkYDJY2ZRqQof4YWz1m4P4+Jbb/BBfH3x8/PDx8QVfX3x8/PBtFERQSHOCmzQnOKQ5wY0aEQw/y1RlMBjcQ3BwMLNnz+bGG2/k/vvvr1S+ulWrVhfUc1ZaurL2KiMkJISIiAiWLl3KjTfeSGFhISUlJU7bVZ9wZk5hD7CndF9E4u0vh9j/5mBNRl+PtX7hYp1CNtCh3H6E/Vh5G17BkulGRHJE5MeLPEcp4VgjG8OFmH6pnAbTNytXrowtKSlxKtd6SUmJn6+vr8vzsttstuC0tLSzAP7+/nTs2DHgL3/5S/ENN9xQMmTIEL+EhAR/gODgYH322WcLIyMj9dy5c0Hp6en5oaGh3HTTTTzzzDONunTp4quqtGvXzjZv3rzC/fv3++Xk5PikpaWdA2jXrh2O2vPx8SE/Pz8wLS0tH+DgwYN+Z8+elbS0tKLHH39cnnrqqYBp06aJn5+fPv/884WRkZFaoR2effbZgsjIyKrlp93M4cOH/Xr27FlxUqijM3Wrlc52NyLiB3wPXIXlDDYBt6vqDjeca7Mz0rENDdMvldOQ+mbbtm2Z8fHxTjnAtLS0HjExMTvdbVN9w1v6Zdu2beHx8fFRNanr8WBdVS0WkV8Bn2GFpL7uDodgMBgMhuqp1imISJiqHnenEar6KfCpO89hMBgMhupxZrXT1yLyvoiMFotOFQtUcqyDiKwRkXQR2SEiDzkoM1RETolIqn17soafw1lecXP79RXTL5Vj+sYB4eHhOZ62wRu5FPrFmcdHXYHhwD3AbKCJiAxW1e/LlVnEz1VSi4GHVXWLiIQAKSKy0sGitK9U9boa2n9R2CesDRUw/VI5DaxvbDabTXx8fKqdaGzTpk2DmHy/WLyhX2w2m2CpTdQIZ6KPFFgpIgeA8cCTWHpImVgZ1w5jrV+oWO8QVi5nVDVXRHZirUmo1aK08PBwjYqKqk0TbkFtJZQUF1F+4l4BLmYi32gS2fF8P1yUBS4z1/OfG7hw1H8RJol32O9RRHzw9R5dpQsuPikpKcdUtdrIeqfmFIA7gKlAAJAPLAZCgceAN4D7qmkjCkgEvnHwdn8R2QYcBB6pbpI5KiqKzZu9RJTVZmP3yn/SKOUfdDq3z9PWGAwGLyDTpwOHukwk8caHCAyqKErvOZwN5a82JFVEvscaEbyhqlki0l9VN9rf+311qThFpAnwJfCnigvbRKQpYFPVPBEZDbykql0ctFF+8VrSjz/WdJmC68g/cZCs126ny9mt7JFIstqOpFFYR8TXHxHBR8BHQJy9+69haLBQ05DiGtarRQSzM7Y67obK6lXXXrlR28XYfRFlKxat6jNW/b9Wi++xRlVr+l04/ozOmaAXU7isqLO/8Z/bW5twe3X4stpaBbm0yFpFt6Kd7PXphO+tb9GpW3z1FesAEUlxJrzaGacwXlXfK7ffEkvRNI9yIw1VvcdBXX/gY+AzVX3BCaMzgd6qWulzud69e6unRwp5R3/k1D+uoUXxcdZd/ghDJvyGgCpWQxoMhgaEKt+tfocO636HDeHIDe/SI3GAp61y2ik4E300vcL+MmAYlvbRJ+W2igYI8E9gZ2UOQUTa2MshIn3t9rg1/LW2FOad4PQro2la/BPbk9/k6km/Mw7BYDCcR4TY4beTP+m/FIs/LZfdxv4fvq++npdQlUrqKCxto/YiMrvcW92xVE3fc1yzjAHAJOA7EUm1H3sUS10VVZ0PjAP+V0SKseYqJqinl1hXhc3GD69MpHPRITYMfIMhQ0d72qJ6Q1FREVlZWRQUFHjaFEMtCAwMJCIiokqdIINF286xHLx9MU0XjOLE2xPI/e2XhDQJ8bRZ1VLVRPNBrDSbY4CUcsfbAu9X17CqrqOa2AVVfRl4uXozvYOdy/5Gj9Mb+CzqEUaOuMHT5tQrsrKyCAkJISoqyvl5FoNXoaocP36crKwsOnX62dIkgwPadUlk17DZdP/8Pr58axpDHpjvaZOqpSqV1G3ANhFZYJeiyKV03gduFpG3gCL7vqpq0zqx2EOcPriXqG1/Y5N/b5LveNTT5tQ7CgoKjEOo54gIYWFh5OTU+/VZdUr3wePZmvYJA4+8y5b1Y+k1YKSnTaqSSucURKT08dBWEdkO/ABk2v+mqWqQqjZV1ZBL3SEAZL/7ICUqNL3lZRr5+3ranHqJcQj1H/Md1owed77EMZ8wGq+ezrkil4vLupSqHh+VylJUXG0cDSAivcodOwX8qKre/WlrSGbKCnqcXs+qiCkM79rD0+YYDIZ6RmCT5mT0m0H0xof5csnLDBn/a0+bVCmVjhTsK5JLyxxR1R9V9UfgD8BS4FX79jXWHMNuEbnazfbWORmfzibqo1s4Qih9xj/maXMMtcDX15eEhISy7dlnK88utnTpUtLTzy++f/LJJ1m1alWtbTh58iRz58696HozZ84sSzFZHampqXz6afX6ks6WM7iG6BH3kNGoO93TZ3E6rzbJKt2LMyGp73OhjsZBYLeqJqlqEpAA7ANGAH91vYkexGaj87dPAJAa9QuaNbvkn5Jd0pSmeizdpk+vGG19nopO4emnny5LAF8bauoULgbjFLwUHx98hj9Ja35iyzL3/gZqgzNOwU9Vz5Xb70I5J2EXuOuuqpeczkPmJmv5xcclV3DlrY942BqDu5g+fTo9e/YkLi6ORx55hA0bNvDhhx8ybdo0EhISyMjI4O6772bRokWAJbUyY8YMEhIS6N27N1u2bGHkyJF07tyZ+fOt6JK8vDyuuuoqevXqRWxsLMuWLSs7V0ZGBgkJCUybNg2A5557jj59+hAXF8cf/vCHMrv+9Kc/0bVrVwYOHMju3bsd2v7+++8TExNDfHw8gwcP5ty5czz55JMsXLiQhIQEFi5cyLfffkv//v1JTEzkyiuvZPfu3Q7LnTlzhnvuuYe+ffuSmJhYZrPBdXTqM5qMRt25fM9rnPXS8GxnlJtyRGSMqn5o3/8J6CQipek4bwXSRSQAKxrpkiFvw6uc0BAGTfuAkKCA6isYnOKpj3aQfvC0S9vs2a4pf7g+usoy+fn5JCQklO3PmDGD4cOHs2TJEnbt2oWIcPLkSZo3b86YMWO47rrrGDdunMO2IiMjSU1N5Te/+Q13330369evp6CggJiYGKZMmUJgYCBLliyhadOmHDt2jH79+jFmzBieffZZ0tLSSE21lu6sWLGCPXv28O2336KqjBkzhrVr19K4cWPeffddUlNTKS4uplevXiQlVRQitkYwn332Ge3bt+fkyZM0atSIp59+ms2bN/Pyy1a09+nTp/nqq6/w8/Nj1apVPProoyxevPhn5R599FGGDRvG66+/zsmTJ+nbty/Dhw+/IOG9oZaIoIMeJmL1fXzx4SsMHf+gpy36Gc44hSnAAhGZY9/PBv4FlM6UrAcewXIIyS630EOcOXaA7ie/4qvwW0lu2sTT5hhcQOnjo/IUFxcTGBjIvffey3XXXcd11zmn4j5mzBgAYmNjycvLIyQkhJCQEAICAjh58iSNGzfm0UcfZe3atfj4+JCdnc2RI0d+1s6KFStYsWJFWXL5vLw89uzZQ25uLmPHjiU4OPiC81VkwIAB3H333YwfP56bbrrJYZlTp05x1113sWfPHkSEoiLH924rVqzgww8/LJu7KCgoYP/+/fToYYIrXMnlA8ax/8s/0m7nG5SU/ApfX2ce2NQdzkhnZwD97MJ2qGpeFcWreq9eseez+SSIjVbJv/S0KZcc1d3R1yV+fn58++23rF69mkWLFvHyyy/z+eefV1svIMAaOfr4+JS9Lt0vLi5mwYIF5OTkkJKSgr+/P1FRUQ5Xc6sqM2bM4Je/vPB3NmvWLKfsnz9/Pt988w2ffPIJSUlJpKSk/KzME088QXJyMkuWLCEzM5OhQ4c6bEtVWbx4Md26dXPq3IYa4uPDqZi7iU19is1fr6L3AO+Kz6nWRYlIMxF5AdgPfCEiOSKSJiLbK2ytRGSsiDwgIveISF8R8S4X6CRafI72e99lq188PaMTqq9gqLfk5eVx6tQpRo8ezYsvvsi2bdsACAkJITe35hEip06dolWrVvj7+7NmzRpKlX0rtjty5Ehef/118vKs+6ns7GyOHj3K4MGDWbp0Kfn5+eTm5vLRRx85PE9GRgZXXHEFTz/9NC1btuTAgQM/O8epU6do3749AG+++WbZcUe2/P3vfy9Tc926dWuNP7+harpffS9nCKRwg/flcHLmov06kAuMwkqy8zZwALjevv0Za57hE3uZtkBP4HEs3aOn7BLZ9YadK9+gpR4jL/GXZrHOJUTpnELpNn36dHJzc7nuuuuIi4tj4MCBvPCCpd04YcIEnnvuORITE8nIyLjoc02cOJHNmzcTGxvLv/71L7p37w5AWFgYAwYMICYmhmnTpnH11Vdz++23079/f2JjYxk3bhy5ubn06tWLW2+9lfj4eEaNGkWfPn0cnmfatGnExsYSExPDlVdeSXx8PMnJyaSnp5dNIP/ud79jxowZJCYmUlx8filRxXJPPPEERUVFxMXFER0dzRNPPFGDXjY4g39wM/a2uZbeeV+QlZXlaXMuwBnp7FRVTajsmIg8BxxQ1dkO6vphLX7zVdXFrjDY7dLZNhsH/hxPYYkQ+ehWs3rZRezcudM8m75EMN+laziWsYXwt5P5POq3DLv7D9VXqCWulM7OF5GBItJURGaIyCKgkVhMBSYAVzmqqKrFqrrUVQ6hLtizfhEdiveTHT3ZOASDweA2wjv34gf/LgzLfIHPPq/9wkhX4YxT+F9gDlYu5seAvliPj9ZgSV8HAY1F5F4Rae4uQ+sCLSnG/8tnyKIVfa6919PmGAyGS5zcblbI88i1N5NzzDtSyVTrFFQ1VVXjsYTw2qlqJFaehZ7ASKA18BwwEEvqYpmITBCRIDfa7RbSP3uNqOJ97Iv7LcFB9c58g8FQz+hy1d1lr9MW/cljdpSnqiQ7v61wqBnwi3ITr1mqWhpj9xnwmYg0wppsngDMEpHVqjrRxTa7hcIzJ2m56a/s9ulM/zH3edocg8HQAAhq0QYeO8J3L9/KFYf+zZ69U+hyeVeP2lTVSCGkwtYOK9Loz8AzQJyInBaRXBE5DWCXw0gHdgKngXozG5X+9iOE206QN+zP+Ps5s6bPYDAYXIB/IB1vfQ5fsXH8vQexldiqr+NGqlJJfarC5qOqgfYtQFX9SvMpANEiMk1EtgAf29sdo6q9Kmvfm9i3+TPiDy1iXehYkgZe42lzDAZDA6Npu67s6fkg/c5tZNV7f/eoLc4sXusqIqtFJM2+Hycij5d7fwOwDmgF3Keq3VR1pqrucpvVLuSnI/tp9vFkDvi0JfbO5z1tjsGNlEpnx8TEcP3113Py5Mlq68yePZsePXowcWK9eApqqMdE3/woGUExXLnrz6RuWucxO5yJPnoVmIFd7E5Vt2PNGZQyHYhS1WmqesEaexG5RkR2i8heEfmZTrGIBIjIQvv734hIVE0/SE04c+o4J14dS6DmU3DTW7RoEVqXpzfUMaXaR2lpaYSGhjJnzpxq68ydO5eVK1eyYMECp85RfnGYwXAxiK8fbe99hwKfYFp9fBe7du30iB3OOIVgVf22wrHyv/zBwM9CUUXEFyuU9WkswbzbRKRnhWL3Aj+p6uXAi8BfnDW8thw9sJfDfx9Bh6If2DFgNt1i+9bVqQ1eQP/+/cnOzi7bdyRfPWXKFPbt28eoUaN48cUXK5WWfvPNNxkzZgzDhg3jqquuqrS9zMxMevTowX333Ud0dDRXX301+fn5AOzdu5fhw4cTHx9Pr169ylZRVyarbbg0CQ6PRCe8Q1M5S/N3ryVl0/o6t8GZGdVjItIZUAARGQccKvf+d8DHIlIAbAFygECgP9Yjpd5Yk9PvAjdgTUSXcgMw0/56EfCyiIhWt8y6Fhw/coC9K1+jx95XCVIb2wfOo++IW911OoMj/jsdDn/n2jbbxMKoyjOplaekpITVq1dz773WWpTK5Kvnz5/P8uXLWbNmDeHh4ZVKSwNs2bKF7du3ExoaWml7kZGR7Nmzh3feeYdXX32V8ePHs3jxYu644w4mTpzI9OnTGTt2LAUFBdhstkrbGTx4sGv7zuBVtOzWj8O3LaPRu7cQ8/ENrPpmAh1G3E/ny7vjVweKqs44hQeAV4DuIpKNtV6h7AGrqi4DlolIF2AAlvbRaWAzcFhVfwMgIlnAFRXabo+1EA5VLRaRU0AYcKw2H8oRW1f8m8s2/I4wzhAGbAtIovnNL9K7a7yrT2XwUkq1j7Kzs+nRowcjRowAKpevrnjxrUxaGmDEiBGEhoZW2V5kZCSdOnUqy+mQlJREZmYmubm5ZGdnM3bsWAACAwMvyi7DpUebbn05M3Uje/89lWE5/8bnnbc5rcFsj5zEwHvdm+DSGafwo6oOF5HGgI+qOpSOVNU9wJ7SffuIoq0rjBSRycBksJKb1ISmbS5jV/hItGkErXpdR1x0XyN25ymcvKN3NaVzCmfPnmXkyJHMmTOHBx98sFL56opUJi39zTffXJCIprL2MjMzL5DZ9vX1LXt8VNn5nLHLcGnSOLQd0Q8u5lTWLn74ehl6bA/Notx/E+uMU/hBRJYDC4HqhebPkw10KLcfYT/mqEyWXTyvGfCztd6q+grWaAW7dPePF2FHecKBY/DHGla/ZLH3i/tYuXJlbElJiUdnYW02W3BaWtpZgKlTp/o89NBDAYMHD87v0qWL79///nf/hISEgsaNG3P48GHx9/fXsLAwzp07F5yenn42NDSUhIQE/yeffFIef/zxcyJCenq6T8+ePW379+/3y8nJ8UlLSzsHUFl7+fn5kp+fH5iWlpYPcPDgQb+zZ8/Kjz/+WNSiRYvAWbNmFQ0fPryksLAQm81WaTthYWGe7EYOHz7s17Nnz0O4+TdTT3Hz/9I/gTtqWrmjM4WccQrdsZROHwD+KSIfA++qanUxU5uALiLSCeviPwG4vUKZD4G7gI1YOkqfVzefoKotnbDZISKy2RmVwIZGXfTLtm3bMmNiYjx9EUmMiYnZCRATE8P8+fMvX79+/YkHHnjgRE5OTqtJkyaFAwQHB9sWLFjwQ3R0dCHQq0uXLnvatm1b/NJLL8nkyZMjb7755sY2m006dOhQuGbNmr2ff/55WEBAQOOYmJj9pW07as/Pz099fHy6lNrQpEmT1oBvTEzMwf/85z8B9913X8e5c+f6+fv76/vvv58xZcqUc1XY5TFKSkrCgWPmf+nnXArXmGqlsy8oLNICeAmYqKrVSoiKyGhgFuALvK6qfxKRp4HNqvqhiARi5WdIBE4AE1R1Xw0+h7P21/svzB3UlVOIj4/3tFO4aNLS0nqUXsQNFtu2bQtPSEgwTsEBl8I1xik9BxEZAtwKXIM1gTzeQZmuwDygtarGiEgc0EtVLxDyUNUny70uAG6pufkGg8FgcCXOrGjOBH4NfAXEqur4SvIjVLfIzRvwvtx33oHpl0oIDw/P8bQNXor5zTim3veLMyOFOFU97US5YFX9tkJEj1ct77RPWBsqUEf9YrPZbOLj4+O2NSjuoE2bNvXukZc7sdlsAtjM/5JjLoV+qdYpOOkQoPpFbi4hPDxco6KiXN2soW7o5GkDDC6jXjl3A6SkpBxzJlDHlRrRjha51Th2qjKioqJwa45mJzmeV8h7m7NY+30Oh08X0DjAl4jmwUS0CCLQpPE0XARVLZepciVNFRWrW4FT9TmraLemtlZXt4Zrhqqr5o7PUlW92PbN6d/ZsyHDleFsKH+1TkFEOqnqD9Uds0cNVbvI7VLgvU0H+L9P0sktKCa2fTOi2zUlr7CYPUdzWbP7KMU2cxNlcI6qov+q+hW5TwjGUFuGdW/FX8fFEd4koPrCXogzI4XFQMW8CIuApPIHKmZqs3v+U0CKqqbWwkavwWZT/vzpTl5b9wP9LgvlqTExdGsT4mmzDIaLokpHVIWzqdpJ1cy5VX/OmtlaHe44Z3GJsnDzfv624nuum72Of//iCi5v1aTmRnqIqtJxdgeigWYiclO5t5piCd5VpLd9+8i+fx2wHZgiIu+rqnsFO+qAZ5fv4rV1P3D3lVE8cV1PfH2MTIah/lHVo5qaK7+Y/wWAyYM7c2XncO5+YxMTXtnIkvsH0CE02NNmXRRVhaR2w7qwNweuL7f1AhwlMY7AWpfwsKo+jDWSaIUlrX23C22uU47lFbLz0Gne3pjJK2v3cWf/jvzheuMQDAaDY2LaN+Pdyf04V2zjvn9tJq/Qq4Iwq6XSkUI59dP+qrrRibZaAeWX3xdhLWTLFxGPLsuvDb3/uAoAH4HhPVrxh+ujjZCewWCokstbNWHOxF7c/cYmnlyWxgvjEzxtktM4M6ewV0QeBaLKl1fVeyqUWwB8IyLL7PvXA/+xTzynUw8p7+G7tg7hpQmJZoRgMBicYlCXltw/tDN//3wvo2PaMrxna0+b5BTOOIVlWKuZVwEllRVS1f+zq6leaT80RVVLY0erTHBrXzWda2+/2Fu0Qz5LO1z2+pbeHWgc4MoIXoPBcKkzdVgXVu08ymNLv6N/57B6cQ1xxsJgVf29M42p6iZ7LGwggIhEqup+J21JVlWvWj26ZOt5pe9GvmaE4A6KiorIysqioKDA06YYyhEYGEhERAT+/v6eNqVe08jPhz/eGMPN8zbwjy8z+O3V3aqv5GGccQofi8hoVf20qkIiMgZ4HmgHHAUigV1YEUz1jiOnC1ifcd5H+ddBGryGSFZWFiEhIURFRZm5Gi9BVTl+/DhZWVl06mQWodeWpI4tGBPfjn+s3ceEvpG0ax7kaZOqpNIrnYjkishp4CEsx5AvIqfLHa/I/wH9gO9VtRMwHPjaSTsUWCEiKfYsaxVtmSwim0Vkc05O3eiTfZh6EFXoFdkcAB9zwXILBQUFhIWFGYfgRYgIYWFhZvTmQn53TTdsqsz/MsPTplRLpU5BVUNUtan9r4+qBpXbb+qgSpGqHgd8RMRHVddgrVtwhoGq2gsYBTwgIhckoVXVV1S1t6r2btmyxjl2nEZVWbwli/iIZkSF29MsmmuW2zAOwfsw34lriWgRzLikCN7ddICjpy90tjM+2M4fP/aeWBxnpLN7Odg629NnlpYJBBqJyFwgGMgQkXWAzRkjVDXb/vcosAToW5MP4yq27D/JrsO5jO/ToWw5pvkXuXQ5fPgwEyZMoHPnziQlJTF69Gi+//77GrU1a9Yszp49e9H1hg4delGaXrt27SIhIYHExEQyMjKYPXs2PXr0YOLEKmM6LiA1NZVPP63yqbDBhfzvkMspsSmvfnVhHrF3vj3Aa+t+qKRW3ePMg/K5WI+BXrVvXwPvA7tF5GoReQrYAKwB1mMJ4y0BcoAjIrLSnnDHISLSWERCSl8DVwNpNf9ItWfB1z/SJMCPGxLalx0zd06XJqrK2LFjGTp0KBkZGaSkpPDMM89w5MiRGrVXlVMoKak0eO+iWbp0KePGjWPr1q107tyZuXPnsnLlShYsWOBU/eLiYuMU6pjIOvrnhAAAHSlJREFUsGDGxLfj31/v51R+kafNqRRnnMJBIFFVk1Q1CUgA9gEjgL8C39of/RSo6gJVXaGqv1XVscA2rHDURlW03xpYJyLbgG+BT1R1eS0+U6346cw5Pv7uEDcmtqNJgF+ZCopxCZcma9aswd/fnylTppQdi4+PZ9CgQagq06ZNIyYmhtjYWBYuXAjAF198wdChQxk3bhzdu3dn4sSJqCqzZ8/m4MGDJCcnk5ycDECTJk14+OGHiY+PZ+PGjaxevZrExERiY2O55557KCysel1nSkoKQ4YMISkpiZEjR3Lo0CE+/fRTZs2axbx580hOTmbKlCns27ePUaNG8eKLL3LixAluvPFG4uLi6NevH9u3bwdg5syZTJo0iQEDBjBp0iSefPJJFi5cSEJCQtlnM7iXewd2Ir+ohMUpWZ42pVKciT7qqqo7SndUNV1EuqvqPvvdc7CIBGA5iYqhq6Ps4axHK2vcrq4af/Gmu4f3Uw5wrtjGxCs6AueFvsxAwf089dEO0g86m77DOXq2a8ofrq88AC4tLY2kpCSH733wwQekpqaybds2jh07Rp8+fRg82Jru2rp1Kzt27KBdu3YMGDCA9evX8+CDD/LCCy+wZs0awsPDAThz5gxXXHEFzz//PAUFBXTp0oXVq1fTtWtX7rzzTubNm8evf/1rh+cvKipi6tSpLFu2jJYtW7Jw4UIee+wxXn/9daZMmUKTJk145JFHAFi+fHnZeadOnUpiYiJLly7l888/58477yQ11dKkTE9PZ926dQQFBfHmm2+yefNmXn755Rr3r+HiiGnfjMTI5vz76x+5+8oofLxwMawzI4UdIjJPRIbYt7lAut0RFAGPAWeAOBH5QUS227cfsATx6g2FxSX8066A2qOtNZdeNlLwvu/O4GbWrVvHbbfdhq+vL61bt2bIkCFs2rQJgL59+xIREYGPjw8JCQlkZmY6bMPX15ebb74ZgN27d9OpUye6drXSlt91112sXbu20vPv3r2btLQ0RowYQUJCAn/84x/Jyqr+DnPdunVMmjQJgGHDhnH8+HFOn7ac7ZgxYwgK8u6QyEudO/t3ZN+xMxeEvHsTzowU7gbux8rTDNa8wSNYDiEZ8AU6AK8B+VjrElYA76rqxy62160s2ZLNkdOFPDfu/MDlV8mXk5Z9iuRurTxoWcOgqjt6dxEdHc2iRYsuul5AwHmtfF9fX4qLHYueBQYG4utbs6RLqkp0dDQbNzojPeYcjRs3dllbhpoxOrYtf/x4Jwu+3s+gLu6PprxYqh0pqGq+qj6vqmPt299U9ayq2lQ1D8spHARGAzcD/YEU4Fl7BrZ6QYlN+cfafcS0b8qgLuFlx7u0DmH1w0NpHlzVtIihvjJs2DAKCwt55ZXzqXW3b9/OV199xaBBg1i4cCElJSXk5OSwdu1a+vatOjAuJCSE3FzH+aW6detGZmYme/fuBeDtt99myJAhlbbVrVs3cnJyypxCUVERO3bsqLR8KYMGDSqbcP7iiy8IDw+nadOfR5FXZavBfQT4+XJjYntW7zrCybPnPG3Oz6hq8dp79r/flXskVLaVK5oCbLZvW4FvgD8D3YF6c1uydGs2Pxw7w/1DLzeRRg0IEWHJkiWsWrWKzp07Ex0dzYwZM2jTpg1jx44lLi6O+Ph4hg0bxl//+lfatGlTZXuTJ0/mmmuuKZtoLk9gYCBvvPEGt9xyC7Gxsfj4+FwwwV2RRo0asWjRIn7/+98THx9PQkICGzZsqPYzzZw5k5SUFOLi4pg+fTpvvfWWw3LJycmkp6ebiWYPcFOv9hSVKB9td3ka+1ojlWVMEpG2qnpIRDo6el9Vf7SXawKMBW4DEoEPgXeBL7SqdEw1pHfv3urqHM0FRSUk/+0LWoYEsPT+AV45+XOpsnPnTnr06OFpMwwOMN+N+1BVRr30FUGNfNm6/yQAmc9e69ZzikiKM2KjVa1oPmT/+2P5DTgADCxXNBMYibWe4X4stdNr7Vu94LWv9nHoVAGPju5hHILBYHA7IsJNvdqXOQRvoqrHR01FZIaIvGxfpCYiMhVrjcL4ckU7qOodWI7iV1i5E9KBh0Tkz+403hXsy8lj9ud7GRXThn6XhXnaHIPB0EAovzjWm6gq+uht4CdgI/AL4FGsNVw3qmpquXILReQVrInmBFW1AYjIW1jhrMVApqq+7o4PUBuKS2z8fvF2Av18eGpMvRRzNRgM9ZTWTQNJ6NCc1AP2x0fHzpzXWvMgVUUfXaaqd6vqP7DmC3oCIys4BIDJWHmYuwGbReRTEfkcyADaAyne6BAA/rbiezZl/sTMMdG0ahroaXMaLG6YejLUEvOd1A0jo88HLtzxz284mut5ZdqqnEKZOIeqlgBZqvozi1X1sKr+Dms9Qyus9V559rd/Yc/1XCUico2I7BaRvSIy/WI+QE1ZnJLF/C8zuP2KSG7qFVEXpzQ4IDAwkOPHj5uLkBdRmk8hMNDcKLmb6+LaAjAyujXH885x75ubOVPoeM1LXVFV9FEJ1kplsB4bBQFn7a/VkXy2iLQF+th3v1XVwxXLOKjjC3yPJZORBWwCblNVh1qyrog+WrhpPzM++I5+l4Xxxv/0IcCvZouLDLXHZF7zTkzmtbrjaG4BocGN+PL7HO7712biOzTn1Tt7E94koPrKF4Gz0UeVOoUanPAj4D/Ah6p6prry5er1B2aq6kj7/gwAVX3GUfnaOIUjpwv4y/JdfLAlm0FdwvnHpCSCG3l/zlSDwdAwWJ52iIfeTSWscSOevD6aq3u2LouILLEp54ptBDWq2U2ss07BlVfEvwG3Yq1k3oS1VuFjR4+cKtAeK8y1lCzgChfaBcCy1Gx+szAVXx9h6rDLeeiqLviZFJsGg8GLuCamLe/9MohH3t/GlH+n0K5ZINHtm3Gu2MbW/T/xi0GX8eBVXdxqg8ucgqp+KSLfAn8HIoD7gNcBR1naLgp7is7JAJGRkTVqI6ljCx5IvpxxSRF0DPP8DL/BYDA4Ir5Dcz55cBD/TTvEf787zL5jefj7+jA6ti1JHVu4/fyufHx0PfA80Bz4Citfc6GqXlZNvTp7fGQwGAwNFU/MKZzAWs3cGLgF+BLYpqqx1dTzw5povgrIxppovr18DocK5XOAH2toZjjgnXq1nsX0S+WYvnGM6RfHeHO/dFTVamVZXTmncASIATar6hoAEanW46hqsYj8CvgMS3H19cocgr18jbVmRWSzM56yoWH6pXJM3zjG9ItjLoV+caVT2IA10ewrIl2AB+3HqkVVPwVMsliDwWDwMK4Mv5mKlWCnEHgHOM35xDwGg8FgqAe4MvroLFZqzsdc1aYbeKX6Ig0S0y+VY/rGMaZfHFPv+8WVE805WOJ55ekDPAv8w4n1CgaDwWDwMLUeKYhIIBBs3y0EPrC/Hg8EAl2BV4FJtT0XQHh4uEZFRbmiqVqTX1RCXkExRSU2fHyERr4+NPL1wSRuM1wUVfxeav5TqvsfodvO6KaG3dFsIz8ffLz0ApCSknKsrqKPfok1dxAGJAGlM++ngdOq+oCIVJ9Y1kmioqLw9DqFvUfzeHJZGhsyjiNAeKAf+UUlFJUoZjhkMDRcmgX5M3V4F+7qH+V1CbtExKlQflc4hYOq2klEDgNDVXW/3YBIrDBTAO/LTl1DPt91hF/9Zyt+PsLj1/bgpl4RhDZuRIlNOXK6gKyf8ikqsXnaTEM9oaqnt0rlb1Zdr7pzVtFulRWreqtmtlb3flVVa/w5qjlnVbWrqldkU97ffICnPkpn/d5j/P22XjXWKfIkrnAKM4D3seSy14lIBtbIrBNwv4g0BhxnDq9nLE87zP0LUujZrin/vKsPrcvlYPD1Edo1D6Jd8yAPWmgwGDzJ9XFteXNDJk9/nM7db3zLW/f0JdC/fjkGV4SkHheRFViPj7Zz/lHdd8AvVfWMqs5ywXk8gs2m2GzK1v0/8dC7W4mLaM7Cyf0vcAgGg8EAVu7l/xnQiVm3JvDNDyeYvnh7vcsV4oqRwrVAL6z0nYuAjkAjF7TrFdz3r82s3nWU8CaNaN00kNfu6k3jACO3bTAYKueGhPYcOHGWv634nriI5twzsJOnTXKaWo8UVPWcqn6NFXV0F3A/0A64FytFZ72luMTG6l1HASgstvH63X1cnvjCYDBcmjyQfDlXdW/FX5bvIiMnr/oKXoIrVzSPA1oDLVT1f7DyOjuVF0FEMkXkOxFJFRGvkUDduO942espQzpzeasmHrTGYDDUJ0SEZ26KJdDfl98t2o7NVj8eI7nyOUhroAewW0SaAl9g5Wx2lmRV9Sp1wSVbs8tehwSaR0buwKTj9E5MOk7X0KppII9f24Npi7bz0faD3JDQ3tMmVYsrr3RnsKSzjwEpWNFITqfl9DbOnivms7TzKab9TZY2t5CVlUVISAhRUVGIly76aWioKsePHycrK4tOnerPs3Bv5eZeEfxr4488+99dXN2zjdeHqbrySvcV0BPLKYwCPgdWOFlXgRUikmLPsuZxVqYf4cy5EjqEWiGmvuaC5RYKCgoICwszDsGLEBHCwsLM6M1F+NjXNB06VcCCb2qaCqbucKVTaAU8gJVzeQPW46S2TtYdqKq9sJzJAyIyuPybIjJZRDaLyOacnBwXmlw5H2zJpl2zQPp0DLUbUSenbZAYh+B9mO/EtVxxWRhXdg7jH2v3UVBUcsF7a3YdZf1e73lyXmunICKBIhIKNAN+hTWv0B143P63WlQ12/73KLAE6Fvh/VdUtbeq9m7ZssY5dpwm66ezrN2Tw029IsqcgfkXuXQ5fPgwEyZMoHPnziQlJTF69Gi+//77GrU1a9Yszp49e9H1hg4delHyLbt27SIhIYHExEQyMjKYPXs2PXr0YOLEiU63kZqayqefmjQmdcWvhl1OTm4h728+cMHx/3lzExNf+8ZDVv0cV4wUfok1h9Ad2GJ/nQIsA6qdpRKRxiISUvoauBpIc4FdNebdbw8gwG1XRJateDd3TpcmqsrYsWMZOnQoGRkZpKSk8Mwzz3DkyJEatVeVUygpKXF4vCYsXbqUcePGsXXrVjp37szcuXNZuXIlCxYscKp+cXGxcQp1TP/Lwkjq2IL5X+6j2IulcFyxTuElVe0EPKKqncpt8Tg30dwaSx5jG/At8ImqLq+tXTXlXLGNdzcdILlbK9o3DypTQTEu4dJkzZo1+Pv7M2XKlLJj8fHxDBo0CFVl2rRpxMTEEBsby8KFCwH44osvGDp0KOPGjaN79+5MnDgRVWX27NkcPHiQ5ORkkpOTAWjSpAkPP/ww8fHxbNy4kdWrV5OYmEhsbCz33HMPhYWFVdqXkpLCkCFDSEpKYuTIkRw6dIhPP/2UWbNmMW/ePJKTk5kyZQr79u1j1KhRvPjii5w4cYIbb7yRuLg4+vXrx/bt2wGYOXMmkyZNYsCAAUyaNIknn3yShQsXkpCQUPbZDO5DRJg8+DKyT+azaudRT5tTKa6Qzr7J/jK73OtSqtWCUNV9QHxt7XAVK9IPcyyvkDv6dQTOi26ZgYL7eeqjHaQfPO3SNnu2a8ofro+u9P20tDSSkpIcvvfBBx+QmprKtm3bOHbsGH369GHwYGu6a+vWrezYsYN27doxYMAA1q9fz4MPPsgLL7zAmjVrCA8PB+DMmTNcccUVPP/88xQUFNClSxdWr15N165dufPOO5k3bx6//rXjBIVFRUVMnTqVZcuW0bJlSxYuXMhjjz3G66+/zpQpU2jSpAmPPPIIAMuXLy8779SpU0lMTGTp0qV8/vnn3HnnnaSmpgKQnp7OunXrCAoK4s0332Tz5s28/PLLNe5fw8VxVfdWtGsWyL82ZnJNTBtPm+MQV4SkLsSxrKAA3h17VQFV5dWvfiAyNJjBXa25i7KRgnEKDY5169Zx22234evrS+vWrRkyZAibNm2iadOm9O3bl4iICAASEhLIzMxk4MCBP2vD19eXm2++GYDdu3fTqVMnunbtCsBdd93FnDlzKnUKu3fvJi0tjREjRgDW46e2bauP3Vi3bh2LFy8GYNiwYRw/fpzTpy1nO2bMGIKCjGijp/Dz9WFiv44899lu9h7N5fJWIZ426WfU2imo6iWzumVjxnG2HTjJn8bG4GvXQh/eozXLUg/Ss20zD1t36VPVHb27iI6OZtGiRRddLyDgvNyJr68vxcXFDssFBgbi61uzeyNVJTo6mo0bKyY0rDmNGzd2WVuGmnFrnw68tGoP//56PzPH1P1vvjpcFpIqIs1E5IXS0FEReV5E6tWVdO4XGbQMCeDmXhFlx66Pb8fOp6+hWxvv8+iG2jNs2DAKCwt55ZXzqXW3b9/OV199xaBBg1i4cCElJSXk5OSwdu1a+vbtW0VrEBISQm5ursP3unXrRmZmJnv37gXg7bffZsiQIZW21a1bN3JycsqcQlFRETt2VJ+vatCgQWUTzl988QXh4eE0bdr0omw1uI/wJgGMiG7NstRszhV734SzK9cpvI61onm8fTsNvOHC9t3Klv0/sW7vMe4d2Oln+ufevgLRUHNEhCVLlrBq1So6d+5MdHQ0M2bMoE2bNowdO5a4uDji4+MZNmwYf/3rX2nTpurnwJMnT+aaa64pm2guT2BgIG+88Qa33HILsbGx+Pj4XDDBXZFGjRqxaNEifv/73xMfH09CQgIbNmyo9jPNnDmTlJQU4uLimD59Om+95TidSXJyMunp6Wai2QOM6xXBT2eL+GK39004i6u0vkUkVVUTqjtWW3r37q2uTsepqtwyfyOZx8/y5bShRhq7Dtm5cyc9evTwtBkGB5jvxn0Ul9jo98xqencMZfkOS04n89lr3XpOEUlR1d7VlXPlSCFfRMpm2kRkAJDvwvbdxmc7DrP5x5/47YiuxiEYDAa34+frww0J7Vm9q2brYdyJK53C/wJz7DLYmcDLWAvbvJrcgiKe+iidrq2bML53RPUVDAaDwQWMTWxPUYn3yWm78rb4O1WNt8tmo6quDTh3E39ZvovDpwuYM/FK/IwSqsFgqCOi2zUlMjSY/SesFfD550q8Yv7SlVfBH0TkFaAP1oSz17M87RD//no/9wzoRK/IFp42p8FS33LYNgTMd+J+RISre7Yu2//Vf7Z4hfyFK51Cd2AVllLqDyLycvk5hqoQkWtEZLeI7BWR6S60qVJ2H87l4fe2Ed+hOb+7pl5nDa3XBAYGcvz4cXMR8iJK8ykEBlYrSGCoJaPjzi9GXL3rKE8sS/P4/4LLHh+p6lngPeA9EWkBvAR8STWrmkXEF5gDjACygE0i8qGqprvKtop8fySXia99Q+MAP+bf0YsAP88P2RoqERERZGVlUVeS6AbnKM28ZnAvvSJbMOf2XvS7LJR/rvuBuV9k0CTAjxmjeuDj4xkZBZeG2ojIEOBW4BpgM9Z6heroC+y1ayAhIu8CNwAudwqqyrLUgzy+NI2gRr78575+tG1mlvx7En9/f5Pdy9CgudY+Wpg2shu5BcW8+tUP7D9xlj/eGEvLkIBqarselzkFe8TRVqzRwjRVdTYVZ3ugvMB4FnCFq+wqZcPeY/zfJzvZeeg0CR2aM3diL9o1Nw7BYDB4ByLC0zdE0zEsmL8s38XQ59ZwbVxbYiOaU1hUwtb9JxnWvRU3J7l3BOfKkUKcuyKO7Ck6JwNERkbWqI2gRr408vPhLzfHMi6pQ5m2kcFgMHgLIsIvBl3G0G6tmPdFBp9+d5j3NmcB0LZZIH07hbrfBk9PaohIf2Cmqo60788AUNVnHJV3x4pmg8Fg8EZsNuVobiH+vkJo40a1Svbl7Ipmb3AKfsD3wFVANrAJuF1VHSp/iUgOUNPs1+GA9yRD9R5Mv1SO6RvHmH5xjDf3S0dVrTafsSvnFDqp6g/VHauIqhaLyK+Az7AilV6vzCHYy9c4SbOIbHbGUzY0TL9Ujukbx5h+ccyl0C+unFNYDPSqcGwR4DitVTlU9VPAJIs1GAwGD+OKdJzdgWigWYV0nE1xIh2nwWAwGLwHV4wUugHXAc2B68sdzwXuc0H7ruSV6os0SEy/VI7pG8eYfnFMve8XV+ZT6K+qrssbaDAYDIY6x5VOoSXWyCCKciMQVb3HJScwGAwGg9txpSDeMqAZlijeJ+U2r8ATonv1AXv+i+9EJFVEGuwCEBF5XUSOikhauWOhIrJSRPbY/zY4Kd1K+mWmiGTbfzOpIjLakzZ6AhHpICJrRCRdRHaIyEP24/X+N+PWdJzegl1073vKie4Bt7lTdK++YJcn6a2q3hpbXSeIyGAgD/iXqsbYj/0VOKGqz9pvJFqo6u89aWddU0m/zATyVPVvnrTNk4hIW6Ctqm4RkRAgBbgRuJt6/ptx5UjhYy++YygT3VPVc0Cp6J7BAICqrgVOVDh8A1Ca9f4trH/6BkUl/dLgUdVDqrrF/joX2Iml41bvfzO1dgoikisip4GHsBxDvoicLnfcG3AkutfeQ7Z4GwqsEJEUu8aU4TytVfWQ/fVhoHVVhRsYvxKR7fbHS/XuEYkrEZEoIBH4hkvgN1Nrp6CqIara1P7XR1WDyu03dYWRBrcyUFV7AaOAB+yPCwwVUOs5q8kEZDEP6AwkAIeA5z1rjucQkSZYC3d/XVEQtL7+Zlwpc1FxNTPAKeBHVS121XlqSDbQodx+hP1Yg0dVs+1/j4rIEqxHbWs9a5XXcERE2qrqIfsz5KOeNsgbUNUjpa9F5FXgYw+a4zFExB/LISxQ1Q/sh+v9b8aVcwpzga+BV+3b18D7wG4RudqF56kJm4AuItJJRBoBE4APPWyTxxGRxvZJMkSkMXA1kFZ1rQbFh8Bd9td3YUXYNXjsF7tSxtIAfzNiyZX+E9ipqi+Ue6ve/2ZcGX30AfBEqZidiPQEngZ+B3zg6cgk+yT4LM6L7v3Jk/Z4AyJyGbDEvusH/Keh9ouIvAMMxVK5PAL8AViKlTQqEkuZd7yqNqhJ10r6ZSjWoyMFMoFflnuO3iCw55//CvgOsNkPP4o1r1CvfzOudApppSFrFY95c7iqwWAwGM7jSpXUHSIyDyvcE6xczekiEgAUufA8BoPBYHATrhwpBAH3AwPth9ZjzTMUAMGqmueSExkMBoPBbXg885rBYDAYvAdX5FN4T1XHi8h3OIjJVdW42p7DYDAYDHVDrUcK5WJyOzp6X1Vrmk/ZYDAYDHVMrUcKpaFoFS/+IuID3IYVlmUwGAyGeoArtI+aisgMEXlZRK4Wi6nAPmB87U00GNyDiISVk38+XEEOeoObzpkoIv+s4v2WIrLcHec2GJzBFY+PlgE/ARuBq4BWgAAPqWpqrS00GOqAupKDFpH3gT+q6rYqyrwBvKaq691pi8HgCFesU7hMVWMBROQ1LIGsSFUtcEHbBoNHEJE8VW0iIkOBp4CTQCzWatXvsFSBg4AbVTXDnnlwPtZKVrAE0tZXaDMEiCt1CCIyBHjJ/rYCg+0yzEuBiVhh3QZDneIK7aOyhWmqWgJkGYdguMSIB6YAPYBJQFdV7Qu8Bky1l3kJeFFV+wA329+rSG8u1Al6BHjAvtp/EJBvP77Zvm8w1DmuGCnEl8ubIECQfV+w1GONfLahvrOpNKBCRDKAFfbj3wHJ9tfDgZ6WThoATUWkSYVFm22BnHL764EXRGQBlj5Ylv34UaCd6z+GwVA9rog+8nWFIQaDF1NY7rWt3L6N8/9DPkC/akbJ+UBg6Y49ZeMnwGhgvYiMVNVd9jL5lbRhMLgVV0pnGwwNmRWcf5SEiDgSgNwJXF6uTGdV/U5V/4Il797d/lZXGqActcE7ME7BYHANDwK97Skq07HmIC7APgpoVprDAvi1iKSJyHasubn/2o8nA5/UhdEGQ0WM9pHBUIeIyG+AXFV1NBFdWmYtcIOq/lR3lhkMFmakYDDULfO4cI7iAuyhrS8Yh2DwFGakYDAYDIYyzEjBYDAYDGUYp2AwGAyGMoxTMBgMBkMZxikYDAaDoQzjFAwGg8FQxv8Djrcw9zaXnfQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "ename": "FileNotFoundError",
     "evalue": "[Errno 2] No such file or directory: 'drivetrain10.csv'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mFileNotFoundError\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-20-0f18c1e94cc0>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m    117\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    118\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 119\u001b[0;31m \u001b[0mdata\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mread_csv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"drivetrain10.csv\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    120\u001b[0m \u001b[0ms\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m5\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    121\u001b[0m \u001b[0me\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"time\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/.virtualenvs/mechsim/lib/python3.6/site-packages/frc3223_azurite/data.py\u001b[0m in \u001b[0;36mread_csv\u001b[0;34m(fnom)\u001b[0m\n\u001b[1;32m     10\u001b[0m     \u001b[0;34m:\u001b[0m\u001b[0mreturns\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mdictionary\u001b[0m \u001b[0mmapping\u001b[0m \u001b[0mheader\u001b[0m \u001b[0mtext\u001b[0m \u001b[0mto\u001b[0m \u001b[0mcolumn\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     11\u001b[0m     \"\"\"\n\u001b[0;32m---> 12\u001b[0;31m     \u001b[0;32mwith\u001b[0m \u001b[0mopen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfnom\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'r'\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     13\u001b[0m         \u001b[0mreader\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcsv\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreader\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     14\u001b[0m         \u001b[0mheaders\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnext\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mreader\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mFileNotFoundError\u001b[0m: [Errno 2] No such file or directory: 'drivetrain10.csv'"
     ]
    }
   ],
   "source": [
    "import frccontrol as frccnt\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import control\n",
    "import numpy\n",
    "from frc3223_azurite.data import read_csv\n",
    "from frc3223_azurite.conversions import *\n",
    "\n",
    "class Drivetrain(frccnt.System):\n",
    "    def __init__(self, dt):\n",
    "        \"\"\"Drivetrain subsystem.\n",
    "        Keyword arguments:\n",
    "        dt -- time between model/controller updates\n",
    "        \"\"\"\n",
    "        state_labels = [\n",
    "            (\"Left position\", \"m\"),\n",
    "            (\"Left velocity\", \"m/s\"),\n",
    "            (\"Right position\", \"m\"),\n",
    "            (\"Right velocity\", \"m/s\"),\n",
    "        ]\n",
    "        u_labels = [(\"Left voltage\", \"V\"), (\"Right voltage\", \"V\")]\n",
    "        self.set_plot_labels(state_labels, u_labels)\n",
    "\n",
    "        self.in_low_gear = True\n",
    "\n",
    "        # Number of motors per side\n",
    "        self.num_motors = 2.0\n",
    "\n",
    "        # Drivetrain mass in kg\n",
    "        self.m = lbs_to_kg(110)\n",
    "        # Radius of wheels in meters\n",
    "        self.r = inch_to_meter(3)\n",
    "        # Radius of robot in meters\n",
    "        self.rb = inch_to_meter(23)\n",
    "        # Moment of inertia of the drivetrain in kg-m^2\n",
    "        self.J = 3.0\n",
    "\n",
    "\n",
    "        self.Gl = self.Gr = 10.75\n",
    "\n",
    "        self.model = frccnt.models.drivetrain(\n",
    "            frccnt.models.MOTOR_CIM,\n",
    "            self.num_motors,\n",
    "            self.m,\n",
    "            self.r,\n",
    "            self.rb,\n",
    "            self.J,\n",
    "            self.Gl,\n",
    "            self.Gr,\n",
    "        )\n",
    "        \n",
    "        A=numpy.array([\n",
    "                [  0.        ,   1.        ,   0.        ,   0.        ],\n",
    "                [  0.        , -18.70879036,   0.        ,  15.90601316],\n",
    "                [  0.        ,   0.        ,   0.        ,   1.        ],\n",
    "                [  0.        ,  15.90601316,   0.        , -18.70879036]])\n",
    "        B=numpy.array([\n",
    "                [ 0.        ,  0.        ],\n",
    "                [ 6.61359246, -5.33282046],\n",
    "                [ 0.        ,  0.        ],\n",
    "                [-5.33282046,  6.61359246]])\n",
    "        C=numpy.array([[1, 0, 0, 0],\n",
    "                           [0, 0, 1, 0]])\n",
    "        D=numpy.zeros(shape=(2,2))\n",
    "        #self.model = control.ss(A, B, C, D)\n",
    "        u_min = np.matrix([[-12.0], [-12.0]])\n",
    "        u_max = np.matrix([[12.0], [12.0]])\n",
    "        frccnt.System.__init__(self, self.model, u_min, u_max, dt)\n",
    "\n",
    "        q_pos = 0.12\n",
    "        q_vel = 1.0\n",
    "\n",
    "        q = [q_pos, q_vel, q_pos, q_vel]\n",
    "        r = [12.0, 12.0]\n",
    "        self.design_dlqr_controller(q, r)\n",
    "\n",
    "        qff_pos = 0.005\n",
    "        qff_vel = 1.0\n",
    "        self.design_two_state_feedforward(\n",
    "            [qff_pos, qff_vel, qff_pos, qff_vel], [12.0, 12.0]\n",
    "        )\n",
    "\n",
    "        q_pos = 0.05\n",
    "        q_vel = 1.0\n",
    "        q_voltage = 9.0\n",
    "        q_encoder_uncertainty = 2.0\n",
    "        r_pos = 0.0001\n",
    "        r_gyro = 0.000001\n",
    "        self.design_kalman_filter([q_pos, q_vel, q_pos, q_vel], [r_pos, r_pos])\n",
    "        \n",
    "\n",
    "dt=0.02\n",
    "drivetrain = Drivetrain(dt=dt)\n",
    "try:\n",
    "    import slycot\n",
    "\n",
    "    plt.figure(1)\n",
    "    drivetrain.plot_pzmaps()\n",
    "except ImportError:  # Slycot unavailable. Can't show pzmaps.\n",
    "    pass\n",
    "\n",
    "t, xprof, vprof, aprof = frccnt.generate_s_curve_profile(\n",
    "        max_v=2.5, max_a=3.5, time_to_max_a=1.0, dt=dt, goal=50.0\n",
    ")\n",
    "\n",
    "refs = []\n",
    "for i in range(len(t)):\n",
    "    r = np.matrix([[xprof[i]], [vprof[i]], [xprof[i]], [vprof[i]]])\n",
    "    refs.append(r)\n",
    "    \n",
    "plt.figure(2)\n",
    "state_rec, ref_rec, u_rec = drivetrain.generate_time_responses(t, refs)\n",
    "drivetrain.plot_time_responses(t, state_rec, ref_rec, u_rec)\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "data = read_csv(\"drivetrain10.csv\")\n",
    "s = 5\n",
    "e = len(data[\"time\"])\n",
    "ts = data[\"time\"][s:e]\n",
    "bus_voltages = data[\"voltage\"][s:e]\n",
    "percentVLeft = data[\"VRL\"][s:e]\n",
    "percentVRight = -data[\"VPR\"][s:e]\n",
    "voltages_l = (bus_voltages * percentVLeft)\n",
    "voltages_r = bus_voltages * percentVRight\n",
    "encPosL = data[\"enc_pos_l\"][s:e]\n",
    "encPosR = -data[\"enc_pos_r\"][s:e]\n",
    "\n",
    "vsl=data[\"enc_vel_l\"][s:e]\n",
    "vsr=-data[\"enc_vel_r\"][s:e]\n",
    "sim_encpos_l = numpy.zeros(shape=ts.shape)\n",
    "sim_encpos_r = numpy.zeros(shape=ts.shape)\n",
    "sim_encvel_l = numpy.zeros(shape=ts.shape)\n",
    "sim_encvel_r = numpy.zeros(shape=ts.shape)\n",
    "\n",
    "print(vsl[0], vsr[0], encPosL[0], encPosR[0])\n",
    "drivetrain.reset()\n",
    "drivetrain.x[0] = encPosL[0] / 630. / 3.28\n",
    "drivetrain.x[1] = vsl[0] / 630 / 3.28 * 10\n",
    "drivetrain.x[2] = encPosR[0] / 630. / 3.28\n",
    "drivetrain.x[3] = vsr[0] / 630 / 3.28 * 10\n",
    "print(drivetrain.x)\n",
    "for i, t in enumerate(ts):\n",
    "    sim_encpos_l[i] = drivetrain.x[0] * 630 * 3.28\n",
    "    sim_encpos_r[i] = drivetrain.x[2] * 630 * 3.28\n",
    "    sim_encvel_l[i] = drivetrain.x[1] * 630 * 3.28 / 10\n",
    "    sim_encvel_r[i] = drivetrain.x[3] * 630 * 3.28 / 10\n",
    "    u = numpy.matrix([\n",
    "        [voltages_l[i],],\n",
    "        [voltages_r[i],],\n",
    "    ])\n",
    "    drivetrain.x = drivetrain.sysd.A * drivetrain.x + drivetrain.sysd.B * u\n",
    "    drivetrain.y = drivetrain.sysd.C * drivetrain.x + drivetrain.sysd.D * u\n",
    "    \n",
    "\n",
    "plt.plot(ts, voltages_r)\n",
    "plt.plot(ts, voltages_l)\n",
    "plt.legend([\"right voltage\", \"left voltage\"])\n",
    "plt.show()\n",
    "\n",
    "plt.plot(ts, encPosL, color=\"green\")\n",
    "plt.plot(ts, sim_encpos_l, color=\"orange\")\n",
    "plt.ylabel(\"left position\")\n",
    "plt.legend([\"actual\", \"simulated\"])\n",
    "plt.show()\n",
    "\n",
    "plt.plot(ts, encPosR, color=\"green\")\n",
    "plt.plot(ts, sim_encpos_r, color=\"orange\")\n",
    "plt.ylabel(\"right position\")\n",
    "plt.legend([\"actual\", \"simulated\"])\n",
    "plt.show()\n",
    "\n",
    "plt.plot(ts, vsl, color=\"green\")\n",
    "plt.plot(ts, sim_encvel_l, color=\"orange\")\n",
    "plt.legend([\"actual\", \"simulated\"])\n",
    "plt.ylabel(\"left velocity\")\n",
    "plt.show()\n",
    "\n",
    "plt.plot(ts, vsr, color=\"green\")\n",
    "plt.plot(ts, sim_encvel_r, color=\"orange\")\n",
    "plt.legend([\"actual\", \"simulated\"])\n",
    "plt.ylabel(\"right velocity\")\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A =  matrix([[1.        , 0.01631643, 0.        , 0.00238268],\n",
      "        [0.        , 0.66737266, 0.        , 0.20542149],\n",
      "        [0.        , 0.00238268, 1.        , 0.01631643],\n",
      "        [0.        , 0.20542149, 0.        , 0.66737266]])\n",
      "\n",
      "B =  matrix([[ 0.00123499, -0.00079884],\n",
      "        [ 0.11152021, -0.06887181],\n",
      "        [-0.00079884,  0.00123499],\n",
      "        [-0.06887181,  0.11152021]])\n",
      "\n",
      "C =  matrix([[1, 0, 0, 0],\n",
      "        [0, 0, 1, 0]])\n",
      "\n",
      "D =  matrix([[0, 0],\n",
      "        [0, 0]])\n",
      "\n",
      "K =  matrix([[56.82612189,  6.03969859, 18.60045886,  3.51953103],\n",
      "        [18.60045886,  3.51953103, 56.82612189,  6.03969859]])\n",
      "\n",
      "Kff =  matrix([[731.26285269,   1.74253981, 334.3110478 ,   0.86234499],\n",
      "        [334.3110478 ,   0.86234499, 731.26285269,   1.74253981]])\n",
      "\n",
      "L =  matrix([[1.12809912, 0.08747579],\n",
      "        [5.70458841, 4.3576656 ],\n",
      "        [0.08747579, 1.12809912],\n",
      "        [4.3576656 , 5.70458841]])\n",
      "\n",
      "Ainv =  matrix([[ 1.        , -0.02579361,  0.        ,  0.0043692 ],\n",
      "        [ 0.        ,  1.65523823,  0.        , -0.5094927 ],\n",
      "        [ 0.        ,  0.0043692 ,  1.        , -0.02579361],\n",
      "        [ 0.        , -0.5094927 ,  0.        ,  1.65523823]])\n",
      "A continuous:  matrix([[  0.        ,   1.        ,   0.        ,   0.        ],\n",
      "        [  0.        , -22.70879036,   0.        ,  15.90601316],\n",
      "        [  0.        ,   0.        ,   0.        ,   1.        ],\n",
      "        [  0.        ,  15.90601316,   0.        , -22.70879036]])\n",
      "\n",
      "B continuous:  matrix([[ 0.        ,  0.        ],\n",
      "        [ 7.61359246, -5.33282046],\n",
      "        [ 0.        ,  0.        ],\n",
      "        [-5.33282046,  7.61359246]])\n"
     ]
    }
   ],
   "source": [
    "for a in [\"A\", \"B\",\"C\",\"D\"]:\n",
    "    print (a+\" = \", repr(getattr(drivetrain.sysd, a)))\n",
    "    print(\"\")\n",
    "    \n",
    "for a in [\"K\", \"Kff\", \"L\"]:\n",
    "    print(a+\" = \", repr(getattr(drivetrain, a)))\n",
    "    print(\"\")\n",
    "    \n",
    "ainv = numpy.linalg.inv(drivetrain.sysd.A)\n",
    "print(\"Ainv = \", repr(ainv))\n",
    "\n",
    "print(\"A continuous: \", repr(drivetrain.sysc.A))\n",
    "print(\"\")\n",
    "print(\"B continuous: \", repr(drivetrain.sysc.B))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Gl',\n",
       " 'Gr',\n",
       " 'J',\n",
       " 'K',\n",
       " 'Kff',\n",
       " 'L',\n",
       " 'P_steady',\n",
       " 'Q',\n",
       " 'R',\n",
       " '_System__default',\n",
       " '_System__make_cost_matrix',\n",
       " '_System__make_cov_matrix',\n",
       " '_System__update_observer',\n",
       " '__class__',\n",
       " '__delattr__',\n",
       " '__dict__',\n",
       " '__dir__',\n",
       " '__doc__',\n",
       " '__eq__',\n",
       " '__format__',\n",
       " '__ge__',\n",
       " '__getattribute__',\n",
       " '__gt__',\n",
       " '__hash__',\n",
       " '__init__',\n",
       " '__init_subclass__',\n",
       " '__le__',\n",
       " '__lt__',\n",
       " '__module__',\n",
       " '__ne__',\n",
       " '__new__',\n",
       " '__reduce__',\n",
       " '__reduce_ex__',\n",
       " '__repr__',\n",
       " '__setattr__',\n",
       " '__sizeof__',\n",
       " '__str__',\n",
       " '__subclasshook__',\n",
       " '__weakref__',\n",
       " 'correct_observer',\n",
       " 'design_dlqr_controller',\n",
       " 'design_kalman_filter',\n",
       " 'design_two_state_feedforward',\n",
       " 'export_cpp_coeffs',\n",
       " 'extract_row',\n",
       " 'generate_time_responses',\n",
       " 'in_low_gear',\n",
       " 'm',\n",
       " 'model',\n",
       " 'num_motors',\n",
       " 'place_controller_poles',\n",
       " 'place_observer_poles',\n",
       " 'plot_pzmaps',\n",
       " 'plot_time_responses',\n",
       " 'predict_observer',\n",
       " 'r',\n",
       " 'rb',\n",
       " 'reset',\n",
       " 'set_plot_labels',\n",
       " 'state_labels',\n",
       " 'sysc',\n",
       " 'sysd',\n",
       " 'u',\n",
       " 'u_labels',\n",
       " 'u_max',\n",
       " 'u_min',\n",
       " 'update',\n",
       " 'x',\n",
       " 'x_hat',\n",
       " 'y']"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dir(drivetrain)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'ss(A, B, C, D[, dt])\\n\\n    Create a state space system.\\n\\n    The function accepts either 1, 4 or 5 parameters:\\n\\n    ``ss(sys)``\\n        Convert a linear system into space system form. Always creates a\\n        new system, even if sys is already a StateSpace object.\\n\\n    ``ss(A, B, C, D)``\\n        Create a state space system from the matrices of its state and\\n        output equations:\\n\\n        .. math::\\n            \\\\dot x = A \\\\cdot x + B \\\\cdot u\\n\\n            y = C \\\\cdot x + D \\\\cdot u\\n\\n    ``ss(A, B, C, D, dt)``\\n        Create a discrete-time state space system from the matrices of\\n        its state and output equations:\\n\\n        .. math::\\n            x[k+1] = A \\\\cdot x[k] + B \\\\cdot u[k]\\n\\n            y[k] = C \\\\cdot x[k] + D \\\\cdot u[ki]\\n\\n        The matrices can be given as *array like* data types or strings.\\n        Everything that the constructor of :class:`numpy.matrix` accepts is\\n        permissible here too.\\n\\n    Parameters\\n    ----------\\n    sys: StateSpace or TransferFunction\\n        A linear system\\n    A: array_like or string\\n        System matrix\\n    B: array_like or string\\n        Control matrix\\n    C: array_like or string\\n        Output matrix\\n    D: array_like or string\\n        Feed forward matrix\\n    dt: If present, specifies the sampling period and a discrete time\\n        system is created\\n\\n    Returns\\n    -------\\n    out: :class:`StateSpace`\\n        The new linear system\\n\\n    Raises\\n    ------\\n    ValueError\\n        if matrix sizes are not self-consistent\\n\\n    See Also\\n    --------\\n    StateSpace\\n    tf\\n    ss2tf\\n    tf2ss\\n\\n    Examples\\n    --------\\n    >>> # Create a StateSpace object from four \"matrices\".\\n    >>> sys1 = ss(\"1. -2; 3. -4\", \"5.; 7\", \"6. 8\", \"9.\")\\n\\n    >>> # Convert a TransferFunction to a StateSpace object.\\n    >>> sys_tf = tf([2.], [1., 3])\\n    >>> sys2 = ss(sys_tf)\\n\\n    '"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frccnt.models.cnt.ss.__doc__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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