diff --git a/README.md b/README.md index ff6dea2c..682ed5bf 100644 --- a/README.md +++ b/README.md @@ -1,4 +1,4 @@ -# AAE497 Fall 2019 [![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/jgoppert/aae497-f19/master) [](https://mybinder.org/v2/gh/jgoppert/aae497-f19/master?urlpath=lab) [![nbviewer](https://img.shields.io/badge/view%20on-nbviewer-brightgreen.svg)](http://nbviewer.jupyter.org/github/jgoppert/aae497-f19/tree/master) +# AAE497 Fall 2019 [![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/cohen39/aae497-f19/master) [](https://mybinder.org/v2/gh/cohen39/aae497-f19/master?urlpath=lab) [![nbviewer](https://img.shields.io/badge/view%20on-nbviewer-brightgreen.svg)](http://nbviewer.jupyter.org/github/cohen39/aae497-f19/tree/master) Class notebook. diff --git a/homework/1-F16-Pitch.ipynb b/homework/1-F16-Pitch.ipynb deleted file mode 100644 index 3c4f1386..00000000 --- a/homework/1-F16-Pitch.ipynb +++ /dev/null @@ -1,58 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import sys\n", - "sys.path.insert(0, '../python/casadi_f16')\n", - "import f16\n", - "import control\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from analysis import loop_analysis" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Pitch Autopilot Design\n", - "\n", - "* See Pitch Autopilot design example in section 4.6 of Stevens and Lewis.\n", - "* Homework 1: Due 8/30 @ 11 pm: Trim the F16 model around a VT=550 ft/s, 20 deg/s yaw rate turn.\n", - "* Find the A, B, C, D matrices for the state space model.\n", - "* Find the transfer function for the aileron to pitch rate (Q).\n", - "* Design a PID controller attempting to meet the following specifications\n", - " * Maximum overshoot: 20%\n", - " * Rise time: 0.1 second\n", - " * Settling time 1 second\n", - "* Simulate and plot the response of your controlled system and the linear model for a step response in pitch rate of 10 deg/s and 100 deg/s. How do the nonlinear and linear responses compare?\n", - "* Using git, fork aae497-f16 on github. Complete the homework. Submit your homework via pull request on aae497-f16." - ] - } - ], - "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": "3.7.3" - } - }, - "nbformat": 4, - "nbformat_minor": 4 -} diff --git a/homework/6-Casadi-Brach.ipynb b/homework/6-Casadi-Brach.ipynb index 4b3f21af..48479cf6 100644 --- a/homework/6-Casadi-Brach.ipynb +++ b/homework/6-Casadi-Brach.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": 5, "metadata": {}, "outputs": [], "source": [ @@ -23,7 +23,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 51, "metadata": {}, "outputs": [], "source": [ @@ -34,24 +34,49 @@ " starts at a height of 1 m and ends at a height of 0 m and the length of the path is\n", " x_end m.\n", " \"\"\"\n", - " x = np.linspace(0, x_end, n_x) # x position where path changes\n", - " dx = x[1] - x[0] # path steps width\n", + " x_pos = np.linspace(0, x_end, n_x) # x position where path changes\n", " n_dy = n_x - 1 # number of height changes we need to find\n", - " dy0 = -(1/n_dy)*np.ones(n_dy) # initial guess for height change along path\n", + " dy_pos_guess = -(1/n_dy)*np.ones(n_dy) # initial guess for height change along path\n", " \n", - " for i in range(n_dy):\n", - " # find average velocit of this track segment\n", - " # find length of this track segment\n", - " # use the above to find the d\n", + " x_1 = x_pos[0]\n", + " x_2 = x_pos[-1]\n", + " y_1 = 1\n", + " y_2 = 0\n", + " \n", + " dy_pos = ca.SX.sym('y_pos',n_x-1)\n", + " nlp = {'x': dy_pos, 'f': t12(x_pos,dy_pos), 'g': y_1+ca.sum1(dy_pos)}#Vary dy_pos to minimiz OF 'f' constrained by the sum of dy's = -1\n", + " tmin = ca.nlpsol('tmin', 'ipopt', nlp, {\n", + " 'print_time': 0,\n", + " 'ipopt': {\n", + " 'sb': 'yes',\n", + " 'print_level': 0,\n", + " }\n", + " })\n", + " res = tmin(x0=dy_pos_guess,lbg=y_2,ubg=y_2) \n", + " dy_opt = res['x']\n", + " y_opt = np.concatenate((np.array([y_1]),y_1+np.cumsum(dy_opt)),axis=0)\n", + " return x_pos, y_opt\n", + "\n", + "\n", + "def t12(x_pos,dy_pos):\n", + " g = 9.81\n", + " y = 1 #set initial height\n", + " t_total = 0\n", + " dx = np.mean(np.diff(x_pos))\n", + " \n", + " for i in range(len(x_pos)-1):\n", + " dy = dy_pos[i]\n", + " length = ca.sqrt(ca.power(dy,2)+ca.power(dx,2))\n", + " dt = 2*length/(ca.sqrt(2*g*(1-y))+ca.sqrt(2*g*(1-y-dy)))\n", + " t_total = t_total + dt\n", + " y = y + dy\n", " \n", - " dy_opt = dy0 # TODO, find optimal change in y along path\n", - " y_opt = ca.vertcat(1, 1 + np.cumsum(dy_opt))\n", - " return x, y_opt" + " return t_total" ] }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 52, "metadata": {}, "outputs": [], "source": [ @@ -81,22 +106,22 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 4, + "execution_count": 53, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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aGkp8fDwzZsxg6NChJCYmMmzYMEaMGMErr7zC008/TWzsny+Q3r9/P2PGjCElJYWoqKizc1q0bNmSlJQUKlSowOzZs/nnP/9ZqFIgRaWJIi/16sHatXDyJFSqVGabFRH6tIwgvnktvlm5m2d/WM+Yd5fQsWE49w9oQfcmzpYFUaq8yi7jDZwt4x0YGHh2HCAmJoZZs2YBkJqaypVXXsnu3bs5ffo0UVFRf1nf6NGjmTRpEkOHDuXtt9/mjTfeKHD7CxcuJC4u7uy6qlWrBsCRI0e44YYb2LhxIyLyp1LlpUkTRV7q1bP//v47NG1a5pv38xOGRNflora1+WxpKi/+uJFr3lhEz6Y1uG9ACzo0CC/zmJTyCAXtAQQEFLw8OLjQexA55SzjHRwcTHx8POnp6QQEBJzd0/f39ycjIwOAO++8kwkTJjBkyBCSk5N59NFH/7LOHj16sG3bNubOnUtmZiZt27YtMAZjTJ5HFR555BESEhKYNm0a27Zto3fv3kXuX2HoGEVe6taF+HhwZW2nBPj7cXXnhiTdF8/DF7dize6jDH3lJ8a+u4T1ezx3MnilfEnOMt7r1q07bxnvI0eOUM/1Y/Odd97Jt93111/P1VdfzY03npuPLTQ0NM/5Mbp168bcuXPZunUrwNlDTzm3NTWvw3KlRBNFXipW9IhEkS0owJ/RvRqTMjGBCf2b8/PmAwx8IYV7Pv5Ny4Io5WY5y3g/8sgj5y3j/eijjzJixAh69epFjRr5Hy6+9tprOXToEFdffW7+tlGjRnHrrbeeHczOVrNmTSZPnszll19OdHQ0V155JQATJ07koYceokePHmRmuvH0emOMT91iYmJMSSQlJdk7p04Zs2mTMZmZJVqfOxxMO2X+M2ONaf63mabJQzPM/32xwuw5cvJPbc72wwdoXzxTWfRlzZo1bt/G0aNH3b6NvHz66afmuuuuK9V1FrYvef1dgSUmn+9VHaPIz7p18MUXcOutULu209H8SdXKgTw0qBU39Yzi5Tmb+GjxDj5bmsqo7pHc2rsJVSsHOh2iUqoAd955J99++y0zZ850OpRC0USRn0aN7L/bt3tcosgW4SoLMqZXY57/cQOT523hg0U7GNOrMc3RazCU8lQvvfSS0yEUiY5R5CcsDMLDYds2pyM5r4bVg3n2ig58Pz6OHk2r89zsDUyce4Ip87QsiPJ+xsdm4XRacf6emigKEhlpE4WXfFCbR4Tyv5GxfHVHDxpW8ePxGWtJeDqZjxZrWRDlnYKCgjhw4IAmi1JijOHAgQMEBQUV6XV66KkgUVHw22+wd6/HHn7KS3SDcO7vVInABm156vv1PPTFSv43dzP39G/O4PZ18fPTq7yVd6hfvz6pqans37/fbdtIT08v8henpypMX4KCgqhfxKkUHE0UIjIQeAHwB6YYY/6ba3lD4B0g3NXmQWNM2Y3+NG8Ot9wCERFltsnS1L1JDb64rTpz1u3jqe/PlQW5f0AL+rTUsiDK8wUEBOR5ZXNpSk5OpmPHjm7dRllxV18cO/QkIv7AK8BFQGvgahHJXSbxYeATY0xH4Crg1TINslIlW/fJi79QRYS+rSKYeVcvXriqA+lnMrn5nSUMe20BP28u+tzgSqnyx8kxis7AJmPMFmPMaSARuDRXGwNUcd0PA8q2Uh/Anj0wY4bb5qcoK35+wqUd6jFrQm/+c1k7dh1O5+o3FjLyzUUs33nY6fCUUh5MnBokEpHhwEBjzGjX45FAF2PMuBxt6gA/AFWBykA/Y8zSPNY1FhgLEBEREZOYmFjsuNLS0ggJCTn7uFJqKhGzZ7Onf3/Ss2tAeYHc/cjtdKZhzo4MvtlymrQzEBPhz+XNAqkX4nnnN5yvL95E++J5fKUfULK+JCQkLDXGxOa5ML8r8dx9A0ZgxyWyH48EXsrVZgJwr+t+N2AN4FfQekvtyuxsp08b869/GfPttyVab1kr7FWzx9LPmOdnbTBt/v6diXzwG3PPx8vMjgPH3RtcEenVzJ7JV/riK/0wpmR9oYArs538+ZgKNMjxuD5/PbR0M/AJgDHmZyAIKNta2wEB9jRZN00I4rSQihW4u18z5k1MYEyvxsxYsZs+zyTzyJer2Hc03enwlFIewMlE8QvQTESiRCQQO1g9PVebHUBfABFphU0U7jtPLj/NmsGBA/bmo6pWDuT/BrUiZWICV3ZqwEeLdxD3VBJPfLuWQ8dPOx2eUspBjiUKY0wGMA74HliLPbtptYg8JiJDXM3uBcaIyHLgI2CUaxepbLVoAaGhcNj3B30jqgTx+NB2/Hhvby5qW4fJKVuIm5TEiz9uJO1UhtPhKaUc4Oh1FMZeEzEz13N/z3F/DdCjrOP6i/BwmDDBq0+TLapG1Svz3JUduLV3E575YT3PztrAOwu2cXtCU67t0pCgAH+nQ1RKlRHPO8XFU4nYUh7urPnugVrUDmXy9bFMu707repU4V/frKHP08kkLt5BhpYFUapc0ERRWEePwrPPwsqVTkfiiI4Nq/L+6C58OLoLtaoE8eAXK+n/XArTl+8iK0vr8CjlyzRRFFZoKPj5wdq1TkfiqO5NazDt9u68cX0sgf5+3PXRMi5+aT5z1u3Vwm1K+ShNFIUlAq1awebNcOqU09E4SkTo3zqCb++2ZUFOnM7gpqlLGP76zyzc4rtnhilVXmmiKIrWrSEjAzZscDoSj5BdFmS2qyxI6qETXDV5Ide/tZiVqUecDk8pVUo0URRFgwb2ENTq1U5H4lEC/P24pktD5t6fwN8GtWJl6mEGvzyfW99byqZ9x5wOTylVQjofRVGIwIUXQuXKTkfikYIC/BkT15irOjdgyrytvDl/Kz+s2cNlHeszvl8zGlQLdjpEpVQxaKIoqnbtnI7A44UGBXBP/+bc0D2S15I38c7P25m+/Heu6dyQO/o0pVaob0wSo1R5oYeeimP/fvj1V6ej8HjVKgfyt4tbk3J/AiNiG/DBoh3ETUriv9+u4/AJLQuilLfQRFEcK1bAN99AWprTkXiF2mFB/Oeydsye0JsBbWrzv5TN9JqUxMtzNnJcy4Io5fE0URRH+/aQlQWrVjkdiVeJrFGZF67qyLd396JLVHWe/mEDcZOSeGv+VtLPlK8r3pXyJpooiqNmTahbF5YvdzoSr9SydhWm3BDLF7d3p3lEKI+5yoJ88stOLQuilAfSRFFc0dGwezfs3et0JF7rgoZV+WhsVz4Y3YWaVYKY+PkKLnwuhW9WaFkQpTyJJoriatsWgoJg3z6nI/F6PZrW4MvbuzN5ZAwV/IVxHy7jkpfmk7Run5YFUcoD6OmxxVW5Mtx3H1TQP2FpEBEubFObvq0imL78d56btZEbp/5CbKOq9I/IJN7pAJUqx3SPoiSyk8SZM87G4UP8/YTLOtZn9oTePD60LTsOnuCJxelaFkQpB2miKKkPP4RPP3U6Cp8TWMGP67o2Yu79CVzZIpAVrrIgt72vZUGUKmuaKEoqIgI2boQj+mvXHSoF+nNRVAApExO4q28zUjbs58LnUrjv0+XsPHjC6fCUKhc0UZRUTIz9d9kyZ+PwcVWCApjQvzkpExO4qUcU05fvos8zyfzjq1XsO5budHhK+TRNFCUVHg5NmtiSHll6DYC7VQ+pyMOXtGbu/fEMj2nA+4t20HtSMk9+t44jJ3SsSCl30ERRGmJj7VSpOk9FmakTVoknLrdlQfq3juD1uZvpOWkOryRt0rIgSpUyTRSloXlzGDrU7lmoMhVVozIvXt2RmXf1oktUNZ76fj29n0ri7Z+2cipDy4IoVRo0UZQGPz/o0AECApyOpNxqVacKU27oxOe3dadprRD++fUa+jw9V8uCKFUKHE0UIjJQRNaLyCYReTCfNleIyBoRWS0iH5Z1jEWyZAnMn+90FOVaTKOqfDSmK+/f3IUaIYG2LMjzKcxYsVvLgihVTI4lChHxB14BLgJaA1eLSOtcbZoBDwE9jDFtgPFlHmhR7NwJKSmQrmfhOElE6NmsBl/e0YPXr4vBX4Q7PvyVwS/PJ2m9lgVRqqic3KPoDGwyxmwxxpwGEoFLc7UZA7xijDkEYIzx7MJKXbrA6dN6qqyHEBEGtq3Nd+PjePaKaI6mn+HGt3/hiv/9zOKtB50OTymvIU79uhKR4cBAY8xo1+ORQBdjzLgcbb4ENgA9AH/gUWPMd3msaywwFiAiIiImMTGx2HGlpaUREhJS7NfX/vZbKhw/Turll9uxC4eUtB+epLT6kpFlSEnNYPrmMxw+ZWhfw5/LmwUQGeZfClEWjr4vnsdX+gEl60tCQsJSY0xsnguNMY7cgBHAlByPRwIv5WrzDTANCACigFQgvKD1xsTEmJJISkoq0evNmjXG/OMfxqxeXbL1lFCJ++FBSrsvJ05lmNeSN5nof35vGj3wjbn9/aVm495jpbqN/Oj74nl8pR/GlKwvwBKTz/eqk4eeUoEGOR7XB3bl0eYrY8wZY8xWYD3QrIziK54WLWwJ8uBgpyNR+agU6M+tvZucLQuSvH4fFz43l/s/XU7qIS0LolRuTiaKX4BmIhIlIoHAVcD0XG2+BBIARKQG0BzYUqZRFpWfHwwfDpGRTkeiziNnWZAbe0Tx1fJd9Hl6Lo9OX83+Y6ecDk8pj+FYojDGZADjgO+BtcAnxpjVIvKYiAxxNfseOCAia4Ak4H5jzAFnIi6i48dhxQqno1CFUD2kIo9c0prk++K5/IJ6vLdwO3GTknjqey0LohQ4PHGRMWYmMDPXc3/Pcd8AE1w37/LLL5CcDHXq2Dm2lcerG16J/w5rzy29m/DcrA28krSZ937ezi29m3Bjj0iCA3WSKlU+6ZXZ7tK5s71SWy/A8zo5y4J0irRlQeImJfPOgm1aFkSVS5oo3CU42BYLXLkSDh1yOhpVDK3rVuHNUZ34/LZuNKlZmX9MX02fp+fy6RItC6LKF00U7tS9O4jATz85HYkqgZhG1Ugc25X3bu5M9ZBA7v9sBQOeT2HmSi0LosoHTRTuFBoKHTvCqVOgZSO8mojQq1lNvrqjB69fdwF+Itz+wa8MeWU+yVoWRPk4HZ1zt0GDHL1CW5UuWxakDv1b1+bLZb/z3OwNjHr7FzpHVuP+gS3oFFnN6RCVKnX6DeZu2Unijz8gLc3ZWFSp8fcThsXUZ8698fzr0jZsPXCcEa//zI1vL2bV7zp/uvItmijKwokT8PrrMG+e05GoUhZYwY+R3SJJuT+BBwa25Ncdh7nkpfnc8eGvbN6vPwyUb9BEURaCg6F9e1i61E6ZqnxOpUB/bot3lQXp05Skdfu48LkUHvhsBb8fPul0eEqViCaKshIXZwe05851OhLlRmGVAphwYQtSJiZwQ7dIpi37nYSnkvnn16v5I03LgijvpImirISHQ0yMnavioM6F4OtqhFTk74Nbk3R/PJd1rMe7P9uyIJ9vOM2Rk1oWRHkXTRRlKS4OKlaE3393OhJVRuqFV+LJ4e354Z44+rSsxddbztDryTm8mryJE6cznA5PqULR02PLUkgITJhgS3uocqVJzRBevuYCOoX8yNyDVZj03Xre/mkbd/ZpylWdGhJYQX+zKc+ln86ylp0kduWeekOVB42q+PPWqE58dms3ompU5u9frabPM8l8tjSVTL3KW3koTRROWLkSJk+GbducjkQ5JDayGh+P7co7N3UmPDiA+z5dzoDnU/h25W69ylt5HE0UTmjZEqpUgVmztLRHOSYi9G5ek6/H9eS1ay/AGMNtH/zKkJd/ImXDfk0YymNoonBCQAD06WMHtVetcjoa5TAR4aJ2dfjhnt48PSKag8dPc/1bi7lq8kKWbtcz5JTzNFE4pX17qF0bZs+GM3q6pLJlQYbH1GfOfb3555A2bN5/nGGv/cxNU39hzS69UFM5RxOFU/z8YOBAyMiwdaCUcqlYwZ8bukeSMjGeiQNbsGTbQQa9OI9xH/7KFi0Lohygp8c6KTISxo/X02VVnoIDK3B7fFOu7dKIN1K28Ob8rXy7ag/DL6jP3f2aUTe8ktMhqnJC9yicFhAAWVmwZYvTkSgPFVYpgPsG2LIgI7s2Ytqy34l/KpnHvl6jZUFUmShUohCRqiLSXkQuyL65O7By5eef4d139YptVaCaofjTT48AACAASURBVBV5dEgb5tzXm6Ed6zJ1wVZ6T0rimR/Wa1kQ5VbnTRQi8i9gBfAi8Izr9rSb4ypfYmPtbHgzZ+rpsuq86lcNZtLwaGZN6E18y1q8NGcTcZOSeC15MydPZzodnvJBhdmjuAJoYoyJN8YkuG593B1YuVKxIvTvb/cofvvN6WiUl2hSM4RXrrmAb+7sSceG4Tz53TrinkrivZ+3cTojy+nwlA8pTKJYBYS7Y+MiMlBE1ovIJhF5sIB2w0XEiEisO+LwCO3aQcOG9nTZkzp/gSq8tvXCmHpjZz69tRtR1SvziKssyOdaFkSVksIkiieAZSLyvYhMz76VdMMi4g+8AlwEtAauFpHWebQLBe4CFpV0mx5NxM6vHRqqU6aqYukUWY2Pb+nK2zd2IqxSAPd+upyBz6fw3SotC6JKpjCnx74DPAmsBEpzf7YzsMkYswVARBKBS4E1udr9C5gE3FeK2/ZMtWvDLbfYpKFUMYgICS1q0btZTb5bvYdnfljPre//Svv6Ydw/oAU9m9ZA9POlikjO90tDROYaY3qX+oZFhgMDjTGjXY9HAl2MMeNytOkIPGyMGSYiycB9xpgleaxrLDAWICIiIiYxMbHYcaWlpRESElLs15cGv9OnCV23jiNt29oL84rBE/pRWrQvxZeZZViwK4MvN53hQLqhZTU/hjcLpGlV/xKv21feF1/pB5SsLwkJCUuNMXke3i/MHsVSEXkCmA6cPWnbGPNrsaI5J6+fNWezloj4Ac8Bo863ImPMZGAyQGxsrImPjy92UMnJyZTk9aVi7VpYsAAqVYJu3Yq1Co/oRynRvpRMX2BiRiYfLtrBK0mbeHxROn1b1uLeC1vQum6VYq/XV94XX+kHuK8vhUkUHV3/ds3xnAFKeuZTKtAgx+P6QM5JGkKBtkCya1e5NjBdRIbktVfhU1q2hObNYc4ce79qVacjUl6uYgV/buwRxZWdGvD2T9v439zNDHpxHkOi63JP/+ZE1ajsdIjKg533uEaOU2ITSvn02F+AZiISJSKBwFXYvZbs7R4xxtQwxkQaYyKBhYDvJwmwYxQXX2z//eYbvbZClZrgwArckdCUeRP7cEdCE2at2Uu/Z+fy4Ocr2HVYz7ZTeXOshIcxJgMYB3wPrAU+McasFpHHRGSIU3F5jLAw6NcPNm+GFSucjkb5mLDgAO4f0JK5E+O5rktDPv81lfink/nXN2s4oGVBVC6OFgU0xswEZuZ67u/5tI0vi5g8SqdOcOiQvb5CKTeoFRrEPy9ty+hejXnxx428/dNWEhfv4OaeUYyOa0yVIC1YqbQooGcTgQED7BiFMXoISrlNg2rBPDUimh/u6U18i1q86CoL8vpcLQuiipEoRCRWROq5IxiVj/R0+OgjWL3a6UiUj2taK4RXrrVlQaLrh/Pfb9fR+6kk3lu4XcuClGPF2aO4E/hGRD4u7WBUPgID4fhxWzRQr9pWZaBtvTDeuakzH4/tSqPqwTzy5Sr6PpvMF79qWZDyqMiJwhhzgzGmIzDaDfGovPj5wdChcPq0ngWlylSXxtX55JZuvH1jJ6oEBTDhk+Vc9EIK363ao2VBypHClBn/UUQG5XpusjHmmPvCUn9Rsyb06QPr1sHy5U5Ho8qR7LIgX4/rySvXXEBGluHW95fy2MJ05m/UaXzLg8LsUUQBD4jIP3I857tVXD1Z167QqBHMn29nxVOqDPn5CRe3r8MP4+OYNKw9R08ZrntzEde8sZBfdxxyOjzlRoU5PfYwtgrAiyLyNXCde0NS+fLzg2HDoEKFYteAUqqkKvj7cUWnBlQ9tonUipG8krSJy19dQL9WEdx7YXNa1Sl+WRDlmQrzbSPGmAxjzO3A58B8oJZ7w1L5qlIFgoMhMxO2b3c6GlWOBfgJN/aIYu79Cdw/oAWLth5g0IvzuDtxGdv+OO50eKoUFSZRvJ59xxgzFVuk7wc3xaMKKyUF3nlH59lWjqtc0ZYFmT+xD7f2bsIPq/fS99m5PPTFSvYcSXc6PFUKClPr6X+5Hi81xtzkvpBUoXTrZic5+uwzOKUlF5TzwoIDeGDgubIgny3dSdxTSfx7xhoOHj/tdHiqBPRAt7cKCrLjFYcPw4wZTkej1FnZZUHm3BvPkOi6vDl/K72enMNzszZwLP2M0+GpYtBE4c0aNoTevW3RQD1lVnmYBtWCeXpEND/cE0dc85q88ONGek1KYnLKZtLPaFkQb6KJwtvFxUHHjhAR4XQkSuWpaa1QXrsuhq/H9aR9/XD+M9OWBXl/4XbOZOpp3t5AE4W38/ODSy+1822DXl+hPFa7+mG8e1NnEsd2pX7VYB7+chV9n5nLl8t+17IgHk4Tha8wxpb3+OorLfGhPFrXxtX57NZuvD2qEyEVKzD+498Y9MI8flitZUE8lSYKXyECISF2rOLXkk5nrpR7iQgJLWvxzZ09efmajpzJzGLse0sZ+uoCftqkZUE8jSYKXxIXB02awMyZBO7f73Q0Sp2Xn59wSfu6/HBPHE8Oa8f+o+lcO2UR105ZyDItC+IxNFH4kuwSH6Gh1EpOtqXJlfICFfz9uLJTQ+bcF8/fL2nNut3HuOzVBYx5dwnr9hx1OrxyTxOFrwkOhiuvRDIzQfcqlJcJCvDnpp5RpExM4L4Lm7Nw8wEuemEe4xOXsf2A/vBxiiYKX1SnDqnDhkFkpNORKFUslStWYFyfZsx7IIFb4prw3eo99H1mLn+bpmVBnKCJwkeZgAB79tPixfaCPKW8UHhwIA9e1JKU+xO4pktDPlmyk95PJfGfmWu1LEgZ0kThy4yBtWth+nRITXU6GqWKrVaVIB5zlQW5pH1dpszbQtykJJ6frWVByoImCl/m5wcjRtjigR9/DEd1UFB5twbVgnnmimi+Hx9Hr2Y1eH72RuImJTFl3hYtC+JGjiYKERkoIutFZJOIPJjH8gkiskZEVrimZG3kRJxeLTgYrr7aVphNTLTzbivl5ZpF2LIg08f1oG29MB6fsZb4p5L5cNEOLQviBo4lChHxB14BLgJaA1eLSOtczZYBscaY9sBnwKSyjdJH1KoFw4fDnj2webPT0ShVatrXD+e9m7vw0Ziu1A0P4v+mraTfs3P56rffydKyIKXGyT2KzsAmY8wWY8xpIBG4NGcDY0ySMeaE6+FCoH4Zx+g7mjeHO++EVq2cjkSpUtetSXU+v607b42KJTiwAncn/sagF+cxe81eLQtSCsSpP6KIDAcGGmNGux6PBLoYY8bl0/5lYI8x5vE8lo0FxgJERETEJCYmFjuutLQ0QkJCiv16T1FQP4J276ZCWhppzZqVcVTF4yvvCWhfykKWMSzek8m0jafZe8LQJMyPYc0DaV3dP8/2ntqP4ihJXxISEpYaY2LzWlahRFGVjOTxXJ5ZS0SuA2KB3nktN8ZMBiYDxMbGmvj4+GIHlZycTEle7ykK7EdiIuzebeeyaN68TOMqDl95T0D7Ulb6APdmZvH50lRe+HEjk35Jp2fTGtw3oAUdGoT/qa0n96Oo3NUXJw89pQINcjyuD+zK3UhE+gF/A4YYY3TOz9Jw+eW2LPmnn+pps8pnBfj7cVXnhiTdF8/DF7dize6jDH3lJ8a+u4T1e445HZ5XcTJR/AI0E5EoEQkErgKm52wgIh2B/2GTxD4HYvRNgYFwzTX2tNkPP4QDB5yOSCm3CQrwZ3SvxqRMTGBC/+b8vPkAA19I4Z6Pf9OyIIXkWKIwxmQA44DvgbXAJ8aY1SLymIgMcTV7CggBPhWR30Rkej6rU0UVEgLXXWfLk2tZclUOhFSswF19m5EyMYGxcY35dtVu+j4zl3dWn2LvUS0LUhAnxygwxswEZuZ67u857vcr86DKk2rVYMwYCAtzOhKlykzVyoE8dFErbuoRxctzNvHhou3ETUpiVPdIbu3dhKqVA50O0ePoldnlXXi43as4dAg+/1wvyFPlRkSVIP41tC1P9KrExe3qMNlVFuSF2RtJO5XhdHgeRROFsvbtg1WrbKmPDP1PosqPWsF+PHtlB74fH0f3ptV5bvYGLQuSiyYKZbVoAUOG2Cu3v/gCsrQMgipfmkeE8r+RsXx1Rw/a1K3C4zPWkvB0Mh8t1rIgmijUOR07woABsGYNTJumyUKVS9ENbFmQD8d0oXZYEA99sZL+5bwsiCYK9WfdukG/fnDwIJzR8s2q/OrepAZf3NadKdfHEhTgX67Lgjh61pPyUD17QteuUKGCHa/w97cD3kqVMyJCv9YR9GlZi69X7OK5WRsY/e4SOjYM5/4BLejepIbTIZYJ3aNQeatQATIz4aOPYMYMOwmSUuWUn59waYd6zJrQmycub8fuw+lc88YiRr65iOU7DzsdnttpolD58/ODOnVgyRL4+mtNFqrcC/D34+rODUm+35YFWfX7ES595SdueW8JG/b6blkQPfSk8icCffvahJGSYge3hwyxj5Uqx7LLglzZqQFvzd/GlHlb+GFNCpd1qMf4fs1pWD3Y6RBLlSYKVTAR6NPHjlMkJUHFinDRRU5HpZRHCA0K4O5+zbi+WyNen7uZqQu2MX35Lq7q3IC7+jSjVpUgp0MsFZooVOH07m2LCTZu7HQkSnmcqpUDeWhQK27qGcVLczaSuHgnny1N5Ybukdwa5/1lQfQYgiq8bt0gIsKOVfz6q5b7UCqXiCpBPD60HXPujWdQ2zpMTrFlQV780bvLgmiiUEW3b58d3H7vPTh50ulolPI4DasH8+yVHfju7ji6NanOs7O8uyyIJgpVdBERcMUVsGsXTJ0Kx3z3bA+lSqJF7VAmXx/Ll3f0oHWdc2VBEhfvIMOLyoJoolDF06qVnfzo0CGYMgX273c6IqU8VocG4bw/ugsfju5CRJUgHvxiJf2fS+Hr5bu8oiyIJgpVfE2awI032tNm//jD6WiU8njdm9Zg2u3dmTwyhkB/P+78aBkXvzSfH9d6dlkQTRSqZOrUgTvvtHsYAEePOhuPUh5ORLiwTW1m3t2LF67qwInTGdz8zhKGv/4zC7d45rTEmihUyQW6Tv3bvh1eeAF+/lmv4lbqPPxdZUFmT+jNfy5rR+qhE1w1eSEj31zEytQjTof3J5ooVOmpWxeaN4fvv4eZM7VMuVKFEODvxzVdGjL3/gT+b1BLVv1+hMEvz+e295ey0UPKgmiiUKUnIMCeDdWzJ/zyC3zwAaTrpPVKFUZQgD9j45qQMjGB8f2aMW/jHwx4PoV7P1nOzoMnHI1NE4UqXSJ2PoshQ2DrVli50umIlPIqoUEBjO/XnJSJCdzcM4qvV+yizzPJ/P2rVew76swPLy3hodzjggugXj2oVcs+PnXK1olSShVKtcqB/O3i1tzUM4oXf9zEh4t28MmSnYzqHsWtvRsTHlx2ZUF0j0K5T0SE3cM4dAhefBEWLNBBbqWKqE5YJZ64vB2zJ/RmYJva/C9lM70mJfHynI0cL6OyII4mChEZKCLrRWSTiDyYx/KKIvKxa/kiEYks+yhViVWuDI0awQ8/wBdfaI0opYohskZlnr+qI9/e3Yuujavz9A+2LMhb87e6vSyIY4lCRPyBV4CLgNbA1SLSOlezm4FDxpimwHPAk2UbpSoVgYEwYoQtV75qlb2SWy/QU6pYWtauwhvXxzLt9u60qB3KY9+soc/TyXz8yw4y3XSVt5N7FJ2BTcaYLcaY00AicGmuNpcC77jufwb0FdHJm72SCMTFwXXXQVqaPQyllCq2jg2r8uGYrnwwuguRFc7w0luz+feidLdc4S1OXTYuIsOBgcaY0a7HI4EuxphxOdqscrVJdT3e7GrzR651jQXGAkRERMQkJiYWO660tDRCQkKK/XpP4cn98E9LI6tiRUxAAP7Hj5MZFGQnRsqHJ/elqLQvnsfb+1Fpxw5qzJvHjtMB/NhzAP2ahRVrPQkJCUuNMbF5LXPyrKe89gxyZ63CtMEYMxmYDBAbG2vi4+OLHVRycjIleb2n8Ip+ZGXB669DhQowfDhUq5ZnM6/oSyFpXzyP1/YjMxNmz4YtWyA2liYjRiArVrilL04eekoFGuR4XB/YlV8bEakAhAEHyyQ65X5+fpCQAAcP2oSxYoXTESnlHU6dgrfesuVyunSBm2/O94dWaXByj+IXoJmIRAG/A1cB1+RqMx24AfgZGA7MMZ5cYlEVXatWtvTH55/bM6I2b4ZLLrFXeSul8hYYaP/f9OgBrXOfA1T6HNujMMZkAOOA74G1wCfGmNUi8piIDHE1exOoLiKbgAnAX06hVT4gLAxGjbLzcu/fb/c0lFJ/dvKk/TG1f789OeTii8skSYDDV2YbY2YCM3M99/cc99OBEWUdl3JA9mGouDg7sH3ypK0X1b2705Ep5bxNm2D6dDh+3M4DU7NmmW5eS3goz5J99tO6dTBnDqxeTUBEhLMxKeWUU6fshapLl9rkcNVV9pBTGdNEoTxTx44QHAzTp1P3l1/sQF2vXgWeRquUz1m4EH791Y5FJCTYMwQdoAeDledq0QLuuIPjkZGQnGx/WSnl69LTYe9ee797dxg9Gvr3dyxJgO5RKE8XHMwfcXF2d7t2bfvcsWO2Em1g2VXPVMrtjIE1a+Dbb+3n+4477Nl/9eo5HZkmCuUlmjc/d//LL+HAARg06M/PK+Wtjhyxs0KuX2/noR882KPO/tNEobxPXBzMmAEffmivwxg40J5iq5Q32rfPFso0BgYMsBfQeVCSAB2jUN6oUSO45RY7k96mTfDKK7Btm9NRKVU0x1zzYdesCZ062UNN3bp5XJIA3aNQ3srf387N3batHeiuU8c+f+IEVKpkL0hSyhMdPmxPzNiyBe68087X0r+/01EVSBOF8m7h4TB0qL2fmQlvvw1VqtjDUWV8UZJSBTp1CubNs6e8itjTvb1kemBNFMp3iEBsLCQlwauv2nm74+MhNNTpyFR5d+KEPUR6/DhER9tJvLxoXE0ThfIdfn52ILBdO0hJsSVAVqyAm246d2hKqbJiDOzZYz97wcHQuTM0a+bIldUlpYlC+Z7gYHvoqUsXmyyyS4Ds2mUPR2llWuVOxtjxhx9/tInijjugenVb9NJLaaJQvqtqVbjwQnv/zBl4/307CN6rlz0s5eCVrspH7dxpa5Rt3WoPLQ0ebD+HXk7/p6jyISAArrjCjl/MnAnz59vrMTp00IShSsfx4zB1KgQFwUUXQUyMz3y2fKMXShVGZKSd92LbNvur75tvoFYtaNjQ4cCUV8o+xLRpk71QrnJluPZaqF/f58rLaKJQ5YsIREXZAe7ff7f/qcEeTxax4xqVKzsbo/JsmZm2JtOCBbB7tz0du2dP+7lp3Njp6NxCE4Uqn0TOJQlj7EVQK1fa//zR0dC1q16Hof5q925ITLS1mWrUsGMQ0dE+c4gpP77dO6UKQwSGDbNjFgsXwvLldqKYiy6yexiqfDtwwI4/NGxoz16KiDhXkLKcVADQRKFUtpo17S/Evn1tomjSxD6fmgrbt9uBbz0sVT5kZcHGjbB4MWzebK+FuOUWO/ZwzTVOR1fmNFEolVtwsD2FNtumTbae1Jw5djL7mBhbmLCc/Josd5Yvt+/1kSN2/KFPH3s6dTmmiUKp84mPtwli6VL7JbJypU0UN97odGSqFEhGhn1Po6IgJMRe4V+jhj2TqWVLj6zmWtY0UShVGLVq2TGLfv1g9Wp75gvYQxSffWZLM7RqZc+hV54vK8teFLdyJQ1mzLCzyA0aZMtstGtnb+osRxKFiFQDPgYigW3AFcaYQ7nadABeA6oAmcC/jTEfl22kSuUSEGDHKrIdPWrnN16zxl6X0bQptGlj5/v2ksqg5c6ZM/Dii2en1D3eqJEdd4iKcjoyj+XUHsWDwI/GmP+KyIOuxw/kanMCuN4Ys1FE6gJLReR7Y8zhsg5WqXyFh8O4cfaajNWrbcJYvx5GjrSD4Wlptl1IiLNxlleZmfYCy7Vr4fRpuPxym+xjYuxeYrNmHPjpJ5+9/qG0OJUoLgXiXfffAZLJlSiMMRty3N8lIvuAmoAmCuVZsq/JqF/f1pZKTT1XIXThQvjpJ3too0ULAg4etNdt6EC4e23eDMuW2RMR0tPt2UotWpz728fHOx2hV3EqUUQYY3YDGGN2i0itghqLSGcgENhcFsEpVWwi0KDBucfR0fYX7Pr18OOP1Nu2zV60dfvttu2ZM1rNtqQyMmxy3rwZune3Mxzu2WP3JFq1sgPSjRvr37kExBjjnhWLzAZq57Hob8A7xpjwHG0PGWPyLLEoInWwexw3GGMW5tNmLDAWICIiIiYxMbHYcaelpRHiA4cJfKUf4Dt98T9xArNhAyEVKnC0bVsA6k6bBiKk167NqYgI0mvVItNLrtVw8n3xP36c0I0bCdqzh4r79yOZmRgR9vbvT3rduvaxn1+h9tx85fMFJetLQkLCUmNMbF7L3LZHYYzpl98yEdkrInVcexN1gH35tKsCzAAezi9JuLY1GZgMEBsba+JLsFuZnJxMSV7vKXylH+BjfQkO5oLsvhhjSz9s2XLuor7t2235kIED7fLUVKhd2yN/DZfJ+2IMHDpk/w6pqXbcp0UL+OMPWLLE7in06WMLPjZsSFQxzjrzqc+Xm/ri1KGn6cANwH9d/36Vu4GIBALTgHeNMZ+WbXhKlQERW0yuZ097uuaePbBjhx1kBfsF+eab9jz+mjXtuEdEhC0dUa2as7G7Q0aGHU8ICbGD0O+9Z/8m6el2eWCgneOhRQtbSuOBB/R05DLiVKL4L/CJiNwM7ABGAIhILHCrMWY0cAUQB1QXkVGu140yxvzmQLxKuZefn00EOafJDAmBq66yM/Pt3g0bNtgB2rAwmyhSU2HWLPulWa2anSCnWjWbVDy1SF1W1rkL2JYvt307cMDuIRw5YpPg1VfbCaYqVYK2bW35jPr1bb+yXyuiSaIMOfJpMsYcAPrm8fwSYLTr/vvA+2UcmlKeIzDQDsS2bHnuuePHzx2Gysiwh2bWr7fPZxszxp5ltXatPTwTGmpLUVSubL98W7a06z51yv5yDwiwiaU4Z2JlZdn1ZN8yM88lu99+s6cNp6XZ600OH7Zx3HKLXb5kib0GpXp1mwg6dLBxZ7vyyqLHo9zCQ392KKXylHOgOzLSzqsB9kv60CF7yy6Pnv0lvn+//bLOyrLP33efTRQLFsDcufY5EZswAgLg7rvt8pQU+6s/O4FkX41+990AVF+wwNbAyqlSJXtICGxRva1bbcxVqthDRjlLt197rb0oUU8V9niaKJTyBRUr2kHv2jlONGzTxt7AJon0dDhxwhY9BFt2pFIlu2dy+rQ9VffMmXOHrcLC7N5BdoLx97c317UIJ+vWtVczV6xob0FBf74affjwgpOAHjryGpoolCoP/PxsgshOEnDuIsH8REfbWz5OREZC7975v173FHyGlkVUSilVIE0USimlCqSJQimlVIE0USillCqQJgqllFIF0kShlFKqQJoolFJKFUgThVJKqQK5bT4Kp4jIfmB7CVZRA/ijlMJxkq/0A7QvnspX+uIr/YCS9aWRMaZmXgt8LlGUlIgsyW/yDm/iK/0A7Yun8pW++Eo/wH190UNPSimlCqSJQimlVIE0UfzVZKcDKCW+0g/QvngqX+mLr/QD3NQXHaNQSilVIN2jUEopVSBNFEoppQpULhOFiAwUkfUisklEHsxjeUUR+di1fJGIRJZ9lIVTiL6MEpH9IvKb6zbaiTjPR0TeEpF9IrIqn+UiIi+6+rlCRC4o6xgLqxB9iReRIznek7+XdYyFISINRCRJRNaKyGoRuTuPNl7xvhSyL97yvgSJyGIRWe7qyz/zaFO632HGmHJ1A/yBzUBjIBBYDrTO1eZ24HXX/auAj52OuwR9GQW87HSshehLHHABsCqf5YOAbwEBugKLnI65BH2JB75xOs5C9KMOcIHrfiiwIY/Pl1e8L4Xsi7e8LwKEuO4HAIuArrnalOp3WHnco+gMbDLGbDHGnAYSgUtztbkUeMd1/zOgr4hHzutYmL54BWNMCnCwgCaXAu8aayEQLiJ1yia6oilEX7yCMWa3MeZX1/1jwFqgXq5mXvG+FLIvXsH1t05zPQxw3XKflVSq32HlMVHUA3bmeJzKXz8wZ9sYYzKAI0D1MomuaArTF4BhrsMCn4lIg7IJrdQVtq/eopvr0MG3ItLG6WDOx3XooiP212tOXve+FNAX8JL3RUT8ReQ3YB8wyxiT7/tSGt9h5TFR5JVVc2fjwrTxBIWJ82sg0hjTHpjNuV8Z3sZb3pPC+BVbVycaeAn40uF4CiQiIcDnwHhjzNHci/N4ice+L+fpi9e8L8aYTGNMB6A+0FlE2uZqUqrvS3lMFKlAzl/V9YFd+bURkQpAGJ55KOG8fTHGHDDGnHI9fAOIKaPYSlth3jevYIw5mn3owBgzEwgQkRoOh5UnEQnAfrF+YIz5Io8mXvO+nK8v3vS+ZDPGHAaSgYG5FpXqd1h5TBS/AM1EJEpEArEDPdNztZkO3OC6PxyYY1yjQh7mvH3Jdbx4CPbYrDeaDlzvOsumK3DEGLPb6aCKQ0RqZx8vFpHO2P+HB5yN6q9cMb4JrDXGPJtPM694XwrTFy96X2qKSLjrfiWgH7AuV7NS/Q6rUNwXeitjTIaIjAO+x5419JYxZrWIPAYsMcZMx36g3hORTdgsfJVzEeevkH25S0SGABnYvoxyLOACiMhH2LNOaohIKvAP7CAdxpjXgZnYM2w2ASeAG52J9PwK0ZfhwG0ikgGcBK7y0B8iPYCRwErX8XCA/wMagte9L4Xpi7e8L3WAd0TEH5vMPjHGfOPO7zAt4aGUUqpA5fHQk1JKqSLQRKGUUqpAmiiUUkoVSBOFUkqpAmmiUEopVSBNFEoppQqkiUIppVSBNFEoVUIi0slVdDFIRCq75gjIXXsn92vSRORJEVkqIrNFpLOIJIvIFtcFkkp5DL3gTqlSB/JVlAAAAOlJREFUICKPA0FAJSDVGPPEedobYJAx5lsRmQZUBi4GWgPvuAq+KeURNFEoVQpctbZ+AdKB7saYzPO0PwUEGWOMq/TCKWPMv0XEDzhojAl3f9RKFY4eelKqdFQDQrCzpwUVov2ZHHWEsoBTAMaYLMphDTbl2TRRKFU6JgOPAB8AT2Y/KSK5q3oq5XX0l4tSJSQi1wMZxpgPXRU9F4hIH2AFeU8go5RX0TEKpdxERC4BGhtjXnQ6FqVKQhOFUkqpAukYhVJKqQJpolBKKVUgTRRKKaUKpIlCKaVUgTRRKKWUKpAmCqWUUgX6f/c+MHbON26EAAAAAElFTkSuQmCC\n", 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\n", 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" ] @@ -120,12 +145,33 @@ "# plot\n", "plt.title('brachistochrone')\n", "plt.plot(x, y_opt, label='numerical')\n", - "plt.plot(xa, ya, 'r--', label='analytical', alpha=0.5)\n", + "plt.plot(xa, ya, 'r--', label='analytical')\n", "plt.grid(True)\n", "plt.xlabel('x, m')\n", "plt.ylabel('z, m')\n", "plt.legend()" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { @@ -144,7 +190,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.4" + "version": "3.7.3" } }, "nbformat": 4, diff --git a/homework/7-Quad-Tree.py b/homework/7-Quad-Tree.py new file mode 100644 index 00000000..afb5078c --- /dev/null +++ b/homework/7-Quad-Tree.py @@ -0,0 +1,231 @@ +# -*- coding: utf-8 -*- +""" +Created on Sun Oct 20 14:51:58 2019 + +@author: cohen +""" + +import matplotlib +import matplotlib.pyplot as plt +import numpy as np +from random import random +from random import seed +import timeit + +seed(4) + +class Quad(object): + def __init__(self,left,right,down,up): + self.leftb = left + self.rightb = right + self.downb = down + self.upb = up + self.childQuads = [None,None,None,None] + self.particles = None + +#Use this method to see which particles from any list of particles are enclosed by the quad. + def getPartsInQ(self,parts): + partsInQ = [] + externParts = [] + for aPart in parts: + if((aPart.xpos > self.leftb) and (aPart.xpos < self.rightb) and (aPart.ypos > self.downb) and (aPart.ypos < self.upb)): + partsInQ.append(aPart) + else: + externParts.append(aPart) + + return externParts, partsInQ + + def doesRectOverlap(self,rectLb,rectRb,rectDb,rectUb): + doesOverlap = not((self.rightbrectRb)or(self.upbrectUb)) + return doesOverlap + + def isQuadEnclosed(self,rectLb,rectRb,rectDb,rectUb): + isEnclosed = (self.rightbrectLb)and(self.upbrectDb) + return isEnclosed + +class particle(object): + def __init__(self,x,y): + self.xpos = x + self.ypos = y + +def buildQuadTree(quadBase,recurseCount): + + leftOvParts = quadBase.particles + leftRightCent = quadBase.leftb + (quadBase.rightb - quadBase.leftb)/2 + upDownCent = quadBase.downb + (quadBase.upb - quadBase.downb)/2 + + subQuad1 = Quad(quadBase.leftb, leftRightCent, upDownCent, quadBase.upb) + subQuad2 = Quad(leftRightCent, quadBase.rightb, upDownCent, quadBase.upb) + subQuad3 = Quad(quadBase.leftb, leftRightCent, quadBase.downb, upDownCent) + subQuad4 = Quad(leftRightCent, quadBase.rightb, quadBase.downb, upDownCent) + + if leftOvParts != None: + leftOvParts, subQuad1.particles = subQuad1.getPartsInQ(leftOvParts) + if (subQuad1.particles != []) and (len(subQuad1.particles)>1) and (recurseCount < 500): + buildQuadTree(subQuad1,recurseCount+1) + quadBase.childQuads[0] = subQuad1 + + if leftOvParts != None: + leftOvParts, subQuad2.particles = subQuad2.getPartsInQ(leftOvParts) + if (subQuad2.particles != []) and (len(subQuad2.particles)>1) and (recurseCount < 500): + buildQuadTree(subQuad2,recurseCount+1) + quadBase.childQuads[1] = subQuad2 + + if leftOvParts != None: + leftOvParts, subQuad3.particles = subQuad3.getPartsInQ(leftOvParts) + if (subQuad3.particles != []) and (len(subQuad3.particles)>1) and (recurseCount < 500): + buildQuadTree(subQuad3,recurseCount+1) + quadBase.childQuads[2] = subQuad3 + if leftOvParts != None: + leftOvParts, subQuad4.particles = subQuad4.getPartsInQ(leftOvParts) + if (subQuad4.particles != []) and (len(subQuad4.particles)>1) and (recurseCount < 500): + buildQuadTree(subQuad4,recurseCount+1) + quadBase.childQuads[3] = subQuad4 + + return + +def plotQuadTree(quadBase): + if quadBase.childQuads[0] != None: + leftRightCent = quadBase.leftb + (quadBase.rightb - quadBase.leftb)/2 + upDownCent = quadBase.downb + (quadBase.upb - quadBase.downb)/2 + + plt.plot([quadBase.leftb,quadBase.rightb],[upDownCent,upDownCent],'k') + plt.plot([leftRightCent,leftRightCent],[quadBase.downb,quadBase.upb],'k') + + plotQuadTree(quadBase.childQuads[0]) + plotQuadTree(quadBase.childQuads[1]) + plotQuadTree(quadBase.childQuads[2]) + plotQuadTree(quadBase.childQuads[3]) + +def plotQuadTreeSearchRegress(topQuad,rectLb,rectRb,rectDb,rectUb,ax): + if topQuad.doesRectOverlap(rectLb,rectRb,rectDb,rectUb): + if topQuad.isQuadEnclosed(rectLb,rectRb,rectDb,rectUb) or topQuad.childQuads[0]==None: + #good just return all of topQuad points (assuming it has them and that this has been checked?) + rect = matplotlib.patches.Rectangle([topQuad.leftb,topQuad.downb], topQuad.rightb - topQuad.leftb, topQuad.upb - topQuad.downb, angle=0.0,color='gray') + ax.add_patch(rect) + + else: + #continue down the list for each quad + plotQuadTreeSearchRegress(topQuad.childQuads[0],rectLb,rectRb,rectDb,rectUb,ax) + plotQuadTreeSearchRegress(topQuad.childQuads[1],rectLb,rectRb,rectDb,rectUb,ax) + plotQuadTreeSearchRegress(topQuad.childQuads[2],rectLb,rectRb,rectDb,rectUb,ax) + plotQuadTreeSearchRegress(topQuad.childQuads[3],rectLb,rectRb,rectDb,rectUb,ax) + +def plotQuadTreeSearch(topQuad,rectLb,rectRb,rectDb,rectUb): + fig,ax = plt.subplots(1) + plotQuadTreeSearchRegress(topQuad,rectLb,rectRb,rectDb,rectUb,ax) + + +def getPointsOfQuadOverlap(topQuad,rectLb,rectRb,rectDb,rectUb): + if topQuad.doesRectOverlap(rectLb,rectRb,rectDb,rectUb): + if topQuad.isQuadEnclosed(rectLb,rectRb,rectDb,rectUb) or topQuad.childQuads[0]==None: + #good just return all of topQuad points (assuming it has them and that this has been checked?) + return topQuad.particles + + else: + #continue down the list for each quad + partList = [] + partList = partList + getPointsOfQuadOverlap(topQuad.childQuads[0],rectLb,rectRb,rectDb,rectUb) + partList = partList + getPointsOfQuadOverlap(topQuad.childQuads[1],rectLb,rectRb,rectDb,rectUb) + partList = partList + getPointsOfQuadOverlap(topQuad.childQuads[2],rectLb,rectRb,rectDb,rectUb) + partList = partList + getPointsOfQuadOverlap(topQuad.childQuads[3],rectLb,rectRb,rectDb,rectUb) + + return partList + else: + #dont get any of these points + return [] + +def getPtsCircQuadTree(topQuad,centX,centY,radius): + rectRb = centX + radius + rectLb = centX - radius + rectUb = centY + radius + rectDb = centY - radius + partCandidates = getPointsOfQuadOverlap(topQuad,rectLb,rectRb,rectDb,rectUb) + + enclosedParts = [] + for aPart in partCandidates: + dist = np.sqrt((aPart.xpos - centX)**2 + (aPart.ypos - centY)**2) + if dist<=radius: + enclosedParts.append(aPart) + + return enclosedParts + +def getPtsCircBrute(parts,centX,centY,radius): + enclosedParts = [] + for aPart in parts: + dist = np.sqrt((aPart.xpos - centX)**2 + (aPart.ypos - centY)**2) + if dist<=radius: + enclosedParts.append(aPart) + + return enclosedParts +#END CLASS AND HELPING METHOD DEFINITIONS---------------------------------------------- +#BEGIN EVALUATION/"MAIN" CODE-------------------------------------------------- + +#Problem parameters +numParticles = 1000 +particles = [] +xlims = [0,60] +ylims = [0,30] +radius = 10 +centX = 30 +centY = 15 +#------------------ + +#set particle positions +for i in range(0,numParticles-1): + particles.append(particle(random()*(xlims[1]-xlims[0])+xlims[0],random()*(ylims[1]-ylims[0])+ylims[0])) +#---------------------- + +#build Quad +def build_quad(): + initialQuad = Quad(xlims[0],xlims[1],ylims[0],ylims[1]) + initialQuad.particles = particles + buildQuadTree(initialQuad,0) + return initialQuad + +t_build_quad = timeit.timeit(build_quad, number = 1) +print(t_build_quad) + +initialQuad = build_quad() +#---------- + +#search Quad +def search_quad(): + encParticles = getPtsCircQuadTree(initialQuad,centX,centY,radius) + return encParticles + +t_search_quad = timeit.timeit(search_quad, number = 1) +print(t_search_quad) + +encParticles = search_quad() +#----------- + +#compute Brute +def search_brute(): + return getPtsCircBrute(particles,centX,centY,radius) + +t_search_brute = timeit.timeit(search_brute, number = 1) +print(t_search_brute) +#------------- + +#plot Quadtree Visual +rectRb = centX + radius +rectLb = centX - radius +rectUb = centY + radius +rectDb = centY - radius +plotQuadTreeSearch(initialQuad,rectLb,rectRb,rectDb,rectUb) +plt.plot([particleX.xpos for particleX in particles], [particleY.ypos for particleY in particles],'.') +plotQuadTree(initialQuad) +plt.gca().set_aspect('equal', 'box') +circ = plt.Circle((centX, centY), radius, color='g', fill=False) +plt.gca().add_artist(circ) + +plt.plot([particleX.xpos for particleX in encParticles], [particleY.ypos for particleY in encParticles],'r.') +plt.show() +#-------------------- + + + + + + diff --git a/homework/HW1.ipynb b/homework/HW1.ipynb new file mode 100644 index 00000000..9140a6a7 --- /dev/null +++ b/homework/HW1.ipynb @@ -0,0 +1,401 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 139, + "metadata": {}, + "outputs": [], + "source": [ + "import sys\n", + "sys.path.insert(0, '../python/casadi_f16')\n", + "import f16\n", + "import control\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import scipy.linalg\n", + "\n", + "import analysis\n", + "from analysis import loop_analysis, rlocus, bode" + ] + }, + { + "cell_type": "code", + "execution_count": 140, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Requirement already satisfied: casadi in /home/kevin/anaconda3/envs/aae497-f19/lib/python3.7/site-packages (3.4.5)\n" + ] + } + ], + "source": [ + "!pip install casadi" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Roll Autopilot Design\n", + "\n", + "* See Roll Autopilot design example in section 4.6 of Stevens and Lewis.\n", + "* Homework 1: Due 8/30 @ 11 pm: Trim the F16 model around a VT=550 ft/s, 20 deg/s yaw rate turn.\n", + "* Find the A, B, C, D matrices for the state space model.\n", + "* Find the transfer function for the aileron to roll rate (P).\n", + "* Design a PID controller attempting to meet the following specifications\n", + " * Maximum overshoot: 20%\n", + " * Rise time: 0.1 second\n", + " * Settling time 1 second\n", + "* Simulate and plot the response of your controlled system and the linear model for a step response in roll rate of 10 deg/s and 100 deg/s. How do the nonlinear and linear responses compare?\n", + "* Using git, fork aae497-f16 on github. Complete the homework. Submit your homework via pull request on aae497-f16." + ] + }, + { + "cell_type": "code", + "execution_count": 141, + "metadata": {}, + "outputs": [], + "source": [ + "p = f16.Parameters()\n", + "x0, u0 = f16.trim(x=f16.State(VT=550), p=p, phi_dot=0, theta_dot=0, psi_dot=20.0*np.pi/180, gam=0)" + ] + }, + { + "cell_type": "code", + "execution_count": 142, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "State(VT=550, alpha=DM(0.251546), beta=DM(0.00040503), phi=DM(1.41001), theta=DM(0.0415563), psi=0, P=DM(-0.0145017), Q=DM(0.344266), R=DM(0.0558364), p_N=0, p_E=0, alt=0, power=DM(86.8792), ail_deg=DM(0.0832868), elv_deg=DM(-1.41359), rdr_deg=DM(-0.3512))" + ] + }, + "execution_count": 142, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x0" + ] + }, + { + "cell_type": "code", + "execution_count": 143, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Control(thtl=DM(0.939641), ail_cmd_deg=DM(0.0832868), elv_cmd_deg=DM(-1.41359), rdr_cmd_deg=DM(-0.3512))" + ] + }, + "execution_count": 143, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "u0" + ] + }, + { + "cell_type": "code", + "execution_count": 144, + "metadata": {}, + "outputs": [], + "source": [ + "ss = f16.linearize(x0, u0, p)\n", + "#ss" + ] + }, + { + "cell_type": "code", + "execution_count": 145, + "metadata": {}, + "outputs": [], + "source": [ + "#sys = control.ss2tf(ss.A,ss.B,ss.C,ss.D);\n", + "#sys = control.minreal(sys,1e-7);\n", + "#sys" + ] + }, + { + "cell_type": "code", + "execution_count": 146, + "metadata": {}, + "outputs": [], + "source": [ + "def select(n, i):\n", + " D = np.zeros((1, n))\n", + " D[0, i] = 1\n", + " return control.ss([], [], [], D)" + ] + }, + { + "cell_type": "code", + "execution_count": 147, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "A = [[-1.15177248e+00 9.03393838e-01 -2.34025343e-03 0.00000000e+00]\n", + " [ 3.98296410e+00 -1.48073989e+00 -2.35589930e-01 0.00000000e+00]\n", + " [ 0.00000000e+00 0.00000000e+00 -2.02020000e+01 2.31497868e+03]\n", + " [ 1.00000000e+00 0.00000000e+00 0.00000000e+00 -1.00000000e+01]]\n", + "\n", + "B = [[ 0. ]\n", + " [ 0. ]\n", + " [-1157.48933772]\n", + " [ 0. ]]\n", + "\n", + "C = [[1. 0. 0. 0.]\n", + " [0. 1. 0. 0.]]\n", + "\n", + "D = [[0.]\n", + " [0.]]" + ] + }, + "execution_count": 147, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "s = control.tf([1, 0], [0, 1])\n", + "G = -(180/np.pi)*ss.sub_system(x=['alpha', 'Q', 'elv_deg'],\n", + " u=['elv_cmd_deg'], y=['alpha', 'Q']).to_control()\n", + "sys3 = control.feedback(G, 0.2*10/(s+10)*select(2, 0))\n", + "sys3\n" + ] + }, + { + "cell_type": "code", + "execution_count": 148, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "3 states have been removed from the model\n" + ] + }, + { + "data": { + "text/plain": [ + "[-21, 0, -8, 8]" + ] + }, + "execution_count": 148, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from analysis import rlocus\n", + "H = (10/(s+10))*select(2, 0)\n", + "plt.figure()\n", + "kalpha = 0.2\n", + "rlocus('alpha', control.minreal(H*G), kvect=np.linspace(0, 10, 1000), k=kalpha*2);\n", + "plt.plot([0, -2], [0, 2], '--')\n", + "plt.axis([-21, 0, -8, 8])" + ] + }, + { + "cell_type": "code", + "execution_count": 149, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[-20, 0, -5, 5]" + ] + }, + "execution_count": 149, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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kJLB+/fpmu/C+/vrrASgrK6O0tPRYB37uugNX6lQl0pXcnNeI6tKHFSt/yIEDn9odySMjr86g3/Bkvpizha2F++yO02Gdv0DEx1vPG1rpHKyhF9WEhDY38eKLL7Jjxw7uv/9+jDHk5eVRWFhIYWEha9eu5bnnnjs2bHR0dJunr9SpKDy8Gzk5rxIVlcGWLX/HmMA/ACwiXHjzQJL7dOXD59ewb2e53ZE6pPMXiLFjrTOV5s2D4mL3wxQVWccnHA5r+DZYvnw5jz76KK+++ioOh4ORI0fy5ZdfttqFd1xcHAkJCXz6qfWfkbvuwJU61YWHJ5Kb8wpnnvkcIsGxugoND+GyHw8lMjqM955aSVVF4Hcl0pzgmOMd0bs3XHMN1NZaxxmaHoQuKoKrr4a6Omu4Nl40N3XqVA4ePEheXh7Z2dnce++9PPXUUx514f3SSy/x61//mqysLAoLC/nDH/7Q3m+pVKcVFpZAREQSTmcda9b8gn37PrI7Uqui4yK47MdZVJXX8tHza4O236bO3903WD21FhRAfj5kZFiFIjPT2q00d65VHDIyYNq0Nk/6hRdeOOm98vJyt114b9++/YSfs7OzWbp0aZvbVOpU5HRWceTINlatnsLQIY+TlPRtuyO1KKl3LOdedwaLXt/A8g+2M/yy4Lm+o0Hn34IASEmBJUusC+OcTuvCuIcesp6dTuv9zz+HHj3sTqqUakZoaCw5OS8TGzuYVavvZO/eD+yO1KrB5/Uic0QPvnp7G8XrD9odp81OjQIBVpGYNQu2b7e2KB54wHrevt16X4uDUgEvNDSWnOwX6Ro7lNVrfkrJ3vftjtQiEWH09/oT3yOKD59fS3VFrd2R2uTUKRAN0tKsK6Z/9zvr2csd9SmlfCs0NJbs7BdJTDyXiIgW7vMSIMIjQ7n4+4OprqwNuovoTr0CoZQKeqGhMWSf+TzxccMAqKzcYnOiliWlxTLiynQ2L9/Lpq+Dp8+3zl8gRNr2UEoFlZK977H0y0vZvfstu6O0KOfi3qRkdGXx9I1UHKqxO45HOn+BUEp1at275ZGQcDZr1/2aXbtn2R2nWY4QBxfeMoj6OmfQ7Go6dQqEMS0/vOyPf/wjjz76qNen22DMmDF8/fXJvV02975dFi5cyBVX+KYfRqUAQkK6cGbWMyQmnMO6db9h166ZdkdqVnxyFCOuyGD7yv1sK9xvd5xWnToFQinVaYWEdCEr6z8kJp7LuvX3Ulm52e5Izcq6MJVuqTEsfnMjR6vq7I7TIi0QXvDyyy+TlZXFmWeeyU033XTS58116/34448zaNAgsrKyuOGGGwCorKzktttu46yzziInJ4e5c+cCUFVVxQ033EBWVhbXX389VVVVreaaPn06Q4cOZciQIdxzzz0nvX/22Wef8H5MTAy//OUvyc3N5cILL2TfvpM7G7vllluYPHky5513HpmZmbzzzjsAVFdXc+uttzJ06FBycnJYsGDBSeM2992U8oaQkEiyhv6brKFPER0dWPepbywkxMGYCf2pLKvhy3lb7Y7TIi0QHbRmzRoefPBBPvnkE1asWMG//vWvk4Zprlvvhx9+mIKCAlauXMnTTz8NwIMPPsgFF1zAsmXLWLBgAb/+9a+prKzkqaeeIioqipUrV3LfffexfPnyFnPt2rWLe+65h08++eRYd+Rz5sw54f0lS5Ycex+sFXhubi75+fmMHj262e7Ht2/fzqJFi3j33XeZPHky1dXVTHNdhb5q1SqmT5/OpEmTqK6uPmG85r6bUt4SEhJBUtLFABwqXUbxN6/bnMi9lPQ4hpx/GisXFgd0h35aIDrok08+4dprr6V79+4AJCYmnvB5S916Z2VlMWHCBF599VVCQ61eT+bPn8/DDz9MdnY2Y8aMobq6mp07d7J48WImTpx4bLysrKwWcy1btowxY8aQlJREaGgoEyZMYPHixc2+D+BwOI51Rz5x4kQ+++wzt9O+7rrrcDgcnHHGGWRkZLB+/Xo+++yzY1tPAwYMoE+fPid1Utjcd1PKF3Z9M50NG35PUdGLdkdxa+RVGURGhbFk1qaAPWB9avTF5EPGGKSdp8e+++67LF68mHnz5vHAAw+wZs0ajDHMnj2b/m7uX9GWdppb4NqyIDbXXtP3RcSj6bb03ZTytoEDH6beWcXGTQ9gjJPevW+zO9IJIqLCGHFlOovf2Mi2FfvJyE6yO9JJdAuigy688EJmzJjBgQMHADh48MT+Vprr1tvpdFJUVEReXh5/+9vfKC0tpaKigksuuYQnnnji2Aq3oKAAgPPPP5/XXnsNgNWrV7Ny5coWc5199tksWrSI/fv3U19fz/Tp0xk9enSz7wM4nU5mzbJOE3z99dc599xz3U575syZOJ1OtmzZwtatW+nfv/8J+TZu3MjOnTtPKgTNfTelfMHhCGfI4MdJTvoOmzY/yI6dz9gd6SSDz+tFQkoUn8/eTH1d4N3vQrcgOmjw4MHcd999jB49mpCQEHJycnjiiSdOGOall15i8uTJHDlyhIyMDF544QXq6+uZOHEiZWVlGGP4+c9/Tnx8PL///e/52c9+RlZWFsYY+vbtyzvvvMOPf/xjbr31VrKyssjOzmbEiBEt5urZsycPPfQQeXl5GGO47LLLuOqqqwCOvV9fX88VV1xx7P3o6GjWrFnDsGHDiIuL480333Q77f79+zN69GhKSkp4+umniYyM5Cc/+QmTJ09m6NChhIaG8uKLLxIREXHCeM19N6V8xeEIY/Dgf8Jaobx8bYe2+H3BEeLgnHH9eHfaSlYtLCb7ot52RzqRMSZoHpmZmaaptWvXnvTeCVq/AuLEhxccPnzYK9PxtaY5o6OjWx1n0qRJZubMmb6KZIw58Xe6YMECn7blLZrTu7yds76+1tTX1xpjjKmtrfDadL2R0+l0mrn/l2+e/cViU1NV2/FQbgBfm3asc3UXk1Kq03M4QnE4Qjl69CBfLRvLtm1PtD6Sn4gIZ489nerKWlZ+UtT6CH7U+XcxBejZAYGooqKi1WFefPFF3wdRykfCwuKIj8tl67b/wxgn6ek/DYhdTj3Su9I3qzuFHxUxdEwqEVFhdkcCOslBaqNFoNPQ36XyJZEQBg58mJ49r2Xb9sfZuu2fAbPMnT02nZojdRR+FDhbEUG/BREZGcmBAwfo1q1bQPwnoNrPGMOBAweIjIy0O0rg2rkT5s2D0lKIj7dun6v3NGkTkRAGDngIwcH27dMID+tGWtoku2PRPTWW03OTWPFJEWdekEZkjP1bEUFfIFJTUykuLnbbLYRdqqurg2IlF4g5IyMjSU1NtTtG4NmzB6ZMgbfesm6T2+Cuu+Caa6y7I6ak2JcvyIg4GDDgQSK7pNKjR+B0JnnWFelsyd/HygVFjLgyw+44wV8gwsLCSE8PrJuBL1y4kJycHLtjtCpYcp7y9uyBUaNg61YIC7MKQv/+sGEDzJ1r3Vu9oEDvq95GIg7S+94BgNN5lD0l8+iZMs7WPRHdesXQN6s7qxZ+Q863+xAWEWJbFugkxyCU6tSmTLGKQ26u9TxrFjz4oPW8bdvx9++4w+6kQWvPnrmsW3cPmzb9xfZjErnf7k11ZS3rPt9law7QAqFUYNu509qtFBZmbS003f2Wmgpz5kBoqDVcUeAc4AwmPXteS1rarRQVv8jGTX+2tUj07BdPz9PjKPywCGe9vVdXa4FQKpDNm2cdcxg79uTi0CAtzTpY7XRaw6s2ExHO6HcfvXv/gOLil9mw8X6MsW/lnHNJH8oPVrN5+V7bMoAWCKUCW2mp9dxaB4eZmdaz614jqu1EhH6n/4Y+vX9ESck8qquLbcvSd0g3EnpGU/DhTlu3ZrRAKBXI4uOt5w0bWh6uoWv1hATf5unkRITTT/81Z494jy5drH6R7FhBi0M484JU9hdVsGfrYb+330ALhFKBbOxYcDisXUfFzfxHW1RkHZ9wOKzhVYeICJGRvQDYvuPfrFt3D8bU+z1H5ogUwruEsmqhfVsyWiCUCmS9e1untdbWWscZmh6ELiqCq6+GujprOL1ozquczhp275nN2nV3+71IhEWEMPBbPdmSv5fKshq/tt3AtusgRCQNeBlIAZzAf4wxJ9+vU6lT3dSp1nUO+fmQkWEVisxMa7fS3LlWccjIANdtX5X3ZKT/FMHB1m3/BGMYOPBvOBz+W20OGX0aKz4pYu1nuzjrcv9f72XnhXJ1wC+NMfkiEgssF5EPjTFrbcykVOBJSYElS45fST179vHPHA4YN84qDnqRnE+kp09BJIQtWx/FYBg86DG/XUwX3yOK3oMSWfPpLnIv7UNIiH93+thWIIwxu4HdrtflIrIOOA3QAqFUUykp1oVxRUXW8YhDh6wD0mPH6m4lP+jb98eIhBAa2tXvV1oPGZPKe0+uZFvhfvoNS/Zr2wHR1YaI9AVygC/tTaJUgEtL0yumbdKnz+3HXpeXryE6OtM/7Q7pRkxiBOuW7PJ7gRC7LysXkRhgEfCgMea/bj6/HbgdICkpadiMGTP8nLDtKioqiImJsTtGq4IhZzBkBM3pbYGc05hDOM1vgcFUHZlITEy8z9vcu8rJvjWQeaUQFt32LZi8vLzlxpjhbR6xPbeh89YDCAP+B/zCk+Hd3XI0EJ2qt3X0hWDIaIzm9LZAz7lz54vmo48zzEcff9fU11f7vL2yfUfM1B99bJa9u7Vd4xNstxwVa0fec8A6Y8xjduVQSqm2SkubRP/MPwGFrFx1B06nb09D7dq9C6f1T2Dd57sxTv/t9bHzOohRwE3ABSJS6HpcZmMepZTyWGrqRERu4sCBBXzzzXSftzfwnJ4c3l/Nrk2lPm+rgZ1nMX0G6C3glFJByyFjODP7UuLjz/J5Wxk5SYRPD2Hd57s5rb9/ulTRK6mVUqoDEhJGIhJCdfUu1q77DfX1VT5pJyw8hDPO6sGW/L0crarzSRtNaYFQSikvKDtcyO7ds1ix8ofU1x/xSRsDz+lFXa2TTV+X+GT6TWmBUEopL+iRfBmDBj3KoUNfUrjiB9TVVXq9jeS+sST2imbd57u9Pm13tEAopZSX9Ey5msGD/kFp6TJWrPg+dXUVXp2+iDBgZE9Kth2mtMQ3WymNaYFQSikvSkkZy5DB/8TprMEY7x8ryBzRAwQ2fLnH69NuSguEUkp5WY8eVzB8+CzCwuKpr6+hrq7ca9OOjo8gtX8CG7/a4/ObGWmBUEopHxAJwRjD6jU/paDwFmprvXdnuP4jUzi8v9rnd5vTAqGUUj4iIvTqeS3l5WsoKLyZ2toyr0w3IzuJ0DCHz3czaYFQSikfSkq6mKFDp1FRsYGCwpuore34ldDhkaGkZyex+esS6uucXkjpnhYIpZTysaTuF5I19EkqKjaxevVPvTLN/menUHOkjh2rD3hleu4ExP0glFKqs+vePY8zs/5NeHg3r0wvbWACXWLD2PjlHjKyk7wyzaZ0C0IppfykW7fziY0dDEBx8WscPbq/3dNyhDg4Y3gPtq3aT82RWm9FPLENn0xVKaVUs6qqitm0+a/kF0ykpgNFov/IFJx1hs3L93ox3XFaIJRSys+6dEnlzDOfpaqqmPz8CdTU7GvXdJJ6xxLfI4qNX/mmbyYtEEopZYPEhG+Rfebz1NTsIr/ge9TUtH0lLyJkjujBrs2lVJZ6/6ZFWiCUUsomCQkjyD7zBWpq9lJalt+uaZyemwwGthR4fzeTFgillLJRfPxwRp2zkB7J3wHA6Wxb/02JPaNJ7BXtk+MQWiCUUspmYWHWHeIOHFjMl19dTnX1rjaN329YMru3lHl9N5MWCKWUChChYXEcPVrC8vwbqaoq9ng8X+1m0gKhlFIBIq7rmeRkv0xd3WHy82+kqqrIo/EadjNtyW/f2VDN0QKhlFIBpGvXLHJyXqGuvpLl+Td6fAps36zu7N5SRo0X71etBUIppQJM19gh5Oa8So8el3vcNUefId0wTkPR2oNey6F9MSmlVACKjR1EbOwgAKqqdmJMPVFR6c0On5LelYioUHauOUC/YcleyaBbEEopFcCMMaxefRfL82+ksnJLs8M5QhykDUxkx5oDXrvTnBYIpZQKYCLCwIGPYIyT/ILvUVG5qdlhT+ufwJGyo5Ttq/JK25gYf6IAABo0SURBVFoglFIqwMXEZDIs93VAyM+fQEXFBrfD9Tw9DoA9W7xz5zotEEopFQSio/uRm/M6IiFs2fKo22ESe0YTERXKbi8VCD1IrZRSQSI6OoNhuW8cu/K6KXEIPdLjvFYgPNqCEJFEN48wryRQSinlsaioPoSFdaW+vppVq+/kcPnqEz5P7hNLackR6ms7fq9qT3cx5QP7gI3AJtfrbSKSLyLDOpxCKaVUm9TWHuRwWSEFBTdx+PCqY+8npERhnIbSfUc63IanBeID4DJjTHdjTDfgO8AM4CfAkx1OoZRSqk0iI3uRmzud0NCuFBTeRNnhFQAkpEQDcGi3/wrEcGPM/xp+MMbMB843xiwFIjqcQimlVJt16ZJKbs7rhIbGU1BwM2VlBcT3iALg0J7KDk/f0wJxUETuEZE+rsfdwCERCQE6vqOrLfbuhWnT/NqkOoVMm2YtYyJtevR55RWYOhWKPOtcTXViDctQcxqvw9q4nLlrq0t5GMNyXycm+gxCQqIIe/ZpEhwVVtffHVxfelogvgekAnOAuUBv13shwHXtbr2NpL4e8vJgyhQtEsr7pk2zlq28vDaPmv7883DnndC3L1x7LezZ4/18KvA1XobcFYm9e723DmvUVuThUIYNm0nMSx9hpkzhokU/w7Fh3bG2UiCpPU14VCCMMfuNMXcaY3KMMdnGmCnGmH3GmKPGmM3tabg9ooqKYO1aGDQIxo/3V7PqVDF+vLVsrV17/D1jrEdJifUZQGYm9Olzwqg7JkyAcePA4YDZs2HUKGscdWppvAw1LRINxcHdOiwjw3oOC7OWo9/+1noObeFKhCZtyb59MH48RT/JZO3fDIPfvvlYWwfgUHu+jqenuSaJyN9F5D0R+aTh0Z4Gm0z3UhHZICKbReQ3rYY9etSaIQsWQLJ3OqNS6pjkZGvZaigEYP1RN/3DzsyEHTsgN/fYYNt+8AOYNQu2bbPe37oV7rjDhi+hbNV4GWpcJJouQ03XYVu3Hl9uZs2CBx88cXnytC2gx4+eJWJfPSv/0p2Dw2Jhxox2fx1PdzG9BqwH0oE/AduBZe1uFXAdv5iGdUbUIOBGERnU0jjO8HAtDsq3Gv7oGgwZYj0a/rBfeQXee8/6T2/u3JPHT02FOXOs//zeekuPSZyKmq64my5D7tZhDctTauqJ7zcsTw2aLk9u2oq4aBy5v9hFZEk9K/7cjf13XMhgGNyer+JpgehmjHkOqDXGLDLG3AaMbE+DjYwANhtjthpjjgJvAFe1NMKRtDQtDsr3Gi9j+/ZZj7go6w/x88/B6YSxY0/+Y26QlgZXXWUNN2+efzKrwNKw4k5KOrYMHY6L5Ke/H8qt+fdw6we3cusHtx4bfNmIXty6+vfH3n/kq0eOTyst7fhrd8uTqy3TqK2I0EQyM14gco+T1b/qQkg7e83wdKRa1/NuEbkc2IV10LojTgMal8Ni4OymA4nI7cDtACndurFw4cIONut7FRUVmtNL7Mo4psnP9c56li5ZQq+CAtKBHZGRbFu48NhwTXOmR0TQB9iWn8+OAJrHwfA7h86RM+zQIc6qrSXc9bMxTg6XHaaMmpOG3ZEUQWlp6bGfi48Us/DI8emOcT03tzyFHTrEWUePHmurtqqKLdt2MvSP5VSlntyex4wxrT6AK4A4YAiwAFgOjPVk3BamOR54ttHPNwFPtDROTni4MSUlJtAtWLDA7ggeCYactmQsKWk4NG1MUpL1AGMGDTLmr3+1Xo8bZw3rGu6knOPGWZ9Nner3+C0Jht+5MZ0gZ0mJtby4W4Yar8MalrOG5ak5DcO5W54ateXs3t3UhYdbr8PCrOekJJNt7f1p83ra07OY3jHGlBljVhtj8owxw4wxHd12LgYabTuRirVl0izH0aPNnz6mlDc0HExssHq19WjYx/vCC9aZSvPmQXGx+2kUFVn7kx0Oa1eUOrU0PSDddBlytw5rbXlq0HR5atKWrFmDWbgQpwhSWwsREciCBayBNe35Kp6exZQuIo+JyH9FZF7Doz0NNrIMOMM17XDgBqDFaTrDw5ufwUp1VOM/tgbJySceCNy0CaKjobbWOs7QVFERXH011NXBNdecuP9YdX7Nna3U3NlNDRqWp6YHoRuWpwaNlyd3bQGhP/gBDmNwOhxQUwPXtf9SNU+PQcwBngPexktXThtj6kRkCvA/rAvunjfGtFjljqSlQUSENUNmztTTCJV3zZx5/I+toUi4u3q1vNx6zs8/9lb6M89YV1LPnWsVh4wMvZjzVNR4GWp6tlJDkWhYqc+ceeK4+fnQu3fH2po2Ddau5WhsLAe+cxk9V6+CtWvpBu77B2+FpwWi2hjzeHsaaIkx5j3gPY+HDwmxZoQWB+ULDcvU+PHQo0ebRu3z+uvWC4fDusBp2rQ2T0N1Ao2XIXdnXDYUiYZ12JQp3m3L9V7xy68QeUY/eOJxmDmTPVOm7GtPE54WiH+JyP3AfDh+CN4Yk9/8KD6SnKzFQflOw7Ll6U3fi4pg3jy25eeTnptr7SPW3UqnttbWT43XYU2XM9fyxKFDkJDQ+vLkpi3zwx9S8+RTxDbs2upAIfK0QAzFOsvoAo7vYjKun5U6daWlwR13sGPhQtLHjLE7jQp2ruWpI47u2AH19YSnZ3Q4jqcF4hogw1gXtCmllApQNVu2AhBxescLhKdXUq8A4jvcmlJKKZ+q2boFgPC+fTs8LU+3IHoA60VkGSceg9CTvJVSKoDUrFtPWFoajqioDk/L0wJxf4dbUkop5VPGGI4UFBB9zre8Mj2PCoQxZpFXWlNKKeUztcXF1O/fT1RzXYS3UYsFQkQ+M8acKyLlWGctHfsIMMaYrl5JoZRSqsOqXBdvdsnJ8cr0WiwQxphzXc+xXmlNKaWUz1R+9RWOrl2J6NfPK9Pz9CwmpZRSAcwYQ+XiT4kedQ4SEuKVaWqBUEqpTqBm/Xrq9u0j5rzzvTZNLRBKKdUJVCxaDEDMeed6bZpaIJRSqhOoWLiQyEGDCE1K8to0tUAopVSQq929m6rCQmK/fbFXp6sFQimlglz5/PkAxF5yiVenqwVCKaWC3OH3PyBiwAAi0tO9Ol0tEEopFcQadi91vdS7Ww+gBUIppYKar3YvgRYIpZQKamXvvkfEwIFe370EWiCUUipo1WzbRvXKlcRdeaVPpq8FQimlgtTht98GEbpefrlPpq8FQimlgpAxhrJ5bxP9rZGE9Uj2SRtaIJRSKghVFRRQW1xM17G+u7GnFgillApCZfPmIZGRxF7k3aunG9MCoZRSQcYcPcrh9z8g9qKLCImJ9lk7WiCUUirIVCxejLOsjLixvjl7qYEWCKWUCjJl894mpFs3os85x6ftaIFQSqkgUn/4MBULFtD18suQ0BbvGt1hWiCUUiqIHP7gA0xtLXFX+u7spQZaIJRSKoiUzZlLeEYGkUMG+7wtLRBKKRUkarZuoyo/n/hx30VEfN6eFgillAoSZW/9F0JCiPPhxXGNaYFQSqkgYOrqKJ0zh5jRo7163+mWaIFQSqkgUPHpp9Tv20/8uO/6rU1bCoSI/F1E1ovIShF5S0Ti7cihlFLBouy//yWkWzdizj/fb23atQXxITDEGJMFbATutSmHUkoFvLqDBylfsJC4q65CwsL81q4tBcIYM98YU+f6cSmQakcOpZQKBmXz5kFdHfHfvcav7QbCMYjbgPftDqGUUoHIGEPZ7P8SeWYWEf36+bVtMcb4ZsIiHwEpbj66zxgz1zXMfcBw4LummSAicjtwO0BSUtKwGTNm+CSvN1VUVBATE2N3jFYFQ85gyAia09s053FhmzeT+Og/ODxhAlXnnduuaeTl5S03xgxv84jGGFsewCTgCyDK03EyMzNNMFiwYIHdETwSDDmDIaMxfsy5Y4cxTzxhzAMPWM87d7ZpdJ2f3uWPnMU//4VZf9YIU19Z2e5pAF+bdqynfdvTUzNE5FLgHmC0MeaIHRmUCip79sCUKfDWW+B0Hn//rrvgmmtg6lRIcbfBroJZ7d69HJ4/n8QJE3BERfm9fVsKBDAViAA+dF0uvtQYM9mmLEoFtj17YNQo2LoVwsKsgtC/P2zYAHPnwuzZUFAAn38OPXrYnVZ5UenMmVBXR8L3brSlfVsKhDHGv0dalApmU6ZYxSE31yoIqY1O+isuhquugvx8uOMOmDXLvpzKq0xtLaVvvEn0eecR3qePLRkC4SwmpVRzdu60diuFhZ1cHMD6ec4cCA21hisqsien8rryjz+mbt8+EiZ8z7YMWiCUCmTz5lnHHMaOPbk4NEhLs7YinE5reNUpHHz5FcJSU4k57zzbMmiBUCqQlZZaz/37tzxcZqb1fOiQb/MovziSn09Vfj6JkyYhISG25dACoVQgi3d1U7ZhQ8vDbdxoPSck+DaP8osDzz5HSHy8Xzvmc0cLhFKBbOxYcDisXUfFxe6HKSqyjk84HNbwKqjVbN5MxSefkGDTqa2NaYFQKpD17m2d1lpbax1naHoQuqgIrr4a6uqs4dLS7MmpvObA8y8gkZEkTJxgdxTbroNQSnlq6lTrOof8fMjIsApFZqa1W2nuXKs4ZGTAtGl2J1UdVLtnD2Vvv03CddcRGgC7C7VAKBXoUlJgyZLjV1LPnn38M4cDxo2zioNeJBf09v/73wAk3nqrzUksWiCUCgYpKdZFcEVF1vGIQ4esA9Jjx+pupU6i9ptvKJ01m/hx3yU89TS74wBaIJQKLmlp1hXTqtPZ99RTiAjdJwdOr0N6kFoppWx2dMcOyt6aQ/z11xMWQJ0uaoFQSimb7Zs6DQkLo/vtP7Q7ygm0QCillI2qVq3i8Ntvk3jTREKTkuyOcwItEEopZRNjDCUPPUxIYiLdfvQju+OcRAuEUkrZpPx/86nKzyfppz8lJABvsaoFQimlbOCsqWHvo48SccYZxF87zu44bulprkopZYODzz9PbXExac89i4QG5qpYtyCUUsrPju7Ywf6nnib2kkuIGTXK7jjN0gKhlFJ+ZIxhz5/+hISF0eO3v7U7Tou0QCillB8dfuddKj//gqRf/JywHsl2x2mRFgillPKTuoMHKXnoISKzski44Qa747RKC4RSSvmBMYY999+Ps7ycng88YOutRD2lBUIppfzg8Lx5lH/4EUk/u4vI/pl2x/GIFgillPKx2t272fPAX+gyfBiJt9xidxyPaYFQSikfMnV17Lr7HnA66fXQQ0Gxa6lBYF6doZRSncS+J6ZyZNkyej78EOFBdnMn3YJQSikfqVi0iAP//jfx468l/uqr7Y7TZloglFLKB2p37WLX3fcQMWAAPe67z+447aIFQimlvMx55AhFU6Zg6upI/b9/4oiMtDtSu+gxCKWU8iLjdLLrnnuoWb+B1CenEd63r92R2k23IJRSyov2/fP/KP/wI3rcczexY8bYHadDtEAopZSXlM6ezYFnniH++utJuPlmu+N0mBYIpZTygsPz57P7938getQoUn53HyJid6QO0wKhlFIdVPn55+z65a/okpVF6hOPI2FhdkfyCi0QSinVAUfyCyiacifh6emk/ftpHFFRdkfyGlsLhIj8SkSMiHS3M4dSSrVH2MaN7PzBDwhN6k7as88QEhdndySvsq1AiEgacDGw064MSinVXhVLlpDwxFTCevakzyuvEJYc2Df/aQ87tyD+CdwNGBszKKVUm5V//DHFP/4JdcnJ9Hn5pU5ZHADEGP+vn0VkLHChMeYuEdkODDfG7G9m2NuB2wGSkpKGzZgxw39B26miooKYmBi7Y7QqGHIGQ0bQnN4WyDm7LFhA7IyZ1PXuTfFttxLVo4fdkVqVl5e33BgzvM0jGmN88gA+Ala7eVwFfAnEuYbbDnT3ZJqZmZkmGCxYsMDuCB4JhpzBkNEYzeltgZjTWVdn9vz1r2Zt/wFm50/uMPWVlQGZ0x3ga9OO9bjPutowxlzk7n0RGQqkAytc5wmnAvkiMsIYs8dXeZRSqr3qy8rYdfc9VCxaROKkm0m+++6guq9De/m9LyZjzCrg2A671nYxKaWUnarWrOGbu35GbUkJKff/gYQbb7Q7kt9oZ31KKeWGMYbSGTMpefBBQhIT6fvKy3TJzrY7ll/ZXiCMMX3tzqCUaqO2diNhw8kwHVG7dy97fv8HKhYtIvqcb9Hr0UcJTUy0O5bf2V4glFIqUBhjKH//ffb86c84q6vp8dt7SZg4EXGcmp1OaIFQSrVfa1sGQdRhXc22bZT85UEqlywhcuhQej3yMBEZGXbHspUWCKXUKa2+vJwDzzzLgRdewBERQY/77iPhxhuQUF096hxQSp2SnFVVHHr9dQ785xnqy8qIu2osyb/+NaHdtWu4BloglFKnlPqyMkpnzuTgSy9Tt28f0eefR9Jdd9Fl8GC7owUcLRBKqVNCzdatHJr+BqWzZ2OOHCFq5EhO++djRA1vew8UpwotEEqpTqvu0CEOv/8+ZXPmUr1yJYSFEXfZZSTeMonIgQPtjhfwtEAopToN43RSs2kzlZ8upnzBQqoKCsDpJCIzk+S77ybuyisITUqyO2bQ0AKhlAp6lUuXcvCll6nKz6e+rAyAiEED6T55MrEXX6RbC+2kBUIp1X4Bcp1Dfdlhjm7fTszFFxGVO4zoc75FWEqK3bGCnhYIpVTQi/32xXS95Nt2x+h0tEAopdouwPpWkgDZkulsTs0ORpRSSrVKC4RSSim3tEAopZRySwuEUkopt8QE2MGmlohIObDB7hwe6A4Ewy1UgyFnMGQEzeltmtO7+htjYts6UrCdxbTBGBPwHaeIyNea0zuCISNoTm/TnN4lIl+3ZzzdxaSUUsotLRBKKaXcCrYC8R+7A3hIc3pPMGQEzeltmtO72pUzqA5SK6WU8p9g24JQSinlJ1oglFJKuRVwBUJE/i4i60VkpYi8JSLxjT67V0Q2i8gGEbmkmfETReRDEdnkek7wUc7xIrJGRJwiMrzR+xNEpLDRwyki2W7G/6OIfNNouMv8mLGviFQ1avvpZsa3e15eLCLLRWSV6/mCZsb3+bxsKafrs4BZNpu0+Waj+bJdRAqbGW67az4XtveUyA7m9Oh3KCKXuubxZhH5jQ05m10/NRnO7/OztXkjlsddn68UkdxWJ2qMCagH8G0g1PX6EeAR1+tBwAogAkgHtgAhbsb/G/Ab1+vfNIzvg5wDgf7AQmB4M8MMBbY289kfgV/5eF66zQj0BVZ7ML6t8xLIAXq5Xg8BvrFrXraSM6CWzRby/wP4QzOfbQe6+zNPW3+HQIhr3mYA4a55PsjPOd2un+yen57MG+Ay4H1AgJHAl61NN+C2IIwx840xda4flwKprtdXAW8YY2qMMduAzcAIN5O4CnjJ9fol4Gof5VxnjGntqu4bgem+aN8THmZsia3z0hhTYIzZ5fpxDRApIhG+yOCJFuZnQC2b7ojVH/Z12Lg8esEIYLMxZqsx5ijwBtY89ZsW1k9282TeXAW8bCxLgXgR6dnSRAOuQDRxG1bFAzgNKGr0WbHrvaZ6GGN2A7iek32asGXX0/If5BTXpt7z/tjd0ES6iBSIyCIROa+ZYQJpXo4DCowxNc18bue8DIZl8zygxBizqZnPDTDftSvvdj/maqy136Gn89lfGq+fmvL3/PRk3rR5/tnS1YaIfAS4ux/gfcaYua5h7gPqgNcaRnMzvE/P0fUkZwvjng0cMcasbmaQp4AHsL7DA1ib/7f5KeNuoLcx5oCIDAPmiMhgY8zhtrbv45wN4w7G2pxv7pZhXpmXHcjp92XzhMY9y9za1uwoY8wuEUkGPhSR9caYxf7KiWe/Q7/M53aun5ry+fxswpN50+b5Z0uBMMZc1NLnIjIJuAK40Lh2nmFVu7RGg6UCu5qOC5SISE9jzG7X5tNeX+VsxQ208AdpjClpeC0izwDvtKeR9mR0/Rde43q9XES2AJlA04Npts9LEUkF3gJuNsZsaWbaXpmXrmm1J6ffl83GPPh7CgW+CwxrYRq7XM97ReQtrF0WXl2heTpvW/gdejqfO6Sd66em0/D5/GzCk3nT5vkXcLuYRORS4B5grDHmSKOP5gE3iEiEiKQDZwBfuZnEPGCS6/UkoMX/Tn1BRBzAeKz9gM0N03jf3zVAc1saXiciSSIS4nqdgTUvt7oZ1NZ56TpD5F3gXmPMkhaGs21eugT6snkRsN4YU+zuQxGJFpHYhtdYW2p+nYce/g6XAWeISLqIhGP9EzbPH/katLB+ajyMHfPTk3kzD7jZdTbTSKCsYZdns/x1lL0NR+M3Y+0nK3Q9nm702X1YR+o3AN9p9P6zuM4qAboBHwObXM+JPsp5DVZFrgFKgP81+mwMsNTNOI1zvgKsAla6fnE9/ZURa3/+GqwzHfKBKwNxXgK/AyobLQuFQLId89KD33nALJtucr8ITG7yXi/gPdfrDNeysMK1XNznj1xN8rj9HTbO6fr5MmCja17bkdPt+ikQ5qe7eQNMbvjdY+1imub6fBXNnH3Z+KFdbSillHIr4HYxKaWUCgxaIJRSSrmlBUIppZRbWiCUUkq5pQVCKaWUW1oglPIDEXlRRK61O4dSbaEFQqk2cl1opH87qtPThVwpD4h1D411IvIk1sWFN4nIFyKSLyIzRSTGNdwfRGSZiKwWkf+4elFVKihpgVDKc/2Bl4GLge8DFxljcrH6sPqFa5ipxpizjDFDgC5YffYoFZRs6axPqSC1wxizVESuwLpJ0BLXBkI48IVrmDwRuRuIAhKxulp4246wSnWUFgilPFfpehbgQ2PMjY0/FJFI4EmsPm6KROSPQKR/IyrlPbqLSam2WwqMEpF+ACISJSKZHC8G+13HJPSsJRXUdAtCqTYyxuwTkVuA6Y1ugfo7Y8xG170MVmHdk3iZTRGV8grtzVUppZRbuotJKaWUW1oglFJKuaUFQimllFtaIJRSSrmlBUIppZRbWiCUUkq5pQVCKaWUW/8PhUGMqIU/pBUAAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure()\n", + "sys3 = control.feedback(G, kalpha*(10/(s+10))*select(2, 0))\n", + "k = 2.2;\n", + "rlocus('p', (s**2*0.06+s+4.5)/s*sys3[1, 0], kvect=np.linspace(0, 1, 1000), k=k)\n", + "plt.plot([0, -10], [0, 10*np.cos(0.707)], '--')\n", + "plt.axis([-20, 0, -5, 5])" + ] + }, + { + "cell_type": "code", + "execution_count": 150, + "metadata": {}, + "outputs": [], + "source": [ + "#bode('test', (s+5)/s*sys3[1, 0], omega=np.logspace(-2, 4), margins=True, Hz=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 151, + "metadata": {}, + "outputs": [], + "source": [ + "sys4 = control.feedback((s**2*0.06+s+4.5)*k/s*sys3[1, 0], 1)\n", + "sys4\n", + "\n", + "#def f_control(t, x, x_dot, x_int):\n", + "# return f16.Control(\n", + "# thtl=u0.thtl,\n", + "# ail_cmd_deg=u0.ail_cmd_deg,\n", + "# elv_cmd_deg=u0.elv_cmd_deg + x.alpha*k + x_dot.alpha*0.06*k + x_int.alpha*4.5*k,\n", + "# rdr_cmd_deg=u0.rdr_cmd_deg)" + ] + }, + { + "cell_type": "code", + "execution_count": 152, + "metadata": {}, + "outputs": [], + "source": [ + "#By frmdstryr | https://sourceforge.net/p/python-control/discussion/1022992/thread/3d038097/\n", + "def step_info(t,yout):\n", + " print(\"Overshoot :\" + str((yout.max()/yout[-1]-1)*100) + \"%\")\n", + " print(\"Rise Time :\" + str(t[next(i for i in range(0,len(yout)-1) if yout[i]>yout[-1]*.90)]-t[0]))\n", + " print(\"Settling Time:\" + str(t[next(len(yout)-i for i in range(2,len(yout)-1) if abs(yout[-i]/yout[-1])>1.02)]-t[0]))" + ] + }, + { + "cell_type": "code", + "execution_count": 154, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Overshoot :7.21002358449685%\n", + "Rise Time :0.08163265306122448\n", + "Settling Time:0.5510204081632653\n" + ] + }, + { + "data": { + "image/png": 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XqAtHCqcAL4IHXmrjY99+kvbUIB9588l8YOWJevMsouqqKsbsgx/m7qQGM+zdH3zIae/+QTpSg3SkhujoHaQ9NUR7apDt2/voSA0eNmzy0OMlqUnkaHniAWbVVjC7toqm2opgJE9tJU01FeF1JY01FdRXV9BYEwzlbKip0AtAzB01wM3sa8DlwF53PyNc1gx8C1gKtALvdPfOqStzZuofyvK5+57nzodaOXF+PXe890LOXKSz7nJnZjTWVNJYE3wq9mgGM1m6+tLsC+er2dcXXHf3p+nqS/P81h3UNNXS059mc1uK/QMZegbS9B0h+IdVJRPUVyepq6qgvjpJfXUF9VUV1FUFP9dUJqmrSlJbmaQ277qmMkFNRZKaqmRwXZmgpjJJdUWC6uHrcL6cqmRCb7rPUOM5A78TuA34Rt6ym4FfuPtnzezm8PZNxS9v5trclmL1Nzawua2Xa1+3lJsvPVVjkmVU1RVJWpqStDTVjLp+3bq9rFy54rDl6WwuCPNweoPUQIb9gxlSAxlSg8GlZyBN32CW3qHMweuhLO2pQfqGsvQNZRlIZ+kbyhz2Bu5EDAd5VUWCyqSF18GyiqRRmUxQmUhQWWFUJIJtKvKmcahIBsuSiWD57pcHebjvORKJYH0yYSTNSCSMhBnJBOF1cDEL1xsHtklYsI2F18PLLFxmHLqecJmZhddgHNyW8DUqf9nwC1f+69fwjweXHbrNWC91veniz1t01AB39/vNbOmIxVcAK8Ofvw6sI0YB/tzuHq756qO4wzevO4+LTppX6pKkDFUmEwfGzE+WuzOUDea9GQ71gXSOgUzw82A6R396eH6cg/PkDGZyDKazDGWdoUyOdDZ34HowmyOdGZ71Mlg2kM6RyWYYyjrZXI5M1snkDs6ImcnmyOacoXSG9btayeaC9T41c7LNKH+5vLro+zQfxyMXBvi9eV0oXe4+O299p7sfPq4rWLcaWA3Q0tKyfM2aNQUVmkqlaGg4+r+rU21LV5bPbxygOml8bEUNCxqmrq97prR5OqnN8TCyzTl3cg4O5PzgxR1y4XofXgaH/XxgWbgt4W0IluEHr4cTz/O2ObBsxO38ZYcu9zG3H8v8igEWzCnseV61atVGdz/83zR3P+qFoK/76bzbXSPWd45nP8uXL/dCrV27tuD7FsvDm9v9tL/5iV/8uV/69o7eKT/eTGjzdFOb40Ftnhhgg4+SqYWePr5iZgsAwuu9Be4nMta9sJf3fe3XLJhdy7dvuIDFzaOPNRYRmS6FBvgPgPeFP78PuKc45cxMP3lqN9d/YwOvOqaBb60+f8w3o0REptNRA9zM7gIeBk4xs51mdh3wWeDNZvYS8Obwdlm67+nd/Ol/PcaZC2fxX9efz9yG4r8RISJSiPGMQvnDMVa9sci1zDit7b189NtP8ppFs/mP686jXnNiiMgMoo8LjmEwk+VDd/2WhMGXrj5H4S0iM45SaQyf+8kLPPVyN/92zXIWzo7XnN0iEg06Ax/Fz599ha/9aivvu2AJl5x+bKnLEREZlQJ8hN3d/Xz07ic4bUETH7/s1aUuR0RkTArwPJlsjhvvepyhTI7b3v1azW0iIjOa+sDz3PqLl/h16z7+5aqzjjidqIjITKAz8NBDm9r54tpNXLl8EW9/7aJSlyMiclQKcCCbc/7q+0+zbG49f3vF6aUuR0RkXBTgwI+e2s3W9l4+dskp1FWpV0lEoiH2AZ7LOV9eu4lXHdOgIYMiEimxD/BfPL+X5/fs54MrT9Q3iotIpMQ6wN2d29ZuYnFzLW8767hSlyMiMiGxDvBfbergiR1d3PAGfYu8iERPrFPri798iZamaq5crmGDIhI9sQ3wDa37eHTrPq6/+ASqK/SJSxGJntgG+G1rN9FcX8W7zzu+1KWIiBQklgH+9MvdrHuhjesuWqZx3yISWbEM8C+t3URjTQXXXLCk1KWIiBQsdgH+0iv7+cnTe3jfBUtpqqksdTkiIgWLXYB/ed1maiuT/NFFy0pdiojIpMQqwFODGe59chdXnbuY5vqqUpcjIjIpsQrwhzd3kM46bzm9pdSliIhMWqwCfP2Le6mrSrJiSXOpSxERmbTYBLi7s+6FNl534jyqKmLTbBEpY7FJsq3tvezs7OcNp8wvdSkiIkURmwC//8U2AN5wkgJcRMpDbAJ8/YttLJtXz/Fz60pdiohIUUwqwM3sL8zsGTN72szuMrOaYhVWTAPpLA9v6eANJ+vsW0TKR8EBbmYLgT8HVrj7GUASeFexCium37TuYyCdU4CLSFmZbBdKBVBrZhVAHbBr8iUV3/oX2qhKJjjvBA0fFJHyUXCAu/vLwD8B24HdQLe7/0+xCium9S+28TvLmjXzoIiUFXP3wu5oNgf4DnAV0AV8G7jb3b85YrvVwGqAlpaW5WvWrCnoeKlUioaGhgnfr6M/x0fW93PVKVVcuixak1cV2uYoU5vjQW2emFWrVm109xWHrXD3gi7AO4Cv5t1+L/DlI91n+fLlXqi1a9cWdL+7Ht3mS26611/Y01PwsUul0DZHmdocD2rzxAAbfJRMnUwf+HbgfDOrMzMD3gg8N4n9TYn1L7axYFYNJx0Tr1d7ESl/k+kDfxS4G3gMeCrc1+1Fqqso0tkcD77UzutPmk/wGiMiUj4m9a6eu38K+FSRaim6x3d0sX8wo4/Pi0hZKutPYq5/oY1kwrjwVfNKXYqISNGVdYDf/1Ibr108m1m10Rp9IiIyHmUb4O2pQZ7c2c3r9elLESlTZRvgD77UDqCPz4tI2SrbAF//YhvN9VWcuXBWqUsREZkSZRnguZxz/4ttXHzSPBIJDR8UkfJUlgG+qS1FR+8QF2n0iYiUsbIM8C1tKQBOObaxxJWIiEydsgzwre19ACydV1/iSkREpk5ZBnhrey9z66toqtH4bxEpX2UZ4Fs7enX2LSJlrywDvLW9l6VzFeAiUt7KLsB7BzPs3T/Isnn69nkRKW9lF+CtHb2A3sAUkfJXfgE+PAJFXSgiUubKL8B1Bi4iMVF2Ab61vZf5jdU0VOsb6EWkvJVdgLe297JM3SciEgPlF+AdvSzVCBQRiYGyCvD9A2naU0Pq/xaRWCirAB8egaIuFBGJg7IK8K0agSIiMVJWAd7aHga4zsBFJAbKLsCPbaqhtipZ6lJERKZcWQX41o5elqn7RERioqwCvLVd08iKSHyUTYB396Xp7EtrFkIRiY2yCfADI1D0BqaIxMSkAtzMZpvZ3Wb2vJk9Z2YXFKuwiRoegaI+cBGJi8nO+PQF4D53v9LMqoCS9V9sbe/FDBY3qwtFROKh4AA3sybg9cC1AO4+BAwVp6yJa+3o5bhZtdRUagihiMSDuXthdzQ7G7gdeBY4C9gI3OjuvSO2Ww2sBmhpaVm+Zs2ago6XSqVoaGgYc/2nH+6nrgI+dm5tQfufiY7W5nKkNseD2jwxq1at2ujuKw5b4e4FXYAVQAY4L7z9BeDvjnSf5cuXe6HWrl075rpcLudnfuo+/6vvPVnw/meiI7W5XKnN8aA2TwywwUfJ1Mm8ibkT2Onuj4a37wbOmcT+CtbZl6ZnIKMRKCISKwUHuLvvAXaY2SnhojcSdKdMu60agSIiMTTZUSgfAv4zHIGyBXj/5EuauAOTWCnARSRGJhXg7v44QV94SbV29JIwWDxHQwhFJD7K4pOYW9t7WTSnjqqKsmiOiMi4lEXiBd+Dqe4TEYmXyAe4u9Pa3seyueo+EZF4iXyAt6eGSA1mdAYuIrET+QBv1fdgikhMRT7AD4wB14d4RCRmIh/gre29VCSMRXPKZw4UEZHxiH6Ad/SyuLmOimTkmyIiMiGRT72t7X0s1QgUEYmhSAe4u7NNY8BFJKYiHeB79w/SN5TVJFYiEkuRDvDhESiaRlZE4ijSAb5jXx8AS9QHLiIxFOkA7+pLAzCnvqrElYiITL9IB3h3f5qEQUPVZKc1FxGJnsgHeFNtJYmElboUEZFpF/kAn11bWeoyRERKIvIBPksBLiIxFfkAb1KAi0hMRT7AdQYuInGlABcRiajIBri7K8BFJNYiG+C9Q1myOWd2nQJcROIpsgHe3R98ClNn4CISV5EN8K6+IUABLiLxFdkAHz4D1zBCEYmryAZ4j7pQRCTmIhvgw2fgs+s0E6GIxNOkA9zMkmb2WzO7txgFjZfexBSRuCvGGfiNwHNF2M+EdPWlSSaM+qrkdB9aRGRGmFSAm9ki4PeBrxSnnPEb/hCPmaaSFZF4Mncv/M5mdwP/ADQCH3X3y0fZZjWwGqClpWX5mjVrCjpWKpWioaHhwO0vPz7Atp4cn3t9+X6d2sg2x4HaHA9q88SsWrVqo7uvGLm84K+yMbPLgb3uvtHMVo61nbvfDtwOsGLFCl+5csxNj2jdunXk3/ermx9lQWWGlSsvLGh/UTCyzXGgNseD2lwck+lCuRB4m5m1AmuA3zWzbxalqnHo0TwoIhJzBQe4u3/c3Re5+1LgXcAv3f09RavsKDSRlYjEXWTHgXcpwEUk5oryde7uvg5YV4x9jUcu5+pCEZHYi+QZeGooQ87RVLIiEmuRDPDuPk1kJSISzQDXx+hFRBTgIiJRpQAXEYkoBbiISERFOsA1CkVE4iyyAV6ZNGorNZWsiMRXJAO8q09TyYqIRDLAe/rTGgMuIrEXyQDXRFYiIhEO8NkKcBGJucgGuM7ARSTuIhngXX1DCnARib3IBXgu5+wfzCjARST2Ihfg+wcyuGsmQhGRyAX4wU9hVpW4EhGR0opsgKsLRUTiTgEuIhJRkQvwrv4hQAEuIhK5ANcZuIhIQAEuIhJRkQzwqooENZWRK11EpKgil4I9/ZpKVkQEIhjgw3OBi4jEXeQCXBNZiYgEFOAiIhEVyQDXXOAiIpMIcDNbbGZrzew5M3vGzG4sZmFj6dbXqYmIAFAxiftmgI+4+2Nm1ghsNLOfufuzRartMNmcs39AU8mKiMAkzsDdfbe7Pxb+vB94DlhYrMJG06MP8YiIHGDuPvmdmC0F7gfOcPeeEetWA6sBWlpalq9Zs6agY6RSKXqtjpse6Of6M6u4cGH5h3gqlaKhoaHUZUwrtTke1OaJWbVq1UZ3X3HYCnef1AVoADYCf3C0bZcvX+6FWrt2rT++vdOX3HSv//zZPQXvJ0rWrl1b6hKmndocD2rzxAAbfJRMndQoFDOrBL4D/Ke7f3cy+xoPzYMiInLQZEahGPBV4Dl3/+filTS2LgW4iMgBkzkDvxC4BvhdM3s8vFxWpLpGpTNwEZGDCh5G6O4PAtM6o9TwKBSNAxcRidgnMbv709RUJqipTJa6FBGRkotWgGsmQhGRA6IV4JrISkTkgEgFeFf/kAJcRCQUqQDv7tc8KCIiwyIV4D2aiVBE5IBIBXgwF3hVqcsQEZkRIhPgmZyTGlQXiojIsMgEeF8muJ5VO5kpzEVEykd0AjwdTHs7q05n4CIiEKEA7x0OcHWhiIgAkQxwvYkpIgIRCvC+YB4rnYGLiIQiE+ApdaGIiBwiMgHel1GAi4jki0yA96ad2sokVRWRKVlEZEpFJg370jBbQwhFRA6ITID3pl3dJyIieSIV4JrISkTkoEgFuM7ARUQOikyA92U0AkVEJF9kArw37cxWgIuIHBCJAE9ncwxmdQYuIpIvEgHe3R98jl4zEYqIHBSJAO8KJ0LRGbiIyEGRCPDhM3ANIxQROSgSAd7TrzNwEZGRIhHgw2fgGoUiInLQpALczH7PzF4ws01mdnOxihqpW2fgIiKHKTjAzSwJfAm4FDgN+EMzO61YheUbfhNTfeAiIgdN5gz8d4BN7r7F3YeANcAVxSnrUN39aWqSUJmMRI+PiMi0qJjEfRcCO/Ju7wTOG7mRma0GVgO0tLSwbt26CR/Iu9O8dp4XdN8oS6VSanMMqM3xMBVtnkyA2yjL/LAF7rcDtwOsWLHCV65cOeEDrQTWrVtHIfeNMrU5HtTmeJiKNk+mT2InsDjv9iJg1+TKERGR8ZpMgP8GOMnMlplZFfAu4AfFKUtERI6m4C4Ud8+Y2Z8BPwWSwNfc/ZmiVSYiIkc0mT5w3P3HwI+LVIuIiEyAxuWJiESUAlxEJKIU4CIiEaUAFxGJKHM/7LM3U3cwszhUpn4AAATrSURBVDZgW4F3nwe0F7GcKFCb40FtjofJtHmJu88fuXBaA3wyzGyDu68odR3TSW2OB7U5HqaizepCERGJKAW4iEhERSnAby91ASWgNseD2hwPRW9zZPrARUTkUFE6AxcRkTwKcBGRiJpxAX60L0q2wK3h+ifN7JxS1FlM42jz1WFbnzSzh8zsrFLUWUzj/UJsMzvXzLJmduV01lds42mvma00s8fN7BkzWz/dNRbbOH6vZ5nZD83sibDN7y9FncVkZl8zs71m9vQY64ubX+4+Yy4E09JuBk4AqoAngNNGbHMZ8BOCbwQ6H3i01HVPQ5tfB8wJf740Dm3O2+6XBDNeXlnquqf4OZ4NPAscH94+ptR1T0ObPwF8Lvx5PrAPqCp17ZNs9+uBc4Cnx1hf1PyaaWfg4/mi5CuAb3jgEWC2mS2Y7kKL6KhtdveH3L0zvPkIwbcfRdl4vxD7Q8B3gL3TWdwUGE973w181923A7h7HNrsQKOZGdBAEOCZ6S2zuNz9foJ2jKWo+TXTAny0L0peWMA2UTLR9lxH8AoeZUdts5ktBN4O/Os01jVVxvMcnwzMMbN1ZrbRzN47bdVNjfG0+Tbg1QRfxfgUcKO756anvJIpan5N6gsdpsB4vih5XF+mHCHjbo+ZrSII8IumtKKpN542/1/gJnfPBidokTae9lYAy4E3ArXAw2b2iLu/ONXFTZHxtPkS4HHgd4ETgZ+Z2QPu3jPVxZVQUfNrpgX4eL4oudy+THlc7TGz1wBfAS51945pqm2qjKfNK4A1YXjPAy4zs4y7f396Siyq8f5et7t7L9BrZvcDZwFRDfDxtPn9wGc96BzeZGZbgVOBX09PiSVR1PyaaV0o4/mi5B8A7w3fzT0f6Hb33dNdaBEdtc1mdjzwXeCaCJ+R5Ttqm919mbsvdfelwN3AByMa3jC+3+t7gIvNrMLM6oDzgOemuc5iGk+btxP8x4GZtQCnAFumtcrpV9T8mlFn4D7GFyWb2Q3h+n8lGJFwGbAJ6CN4FY+scbb5k8Bc4MvhGWnGIzyT2zjbXDbG0153f87M7gOeBHLAV9x91KFoUTDO5/jvgDvN7CmCroWb3D3SU8ya2V3ASmCeme0EPgVUwtTklz5KLyISUTOtC0VERMZJAS4iElEKcBGRiFKAi4hElAJcRCSiFOBSdsxstpl9sNR1iEw1BbiUo9mAAlzKngJcytFngRPDubX/cayNzCxpZnea2dNm9pSZ/UW4/EQzuy+cVOoBMzs1XN5iZt8L569+wsxeN03tERnVjPokpkiR3Ayc4e5nH2W7s4GF7n4GBF0v4fLbgRvc/SUzOw/4MsGES7cC69397WaWJJgCVaRk9ElMKTtmthS4dziYj7DdHGADwcebfwT8D1AHtAEv5G1a7e6vNrM2YJG7D05F3SITpTNwiS137wy/nu4S4E+BdwIfBrrGcfYuUnLqA5dytB9ozF9gZs+P3MjM5gEJd/8O8DfAOeFc1FvN7B3hNmYHv4P0F8AHwuVJM2uawjaIHJUCXMpOOF/6r8I3J/8xDOrRJtJfCKwzs8eBO4GPh8uvBq4zsyeAZzj4VWA3AqvC2fM2AqdPYTNEjkp94FL2zOxy4AR3v7XUtYgUkwJcRCSi1IUiIhJRCnARkYhSgIuIRJQCXEQkohTgIiIRpQAXEYmo/w/5fmLRLUMJ8gAAAABJRU5ErkJggg==\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "analysis.step_reponse('Linear 10 Deg Pitch',10*sys4,np.linspace(0,1));\n", + "t, y = control.step_response(sys4,np.linspace(0,1));\n", + "step_info(t,y)\n", + "\n", + "#res = f16.simulate(x0, f_control, p, 0, 20, 0.005)\n", + "#plt.plot(res['t'], np.rad2deg(res['x'][:, f16.State().name_to_index('alpha')]))\n", + "#plt.xlabel('t ,sec')\n", + "#plt.ylabel(r'$\\alpha$, deg')\n", + "#plt.grid()\n", + "#plt.title('Nonlinear 10 Deg Pitch Step Response')" + ] + }, + { + "cell_type": "code", + "execution_count": 138, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Overshoot :7.21002358449685%\n", + "Rise Time :0.08163265306122448\n", + "Settling Time:0.5510204081632653\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "analysis.step_reponse('Linear 100 Deg Pitch',sys4*100,np.linspace(0,1));\n", + "t, y = control.step_response(sys4,np.linspace(0,1));\n", + "step_info(t,y)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.7.3" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} + diff --git a/homework/HW3.ipynb b/homework/HW3.ipynb new file mode 100644 index 00000000..96fa6000 --- /dev/null +++ b/homework/HW3.ipynb @@ -0,0 +1,529 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "import casadi as ca\n", + "import numpy as np\n", + "import control\n", + "import matplotlib.pyplot as plt\n", + "\n", + "from casadi.tools.graph import dotgraph\n", + "from IPython.display import Image\n", + "\n", + "def draw_graph(expr):\n", + " return Image(dotgraph(expr).create_png())\n", + "\n", + "# make matrix printing prettier\n", + "np.set_printoptions(precision=3, suppress=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This notebook will walk through trimming and control design for a transport aircxraft using casadi." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "def rhs(x, u):\n", + " s = 2170\n", + " cbar = 17.5\n", + " mass = 5.0e3\n", + " iyy = 4.1e6\n", + " tstat = 6.0e4\n", + " dtdv = -38.0\n", + " ze = 0.0\n", + " cdcls = 0.042\n", + " cla = 0.085\n", + " cma = -0.022\n", + " cmde = -0.016\n", + " cmq = -16.0\n", + " cmadot = -6.0\n", + " cladot = 0.0\n", + " rtod = 57.29578\n", + " gd = 32.17\n", + " \n", + " thtl = u[0]\n", + " elev_deg = u[1]\n", + " xcg = u[2]\n", + " land = u[3]\n", + " \n", + " vt = x[0] # velocity, ft/s\n", + " alpha = x[1]\n", + " alpha_deg = rtod*alpha # angle of attack, deg\n", + " theta = x[2] # pitch angle, rad\n", + " q = x[3] # pitch rate, rad/s\n", + " h = x[4] # altitude, ft\n", + " pos = x[5] # horizontal position from origin, ft (not used in dynamics)\n", + " \n", + " r0 = 2.377e-3\n", + " tfac = 1.0 - 0.703e-5*h\n", + " temperature = ca.if_else(h > 35000, 390.0, 519.0*tfac)\n", + " rho = r0*(tfac**4.14)\n", + " mach = vt/ca.sqrt(1.4*1716.3*temperature)\n", + " qbar = 0.5*rho*vt**2\n", + " \n", + " qs = qbar*s\n", + " salp = ca.sin(alpha)\n", + " calp = ca.cos(alpha)\n", + " gam = theta - alpha\n", + " sgam = ca.sin(gam)\n", + " cgam = ca.cos(gam)\n", + " \n", + " aero_p = ca.if_else(\n", + " land,\n", + " (1.0, 0.08, -0.20, 0.02, -0.05),\n", + " (0.2, 0.016, 0.05, 0.0, 0.0))\n", + " cl0 = aero_p[0]\n", + " cd0 = aero_p[1]\n", + " cm0 = aero_p[2]\n", + " dcdg = aero_p[3]\n", + " dcmg = aero_p[4]\n", + " \n", + " thr = (tstat + vt*dtdv)*ca.fmax(thtl, 0)\n", + " cl = cl0 + cla*alpha_deg\n", + " cm = dcmg + cm0 + cma*alpha_deg + cmde*elev_deg + cl*(xcg - 0.25)\n", + " cd = dcdg + cd0 + cdcls*cl**2\n", + " \n", + " x_dot = ca.SX.zeros(6)\n", + " x_dot[0] = (thr*calp - qs*cd)/mass - gd*sgam\n", + " x_dot[1] = (-thr*salp - qs*cl + mass*(vt*q + gd*cgam))/(mass*vt + qs*cladot)\n", + " x_dot[2] = q\n", + " d = 0.5*cbar*(cmq*q + cmadot*x_dot[1])/vt\n", + " x_dot[3] = (qs*cbar*(cm + d) + thr*ze)/iyy\n", + " x_dot[4] = vt*sgam\n", + " x_dot[5] = vt*cgam\n", + " return x_dot" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "def constrain(s, vt, h, q, gamma):\n", + " \n", + " # s is our design vector:\n", + " # s = [thtl, elev_deg, alpha]\n", + " thtl = s[0]\n", + " elev_deg = s[1]\n", + " alpha = s[2]\n", + " \n", + " pos = 0 # we don't care what horiz. position we are at\n", + " xcg = 0.25 # we assume xcg at 1/4 chord\n", + " land = 0 # we assume we do not have flaps/gear deployed\n", + " theta = alpha + gamma\n", + " \n", + " # vt, alpha, theta, q, h, pos\n", + " x = ca.vertcat(vt, alpha, theta, q, h, pos)\n", + " \n", + " # thtl, elev_deg, xcg, land\n", + " u = ca.vertcat(thtl, elev_deg, xcg, land)\n", + " return x, u\n", + "\n", + "def trim_cost(x, u):\n", + " x_dot = rhs(x, u)\n", + " return x_dot[0]**2 + 100*x_dot[1]**2 + 10*x_dot[3]**2\n", + "\n", + "def objective(s, vt, h, q, gamma):\n", + " x, u = constrain(s, vt, h, q, gamma)\n", + " return trim_cost(x, u)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "def trim(vt, h, q, gamma):\n", + " s = ca.SX.sym('s', 3)\n", + " nlp = {'x': s, 'f': objective(s, vt=vt, h=h, q=q, gamma=gamma)}\n", + " S = ca.nlpsol('S', 'ipopt', nlp, {\n", + " 'print_time': 0,\n", + " 'ipopt': {\n", + " 'sb': 'yes',\n", + " 'print_level': 0,\n", + " }\n", + " })\n", + " # s = [thtl, elev_deg, alpha]\n", + " s0 = [0.293, 2.46, np.deg2rad(0.58)]\n", + " res = S(x0=s0, lbg=0, ubg=0, lbx=[0, -60, -np.deg2rad(5)], ubx=[1, 60, np.deg2rad(18)])\n", + " trim_cost = res['f']\n", + " trim_tol = 1e-10\n", + " if trim_cost > trim_tol:\n", + " raise ValueError('Trim failed to converge', trim_cost)\n", + " assert np.abs(float(res['f'])) < trim_tol\n", + " s_opt = res['x']\n", + " x0, u0 = constrain(s_opt, vt, h, q, gamma)\n", + " return {\n", + " 'x0': np.array(x0).reshape(-1),\n", + " 'u0': np.array(u0).reshape(-1),\n", + " 's': np.array(s_opt).reshape(-1)\n", + " }" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "def power_required_curve():\n", + " throttle = []\n", + " vt_list = np.arange(190, 500, 5)\n", + " for vt in vt_list:\n", + " res = trim(vt=vt, h=0, q=0, gamma=0)\n", + " throttle.append(res['s'][0])\n", + " plt.plot(vt_list, 100*np.array(throttle))\n", + " plt.grid()\n", + " plt.ylabel(r'throttle, %')\n", + " plt.xlabel('VT, ft/s')\n", + " plt.title('power required curve')\n", + " \n", + "power_required_curve()" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "def linearize(trim):\n", + " x0 = trim['x0']\n", + " u0 = trim['u0']\n", + " x = ca.SX.sym('x', 6)\n", + " u = ca.SX.sym('u', 4)\n", + " y = x\n", + " A = ca.jacobian(rhs(x, u), x)\n", + " B = ca.jacobian(rhs(x, u), u)\n", + " C = ca.jacobian(y, x)\n", + " D = ca.jacobian(y, u)\n", + " f_ss = ca.Function('ss', [x, u], [A, B, C, D])\n", + " return control.ss(*f_ss(x0, u0))" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "def pitch_rate_control_design(vt, H, xlim, ylim, tf=3):\n", + " trim_state = trim(vt=vt, h=0, q=0, gamma=0)\n", + " print(trim_state)\n", + " sys = linearize(trim_state)\n", + " G = control.minreal(control.tf(sys[3, 1]), 1e-2)\n", + " control.rlocus(G*H, kvect=np.linspace(0, 1, 1000), xlim=xlim, ylim=ylim);\n", + " Go = G*H\n", + " Gc = control.feedback(Go)\n", + " plt.plot([0, -3], [0, 3*np.arccos(0.707)], '--')\n", + " #plt.axis('equal')\n", + " plt.grid()\n", + " \n", + " plt.figure()\n", + " control.bode(Go, margins=True, dB=True, Hz=True, omega_limits=[1e-2, 1e2], omega_num=1000);\n", + " plt.grid()\n", + "\n", + " plt.figure()\n", + " t = np.linspace(0, tf, 1000)\n", + " r = np.array(t > 0.1, dtype=float)\n", + " t, y, x = control.forced_response(Gc, T=t, U=r)\n", + " _, u, _ = control.forced_response((1/G)*Gc, T=t, U=r)\n", + "\n", + " u_norm = np.abs(u)\n", + " max_u_norm = np.max(u_norm)\n", + " print('u_norm max', max_u_norm)\n", + "\n", + " plt.plot(t, y, label='x')\n", + " plt.plot(t, r, label='r')\n", + " plt.plot(t, u_norm/max_u_norm, label='u normalized')\n", + " plt.gca().set_ylim(0, 1.5)\n", + " plt.grid()\n", + " plt.legend()" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'x0': array([500. , 0.01, 0.01, 0. , 0. , 0. ]), 'u0': array([0.293, 2.328, 0.25 , 0. ]), 's': array([0.293, 2.328, 0.01 ])}\n", + "1 states have been removed from the model\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/kevin/anaconda3/envs/aae497-f19/lib/python3.7/site-packages/control/xferfcn.py:896: ComplexWarning: Casting complex values to real discards the imaginary part\n", + " num[i, j, np + 1 - len(numpoly):np + 1] = numpoly[::-1]\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "u_norm max 853.5644468055459\n" + ] + }, + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "s = control.tf([1, 0], [0, 1])\n", + "# this is a PID controller with an extra pole at the origin\n", + "pitch_rate_control_design(500, -900*((s + 2 + 1j)*(s + 2 - 1j)/s**2), [-8, 2], [-4, 4])" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'x0': array([200. , 0.273, 0.273, 0. , 0. , 0. ]), 'u0': array([ 0.233, -18.347, 0.25 , 0. ]), 's': array([ 0.233, -18.347, 0.273])}\n", + "1 states have been removed from the model\n", + "u_norm max 990.9811402584778\n" + ] + }, + { + "data": { + "image/png": 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\n", 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "pitch_rate_control_design(200, -1000*((s+0.5)/s)**2, [-3, 1], [-2, 2])" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [], + "source": [ + "def lqr_design(out_num, in_num, tf=3, R=1e-5, y_max=1.5):\n", + " trim_500 = trim(vt=500, h=0, q=0, gamma=0)\n", + " # input: thtl, elev, xcg, land\n", + " # state: vt, alpha, theta, q, h, pos\n", + " sys = control.minreal(linearize(trim_500)[out_num, in_num], 1e-3)\n", + " assert np.linalg.matrix_rank(control.ctrb(sys.A, sys.B)) == sys.A.shape[0]\n", + " assert np.linalg.matrix_rank(control.obsv(sys.A, sys.C)) == sys.A.shape[0]\n", + "\n", + " Q = sys.C.T.dot(sys.C)\n", + " K, S, E = control.lqr(sys, Q, R)\n", + " sys_c = control.ss( sys.A - sys.B*K, sys.B, sys.C, sys.D)\n", + " final_value = float(sys_c.horner(0))\n", + " N = 1.0/final_value\n", + " sys_c = control.ss( sys.A - sys.B*K, sys.B*N, sys.C, sys.D)\n", + "\n", + " t = np.linspace(0, tf, 1000)\n", + " r = np.array(t > 0.1, dtype=float)\n", + " t, y, x = control.forced_response(sys_c, T=np.linspace(0, tf, 1000), U=r)\n", + " u_norm = np.linalg.norm(K.dot(x), axis=0)\n", + " max_u_norm = np.max(u_norm)\n", + " print('u_norm max', max_u_norm)\n", + "\n", + " plt.plot(t, r, 'r--', label='r')\n", + " plt.plot(t, y, 'b-', label='y')\n", + " plt.plot(t, u_norm/max_u_norm, 'g-', label='u normalized')\n", + " plt.gca().set_ylim(-0.1, y_max)\n", + " plt.grid()\n", + " plt.legend()" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1 states have been removed from the model\n", + "u_norm max 324.1938796680499\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "lqr_design(2, 1, tf=10, R=1e-5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we see that the LQR is not able to design a reasonable pitch rate controller." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1 states have been removed from the model\n", + "u_norm max 63670.60717497369\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "lqr_design(3, 1, tf=10, R=1e-5, y_max=1.5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we see the LQR is doing a poor job of designing a pitch rate controller. This is likely because none of the\n", + "states provide derivative of the pitch rate signal to prevent overshoot." + ] + } + ], + "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": "3.7.3" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/homework/hw7/plotTimes.py b/homework/hw7/plotTimes.py new file mode 100644 index 00000000..d1147ba5 --- /dev/null +++ b/homework/hw7/plotTimes.py @@ -0,0 +1,12 @@ +from numpy import * +from matplotlib import pyplot as plt + +data = loadtxt("build/timingResolutions.dat",delimiter=",") +plt.plot(data[:,0],data[:,3]) +plt.ylabel("Search Time QuadTree (ns)") +plt.xlabel("Resolution") +plt.figure() +plt.plot(data[:,0],data[:,2]) +plt.ylabel("Build Time QuadTree (ns)") +plt.xlabel("Resolution") +plt.show() \ No newline at end of file diff --git a/homework/hw7/quadTreeBuild_ResolutionVTime.png b/homework/hw7/quadTreeBuild_ResolutionVTime.png new file mode 100644 index 00000000..6032867c Binary files /dev/null and b/homework/hw7/quadTreeBuild_ResolutionVTime.png differ diff --git a/homework/hw7/quadTreeSearch_ResolutionVTime.png b/homework/hw7/quadTreeSearch_ResolutionVTime.png new file mode 100644 index 00000000..a9ecad7e Binary files /dev/null and b/homework/hw7/quadTreeSearch_ResolutionVTime.png differ diff --git a/homework/hw7/quadtree.cpp b/homework/hw7/quadtree.cpp index 80e881eb..0e7e17ff 100644 --- a/homework/hw7/quadtree.cpp +++ b/homework/hw7/quadtree.cpp @@ -80,7 +80,6 @@ class QuadTree if (m_size < m_resolution) { m_landmarks.push_back(lm); - //std::cout << "resolution reached, adding landmark: " << m_landmarks.size() << std::endl; } else { @@ -121,16 +120,50 @@ class QuadTree std::list search(const Position &position, double radius) { std::list close_landmarks; - // just fill in your logic here + //If search area overlaps quad being checked + if(overlap(position,radius)) + { + //Check for each child if it's been created. If so, search inside the child quad as well + if(m_NE) close_landmarks.splice(close_landmarks.end(),m_NE->search(position,radius)); + if(m_NW) close_landmarks.splice(close_landmarks.end(),m_NW->search(position,radius)); + if(m_SW) close_landmarks.splice(close_landmarks.end(),m_SW->search(position,radius)); + if(m_SE) close_landmarks.splice(close_landmarks.end(),m_SE->search(position,radius)); + //If there's no more children then look at the points in this root + if(!(m_NE||m_NW||m_SW||m_SE)) + { + //Check each landmark to see if it is inside the search area. If so, add to close_landmarks + for (auto &lm : m_landmarks) + { + double dx = position.x - lm.pos.x; + double dy = position.y - lm.pos.y; + double d = sqrt(dx * dx + dy * dy); + if (d < radius) + { + close_landmarks.push_back(lm); + } + } + //close_landmarks.splice(close_landmarks.end(),m_landmarks); + } + } return close_landmarks; } + bool overlap(const Position &position, double radius) + { + double quadRadius = sqrt(2)*m_size; + double dx = (position.x-m_center.x); + double dy = (position.y-m_center.y); + double dist = sqrt(dx*dx+dy*dy); + bool isOverlap = (quadRadius+radius)>dist; + return isOverlap; //implement + } + private: void subInsert(std::shared_ptr &tree, const Landmark &lm, const Position &pos) { if (!tree.get()) { - tree = std::make_shared(pos, m_size / 2, m_depth + 1); + tree = std::make_shared(pos, m_size / 2, m_resolution, m_depth + 1); } tree->insert(lm); } @@ -146,15 +179,17 @@ class QuadTree int main(int argc, char const *argv[]) { + double resolution; srand(1234); // seed random number generator Position center{0, 0}; // center of space double size = 1000; // size of space - double resolution = 1; // smallest cell in quadtree int n_landmarks = 1000; // number of landmarks - QuadTree tree(center, size, resolution); double search_radius = 50.0; // radius we want to find landmarks within - std::cout << "size: " << size << " resolution: " << resolution << " n_landmarks: " << n_landmarks << std::endl; + + std::FILE * pFile; + pFile = std::fopen ("timingResolutions.dat","w"); + // create random landmarks std::list landmarks; @@ -165,63 +200,145 @@ int main(int argc, char const *argv[]) //std::cout << "inserting landmark id: " << id << " x: " << x << " y: " << y << std::endl; landmarks.push_back(Landmark{x, y, id}); } - std::cout << "created " << landmarks.size() << " landmarks" << std::endl; // where you are float x = size * 2 * (double(rand()) / RAND_MAX - 0.5); float y = size * 2 * (double(rand()) / RAND_MAX - 0.5); Position vehicle_position{x, y}; - std::cout << "searcing at x: " << x << " y: " << y << " radius: " << search_radius << std::endl; - // brute force search - std::list close_landmarks_brute_force; - auto start = std::chrono::high_resolution_clock::now(); - for (auto &lm : landmarks) + for(int i = 1; i<1001;i++) { - float dx = vehicle_position.x - lm.pos.x; - float dy = vehicle_position.y - lm.pos.y; - float d = sqrt(dx * dx + dy * dy); - if (d < search_radius) + resolution = i*1000.0/1000; + + QuadTree tree(center, size, resolution); + + // brute force search + std::list close_landmarks_brute_force; + auto start = std::chrono::high_resolution_clock::now(); + for (auto &lm : landmarks) { - close_landmarks_brute_force.push_back(lm); + float dx = vehicle_position.x - lm.pos.x; + float dy = vehicle_position.y - lm.pos.y; + float d = sqrt(dx * dx + dy * dy); + if (d < search_radius) + { + close_landmarks_brute_force.push_back(lm); + } } - } - double elapsed_brute_force_search = std::chrono::duration_cast( + double elapsed_brute_force_search = std::chrono::duration_cast( + std::chrono::high_resolution_clock::now() - start) + .count(); + + // insert random landmarks into quadtree + start = std::chrono::high_resolution_clock::now(); + for (auto &lm : landmarks) + { + tree.insert(lm); + } + double elapsed_quadtree_insert = std::chrono::duration_cast( std::chrono::high_resolution_clock::now() - start) .count(); - std::cout << "search landmarks brute force,\telapsed time " - << elapsed_brute_force_search << " ns" << std::endl; - // output close landmarks - for (auto &lm : close_landmarks_brute_force) - { - std::cout << "id: " << lm.id << " x: " << lm.pos.x << " y: " << lm.pos.y << std::endl; - } + double cum_quadtree_search = 0; + start = std::chrono::high_resolution_clock::now(); + for(int smoothIter = 0;smoothIter<1000;smoothIter++) + { + std::list close_landmarks_quadtree = tree.search(vehicle_position, search_radius); + } + double elapsed_quadtree_search = std::chrono::duration_cast( + std::chrono::high_resolution_clock::now() - start) + .count(); + double avg_quadtree_search = elapsed_quadtree_search/1000; - // insert random landmarks into quadtree - std::cout << "quadtree inserting landmarks"; - start = std::chrono::high_resolution_clock::now(); - for (auto &lm : landmarks) - { - tree.insert(lm); - } - double elapsed_quadtree_insert = std::chrono::duration_cast( - std::chrono::high_resolution_clock::now() - start) - .count(); - std::cout << ",\telapsed time " << elapsed_quadtree_insert << " ns" << std::endl; - - // quadtree search - std::cout << "quadtree searching"; - start = std::chrono::high_resolution_clock::now(); - std::list close_landmarks_quadtree = tree.search(vehicle_position, search_radius); - double elapsed_quadtree_search = std::chrono::duration_cast( - std::chrono::high_resolution_clock::now() - start) - .count(); - std::cout << ",\t\telapsed time " << elapsed_quadtree_search << " ns" << std::endl; - for (auto &lm : close_landmarks_quadtree) - { - std::cout << "id: " << lm.id << " x: " << lm.pos.x << " y: " << lm.pos.y << std::endl; + char output[61]; + std::sprintf(output,"%8e,%8e,%8e,%8e\n",resolution,elapsed_brute_force_search,elapsed_quadtree_insert,avg_quadtree_search); + if (pFile!=NULL) + { + std::fputs (output,pFile); + } } + std::fclose (pFile); + // double res = 1; + + // std::cout << "Enter the resolution (smallest quadtree): " << std::endl; + + // std::cin >> res; + + // srand(1234); // seed random number generator + + // Position center{0, 0}; // center of space + // double size = 1000; // size of space + // double resolution = res; // smallest cell in quadtree + // int n_landmarks = 1000; // number of landmarks + // QuadTree tree(center, size, resolution); + // double search_radius = 50.0; // radius we want to find landmarks within + // std::cout << "size: " << size << " resolution: " << resolution << " n_landmarks: " << n_landmarks << std::endl; + + // // create random landmarks + // std::list landmarks; + // for (int id = 0; id < n_landmarks; id++) + // { + // float x = size * 2 * (double(rand()) / RAND_MAX - 0.5); + // float y = size * 2 * (double(rand()) / RAND_MAX - 0.5); + // //std::cout << "inserting landmark id: " << id << " x: " << x << " y: " << y << std::endl; + // landmarks.push_back(Landmark{x, y, id}); + // } + // std::cout << "created " << landmarks.size() << " landmarks" << std::endl; + + // // where you are + // float x = size * 2 * (double(rand()) / RAND_MAX - 0.5); + // float y = size * 2 * (double(rand()) / RAND_MAX - 0.5); + // Position vehicle_position{x, y}; + // std::cout << "searcing at x: " << x << " y: " << y << " radius: " << search_radius << std::endl; + + // // brute force search + // std::list close_landmarks_brute_force; + // auto start = std::chrono::high_resolution_clock::now(); + // for (auto &lm : landmarks) + // { + // float dx = vehicle_position.x - lm.pos.x; + // float dy = vehicle_position.y - lm.pos.y; + // float d = sqrt(dx * dx + dy * dy); + // if (d < search_radius) + // { + // close_landmarks_brute_force.push_back(lm); + // } + // } + // double elapsed_brute_force_search = std::chrono::duration_cast( + // std::chrono::high_resolution_clock::now() - start) + // .count(); + // std::cout << "search landmarks brute force,\telapsed time " + // << elapsed_brute_force_search << " ns" << std::endl; + // // output close landmarks + // for (auto &lm : close_landmarks_brute_force) + // { + // std::cout << "id: " << lm.id << " x: " << lm.pos.x << " y: " << lm.pos.y << std::endl; + // } + + // // insert random landmarks into quadtree + // std::cout << "quadtree inserting landmarks"; + // start = std::chrono::high_resolution_clock::now(); + // for (auto &lm : landmarks) + // { + // tree.insert(lm); + // } + // double elapsed_quadtree_insert = std::chrono::duration_cast( + // std::chrono::high_resolution_clock::now() - start) + // .count(); + // std::cout << ",\telapsed time " << elapsed_quadtree_insert << " ns" << std::endl; + + // // quadtree search + // std::cout << "quadtree searching"; + // start = std::chrono::high_resolution_clock::now(); + // std::list close_landmarks_quadtree = tree.search(vehicle_position, search_radius); + // double elapsed_quadtree_search = std::chrono::duration_cast( + // std::chrono::high_resolution_clock::now() - start) + // .count(); + // std::cout << ",\t\telapsed time " << elapsed_quadtree_search << " ns" << std::endl; + // for (auto &lm : close_landmarks_quadtree) + // { + // std::cout << "id: " << lm.id << " x: " << lm.pos.x << " y: " << lm.pos.y << std::endl; + // } - std::cout << "quadtree speed up: " << elapsed_brute_force_search/elapsed_quadtree_search << std::endl; + // std::cout << "quadtree speed up: " << elapsed_brute_force_search/elapsed_quadtree_search << std::endl; return 0; } diff --git a/lectures/10-Multirotor.ipynb b/lectures/10-Multirotor.ipynb index 098dc8ea..244b586b 100644 --- a/lectures/10-Multirotor.ipynb +++ b/lectures/10-Multirotor.ipynb @@ -22,7 +22,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 18, "metadata": {}, "outputs": [], "source": [ @@ -82,20 +82,20 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 122, "metadata": {}, "outputs": [], "source": [ "def quadrotor_model():\n", " # state space model\n", " \n", - " #x: state: (position, orientation, velocity (body frame), angular velocity (body frame))\n", - " x = NamedSXVect.from_string('P, Q, R, v_X, v_Y, v_Z, r0, r1, r2, p_N, p_E, p_D, rpm0, rpm1, rpm2, rpm3')\n", + " #x: state: (angular velocity (body frame), velocity (body frame), orientation, position, motor rpms)\n", + " x = NamedSXVect.from_string('P, Q, R, v_X, v_Y, v_Z, r0, r1, r2, p_N, p_E, p_D, duty0, duty1, duty2, duty3')\n", " omega_b = ca.vertcat(x['P'], x['Q'], x['R'])\n", " v_b = ca.vertcat(x['v_X'], x['v_Y'], x['v_Z'])\n", " r_nb = ca.vertcat(x['r0'], x['r1'], x['r2'], ca.SX.sym('r3'))\n", " p_n = ca.vertcat(x['p_N'], x['p_E'], x['p_D'])\n", - " rpm = ca.vertcat(x['rpm0'], x['rpm1'], x['rpm2'], x['rpm3'])\n", + " duty = ca.vertcat(x['duty0'], x['duty1'], x['duty2'], x['duty3'])\n", "\n", " #u: control\n", " u = NamedSXVect.from_string('u_roll, u_pitch, u_yaw, u_thrust')\n", @@ -123,12 +123,12 @@ " [1, 1, -1, -1], # yaw\n", " [1, 1, 1, 1] # thrust\n", " ])\n", - " u_rpm = ca.mtimes(ca.inv(mix_matrix), u)\n", + " u_duty = ca.mtimes(ca.inv(mix_matrix), u)\n", " F_b = ca.mtimes(C_nb.T, ca.vertcat(0, 0, p['m']*p['g']))\n", " M_b = ca.SX.zeros(3)\n", - " for theta_deg, rpm_i, motor_dir in zip(arm_angles_deg, rpm, motor_dirs):\n", + " for theta_deg, duty_i, motor_dir in zip(arm_angles_deg, duty, motor_dirs):\n", " theta = theta_deg*ca.pi/180\n", - " omega = rpm_i*p['V']*p['kV']*(2*ca.pi/60)\n", + " omega = duty_i*p['V']*p['kV']*(2*ca.pi/60)\n", " q = p['rho']*(omega*p['r'])**2/2\n", " s = ca.pi*p['r']**2\n", " arm_b = ca.vertcat(ca.cos(theta), ca.sin(theta), 0)\n", @@ -142,7 +142,7 @@ " F_b/p['m'] - ca.cross(omega_b, v_b),\n", " so3.Mrp.kinematics(r_nb, omega_b)[:3],\n", " ca.mtimes(C_nb, v_b),\n", - " (u_rpm - rpm)/p['tau']\n", + " (u_duty - duty)/p['tau']\n", " )\n", " \n", " rhs = ca.Function('rhs', [x, u, p], [x_dot])\n", @@ -153,17 +153,56 @@ " 'x_dot': x_dot,\n", " 'u': u,\n", " 'p': p,\n", - " 'rhs': rhs\n", + " 'rhs': rhs,\n", + " 'mix': mix_matrix\n", " }\n", "\n", "def trim_hover(model):\n", " # motor time constant 0.015 s, https://flyingmachinearena.org/wp-content/publications/2014/mueIEEE14.pdf\n", - " p0 = ca.vertcat(1, 1, 9.8, 1, 1, 1, 0.1, 0.015, 1.225, 0.1, 11.1, 1550, 1e-3, 1e-4)\n", + " p0 = ca.vertcat(1, 1, 9.8, 1, 1, 1, 0.1, 0.015, 1.225, 0.1, 11.1, 880, 7e-1, 1e-4)\n", "\n", " # TODO trim\n", - " u0 = ca.vertcat(1000, 1000, 1000, 1000)\n", - " x0 = ca.vertcat(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, u0)\n", - " return x0, u0, p0\n", + "# u0 = ca.vertcat(1000, 1000, 1000, 1000)\n", + "# u_in = ca.SX.sym('u',4)\n", + "# x0 = ca.vertcat(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, u0)\n", + " \n", + "# model = quadrotor_model()\n", + " \n", + "# nlp = {'x':u_in, 'f':0,'g':model['rhs'](ca.vertcat(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, u_in),u_in,p0)}\n", + "# S = ca.nlpsol('S', 'ipopt', nlp, {\n", + "# 'print_time': 0,\n", + "# 'ipopt': {\n", + "# 'sb': 'yes',\n", + "# 'print_level': 0,\n", + "# }\n", + "# })\n", + "# res = S(x0=u0, lbg=np.zeros((1,16)), ubg=np.zeros((1,16)) )\n", + " \n", + "# x = ca.vertcat(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,res['x'])\n", + "# u = res['x']\n", + "# p = p0\n", + "\n", + " throt = ca.SX.sym('throt',1)\n", + " u = np.array([0,0,0,throt])\n", + " duties = ca.mtimes(ca.inv(model['mix']),u)\n", + " x = ca.vertcat(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, duties) \n", + " \n", + " nlp = {'x':throt, 'f':0,'g': model['rhs'](x,u,p0)[5]}\n", + " S = ca.nlpsol('S', 'ipopt', nlp, {\n", + " 'print_time': 0,\n", + " 'ipopt': {\n", + " 'sb': 'yes',\n", + " 'print_level': 0,\n", + " }\n", + " })\n", + " res = S(x0=0.5, lbg=0, ubg=0)\n", + " \n", + " u = np.array([0,0,0,res['x']])\n", + " duties = ca.mtimes(ca.inv(model['mix']),u)\n", + " x = ca.vertcat(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, duties)\n", + " p = p0\n", + "\n", + " return x, u, p\n", "\n", "def linearize(model, x0, u0, p0):\n", "\n", @@ -182,12 +221,39 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 123, "metadata": {}, "outputs": [], + "source": [ + "# model = quadrotor_model()\n", + "# u0 = ca.vertcat(1000, 1000, 1000, 1000)\n", + "# x0 = ca.vertcat(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, u0)\n", + "# states = ca.SX.sym('states',16)\n", + "\n", + "# u = states[12:16]\n", + "# print(u)\n", + "# #nlp = {'x':states, 'f':0,'g': model['rhs'](states,states[12:15],p0)}" + ] + }, + { + "cell_type": "code", + "execution_count": 125, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0. 0. 0. 0.527]\n", + "[-0, 4.44089e-16, 0, 0, 0, -1.00018e-11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n" + ] + } + ], "source": [ "model = quadrotor_model()\n", "x0, u0, p0 = trim_hover(model)\n", + "print(u0)\n", + "print(model['rhs'](x0,u0,p0))\n", "sys = linearize(model, x0, u0, p0)" ] }, @@ -200,28 +266,28 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 126, "metadata": {}, "outputs": [ { "data": { "text/latex": [ - "$$\\frac{5.949e+04}{s^2 + 66.67 s + 5.515e-12}$$" + "$$\\frac{1770}{s^2 + 66.67 s + 5.553e-16}$$" ], "text/plain": [ "\n", - " 5.949e+04\n", + " 1770\n", "-------------------------\n", - "s^2 + 66.67 s + 5.515e-12" + "s^2 + 66.67 s + 5.553e-16" ] }, - "execution_count": 5, + "execution_count": 126, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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" ] @@ -241,14 +307,14 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 127, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "(inf, 61.44275238117672, nan, 72.82566417153188)\n" + "(inf, 88.64946081735565, nan, 2.6532664584571592)\n" ] }, { @@ -262,7 +328,7 @@ }, { "data": { - "image/png": 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\n", 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\n", 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\n", 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\n", 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" ] @@ -313,23 +379,23 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 128, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "(4.868953480974533, 68.7936060131583, 108.17677828605653, 30.80793431496759)\n" + "(3.808742835197417, 12.562278560373215, 17.35581047691042, 8.808252479772401)\n" ] }, { "data": { "text/plain": [ - "[]" + "[]" ] }, - "execution_count": 7, + "execution_count": 128, "metadata": {}, "output_type": "execute_result" }, @@ -344,7 +410,7 @@ }, { "data": { - "image/png": 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p06Y1bo8fP57p06cnNx7/MexIW31zx7u89dD7z3/WWWcxe/bsxu3i4mLmz5/fuJ1IJNr1ey+RSFBdXc3NK579yO+9xI8fYuiVc/jXu8sYN3c1o27+H4ZeOYdxc1czbu5qTv/RMo676u7G7c/f9CDHT5rXuP25qQ9wwrfnN26PvPF+hl29oHH7tB8u5ZOT72ncPvWGJQz/7sLG7c9M+T+M+N6ixu1Trr+PE6/5ZeN20Q8WM2nOI3y8R2f+456nOPH79/G1eX9k1kUnMnJIwYF97wEXXHDBHgPf55xzDjNnzmzV996+ZDqVtTST8w6g/kB1k+0a4DNNTzCzicBEgM6dO7desnagw6736N29MxU1dZze+11efqv6gx/UHtXVtLi7+27N0s5lPbrk8dbv72Tztl189kvnNP7hlGv2uXyGmf3J3T9nZm+TnJ3UeIjkkt09shLK7ELgS+5+eWr7EuAUd/92S+dr+YwPp6GpfPFnCln85MuNfxnlnJ8NS3UppckfCN9d3/p5pE0o21jLBV+fzCf751N73Hnt+vdjv5fPcPfPpb53d/ceTb66Z6swpNQAA5tsDwBeyeLr5YyGwjDrohP53heHMuuiE/cYg8gpo6dCXtqHnfK6JvdLTmr4/Xjwnjv4/a/vyunfj0xXZe3VwldeFnOVA8eY2VFmdggwHsjaAHguWVdTt8dfQiOHFDDrohNZV5ODXSnD/xXG3plsKWDJ72PvTO6XnKTfj/dluirr30n+Jf8GyS6lnsAm4FXgG+6+9oAHMzsbuAPoCCx095/s7Vx1K4nIgdQwiaJhgLe9+sh3ggNWAv/j7r9LPeEXgTHA/cBs0gaLDwR3fwR45EA/r4jIBxk6dGh0hHCZthzWpFeXhn1mVuHuI7KWMANqOYiIfHgHouXwupn9gOTnDSB5V7g3Uh9W230AMoqISBuS6YfgLiI5Y+gh4GGgMLWvI6DROxFpV8aPH7/HhzlzUaYfgqslef/olmw4cHFEROKNGBHaU94mZLpkdx/g+8AJQJeG/e5+RpZyiYiEuf56rfWZabfSr4EXSN43+mbg7yQ/iyAiIu1QpsWht7vfA+xw91J3nwCcmsVcIiJhLrjggj0WlMxFmc5W2pH6vsnMvkxyKYsB2YkkIhLrtNNOi44QLtPicIuZ5QPXAD8HegDfzVoqEZFATZfmzlWZzlb6TerHOuAL2YsjIiJtQaazlY4iOZV1UNPHuPs5e3uMiMjBquGGVsuX5+56n5l2Kz0E3AOsQJ+IFpF2bvTo0dERwmVaHN5z9zuzmkREpI34zne+Ex0hXKbFYaaZ3QT8HtjWsNPdn85KKhERCZVpcfgkcAlwBu93K3lqW0SkXTnrrLMAePTRR4OTxMm0OHwFGOzu27MZRkSkLRg7dmx0hHCZFoc/k7z726tZzCIi0iZceeWV0RHCZVocPg68YGbl7DnmoKmsIiLtUKbF4aasphARaUOKi4sBKCkpCU4SJ9NPSJdmO4iISFsxbty46Ajh9lkczOxtkrOSmh0C3N177M+LmtltwFhgO7ARuMzd30wdmwJ8HdgFXO3uv9uf1xAR2V/f+MY3oiOE2+eS3e7e3d17tPDVfX8LQ8pjwDB3Hw78FZgCYGbHA+NJ3lRoDDA7dZ9qERFpRZnez+GAcvffu/vO1OYTvL/897nAEnff5u4vkrwF6SkRGUUkdyUSCRKJRHSMUJkOSGfTBGBp6uf+JItFg5rUPhGRVvO1r30tOkK4rBUHMysB+rVw6Ifu/nDqnB8CO0nehhSSYxnpWhrzwMwmAhMBCgsLP3JeEZEGKg5ZLA7uXryv42Z2KfAvwGh3bygANcDAJqcNIHnXuZaefx4wD6CoqKjFAiIisj927Eje/DIvLy84SZyQMQczGwP8ADjH3eubHFoOjDezzql7SBwDPBWRUURy15lnnsmZZ54ZHSNU1JjDLKAz8JiZATzh7t9092fN7H7gOZLdTVe5+66gjCKSoy6//PLoCOHs/R6dg1dRUZGvWbMmOoaIyEHFzNa6e1FLx0K6lURE2rL6+nrq6+s/+MR2rC1MZRURaVPOPvtsAFatWhUbJJCKg4hImm9961vREcKpOIiIpNHCexpzEBFppq6ujrq6uugYodRyEBFJc+655wIacxARkSauvvrq6AjhVBxERNKcf/750RHCacxBRCRNbW0ttbW10TFCqeUgIpLmq1/9KqAxBxERaeKaa66JjhBOxUFEJM3YsWOjI4TTmIOISJrNmzezefPm6Bih1HIQEUkzfvx4QGMOIiLSxPXXXx8dIZyKg4hImjFjxkRHCKcxBxGRNNXV1VRXV0fHCKWWg4hImksuuQTQmIOIiDRx4403RkcIp+IgIpKmuLg4OkI4jTmIiKSpqqqiqqoqOkao0OJgZteamZtZQWrbzOxOM9tgZuvM7KTIfCKSmyZMmMCECROiY4QK61Yys4HAmcDLTXafBRyT+voMMCf1XUSk1dx8883REcJFjjn8DPg+8HCTfecCv3J3B54ws55mdri7bwpJKCI5adSoUdERwoV0K5nZOcA/3P3PaYf6A00nF9ek9rX0HBPNbI2ZrXnttdeylFREclFlZSWVlZXRMUJlreVgZiVAvxYO/RC4AfhiSw9rYZ+39PzuPg+YB1BUVNTiOSIi++OKK64A9DmHrHD3FueCmdkngaOAP5sZwADgaTM7hWRLYWCT0wcAr2Qro4hIS2699dboCOFafczB3f8C9G3YNrO/A0XuXmtmy4FJZraE5EB0ncYbRKS1jRw5MjpCuLb2IbhHgLOBDUA9cFlsHBHJRevXrwdg2LBhwUnihBcHdx/U5GcHropLIyICkyZNAjTmICIiTdx2223REcKpOIiIpDn55JOjI4TT2koiImkqKiqoqKiIjhFKLQcRkTSTJ08GNOYgIiJN3HHHHdERwqk4iIikGTFiRHSEcBpzEBFJU15eTnl5eXSMUGo5iIikue666wCNOYiISBOzZs2KjhBOxUFEJE0uL5vRQGMOIiJpysrKKCsri44RSi0HEZE0N9xwA6AxBxERaWLu3LnREcKpOIiIpBk6dGh0hHAacxARSVNaWkppaWl0jFBqOYiIpLnpppsAjTmIiEgTCxcujI4QTsVBRCTN4MGDoyOE05iDiEiakpISSkpKomOEUstBRCTNLbfcAkBxcXFwkjgqDiIiae69997oCOHCupXM7NtmVmlmz5rZfzXZP8XMNqSOfSkqn4jkroEDBzJw4MDoGKFCWg5m9gXgXGC4u28zs76p/ccD44ETgCOAEjM71t13ReQUkdy0cuVKAMaMGROcJE5Ut9K3gOnuvg3A3V9N7T8XWJLa/6KZbQBOAVbHxBSRXDR9+nRAxSHCscDnzewnwHvAte5eDvQHnmhyXk1qXzNmNhGYCFBYWJjdtCKSU5YsWRIdIVzWioOZlQD9Wjj0w9TrHgacCpwM3G9mgwFr4Xxv6fndfR4wD6CoqKjFc0RE9ke/fi3915VbslYc3H2vc8DM7FvAMnd34Ckz2w0UkGwpNB0FGgC8kq2MIiItWbFiBQBjx44NThInarbSQ8AZAGZ2LHAIUAssB8abWWczOwo4BngqKKOI5Kjbb7+d22+/PTpGqKgxh4XAQjNbD2wHLk21Ip41s/uB54CdwFWaqSQire2BBx6IjhAupDi4+3bg4r0c+wnwk9ZNJHJwe2/HLmreqOelLfW8/Ho91a+/y+tbt/FG/Q7erN/O1u272L3b2e2OA13zOtKjSx49unaiT/cuFPbqxsBeXTm676Ec3edQOnXM7ZV1CgoKoiOE0yekRQ4y23fuZl3Nm6yrqWP9K3U898pb/O3Vd9i1+/15Gd0O6UjBoZ3p2S2Pnt0OYcBhnejQweiQmvKxddsu3n5vB/948z3WvvQGb9TvaHxsl7wOnHBEPicV9mTUsX0pGnQYXfI6tvY/M9SyZcsAOP/884OTxLFkb87BraioyNesWRMdQ+Qjubt0I8MH5DNyyPt/tZZtrKXi5Tc5+ahePLFxC0+8uIW1L73Bezt2A9Cne2eGHdGDE47I5+i+h1LYuxuFvbrR+2OHYNbS5L+WvbNtJy9vqeev/3ybdTV1jcVn+67ddMnrwOeP6cN5I/oz+hN9c6JQJBIJoP3fz8HM1rp7UYvHVBxE2oayjbVMuu8ZZl10IsP65zP/f6uYW1pFXidj67ZdmMFx/Xpw6uBefOao3pxU2JO+PbpkLU/99p08UbWF0srXWPnsZv751ja6d+7El4cfzsWnHsmw/vlZe+1odXV1AOTnt99/I6g4iBw0yjbWcunCp9i129nt0L1LJ750Qj9GH9eX04b0pme3Q0Jy7drtPFG1hWVP/4Pf/uUVRg4pYOHXTg7JIgfOvoqDxhxE2pCRQwoY3j+ftS+/yYWf7s/0Cz5Fxw6Zdw9lS8cOxmePLuCzRxcwdezx1DUZo2iPli5dCsC4ceOCk8TJ7SkJIm1M2cZaXtxSz9VnHM3jL7zGky9uiY7UTH7XPAp7d4uOkVVz5sxhzpw50TFCqeUg0kY0HXMYOaSAU4f03mNbWs8jjzwSHSGcWg4ibcS6mro9CsHIIQXMuuhE1tXUBSfLPd26daNbt/bdOvogGpAWEUmzePFiAC6+uMXP6rYbGpAWEfkQFixYALT/4rAvKg4iImkee+yx6AjhVBxERNLk5eVFRwinAWkRkTSLFi1i0aJF0TFCqTiIiKRRcWgns5XM7DXgpegcWVRA8mZIsm+6TpnRdcpMLlynI929T0sH2kVxaO/MbM3eppvJ+3SdMqPrlJlcv07qVhIRkWZUHEREpBkVh4PDvOgABwldp8zoOmUmp6+TxhxERKQZtRxERKQZFQcREWlGxaGNMbMLzexZM9ttZkVN9g8ys3fNrCL1dXeTY582s7+Y2QYzu9M+zJ3lD1J7u06pY1NS16LSzL7UZP+Y1L4NZnZ966eOZWY/MrN/NHkPnd3kWIvXLBfl+vukgdZWanvWA+cDc1s4ttHdR7Swfw4wEXgCeAQYAzyatYRtQ4vXycyOB8YDJwBHACVmdmzq8F3AmUANUG5my939udaL3Cb8zN1nNN2xt2vm7rsiAkYys47ofQKo5dDmuPvz7l6Z6flmdjjQw91Xe3J2wa+A87IWsI3Yx3U6F1ji7tvc/UVgA3BK6muDu1e5+3ZgSepc2fs1y0V6n6SoOBxcjjKzZ8ys1Mw+n9rXn+RfOA1qUvtyVX+gusl2w/XY2/5cM8nM1pnZQjM7LLVP1+Z9uhYp6lYKYGYlQL8WDv3Q3R/ey8M2AYXuvsXMPg08ZGYnAC2NL7SL+cn7eZ32dj1a+kOoXVynpvZ1zUh2P04j+e+eBtwOTKAdv4f2g65FiopDAHcv3o/HbAO2pX5ea2YbgWNJ/mUzoMmpA4BXDkTOaPtznUhej4FNtptej73tbzcyvWZmNh/4TWpzX9cs1+hapKhb6SBhZn1Sg2WY2WDgGKDK3TcBb5vZqalZSv8B7O2v6lywHBhvZp3N7CiS1+kpoBw4xsyOMrNDSA7ALg/M2epS41MNvkJyUB/2fs1yUc6/Txqo5dDGmNlXgJ8DfYDfmlmFu38JOB34sZntBHYB33T311MP+xawCOhKcpZSe5+ptNfr5O7Pmtn9wHPATuCqhlk3ZjYJ+B3QEVjo7s8GxY/yX2Y2gmQ3yd+BKwD2dc1yjbvv1PskSctniIhIM+pWEhGRZlQcRESkGRUHERFpRsVBRESaUXEQEZFmVBxE9pOZ7UqtbrrezFaYWc+P8Fx/N7OCA5lP5KNQcRDZf++6+wh3Hwa8DlwVHUjkQFFxEDkwVtNkgTYzu87MylOL3N3cZP9DZrY2dS+KiSFJRTKg4iDyEaWWNRlNapkFM/siySUoTgFGAJ82s9NTp09w908DRcDVZtY7ILLIB1JxENl/Xc2sAtgC9AIeS+3/YurrGeBp4DiSxQKSBeHPJG/MNLDJfpE2RcVBZP+9m7oz35HAIbw/5mDAT1PjESPc/Wh3v8fMEkAxcJq7f4pk8egSEVzkg6g4iHxE7l4HXA1ca2Z5JBdtm2BmhwKYWX8z6wvkA2+4e72ZHQecGhZa5ANoVVaRA8Ddn0l1F41393vN7BPA6uQq6rwDXAysBL5pZpg9fWEAAAA+SURBVOuASpJdSyJtklZlFRGRZtStJCIizag4iIhIMyoOIiLSjIqDiIg0o+IgIiLNqDiIiEgzKg4iItLM/wcBBN3GlOBZfgAAAABJRU5ErkJggg==\n", 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\n", 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\n", 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\n", "text/plain": [ "
" ] @@ -392,28 +458,28 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 129, "metadata": {}, "outputs": [ { "data": { "text/latex": [ - "$$\\frac{8413}{s^2 + 66.67 s + 4.153e-12}$$" + "$$\\frac{0.3575 s^2 + 5.716e-15 s - 4.573e-14}{s^4 + 66.67 s^3 + 9.352e-13 s^2 - 8.447e-12 s + 1.075e-11}$$" ], "text/plain": [ "\n", - " 8413\n", - "-------------------------\n", - "s^2 + 66.67 s + 4.153e-12" + " 0.3575 s^2 + 5.716e-15 s - 4.573e-14\n", + "---------------------------------------------------------\n", + "s^4 + 66.67 s^3 + 9.352e-13 s^2 - 8.447e-12 s + 1.075e-11" ] }, - "execution_count": 8, + "execution_count": 129, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -433,14 +499,14 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 130, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "(inf, 57.45311890021898, nan, 42.54807839872257)\n" + "(587.8590314250265, 0.23140106104864344, 0.0, 8.663626371934768e-06)\n" ] }, { @@ -454,7 +520,7 @@ }, { "data": { - "image/png": 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cPMprtI8G+Li986hjOMo++X4fHXUMe/nk++1q2oYqmn3c3t3sWA4cbFGj3RY/8El7T/N2vH+g+afb+z95/b4Wx/He/mYQtataHce2fU05+HG7PVv3NuHAlp24O1WtjqNbq/384JsXcH63Y7hseAGF/+zDTyb9kQMHnaatO7J5j7Fny0727z9AVav2vLsbdm3Zyf79+1PtXfDRlp1UVVVR1ao9mz5ydmzZyb59n7Q/ZCd796bab+88wAcHd7JnT9TesZ/39+9kz57U93trx362Ve1k9+5Ue+P2Krbu3cmuXamfX7m9ihZ7dvLRR05Vq/a8+cE+mu9ydla3399Ds50H2Lkr9d/7z/f30LTpfnbsTrX/8d4emjat4sM9RlWr9vx9226aNNnL9qi9YesujjrK+GBvEw42bcl7C6ayYL8z5P9dz5sf1vw1l2xi9a0xm9lL7n6hme0gdXbSx5sAd/djMxLK7FvA1939uqg9Aujr7t+va/+8vDxfsWJFJqJIDNXTA8PP60bBsjeZ/u1z6HdSTuhYwb39wW76TfojHY5uztVf6crQPrn06HhM6FhBla7fylXfHcOZXdqy9cvf1HslMDNb6e55dW2rd+Tg7hdGX9tkIlg9NgK5NdpdgbcTziAxVBeG6l/y80/q8Kn2kWxPVeqs77sHnc7g3l0Cpwmv+r0y94mp9Dspp9Z7R7JL3Kuytq/j0SyDuZYDp5jZiWbWHBgGZGwBXD6/NRu3f+qXu99JOUz/9jms2agP0Mun6b1yeIm7IL2K1F/y75OaUmoHbDKzzcD17r6yIUO5+34zGw28ADQBnnT31xryZ0jD+N5FJ9Xq63dSjv4SlFqq3yvDhw8HoKCgQO+VLBa3OCwEfufuLwCY2WXAAOBZ4GE+s1jcENx9AbCgob+viIRVfaaYZLfYn5B29+9VN9z9RTO7z93/08x0qpCIxFZ9aqdkt7jF4T0z+xFQGLWHAu9HH1Y7mJFkIiISTNxPSH+b1BlDvwfmA92ivibAf2Qmmog0RsOGDWPYsGGhY0gacT8Et5XU/aPrsq7h4ohIY9e7d+/QESSGuJfs7gj8EDgDaFnd7+4XZyiXiDRS1ZePkOwWd1rpGeCvpO4bPRH4B6nPIoiISCMUtzh0cPcngCp3L3H3kcD5GcwlIo3UVVddxVVXXRU6hqQR92ylqujrJjO7gtSlLLpmJpKINGYXXHBB6AgSQ9zicK+ZtQVuA/4bOBb4QcZSiUijVX2Jaslucc9W+kP0dDvwtczFERGRbBD3bKUTSZ3K2r3ma9z9yszEEpHG6sorU/9sVN+0R7JT3Gml3wNPAEXoE9Ei8gVccskloSNIDHGLwx53n5bRJCJyRKi+DaZkt7jF4UEzmwC8COyt7nT3VRlJJSIiQcUtDmcCI4CL+WRayaO2iEhsl19+OQDPP/984CRSn7jF4d+BHu6+L5NhRKTxGzRoUOgIEkPc4rCa1N3fNmcwi4gcAW666abQESSGuMXhS8BfzWw5n15z0KmsIiKNUNziMCGjKUTkiJGfnw9AcXFx4CRSn7ifkC7JdBAROTIMHTo0dASJod7iYGY7SJ2VVGsT4O5+bEZSiUijdf3114eOIDHUWxzcvU1SQUREJHvEvZ+DiEiD6N+/P/379w8dQ9KIuyAtItIgrr322tARJAYVBxFJlIrD4UHTSiKSqKqqKqqqqtLvKEFp5CAiibr00ksBWLJkSdggUi8VBxFJ1HXXXRc6gsSg4iAiiRo+fHjoCBKD1hxEJFG7du1i165doWNIGho5iEiiBg4cCGjNIdupOIhIom688cbQESQGFQcRSZQuvHd4CLLmYGaTzeyvZrbGzH5nZu1qbLvDzNaZWYWZfT1EPhHJnO3bt7N9+/bQMSSNUAvSi4Be7n4W8AZwB4CZnQ4MA84ABgAPm1mTQBlFJAMGDx7M4MGDQ8eQNIJMK7n7izWaLwNXR88HA4Xuvhf4u5mtA/oCSxOOKCIZcsstt4SOIDFkw5rDSGB29LwLqWJRbWPUV4uZjQJGAXTr1i2T+USkAQ0ZMiR0BIkhY8XBzIqBTnVsutPd50f73AnsB56pflkd+9d1syHc/THgMYC8vLw69xGR7LN161YAcnJyAieR+mSsOLh7fn3bzewa4BvAJe5e/Y/7RiC3xm5dgbczk1BEQrj66tQssj7nkN2CTCuZ2QDgR8BF7l7zo5LPAb8xs18A/wKcArwSIKKIZMhtt90WOoLEEGrNYTrQAlhkZgAvu/v33P01M3sWeJ3UdNPN7n4gUEYRyYBBgwaFjiAxhDpb6eR6tv0X8F8JxhGRBL3zzjsAdOpU15KkZItsOFtJRI4gw4YNA7TmkO1UHEQkUePGjQsdQWJQcRCRRA0YMCB0BIlB93MQkURVVlZSWVkZOoakoZGDiCRqxIgRgNYcsp2Kg4gk6q677godQWJQcRCRROXn13vxBMkSWnMQkURt2LCBDRs2hI4haWjkICKJGjlyJKA1h2yn4iAiiZo4cWLoCBKDioOIJOqiiy4KHUFi0JqDiCSqoqKCioqK0DEkDY0cRCRRN9xwA6A1h2yn4iAiibrvvvtCR5AYVBxEJFH9+vULHUFi0JqDiCSqvLyc8vLy0DEkDY0cRCRRo0ePBrTmkO1UHEQkUZMnTw4dQWJQcRCRRPXp0yd0BIlBaw4ikqiysjLKyspCx5A0NHIQkUSNGTMG0JpDtlNxEJFETZ06NXQEiUHFQUQS1bt379ARJAatOYhIopYvX87y5ctDx5A0NHIQkUTdfvvtgNYcsp2Kg4gkavr06aEjSAwqDiKSqF69eoWOIDFozUFEElVaWkppaWnoGJKGRg4ikqjx48cDWnPIdioOIpKoRx99NHQEiUHFQUQS1bNnz9ARJAatOYhIokpKSigpKQkdQ9IIWhzMbKyZuZnlRG0zs2lmts7M1pjZuSHziUjDmzBhAhMmTAgdQ9IINq1kZrnApcCbNbovB06JHucBj0RfRaSRePLJJ0NHkBhCjhx+CfwQ8Bp9g4Ffe8rLQDsz6xwknYhkRI8ePejRo0foGJJGkOJgZlcCb7n76s9s6gJU1mhvjPrq+h6jzGyFma3YsmVLhpKKSEMrLi6muLg4dAxJI2PTSmZWDHSqY9OdwHjgsrpeVkef19GHuz8GPAaQl5dX5z4ikn3uvfdeAPLz8wMnkfpkrDi4e53/583sTOBEYLWZAXQFVplZX1Ijhdwau3cF3s5URhFJ3qxZs0JHkBgSX5B2978Ax1e3zewfQJ67bzWz54DRZlZIaiF6u7tvSjqjiGRObm5u+p0kuGz7ENwCYCCwDtgFfCdsHBFpaAsXLgRgwIABgZNIfYIXB3fvXuO5AzeHSyMimTZp0iRAxSHbBS8OInJkKSwsDB1BYlBxEJFEdepU10mMkm10bSURSVRRURFFRUWhY0gaGjmISKIeeOABAAYNGhQ4idRHxUFEEjVnzpzQESQGFQcRSVROTk7oCBKD1hxEJFHz5s1j3rx5oWNIGho5iEiipk2bBsCQIUMCJ5H6qDiISKLmz58fOoLEoOIgIolq27Zt6AgSg9YcRDLk6BZNGXhmJzq3bRU6SlaZPXs2s2fPDh1D0rDU5YwOb3l5eb5ixYrQMUQkhv79+wOwZMmSoDkEzGylu+fVtU3TSiKSqAULFoSOIDGoOIhIolq3bh06gsSgNQcRSVRBQQEFBQWhY0gaGjmISKJmzJgBwPDhwwMnkfqoOIhIohYtWhQ6gsSg4iAiiWrWrFnoCBKD1hxEJFEzZ85k5syZoWNIGioOIpIoFYfDQ6P4EJyZbQH+mfCPzQG2Jvwz/7cOh4ygnA3pcMgIytmQvkjGE9y9Y10bGkVxCMHMVhzqk4XZ4nDICMrZkA6HjKCcDSlTGTWtJCIitag4iIhILSoOn99joQPEcDhkBOVsSIdDRlDOhpSRjFpzEBGRWjRyEBGRWlQcRESkFhWHNMzsW2b2mpkdNLO8z2y7w8zWmVmFmX29Rv+AqG+dmY0LkLm3mb1sZmVmtsLM+kb9ZmbTolxrzOzcpLPVkfX70bF6zcx+XqO/zmMbipmNNTM3s5yonVXH0swmm9lfoyy/M7N2NbZlzbEM/btxKGaWa2Z/MrO10Xvx1qi/vZktMrO/RV+Py4KsTczsVTP7Q9Q+0cyWRRlnm1nzBvlB7q5HPQ/gNKAnsATIq9F/OrAaaAGcCKwHmkSP9UAPoHm0z+kJZ34RuDx6PhBYUuP584AB5wPLAh/brwHFQIuofXx9xzZgzlzgBVIftMzJ0mN5GdA0ev4z4GfZdiyz4XejnmydgXOj522AN6Jj93NgXNQ/rvq4Bs76n8BvgD9E7WeBYdHzXwE3NsTP0cghDXdf6+4VdWwaDBS6+153/zuwDugbPda5+wZ33wcURvsmyYFjo+dtgbdrZP61p7wMtDOzzglnq+lGYJK77wVw981R/6GObSi/BH5I6rhWy6pj6e4vuvv+qPky0DV6nk3HMht+N+rk7pvcfVX0fAewFuhCKt/T0W5PA98MkzDFzLoCVwAzorYBFwNzol0aLKOKw+fXBais0d4Y9R2qP0ljgMlmVglMAe6I+rMhW02nAv8aDYlLzKxP1J81Oc3sSuAtd1/9mU1Zk7EOI0mNaiC7cmZTlkMys+7AOcAy4EvuvglSBQQ4PlwyAKaS+kPlYNTuAHxQ4w+DBjumumQ3YGbFQKc6Nt3p7vMP9bI6+py6C26Dny9cX2bgEuAH7j7XzP4DeALI59CZMyZNzqbAcaSmZfoAz5pZDxLOmSbjeFJTNrVeVkdfsGNZ/T41szuB/cAz1S+rY/9Q569nU5Y6mdkxwFxgjLt/mPrDPDuY2TeAze6+0sz6V3fXsWuDHFMVB8Dd8z/HyzaSmouu1pVPpm8O1d9g6stsZr8Gbo2avyUaglJ/5oxIk/NGYJ6nJktfMbODpC4ilmjOQ2U0szNJzdOvjv6R6Aqsihb4s+pYApjZNcA3gEuiYwoBctYjm7LUYmbNSBWGZ9x9XtT9rpl1dvdN0bTh5kN/h4z7KnClmQ0EWpKaOp5KakqzaTR6aLhjGnpx5XB5UHtB+gw+vdC3gdSCW9Po+Yl8suh2RsJZ1wL9o+eXACuj51fw6UXUVwIf0+8BP42en0pqysEOdWyz4D3wDz5ZkM62YzkAeB3o+Jn+rDmW2fC7UU82A34NTP1M/2Q+vSD989BZoyz9+WRB+rd8ekH6pgb5GaH/I7P9Afw7qb949gLvAi/U2HYnqbMvKojODor6B5I622E9qSF/0pkvBFZGv3zLgK9E/QY8FOX6S81iF+jYNgcKgHJgFXBxumMbOG/N4pBtx3JdVFzLosevsvFYhv7dqCfXhaSmY9bUOIYDSc3pLwb+Fn1tHzprlLdmcegBvBK9B35LdPbfF33o8hkiIlKLzlYSEZFaVBxERKQWFQcREalFxUFERGpRcRARkVpUHEQ+JzM7EF35ttzMimpeCfVzfK9/VF/xVSQbqDiIfH673b23u/cC3gNuDh1IpKGoOIg0jKXUuOCZmd1uZsuj+ytMrNH/ezNbGd0zYFSQpCIxqDiIfEFm1oTUZUqei9qXAaeQukR1b+ArZvZv0e4j3f0rQB5wi5l1CBBZJC0VB5HPr5WZlQHbgPbAoqj/sujxKqnLgnyZVLGAVEFYTeqeC7k1+kWyioqDyOe32917AyeQuk5U9ZqDAfdH6xG93f1kd38iusxyPnCBu59Nqni0DBFcJB0VB5EvyN23A7cAY6PLPr8AjIzuDYCZdTGz40ndle99d99lZl8mdTVXkayk+zmINAB3fzWaLhrm7rPM7DRgaXQfiJ3AcGAh8D0zW0PqCqkvBwsskoauyioiIrVoWklERGpRcRARkVpUHEREpBYVBxERqUXFQUREalFxEBGRWlQcRESklv8PWpXPir7uSS0AAAAASUVORK5CYII=\n", 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UVPDY+X5DurngVxYRkbdlxowZwWKfsDiY2Stk7krqdQhwdz8tSFYiItKnr3zlK8Fin7A4uPsfBbuyiIgkVr7PcxARkYSJoogoioLEzrchLSIiCfOlL30pWGwVBxGRlApZHDStJCKSUocPH+bw4cN9n9gPGjmIiKTUZz/7WQB27txZ8NgqDiIiKfXlL385WGwVBxGRlKqsrAwWWz0HEZGUOnToEIcOHQoSWyMHEZGUuvLKKwH1HEREJMsNN9wQLLaKg4hISoVceE89BxGRlDp48CAHDx4MElsjBxGRlJo6dSqgnoOIiGS56aabgsVWcRARSalp06YFi12UnoOZXWNmT5nZm2ZWdsyxhWa218w6zOyKYuQnIpIGBw4c4MCBA0FiF2vk0A5MA+7N3mlm5wEVwPnAR4AmMzvX3d8Y+BRFRJLtC1/4AjCIeg7u/gyAmR17aCqwyd1fA35tZnuBi4BdA5uhiEjy3XzzzcFiJ63ncCawO2t7X7yvFzOrAqoARo0aFT4zEZGEmTJlSrDYwYqDmTUBI3IcWuTuW473thz7PNeJ7r4WWAtQVlaW8xwRkcFs//79AIwYkeuv2rcnWHFw9/J+vG0fUJq1PRL4bWEyEhEZXCoqKoBB1HM4ga3AD83sH8g0pM8Bfl7clEREkmnBggXBYhelOJjZ54HvAsOBH5tZm7tf4e5PmdmDwNPAEeBG3akkIpLbpEmTgsUu1t1KDwMPH+fYHcAdA5uRiEj6dHV1AVBaWtrHmScvadNKIiKSp5kzZwLvjJ6DiIjk6bbbbgsWW8VBRCSlysv7c1NofvQ8BxGRlOrs7KSzszNIbI0cRERSas6cOYB6DiIikmXp0qXBYqs4iIik1KWXXhostnoOIiIp1dHRQUdHR5DYGjmIiKTUddddB6jnICIiWe68885gsVUcRERSasKECcFiq+cgIpJS7e3ttLe3B4mtkYOISErNnTsXUM9BRESyLF++PFhsFQcRkZQaP358sNjqOYiIpFRbWxttbW1BYmvkICKSUvPmzQPUcxARkSwrV64MFlvFQUQkpcaNGxcstnoOIiIp1draSmtra5DYGjmIiKTULbfcAqjnICIiWVavXh0stoqDiEhKXXDBBcFiq+cgIpJSLS0ttLS0BImtkYOISErdeuutgHoOIiKS5d577w0WW8VBRCSlxo4dGyy2eg4iIinV3NxMc3NzkNgaOYiIpNSSJUsA9RxERCTLhg0bgsVWcRARSakxY8YEi62eg4hISjU1NdHU1BQktkYOIiIpdfvttwNQXl5e8NgqDiIiKbVx48ZgsVUcRERSqrS0NFhs9RxERFKqsbGRxsbGILGLUhzMbLmZ/dLMnjSzh83s/VnHFprZXjPrMLMripGfiEgaVFdXU11dHSR2saaVtgML3f2ImX0HWAh808zOAyqA84GPAE1mdq67v1GkPEVEEmvTpk3BYhdl5ODuP3H3I/HmbmBk/HoqsMndX3P3XwN7gYuKkaOISNKNGDGCESNGBImdhJ7DHODR+PWZQFfWsX3xvl7MrMrM9pjZnt///veBUxQRSZ6GhgYaGhqCxA42rWRmTUCukrbI3bfE5ywCjgAPdL8tx/meK767rwXWApSVleU8R0RkMLvrrrsAmDJlSsFjBysO7n7Cb2WY2SzgL4GJ7t79l/s+IPverJHAb8NkKCKSbps3bw4Wu1h3K00Cvglc5e6Hsg5tBSrM7BQzOws4B/h5MXIUEUm6kpISSkpKgsQu1t1Kq4FTgO1mBrDb3a9396fM7EHgaTLTTTfqTiURkdzq6+sBmDZtWsFj21szOulVVlbme/bsKXYaIiIDKooioP/PczCzx9y9LNcxLZ8hIpJSW7ZsCRZbxUFEJKWGDRsWLHYSvucgIiL9UFdXR11dXZDYGjmIiKTUPffcA8CMGTMKHlvFQUQkpbZt2xYstoqDiEhKnXrqqcFiq+cgIpJStbW11NbWBomtkYOISEqtX78egMrKyoLHVnEQEUmp7du3B4ut4iAiklJDhw4NFls9BxGRlKqpqaGmpiZIbBUHEZGUClkcBsXCe2b2CtBR7Dz6oQQ4UOwk+iGNeacxZ1DeAymNOcPby/uj7j4814HB0nPoON7KgklmZnuU98BIY86gvAdSGnOGcHlrWklERHpRcRARkV4GS3FYW+wE+kl5D5w05gzKeyClMWcIlPegaEiLiEhhDZaRg4iIFJCKg4iI9JLq4mBmdWbWFv88Z2ZtWccWmtleM+swsyuKmWcuZva1OLenzOzvs/YnMm8z+5aZ/VfW531l1rFE5pzNzOabmZtZSda+ROZtZsvM7Mn4c/6JmX0k61gicwYws+Vm9ss494fN7P1Zx5Kc9zXxf4dvmlnZMceSnPekOK+9Zrag4Bdw90HxA9wFLI5fnwc8AZwCnAU8Cwwpdo5ZuX4GaAJOibc/mPS8gW8B83PsT2zOWTmWAv8C/CdQkvS8gdOyXt8EfD/pOcf5XQ68K379HeA7Kcn7Y8BYYCdQlrU/sXkDQ+J8xgDvjvM8r5DXSPXIoZuZGfBF4J/jXVOBTe7+mrv/GtgLXFSs/HK4Aah299cA3P2FeH/S884lDTn/I/ANIPvui8Tm7e7/nbX5h7yVd2JzBnD3n7j7kXhzNzAyfp30vJ9x91wrLCQ574uAve7e6e6vA5vI5Fswg6I4AJ8Gfufuv4q3zwS6so7vi/clxbnAp83sZ2bWbGbj4/1Jz3tuPGWwwcw+EO9LdM5mdhXwX+7+xDGHkp73HWbWBfw1sDjeneicjzEHeDR+naa8syU57+C5JX75DDNrAkbkOLTI3bfEr/+Kt0YNAJbj/AG9Z/dEeZP53D8AXAyMBx40szEUOe8+cr4HWBbns4zMNN4ckv9Z30pmuqPX23LsS8Rn7e5b3H0RsMjMFgJzgSUk/LPu/u/RzBYBR4AHut+W4/zE5Z3rbTn2JeXe/+C5Jb44uHv5iY6b2buAacAns3bvIzPP3G0k8NvCZ3d8J8rbzG4A6j0zefhzM3uTzOJZRc27r8+6m5mtA34Ubyb2szazPyUzV/xEZuaRkcDjZnYRKfmsgR8CPyZTHBL7WXczs1nAXwIT499vSEHex1H0vE8gfG7FbqwUoDEzCWg+Zt/5HN1I6iQhjaQ4v+uBb8evzyUzPLQk5w18OOv135KZi038Z33M/4bneKshndi8gXOyXn8N2Jz0nOP8JgFPA8OP2Z/ovLPy3MnRDenE5k3mH/adcV7dDenzC3mNxI8c8lDB0VNKuPtTZvYgmV/UI8CN7v5GMZI7jg3ABjNrB14HZnnm//Ek5/33ZjaOzND1OeA6SMVnnVPC8642s7HAm2TusLoeEp8zwGoyf5Fuj0dqu939+qTnbWafB74LDAd+bGZt7n5FkvN29yNmNpfMXXhDgA3u/lQhr6HlM0REpJfBcreSiIgUkIqDiIj0ouIgIiK9qDiIiEgvKg4iItKLioNIP5nZG/HKqe1m1pC9Cmk/Yj2XvWKsSLGpOIj036vuPs7dLwBeAm4sdkIihaLiIFIYu8ha+MzMbjGz1nihwqVZ+x8xs8fi5wdUFSVTkTyoOIi8TWY2BJgIbI23LwfOIbOs8jjgk2b2F/Hpc9z9k0AZcJOZnVGElEX6pOIg0n/vjZ8++CJwOrA93n95/PML4HHgT8gUC8gUhCfIPO+gNGu/SKKoOIj036vuPg74KJnFz7p7Dgb8XdyPGOfuf+zuPzCzCCgHLnH3T5ApHu8pRuIifVFxEHmb3P0gmcd5zjezoWQWQ5tjZu8DMLMzzeyDwDDgZXc/ZGZ/QuZ5HiKJNBhWZRUpOnf/RTxdVOHuG83sY8CueHXS/wEqgUbgejN7EuggM7UkkkhalVVERHrRtJKIiPSi4iAiIr2oOIiISC8qDiIi0ouKg4iI9KLiICIivag4iIhIL/8P5Fr/bofQhPQAAAAASUVORK5CYII=\n", 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\n", 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\n", 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" ] @@ -503,14 +569,14 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 131, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "(4.444444444444475, 71.91755280227125, 58.00868819458393, 15.329741102247425)\n" + "(4.444444442107674, 0.5310146996565663, 0.3781637566207558, 0.17937496801506117)\n" ] }, { @@ -524,7 +590,7 @@ }, { "data": { - "image/png": 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G+52BV3dxBpHYaxhjuP+2qU3GHFQgZFsyXZX1wGY+rbOYqwI4zMy6m9kewEhgSRb/PZG8tHpD3RaFoF/PAqaffSyrN2iBA9m2TGcrrSL9l/zbpLuU2gGvmdnrwE/cfWVLhnL3T8zsYuARoBVwu7s/25L/hkgS/LR/T4DNA7PFxcX061mgVoNsV6bFYSnwR3d/BMDMTgEGAfcBM/jCYHFLcPeHgIda+ueKJFGvXr1CR5CYyfR9DpVfHLRoOGZmVe7eJ2sJM6ABaRGRHfel3yENvGVmvyL9vAGk3wr3dvSw2mctkFFERHJIpg/BnU16xtADwGKga3SsFfCD7EQTkZYycuTILR4QE9meTB+CqyX9/ujmrG25OCKSDX36BO35lRjKdMnuDsAvgaOBvRqOu/uALOUSkRZ01VVau1J2TKbdSvcAL5B+b/RE4CXSzyKIiEgeyrQ4tHf324B6dy9z99HAt7KYS0Ra0JlnnrnFInUi25PpbKX66OtrZnYa6aUsOmcnkoi0tBNOOCF0BImZTIvDdWbWFrgc+D2wP/DzrKUSkRbVeKlpkUxkOlvpwWizDjgpe3FERCQXZDpbqTvpqazdGn9Ptt4EJyItq+ElOUuWaP1KyUym3UoPALcBJeiJaJHYGThwYOgIEjOZFocP3f3mrCYRkay59NJLQ0eQmMm0OEwzswnAo8BHDQfdfVVWUomISFCZFoevAecAA/i8W8mjfRHJcYMHDwbg4YcfDpxE4iLT4vBvQA93/zibYUQkO4YMGRI6gsRMpsXhGdJvf3s9i1lEJEvGjh0bOoLETKbF4WDgBTOrYMsxB01lFRHJQ5kWhwlZTSEiWVVUVARAaWlp4CQSF5k+IV2W7SAikj0jRowIHUFiZpvFwczeIz0rqckpwN19/6ykEpEW9ZOf/CR0BImZbRYHd99vVwUREZHcken7HEQkxlKpFKlUKnQMiZFMB6RFJMZ+/OMfh44gMaPiIJIAKg6yo9StJJIA9fX11NfXb/9CkYhaDiIJcPLJJwOwfPnysEEkNlQcRBLg/PPPDx1BYkbFQSQBRo0aFTqCxIzGHEQSYNOmTWzatCl0DIkRtRxEEuDUU08FNOYgmVNxEEmACy+8MHQEiRkVB5EE0MJ7sqOCjDmY2Q1m9oKZrTazP5pZu0bnxpnZWjOrNrPvhcgnkm/q6uqoq6sLHUNiJNSA9DKgt7sfA/wNGAdgZkcBI4GjgUHADDNrFSijSN4YNmwYw4YNCx1DYiRIt5K7P9po9wngrGh7GDDf3T8C/m5ma4G+wIpdHFEkr1xyySWhI0jM5MKYw2hgQbTdiXSxaLAhOtaEmY0BxgB07do1m/lEYm/48OGhI0jMZK04mFkp0LGZU9e4++LommuAT4B7Gr6tmeube9kQ7j4bmA1QWFjY7DUiklZbWwtAQUFB4CQSF1krDu5etK3zZnYucDow0N0b/ue+AejS6LLOwKvZSSiSHGedle651XMOkqkg3UpmNgj4FdDf3Rs/trkEuNfMbgK+AhwGPBUgokheufzyy0NHkJgJNeYwHdgTWGZmAE+4+0/d/Vkzuw94jnR300Xu/mmgjCJ5Y8iQIaEjSMyEmq106DbO/Rr49S6MI5L3Nm7cCEDHjs0NA4o0lQuzlUQky0aOHAlozEEyp+IgkgBXXXVV6AgSMyoOIgkwaNCg0BEkZvQ+B5EEqKmpoaamJnQMiRG1HEQS4JxzzgE05iCZU3EQSYBrr702dASJGRUHkQQoKtrmggUiTWjMQSQB1q9fz/r160PHkBhRy0EkAUaPHg1ozEEyp+IgkgATJ04MHUFiRsVBJAH69+8fOoLEjMYcRBKgurqa6urq0DEkRtRyEEmACy64ANCYg2ROxUEkAa6//vrQESRmVBxEEqBfv36hI0jMaMxBJAHWrFnDmjVrQseQGFHLQSQBLr74YkBjDpI5FQeRBLjhhhtCR5CYUXEQSYDjjz8+dASJGY05iCRAVVUVVVVVoWNIjKjlIJIAl112GaAxB8mcioNIAkydOjV0BIkZFQeRBOjTp0/oCBIzGnMQSYCKigoqKipCx5AYUctBJAGuvPJKQGMOkjkVB5EEmD59eugIEjMqDiIJ0Lt379ARJGY05iCSAOXl5ZSXl4eOITGiloNIAlx99dWAxhwkcyoOIgkwa9as0BEkZlQcRBKgV69eoSNIzGjMQSQBysrKKCsrCx1DYiRocTCzK8zMzawg2jczu9nM1prZajM7LmQ+kXwxYcIEJkyYEDqGxEiwbiUz6wKcDLzS6PBg4LDo801gZvRVRL6E22+/PXQEiZmQLYffAb8EvNGxYcBdnvYE0M7MDgmSTiSP9OjRgx49eoSOITESpDiY2VDgH+7+zBdOdQJqGu1viI419zPGmFmlmVW+8cYbWUoqkh9KS0spLS0NHUNiJGvdSmZWCnRs5tQ1wNXAKc19WzPHvJljuPtsYDZAYWFhs9eISNp1110HQFFRUeAkEhdZKw7u3uxvoZl9DegOPGNmAJ2BVWbWl3RLoUujyzsDr2Yro0hS3H333aEjSMzs8gFpd/8rcFDDvpm9BBS6e62ZLQEuNrP5pAei69z9tV2dUSTfdOnSZfsXiTSSaw/BPQScCqwFNgHnhY0jkh+WLl0KwKBBgwInkbgIXhzcvVujbQcuCpdGJD9NnjwZUHGQzAUvDiK5zN15/b2P2Fj3Ie98UE/XA9vQvWCf0LF22Pz580NHkJhRcRBp5OU33+fJv7/Fypfe5pkN7/Dym5v4oP7Tzed/cfLhXDLwsIAJd07Hjs1NHBTZOhUHSbwXNr7Lg8+8xiPPbuTF1/8FQNu9W3Ns13Z8+9ACurVvwyFt9+aAfVrT5cA2gdPunJKSEgCGDBkSOInEhYqDJNKH9Z9S8syr3PvUKzz9yjvsZtC3+4Gc/c2jOPHQAnp22JfddmvusZt4uvHGGwEVB8mcioMkyvsffcI9T77M7L/8ndp/fUSPDvtw7WlHMvy4zhy4zx6h42XNwoULQ0eQmFFxkET4+JPPuGvFS9zy+Fre3lTPiYcWMPakPpzQoz3Rw5h5raCgIHQEiRkVB8lr7s6fX3idX//pedbXvs93Divg5ycfznFdDwgdbZdatGgRAMOHDw+cROJCxUHyxq1l6zimc1v69Uz/lbyx7kMuvGclT7/yDj067MMd5x3PSb0O2s5PyU8333wzoOIgmVNxkLxxTOe2XHzv0/z+3/vwj7c/5D9LnmXTx59y9je7MnHo0bRuldwXHy5evDh0BIkZFQfJG/16FjB1xNf58R0V1H/q7L6bcdMPvs7w4zqHjhZc27ZtQ0eQmEnun1KSl757+EEcdcj+AFzYv4cKQ2TBggUsWLAgdAyJERUHySvl62qpefsDLhlwKPc8VUP5utrQkXLCzJkzmTlzZugYEiPqVpK8Ub6ulovvfZrpZx9Lv54FfKtn+y32k+yhhx4KHUFiRi0HyRurN9RtUQj69Sxg+tnHsnpDXeBk4bVp04Y2beK59IeEYelVsuOtsLDQKysrQ8cQyVnFxcUAjBo1KnASySVmttLdC5s7p24lkQSYO3cuoOIgmVNxEEmAZcuWhY4gMaPiIJIArVu3Dh1BYkYD0iIJMG/ePObNmxc6hsSIioNIAqg4yI7Ki9lKZvYG8HLoHI0UALn+9FUcMoJytqQ4ZATlbEnby/hVd+/Q3Im8KA65xswqtzY9LFfEISMoZ0uKQ0ZQzpb0ZTKqW0lERJpQcRARkSZUHLJjdugAGYhDRlDOlhSHjKCcLWmnM2rMQUREmlDLQUREmlBxEBGRJlQcWoiZ9TGzJ8ysyswqzaxvdNzM7GYzW2tmq83suBzI+jMzqzazZ83st42Oj4tyVpvZ90JmbGBmV5iZm1lBtJ8z99PMbjCzF6IcfzSzdo3O5dS9NLNBUZa1ZnZV6DwAZtbFzB43s+ej38VLo+MHmtkyM3sx+npA6KwAZtbKzJ42swej/e5m9mSUc4GZ7ZEDGduZ2cLo9/J5Mzthp++nu+vTAh/gUWBwtH0qsLzR9sOAAd8Cngyc8ySgFNgz2j8o+noU8AywJ9AdWAe0Cpy1C/AI6QccC3LtfgKnALtH278BfpOL9xJoFWXoAewRZTsq5H/bKNchwHHR9n7A36J791vgquj4VQ33NfQH+AVwL/BgtH8fMDLavhW4MAcy3gmcH23vAbTb2fuplkPLcWD/aLst8Gq0PQy4y9OeANqZ2SEhAkYuBCa7+0cA7v56dHwYMN/dP3L3vwNrgb6BMjb4HfBL0ve2Qc7cT3d/1N0/iXafABpeWJ1r97IvsNbd17v7x8D8KGNQ7v6au6+Ktt8Dngc6kc52Z3TZncAZYRJ+zsw6A6cBc6N9AwYAC6NLguc0s/2B7wK3Abj7x+7+Djt5P1UcWs5lwA1mVgNMAcZFxzsBNY2u2xAdC+Vw4DtRc7jMzI6PjudUTjMbCvzD3Z/5wqmcytnIaNItGsi9jLmWpwkz6wYcCzwJHOzur0G6gAAHhUu22VTSf6h8Fu23B95p9MdBLtzTHsAbwB1R99dcM9uHnbyfWrJ7B5hZKdCxmVPXAAOBn7v7/Wb2A9LVu4h098cXZXX+8HZy7g4cQLpL5njgPjPrQe7lvJp0t02Tb2vmWNZybiujuy+OrrkG+AS4p+Hbmrk+5JzxXMuzBTPbF7gfuMzd303/UZ47zOx04HV3X2lmqYbDzVwa+p7uDhwH/MzdnzSzaaS7kXb6h0mG3L1oa+fM7C7g0mj3D0TNT9J/UXRpdGlnPu9yyort5LwQWOTpDsinzOwz0otz5UxOM/sa6b76Z6L/UXQGVkWD/Ls057buJYCZnQucDgyM7ikEuJfbkWt5NjOz1qQLwz3uvig6/E8zO8TdX4u6DF/f+k/YJb4NDDWzU4G9SHcfTyXdpbl71HrIhXu6Adjg7k9G+wtJF4edup/qVmo5rwL9o+0BwIvR9hLgR9Esm28BdQ1NvEAeIJ0PMzuc9KBVLemcI81sTzPrDhwGPBUioLv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\n", 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BLiLRkjPQzawMeAZ4BNgG7DWzbTO0Wwb8HvBSvovMp46+FGuXVVFRFrv/nIhIxAVJtXuBFnc/7e6jwAFg9wztvgR8GUjlsb6808YWIhJVQTbUXA+0TbnfDuyY2sDMtgON7v4DM/uP1zuQme0D9gHU1dWRTCZnXTDAwMDAnF/7TscQjcsTc359WObT51KlPseD+pw/QQLdZnjMrz5plgC+Anwm14HcfT+wH6Cpqcmbm5sDFTldMplkLq91d3p+9Hd88pYNNDdfM2u0oM21z6VMfY4H9Tl/gky5tAONU+43AB1T7i8D7gSSZnYG+AhwcCF+MdozNMbIeFonFYlIJAUJ9JeBrWa22cwqgT3Awckn3b3P3WvdfZO7bwJeBHa5+5GCVDwPV9ega8miiERQzkB393HgCeAw8CbwrLsfN7OnzWxXoQvMp6tr0DVCF5EICjKHjrsfAg5Ne+yp67Rtnn9ZhdHZpxG6iERXrBZjd/SmqCgzapcuCrsUEZG8i1Wgd/YNU7e8ikRipoU7IiKlLV6B3pvSxtAiElmxCvQOnSUqIhEWm0BPp50LV1Laek5EIis2gd41MMLYhLNOI3QRiajYBPq7V08q0ghdRKIpNoE+eVKRdioSkaiKTaC/t/WcplxEJJpiFOgpllSWsWJxRdiliIgURIwCfZh1KxdjppOKRCSa4hPofcPaGFpEIi0+gd6bYr2+EBWRCItFoKfGJugaGNEKFxGJtFgE+vnJ66BrykVEIiwWgd6RvQ66plxEJMriEei9OqlIRKIvFoHemT2p6CZNuYhIhMUi0Dv6hqldWklVRVnYpYiIFEwsAv3d3pSmW0Qk8mIR6J29OqlIRKIv8oHu7ldP+xcRibLIB/qV4XEGRye0ZFFEIi/ygT65Bl1bz4lI1EU/0HUddBGJiegHeva0f025iEjURT/Qe4epKDNqly4KuxQRkYKKfKC39wxTv2IxiYQ2thCRaIt8oLd1D9G4StMtIhJ9kQ/09p4hGmuWhF2GiEjBBQp0M9tpZifNrMXMnpzh+c+b2Qkze93MfmxmG/Nf6uwNjY7TNTBK4yoFuohEX85AN7My4BngEWAbsNfMtk1r9irQ5O4fBL4DfDnfhc5Fe09myWJDjaZcRCT6gozQ7wVa3P20u48CB4DdUxu4+3PuPpS9+yLQkN8y56atO1OSRugiEgflAdqsB9qm3G8Hdtyg/ePAD2d6wsz2AfsA6urqSCaTwaqcZmBgINBrf3J2DIC2N49x5XRpr3IJ2ucoUZ/jQX3OnyCBPlMS+owNzT4NNAEPzvS8u+8H9gM0NTV5c3NzsCqnSSaTBHntCz84weKKc+z6eDNmpR3oQfscJepzPKjP+RMk0NuBxin3G4CO6Y3M7GHgC8CD7j6Sn/Lmp617iIaaxSUf5iIiQQSZQ38Z2Gpmm82sEtgDHJzawMy2A38G7HL3i/kvc27aeoY1fy4isZEz0N19HHgCOAy8CTzr7sfN7Gkz25Vt9t+BpcBfm9kxMzt4ncMVVWYNula4iEg8BJlywd0PAYemPfbUlNsP57mueesbGqM/Na4RuojERmTPFG3rySxZbNBZoiISE9EN9Ktr0DXlIiLxENlAP6uTikQkZiIb6KcvDVC7dBHLqyrCLkVEpCgiG+itXYNsWVMddhkiIkUT7UCvVaCLSHxEMtD7hsfoGhhlswJdRGIkkoHe2jUIwJY1S0OuRESkeCIZ6KcvDQBohC4isRLJQG/tGqQsYWzQkkURiZFIBvrprkEaaxZTWR7J7omIzCiSiXf60qCmW0QkdiIX6BNpp7VrQF+IikjsRC7Qz14eJDWW5rabloVdiohIUUUu0E+e7wfgtpuWh1yJiEhxRS7Q3zzfT8Jga52mXEQkXiIX6G91XmFzbTVVFWVhlyIiUlSRC/STF/q5rV7TLSISP5EK9MGRcc5eHuK2On0hKiLxE6lAP9F5BYDbNUIXkRiKVKC/eq4HgLs2rAy5EhGR4otUoB9r66WhZjG1SxeFXYqISNFFK9DP9XJXo0bnIhJPkQn0zr5hOvpSbN9QE3YpIiKhiEyg/6zlMgD3bVkdciUiIuGITKD/vKWL1dWVuoaLiMRWJALd3flpSxf33byaRMLCLkdEJBSRCPRX23q52D/CQx9YG3YpIiKhiUSg/+3rnVSWJfjYHXVhlyIiEpqSD/TR8TT/77UOHrh1DcurKsIuR0QkNCUf6N879i4X+0f4zfs2hl2KiEioAgW6me00s5Nm1mJmT87w/CIz+3b2+ZfMbFO+C53J8OgEf/KTFm6vX84DW2uL8ZYiIgtWzkA3szLgGeARYBuw18y2TWv2ONDj7rcAXwH+W74LnW5wZJzPP3uMc91D/OEnb8dMq1tEJN7KA7S5F2hx99MAZnYA2A2cmNJmN/DF7O3vAH9iZubunsdaAfj2y+f44+eH6PvxP5AaS/MHn7idf3KzRuciIkECfT3QNuV+O7Djem3cfdzM+oDVQNfURma2D9gHUFdXRzKZnHXBHRfHaViS5q7qCu6tr+TmiXMkk+dmfZxSMzAwMKc/r1KmPseD+pw/QQJ9prmM6SPvIG1w9/3AfoCmpiZvbm4O8Pbv1wxsTyaZy2tLWVJ9jgX1OR4K1ecgX4q2A41T7jcAHddrY2blwAqgOx8FiohIMEEC/WVgq5ltNrNKYA9wcFqbg8C/yd5+DPhJIebPRUTk+nJOuWTnxJ8ADgNlwNfd/biZPQ0ccfeDwF8A3zSzFjIj8z2FLFpERK4VZA4ddz8EHJr22FNTbqeAf5Hf0kREZDZK/kxRERHJUKCLiESEAl1EJCIU6CIiEWFhrS40s0vA2Tm+vJZpZ6HGgPocD+pzPMynzxvdfc1MT4QW6PNhZkfcvSnsOopJfY4H9TkeCtVnTbmIiESEAl1EJCJKNdD3h11ACNTneFCf46EgfS7JOXQREblWqY7QRURkGgW6iEhELOhAX6ibUxdSgD5/3sxOmNnrZvZjM9sYRp35lKvPU9o9ZmZuZiW/xC1In83sU9nP+riZ/VWxa8y3AL/bG8zsOTN7Nfv7/WgYdeaLmX3dzC6a2RvXed7M7KvZP4/Xzezueb+puy/IHzKX6n0H2AJUAq8B26a1+R3ga9nbe4Bvh113Efr8ELAke/u349DnbLtlwPPAi0BT2HUX4XPeCrwK1GTvrw277iL0eT/w29nb24AzYdc9zz4/ANwNvHGd5x8Ffkhmx7ePAC/N9z0X8gj96ubU7j4KTG5OPdVu4P9kb38H+KiZzbQdXqnI2Wd3f87dh7J3XySzg1QpC/I5A3wJ+DKQKmZxBRKkz58FnnH3HgB3v1jkGvMtSJ8dWJ69vYJrd0YrKe7+PDfeuW038Jee8SKw0szq5/OeCznQZ9qcev312rj7ODC5OXWpCtLnqR4n8y98KcvZZzPbDjS6+w+KWVgBBfmcbwVuNbOfmdmLZrazaNUVRpA+fxH4tJm1k9l/4XeLU1poZvv3PadAG1yEJG+bU5eQwP0xs08DTcCDBa2o8G7YZzNLAF8BPlOsgoogyOdcTmbapZnM/8JeMLM73b23wLUVSpA+7wW+4e5/ZGb3kdkF7U53Txe+vFDkPb8W8gg9jptTB+kzZvYw8AVgl7uPFKm2QsnV52XAnUDSzM6QmWs8WOJfjAb93f6+u4+5eytwkkzAl6ogfX4ceBbA3X8BVJG5iFVUBfr7PhsLOdDjuDl1zj5npx/+jEyYl/q8KuTos7v3uXutu29y901kvjfY5e5Hwik3L4L8bn+PzBfgmFktmSmY00WtMr+C9Pkc8FEAM7udTKBfKmqVxXUQ+NfZ1S4fAfrcvXNeRwz7m+Ac3xI/Cpwi8+34F7KPPU3mLzRkPvC/BlqAXwJbwq65CH3+EXABOJb9ORh2zYXu87S2SUp8lUvAz9mAPwZOAP8I7Am75iL0eRvwMzIrYI4BHw+75nn291tAJzBGZjT+OPA54HNTPuNnsn8e/5iP32ud+i8iEhELecpFRERmQYEuIhIRCnQRkYhQoIuIRIQCXUQkIhToIiIRoUAXEYmI/w9x306CvTj5GgAAAABJRU5ErkJggg==\n", 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\n", "text/plain": [ "
" ] @@ -574,28 +640,28 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 132, "metadata": {}, "outputs": [ { "data": { "text/latex": [ - "$$\\frac{8.328e+04}{s^2 + 66.67 s}$$" + "$$\\frac{2478}{s^2 + 66.67 s}$$" ], "text/plain": [ "\n", - " 8.328e+04\n", + " 2478\n", "-------------\n", "s^2 + 66.67 s" ] }, - "execution_count": 11, + "execution_count": 132, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -615,14 +681,14 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 133, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "(inf, 53.14209069059456, nan, 49.97820800873587)\n" + "(inf, 88.40402033571957, nan, 1.857487099451951)\n" ] }, { @@ -636,7 +702,7 @@ }, { "data": { - "image/png": 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\n", 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dyioiMgTl2xyWBE0hIiLHrby8HICmpqaC1873E9LNBX9mERE5IbNmzQpW+5jNwcxeInNVUp9DgLv7aUFSiYhIv7761a8Gq33M5uDufxnsmUVEJLHy/T4HERFJmCiKiKIoSO18J6RFRCRhvvzlLwerreYgIpJSIZuDTiuJiKTUwYMHOXjwYP93HACNHEREUuozn/kMADt37ix4bTUHEZGUuuqqq4LVVnMQEUmpysrKYLU15yAiklIHDhzgwIEDQWpr5CAiklKXXnopoDkHERHJcu211warreYgIpJSIRfe05yDiEhK7d+/n/379weprZGDiEhKTZ8+HdCcg4iIZLnuuuuC1VZzEBFJqRkzZgSrXZQ5BzO73MyeNrPXzazsiGOLzGyPmXWY2SXFyCcikgbd3d10d3cHqV2skUM7MANYm73TzM4BKoBzgfcDTWZ2tru/NvgRRUSS7fOf/zwwhOYc3P1XAGZ25KHpwEZ3fwX4rZntAS4Adg1uQhGR5Lv++uuD1U7anMPpwGNZ23vjfX2YWRVQBTBmzJjwyUREEmbq1KnBagdrDmbWBIzKcegmd998tIfl2Oe57uju64B1AGVlZTnvIyIylO3btw+AUaNyvdWemGDNwd3LB/CwvUBp1vZo4PeFSSQiMrRUVFQAQ2jO4Ri2AA+a2T+SmZA+C/hFcSOJiCTTwoULg9UuSnMws88B3wNGAo+aWZu7X+LuT5vZQ8AzwCFgrq5UEhHJbfLkycFqF+tqpUeAR45y7Fbg1sFNJCKSPl1dXQCUlpb2c8/jl7TTSiIikqfZs2cDb445BxERydPNN98crLaag4hISpWXD+Si0Pzo+xxERFKqs7OTzs7OILU1chARSak5c+YAmnMQEZEsS5cuDVZbzUFEJKUuvPDCYLU15yAiklIdHR10dHQEqa2Rg4hISl199dWA5hxERCTLbbfdFqy2moOISEpNmjQpWG3NOYiIpFR7ezvt7e1BamvkICKSUvPmzQM05yAiIlmWL18erLaag4hISk2cODFYbc05iIikVFtbG21tbUFqa+QgIpJS8+fPBzTnICIiWVauXBmstpqDiEhKTZgwIVhtzTmIiKRUa2srra2tQWpr5CAiklI33HADoDkHERHJsnr16mC11RxERFLqvPPOC1Zbcw4iIinV0tJCS0tLkNoaOYiIpNSNN94IaM5BRESyrF27NlhtNQcRkZQaP358sNqacxARSanm5maam5uD1NbIQUQkpZYsWQJozkFERLJs2LAhWG01BxGRlBo3blyw2ppzEBFJqaamJpqamoLU1shBRCSlbrnlFgDKy8sLXlvNQUQkpe6///5gtdUcRERSqrS0NFhtzTmIiKRUY2MjjY2NQWoXpTmY2XIz+7WZPWVmj5jZO7OOLTKzPWbWYWaXFCOfiEgaVFdXU11dHaR2sU4rbQcWufshM/susAj4tpmdA1QA5wLvB5rM7Gx3f61IOUVEEmvjxo3Bahdl5ODuP3X3Q/HmY8Do+PZ0YKO7v+LuvwX2ABcUI6OISNKNGjWKUaNGBamdhDmHOcC2+PbpQFfWsb3xvj7MrMrMdpvZ7j/+8Y+BI4qIJE9DQwMNDQ1Bagc7rWRmTUCulnaTu2+O73MTcAh4oOdhOe7vueq7+zpgHUBZWVnO+4iIDGV33HEHAFOnTi147WDNwd2P+akMM7sC+DvgInfveXPfC2RfmzUa+H2YhCIi6bZp06ZgtYt1tdJk4NvANHc/kHVoC1BhZieb2RnAWcAvipFRRCTpSkpKKCkpCVK7WFcrrQZOBrabGcBj7n6Nuz9tZg8Bz5A53TRXVyqJiORWX18PwIwZMwpe2944o5NeZWVlvnv37mLHEBEZVFEUAQP/Pgcze9zdy3Id0/IZIiIptXnz5mC11RxERFJq+PDhwWon4XMOIiIyAHV1ddTV1QWprZGDiEhK3XXXXQDMmjWr4LXVHEREUmrr1q3Baqs5iIik1KmnnhqstuYcRERSqra2ltra2iC1NXIQEUmpe+65B4DKysqC11ZzEBFJqe3btwerreYgIpJSw4YNC1Zbcw4iIilVU1NDTU1NkNpqDiIiKRWyOQyJhffM7CWgo9g5BqAE6C52iAFIY+40ZgblHkxpzAwnlvsD7j4y14GhMufQcbSVBZPMzHYr9+BIY2ZQ7sGUxswQLrdOK4mISB9qDiIi0sdQaQ7rih1ggJR78KQxMyj3YEpjZgiUe0hMSIuISGENlZGDiIgUkJqDiIj0kermYGZ1ZtYW/zxnZm1ZxxaZ2R4z6zCzS4qZMxcz+3qc7Wkz+4es/YnMbWbfMbP/zHq9L806lsjM2cxsgZm5mZVk7UtkbjNbZmZPxa/zT83s/VnHEpkZwMyWm9mv4+yPmNk7s44lOffl8X+Hr5tZ2RHHkpx7cpxrj5ktLPgTuPuQ+AHuABbHt88BngROBs4AngVOKnbGrKyfApqAk+Pt9yQ9N/AdYEGO/YnNnJWxFPgJ8B9ASdJzA6dl3b4OuDvpmeN8FwNvjW9/F/huSnJ/CBgP7ATKsvYnNjdwUpxnHPC2OOc5hXyOVI8cepiZAV8A/jneNR3Y6O6vuPtvgT3ABcXKl8O1QLW7vwLg7i/E+5OeO5c0ZP4n4FtA9tUXic3t7v+VtfkXvJE7sZkB3P2n7n4o3nwMGB3fTnruX7l7rhUWkpz7AmCPu3e6+6vARjJ5C2ZINAfgE8Af3P038fbpQFfW8b3xvqQ4G/iEmf3czJrNbGK8P+m558WnDDaY2bvifYnObGbTgP909yePOJT03LeaWRfwf4HF8e5EZz7CHGBbfDtNubMlOXfwbIlfPsPMmoBROQ7d5O6b49tf5I1RA4DluP+gXrN7rNxkXvd3AR8DJgIPmdk4ipy7n8x3AcviPMvInMabQ/Jf6xvJnO7o87Ac+xLxWrv7Zne/CbjJzBYB84AlJPy17vnv0cxuAg4BD/Q8LMf9E5c718Ny7EvKtf/BsyW+Obh7+bGOm9lbgRnAR7N27yVznrnHaOD3hU93dMfKbWbXAvWeOXn4CzN7ncziWUXN3d9r3cPM1gM/jjcT+1qb2YfJnCt+MnPmkdHAE2Z2ASl5rYEHgUfJNIfEvtY9zOwK4O+Ai+K/b0hB7qMoeu5jCJ+t2BMrBZiYmQw0H7HvXA6fSOokIRNJcb5rgL+Pb59NZnhoSc4NvC/r9jfJnItN/Gt9xD/Dc7wxIZ3Y3MBZWbe/DmxKeuY432TgGWDkEfsTnTsr504On5BObG4y/2PfGefqmZA+t5DPkfiRQx4qOPyUEu7+tJk9ROYP9RAw191fK0a4o9gAbDCzduBV4ArP/BtPcu5/MLMJZIauzwFXQype65wSnrvazMYDr5O5wuoaSHxmgNVk3ki3xyO1x9z9mqTnNrPPAd8DRgKPmlmbu1+S5NzufsjM5pG5Cu8kYIO7P13I59DyGSIi0sdQuVpJREQKSM1BRET6UHMQEZE+1BxERKQPNQcREelDzUFkgMzstXjl1HYza8hehXQAtZ7LXjFWpNjUHEQG7mV3n+Du5wF/AuYWO5BIoag5iBTGLrIWPjOzG8ysNV6ocGnW/h+Z2ePx9wdUFSWpSB7UHEROkJmdBFwEbIm3LwbOIrOs8gTgo2b2yfjuc9z9o0AZcJ2ZjShCZJF+qTmIDNzb428ffBF4N7A93n9x/PNL4Angg2SaBWQawpNkvu+gNGu/SKKoOYgM3MvuPgH4AJnFz3rmHAy4PZ6PmODuf+Xu95pZBJQDH3f3vybTPE4pRnCR/qg5iJwgd99P5us8F5jZMDKLoc0xs3cAmNnpZvYeYDjwZ3c/YGYfJPN9HiKJNBRWZRUpOnf/ZXy6qMLd7zezDwG74tVJ/xuoBBqBa8zsKaCDzKklkUTSqqwiItKHTiuJiEgfag4iItKHmoOIiPSh5iAiIn2oOYiISB9qDiIi0oeag4iI9PH/AXUhFXK5h5V9AAAAAElFTkSuQmCC\n", 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\n", 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"execution_count": 15, + "execution_count": 136, "metadata": {}, "output_type": "execute_result" } @@ -754,7 +820,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 137, "metadata": {}, "outputs": [ { @@ -772,13 +838,13 @@ " 'p_N': 9,\n", " 'p_E': 10,\n", " 'p_D': 11,\n", - " 'rpm0': 12,\n", - " 'rpm1': 13,\n", - " 'rpm2': 14,\n", - " 'rpm3': 15}" + " 'duty0': 12,\n", + " 'duty1': 13,\n", + " 'duty2': 14,\n", + " 'duty3': 15}" ] }, - "execution_count": 16, + "execution_count": 137, "metadata": {}, "output_type": "execute_result" } @@ -789,19 +855,19 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 138, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "array([[ 1.03 , -0. , -0.069, -0. , 1.447, 0. , 21.595, 0. , -0.069, -0. , 0.998, -0. , -4.466, 4.302, 4.466, -4.302],\n", - " [ 0. , 1.032, 0. , -1.451, 0. , 0. , 0. , 21.647, 0. , -1. , 0. , -0. , 4.348, -4.348, 4.348, -4.348],\n", - " [ 0.078, 0. , 1.002, -0. , 0.101, 0. , 1.559, 0. , 0.998, -0. , 0.069, 0. , 1.32 , 1.155, -1.32 , -1.155],\n", - " [-0. , -0. , -0. , 0. , 0. , -1.005, 0. , -0. , 0. , 0. , 0. , -1. , 5.238, 5.238, 5.238, 5.238]])" + "array([[ 1.299, -0. , 0. , 0. , 1.497, 0. , 24.353, -0. , 0. , 0. , 1. , 0. , -0.511, 0.511, 0.511, -0.511],\n", + " [-0. , 1.296, -0. , -1.497, -0. , -0. , -0. , 24.324, -0. , -1. , 0. , 0. , 0.507, -0.507, 0.507, -0.507],\n", + " [ 1.031, -0. , 10.313, -0. , -0. , -0. , 0.101, -0. , 1. , -0. , -0. , -0. , 0.119, 0.119, -0.119, -0.119],\n", + " [ 0. , 0. , 0. , -0. , 0. , -1.041, 0. , 0. , 0. , -0. , 0. , -1. , 0.553, 0.553, 0.553, 0.553]])" ] }, - "execution_count": 17, + "execution_count": 138, "metadata": {}, "output_type": "execute_result" } @@ -810,6 +876,27 @@ "K, S, E = control.lqr(sys.A, sys.B, np.eye(16), np.eye(4))\n", "K" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { @@ -828,7 +915,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.4" + "version": "3.7.3" } }, "nbformat": 4,