{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import sympy\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "sympy.init_printing()" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def inv_laplace(Y):\n", " s, t = sympy.symbols('s, t')\n", " # define a function to perform more complicated inv laplace\n", " y = 0\n", " for a in Y.apart().expand().args:\n", " y += sympy.inverse_laplace_transform(a, s, t)\n", " y = y.subs(\n", " {sympy.InverseLaplaceTransform(s, s, t, None): sympy.DiracDelta(t)}\n", " )\n", " return y\n", " \n", "def responses(G, R):\n", " s, t = sympy.symbols('s, t')\n", "\n", " ER = (1/(1 + G)).simplify()\n", " YR = (G/(1 + G)).simplify()\n", " Y = YR*R\n", " \n", " r = sympy.inverse_laplace_transform(R, s, t)\n", " y = inv_laplace(Y)\n", " e = r - y\n", " return locals()\n", "\n", "def f_eval(f):\n", " return sympy.lambdify((t), (f), modules=['numpy', {\n", " 'Heaviside': lambda x: np.heaviside(x, 1)}])\n", "\n", "def plots(res, t_vect):\n", " plt.plot(t_vect, f_eval(res['r'])(t_vect), label='r')\n", " plt.plot(t_vect, f_eval(res['y'])(t_vect), label='y')\n", " plt.plot(t_vect, f_eval(res['e'])(t_vect), 'k--', label='e')\n", " plt.legend()\n", " plt.xlabel('t')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Type 0" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "zeta = 0.75\n", "omega_n = 3\n", "s, t = sympy.symbols('s, t')\n", "G = 1/(s**2 + 2*zeta*omega_n*s + omega_n**2)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\frac{1}{s^{2} + 4.5 s + 9}$" ], "text/plain": [ " 1 \n", "──────────────\n", " 2 \n", "s + 4.5⋅s + 9" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "G" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$K_p = 1/9$\n", "\n", "$e_{ss} = \\frac{1}{1 + K_p} = 9/10$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "res = responses(G, 1/s)\n", "plots(res, np.arange(-1, 3, 0.001))\n", "plt.hlines(9.0/10, -1, 3)\n", "plt.title('unit step');" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "res = responses(G, 1/s**2)\n", "t_vect = np.arange(-1, 3, 0.001)\n", "plots(res, np.arange(-1, 3, 0.001))\n", "plt.title('ramp');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Type 1" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\frac{1}{s \\left(s^{2} + 4.5 s + 9\\right)}$" ], "text/plain": [ " 1 \n", "──────────────────\n", " ⎛ 2 ⎞\n", "s⋅⎝s + 4.5⋅s + 9⎠" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "G2 = G/s\n", "G2" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "res = responses(G2, 1/s)\n", "plots(res, np.arange(-1, 60, 0.1))\n", "plt.title('unit step');" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "res = responses(G2, 1/s**2)\n", "plots(res, np.arange(-1, 60, 0.1))\n", "plt.hlines(9, 0, 60)\n", "plt.title('ramp');" ] }, { "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": [ "res = responses(G2, 1/s**3)\n", "plots(res, np.arange(-1, 60, 0.1))\n", "plt.title('parabolic');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Non-Symbolic Approach" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\frac{1}{s^3 + 4.5 s^2 + 9 s}$$" ], "text/plain": [ "\n", " 1\n", "-------------------\n", "s^3 + 4.5 s^2 + 9 s" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import control\n", "s = control.tf([1, 0], [0, 1])\n", "G = 1/(s*(s**2 + 4.5*s + 9))\n", "G" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/jgoppert/anaconda3/envs/aae364/lib/python3.7/site-packages/control/xferfcn.py:610: RuntimeWarning: divide by zero encountered in double_scalars\n", " polyval(self.den[i][j], s))\n" ] }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFUAAAAUCAYAAAD88XGTAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAD/klEQVRYCe2Z7VEbMRCGMUMBnqQDpwMSKgh04KSDkA5gKIF0QDog0AF0kLE7wB3EuAPnfWStsifrznfnj/xhZ2RJu3p391arLxgsl8sjo8FgMFL7XLyfxnurmyOgmI01YqqYzWzkwIIq4VDMB/UvTOhryR/UH9bJ/dgu7Wj3VpgXlQ8qt97BLrpKY6Uf3X9UFirov5f+qepW1AYfY3Od/FbjiCKaqIysn9eSEdTLnL9tP+rlw5lxHBlvq9Pw0sU3JX1qkzhMXu13GpZa1AqvceidGNYCeinmnTEPVUdn8P48ttl6gk/b1tLHN73mesRjAlMAcrn1u+Kj3ivwFtTWs2dGd1HLkZCdu9CV65DuJxW2s8okmU3VbGUVme93xaNPJUzisfYDDieUp42W/oHoTHb2ZZfsLxF7K1QnX0nr5UW84gd/pnien6hBtjybJl9rANFnGbHBvwj4w+SA1eZQY1KuIx9d0Nr4FXv1Kyw6P6p8VZmrf4dE+r9Tb0vRb9TMG3SFZCrJt8ATxy/oZJkUDyDxOYkZQwAr+5OTgaeE/SSOZzIANh4IcUzCgd1FwW7UHfz3OsU/3WS3L144kmVCpuLA2oxqtuD/VoGIflqmkuGYyRi3kOMpi9V/pwIR3CJF/ciKq6QI6s6stS9V71uo64onjkOCSgAWBQNzBeox8pkBW+KwZpJN4zIhqPndlswm65rug0zMpjEM6UNrSeKU2IRzd62jvngSb3Rcp1UBCYFW4GyfTK8skwlrwcuzjSA3BRSzezuknH8WQOwZWfallWcCq7fFE1RmxQyZXl9zeDw6Q15WFzwmIhw+MZs9xtpk6qbA29g+NRNd+i4LdJ4IuY0+eHTPCCozZoYqimNAyMZ7BOpzcfbE6V1xzmX2rzjwxgNc+5Pati879s6avACxkRM3E97qYSXmQtfvg2crDHoJVPE1JT4Blf1wAwCQbglq00dQeQWpn14sarMXn4L3RTwyaA1bM2bj68fjfFs2eNTkz9RX8ZJPapsva3ba4DN7rM7bE/1wHQpLVXWFBHhW5j2qEBwCk/ZVdQkqB1YlU8VD1yhiOOxKSzxkUAEr6IokW0gHq2iomtfPpswyqK+5C98Ij68Q+/hn75OzU9pjN+KD1n8/fNe3kEFqHPSZKntk85M+qJLBpb7GjVUan5Ql3KF5+KjCA+noWA2Ij/RXpsDc5Y+yZazCPgWxrVg7MBp+zuRonyxtULkXEWdHWPEhqHKaZc2StWWyD6tMXFjKKI82G+3IH2a/6T7ZiD+UMPrJ2bJ6AKlhWwAf0GpJGqZLLd3sy1cqYc9tgwXTZtz/HiM/OZfSkzz95V9Mrkxk6tu/UwhGS1LMSJZnTWw66P4CeKKqY2hdUX4AAAAASUVORK5CYII=\n", "text/latex": [ "$\\displaystyle \\left( inf, \\ 0.0\\right)$" ], "text/plain": [ "(inf, 0.0)" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Kp = np.real(control.minreal(G, verbose=False).horner(0)[0][0])\n", "ess_step = 1/(1 + Kp)\n", "Kp, ess_step" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\left( 0.11111111111111109, \\ 9.000000000000002\\right)$" ], "text/plain": [ "(0.11111111111111109, 9.000000000000002)" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Kv = np.real(control.minreal(s*G, verbose=False).horner(0)[0][0])\n", "ess_ramp = 1/Kv\n", "Kv, ess_ramp" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/jgoppert/anaconda3/envs/aae364/lib/python3.7/site-packages/ipykernel_launcher.py:2: RuntimeWarning: divide by zero encountered in double_scalars\n", " \n" ] }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFcAAAAUCAYAAAD4BKGuAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAEOElEQVRYCe2Z7VEbMRCGMUMBnqQDpwMSKgjpwEkHIR3AUALpgHRAoAPoIIM7wB0E3AF5H1m72TtLd0fODPmBZmSt9kvSq9XqNJ48Pj7uWJlMJjPRh+L9MN5rOwwBYTeX5kLYLc1iYuBKOBXzUv1PJrRWsjPRv1VXqu9UL6S3UDuojLUfNEhQ0niX6k5LawlqTyYzRmBxpwoOZxrjL5jrcU+cJ2KHqnKrOrO+tZk/D302AecbuqYT27H20ddQWmMC7tFQ/aF62S/gEqWA5rjgQwVsbs2fAXsk5rkxrRUP/oP1rRWPAdyJ8dvtWPu2v5fsay0AB4KHmSZ9JvxiKxnYHMMzcIuRKKVrVVJFw4l4tnMcvYYs9sfaR18vTdua++YhPTYhBeSu8giXGAB57qCfC7tUKqvMrMnNpiYfam9+/of2QJMoYdSYm3BkbUvhergngii8aWiok5M37Pu2LPTTxoS+k2Pt3dFAIo9HGuOiudMiv5spCxXNRc18TzKfdVM29Nfs9a9s8fle9YvqvfrnSOT/G22lgOdnZBz9jeQvHhMhx3AjNo6+ePtZlnJLW05fZZR9yWcXT+OleaoFyMY9EWSslerzFs0xZsKdF3TWcbueubAht0QuIHRFJ4PXytuaIPDH2gdXZVLRxBp+ZSkR48dXMgLBZOitBIxHtfpvVCnVeWb/6GyccJiFAp5TwMX5qqJQYCeWTYhv31rp2rAh9jW/Jf69ALvKAqLGjj6spWQLAQR4gNv+jifSOZkL2krZh9+jE03Z3Nlu5ERajgxwAyKKbZc9QqIQeqx9219X38YSgJZH/YVpMtkbiO3oA+wuYBl60GWGYiyAm0I4MgPNRAzIwPaj1J5o1IEea9/219fnkrkKgEb9GohsSLqkcnRHG6OJ3L4NMF1aAnIJuERfKTrFTi+dDxCtwg3LO9qiuyX2Li+lMfbuqI/IwBCdF+iqz8d8LNz2jWAIkf4zK55Gg0CzBsvbgV0lST8JGyax8ToTcOkLQTIeGP7ME00kP6juBx143LgbrzbxRtnbGH2txgFYqfmXin8Bic9iETReVeqz9jRnteRqX5ONJ56trWFr8lIrG07C2Z5++DRJx0JtqfCNd6pdZoIU8s9HOfVjInolOSeglIOfYj+VH159adcZbGiRzY1sr1QBCZQ976rL3LnYGpErHuueZRsuRV+T+FbSySvYmrzUYvM1Rmfnd56cJ93nbDWhuWrnk/o5xy/51nyI7uuSrMRj/qo8YnZ2RVBwED9fEvMFfg40qSdH7bbnqUieq3JfUEg3RidGzw95O2WCBK4WxBHieNjR77Hfvlhjs+Nd383bH7TukWBLKQqVjE9dO0vyGsjN60eKCEsNLG5w+JvdtlqN7RfQtnz+qx/monqsmnLyUD/S5/7y9Or/RIjJ5wuRC/LxMkD0WnoQEHZsyI2w80v9D9QA1Dm0pEzIAAAAAElFTkSuQmCC\n", "text/latex": [ "$\\displaystyle \\left( 0.0, \\ inf\\right)$" ], "text/plain": [ "(0.0, inf)" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ka = np.real(control.minreal(s**2*G, verbose=False).horner(0)[0][0])\n", "ess_parab = 1/Ka\n", "Ka, ess_parab" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'unit step')" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t, y = control.step_response((G/(1 + G)))\n", "r = np.ones(len(t))\n", "plt.plot(t, r, label='r')\n", "plt.plot(t, y, label='y')\n", "plt.plot(t, r - y, 'k--', label='e')\n", "plt.legend()\n", "plt.title('unit step')" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'ramp')" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t = np.linspace(0, 60)\n", "t, y = control.step_response((G/(1 + G))/s, t)\n", "r = t\n", "plt.plot(t, r, label='r')\n", "plt.plot(t, y, label='y')\n", "plt.plot(t, r - y, 'k--', label='e')\n", "plt.legend()\n", "plt.title('ramp')" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'parabolic')" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t = np.linspace(0, 60)\n", "t, y = control.step_response((G/(1 + G))/s**2/2, t)\n", "r = t**2/2\n", "plt.plot(t, r, label='r')\n", "plt.plot(t, y, label='y')\n", "plt.plot(t, r - y, 'k--', label='e')\n", "plt.legend()\n", "plt.title('parabolic')" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "G = (s-2)/(s+1)\n", "control.rlocus(G, np.linspace(0, 0.5));" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "G = (s+2)/(s*(s-2))\n", "control.rlocus(G, np.linspace(0, 100));" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'step')" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t = np.linspace(0, 60)\n", "G = (s+1)/((s+2)*(s+3))\n", "t, y = control.step_response((G/(1 + G))*2, t)\n", "r = 2*np.ones(len(t))\n", "plt.plot(t, r, label='r')\n", "plt.plot(t, y, label='y')\n", "plt.hlines(12.0/7, t[0], t[-1])\n", "plt.plot(t, r - y, 'k--', label='e')\n", "plt.legend()\n", "plt.title('step')" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'step')" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t = np.linspace(0, 30)\n", "G = (s+1)/(s*(s+2)*(s+3))\n", "t, y = control.step_response((G/(1 + G))*10/s, t)\n", "r = 10*t\n", "plt.plot(t, r, label='r')\n", "plt.plot(t, y, label='y')\n", "plt.plot(t, r - y, 'k--', label='e')\n", "plt.hlines(60, 0, 30)\n", "plt.legend()\n", "plt.title('step')" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "G = (s+2)/(s-2)\n", "control.rlocus(G, np.linspace(0, 1, 1000));\n", "plt.grid();\n", "\n", "plt.figure()\n", "control.bode(G);" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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j05ldkEXRuIxAh2xChKeJYr6IfF5V3/RpNMaYNrmpsXztnHy+dk4+tY0tvLftcNuTVG9uOIQIjEh0sL51K7MLMpk4NNH6bBif8DRRfBf4sYg0As24emirqib6LDJjTJu4qHAunpjNxROzUVU2HjhJcVklryzfxgMLt/DAwi1kJ0Yzy32J6tzRacRG2qx+pn94Oh+FjbdsTJAQESblJDEpJ4nTwvYzsfBsSt2DGL6+7gAvLN9DZLiDs0emkRvWzKijdeSm2og7xnuePvXU2eB/J4Ddqmoz3RkTQBkJUVw9NZerp+bS1OKe1c89HtWSw008t7mEsVnxzHJPBXvm8GTCbVY/0wuenps+imuk2A3uz5OBdUCaiNymqu/4IjhjTO9EuodDP3d0Oj+9dALz3iimJjGfkvJKnnh3J39ZsoOkGNcghtnawum1TaTYrH6mB54mil3ALaq6EUBEJgA/An4BvAxYojAmCGXHOSg6fyRfP38k1Q3NLNt6mMVllZSWV3K4ponHNyykMC+lrYf42CwbhMF8lqeJouBUkgBQ1U0iMkVVd/j6KQsRGQn8BEhS1at8ujNjBrGE6AgumTyESya7ZvV7+rVijscOo7i8kt++XcZv3y4jJzmGcYnN6JBKzh6ZZrP6GcDzRFEuIn8C5rk/Xwtscc9y19zVRiLyJHApUKmqk9qVzwX+CIQBj6vqb7qqQ1V3ALeIyIsexmqM6YHDIYxMDqOoaBw/uHgch040tD16u3RLBcVPrSA6wuEexDCL6AZnoEM2AeRporgR+G/ge7gejV0G/BBXkpjVzXZPAw8Dz54qEJEw4BHgImAfsEJEXsOVNH7dYfubVbXSwxiNMV7KTorm+unDuX76cN5ZXEJU7iSKN1ewuKySRZtdh+Bfy99ljnvk2zNykwMcsfEnTx+PrQd+7351VNPNdktFJL9D8XRgm/tMARGZB1yuqr/GdfZhjAmgyDBh5tgMZo7N4OdfULZV1vDXNz5gV3M4f1qynYdLtpEaF0lBkpOa1AOcPyaDpBib1W8wE1XteSWRMbj+2p8AtA2ir6ojPdg2H5h/6tKTiFwFzFXVr7s/3wDMUNVvdbF9GnAfrjOQx90JpbP1bgVuBcjKyiqcN2/ep5bX1NQQHx/vVZk/9Nd+vanH0216Wq+75V0t86QNAtUm/bnv3tYTrG1S26xsONzKusoW1lW1UNcihAmMSXFwekY4Z2SEkR0nPu0hHorHiqdt1ZfvZtasWatUdWqnC1W1xxeuS01zgPVAHvBz4B4Pt80HPm73+Wpcv/BPfb4BeMiTujx9FRYWakclJSVel/lDf+3Xm3o83aan9bpb3tUyT9ogUG3Sn/vubT3B3iaqqosWF+vynUf0N29t1osfWKJ5t8/XvNvn6wW/K9afv/axvrulShubW7uNzxuheKx42lZ9+W6AldrF71RP71HEqOpiERFV3Q38XETeBe72InHtA3LbfR4GHPCiHmNMAIU5hGn5qUzLT+X2uQXsO1ZHibuj3/Mf7eGp93YRFxnG+WMymF2QSVFBBpkJNqvfQORpomgQEQewVUS+BewHMr3c5wpgjIiMcNdzHfCfXtZljAkSw1JiueHsfG44O5/6plbe3+7qs1FSVsnbGw8BcNqwpLYh0ycNtVn9BgpPE8X3gFjgO7g62c0GvtbTRiLyAlAEpIvIPuBuVX3CnWwW4HrS6Ult10fDGDPwxUSGMWd8FnPGZ6GqbD5YTXFZBcVllfxx8Vb+sGgrGQlRzB7neorqvDHpxEfZIIbBytOnnla439YAN3lauape30X5m4ANWW5MCBARJgxNZMLQRL41ewxHahopLa+iuLySNzcc5B8r9xIZ5mDGyNS2s428NJvVL5h0myjc/Ru6pKpf6N9wjDGDXVp8FFcWDuPKwmE0tzpZuesYJeWVLNpcwT2vb+Ke1zcxKuPUrH5ZTM1PIcIGMQyons4ozgb2Ai8AH+HqbGeMMf0iIszB2aPSOHtUGj/+/Hh2H6ltG/n2mfd389d3d5IQHc4FYzOYU5BJ0Thvb42avugpUWTj6r9wPa4bzm8AL9g9BWOML+SlxXHTuSO46dwR1DS2sGzrYYrLKigpr+KN9QcRgVFJDjbqNmYXZFKQnWCz+vlBt4lCVVuBt4G33eM6XQ+Uisi9qvqQPwI0xoSm+Khw5k7KZu6kbJxO16x+i8sqeHX5du5fUM79C8oZkhTtnmcjk3NGpRMTaYMY+kKPN7PdCeI/cCWJfOBBXEOLG2OMXzgcwuRhSUwelsQZ4QeYcOZZlLhn9Xt1zX6e/2gPUeEOzhmV5rq3MT6LnOSYQIc9aPR0M/sZYBLwFq6e2B/7JSpjjOlGZmI0104bzrXThtPY0srynZ/M6lfy6kZ++upGCrIT2s42pgxPIcz6bHitpzOKG4BaYCzwnXbXAgVQVU30YWzGGNOjqHBX7+/zx2Tws0snsL2qtq2H+F+X7uBPpdtJjo2gaGwGswoyKRqbSVKsDWLYGz3do7Bn0owxA4aIMDozntGZ8XzjgpGcqG/m3a1VFJdVUlpexStrDxDmEArzUsiPaCJnfDWjM+PthngPrCukMWbQSoqJ4NLThnLpaUNpdSpr9x6npKySxWWV/HNnM//cspTc1Bhmj3Pd15gxItVm9euEJQpjTEg4dSZRmJfCDz83jpfeKqYhdRQlZZX8Y+VenvlgNzERYZw3Jr2th3hWog1iCJYojDEhKi3GQdGMPL48I4+G5lY+2HGE4s2uexsLN1UAMHFoInPcT1GdlpMU4IgDxxKFMSbkRUeEMWtcJrPGZXKvKlsqalhcVkHx5koeLtnGg8XbSI93zepXn3aQ88akkxAdOjfELVEYY0w7IsK47ATGZSfw30WjOVbbxJItrhviizYeYNnfVxMRJkwfkcqscZnMGZ/FiPTBPYihJQpjjOlGSlwkV0zJ4YopOSwuPk7CiNNZXFZBSVklv3xjM798YzMj0uPa7mtMy08NdMj9zhKFMcZ4KMzhOpOYPiKVOy8Zz96jdZSUV7J4cyV/+3A3TyzbSXxUOAXJSlX8XmYVZJIeHxXosPvMEoUxxngpNzWWr56dz1fPzqeuqYX3th2huKyCt9bt40cvrkcEThuW7LohXpDJxKGJA7LPhiUKY4zpB7GR4Vw0IYuLJmRxccoRMsae2dZn4/8WbeGBhVvISoxidkEmGc0tTG9qITZyYPwKHhhRGmPMACIiTMpJYlJOEt+eM4bDNY2UlFVSUl7J/HUHqW5s4c8bFnLWyLS2s43c1NhAh90lSxTGGONj6fFRXD01l6un5tLU4uTxV0s4GjWE4rJK7n5tI3e/tpExmfHMLsgktaGV81qdhAfRrH6WKIwxxo8iwx1MSAujqGgCd106gZ2HT83qV8GT7+2kuVV5ZP1CZo5zjXw7c2xGoEO2RGGMMYE0Ij2OW84bwS3njaC6oZk/v7KEirAMSssreX3dARzuWf024ZrVb1yW/2f1s0RhjDFBIiE6gmnZ4RQVnY7Tqazff4LizRW8unIHv3u7nN+9XU5OcgyzCjKYU5BFc6v6JS5LFMYYE4QcDuGM3GTOyE3mzMiDjD/zrLanqF5evZ/nPtxDpAPO37uC2eNdN8R9xRKFMcYMAFmJ0Vw3fTjXTR9OQ3MrH+08yt8Wraa8sprFZZUA5CY4eHVaE6lxkf26b0sUxhgzwERHhDFzbAZ6IIqZM2eyvaqGxZsrWbRmKyk+mL3PEoUxxgxgrln9EhidmcA43euTG93B86CuMcaYoGSJwhhjTLdE1T+PV/mTiFQBuzsUJwEnPChLBw77KLTudBaLv+rxdJue1utueVfLPGmXQLVJZ7H4q55gbxOwY6Uv6/W2XTxtq760SZ6qdt67T1VD4gU85mHZymCJz1/1eLpNT+t1t7yrZZ60S6DaJJDtEuxtEsh2CcVjxdO28lWbhNKlp9c9LAuU/orFm3o83aan9bpb3tUya5e+rW9t4t96AtUuvWmrfjcoLz31hYisVNWpgY7DfMLaJDhZuwQfX7VJKJ1ReOqxQAdgPsPaJDhZuwQfn7SJnVEYY4zplp1RGGOM6ZYlCmOMMd2yRGGMMaZblih6QURGisgTIvJioGMJZSISJyLPiMhfReTLgY7HuNjxEXxE5Ar3cfKqiFzsbT0hkyhE5EkRqRSRjzuUzxWRchHZJiJ3dFeHqu5Q1Vt8G2lo6mX7fAl4UVW/AXzB78GGkN60ix0f/tHLNnnFfZzcCFzr7T5DJlEATwNz2xeISBjwCHAJMAG4XkQmiMhkEZnf4eW7WUEM9KJ9gGHAXvdqrX6MMRQ9jeftYvzjaXrfJne5l3slZIYZV9WlIpLfoXg6sE1VdwCIyDzgclX9NXCpfyMMbb1pH2AfrmSxltD6Y8fvetkum/wbXWjqTZuIyGbgN8Bbqrra232G+kGWwyd/mYLrF1BOVyuLSJqI/BmYIiJ3+jo402X7vAxcKSJ/IriGlggVnbaLHR8B1dWx8m3gQuAqEbnN28pD5oyiC53N8NFlD0RVPQJ4/WWbXuu0fVS1FrjJ38GYNl21ix0fgdNVmzwIPNjXykP9jGIfkNvu8zDgQIBiMZ9l7ROcrF2Cj0/bJNQTxQpgjIiMEJFI4DrgtQDHZD5h7ROcrF2Cj0/bJGQShYi8AHwAjBORfSJyi6q2AN8CFgCbgX+q6sZAxhmqrH2Ck7VL8AlEm9iggMYYY7oVMmcUxhhjvOPXp55EJBd4FsgGnLim8fujiPwDGOdeLRk4rqpnuLe5E7gFV8eq76jqgp72k56ervn5+Z8qq62tJS4uzqsyf+iv/XpTj6fb9LRed8u7WuZJGwSqTfpz372tJ9jbpDcx9rdQPFY8bau+fDerVq06rMEwZzYwBDjT/T4B2AJM6LDO74Gfud9PANYBUcAIYDsQ1tN+CgsLtaOSkhKvy/yhv/brTT2ebtPTet0t72qZJ20QqDbpz333tp5gbxNP9u0roXiseNpWfflu6Ga+bb9eelLVg+ruHaiq1bhuurR1cBMRAa4BXnAXXQ7MU9VGVd0JbMPVA9EYY4yfBOxmtrsL+lJgkqqedJddADyg7jlfReRh4ENVfc79+QlcXdE/MzqliNwK3AqQlZVVOG/evE8tr6mpIT4+3qsyf+iv/XpTj6fb9LRed8u7WuZJGwSqTfpz372tJ9jbpDcx9rdQPFa6Wr+6uoaYuDhanNDshBPVtQxL8+67mTVr1irtYr7tgPTMFpF44CXge6eShNv1fHI2Ab3oOa2qj+GeL3bq1KlaVFT0qeWlpaV4W+YP/bVfb+rxdJue1utueVfLPGmDQLVJf+67t/UEe5v0Jsb+NlCOlZkzZ1Lf3EpNYwu1ja3UNrZQ19RKbVMLm9esJz97FPXNrdQ1tVLf1EpDcyv1za3s3NNIUloiDc1OGppbaWxppepoGBHRQmPLqTInjS2tNDYLSl27PQvb7ruA8LD+vVjk90QhIhG4ksTfVfXlduXhuIaPLmy3uvUANcYEhKpysqGFE3XNnKhv5nh9E8sPtrDvw92cqG/mZEMz1Q0t7lczJ+tdn2saWzhe20DjgjdxdnfBZu36T32MCncQExmGw9lKcuNJoiLCiIlwEBUeRmKUkJMZT1S4g+iIMKLCHURFhHFw317GjhpBZLiDqHAHu3Zs88l34e+nngR4Atisqg90WHwhUKaq+9qVvQY8LyIPAEOBMcByvwRrjBlUVJWaxhaqqhs5XNPEikMt7PlgF4erGzlc28Sx2iaO1jZxrK6Jo7XNHK9roqWz3/TrXNNARIY7SIwOJyE6goTocBKiw8lKjCY+Kpzjhw8xbmQ+cVHhxEeFERcV7npFhhMTGcam9WuYec5ZxEaFERsZRnR4GA6H6wJK12dvhR0jobS0gqKiMZ98bt7d72cT4P8zinOBG4ANIrLWXfZjVX0TV5fz9pedUNWNIvJPXMMXtwDfVFWbf8AY8ylOp3K4tpEDxxs4cLyeA8frqaxu5NCJBipONrS9r2/u8Otj7UZEIDU2ktS4SFLiIhmZHk9hXiSpcRGkxEaSHBtJUkwESTERbP14LRfOPIekmAiiI8K6jKe09BhFReO6XF6908HwtNj++vF9zq+JQlWX0fl9B1T1xi7K7wPu8/rnvesAAB7QSURBVGFYxpgB4ERdM7uP1vLRwRY2lmxj95Fa9h+vZ/+xeg6caKCpxfmp9SPDHWQnRpOdGM3EoYnMLsgkKzGK9HjXa3f5BuYWnUtqXCRhjk5/LX1G3W4HWYnRvvjxglqoDzNujAkijS2t7D5Sx46qGrZX1bK9sobtVTXsOlLHifrmT1ZcV056fBS5qTFMyknicxOzGZocQ05yDEOTYxiaHE1STASuq92dKz3gICMhyg8/1cBnicIY43dOp7LnaB1lh6opO3SSsoPVlFdUs/tI7aduAA9NimZkRjyXnT6EvNQ4hqfFUrljE1+6+ALiouzXl78MqkEBReQy4LKcnJxvPPfcc59aZs+G930b60fhv3qCvU16E2OrUzlQq+w60crOk052nXCyv8ZJo/t2gQBZscKwBAdD4x0MiXMwJE7IjnMQHf7ZM4JQPFY8bau+fDfd9aPw6xAe/nrZEB6+2caG8PBfPcHeJt1tf/B4vb62dr/e89pGvfLR97Tgrrc07/b5mnf7fJ30s7f1mj+/r3e/+rHOW75b1+45pnWNLd3+DJ7ut7cG0rES6CE87NzNGOM1p1PZVlXDil1HWbnrGCt2HWXfsXoAoiMcTByaxHXTczltWBKnDUtmRFpc22OgZuCwRGGM6ZW9R+tYtu0w/17bwPeXLuRYnesmc3p8FNNHpHDzuSOYlp/K+CEJPnmm3/ifJQpjTLdqGltYcaiFd/69gfe2HWb3EdeQEclRwuyJ2Zw1Mo3p+ankpcV2+5SRGbgsURhjPmP/8XoWb65g0eZKPtx+hKZWJ/FRBzhrZCo3npPP+WPS2btxJbNmnRHoUI0fWKIwxgBQfqiaNzYc5JXl9ex5uxiA/LRYvnZOHmmNB7nl8llEtLuUtG+TnT2ECksUxoSwnYdrmb/uAK+vP8CWihocAqOTHdx5SQFzxmcxKiMOEaG0tPJTScKEFutHYf0ogv6ZfetH4f16nS0/1uDkw4OtvL+/kb01rrOCsSkOpmeHMy07nLDmWjtW+riN9aMYAC/rR+Gbbawfhf/q6e82aWpp1bc2HNSbnlquI+5w9Wkouu9NfWzJdt1/rK7HOu1Y6d021o8CEJFhuEZ7PR/X8N/1wMfAG7hmoHN2s7kxxk8O1Dj51ZubeXn1Pg7XNJGZEMVtM0dx9dRcdn+8gqILRgY6RDMA9DpRiMhTuOa5ng/8FqgEooGxwFzgJyJyh6ou7c9AjTGeaWl1snBTBU+9v4vlO+sJd+xkdkEm107LZebYjLa+DbsDHKcZOLw5o/i9qn7cSfnHwMsiEgkM72xDEckFngWyASfwmKr+UUTuBy4DmoDtwE2qetw9r/ZmoNxdxYeqepsXMRsz6J2oa2beij08+8Fu9h+vZ1hKDNeMjeBHV8+0UVJNn/Q6UXSRJNovbwK6mo+vBfh/qrpaRBKAVSKyEFgI3KmqLSLyW+BO4Hb3NttV1R7WNqYL2yqrefK9Xfx79X7qm1s5a2QqP710AhdNyOLdpUssSZg+8/rxWBHZAHR8ZOoEsBL4paoe6biNqh4EDrrfV4vIZiBHVd9pt9qHwFXexmVMqNiw7wQPrWlg1dtLiQx3cMUZQ7nxnBFMGJoY6NDMINOXfhRvAa3A8+7P17n/PQk8jetSUpfcl5WmAB91WHQz8I92n0eIyBp3vXep6rt9iNmYAW/5zqM8UrKNJVuqiAmHb88ezY3n5JMWb2cOxje87kchIu+p6rmdlYnIBlWd3M228cAS4D5Vfbld+U+AqcCXVFVFJAqIV9UjIlIIvAJMVNWTndR5K3ArQFZWVuG8efM+tdz6UfR9G+tH4b96Oq6vqmw84uT17U2UH3OSEAmfy4tgRloTGcnBPR9FfwvFY2XA9qMA1gEz2n2eDqxzv1/TzXYRwALgBx3KvwZ8AMR2s20pMLWn2KwfhW+2sX4U/qun/fordh7Rq//0vubdPl9n3LdIn3h3R9scDsE4H4WvheKxMiD7Ubh9HXjSfXYAUA18XUTigF93toG4hpZ8Atisqg+0K5+L6+b1TFWta1eeARxV1VYRGQmMAXb0IWZjBoxNB07y+3fKWVxWSXp8FPdePpFrp+USFR4W6NBMiPE6UajqCmCyiCThuoR1vN3if3ax2bnADcAGEVnrLvsx8CAQBSx0D1N86jHYC4B7RaQF1/2Q21T1qLcxGzMQ7Dpcy5/XNfDRgndJiArnR58bx03n5hMbaUOzmcDoy1NPWcCvgKGqeomITADOVtUnutpGVZfhmiK3oze7WP8l4CVvYzRmIDle18QfFm3luQ9340C5beYobrtgFEmxEYEOzYS4vvyJ8jTwFPAT9+ctuJ5W6jJRGGM+q6XVyfPL9/DAwi2crG/m2mnDmRFbxRVzCwIdmjFA3xJFuqr+U0TuBFBXZ7nWforLmJDw7tYqfjF/E1sqajh7ZBo/u2wC44ckUlpaGujQjGnTl0RRKyJpuDvdichZuDrcGWN6sOtwLb98YxOLNlcyPDWWv9xQyMUTsmwqUROU+tKP4kzgIWASrnGeMoCrVHV9/4XX65hsPooB9Gx4V+WDuR9FU6vyxo5m3tjZTLjAF0ZFcFF+BBEO6XT9vsZn/Sj6tx7rR+FdX4pwYCKuZBHRl7r682X9KHyzjfWj6Fs9S8ordebvijXv9vn67edXa8WJ+j7v1/pR+Lce60fhIRH5UheLxooI2q6ntTEGKk428OjaBpa/vZwR6XE8d8sMzhuTHuiwjPGYN/coTo3hlAmcAxS7P8/C1XPaEoUxQKtT+dsHu/jfd7bQ0NzK9y8cy3/NHEl0hHWYMwOLN8OM3wQgIvOBCeoaERYRGQI80r/hGTMwba2o5n9eWs+aPcc5f0w6l2bXcu2FYwIdljFe6ctTT/mnkoRbBa5Z7owJWU0tTv5Uup1HSrYRGxXG/117OleckcOSJUsCHZoxXutLoigVkQXAC7gekb0OKOmXqIwZgNbuPc7tL66nvKKay04fyt2XTSDdhv42g0Bfxnr6loh8Edd4TOCa1vTf/ROWMQNHfVMrDyws54llO8lMiObxr07lwglZgQ7LmH7T634UIiLaw0aerOML1o9iYD0b3lX5QOpHsfVYK49vaKSiTikaFs414yKJjfhsp7m+zkfh7XrWj6J/67F+FJ73nSgFvg0M71AeCcwGngFu7G29/fmyfhS+2cb6UXyivqlFf/H6Rs2/Y76e8+vFumxrlVf19HV960fh33qsH4Xn5uKarvQFERkBHAdiAAfwDvB/qrq2m+2NGdBW7T7Gj/61jh2Ha/nyjOHc+fnxxEfZEOBm8PLm8dgG4FHgURGJANKBev30fBTGDDoNza08sHALj7+7gyFJMfz96zM4d7R1nDODn6MvG6tqs6oe7E2SEJEnRaRSRD5uV3aGiHwoImtFZKWITG+37E4R2SYi5SLyub7Ea4y31u09zqUPLeOxpTu4bvpwFnz/AksSJmQE4nz5aeBh4Nl2Zb8D7lHVt0Tk8+7PRe7JkK7DNZ7UUGCRiIxVVRvO3PhFi1P5/TvlPFq6ncyEKP52y3TOH5MR6LCM8Su/JwpVXSoi+R2LgUT3+yTggPv95cA8VW0EdorINmA68IEfQjUhbvPBk9zzQQN7q7dxVeEwfnrpBJJibLY5E3q8HmYcQETygDGqukhEYoBwVa32YLt8YL6qTnJ/Hg8swDVNqgM4R1V3i8jDuObPfs693hPAW6r6Yid13grcCpCVlVU4b968Ty23R/76vk2oPB7b6lTe3NnMK9uaiQ1Xbp4czZTMvv1NZY/H9p9QPFYG3OOxp17AN4AVwHb35zHAYg+3zQc+bvf5QeBK9/trgEXu948AX2m33hOn1uvuZY/H+mabUHg8dmvFSf3Cw8s07/b5+t9/X6WvLSjul3rt8dj+E4rHSqAfj+3LzexvAucCJ90JZyuuEWW98TU+GXX2X7guLwHsA3LbrTeMTy5LGdNvWp3KY0u38/kHl7H7SC0PXT+FR/7zTBIibcY5Y/pyPt2oqk2npm4UkXDc06J64QAwE1dnvtnAVnf5a8DzIvIArpvZY4DlfYjZmM/YebiWH/1rHSt3H+OiCVnc98VJZCZEBzosY4JGXxLFEhH5MRAjIhcB/w283tNGIvICUASki8g+4G5cl7H+6E42DbjvNajqRhH5J7AJaAG+qfbEk+knTqfy7Ae7+M3bZUSGOXjgmtP54pQcm7famA76kijuAG4BNgD/BbwJPN7TRqp6fReLCrtY/z7gPi9jNKZTu4/U8j8vruejnUcpGpfBb750GtlJdhZhTGf6MnqsE/gr8FcRSQWGuW+IGBO0Wp3K0+/v4v4FZUQ4HPz2yslcMzXXziKM6YbXiUJESoEvuOtYC1SJyBJV/UE/xWZMv9peVcP/vLieVbuPMWtcBr/60mSGJMUEOixjgp7X/ShEZI2qThGRrwO5qnq3iKxX1dP6N8RexWTDjA+gZ8O7Ku/vfhStTmXBrmZe3tZMVBj8Z0Ek5wwN9+gsIlDtEuxt0psY+1soHisDuR/FBmAIrhFjp7nL1ntbX3++rB+Fb7YZiP0oPt5/XC976F3Nu32+fuOZFVpxor5X2weqXYK9TTzZt6+E4rES6H4UfbmZfS+u3tTLVHWFiIzkk8dajQmouqYW/rhoK48v20lKbAQPXT+FS08bYvcijPFCX25m/wtX57hTn3cAV/ZHUMb0RWl5JXe98jH7jtVz3bRc7rikgOTYyECHZcyA1Zeb2dG4Ho+dCLQ9V6iqN/dDXMb0WlV1I7+Yv4nX1h1gZEYc/7j1LGaMTAt0WMYMeH259PQ3oAz4HK7LUF8GNvdHUMb0RqtTef6j3dy/oJyGZiffnTOG/541iqjwsECHZsyg0JdEMVpVrxaRy1X1GRF5Htc9C2P8ZuWuo/zs1Y1sOniSc0alce/lExmdmRDosIwZVPqSKJrd/x4XkUnAIVyjwhrjc5UnG/jNW2W8vGY/Q5KieeQ/z+Tzk7PtZrUxPtCXfhRfB14CTgOeAuKBn6nqn/svvF7HZP0oBtCz4V2Vd/dseItTWbS7hVe2NdHihLkjIrhsZARR4b5JENaPondl/hCKx8qA7UcRzC/rR+GbbQLZj8LpdOob6w/ozN8Va97t8/VrT36kO6pqug+4H1g/it6V+UMoHisDth+FiEThehw2n3aXsFT1Xm/rNKYzW4+18uCf3mf1nuOMy0rgqZumUTQ2wy4zGeMnfblH8SpwAlgFNPZPOMZ8YufhWn73dhlvfdxAZoLy2ysnc1VhLmEOSxDG+FNfEsUwVZ3b241E5EngUqBSP5kz+xfA5YATqARuVNUD7rm1NwPl7s0/VNXb+hCzGQCO1Dv58b838M8Ve4kMd/DF0RHc99UiYiP7Nm+1McY7fTny3heRyaq6oZfbPQ08DDzbrux+Vf0pgIh8B/gZcCohbFfVM/oQpxkgDp6o59GS7Tz/UT0Ox16um57Ld+aMYdOqDy1JGBNAvT76RGQDrilPw4GbRGQHrktPAqj2MHqsqi51nym0LzvZ7mMc3k+pagagipMNPFqyjReW78Wpyvk54fzyy+czLCUWcE1vaIwJHG/+TLu036MAROQ+4Ku47nvMardohIisAU4Cd6nqu77Yv/G/PUfq+NumRt5dVILTqVxVOIxvzhrN9vXL25KEMSbwet2Pwj3G023AaFxDjT+hqi29rCMfmH/qHkWHZXcC0eqa3yIKiFfVIyJSCLwCTOxwBnJqu1txz7WdlZVVOG/evE8tt2fD+75Nfz0bvuN4K2/ubGZVRSsOUc7NcfWFyIh1dFpPoNqkP/dt/Sj6TygdKz2tH7T9KIB/AM/hmif7FeCPXtSRD3zcxbK8bpaVAlN7qt/6Ufhmm748G764uFgXbTqkV//5fc27fb5Ouvtt/c1bm/Xltxb3WE+g2qQ/9239KPrPYD9WBks/igmqOhlARJ4AlntRx6eIyBhVPTWXxRdwDTaIiGQAR1W11T3fxRhgR1/3Z/znRF0zL63ex2PL6jlUu5KhSdHc9R/juW76cOKjwiktPRToEI0xPfAmUZwa4wlVbeltpycReQEoAtJFZB9wN/B5ERmH6/HY3XzyxNMFwL0i0gK0Arep6lEvYjZ+tm7vcZ77cDevrz9AQ7OTkUkO/nDt6fzHaUOICHMEOjxjTC94kyhOF5FT9wgEiHF/PvXUU2J3G6vq9Z0UP9HFui/hGk/KDAD1Lco/VuzhuQ/3sGH/CWIiwvjilBy+PCOPw1vXUDQlJ9AhGmO80OtEoao2yL9p09Lq5N1th3l59X7e3lBHs3MDY7PiuffyiVwxJYfE6AgASm2SXGMGLOvFZHpNVdl44CT/XrOfV9ce4HBNI8mxEZw/LJxvXTqdKbnJNg6TMYOIJQrjEVVlx4lWPnyrjLc/PsiuI3VEhAmzCzL50pnDmDUuk/eXLeXM4SmBDtUY08+8no8iGNl8FP37bLhTla3HnKysaGFVRStHG5QwgfGpYRRmhTEtO5z4SOmxnu6W9XY+Cn+zfhS9K/OHYDxWerveoO9HMRBe1o/C+22qqhv0pVV79dvPr9Yz7lmgebfP1zE/eVNveXqF/uK5d/RYbaNX++7rfBSBYv0oelfmD8FyrPRlvVDoR2EGkcaWVsqPtrLqnXJKy6vYsP8EAOnxkcwqyGR2QSZF4zLdfR5KSY6NDHDExhh/s0QRYhpbWlm/7wQfbj/ChzuPsGr3MRqanThkG2cOT+GHF4+laFwmE4Yk4rB5H4wxWKIY9A7XNLJ2z3FW7znGmj3HWbPXlRhEoCA7keunDye+7iBfv2wmSbERgQ7XGBOELFEMIrWNLWw91squ93ayZu9x1uw5zp6jdQCEO4SCIQlcP304Z41MY8aI1LbLSKWlVZYkjDFdskQxAKkqVdWNlB2qZuOBk2w8cIJNB06y80gtrofYNpGVGMWZw1P4ylnDmTI8hUlDk4iJtL6Sxpjes0QRxJxOpaK6ge2VtWytrGZLRQ1bK6rZUlHNyYZPRnbPSY5h4tBELj8jB+fR3Vz3uXPJToy2Tm/GmH5h/SgC/Gy4U5XjjcqeI3VUaxQVdcqhWicVdUpFnZOm1k/WjYuAnHgHQ+Md5LhfwxMcHvdl6EqwP7Nv/Si8X8/6UfRvPdaPYhC9gqkfRV1ji+6oqtH3tlXpiyv36sPFW/WOl9bpl//6oc78XbGO/vEbmnf7/LbXqDvf0Fn3l+hNTy3Xe17bqM++v1OXba3SipP16nQ6e9zfQHo2vKty60cR/G3iyb59xfpRdF1u/SiCiKpysr6FI7WNHK5poqq6kcrqBiqrG93vG6k82cChkw0cr2v+zPbp8ZHkpMQyKSeJuZOGkJsaw7G9W7m06GyGpcQQbsNwG2OCiCWKdjbsO8HayhaOrt7HsbpmTtQ1cayumeP1zRyrbeJwTSNHa5s4WttEi/Ozl+zCHUJGQhSZCVEMS4lhan4KQ5JiGJIUTXZSdNv76IjP3lQurd9JfnqcP35MY4zplaBKFCLyXeAbuOa2+Kuq/kFEUnFNv5oP7AKuUdVjvtj/d/+xhh1VjbB6nTseSIqJICU2kuTYCIalxHL6sGTS4iNJjYskPT6K1LhIMhOjyEyIJjkmwjqpGWMGnaBJFCIyCVeSmA40AW+LyBvussWq+hsRuQO4A7jdFzHcf9VprF2zhjnnnUVybASJ0faL3xhjguli+HjgQ1WtU9UWYAnwReBy4Bn3Os8AV/gqgMK8VEYlh5GfHkdybKQlCWOMIYgejxWR8cCrwNlAPbAYWAncoKrJ7dY7pqqfmfRARG4FbgXIysoqnDdv3qeW2yN/fd/GHo/1Xz3B3ia9ibG/heKxYo/HtnsBtwCrgaXAn4H/A453WOdYT/UE0+OxngrFR/66KrfHY4O/TTzZt6+E4rES6Mdjg+aMoiMR+RWwD/guUKSqB0VkCFCqquN62LYK2N2hOAk44UFZOnDY68C911ks/qrH0216Wq+75V0t86RdAtUmncXir3qCvU3AjpW+rNfbdvG0rfrSJnmqmtHpkq4ySCBeQKb73+FAGZAC3A/c4S6/A/idl3U/5mFZl1nVxz/7Z2LxVz2ebtPTet0t72qZJ+0SqDYJZLsEe5sEsl1C8VjxtK181SZB89ST20sikgY0A99U1WMi8hvgnyJyC7AHuNrLul/3sCxQ+isWb+rxdJue1utueVfLrF36tr61iX/rCVS79Kat+l3QXnoKFBFZqV3d0DEBYW0SnKxdgo+v2iSYHo8NFo8FOgDzGdYmwcnaJfj4pE3sjMIYY0y37IzCGGNMtyxRGGOM6ZYlCmOMMd2yRNELIjJSRJ4QkRcDHUsoE5E4EXlGRP4qIl8OdDzGxY6P4CMiV7iPk1dF5GJv6wmZRCEiT4pIpYh83KF8roiUi8g29+i0XVLVHap6i28jDU29bJ8vAS+q6jeAL/g92BDSm3ax48M/etkmr7iPkxuBa73dZ8gkCuBpYG77AhEJAx4BLgEmANeLyAQRmSwi8zu8Mv0fckh5Gg/bBxgG7HWv1orxpafxvF2MfzxN79vkLvdyrwRbz2yfUdWlIpLfoXg6sE1VdwCIyDzgclX9NXCpfyMMbb1pH1xjgA0D1hJaf+z4XS/bZZN/owtNvWkTEdkM/AZ4S1VXe7vPUD/IcvjkL1Nw/QLK6WplEUkTkT8DU0TkTl8HZ7psn5eBK0XkTwTX0BKhotN2seMjoLo6Vr4NXAhcJSK3eVt5yJxRdKGzmYm67IGoqkcAr79s02udto+q1gI3+TsY06ardrHjI3C6apMHgQf7Wnmon1HsA3LbfR4GHAhQLOazrH2Ck7VL8PFpm4R6olgBjBGRESISCVwHvBbgmMwnrH2Ck7VL8PFpm4RMohCRF4APgHEisk9EblHX3NzfAhYAm4F/qurGQMYZqqx9gpO1S/AJRJvYoIDGGGO6FTJnFMYYY7xjicIYY0y3LFEYY4zpliUKY4wx3bJEYYwxpluWKIwxxnTLEoUZMESkVUTWtnvlBzqm/iQiU0Tk8T7W8bSIXNXu8/Ui8pO+Rwci8i0RsaFTQlCoj/VkBpZ6VT2jq4UiEu7ueDRQ/Rj4ZcfCPv5cc+mHsX7cngTeA57qp/rMAGFnFGZAE5EbReRfIvI68I677EciskJE1ovIPe3W/Yl7YpdFIvKCiPzQXV4qIlPd79NFZJf7fZiI3N+urv9ylxe5t3lRRMpE5O8iIu5l00TkfRFZJyLLRSRBRN4VkTPaxfGeiJzW4edIAE5T1XXuzz8XkcdE5B3gWRHJd9ez2v06x72eiMjDIrJJRN4AMtvVKcAZwGoRmdnuTGyNe3/dfVdfdZetE5G/AahqHbBLRKb3R9uZgcPOKMxAEiMia93vd6rqF93vz8b1S/aouKZ7HINrfH4BXhORC4BaXOPfTMH1/341sKqH/d0CnFDVaSISBbzn/sWNu56JuAZeew84V0SWA/8ArlXVFSKSCNQDj+OaYex7IjIWiFLV9R32NRX4uENZIXCeqtaLSCxwkao2iMgY4AX3Nl8ExgGTgSxcc0I82S7Gdaqq7qT4TVV9T0TigYZuvqsjwE+Ac1X1sIiktotpJXA+sLyH784MIpYozEDS1aWnhap61P3+YvdrjftzPK5fhgnAv91/FSMingyYdjFwWrtr/knuupqA5aq6z13XWiAfOAEcVNUVAKp60r38X8BPReRHwM24ZijraAhQ1aHsNVWtd7+PAB52n5m0AmPd5RcAL6hqK3BARIrbbT8XeMv9/j3gARH5O/Cyqu5zJ4rOvqvTcU01e9j9cxxtV2clUND512UGK0sUZjCobfdegF+r6l/aryAi36PruUZa+OQybHSHur6tqgs61FUENLYrasV1LEln+1DVOhFZiGsWuGtwnQl0VN9h3/Dpn+v7QAWuX+IOoKH9Ljr7oXAlgSvdMfzGfWnq88CHInIhXX9X3+mmzmh3rCaE2D0KM9gsAG52X15BRHLENd/5UuCLIhLjvj5/WbttduG6zANwVYe6/j8RiXDXNVZE4rrZdxkwVESmuddPEJFTf4w9juum8ooOf6GfshkY3U3dSbjOVpzADUCYu3wpcJ37fsoQYJZ730lAuHsyIURklKpuUNXf4rp8VEDX39Vi4BoRSXOXt7/0NJbPXiIzg5ydUZhBRVXfEZHxwAfu+8s1wFdUdbWI/APXPNu7gXfbbfa/wD9F5Aag/aWbx3FdUlrtvjFcBVzRzb6bRORa4CERicH1l/eFQI2qrhKRk3TxxJCqlolIkogkqGp1J6s8CrwkIlcDJXxytvFvYDawAdgCLHGXXwQsarf990RkFq6zn0245lBu7OK72igi9wFLRKQV16WpG931nAvcgwkpNsy4CUki8nNcv8D/10/7GwqUAgXus4LO1vk+UK2qfepL4a7rceBxVf2wr3W1q3MK8ANVvaG/6jQDg116MsbHROSrwEfAT7pKEm5/4tP3Prymql/vzyThlg78tJ/rNAOAnVEYY4zplp1RGGOM6ZYlCmOMMd2yRGGMMaZbliiMMcZ0yxKFMcaYblmiMMYY063/H5pTV/O1/InwAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "G = (s+2)/(s*(s-2))\n", "control.rlocus(G, np.linspace(0, 20, 1000));\n", "plt.grid();\n", "\n", "plt.figure()\n", "control.bode(G);" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "G = 1/s\n", "control.rlocus(G, np.linspace(0, 2, 1000));\n", "plt.grid();" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "G = 1/(s*(s+2))\n", "control.rlocus(G, np.linspace(0, 2, 1000));\n", "plt.grid();" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "G = (s+2)/(s*(s+1))\n", "#control.rlocus(G, np.linspace(0, 1, 1000));\n", "#plt.grid();" ] } ], "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 }