{ "cells": [ { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A = [[ 0. 0. 1. 0. ]\n", " [ 0. 0. 0. 1. ]\n", " [-100. 100. -1.8 0.9]\n", " [ 100. -100. 0.9 -0.9]]\n", "\n", "B = [[0. 0.]\n", " [0. 0.]\n", " [1. 0.]\n", " [0. 1.]]\n", "\n", "C = [[1. 0. 0. 0.]\n", " [0. 1. 0. 0.]]\n", "\n", "D = [[0. 0.]\n", " [0. 0.]]\n", "\n" ] } ], "source": [ "import matplotlib.pyplot as plt\n", "from scipy import signal\n", "import numpy as np\n", "import control as ctl\n", "import scipy.linalg as la\n", "from control import (TransferFunction, step_response, bode_plot,\n", " impulse_response, series, feedback, rlocus,\n", " margin, nyquist_plot)\n", "\n", "\n", "m1 = 1\n", "m2 = 1\n", "b1 = 0.9\n", "b2 = 0.9\n", "k1 = 0\n", "k2 = 100\n", "\n", "A = np.array([[0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 1.0], [-(k1+k2)/m1, k2/m1, -(b1+b2)/m1, b2/m1 ],[k2/m2, -k2/m2, b2/m2, -b2/m2 ]])\n", "\n", "B = np.array([[0.0, 0.0], [0.0, 0.0], [1/m1, 0.0],[0.0, 1/m2]])\n", "\n", "C = np.array([[1.0, 0.0, 0.0, 0.0],[0.0, 1.0, 0.0, 0.0]])\n", "\n", "D = np.array([[0.0, 0.0],[0.0, 0.0]])\n", "\n", "sys = ctl.ss(A,B,C,D)\n", "print(sys)\n", "\n" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-1.12477103e+00+14.090123j -1.12477103e+00-14.090123j\n", " -5.82980180e-15 +0.j -4.50457945e-01 +0.j ]\n" ] } ], "source": [ "poles_sys= ctl.pole(sys)\n", "print(poles_sys)\n", "\n", "# alternativa\n", "#eigvals, eigvecs = la.eig(A)\n", "#print(eigvals)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-0.45+9.98986987j -0.45-9.98986987j]\n", "[-111.11111111+0.j]\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "A = np.array([[0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 1.0], [-(k1+k2)/m1, k2/m1, -(b1+b2)/m1, b2/m1 ],[k2/m2, -k2/m2, b2/m2, -b2/m2 ]])\n", "\n", "BU1 = np.array([[0.0], [0.0], [1/m1],[0.0]]) # entrada na massa 1\n", "\n", "BU2 = np.array([[0.0], [0.0], [0.0],[1/m2]]) # entrada na massa 2\n", "\n", "CQ1 = np.array([[1.0, 0.0, 0.0, 0.0]]) # saída Q1\n", "\n", "CQ2 = np.array([[0.0, 1.0, 0.0, 0.0]]) # saída Q2\n", "\n", "D0 = np.array([0.0])\n", "\n", "sys_Q1U1 = ctl.ss(A,BU1,CQ1,D0) # colocado\n", "sys_Q1U2 = ctl.ss(A,BU2,CQ1,D0) # não colocado\n", "sys_Q2U1 = ctl.ss(A,BU1,CQ2,D0) # não colocado\n", "sys_Q2U2 = ctl.ss(A,BU2,CQ2,D0) # colocado\n", "\n", "w = np.linspace(0.1, 100, 1001)\n", "\n", "plt.figure()\n", "mag, phase, omega = bode_plot(sys_Q1U1, omega=w, dB=True)\n", "mag, phase, omega = bode_plot(sys_Q1U2, omega=w, dB=True)\n", "plt.legend([\"Q1/U1\", \"Q1/U2\"])\n", "plt.title(\"Bode plot FRFs Q1U1 Q1U2\")\n", "plt.show\n", "\n", "\n", "\n", "zeros_sys= ctl.zero(sys_Q1U1)\n", "print(zeros_sys)\n", "\n", "zeros_sys2= ctl.zero(sys_Q1U2)\n", "print(zeros_sys2)\n" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "image/png": 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nFH2GXsu+ogY8f6weq1b+yJh627m5zQnq52yDtR9D/slSSnJm+G7QvdDtakg6M3nx8xX7uP/DlXRsksQzchd/P/Ecs996jMG3/424aJN4DzcV5jRUdT3whxryxWAw1FISo4UXb+jLrB7NefyztfxzTSH3De/IXb9oT5QWQe4xK5fkjLGCfnT5q+ieKnDx7Jcb6NemHh/+aiAeHcK6V5cwZP873PuvdB7/2VWkNQry3BRDpQjdvbzBYKhzXNa9GbN+dyGXd2/G32dt5trXFrL1WKE1RFWvtXXX6CdgALw5fweZ2QX8YXQ3op0OYqOcdP/lv3HEJnJX1ktc+a/vmbF6v199Q+gxQcNgMASVBokxvHJzP165uS+7j+Uy6uUf+GxF4NRnZnYBr3+/jRHdm5V8jDepCdEjnqUfG7k75QfueX8Fj326hqx8s0NDOIi4oCEiT4rIPhFZ6T1G+ZQ9JiJbRWSTiFweTj8NBkPFXNGrBbN+dxH92tTjdx+u4oWZG/F4Sq9GdoaXZ28h3+Xh9yM6ly3seyukXcCvCifx4MBkPvxxN8P/7zuWHnSVWEPNEHoCBg2xuFVE/uQ9byMioV5o/x+q2sd7fOlttxtwI9AdGAFMEBGTFTMYIpjGybFMvv08bhrQmlfnbuPu95eTX7zSrw/bM3P4YOlubhrQmnaNk8oaEoErX0LcRdyb/zqf3z2YpimxTFhZwM1vLGHVnhM18GkMYO9OYwIwECieYZMNvBoyj/xzFTBFVQtUdQfW0/pmlxiDIcKJiXLw3DU9eWJ0V75ae5CfvbWUk7klh5ZemLmJmCgH9w3v5N9Qw/bWBlMbptMrez6f/2Ywt3aNYdOhbK56dQG/eS+DrYdzQvxpDBLo1k5ElqtqPxFZoap9vbJVqto7JA6JPAncBmQBy4AHVfW4iLwCLFbVd7313gK+UtWPy7ExDhgH0LRp0/QpU6aUKM/JySEpKalKspogWO1WxY5dnUD1Kir3V2anD8LVJ8Fsu7J2Ir1PKuPjkgMu3lhdQJNE4cH0OBrGO1h7xMXflxVwTYdorupQ8VwM8bhIz3iImMJjLOv/D44VxeKMS+TrHUV8vbOIQjekN3Uyul00bVPtD0TUpmvFbl9V9+912LBhGarav0yBevcf8HcASwAnsNx73hhYEUgvgM1vseYElz6uApp623MAzwITvTqvArf62HgLuDZQW+np6VqauXPnVllWEwSr3arYsasTqF5F5f7K7PRBuPokmG1X1k6k94mdtn1ZuPWI9hj/tQ549hv9aNkePe/Zb3XYC3M1r9Blz8ChDarPNFN9a4TOm/3tafGR7Hx94euN2mP813rOIzP0ljcW6/ebD6vH4wlosjZdK3b7qrp/r8AyLec31c7w1MvAZ1j7hD8L/AA8V4XA5RuoLlHVHuUcU1X1kKq6VdWDtc1s8RDUXqC1j5lWgHn2zmCoZQxs35CP7hqIIDz00SoKXG7+dXNf+xP3mnSBK1+G3Qtpu+O/p8UNk2J56PLOLHz0Yh4d2YWNB7MZ+9ZSLnnxOyYt3ElOQem10gxVwc6Che+JSAbWsiECXK2qGwKoVRkRaa6qB7yn13BmlaJpwPsi8iLW0uwdgSrsMGQwGMJNl2YpzHrgQtbty6J7yxRS4qIrZ6DXdbB7EW2WvQWrRkLvG04XJcdFc9dF7bltUBpfrjnApIU7GT9tHS/M3MS1/VoydmAaHZqEZ4jzbKCiBQt9N2I4DHzgW6aqx8pqBYW/iUgfrKVRdwK/AlDVdSLyP2A94ALuVtWyj2EYDIZaQUpcNAPbN6y6gRHPc3zrEupPvdtaliRtcIniuGgnY/q1Yky/Vqzcc4JJC3fywdI9TFq0iwFpDbj+3NaM6tmMhBg7O0QYigm03ati3V20AY5739cDdgNtQ+GQqo6toOxZrDyHwWCo60TFsK77YwzZ+CRMuRnu+BYadSy3ap/W9ehzQx8eH9WVjzL28NGyvTz00SqenLaOK3u3oKPDzUWqZg90G/jNaahqW1VtB8wErlTVRqraELgC+LSmHDQYDAZ/uKKT4JaPrKXv/3sNnNhTYf3GybH8ZmgH5jx4ER+OO5/LujflsxV7eXpxPiNfms/EH3Zw7FRhhTbqOnYS4eeqd4IdgKp+hbV7n8FgMISfBm3h1k8gPwsm/8TaWjcAIsJ57Rry4vV9WPqHS/h5txhiohw8PWM9A579ljsm/ciM1fvLnYhY17EzmHdERJ4A3sUarroVOBpSrwwGg6EytOgDt34Mk6+2jtu+gER7+ZKUuGiGtYnmqaFD2HAgi89X7OPzlfv4dsNhkmOjGNWzOdf0a8mAtAY4HGb4yk7QuAlrs6XPvOffc2Z2uMFgMEQGrQfAzVPgveusO46xn0FSk0qZ6No8ha7NU/j9iC4s2naUT1fsZfrq/Xy4bA8t68VzVZ8WjOnXkg5NkkP0ISIfO4/cHgPuqwFfDAaDoXq0vRBummIlxt8eCT+bBqktK23G6RCGdGzEkI6NeOZqF9+sP8Sny/fx7++2MWHeNnq2TKVHchFds/JpmuJ/qfezkYBBQ0TmYg1LlUBVLw6JRwaDwVAd2g+DWz+F96+Ht0fAz6aW2RGyMiTERHFVn5Zc1aclh7Pzmb7qAJ+t2MsHGwuZ8pfZnNe2AVf2bsGoHs2pn3j2b0lrZ3jqIZ/3ccC1WPMkDAaDITI5ZyD8fBr8dwxMHGklypv1qLbZJslx/HJIW345pC3vz5jD4bhWTFu1nz98tpbxU9cxpGMjftK7BZd2a0pyZScs1hLsDE9llBItEJHvQuSPwWAwBIcWfeEXX1qB4+2RcP1k6y4kWOaTHNw8tBP3De/I+gNZTFu1nxmrDvDA/1YRE+Xg4s5N+EmfFkS5z679PuwMT/nODHcA6UCzkHlkMBgMwaJJV2vS33vXwXs/tdas6ntLUJsQEbq3SKV7i1QeHdGF5btPMH3VfmasPsDX6w4S54SRR1ZyZe/mDOnQmJioiNv7rlLYGZ7ynRnuAnYAvwylUwaDwRA0UlvC7V/B/34GU38DJ/dY+3KEYPa3iJB+Tn3Sz6nPH6/oxuLtR/nP1xnM2XiYz1bso15CNCN7NOPKXi04r11DnLXwEV47QaOrqub7CkQkNkT+GAwGQ/CJS4WbP4Lp98G8v8DRbfCTlyE6PmRNOh3C4A6NKOoRy6AhFzJ/SybTVu1n6sr9fLB0D42SYhjRoxkt3W4u8GitCSB2gsZCoF8p2aJyZAaDwRC5RMXA1ROsJ6nmPgNHt8AN71XpkdzKEhPlYHjXpgzv2pS8QjdzNh7myzUH+DhjL/lFHt7aMJtRPZsxqmdzzk1rENEBpKJVbpsBLYF4EemLNTwFkAIk1IBvBoPBEFxE4KKHoWk3+HQcvD4Ubni3Rl2Ij3EyuldzRvdqTm6hi1c+mccOd33+t2wPkxftonFyLKN6NGN0rxZ4AuysGg4qutO4HGvb1VbAiz7ybODxEPpkMBgMoaXLaCtB/sFN8M5omnX8FTC0xt1IiIliQPMofj80nVMFLuZsPMwXqw8w5UdrCfd6scLV2esY3as56W3qR8QyJn6DhqpOAiaJyLWq+kkN+mQwGAyhp0lXuHMOfHw7XTa9AjNyYcTzEBWelG1ibBRX9m7Blb1bkOMNIJPmrOb9pbt5Z+FOmqXEMbJnM1q43Fzo0bAFkIqGp25V1XeBNBF5oHS5qr5YjprBYDDUHhIawC0fs/udO2izbCLsWw7XT4L6aWF1Kyk2ip/0bkHK8c30HziE2RsOMWP1Ad5bsptCl4eJG+cwsoc1xNW3db0aDSAVDU8lel/NvogGg+HsxRnF9va30WbwdfDZr+E/F8I1/4HOI8PtGWAFkOJlTLLzi/jXp9+xvSiVdxfvYuKCHbRIjWNUz+Y0d9XMRlIVDU/9x/v6VEg9MBgMhkigy2j41XfWfI4PboTB98PFfwRn5GwHmxwXzaAWUTw+tD9Z+UXM3nCIL1YfYPKiXRS6PUzcOJdRPa0kuoYoiW5nRnhj4E4gzbe+qt4eEo8MBoMhXDRoC7/8Br5+FBb8E/b+CNe+BSnNw+1ZGVLiormmbyuu6duKk3lFvPLpPLYVJfPOwp28MX8HDeOEr/sX0Dg5uDkaOyF0KjAf+BYw21gZDIazm+g4uPKf0GYgzLgf/j0YrpoAnUeE2zO/pMZHM7hlNH8Yei4n84r4Zv0hpi1aR6Ok4K+6aydoJKjqI0Fv2WAwGCKZ3jdYix5+cjt8cAMM+BVc+rQVVCKY1PhofpreikbZW0OS37CzctYMERkV9JYNBoMh0mncCe6YDef/Bpb+B964GA5vDLdXYcVO0LgPK3DkiUiWiGSLSFaoHTMYDIaIICoWRvzFWrsq5xC8fhH8+BZE4GztmiBg0FDVZFV1qGq8qqZ4z1NqwjmDwWCIGDpdBr9eCOcMgi8eoPu65yH3WLi9qnECBg0R6VfO0V5EIuc5NIPBYKgJkpvCLZ/AZc/Q8OgymDAQtnwbbq9qFDvDUxOAxcAb3mMxMAXYLCKXhdA3g8FgiDwcDhh0L8v7vQDx9eC9a2HGA1B4Ktye1Qh2gsZOoK+qpqtqOtAHWAtcAvwthL4ZDAZDxJKT3A7GfQcD74FlE+HfQ2DP0nC7FXLsBI0uqrqu+ERV12MFke2hc8tgMBhqAdFxcPmzcNsMcLtg4uUw+2lwFYbbs5BhJ2hsEpHXROQi7zEBa2gqFigKsX8Gg8EQ+aQNgV8vgD43w/z/gzcvhkPrw+1VSLATNG4DtgL3A78DtntlRcCwUDlmMBgMtYq4FLjqVbjxfcg6YD2au+Bl0LNrIY2AT0Cpah7wf96jNDlB98hgMBhqM11GQ6sB1hIk3/yRvimdocd/oXHncHsWFOw8cttRRD4WkfUisr34qAnnDAaDoVaS1NjaRnbMmyTk7od/XwDzX7TyHrUcO8NTbwOvAS6s4ajJwH+r27CIXCci60TEIyL9S5U9JiJbRWSTiFzuIx/hlW0VkUer64PBYDCEDBHodR1LB7wCnS6H2U/BW5fU+lyHnaARr6qzAVHVXar6JHBxENpeC4wBvvcVikg34EagOzACmCAiThFxAq8CI4FuwE3eugaDwRCxFMXUgxv+C9e9Ayf2WJs8ffcCuGvnc0R2ZnXni4gD2CIi9wD7gCbVbVhVNwDlrcJ4FTBFVQuAHSKyFRjgLdta/KiviEzx1q3dYdtgMNQNul8DaRfAV7+Huc/AhqnWkuu1DDt3GvcDCcBvgXRgLPDzEPrUEtjjc77XK/MnNxgMhtpBYiP46UQr35F9CN4YRtqO92vVvA4J1ZaAACLyLdCsnKI/qOpUb515wEOqusx7/iqwSFXf9Z6/BXyJFeAuV9U7vPKxwABVvbecdscB4wCaNm2aPmXKlBLlOTk5JCUlVUlWEwSr3arYsasTqF5F5f7K7PRBuPokmG1X1k6k90llfAw2tflaiSrKpsPWN2l2aB6nElqzqfPdZKV2Dahrt6+q+90MGzYsQ1X7lylQ1XIPYFpFhz+9yh7APKC/z/ljwGM+5zOBgd5jpr96/o709HQtzdy5c6ssqwmC1W5V7NjVCVSvonJ/ZXb6IFx9Esy2K2sn0vvETtuh4my4VlZ9/ILqi91Vx6eoTr9fNe9Ehbp2+6q63w2wTMv5Ta0opzEQazjoA2AJEPwtoMpnGvC+iLwItAA6Aku97XcUkbZYeZUbgZtryCeDwWAICcca9ocr7oK5z8GS12DjlzDqBej2k3C7Vi4V5TSaAY8DPYCXgEuBI6r6nap+V92GReQaEdmLFZy+EJGZAGqtc/U/rAT318DdqupWVRdwD9adxwbgf+qzJpbBYDDUWmKTYMRzcMe3kNgY/jcWptxCbP6RcHtWBr93GqrqxvrR/tq7ztRNwDwReVpV/1XdhlX1M+AzP2XPAs+WI/8SK79hMBgMZx8t02HcXFg8Aeb+hXN1NjQ4Dv1vB4cz3N4BAZ6eEpFYERkDvAvcDbwMfFoTjhkMBkOdxBkNg++D3ywkK6UTfPmQtXruocgYWPF7pyEik7CGpr4CnlLVtTXmlcFgMNR1GrRjda+nGNrgEHz9mDUpcNC9OOT8sLpVUSJ8LHAK6AT81mcSngCqZp9wg8FgCC0i0PtG6HApzOop3joAACAASURBVHoCfvgHA2IbQ8uXoPMoq7yG8Ts8paoOVU32Hik+R7IJGAaDwVCDJDaEa16D277E7YyHKTfDBzfC8Z017oqdGeEGg8FgiATSBrOs/z/g0j/Djvnw6nnw/QvgKqgxF0zQMBgMhlqEOqJg8G/hnh+t1XPnPAOvDaL+sZU10r4JGgaDwVAbSW0J10+GWz4Bj5veq8fDR7+wdg0MISZoGAwGQ22m4yXwm8XsSLsJNn4Br5wLiyYgntBsM2uChsFgMNR2ouPYlXYj3L0Y2pwPMx8jPeN3IbnrMEHDYDAYzhYatINbPoIb3iM3oSUkNQ16E3Y2YTIYDAZDbUEEul7B+kNJNHEE/77A3GkYDAaDwTYmaBgMBoPBNiHduS8SEJFMYFcpcSpw0oasERCOtYnL86Wm7NjVCVSvonJ/ZXb6JVx9Up4vNWUn0vsEzLVSnXqV7Re7fVXdPjlHVRuXkZa3M9PZfgCv25SVu3NVOPyrKTt2dQLVq6jcX5mdfglXn4SzXyK9T8LZL3XxWrHbV6Hqk7o6PDXdpixcBMuXqtixqxOoXkXl/spMv1SvvumTmrUTrn6pTF8FnbN+eKo6iMgyLW9jdUPYMH0SmZh+iTxC1Sd19U7DLq+H2wFDGUyfRCamXyKPkPSJudMwGAwGg23MnYbBYDAYbGOChsFgMBhsY4KGwWAwGGxjgobBYDAYbGOCRhURkXYi8paIfBxuX+oyIpIoIpNE5A0RuSXc/hgszPUReYjI1d7rZKqIXFZVO3UyaIjIRBE5LCJrS8lHiMgmEdkqIo9WZENVt6vqL0Prad2kkv0zBvhYVe8EflLjztYhKtMv5vqoGSrZJ597r5PbgBuq2madDBrAO8AIX4GIOIFXgZFAN+AmEekmIj1FZEapo0nNu1yneAeb/QO0AvZ4q4VmqzJDMe9gv18MNcM7VL5PnvCWV4k6uZ+Gqn4vImmlxAOAraq6HUBEpgBXqepfgCtq1sO6TWX6B9iLFThWUnf/CaoRKtkv62vWu7pJZfpERDYAzwNfqeryqrZpLrIztOTMf6xg/Ri19FdZRBqKyL+BviLyWKidM/jtn0+Ba0XkNSJrTaS6Qrn9Yq6PsOLvWrkXuAT4qYjcVVXjdfJOww9SjszvdHlVPQpU+Ys3VJpy+0dVTwG/qGlnDKfx1y/m+ggf/vrkZeDl6ho3dxpn2Au09jlvBewPky+Gspj+iUxMv0QeIe0TEzTO8CPQUUTaikgMcCMwLcw+Gc5g+icyMf0SeYS0T+pk0BCRD4BFQGcR2Ssiv1RVF3APMBPYAPxPVdeF08+6iumfyMT0S+QRjj4xq9waDAaDwTZnfSK8UaNGmpaWVkJ26tQpEhMTqySrCYLVblXs2NUJVK+icn9ldvogXH0SzLYrayfS+6QyPgabunit2O2r6n43GRkZR7ScPcJrXdAQkRHAS4ATeFNVn/dT70rgypYtW/L3v/+9RFlOTg5JSUlVktUEwWq3Knbs6gSqV1G5vzI7fRCuPglm25W1E+l9Uhkfg01dvFbs9lV1v5thw4btKrcgFBuPh+rAChTbgHZADLAK6FaRTnp6upZm7ty5VZbVBMFqtyp27OoEqldRub8yO30Qrj4JZtuVtRPpfWKn7VBRF68Vu31V3e8GWKbl/KbWtjuNGpt9um/7BnIyd7Nr00rE56lnKXFy5jkC8T4aLQ7fR6R9yksa8X3xvj9TN/fEYQ7u2VpCz7fc15b4PpJdom0hP/s4Rw/tLV+vHHsiQsGpLE4ePVTis1FCz3pflH+K7JPHyrHrLS/IJTfnZLltuQrzyc/NKWPX5SqksCC/hMztKqKosOC0XY/bhdvl8tsugDjq5PMdBkONUNuCRnkzHc8LRUNF717HFZ49EIbnQEaBtShGNRkBkFE5ncvBemAvAJcCLA5Qvqj8sksAFvqR/1BSNryU7GKA+RX75lHBg6Dew4PgwXH6vYrDW+44Xc/jDfDF9XzrqFivbTzK9u+jTpcDqHjr4zj93i1O3BKFR6LxSBQeRzTqiEId1ntXXiEL172HOmLAGQWOaHDGgDMajU6A2CSi4qwjOi6ZYwf2sn1LY+KTUklIbkRKYmzJf0IMhhqkVj09JSLXAZer6h3e87HAAFW9t1S9ccA4gKZNm6ZPmTKlhB0744Qnty+hKDeL6Ch/cVXLvvf5LsXPZPLi71vK0/dSVOQiOjrKx56v3RLGfCyUreMqKiLqtP9++rmUPy6Xy0enZBu+Ns7U82nXp67L7SLK6SzdGABulxun0/cuzcLtduE8reNb94yd4jr+vl9Rj6Wr1k/5mdcz4aFYVuK9txwU8Sm3PpO3zOPGIZwJR1ochjhdV/DgxI1T3UTh8r53EYWLKNw4cROt1vsoXETjwin2r0GXOjhGCscklZNSj2xnfbLiWpCf1IbChBa0atWGKEf5AcXkNM4gIiQmJp7+21LVSgdiuzqB6lVUXl6Zv/ql5Xb9c7vdnDp1itKxYNiwYRmq2r/chmrLAQwEZvqcPwY8VpGOyWmERsfkNIJox+1WV0Ge5mUf0+zMPXpk13rdu36xbls2SzfO/1RnvPG0rpj2imZ8+Jwuf/sBXfnqWF33wgjd9mx/PfJkmur4lNPHrj911G9f/IUuXvyDut0e2/7XtZzG9u3bNTMzUz0e6zvKysqqtA27OoHqVVReXpm/+qXldvzzeDyamZmp27dvL1PGWZLTOD3TEdiHNdPx5vC6ZDBUE4cDZ0wczpg4SKpP6f+bD7jq02foUL/q7tzjZG5fzbrvP6NF/mYuPDmV6K8+YcHswbS4+VXaprUNqfu1kfz8fNLS0ur8MJ+I0LBhQzIzM23r1KqMoZrZpwZDGZwJ9WnW4yKc3a6m6wNfog9sZF3ne0gv/JG4t4ezYcOacLsYkdT1gFFMZb+HWpXTqAw+8zTufPfdd0uUna3jtMGwE+lzAsw8Dfv13Ee2cO7a8RykIdsHvYirsMDkNLykpqbSoUOH0+dud8ncmR3s6gSqV1F5eWX+6peWV+Yzbd26lZMnT5aQnRU5jaocJqcRGh2T06g5O9Xpk63zP1Qdn6KzJ/7J5DR8WL9+fYnzcOU09uzZo6NGjdIOHTpo27Zt9e6779b8/HydNWuW9uvXT7t166b9+vXT2bNnl7D33HPP6bvvvqs///nP9aOPPirRTmJioqqq/vDDD3r++edrt27dtGfPnjplyhS/fpT+PlT95zRq1fCUwWCoHO2HXM/muF502vUBLrfZDTeSUFXGjBnDFVdcwZYtW9iyZQt5eXn8/ve/p1GjRkyfPp3FixczadIkxo4dW0J31qxZXHbZZRXaj4+PZ/Lkyaxbt46vv/6a+++/nxMnTlTbbzM8VUlZTWCGp/zLzPBU5evlb53LiL3/5L1mf6BllwGV0j1br5VIGJ6aN28ezz//PF988cXp8qysLHr06MH69etJSkrC7XbjcDhIS0tj8+bNxMbGcvz4ca6//nq++eYb7rrrLkaMGMHVV199up3mzZtz4MCBMu0OGjSIyZMnl/jcxVRmeCpin54SkYeAF4DGqnpERIYCU4Ed3iqfqurT/vRVdTowvX///ncOLfXkybx586iqrCYIVrtVsWNXJ1C9isr9ldnpg3D1STDbrqyd6vZJfv/euF94idTsTQwd+vtK6Z6t18qGDRtITk4G4Knp61iz53hQg0a3FimMv7I7ANnZ2afb8mXHjh0MGDAAp9N5ujw5OZm0tDQOHTpE8+bNyc7OZubMmfTr149GjRoBMG3aNC677DKSk5OJjo4mPj6e5OTkEu2UPl+6dCkul4vevXvjKGfFhLi4OPr27Wvrc0dk0BCR1liTineXKpqvqleEwSWDodYSl1Sf7dHtaJm7IdyuGHzQCibpFbNhwwYeeeQRZs2adVr27bffMm7cOKD8J59Kyw4cOMDYsWOZNGlSuQGjskRk0AD+Afwe687CYDBUk2ON0ul+4HMKCguIjYkNtzsRxfgru/u9G6iIquj40r17dz755JMSsqysLA4dOkTnzp3Zu3cvN998M5MnT6Z9+/an62RkZDBggDXM2LBhQ44fP3667NixY6fvSIrtjR49mmeeeYbzzz+/yr76EnE5DRH5CTBcVe8TkZ1Af5/hqU+w1pvaDzykfuZoBGMZEX+ymsDkNPzLTE6javVy1n/NFYdfY3qv/5DcoJlt3bP1WomEnIaqMnToUMaNG8ctt9yC2+3m/vvvp02bNtx5552MGjWKhx9+mGuuuea0zoYNG3j++eeZNGkSAF999RWvvfYaH3/8MU6nk9dee43169czYcIE8vLyuP766xkxYgR33313hT5G/CO3wLfA2nKOq4AlQKq33k6gkfd9CpDkfT8K2GKnLfPIbWh0zCO3NWcnGH2yceEM1fEpumLe55XSPVuvlUh55Hb37t06cuRI7dChg6ampuq4ceNUVfXPf/6zJiQkaM+ePbV3797au3dvPXTokL7wwgv62muvlbDx5JNPao8ePbRnz546ZswYPXz4sKqqvv766xoVFXVav3fv3rpixYpy/ajMI7dhGZ5S1UvKk4tIT6AtsMo7LtcKWC4iA1T1oI/+lyIyQUQaqeqRGnHaYKjFNGzVEYC8w9vC7InBl9atW/Phhx+SnJzMwoULuemmm8jIyOCJJ57giSeeKDMENnPmTCZMmFDCxvjx4xk/fnyZujfeeCN33nln0H2OqJyGqq4BmhSflxqeagYcUlUVkQFYS6AcDY+nBkPtomGLthSpE8+xHYErG8LCoEGD2LWr/M3yivnmm2/Izs6uIY/KJ+JyGr6UChr3AL8GXEAe8ICqlrMrw2ldM0/D5DSCSm3OaQC0nzeOXdHtcA1+1Lbu2XqtREJOw065WUbELCNiC5PT8C8zOY2q11vx9CDd8OcBldI9W6+VSMlpBCoP9dLoxQQtpyEirbCWH78AaIH1H/5a4AvgK1X12ApjBoMh7Jxy1qNx4ZZwu2Go5fgNGiLyNtb2qjOAvwKHgTigE9ZOon8QkUdV9fuacNRgMFSP/OhU6hec8DupzGCwg9+choj0UNW1fhVFYoA2qro1VM5VB5PTMDmNYFPbcxrZGR9wZfYUvj7/A+LiEmzpnq3XislplKRW5zSA3sAiYA0wHUjxKXsM2Apswtor3OQ0gmzH5DT8U9tzGtMmPKY6PkV3bF5jW/dsvVYiJacRyqXRs7Ky9PLLL9fU1FQdPXp0hT4GdWl0EVkjIqtLHfNF5B8i0tBWGKscbwKPqmpP4DPgYa8f3bDyK92xhscmiEjl/jUwGOoycfUByDm6P8yOGCD0S6MDPPzww/z3v/8Nqt92Vq/6CivxfYv3mA58DxwE3gmqNxadvfYBvgGu9b6/CpiiqgWqugPrjqP8dZ4NBkMZJMEKGvnHIy9o5Ba6uG/KCn75zo8czsoPtzs1wpw5c4iLi+PWW28FwOl08o9//IPJkyfTsWNHWrRoAVhrVOXn51NQUABY60kVFhbSuHHjgG0MHz68WutjlYedyX2DVXWwz/kaEVmgqoNF5NagemOxFvgJ1mKF1wGtvfKWwGKfenu9sjKUWnuKefPmlSjPycmpsqwmCFa7VbFjVydQvYrK/ZXZ6YNw9Ukw266snWD1iQtrocJ9W9eSY/NvvaaulYlrC5i/14VDYOxrc3l0QJytZH1V201NTT09SS527njiD63DVclnA+IVvzqeJt0pGPYUYOUWypuQl5GRQc+ePUuUiwht2rRh1apV9OrVC7fbzbvvvkuvXr0oLCyksLCQOXPmMGTIELKzsykqKiIvL4/s7OwSdnzPc3NzcblcFU4KzM/Pt/092gkaSSJynqou8X6oAUBx5sllq5VSiMi3QNlV0+APwO3AyyLyJ2AaUFisVk79crP4qvo68DpA//791eynEXwds59GzdkJVp/Mnf0NAI3jlUE2/9Zr4lo5lJXPom/m8LOB59C+SRJ/mrqOuDa9GNg+8Oh3MPbTIDoGl0CUs3ILZLjcLv860THEeO37Ww03NjaW2NjYEvtpgBU4EhMTSU5OZunSpTz55JPMmjXrdJ05c+Ywbtw4kpOTiYmJKbOfhoiUOE9ISCAqKqrCO45g76dxBzBRRIoDRTZwh4gkAn+x1Uop1M/aUz5cBiAinYDRXtleztx1gLUuVeTdZxsMEYo4ozlBMo7czHC7UoJZ6w9R5FbGDkyjVf14Xvh6E58u32sraASFkc+TV4Vlzqui40tNLI0eCgLmNFT1R29Sug/QV1V7qepSVT2lqv8LtkMi0sT76gCeAP7tLZoG3CgisSLSFugILA12+wbD2cxJR32i8yNrybZF247QIjWO9o0TiYt2cmm3pt5AcnbPHR4+fDi5ubm8//77gDWM9eCDD3LPPfdQUFDA6NGjefLJJxk8+Ex2YN26dXTs2PH0o7RDhw7lww8/pLDQGpB55513GDZsWEj9Drj2lIg0BZ4DWqjqSO9TTANV9a2QOCRyH1C8+PunwGPex78QkeLhKxdwv6p+VYEdM0/DzNMIKrV9nkZOTg6tlz+HU4s4ctELtnRDfa14VLlvTi69GkdxZy8r57LisIuXlhfwUP9YejSqeDCkts/T2Lt3Lw888ACbN2/m6NGjjBkzhpdeeom//e1vvPjii7Rr1+50bufzzz/ngw8+oH79+iWepvrLX/7C1KlTcTgctGvXjn/+8580atQIt9vNqFGj2Lx5M6dOnaJBgwa88sorXHJJ2YGeoM7TwHp66npglfc8ClgTSC9SDjNPIzQ6Zp5GzdkJZp9k/N/VuufJTrZ1Q32trN9/Us95ZIZ+tGzPaVlugUs7/eFLfXLa2oD6tX2ehm/5ggULtE2bNrps2TK/updccolu3rzZVjuhWnvKziO3jdQahvJ4g4wLcNvQMxgMEYYrvjH1PCeK/yEMO4u2WUNlvvmL+Bgng9o3ZO7Gw+FyKywUL42enp7ut84333xDs2blPUNUc9gJGqe8k/iKh4jOB05WrGIwGCKSxMYkST7ZOVnh9gSAhduOck7DBFrWiy8hv7hLE3YezWV7Zk6YPDP4w05Oox/wL6AH1hyKxsBPVXV16N2rOianYXIaweZsyGmw+weuOPwa03q+RkrDFgF1Q3mteFS5e3YuA5pF8YsesSXKMnM9PPx9Hjd1ieHytOgKP1NVcxrt27c/nS+oy2tPqSrbtm0L7tpTWHmM7liBI9qOTgB71wHrsIa8+vvIBwArvccq4Bqfsp1Y61GtxM9YW3mHyWmERsfkNGrOTjD7ZOOCqarjU3T5d1Nt6YbyWlm157ie88gM/XzF3nLLL/m/eXrLG4srtFHVPtm+fbtmZmaqx+NR1cjIadgtC+Z+Gh6PRzMzM3X79u1lyvz9zla0NPoYP0WdRARV/TRgCPPPWmAM8J9y5P1V1SUizbH2Cp+uVh4FYJiaPcENhirTOK07ALn7N2ItvBA+FpaTz/Dl4i5NmLhgBzkFLpJig7szdatWrdi7dy+Zmdaclfz8fOLi4iplw65OoHoVlZdX5q9+abld/+Li4mjVqlXAesVU1BNXel+bAIOAOd7zYcA8rMdhq4SqbgDKLBOgqrk+p3H4mfFtMBiqRv1maeQRgx4J/44GC7cdpUOTJJokl//DNrRzE/7z/XZ+2HKEET2Cm/yNjo6mbdu2p8/nzZtne0Z0ZXUC1auovLwyf/VLy6vymexgJ6cxA7hTVQ94z5sDr6qqvzsR+42LzAMeUtVlPrLzgInAOcBYVf3MK98BHMcKJP9Ra6kQf3Z9155KnzJlSolyk9Oovo7JadScnWD3SavvfssxaUDuhU8G1A3VtZLvUu6Zk8vFraO4uWtsuXVcHuXeObmc2yyK23uUX6cuXit2+6q630115mmsLXXuKC3zo/ct1nBT6eMqnzrz8MlplNLvijXjO8573sL72gQr33FhIB/U5DRCpmNyGjVnJ9h9suL/rtZ949ur2+0JqBuqa+WrNQf0nEdm6MKtRyqs95t3MzT9z99ooctt27+qUJuuFbt9Vd3vhmrM05gnIjNF5DYR+TnWMulzAymp6iWq2qOcY6qNNouHsE5hJd9R1f3e18NY+2yYZdENhiqgrc6lBZls27ohbD58s/4QqfHR9E+rX2G9n6a34khOAV+uOVBDnhkCYWftqXuw1n/qjbX+1Ouqem8onBGRtiIS5X1/DtbeGjtFJFFEkr3yRKwFDf1uRWswGPzTst8IAPavmBmW9nMKXHy99gCXdWtKtLPin6CLOjWmXaNE3py/I2ImJNZ1KtojXDRAL9mp40fvGqy5H42BE8BKVb1cRMYCjwJFWI/jPq2qn4tIO6y7C7CS9++r6rMB2jDzNGrROK0/uclphKBPVOn23e1sl9bkXfgUIlKjOY2ZO4v4YGMhfzw/jvb1As8jmL+3iLfWFnJHzxiGtCw5Z6MuXisRm9PAyjfcC7QpJY8BLgYmAbf504+Uw+Q0QqNjcho1ZycUfbL63UdVx6foosU/VKgb7Gvl+KkC7ff0LL3p9UWn50gEwu326DWv/qC9n5qpO4/kVKndQNSmayWScxojsNaY+kBE9ovIeu8TTFuAm4B/qOo7VQ5jBoMhbHS64n6ySSTu6wc5eMz/jm7BxOX28NBHqzmZV8Tjo7ra2pkPwOEQXry+DwA/m7jULC0SZvwGDVXNV9UJam31eg4wHGs/jXNU9U5VXVljXhoMhqASm9qUE8Oeo49uYMu/rmLLodAuYngyr4h73l/BtxsO8cTorvRomVop/bRGiUy87Vyy811c9eoCJi/aiess328jUgk4TyNkDYtcBzyJ9WjtAPXO1RCRaOBNoB9W/mKyqv7FWzYCeAlwAm+q6vMV2Dc5jVo0TutPbnIaoe2TuO1fkr77TY5rMh9HXcmx5hfRtmlDmicJDj+5jspcK4dzPSw+4OLbXUXkFMENnSteSyoQmbkeJq4tYMMxD/VihQGNPZzbMp62qQ6iHJXc5NuG/8HQOdtyGuEMGl2xkt3/wWeCn4jcDPxEVW8UkQRgPTAU2ANsBi7F2vr1R+AmVV1fUTv9+/fXZcuWlZCZPcKrr2P2CK85O6Huk4JdP7Lvg/tol78OtwrLtSMr6czhlJ4c1IY0bJ9Oo3pJJMVGkRAbxc4tm0jv0xMAj4Lbo6xeu5bW7TpxPLeQozmFbMvMYfPBbPafzAdgaOfGPHBpJ3q1qmf7c/tDVZm3KZPJi3Yyb1MmCsRFO+jUNJnOTZNJa5RI89Q4mqXG0SwljnoJMSTHRVX4pFZtulbsXj/V/XsVkXKDRnAXdKkE6mcpEawZ34neR2/jgUIgC2texlZV3e7VmwJchRVUDAZDFYk951x2n/8c7bo1JWfZh7TfMpt+J77CmTMdANdqB3s8jdmpzditTSjQJny45gd2a1P2aGNO4V3WfOUawPoBb9soiXPbNqBP63pc3KUJ5zRMDJq/IsKwLk0Y1qUJX3wzF0ezLvy48zibDmUxd9NhjmQUlqsXH+0kJT6KlLhoEmKcxEY7iY1yEBvlJOt4PtMPryI22kFclJOYKOvOxekQ69XpfXWckW/bU0Tmsj1EOUvKHSI4BBwiILA204VzSyYOEcTrv0POvG497iZl9/HTeoIgXv092R42Hcz21rd0Dp7ysPPIKcueVw5wNM/D/hN5lgzheL4HVbWdO7KLraDhnTPRUVW/FZF4IEpVQ5U9+xgrGBwAEoDfqeoxEWmJdbdRzF7gvBD5YDDUPZp0JXXUk8CTUJQPh9ax4YfpdG0SRZvMLbQ+ug3HiSU4CkvuxeGKa8hxZ0MSW3UnumE7ohu1hfpJUL8RpLQEh505xFUjMVoY2rM5I3s2Py3LLXRx8GQ+B0/mcyg7n5O5RWTlu8jKKyI738XJvCLyitzkF7nJzndxxFXI8SwP+/KPUuByk1/kodDlweXx4Ak0ELPO5g4RGUsrLl+y0H/Zgu/LyubPK7/ud3NKnI4c7iEuunJLvgfCztpTd2Kt49RAVduLSEfg36o6PKBxkW+B8lYa+4N6Z4aXXn9KRAYDvwFuA+oD84GRQDpwuare4a03FisXUmaioVl7qup2TE7DP2djTiNQWXnyghOHaOjMJj7vEHH5B4nPO0R0zj6Sio4Ql38Y4UyC2uVM5GRqF06mduNIowHkJrYJ+DkqQ6j7RFWtITil1KuSnZNLXHxCGbmqNVyiao2/5+bmER8fj8dH7vuam5dHXFycnzJrpdpiWyjk5ecTE2utxVVsEyA/v4DY2Ngz5wUFXNY+0brjqQLVWXtqJdbcjBU+sqDtEU6p9aeAV7EWKiw+n4i1R/lAYKaP/DHgsUD2zTyN0OiYeRo1ZyfS+6SEzFWkemyH6ra5qj9OVJ32W9VXBqiOT7GOf52ruug11YKcMjaqQl28VsI9T8PO8FSBqhYWj4t5cw2hzJ7vBi4WkXexhqfOB/6JlbvoKCJtgX3AjcDNIfTDYDBUFmcU1E+zjnZDz8izD8KG6bD6Q/j6Efj+b3DZM9D7pjOD8oZagZ3Bxu9E5HEgXkQuBT4Cple3YRG5RkT2Yt1BfCEixQvhvAokYa0t9SPwtqquVmsjpnuAmcAG4H+quq66fhgMhhoguRkMuBPu+BZunwkNO8Dnv4ZP7rDyJ4Zag52chgP4JdYigYL1o/2mBlIMM2aehslpBBuT06icrELUQ5vdn9Jux385Xq8Xq3v9CXVUfv5GXbxWwj1Po7L5hwZAr8rohPswOY3Q6JicRs3ZifQ+sdO2X5a/a+U6pt1XJfW6eK2EO6cRcHhKROaJSIqINMBKir8tIi9WOXwZDAZDMX1vgUH3QsbbsOXbcHtjsIGdnEaqqmYBY7DyC+nAJaF1y2Aw1BmGPQEN2sM3fwSPO9zeGAJgJ6exBiufMQlrfsWPIrJaVXtVuVGRF4ArsWZ7bwN+oaonvIn257Ee8S0EHlbVOV6deUBzIM9r5jK1dvHz14bJadSicVp/cpPTiPw+49tSqQAAEptJREFUqYyP/mh8+Ae6r3+Bdd0eIrPJBbb16uK1EvE5DeA6YDUwwXveDvgkkF4Am5dhzSoH+CvwV+/7vpzZC7wHsM9HZx5+9hOv6DA5jdDomJxGzdmJ9D6x03ZA3G7Vf/ZSnTiqUmp18VqJ+JyGqn6kqr1U9Tfe8+2qem2Vw5dlY5Zaj9ACLAZaeeUr1LsXOLAOiBOR2Oq0ZTAYagEOB/T7Gez6AY5sDbc3hgqwkwiPE5G7RWSCiEwsPoLow+3AV+XIr8WahV7gI3tbRFaKyB8l2KtwGQyG8NL7Jut1w7Tw+mGoEDs5jY+AjVizr58GbgE2qOp9AfTsrDv1B6A/MEZ9HBGR7sA0rLzFNq+sparuE5Fk4BPgXVWd7Kdts/ZUFe1E+vi5yWlUvV4k5zSK6ZfxICpOVvT7m636dfFaqQ05jRXe19Xe12hgTiA9G3Z/DiwCEkrJW2HtmzG4At3bgFfstGNyGqHRMTmNmrMT6X1ip23bzPur6vhU1ezDtqrXxWsl4nMaQJH39YSI9ABSgbSqxS4L7w58j2BttpTrI68HfIG1EOECH3mUiDTyvo8GrsBaZsRgMJxNtBsGKOxaELCqITzYCRqvi0h94I9YQ0brAXv3jv55BUgGvvHmKP7tld8DdAD+6JWvFJEmQCwwU0RWY00w3Ae8UU0fDAZDpNG8N0QnwK4K9pcwhJWwbfcaasw8jdo1TutPbnIakd8nlfHRDr1X/pEoVzYZ/f8ZsG5dvFZqQ04jFisJ/jjwp+IjkF6kHCanERodk9OoOTuR3id22q4Uc5+38hq5xwNXrYPXSm3IaUzF2n7VBZzyOQwGgyH4nDMQUNizJNyeGMrBziO3a1W1Rw35EzTM8FTtuuX2JzfDU5HfJ5Xx0Q4Odz4XzL+J3W3GsKPd2Arr1sVrpTYMT70O9AxUrzIH8ALW3I/VwGdAPa/8FqxEd/HhAfp4y9L/v70zD7K7qvL455tOL1k6CQkSsilrQsCwGQKKQEeWySgMoFHAGRCBGXEUCyysERlLGIcSlbKKyIhgwIgiwyIgYCFhmSZMICYhBgKEJUCALGOHBLqzdTrdfeaPezv98tKv+9ev39b9zqfqV/1793fvuee9U/edd+/pey6wAlgFzCE6vJ4uX57KTxtfniqcnFK3SZK+e80tJ5n9+nM9VivHsVKyy1OSVsT/Vvo0sEzSa5JeTCnvC48DH7eQ9PB1wnnfmNmdZnakmR0JnA+sNrPlsc3NhA17B8drVh91cBynVJl0LKxZCm07e67rFJTuzgg/PV+dmtn8lJeLgNldVDsPuAtA0jhghJk9F1/fAZxF1+lHHMfp70w6Fv7yS/i/FTDh6GJr46SQMaYhqQa4lLBvYgVwm3UmGcydAtLDwN1m9ru08jeBM83sJUnTgevN7JT47ATg38ysS8fmaUSyl1Pq6+ce08i+Xn+JaQBUN7/PJxddzBsHXcLaiWdkrFeOY6VkYxrA3cDvgK8BDwI3Zqqbof0ThF3b6deZKXWuJsQ0lNb2WGBFyutjgCdSXp8APJxED49p5KeNxzQKJ6fUbZKk76z42WFm93yl2yrlOFaKHdPobnnqUDObBiDpNmBxb7yUxVlBJiR9hbAEdnJUMJVziUtTkTXE9OmRicA6HMcZuEyaAe88B2bgSa1Lhu72aeyKQFmOl6Uy5Z6KzwYRDn7ataZkZuuBzZKOiynRLyDsH3EcZ6Ay6TjYvA4a1xRbEyeF7mIabXRu4hMwBNgW783MRmTdqbSKsNN8YyxaZGaXxmd1hPjFcWltpgPzoh6PApd1MUNJre/7NPrROm2mco9plL5NeqNjbxi++U2mP/9tXpl6BQ1j67qsU45jpWRjGgPl8phGftp4TKNwckrdJkn6zoq2VrMfH2B270UZq5TjWCl2TCNJGhHHcZzCM6gCpsyCN+ZDa0uxtXEi7jQcxyldpnwOdjTB6meKrYkT8dTovSwrBOW4Tpup3GMapW+T3ujYWwa17eBTz36VjWOOZuWhVybSLxv601gpy5gG8ENC3qnlwHxgfCw/hHAE7A7gyrQ2qwmbDJeTYa2tq8tjGvlp4zGNwskpdZsk6btPPHqV2bWjzRrX5a3f/jRWyjWm8VMzO9xCjqlHCGd0AGwCvgXckKHdTAu5qfb0fo7jDExmXALtbfDsnGJr4lCkmIaZNaW8HAZYLG8wsyWk7BFxHKfMGX0AHH0BLL4VGlYWW5v+wfYPqG16Iy+iixbTkHQdYZNeI2EGsSHl2TXAFjO7IaXsbeADgoO5xcxu7Ua2557KUk6pr597TCP7ev0xptFBZUsjMxZ/gx3Vo1l29E9or6jJab/9aax0lKm9jZrmBoZsX8vQbeuobHqbkS0NDN32HlU7GzHEMyfcTXtFda/eVwcFj2mQIPdUrHcVcG1a2TXsGdPoiHvsA7wAnJhED49p5KeNxzQKJ6fUbZKk75yw6kmza0aZ3f5Zs+amnPZbsmPlqafMGteavfW02ZLbzP78Pdsw52SzOZ8IcZ4fjNh1tfxwvNncU80e/Fez/73RXrz3J2Y7m5O/oTTIIvdUn7Aeck+l8HvgT8APepC3Lv5tkPQAMANY0CclHcfpPxz4Gfj8r+D+f4Fb6+Csm4utUU4Y1NYclt0+fBc+eAc+jNcHqzmh4Q14urmz8uAaaqrHwkePgKlnwJiDYMyBMPpAFi55ibqZM3dV3VhfD4Ozm2V0R96cRndIOtjMOhbc/oFwil939YcBg8xsc7w/DfiPPKvpOE6pMW02DB8LD34dbjuVj485Bia2wv4nQUVlsbXbk7adVDdvCAdKNa2DzevD3w/fjc7hXU7cugFSt6EMHgKjPgp7fYx1g/dj0hF10TkcBLXjWbpgAXV1dXv2VaCkjkWJaUj6AzCFcJzrO8ClZrZW0r7AUmBEfLYFOBTYm5BCHYKj+72ZXddDH75Pox+t02Yq95hG6dukNzrmiorWbUxc8wgT3vsjVW1baKkcwYejptE04hC2DN+fbUPH01K1FyjZ//ok1t+MirZmKnc2sbPpb4wc3ErlzqbdrqqWTVTv2ERVyyaqWj5E7P4d267BNNd8hOaasTTX7EPjoFHYiEk014xl+5Cx7KwcucsBlOI+jQG7ua+D6dOn29KlS3crq6+v38NTJy0rBLnqNxs5Sdv0VK+755meJbFBsWySy757K6fUbdIbHXPNgifnc+L4Flj5UEij3vhu58PBQ2D4PjB0NAwdAzWjwnJNRSVUVIULoL2Vte+9w4RxY6GtFdpbYedW2LEFWrZAS8f95vC3PcM/d6oi9DV8X6jdF0aMg9rxvLa+iSnT66B2XLiGjoFBnc6st3ZJaqu+2kRSl06jKMtTjuM4uaC9ogqmngZTTw8FTethw6uw6a1wbWmA7Ztg26bwum0ntLWEq7Ul/KIfVMFH2gyahsCgwSHnVeUwqB4OVcPCclh1LVQND2VD9oKhY1jx5jqmHVsXnMDQ0VA9cjdn0MH6+nqmTK4r6OeST9xpOI4zcBgxLlwHzuy5bgrPZvGrfGNjfTgoqswYsMtTHtPwmEau8ZhG78oKQTmOlWLHNIp2zgUZ8k/FZ3Wx/GXg6ZTyWcBrwCrgu0n68X0a+Wnj+zQKJ6fUbZKk73xRjmOlXHNPQYb8U5JGAb8gHAV7GOHoVyRVAP8F/D3hP6rOk3RoUTR3HMcpU4rmNCxD/ingy8D9ZvZurNcQy2cAq8zsLTNrIZwhfmah9HUcx3GKHAhPzz8ViycDlZLqgVrgRjO7A5gAvJfSfA1wbAa5u3JPAVskvZZWZWTss6eyvYH3k76fHNKVLoWSk7RNT/W6e57pWRK7FMsmXelSKDmlbhPwsdKXer21S1Jb9dUmH+uytKs1q1xdZJF/CrgJWESYfewNvEFwJF8E5qa0OR/4eZZ63ZqwLPG5HTn+3PbQpVBykrbpqV53zzM9S2KXYtmkmHYpdZsU0y7lOFaS2ipfNsnrTMOyyz+1BnjfzLYCWyUtAI6I5ZNS2kwE1mWp2sMJy4pFrnTJRk7SNj3V6+55pmdul77Vd5sUVk6x7NIbW+WcYqZG35V/StJlwElmNlvSVMJs4++AKmAxcC4hP9XrwMnAWmAJ8GUzezmPOi41P/CppHCblCZul9IjXzYpZkzjekm75Z8CMLOVkv5M+HfcdsKS1EsAkr4JPAZUALfn02FEMp7Z4RQNt0lp4nYpPfJikwG7uc9xHMfJPcXcp+E4juP0M9xpOI7jOIlxp+E4juMkxp1Glkg6QNJtku4rti7ljKRhkn4j6VeS/rHY+jgBHx+lh6Sz4jj5o6TTspVTlk5D0u2SGiS9lFY+S9JrklZJ+m53MiykM7k4v5qWJ720z+eB+8zsnwlHBzt5ojd28fFRGHppkwfjOLkQOCfbPsvSaQDzCBlzd5EpIaKkaZIeSbv2KbzKZcU8EtqHsMmzI71MWwF1LEfmkdwuTmGYR+9t8u/xeVaU5SFMZrZA0n5pxbsSIgJI+m9CupMfAacXVsPypjf2IWQKmEhIpV+uP4IKQi/t8kphtStPemMTSSuB64FHzWxZtn36IOukq4SIEzJVljRG0i+BoyRdlW/lnIz2uR/4gqSbKa30FuVCl3bx8VFUMo2Vy4BTgNmSLs1WeFnONDKgLsoy7nw0s43EXexOQejSPjFH2VcLrYyzi0x28fFRPDLZZA4wp6/CfabRSS4TIjq5x+1TmrhdSo+82sSdRidLgIMl7S+pipAk8aEi6+R04vYpTdwupUdebVKWTkPSXcBzwBRJayRdbGatQEdCxJXAPQVIiOh0gdunNHG7lB7FsIknLHQcx3ESU5YzDcdxHCc73Gk4juM4iXGn4TiO4yTGnYbjOI6TGHcajuM4TmLcaTiO4ziJcafh9EsktUlannLtV2ydcomkoyTN7aOMeZJmp7w+T9LVfdcOJH1TkqdvKUM895TTX9luZkdmeihpcNzk1F/5HvCf6YV9fF+zyEHuocjtwELg1zmS5/QTfKbhDBgkXSjpXkkPA/Nj2XckLZH0oqRrU+peHQ+peULSXZKujOX1kqbH+70lrY73FZJ+miLra7G8Lra5T9Krku6UpPjsGEnPSnpB0mJJtZKekXRkih4LJR2e9j5qgcPN7IX4+hpJt0qaD9whab8oZ1m8PhXrSdJNkl6R9CdgnxSZAo4Elkk6KWWG9tfYX3ef1QWx7AVJvwUws23AakkzcmE7p//gMw2nvzJE0vJ4/7aZnR3vP0n4wt2kcKTlwYTzBQQ8JOlEYCshH89RhDGwDHi+h/4uBhrN7BhJ1cDC+CVOlHMYISncQuB4SYuBu4FzzGyJpBHAdmAu4eS0yyVNBqrN7MW0vqYDL6WVfQL4tJltlzQUONXMmiUdDNwV25wNTAGmAWMJZ1rcnqLjC2Zm0UF+w8wWShoONHfzWW0ErgaON7P3JY1O0WkpcAKwuIfPzhlAuNNw+iuZlqceN7NN8f60eP01vh5O+GKsBR6Iv5aRlCSZ22nA4SkxgpFRVguw2MzWRFnLgf2ARmC9mS0BMLOm+Pxe4PuSvgNcRDh5LZ1xwIa0sofMbHu8rwRuijOWNmByLD8RuMvM2oB1kp5KaT8LeDTeLwR+JulO4H4zWxOdRlef1RGE43Tfj+9jU4rMBuCQrj8uZ6DiTsMZaGxNuRfwIzO7JbWCpMvJfFZKK53LtjVpsi4zs8fSZNUBO1KK2gjjSl31YWbbJD1OON3uS4QZQjrb0/qG3d/XFcDfCF/og4Dm1C66elMEh/CFqMP1cfnqs8AiSaeQ+bP6Vjcya6KuThnhMQ1nIPMYcFFcgkHSBIXz3RcAZ0saEtfzz0hps5qwFAQwO03W1yVVRlmTJQ3rpu9XgfGSjon1ayV1/EibSwhIL0n75d7BSuCgbmSPJMxi2oHzgYpYvgA4N8ZfxgEzY98jgcHxYCQkHWhmK8zsx4QlpkPI/Fk9CXxJ0phYnro8NZk9l9GcAY7PNJwBi5nNlzQVeC7GprcA/2RmyyTdTThX/B3gmZRmNwD3SDofSF3emUtYdloWg8obgLO66btF0jnAzyUNIfwiPwXYYmbPS2oiw38emdmrkkZKqjWzzV1U+QXwB0lfBP6HzlnIA8BngBXA68DTsfxU4ImU9pdLmkmYFb1CODN6R4bP6mVJ1wFPS2ojLF9dGOUcD1yLU1Z4anSn7JF0DeHL/IYC9TceqAcOibOFrupcAWw2sz7t1Yiy5gJzzWxRX2WlyDwK+LaZnZ8rmU7/wJenHKeASLoA+AtwdSaHEbmZ3WMlWWNml+TSYUT2Br6fY5lOP8BnGo7jOE5ifKbhOI7jJMadhuM4jpMYdxqO4zhOYtxpOI7jOIlxp+E4juMkxp2G4ziOk5j/B0dcjfb16+rbAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.title(\"Bode plot FRFs Q2U1 Q2U2\")\n", "mag, phase, omega = bode_plot(sys_Q2U2, omega=w, dB=True)\n", "mag, phase, omega = bode_plot(sys_Q2U1, omega=w, dB=True)\n", "plt.legend([\"Q2/U2\", \"Q2/U1\"])\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.6" } }, "nbformat": 4, "nbformat_minor": 4 }