{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapter 7" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "ライブラリの読み込みと関数の定義" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "plt.rcParams['font.family'] ='sans-serif' #使用するフォント\n", "plt.rcParams['xtick.direction'] = 'in' #x軸の目盛線が内向き('in')か外向き('out')か双方向か('inout')\n", "plt.rcParams['ytick.direction'] = 'in' #y軸の目盛線が内向き('in')か外向き('out')か双方向か('inout')\n", "plt.rcParams['xtick.major.width'] = 1.0 #x軸主目盛り線の線幅\n", "plt.rcParams['ytick.major.width'] = 1.0 #y軸主目盛り線の線幅\n", "plt.rcParams['font.size'] = 10 #フォントの大きさ\n", "plt.rcParams['axes.linewidth'] = 1.0 # 軸の線幅edge linewidth。囲みの太さ\n", "plt.rcParams['mathtext.default'] = 'regular'\n", "plt.rcParams['axes.xmargin'] = '0' #'.05'\n", "plt.rcParams['axes.ymargin'] = '0.05'\n", "plt.rcParams['savefig.facecolor'] = 'None'\n", "plt.rcParams['savefig.edgecolor'] = 'None'\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# 線種を変更するジェネレータ\n", "def linestyle_generator():\n", " linestyle = ['-', '--', '-.', ':']\n", " lineID = 0\n", " while True:\n", " yield linestyle[lineID]\n", " lineID = (lineID + 1) % len(linestyle)\n", "\n", "# 時間応答のグラフを整える関数\n", "def plot_set(fig_ax, *args):\n", " fig_ax.set_xlabel(args[0])\n", " fig_ax.set_ylabel(args[1])\n", " fig_ax.grid(ls=':')\n", " if len(args)==3:\n", " fig_ax.legend(loc=args[2])\n", "\n", "# ボード線図を整える関数\n", "def bodeplot_set(fig_ax, *args):\n", " fig_ax[0].grid(which='both', ls=':')\n", " fig_ax[0].set_ylabel('Gain [dB]')\n", "\n", " fig_ax[1].grid(which='both', ls=':')\n", " fig_ax[1].set_xlabel('$\\\\omega$ [rad/s]')\n", " fig_ax[1].set_ylabel('Phase [deg]')\n", "\n", " if len(args) > 0:\n", " fig_ax[1].legend(loc=args[0])\n", " if len(args) > 1:\n", " fig_ax[0].legend(loc=args[1])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## オブザーバ" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "from control.matlab import ss, acker, lsim\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ ": sys[2]\n", "Inputs (1): ['u[0]']\n", "Outputs (1): ['y[0]']\n", "States (2): ['x[0]', 'x[1]']\n", "\n", "A = [[ 0. 1.]\n", " [-4. -5.]]\n", "\n", "B = [[0.]\n", " [1.]]\n", "\n", "C = [[1. 0.]]\n", "\n", "D = [[0.]]\n", "\n" ] } ], "source": [ "# A = '0 1; -4 -5'\n", "# B = '0; 1'\n", "# C = '1 0'\n", "# D = '0'\n", "\n", "A = [[0, 1], [-4, -5]]\n", "B = [[0], [1]]\n", "C = [1, 0]\n", "D = [0]\n", "P = ss(A, B, C, D)\n", "print(P)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### オブザーバゲインの設計(極配置)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "acker関数を用いてオブザーバゲインを設計するために,A行列とC行列の転置をとったものを用いる\n", "\n", "得られるゲインの転置をとることでオブザーバゲインが得られる" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-15.]\n", " [-46.]]\n" ] } ], "source": [ "# オブザーバ極\n", "observer_poles=[-10+5j,-10-5j]\n", "\n", "# オブザーバゲインの設計(状態フィードバックの双対)\n", "L = -acker(P.A.T, P.C.T, observer_poles).T\n", "print(L)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A+LCの固有値が指定極になっている" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([-10.+5.j, -10.-5.j])" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.linalg.eigvals(P.A + L @ P.C)\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "G = ss(P.A, P.B, np.eye(2), [[0],[0]])\n", "Obs = ss(P.A + L@P.C, np.c_[P.B, -L], np.eye(2), [[0,0],[0,0]] )\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAkAAAADcCAYAAACYoR4nAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAA9hAAAPYQGoP6dpAABRuElEQVR4nO3deXxU1f34/9e9s2RfyB5Iwq6AYd8EAQFbUKwLba2fj7h9pPZjbWtt+/l8WuX3qdW21n61/VBttXSxWNq61Fq1igUsIipKEgiyCMgSCGQhe8gyk1nu/f0xZEjIzCWTSTKTmffz8cgjJzczd859z5wz555z7zmKrus6QgghhBBRRA11BoQQQgghBps0gIQQQggRdaQBJIQQQoioIw0gIYQQQkQdaQAJIYQQIupIA0gIIYQQUUcaQEIIIYSIOtIAEkIIIUTUkQaQEEIIIaKONICEEEIIEXWGfANo+/btXHfddQwfPhxFUXj11VdDnSUhRISTekeIoW/IN4Da2tqYOnUqv/zlL0OdFSFElJB6R4ihzxzqDATrmmuu4Zprrgl1NoQQUUTqHSGGviHfAySEEEIIEagh3wMUqLq6Ol544QXi4+OJiYnxbs/IyCAzMzOEORNiaLPZbJw4cYLly5eTkZER6uyEDalzhBg4wdQ7UdcA2rRpE9/4xjdCnQ0hItaf/vQnVq1aFepshA2pc4QYeH2pd6KuATRq1CgAHnnkEcaMGYOmaQBkZWWRlpYGgMlkwuVyoSiKN62qKqqq9jptMplQFMWbBnC73d3SZrMZXde9aU3T0DSt12m3242u6950Z979peWY5JgG8pg+/fRTbr31Vm8ZEx5S58gxyTEN3DEdOHCA22+/vU/1TtQ1gOLi4gBYvnw5c+bMCXFuwo/L5aKoqIg5c+ZgNkfdx8OQxMaYruvA+TImPKTOMSblypjEx5jL5QL6Vu8M+Wi2trZy9OhR799lZWXs2bOHtLQ0CgoK/D5PVeX6b19UVWXEiBESHx8kNsaiKS59qXeiKT6BkHJlTOJjLJi4DPkGUElJCUuWLPH+/e1vfxuAO+64g/Xr1/t9nnyYfFNVlZEjR4Y6G2FJYmMsmspUX+qdaIpPIKRcGZP4GIvqBtDixYu9Xe+B6Ow288XtduN0OoPJ1pBksVjQdZ0dO3Ywf/586W69gMvlktgYMCpTkaYv9U40xScQUq6MSXyMBVOuojaavlqNuq5TXV1NU1PT4GcoTKSkpDBmzBg5W/VBVVXGjh0rsfFD4mJM4uOblCtjEh9jUd0D1Fe+gtbZ+MnKyiI+Ph5FUUKQs9DQdZ329nZqampITU2VwuZD51i88E0+M8YkPr5JuTIm8TEmDaA+uLDbzO12exs/6enpIcpVaMXFxaHrOidPniQtLa3bpG3C85nZvn07ixYtkq5oH2SIx5jExzcpV8YkPsaCKVdRe0pyYaux85qf+Pj4UGQnbHTOVts5z4I4T1VVCgsL5UzeD4mLMYmPb1KujEl8jEkPUB/4C1o0DXv5oqoqJpNJCpsPqqqSlZUV6myELfnMGJP4+CblypjEx1gw5SpqS6R0R/umaRo2my0q74K7GKfTyaZNmyQ2fkiZMtbX+NS2dPDup7XsPF7fbfsru0/z8q7T/OPjSj44Wsfh6hbqWztwa4HfFRtKUq6MSXyMyV1gfSBnY74pikJMTIx3CnNxnslkYvbs2RIbP6RMGbtYfBwujaKyBorK6lk5I4/RGQkAbD10hu/+bR8Lx2cwd8z56xMfev0ALfaelb9JVchJjmV0RgIj0+PP/U5gfFYiBWnxqGp49XJLuTIm8TEmQ2B9IJW1b4qieNd4Ed2pqupdu0n0JJ8ZY77i49Z03jtSy8u7TvPOoRraHJ5r74anxnkbQAVpCUzISWJsZmK35y66JJNWuwub001Dm4P61g4a2524NZ2KJhsVTTbeP9r99X50YyG3Xu6ZVK+mxc6phnYm5aYQZw3dl6uUK2MSH2PSAOqDSOqur62tZfLkydx33308+OCDAOzcuZOFCxfyxhtvsGzZsl7vq+sQWGxs7EBleUhyOp1s3ryZZcuWYbFYQp2dsBNJZWogdI2P3enmpZJTrHv3OBVNNu/2jMQYFo3PYGR6gnfbvLHp/PP+RT3296tbZvTY5nRr1Lc6ON3YTlldGyfr2zlR30ZZXRtHa1qZmJvkeaCtiY93vMef3/2YqdkxfGv5JIgbBnHDKHOkUDA8F9Mg9RRJuTIm8TEmQ2B9EEndiZmZmTz77LPceOONLFu2jAkTJnDrrbdy7733BtT4gfNDYHK7ZU9ms5mFCxdKbPyIpDI1EEwmE7qu8+qeCn6y8RA1LR0ApMZbuHHaCFZOH8HkESlBDVFZTCo5KbHkpMQya1SXXgNdx1X2PurHP4C//QvOnuazwGetQCPwwvmHjgbq9BRqYwqwp47FkjeD4ZOuIG30VDD1/xewlCtjEh9jwdQ7URvRQO72ancE3sK0mlTMJk/XnMut4XBrqIpCrOX8m+Vvv/HWwN+WFStWcPfdd7Nq1Spmz55NbGwsjz32mPf/K1euZNu2bVx11VW8/PLLfvfTOQQW7XfD+aIoCsnJyaHORtiSz4yx6mY7//abj9hZ1gDA8JRYvrp4LDfNyu9WL/S78o/gre9irtrTfXvScPTELHRzLKrmAnsTrtZ6zB2NZCjNZDj2Qc0+qHkVdkMHVk7HjseWOZWEsZczfPJiYtIKIMj3XcqVMYmPsWDqnahtAAXSbTbp+5sC3v+vbpnBtVNyAdh04Axf+8tu5o5O48X/nOd9zIKfvkNDm6PHc088dm3ArwfwxBNPUFhYyEsvvURJSUm3Iaz77ruPu+66i+eee85wH5qm0d7eLkNgPjidTjZu3MiKFSukK9oHGQIz9o0XStHSRhNrUfnG0vF8eeFoYswD2PBxO2HL9+Gjpz1/m+Ngyk0w6QbImw2xKShA168PM+C2NXPqyF6qju3DXrmflMYDjHN+SrLSzlj7ATh1AE79BbZBvZrOmeQpjJu5BOvIyyF3KlgCqzekXBmT+BiTIbA+iMTu+uPHj1NZWYmmaZw8eZIpU6Z4/7dkyRK2bdt20X0oikJcXJx0t/pgNptZtmyZxMaPSCxT/cnmcLNg1DB+/qVp5KcN8ISrHa3wwr9D2XbP3zNuh6segoSMiz7VFJfCqCkLGTVloXdbq93B7k8+pv7TD1ErS8g9u49L9BOka/WkN70D/3rn3JOt1CRcSlXyZEZMXkzGhAWQYryMg5QrYxIfYzIENsA+eWR5wM+xms5fmb78smw+eWQ56gVdde9/d0nQeevkcDhYtWoVN998MxMmTGD16tXs27eP7OzsfnsNgVRCos9unpXPE3df7h0aHzBOGzz/b3DiPbAmwsp1MPFzQe0yMdbKjBmzYcZswLN24KkzdZzct4P4ml3MVI/C6SJoqyXr7D6yzu6D03+Bt4DkETSnT+NE3GVkTlpI7qVzUC7oJZJyZUziMzCiNqqBLPXQl2tyujJ3uR6oP/fb1Zo1a2hububJJ58kMTGRt956i9WrV/PGG28EtB9d17HZbDKc4YPL5ZKuaAOyfIqxW+bkDXzjR9fhta+da/wkwe2vQd7Mfn8ZRVEoyMmkIOcG4Abva2v1Zby79U3UimIWxJZhqjkAZytIOVvBVN6ET/4fHVg4FTOesxkziBszj5xJV7C9aK+UKz+k3jEWTL0TtQ2gSOqu37ZtG2vXruWdd97xXiy3YcMGpkyZwjPPPMNXv/rVXu9LhsD8M5vNrFixQmLjRySVqYEwKPEp/h3s/xuoZrjlhQFp/PilKKgZY1jypW+c3+Zog4rdlO7YjPvkR4ztOMgwpYVxHZ9AxSdQ8Sd4Dy5XMvnk+HrcI2aTMv4K8ifNxRoj1yCC1DsXI0NgUW7x4sU9pkkvKCigqakpNBmKYC6XSyoiEZ7qj8GmNZ70Zx+BUQtCmx8AawKMXsj00Z7riRxONwcP76Xu4Hsop4vJPruXMdpJsqklu3krNG+FT8DxqokzCePIvnQ25ExBy56MLW0iCcnDQnxAoSH1zsCI2ohGW3f98uXL2b17N21tbeTl5fH3v/+d2bNn93icDIH553K52Lx5s3RF+xFtZSpQAxofXYc3vw3uDhi7FC6/d+BeKwhWi4mJhdOhcLp3W/WZat7+2x8osDSQVLeH0R2fkKq0kt1+GEoPA55FK+N0hQpTLsMnzkXJmQK5U2hNnUBC2nCUCJ6FXOodYzIE1gfR1pretKl3t/Krqkp8fLwUNB8sFgs33HBDqLMRtqKtTAVqQOPzyatwfBuYYuDanwU9N89gysnO4dZ7H/D+rWsalSc/JbHxAMlNB6FqL/bTe4i1nWGEVgkH/u75ARKBRpKoso7ibPI4lMyJJOVPZvglM0jNyAnREfUvqXeMBVOuorbG0vWhtWLyYNF1HU3TJD4+6LpOS0sLSUlJMumfD/KZMTZg8dHc8M6jnvSC+yFtzMC8zgC5sFwpqsrw0RNg9ATvY2KB+jOnsZ/awwj7Eajai161F73+GMOUFoY59kHdPqj7OxwENkM9qVTFjKYtZRxkTSJxxCSyxlxGRuaIIdVjJPWOsWDKVdQ2gKS73jdd1+no6JAhMB9cLhfvvfeerMnjh5QpYwMWn30vQ92nEJsK874+MK8xgHpbrtKz8yA7z/u3AnS0t1Jx9GMaT3yMq/ogsY2fkmU/znC9hnSaSO8ohZpSqAH2e57ntCRhyRwP6eNoiCvguJ5D9qjLyB83GWKSBvZg+0DqHWMyBNYH0l3vm6qqxMXFSUHzwWKxcO21fZulOxpImTI2IPHRNNj+uCd9xX0QO/SWTAimXMXGJzJ2yhUw5Ypu21tbmqg8soemE3txn/mEhOYjZHScIkerweJsgcrdULmbNCANoPjcExNz0NPHUtycgju5AHP6KJJyxpKefwnp2fmoIbjTUeodYzIE1geapoU6C2GpcwhM4tOTpmk0NTWRmpqKOoS60AeLfGaMDUh8jm2F+iMQkwxzvtL/+x8EA1GuEpNSuWTGYpixuNt2u60NS/NJTI3HoP4oZYf3Yq8+zEiqiHc2QGs1Sms1cwCagPIuz9Ut1JiyaLIOx5aQh55aQEzGaBKyxzJs+CjSM0cMSANJ6h1jwZQraQCJbjqHwGQ4oye3201xcTFLly6VisgHKVPGBiQ+Res8v6etCsvhm94YzHIVG5cAcZMgZxIAo7vOFGBrgoZjtFQc4sCBvZiay4lvP02as4osrY5YxUmBVkGBvQLsxVAPHDv/dE21QHIuJI+gmnROOFLIGDGGcWMvgZQR6EnD0eMzUQPssZB6x5g0gPpAuut9kyEw/ywWC8uXB74sSrSQMmWs3+PTcByObPGk59zdv/seRGFTruJSYcRMkkbM5PI5q7r9y+nooPr0cRorPqWt5jha/QksLadItFWQ7jpDut6EqjmhqRyayskBcgCqgV2efSiASzdRowzjrDmNNmsGjtgMtIQs1KRsLCm5xKflkpyRx7CsEcQleBq0YROfMCVDYH0gZ6u+6bqO2+2W+PigaRp1dXVkZGTImZgP8pkx1u/x2fM8oMPYqyB9bP/uexANhXJlscYwYsxERoyZ6PP/TkcHSvsZlLNVcPY0nx45TEPVCcbENJOl1cHZSvTWaiy4yaGOHFcduD6FdqDB92u26nE0qsPIzM2HuGHEpOZyuiOeCkc8ObkjGJWXD/FpuOPSsFlSSUhIHlJ3t/UX6QHqA6ms/XM6nRIfHzRNY//+/SxatChsK+pQks+MsX6Nj67D3hc96Wm39N9+QyASypXFGgPWAkgtAOZySWHPx7idDmqrT9FSc5L2hiocTVVoLWdQ2mqw2muJ76gnyd1ImtZArOIkUbGRqNugstK7j/xzP3x6fr8mPPMhOXQzTUoyrWoy7ZZUHJYUnDHD0GJSIS4VNT4Vc3wq1oRhxCSmMXJELjGJaZ4L501Dt8dfGkB9IN31vimKQmxsrMTHB7PZzNKlS0OdjbAlnxlj/RqfUzuh6aRntfdLV/TffkMgWsqV2WIlN38sufnGvXW6ptHS0kRTzSla6iqZkGRHbauB9gaOnjhJc0M1I+M6yFBboL0Bra0W1e3AqrjIooEsrQE68Py09i5vDjWOJi0OU3wq6elZEJuCw5JEaY2GZk0EayJKTBJqbCLm2CTMcclY45OJSUgmJj6F+MQU4pNSPeu3DfJcRTIE1gdytuqbruu4XC6Jjw+aplFVVUVubu6QPVMdSNH4mXn66ad5/PHHqaqq4rLLLmPt2rUsXLjQ52P7NT6dvT8TrwNrfP/tNwSkXHWnqCpJKWkkpaTB+KlomkbFufiMW9IzPoqm0d7eQnP9GVoba7A11+A4W4uzpR6lvQ6loxnVcRaLswWrq4U4VytxWitZVjuqw9NCsmo2srBBewO0H/dsA+YGmHenbkKJTcQcmwzWRBpcFirbTSSlDGNkdgZY4nCZYik+bQNLPFjjUC3xKNZ4TDFxmGISMMfEY45NwHruJyYuEWt8IokJSZgsMT0aWNID1AeRWlk3Njby5JNP8pWvfIXc3Nw+7UMaQL5pmsaxY8fIzs6WitqHaPvMvPjii9x///08/fTTXHHFFaxbt45rrrmGTz75hIKCgh6P77f4aG44+A9PevIX+2efISTlytjF4qOoqqcHJjEFRl4S2M7dLug4S319DQ31tQxTbWSYbWBvprW5nv3HToKjDZOjDZOrFbOrHYu7HavWTqzWTqxuJ163Eac4ALAobuho9vzA+XmWas794Gl0zOtrMFDAEo9diaHJoWKOiUNp7vtnJmobQJHaXX/ffffR2NhIaWkpr776asDPlyEw/8xmM4sWLQp1NsJWtH1mfv7zn7N69Wq+/OUvA7B27Vo2bdrEM888w09+8pMej++3+JwugbZaz9w/o4b+51HKlbEBjY/JDPFppMenkZ4/odu/EoHLl/RuNy6ng7bWs9ham0m3OLC42sHRyqkzNVTX1JEd66QgSQWnDbutlY+PV6K47KguGya33fOj2bFoHVg1O1a9A6veQYzeQRwdmJXOkwcdnG3E0ua5y64DyhtlJuiAReLZ6uuvv05raytvvPEGd955J3/+859ZtWrVxZ/YhQyB+adpGqdOnSI/P1/OVH2Ips+Mw+Fg165dfO973+u2fdmyZezYscPnc7TTu2HGjOBf/PCbnt/jl4HZGvz+QkzKlbGhEB+zxUrKsAxShmV0254/5txF213EEtjQmq7rOBwOTG4bJncHONtpbG6mruksCSYX2vFP4Tdf7Vu++/SsCBCJlfX111/P9ddfD8D69ev7vB+5Dd43TdOoqKhgxIgRYVsRhVI0fWbq6upwu91kZ2d3256dnU11dbXP55zZ9w6782Z4JxnNy8sjKysLAJPJhMvlQlEUb1pVVVRV7Z52OjEdfMMzp8z45aiahqqqOJ1OzGYziqJ40+AZzu6atlgs3pMci8WCpmm43W5vWtM0zGaz37Tb7UbXdW+6M+/+0r05JofDwenTpxkxYgRutxuTyTTkj6lr2ul0BnVMiqJw+vRpsrOziY2NjYhjCvR9ssbE4HabcemJmJOySU5xk1zgyXt5e9+vgYvaWjzauut7S1EUYmJiJD4+mM1m5s+fL7HxIxrjcuHq3Lqu+12x+41X/8rMmTOZM2cOc+bMYd26dezdu5cjR44AUFpaSllZGQBFRUWcOnUKgB07dlBVVQVAyaYXUBqOgWph22kLTU1NAGzevJmWlhYANm7ciN1ux+VysXHjRlwuF3a7nY0bNwLQ0tLC5s2bAWhqamLr1q2Ap1G3fft2AKqqqrw9WadOnaKoqAiAsrIySktLAThy5Ah79+4F4ODBgxw8eBAg4GPasWMH48ePx2w2s3Xr1og4pu3bt1NXVwcQ9DGZzWYmTpzIu+++GzHH1J/vU3l5l/VKAqTowawlPwTt3r2bmTNnUlRUxOzZs73b7XY7ZWVljB49mtjY2BDmMLRsNhtHjhxh7NixJCQkhDo7YcXtdns/I6YQLIoY7oqLi5kzZw67du1iRn8M9YQxh8NBfHw8f/3rX1m5cqV3+ze/+U327Nnj/bKC83XOPx/6HJnXPxxUD5B7x68wbX4QRi/CecsrEdFb0tHRQXl5OWPGjEHTtIg4pv7sLVFVlePHj1NQUEBMTExEHFN/vk87d+7k8ssv71O9E7U9QJHU7qutrSUnJ4dHH33Uu23nzp1YrVZvazsQmqZFVHz6i67rNDY2Smz8iKa4WK1WZs6cyZYtW7pt37JlC/Pnz/f5nPTkeGbMmMHs2bOZPXs2ubm5mEwmb2PabDZ3S3cOs3ZNm054zpIZuxSLxeLdbrFYvD1PnWlFUXqkgW5pVVW7pTu/sPylTSZTt3Rnfv2le3VMJhNNTU3ouh4xx9Q1Hewx6bpOU1OT9zUj4Zj6833y1+PaG9HXZ31OJHXXZ2Zm8uyzz3LjjTeybNkyJkyYwK233sq9997LsmXLAtqXDIH5Zzabu/Uaiu6i7TPz7W9/m9tuu41Zs2Yxb948fvOb31BeXs4999zj8/Gqyx7cC7occOJ9T3ps5EwcKOXKmMTHmEyE2Ae9Wu1c18HZPvCZ8cUSH9CMmitWrODuu+9m1apVzJ49m9jYWB577DHv/1euXMm2bdu46qqrePnll/3uR9d1nE6nrAbvg9vt5siRI4wfP16GwHyIts/MzTffTH19PY888ghVVVUUFhayceNGRo4c6fPxutMW3AueLgZHK8RnQPbk4PYVRqRcGZP4GAum3onaBlCvONvh0eGhee0HK8Ea2DU4TzzxBIWFhbz00kuUlJR0u5bpvvvu46677uK555676H6iaSgjUDZbkF9iIqLce++93Hvvvb17sDPIHqDj73h+j1kMEXYXopQrYxKfgRFZpSgAkdiSPn78OJWVlWiaxsmTJ7v9b8mSJSQlJV10H4qiYLVaIzI+wTKZTEyfPl1i44fExZgS7BDYiQ88v8dcGXxmwoiUK2MSH2PBxCVqe4B61W1miff0xISCJbC5DRwOB6tWreLmm29mwoQJrF69mn379vWYp+RiOiedirbhjN5wu90cPHiQiRMnSmXkg3xmjOmuIIbTXR1QscuTLvB9kfVQJeXKmMTHWDD1TsT0AD399NPeW9hnzpzJe++9F/xOFcUzDBWKnwCvbF+zZg3Nzc08+eST/M///A8TJ05k9erVwcdACNE/ghkCqywFdwckZEK68WriQojeiYgGUOeihGvWrKG0tJSFCxdyzTXXGE6QFEkt6W3btrF27Vo2bNhAcnIyqqqyYcMG3n//fZ555pmA9iVDYP6ZTCYKCwslNn5IXIwFNQRW/qHnd8HlAZ8chTspV8YkPsaCiUtENIC6Lko4ceJE1q5dS35+vuGXfyR11y9evBin08mCBQu82woKCmhqauKrXw1sjRQZAvPP7XZTWloqsfFD4mIsqLvAyj/y/C7o+zra4UrKlTGJj7GoHgLrXJTwwvlujBYljEbLly/npptuYuPGjeTl5VFcXOz3scFMLBXp4uLiQp0FMUQp7g7Q+lBZa1qXBtDl/ZupMCHlypjEZ2AM+Yug+7IoIcChQ4e6TQeenZ2NruveW8A7fyuK0qu0pmneWS99pTv32TWtqqr3NX2lA3n9i6U3bdrUY3tnfrpuh/OzgobTdOfhMIW7pmlMmDABTdNwOp0RcUz9/T6Ji3C2Q8zF78bspvYQ2JvAkgA5UwckW6FkMpmYMGFCqLMRtiQ+xqJ+CAwCW5QQ4Pbbb++2MOFLL72E0+mko6MDgPb2dm+6ra0Nh8MBQGtrK06nE/As7OZyubzpzi+Cs2fPelfGPnv2rLexcWEaPMtOdKbdbrd3UTmXy+VNO51OWltbAU+PV1tbGwAdHR20t3vuLLHb7d65Iux2O3a753oDm83mTffmmNra2ujo6MDlcoXVgnfhsohfcXEx9fX1EXVM/fU+dZYFYcDRhzvBys/1ZOfNAtOQP2ftweVyUVxcLJ8fPyQ+xoKJy5BfDDWQRQnh/MKE69evZ/Lkyd16gFpbWxk9ejRxcXER1wPU23R7eztHjx5l7Nix3ouhw6FnIRx6Szo6Ojh9+rR3pt9IOKZevU9uN2bdgWZvobqunva2FtItDpKVDkyanbr6Oo5W1FBx8gRf/O6vo2Ix1EB01jm7vpLAjEc/Dvwurr99Gfb9Fa78Hix5YGAyGUKyyLAxiY+xYBZhHvKnE10XJezaANqyZQs33HCD3+dNnjy5W7DsdjttbW3eBkrX3qPepDsXhjNK+3puZ0PJVzqQ1++vdOcCdSaTybtQHRBQ+sIF7zpj0Jt01wLem3TXdWB6kw7mmGJjYxk3bhxdhfMxmU0quq0Z1dmKxX6WhsZ6yquqcbY3o9la0OzNYG9BcbSgOlowu1qxuFqJcbURo7UTp7WTQDsJ2AEdFfA1L3rGuZ/dVXKR5kU52gJ/zulz1+sVzO3fvIQJk8nUo1yJ8yQ+xqJ+IsRAFyUEcDlkanFfOns6pLu1J5fLRVFREXPmzBnUhT8ddhvNDTWcbazBdraejpZ63K0NuNsbwdaI0tFIvLuVKWka2BrB3kRLUy3x7lZMyvkO3rRzP8Gwq3G0aTHExCeRmJQK1nha9Rg+bdQpG+YAtlxsF9GtoyWwx7c3QOMJT3r49H7PTjgIVbkaKiQ+xoL5roqIaAa6KCGAam8avAwOMZ3DKaI7VVUZMWJE8LFxdUBbHbTXcfDocVoaqpmY3EGSuwnaaqk9U0lDTQVJ7iZStGYSFDuZQObF9tt4PpkE0NmxZ7JCTDI2UzyV7RY6TAk4zIm4zAm4rUlo1kSISUKJSUGNS8Ycn4w1LgVrQgoxiakU5GShxCSCOY5YVSX2gpdNBGYAWkkJ/FQaQIYCbQBVfez5PWw0xA3r//yEgX4rVxFK4mMsmLhERAMIAlyUEFDb631uH+KXRPULs9kshc0HVVX9r/St67SebaSx5hQtNaexNZzG3VyF3lKNpf0M8R21JDnrSaWZRP38MMhEH/vq1tg514hx6wotSiKtSiLtpiTs5hSc1mRc1hT02GEQl8rcSWNR4tMgNpVadxx6bBopaenExHoW1Y0DBnIOYfnM9ELH2cAeX+m50DxSe3/AuFwJic/FSAOoD9wtNd3+7rx2or29ParnXGhra8Nms8lcQBdoaW6gpvwwTYc+YFp+EqaWSqpPH6Ou6iTJzjrStQaSFDu9vsFZNUN8OtXuJOq0JHJy88jIzoOEdJqUVI63xxKbmkPCsGxS0nNITk0n1WQitZe7v2hv0QCQYdNekAZQDy6Xix07djB//nwZ4vFB4mMs6ofA+kKx1XX722QykZqaSk2Np2EUHx8fVY0AXddpb2+ntraWhISEbhfTRjpd02iur6am/BBnq4/hqCsn3lbJtORWaDoFzadJ6mg+37g54PmVc+4H8PbUtOpxNJjSOGvOwBaTiSs+C5JyMKeOIC5tOEnpwynIL0CJTQVV7b6Pc1LxDCkNNdID1Av2QBtAezy/h0/r75yEDVVVGTt2rHx+/JD4GAv7HqBdu3Yxc+bMwXipXvM1BJaT4/kq6mwERaPU1FRycnIirvHncrmoqSij4dQh2qqPotUfJ6blBMm2CnLclaRi69m7csE8mo0koaTkkZozBlLzOWvN4lNbEgnpeSRl5pOWk09iYiqJg3RM4SZUFbTNZqOhoYERI0Z0237gwAEuu+yykOTJr0CuAWqrh+Zz6xnmRt4EiJ06r3ERvkl8jIV9A2jlypWGC5OGgtbas5GjKAq5ublkZWV5JwaMJp1zw7zzzjssWrRoSHa3tjQ3UHVsLzkdJ0luPQ51n9JaeRjL2XKGK06ft3F3OkM69ZZc2uNzcSeOYObUqZiHFUBqPq7EXJIs8Wzfvt0bm2Rg1mAd2BAQiiGwl19+mW9961ukpaWh6zq//e1vmTvXc7v4bbfdxu7duwc9T4YCGQKrOjf8lT4OYlMGJj9hwOVydStXojuJj7GwGAL70pe+5HO7rus0NDT018v0G8XPRdDgGQ6L1gmnNE2jsLAw7Ltbm2oqqDhSSmvFAeYk1KLUH4HaT0lqqexxHU4igAJO3cQZNYuGmDxsifnoaWOIzRpHat6lZBdcSnZ8Atk+Xgs8BWWoxCZUQhGXH/3oR+zevZvMzExKSkq44447WLNmDbfcckt43tAQSA9QFFz/A57PjZQr/yQ+xsKiB+jtt99mw4YNJCZ2HwDQdd07rX44UdrqLv6gKKSqKllZWaHOhpejo4PTxz6m4ehuXFV7iW88zHD7UTJo8ntBcB2pOIaNZ/i4qZBxCc7UsdTFjCArbxx5Zgt5fcxLuMUm3ISignY6nWRmei75njVrFtu3b+fzn/88R48eDc9h3ECuAfJe/xP5DSApV/5JfIyFRQNo8eLFJCYmcuWVV/b43/Tp4VeA9fZ60HUIx0oyhJxOJ1u3bmXp0qWDfiG0o72F4/s/pPnoTpQz+0lr/ZQCVzljFBdjLnispitUqVnUxY5i9MQZJOddBpmX4k4bT0ZC9/lSLEBuP+QvlLEZCkIxBJaVlcXevXuZMmUKAOnp6WzZsoU77rjDu+ZaWOlLD1DutAHJSriQcmVM4mMsLIbAXnnlFb//++c//9lfL9NvFJfNM2tufLBz40YWk8nE7NmzB3wIsMPezslPiomv20te+yGo3I2l9hATdK37AxXPnVWnraNpTpkA2YWkjJrGiEtnMCJ5GBdeGjiQuR6s2AxVoegB2rBhQ4/rIqxWK88//zxf//rXBz0/F9XR3LvHtdbA2QpAgdwpA5qlUJNyZUziYyykPUBvv/02n/nMZ3z+b926dfznf/5nsC8xcBpPSAPoAqqqkpbW/zE5U36EpLpdxFeVQEUJ5qr9XKJ3v9BcAeqUdE7FXoo9s5D4/KlkXzKL7PzxTFBDX/gHKjaRYjAbQJ31Tl5ezwHNznrniiuuGLT89Fpve4A6h78yLoGYXs8uNSRJuTIm8TEWTL0T8DOff/75bn9fe+21fOc738HhcHi31dbWct111/HAA2G+cnFjWahzEHacTidvvvlmUHfBuZxOjn78AR89/xNKfraSMz8YQ/azs4h//T+h+LdQWYpJd9JEIocS5sCi/4Z/ex6+c5iMh44z/btvMe+ux5n62VvJGTkBJQwaP9A/sYlkAzkEFjH1jr2XPUBRcgE0SLm6GImPsUEZAquurubee+8lNTWVf//3f/du3759O7fddhtvv/02f/nLXzhx4gR33XUXkyZN4uOPP+5zxgZFgzSALmQ2m1m4cGFAt1u6nA6OffwejQf+RULlh4y2H2ScYqPr+sUuXaU+aQLZl10J+bPRcmeQMmwkqUPozoa+xCaaDEQXfcTVO7Ym0NxwsUZ9FDWApFwZk/gYG5TV4H/zm9/gcrl49tlnu22fO3cupaWl3HPPPcycORNN0/jRj37Ef//3f4fnXRhdSQ9QD4qikJycbPwgTePEJ0VUf7yJuNMfMLZ9L5cqti47gVbiOB57Ge3Zs0gcv4DRUxeRnXR+LpOh0+w5r1exiWIDUd4jr97RPb1AFxt69zaApg14jkJNypUxiY+xYMp7r7+H7rvvPlJTU/nCF77Q43+HDx+muLiYvLw8zGYzhw4dor29vc+ZGjQNJ0Kdg7DjdDp57bXXenS31lYcRy9ZDy/dDo+PZdTLy7n8yM+ZattJomKjmQR2xy/ko0u/x/EvbiL+/zvNlO/9i8v/46cULriOhKShP5Gbv9gIj4EYAoukekc3n1tjsP0i86KdrYLWalBUyJk88BkLMSlXxiQ+xoKpd3rdAEpNTeWPf/wjd955Z7ftjz32GPPmzeOzn/0s+/fvp7i4mNLSUqZMmcKHH37Y54wNCukB6sFsNrNs2TLMig4n3kff/H1O/HAqmb+djvLGN+GT18DWgMscz8dxc/ho3Lc4unIjif97ihn/8waX//sDjCm8HDUCu2u9sYnAY+sPAzEEFlH1TudszraLNICq9nh+Z04Aa8KAZikcSLkyJvExNihDYJ2uu+66bn//4he/4NVXX+Waa64B4LLLLqOoqIgHH3yQxYsX09HR0efMDbizleC0gyU21DkJCw1nTnH0g1dIOLmVSfbd0HEWBRiFZ96dxmFTSJ92LYxZjHnEDKaaom9OCqmEQiMi6p3YZKDWM/2GkSi6/qeTlCtjEp+BEXRU9+3bR0ZGRrdtFouFxx9/nM997nPB7n7AeLqjHdBUDpmXhDo7IVNZdojyHS+ScmITlzo+YY7SZfmA+HQY9xnOZC/CcslVpGf2x3SCQ5fL5WLjxo2sWLFCJiTzwe12D9prhbre+fGPf8ybb77Jnj17sFqtNDU1XfQ5ujUJdC4+BBZlDSApV8YkPsaCqXeCbgBdWAl15WtW6LCRPBw44RkGi6IGkK5pHD9QTE3xy2RVbGGsu+z8AqEKfGoaT93wxUxY+AXSxs0FVfW7Pla0MZvNrFixQs7G/BjMidpCXe84HA5uuukm5s2bx+9///tePUeJS4F2jIfAdD1qZoDuJOXKmMTH2KAOgUWMlBFgPwENx0Odk0FRfrCYqvf/RF7lPxmrVzP23HaXrnIoZjKto69m5BU3MT5/HPl2O7GxsbJMiA8ul0sqIsHDDz8MwPr163v/pJhzDSCjHqCzldBWC4oJcgqDyuNQIuXKmMRnYERtRLWkfLADtYdCnZWB01AG+1+mfPufKHCdoODcZrtu4VDCbBzjVzB+4U0UZuR4n+J0Otm8ebN0t/rgcrkkNgYGcwhsKNKs5xaKNuoB6uz9yZoElriBz1QYkHJlTOJjLKRDYEOVKXMc1AJnDoQ6K/2qrvoUJ979IzPPbkWpKAGgAHDoZg7Ez8F12ReYdOUXmZaU6vP5FouFG264YfAyPIRIbIzJGaqxmrOeWasbTn/KsXO373eu8m0ymXC5XKgVu1EBLXcqaBqqqnq2q2qPtNPpxGQyedNmsxlFUbxp6N5z4HK5sFgs6LruTWuahtvt9qY1TcNsNvtNu91udF33pjvz7i/tcrlQFOX88fk4DkVRuO666yLqmPr7fbruuuu8eYiUY+qv92lQ5gGKNHraufXFz3wCmmb84HDndsLBN9D+8m+k/Hoqsw7+P0/jR1FhzGKal/0ftm8eYvp332L2575Mgp/GD4Cu65w9exZd1/0+JlpJbIwN9bj84Ac/QFEUw5+SkpI+7/9nv34OgEPF25gzZw7r1q1j7969HDlyBIDS0lJsx3YAUNaRyqlTpwDYsWMHVVVVgGcG7Lq6OgC2bt3qvfh68+bNtLR41hnbuHEjdrvde/Gsy+XCbrezceNGAFpaWti8eTMATU1NbN26FYC6ujq2b98OQFVVFTt2ePJy6tQpioqKPPkqK6O01NNLdeTIEfbu3QvAwYMHOXjwIECPYyor80w3UlRU5PeYTp48ia7rEXVM/fU+6bpORUVFRB1Tf75Px4/3/TIWRR/AWktVVRYvXszjjz/OzJkzB+plArJ7925mzpzJzg8/YM6WG8HdAd/YDeljL/rccHNsfxEtH61nauNmlLZa7/bD5kuxTv83Ri9aBUmBXcLcOQS2bNky6W69gMTGWFFREXPnzmXXrl3MmDEjZPnoa71TV1fnreD9GTVqlOf6uHPWr1/P/fffb3gXWGed88KT/8vN9b+gIy6bvUv/3LMHyOnE9PPxKLZGXHdtQc2bNWTOwoPpWbDZbPzrX/9i+fLl3ucN9WPqz/cJYNOmTVx11VXExcVFxDH15/v04YcfMn/+/D7VOwPaZ/3ss89y8uRJ7rvvPj744IOBfKmAma2xkDUBqj72DIMNkQZQS8tZPt60nsyDG7jU/en5fyRkwdSbcUy+hUtzJ/V5/xaLhWuvvbYfchp5JDbGwmUIrK/1TkZGhuHdZcEaP2UuvAMxjkZmz5rV4yYD89lyzxxBphjMw6fBuXXyusa1a7prIzyQtKIo3nTnF1pv013vuOlN2l/eu6bj4uJ8Tl0wlI+pv9+nrvGJlGPqr/cpJiaGvhrQGqtz9taHHnpoIF+mTzRNg+zJ5xtAk64PdZYMHT64l+qtTzO15h8sUFoBcOomDiReTvqC1eTPuR5MFqxBvo6maTQ1NZGamur94AkPiY0xLUyGkgej3ikvL6ehoYHy8nLcbjd79uwBYNy4cSQmJvp8jhY7zJNwOzwNnQvXAzt9bngtdwqYgy3JQ4eUK2MSH2PB1DuDEs1du3YNxssExNMAuszzx5n9oc2MH3aHi/feeoGSRz/D+BcWcWXt86QqrZxRMikZ+w3avraXaf+9kfx5X4B+mpXZ7XZTXFwsd/T4ILExFqoGkM1mo6Kiosf2AwcG7gaH73//+0yfPp2HHnqI1tZWpk+fzvTp0w2vEdIUM8SdawS1VPd8wLmbFhgxawByHL6kXBmT+BgLpt4ZlD7rlStXUl5ePhgv1WtmsxkyzjWAqveFNjMXOHGmiT3//D2TytazkHNxU+Bg/CzUuV/hkgVfINs0MG+dxWLxjsWL7iQ2xkIxBPbyyy/zrW99i7S0NHRd57e//S1z584F4LbbbmP37t0D8rrr168PbA4gzsUnKdfT+9NaDdkXDFV39gDlRVcDSMqVMYmPsWDqnX6rsb70pS/53K7rOg0NF5n6PQQ0TYPcqYACTSc9Z2RJORd93oDqaKHklf9j+KE/cKPiiVk7sRwZsZL85d9kYsHEAc+CpmnU1dWRkZEh3a0XkNgYC0UP0I9+9CN2795NZmYmJSUl3HHHHaxZs4Zbbrkl7O5K0zTN0wCq+QSaL+ixctrPn4iNCI8bRgaLlCtjEh9jYdED9Pbbb7Nhw4Ye49+6rntvbwsnmqZBXCrkTIbqvXDyAyj8wqDno8PlpvVsE+kHnoMdTzLL1ggKNKvDqCv8D0Ytv4+pCcMGLT+aprF//34WLVokhe0CEhtjoWgAOZ1OMjMzAZg1axbbt2/n85//PEePHg1qfpCBoGkapI2GY3iW4Omqei9oTs/6e8NGhSJ7ISPlypjEx1hYNIAWL15MYmKiz3V4pk8Pv0X9vN1mI6/wVD4nBr8B9K+9Zex/9WesVl4Hd7NnY9pYmmbcS+rcW0kJwSr1ZrOZpUuXDvrrDgUSG2OhGALLyspi7969TJkyBYD09HS2bNnCHXfc4Z0nJFyYzWbonH/swiV4ys6dJBbMi7olaKRcGZP4GAum3um35uQrr7zidxHCf/7zn/31Mv3G22ocdYXn98nBuU1f03TQ3LBrPYve+izf1DaQ6G5GGzYGVv4Gvl5M6oIvQwgaP578aVRUVITNHT3hRGJjLBRx2bBhg3cunU5Wq5Xnn3+ed999d9DzY8TTA+SvAXQur2MWD2qewoGUK2MSH2MhvQvs7bff9vu/devWBbv7AeMNWsF8z+/aQ9BmPAlaMPadbubeP+/iuT//AX69EP7xTSy2WmyJ+biufxr168Uw9WZQB29FbV80TePYsWNS2HyQ2BgbzLh01jt5eXnk5HS/dq+z3rniiisGLT+9oWkaDBvt+aOhzLPyO4DTBuU7PenRA7+SfbiRcmVM4mMspA2ga6+9lu985zs4HA7vttraWq677joeeOCBYHc/YLzdZgnpkHnu4uIT7/Xra+i6zo5jddz2+518/Vcv84VD3+E/jn0Lag5AbCpc/Rhx9+/GPGMVDNBdXYEym80sWrQobCa1CycSG2ODGZehWO+YzWbP9T2KCh1nz98Kf2qnZ0b6pFzIGB/SPIaClCtjEh9jIR0C2759O//4xz+YPXs2Bw4c4M0336SwsJDW1lY+/vjjYHc/YLq1Gsdd5fl9aGM/7Vtn84FqVj69g9t+u4OJx//AJut3ucpUiq6aYe5X4b5SuPyrYTfhmaZpnDx5Us42fJDYGBvMuAzFekfTNM/QducJV8W5+dGOnxv+Gn1l1F3/A1KuLkbiYyykPUBz586ltLSUKVOmMHPmTFauXMl3vvMdtm7dSn5+frC7HzDdgjbh3DTjn24CV0ef9+l0a7yy+zRX/2I7X9mwi47TH/NazEM8aHmeWMUJo69EufcjuOaxnrPAhgkZb/ZPYmNsMOMyFOsdb3w65/k5XewZBjt87sQrCq//ASlXFyPxMRbyu8AOHz5McXExeXl5VFZWcujQIdrb20lISOiP3Q+Ibt1m+XM83c8tVZ5GUIDLYtidbl4qOcW6d49T0WQjBgcPxrzGavV1TLobYlNg+aMwbVXYn+GZzWbmz58f6myEJYmNscHuoh9q9Y43PnmzYPdzcHKH5w7U2kNgioEJK0KbwRCRcmVM4mMspENgjz32GPPmzeOzn/0s+/fvp7i42Htm9uGHHwa7+wHTbVpx1QRTbvakSzcEtJ+/l55mwU+38v3XDlDRZOOqhGN8NOwhvqL83dP4mXg9fK0Ipt8a9o0f8MTl6NGjMu26DxIbY4MZl6FY73jjM/Yqz3VAp4vgla94tl16jedEKQpJuTIm8TEWTFyCbgD94he/4NVXX+Wpp54iNjaWyy67jKKiIj7/+c+zePHiYHc/YHrMEjv9NkCBI5uh9nCv9xNnMVHX6uCSVJ1N41/j9+7/ZZjtJCRmw5c2wM0bQj/DdAB0XaexsTHsZtENBxIbY4MZl6FY73jjkzICxi/zpGsPAQos+q+Q5SvUpFwZk/gYCyYuQfdZ79u3j4yMjG7bLBYLjz/+OJ/73OeC3f2A6dFtljEOLl0Bh9+EbY/BTX/o8ZxTDe2s236MUekJfHmhZz6PZZNy+OvSs8za/0OUU+emt59+Gyz74fmFD4cQs9nM7NmzQ52NsCSxMTaYQ2BDsd7pFp/P/hDOfAJnK+AzD6FnF+JyOqPyLN9kMjFr1qywm7k7XEi9Yyyka4FdWAl15W9ixHDgs6JZ8oDngsQDr8DMO3pclFh8ooE/fVRORqKVWy8fSaztDOpb32X2wdc9Dxg2Cq77xZC+mNHtdnPkyBHGjx+PyRTaOYnCjcTG2GB+eQ/FeqdbfDIvgW+UgL0ZhzWVqvJy2tvbQ5e5ENJ1HafTySWXXEJcXFyosxN2pN4xFky9IxMLdJUzGWavhuLfwStfYd/VL1NrzmbphGwArps6nPeP1HHz1HRidj4F258ARwsoJph3Lyx+AKzheQFmIGw2W6izELYkNqLfmGPQ4jMoO3IEk8nE8OHDsVqtUdUTous6DoeDyspKTp48ySWXXCLrXfkg9c7AiNoGkL+WtHbVw7R9up2k5k/J+ut1vGC9m4XfuR+LJRZL/RF+nvUWvP5baK/3PCFvNnzu/zyNpwhgMpnCcu22cCCxMSZnp8Z8xcfhcKBpGvn5+cTHx4cgV6EXFxeHxWLh5MmTOBwOYmNDswxQuJJ6x1gw9c6Qb2r/+Mc/Zv78+cTHx5Oamtrr513YbdbW4WL9B2UsfaqYz5y5j0NaPtlKEz92Po7lsRHwoyx4+nJ49zFP42fYaLjxGbhrc8Q0fsATl/3790fltQgXI7ExJnExZhSfaO716OwFkot8fZN6x1hUD4E5HA5uuukm5s2bx+9///uAn3+6sZ0/fniS54vKabG7AEiOzeKNWX9khOl1kg78BVrPgO4GcyyMWui5Zf6ylWGzfIUQQgghAjPkv8EffvhhANavXx/Q8z463sAv9xWx/Uitd03CMRkJ/McVo/jCzDzirWZgBlzzA7A1gaPNM1lihJ+pmUwmCgsLQ52NsCSxMSZDYMYkPr4pikJsbGxUXfsUCKl3jAVTroZ8A6ivHn3rEDE54wBYMC6D1QtGc+Ulmaiqj0IYl+r5iQJut5u9e/cyZcoUqbAvILExJl30xiQ+vum6js1mkyEwP6TeMRbSiRCHquQYlS9MTOCp5Wl8c6rKhBQ3uq55g+lyubqlO9cb8Zd2Op3d0p2FuTPdeatn1zTQLa1pWre0y+UyTLvd7m7pzvz6S/f2mDovQoykY+qv9ykuLi7ijqk/3ych+kJ6f4zJ9AADIywbQD/4wQ9QFMXwp6SkJKjX+PQ33+Tndy7h+qXzmTNnDuvWrWPv3r0cOXIEgNLSUsrKygAoKiri1KlTAOzYsYOqqirAsyJ1XV0dAFu3bqWpqQmAzZs309LSAsDGjRux2+24XC42btyIy+XCbrezcaNnAcSWlhY2b94MQFNTE1u3bgWgrq6O7du3A1BVVcWOHTsAOHXqFEVFRQCUlZVRWloKwJEjR9i7dy8ABw8e5ODBgwABH9MHH3xAeno6JpMpYo6pv96nf/3rX0yYMIGWlpaIOab+fJ/k7NRYpMWntraWnJwcHn30Ue+2nTt3YrVavZ+r3pAhMGMmk4kJEyZE3OenvwQTF0UPw37Huro6b+Xuz6hRo7rdLrl+/Xruv/9+7xeBP7t372bmzJmsX7+eyZMne89c8/LyyMrKAjwBdblcKIriTauqiqqqftNOpxOTyeRNm81mFEXxpsFz1t41bbFY0HXdm9Y0Tw9UZ1rTNMxms9+02+1G13VvujPv/tK9OSa73c7evXuZMWMGuq5HxDH11/tkt9vZv38/U6dORVGUiDim/nyfdu3axdy5c9m1axczZswwLIfRpLPO2blzJ3PmzOn2P7vdTllZGaNHj+5x+3e7wxXwa1lNKmaT57zW5dZwuDVURSHWcv5Lwt9+Pdc9Bmbjxo3ceOON7NixgwkTJjB9+nSuvfZa1q5d2+t9dC71UF1dzZgxY+Q2+Au4XC5KS0uZPn36oC84PBQUFRX1ud4Jy2hmZGQYzvTaHyZNmmQYrK4ftN6kLRZLn9KdX6SA9wutt+muLd/epHt7HGlpaSiK0ufjC7dj6q/3yWq1MmzYMEwmkzcPQ/2Y+vN9kjN4Y4HGZ9L3NwX8Gr+6ZQbXTskFYNOBM3ztL7uZOzqNF/9znvcxC376Dg1tjh7PPfHYtQG/3ooVK7j77rtZtWoVs2fPJjY2lsceewzw9Bjedttt1NTUYDab+d///V9uuukmn/uR3g3/FEVh2LBhUr78CCYuYdkACkR5eTkNDQ2Ul5fjdrvZs2cPAOPGjSMxMdHv86TA+WYymRg3blyosxGWJDbGpEwZi9T4PPHEExQWFvLSSy9RUlLi7cExm82sXbuWadOmUVNTw4wZM1ixYgUJCd1ny1cUhZiYGPmC90PqHWNRfRfY97//fZ577jnv350zZr7zzjuGq0J3XsApunO5XBQVFTFnzhzpbr2AxMaYlCljgcbnk0eWB/waVtP5yzqXX5bNJ48sR72gYfH+d5cEvF8jx48fp7KyEk3TOHnyJFOmTAEgNzeX3FxPb1RWVhZpaWk0NDT0aADpuk5bW5vcBeaH1DvGgql3hnw0169fH/AcQBDdM68aUVWVESNGSHx8kNgYk7gYCzQ+fbkmpytzl+uB+nO/XTkcDlatWsXNN9/MhAkTWL16Nfv27SM7O7vb40pKSrxLfvjSdYhWdCf1jrFg4jLkG0B9JR8m31RVZeTIkaHORliS2BiTMmUsEuOzZs0ampubefLJJ0lMTOStt95i9erVvPHGG97H1NfXc/vtt/O73/3O5z46r6+TITDfpN4xFky5irwS2UvSXe+by+Vi+/btEh8fJDbGJC7GIi0+27ZtY+3atWzYsIHk5GRUVWXDhg28//77PPPMMwB0dHSwcuVKHnjgAebPn+9zPzIEZkzqHWNRPQTWV5F4NtYfVFVl7NixEh8fJDbGoiUuJ06c4Ic//CFbt26lurqa4cOHc+utt7JmzRqsVqvf50VafBYvXuydPLNTQUGBdyoSXde58847Wbp0KbfddpvhvmQIzD+pd4zJEFgfyIfJt87xZtGTxMZYtJSpQ4cOoWka69atY9y4cezfv5+7776btrY2nnjiCb/Pi5b4dPrggw948cUXmTJlCq+++ioAGzZsYPLkyd0eJ0NgxqTeMSYNoD6Q7kTfOrtbFy1aJHccXEBiYyxaytTVV1/N1Vdf7f17zJgxHD58mGeeecawARQt8em0YMEC7xItRnRdp7W1VYbA/JB6x1gw5Sq6Tkm6iLazsd5SVZXCwkKJjw8SG2PRHJfm5mbS0tIMHxPN8bmYmJiYUGchbEm9Y0x6gPpAPky+qarqXRJEdCexMRatZerYsWM89dRT/OxnPzN83MGDB1FVtdvyO8nJyd6ej87fiqL0Kq1pmndtRF/pzn12Tauq6l0U11c6kNfvrzTQbfkWq9Ua8mVdwm2pmoyMDNxuN6qqRswx9df7FEzPYXTWWERfd3RvOZ1ONm3a1OPiRiGxuZihXqb6sghzZWUlV199NTfddBNf/vKXDfd/++23M3PmTObMmeNdgPnw4cPeuLW3t9PR0QFAW1sbDodnuYrW1lbvZ66lpcX7+JaWFu8XwdmzZ73DTWfPnvU2bC5MA2ia5k273W7v4rkul8ubdjqdtLa2Ap65ftra2gDPXV3t7e2AZx0zm83mTdvtdgBsNps33dtj6hwC27lzZ1gs7Avhs1hxZ70TScfUn+/TsWPH6KuwXAx1IHUuTFhcXMysWbNCnZ2wo2kaTU1NpKamRu0ZvT8SG2MlJSXMnj17yC6GGugizJWVlSxZsoS5c+eyfv16v5+Jzjrnueeeo7CwsEcP0MmTJxkzZox3GCjaeoA0TaO9vZ3y8nLy8/NJSEgIi56FcOktMZlMNDY2kpSUhNVqjYhj6s/3KeIWQx0M8gXmm6qqF72WIVpJbIwN9TIVyCLMFRUVLFmyhJkzZ/KHP/yhV8deWFjYo4K22+3eBkrXu6B6k+76mv7Svp7b2VDylQ7k9fsrraqq9wvUYrF48y8LMJ8/pvT0dO//I+WY+ut9CubC8KFdYwVhqHfXDxSn08mbb74pwzw+SGyMRUuZqqysZPHixeTn5/PEE09QW1tLdXU11dXVhs+LlvgEqnNILsoGI3pN6h1jMhFiH0TqyszBMpvNLFy4UG639EFiYyxaytTmzZs5evQoR48eJS8vr9v/jL7EoyU+gVIUhYSEBOrr60OdlbAk9Y6xYMpV1PYAyaRbvimKQnJyssTHB4mNsWiJy5133um9dubCHyPREp9AdV57InyTesdYMHGJ2gaQdEf75nQ6ee2116S71QeJjTEpU8YkPr7JEJgxqXeMyUSIfSBnHL6ZzWaWLVsm3a0+SGyMSZkyFsnxaWxs5OGHH/beMh0IRVFITEyUHg4/pN4xFky5koiKHqSg+SexEaKn++67j8bGRkpLS73rfon+I/XOwIjaHqDOeQREd10nsBLdSWyMSZkyFqnxef3112ltbeWNN94gNTWVP//5zwE9X9YCMyb1jrFgylXUNisjuTs6GGazmRUrVsgZhw8SG2NSpoxFanyuv/56rr/+egDWr18f8PM7h8DkLjDfpN4xJneBiX4lZxr+SWyEEINN6p2BEbUNoEjtjg6Wy+Vi8+bNUuB8kNgYkzJlTOLjmwyBGZN6x1gw5SpqG0DSneibxWLhhhtu6DaNufCQ2BiTMmUs0uJTW1tLTk4Ojz76qHfbzp07sVqt3gUve0NVVZnnxoDUO8ZkKYw+kLMN37quIC26k9gYk7gYi7T4ZGZm8uyzz/KDH/yAkpISWltbufXWW7n33ntZtmxZr/ej67r0jhmQesdYMHGJ2gaQFDjfXC4X7733nnS3+iCxMSZlyliv46Pr4GgLzU+AXyYrVqzg7rvvZtWqVdxzzz3Exsby2GOPAXDq1CkWL17MpEmTmDJlCn/961/9HK5OW1ubfMH7IfWOMbkLrA8irTu6v1gsFq699tpQZyMsSWyMSZky1uv4ONvh0eEDmxl/HqwEa0JAT3niiScoLCzkpZdeoqSkhNjYWMBzvGvXrmXatGnU1NQwY8YMVqxYQUJC9/13DoHJXWC+Sb1jTIbA+kDTtFBnISxpmkZDQ4PExweJjTGJi7FIjc/x48eprKxE0zROnjzp3Z6bm8u0adMAyMrKIi0tjYaGhh7P13Udl8slPUB+SL1jLJi4RO0pm3yYfHO73RQXF7N06VJUNWrbxz5JbIxJmTLW6/hY4j09MaFgiQ/o4Q6Hg1WrVnHzzTczYcIEVq9ezb59+8jOzu72uJKSEjRNIz8/v8c+dF3HZrMFle1IJvWOMWkA9YF01/tmsVhYvnx5qLMRliQ2xqRMGet1fBQl4GGoUFmzZg3Nzc08+eSTJCYm8tZbb7F69WreeOMN72Pq6+u5/fbb+d3vfudzH6qqkpSURF1d3WBle0iReseYDIH1gZyt+qZpGjU1NRIfHyQ2xiQuxiItPtu2bWPt2rVs2LCB5ORkVFVlw4YNvP/++zzzzDMAdHR0sHLlSh544AHmz5/vcz+6ruN0OmUIzA+pd4wFExdpAIluNE1j//79Eh8fJDbGJC7GIi0+ixcvxul0smDBAu+2goICmpqa+OpXv4qu69x5550sXbqU2267zXBfHR0dA53dIUvqHWPSAOoD6a73zWw2s3TpUomPDxIbYxIXY9EWnw8++IAXX3yRV199lWnTpjFt2jT27dvX43Gda4HJRIi+Sb1jLJi4RG1EpTXtm6ZpVFVVkZubKxfcXUBiY0zKlLFoi8+CBQt6dcy6ruNwOGQIzA+pd4xJD1AfRFtl1FuapnHs2DGJjw8SG2MSF2MSH/+cTmeosxC2pN4xJneB9YF0J/pmNptZtGhRqLMRliQ2xqRMGZP4+KYoCgkJCTIE5ofUO8bkLrA+kNa0b52TmUl8epLYGJO4GJP4+CZDYMak3jEmQ2B9IB8m3zRNo6KiQuLjg8TGmMTFmMTHPxkC80/qHWMyBNYH0h3tm9ls9jtfR7ST2BiTMmVM4uObDIEZk3rHmAyB9YGsXO2b2+3m6NGjEh8fJDbGJC7GjOITzcM/uq5jt9ujOgZGpN4xFkxcorYBJIXNN13XaWxslPj4ILExJnEx5is+FosFgPb29sHOTljpPP7OeIjzpN4xFkxcorZPVrqjfTObzcyePTvU2QhLEhtjUqaM+YqPyWQiNTWVmpoaAOLj46NqKEjXddrb22lubmbYsGGYTKZQZynsSL1jTCZC7APpTvTN7XZz5MgRxo8fL5XRBSQ2xqRMGfMXn5ycHABvIyja6LqOy+UiMzMz1FkJS1LvGAum3onaBpDwz2azhToLYUtiI/qboijk5uaSlZUVlXdDqarKgQMHoqrnK1BS7wyMId0AOnHiBD/84Q/ZunUr1dXVDB8+nFtvvZU1a9ZgtVp9Pqe2thaAhoaGwczqkFFTU8Nrr71GTk4Oubm5oc5OWJHYGOssU51lLJJdf/317Nmzh5qaGoYNG8ZnPvMZfvrTnzJ8+PAej+1tnWMymaLyDL+qqkrKlQGpd4wFU+8M6YugDx06hKZprFu3jgMHDvB///d//PrXv+bBBx/0+5y6ujogerubL+b06dM8/PDDnD59OtRZCTsSG2OdZaqzjEWyJUuW8NJLL3H48GH+9re/cezYMb74xS/6fKzUOcakXBmT+BgLpt4Z0j1AV199NVdffbX37zFjxnD48GGeeeYZnnjiiRDmTAgRyb71rW950yNHjuR73/seN954I06nU+5kEmKIGNI9QL40NzeTlpZ20cfJqrq+dXbBR2NX/MVIbIxFa5lqaGjgz3/+M/Pnzzds/ERrfC5GypUxiY+xYMrVkO4ButCxY8d46qmn+NnPfub3MR0dHQC89957wPlptLOysrwNJ5PJhMvlQlEUb1pVVVRV7XXaZDKhKIo3DZ6r1bumzWYzuq5705qmoWlar9Nutxtd173pzrz7S/fmmPbt24eiKBw4cCBijqm/3qf9+/cDsH//flwuV0QcU3++T8ePH+9WxiLdd7/7XX75y1/S3t7O5ZdfzhtvvOHzcVLnSJ0TzDEdPnwYRVHYt2+f9/Mz1I+pP9+nY8eOdStnAdHD0EMPPaQDhj/FxcXdnlNRUaGPGzdOX716teG+n3rqqYvuW37kR376/vPUU08NZPUwYAKtd2pra/XDhw/rmzdv1q+44gp9xYoVuqZpPfYrdY78yM/A//Sl3lF0Pfyml6yrq7voBU2jRo0iNjYWgMrKSpYsWcLcuXNZv369YZdYXV0dL7zwAvHx8cTExHi3Z2RkyDwUQgTBZrNx4sQJli9fTkZGRqizE7BA652uTp8+TX5+Pjt27GDevHk99it1jhADI5h6JywbQIGoqKhgyZIlzJw5kz/96U8yTiqEGHSnTp2ioKCAd955h8WLF4c6O0KIXhjSDaDKykquvPJKCgoK+OMf/9it8dM5u6oQQvSnoqIiioqKWLBgAcOGDeP48eN8//vfp6qqigMHDnTr5RFChK8hfRH05s2bOXr0KEePHiUvL6/b/4Zwu04IEcbi4uJ45ZVXeOihh2hrayM3N5err76aF154QRo/QgwhQ/q+zDvvvBNd133++PL0008zevRoYmNjmTlzpveuDAHbt2/nuuuuY/jw4SiKwquvvhrqLIWNn/zkJ8yePZukpCSysrK48cYbOXz4cKizFTaeeeYZpkyZQnJyMsnJycybN4+33nor1NkaMJMnT2br1q3U19djt9spKyvjmWeeYcSIET4fL/WOf1Lv+Cf1jrH+qHeGdAMoEC+++CL3338/a9asobS0lIULF3LNNddQXl4e6qyFhba2NqZOncovf/nLUGcl7Lz77rt87Wtf46OPPmLLli24XC6WLVtGW1tbqLMWFvLy8njssccoKSmhpKSEpUuXcsMNN3DgwIFQZy3kpN4xJvWOf1LvGOuXeifg+8aGqDlz5uj33HNPt20TJkzQv/e974UoR+EL0P/+97+HOhthq6amRgf0d999N9RZCVvDhg3Tf/e734U6GyEn9U7vSb1jTOqdiwu03omKHiCHw8GuXbtYtmxZt+3Lli1jx44dIcqVGKqam5sBejXjeLRxu9288MILtLW19bgdPNpIvSP6k9Q7/vW13hnSF0H3Vl1dHW63m+zs7G7bs7Ozqa6uDlGuxFCk6zrf/va3WbBgAYWFhaHOTtjYt28f8+bNw263k5iYyN///ncmTZoU6myFlNQ7or9IveNbsPVOVDSAOimK0u1vXdd7bBPCyNe//nX27t3L+++/H+qshJVLL72UPXv20NTUxN/+9jfuuOMO3n333ahvBIHUOyJ4Uu/4Fmy9ExUNoIyMDEwmU4+zrpqamh5nZ0L4841vfIPXX3+d7du395h2IdpZrVbGjRsHwKxZsyguLuYXv/gF69atC3HOQkfqHdEfpN7xL9h6JyquAbJarcycOZMtW7Z0275lyxbmz58folyJoULXdb7+9a/zyiuvsHXrVkaPHh3qLIU9XdejZlFUf6TeEcGQeidwgdY7UdEDBPDtb3+b2267jVmzZjFv3jx+85vfUF5ezj333BPqrIWF1tZWjh496v27rKyMPXv2kJaWRkFBQQhzFnpf+9rX+Mtf/sJrr71GUlKS94w+JSWFuLi4EOcu9B588EGuueYa8vPzaWlp4YUXXmDbtm3885//DHXWQk7qHWNS7/gn9Y6xfql3BuBOtLD1q1/9Sh85cqRutVr1GTNmyO2EXbzzzjs+V9i94447Qp21kPMVF0D/wx/+EOqshYW77rrLW64yMzP1q666St+8eXOosxU2pN7xT+od/6TeMdYf9c6QXgtMCCGEEKIvouIaICGEEEKIrqQBJIQQQoioIw0gIYQQQkQdaQAJIYQQIupIA0gIIYQQUUcaQEIIIYSIOtIAEkIIIUTUkQaQEEIIIaKONICEEEIIEXWkASTC1uLFi7n//vtDnQ0hRBSReid6SANICCGEEFFH1gITYenOO+/kueee67atrKyMUaNGhSZDQoiIJ/VOdJEGkAhLzc3NXHPNNRQWFvLII48AkJmZiclkCnHOhBCRSuqd6GIOdQaE8CUlJQWr1Up8fDw5OTmhzo4QIgpIvRNd5BogIYQQQkQdaQAJIYQQIupIA0iELavVitvtDnU2hBBRROqd6CENIBG2Ro0axc6dOzlx4gR1dXVomhbqLAkhIpzUO9FDGkAibP3Xf/0XJpOJSZMmkZmZSXl5eaizJISIcFLvRA+5DV4IIYQQUUd6gIQQQggRdaQBJIQQQoioIw0gIYQQQkQdaQAJIYQQIupIA0gIIYQQUUcaQEIIIYSIOtIAEkIIIUTUkQaQEEIIIaKONICEEEIIEXWkASSEEEKIqCMNICGEEEJEHWkACSGEECLq/P/9Nx4fi0vOHwAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,2, figsize=(6, 2.3))\n", "\n", "Td = np.arange(0, 3, 0.01)\n", "X0 = [-1, 0.5]\n", "# 入力 u = Fx\n", "u = np.zeros_like(Td)\n", "# u = 10*np.sin(10*T)\n", "\n", "x, t, _ = lsim(G, u, Td, X0)\n", "ax[0].plot(t, x[:, 0], ls='-.', label='${x}_1$')\n", "ax[1].plot(t, x[:, 1], ls='-.', label='${x}_2$')\n", "\n", "# 出力 y = Cx\n", "y = x[:, 0]\n", "# オブザーバで推定した状態の振る舞い\n", "xhat, t, _ = lsim(Obs, np.c_[u, y], Td, [0, 0])\n", "ax[0].plot(t, xhat[:, 0], label='$\\hat{x}_1$')\n", "ax[1].plot(t, xhat[:, 1], label='$\\hat{x}_2$')\n", "\n", "for i in [0, 1]:\n", " plot_set(ax[i], 't', '', 'best')\n", " ax[i].set_xlim([0, 3])\n", "\n", "ax[0].set_ylim([-2, 1])\n", "ax[1].set_ylim([-3, 1])\n", "ax[0].set_ylabel('$x_1, \\hat{x}_1$')\n", "ax[1].set_ylabel('$x_2, \\hat{x}_2$')\n", "\n", "fig.tight_layout()\n", "# fig.savefig(\"obs.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 出力フィードバック" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "オブザーバ併合レギュレータを設計します" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-25. -5.]]\n" ] } ], "source": [ "from control.matlab import tf, feedback, initial\n", "\n", "# レギュレータ極\n", "regulator_poles = [-5+2j, -5-2j]\n", "# 極配置\n", "F = -acker(P.A, P.B, regulator_poles)\n", "print(F)\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "K:\n", " : sys[5]\n", "Inputs (1): ['u[0]']\n", "Outputs (1): ['y[0]']\n", "States (2): ['x[0]', 'x[1]']\n", "\n", "A = [[-15. 1.]\n", " [-75. -10.]]\n", "\n", "B = [[15.]\n", " [46.]]\n", "\n", "C = [[-25. -5.]]\n", "\n", "D = [[0.]]\n", "\n", "----------------\n", "K(s)= \n", " -605 s - 2725\n", "----------------\n", "s^2 + 25 s + 225\n", "\n" ] } ], "source": [ "# 出力フィードバック(オブザーバ+状態フィードバック)\n", "K = ss(P.A+P.B@F+L@P.C, -L, F, 0)\n", "print('K:\\n', K)\n", "print('----------------')\n", "print('K(s)=', tf(K))\n", "\n", "# フィードバック系\n", "Gfb = feedback(P, K, sign=1)\n" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(-1.5, 0.5)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(3, 2.3))\n", "Td = np.arange(0, 3, 0.01)\n", "\n", "y, t = initial(P, Td, [-1, 0.5])\n", "ax.plot(t,y, ls='-.', label='w/o controller')\n", "\n", "y, t = initial(Gfb, Td, [-1, 0.5, 0, 0])\n", "ax.plot(t,y, label='w/ controller')\n", "\n", "plot_set(ax, 't', 'y', 'best')\n", "ax.set_xlim([0, 3])\n", "ax.set_ylim([-1.5, 0.5])\n", "\n", "# fig.savefig(\"obs2.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 外乱オブザーバ" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "出力に0.5の定値外乱が加わるとすると,推定がうまくいきまんせん" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,2, figsize=(6, 2.3))\n", "\n", "Td = np.arange(0, 3, 0.01)\n", "X0 = [-1, 0.5]\n", "d = 0.5*(Td>=1.5)\n", "\n", "G = ss(P.A, P.B, np.eye(2), [[0],[0]])\n", "x, t = initial(G, Td, X0)\n", "ax[0].plot(t, x[:, 0], ls='-.', label='${x}_1$')\n", "ax[1].plot(t, x[:, 1], ls='-.', label='${x}_2$')\n", "\n", "# 入力 u\n", "u = np.zeros_like(Td)\n", "# 出力 y = Cx+d\n", "y = x[:, 0]+d\n", "Obs = ss(P.A + L@P.C, np.c_[P.B, -L], np.eye(2), [[0,0],[0,0]] )\n", "\n", "xhat, t, _ = lsim(Obs, np.c_[u, y], Td, [0, 0])\n", "ax[0].plot(t, xhat[:, 0], label='$\\hat{x}_1$')\n", "ax[1].plot(t, xhat[:, 1], label='$\\hat{x}_2$')\n", "\n", "for i in [0, 1]:\n", " ax[i].grid(ls=':')\n", " ax[i].set_xlim([0, 3])\n", " ax[i].set_xlabel('t')\n", " ax[i].legend()\n", "\n", "ax[0].set_ylim([-2, 2])\n", "ax[0].set_ylabel('$x_1, \\hat{x}_1$')\n", "ax[1].set_ylabel('$x_2, \\hat{x}_2$')\n", "\n", "fig.tight_layout()\n", "# fig.savefig(\"dis_obs.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "拡大系を構成し,外乱もオブザーバで推定できるようにする" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 75.75]\n", " [-91. ]\n", " [-93.75]]\n" ] } ], "source": [ "# オブザーバ極\n", "observer_poles=[-10+5j,-10-5j, -3]\n", "\n", "# オブザーバゲインの設計(状態フィードバックの双対)\n", "\n", "Abar = np.block( [ [P.A, np.zeros([2,1])], [np.zeros((1,3))] ])\n", "Bbar = np.block( [ [P.B], [0] ])\n", "Cbar = np.block( [ P.C, 1 ] )\n", "\n", "Lbar = -acker(Abar.T, Cbar.T, observer_poles).T\n", "print(Lbar)\n", "\n", "Aob = Abar + Lbar@Cbar\n", "Bob = np.block([Bbar, -Lbar])\n", "Obs = ss(Aob, Bob, np.eye(3), np.zeros([3,2]) )\n" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([-10.+5.j, -10.-5.j, -3.+0.j])" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Obs.poles()\n" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(-0.5, 2.0)" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,2, figsize=(6, 2.3))\n", "\n", "Td = np.arange(0, 3, 0.01)\n", "X0 = [-1, 0.5]\n", "d = 0.5*(Td>=1.5)\n", "x, t = initial(G, Td, X0)\n", "ax[0].plot(t, x[:, 0], ls='-.', label='${x}_1$')\n", "ax[1].plot(t, x[:, 1], ls='-.', label='${x}_2$')\n", "\n", "\n", "# 入力 u = Fx\n", "u = np.zeros_like(Td)\n", "# 出力 y = Cx+d\n", "y = x[:, 0]+d\n", "xhat, t, _ = lsim(Obs, np.c_[u, y], Td, [0, 0, 0])\n", "#xhat, t, x0 = lsim(Obs, x[:, 0]+d, T, [0, 0, 0])\n", "ax[0].plot(t, xhat[:, 0], label='$\\hat{x}_1$')\n", "ax[1].plot(t, xhat[:, 1], label='$\\hat{x}_2$')\n", "\n", "for i in [0, 1]:\n", " ax[i].grid(ls=':')\n", " ax[i].set_xlim([0, 3])\n", " ax[i].set_xlabel('t')\n", " ax[i].legend()\n", "\n", "ax[0].set_ylabel('$x_1, \\hat{x}_1$')\n", "ax[1].set_ylabel('$x_2, \\hat{x}_2$')\n", "\n", "fig.tight_layout()\n", "# fig.savefig(\"dis_obs2.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n", "\n", "fig, ax = plt.subplots(figsize=(3, 2.3))\n", "ax.plot(t, xhat[:, 2], label='$\\hat{x}_2$', color='k')\n", "ax.grid(ls=':')\n", "ax.set_xlabel('t')\n", "ax.set_ylabel('$\\hat{d}$')\n", "ax.set_ylim([-0.5, 2])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "外乱 0.5 が推定できていて,状態推定もできています" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 定常カルマンフィルタ" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "from control.matlab import ss, lqe, lsim\n" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ ": sys[12]\n", "Inputs (1): ['u[0]']\n", "Outputs (1): ['y[0]']\n", "States (2): ['x[0]', 'x[1]']\n", "\n", "A = [[ 0. 1.]\n", " [-4. -5.]]\n", "\n", "B = [[0.]\n", " [1.]]\n", "\n", "C = [[1. 0.]]\n", "\n", "D = [[0.]]\n", "\n" ] } ], "source": [ "# A = '0 1; -4 -5'\n", "# B = '0; 1'\n", "# C = '1 0'\n", "# D = '0'\n", "\n", "A = [[0, 1], [-4, -5]]\n", "B = [[0], [1]]\n", "C = [1, 0]\n", "D = [0]\n", "P = ss(A, B, C, D)\n", "print(P)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-0.0245608 ]\n", " [-0.00030162]]\n" ] } ], "source": [ "QN = 1\n", "RN = 1\n", "L, _, _ = lqe(P.A, P.B, P.C, QN, RN)\n", "L = -L\n", "print(L)\n" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.0633029256172646\n", "-0.009360534572358931\n", "[[-0.0245608 ]\n", " [-0.00030162]]\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Td = np.arange(0, 6, 0.01)\n", "u = 0.5 * np.sin(6*Td) + 0.5 * np.cos(8*Td)\n", "\n", "QN, RN = 1, 1\n", "w = np.random.normal(loc=0, scale=np.sqrt(QN), size=len(Td))\n", "v = np.random.normal(loc=0, scale=np.sqrt(RN), size=len(Td))\n", "\n", "print(np.var(w))\n", "print(np.mean(w))\n", "\n", "L, _, _ = lqe(P.A, P.B, P.C, QN, RN)\n", "L = -L\n", "print(L)\n", "# L = np.matrix([[-1], [-1]])\n", "Obs = ss(P.A + L@P.C, np.block([P.B, -L]), np.eye(2), np.zeros([2,2]))\n", "\n", "X0 = [-0.3, 0.2]\n", "_, t, x = lsim(P, u+w, Td, X0)\n", "_, t, xorg = lsim(P, u, Td, X0)\n", "\n", "# 出力 y = Cx\n", "y = x[:, 0]+v\n", "\n", "fig, ax = plt.subplots(2,2, figsize=(6, 4.6))\n", "ax[0,1].plot(t, y, ls='-.', label='$y$', c='gray', lw=0.5)\n", "ax[1,0].plot(t, xorg[:,0], ls='--', label='$x_1$', c='k')\n", "ax[1,1].plot(t, xorg[:,1], ls='--', label='$x_2$', c='k')\n", "ax[0,0].plot(t, u+w, ls='-.', label='$u+w$', c='gray', lw=0.5)\n", "\n", "# 入力 u = Fx\n", "#u = [ [F[0,0]*x[i,0]+F[0,1]*x[i,1]] for i in range(len(x))]\n", "#u = np.sin(T)\n", "#u = 0*(T>0)\n", "\n", "# オブザーバで推定した状態の振る舞い\n", "xhat, t, _ = lsim(Obs, np.c_[u, y], Td, [0, 0])\n", "ax[1,0].plot(t, xhat[:, 0], label='$\\hat{x}_1$', c='k')\n", "ax[1,1].plot(t, xhat[:, 1], label='$\\hat{x}_2$', c='k')\n", "ax[0,0].plot(t, u, label='$u$', c='k', ls='--')\n", "\n", "for i in [0, 1]:\n", " for j in [0, 1]:\n", " plot_set(ax[i,j], '$t$', '', 'best')\n", " ax[i,j].set_xlim([0, 6])\n", "\n", "ax[0,1].set_ylim([-4, 4])\n", "ax[0,1].set_ylabel('$y$')\n", "ax[0,0].set_ylabel('$u$')\n", "ax[0,0].set_ylim([-4, 4])\n", "ax[1,0].set_ylim([-0.4, 0.4])\n", "ax[1,0].set_ylabel('$x_1$')\n", "ax[1,1].set_ylim([-0.4, 0.4])\n", "ax[1,1].set_ylabel('$x_2$')\n", "\n", "\n", "fig.tight_layout()\n", "# fig.savefig(\"ex_kalman.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## ロバスト制御" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "from control.matlab import tf, bode, logspace, mag2db, ss2tf, step, feedback\n" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "g = 9.81 # 重力加速度[m/s^2]\n", "l = 0.2 # アームの長さ[m]\n", "M = 0.5 # アームの質量[kg]\n", "mu = 1.5e-2 # 粘性摩擦係数\n", "J = 1.0e-2 # 慣性モーメント\n", "\n", "P = tf( [0,1], [J, mu, M*g*l] )\n", "\n", "ref = 30 # 目標角度 [deg]\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 乗法的不確かさ" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# 垂直駆動アームのノミナルモデル\n", "Pn = tf( [0,1], [J, mu, M*g*l] )\n", "\n", "# Pn = tf( [0, 1], [1, 1])\n", "# 不確かさ\n", "delta = np.arange(-1, 1 , 0.1)\n", "WT = tf( [10, 0], [1, 150])\n", "\n", "fig, ax = plt.subplots(1, 2, figsize=(6,2.3))\n", "# fig, ax = plt.subplots(1, 2)\n", "\n", "for i in range(len(delta)):\n", " # 不確かさをもつ制御対象\n", " P = (1 + WT*delta[i])*Pn\n", " mag, _, w = bode(P, logspace(-3,3), plot=False)\n", "\n", " ax[0].semilogx(w, mag2db(mag), color = 'k', lw = 0.3)\n", "\n", " # 乗法的不確かさ\n", " DT = (P - Pn)/Pn\n", " mag, _, w = bode(DT, logspace(-3,3), plot=False)\n", "\n", " ax[1].semilogx(w, mag2db(mag), color = 'k', lw = 0.3)\n", "\n", "mag, _, w = bode(Pn, logspace(-3,3), plot=False)\n", "ax[0].semilogx(w, mag2db(mag), lw =2, color='k')\n", "\n", "mag, _, w = bode(WT, logspace(-3,3), plot=False)\n", "ax[1].semilogx(w, mag2db(mag), lw =2, color='k')\n", "\n", "ax[0].set_ylim(-100, 50)\n", "ax[1].set_ylim(-100, 50)\n", "bodeplot_set(ax)\n", "ax[0].set_xlabel('$\\omega$ [rad/s]')\n", "ax[0].set_ylabel('Gain of $P$ [dB]')\n", "ax[1].set_ylabel('Gain of $\\Delta W_T$ [dB]')\n", "#ax.grid(which=\"both\", ls=':')\n", "#ax.set_ylabel('Gain [dB]')\n", "#ax.set_xlabel('$\\omega$ [rad/s]')\n", "\n", "fig.tight_layout()\n", "# fig.savefig(\"robust_plant.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 混合感度問題" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "K= \n", " 7.21 s^4 + 1098 s^3 + 3259 s^2 + 1.081e+05 s + 9.032e+04\n", "---------------------------------------------------------------\n", "s^5 + 165.1 s^4 + 2448 s^3 + 2.449e+04 s^2 + 2.273e+04 s + 5540\n", "\n", "gamma = 0.9527651218302327\n" ] }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAk0AAADbCAYAAABwWqUvAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAA9hAAAPYQGoP6dpAABdMUlEQVR4nO2dd1gU1/rHv7O7VGkq4tpRscZeYwVUQLBGr16j10gSvRpbbDGJSdTcFG/UxG4sSSwxxhiNioqKBXsBUaOJaNQLYkNAUTpsOb8/+O2EZRdYYGZny/t5nn04zM6eec935333zKkcY4yBIAiCIAiCKBWZ1AYQBEEQBEFYA1RpIgiCIAiCMAGqNBEEQRAEQZgAVZoIgiAIgiBMgCpNBEEQBEEQJkCVJoIgCIIgCBOgShNBEARBEIQJUKWJIAiCIAjCBKjSRBAEQRAEYQJUaSIIgiAIgjABq600LVq0CBzHYcaMGfwxxhgWLlyI2rVrw8XFBQEBAfjzzz+lM5IgCLuA4hFB2AdWWWmKjY3Fhg0b0KZNG73jixcvxjfffIPVq1cjNjYWSqUSQUFByMzMlMhSgiBsHYpHBGE/WF2lKSsrC2PGjMHGjRtRtWpV/jhjDMuXL8dHH32EYcOGoVWrVtiyZQtycnKwfft2CS0mCMJWoXhEEPaFQmoDysuUKVMwYMAA9OvXD59//jl/PCEhAcnJyQgODuaPOTk5wd/fH+fPn8fEiRMN8kpLS8OOHTvg6uoKJycn/ri3tzdq1KghbkEIwobIzc1FYmIiQkJC4O3tLbU5ZoPiEUFYHmLGI6uqNO3YsQNXrlxBbGyswXvJyckAgJo1a+odr1mzJu7fv280vyNHjmDatGnCG0oQdsq2bdswZswYqc0wCxSPCMKyESMeWU2l6cGDB3j33XcRFRUFZ2fnEs/jOE7vf8aYwTEdvr6+AICFCxfCz88PWq0WAODj44Nq1aoBAORyOdRqNTiO49MymQwymczktFwuB8dxfBoANBqNXlqhUIAxxqe1Wi20Wq3JaY1GA8YYn9bZXlK6tDIxxnD16lW0bdsWDg4ONlGmyn5PN2/exBtvvIEvvvgC1apVQ5s2beDs7GzVZRLye7p58ybCw8N5n7J1KB6Z9z7XarW4cuUK2rdvDwcHB71zYmJi8O6776Jbt2744osv+O/D0sskxPcEAFeuXKF4ZMZ4ZDWVpri4OKSkpKBjx478MY1Gg9OnT2P16tW4ffs2gMInvFq1avHnpKSkGDzt6XBxcQEADBgwAJ06dRLReutCq9WiYcOG8Pb2hkxmdcPeRGHlypVo0qQJ3nvvPaSnp5M2xdBVBHQ+ZetQPDIvWq0Wvr6+Rv2uQ4cOqF+/PoYMGYJ169Zhy5YtduObpeliz4gZj6xG5b59++LGjRu4du0a/+rUqRPGjBmDa9euoVGjRlAqlTh69Cj/mYKCApw6dQrdu3cvNW+62fSRyWTw8fEhXYqwZs0a7N69Gw4ODqSNEexND4pH5qWsmBQWFobt27dj7969uHnzppmtkw6K1cYRUw+raWlyd3dHq1at9I5VqVIF1atX54/PmDEDX375JZo0aYImTZrgyy+/hKurK0aPHl1q3mq1WjS7rRGVSoUTJ06gT58+cHBwkNocycnOzoabmxtat25N2pSAvfkQxSPzYorfjRgxAoGBgfD29gZjDIBh96itQfHIOGL6kNVUmkxh7ty5yM3NxeTJk5Geno6uXbsiKioK7u7upX6urFqpRqOBSqUS0lSLRqvVom3btlCpVHx/dmVxcHDg+62tiaSkJLRu3Rp79uxBnz59IJfL0blzZ6ssi5jQk64hYsUje8RUv/P29oZWq0V4eDiaN2+OefPmmclCaaB4ZBxqaSqBkydP6v3PcRwWLlyIhQsXliufkgRmjCE5ORkvXryomIFWTnp6uqD5eXl5QalUWtXTn4eHB95//3106dIFQOG9ohuUS/wN/dCLH4/smfL4nUwmg5+fHz766CN4eHhg6tSpIlsnHRSPjEOVJpEpqSlPV2Hy8fGBq6urVf3YVwatVousrCy4ubkJcvMxxpCTk4OUlBQA0BsYa+l4eXnpPa2qVCpERUUhODiYmsOLQF1KwkFaGlJev/vkk0/w8uVLTJs2De7u7hg3bpwZrDQ/FI+MQ91zImOsaVOj0fAVpurVq0tglXQwxuDk5ASZTCZYRVE3iyElJQU+Pj5W0Zz81VdfQaVS4eOPP+aPKRQK9OrVCwoFuU5RrOH7tBZIS0PK63ccx2Hp0qXIyMjAW2+9hWbNmuHVV18V2UrzQ/HIOGL6ELUDw/hgQd0YJldXV3ObIzm6dTiEblnTaWkN48MyMjKwaNEigy5KjuPg4eFhN62OpkJ6CAdpaUhF/I7jOKxbtw4bN25E586dRbROOigeGUdMPajShNKb8uzxZtRqtXjx4gW/uJ5QWJOW3377LXJzczFr1iy94yqVCvv27bOKip85oS4l4SAtDamo38nlcrz11luQy+U4duwYzp49K5KF0kDxyDhi+hBVmkDN4cWx96eX3NxcLFu2DOPGjUOdOnX03lMoFAgODqbm8GKQDwkHaWlIZf2OMYavv/4aAwYMwJUrVwS2TjooHhmHuucIwoxs3rwZqampmDt3rtH3KUARhPmpjN9xHIedO3eiefPmCAkJQXx8vICWSQvFI/NClSZAsLWIbAXGGDIyMvgF4uwJtVqNxYsXY+TIkfDz8zP6fmRkJHWhFIN8SDhIS0OE8Dt3d3ccOnQISqUS/fr1Q0JCgoAWSgPFI+OI6UNUaYLtNYenpKRg4sSJqF+/PpycnKBUKhESEoILFy6Y9Hl77p7bsWMHEhMT8cEHHxh9X6FQICwsjJ7uimFrPiQlpKUhQvldtWrVcPToUTRv3twmxgFRPDKOmD5EStsgw4cPh0qlwpYtW9CoUSM8ffoUx48fx/Pnz6U2zaLRarVYtGgRBgwYgLZt25Z4nlqtpiBFEGZGKL9TKpU4fvw4ACAzMxMFBQVWvawMxSPzQkrDtprDX7x4gbNnz+LkyZPw9/cHADRo0IBf0doUdN1z9tbapNFoMGXKlFJ3mFer1YiKikJYWBgtJlcEW/IhqSEtDRHL78aMGYPHjx/jxIkT8PDwECxfc0HxyDhi+hBVmmD6QLpOnTohOTlZZGsMUSqVuHz5sknnurm5wc3NDXv37sWrr74KJyencl9PJpPBy8ur3J+zdhwcHDB58uQyzxkyZIiZLLIe6ElXOEhLQ8Tyu88++wwBAQEYOHAgDh8+bHXr8lE8Mo6YPkTeCZg84Dk5ORmPHj0S2ZrKoVAosHnzZkyYMAHr1q1Dhw4d4O/vj1GjRqFNmzYm5cEYg1arFXRFcEsnOjoaO3bswLJly0oNnIwxZGZmwt3d3W60MQV7nDQgFqSlIWL5Xdu2bREZGYmgoCAMHz4c+/btg6Ojo2D5iw3FI+OI6UNUaYLpTXlKpVJkS4S57vDhwzFgwACcOXMGFy5cwOHDh7F48WJ89913CA8PL/PzOke0p+651NRUPHz4kN/upSTUajXOnDlDez0Vg7qUhIO0NERMv+vWrRv27duHAQMG4NChQ1bVckPxyDjUPScypjblmdpFZgk4OzsjKCgIQUFBmD9/PsaPH48FCxaYVGmyx+65kSNHYuTIkWWe5+DggAEDBpjBIuuCupSEg7Q0RGy/69u3L27fvo0GDRqIdg0xoHhkHDF9iJYcAATfLsQSadmyJbKzs006lzEGtVptN90E33//vcndrlqtFs+fP7eLe6Y8kB7CQVoaYg6/01WYVq5ciRkzZlhF/KN4ZBwx9aBKE2wrSD179gx9+vTBtm3bcP36dSQkJODXX3/F4sWLTW52ZowhOzvbKoJGZfnjjz8wfvx4HDt2zKTzNRoNYmNjqQulGLbkQ1JDWhpiTr9zdHTEihUrsGDBAtGvVVkoHhlHTB+idmDYVnO4m5sbunbtimXLluHevXtQqVSoV68eJkyYgHnz5pmUh0wmg6enp8iWWgaLFi1C/fr1MXr0aJPOd3BwQEhIiMhWWR+25ENSQ1oaYk6/mzRpEjIyMvD+++/D09MTs2fPNst1KwLFI+PQ7DmRsaUnOycnJyxatAiLFi2qcB667jmFQmHTA8Hv3buHHTt2YMWKFSYPotRqtUhLS4O3tzdkMmqo1WFLPiQ1pKUh5va7uXPnIiMjA3PmzEH9+vUxYsQI0a9ZESgeGYe650SGgpQhubm5UpsgOl999RVq1KiBt99+2+TPaLVa/PHHH3TPFIP0EA7S0hAp/O6zzz7DihUrEBQUZLZrlheKR8ahSpPIUHO4Pvaw99yjR4+wefNmzJo1q8xlBoqiUCjQp08fumeKQXoIB2lpiBR+x3Ecpk+fDi8vL/zvf//D4cOHzXZtU6F4ZByaPScyVEvXhzGGgoICmx4IvnTpUlSpUgWTJk0q1+e0Wi0ePXpE90wxSA/hIC0Nkdrvli5diqFDh+LEiROSXL8kpNbFUqGWJpGhG86Q/Px8qU0QjdTUVGzYsAHTp08v935TWq0W9+7do3umGKSHcJCWhkjtd8uWLUNAQAAGDx6MixcvSmKDMaTWxVKhSpPIUNOmPhzH2fSy/Pfv30fTpk0xffr0cn9WoVCgd+/edM8Ug/QQDtLSEKn9zsnJCb/99hs6dOiA0NBQ/P7775LYURypdbFUqHtOZKiWrg9jDPn5+TbbPdepUydcuXIF1atXL/dntVot7t+/T/dMMUgP4SAtDbEEv3N1dcX+/fvRqlUrPHnyRDI7imIJulgi1NIkMnTDGaJSqaQ2QRQOHDiA+Pj4Crei0RgC45AewkFaGmIpfufp6YnTp0+jf//+/HR/KbEUXSwNqjSJDDVt6sNxHNzc3Gyue44xhgULFmDFihUVzkOhUKB79+50zxSD9BAO0tIQS/I7XVz8+OOP0a1bNyQnJ0tmiyXpYklQ9xwKV27u3Lkz3N3d4ePjg6FDh+L27dt65zDGsHDhQtSuXRsuLi4ICAjAn3/+WWbetAS9Powx5OXl2Vz3HMdxOH/+fKUW/tRoNLh79y7dM8WwRz3Eikn2qGVZWKLfjR8/HtnZ2QgODsbz588lscESdbEExNTDaipNp06dwpQpU3Dx4kUcPXoUarUawcHBepvQLl68GN988w1Wr16N2NhYKJVKBAUFITMzs9S8ba1yIAS25oT5+flITEyEk5MTqlatWuF8GGNIT0+ne6YY9qiHWDHJHrUsC0v0u0aNGuHYsWN4/PgxwsLCyvydEQNL1MUSEFUPZqWkpKQwAOzUqVOMMca0Wi1TKpXsv//9L39OXl4e8/T0ZOvWrTOaR1xcHAPA4uLiDN7Lzc1lN2/eZLm5ueIUQEROnTrFBg4cyGrVqsUAsD179hg9b9y4cez9999n3377LXNzc2MqlYp/LzMzkykUCtazZ0+9z5w+fZoBYLdv3y63XVJqum7dOubo6MiePn1q9mvbA6X5kr1Q2ZhEGlonly9fZh4eHuyLL76Q2hTi/xHTl6ympak4L1++BABUq1YNAJCQkIDk5GQEBwfz5zg5OcHf3x/nz58vNa8bN27gypUriI2NRWxsLJ48eQKNRsPXVhlj5UprtdpS04wxg7Quj5LS5bl+VlYW2rRpg9WrV/PvFT9Ho9Hg4MGDGDJkCAICApCVlYXLly/z1z127BiUSiViY2ORk5PD23vy5EnUrl0bTZo0qVCZimqhVqtLTWs0Gr20rvWrpLRardZL666bm5uL//73v3jttddQrVo1/rhKpdJL62zTpRljBmmNRoP4+Hjk5eXx9uoGzZuzTCWlK1Im3XdTtBzlLZOtThwoD0LFpJLikbXdE0Le5xqNBjdv3uRtsKQytWvXDufPn8f7779v9u+J4pH545FVVpoYY5g1axZ69uyJVq1aAQA/GK9mzZp659asWbPMgXrh4eHo2LEjunTpgi5dumD9+vW4ffs2/yXk5OTwiz1mZ2ejoKAAQGHlRPflZGZm8udnZmbyN1ZGRgZ/02RkZPA3R/E0UPjF69IajYZv7lWr1XxapVIhKysLAFBQUMB3BeTn5yMnJwcAEBgYiI8++gjDhg3jzwMKKw865zp+/DhkMhm6du2KunXronbt2jh58iSysrKgVqtx+vRphIaGolGjRjh//jxfppMnT6JHjx4VLpPu+mlpaTh9+jQA4MmTJ/yPyIMHDxATEwOg8Efn6tWrAIA7d+7g+vXrAID4+HjEx8cDAK5fv447d+4AAK5evYqEhAQAQExMDB48eACgcA+pxMREzJs3D6dPn+ZnvJw4cQIvXrwAAERFRfEaR0ZGIi8vD2q1GpGRkVCr1cjLy0NkZCRf5uPHjwMAXrx4wa8SbM4ynT9/np/2LESZMjMzERUVVeEyFR/LY28IGZOMxSNrvCeEvs8TExMttkyMMcjlcnz//fcYNWoUNBqN2b4nikdmjkflbZqyBCZPnswaNGjAHjx4wB87d+4cA8AeP36sd+748eNZSEiI0Xx0TXhbt25lcXFxLCYmhsXExLDHjx+zrKws9ueff7Lc3Fym1WqZVqtljDGT0hqNptS0Vqs1SOvyKCldnusXTQNgv/32m8Hx2bNns7feeos/Pnr0aBYcHMyf07lzZ7Zz5042adIkNm/ePKbRaFheXh5zcXFhGzZsqFCZcnJyeE01Gg3fHVhSWq1W66XVanWpaZVKpZfWaDRMrVazpk2bssGDB+sdZ4yxgoICvbSuTLq0Vqs1SOvKpEtrNBq9tDnKVFpaqjJdunTJrruWhIhJpcUja7wnbPE+L6tMO3fuZDKZjE2YMIEVFBTYRJms8XsSMx5Z3TzFadOmISIiAqdPn0bdunX540qlEkDh012tWrX44ykpKQZPesVp3rw5OnTooHcsLy+Pn1padOp9cnJymQub1a9fH97e3khLS0NSUhKf9507d/QGiRqjVatWcHR0REJCAjQaDZo0aaJ3/fKmi/5f9Pj+/fuxdOlS/nhAQABmzpwJjUaDnJwcXL16Fb1794ZWq8XKlSshk8lw6dIl5Obmom/fvnxen3/+OXbu3AmO4+Dk5IRff/0VDRs21LumsbRMJoNMJis1LZfLeXtNSRedZqpL//LLL/jrr7+wbds2g3McHBzKndY1h7do0cLkcghdptLSFSkTUPjd6NIVKZOtLU9RHoSOScbiUVGs5Z7QIcR9rtFocOvWLd7vLLVMI0aMQHZ2Nt588014eHhgyZIlJpWvomWieGT+eGQ1lSbGGKZNm4Y9e/bg5MmTaNiwod77DRs2hFKpxNGjR9G+fXsAhd1Sp06dwldffSWYHevXr8enn35a6jkbN27E+PHjsXfvXkyYMIHvxw0PDy9z36IHDx6gbt26eP/995GRkYEjR44IZruO+Ph4PHz4EP369eOPBQYGIjs7G7GxsXj+/DmaNGkCHx8f+Pv7Y+zYscjOzsbJkydRv359NGrUCEBhk+zJkydx7do1KBQKPHz4EFWqVBHc3oqi1Wrx+eefIyQkBJ07d5baHMLGsJSYRFgW4eHhyMzMxPTp06FUKjFnzhypTSIExGoqTVOmTMH27duxb98+uLu782MCPD094eLiAo7jMGPGDHz55Zdo0qQJmjRpgi+//BKurq4YPXp0qXkXrUmXxcSJEzF48OBSz6lfvz4AYOjQoXpPjJs3by6zpcnHxwcA8NVXX4k27T8iIgJBQUFwcXHhj/n5+aFu3bqIjo5Geno6AgICwHEclEolGjZsiHPnziE6Ohp9+vThP5OcnIyqVavyTxZFn7ItgYiICPzxxx9Yu3atYHnK5XJ+zArxN+XxIVtBrJhkj1qWhbX53bRp0wAAQUFBol7H2nQxF6L6kOAdfiIBwOhr06ZN/DlarZYtWLCAKZVK5uTkxHr37s1u3LhRYp66MQQxMTEG71nzkgNFgZElB7p168a+//57g3PHjh3LgoKCWKdOndjWrVv5/ucJEyawWbNmMWdnZ7Zlyxb+/IyMDNaqVSvWvHlzNn36dKM6FsXcmr7++ussICBA0DzVajW7cuUK369PFBITE2N3Y5qEjkmlxSN7x5r9LjMzkx08eFCUvK1ZFzERMx5ZTUsTM2GxKo7jsHDhQixcuFB8gyyYrKws3L17l/8/ISEB165dQ7Vq1eDs7IzY2Fjs3bvX4HOBgYGYMmUKVCoVevXqxR/39/fHO++8g7y8PAQGBvLH3d3dcfXqVURHR+PYsWMICgrCzp079aZYS8m2bdvw7NkzwfMt2kJH2C8Uk8yLtfrd+vXrMXfuXOzYsQMjRowQPH9r1cVaManSpJu6Xh7WrVvHdzVZOrbWHH758mW9ys2sWbMAAOPGjUOvXr3QtWtXo99NYGAgcnNz0bx5c/j6+vLH/f39kZmZicaNG6NevXp6n1EoFAgKCkJQUBC8vb0REREheaWJMYb4+Hi0bNkSNWrUEDRvuVyO5s2bC5qnLWBuH7LlmGRr8UgIrNnvZs6ciatXr2LMmDGoUqUKwsLCBMvbmnUREzF9yKR1mvbu3QtHR0d4enqa9Dp48CC/lpA1oFtfyVYICAjg10sq+tq8eTP27dtX4pgsX19fMMZw8+ZNZGdn80/SdevWBWNMr/UKAG7fvo179+4BKKyo/Pnnn2jQoIG4hTOBY8eO4ZVXXsG1a9cEz1utViM2Ntbm7pnKYm49bDkm0b1liDX7nUwmw6ZNmxAWFobhw4fj1KlTguVtzbqIiZh6mNw9t3LlSpOf0nbt2lVhg6TAnqZL9+zZE6+//nqZ55lSU8/KysLUqVP5xSs7duyIqVOnVtrGyhIYGIiIiAi0bdtW8Lw5jkPVqlXt6p4xBSn0sNWYRPeWIdbudw4ODtixYwcGDRqEy5cvw9/fX5B8rV0XsZB8yYHo6Gh+awBTOHToEOrUqVNho8yNPTWHz507t8xzOI6Ds7Nzmed17NgRFy5cEMIswVCpVHBwcMCgQYNEyV8ul8PPz0+UvK0Zc/uQLccke4pHpmILfufs7IxDhw7xs40zMzPh7u5eqTxtQRcxkLx7zt/fX2/BqrLo2bMnnJycKmyUuaGmTX0YY8jKyrK6nbMZY+jbty/+85//iHYNtVqN8+fP0z1TDHPrYcsxie4tQ2zF73T37I4dO9C8eXODIQ/lxVZ0ERox9ajU3nOMMZw4cQIHDx5Eenq6UDaZHd1KosTfFF2l1VqIjo7GmTNn0KlTJ9GuIZPJUKdOHbpnimEpethCTLIULS0JW/O7Pn36wN3dHf369eP3b6sItqaLUIiph8k5v3jxAuPGjUPr1q0xYcIEZGRkoFevXujXrx8GDRqE5s2b85v9WRt0w+mj2xLFmvrJGWNYsGABOnbsiNDQUNGuI5PJ0KBBA7pniiGFHrYak+jeMsTW/M7HxwdHjx4FYwxBQUFISUmpUD62potQWESlac6cObhw4QL++c9/4saNG+jfvz80Gg0uXLiAS5cuoWXLlvjoo49EM1RMqGlTH8YYMjMzrap77ujRozh79iz+85//iFrZU6vVOH36NN0zxZBCD1uNSXRvGWKLflevXj0cP34cL1++xOzZsyuUhy3qIgQWMXvu0KFD2L59O/z9/fHmm2+iXr16OHHiBLp27QqgcNuPsrYXsVRKq5VaU8VBSMQY/yGWlowxfPLJJ+jatauorUxA4b3SuHFjerIrhhR62GpMonvLEFv1Oz8/P0RHR5e5qXxJ2KoulcUiWpqePn2Kpk2bAgDq1KkDZ2dnvYUO69evj9TUVOEtNAPGBNaN6cnJyTG3OZLDcRwcHR0Fb7HRaSn0eKnIyEjExMTgs88+E71LkcYQGEcKPWw1JtG9ZYgt+13z5s1RtWpVJCYmYvz48cjLyzP5s7asS2UQUw+TW5q0Wq3eND65XK73A2VN41+KY6wpTy6Xw8vLi+9rdnV1teoylgfGGLKzs1GlShVByswYQ05ODlJSUuDl5SXodFDGGObPn8+PZREbXXN47969yzV7y9aRonvAVmMSdbUYYg9+l5SUhJ9++glpaWn49ddfTXq4tAddKoJFdM8BwHfffQc3NzcAhUZt3rwZ3t7eAArXnLBWSqqVKpVKAKjwID1rhTEGrVYLmUwm6A+Pl5cXr6lQHD9+HFeuXEF0dLRZfiRlMhlatWpFT3bFkEoPW4xJdG8ZYg9+17t3b+zevRtDhgzBm2++ia1bt5ZZXnvQpSJYREtT/fr1sXHjRv5/pVKJH3/80eAca6QkgTmOQ61ateDj4wOVSmVmq2wLBwcHURYc69u3L86ePYsePXoInrcxZDKZVexfZm6kCNq2GpPoB9AQe/G7sLAwbN++HaNGjULVqlWxatWqUs+3F13Ki0VUmhITE0UzQmrKasqTy+V2tUqvSqXCiRMn0KdPH4ter+nFixfw8vIyW4UJsB5tzI0UXUq2GpOoe84Qe/K7ESNGIDs7G9WrVy/zXHvSpTxY7OKWtgI92ekjl8vRuXNni64oqtVqdO/eHfPnzzfrda1BGykgHxIO0tIQe/O78PBwDBo0CIwxHDt2rMTz7E0XU5G8pWnlypUmZzh9+vQKGyMVFKT0kclk5drXSwrkcjn+85//mH3fJWvQRgrM7UO2HJMoHhlir3538OBBDBo0CCtWrDB6H9urLmUheaVp2bJlev+npqYiJycHXl5eAAq7SVxdXeHj42N1AQqg5vDiqFQqREVFITg42CKbfBlj4DgO//jHP8x+bUvXRirM7UO2HJMoHhlir343YMAAzJkzB++++y7c3d3x5ptv6r1vr7qUheTdcwkJCfzriy++QLt27RAfH4/nz5/j+fPniI+PR4cOHfDZZ5+JZqiYUNOmPgqFAr169bLYKayLFy/GiBEjJFl41NK1kQpz+5AtxySKR4bYq99xHIfFixfj3//+N8aPH49ff/1V73171aUsxPShcrdhffLJJ1i1ahWaNWvGH2vWrBmWLVuGjz/+WFDjzIW1ruciFhzHwcPDwyJ1ef78ORYtWgSlUimJfZasjZRIqYetxSS6twyxZ7/jOA5r167FqFGjsGfPHoP37FWX0hBTj3JXmp48eWJ0+r1Go8HTp08FMcrcUHO4PiqVCvv27bPIZRYWLVoEjUaDTz75RJLrW7I2UiKlD9laTKJ4ZIi9+51cLsfmzZuxdetWAOBXDbd3XUpC8u65ovTt2xcTJkzA5cuX+e6Ry5cvY+LEiWZZkVkMqDlcH4VCgeDgYItr8k1KSsKqVaswZ84cs61NotVqcfToUWzYsAGLFy/G/PnzcfDgQaxatYp+3IogpQ/ZWkyieGSIpcYkc+Lg4ACFQoG4uDg0btwYMTExpEsJiOlD5Vb6hx9+wLhx49ClSxd+4JlarUZISAi+++47wQ0kpMESnXDBggXw9PTErFmzzHI9lUqF4cOHY//+/Ubfv3r1KjZv3kw/chJDMck+sMSYJAXNmjWDr68v+vfvj5MnT6JFixZSm2RXlPsurFGjBiIjI3Hnzh3Ex8eDMYYWLVrwG2daIxqNRmoTLAq1Wo3IyEiEhYVZzIyM33//HVu2bMGqVavg7u4u+vUYY5gwYUKJFSYA2LZtGxQKBb7//nu7nyYupQ/ZWkyieGSIJcYkqXBzc8PBgwcRGBiI4OBgLFiwAOPHj7d7XYoipg9VuOrepEkTNGnSREhbJINaCvRRKBQICwuzmCc7xhimTZuGZs2aYcKECWa55ocffogtW7YAABwdHfHVV1+hXr168PT0REJCAiZPnszvdaZQKLB+/Xq7rjhZgg/ZSkyyBC0tDUuLSVLj5eWFqKgo9O7dGxs3bsTEiROlNsmikHz23KxZs5CdnW1yph9++CGeP39eYaMI6bGk8TqnT5/GmTNnsHLlSjg6Oop+veXLl+Orr74CUDgLY/v27ZgxYwaGDx+Ovn374l//+hd+/vln3jG/++47TJkyRZIlEOwVikn2hyXFJEugRo0aOHr0KL777juaPWdGTKo0rVixAjk5OSZnumbNGrx48aKiNpkdag7XR61WIyoqymKClL+/P+Li4hAUFCT6tX7++WfMnDmT/3/NmjUYPnw4/79OmyFDhmD79u1869K6desQEhKCv/76S3QbLRFz+5AtxySKR4ZYWkyyFGrWrIkHDx7g5cuXmDp1Kp49eya1SRaB5N1zjDE0bdrU5NpseZ4ALQFq8tXHwcEBQ4YMkdoMAMCff/6Jli1bokOHDqJf6/jx4xg3bhz///z58/HOO+/onVNUm5EjR0KtVmPs2LH8LLtWrVrhvffew7x581ClShXRbbYUzO1DthyTKB4ZYkkxyZLQ6XLnzh388ssvuHTpEo4fPw4PDw+pTZMUMX3IpJw3bdpU7oxr1qxZ7s8Ixdq1a7FkyRI8efIEr7zyCpYvX45evXqVeD51q+jDGENmZibc3d0lbfZ99OgR2rdvj/Xr1xtsHyA0165dw2uvvcavd/Lvf/8bCxcuNDivuDajR4+Gl5cX3nnnHSQlJUGlUuHLL7/Etm3bMGnSJHTt2hWdOnWy+SBmbh+ypphE8ajyWEpMsjR0uvj5+SEqKgqBgYEYOHAgDh8+DFdXV6nNkwwxfcikSlPRp29L55dffsGMGTOwdu1a9OjRA+vXr0doaChu3ryJ+vXrG/0MNYfro1arcebMGcn3M6pTpw4OHDhQ6g+MECQmJiI0NBSZmZkAgMGDB2PNmjVGg7MxbcLCwhAfH48vv/wSS5YsQUFBAZKSkjBv3jwAheOiWrRogWbNmqFq1aqoVq0aqlatCg8PDzg6OsLBwYH/K5PJ9F46G4raUtwuS/gRuX37tlmvZy0xieKRMFhKTDIHWq0WKSkpePToER49eoTHjx8jPz8fQKGvcxyHWrVqYdiwYdBoNLwu7du3x6FDhxAUFIRhw4bhwIEDdttqKaYPcczGHmu6du2KDh064Ntvv+WPtWjRAkOHDsWiRYv0zr1y5Qo6duyIrVu34pVXXuGFrlu3Lr94olwuh1qtBsdxfFr3g1ZSWqVSQS6X82mFQgGO4/g0UBgEiqYdHBzAGOPTWq0WGo2GT2u1WigUihLTGo0GjDE+rbO9pLSll+np06d8y4CYZXrx4gV69erF/+i/+uqrOHz4MN8yVN4y3bp1CzNnzkRUVFRlb2WrJC4uzixdqdZCReLR5MmTUa9ePWi1WgBAtWrV4OnpCaBw93aNRgOO40xOF7//5XI5OI7j00Dhj0zRtEKhAGOMTxf3UcYY5HK5XloXg4of15VDJpOVmNbZy3GcQTmMnaPz9aKxCQCf1tnOcZxeWqvV8p9Vq9X8GCmNRgO1Ws2/r1KpwBiDSqUqMa1Wq/nPaTQaPhboylU0rdNDFzt05+ryyc7O1nvpPlca7733HhYvXmwQj44dO4bLly/j/fff538T7OV3Q1eOuLg4dO3aVZx4xGyI/Px8JpfL2W+//aZ3fPr06ax3794G58fFxTEABq8FCxawK1eusPj4eMYYYzExMezOnTuMMcbOnTvHEhMTGWOMnTp1ij18+JAxxtjx48fZ06dPGWOMHT58mD179owxxtiBAwfYy5cvGWOM7d27l+Xk5LCCggK2d+9eVlBQwHJyctjevXsZY4y9fPmSHThwgDHG2LNnz9jhw4cZY4w9ffqUHT9+nDHG2MOHD9mpU6cYY4wlJiayc+fOMcYYu3PnDouJiWGMMRYfH8+uXLnCGGPsxo0b7MaNG4wxZnKZHjx4wJ49e8aOHTsmSZkOHTrEatWqxWbOnClYmYx9T3v37mVdunThv3c/Pz+Wmppaapk0Gg1LSkoqs0ynTp1iH374IXvnnXdYq1atmFwuN3qv2dorLi6uuJvZLULFI3rRy9iL4zh2/PjxUuPRsmXLmFqtNsvvhiX9Fm7ZsoUB4sQjm2ppevz4MerUqYNz586he/fu/PEvv/wSW7ZsMehC0D3Zbdq0CW3atKGWpv8vh0ajwcmTJ9G7d284OTmZvUxjxozB4cOH8fvvv6N27dqiPAWp1WoMGTIEhw8fBgAolUqcO3cOjRo1KrVMQOGA8d69e8PV1dXkMuXm5iI9PR1paWlIT0/Hy5cv8fLlS/5JMz8/HwUFBfwTcPEn1KJP5ronZl23nC6te0rXdesZS+vOL5rWPZmXlNZdv6S0VqvFo0ePsHHjRmppKkJF4xFhP8jlcigUClSpUoV/ubm5wcfHB3Xr1kWdOnVQs2ZNeHh48C1msbGxWLVqFQCgXr16+OabbxAWFmYQj/73v/+hWbNmCA8Px7p164y2OtlqS1NMTAy6d+8uSjyyyQ7P4mM8GGOljvto06ZNqcIW7Rc2JV20z708aY7j+LTupjM1XXQxL1PSpZVDoVAgJCRETwNzlem3337Djh07sG3bNr0xH5UtU9G0RqPB2LFj+QqTu7s7IiMj0ahRI5PK1L9/f/6Yqd+TLiDWrVsXtsiVK1ewceNGqc2wSMobj2bNmoV69eqJbZZZqMh4O2OfKWscX9Gxf7q07oFB9yo+VlAul/M/6Lq/uvine0/3v+5Y8f+Lv3R56a5X9Lo6O4qeWxF9Ro8ejRs3buDkyZN48OABfvvtN/zjH//gy6yLO40aNcJ3332H8PBwVKlSBcuWLTM4R8jfDWNpqX4LnZycissmGDZVafL29oZcLkdycrLe8ZSUlFJnzpjSf2xPaLVapKWlwdvb26yrXD99+hTvvPMOhg0bhtGjR4tyDcYYJk2ahJ07dwIAnJ2dceDAAbRv396kz0uljaVDPmRIRePR66+/jk6dOoltnlVBfvc3crkcW7duRevWrfHy5Uv8/PPPCAsLw7/+9S+Dc8eNG4ecnBxMnjwZVapUwRdffCGBxeZHzHhU7rsvOzsbn3zyCbp37w4/Pz80atRI7yUljo6O6NixI44ePap3/OjRo3rN48WhgK+PVqvFH3/8YVZddJUZjuPw7bffijIjjDGGOXPm8Ju4KhQK7N69G7179zY5Dym0sQak1MNSYxLFI+Egv9OnXr16WLduHf//1KlTcf/+faPnvvPOO1iyZAn2799vVeuVVQYx75NytzSNHz8ep06dwtixY1GrVi2LmO5clFmzZmHs2LHo1KkTunXrhg0bNiApKQmTJk0q8TP2Oi2zJBQKBfr06WPWa27btg179+7Fb7/9xo8nE5rPP/8c33zzDYDC5t+ffvoJYWFh5cpDCm2sASl9yJJjEsUjYSC/M2TUqFE4cOAAfvrpJ7x8+RLTpk1DRESE0XPnzJmDKVOmwMXFBbm5uXBxcTGzteZFVB8q78hxT09Pdvbs2UqNPhebNWvWsAYNGjBHR0fWoUMHfoR9cXSzVWJjY81soWWj0WjYw4cPmUajMcv1bty4wapUqcLGjh0r2jWWL1+uN/Nk48aNFcrH3NpYC7GxsaLNVikLS49JFI8qD/mdcZ49e8Zq1qzJADC5XM7PVCuJ9PR01rRpU7ZmzRozWSgNYsajcnfP6Rbns2QmT56MxMRE5OfnIy4urszuF2ry1Uer1eLevXtm06V+/fqYOHGi3lo2QvLDDz9gxowZ/P9Lly7F+PHjK5SXubWxFqTUw9JjEsWjykN+ZxwPDw/4+/sDKFwXKjIystTzPT09ERYWhilTpuCHH34wh4mSYFFjmj777DPMnz+/XJtlWjrUHK6PQqFA7969RdclLy8PCQkJ8PDwwNdffy3KXm07d+7EhAkT+P8XLFiA2bNnVzg/c2ljbUiph63FJLq3DCG/M45CocCUKVP4/0vqntPBcRy++eYbTJo0CePHj8e2bdvENlESJN97rihff/017t27h5o1a8LX19dgSfsrV64IZpy5oKcXfbRaLR48eIB69eqJOlNlwYIF+Omnn3D37l04OzsLnn9kZCTGjBnDf78zZ87EggULKpWnubSxNqT0IVuLSRSPDCG/M45Wq0WdOnVQvXp1PHv2DIcOHUJ+fn6pU+45jsOaNWuQn5+P8ePHIzAwEHXq1DGj1eJjUQPBhw4dKoIZ0kJBSh/dYoV16tQRNUB98MEHCA4OFqXCdPr0aQwfPpxfkHL8+PH4+uuvKz1I2FzaWBtS+pCtxSSKR4aQ3xlHt+VUaGgotm3bhqysLERHR+utJWcMmUyGjRs3YuLEiTZXYQIsrNJU2Sd1S4SafPVRKBSlTomuLGvXrkVYWBh8fX3Rt29fwfO/cuUKBg0ahLy8PADAP//5T6xbt06QWVVia2OtSOlDthaTKB4ZQn5nHJ0uycnJfFdbREREmZUmoHC9p65du4Ixhg8//BDdunXDkCFDxDbZLIjpQ1RlB+0qXhyNRoO7d+8KrotWq8Xs2bMxZcoU7Nu3T9C8ddy+fRv9+/dHRkYGACA0NBRbt27VW9W2MoiljbVDeggHaWkI+Z1xdLr07duX75KLiIgAK8fuaLpB9iNGjMCBAwfEMtWsiHmfmFRpqlatGtLS0gD8PVOlpJc1Up4bzB5gjCE9PV1QXQoKCjB27FgsW7YMK1euxLvvvitY3joePHiAoKAgpKamAgB69OiBXbt2wdHRUbBriKGNLWBuPWw5JtG9ZQj5nXF0ulSpUgX9+vUDADx69AhxcXEm5yGXy7F9+3YMHDgQw4YNw/79+8Uy12yIeZ+Y1Ia1bNkyuLu7AwCWL18umjFSQc3h+igUCnTu3Fmw/DIyMvCPf/wDp06dwi+//IIRI0YIlreO1NRUBAUF4cGDBwCAdu3a4cCBA3B1dRX0OkJrYyuY24dsOSZRPDKE/M44RXUZPHgwDh48CKCwtak8W/E4ODjgl19+weuvv47hw4fj5MmTVt0dalGLW9oSusXkYmJipDbFolCr1Sw+Pp6p1epK57Vnzx5Wp04d5uHhwU6cOCGAdYZkZmayzp078wtXNmnShCUnJ4tyLSG1sSViYmIkW9zSVqB4VDLkd8Ypqsvjx4/5GNimTZsK5VdQUMCWLFnC8vLyBLbUvIgZjyo1pik3NxcZGRl6L8I2yM3NrdTnGWMYOXIkXnvtNbRv3x7Xr19HYGCgQNb9TUFBAYYNG4bY2FgAQO3atXH06NFSN0StLJXVhhAPikm2C/mdcXS61KpVC127dgUAXL9+HQkJCeXOy8HBAXPmzIGTkxMuX76MPXv2CGqrLVChDXunTp0KHx8fuLm5oWrVqnova0SoQcK2glwuR/v27SukS1paGjIyMsBxHDp16oRff/0VERERaNCggeB2arVavPHGG/yGqF5eXjhy5Igo19JRGW1sGSn1sLWYRPeWIeR3ximuS9HZb5Udm/Tdd99hxIgR+PHHHyuVjxSIeZ+Uu+Nv7ty5iI6Oxtq1a/HGG29gzZo1ePToEdavX4///ve/YtgoOjQjQx+NRoP4+Hi0aNGiXDdfTk4OGjdujPnz52P27NmYO3euaDYyxvDuu+/il19+AQC4uLjgwIEDaNWqlWjXBCquja0jpQ/ZWkwqS0uNRgOVSmUmaywDjUaDe/fuoXHjxoL5nYODg9X7cPF4NHjwYMybNw8AsG/fPkyfPr3Cea9ZswZqtRpvvPEGsrKy8M477whltuiIGY/KXWnav38/tm7dioCAALz11lvo1asX/Pz80KBBA/z0008YM2aMGHYSFkZGRgbOnDmD6OhoxMTE4MiRI3B1dcW2bdvQrVs30a//xRdfYPXq1QAKnyp+/fVX9OjRQ/TrEpaHvcQkxhiSk5Px4sULqU0xO4wxMMZw//59QdZb0+Hl5QWlUilonlLSsmVLNG7cGPfu3cOpU6eQnp5e4dZWuVyOjRs3wt3dHZMnT4Zarca0adMEttj6KHel6fnz52jYsCGAws0Cnz9/DgDo2bOnVdVEi2LtTxtCI5fL9VpsHjx4gBs3buDWrVu4ffs2rl27hri4OGg0GtSpUwd9+vTB8+fPUadOHQwaNEh0+7777jt88skn/P/ff/89BgwYIPp1AUNtiEKk9CFbi0klaamrMPn4+MDV1dVmfuilgDGGnJwcpKSkACgcD2SNFI9HHMdh8ODBWLZsGTQaDY4ePYqRI0dWOH/dXnU1atSwqtl0FtU916hRIyQmJqJBgwZo2bIldu7ciS5dumD//v3w8vISwUTxuX//Pjw9PY2+V6VKFSiVSqjVaty/fx9KpRJVqlRBeno6H5xLwtvbG56ensjIyEBqaioaNWoEjuPw8OFDfrVqHazYuhK6PbQeP34MjUaDevXqQavV4vbt2/xTF2MMWq1WL+3o6Mg70cWLF1G3bl3UrVsXT548weXLl1FQUID8/Hzk5eUhLy8Pubm5yMzMRGZmJnr06MEPqh41ahSOHj2KRo0a4YMPPsD27dvh4uKCZs2aoWXLlnj77bcRGBgIPz8/swbviIgITJw4kf//q6++wrhx48x2fY1Gg+vXr6NNmzZU2S6ClN1zthaTjGmp0Wj4ClP16tUlsEpaGGPIzc2Fi4uLYPHGxcUFAJCSkgIfHx+r9Gdj8Sg0NBTLli0DABw6dKhSlSagsOKk6/LLz8/HypUrMWPGDIM9Hi0JUeNReafbffPNN2zFihWMMcZOnDjBXFxcmKOjI5PJZGz58uVCzOgzG7opvqW9XnvtNcYY46dzHjhwgDHG2GeffVbmZ9etW8cYY2zTpk0MAD9dtkePHmV+NiEhgTHG2KhRo1jfvn0ZY4xlZWWV+bmmTZvy5fPy8mKLFy9mjDG2e/dug3MdHByYu7s7q127NmvevDn76quvGGOM/e9//2Njx45l9+/fZ4wxdu/ePXb//n2m0WhE/kZK5+zZs8zZ2Zm3f+bMmUyr1ZrVBpr6bBwplxywlZhU2pIDubm57ObNmywnJ0cCy6RHq9WynJwcwf09JyeH3bx5k+Xm5gqar7kwFo/y8vKYq6srA8CUSqWgcfv06dPMwcGBBQUFsZcvXwqWr9CIGY84xiq3dGZSUhIuX76Mxo0bo23btpXJyuxcuXIFHTt2xLp169C0aVOj53h7e6N169bIz8/H+fPn0bp1a3h7eyMxMVFvSqexp5+mTZuidu3aSE5Oxq1bt+Dv7w+O43D16lWjU6GL5tGlSxc4Ozvj1q1bUKlUaN26NTQaDS5dusSfy3EcZDKZ3l8XFxe0aNECAHDnzh1Ur14d1apV46diOzo6wtnZGU5OTla18eXNmzfRs2dPpKenAwBGjx6NH3/80arKYMvofCkuLg4dOnSQ1BZrjUmlaZiXl4eEhAQ0bNhQlA2u7RVb1XXQoEH8lihXr15Fu3btBMs7Ojoar732Gho0aICDBw+ibt26guUtFGLGo0ovm1m/fn3Ur19fCFsko3379ujSpUup5zg5OemtM+Tr6wtfX1+T8lcqlVAqlXrXM5XmzZvzablcXq5+5SZNmvBpFxcXvjm6LNRqNa5evYr27dtbxOrESUlJCAkJ4StMQUFB2LRpkyQVJkvTxlJQq9VSm8Bj7THJkrS0FNj/j0GisVz6lBSPQkND+UrToUOHBK00BQYG4ty5cwgNDcWrr76KGzduWNzSHmL6kMlRPzc3F8ePH8fAgQMBAB9++CHy8/P59+VyOT777DOrrK2TE+rDcRyqVq1qEbqkpqYiODgYDx8+BAB06NABu3fvFnQ/ufJgSdpYElLoYasxie4t41jjmCOxKSkehYaG8ulDhw7hww8/FPS6r7zyCi5evIiff/7Z4ipMgLg+ZHKlaevWrThw4AAfoFavXo1XXnmFb724desWateujZkzZ4pjqYiQM+ojl8vh5+cntRnIzMxEWFgYbt++DaCw5ezQoUP8nmNSYCnaWBpS+JCtxiSKR4ZwHGd1lV9zUFI8atiwIZo1a4bbt2/j/PnzePHiheCTImrXro3Zs2cDADZt2oQzZ85gzZo1JvdoiImYPmRy/8ZPP/2Et956S+/Y9u3bER0djejoaCxZsgQ7d+4U3EBzQM3h+qjVapw/f15SXfLz8/Haa6/h8uXLAAodNCoqCj4+PpLZBFiGNpaIFHrYakyytXtLN/6ypFd4eHiZeTDGkJWVJeru9dZIafFI19qk0Whw7NgxUe1wdHTEjh070K1bN9y5c0fUa5mCmD5kcqXpr7/+0hss7ezsrDempEuXLrh586aw1pkJGkysj0wmQ506dSTTRa1W41//+heOHz8OAKhatSqOHDli8hgyMZFaG0tFCj1sNSbZ2r315MkT/rV8+XJ4eHjoHVuxYoVJ+VjyFHepKC0e9e/fn08fOnRIVDvGjBmDixcvIjs7G23btsXXX38t6TIkYvqQyd1zL1++1Btolpqaqve+VqvVG09gTdhakKosMplM1P3bSkOj0SA8PBy7du0CYL7tUUxFSm0sGSl8yFZjkq3Fo6KTYDw9PcFxnN4xU+A4Dk5OTkKbZvWUFo/8/f3h4uKC3NxcHD58GIwxUcf6tGnTBlevXsXHH3+MPXv2YMaMGaJdqywsotJUt25d/PHHH2jWrJnR969fv26RUw9NwdaawyuLrsm3e/fuZp0hptFo8NZbb+Gnn34CUPhkuXv3botaiVYqbSwdKXzIVmNSebTs1KkTkpOTRbTGOEqlku86Nwe67jk3NzcaKF+E0uKRs7MzAgMDERkZicePH+P69euiL8Hh5uaG5cuXQ6VSQS6X49y5c9i/fz/mzp2LatWqiXrtoljE7LmwsDDMnz8fAwYMMBiQl5ubi08//dRsW1kIja092VUWmUyGxo0bm1UXrVaLf//739i6dSsAQKFQYNeuXXqzQCwBKbSxBqTQw1ZjUnm0TE5OxqNHj0S0xnKgliZDyopHoaGhiIyMBFDYRWeudct0Xak3b97EypUrsXbtWkyfPh0zZ840y4r2FtHSNG/ePOzcuRPNmjXD1KlT0bRpU3Ach1u3bmH16tVQq9X8UuvWBv0A6qPrJzcXWq0W77zzDn744QcAhTMfdu7cicGDB5vNBlMxtzbWghQ+ZKsxqTxalrebSyjMfV2O4yRbZsSSKSseFV964IMPPjCHWTwTJkzA4MGDsXTpUixbtgwrVqzAvn370KdPH1GvK2o8Ks/y4f/73/9YSEgIk8lkjOM4xnEck8lkLCQkhN27d0/w5crFRrdtwaVLl6Q2xaJQqVTs+PHjTKVSiX6t/Px8NmbMGH5rFLlcznbu3Cn6dSuKObWxJi5duiTJNiq2FJNKi0e6bVSsdbsPHZs2bWKenp7l/pxWq2UvX74UfBsVa9fVlHjUpEkTBoApFAr24sULM1qnz9OnT9lHH33E27B06VK2Zs0alpqaKvi1xIxH5aqONWzYEIcPH0ZqaiouXryIixcvIjU1FYcPH0ajRo0Er9DpSExMxNtvv42GDRvCxcUFjRs3xoIFC1BQUKB3XlJSEgYNGoQqVarA29sb06dPNzjHGNTSpI9MJkOrVq1E1+XFixfo378/P4ZJJpNh27ZtGDFihKjXrQzm0sbakEoPW4xJdG8ZxxLW/7E0TIlHull0arWan5EsBT4+Pvj888/h6ekJoHB7l+nTp6NWrVro3bs35s2bhwcPHghyLYvonitKtWrVytx2REhu3boFrVaL9evXw8/PD3/88QcmTJiA7OxsLF26FEDhIOIBAwagRo0aOHv2LJ49e4Zx48aBMYZVq1aVmj8FKX1kMpno6yE9ePAAoaGh+PPPPwEUBsSff/4ZQ4YMEfW6lcUc2lgjUvuQLcUkqbW0RDiOoyUHjGBKPAoLC+Pvt4MHD2LYsGHmMK1Mtm3bhmXLlmHXrl04fvw4fvjhB7z55psAgP/85z+4du0amjZtiqZNm6JJkyZo3rw5atSoYVLeFtM9Z0ksXryYNWzYkP8/MjKSyWQy9ujRI/7Yzz//zJycnErcjVnXHL5p0yYWFxfHYmJiWExMDHv8+DFTq9X8ztEqlUovrds1uqR0QUGBXlrXpKxLa7VagzRjTC+t0Wj00rrm15LSarVaL62zt6R0aWXKy8tjhw8fZjk5OaKU6fLly6x27dp8l5y3tzc7e/asqGUS6nsqKChghw4dYtnZ2ZJ/T5Z0750/f16S7jlLorIxqbR4lJWVxf7880+Wm5vLf3eMMZPSGo2m1LRWqzVI6/IoKV2e6xdN//DDD3z3XHk+q9Fo2IsXL3gbhCpTdnY2u3nzJsvOzrZK3zUlHuXk5DAXFxcGgCmVSqZSqSyyTBqNhuXn5zPGGFu+fDkLCgpivr6+jOM4BoB98803TKPRsN27dzNfX1/Wvn171rt3bzZw4ED24Ycf8uV477332FtvvWUZ3XOWxMuXL/WmMF64cAGtWrVC7dq1+WMhISHIz89HXFxcqXm9+eab6NixI7p06YIuXbpg/fr1uH79Or+y6dWrV5GQkAAAiImJ4ZsQz58/jydPngAATp8+jbS0NADAiRMn8OLFCwBAVFQUMjMzAQCRkZHIy8uDWq1GZGQk1Go18vLy+NkNmZmZiIqKAlDYdXXixAkAQFpaGk6fPg2gcKG48+fPAyhsrYmJiQEAJCQk4OrVqwCAO3fu4Pr16wCA+Ph4xMfHA4DJZUpNTUXnzp1x/vx5QcuUlpaGf//733j11Vfx+PFjAICfnx/27NnDL4QmVpmE+p7kcjleeeUVREdHS/49WdK9ZwmrAEuNUDHJWDy6ffs2P406JyeHX38qOzub7+7LysqCSqUCUPh96s7PzMzk/SsjIwNarZZPM8bAGDNIA4UTNHRpjUbD30tqtZpPq1QqZGVlAQAKCgqQnZ0NoHBF/5ycHABAXl4ecnNzAQCjRo3i79vc3Fzk5eWZVCbd6uG6cghVJp296enpVum7psQjFxcX9OzZE0DhbMvDhw9bZJny8/P5RTjffPNNvPvuu0hISMDDhw+xfv16jB49GmlpaXj27BlGjRqFVq1a8ZMDnjx5gpiYGGg0GuzcuRN79uyBaAheDTMDd+/eZR4eHmzjxo38sQkTJrCgoCCDcx0dHdn27duN5qN7stu6dSu1NIlcprt377Ju3brxrUsAWNeuXVlKSorVlskWv6eKlkmqgeCWghAxqbR4ZCstTUKlqaWpfL67du1aPu4uWLDAJsokVTyStKVp4cKFZe5LVHwBtcePH6N///4YMWIExo8fr/eesUXPmAmroDZr1gwdOnRA586d0blzZ9SqVQtyuZzf9E+hUOildf2lJaUdHBz00rrr69K6/vmiaZ39urRMJtNL6xYuKyktl8v10jp7S0qXViaNRoODBw+CMVbpMhUUFGDdunVo27YtLly4wNs9b948nD59GjVq1DBLmYT6nlQqFd86I/X3ZEn3nq1gCTGppHik+4zODlPTMpms1DTHcQZpXR4lpStqS0XTWq0WL1++5PeeE7pM1uq7psajQYMG8edERkZadJl0342lxiNJlzSeOnUqRo0aVeo5Rfcbe/z4MQIDA9GtWzds2LBB7zylUolLly7pHUtPT4dKpULNmjVLvYYtBX0hUCgU6NWrV6VWvM7Pz8emTZvw5Zdf6s2IaNSoEX788UeLWuW7PAihjS1iKz5kCTHJVrQUEo7j4O7uTquBF8PUeFS3bl20bdsWv//+O2JjY5GcnCzZGl/mQEwfkjTye3t7w9vb26RzHz16hMDAQHTs2BGbNm0yGB3frVs3fPHFF3jy5Alq1aoFoLAP1cnJCR07diw1b3JEfTiOg4eHR4U+m5aWhh07dmDx4sUG00cnTJiAb775Bm5ubkKYKQmV0caWsRUfsoSYZCtaCgnHcVSZNEJ54tHAgQPx+++/Ayhc6FI3U80WEdOHrGIg+OPHjxEQEIB69eph6dKlSE1NRXJyst6eS8HBwWjZsiXGjh2Lq1ev4vjx45gzZw4mTJhQ5k1Fe8/po1KpsG/fPn5QaVmkpaVh48aNCA4OhlKpxLRp0/QqTAMHDkRMTAw2bNhg1RUmoPza2Av25kNixiR709IUtFotXrx4wQ/4JgopTzwquqXQwYMHxTRLcixi7zkpiYqKwt27d3H37l2DDTh1fdxyuRwHDx7E5MmT0aNHD7i4uGD06NH8mimlQU8w+igUCgQHBxtt8s3JycGtW7cQGxuLmJgYxMbG4s8//zQazAYOHIgFCxagU6dO5jDbLJSmjT1jbz4kZkyyNy1NQdeiQq1w+pQnHnXp0gXe3t5IS0tDVFQUCgoKbHZrGpvtnjOV8PBwhIeHl3le/fr1ceDAAfENsnIYY1CpVCgoKEBeXh6ys7P1Xs+ePUNqairS09Px/PlzPHz4EImJiUhISMDTp09LzdvX1xcjR47E6NGjzbY5pLmhChNBMYmwFEyNR3K5HKGhofjxxx+RmZmJM2fOoG/fviJbZ3tQ9Efh2iFVqlQRLD/dk2ZlPqP739jf4mmtVquXLvrSaDRQq9VQq9XQaDRQqVT8eihCIJfL0bp1awQFBWHkyJHo2LGjTT8N6tYVCQsLoxWKi6BbM4eoPKSlIez/11qi1iZ9yhuPBgwYgB9//BEAcODAAZutNInpQ1RpAnD37l2pTbAKateuDV9fXzRq1IhffK9du3ZwdXWV2jSzoVAoEBYWRq1NxaAuJeEgLQ2h7jnjlDcehYSEQC6X88vKLFu2TGQLpcHuu+fExtHRUfT9nkxx9uLnFF2rpPhfY+uS6GaYyGQy/rhCoeDX1tClnZyc4OTkBEdHRzg5OaFKlSp6Ly8vL3h6ekKpVMLb2xs1a9ZEgwYN4OzsLKQkVotaraZKE0EQFkF54pGXlxd69uyJU6dO4c6dO/jrr7/QtGlTkS20LSjyAzhz5oxZN/u0dHQLplEXlCFqtRpRUVGkTTGoS0k4bFHL06dPY8mSJYiLi8OTJ0+wZ88eDB061OC88PBwKJVK+Pr64r333kN6ejoUCgUYY3j8+DEaNmyIV199FWfOnOE/c+bMGfTu3Ru3b9+2uwpAReLRgAEDcOrUKQCFs+hsUTMxfcgqlhwQG2o10MfBwQFDhgyhSoERSBvjkA8Jhy1qmZ2djbZt22L16tUlnqPVanHw4EEMGTIEgYGByMrK4ldfl8lkuHHjBpRKJWJjY/l97QDg5MmTqF27tk3++JdFReLRwIED+bStTlIQ04eo0oSKDdy2ZViRzS4JfUgb45AewmGLWoaGhuLzzz/HsGHDSjzn3LlzkMlk6Nq1K5o1a4batWvj5MmTAAo1OXHiBAYPHozGjRvzG+oChZWmwMBAsYtgkVQkHjVv3hyNGjUCUNgC+PLlS7HMkwwxfYgqTbDN5vDKoFarcebMGVpkzwikjXHIh4TDXrWMiIjAoEGD+PGlAQEBiI6OBvB3pcnf3x/+/v788YKCAly4cMFuK00ViUccx/F70anVahw+fFgs8ySDZs+JjC02h1cGBwcHvdVjib8hbYxDPiQc5dXyyZMnePLkid6xqlWromHDhsjLy8PNmzcNPtOhQwcAwO3bt5Gdna33nq+vL6pVq4bU1FSDrZDc3d3RpEmTctlnKhEREXoLfwYEBGDmzJlQq9XIzc3F9evXERAQAMYYVq5cCQC4ePEicnNzERgYCI1Gw29Pk5ycDIVCAW9vb7i7u+uNgbIlKhqPBg8ejBUrVgAo1P2f//yn0KZJipjxiCIdQEvzF0O3ZYGXl5foswqtDdLGOORDwlFeLdevX49PP/1U79iYMWOwbds2PHz40Og+d7rui/DwcFy8eFHvvR9//BH/+te/sHPnTkydOlXvveDgYBw5cqRc9plCfHw8Hj58iH79+vHHAgMDkZ2djdjYWDx//hxNmzZFjRo14O/vj7FjxyI7OxsnT55E/fr1+e6ma9euAQAWLlwIb29vA/ttjYrGo169esHT0xMvX75EZGQkVCqVTY3TFDMeUaUJFPCLo9FoEBsbiz59+lDFoBikjXHIh4SjvFpOnDgRgwcP1jtWtWpVAIW728fFxZX42c2bNxttaQKAkSNHolu3bnrvubu7l8s2U4mIiEBQUBBcXFz4Y35+fqhbty6io6Px/PlzdOvWDYwxKJVKNGzYEOfOnUN0dDT69Okjik3WQEXjkYODA0JDQ7Fjxw68ePEC586dQ0BAgHiGmhmqNIkMdS3o4+DggJCQEKnNsEhIG+OQDwlHebWsVasWatWqZfQ9Z2dnvivOGM2aNSvxvRo1aqBGjRrlsqWi7Nu3D+PHjzc4HhgYiJMnTyI9PR3vvfceXzHw9/fHkSNHcPHiRbz55ptmsdESqUw8GjRoEHbs2AEA2L9/v01Vmmj2nMjQU7I+Wq0WKSkppIsRSBvjkB7CYYtaZmVl4dq1a3z3WUJCAq5du4akpCSkpKQgNjZWbyq8jsDAQJw9exbXrl1D9+7d+W5Ff39/bNy4EXl5eXY7CByoXDwKDQ3lV86OiIiwqVmbYvoQVZpgm0GqMmi1Wvzxxx+kixFIG+OQHsJhi1pevnwZ7du3R/v27QEAs2bNQvv27TF//nzs378fXbt2hY+Pj8HnAgMDkZubCz8/P3h4ePDH/f39kZmZicaNG6NevXpmK4elUZl4VLVqVfTq1QtA4VZit2/fFto8yaDuOZGhrgV9FAqFXY8TKA3SxjjkQ8Jhi1rqZr0ZY/DgwQZjsnT4+voa/VzdunVtqmWkolQ2Hg0ePJhfCysiIgLNmzcXyDJpoe45kbHFJ7vKoNVq8ejRI9LFCKSNcUgP4bA3LXv27InXX3+91HMYYygoKKCKUjEqG4906zUBheOabAVqaRIZewtSZaHVanHv3j3UrFmTZogVg7QxDvmQcNiblnPnzjXpvPz8fJOnxS9cuLASFlkPlY1Hfn5+aNGiBeLj43H+/HmkpaXB29tbBEvNC41pEhlbbA6vDAqFAr179yZdjEDaGIf0EA7S0hCO4+Du7g6O46Q2xaIQIh7pWpu0Wi0iIyOFMk1SqHtOZOztya4stFot7t+/T7oYgbQxDukhHKSlIYwx5OfnU/dcMYSIR0XHk0VERAhhluRQS5PIUJDSh8btlAxpYxzSQzhIS+OoVCqpTbA4hIhHr776Kt8ld+TIEeTn5wtlnmRQpUlkqDlcH4VCge7du5MuRiBtjEN6CAdpaQjHcXBzc6PuuWIIEY/kcjm/f11WVha/GbI1Q91zImOvu4qXhEajwd27d0kXI5A2xiE9hKM0Le21e4oxhry8PMHLb+16ChWPinbR7du3r7JmSY6Y8YgqTbB+xxEaxhjS09NJFyOQNsYhPYTDmJa6WWM5OTnmNsdiEOOHUKentW5WK1Q8Cg4OhpOTE4DCcU3W3kUsZjyidmBQc3hxFAoFOnfuLLUZFglpYxzyIeEwpqVcLoeXlxdSUlIAAK6urnbXVSWXywUbb8MYQ05ODlJSUuDl5cVvJ2JtCBWP3Nzc0K9fPxw8eBCPHz9GXFycVcc5MeMRRTpQ10JxNBoN7ty5gyZNmlhtMBEL0sY45EPCUZKWSqUSAPiKkz3BGINarYZCoRC0sujl5cXrao0IGY+GDBmCgwcPAihsbbLmSpOY8YgqTYRRcnNzpTbBYiFtCCngOA61atWCj4+P3c0k02g0uH37Nho3bizYw4qDg4NNPPgIFY+Krg6+b98+fPbZZ4Lka2vYdaUpNTUVAPD8+XOJLbEsUlJSsG/fPiiVStSqVUtqcywK0sY4Oh/S+RRRfkyNR3K53CZ+7MvDkydPEBERgYkTJ5LfFUHIeKRUKtG1a1dcunQJN27cQEJCAho2bCiQpeZFzHhkdQPB8/Pz0a5dO3Ach2vXrum9l5SUhEGDBqFKlSrw9vbG9OnTUVBQUGJeaWlpAOyzubs0Hj58iE8//RQPHz6U2hSLg7Qxjs6HdD5lTwgVkygelQz5nXGE1mXIkCF82ppn0YkZj6yu0jR37lzUrl3b4LhGo8GAAQOQnZ2Ns2fPYseOHdi9ezdmz54tgZUEQdgLFJMIW8FWKk1iYlWVpkOHDiEqKgpLly41eC8qKgo3b97Etm3b0L59e/Tr1w9ff/01Nm7ciIyMjFLzpY1X9dE1/dtbF4ApkDbGsVcfEiMm2auWpUF+ZxyhdWnRogX8/PwAAGfOnLHaoSti+pDVjGl6+vQpJkyYgL1798LV1dXg/QsXLqBVq1Z6T3whISHIz89HXFwcAgMDDT6jm7565swZAH8vve7j44Nq1aoBKLwZ1Wo1OI7j0zKZDDKZzOS0XC4Hx3F8Gih8Ci2aVigUYIzxaa1WC61Wa3Jao9GAMcandbaXlC6tTLdu3QIA3LhxA1qt1ibKJNT3dPv2bXAchxs3bvD3jLWXSYjv6e7du3o+ZQ8IHZMoHpVcpvj4eDg6OuKPP/4AAJsok6XGo1dffZVfMHPNmjXo37+/1d17YsYjq6g0McYQHh6OSZMmoVOnTkhMTDQ4Jzk5GTVr1tQ7VrVqVTg6OiI5OdlovrqFzdavX4/169cLbre1Ex4eLrUJFgtpYxx7WXxRjJhE8ahsxo0bJ7UJFolY8Wj+/PmYP3++KHmbAzHikaSVpoULF+LTTz8t9ZzY2FicP38eGRkZ+PDDD0s919j6HYyxEtf1GDVqFIDCheJ0q6ECgLe3N2rUqFGW+QRB/D+5ublITExESEiI1KZUCiljEsUjghAGMeMRxyTc/yAtLa3M0e2+vr4YNWoU9u/frxdodE16Y8aMwZYtWzB//nzs27cPv//+O39Oeno6qlWrhhMnThjtniMIgigKxSSCIEpD0kqTqSQlJekNnHz8+DFCQkKwa9cudO3aFXXr1sWhQ4cwcOBAPHz4kF+v4pdffsG4ceOQkpICDw8PqcwnCMLGoJhEEPaJVVSaipOYmIiGDRvi6tWraNeuHYDCp7x27dqhZs2aWLJkCZ4/f47w8HAMHToUq1atktZggiBsGopJBGEf2MzcVrlcjoMHD8LZ2Rk9evTAyJEjMXToUKNTgQmCIMSGYhJB2B5W2dJEEARBEARhbmympUlMMjMz0blzZ7Rr1w6tW7fGxo0bpTbJonjttddQtWpV/OMf/5DaFEkhHQwh3xEH0rVkyA//hrQwpLK+Qy1NJqDRaJCfnw9XV1fk5OSgVatWiI2NRfXq1aU2zSKIjo5GVlYWtmzZgl27dkltjmSQDoaQ74gD6Voy5Id/Q1oYUlnfoZYmE5DL5fyKv3l5efwqqkQhgYGBcHd3l9oMySEdDCHfEQfStWTID/+GtDCksr5jE5Wm06dPY9CgQahduzY4jsPevXsNzlm7di0aNmwIZ2dndOzYkd+qwFRevHiBtm3bom7dupg7dy68vb0Fsl5czKGNLUA6GUcIXazVdyoDxSTjkJ+ZDmllHKljkk1UmrKzs9G2bVusXr3a6Pu//PILZsyYgY8++ghXr15Fr169EBoaiqSkJP6cjh07olWrVgavx48fAwC8vLzw+++/IyEhAdu3b8fTp0/NUrbKYg5tbAEhdLJFhNDFWn2nMlBMMg7FI9OhmGQcyWMSszEAsD179ugd69KlC5s0aZLesebNm7MPPvigQteYNGkS27lzZ0VNlAwxtYmOjmbDhw+vrIkWQWV0siUdiiPE/WOtvlMZKCYZh+KR6VBMMo4UMckmWppKo6CgAHFxcQgODtY7HhwcjPPnz5uUx9OnT/nVfzMyMnD69Gk0a9ZMcFvNjRDa2AOkk3FM0cVWfacyUEwyDvmZ6ZBWxjFHTJJ0w15zkJaWBo1GY7DbeM2aNY3uNG6Mhw8f4u233wZjDIwxTJ06FW3atBHDXLMihDYAEBISgitXriA7Oxt169bFnj170LlzZ6HNlQxTdbJ1HYpjii626juVgWKScSgemQ7FJOOYIybZfKVJR/FdxVkJO40bo2PHjrh27ZoIVlkGldEGAI4cOSK0SRZJWTrZiw7FKU0XW/edykAxyTgUj0yHYpJxxIxJNt895+3tDblcbvCkkpKSYlAbtTdIG9MgnYxDulQM0s04pIvpkFbGMYcuNl9pcnR0RMeOHXH06FG940ePHkX37t0lssoyIG1Mg3QyDulSMUg345AupkNaGcccuthE91xWVhbu3r3L/5+QkIBr166hWrVqqF+/PmbNmoWxY8eiU6dO6NatGzZs2ICkpCRMmjRJQqvNA2ljGqSTcUiXikG6GYd0MR3SyjiS62LyPDsLJjo6mgEweI0bN44/Z82aNaxBgwbM0dGRdejQgZ06dUo6g80IaWMapJNxSJeKQboZh3QxHdLKOFLrQnvPEQRBEARBmIDNj2kiCIIgCIIQAqo0EQRBEARBmABVmgiCIAiCIEyAKk0EQRAEQRAmQJUmgiAIgiAIE6BKE0EQBEEQhAlQpYkgCIIgCMIEqNJEEARBEARhAlRpIgiCIAiCMAGqNBEEQRAEQZgAVZoIsxIQEACO48BxHK5duyZK/jNmzKjw58PDw3n79u7dK5hdBEFYHhSPiPJClSbC7EyYMAFPnjxBq1atzHbN8PBwfPDBB2Wet2LFCjx58sQMFhEEYQlQPCLKg0JqAwj7w9XVFUqlssT3CwoK4OjoKNj1tFotDh48iIiIiDLP9fT0hKenp2DXJgjCsqF4RJQHamkiysWePXvg5OSE1NRUg/fmzJmD9u3blzvPgIAATJ06FbNmzYK3tzeCgoIAAIcPH0bPnj3h5eWF6tWrY+DAgbh37x7/uezsbLzxxhtwc3NDrVq18PXXXxvN/9y5c5DJZOjatSsAYNeuXWjdujVcXFxQvXp19OvXD9nZ2eW2myAIaaF4RJgbqjQR5WLLli0IDQ1FjRo1DN4bPXo0rl27huvXr1coX4VCgXPnzmH9+vUACoPQrFmzEBsbi+PHj0Mmk+G1116DVqsFALz33nuIjo7Gnj17EBUVhZMnTyIuLs4g74iICAwaNAgymQxPnjzB66+/jrfeegvx8fE4efIkhg0bBsZYuW0mCEJaKB4RZocRhIloNBrm7u7OVq9eXeI5np6ebOnSpSW+7+/vz959912DY+3atSvz+ikpKQwAu3HjBsvMzGSOjo5sx44d/PvPnj1jLi4uBvk3bdqURUREMMYYi4uLYwBYYmJiqdcCwPbs2VOmTQRBSAPFI0IKqKWJMJmUlBRkZmbCz8+PPzZ27Fjs2rWL/79x48a4c+dOufPu1KmTwbF79+5h9OjRaNSoETw8PNCwYUMAQFJSEu7du4eCggJ069aNP79atWpo1qyZXh7x8fF4+PAh+vXrBwBo27Yt+vbti9atW2PEiBHYuHEj0tPTy20vQRDSQvGIkAKqNBHlRq1W8+lr164hKSmJ/18mk4HjuHLnWaVKFYNjgwYNwrNnz7Bx40ZcunQJly5dAlA4MJOZ2HwdERGBoKAguLi4AADkcjmOHj2KQ4cOoWXLlli1ahWaNWuGhISEcttMEIT0UDwizAlVmgiT8fHxgaurK/766y8AQH5+Pu7cuYObN28CKJwVkpCQAF9f30pf69mzZ4iPj8fHH3+Mvn37okWLFnpPYH5+fnBwcMDFixf5Y+np6bxtOvbt24fBgwfrHeM4Dj169MCnn36Kq1evwtHREXv27Km0zQRBmA+KR4QU0JIDhMnIZDIMGTIEq1evhr+/P3bv3o0+ffpgz549ePvttxEdHY3nz59j0KBBlb5W1apVUb16dWzYsAG1atVCUlKS3rombm5uePvtt/Hee++hevXqqFmzJj766CPIZH8/B6SkpCA2NlZvUbhLly7h+PHjCA4Oho+PDy5duoTU1FS0aNGi0jYTBGE+KB4RUkCVJqJcrFixAm+88Qa6d++Opk2bYteuXThw4ABCQ0Ph7OyMb7/9Fi1btqz0dWQyGXbs2IHp06ejVatWaNasGVauXImAgAD+nCVLliArKwuDBw+Gu7s7Zs+ejZcvX/Lv79+/H127doWPjw9/zMPDA6dPn8by5cuRkZGBBg0a4Ouvv0ZoaGilbSYIwrxQPCLMDcdM7YwlCAEICAhAu3btsHz5ctGvNXjwYPTs2RNz584t92c5jsOePXswdOhQ4Q0jCMIioHhElBca00SYnbVr18LNzQ03btwQ9To9e/bE66+/Xq7PTJo0CW5ubiJZRBCEpUHxiCgP1NJEmJVHjx4hNzcXAFC/fn1BtycQgpSUFGRkZAAAatWqZXQWDUEQtgHFI6K8UKWJIAiCIAjCBKh7jiAIgiAIwgSo0kQQBEEQBGECVGkiCIIgCIIwAao0EQRBEARBmABVmgiCIAiCIEyAKk0EQRAEQRAmQJUmgiAIgiAIE6BKE0EQBEEQhAlQpYkgCIIgCMIE/g8iBx1PvcIt0AAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from control import mixsyn\n", "\n", "WS = tf( [0, 1], [1, 1, 0.25]) # 感度関数に対する重み関数\n", "WU = tf(1,1)\n", "WT = tf( [10, 0], [1, 150]) # 相補感度関数に対する重み関数\n", "\n", "# 混合感度問題\n", "K, _, info = mixsyn(Pn, w1=WS , w2=WU, w3=WT)\n", "\n", "print('K=', ss2tf(K))\n", "print('gamma =', info[0])\n", "\n", "fig, ax = plt.subplots(1, 2, figsize=(6,2.3))\n", "\n", "# 感度関数\n", "Ssys = feedback(1, Pn*K)\n", "mag, _, w = bode(Ssys, logspace(-3,3), plot=False)\n", "ax[0].semilogx(w, mag2db(mag), ls= '-', lw =2, label='$S$', color='k')\n", "\n", "mag, _, w = bode(1/WS, logspace(-3,3), plot=False)\n", "ax[0].semilogx(w, mag2db(mag), ls= '-.', lw =1, label='$1/W_S$', color='k')\n", "\n", "# 相補感度関数\n", "Tsys = feedback(Pn*K, 1)\n", "mag, _, w = bode(Tsys, logspace(-3,3), plot=False)\n", "ax[1].semilogx(w, mag2db(mag), ls = '-', lw =2, label='$T$', color='k')\n", "\n", "mag, _, w = bode(1/WT, logspace(-3,3), plot=False)\n", "ax[1].semilogx(w, mag2db(mag), ls= '--', lw =1, label='$1/W_T$', color='k')\n", "\n", "for i in range(2):\n", " ax[i].set_ylim(-40, 40)\n", " ax[i].legend()\n", " ax[i].grid(which=\"both\", ls=':')\n", " ax[i].set_ylabel('Gain [dB]')\n", " ax[i].set_xlabel('$\\omega$ [rad/s]')\n", "\n", "fig.tight_layout()\n", "# fig.savefig(\"robust_design.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "設計したコントローラのボード線図とノミナルモデルのボード線図" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(6,2.3))\n", "\n", "mag, _, w = bode(K, logspace(-1,3,1000), plot=False)\n", "ax.semilogx(w, mag2db(mag), ls= '-', lw =2, label='$K$', color='k')\n", "\n", "mag, _, w = bode(Pn, logspace(-1,3,1000), plot=False)\n", "ax.semilogx(w, mag2db(mag), ls= '-.', lw =1, label='$Pn$', color='k')\n", "\n", "ax.legend()\n", "ax.grid(ls=':')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "ステップ応答" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.0, 60.0)" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(3, 2.3))\n", "\n", "for i in range(len(delta)):\n", " P = (1 + WT*delta[i])*Pn\n", " Gyr = feedback(P*K, 1)\n", "\n", " y, t = step(Gyr, np.arange(0,5,0.01))\n", "\n", " ax.plot(t, y*ref, color ='k', lw =0.3)\n", "\n", "Gyr = feedback(Pn*K, 1)\n", "y, t = step(Gyr, np.arange(0,5,0.01))\n", "ax.plot(t, y*ref, lw =2, color='k')\n", "\n", "plot_set(ax, 't', 'y')\n", "ax.set_xlim(0, 2)\n", "ax.set_ylim(0, 60)\n", "\n", "# fig.savefig(\"robust_step.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### PID制御との比較" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "ステップ応答" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "kp = 2\n", "kd = 0.1\n", "ki = 10\n", "\n", "# fig, ax = plt.subplots()\n", "fig, ax = plt.subplots(figsize=(3,2.3))\n", "\n", "for i in range(len(delta)):\n", " Kpid = tf([kd, kp, ki], [1, 0])\n", "\n", " P = (1 + WT*delta[i])*Pn\n", " Gyr = feedback(P*Kpid, 1)\n", " y, t = step(Gyr, np.arange(0,5,0.01))\n", " ax.plot(t, y*ref, color ='k', lw =0.3)\n", "\n", "ax.set_xlim(0, 2)\n", "ax.set_ylim(0, 60)\n", "plot_set(ax, 't', 'y')\n", "\n", "# fig.savefig(\"robust_comp.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "ナイキスト線図で不確かさの影響を確認する" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "from control.matlab import nyquist\n" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/minami/opt/anaconda3/envs/bookpython/lib/python3.11/site-packages/control/freqplot.py:943: UserWarning: number of encirclements was a non-integer value; this can happen is contour is not closed, possibly based on a frequency range that does not include zero.\n", " warnings.warn(\n", "/Users/minami/opt/anaconda3/envs/bookpython/lib/python3.11/site-packages/control/matlab/wrappers.py:113: UserWarning: number of encirclements does not match Nyquist criterion; check frequency range and indent radius/direction\n", " _, contour = nyquist_plot(syslist, omega, *args, **kwargs)\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,2, figsize=(6, 3))\n", "\n", "for i in range(len(delta)):\n", "# ロバスト制御:閉ループ系が安定になる\n", "\n", " P = (1 + WT*delta[i])*Pn\n", "\n", " x, y, _ = nyquist(P*K, logspace(-3,5,1000), plot=False)\n", " ax[0].plot(x, y, lw = 0.5, color='k')\n", " #ax[0].plot(x, -y, ls='--', color='k')\n", " ax[0].scatter(-1, 0, color='k')\n", " plot_set(ax[0], 'Re', 'Im')\n", "\n", "# PID制御:閉ループ系が不安定になる\n", " xpid, ypid, _ = nyquist(P*Kpid, logspace(-3,5,1000), plot=False)\n", " ax[1].plot(xpid, ypid, lw = 0.5, color='k')\n", " #ax[1].plot(xpid, -ypid, ls='--', color='k')\n", " ax[1].scatter(-1, 0, color='k')\n", " plot_set(ax[1], 'Re', 'Im')\n", "\n", "x, y, _ = nyquist(Pn*K, logspace(-3,5,1000), plot=False)\n", "ax[0].plot(x, y, lw = 2, color='k')\n", "ax[0].set_xlim(-1.2, 1.2)\n", "ax[0].set_ylim(-1.2, 1.2)\n", "\n", "xpid, ypid, _ = nyquist(Pn*Kpid, logspace(-3,5,1000), plot=False)\n", "ax[1].plot(xpid, ypid, lw = 2, color='k')\n", "ax[1].set_xlim(-1.2, 0.5)\n", "ax[1].set_ylim(-1.2, 0.5)\n", "fig.tight_layout()\n", "\n", "# fig.savefig(\"nyquist_robust.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "左:ロバスト制御,右:PID制御" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### おまけ" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "from control import augw, hinfsyn\n", "G = augw(P, w1=WS, w2=WU, w3=WT)\n" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\frac{5.264 s^5 + 1592 s^4 + 1.227 \\times 10^{5} s^3 + 4.366 \\times 10^{5} s^2 + 1.19 \\times 10^{7} s + 9.958 \\times 10^{6}}{s^6 + 320.4 s^5 + 2.892 \\times 10^{4} s^4 + 3.768 \\times 10^{5} s^3 + 2.799 \\times 10^{6} s^2 + 2.53 \\times 10^{6} s + 6.109 \\times 10^{5}}$$" ], "text/plain": [ "TransferFunction(array([5.26385918e+00, 1.59156522e+03, 1.22682223e+05, 4.36556203e+05,\n", " 1.19037009e+07, 9.95839882e+06]), array([1.00000000e+00, 3.20437726e+02, 2.89216312e+04, 3.76842182e+05,\n", " 2.79873805e+06, 2.53046728e+06, 6.10856797e+05]))" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "k, cl, gam, ro= hinfsyn(G, 1, 1)\n", "ss2tf(k)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## ディジタル実装" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "from control.matlab import tf, c2d, step, lsim\n" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "連続時間システム \n", " 1\n", "---------\n", "0.5 s + 1\n", "\n" ] } ], "source": [ "P = tf([0, 1], [0.5, 1])\n", "print('連続時間システム',P)\n" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "離散時間システム(zoh) \n", " 0.3297\n", "----------\n", "z - 0.6703\n", "\n", "dt = 0.2\n", "\n", "離散時間システム(tustin) \n", "0.1667 z + 0.1667\n", "-----------------\n", " z - 0.6667\n", "\n", "dt = 0.2\n", "\n" ] } ], "source": [ "ts = 0.2\n", "\n", "Pd1 = c2d(P, ts, method='zoh')\n", "print('離散時間システム(zoh)', Pd1)\n", "\n", "Pd2 = c2d(P, ts, method='tustin')\n", "print('離散時間システム(tustin)',Pd2)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "ステップ応答" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,2, figsize=(6, 2.3))\n", "\n", "Tc = np.arange(0, 3, 0.01)\n", "y, t = step(P, Tc)\n", "ax[0].plot(t, y, ls='-.')\n", "ax[1].plot(t, y, ls='-.')\n", "\n", "\n", "Td = np.arange(0, 3, ts)\n", "y, t = step(Pd1, Td)\n", "ax[0].plot(t, y, ls='', marker='o', label='zoh')\n", "\n", "y, t = step(Pd2, Td)\n", "ax[1].plot(t, y, ls='', marker='o', label='tustin')\n", "\n", "for i in [0, 1]:\n", " plot_set(ax[i], 't', 'y', 'best')\n", " ax[i].set_xlim([0, 3])\n", "\n", "fig.tight_layout()\n", "# fig.savefig(\"c2d_step.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "特定の周波数の信号を印加したときの応答" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/minami/opt/anaconda3/envs/bookpython/lib/python3.11/site-packages/control/timeresp.py:940: UserWarning: return_x specified for a transfer function system. Internal conversion to state space used; results may meaningless.\n", " warnings.warn(\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,2, figsize=(6, 2.3))\n", "\n", "Tc = np.arange(0, 3, 0.01)\n", "Uc = 0.5 * np.sin(6*Tc) + 0.5 * np.cos(8*Tc)\n", "\n", "y, t, x0 = lsim(P, Uc, Tc)\n", "ax[0].plot(t, y, ls='-.')\n", "ax[1].plot(t, y, ls='-.')\n", "\n", "\n", "T = np.arange(0, 3, ts)\n", "U = 0.5 * np.sin(6*T) + 0.5 * np.cos(8*T)\n", "\n", "y, t, x0 = lsim(Pd1, U, T)\n", "ax[0].plot(t, y, ls='', marker='o', label='zoh')\n", "\n", "y, t, x0 = lsim(Pd2, U, T)\n", "ax[1].plot(t, y, ls='', marker='o', label='tustin')\n", "\n", "for i in [0, 1]:\n", " plot_set(ax[i], 't', 'y', 'best')\n", " ax[i].set_xlim([0, 3])\n", " ax[i].set_ylim([-0.3, 0.3])\n", "\n", "fig.tight_layout()\n", "# fig.savefig(\"c2d_time.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [], "source": [ "from control.matlab import bode, logspace, linspace, mag2db\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "ボード線図" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(2, 1, figsize=(4, 3.5))\n", "\n", "mag, phase, w = bode(P, logspace(-2,2), plot=False)\n", "ax[0].semilogx(w, mag2db(mag), ls = '-.', label='continuous')\n", "ax[1].semilogx(w, np.rad2deg(phase), ls = '-.', label='continuous')\n", "\n", "# 離散時間システム (0次ホールドによる離散化)\n", "mag, phase, w = bode(Pd1, linspace(0.01, np.pi/ts-0.001, 1000), plot=False)\n", "ax[0].semilogx(w, mag2db(mag), ls = '--', label = 'zoh')\n", "ax[1].semilogx(w, np.rad2deg(phase), ls = '--', label= 'zoh')\n", "\n", "# 離散時間システム (双一次変換による離散化)\n", "mag, phase, w = bode(Pd2, linspace(0.01, np.pi/ts-0.001, 1000), plot=False)\n", "ax[0].semilogx(w, mag2db(mag), ls = '-', label = 'tustin')\n", "ax[1].semilogx(w, np.rad2deg(phase), ls = '-', label = 'tustin')\n", "\n", "bodeplot_set(ax, 3)\n", "\n", "# ナイキスト周波数 w = pi/ts のところに線を引く\n", "ax[0].axvline(np.pi/ts, lw = 0.5, c ='k')\n", "ax[1].axvline(np.pi/ts, lw = 0.5, c ='k')\n", "\n", "ax[0].set_ylim([-43, 3])\n", "# ax[0].set_xlim([0.01, np.pi/ts])\n", "# ax[1].set_xlim([0.01, np.pi/ts])\n", "\n", "fig.tight_layout()\n", "# fig.savefig(\"c2d_bode.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "サンプリング周期を0.05にしたときのボード線図" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "離散時間システム(zoh) \n", " 0.09516\n", "----------\n", "z - 0.9048\n", "\n", "dt = 0.05\n", "\n", "離散時間システム(tustin) \n", "0.04762 z + 0.04762\n", "-------------------\n", " z - 0.9048\n", "\n", "dt = 0.05\n", "\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ts = 0.05\n", "\n", "Pd1 = c2d(P, ts, method='zoh')\n", "print('離散時間システム(zoh)', Pd1)\n", "\n", "Pd2 = c2d(P, ts, method='tustin')\n", "print('離散時間システム(tustin)',Pd2)\n", "\n", "fig, ax = plt.subplots(2, 1, figsize=(4, 3.5))\n", "\n", "mag, phase, w = bode(P, np.logspace(-2,2), plot=False)\n", "pltargs = {'ls': '-.', 'label': 'continuous'}\n", "ax[0].semilogx(w, mag2db(mag), **pltargs)\n", "ax[1].semilogx(w, np.rad2deg(phase), **pltargs)\n", "\n", "# gain, phase, w = bode(Pd1, np.logspace(-2,2), plot=False)\n", "mag, phase, w = bode(Pd1, plot=False)\n", "pltargs = {'ls': '--', 'label': 'zoh'}\n", "ax[0].semilogx(w, mag2db(mag), **pltargs)\n", "ax[1].semilogx(w, np.rad2deg(phase), **pltargs)\n", "\n", "\n", "# gain, phase, w = bode(Pd2, np.logspace(-2,2), plot=False)\n", "mag, phase, w = bode(Pd2, plot=False)\n", "pltargs = {'ls': '-', 'label': 'tustin'}\n", "ax[0].semilogx(w, mag2db(mag), **pltargs)\n", "ax[1].semilogx(w, np.rad2deg(phase), **pltargs)\n", "\n", "bodeplot_set(ax, 3)\n", "\n", "# 周波数が w = pi/ts のところに線を引く\n", "ax[0].axvline(np.pi/ts, lw = 0.5, c ='k')\n", "ax[1].axvline(np.pi/ts, lw = 0.5, c ='k')\n", "\n", "ax[0].set_ylim([-43, 3])\n", "# ax[0].set_xlim([0.01, np.pi/ts])\n", "# ax[1].set_xlim([0.01, np.pi/ts])\n", "\n", "fig.tight_layout()\n", "# fig.savefig(\"c2d_bode2.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### プログラム実装(おまけ)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "離散時間システム(コントローラ)プログラムに実装する方法" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [], "source": [ "from control.matlab import tf, tfdata, c2d, step\n" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [], "source": [ "zeta, omega_n = 0.2, 10\n", "P = tf([omega_n**2], [1, 2*zeta*omega_n, omega_n**2])\n", "\n", "ts = 0.2\n", "Pd = c2d(P, ts, method='zoh')\n", "[[[b]], [[a]]] = tfdata(Pd) # 分子・分母多項式の係数を取得\n", "\n", "b1, b2 = b\n", "a1, a2 = a[1:]\n" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.0, 3.0)" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(3, 2.3))\n", "\n", "Tc = np.arange(0, 3, 0.01)\n", "y, t = step(P, Tc)\n", "ax.plot(t, y, ls='-.', label='continuous', color='k')\n", "\n", "Td = np.arange(0, 3, ts)\n", "y, t = step(Pd, Td)\n", "ax.plot(t, y, ls='', marker='o', label='zoh', color='k')\n", "\n", "plot_set(ax, 't', 'y', 'best')\n", "ax.set_xlim([0, 3])\n" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.0, 3.0)" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(3, 2.3))\n", "\n", "# 離散時間システムのステップ応答\n", "uold, uold2 = 0.0, 0.0\n", "yold, yold2 = 0.0, 0.0\n", "\n", "Td = np.arange(0, 3, ts)\n", "u = 1.0*(Td>=0) # 単位ステップ入力\n", "\n", "# プログラム ===============\n", "for k in range(len(Td)):\n", " y[k] = b1*uold + b2*uold2 - a1*yold - a2*yold2\n", "\n", " yold2 = yold\n", " yold = y[k]\n", " uold2 = uold\n", " uold = u[k]\n", "# ========================\n", "\n", "ax.plot(Td, y, ls='', marker='o', label='discrete', color='k')\n", "\n", "#連続時間システムのステップ応答\n", "yc, t = step(P, np.arange(0, 3, 0.01))\n", "ax.plot(t, yc, ls='-.', label='continuous', color='k')\n", "\n", "plot_set(ax, 't', 'y', 'best')\n", "ax.set_xlim([0, 3])\n", "\n", "# fig.savefig(\"c7_system2program_plot.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.0, 3.0)" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(3, 2.3))\n", "\n", "Tc = np.arange(0, 3, 0.01)\n", "yc, t = step(P, Tc)\n", "ax.plot(t, yc, ls='-.', label='continuous', c='k')\n", "\n", "xold, xold2 = 0.0, 0.0\n", "\n", "Td = np.arange(0, 3, ts)\n", "u = 1.0*(Td>=0)\n", "\n", "# プログラム ================\n", "for k in range(len(Td)):\n", " x = u[k] - a1*xold - a2*xold2\n", " y[k] = b1*xold + b2*xold2\n", "\n", " xold2 = xold\n", " xold = x\n", "# ========================\n", "\n", "ax.plot(Td, y, ls='', marker='o', label='discrete', c='k')\n", "\n", "plot_set(ax, 't', 'y', 'best')\n", "ax.set_xlim([0, 3])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 最適制御" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [], "source": [ "import control as ct\n", "import control.optimal as obc\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 有限時間最適制御" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "1次系" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1.+0.j]\n" ] } ], "source": [ "P = ct.ss(1, 1, 1, 0) # システム dxdt=x+u,y=x の記述\n", "sys = ct.ss2io(P) # 状態空間モデルを入出力モデル変換\n", "print(sys.poles())\n" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [], "source": [ "xf = 0 # 基準状態,終端状態\n", "uf = 0 # 基準入力\n", "Q = 50 # 状態に関する重み\n", "R = 0.1 # 入力に関する重み\n", "\n", "# 評価関数の設定\n", "cost = obc.quadratic_cost(sys, Q, R, x0=xf, u0=uf)\n", "\n", "# traj_cost = obc.quadratic_cost(sys, R, R, x0=xf, u0=uf)\n", "# term_cost = obc.quadratic_cost(sys, Q, None, x0=xf)\n", "\n", "# P = 100\n", "# term_cost = opt.quadratic_cost(sys, P, 0, x0=xf)\n", "\n", "# 制約条件の設定\n", "umin, umax = -4, 4\n", "constraints = [ obc.input_range_constraint(sys, [umin], [umax]) ]\n", "terminal = [ obc.state_range_constraint(sys, [xf], [xf]) ]\n" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Summary statistics:\n", "* Cost function calls: 3535\n", "* Constraint calls: 3672\n", "* Eqconst calls: 3672\n", "* System simulations: 1\n", "* Final cost: 5.585715123369499\n", "最適化成功: True\n" ] } ], "source": [ "Td = np.arange(0, 0.5, 0.01) # シミュレーション時間\n", "x0 = 1 # 初期状態\n", "\n", "# 最適制御問題を解く\n", "result = obc.solve_ocp(sys, Td, x0, cost=cost,\n", " constraints=constraints, terminal_constraints=terminal)\n", "# result = obc.solve_ocp(sys, Td, x0, cost=traj_cost, terminal_cost=term_cost,\n", "# constraints=constraints)\n", "print('最適化成功:', result.success)\n" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Final_computed_state: [0.]\n" ] } ], "source": [ "print(\"Final_computed_state:\",result.states[:,-1]) # 終端状態\n" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Final_simulated_state: [0.00570882]\n" ] }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlYAAADWCAYAAAATiszuAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAA9hAAAPYQGoP6dpAABV1UlEQVR4nO2deVxU1f//X7OxuKMI4gaIJiqliGAu4A4KlpkmbS79tPJhi8unTx/Nvp+sbPHzqdQWSz9Z2KKSmVuOAoYsijkwjhqCSopCOKAYEKDA3Jnz+wPnxggzbPfOnSPn+XjMw8Pl3MPzvO+5xzPn3EVGCCFgMBgMBoPBYLQaudQCDAaDwWAwGPcKbGDFYDAYDAaDIRBsYMVgMBgMBoMhEGxgxWAwGAwGgyEQbGDFYDAYDAaDIRBsYMVgMBgMBoMhEGxgxWAwGAwGgyEQbGDFYDAYDAaDIRBKqQWkpri4GHFxcfDx8YGrq6vUOgzGPc/t27dx5coVREREwN3dXWodh4L1RwyGfRGjP2rzA6u4uDg8/fTTUmswGG2O7777Dk899ZTUGg4F648YDGkQsj9q8wMrHx8fALVBHTRokLQyDEYbIDs7G08//TR/7jH+hvVHDIZ9EaM/avMDK/N0+4ABAzB8+HCJbZoGx3HQaDQICQmBUun4h5D5iguNvgDYUlcD0NYf0dj2aPIF6HOm0RcQtj+S9OL1lJQUPPTQQ+jZsydkMhn27t3b6D7JyckICgqCi4sL+vXrhy+++KJent27d2Pw4MFwdnbG4MGDsWfPnkbLlcvpuY5fLpejV69e1DgzX3Gh0ZdhG1piRGPbo8kXoM+ZRl/ByxS8xGZQWVmJoUOH4tNPP21S/tzcXERGRiI0NBQ6nQ6vvfYaXn75ZezevZvPc+LECURHR2Pu3Lk4c+YM5s6dizlz5uDkyZM2y6alEQC1rt7e3tQ4M19xodGXYRtaYkRj26PJF6DPmUZfwcsUvMRmMG3aNKxduxaPPvpok/J/8cUX6Nu3LzZs2IBBgwZh0aJF+H//7//hgw8+4PNs2LABU6ZMwapVq+Dv749Vq1Zh0qRJ2LBhg82yy8vLW1MVu8JxHFJSUvgpTEeH+YoLjb4M29ASIxrbHk2+AH3ONPoKDR1DyjucOHEC4eHhFtsiIiKQkZEBg8FgM09aWprNsp999lmkpKQgPT0d6enp0Ov1MBqNMBqNAGqDXzdtMplspg0Gg0WaEGKRJoTUSwOwSJtMJot03Qbg4+MDuVxusd1oNFqkzb7W0vaqk0wms/BtqE7W0lLUSS6Xw8fHBzKZrFXHyV51MvuaEbPtCVEnWr7JSgktMZLL5fDz82O+IkKbM42+gpcpeIkiUlhYCE9PT4ttnp6e4DgOxcXFNvMUFhbaLDsnJwfjxo1DSEgIQkJCsHnzZpw9exY5OTkAAJ1Oh9zcXACARqNBfn4+ACAtLQ16vR5A7TVjZo/ExESUlpYCAOLj4/kZMbVajaqqKnAcB7VaDY7jUFVVBbVaDaB25iw+Ph4AUFpaisTERAC1z7dJSUkBABQVFeHKlSuQy+XIz8+HRqMBULtUqtPp+PqcPXsWQO1dD9nZ2QAgSZ0qKyvx22+/QS6XW62TXq/nB79S10kul0On06GmpqZVx8ledZLL5fj999/x559/tuo42atOtHS4UkJLjGi8noYmX4A+Zxp9BYc4CADInj17bOYZMGAAeffddy22HTt2jAAger2eEEKISqUi27dvt8jz3XffEWdn5wbL1Gq1BABp3749AUD8/f1JQkICuXbtGuE4jnAcRwghxGAwWKSNRqPNdE1NjUXaZDJZpE0mU700IcQibTQaLdIGg4EQQkh1dTU5cuQI//fM2zmOs0ibfa2l7VWnmpoaC9+G6mQtLUWdDAYDOXLkCP9zS4+Tvepk9q2urm7VcbJXnU6ePEkAEK1WSxiWmPujkydPSq3SJAwGA/nll1/4Y+/o0OZLCH3OtPmK0R/RMaS8Q48ePerNPF2/fh1KpRLdunWzmefuWay72bJlC9zd3XH+/Hm88sorUCqVUCgUUCgUAMD/bE6bR7nW0iqVyiItk8ks0jKZrF4agEVaLpdbpM23riqVStx///2Qy+UW2xUKhUXa7Gstba86KRQKC9+G6mQtLUWd5HI57r//figUilYdJ3vVyexrLlPMtidEnWj5JisltMRILpcjICCA+YoIbc40+gpepuAlisioUaOQkJBgsS0+Ph4jRozg/xOwlmf06NE2y/b390dSUhI8PT1x5swZTJgwAUVFRcJWQCDkcjk8PDyoarjMVzxo9GXYhpYY0dj2aPIF6HOm0VfwMgUvsRlUVFTg9OnTOH36NIDa6zROnz6NvLw8AMCqVaswb948Pv/ixYtx9epVrFixAtnZ2fjqq6+wdetWvPLKK3yepUuXIj4+HuvWrcP58+exbt06HDlyBMuWLbPpwnEchgwZguTkZPTs2RPnzp3DhAkTGr02SwoMBgPi4uL4i4sdHeYrLrT50nK3kJTQEiPa2h5tvgB9zrT53nN3BWZkZCAwMBCBgYEAgBUrViAwMBD//ve/AdReKGseZAGAr68v1Go1kpKSMGzYMLz99tv4+OOPMWvWLD7P6NGjsXPnTnz99dd44IEHEBMTg9jYWIwcOdKmi3nUOnDgQCQnJ6N3797Izs7G+PHjce3aNaGr3ioUCgWCg4P5JRZHh/mKC22+tHyTlRJaYkRb26PNF6DPmTZfMc41SZ83P378eP5W8IaIiYmpt23cuHE4deqUzXJnz56N2bNnN8ulbnD79++P5ORkTJgwARcuXMD48eORmJiI3r17N6tMsZDL5ejatavUGk2G+YoLjb4M29ASIxrbHk2+AH3ONPoKXqbgJVLK3dOB/fr1Q3JyMnx8fJCTk4Px48fzt7lLjcFgwMGDB6mZamW+4kKbLy3LXFJCS4xoa3u0+QL0OdPme88tBToSDU1b+vj4ICkpCf369cOlS5cwfvx4i6VJqVAqlQgNDaXiBZcA8xUb2nxpWSKQElpiRFvbo80XoM+ZNl8xzjU2sLqD+Zb0u/H29kZSUhL8/Pxw+fJljB8/HlevXrWznSUymQydOnWy6uxoMF9xodGXYRtaYkRj26PJF6DPmUZfoWEDqzvYmg7s06cPP7jKzc3F+PHjceXKFfvJ3YXBYMC+ffuomWplvuJCmy8ty1xSQkuMaGt7tPkC9DnT5suWAkWksenA3r17IykpCf3798eVK1ckHVwplUqEh4dTM9XKfMWFNl9alrmkhJYY0db2aPMF6HOmzZctBUqMeXA1YMAAXL16VfLBFU0wX3GhzZdx70Bb26PNF6DPmTZfoWEDqzsYjcYm5evVqxeOHj3KD64mTJhg92uu6r5ElwaYr7jQ5tvUc60tQ0uMaGt7tPkC9DnT5ivGucYGVndoznRg3cGVeVnQnoMrpVKJyMhIar4VMF9xoc2XlmUuKaElRrS1Pdp8AfqcafNlS4EOhHlwZb7masKECXZ9FAMt3wbMMF9xoc23rbFp0yb4+vrCxcUFQUFBSE1NlVpJMGhre7T5AvQ50+YrNGxgdYeWTAeaB1d17xa0x0NEOY5DfHw8NY2X+YoLbb60LHMJRWxsLJYtW4bVq1dDp9MhNDQU06ZNs/lFjJYY0db2aPMF6HOmzVeMc01GbL1Tpg1w6tQpBAUFQavVYvjw4S0qIz8/HxMmTMClS5fg5+eH5ORk9OrVS2BTBuPeQIhzjiZGjhyJ4cOH4/PPP+e3DRo0CI888gjee+89i7xtLTYMhtSIcc7RsQhqB1ozvuzTpw+OHj2KcePG4dKlS5gwYQKSk5Ph5eUloOHfEEJQXl6Ojh07UvEQNuYrLjT6thVqamqg1WqxcuVKi+3h4eFIS0uzul9mZiaAv79N9+7dGx4eHgBqrwnhOA4ymYxPy+VyyOVyq2mDwQCFQsGnlUolZDIZnwZqZxrqplUqFQghfNpkMsFoNPJpk8kEhUKBsrIytG/f3mK7UqmE0WgEIYRPm92tpe1RJ6VSib/++guurq5wcnJqsE5KpdJqWoo6AUBJSQm6dOkCmUzWouNkzzrJZDKUlJSgc+fOUCgUzT5OBoMBJpMJt2/fRlVVFX8eVVVV8WWYHTiO4/8ux3EwGo0WaYVCgZKSEly/fh3Xr19HYWEhioqKsHDhQkycOBGAOP0RWwq8Q2unA82DK29vb+Tk5GDChAkoLCwUyM4SjuOQmppKzVQr8xUX2nxpWeYSguLiYhiNRnh6elps9/T0tNk/zJ8/H0FBQQgJCUFISAg2b96Ms2fPIicnBwCg0+mQm5sLANBoNPwlCGlpadDr9QCAlJQUFBcXAwASExNRWloKAIiPj0d5eTkAQK1Wo6qqyuJOrqqqKqjVagBAeXk54uPjAQClpaVITEzk65WSksK3PfMgMT8/HxqNBgCQm5sLnU4HAMjJycHZs2cBANnZ2cjOzgYAu9fJ7JuQkGC1TgCg1+sdpk5m54qKihYfJ3vWieM4JCUl4ezZs9BoNHjrrbfw4Ycf4u2338bs2bPxxBNPICoqCsOGDUNgYCDuu+8+eHp6okuXLnB1dYWzszNcXV3RtWtX9OzZEz179oSPjw/8/f1x3333YciQIRg6dCgeeOABDB8+HCEhIRgxYgQefPBBjBkzBqNGjUJoaCjGjx+P0NBQPPzww1i0aBFee+01fPzxx4iNjcWZM2f4OrGlQBEQehowNzcX48aNQ35+PgYNGoSkpCT+myaDwWhby13Xrl1Dr169kJaWhlGjRvHb33nnHXz77bc4f/68RX5zbL755hsMGTLE4WesHG12h9XJvnW6ceMGfvvtN1y8eBFZWVm4cOECLl68iD/++EOwL3pyuRwqlQoKhQJKpRIKhYKPkVwu59MymQwymYzfbv65Q4cO8PDwQI8ePdC9e3d4enpi4sSJGDp0KADgzJkzbClQLEwmkyDl+Pr68suC2dnZmDx5MhITE+Hu7i5I+UCta2lpKbp06QK53PEnHZmvuNDo21Zwd3eHQqGoNzt1/fr1erNYdRk0aJDNTr7urexNSatUqhalZTIZnzb/h1U3Xbft3Z2n7m3sTUnbo062fJuSlqJOJpMJ5eXl/PndkuMkRJ0IITh9+jTS0tJw8uRJ/Prrr7h48SKsIZfL4eXlhd69e8PLywvu7u7o1q0b3N3d0bVrV3Tq1AkdOnTgP+3bt4eLiwv/cXJygkqlEr1PE6M/YgOrOwgZXD8/P35w9dtvv2HKlCn45Zdf0LVrV0HKNxqNSE9Px8SJE6n4j5T5igttvm1pYOXk5ISgoCAkJCRg5syZ/PaEhATMmDHD6n60xIi2tkebLyCtc1lZGY4cOQK1Wo1Dhw7xy5d18fX1xeDBg+Hv7w9/f3/4+fmhoKAAs2bNgqurq119WwIbWImI0A8zGzBgABITEzFu3DicPn0aEREROHLkCDp37tzqslUqFSIiIgSwtA/MV1xo86XlwYFCsWLFCsydOxcjRozAqFGjsGXLFuTl5WHx4sVW96ElRrS1Pdp8Afs719TU4ODBg/j6669x6NAhiyW99u3bY+zYsRg5ciRGjhyJkJAQQVdjpECMc42Os9cOiDFq9ff3xy+//IIJEyYgIyMDU6dORXx8PDp27Niqck0mE4qLi+Hu7k7Fty7mKy40+rYloqOjcfPmTbz11lvQ6/UICAiAWq2Gt7e31X1oiRGNbY8mX8B+zllZWfjyyy/x3Xff4caNG/x2f39/REZGIjIyEmPHjoWzs7ND+AqFGOea49faTojVkQUEBODIkSNwc3PDr7/+iqioKFRWVraqTJPJhMzMTKo6X+YrHjT6tjWWLFmCK1euoLq6GlqtFmFhYTbz0xIjGtseTb6A+M46nQ6PPvoohgwZgvXr1+PGjRvo0aMHXn31VWRlZSE7OxsffvghJk2a1Oigyh6+QsOWAkVEzKn3oUOHIiEhAZMmTUJqaipmzJiBAwcOtHj9WalU8s/goAHmKy40+jJsQ0uMaGx7NPkC4jlrNBq8/fbb+PnnnwHUXgBvfjTB1KlTW9wGaYuxGOcam7G6g9ij66CgIBw+fBgdOnTAL7/8gtmzZ6O6urpFZZlMJhQUFFD1jYD5igeNvgzb0BIjGtseTb6A8M5FRUV4+umnMXLkSPz888+Qy+V48sknkZmZib1792L69OmtGmzQFmO2FCgi9mgEDz74IA4ePAhXV1eo1Wo8/vjjMBgMzS7HZDLh0qVLVDVc5iseNPoybENLjGhsezT5AsI5m0wmbN68Gf7+/vj+++8hk8kwf/58ZGdn4/vvv8fgwYMdytdesIGViNhr6j0sLAz79++Hs7Mz9u7di7lz5zb7ya9KpRJhYWFULRcwX/Gg0ZdhG1piRGPbo8kXEMb53LlzGDt2LBYvXozS0lIMHz4cGo0GMTExuO+++wS0pS/GbClQROw5up48eTJ2794NlUqF2NhYLFq0qFl/32Qy4erVq1R9I2C+4kGjL8M2tMSIxrZHky/QeudvvvkGwcHBOHHiBDp06IANGzbg5MmTGDFihMCmtdAW43tyxmrTpk3w9fWFi4sLgoKCkJqaajXvggUL+MfU1/0MGTKEzxMTE9NgHvPLHK1h70YQFRWFnTt3QqFQICYmBi+99FKTXwZJ4xo28xUPGn0ZtqElRjS2PZp8gZY7V1dXY8mSJZg/fz5u376NiIgIZGdnY+nSpaLOJtEW43tuYBUbG4tly5Zh9erV0Ol0CA0NxbRp05CXl9dg/o0bN0Kv1/Of/Px8dO3aFY899phFvk6dOlnk0+v1cHFxsekixbTlo48+im3btkEmk2HTpk3417/+1aTBlVKpxOjRo6maamW+4kGjL8M2tMSIxrZHky/QMuf8/HyEhYXh888/h0wmwxtvvAG1Wo3evXuLaFoLbTG+55YCP/roIyxcuBCLFi3CoEGDsGHDBvTp0weff/55g/k7d+6MHj168J+MjAyUlJTgmWeescgnk8ks8vXo0aNRFzHecN0UnnrqKWzevBkA8N///hdvvfVWo/sYjUb8/vvvkjk3F+YrLjT6MmxDS4xobHs0+QLNd87IyEBQUBA0Gg3c3Nxw8OBBrFmzxm4P66QtxmJ4SjawqqmpgVarRXh4uMX28PBwpKWlNamMrVu3YvLkyfWeYFxRUQFvb2/07t0b06dPh06na7SsrKwsnDp1Cunp6UhPT4der4fRaOSDznGcRdo8fWgtbTAYLNLmmShzmhDCpxctWoQPP/wQALBmzRqsW7cOQO0UpfmuQZPJxL9awGg04ubNmyCE1NteN232tZYWs07mtNm9rm9DdbKWlqJOhBDcvHkTJpPJap3urp+UdTL7mvO09DjZq05NXfJuy9ASI0IISkpKmK+INMc5LS0NkyZNwo0bNxAYGAitVotp06bZwfJvaIuxGJ6SDayKi4thNBrrveHd09Oz3pvgG0Kv1+PQoUNYtGiRxXZ/f3/ExMRg//792LFjB1xcXDBmzBjk5OTYLG/BggUICgpCSEgIQkJCsHnzZpw9e5bfT6fTITc3F0Dtg9Xy8/MB1DZk84spU1JSUFxcDABITExEaWkpACA+Ph7l5eUAALVajaqqKnAcB7VaDY7jUFVVBT8/P7zzzjsAgJUrV2Lz5s0oLS1FYmIiH6+UlBQAwI0bN1BdXQ2lUon8/HxoNBoAQG5uLj+IzMnJwdmzZwEA2dnZyM7OBgC71kmtVgMAbt++jeLiYiiVSqt10uv1/IBa6joplUoUFhaC4zirdSovL0d8fDwASF4npVKJyspKvh4tPU72qhMtSwRSQkuMlEolgoODma+INNU5KSkJ4eHh+OuvvxAWFobk5GT4+vrayfJvaIuxKJ5EIgoKCggAkpaWZrF97dq1ZODAgY3u/+6775Ju3bqR6upqm/mMRiMZOnQoeemllxr8vVarJQBITEwM0Wq1RKPREI1GQ65du0Y4jiMcxxFCCDEYDBZpo9FoM11TU2ORNplMFmmTyVQvTQghK1euJACITCYj33zzDb/daDQSg8HAl3Hu3DnCcZzFdo7jLNJmX2tpe9XJYDCQzMxM3rehOllLS1EnjuNIZmYmMRgMVutUNy11nTiOI+fOneMdWnqc7FUnjUZDABCtVksYlpj7I41GI7VKk+A4jmRnZ/PH2NGhzZeQpjkfPnyYuLi4EABkypQppLKy0o6GltAWYzH6I8mGlO7u7lAoFPVmp65fv15vFutuCCH46quvMHfuXDg5OdnMK5fLERwc3OiM1eDBgzF8+HCrv687qm1KWqVStSj97rvvoqKiAp9++imeeeYZdOzYEY888gjkcjm/Ri6Xy/mnttfdrlAo+PKakrZXnWQyGWpqaur5NiUtVZ1qamr4O0qt1cmclrpORqMR1dXVfPmtOU72qhPj3uH27dtSKzQL2nwB285qtRozZ85ETU0Npk+fjl27djV6s5bY0BhjIZFsKdDJyQlBQUFISEiw2J6QkIDRo0fb3Dc5ORm///47Fi5c2OjfIYTg9OnT8PLyspnPUTp9mUyGjRs3Yv78+TAajYiOjq4XI4VCgcDAQIdxbgzmKy40+jJsQ0uMaGx7NPkCtp11Oh0ee+wx1NTUYNasWdi9e7fkgyraYiyGp6R3Ba5YsQJffvklvvrqK2RnZ2P58uXIy8vD4sWLAQCrVq3CvHnz6u23detWjBw5EgEBAfV+9+abbyIuLg6XL1/G6dOnsXDhQpw+fZov0xqOdAeDXC7Hl19+iVmzZqGmpgaPPPIIjh8/zv/eaDQiMzPToZxtwXzFhUZfhm1oiRGNbY8mX8C6c0FBAR566CHcunULU6ZMwY4dOxpdwbEHtMVYDE9Jry6Ljo7GzZs38dZbb0Gv1yMgIABqtZq/y0+v19d7plVZWRl2796NjRs3NlhmaWkpnnvuORQWFqJz584IDAxESkoKQkJCRK+PkCiVSmzfvh0zZszA4cOHERUVhaSkJAwbNkxqNQaDwWBISGVlJR5++GEUFBRg0KBB+OGHHyyW9xnSIiOEknsiReLUqVMICgqCVqu1eY2VVNy6dQsRERE4duwYPDw8kJqaKvi7nRgMe+Lo55yUsNgwGsNkMmH27NnYs2cP3N3dcfLkSfTr109qLWoR45yT/JU2joKjTlu2a9cOP//8MwIDA3H9+nVMnjyZv7XdUZ3vxmg0Ml8RodGXYRtaYkRj26PJF6jvvHr1auzZswdOTk7Yu3evww2qaIvxPfWAUEbT6dy5M+Li4uDv74/8/HxMnToVt27dklqrWbi6ukqt0CyYL4PRNGhre7T5An87Hzx4EO+//z4A4KuvvsKYMWOk1LIKjTEWEjawuoOj38HQvXt3JCQkwNvbGxcvXsSLL76IiooKqbWahEKhgL+/v8PH2AzzFRdaPKWElhjR2PZo8gX+dv7zzz/5O+GXLVuGp556SmKzhqEtxvfcXYGOhPl1HI5M7969kZCQAA8PD5w+fRrTp0+n4nkhHMchPT2dihgDzFdsaPGUElpiRGPbo8kXqHXWaDR49tlnUVRUhCFDhuC9996TWssqtMVYDE82sLqDTCaTWqFJDBgwAGq1Gh06dMCxY8fw2GOP8e90c1RkMhnc3NyoiTHzFRdaPKWElhjR2PZo8gVqnRMTE7Fv3z6oVCp89913kj+ryha0xVgMTzawugMt05YAEBQUhEOHDsHV1RUHDx7EM888w7901xFRKBTo378/NTFmvuJCi6eU0BIjGtseTb4AkJeXx79H9u2333b4R+7QFmO2FCgitExbArWucrkcsbGxUCqV+P7777F06VKHfZs4x3FIS0ujJsbMV1xo8ZQSWmJEY9ujyddoNOLpp59GRUUFxo4di1deeUVqpUahLcZsKVBEzO88owG5XI5evXohKioK27Ztg0wmw6effoq3335barUGMfvSEmPmKy60eEoJLTGise3R5Pvxxx8jLS0NHTp0wLZt26iYBaItxmJ40lFzO0BLIwBqXb29vSGXy/Hkk0/i448/BgC88cYb+PzzzyW2q09dXxpgvuJCi6eU0BIjGtseLb5FRUVYs2YNAOCjjz5yuOdVWYOmGANsYCUqtExbArWuKSkpvPOLL76If//73wCAF154AT/88IOUevW429fRYb7iQounlNASIxrbHi2+r7/+Ov766y8MHz4cAwYMoMIZoCvGAFsKFBVaRtdAraufn5+F85o1a7BkyRIQQvD0008jISFBQkNLGvJ1ZJivuNDiKSW0xIjGtkeDr06nw9atWwEAGzZswIABAxze2QwtMTbDZqxEhJZGADS8hi2TyfDxxx8jOjoaBoMBM2fOhEajkdDyb2hcc2e+4kGLp5TQEiMa256j+xJC+JuRnnjiCYSGhjq8c11oiHFd2MBKRGiZtgRqXRMTE+s5KxQKfPPNN5gyZQoqKysRFRWFCxcuSGT5N9Z8HRXmKy60eEoJLTGise05uu+uXbuQmpoKV1dXrFu3jgrnutDoKzRsYHUHWkbXQK1rQEBAg85OTk7YvXs3RowYgeLiYkRERODatWsSWP6NLV9HhPmKCy2eUkJLjGhse47se+vWLfzzn/8EAKxcuRJ9+vRxeOe7odFX8DIFL5FSaGkEQK2rh4eHVeeOHTvi4MGDGDBgAK5evYqpU6eitLTUvpJ1aMzX0WC+4kKLp5TQEiMa254j+37wwQfIy8tD3759+WdWObrz3dDoK3iZgpdIKbRMWwKAwWBAXFyczVfZeHh4IC4uDj169MBvv/2Ghx9+WLL3CjbF15FgvuJC07kmFbTEiLa258i+N2/exH/+8x8AwH//+1+0a9cOgGM7NwRtvmwpUERoGV0DtddSBQcHN/qwOF9fX8TFxaFTp05ITU3Fk08+CaPRaCfLv2mqr6PAfMWFpnNNKmiJEW1tz5F9N27ciMrKSgQGBuKxxx7jtzuyc0PQ5stmrESElo4MqHXt2rVrk5wfeOAB7N+/H87Ozti7dy9eeOEFu7/6pjm+jgDzFRdaPKWElhjR2PYc0besrIx/0PPrr79u8WJgR3W2Bo2+gpcpeImUQsvUO1A71Xrw4MEmT7WOGzcO33//PWQyGTZv3oy1a9eKbGhJc32lhvmKC03nmlTQEiPa2p6j+n722WcoKyvD4MGD8cgjj1j8zlGdrUGbL1sKFBFapi0BQKlUIjQ0FEqlssn7zJo1C59++ikA4N///je+/PJLsfTq0RJfKWG+4kLTuSYVtMSItrbniL6VlZVYv349AOC1116rN4PiiM62oM1XjHONDazuUHfq1dGRyWTo1KlTs52XLFmC1157DQDw/PPP48CBA2Lo1aOlvlLBfMWFFk8poSVGNLY9R/PdsmULiouL4efnh+jo6Hq/d0RnW9DoKzRsYHUHWqbegdqp1n379rVoqnXt2rVYsGABTCYToqOj8euvv4pgaElrfKWA+YoLTeeaVNASI9ranqP5VlVV4YMPPgBQ+9yqhmZ5HM25MWjzZUuBIkLL1DtQO9UaHh7eoqlWmUyGLVu2IDIyErdv38b06dNx8eJFESz/pjW+UsB8xYWmc00qaIkRbW3P0XxjYmJw7do19O7dG/PmzWswj6M5NwZtvmwpkMHTmkarUqkQGxuLESNG4ObNm5g6dSqKiooEtKsPLSeZGebLYDQN2tqeo/gaDAa8//77AIB//etfcHJysprXUZybCm2+QsMGVneQ4vlOLYXjOKjV6lZNYXbo0AEHDx6En58fcnNzERUVhYqKCgEt/0YIX3vCfMWFpnNNKmiJEW1tz5F8d+3ahatXr8LT0xMLFy60ms+RnJsCbb5inGuSD6w2bdoEX19fuLi4ICgoCKmpqVbzJiUlQSaT1fucP3/eIt/u3bsxePBgODs7Y/DgwdizZ0+jHrRMvQO13wYiIyNb/a3Aw8MDhw8fhru7O7RaLR577DFR1sWF8rUXzFdcaDrXWsOVK1ewcOFC+Pr6wtXVFX5+fnjjjTdQU1PT6L60xIi2tudIvl988QWA2puKXF1dreZzJOemQJuvQywFHjlyxOrvNm/e3KyyYmNjsWzZMqxevRo6nQ6hoaGYNm0a8vLybO534cIF6PV6/jNgwAD+dydOnEB0dDTmzp2LM2fOYO7cuZgzZw5OnjzZLDdHR6hvA/3798fPP/8MV1dXHD58GM8//7woDxCl5duLGebLaC3nz5+HyWTC5s2bce7cOaxfvx5ffPEFf2fuvQJtbc8RfM+dO4fU1FQoFAosWrSo0fyO4NwcaPMVHNJMnJycyIoVK0h1dTW/7fr162T69OnEzc2tWWWFhISQxYsXW2zz9/cnK1eubDD/0aNHCQBSUlJitcw5c+aQqVOnWmyLiIggjz/+eIP5tVotAUBOnjzZLHcpqampIXv37iU1NTWClXngwAEil8sJALJmzRrByiVEHF8xYb7icvLkSQKAaLVau/7dN9980+bHHvznP/8hvr6+Vn9PW39EW9tzFN+XXnqJACCPPvpoo3kdxbmp0OYrRn/U7BmrlJQUHDhwAMHBwTh37hwOHjyIgIAAVFRU4MyZM00up6amBlqtFuHh4Rbbw8PDkZaWZnPfwMBAeHl5YdKkSTh69KjF706cOFGvzIiIiEbLvHDhAk6dOoX09HSkp6dDr9fDaDTy668cx1mkTSaTzbTBYLBIkzuzQOY0IaReGoBF2mQyWaTN3wIUCgWioqKgUqksthuNRou02ddaum6dpk6dyj9AdM2aNdi6datgdTJPDZt9G6qTtXRr6tTS46RSqfip7NYcJ3vVSaVSISoqip/SFrPtCVEnqZYI9uzZY/H54YcfsG7dOnz44YfYu3evXRzKysrQtWvXRvPR0h+pVCo89NBD/LOApD53G6uTSqXCww8/zMdZinO3srIS33zzDQBg8eLFrD+6B/ujZg+sRo4cCZ1OhwceeABBQUGYOXMm/vGPfyAxMRF9+vRpcjnFxcUwGo3w9PS02O7p6YnCwsIG9/Hy8sKWLVuwe/du/PTTTxg4cCAmTZqElJQUPk9hYWGzyjQzb948BAUFISQkBCEhIdi8eTPOnj2LnJwcAIBOp0Nubi4AQKPRID8/HwCQlpYGvV4PoHbQWVxcDABITExEaWkpACA+Ph7l5eUAALVajaqqKosL/KqqqqBWqwEA5eXliI+PBwCUlpYiMTGRj5e5nnq9HqmpqSCEID8/HxqNBgCQm5sLnU4HAMjJycHZs2cBANnZ2cjOzgYAm3WKjIzEqlWrANSe8PHx8YLU6a+//kJcXBwIITbrZB78ClmnlhwnQgjUajVu377d6uNkjzoRQnD06FHcuHGjVcfJXnUyd6z2RqfTWXwyMzOh1+sxadIkLF++XPS/f+nSJXzyySdYvHhxo3lp6Y8IIbh8+bLDnLuN1YkQgsLCQknP3djYWJSVlcHb25v//4v1R/dYf9SSaS6tVksGDhxI/Pz8iKurK3nmmWdIRUVFs8ooKCggAEhaWprF9rVr15KBAwc2uZzp06eThx56iP9ZpVKR7du3W+T57rvviLOzc4P7m6fev/76a6LVaolGoyEajYZcu3aNcBxHOI4jhBBiMBgs0kaj0Wa6pqbGIm0ymSzSJpOpXpoQYpE2Go0WaYPBQAghpKqqihw4cID/G+btHMdZpM2+1tIN1clkMpEnnniCACAdOnQg6enpra5TdXW1hW9DdbKWFqJOzT1ONTU15MCBA6S6urpVx8ledTL7VlVVid72hKiTVEuB1vjtt9+It7d3k/O/8cYbBIDNT3p6usU+BQUFpH///mThwoU2y6atPzK3vVu3bllsJ0Sac7exOpl9KysrrdbJVlqIOgUHBxMAZN26dU2qE+uP6OuPmj2weu+994iTkxN58cUXye3bt0lmZiYZNmwY6devX71Bki2qq6uJQqEgP/30k8X2l19+mYSFhTW5nLVr1xJ/f3/+5z59+pCPPvrIIs9HH31E+vbt2+D+5o7MUTp5R6C6uppMmDCBACBeXl7k6tWrUisx7iEc7ZxLTU0lXbp0aXL+GzdukOzsbJuf27dv8/kLCgrIfffdR+bOncv/B2MNR4sNQ1gyMjIIAOLk5ESuX78utQ6DiHPONXtxcePGjdi7dy+mTZsGABgyZAg0Gg1ee+01jB8/HtXV1U0qx8nJCUFBQUhISMDMmTP57QkJCZgxY0aTfXQ6Hby8vPifR40ahYSEBIup/fj4eIwePdpmOeY1YBowmUwoLS1Fly5d6r2wUwicnJzw008/YezYsTh37hyioqJw7NgxdO7cuUXlie0rNMxXXKQ61z7++GOLnwkh0Ov1+PbbbzF16tQml+Pu7g53d/cm5S0oKMCECRMQFBSEr7/+usnHh5b+iMa2J6Wv+c752bNno3v37k3aR2rn5kKjr+A0dyR248YNq79LSkpqVlk7d+4kKpWKbN26lWRlZZFly5aR9u3bkytXrhBCCFm5ciWZO3cun3/9+vVkz5495OLFiyQzM5OsXLmSACC7d+/m8xw/fpwoFAry/vvvk+zsbPL+++8TpVJJfv311wYdaLsLh5DaKdTDhw+LftfF1atXiZeXFwFAJk2aZHEnaHOwl69QMF9xkWop0MfHx+LTr18/MnLkSLJq1Sry119/Cf73zMt/EydOJH/88QfR6/X8xxq09Ue0tT0pfUtLS0n79u0JAJKSktLk/ViMxcUhlgKF5rPPPiPe3t7EycmJDB8+nCQnJ/O/mz9/Phk3bhz/87p164ifnx9xcXEhbm5uZOzYseTgwYP1yty1axcZOHAgUalUxN/f32LgdTds6t02p06dIh06dCAAyPz58/n1cQajpbSVc+7rr7+2eg2WNdpKbNoin332GQFABg8ezPpRB0KMc07ygZXUmIN698WmjozRaCRFRUWNXq8hFGq1migUihY/48revq2F+YpLeno6GzxYgbb+iLa2J6Xv8OHDCQCycePGZu3HYiwuYvRHjr8AaidouaYBqHXNzMy0m/O0adOwadMmALXPuNq2bVuz9re3b2thvuJCi6eU0BIjGtueFL4XL17EqVOnoFAo8OSTTzZrXxZjcRHDkw2s7kDLe42AWteJEyfa1fm5557DypUrAQCLFi3inynSFKTwbQ3MV1xo8ZQSWmJEY9uTwjc2NhYAMGXKlCbf+GCGxVhcHOIBofcqtIyugVrXgoICuzu/8847iI6OBsdxePTRR5GVldWk/aTybSnMV1xo8ZQSWmJEY9uzty8hBDt27AAAPP74483en8VYXNiMlYjQ0giAWtdLly7Z3VkulyMmJgZjxoxBWVkZIiMjG32iPSCdb0thvuJCi6eU0BIjGtuevX0zMzORnZ0NJycnPPLII83en8VYXNjASkRombYEal3DwsIkcXZxccHevXvRv39/XL16FQ8//DBu3bplcx8pfVsC8xUXWjylhJYY0dj27O27c+dOAEBkZGSLngXIYiwubClQRGgZXQO1rlevXpXM2d3dHWq1Gt26dUN6ejqeeuop/sWWDSG1b3NhvuJCi6eU0BIjGtuePX0JIfzAqiXLgACLsdiwGSsRoaURAI6xhj1gwADs27cPzs7O2Lt3L1599VWreR3BtzkwX3GhxVNKaIkRjW3Pnr4ZGRm4fPky2rVrh+nTp7eoDBZjcWEDKxGhZdoSqHUdPXq05M5jxoxBTEwMAOCjjz7iH8lwN47i21SYr7jQ4ikltMSIxrZnT1/zbNXDDz+M9u3bt6gMFmNxYUuBImJrKcvRMBqN+P333x3C+fHHH8c777wDAHjppZegVqvr5XEk36bAfMWFFk8poSVGNLY9e/maTCb+MQstXQYEWIzFRgxPNrC6AyFEaoUmQwhBSUmJwzivWrUKzzzzDEwmE6Kjo3HmzBmL3zuab2MwX3GhxVNKaIkRjW3PXr7Hjx9HQUEBOnfu3KyXfN8Ni7G4iOHJBlZ3oGXaEqh1DQ4OdhhnmUyGL774AhMnTkRFRQWioqJQUFDA/97RfBuD+YoLLZ5SQkuMaGx79vI1LwM+8sgjcHZ2bnE5LMbiwpYCRYSWaUug1vX8+fMO5ezk5ITdu3dj0KBBKCgowEMPPYSKigoAjulrC+YrLrR4SgktMaKx7dnDl+M47Nq1C0DrlgEBFmOxYUuBDJ7bt29LrVCPLl264ODBg+jevTt0Op3FYxgc0dcWzJfBaBq0tT17+B4/fhw3btxA165dMWnSpFaXx2JMF2xgdQeFQiG1QpNRKBQIDAx0SGdfX1/+MQz79+/HP//5T4f2bQjmKy60eEoJLTGise3Zw/fgwYMAah8KqlKpWlUWi7G4iOHJBlZ3oGXaEqh1zczMdFjnUaNGYdu2bQCA9evX47PPPnNo37tx9PjeDY2+DNvQEiMa2549fM0Dq6ioqFaXxWIsLmwpkEEN0dHRWLt2LQBg6dKlOHbsmMRGDAaDIT5XrlxBVlYWFAoFIiIipNZhSAAbWN2BlmlLoNY1ICDA4Z1fe+01zJ8/H0ajEa+++iqysrKkVmoStMTXDI2+DNvQEiMa257YvubZqtGjR8PNza3V5bEYiwtbChQRWqYtgVpXnU7n8M4ymQxbtmxBWFgYysvLMX36dBQWFkqt1Si0xNcMjb4M29ASIxrbnti+Qi4DAizGYsOWAhk8rq6uUis0CScnJ+zatQve3t7Iy8vDjBkzcOvWLam1GoWW+JqhzZdx70Bb2xPT99atWzh69CgA4QZWAIsxbbCB1R1ombYEal39/f2pcfbw8EBCQgK6du0KjUaD+fPnO/QLOmmLL42+DNvQEiMa256YvkePHkVVVRX69u2LIUOGCFImi7G4sKVAEeE4TmqFJsNxHNLT06lx5jgOpaWl+PHHH6FSqfDjjz9i9erVUmtZhcb40ubLsA0tMaKx7YnpW/cxCzKZTJAyWYzFRQxPNrC6g1AngT2QyWRwc3OjxtnsGxYWhi+//BIA8P777+Prr7+W2KxhaI0vTb4M29ASIxrbnli+hBDBr68CWIzFRgxPNrC6Ay3TlkCta//+/alxrus7b948vP766wCA559/HklJSdLKNQDN8aUBWjylhJYY0dj2xPI9d+4c8vLy4OLigokTJwpWLouxuLClQBGhZdoSqHVNS0ujxvlu3zfffBNz5syBwWDAo48+iosXL0psaAnt8XV0aPGUElpiRGPbE8tXrVYDACZMmIB27doJVi6LsbiwpUARkcvpCYVcLkevXr2ocb7bVy6XIyYmBiNHjkRJSQmmT5+OmzdvSmz5N7TH19GhxVNKaIkRjW1PLF8xlgEBFmOxEcNT8ppv2rQJvr6+cHFxQVBQEFJTU63m/emnnzBlyhR0794dnTp1wqhRoxAXF2eRJyYmBjKZrN6nqqrKpgctjQCodfX29qbGuSFfV1dX7Nu3D97e3sjJycGsWbNQU1MjoeXf3AvxdWRo8ZQSWmJEY9sTw7ekpATHjx8HUHvhupCwGIvLPTewio2NxbJly7B69WrodDqEhoZi2rRpyMvLazB/SkoKpkyZArVaDa1WiwkTJuChhx6CTqezyNepUyfo9XqLj4uLi00XWqYtgVrXlJQUapyt+Xp6euLnn39Gx44dkZycjOeeew6EEIks/+Zeia+jQounlNASIxrbnhi+8fHxMBqNGDRoEHx9fQUtm8VYXO65pcCPPvoICxcuxKJFizBo0CBs2LABffr0weeff95g/g0bNuDVV19FcHAwBgwYgHfffRcDBgzAgQMHLPLJZDL06NHD4tMYtIyugVpXPz8/apxt+QYEBGDXrl1QKBTYtm0b3n//fQkMLbmX4uuI0OIpJbTEiMa2J4bv4cOHAQi/DAiwGIvNPTVjVVNTA61Wi/DwcIvt4eHhSEtLa1IZJpMJ5eXl6Nq1q8X2iooKeHt7o3fv3pg+fXq9Ga2GyM7OxqlTp5Ceno709HTo9XoYjUb+cfccx1mkzQ+4tJY2GAwWafNMjDlNCKmXBmCRNplMFum6I2tPT0/I5XKL7Uaj0SJt9rWWtledZDIZPDw8eN+76xQREYGNGzcCqH2/4A8//CBpneRyOTw8PCCTyVp1nKylha6TXC6Hp6cn3zbEbHtC1ImWDldKaIkRjdfTCO1LCEFiYiIAYMqUKYKVa4bFWFzuqYFVcXExjEajxX8IQO2Aoanvk/vwww9RWVmJOXPm8Nv8/f0RExOD/fv3Y8eOHXBxccGYMWOQk5Njs6x58+YhKCgIISEhCAkJwebNm3H27Fl+P51Oh9zcXACARqNBfn4+ACAtLQ16vR5A7VJlcXExACAxMRGlpaUAaqeJy8vLAdTeOVJVVQWO46BWq8FxHKqqqvg7SsrLyxEfHw8AKC0t5U/Y4uJipKSkAAAKCgpw6NAhcByH/Px8aDQaAEBubi4/iMzJycHZs2cB1A4as7OzAUCSOpWWlvLbrdXpkUcewezZs/ljERMTI1mdzPWoqKho1XHS6/X8lwQxjxPHcTh06BCKiopadZzsVSdalgikhJYYcRyHxMTENu17+fJl5OXlQaVSYcyYMYKVa4bFWFxE8SQSUVBQQACQtLQ0i+1r164lAwcObHT/7du3k3bt2pGEhASb+YxGIxk6dCh56aWXGvy9VqslAMi2bduIVqslGo2GaDQacu3aNcJxHOE4jhBCiMFgsEgbjUab6ZqaGou0yWSySJtMpnppQohF2mg0WqQNBgP/d65du0aMRqPFdo7jLNJmX2tpe9WJ4zhSUFDA+zZUJ6PRSKqqqkhUVBQBQDw9PcmVK1ckqZPRaCQFBQWE47hWHSdraaHrZDQaybVr1/gyxWx7QtQpPT2dACBarZYwLDH3R+np6VKrNAmj0UiKior49uboiOG7ZcsWAoCEhYUJVmZdWIzFRYz+SCn8UK1puLu7Q6FQ1Judun79er1ZrLuJjY3FwoULsWvXLkyePNlmXrlcjuDg4EZnrAICAjB8+HCrv1cqlc1Kq1SqFqVlMhmflsvlFo8oMKeVSiW8vLws6ghYPuisKWl71UmhUKBnz571fO+un7OzM3bs2IHQ0FCcOXMG06dPx/Hjx9GpUye71kkmk1n4tvQ4WUuLcZzqtgcx254QdaJliUBKaImRedmcFsTw/eWXXwBA0IeC1oXFWFzuqaVAJycnBAUFISEhwWJ7QkICRo8ebXW/HTt2YMGCBdi+fXuTLhQkhOD06dMW//E0BC3TlkDttTJxcXH8NTCOTnN8O3bsiAMHDsDLywuZmZmIjo62+7G5l+PrCNB0rkkFLTGire0J7UvqXF8l1sCqrcdYbO65uwJXrFiBL7/8El999RWys7OxfPly5OXlYfHixQCAVatWYd68eXz+HTt2YN68efjwww/x4IMPorCwEIWFhSgrK+PzvPnmm4iLi8Ply5dx+vRpLFy4EKdPn+bLtAYt3xCB2m/+wcHBVL0yoDm+ffr0wYEDB9CuXTscPnwYS5cutetjGO71+EoNTeeaVNASI9rantC+586dw40bN+Dq6oqRI0cKUubdtPUYi809NWMFANHR0diwYQPeeustDBs2DCkpKVCr1fD29gZQe6Fs3Wdabd68GRzH4YUXXoCXlxf/Wbp0KZ+ntLQUzz33HAYNGoTw8HAUFBQgJSUFISEhNl1o6ciAWteuXbtS49wS36CgIHz//feQyWTYtGkTPvnkExENLWkL8ZUSWjylhJYY0dj2hPQ1z1aFhobCyclJkDLvpq3HWGzuuYEVACxZsgRXrlxBdXU1tFotwsLC+N/FxMRYvKQ3KSmJv0W87sd8BxkArF+/HlevXkV1dTWuX7+OuLg4jBo1qlEPWqbegdqp1oMHD1Iz1dpS30ceeQT/+c9/AADLly/Hzz//LIZePdpKfKWCpnNNKmiJEW1tT2hf88Bq0qRJgpTXEG09xmJzzy0FOhK0TFsCtRcth4aGWly87Mi0xvcf//gHnn32WZhMJjz++ONNeiZZa2lL8ZUCms41qaAlRrS1PSF9OY7jv/iLdX0V0LZjbA/EONfYwOoOMplMaoUmI5PJ0KlTJ2qcW+Mrk8nw2WefYfLkyaisrERkZCT/TCexaEvxlQJaPKWElhjR2PaE8tXpdCgrK0Pnzp0RGBgogF3DtOUY2wMxPNnA6g60TL0DtVOt+/bto2aqtbW+KpUKP/74Ix544AEUFhZi6tSp/AM+xaCtxdfe0HSuSQUtMaKt7Qnpa14GHD9+vKgzjG05xvaALQWKCC1T70DtVGt4eDg1U61C+Hbu3BmHDh1C3759cfHiRTz00EO4deuWgJZ/0xbja09oOtekgpYY0db2hPQV+zELZtpyjO0BWwpk8NDSaM0I4duzZ08cPnwYbm5u+PXXX/HEE0+I9s2+LcaXwWgJtLU9IXxramqQmpoKQNwL1820xRjTDBtY3cH8olgaqPuuNxoQ0nfQoEHYv38/XFxcsH//fjz33HOCH7u2HF97QNO5JhTV1dUYNmwYZDIZTp8+3Wh+WmJEW9sTyvfkyZO4ffs2PDw8MHjwYIHsGqatxtheiHGusYHVHWiZegdqvw1ERkZS861AaN+xY8di+/btkMvl+Prrr/H0008Lup7f1uMrNjSda0Lx6quvWrwmqTFoiRFtbU8o37qvsRH7Iu22GmN7Ica5RkfNGfXgOI6ahgsI7ztz5kzs2LEDTz31FHbu3InKykr88MMPcHFxEaT8th5fhnAcOnQI8fHx2L17Nw4dOtSkfb766ivEx8eLbNZ6CCF826PhLjChfGNjYwGIf32VGdrOb9p8habt1vwuaJl6B2obbXx8PCIjIy1epuuoiOU7Z84cdOjQAbNmzcKBAwcQFRWFffv2oUOHDq0ql8VXXGg611pLUVERnn32Wezduxft2rVr8n6bNm0S0YohFOPGjQPwd5tWKBQWaY7jIJPJ+LT5xeXW0gaDAQqFgk8rlUr+/J42bRpUKpXFoIXjOKhUKn7AqFKpYDKZYDQa+bTJZIJSqbSaNhqNIITw6Ybq0Zw6GY1GxMfHY+rUqXB2dm6wTjKZjE+b6yFVncToj9jA6g40ja5VKhVmzJghtUaTEdM3MjIShw8fxvTp05GYmIjJkydj37598PT0bHGZLL7iQtO51hoIIViwYAEWL16MESNG4MqVKy0uKzAwEN7e3lAoFOjSpQtu3LgBZ2dndOrUCUVFRWjfvj06dOiAwsJCdOzYEe3bt8e1a9fg5uYGV1dX/PHHH+jevTucnZ2Rn58PT09PODk54erVq+jVqxfkcjny8/PRp08fmEwmFBQUwNvbGzU1NSgqKkKfPn1QXV2NGzduoHfv3rh9+zZKSkrQs2dPVFZWory8HD169EBFRQUqKyvh6emJv/76C9XV1ejevTtKS0thNBrRrVs3lJSUAADc3Nxw8+ZNauvUt29fVFZWAgCys7MBAAEBATh79ixcXV3h7+8PnU4HNzc39O/fHxqNBr169YK3tzfS0tLg5+eHXr16ISUlBQEBAfDw8EBiYiKCg4PRtWtXxMfHIzQ0FJ06dQJQOwCQyWRQq9WIjIzkB1wzZsxAeXk5UlNTERUVhdLSUqSnpyMiIgLFxcXIzMzExIkTodfrcenSJYSFhSE/Px8FBQUYPXo0cnNzUVJSguDgYOTk5OD27dsIDAxsVZ06duyIsrIym3VSq9X83YNS1kmU/oi0cbRaLQFAMjIypFZpMiaTiZSVlRGTySS1SpOwh69GoyFdu3YlAEjPnj3J8ePHW1wWi6+4ZGRkEABEq9VKrdIi3njjDQLA5ic9PZ1s3LiRjB49mnAcRwghJDc3lwAgOp3Oatnm/mjbtm1Eq9USjUZDNBoNuXbtGuE4ji/LYDBYpI1Go810TU2NRdrcVsxpk8lUL00IsUgbjUaLtMFgICaTiZSUlNTbTgghHMdZpM2+1tL2qJPJZCKlpaWkurraap1spaWok8lkIjdv3iRGo7HFx8medTL7mvOI1faEqpMY/RG7eP0ONC1PcByH1NRUau66sIdvcHAw0tLSMGjQIFy7dg3jxo3DJ598AkJIs8ti8RUXms61hnjxxReRnZ1t8xMQEIDExET8+uuvcHZ2hlKpRP/+/QEAI0aMwPz5823+DX9/fwwfPhzBwcEIDg6Gl5cXFAoFf6GtUqm0SJtfJGstrVKpLNLm64vMaZlMVi8NwCItl8st0uZlquPHj/Pe5u1A7XJL3bTZ11raHnXiOA7Hjh3j8zZUJ1tpKerEcRxOnDjBz1i15DjZs05mX5PJ1OLjZM86idEfyUhL/ue5hzh16hSCgoKg1WoxfPhwqXUYraSiogILFy7EDz/8AAB44oknsGXLllZfd8UQjrZyzuXl5eGvv/7if7527RoiIiLw448/YuTIkejdu3e9fdpKbBgMR0GMc47NWN3BPLqmAZPJhD///JMaZ3v6dujQATt37sT69euhUCiwY8cO3H///c26w4rFV1xo8Wwtffv2RUBAAP+57777AAB+fn4NDqrqQkuMaGx7NPkC9DnT6Cs0bGB1B1oaAVC7lJKenk7Nkoq9fWUyGZYtW4ajR4+iT58+uHLlCiIiIjBv3rwmvWOQxVdcaDrXpIKWGNHW9mjzBehzps2XDaxEhKY7lVQqFSIiIqi4tR6Qzjc0NBTnzp3Dyy+/DJlMhm+//RaDBg3Ctm3bbJ5MLL7iQtO5JiQ+Pj4ghGDYsGGN5qUlRrS1Pdp8AfqcafMV41xjA6s70PINEah1vX79OjXOUvp27NgRGzduxIkTJxAQEIDi4mIsWLAAQ4cOxZ49exq8uJ3FV1xo8ZQSWmJEY9ujyRegz5lGX6FhA6s70NIIgFrXzMxMapwdwXfkyJHQarV4//330blzZ2RmZuLRRx9FSEgI4uLiLAZYjuDbHGj0ZdiGlhjR2PZo8gXoc6bRV2jYwOoOtEy9A7WuEydOpMbZUXydnJzwr3/9C7m5uVi9ejXat2+PjIwMTJ06FQ888AA+//xzlJeXO4xvU6HRl2EbWmJEY9ujyRegz5lGX6FhA6s70DK6BsA/RZgWZ0fzdXNzw9q1a3H58mUsX74c7dq1Q2ZmJpYsWYJevXrhhRdeQFxcHFUXXzpSfBuDFk8poSVGNLY9mnwB+pxp9BUaNrC6Ay2NAKh1vXTpEjXOjurr4eGBjz76CAUFBdi4cSMGDhyI8vJybNq0CVOnTsXAgQOxcuVKZGRktOhBo/bCUeNrDVo8pYSWGNHY9mjyBehzptFXaNjA6g60TFsCta5hYWHUODu6b5cuXfDyyy8jOzsbR44cwezZs+Hi4oJLly5h3bp1CA4Oho+PDxYuXIjt27ejsLBQamULHD2+d0OLp5TQEiMa2x5NvgB9zjT6Cg0bWN2BltE1UOt69epVapxp8ZXJZJg0aRJiY2Oh1Wqxc+dOPPbYY2jXrh3y8vLw1Vdf4amnnoKXlxeGDBmCZ599Fps3b4ZWq0VNTY1k3rTE1wwtnlJCS4xobHs0+QL0OdPoKzR0DCntAC2NAPh7Ddv8BndHh0bf0tJSzJo1C9HR0bh16xaSk5ORmJiIX375BadPn0ZWVhaysrLw5ZdfAqi9MH7IkCEYNGgQ/P39+Y+vr6/or9OhMb4M29ASIxrbHk2+AH3ONPoKjeQDq02bNuG///0v9Ho9hgwZgg0bNiA0NNRq/uTkZKxYsQLnzp1Dz5498eqrr2Lx4sUWeXbv3o3/+7//w6VLl+Dn54d33nkHM2fOtOlBy7QlUOs6evRoqTWaDO2+7dq1w7Rp0zBt2jQAwM2bN5GSkoL09HRkZGQgIyMDJSUl0Ol00Ol09crr1q0bvL294ePjg969e6NHjx7w8vKCl5cXPD094e7ujm7dusHV1VUQX0eHpnNNKmiJEY1tjyZfgD5nGn0FL1PwEptBbGwsli1bhk2bNmHMmDHYvHkzpk2bhqysLPTt27de/tzcXERGRuLZZ5/Fd999h+PHj2PJkiXo3r07Zs2aBQA4ceIEoqOj8fbbb2PmzJnYs2cP5syZg2PHjmHkyJFWXWi5Awyodc3NzYWvry//pm5H5l7z7datG2bOnMkP1gkhuHz5MjIzM3H+/HlkZ2fj/PnzuHDhAkpLS3Hz5k3cvHkTp06dsvl327Vrh27dusHNzQ2dO3dGly5d0LlzZ3Tu3BkdOnSw+Li6uvIfJycn/Pnnn/Dx8UG7du3g7OwMZ2dnqFQqODk5wcnJCSqVyuIt81JC07kmFbTE6F47tx0R2pxp9BUaSQdWH330ERYuXIhFixYBADZs2IC4uDh8/vnneO+99+rl/+KLL9C3b19s2LABADBo0CBkZGTggw8+4AdWGzZswJQpU7Bq1SoAwKpVq5CcnIwNGzZgx44dVl0c+a6vuyGEoKSkBD4+PlKrNIl73Vcmk8HPzw9+fn6YMWOGxe/Kyspw9epVXLlyBVevXkVBQQH0ej0KCwuh1+tRVFSEmzdvwmg04tatW7h16xby8/NFqFUtcrmcH2QplUr+37s/CoWi0e3mtLVtdT/9+/fHCy+8AICuc00qaInRvX5uOwK0OdPoKzSSDaxqamqg1WqxcuVKi+3h4eFIS0trcJ8TJ04gPDzcYltERAS2bt0Kg8EAlUqFEydOYPny5fXymAdj1rhw4QKUSiU/eu3duzc8PDwAAAqFAhzHQSaT8Wm5XA65XG41bTAYoFAo+LRSqYRMJuPTAMBxnEVapVKBEMKnTSYTjEYjnzaZTFAqlZDL5QgMDIRSqbTYbjQaQQixqIdCobCatledFAoFhg0bxvs2VCdraSnqpFQqMWzYMCgUCv54tOQ4mUwmtG/fHg888AACAgKs1okQgoqKCly/fh03b95EeXk5/vzzT5SVlaG8vBylpaWoqKjArVu3UF5ejvLyclRXV+PWrVuoqqrC7du3UVVVhZqaGlRXV/Ofhi6oN5lM/O/tSVhYGL9kT8syl5TQEiOlUong4GCpNZoMbb4Afc40+gpepuAlNpHi4mIYjUZ4enpabPf09LR6O3thYWGD+TmOQ3FxMby8vKzmaewW+Xnz5ln8/MYbb2DGjBlwdXWFv78/dDod3Nzc0L9/f2g0GvTq1Qve3t5IS0uDn58fevXqhZSUFAQEBMDDwwOJiYkIDg5G165dER8fj9DQUHTq1AlqtRrh4eFQKpVQq9WIjIwEx3GIj4/HjBkzUF5ejtTUVERFRaG0tBTp6emIiIhAcXExMjMzMXHiRBQUFCArKwuTJ0/GH3/8gYKCAowePRq5ubkoKSlBcHAwcnJycPv2bQQGBiI7OxsAEBAQgLNnz9q9TmVlZUhNTUVkZCTKysoarJNer8elS5cQFhaG/Px8SevUvn17qNVqTJo0Cc7Ozi0+Ts2t0x9//IGOHTti1KhR0Ol0fJ3S09P5OqWlpfF1SklJgZ+fH3r06IH4+HgMGzYMXl5eiIuLQ3BwMNzc3HDgwAGMHDkSzs7OOHDgAMaMGQNCCBISEjBmzBjU1NQgNTUVoaGhKC0txalTpxASEoI///wTWVlZGDp0KG7evInc3FwMHjwYRUVF0Ov1GDBgAIqKilBcXAxvb28UFhaioqICXl5e0Ov1qK6uhqenJ/R6PUwmE4KDg/njRMsyl5TQEiOj0YicnBwMGDCAmmUfmnwB+pxp9BUcIhEFBQUEAElLS7PYvnbtWjJw4MAG9xkwYAB59913LbYdO3aMACB6vZ4QQohKpSLbt2+3yPPdd98RZ2fnBsvUarUEAImJiSFarZZoNBqi0WjItWvXCMdxhOM4QgghBoPBIm00Gm2ma2pqLNImk8kibTKZ6qUJIRZpo9FokTYYDHwZGRkZhOM4i+0cx1mkzb7W0vaqk8FgsPBtqE7W0lLUieM4kpGRQQwGQ6uOk73qZPY1O4jZ9oSok0ajIQCIVqslDEvM/ZFGo5FapUlwHEdOnTrFH2NHhzZfQuhzps1XjP5Ishkrd3d3KBSKejNJ169frzfjZKZHjx4N5lcqlejWrZvNPNbKvHHjBr/f8OHDrfrWnS5sSlqlUrUoLZPJ+LR5uerudHFxMQ4cOICePXvCy8uL317320FT0vaq040bNxr0tVa/umkp6nT9+nUL35YeJ3vVSa/XN+rblLS96vTnn38C+PvcY/yNOSbmGDk6169fx759+/g7XR0d2nwB+pxp8xWjP5LsFiEnJycEBQUhISHBYntCQoLVWzVHjRpVL398fDxGjBjB/4dgLY+1MouLiwHUNgZa+OOPP/Dmm2/ijz/+kFqlSTBfcaHN13yumc89xt/Q1h/R1vZo8wXoc6bNV4z+SNIrJFesWIG5c+dixIgRGDVqFLZs2YK8vDz+ItdVq1ahoKAA33zzDQBg8eLF+PTTT7FixQo8++yzOHHiBLZu3Wpxt9/SpUsRFhaGdevWYcaMGdi3bx+OHDmCY8eOSVJHBoPBYDAYbQdJB1bR0dG4efMm3nrrLej1egQEBECtVsPb2xtA7RJHXl4en9/X1xdqtRrLly/HZ599hp49e+Ljjz/mH7UAAKNHj8bOnTvx+uuv4//+7//g5+eH2NhYm8+wAuAQz/dpKuYlFRouDASYr9jQ5kvTuSYVtMSItrZHmy9AnzNtvmKca5Lf07tkyRIsWbKkwd/FxMTU2zZu3LhGH7Q4e/ZszJ49u0l/33zb+eXLlxst11E4d+6cxb+ODvMVF9p8L1++DAB2f+QDDdDWH9HW9mjzBehzps1XlP5IsMvgKeWTTz4hANiHfdjHzp9PPvlE6tPf4WD9EfuwjzQfIfsjyWespObxxx+Hm5sbfHx8WvyuNgaD0XRu376NK1euICIiQmoVh4P1RwyGfRGjP5IRQsm7ExgMBoPBYDAcHDqukGQwGAwGg8GgADawYjAYDAaDwRAINrBiMBgMBoPBEIg2MbDatGkTfH194eLigqCgIKSmptrMn5ycjKCgILi4uKBfv3744osv7GRaS3N89Xo9nnzySQwcOBByuRzLli2zn2gdmuP8008/YcqUKejevTs6deqEUaNGIS4uzo62zfM9duwYxowZg27duvEvRl6/fr0dbZvfhs0cP34cSqUSw4YNE1fwLprjm5SUBJlMVu9z/vx5OxrbD9YfiQvri8SFtr4IkKA/Euz+Qgdl586dRKVSkf/9738kKyuLLF26lLRv355cvXq1wfyXL18m7dq1I0uXLiVZWVnkf//7H1GpVOTHH390SN/c3Fzy8ssvk23btpFhw4aRpUuX2sWzLs11Xrp0KVm3bh3RaDTk4sWLZNWqVUSlUpFTp045pO+pU6fI9u3bSWZmJsnNzSXffvstadeuHdm8ebND+popLS0l/fr1I+Hh4WTo0KF2cSWk+b5Hjx4lAMiFCxeIXq/nP7S8xLU5sP7IsXxZXySurxmp+iJCpOmP7vmBVUhICFm8eLHFNn9/f7Jy5coG87/66qvE39/fYtvzzz9PHnzwQdEc69Jc37qMGzdOkoFVa5zNDB48mLz55ptCqzWIEL4zZ84kTz/9tNBqDdJS3+joaPL666+TN954w66dWXN9zR1ZSUmJHeykhfVH4sL6InGhrS8iRJr+6J5eCqypqYFWq0V4eLjF9vDwcKSlpTW4z4kTJ+rlj4iIQEZGBgwGg2iuQMt8pUYIZ5PJhPLycnTt2lUMRQuE8NXpdEhLS8O4cePEULSgpb5ff/01Ll26hDfeeENsRQtaE9/AwEB4eXlh0qRJOHr0qJiaksD6I3FhfZG40NYXAdL1R/f0A0KLi4thNBrh6elpsd3T0xOFhYUN7lNYWNhgfo7jUFxcDC8vL4fylRohnD/88ENUVlZizpw5Yiha0Brf3r1748aNG+A4DmvWrMGiRYvEVAXQMt+cnBysXLkSqampUCrte4q3xNfLywtbtmxBUFAQqqur8e2332LSpElISkpCWFiYPbTtAuuPxIX1ReJCW18ESNcf3dMDKzMymcziZ0JIvW2N5W9ou1g019cRaKnzjh07sGbNGuzbtw8eHh5i6dWjJb6pqamoqKjAr7/+ipUrV6J///544oknxNTkaaqv0WjEk08+iTfffBP33XefXdwaojnxHThwIAYOHMj/PGrUKOTn5+ODDz64pwZWZlh/JC6sLxIX2voiwP790T09sHJ3d4dCoag3Mr1+/Xq9EayZHj16NJhfqVSiW7duorkCLfOVmtY4x8bGYuHChdi1axcmT54spiZPa3x9fX0BAPfffz+KioqwZs0a0Tuz5vqWl5cjIyMDOp0OL774IoDa5Q1CCJRKJeLj4zFx4kSH8bXGgw8+iO+++05oPUlh/ZG4sL6I9UWtdbZGc/uje/oaKycnJwQFBSEhIcFie0JCAkaPHt3gPqNGjaqXPz4+HiNGjIBKpRLNFWiZr9S01HnHjh1YsGABtm/fjqioKLE1eYSKMSFE2LehW6G5vp06dcJvv/2G06dP85/Fixdj4MCBOH36NEaOHOlQvtbQ6XSiLnNJAeuPxIX1ReJCW1/UEmdrNLs/avFl75RgvtVy69atJCsriyxbtoy0b9+eXLlyhRBCyMqVK8ncuXP5/Obbm5cvX06ysrLI1q1bJbm9uam+hBCi0+mITqcjQUFB5MknnyQ6nY6cO3fOLr4tcd6+fTtRKpXks88+s7idtbS01CF9P/30U7J//35y8eJFcvHiRfLVV1+RTp06kdWrVzuk793Y+06c5vquX7+e7Nmzh1y8eJFkZmaSlStXEgBk9+7ddnO2F6w/cixf1heJ63s3UtwVKEV/dM8PrAgh5LPPPiPe3t7EycmJDB8+nCQnJ/O/mz9/Phk3bpxF/qSkJBIYGEicnJyIj48P+fzzzx3aF0C9j7e3t8M6jxs3rkHn+fPnO6Tvxx9/TIYMGULatWtHOnXqRAIDA8mmTZuI0Wh0SN+7kaIza47vunXriJ+fH3FxcSFubm5k7Nix5ODBg3b1tSesP3IcX9YXiet7N1L0RYTYvz+SEXLnSkgGg8FgMBgMRqu4p6+xYjAYDAaDwbAnbGDFYDAYDAaDIRBsYMVgMBgMBoMhEGxgxWAwGAwGgyEQbGDFYDAYDAaDIRBsYMVgMBgMBoMhEGxgxWAwGAwGgyEQbGDFYDAYDAaDIRBsYMVgMBgMBoMhEGxgxaCS8ePHY9myZVJrMBgMBuuPGBawgRWDwWAwGAyGQLB3BTKoY8GCBdi2bZvFttzcXPj4+EgjxGAw2iysP2LcDRtYMaijrKwM06ZNQ0BAAN566y0AQPfu3aFQKCQ2YzAYbQ3WHzHuRim1AIPRXDp37gwnJye0a9cOPXr0kFqHwWC0YVh/xLgbdo0Vg8FgMBgMhkCwgRWDwWAwGAyGQLCBFYNKnJycYDQapdZgMBgM1h8xLGADKwaV+Pj44OTJk7hy5QqKi4thMpmkVmIwGG0U1h8x6sIGVgwqeeWVV6BQKDB48GB0794deXl5UisxGIw2CuuPGHVhj1tgMBgMBoPBEAg2Y8VgMBgMBoMhEGxgxWAwGAwGgyEQbGDFYDAYDAaDIRBsYMVgMBgMBoMhEGxgxWAwGAwGgyEQbGDFYDAYDAaDIRBsYMVgMBgMBoMhEGxgxWAwGAwGgyEQbGDFYDAYDAaDIRBsYMVgMBgMBoMhEGxgxWAwGAwGgyEQ/x9eFND3CxUFwwAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "resp = ct.input_output_response(sys, Td, result.inputs, x0)\n", "# t, y = ct.initial_response(sys, Td, x0)\n", "\n", "print(\"Final_simulated_state:\", resp.states[:,-1]) # 終端状態\n", "\n", "fig, ax = plt.subplots(1, 2, figsize=(6, 2.3))\n", "ax[0].plot(resp.time, resp.outputs, c='k')\n", "ax[1].plot(resp.time, resp.inputs, c='k')\n", "# ax[0].plot(t, y)\n", "\n", "ax[0].set_xlim([0,0.5])\n", "# ax[0].set_ylim([0,1])\n", "ax[1].set_xlim([0,0.5])\n", "ax[1].set_ylim([-5,1])\n", "plot_set(ax[0], 't', 'x')\n", "plot_set(ax[1], 't', 'u')\n", "plt.tight_layout()\n", "# fig.savefig(\"c7_obc.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "2次系" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [], "source": [ "A = [ [0, 1], [-4, -5] ]\n", "B = [ [0], [1] ]\n", "C = np.eye(2)\n", "D = np.zeros([2,1])\n", "P = ct.ss(A, B, C, D)\n", "sys = ct.ss2io(P)\n" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [], "source": [ "xf = [0, 0]\n", "uf = 0\n", "Q = np.diag([100, 1])\n", "R = 0.1\n", "cost = obc.quadratic_cost(sys, Q, R, x0=xf, u0=uf)\n", "\n", "constraints = [obc.input_range_constraint(sys, [-15], [15])]\n" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Summary statistics:\n", "* Cost function calls: 15351\n", "* Constraint calls: 15704\n", "* System simulations: 1\n", "* Final cost: 29.16562957646857\n", "最適化成功: True\n" ] } ], "source": [ "Td = np.arange(0, 1, 0.01)\n", "x0 = [1, 0]\n", "result = obc.solve_ocp(sys, Td, x0, cost=cost, constraints=constraints)\n", "print('最適化成功:', result.success)\n" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "resp = ct.input_output_response(sys, Td, result.inputs, x0)\n", "\n", "fig, ax = plt.subplots(1, 2, figsize=(6, 2.3))\n", "ax[0].plot(resp.time, resp.outputs[0], label='x1')\n", "ax[0].plot(resp.time, resp.outputs[1], label='x2')\n", "ax[1].plot(resp.time, resp.inputs[0])\n", "\n", "ax[0].set_xlim([0,1])\n", "ax[1].set_xlim([0,1])\n", "# ax[1].set_ylim([-5,1])\n", "plot_set(ax[0], 't', 'x', 'best')\n", "plot_set(ax[1], 't', 'u')\n", "plt.tight_layout()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### モデル予測制御" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [], "source": [ "A = [ [0, 1], [-4, -5] ]\n", "B = [ [0], [1] ]\n", "C = np.eye(2)\n", "D = np.zeros([2,1])\n", "P = ct.ss(A, B, C, D)\n", "# 離散時間モデル\n", "Pd = ct.c2d(P, 0.1, name='plant')\n", "sys = ct.ss2io(Pd)\n" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [], "source": [ "xf = [0, 0] # 基準状態\n", "uf = 0 # 基準入力\n", "Q = np.diag([100, 1]) # 状態に関する重み\n", "R = 0.1 # 入力に関する重み\n", "\n", "# 評価関数\n", "cost = obc.quadratic_cost(sys, Q, R, x0=xf, u0=uf)\n", "\n", "# constraints = [opt.input_range_constraint(sys, [-10], [10])]\n", "# constraints = opt.state_range_constraint(sys, [-1.5, -2], [1.5, 1.5])\n", "\n", "# 制約条件\n", "xmin, xmax = -1.5, 1.5\n", "umin, umax = -8, 8\n", "constraints = [obc.input_range_constraint(sys, [umin], [umax]),\n", " obc.state_range_constraint(sys, [xmin, xmin], [xmax, xmax]) ]\n" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [], "source": [ "# MPC制御器の設計\n", "N = 5 # 予測ホライズン\n", "ctrl = obc.create_mpc_iosystem(sys, np.arange(0, N)*0.1,\n", " cost, constraints, name='controller')\n", "\n", "# print(ctrl)\n", "# print(sys)\n" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [], "source": [ "# 閉ループ系の定義\n", "loop = ct.interconnect(\n", " [sys, ctrl], #制御対象と制御器の結合\n", " connections=[ #信号の接続\n", " ['plant.u[0]', 'controller.u[0]'],\n", " ['controller.x[0]', 'plant.y[0]'],\n", " ['controller.x[1]', 'plant.y[1]']\n", " ],\n", " outlist=['plant.y[0]', 'plant.y[1]', 'controller.u[0]']\n", ")\n", "\n", "# Define an I/O system implementing model predictive control\n", "# loop = ct.feedback(sys, ctrl, 1)\n", "# print(loop)\n" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [], "source": [ "# シミュレーション\n", "Td = np.arange(0, 2.1, 0.1) #シミュレーション時間\n", "X0 = [1, 0, 0, 0, 0, 0, 0] # 初期状態 [1,0]+予測ホライズンの初期値\n", "resp = ct.input_output_response(loop, Td, 0, X0)\n" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 2, figsize=(6, 2.3))\n", "ax[0].plot(resp.time, resp.outputs[0], label='x1', ls='-.') # 状態のグラフ\n", "ax[0].plot(resp.time, resp.outputs[1], label='x2', ) # 状態のグラフ\n", "ax[1].plot(resp.time, resp.outputs[2]) # 制御入力のグラフ\n", "\n", "ax[0].set_xlim([0,2])\n", "ax[1].set_xlim([0,2])\n", "ax[0].set_ylim([-2,2])\n", "ax[1].set_ylim([-12,12])\n", "# 制約条件をプロット\n", "ax[0].hlines(xmin, 0, 2, colors='black', linestyle='dashed', lw=1)\n", "ax[0].hlines(xmax, 0, 2, colors='black', linestyle='dashed', lw=1)\n", "ax[1].hlines(umin, 0, 2, colors='black', linestyle='dashed', lw=1)\n", "ax[1].hlines(umax, 0, 2, colors='black', linestyle='dashed', lw=1)\n", "plot_set(ax[0], 't', 'x', 'best')\n", "plot_set(ax[1], 't', 'u')\n", "plt.tight_layout()\n", "\n", "# fig.savefig(\"c7_mpc.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.11.3" } }, "nbformat": 4, "nbformat_minor": 4 }