{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapter 5" ] }, { "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": [ "## 垂直駆動アームの角度追従制御" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "from control.matlab import tf, feedback, step, bode, logspace, mag2db\n" ] }, { "cell_type": "code", "execution_count": 4, "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[kg*m^2/s]\n", "J = 1.0e-2 # 慣性モーメント[kg*m^2]\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": [ "ステップ応答のオーバーシュートや整定時間などを調べる" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'RiseTime': 0.12686419245146258,\n", " 'SettlingTime': 3.8820442890147544,\n", " 'SettlingMin': 0.3869097474111556,\n", " 'SettlingMax': 1.8169776184368178,\n", " 'Overshoot': 78.24550436865185,\n", " 'Undershoot': 0,\n", " 'Peak': 1.8169776184368178,\n", " 'PeakTime': 0.32984690037380265,\n", " 'SteadyStateValue': 1.019367991845056}" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from control.matlab import stepinfo\n", "info = stepinfo(P, SettlingTimeThreshold=0.05)\n", "info\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "ピークゲインとバンド幅を調べる" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "ピークゲイン Mp = 16.584713001907232 [dB]\n", "バンド幅 wbw = 15.321579070586944 [rad/s]\n" ] } ], "source": [ "from control.matlab import bode, logspace, mag2db\n", "# from scipy.signal import argrelmax\n", "\n", "# ピークゲイン\n", "mag, _, w = bode(P, logspace(-1,2,1000), plot=False)\n", "print(f'ピークゲイン Mp = {mag2db(mag.max())} [dB]')\n", "\n", "# [maxId] = argrelmax(mag)\n", "# print('wp=', w[maxId])\n", "# print('ピークゲイン Mp=', mag2db(mag[maxId]))\n", "\n", "# バンド幅\n", "print(f'バンド幅 wbw = {P.bandwidth()} [rad/s]')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### P制御" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pゲインと応答の関係" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.0, 50.0)" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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stGlLrLE4e53C2iuHzsyVIqcJ0ypjSxXPnTZtGq+88gqzZs1q1vs6Qkt8N51SiTWXyaqX9SzcsZDZ62ezIX1Ds9yzOdBoNEyfPt3prZRmkVNXXv+PvsqBcyvtO7cJdOjQgW+//bZFiue2FZzenWxrvLr7VdaeWgvAwbiDaCQN13W7roGrLg+1wx+cmSbLubhz/cd6x8I931/8+1+RoK+wfm638XDfuot/LxkEFfl1z1tU3Lh+AsuWLWPhwoUtUjzXmXHKb0FzmKzJ+cmsOrkKgAD3AAqrC/nPwf9wTddrUEmta8AaDAY2btzI9OnTLcIgnI0rRU64WDw3Pj6eMWPGWBxrzuK5rU1LuJNOqcSaw0JJzElEQiK2eyx/G/M3pq6aSmpRKtsytnFN12ua3skmoNVqHaoV2F5pFjlfPF//MekS1+aZVBvnXvLgmn/E+nmNZOjQoRw4cIAVK1YwevToelcpJ0yYYN7psHjxYhYvXmzzvr/++muja0S2BC3hPTilEmuOTQh397+bSRGT0Mk6/Nz9uKX3Law4toKNZza2uhIz5WP39fV16g3DzSKnm3frn2sHPXv25M033+Taa69FrVY3e/HctkJLbBBySiXWXCZrmE+YuR0TEcOKYyvYlbkLWcit6lIaDAa2b99ObGysU7tZV4qcJsLCwti8eTPXXHNNixTPLSsrIzX1orWZlpbGwYMHCQwMpGvXrs0mhy1c7qSdtITJOiR4CD5aHwqrCzmad5RBnQY1+3vYi1ar5frrr2+1979cXClyghIT6e/vj7+/f4sVz923b5/FgsGCBQsAmDNnDsuXL2/y/e3B5U7aSVO3bszbPI8qQxVPjXyKgR0HAqBVaRnbeSybzmxiR+aOVlVisixTVFSEv7+/U+dOu1Lk3LZtm3ljvVqtpn///ly4cKHZ3ycmJqbVc/i3xLYqp/xkNOUfpTfq2ZO1hz3Ze/BUW+Y8HxOmrBodyDnQpP41FaPRSEJCgtMH9V4pcoIyV1ReXt7qSqalaQkl5pSWWFNMVrVKzf+u/x8Hcw/S3a+7xbFBQYPo5NmJYK/gJvawaWi1WqZMmdKqfbgcXClygpKVws/Pz+oxZyqe63In7aQp2l4lqYgMiCQyILLOsX6B/dhy+5amdK1ZkGWZvLw8goKCnNrNulLkBMzupCmvm7PiciftpKXSmbSVD5csyyQlJTl92pYrRU4TpgyqzozLnbSTppisHx/+GG+tN9N6TCPQw/rytRCCCkMF3trmjRWyF41GwzXXtG6s2uXgSpETlAfkpYkunZGWcCddllgtjLKRjw9/zOt7X6dUZ7225Z6sPcR8F8Ojvz/alC42CVmWyczMdHoL5UqRE5QHo06nc03sNwKXEqtFRmkG1cZqPNQedPHpYvUcf3d/CqoKOFV8qtU+cLIsc+rUKaf/cl8pcpowFdtwZlzupJ001mQ9WaRU2enl3wu1ynrKkJ5+PVl5/Up6+PVotTkyjUbD1Vdfbf5bL+t5fc/rbMvYhq+bL0uvXUoXX+tKuD1xqZzOjCRJDWYsdgZc7qSdNFbbnyxUlFjvgN71nqNVaxkYNBAvrVej3qM5kGWZM2fOmOX84OAHfHfiO3IqczhVfIoHNj5AYVVhq/WvubhUTmdGCEF1dbXLnWwELiVWi9PFpwGI9K8bXtGWqD1XlFKQwmdHPgPg2ehnifCNILMsky+PfdnKvWw6V9KcGOD0BVHApcTsprEm69mSswB069DN5nmHcg/xyu5X+OJo86YPtheNRsO4cePQaDR8f+J7BILrul7H7AGz+euIvwLwbcq3VNSX4K+dUFtOZ0eSJHx8fNpMGE9L4XIn7aQx21SEEJwpOQNA1w62d/RnlGbwbcq3bD67uVH9aypGo5HU1FTKqstYd1rJNnpHvzsAJdtGtw7dKNGVmLPStldMcl4p246qqqqc3p105di3k8Z8EPKr8qkwVKCSVPWuTJowuZunik81qn9NRQhBYWEhW89upUxfRrhPOKNCRwHKtqnb+tyGhGRWyu0Vk5zO/sWOiYlh/vz5V4yybm6cUok1xmQ1feHDvMNwU7vZPLerr2KpFVcXU1zd+JzqjUWj0RAdHU1yUTIAU7tPtchvNjNyJltu38Jzo5677H1rTkxyXinupLe3d4u6k6+99hrR0dH4+voSHBzMzJkzSUlJabH3s4bLnbSTxjzRTPNhJgVlCy+tF8GewRbXXU6MRiPHjx/nr8P/yoZbNnBXv7ssjvu5+xHkGXTZ+9XcmOS8UiyUysrKFrU64+LieOyxx9i9ezebNm3CYDAQGxtLeXnTqjQ5gsudbEHOltYosQbmw0yYzjtT2joum2mfXbhPOCHeIfWeJ4v2vbJ3JewnNGFSYC1Vd3LDhg3MnTuXgQMHMmTIED7//HPOnj3L/v37m/V9LjetqsSWLVvG4MGD6dChAx06dGDs2LH8+uuv5uNCCBYtWkTnzp3x9PQkJiaGo0ePNnjfxtS2M0/q22GJwUUlllGS4fB7NRW1Ws2wYcNsyplRksGcX+cw48f2W1DEHjmdBUmS8PLyuqx1J4uLlamQy1kxyenqTnbp0oXXX3+dyEhlonzFihXMmDGDxMREBg4cyJtvvsk777zD8uXL6dOnD6+88gqTJ08mJSXFZnRzY0zW3gG9Ka4upm9gX7vONym71rDEjEYjCzYswOBu4C9D/sKQTkPqnNPRsyOHcg9hFEayy7MJ9Q697P1sKkajkeTkZPr379/oD39jwkzc1G5oVMpXwyAb0Bl1qCQVHhqPBu/b2CBoIQRLlixh0aJFl6XupBCCBQsWMH78eKKiohrV58bgdDn2b7zxRou/X331VZYtW8bu3bsZMGAAS5YsYeHCheay6ytWrCAkJIRvvvmGhx56qFn78siQR6CuLqiX1rTEAA4WH6RAX8CfB/3Z6nEvrRdvx7xNpH8kIV71u5uXm/TidL489iUyMrf1uY0BHQe06PuN/ma0w9e8NfEtpnRXkjFuPruZp+OeZmTISD6f+rn5nKmrplJYXXdXxJE5jSvlZqo7uX37dkaPtuxzS9SdnDdvHocPH2bHjh2Nur4t0WbmxIxGIytXrqS8vJyxY8eSlpZGdnY2sbGx5nPc3d2ZOHEiu3btsnmv48ePc+DAARISEkhISCArKwuj0Wh+ChgMBou2KYq4vrZer7doCyHMltjZ0rMIIcyvm9qARVuWZYu2wWCw2TYajRZtU3+NRiNCCN677j2eGfkMff371ivTtV2vJdwr3DzX0pBMtdstIdOB7APcsvYWvjvxHT+c+IG7193N3qy9deQztYUQZivMnnEy9dX0vo2dJDddJ4QAUc/rdlzrSHvo0KF06tSJ5cuXW/S9doS7LMuMHz+e1NRUZFnm1VdftcudFEJY/I/mzZvH2rVr2bJli9lSc7S/9rStjZPTuZMAR44cYezYsVRVVeHj48OaNWsYMGCAWVGFhFhaESEhIZw5Y9uFu3QuoU+fPoSGhqJWq/Hx8aGoqAitVou3tzcFBQW4e7jj6elJYUEh3t7eeHh4kJeXh6+vL+7u7uTk5BAQEIBWq+XChQt07NgRSSVxJvMMZzjDtC+nUZBbQHBwMEIIcnNzCQ0NxWAwkJ+fT0hICHq9nsLCQoKDg6murqa0tJSgoCCqqqooLy+nY8eOVFZWUllZSWBgIOXl5ej1evz9/SkrK8NoNOLn50dpaanFB2W5erlVmTw9PfH09CQ/P99umTQaDdnZ2XTq1AlJksjJyWk2mfz8/dibvZdqYzV+7n4IWVCiL2Ha+9Po790frUqLr68vxcXFFuNkNBoJDAyksLDQpkydO3dm9uzZSJKERqMxZ0n9ZvQ35jbQYFsIgapSxcmTJxFCEG4I55vR34CAlJQU1Go1QgjeH/Q+arXarHBMbdM5pi+vSqXCaDQiSZLVtkqlorKykq5du/Lpp58yd+5cSkpK+Mc//oEkSeaH08mTJ6mqqmLVqlVMmDCBlJQUYmNjGT16tE2Z/P39OXnyJEajEbVazUsvvcSmTZv46quvMBgMFjKZlMylMtVu2yOTEIKcnBxefPFFysvLLcapJRZqWl2J9e3bl4MHD1JUVMSqVauYM2cOcXFx5uOXxs0IIRqMpVm+fDmDBg0yP9G7dOlCcLASEmF6qkuSZG7HZ8bz5LYnGRs2lg+v+xCVSoXBYEClUqFSqdDr9ajVanPblEI45tsY8qvyefv6t+nj18fiw6PVas0ph7VaLbIsYzQazW1ZltFoNPW2TR8GU9vUd5Olcvr0aXr27IlarbYqk0qlQkbmi6NfkFKQwj+v+icaNA3KZGqb5GgumT4/9jlnE88S4hXC6hmrUQkV9264l5NFJ5nRfwYLRiwwy2eSVafTkZqaSt++fRXlUtP32mNjaut0Ok6fPk337t3x9PRElmUkSUKSJHP70s+P6Z6mh4K1tukz2JJtT09PAgICiImJIS4ujkmTJhEUFMR7772HLMuUlpZy2223ATB+/HheeOEFizTW9so0b948fvnlF3788Uf69etnfn9/f388PDyaTaaqqioAvvzyS7y8vCzGaf/+/YwaNcrm99dRWl2Jubm5mSf2R44cSUJCAu+99x7PPacEamZnZxMWdrGIbU5OTh3r7FIGDRrE8OHD6z1eO+BOo9FwoVIpj+Xj5mPO5V77nNqFW2u3w33Cya/KJ7s8m4FBA+ucI0mSuW360tnbrm12X9peeWIlPlofQuVQ/N38rcoEIAmJFcdWUFBVwD0D7mFwp8ENytRQu7EyTe85nVJdKVFBUXRwUzKYzh8xn8c2P8YPJ3/gL0P+gp/az0JWNzc3BgyoO2dmTVZT30xf5to5+Wu3az8ATe3a113atnVdc7c9PT3p16+fue6kRqOxq+6kvTItW7YMwGLRAODzzz9n7ty5zSaH6W+NRlPn++SU7uSlmFKS9OjRg9DQUDZt2sSwYcMA0Ol0xMXF8cYbb9i8h2kOxl7u7HsnU7tPpdroWFK6SV0n0Sewz2WvfvTRoY8orC7kq6lf4e/hX+95kiTRv2N/dmbu5Fj+MQsldrkJ9wlnwcgFFq9NCJ9ApH8kqUWprDm5hrlRcy2OGwwGEhMTGTZsmFNH7ZvqTpaXl+Pl5dVidSfbwvYtR7+b9tCqn4wXX3yRadOmERERQWlpKStXrmTbtm1s2LABSZKYP38+ixcvpnfv3vTu3ZvFixfj5eXF3XffbfO+jm7dkCSJAI8Ah/v/wKAHHL6mqeRV5lFYXYiERC//Xg2ePyBwgFmJtTUkSeKufnfx8u6XWZ+2vo4SkySJgIAAp8/sYOJKiYdrblpViV24cIHZs2eTlZWFn58fgwcPZsOGDUyePBmAZ599lsrKSh599FEKCwsZPXo0GzdubDADpjN/GEyJG7t26IqPu0+D55sqmCcXJLdov+qjQl/Bq3teJSYihmu7XmuxxxNgcrfJLN6zmOSCZNKL0y1qfarVavNUg7MjSZJ5XupSnKnupNO5k5999pnN45IksWjRIhYtWuTQfR01WZ/f/jz+7v48PPhhm+4ZALIRTm4Eow66jqPC3Zu8yjy7tys1FZMSCzQGWky810f/jv0BSC1MRW/Uo1VrbZ7f3OzI3MHaU2tJzEnkuq7X1Tke4BHAhC4TQIBO1lkcMxgM7N27l1GjRrWKOymEQBYyKknV4tagyZ1s6U3grY3TuZMthSOFVisNleacXI8ObaCCUcl5+HY2ZO4DIM07gJuCffHR+rDrrl2X5cN3ovAEAP2C+tklZ5h3GN5ab8r15ZwpOWO1KHBL0su/F/cOuJdOnp3q/f+8P+l9q8dUKhXh4eGXvXCuEIKi6iIulF/AKIy4qd0I9wlv8ZTktRdSnJWWGMs2E+zanDjyj7pQrkygemm88NXacFNlI6x6QFFg7h0gsBehFUXK+wEVhsuTRdVUzGRUj1F2ySlJEr38lLmz1OLUFu2bNXr59+KZ6GfqzHfVpj7lplKp6Nat22VXYgVVBZwvO49RKOEeOqOO9JL0Fs2UK0kS7u7uTm2FgUuJ2Y0jJmt2RTYAId4htj9Aez+BMztB6w0PboVHduLZeyp/RD7Azju2X5ZCurKQOV2k1AEoTC20W07TAsCpotZJ4mgvmWWZFqmNDAYD8fHxLeKC1EeVoYoLFcqDLcgziL6BffFx80EIwbmycxjllkkLJIQwBzI7My0xlk6pxBzR9tnlihIL9Wpgg7SsBw8/iH0JgiJB6wl3r8TnqidBfXm88uzybKqMVWhUGkb3GW23nK2lxA7mHGRX5i67LJhPj3zK1FVT+ejwR+bXVCoVvXr1uqyW2IWKCwgh8HXzJdgrGI1KQxefLmjVWvRGPXmVLTfJ7u7u3mL3biu4LDE7aZQSayjLw7jH4aljMHyO9eOX4QmaVpwGQDffbnSN6Gq3nKZ02qlFl9edXHF0BQ/9/hBfJ3/d4LlRQVGoJTVlujLza42ZE2uKJVOhrzC/f6h3qNkyV6vUhHqFopJU9dYjbSqSJOHm5uYU7qStMXApMTtxyJ20V4kBuPvAJat7m89s5pHVM/nvp6PgQsvGYpmVWIdubNmyxW45TUrsbMlZdEZdA2c3D0II9l9Qku1Fh0Y3eP6IkBHsumsX713znvk1g8Fgt5ymSfGKisbPW5msLH93/zopyn3dfOkT0KfFMuYKISgpKXEKd9I0BtYWKlyrk3bi0MR+zfxHvUqsOBMK06HrWLBy39zKXHaUnsJNXwEHv4Yprzamy3ZhUmI9/XoSFRFlt5zBXsH4an0p1ZeSVpxmd860ppBRmkFhdSFuKjdzrJottCotWpXlh16lUhEVZZ+carUaf39/cnJyAPDy8nLIqhFCoK/WIxtkfDx8zPv/LkVPy9SGNO1/rKqqcrjf5fpyKg2VaFQafLQ+lz2MpnZfKioqyMnJwd/f32pMWEtYYle8EmtwTizxK9i2GAbdDrd8UudwZ5/OAJzXaODoGpj8slVl1xykl6QD0NO/p3lDuz1IksTM3jOBxiftc5RDuYcAJU7N0S+VQTagUSn77hyRMzRUGUOTImsMkixxvuh8vccFQkmSiKrVlIUJWcgUVhVabJeTJIkA9wCLBI6XG39/f/NYXEqbUGJz587lz3/+M1dffXWzd6a5cMRkNYVY1GuJHV2t/O51jdXD4T5KPqZMrQZKzsG5vdB1jP2ddYDeAb0p05fRzacbv/32G9dcc43dsUXPRj/bIn2qj8O5hwEc2q95uvg0C7cvpNxQztqZa9Hr9WzZssVuOSVJIiwsjODg4Barpr3y+Eq+Sf6GsZ3H8sLoF5rtvnq9nj179jB69Gi7ZNXLev6+8+8czTuKu8adiV0mklqUyumi00qQ+LhFDAse1mz9sxetVmszKr9NuJOlpaXExsYSERHBfffdx5w5c+pNgdta2Kvty/XllOpLAawX2yhMh9zjoNJAv+lW7xHmrWTYKFWpKFFJdDi6psWU2POjngeU5Hhdoru06e1Vh/McV2JBnkEk5ScBSqyWv5s/0dHRDstpSk9kL2W6MgTKimRDjOk6hk+SP0Hrrq13m1BjcHNzY/jw4Xh7e9v1+f1w/4f8fv53vLXerLh2BX0D+6KX9fxt599Yd3odz//xPD/c+AOdvDo1Wx+bgzYxsb9q1SoyMzOZN28e33//Pd27d2fatGn88MMPLfb0cxR7/1E5FYrb4aP1sR7nlVpT4bvLKCW8wgpeWi8C3JXN41kajbIlqYVRqVQEBgY6/IEori7mSG7j0ic7QpWhihMFys6CIUH25/zu4NaBHn49AEjKS2q0nI6yJnUNV397Ne/uf7fBc/sG9GXbHdv4vzH/16x9cFRWlaRCq9Ly0riXzHOcWpWWRWMX0TegLwVVBSw5sKRZ+9gctAklBtCxY0eefPJJEhMT2bt3L5GRkcyePZvOnTvz1FNPcfLkyebup0PYa7LmVuQC1J9K59QW5XekdVfShHleTOsOBachv/njsaqN1eZAS71ez7p16xx6aORV5jF+5Xj+9OufHE455Cinik5hEAYC3AMcLlAyKGgQAEfyjjRKzsaQnJ+MQTbYlVJJkqQ6CxDNgaOyPjH8CTbcsoHY7rEWr3toPFg0bhEAa0+tJSkvqbm72iTaXLBrVlYWGzduZOPGjajVaqZPn87Ro0cZMGAA777b8FOtpbDXlejg3oGbet3ExIiJdQ8a9XC6JsNsZN2Ny7UxKbHM0AHQZxoYrK9sNYUvj31J9NfRvJXwFhqNhgkTJji0KbqjR0f83P0I9Qo1W6AAlGZDwmew69+Q3TxWWkqhUlW6T2Afh+OeaiuxxsjZGBZPWMzamWu5vsf1dl8jhOB4wfFmC1lpjKz1Kd2ooChu7KkU4fkq+atm6V9TKK4u5oktT7Ana0/byGKh1+tZu3Ytn3/+ORs3bmTw4ME89dRT3HPPPeYUOStXruSRRx7hqaeeavYO24O9X5x+gf14dXw9IRHnD4KuFDwDIdS2S2SaF8vuFwvRzzjSVbvJLMtEL+vx1HoiSRIdOnRw6HpJkvj91t8tV62OrYXVfwFDrbznN/0bhtuud9gQpk3qfQMcD+UwKTGTBeGonI3F5Mbay93r7iYpP4mPJn/EuM7jmvz+9o7p9ye+p29A3wbnGh8Z8gjDQoZxU6+bmty3plBtrObBjQ+SXJDMicITvNTtpWZ/D4eVWFhYGLIsc9ddd7F3716GDh1a55wpU6bg7+/fDN1rHM1isoYNgT9vhLLsBkMmTEosqyZcoyX4v9H/x4ODHsRN7YZer2f9+vVMnz7docwHFgrsxEb47l5AKLJ6BSmLGH2mNbmvJiXWJ6CPw9f2CeiDm8qN4upiTheeJml7ksNyOoI9NRus0SewD0n5SWw/t71ZlJg9Y1pUVcTre15HJ+v4/sbv6RfYr977RXSIIKJDRJP71VTcVG5c3/N6citzWTJpCSWpJc3+Hg4rsXfffZfbbrvN5spMQEAAaWlpTepYU7DXZC2sKsRb610nOhsAjRt0ta9modkSMymxogzQeIBP860MqVVqs9sqhCA2NrbxblZZLvz0KCBg6D1w4/vK/s/KIvD0b1I/hRCkFCjuZGOCarVqLf069uNw7mGSC5ObJmcDCCG45edbiPCJ4IXRLzg0fzchfAKrT65mR+YOnuO5JvdFo9E0KGuVsYqpPaaSUZrhkJUrhMAojOaCwJcTSZKYM3AOs3rPwtfNl/3q/c3+Hg7Pic2ePbtZl5Zbkye2PMGIr0aw5eyWJt0n1Ef58GeVZ8HaJ2BJFBxs2bmIxnyxTxae5M+//ZkH1/8JynMheCBc/87FDey1FVjmAdA7PrdXYaigf8f+BHkG0dOvp8PXQ915sZbiTMkZThaeZHvmdnPxEnsZEzYGjaQhvSS92QooNyRrqHcor45/lRVTV9htPa47vY6ZP83k+xPfN0cX7aZCX4FBvugR2RO+0liccu+kvaXSi6qLAAj0uKSKcv4p+GWBMmdkByZLLLcyF11QjQuV3nyVlc+XneeZuGf46JCS4cFgMLB+/XqH3WYPtQcJ2Qkk6vIx3vM9zPwAtFYeSL8thE8mwZ4PHe6rt9abT2M/ZevtW61buHZgVmK5Rxolp72Y9nYO7jTY4Z0MPm4+DAtRgkm3Z25vcl8cGVNH3N+i6iJOF582J/68XLy7/11uXXsr+7L3Wbxu73fTEZxy25G97uTamWsp0ZXgpbnkA3xmF+z7DHJTYEDDE6MB7gHc3ud2QrxDMAQMxQ3g7G4lkWIzZD04VXSKDekbiPSP5KEhD6HRaJg+fbrDVkpnn85oVVqqjdVkhQ6gi28X6yeG1Ox13PVvGP2QknboMmJSYimFKUy+bXKLWWMHcg4AMDy4/vJ+thgfPp6E7AS2Z27n7v62i9c0RENjGn8unmCvYPoG9HVIid3Q8wa0Ki3Te1gP1m4JyvXlbEjfQFF1EbKQLY61xOqkU1pi9iJJEn7ufnX3wGUdVH6H27dtQ5Ik/jb2b/xl8F/wCh8Bbj6gK4Oc5inOkVGquCsRvhcnahtjnagNVXTzVWoBmDaTW2XQ7eAXARV5cPhbh96jOUIOInwj8HP3QyfrSM5vuQInBy4oSmxEyIhGXT8hfAIACdkJVDVDWE19YyoLmVd2v8JtP9/msNXn5+7H7X1vx8et4aIyzYW31pt1s9bx2oTXGBXWvIVyreGUSqzJJuv5ROV32FDHr1WpIbzmyX4uoWn9qOFSJWYwGNi4caPjimzf5/TIPg5c3ExuFbUGxjyitP/4wKFcabf9fBuxP8RyNP+oY32rhSRJRHWMAmDVzlUt4k7mVORwruwcKknFkE727yqoTaR/JCFeIVQbq80KsbHYGtPDuYfJKs/CW+vNqNCmKYXLleqng1sHbuh5Q53XW8KddEolZo/7cTDnIE9ueZLPjlxSccmoh+yaKOfO9m+grdBXcKrolDLJ26Umf9a5fbYvspNzpeeAi0pMq9UyY8YMx8IOhIADX9C9Wsn1ZNMSAxg2G7RekJditzLWGXWcKTlDVnkWnTybtjI7b9g8Vt6wkkW3LGqR8AqT0ukb0LfRVookSYztPBaAP7L+aFJ/bI3p72d+ByAmIqbR2Sl+PvUzd/5yJ7+l/9akfjZEQ5lvW2JqwCmVmD1Pm9PFp9mSscU8uWsm9zgYq8HdDwLsD4BccWwFM3+ayWdJnyl7LaHFLLFGJdC7kAR5KfSoedA3qMQ8OsDAm5V24pd2vYWb2o34O+NZMXVFk5VYVFAUAwIHUFVeZZ+cQlzc62pi2xuw5RUw1HVxTfNhTc30MDasRomdb5oSq29MhRBszdgKwDURtre/2SKtOI2j+UdbdIJfb9Rzy9pbuOOXOzhfZj2dUUtYgk6pxOwxWU1bb+ps3TC7koMdygsW5h2Gr5uvUhy2SzSMfgRimh4/ZCpQAZbu5Pbt2x1zs5JWAdAzTJn/aVCJgRJDBpCyAYz2vVcHtw4MDxneLGmW7ZZTCPjtRfhqlhIaYnrt2E8Q/y/ldZ1lxleTJTY8pHGT+iZGhymxhCmFKU3Kv1+frGnFaZwtPYtWpeWq8KsafX+Ta7cjcweFVYWNvo8tNp/dTEFVAbkVufVmz3A6d/K1114jOjoaX19fgoODmTlzJikpKRbnCCFYtGgRnTt3xtPTk5iYGI4etT3fYo/Jatr8XeefnV+Th94BVxLgpl43seuuXfx97N/BuyNMex2ibnHoHlb7WZlLtbEataQmzEcJ5dBqtVx//fX2u1lCmJVY96g7AMivyqe4utj2dd3GwV0r4clDl60YSm02ZWwiISCB06WnbZ/4x39g9wdK2zR+kgRXPw1uvpC+HX64D2RlpaxUV2reVdDYlUkTHT07miPn92TtafR96hvTLRlKDOOosFFNqqjV078n/QP7YxCGFnMpv01RFoFu6XNLvZvknc6djIuL47HHHmP37t1s2rQJg8FAbGws5eXl5nPefPNN3nnnHZYuXUpCQgKhoaFMnjyZ0tLSeu8ry3K9x0yYLLE6bs/kl+CvJ2DsYw7JopJa5l9pciVDvUPNHwxZlikoKLBLTkBxJYvOgsYT7343ma1Pm5P7oCiCvtPAzb4Yqrf3vc2bCW9alF1rCr+c/oVVJ1eRkG3DLT+3Dzb9XWlPexMG337xWNQsuOd7ZffEiQ3wx1JAmQ8VCCJ8I5ol39bYzmOJ9I9s0megvjFtDlfShMka++X0L02+16WcKjrFvgv7UEtqbuld/8Pb7s+sA7SqEtuwYQNz585l4MCBDBkyhM8//5yzZ8+yf78yTyWEYMmSJSxcuJBZs2YRFRXFihUrqKio4Jtvvqn3vnYpsUpFiYV4WUmG6BsCvo6lkKmDvlIJeK2xgBqLtfAKo9FIQkKC/aZ5yq/K716TwM3LvNnZLpeyNjbmM4QQrEldw5fHvqRcX17veY4Q2zWWa7yvISowyvoJRgP8Mh+EUbF6R/2l7jndxsLU15X25pcg9wSJOcqUQVOtMBPzh89nzYw1TOvR+H2n1sY0rzLPnP9tYhcrmVYcZFqPaagkFYdyDzXbLgMTph0BE7tMtLl9y+mU2KUUFyvuTWCgEkGflpZGdnY2sbEXcya5u7szceJEdu3aVe99muRONoHntz/PzT/drOwdzD0Oy69XIv+bMHDWlJhWq2XKlCn2u5P9b4KYF5QVR6BHB0WJpRen23f97g/hP2NsJnzMqcihuLoYtaSmp3/jthtdysw+M3nv1vcYGjrU+gkHlivpgzz8FSusvnm4EXOh9xSlduivz14Mcm3ifJiJ5rDCrY1pXEYcAsHAjgOtZx52kE5enRgTpmQdXpfWfBP8FfoK1qYqu1tu73u7zXOdzp2sjRCCBQsWMH78eKKilCdvdnZNde4QywEMCQkxH7NGUlISBw4cICEhgYSEBLKysjAajeanXJWuivyqfAAC3QLNTwfjoe8QX90CB7/BYDCYX9fr9RZt0wqLqS2EQK/Xk16cTmpRKmeLz0JIFELjAVVFkJ+KLMvmhHeyLJsncOtrG41GDAaDWYmFe4ebX9fr9eTk5KDX680yGQwGi7apvwaDATmoD8Q8jyEyFlmW6e7XHVBWaBuSSQiByE+F3GQ4ttb8uqm/pvbxAiX+rIdfD7SS1qZMprapv/W1dTod2dnZ5ntYyFRdDvFvKe8R8wJ4B9U/TgYDYurrCI0nsmcA7457lfcnvc+YEOULXZ9MjowTQIWugvMl523KVN84WZN1a83cVUyNJdrgONWSoz6ZpndXIvfXnV5n0femjNO6U+so1ZcS4RtBdHC05Thd0nZqS2zevHkcPnyY//3vf3WOXbrS1VD6lDlz5jBixAhGjRrFqFGj+Oijjzh8+LA542z8vnhkIaOW1KQeTiUjQ1EUF/auRkr9HXKPEx8fT16estq0ZcsWioqKANi4caN5Pm79+vVUVVWZ972ZXNPNCZtBrcUYrGyf4fwBioqK2LJFmaTNy8sjPj4eUBJLmqzKjIwM9u7dCyhWaGJiojlGzFigfGCSk5NJTk4mKSmJI0eOmGVKTEw0Zw7Zu3evWaZdu3aRlZWlyF0j05iwMczwncGsiFkNymQwGND1mqLIkbKO0qICNm5ULLLaMh08dxBQipk0JBPAyZMnOXz4sIVMgMU4JSYmsvPATnac28H6nestZMrOzoKRf6bUuzt53a5veJy8wjA8fpCf3Wbi4xnMmE5jSNiqzLWVlpZalcmRcdqQtoHxK8fz3O/PNSiTtXH6448/OHToELIsEx8XR+6Wt9l9Xnm/cfn5F2XKzYC4N/l13c91xqmqqor169fblGmI9xC0kpb0knTiUuKaZZxWHFoBwG19bmNfwj6bn72WUGKINsC8efNEly5dxOnTpy1eP3XqlADEgQMHLF6/6aabxL333lvnPvv37xeA+OKLL8T+/fvF3r17xd69e8X58+eFwWAQBoNBCCHEweyDImp5lLj2u2uFXq8XRqNRCCGE/MlkIf7RQYhD31m8rtPpLNqyLFu0ZVkWOp1OvL7ndRG1PEq8secN5X7rn1Xut/5ZYTQahU6nE0IIYTQahV6vt9k2GAxCr9eLjw99LOZvmS9S81PNr5vkqN3W6/UWbVN/Dfu+EMYjq4WoLGqUTLIsC9mgE/IbPYT4Rwchp26xkMPUfnrb0yJqeZT49PCnDcpkS45LZZr3+zwRtTxKfH74c3N/a8uh11U3TqaathDCot3YcTqWd0xELY8SN66+Uciy7PA4mdtGozCunS9+fyNERC2PElP+O0gYEr+5KMevLwjxjw7CuPxGIVeVNEqmp7cqY7V49+Imj9OR3CMianmUGP7FcFFQWWBdplpt03d0//79orlo1Q3gQggef/xx1qxZw7Zt2+jRwzK4tEePHoSGhrJp0yaGDVNCHnQ6HXFxcbzxxhv13rd///4MH17/fEdetWJhBXsFX/TRhUDKVVwiQgZY+O615ylstU35vkyLBlJ4zZ68zAOoVCpzkQR72qaNsg8OftCi72q1GlmWyczMJCwszHx+7f7Wlkkd9xqUZMLsH9H0muSwTMqbaqHvdEj8EunEb2hr7lO7vycLladyn4A+Dcpkb1ulUtHVTdnrmVyYbF1W7cVMGfbItOzIMqTKIm42qOkycSFQkze/5pzGjlPfwL78OONHevr1RJKkemWyOk4198zKyqLzkQ9Q7f8vvTRa7vcfjH/Pa1EPuuuiHBHRsN8bVVocrLwb7v4eba1MJCY5bMl0Y+SNbDizgQ3pG3imJhNxY8fJFFYR2z2WAI8AamNNVqdzJx977DG++uorvvnmG3x9fcnOziY7O5vKSiVdsiRJzJ8/n8WLF7NmzRqSkpKYO3cuXl5e3H13/VkDGvpHmSf1a4dXlJyH6mKlPFvH3o2S52KGV8WENseaZR+2O1jUHmRZ5tSpUw1/IPJTFQWmdq9TRu508WnWn17P6aIGYrBM9J6s/E79vc6hamO1OVyjMdlc60OWZXzKlS1Bx/KPXTzw20IlANfBL4QsZL5NWcnHqd9TtHPJxcDYZkAlqejl36vRQb6yLFO64xOk3UoYSPcb3mf+jK+ZO+jPlicOvBnm/KwkGUiLh1+ecmhvKyghIYEegRRUFbA7a3ej+gtK7vwNaRsAuKPvHXZd43RKbNmyZRQXFxMTE0NYWJj559tvL2ZOePbZZ5k/fz6PPvooI0eOJDMzk40bN5rz+VujoRUQc4xY7ZVJU8aJjpFKVlc7KK828MG2VG5dtotr397GNzuV1dXssppFh8Be4N5BKRyS63g2hsKqQi6UX6iTzkSj0XD11Vc3vNJzepvyu+uYOul0Pjz0Ic9tf45t57bZ15keE0FSQ/5JpR5nLU4VncIojPi7+9tVMcheNBoNd8QoX470knTKdGWQd1KJ91p5F5RdcOh+RtnIUyMWMFPTib463cUA2WZGNGJrjUaupt/Zr5U/Jj4PQ22k9ukyAu78GiQVHPoGDqxw6L20Ki1Tuk/B392f/Mp8h/tq4udTP1NlrKJPQJ+GN9HrFcOkJVYnW92dbAhJkli0aBGLFi2y+74NafsBHQcwo9cMyxQsOTVP+uD+dr3Hqdwy5vx3L+cKLxbZOF1gwKcP5FTmojPocNO4KYkHfTtDkOMWyuqTq1lyYAk39brJoqCJLMtkZGQQERFhu46fSYn1jKlzaFDQIC6UX6ibELI+PP2h3/XKpnDZMj7NlI66T4Dj1Y1sIcsypRdK6ezdmfPl50kuSCY6qSY0IPI66BDm0P20ai239rmVW30i4eREOLoGrvsn+DVP8We9Uc+LO15k34V9/DTzJ4eyxcoaT85PW0F41kY2dR+Gx7l4RoeNxl3tbv2CnjFw3SIl0Pe3hUqFev+udr/fY0Mf45noZ5pUfm58+HjOlZ1jQMcB9Y+7EJDwKWx9Fe7b0CKWmFMmRWzoH3Vdt+u4rtslZdgMVcoWleCBDd7/bH4Ft334BwXlOsL9PXlsUiRh/h6sTcxkU6UGSWXgxbU7eGvWNdD/xkbLUaorRS1dzK1vwjQnFh4eXr8SMxogrSb3lBUlNnvAbGYPmO1Yh+6wvhG8KYVBbGGSs39gf86Xn+do7hGiD61UDg77U+Nv3HkodBsPZ3bA3o9h8j+bpb9atZbjBcfJq8wjISuBa7tda/e1sixztgRCYhby3s8zOVt6lrcnvl2nrqQFYx+H4+uVmMT8Uw4pMT9368WgHaG7X3dzVXqr6Kvgx4eVhwXAgRXIgTc3+X0vpc2EWDQnjTJZJz4LL2TAVU/YPK1SZ+QvX+6joFxHVHgH1s67irtHd2VS32DevXMYHT0Ud2pN0lG+TWja9pv5I+aT8KcE7ht4n8XrGo2GcePG2ZYz66Ayx+fhp1QzakFaSomZ5IzqpMRJJZ3ZCqVZShk9B6syCSFYdWIVKQUpintuypeW+JXVLBeNxeHUPLoKyNxvllVWyYwPH0+4T3jDG75VKpj1MTy2V9mN0QhkIXM493CjrrWJvhK+uU1RYCotTHkNYl917mDX5qSh7TjnSs9Zz8QpSaCpx3yv4f0tJzmeXUqQjxuf3DuSjj6W5/fuqETWS5oi/vbTUU5fKIIDXygTsAbHK29rVdo6+d+NRiOpqam25TSlAeo+wWaK7GpjNXrZgQrbQkDWIShIq/lTXKwz2YjqRrYwyTkgYAAARwpqXP7Bt9s9b2kisyyTRX8s4s51dypj32cq+IQq2WtT1jdbn03l23Zk7rBvbmz3B/DJNci/Pk9qaioaNLww+gV+nfWrfRu+A7op2+QaQZWhipk/zeSe9fc4tAXtWP4x5m+dz6HcQ9ZPMBrguznKwoObL8xeDWMfBZXK+bJYtBS2PjzVxmqmrZ5G9NfRDWdxuISTF0r5JF5ZzVt88yDC/OrmnjetUPYI1aEzyPzfT8mITf+Aff9VNmI3A0IICgsLbX9JxjwC85OUeZN6uG/DfUR/Fe3Yk/jXZ+Gjq5UaBIBRGLk/6n5u6HkDvfx72X8fOzDJObDjQNSSmvNCR7ZafTFFkAPsu6AkqIzqGKU8FNQaGHYPeAYouyqaiVGho3BXu5NZlsnJopO2Ty7Ph53vASBCh1iMqcNzi0LA8XWw/R27L/HQeNDNtxu+Wl/7V6mB5UnL2Xx2M98k17N/efM/4eRvoPFUNuD3uLpWN135xOzClslaWFWIu9odd7X7xYnX5F/g3yNg0z9s3veNDSkYZMF1/UOIHWh9k6tJiQ3tAe4aFbtOF5DboWaezZSrzA4ySjP40/o/8c8/6s7XaDQaoqOjGzbN/SMgqP5wEXeNOwLh2EZwU6hGTQJCjUrD3Ki5vDbhtfonoRuJSU4/Tz/61NQGOBjcS8n15iCmTBgjQ0defPGqJ2HBcWVvZTPhpfUy70/clrHN9snx/4LqEggdjHrIHYT1CyMxLxGj3Ahr5fwBJW5syytKgRs7eXH0i/x+2+8Ozd89NOQhZkbO5L6o++oeNOggoyYl0c3LlA34tXC5k3Ziy2QN9Q4l4Z4Ett6+9eLT7kKSElNVnlvvdYcyivg9+QIqCZ6fVn/l5bGdx/LEsCe4td8NPDRRsUx+K6xZRcu0X4mlF6dzKPcQB3MO1jlmNBo5fvx4k01z00Zwh5RYz0nK0n7OMSg+16T3b4jacg4PV9y0A4Pq5m23B1MG35EhtZSYh5/1knVNZFKEMj+19ezW+k8qy4H9nyvtyf/EKAQf7/6YP//2Z/6+6++Ov2n4CCUgWRhh4//ZfVmYT5jD5ep6+ffi5atetl6BXOMGc36BO76+mBm4Fi53spmQJMmymKcd4RVLtyrJ9mYODScyuP6c7MOCh/Hg4AcZHTaaByf0INDbjbiymgwUDlpiYJm9ojamgGCrHPgCvrlDyWxqg0al5PEKhPAaRZD6OwdzDnK66LRFodTmxCTn0OChACTmO+6SZ5VlkVmWiVpSW09HLcvKSm5jLCArTIyYiIREUn4SmWWZ1k/a/YGyIt4lGnpOQgjBrjxlH+P48PGNe+PYV5RJ9JMb66bqbgAhBNvPbbeZnVZvtHPuVOMG/Rv3sGkMTqnEHK5td8GkxAZYPZyeV87vyUpg5aOT7J/38fXQ8pere3JYVlLTiNxk0NmXa8uWElOr1QwbNqx+OU9uUpIAmrKc1kNjlFhJlZ40f8VdKjj8K//YtYgZP81g1/n6UyM1FrOcJRkM8+tDB7cOhHqH1gn+bQjTfNjAjgPrWh1CwH9jYcUNVncjNIYgzyCiQ5ViMb+m/Vr3hKpiSKgpUDN+AUgSJ4tPckF3AXe1e+Nzh3XsdTGn2qZ/OKSUX979Mo9ufpR/JfzL6nGjbOT+jffzXPxzXCi3EmT8xwfw+z8brBrvqjtpJ7ZM1q+Tv+aJLU+wMb0mN5a+CgpOKe16lNjyXekIATF9OxEZ3HA59rTiNOLPxVOhr+CuUV0pdwsiWwQgCVnJf2UHl+bVr43RaCQpKcm6nEIoxX8Buo6z+R49/RTlmlmWSYW+wua5uaXVvLD6CMNf2sST+5WdDur0ONIuyGgkN3p2aNxWLVuY5BTr/krI0jFsj5rPv6/5t8P5u0zzYSNCrdSXlKSLhV32Oxb5bgtTgkTTthwLck8oOyg69VNWSYE1J5VYqgnhExx27yy4+mmlyM2FIw7VDL2lzy2oJBXr09az6cymOsc/PfIpiTmJxJ2Lwygu+dzln1Im83e8A8dtZ411uZPNwKHcQ2zN2HqxGkveCRCykljPSjbXKr2RVQcUhXLfVfZVP3po00M8tvkxThadxM9Ty+3RERypscYwbTJvAFOK566+9gcwAor1VZGn7Jc01b+sh46eHQn0CEQgzLnFrHHgbCHXv7+d/+09i0EWlAVGUazyw0+qpH/61RQeW8RDK06SWWTDxW0kal2JsvPAWI0qtHHxbiZLzGI+rDbD71V+n9gAJVmNeo9LmdxtMhqVhpTCFPOOBjMR0fDkYWXeSKWi0lDJL2nKl39W5KymvbFXIFz9V6W95ZUGLSMTAzsOZM6AOQAs3LGQvVlKWh4hBN+lfMfSg8qezudHPW8ZfC3L8NM8xTXuGdMsdSUcxSmVmC2T1WQKmzNlmubDQgZazQy66dgFSqsMdPbzYEJkkF3v3yegD30D+pqrYf/5qh68YvgTw6o+JCW84UE2ykazO9m1Q10lplariYqKsi6nyQrrMrLBmDdQ8n/BxSwUl7IvvYB7PtlDTmk1vYN9+P7hsWx55hr8bn4H4+yfuOvWWQR4uXM0s5Rbl+0iLa95UlODImd/6TSSbFB2UnRSgmmLHAiJyC7PJqM0A5Wkqj8ddXA/iBitTIof/LoZeq5ExJvy4n+X8l3dE7QeEBQJwMb0jZTqSpUA1y6Nr2hkZtRDEDkZblhi12fAxBPDn+CqzldRaajkwU0P8viWx5mzYQ4v734ZgHsH3MuMXjMsL9r3GZzdBVpvuPH9+rPr1uByJ+3Elslq2vxtzq2v1kLo4HqrG5mssFnDu6BS2Re7s/Tapfxw0w/meZGIQC8GRg2hkA58tqPheJzsimz0sh6tSmsO2aiN0WgkMTHRupxmV3Js3WNW6O1fo8SsxDSl5ZVz3/IEKvVGJvQO4sfHriK6e81ey0G3Qo8JzBzRk3VPTKBXJ2+yiqu49797yC11PKjXGkajkeI/vlD+GDiTC+UXiP0hlthVsXYvJJjqQQ7sONB2kVxTmMWBL5qUTrw2d/S9AwmJYl2xEh9lNCixXLXmqmQhs/zocgDG+YxDyM0QR6X1gD/9AH1iG1QqtdGoNLw76V1u6nUTspDZlrGNxJxENCoNjw19jKdHPm0Zv1Z45mJY0uR/KoG3DeByJ5uIEKJuvcmoW+Dh7TDl1TrnXyipIv6EEnZxy4guTXrvP9e4oj8fyqK0yvYqz5mSMwB08e2Cup5oe0/PuoG2gPJUhDrxOfVRnyVWqTPy8Jf7Ka0yMLyrPx/PHom3u2WMz93r72bmjzMpNJ7m24fG0jXQi4yCSh75aj96YzMogsoiOuTVFDceMJNOXp2oMFSgl/V2L0Zsz1T2jza44jdgpjKXVHQG0rY1vs+1iA6N5tdbfuWtiW8pX/6jq5VYruXXm9PnxGXEkVqUio/Wh+vDr2+W962DnS4lgKfGk1fHv8p3N3zHghEL+NuYv7F2xloeHvKwpQITAn5+AvTlytzryPtboOP24ZRKrD6Ttai6CJ2suHj2pIz5MTETWcCIbgH0CGp8zT9Q7vGc3+98zMvs3mZ7m4tpPqybr/Unm1qtpl+/fnXl1FWAX1cl15RpsroBzJbYJUrsX7+lkHKhlE6+7nz4pxF4ulm+l86o40RBCqeKTxF4dj9BPu4svy8aX3cN+84U8vbGE3a9vy3UJzfUuJIDoFMfVJKKjyZ/xM47d5qVry0MsoHd55V8WQ0qMTcvGHyb0k6xMhnfCCRJItynJkOGELDjXaUdeS1IEnqjniUHlgCK1TYiakTzuluyDDuWwLsDlcl3B+jfsT/3Rd3H7X1vJ6KDlTCfvBOQkaCUw5ux1O5C0y530k7qqxhtssICPQJxU7spZn09yQqFEPywX3Elb3XQCksvTufmn27mph9vMr8mSRJTOpxlgjqJzCPbbF5vssSszYeBIl9CQkJdOd284L518NwZ8LAvDUwv/15ISORX5ZtzS+0/U8DnuxRL581bBxPcoW5A6MnCkxiEEX+jkdAUpaBFz04+vHmrEk3/UfwpEs82rdK0XJP9wNj/4jyM1TCJeqg0VDIjcgZDOg1hYMeGs5Mw5lGYuw6mvYHBKLPucBbzvjnANW9tY8TLm4j511Ye+/oAPx86T7XBMbfozOGv+VB3TtlLGK1k6/0s6TNOF58m0COQe/vda31Mm4JKpZQNrMi7WJuzuejUFx79A2Z9ooR22EmzyleDU6biqW/f2YUKZVLfbIVl7ldM++4TlE2qtUjOKuVkThluGhXXD3Ysb5Wvmy+pRalISOiMOkVhAiH9x0Lu7wSVHCUlu5S+odbDNc6W1lhiHaxbYpIkERAQUP/+OgeqdXtpvejWoRvpJekkFyQzNuwq/u/HowihKO9Jfa1brMdqNmMPqNYhXYgHox7UWqYNCuPmYeGsSczk+VVH+Pnx8bhpGvesFNPfJnfncgKjbm3U9b5uvjw36jn7L+jYCzr2YltKDovWHiU93zLsJL9cR3p+BeuOZBHu78nz0/pxw+CwBvc5FlcXc1fim5QG+NO352gmefoTlxHHBweVpIzPRD+Dn4ef7TFtLLEvw6ktSuhDygboO7X57h3Qza55sNo0u3w4qSVWn8lqUmLmSf2cY2C0noZlQ5Ky1B7TpxMdPBxLHBfoEYinxhOBuBjKAXh3Vyb6B0un+Tah/uKl5vCKeiwxtVpNZGRkXTmrShzqp4mXrnqJn2b+xNiwsaxMOEtyVgkdPDS8YGN7VXK+kqm2v9Ao+/9M++WAv90wgEBvN1IulPJhnGNuTG3Ugd3odOM/UHeKtHj9u5TvuOOXO8yxVc2FwSjzz5+PMvfzBHLyC+jkpebhib346v7RbJg/ga8fGM1jk3oR7OtOZlElj/8vkXn/S6RSZ9sq88s+xn2FhUTq9IwZr+T1N43tnX3v5Poe19c/pk0luP/Favbrn7Y72LpeDq2EUza2UzWAy520k4bcSbMlZkpJbWW70YajSorpqVGOVwKXJIkuvooLagpaBcx5vbqqctl64Bg6g/XJ7/ui7uPeAfcS6R9p9bjBYGDXrl2WclYWwhvd4INxytyYAwwLHkZPv57ojfD+ZmVubP51feqkGaqNKed9f5ObdvJigGSgtxv/uFEJHF66JbXRYRdW5USxbI7lH7MeDV9DenE6OzJ32J1mSGeQefirA3y+M51H1T9ywPsJts+o4Plp/RjfO4h+oR24KjKIZ6b0I/7ZScy/rjcalcS6w1nc+clu2yuyO97lgeISlneahGegssDTw68Hb8e8zQujX0CSpHplbRZinlfmSoszYNvrjb9PXir8PB++nHkx4aaDtIR8TqnE6st2ao4R87okRuwSJXYqt4wTF8rQqiWu7d+4XE1dfGqUWGktJebpjwhUFFNE9Qm2peRYvXZW71k8E/0MQZ7W49JUKlXdrK5n9yhBu4YqZW6sEXy1+wwXSqoJ9/fknjH1B9nqZb05h9iAnjWZR09aRnnfNKQzV/fphM4o8/qvDtYXqCiAr25FdXgl4Z071xnPqd0Vl2hP9p56c8R/lfwVj/z+CK/sfqXBtzMYZeZ/m8jvyRdw16iYNagjHsYyPPZ/bPV8D62a+df14X9/GYO/l5ZDGUXc/MFOMgqsPDz0lVBZgISE34SnLQ5N7jbZvPvA6pg2F27eML1mO9Ef/4Fz+6yellNSxS+Hz/P+5pO88ssx3t6Ywsq9imUuqsvg+7lgqFTqLXRrXDxbS8h3RSkxey2xDUmKFTauVxB+no3LQW62xGorMUAKV+LRBkunWX2gns3BDaBSqejWrdslSqwmk6idoRW1EULwyaHPef/IIlBV8MS1kbhr6jf7UwtT0ct6fLW+dOl/CyBBzlEoviiPJEn87fr+qFUSvx29wO7TDhSkSF4LqZtQ7f2Qbt271xnPiA4RRHWMQhYy69Osr/QGeQbh7+7P9B7Tbb6VEIJnVx1m/ZFstGqJj2aPIHL6k8pG6rN/2Ny0H909kNWPjKNbRy/OFVYy+zMrMXJaT7h/kzIJbmMC3OqYNid9p4JpbrHW1jdZFvxy+Dy3fbiLUYs3M++bRN7ZdIJPd6Tx7y2pPL/6CNPei2frm7fBhSPIXp1g5jK7VyMvxaXE7KQ+k9U8J+YdAuV5F1PvdLKc+zEpsca4kibMlliZpRKj83CMbn5oJSNbjudQXGHp7pwuPs3BnIM2EzYaDAbi4+Mt5TQpsQb2S1pDkiSWJ32N8E6kc3Aes4bbXo1NzFG+2IM7DUbyCVLSwPhFKOXhatE7xJe7RinL86+sO4ZsbyBn0ioAjANuritnDTf3VtK8fJ38tdXA14eHPMzvt/3OqFDboSafbk9j9YFM1CqJpXcPJ6ZvsFKAxJRGZvcym9f37OTDdw+NpUuAJ+n5Fcz5715KLo0DlKQGC9BYHdPm5oZ3FIU6UskDdiijiOnvb2feN4kkpCsryVHhHbh9ZBceurons8d046rIjjzptpZrjLvQCTWzS+fxnwOVDq/OmnC5k3ZSn7a/oecNzIycqaz6maywgO6KuV3DucIKjmQWo5IgdkDjXEmo3xIj+gHUL5zh16D70Bllfjly3uLwt8e/Zfavs/nsyGf13lulUtGrV6+LcuorL9ZQbIQlVqU3UpYziuqcKTw4dhRate2PhUmJmdPa3LUS5h+BiLoKY/51ffB115CUWcKaRDssz9Js83yLFHWLpZy1uKnXTQR6BJJZlslv6b9ZvZW72t3matju0/m8vkHZy/qPGwcwpXaiy7GPKr+P/AAFtndZhHTw4Kv7RxPk486xrBIe/eoABqOsbCivtC/MpM6YtgQeftBlBDqDzFu/pfDgsvWkZBfj66HhiWt7s/uFa/nl8Qm8eesQXpjen5dnRvH14CM8pVI2kn/o9RA79b35128pTHtvO3vTChzugssSs5P6/lH3D7qfl696WQlA1HopUdq9LavJ/HZUsdaiuwfanNhuiNqWmEVKXo0bSBKzhitBkGsucSm9tF6EeYfR3a97vfeuM3+SuR9kvZIzPsC+Teq1WX0gk+ILVxEsT+feaNubxoUQHLigKMzhITXn+nSqd3tLkI87j05S5gHf2XSCKn0DT/BjPwECukSjCuxe7zyRh8aDu/oplbHf2vcWhVWKslhxdAVxGXENpkHOKali3jeJGGXBrGHhzB5zSahA52HK/kNhhPi3bfcZ6B7kzYo/R+PlpmZHah4rv/taiWhfGm3XimCLzonVoqBcx58+3cOP2/5gtfZvrA76hLgno1kwuQ+hflYSRFbVeARXPcnjzy5myR1DCfJx53RuOXd+/AdLt5y038LGpcTsxi6TtcsIuH3FxQnPGrYcV5RYfemn7cW0079cX05RdVGd4zOGhqOWZPadKeRM/sUP+ZPDn2TjrRuZ1bv+bAYGg4EtW7ZclPNMrfkwB+NwZFnw351KYOvccd1RN7A/9Hz5eXIqc9CoNEQFRVkeNOoVS+oS7ruqO6EdPMgsquSr3Wdsd6jGlSTqlrpyXsLcgXPp6deTvMo8Htr0EC//8TJv7XuLeVvmma1FawgheH71EfLKqukX6surNw+ybrHF1JQjO7pGWWxogIGd/XjrtiFIyEQl10TnD5hpYenXR0OyNgencsu4+YOd7E0vYIRbBp1VxQwriyPw8wmw9xMlqr8gTXkompjwV7htBVz3TyRJYuawcDb/dSKzhocjC3hr4wnmfL63zrRIfbjcSTuxpu1LdCWcLTlrvcpRDaVVevacVj6s1/ZrWiVrD40HwZ7KPUwZKcwkfErIf6N5q5MSImCXm1ULlUpFVFTURTnDh8GQu6Gv43vv4k7mkppTho+7hmuiPNiQvsEitu1STEVFBgQOwFNTa//mid/grd7w4yN1rvHQqlkwWclAsXRrat05IxMFaTXxZhIMvLmunJfeV+PBm1e/ia+bL8kFyXx3QskW8ciQRy5aiVb4Yf85thzPwU2t4t93DauzpcpMl5EwZbEyKe9lX5Hh6YPC+HDAMYaqTlEu3Enu/bBd1zUka1M5caGU2z78gzP5FXQJ8GTeo/NR3bdOCb0oOafEkP17OLw/FL6+7WJlLkmCgTMtHo5+nlreuX0o/7p1MB5aFdtP5jFr2U6Lh7EtOZubVlVi8fHx3HjjjXTu3BlJkvjxxx8tjgshWLRoEZ07d8bT05OYmBiOHj3a4H2t/aPiMuK4fs31zNs8T9nHVnimTraC7SfzMMiCnp286d7EvZJwMaAxvSTd8oAQUHSWsR6KVbImMRMhhN2VYFQqFcHBwRfljLxOKcpg2vvnAP/doVhhd0RH8Ob+l3gm7hk2n60/tfHU7lP5acZPPB1tGS5AYC9l/ud0nFWrZdbwcHoH+1BUoeej+gJgq0uV3RO9rgHf0LpyWqFvYF9+mvETf+r/J2ZGzuSdmHd4dOij9Z6fVVzJSz8roTVPTe5D75AGklyOfcyxqPSS88RmKrm33jHcxv2rzpBf1nBWD3tkbSyncsu4+5M95lqpPz52lSJ319EwL0GpCRk+UpliUbspFesLG7CYgdtGRrD6kasI8/PgVG45M/+zs8F5MqdTYuXl5QwZMoSlS5daPf7mm2/yzjvvsHTpUhISEggNDWXy5MmUlpbavK81k7XSUImnxlNZmSw5D+8Nhje7W+yd3JyshGA01QozYSphVqccVmfFSggpTcbLTcWZ/AoOnC3itzO/EfNtDIv3LLZ5X71ez2+//YZe70C9SCukZJey/WQeKklxJceGKYsCOzJ31HuNJEn09O9ZN1d9UCSERClzSMfX1blOo1bx7FRlFfizHWlcKLFiEYcNhrm/wF3/A+yXs5NXJ54b9RwvX/Uyk7tNrvc8IQTPrTpCabWBoRH+PDjBwfnDU1ttJ000GuCH+5GqSzCGDSPOfxbni6t4/H+JykS/DZprTC/lTH45d3+y2+w6mxYgzGg9lEWMBzfDwiz4vxx4ZIc5d1tDDOjcgZ8eu4pB4X4UVuj506d7WJNYfwEZp3Mnp02bxiuvvMKsWXXnf4QQLFmyhIULFzJr1iyioqJYsWIFFRUVfPNNPfXuarCm7W/vezt77t7DorGLILdmZdIn1LzPUJaFOfh0UjMpsRt63sDi8YuZGTnT8kBoFKi0SJX53FWTjGFN4jlOFZ0ivyrfpssLytaN6OhoZQvHuf1KMdtG5MAy5TabGhVKRKAXE7pMAJR0zg2lq7bKgJnK76QfrB6+rn8wI7sFUKWXWfK7jZqMNYn8LORsBr5NyCD+RC5uGhVv3TYETQOrsBbsfE+JVF95d/07IvZ+pKRCcvNFfetnLLt3FF5uanadyudfv9kuo9bcsoKy0n73J3u4UKIktPz6gdH4ezVQdLgRexuDO3jw7UNjmDowFJ1R5qlvD/HuphNWPQuns8RskZaWRnZ2NrGxF1cP3d3dmThxIrt22S5KkZyczIEDB0hISCAhIYGsrCyMRiOyLKNVazFm17ikwf0xGAzIssyhc0Xkl+vwcdcQ3T3Q/DooT8nabdPgmNpCiDptgCGdhjC161S6+3VHlmXz67JKiwhVJsVvDVHmw34+lMWJAuWL3cu/F0aj0fzUMhqN5mRyRqMRIQSBgYHK+215GT66GuPej83n1O57fe2swjJ+PKjMfc0Z0xUhBD069KCLTxf0sp7dWbvryPTpkU/567a/8sc5ZSHBQiZZxjCg5mF0ehuG3FMXX6+RQ5ZlnolVtPZ3+zI4kV1slkk+/D2U5VjIKssyfn5+qFQqu2SyNU7niyp4ZZ3y8Ho6tg+9Onmb+157zOrIZOp73xsQnoFw/gDiy5kYirPMfTeP07A5iD7T4OZlGP270zPIi7duU7aafRR/mnWHszAYDFbHSZZl/P3968ja2M9eVlEld328m8yiSnoEebNi7gg6+rjXGQ9rbVufPWttg8GAu1rig3uG8+D47gC8t/kk81cmUqnTW8h6RSmx7GxllSskxDJWKyQkxHysPu69915GjBjBqFGjGDVqFB999BGHDx/m5ElFSRQc36mcGNyfvXv3kpGRwZbjihU2KsIHrVpFfHw8eXlK+aotW7ZQVFQEwMaNG83u7Pr166mqqsJgMLB+/XoMBgNVVVWsX69EkZeWlrJxo1KQpKioiC1btgCQl5dHhqSEYHQp2EuAu0RxpZ6DWcqXLNI/krS0NBITlRW2kydPcviwMqGenJxMUlIS69at49D+vYiaTK7HKoJIS1Pmt0wyAezatYusLOULV1umV7+NR2eQGRrhT27yXkpLS5U9nzqlX5vSN1nI9Mu6X1h5fCUbz2xk295tVmWKP3JGybMOZK57A4CMjAz27lXytaelpaEqSOe6/iEYZcHff1C2v6Tu24q0+kF4dyDHEuLM47R//37Wr1+PXq+3S6b6xmnduvUsXH2EsmoD3XwE946OsHuc4uPjAciq9uDQgOfB3Q8pY48yCb72CUq/e4QjfyhziCfTz3Gw37PQ/0aSk5NJTk5m+qAwZvZT5lef+eEQa+MSrI7Tzp07WbduHXq9vsmfvZzSKu78+A8yCiuJCPTkg9v6ciRhZ12ZsrLMBsGl41TfZy85WfmM1v4+JSYmKmOrkpgUWMzTEzujVkn8dCiLOz/cSWG5zixTi6y+ijYCINasWWP+e+fOnQIQ58+ftzjvgQceEFOmTLF6j/379wtArFixQuzfv1/s3btX7N27V5w/f1785be/iHm/zxPnS88L+cOrhfhHByGO/ij0er0wGo1i2pJ40e25X8QP+84KIYT5dSGE0Ol0Fm1Zli3asizXaQshhCzLYve53eLrY1+L86Xnza8bjUZhSPpRiH90EPLSUeKVn5NEt+d+FFHLB4uo5VEiqyxLGAwGodfrhRBCGAwGYTAYzG29Xi+Ki4uF4cRmRY5/9RF6nc58Tu2+W2tX6gxi2Eu/iW7P/SLWHsy0kGnf+X0ianmUGPHlCJFbmmsh0/H84+LthLdFWWWZWY7aMun1eiGO/KDI9VZfIYyGi6/X6ntKdono8fwvottzv4j9ZwqEccNCRY7lN1jIqtPpRGFhoZBluUGZbI3Tmv1nRbfnfhGRL64TRzMKrI5TbTnqyFS7fSFZyMvGK/2t+TFuXGR1nEztqmqduPOjXaLbc7+ImH9tEYVllVb7bk1WRz972YVlYvI720S3534RYxf/Ls7mlzcs0yVtW589a229Xl/nsxd/IkcM/PsG0e25X8TEN7eIIxkFwmg0in379glA7N+/XzQXbdYSCw1V4rQutbpycnLqWGeXEhUVxfDhw4mOjiY6Opqg4CD+yPqDbee24SZpkExl3oMHoNFouFBazbGsEiQJJvVT7q3RaMymr1artWibYopMbUmS6rRBmQR/N/FdXtv7Gkn5SebXVSoV6u7jIWQQUs8YbhkRjso9D5Dx1ngT4hWCWq02l3xXq9XmuRLT6x06dEB9piaTQM8YNFqt+ZzafbfWXnvwPAXlejr7eTAtKtRCpuGhw+kb0JdqYzXrz6y3kKlvYF8WjFyAt4e3WY7aMmk0Guh3I4x7HGnuOlCpL75eq+99QnzNiSb/vS4ByVQJe8xjFrJqtVr8/f2RJKlBmeobp8JyHS+vU6LyH5sUyYAuAVbHqbYcdWSq3Q7uh/SXOLj7Oxj/FIx7AlXESKvjZGq7u2lZevdwOvt5kJZXwYLvj2AwynX6bk1WRz57xZV67ltxgBMXygjp4M43D44hItCrYZkuadv67FlrazSaOp+9Cb07sfrRcYT7K9uxbvlwN9/ta5mK8W1WifXo0YPQ0FA2bbqYHUGn0xEXF8e4cbb3B15qsmaXZyMQeKg9CKwqUXbiq93N0e0mV3J41wACvRuY+HSQUWGjmBQxCX93f8sD3h2VVaBpb9AvzJ+IEGVpOkDbrcHEcXq9np9++gn5lOL2mFw4exBC8GnNhP7cq7rXmdyWJInb+94OKJlH8yrzKNOV2X1/NG5KJeoGsn3Ov64P7hoVQzL/h6QrU1Y2+0yxOMckZ1NW7F5ed4z8ch19Qnx4NMZ6aiOHUamUvl63SEk62K/h+LyOPu4s+9MI3DUqthzP4e9rj1pMfDdV1uIKPff+dy/HskoI8nHj6wfGNEuYUFPoE+LLz4+PJ6ZvJ6oNMs+vPsK/t9hY0GkkrarEysrKOHjwIAcPHgQUX/zgwYOcPXsWSZKYP38+ixcvZs2aNSQlJTF37ly8vLy4++67bd730hWe8+XKBHaodyiS1lOpujxirnllcktNaMU1zbQqWZsFIxbw/jXvmysf1UfXMEWJlZU0vFNAo9EQOyEaKeuQ8kJP+ytG70jN48SFMrzc1NwRbT3dzszImfQJ6ENBVQEPbnyQ2B9ieTru6XrT3tjEtG3lEjr7ezIv2ou/qJVwDOOEp+usjGk0GmJjY81WgaPEnchl9YFMJAlev2VwozPMNhdDIvx5785hSBJ8s+csS7dcrNDeFFnzy6q565PdHD5XTICXlq8fGENksI3KTpeRQG83/jsnmuem9kOtkhjQ2b606Y7Qqump9+3bx6RJk8x/L1iwAIA5c+awfPlynn32WSorK3n00UcpLCxk9OjRbNy4EV/fhqtw18YUgd7ZpzN06AzX/cN8rFJnZOcpZRK1JZRYg+ir4HwiBo0ywZuVE0R6XnmDT1Ft5m4khJKBo0Nnm+fW5rOa4NbbR0bUm2bITe3GaxNeY/b62aQWKV+0c6XnzGm27aKiQIkCP7sbHtsD7peMmRA8VPEZblI1CXIfTlcM5w4rt2msAiuvNvDiaiXlzNxx3RneNaBR92lupkaF8s+bBvL3n47y9qYTqFQSj9XsLW2MrFnFldz72V5O5pSZLbD60p63FiqVxCMxvZgyMITCs7ZDTRp1/2a/owPExMSYl4Zr/yxfvhxQXJtFixaRlZVFVVUVcXFxREVF2b4pdWvbZZUrK1nWajjuTM2jSi8T7u9JvxYafCEE2eXZdeO/9JXwr14YP5/KqWJlcOWq8Aa3IRkMBn5NNWK4Z7Xi0thJak4p21JykSRlP6Mt+gT0Ye3MtTw14imejX6WL6d/ia+bA/8frZeSfK8kE355ylyizIwQuHUehEHlxj/19/LahhTyLolsr73y5iiL1yeTWVRJuL8nT8f2dfj6luTesd156jolmPRfv6Xw+q/H0ev1Dsu6/0whN/57Jydzygjt4MG3D41tcwqsNj07+bjqTtpLHXeytiWWth3Kcs3Hfk9WNnxf1z+4RYoYANyz/h4m/zCZAzkHLA9oPSG4P2e0GiqNVWgld2RdJ9YkZtrMDKDRaJh6w0zUkddA32l29+OzHekATO4fQreODc+XhHiH8OeoPzN7wGy0KgeTQ2o9YNbHIKnhyPdKtZ3aAbkqFUx8Bp44hBw6lKIKPS//csziFhqNhunTpztsofx2NJuv9yh1Ct68dXCdepltgSev683C6UqOsQ/jTrHghySuvtY+d9IoC1bsSueujy9G4n//8Fh6dWobLqQtXDn2G4nZEnMLgBU3wFuRUFGALAs210zqNzYNtT2YLMDjBcfrHux1DUnuSoR6/4798HF342xBhdnFrQ9HrZOc0ipzNfP7xzuerqdRdB0DU19T2rveV2KrPhwP2UnmUzT+nXn9lkGoJPjp4Hm2XpKy21E5s4ureG6VEtf00NU9uSrSeorvtsCDV/fk9VmD0KgkfjmcxfX/3sWmYxds7qFNyixm1rJd/GPtUXRGmakDQ1n1yDgiAhuXktwZcEoldqnJarbEqmp22ftFgFcgRzKLyS2txttNzeie9mUpaAwDg5RiGgdzDtY92Gcq+z0UJTai02Bz6MGKXfVvwJV3LSXrv7MxZB6yuw/Ld6ajM8gM6+rPqB4tJ2sdRj8EN3+kVNcuTFNSI8dbpj8a3MWf+2oqpL+w6giF5UoFKoPBwMaNG+1WZDqDzJMrEymq0BMV3oG/tjE30hp3jurKyr+MIdzfg/PFVfzly/1Mf38HH8WdIiG9gNScMg5mFPHl7jPc8+lubvj3Dg5lFOHrruGlGQP54J7hbdLSrI+WcCfbj/QOUNskl4VMdoUSa9a5RHEdTVWHTK7kxL6dbOaUbyrRIcrK5P4L+5GFbC4OoXRqGE/rPLg2O4fwIaGIMd1YviudzccvkFFQUfcJKwTq/Z/Ts+AUFN4JXYY2+P6lVXq+rMnj9cjEXi3mNtfLkDuh3w1warNSsDhidJ1T/hrbh63HczidV84zPxzi49kj0Wq1zJgxw8oN6yKEYOGaI+xJK8DbTc17dw5r9dVIexnZPZCNT01k6dZUlu9MJzmrhOQs6+X3VBLcOKQzL07vT4iVosZtncYu1NiifYyyg9Q2x3MqcjDIBjSShk65NUvaZiVmylrRcq4kKCXhvTRelOhKzFWCzEgSvn2nc3VlFb3OJhAZ7MOE3kEIgXlex4LMA1BwCqHxRFwSV1Uf3+w5S2mVgchgH65rQbfZJu4+MGAGRM0Cv/A6h73cNLx/1zDc1Cp+T87h7U0pCCEoKSmxK0XRsrhTfL//HCoJlt4zvF3MD9XGy03NI+M6s+v5SfzzpoFc0y+YLgGe+HpoCOngzrheHXlmSl/inpnEe3cOa5cKDLBrLB3FKZVYbZPVVIg23DccTbYyV0LYEDKLKknOKkElNV/WivrQqDTmJH0J2Ql1T+h/k/L72E9g0HHv2O4AfJtwtm4658NKvvPzHYZhUDX8Qa7SG81hFX+5uieqBjK3tiZR4X68fssgAP6z9RSfxJ9i+/btDbqTy3em8eYGZXV30U0D661a3pYxGAxs374dHzcVc8Z1579zo9nx3DUcWTSFPS9exzcPjuGxSZHtfu7LtTppJ7VNVlNW1S7eYZBXYwWFDWFzjSs5olvzR+lbwxTs+sf5Pyxef2PvG7xfeJDsqxfAg1tB48Y1/YIJ9/eksEJvGW6hrzKnuQmftsC8lcQWX+0+Q05pNWF+HswcWtcCamvMGt7FHH6w+NcUktS9UKmtuyB6o8wrvxxjUU2Sw4cm9jQ/ANobWq2W66+/3q4xbc+43Ek7kWst5ffv2J9HhjzCdP+BSnFZnxDwDb3oSl4m9yqmSwwAu87vIq9SWXks1ZXyXcp3fJL0KYVDbjdv1VGrJP5cs4K4bNupiwn1kn6AinxEh3AKAoZYyGmNkio9S7cqLvRT1/VpN3NET1wbyZPXKil7lm07xc0f7GTHyTxz2IneKLMhKZsb3t/BpzVW5lPX9eH5qf3qvWdbR5ZlCgoKGhzT9k5LyOeUE/u1/1EDOg5gQMcBSmyYNgj0lZRVG9h9StlCc13/y+N69PTvyaCgQRzJO8L60+u5d+C9uKvdWTxhMQnZCfQLrPUFNBq4a1QE/9maytmCCn46eJ5bhoebayDKIx8gYX8i11xzjc38TB/FnaKoQk9ksI+5ulJ7QJIknprch64BHixcc4TD54r502d78HHXEOTjRnZJFVV6ZYwDvd1YfPOgJtUIbQsYjUYSEhIaHNP2TksoMaf8b1k1WX06wbA/wagHiT+Ri84o072j12WdAJ7RS1lp+zblWyr0Fbip3ZjSfQr/N+b/lBXD3BT4312w5i94uWl4oCZ98ru/n6Bar4OoW8AnBHX0fUyZMsWm65FTUmWeC3tmSl/Hspi2EW4Z2ZX4565lzthu+LprKKs2kJ5fQZVepqO3G4/E9GLzgontXoGB4k42NKbOQEu4k05tiQkh+CPrDyJ8Igj3DTeHNqw7ogS/xg4MvazhBtN7TufDwx9ytvQsV397NfF3xOOlrTVRa9RDipKoj+FzuG/ceFbsSudcYSVf7M7kwasXwNjHkFVa8nJyCAoKqvep/er6ZKr0MsO7+jepCHBrIssyVJXwjxsH8LcbBnAqt5zSKj0B3m706OjdphcpHEWWZfLy8myOqTPgssTsxPSPKqgq4KFND3H9musx7FoK5/ZTXqU3T+rfMLjuXsqWxNfNl39d/S/UkppqYzW5lbmWJ4RGKdk1AH58BM+yMzxzTVc6UcSS309wvqgSNEqK4aSkpHo/EFtTcvjp4HlUkrJad9njwpqJ2nJq1Cr6hvoysnsgvTr5OJUCAxocU2fBNSdmJyaTtVRXSu+A3uiqinHb9Dfo0IXN126iSi/TraMXg8L9LnvfRoaO5POpn3O66HTdHGMAsa9CWjwUnIZlV3GL1osYL7in8mmeXx3I8rnRaDQarrnmGqv3zy2t5pnvlVCSueN6MLiLlfdoJ9iS09m4UmR1rU7aiUnbd/frzuqbVrM2uCYoNGIUPx9StiDdOLhzq1kow4KHcUufW/Bzt6JE3X1g7nolql1fgVSRh5+nls6aYuJP5PKfranIskxmZmadp1qV3shjXx8gr6yaviG+PDOl7W+7sUV9cjojV4qsLkvMTi79R6nO7QGgMiyauF8VF+7GIfbn4LrsdAiD+zZAzlGoKEAbMZppB3PZuuowb286QQcPNT2M5wgJCTHPn1ToDMz7JpG96QX4umv4zz02Klu3E2RZ5tSpUxZyOitXiqwuJWYnJpNVCIEkBGQoUfI7qyPRGfX0DvZp03mXACVVTegg85+3R0eQmlvGx/Gn+cfPydwyvAuh+ZWE+Xmw53QBb/52nBMXynDTqPj43pFEBrdx+exAo9Fw9dVXt3Y3LgtXiqyu1Uk7MWn7Kaum4K9yZ4mxjM5uvnyZ5gMUtm0rzAYvTOuHp1bN+1tOsurAOXNqHRNBPm58NHsEI7pdxiwVLYgsy2RkZBAREeHU1glcObK6ViftRJZl8ivzySrP4nhpOgFGmcrwccSfKgRoF9tvrGEKAl35wCiGhWjR1KzQBfu68+CEHmx6aqLTKDC4cuaJ4MqR1eVO2olGozHnhu+CFk8h2MIghIDxkUF07di+N9GO7tWJNU/FYpQFFToDPu6adhtGYQuNRtNgZStn4UqR1bU6aSdGo9GcRbV3l6vQ/2ktb51TtvXcER3Rml1rFoxGI6mpqSBkfD20TqnA4KKcLZH5oK1xpcjqymJhJ0IIEnOUMuxDQobxS2kvjpV60cnXndiB7TN6vTZCCAoLC1skN1Nb4kqRE64cWV35xOxErVZfVGJBQ/h0u7KHcO647i2awfVyodFoiI6ObhHTvC1xpcgJV46sLnfSTs6XnaegqgCtAN/Ny0k7n4OnVs09o60Xi21vGI1Gjh8/fkW4HleCnHDlyOpyJ+0kpUDJ8jmguprA1F+oxI37ruqOv1fLJz+8XFRWVrZ2Fy4LV4qccGXJ2py0CyX2wQcf0KNHDzw8PBgxYgTbt2+3el5urhKNn5CpBLcOr6rmB/04fD3ceOjqXpetvy1NTk4OP/30Ezk5OQ2f3I65UuSEK0fWgoIC4OJ3tTlo80rs22+/Zf78+SxcuJDExEQmTJjAtGnTOHu2bhGNvDwlY+qhfGU+7NqyKlYYpvDctH74eTlPnqZz587xz3/+k3PnzjV8cjvmSpETrhxZTUra9F1tDtq8EnvnnXe4//77eeCBB+jfvz9LliwhIiKCZcuW1XuNAZlInY7UqhH0jOzD3aOcYy7MhQsXdWnTSkyn07F//35iY2MtXo+NjWXXrl02r51cauA73/t4/85hThdHZSoF3xIl4dsSV4qccOXI2hJbqtr0em5eXh5Go5GQEMvYrpCQELKzs+ucX11dDUDnM2Xs9b6ZqwZXsH7NdwQHBxMYqGzHUavVGAwGJEkyt1UqFSqVyu62Wq1GkiRzG5RVl9ptjUaDEMLclmVZSe5nZ9toNCKEMLdNfTcajSQnJwOQlJRkft/2LpO19pEjR1Cr1Rw9etRpZKpvnI4cOYJKpWpQ1vYkk7X26dOnLb6rzUGbVmImLrWkhBBWrauKigoAtn9+ge18yAo+vCz9ay3mzJnT2l24LNx7772t3YXLxpUiq+m72hy0aSUWFBSEWq2uY3Xl5OTUsc4A7rzzTgC8vLxwd3e3uE+nTp1atrMuXLhokMrKStLT05kyxb7q9fYgiTa+z2H06NGMGDGCDz74wPzagAEDmDFjBq+99lor9syFCxdtgTZtiQEsWLCA2bNnM3LkSMaOHcvHH3/M2bNnefjhh1u7ay5cuGgDtHkldscdd5Cfn89LL71EVlYWUVFRrF+/nm7durV211y4cNEGaNMhFiYeffRR0tPTqa6u5v7772fOnDkNRu+biIuLY8SIEXh4eNCzZ08+/LB9TPbbu0sBYNu2bUiSVOfn+PHjl7HHjhMfH8+NN95I585K0ZYff/yxwWva43g6Kmd7Hc/XXnuN6OhofH19CQ4OZubMmaSkpDR4XVPHtF0oMROORO8DpKWlMX36dCZMmEBiYiIvvvgiTzzxBKtWrbrMPXcMR+U0kZKSQlZWlvmnd+/el6nHjaO8vJwhQ4awdOlSu85vr+PpqJwm2tt4xsXF8dhjj7F79242bdqEwWAgNjaW8vLyeq9pljEV7YhRo0aJhx9+2OK1fv36ieeff97q+c8++6zo16+fxWsPPfSQGDNmTIv1sTlwVM6tW7cKQBQWFl6G3rUMgFizZo3Nc9rreNbGHjmdYTyFECInJ0cAIi4urt5zmmNM240l1pjo/T/++KPO+VOmTGHfvn3o9foW62tTaMouhWHDhhEWFsa1117L1q1bW7KbrUJ7HM+m0N7Hs7i4GMAcaG6N5hjTdqPEHI3eB8jOzrZ6vsFgaNYNqM1JY+QMCwvj448/ZtWqVaxevZq+ffty7bXXEh8ffzm6fNloj+PZGJxhPIUQLFiwgPHjxxMVFVXvec0xpm1+dfJS7I3et3W+tdfbGo7I2bdvX/r2vVjte+zYsWRkZPDWW285XS3D9jqejuAM4zlv3jwOHz7Mjh07Gjy3qWPabiwxR6P3AUJDQ62er9Fo6NixY4v1tSk0Rk5rjBkzhpMnTzZ391qV9jiezUV7Gs/HH3+ctWvXsnXrVrp06WLz3OYY03ajxNzc3BgxYgSbNm2yeH3Tpk31lroaO3ZsnfM3btzIyJEj0WrbZn6xxshpjcTERMLCwpq7e61KexzP5qI9jKcQgnnz5rF69Wq2bNlCjx49GrymWcbU8TWH1mPlypVCq9WKzz77TBw7dkzMnz9feHt7i/T0dCGEEM8//7yYPXu2+fzTp08LLy8v8dRTT4ljx46Jzz77TGi1WvHDDz+0lgh24aic7777rlizZo04ceKESEpKEs8//7wAxKpVq1pLBLsoLS0ViYmJIjExUQDinXfeEYmJieLMmTNCCOcZT0flbK/j+cgjjwg/Pz+xbds2kZWVZf6pqKgwn9MSY9qulJgQQvznP/8R3bp1E25ubmL48OEWy7dz5swREydOtDh/27ZtYtiwYcLNzU10795dLFu27DL3uHE4Iucbb7whevXqJTw8PERAQIAYP368WLduXSv02jFMoQSX/syZM0cI4Tzj6aic7XU8rckIiM8//9x8TkuMaZvfAO7ChQsXtmg3c2IuXLhwYQ2XEnPhwkW7xqXEXLhw0a5xKTEXLly0a1xKzIULF+0alxJz4cJFu8alxFy4cNGucSkxFy5ctGtcSsyFCxftGpcSc9FmiYmJYf78+a3dDRdtHJcSc+HCRbvGtXfSRZtk7ty5rFixwuK1tLQ0unfv3jodctFmcSkxF22S4uJipk2bRlRUFC+99BIAnTp1Qq1Wt3LPXLQ12l16ahdXBn5+fri5ueHl5UVoaGhrd8dFG8Y1J+bChYt2jUuJuXDhol3jUmIu2ixubm4YjcbW7oaLNo5Liblos3Tv3p09e/aQnp5OXl4esiy3dpdctEFcSsxFm+Xpp59GrVYzYMAAOnXqxNmzZ1u7Sy7aIK4QCxcuXLRrXJaYCxcu2jUuJebChYt2jUuJuXDhol3jUmIuXLho17iUmAsXLto1LiXmwoWLdo1Liblw4aJd41JiLly4aNe4lJgLFy7aNS4l5sKFi3aNS4m5cOGiXeNSYi5cuGjX/D9kuM32OJTbLwAAAABJRU5ErkJggg==", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "kp = (0.5, 1, 2) # 比例ゲイン\n", "\n", "LS = linestyle_generator()\n", "fig, ax = plt.subplots(figsize=(3, 2.3))\n", "for i in range(len(kp)):\n", " K = tf([0, kp[i]], [0, 1])\n", " Gyr = feedback(P*K, 1)\n", " y,t = step(Gyr, np.arange(0, 2, 0.01))\n", "\n", " pltargs = {'ls': next(LS), 'label': f'$k_P$={kp[i]}'}\n", " ax.plot(t, y*ref, **pltargs)\n", "\n", "ax.axhline(ref, color=\"k\", linewidth=0.5)\n", "plot_set(ax, 't', 'y', 'best')\n", "\n", "ax.set_xlim(0, 2)\n", "ax.set_ylim(0, 50)\n", "\n", "# fig.savefig(\"pcont.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pゲインと周波数特性の関係" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "LS = linestyle_generator()\n", "fig, ax = plt.subplots(2, 1, figsize=(4, 3.5))\n", "for i in range(len(kp)):\n", " K = tf([0, kp[i]], [0, 1])\n", " Gyr = feedback(P*K, 1)\n", " mag, phase, w = bode(Gyr, logspace(-1,2,1000), plot=False)\n", "\n", " pltargs = {'ls': next(LS), 'label': f'$k_P$={kp[i]}'}\n", " ax[0].semilogx(w, mag2db(mag), **pltargs)\n", " ax[1].semilogx(w, np.rad2deg(phase), **pltargs)\n", "\n", "bodeplot_set(ax, 'lower left')\n", "\n", "ax[1].set_ylim(-190,10)\n", "ax[1].set_yticks([-180,-90,0])\n", "\n", "fig.tight_layout()\n", "# fig.savefig(\"pcont_bode.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### PD制御" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Dゲインと応答の関係" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.0, 50.0)" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "kp = 2 #比例ゲイン\n", "kd = (0, 0.1, 0.2) # 微分ゲイン\n", "\n", "LS = linestyle_generator()\n", "fig, ax = plt.subplots(figsize=(3, 2.3))\n", "for i in range(len(kd)):\n", " K = tf([kd[i], kp], [0, 1])\n", " Gyr = feedback(P*K, 1)\n", " y,t = step(Gyr, np.arange(0, 2, 0.01))\n", "\n", " pltargs = {'ls': next(LS), 'label': f'$k_D$={kd[i]}'}\n", " ax.plot(t, y*ref, **pltargs)\n", "\n", "ax.axhline(ref, color=\"k\", linewidth=0.5)\n", "plot_set(ax, 't', 'y', 'best')\n", "\n", "ax.set_xlim(0, 2)\n", "ax.set_ylim(0, 50)\n", "\n", "#fig.savefig(\"pdcont.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Dゲインと周波数特性の関係" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "LS = linestyle_generator()\n", "fig, ax = plt.subplots(2, 1, figsize=(4, 3.5))\n", "\n", "for i in range(len(kd)):\n", " K = tf([kd[i], kp], [0,1])\n", " Gyr = feedback(P*K, 1)\n", " mag, phase, w = bode(Gyr, logspace(-1,2,1000), plot=False)\n", "\n", " pltargs = {'ls': next(LS), 'label': f'$k_D$={kd[i]}'}\n", " ax[0].semilogx(w, mag2db(mag), **pltargs)\n", " ax[1].semilogx(w, np.rad2deg(phase), **pltargs)\n", "\n", "bodeplot_set(ax, 'lower left')\n", "\n", "ax[1].set_ylim(-190,10)\n", "ax[1].set_yticks([-180,-90,0])\n", "\n", "fig.tight_layout()\n", "# fig.savefig(\"pdcont_bode.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### PID制御" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Iゲインと応答の関係" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.0, 50.0)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "kp = 2 # 比例ゲイン\n", "kd = 0.1 # 微分ゲイン\n", "ki = (0, 5, 10) # 積分ゲイン\n", "\n", "LS = linestyle_generator()\n", "fig, ax = plt.subplots(figsize=(3, 2.3))\n", "\n", "for i in range(len(ki)):\n", " K = tf([kd, kp, ki[i]], [1, 0])\n", " Gyr = feedback(P*K, 1)\n", " y, t = step(Gyr, np.arange(0, 2, 0.01))\n", "\n", " pltargs = {'ls': next(LS), 'label': f'$k_I$={ki[i]}'}\n", " ax.plot(t, y*ref, **pltargs)\n", "\n", "ax.axhline(ref, color=\"k\", linewidth=0.5)\n", "plot_set(ax, 't', 'y', 'upper left')\n", "\n", "ax.set_xlim(0, 2)\n", "ax.set_ylim(0,50)\n", "\n", "# fig.savefig(\"pidcont.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Iゲインと周波数特性の関係" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "LS = linestyle_generator()\n", "fig, ax = plt.subplots(2, 1, figsize=(4, 3.5))\n", "\n", "for i in range(len(ki)):\n", " K = tf([kd, kp, ki[i]], [1, 0])\n", " Gyr = feedback(P*K,1)\n", " mag, phase, w = bode(Gyr, logspace(-1,2,1000), plot=False, wrap_phase = True)\n", "\n", " pltargs = {'ls': next(LS), 'label': f'$k_I$={ki[i]}'}\n", " ax[0].semilogx(w, mag2db(mag), **pltargs)\n", " ax[1].semilogx(w, np.rad2deg(phase), **pltargs)\n", "\n", "bodeplot_set(ax, 'best')\n", "\n", "ax[1].set_ylim(-190,10)\n", "ax[1].set_yticks([-180,-90,0])\n", "\n", "fig.tight_layout()\n", "# fig.savefig(\"pidcont_bode.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 練習問題(外乱抑制)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(-0.05, 0.5)" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "LS = linestyle_generator()\n", "fig, ax = plt.subplots(figsize=(3, 2.3))\n", "\n", "for i in range(len(ki)):\n", " K = tf([kd, kp, ki[i]], [1, 0])\n", " Gyd = feedback(P, K)\n", " y, t = step(Gyd, np.arange(0, 2, 0.01))\n", "\n", " pltargs = {'ls': next(LS), 'label': f'$k_I$={ki[i]}'}\n", " ax.plot(t, y, **pltargs)\n", "\n", "plot_set(ax, 't', 'y', 'center right')\n", "ax.set_xlim(0, 2)\n", "ax.set_ylim(-0.05, 0.5)\n", "\n", "# fig.savefig(\"pidcont_dis.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "LS = linestyle_generator()\n", "fig, ax = plt.subplots(2, 1, figsize=(4, 3.5))\n", "\n", "for i in range(len(ki)):\n", " K = tf([kd, kp, ki[i]], [1,0])\n", " Gyd = feedback(P, K)\n", " mag, phase, w = bode(Gyd, logspace(-1,2,1000), plot=False, wrap_phase=True)\n", "\n", " pltargs = {'ls': next(LS), 'label': f'$k_I$={ki[i]}'}\n", " ax[0].semilogx(w, mag2db(mag), **pltargs)\n", " ax[1].semilogx(w, np.rad2deg(phase), **pltargs)\n", "\n", "bodeplot_set(ax, 'best')\n", "\n", "ax[1].set_ylim(-190,100)\n", "ax[1].set_yticks([-180,-90, 0, 90])\n", "\n", "fig.tight_layout()\n", "# fig.savefig(\"pidcont_dis_bode.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2自由度制御" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "from control.matlab import tf, feedback, lsim\n", "\n", "kp, ki, kd = 2, 10, 0.1\n", "K1 = tf([kd, kp, ki], [1, 0])\n", "K2 = tf([kp, ki], [kd, kp, ki]) # PI-D\n", "K3 = tf([0, ki], [kd, kp, ki]) # I-PD\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### PI-D制御" ] }, { "cell_type": "code", "execution_count": 16, "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": [ "Gyz = feedback(P*K1, 1)\n", "\n", "Td = np.arange(0, 2, 0.01)\n", "r = 1*(Td>0)\n", "\n", "z, t, _ = lsim(K2, r, Td, 0)\n", "\n", "fig, ax = plt.subplots(1, 2, figsize=(6, 2.3))\n", "\n", "y, _, _ = lsim(Gyz, r, Td, 0)\n", "ax[0].plot(t, r*ref)\n", "ax[1].plot(t, y*ref, ls='--', label='PID')\n", "\n", "y, _, _ = lsim(Gyz, z, Td, 0)\n", "ax[0].plot(t, z*ref)\n", "ax[1].plot(t, y*ref, label='PI-D')\n", "\n", "plot_set(ax[0], 't', 'r')\n", "ax[0].set_xlim(0, 2)\n", "ax[0].set_ylim(0,50)\n", "\n", "ax[1].axhline(ref, color=\"k\", linewidth=0.5)\n", "plot_set(ax[1], 't', 'y', 'best')\n", "\n", "ax[1].set_xlim(0, 2)\n", "ax[1].set_ylim(0,50)\n", "\n", "fig.tight_layout()\n", "# fig.savefig(\"2deg1.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "制御入力の計算\n", "\n", "PID制御では,$G_{ur}$ がインプロパーになるので,擬似微分を用いて計算する" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tau = 0.0000001 # ローパスフィルタ\n", "Klp = tf([kd, 0], [tau, 1]) # 擬似微分器\n", "Ktau = tf([kp, ki], [1, 0]) + Klp\n", "\n", "Gyz = feedback(P*Ktau, 1)\n", "Guz = Ktau/(1+P*Ktau)\n", "\n", "Td = np.arange(0, 2, 0.01)\n", "r = 1*(Td>0)\n", "\n", "z, t, _ = lsim(K2, r, Td, 0)\n", "\n", "fig, ax = plt.subplots(1, 2, figsize=(6, 2.3))\n", "\n", "u, _, _ = lsim(Guz, r, Td, 0)\n", "ax[0].plot(t, u, ls='--', label='PID')\n", "\n", "u, _, _ = lsim(Guz, z, Td, 0)\n", "ax[0].plot(t, u, label='PI-D')\n", "\n", "y, _, _ = lsim(Gyz, r, Td, 0)\n", "ax[1].plot(t, y*ref, ls='--', label='PID')\n", "\n", "y, _, _ = lsim(Gyz, z, Td, 0)\n", "ax[1].plot(t, y*ref, label='PI-D')\n", "\n", "ax[0].set_xlim(0, 0.5)\n", "ax[1].axhline(ref, color=\"k\", linewidth=0.5)\n", "plot_set(ax[0], 't', 'u', 'best')\n", "plot_set(ax[1], 't', 'y', 'best')\n", "ax[1].set_xlim(0, 2)\n", "ax[1].set_ylim(0,50)\n", "\n", "fig.tight_layout()\n", "# fig.savefig(\"2deg1_u.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### I-PD制御" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Gyz = feedback(P*K1, 1)\n", "\n", "Td = np.arange(0, 2, 0.01)\n", "r = 1*(Td>0)\n", "\n", "z, t, _ = lsim(K3, r, Td, 0)\n", "\n", "fig, ax = plt.subplots(1, 2, figsize=(6, 2.3))\n", "\n", "y, _, _ = lsim(Gyz, r, Td, 0)\n", "ax[0].plot(t, r*ref)\n", "ax[1].plot(t, y*ref, ls='--', label='PID')\n", "\n", "y, _, _ = lsim(Gyz, z, Td, 0)\n", "ax[0].plot(t, z*ref)\n", "ax[1].plot(t, y*ref, label='I-PD')\n", "\n", "plot_set(ax[0], 't', 'r')\n", "ax[0].set_xlim(0, 2)\n", "ax[0].set_ylim(0,50)\n", "\n", "ax[1].axhline(ref, linewidth=0.5)\n", "plot_set(ax[1], 't', 'y', 'best')\n", "\n", "ax[1].set_xlim(0, 2)\n", "ax[1].set_ylim(0,50)\n", "\n", "fig.tight_layout()\n", "# fig.savefig(\"2deg2.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tau = 0.0000001 # ローパスフィルタ\n", "Klp = tf([kd, 0], [tau, 1]) # 擬似微分器\n", "Ktau = tf([kp, ki], [1, 0]) + Klp\n", "\n", "Gyz = feedback(P*Ktau, 1)\n", "Guz = Ktau/(1+P*Ktau)\n", "\n", "Td = np.arange(0, 2, 0.01)\n", "r = 1*(Td>0)\n", "\n", "z, t, _ = lsim(K3, r, Td, 0)\n", "\n", "fig, ax = plt.subplots(1, 2, figsize=(6, 2.3))\n", "\n", "u, _, _ = lsim(Guz, r, Td, 0)\n", "ax[0].plot(t, u, ls='--', label='PID')\n", "\n", "u, _, _ = lsim(Guz, z, Td, 0)\n", "ax[0].plot(t, u, label='I-PD')\n", "\n", "y, _, _ = lsim(Gyz, r, Td, 0)\n", "ax[1].plot(t, y*ref, ls='--', label='PID')\n", "\n", "y, _, _ = lsim(Gyz, z, Td, 0)\n", "ax[1].plot(t, y*ref, label='I-PD')\n", "\n", "ax[0].set_xlim(0, 0.5)\n", "\n", "ax[1].axhline(ref, color=\"k\", linewidth=0.5)\n", "plot_set(ax[0], 't', 'u', 'best')\n", "plot_set(ax[1], 't', 'y', 'best')\n", "ax[1].set_xlim(0, 2)\n", "ax[1].set_ylim(0,50)\n", "\n", "\n", "fig.tight_layout()\n", "# fig.savefig(\"2deg2_u.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 限界感度法" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 無駄時間要素" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "from control.matlab import tf, pade, rlocus, poles, feedback, step\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[kg*m^2/s]\n", "J = 1.0e-2 # 慣性モーメント[kg*m^2]\n", "\n", "P = tf( [0,1], [J, mu, M*g*l] )\n", "\n", "ref = 30 # 目標角度 [deg]\n" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-400. +0.j -0.75+9.87610753j -0.75-9.87610753j]\n" ] } ], "source": [ "# num_delay, den_delay = pade( 0.005, 5)\n", "num_delay, den_delay = pade( 0.005, 1) # 1次のパデ近似\n", "Pdelay = P * tf(num_delay, den_delay)\n", "Pdelay\n", "print(poles(Pdelay))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "根軌跡を描くと,Pゲインを大きくすることで不安定になることがわかる" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "kvect = np.arange(0, 5, 0.001)\n", "rlist, klist = rlocus(Pdelay, kvect, plot=False)\n", "fig, ax = plt.subplots(figsize=(3,3))\n", "\n", "ax.plot(rlist.real, rlist.imag)\n", "ax.set_xlim(-3, 1)\n", "ax.grid(ls=':')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "無駄時間要素がない場合は,制御対象は2次遅れ系なので,Pゲインを大きくしても不安定にならない" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rlist, klist = rlocus(P, kvect, plot=False)\n", "fig, ax = plt.subplots(figsize=(3,3))\n", "\n", "ax.plot(rlist.real, rlist.imag)\n", "ax.set_xlim(-3, 1)\n", "ax.grid(ls=':')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### チューニング" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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hTqnaoijGtI3qdG5gDIQAhTkelPg9k3SaU6bev47IYInXSd/W65SorSgKiouLwfN8Sp1kWdZIrD7y+3qdZpeofXd2YNyRfkqmEyWM+nL/pGdvdmksiSmKgpKSkkm6Wu2nZDqdigT1F1QWTNJJu0/9Y6b6ycyzN6NIrLOzE9/73vfw2muvITc3+QZ/8aveCSFpV8I/9NBDWLZsGVasWIEVK1bgZz/7GQ4dOoQTJ04AANra2tDR0QEAaG5uRmdnp2b1FAuqpbVv3z7096uLmffs2YO6Ih8AYNfeZi0mt2vXLoRCIUiShF27dkGSJIRCIezatQsAMDo6isbGRgDA0NAQ9uzZAwDo7+/Hvn37AADd3d2aZdnZ2Ynm5mYAqiXafFTdJaJEEHHo0CEAKkG3t7fj7bffRhGvynpucDyhTgDQ1NSE7u7uhDoNDQ0BABobGw3rdPS8uoRnXkU+hoeHJ+lELYymz44n1KmtrQ0AcOLEiRidjh49CgAx/dTa2opdu3ZBFMWUOh0/14OxsAwO0O6JXicxoE56ZwcuOdJPyXT6oke9v8pQz6Rnj96nY+cvAgA++ugjvP322xBFkUk/JdPpaJe63OiKyvxJOklD6n364sKgqX4y8+w5kn0lWcKOHTsIACIIgvYPAOE4jgiCQE6ePEkAkAMHDsR872tf+xp56KGHEl6ztbWVACDbt28nra2tpLm5mTQ3N5MLFy4QSZKIJEmEEEJEUYxpy7JM7vxvH5D6zTvJvuO9Ma8TQkg4HCZP/LqN1G/eSf5l9zGiKIr2uqIoRFGUSW1CSExbluWYtiiKKduSJJHv/eoAqd+8k/x4zxeavJIkEVEUyfDwMPmHPxwm9Zt3kmf+z5GEOqVqh8PhmLZRnV758DSp37yTfOeX+xPq9D/+7QtSv3kneeKNAwl10rf1OiVqh8NhEggEiKIoKXXa39FP6jfvJKu2/t+EOv38j6dI/ead5P95tdmRfkqk03goTOY9tZPUb95JeobGJj17Oz+7QOo37yT3/+SjlLpa7adkOm34l32kfvNOsvtIzySd9h3rIfWbd5I1/3WPqX4y8+zt37+fACCtra2EFbK2PfWdd96Jw4cPx7z2N3/zN1i8eDE2b96MBQsWoKamBrt379bO4wuHw9i7dy+ee+65lNduaGjA0qVLk76vP0qdtnsjWaK6iJmv/4zX60VtJNZz8ZKoWYJerzfmM/FtjuO0Ns/zmiltpC0IAnpH1OB4XUmeFiuh/xcVFaG+XA3Eng+MJ9QpVTud7MnadLuW2mJ/Qtk1F3coFPO6Xnajba/Xi5KSkrQ69Yyo1lddiV/7Lb3s8yvVeqjzg0FH+imR7P1jIghR44RVRX7tmaGyU7ebxumS6Wq1n5LpRPfFm1U6uf/mRe5TVyAEno993lK1zTx7M2o/scLCQjQ0NMT8y8/PR3l5ORoaGrSasa1bt2LHjh1ob2/Hww8/jLy8PDzwwAMpr23WZL00IWF0Qv1OTVFi17a6WH29JwN7LlFQwqgpjpVJFEW89dZbqMz3RmTK3JpOWhJQW5z4PlESO88giE71TJex644kGuLvkyZTJM7JqvTDCChZ1BbnJhy41J1UM9CyYV3tIBiWERhXr19XMnk//9riXAg8h7CsoHfUmefcCXdySh8U8uSTTyIYDOKRRx5BIBDAypUr0djYiMLCwpTfM5vh6YkMzMIcD/JzEt8SSm6Z2DgOUGN/yQjD4/Fg7dq1OH5Rfb83g4vA6b2qLUlMGPQ+9Y1OQFFITH2UWVA99TN6IlyIWH2JBiYArZwhKKrZ5fKCHMsyGQXN4NJsbTyK/V4U5ngwOiHhfGAcV1QWGNKVhUwFOR4U5U7+HY/Ao64kF52DQXQOBjXvgyVm/KaIH3zwAV588UXtb47jsGXLFnR3dyMUCmHv3r2OnM1Hiak6yUwORAdnT4YIYyQoIRip/6pOYB16PB7N8rh4aQJyhg7E6B6JWhiJUFmYA44DJIVggEE5ipFBTS2xZDLleASU56uJmUxZ0pRYk5E9x3GYTV3vSImMkwSmyhQh1pLE1iGQvXIUO5hSJMYKZs+2S+ciAUB1sTp791+acHRZBgUdbKV5Xm2nAQqakSrO4cFz6oEP/QyKS9NBUYhG4jVJZmmvwKMiYunYtVr1mbdUiPZfcsuhOsOWdHcaSwwAaooi92k4ZFhXO4iSWHKZZpdEwgEO1R46ce7kjCQxsyarZokliYcBQEV+Djw8B4WASTV6OkTjPJMfOI/Hgw0bNiA3x4fKQnUgZMJCHBgLQ5QJOA6oKkzukrGyWqme6SyUdJYYEI2X9QxnJn6YzsXVy9Q7MmFYVzvoMiCT07HfGe9OZguadZGCxHie0wZuJggjKlNisqAztkYYGbAwqEyVBTnwCskfnWqGMqWzTERZQV9ks8pkrhtrmYxAC+ybkMnpHSy0zGQqYqUxzQwmsOxiRpKYWZO1x0BMTP9+RkhMy0xOfuAkSUJjYyMkScqom2TE4gGAmmJ27iTVMxl6R0IgBPAKHCry01uHmUqCUBc3tTsZ7TsjutqXKRoTSypTpO+cInsn3MkpnZ20CrMmuRFLTP9+Jq2eRITh9Xpx7733qjJlhVgN3iebMun1TIbu4ahMqTKhTg9OPcYmJAwH1VKGlJaYru+M6GoXWrIhi7FDJ9zlGWmJma0F0gZnGhLLpEuSSiZCCEZG1DWcmZSp2yDZVzGSSa9nMhidgDJpsVK9833CpG2d9NBbYkZ0tQO1ZMdA7DAiU/+lMMIS+wSWE/rNSBIzY7LKCsFAJFBflST+REEtkL4MFJfSQ0kqE8gkSRI+/PBDSJKU0fo1KlOVQYuVhTtJ9bQtU3Hm7hN9PlIlioDofRoYC2MsFE6rqx2MTkgIiUpaucryffBF4p19DhS8utlJgzBjsgbGw6AlVmWRWqJkoKUDmShn0EgsQWGm1+vF3XffDa/XG5PhyphMKTKTADsXV69nMvSluE8xMkUGbmBcdHz/NZq9rkhzn0ryvNoWS4GgnFZXO6DEWpjrmVSyowfHcdpk7gThu+6kQdDtP4yAElJpnjdlxg0AKgpUknP66DZFVyiaiDAURcHg4CAURckOsaYZnHSmHwlJtghDr6ddmYr9XuRECMNpS5pm9lKVoQAqYVRHCKN7OJhWV1syjRqTCdCFTRwoR3FCP5fERlWyqDCwFCVKGM5ujBgYD2sV+ImsQ1mW0dLSAlmWNWIdGhcdPyCWEmU6q6co16O5JHYIX69nMlCrxwhhaFarQ+sC42VKR6xA1ELsDoyn1dWWTAbJXi+TE3FWl8QMwozJ2m/igaOfGRxzdpkPJcmyfF9C69Dr9WLdunXwer0ozfNBiGTlBhwkVzmNdagHx3HaZ+xYiHo9k8HM4NQmIYct6YsjlFhTx8SAqNXTPy6l1dUO+izI5LqTWYQVd9KIJUatIoWo1pJToAOTWlnxUBQFfX19kZ0yOU0uJ11Kah1yXPrYIRCV3Y7VqtczGcyRmPP3CYjG6Yy4bvS5uzgaSqurPZmMu5Os6vwSwbXEDMLMjbpogsS8Ao/SPHWmdHIgpCNWRVHQ3t6u6akNBAdlomRRlpfYOowHi1hdvJ7xkBWCwTHzlpjTMU0zxKpZrKMTKXW1C41Y02TgAWcTWC6JGYQpd5LGxArTWxeA3iVx3hJLNgg8Hg/uuOMOTU/NwnBwcJpxu1WZ7Ltu8XrGY2BsAgoBeA4oT1GtT0Flv+hwTFOzegwQBo0vDoyFU+pqWyYT7qSTz7jrThqEU+6k/nPZtsS6uro0PSszkHAwY10A0UnBriWm1zMedGCWF+RoccGUMmWg78KSom08mC4BAkTv08XRiZS62oUZd5JFPDMZXEvMIKyQmJEHDojW/jg5ENJltxRFwalTp6LuZCZkGrVG9nZc3Hg9J8lktu8yOAF5eA6leUZih9H7lEpXu7howZ0cHA8z33bKJTGDsJKdND44IzNnFgnD4/Hgtttum+xOZkAmo5ZYNNZj3TqM19O+TJm7TxUFOYZ2tdUIYyyMW2+91RF3KyTKGAmpKwEqDbiTZfk+8BxACJifs+q6kwZhlO0VhWhlCVMpJkbdwlSW2NmzZycF9jNiHWbQ6onXc5JMZl1cXd85tUbRrEzlkQlIlAnavzjtiKVCZfJ5+ITbUsdD4DmU5TuTLHItMYMweqOGgyKkSL2XkcAwoI8/Oe+SlCcpZYiPFWWCWCnZlycp+4gHK3cyVZxIm4BMEmtQlDEWdqaodGAsdXlMPHI8Aor9asb76JkLjgxyWt9Xke8zfNqQU6tTXBIzCKMmK+3colyPtoYtHajFRh9W1iCEIDCWenB6PB6sXr1a505mkFgNEgYl+1EbS4/i9YwH7YNkZB+P/BwP8nzqukGnMrn9GtkbP4yEEsbsK692xN2iGxykW8upRzS477qTWYHRpRvU3zdSvElBg7WBMWeO1hoJSpp1WJqfuHpblmWcPHlS05MS66BuuRJr0HtllDCK/NGlR1YPDInXM6lMBq0ewHnCN3uf9DIdOXnOkWVHmhVtQSbW98ndxcIgjMY7rJAY/SzrgCdFf8S6KMzxIMeTeLcBQggCgYCmJyVWQqBtxscShBBthYLRe8VxnEYuVq2eeD3joV+eZRROJ0EGNIvVhEwRq6drYNSRWB19psxYh/oiXJZw9xMzCKMma5TEjHduaWTABEUZQQfiKppMKQaBx+PB8uXLNT29QjRgO+iAmzsSkiDKyRekJwP9rNUlWvF6xmNwLJoJNIporM6ZSWhAs8RMEEZEpryyaofcSSsWqzNZeNedNAjj7mRkKU0Sty0RCnM88ApqcNSJ9ZMDBqwLWZZx7NixGD2jFiJ7S4xaFwU5qfeiioddqzWRnhSEEEP3Kh50IAecsqRtEMbJrj6H3MkI2ZsgVtednCYYsGCJcVy0iNEJl9JoTCUYDMb8Xeqgm2vF7QbA5D7F60mhjx1aiWk6FQ4YMFl3CESfP6firNaINbIcyuElWiyQVRJ76aWXcP3116OoqAhFRUVYtWoV3nnnHe19Qgi2bNmCuro6+P1+rFmzBkeOHEl7XaNn21kJwgL23aTUMlHrMLlMgiBgyZIlMXqWOyjTgEUSs2uJJdIzKlN2rMNUIIRYSjZQT0D25DpyLqPZgm5VJpqFZ3ufZty5k7Nnz8Y//dM/Yf/+/di/fz/uuOMO3HvvvRpRPf/883jhhRewbds2tLS0oKamBnfddRdGR0dTXtfJ7CTg7GxuxDqUZRnt7e0xejoqk1aPlVmyT6SnJpMFsmAhUypYtQ5pX/cELjnjTloi1qjbzTIYP+PcyXvuuQcbNmzAokWLsGjRIvzjP/4jCgoK8Mknn4AQghdffBFPP/007r//fjQ0NGD79u0YHx/H66+/zuT3rZKYvoNZIyqTuc3xnLQwjFiHieCki2slHqaXyQk3Scss5ybPLCcC1WF4gn0hqKJErUMrlpikEG3J0lTFlImJybKMN954A2NjY1i1ahU6OjrQ09ODtWvXap/JycnB7bffjqamppTXOnbsGA4cOICWlha0tLSgu7sbsixrs4AkSZBlWevckjyP9jqtKNa3RVGMadM9xS6OqkdtEUIgimJMG0BMW1GUmDY91Sa+TVPaJX6v9rpedvp/Q0NDzN/FflWHwFg4qR6pdKKzbbwesQH0HFM6lWuEMaHJmkynRG1CCK6++moIgjBJj/7IrgxleV5TOhXnRA7mGA/b6ie9HrR9cUSN35Xn+5LqRJ89fX9QwhgLK1DAWe6nRM/ecFDUagdL83yGdfJwBPmRwmCqlxmdkrWdcCc54tQiMoM4fPgwVq1ahVAohIKCArz++uvYsGEDmpqa8KUvfQldXV2oq6vTPv+3f/u3OHv2LN57771J1zpw4ACWLVs26fVFixahpqYGgiCgoKAAQ0ND8Hq9+LRzDAohWDarAKVF+RgYGEB+fj5yc3PR39+PwsJC5OTkoK+vD6WlpfB6vejt7cUI/Dg7GERZDnBDfQU4jkNfXx+qqqpACMHFixdRU1MDSZIwMDCA6upqiKKIQCCAqqoqTExMYHR0FBUVFQiFQhgbG0N5eTmCwSAOnB9FUCJYXJmLAg9BSUkJLl1S3Yzi4mKMjo5qDywATaeTFwZwZlhCeUEO6vMV+P1++P1+wzqVl5fD4/Ggp6cHlZWVMToduTCC3tEJLKwqxKxin2Gd+NxCtJ4LIFfgcMuiKoyNjUEUxYQ6AUBhYSGGh4dj+kmWZZSVlSEQCMToNCgKOBuYQFkuh2vrig3rdL6nD18Mc+A5DteUKJb7KRgMoqysLEanc31D+GJgAsV+LxaXe5Pq5PV6kZ+fj8HBQfj9fuTm+vFvx3oBALdeWYHR4YClfkr07BWUlOPj0wMQOODLi6tN6dTer662uLrCh1mVpSn7KV6nZM9eMBjEhx9+iNbWVixdupQJh2T9BPCrrroKBw8exNDQEN58801s3LgRe/fu1d6PX+tFCEm7/uvVV1/Fddddp80Os2fPRlVVFQBos/p4WMb1z/xfAMCu/3wXCv0+SJIEnufB83xMWxRFCIKgtX/56Xk8s/NzrL+2Gj/5a5U0JUnSamAkSYLX6wUhRGsrigJZlrW2oijweDyT2qv+aQ96RybwyndX4bpZRfB4PJoegiBoM+Dp06exYMECCIIAQRDwXvsFfPu1Nlw/uxi/+87NCfVIpZPH4wHHcVpbr9Nfv/IpPjo5gP/8FzfgT5bMMqzTqf4g1r24D6V5Xvzh/1sLWZZBCEmoU6J2OBzGyZMncdVVV4EQEqPHf3n7GLZ/fBbfuW0+nvx3iw3rNDIewg3/ZQ8AoPE/3oGSAr+lfqJtvU6/bOrAf/rD51h7TTVe+saShDpJkgSO47Q21WnJM40IjIv40eNfwqLqAkv9lOjZa+0cwV+9/Anml+fhD//hy6Z0+tOffoLPzg9j618vxbqG2qT9lEynRO3W1lasWLEiDSuYQ9ZJzOfz4corrwQA3HTTTWhpacG//Mu/YPPmzQCAnp4e1NbWap/v6+tDdXV1ymted911KVne4/FgeER1kXI8PAoipzTrC/H0bf3hDV6vVwuQDgUljVDjPwOoBEzbtDNTtTmO09LsFYW5mgx6E5yS1uLFi2N0qihUj6YfHAsn1SOVTqnatPasLLKA2KhO1E0airg08Xqka/t8PlxzzTWIh8fjweB49D7R3zWiU1FeLnI8PCYkBaNhghKY7yd9Wy9vIKi6Y+UFvqQ6JeuP8oIcBMZFDAUly/2kb1OdtHhYpALfjE76/ovXw4hOidozLjuZCIQQTExMYP78+aipqcHu3bu198LhMPbu3YvVq1envIaRU5QHdOUVRlf2UziV4RoLywhHNqFLlUmSJAktLS0xejqZbAhYTICURGKHVpdDJdIzXiaz2UmO47RYHeuEg9VEEYCYOKsTMhnZoHGSTA6UWThxwnlWLbEf/OAHWL9+PebMmYPR0VG88cYb+OCDD/Duu++C4zhs2rQJW7duxcKFC7Fw4UJs3boVeXl5eOCBB1Je1wgp0UFQaumBc2YQUJlyPDzyfMm7huM4lJaWxugZDQ7LCImyqdqpVCCEYHDc2kCgy6FGQhIGx8KmB3ciPSnsDs4LwyH2/WfxPgHOTYxWJyAgWns4yDCTa9ZgMIKsklhvby8efPBBdHd3o7i4GNdffz3effdd3HXXXQCAJ598EsFgEI888ggCgQBWrlyJxsZGFBYWpryuEZOV1QNnJEZnFEZnckEQNBecoijXA4HnICsEQ+MiaorZkNh4WEZYUgzJlQjlBTkaiZlFIj0pzC5I18OpchQ7lhhdnD0UZGupWC1UVr8T3aaaFZxwJ7NKYq+88krK9zmOw5YtW7BlyxZT1zVisg4ysMREmeDShITCXDYHntKBWZKGWCVJQnNzM1asWKHFGuhyqP5LExgYm9BOu2Ylk8/Da3txmUFpnhcdsEYYifQEYivj7UxCjlliFp6pksgC/n7G7qQdsnfC7XbCnZxyMTEWoAHKVBiKBIZpLMIM/D4B/oi7xrKDow9capl4nsesWbMm6Um/x3INHr1WWZ752KEqU2RdoIXZPJmeQVHGRMQ6tEIYGokxdt2o21VmgVipJUZPSmImE4OYGMtn3MjYNH1N5lecAjByo+y4k4AzszkljHSWGM/zqK+vT0Bi7AfnoGYdWrM2KbFauU/J9KTX8gm8VpBpSqY89rEeIHqvrFg9NHvImsS0idFkAgRw5hl3ScwgjJisdiwxILrrKstArPbAGXAn9+3bN0lPJzKUQzYGJmBvNk+mJyX70nyvNeuwgD3ZB8MyQqJ167AoRyXjAcZb39iyDl13MnswwvZ2YmKAPkPJ0HXTrMP07uQVV1wxSU8qE8uUuN37VG6DWJPpaduKdiC7TAnRqnVILbFB1u6knQRIhOzHIxlvFnAtMYPIhDtpZ3AmlUmzMNK7k4ljYk7IZIxYk8EOsSbT006wWv89R+6TReuwvCBXuw6rlYB2rUP9BqCsJkaXxAzCnDtp001ywJ1MJ5MkSdizZ88kPTXr0IGYmBV3BLBX/5RMT7vWoRN7ZdkJoAPQFqaz3DViUJdZtmId6jcAZUX4rjtpEOnYXl/AaTlgzbhzAeODk+d5NDQ0TNLTia2XaaDZLmFYDewn0lMr4LRJrMNBEZLMZvsbu9ahP8eLPG9khw1G/aePh1mtZWRN+K4lZhDpblRQtFfACTiTfjaabOB5HlVVVUljYmwzptnL4ibTc9BGPRagZn/pmGaVDbRrHfI8jzK6JTQrErN5nwB9/7FJOEwJEnv44Yexb98+5oKwRDqTlT64PsFaASfAfpmImeU9oijivffe0/aOipeJacDabgIk33pwOJmeWuzQohUt8BxK/Gyzy9paTov3SRRFeCR13y5W/WdXJoD9ATRTwp0cHR3F2rVrtbWMXV1dzIWyi3RsTzu3JM9aEBZgnwnUW4fpCEMQBCxfvnzSEo5SHbGyCg5T69Cq62bndKhketpZ3kPBeofXAZsWqyAImF1ZAoCdOzlgcwIC9GUWM8gSe/PNN9HV1YXHHnsMv/nNbzBv3jysX78ev/3tbyfNmNlCWhKzGb/Qf5dZ/MJEASfP8ygrK5ucnYxbDmUXLGKH+uCwWcJIpqfdzDLA/mAVu88Uz/OoKskHwG5ijMYOrS+L09ZPzrSYWHl5Ob73ve+hra0Nzc3NuPLKK/Hggw+irq4O3//+93HixAnWcpqCUXfS6sAEosWuQ7rtf+1gSCdTOutQFEW8/fbbkyYN/XIoFkuP7C7+prDqeifTk8UkxNqStut2i6KI4d6uyLXYWD1sYmLqc87KYp0S7qQe3d3daGxsRGNjIwRBwIYNG3DkyBFcc801+NGPfsRKRtNIt1LebrBa/11ColXtdmDGRfJ4PLj11lsTnqYczSbZHwh2F3/Hy2R2Nk+kJyHEcD1dKrDO5OrXmFqBx+NBw8J5ANjFn9jExKyvfU2EKbEpoiiKePPNN/HVr34V9fX1+M1vfoPvf//76O7uxvbt29HY2Ihf/vKXeOaZZ5gLaxTpLBk7uw1QeAUehZGdB1hkuAIm3DaO41BUVJRQz1IbaxUnyWRz8XdUJmsklkhP/caRVgkDYJ/JjVo91t3uuvLCiExsLDEWMTHWJRZTYj+x2tpaKIqCr3/962hubsaNN9446TPr1q1DSUkJA/GsIZ3JanfdJEVpng+jIYmJJWZm8zpRFLFr1y5s2LAhZmtiKhPAhljtxsMorK7BS6QnvU+5Xh7+LFiHiaBah/ZcXFEUcaL9IACBeXbSDtlTi5WVTFNiZ9cf/ehH+PM//3Pk5ibfr6q0tBQdHR22BLODdCar3epqitJ8H84NjrOxesaN7WABqK7H2rVrU7qTLIjV7uJvipI8azGxRHoOMhiYAFsSG52IHppr9ZnyeDy440sr8D+Pt7IL7NvYwYKC6jM0rhYGewR7gfkp4U4++OCDKQlsOoBFdkv9fiS4z9CdNDo4ExGYKhO7wWk3WE1Bs2NWkg3xekatQ/sTEMAm1kMtnjyfYGtb8MoidVyxeJ4UhWgToz2328u8MJg1ZmTFfrqj0jV30mL8gqLMooWRCGYyppIkYdeuXQlNc5bupN3F35pMFgkjkZ523TYKlsvGWFj2kiRh/0fqUYWXJiRMSPZ2jRgJRbPmdgjfI/AoZlgYnG5sWsGMJDGj7qTd2Zx+n8WCazOD0+PxYMOGDUncydjYkR3YXfwdlcl6djJeT2bWIcMF/CyKbz0eD+7/6noIfKQw2GaGkspUmOOBz2NvmLPcumhKuJMzAUPMBmfEnWSQEjfr4iYLkDIlVpuLvylKbViskzZE1PqOjXUYEhUEw/asA1bEqiiyZonbJQwW8TAKJ48DZIEZSWKpTNYJScZY5KG1GxNzwhIzMhAkSUJjY2NCImMZ2GdRTwfo3Mkx0dRyqER6siLWfJ8AXyRIbbf/KGHYqceiumrxQ5sy0eJUu30HsD1/0nUnDSJZ0BuIxsMEntPqvKwimrlhaPUYsDC8Xi/uvffeSeUVeplYFEyyC+yr3w/LijaBGEEiPVnFxDiOi24xbnNwDmoL0m3UHUZ0ZbXMh8WqBgqW8cNUY9MqZiSJpZrttaJSvxc8b6/wLrrPvj3CCIkygpEdHowQBiEEIyMjCfXUlkMxWARud/E3hd8nINfCXlmJ9GRVHqO/hm3C0IjVuotLdWWVNaXEyoTEGJ5JwGpjAj1mJImlMlmjJwrZPyuS1a6X9IH18BwKc9LPVJIk4cMPP0yZnZQUglEbi8BZLP7Ww0omN5GeTC0MVoTBYAUI1bXEr/a/3bWKtOqfpSXGIrA/49zJZ599FsuXL0dhYSGqqqpw33334fjx4zGfIYRgy5YtqKurg9/vx5o1a3DkyJGU103tTrIfBENBEYqNReD6bKmRZRlerxd33313Qncy16tfBG79oWO1+JvCytKjRHqycN3syJQILGKHVNcKutc+I0uMxX1iWRg849zJvXv34tFHH8Unn3yC3bt3Q5IkrF27FmNjY9pnnn/+ebzwwgvYtm0bWlpaUFNTg7vuugujo6NJr6soybccZlUsqV5DHVyyQjBqY190s8ugFEXB4OBgUj2jFoZ1N5fV4m8KKxnKeD0JIdokZLfGD2AX62FRYkF1LcnzxFzTukyqJWYn2UDBksRSjU2ryCqJvfvuu3j44Ydx7bXX4oYbbsDPf/5znDt3Dq2trQDUh/bFF1/E008/jfvvvx8NDQ3Yvn07xsfH8frrrye9bqobxWrdJADkeARtgNuZOc0G0GVZRktLS1LTnEXAWr97KotFu1Grxzixxus5ErK/vCehTHYzgQx2i6C6stpxllVSRn8NFoH9GUdi8RgeHgYAlJWVAQA6OjrQ09ODtWvXap/JycnB7bffjqampqTXSWWysioboGBxwpBmXRgkVq/Xi3Xr1iV0J/Uy2RkIA1pMJcfyNfQoy4smHIwiXk86MPNtLu+Jl8lOYakkKxgO2i/7oLpWFvkB2M8u2zlvMh7ljMgemIHupB6EEDzxxBO45ZZb0NDQAADo6ekBAFRXV8d8trq6WnsvEdrb23HgwAG0tLSgpaUF3d3dkGUZsixPClZLkqTNDsnaoijGtGmGRRRFjXj6R4IghIAQom3ip28rihLTpsFqRVHQPxoCoLo39HVZlmPa1BqRZRmiKKKvrw+iKGqvS5KktWlweHAsbEknQohuobXXkk7x7eh20BMJdUrUDofD6Onp0a4xcEm9T6V5Pks6UdlpuyhX0O6TFZ1UfVSZOA4o9PFpddL3k152qmu07yYs6URlpycdlef7TOsU/+zR+xQSFYwGJ/dfMp0StWe0JfbYY4/h0KFD+NWvfjXpvXh3hhCS0sXZuHEjli1bhhUrVmDFihX42c9+hkOHDuHEiROaJSaPq1Zfc3MzOjs7AQBNTU3o7u4GAOzbtw/9/f0AgD179mBoaAgA0NjYqMXjdu3aheLIQ7f3k/2QJAmhUAi7du0CoJ5H0NjYCAAYGhrCnj17AAD9/f3aYSvd3d04cuocAECQQ2hubgagWqFtbW0AgBMnTuDQoUMAgKNHj+Lo0aNob2/H4cOHtV1029ratJ1DwqMBAKolZkWnUCikEWtJnteSTtRS7uzsRHNzs2Ydnu7qS6oTAK2fqE4HDx6Eoihobm7GF2cuAAB8ZMKSTvq1mKFQKLL1DdA/GrSkEwAc/kK958V+LzpOnzKkE+0n/bP38ccf47PPPkNJbnQCIoSY1mnXrl0IibqC7nyfaZ3in71Tx45oS5daPjOuU6JnzwkSA5kCeOyxx8js2bPJ6dOnY14/deoUAUAOHDgQ8/rXvvY18tBDD026TmtrKwFAfvGLX5DW1lbS3NxMmpubyYULF4gkSUSSJPK1bX8k9Zt3kvcOXyCEECKKIpFlOWU7HA7HtBVF0dqPv95K6jfvJD99/wuiKApRFIWEw2FCCIlpy7Ic0xZFUWs/+tp+Ur95J3l570ntdUmSYtqSJKVsi6Kotf/be0dJ/ead5P/93SFLOimKQp57R73Gf/r9YUs6xbffOthF6jfvJH/x048s6SSKIvnVp2dI/ead5KFXPrGkE5WdttvO9JP6zTvJ8h/utqQTIYT88YteUr95J/nyP79vSad4PcYmRFK/eSep37yTjIZE0zqFw2FyYWic1G/eSa78wdtEURTTOiV69lb+4/8l9Zt3kgNnBkzrpG/TMdra2kpYgb2Dao5A8fjjj2PHjh344IMPMH/+/Jj358+fj5qaGuzevRtLliwBoJrde/fuxXPPPZf0uldffTWWLl2a8D1ty95CNZWt99GTtfWxp/g2tTBGJmTNOqSf4ThOa/M8rx2SEN8eCqqme0Vhjva7+oWy8W1FUdDV1YXa2lrtOnp5KyK6BcbClnQCopnNsnxfjB5GdYpv00zgcETXVPpR8DyP7u5u1NbWwuPxIDCufre8ICeh3ul0im9XFedFdI3eJzM6AcBwSLV4yvJ8hnRK1h9U15qaGuR4eExICgJjYcwpyzOt38ClcQCq281xHDiOM6VTItnL8n3oGQlhODS5/4yMIdqece7ko48+itdeew2vv/46CgsL0dPTg56eHgSD6vl7HMdh06ZN2Lp1K3bs2IH29nY8/PDDyMvLwwMPPJD0uqluFKtlKxRWsm7xMFuFrigKTp06lVRPq5sQ6sFif3Y9rGybHa+n2T3X0srE4HSoAUbPE9WVEGJ5J1wKFiUf8WBVGOwEiWXVEnvppZcAAGvWrIl5/ec//zkefvhhAMCTTz6JYDCIRx55BIFAACtXrkRjYyMKCwuTXjdZBiQsKVoVO+uBYGf9pNkqdI/Hg9tuuy3p+9H6JxvEyqAKPUamuDMxjZRtxOupDU4GOzMA0dOhgqKMwJiIwlzzZTesJkW9rqX5PlwYDlnOBrJc1UDB6pzOGZedJJGMSvw/SmCAao1t2bIF3d3dCIVC2Lt3r5a9TIZkbE+JhsXibwq7a90IIaYPXlUUBWfPnk2qp2b1MKhdy6bVE68na5kA+/uKsbJ69LpqMlkkDEo0LEmM1TmdM86ddArJbtSgrh7L7uJvilKbtUZWlvfQmFhSEtNZh8TigtsAY6sndjmUsXsVryfLAk4Ku4XBLEmM6mq3zs8Jd5LV7iguiRlEMpOV5Q4IFKweuBwTy3s8Hg9Wr16ddp99q7EedX9256weo/cqXs9BxnE6wP5OFqwIQ6+r3WU+LAtdKbSdLCweJ9c5OI62cwGMTrgkZgjJluM4M5PHxnrMQh+/MLq8R5ZlnDx5Mqme+pPArRw6MRwUQdezs1hjSmHWzY3X08zGkUZhN2DN6pnS62pbpkvsyd5unPV/7+/En/ykCb/69CwzmShmJIklIxMW5/DFg7qTokxMbfhHYcU6JIQgEAikJM1SG9scU5IpzLW/P3usTObW4On11CdlpqIlZlcmva52d9dw0u22erJ8f2SlBi0OZ4kZSWLJ3Uk2Wxvr4fcKyPGY3/CPwkomyePxYPny5SkzPXYWN7MuQ9FkMkkYej3pfeI5oMhCFjEZ7Fg9RL88i4E7SXW1u3+XE+5keWQNrdWdUfrpdtkF7I97nJEklszNihIGu0HAcZytuJi2F7qJB06WZRw7dizlBnN2Sj+ciB0C5glDr6deJlZJGcDenmJjYRlhmc2ea3pdrdTU6RG1Dtks3gdidwyWLeydR9fMFjGqCtBjRpJYMjg1OKNxMfOzlNVDJmhBcDqZrGSTnAigA9bOxKR6OpFxA+zFemjsKdfLI89nf3BSXe3sByfrkjIs9lyjoH2nEGi7dpgBtcRcd9Igkp1t50QRIKAvs7Bi9ZjfgVMQBCxZsiTlGX5Wtr7RZGJc6KrJZLKcQa+nE3Ee9XrWa+pYncsJxOpaprOizVo9w0ERNFTKcrL2CrxmRVmxEKklVpbvupOGkC47yZzEbLgkVg6ZkGUZ7e3tKd1JmlW0csyWUzGxEpOxHr2eTlmHds5U1PaxZ1BLp9eVPk8KAUZMWj1UpmK/F16B7fAuL7B2ElMwHN1Vg27rwxIzksSSwanBaeUQDArnrB7rg5PVesBkMlnKmDpkien7zuw5CSz3sdfDK/DaihKzFqIT1foUVjPeNKPp8/Dwe9lTzowksWRuVrRi35nBacXqsWIdCoKAhoaG1O6kDZmcKEXRy2SU7PV6OlF8C0StQyuxHpb72Mf3qdZ/JpceORUy0V/TLInReFhFvm/mrZ10ConcrGBYRkhkd3qPHuW0mtnCWjcr1qEsy2hra0vpTtrZCWGQ0Snbk2QqiMpkxOrR6+mUdejzRGM9ZmugWJbsxPdptP/MyeTUfVJlou6kSZki8bCKwpyZd2RbJkGtMFan9+hhdYays7zH7/enlqnAjutGg7DssltAbIZryKDVQ/V0KhQARGM9Zq0elpYYENunVKZ+szJdcsZiVWXyWZJpwIEVBHrMSBJL5GbpXSQWp/foUaYF0c3NUCMha8t7BEHA4sWLU7qT0eJE8xmugHZ6NLs6I0CN9RRHTvOhs3Mq6PV0KikDRAeXWdebpSUW36cVFichLWPKaOG+HhrZm5TpYqSvywtyUj6zVjEjSSzRydhOBYYB61YP/XxhjrnlPZIkoaWlJaGeFDQIS4i5hMOEJGuLxp2czY0MBL2ejpIYlckAserB0hKL71M6CZmXyTmrp8LifdIssQJfymfWKmYkiSWytJyo1qfQnwRuxuoJWJw1OY5DaWlpSovSI/DaiU5myJUuGGe555oe5SYC1lRPwNmAtVULg2XxdHyfaq5bFmWKByXWfrMkFiH7yoIc5l4QMENJLJHJ6mTn0muatXq0JUcmZRIEAVdeeWVa09xKhksvE8vlPRRmgsNUz3GJQJTZHZo7WSZrmUDN6mHgusX3aTROZ80Sc8KdrCi0dp/6NXfS57qTRpHKnXRiJtfHesxYPVatC0mS0NTUlNY0t5KhdNJiBaKDy0hwmOp5cVhdjuP3CvAzTsoA+piYccIQZQUjkUMzWBBrfJ9W2CRWR0IBdAIyGWeNBvZzXHfSKOipLXo4aYkB1gjDarEkz/OYNWtWQj31KLOQpnf6PlWYuE9UT5rJdGICAqxlJynZcxybPdfi+9SKi0sI0XSoKGSblAHUOCvHmfc4tDox3SlVLHHZkJiTMRX9dTNh9fA8j/r6egMkZn4gsHSREstkjsTq6+u1I+0cIzEL2cn+0ajFIzBwu+P7lN7/wHgYkmxsN9SRoKTtquFEYN8j8NrkZjQupihEm0QrCnwuiRlFprOTgLUK+aiLa27WlCQJ+/btM+xOmrEwHLdYC4wHh6mevRF3ssIhYrUSf6LyVzKyeOL7VD0zklo9xmrqaClDYa4HuV72bjdg/pkKjIe1MqLSfDc7aRgJLTFa++TY4DRftR8lDPOW2BVXXGHCnTRj+kdrepyAGbeb6kknhgqnZCqIZpeNWj0XR6l1wUam+D4VeM50/SGViRWxJkKFiUkIiE7qJXnqgnTXEjOIRDdKOxbNoYB1dNdS87O52YFgNCYWrcmyYGE45U6aqBOjeg5EJiAn4jyANasn2nds7lOiPo3WrxmbhKw+T2ZgVyaXxAwi3mSVdX55pUMdXGFhmUg/nc1NDk5JkrBnzx4D7qQFmSKfdWo2168kSGf1UD37RkIAnBucAh/dndco4bMmjER9arYuKzoBTR1LrD9uyZHrThpEPNvr/XKngsOUiC4a7FxCiC5rYz472dDQkHZWo0RkpjiRtZsUj7J8H/iI1ZNumxmqZ9SddKbvgOjApwH7dOhnnAVM1KfU6qF9kg6ZcCcpGRl2J2e6JbZv3z7cc889qKurA8dx+P3vfx/zPiEEW7ZsQV1dHfx+P9asWYMjR46kvW78jaI3vDTPCw/jjeIoKgrMde5IKJpJsuJOVlVVGSaxoXFRO6A3HZx2SQSe0+Jt6QYn1TMTFga9V32jIUOfZy1Toj6tKlR3QTU6MbJ2cROhqojeJ6MkFjsBzTgSGxsbww033IBt27YlfP/555/HCy+8gG3btqGlpQU1NTW46667MDo6mvK68SYrnV2djBVUUavHYOfSB64wx3wmSRRFvPfeexDF1PGbEr9XS/8bcZPGwxLGIztwOhV/AqIDPx2JUT21wemkTIXGZKK4aDEUkAyJ+pQSxsURc66bs8+5Sqx9hmWKTRTNOHdy/fr1+OEPf4j7779/0nuEELz44ot4+umncf/996OhoQHbt2/H+Pg4Xn/99ZTXTWaJOdm59NojIQkhMf2eSVbjYYC6RGX58uVpl3DwPBe1EA24SfQzuV4e+Q5UxlMYJQxBEHDj0mUYjtSJZWISMkpirK2eRH1Kyd6o1eN0KADQW6wmY2Iz1RJLhY6ODvT09GDt2rXaazk5Obj99tvR1NSU8rtHjx7FgQMH0NLSgpaWFpy+cBEAUF6gZiYlSdI2Z5MkCYqipGyLohjTpofW0jYhBHkewCuoVk/v0BgAlYjpzKooSky7J1L7VK6rnVEURWvLshzTpvLKsgxCCMrKykAIidEjkU40hnHxUiitThfjyF6vH5U9lU6J9EikkzYQIgH7eP1oW1EUiIK6x5aH51CUI9jup2Q6leWpi917R0JpdRKl6J7/ZX5P0n5K1E7WT4qioKSkBDzPa69HXbeQIZ30tWss+imRHhW6Q3QnwmJKnSRJ0mJipX4PFEW5vEisp6cHAFBdXR3zenV1tfZeMjz00ENYtmwZVqxYgRUrVmBP034AgEdUiaOtrQ0dHR0AgObmZnR2dgIAmpqa0N3dDUCN1/X39wMA9uzZg6GhIQBAY2Oj5s7u2rULoZBKDu+8846WNHir8X0AwOjoKBobGwEAQ0ND2LNnDwCgv78fn372OQCgwKNopNzZ2Ynm5mYAKom3tbUBAE6cOIFDhw4BUAm6vb0db7/9Ng4ePIgTJ06k1MkjjQNQZ+l0OtFBUJbnhSRJ2LVrFyRJQigUwq5du9LqtG/fPgBAd3d3Sp0oiR3t6NJ0Onr0KADg0KFDmk6tra146z31+oU+oKvrvO1+SqZTd8cXquxDY2l1aj9xBgpRlxyNXLyQtJ8S6ZSsnz766CO8/fbbEEVR0ynquoXS6iSKYox1z6KfEunUe+4UBJ4DIUDL4eMpdWpqakLvsPr8nT/5Ofr7+x1xJ0GmCACQHTt2aH9/9NFHBAC5cOFCzOe+9a1vkXXr1iW8RmtrKwFAtm/fTlpbW0lzczNpbm4m3321idRv3kn+x78dJ4QQIooikSRJa8uynLIdDodj2oqixLQVRSHhcJh89b/vI/Wbd5J3D3cRQoj2OiGEyLIc035u1+ekfvNO8vTvDhFRFLXXaVuSpJg2lZe+Pjw8PEmPRDr9+1+3kfrNO8m2PSfS6vTaJ2dI/ead5JuvNmuy6/VLp1MiPRLp9MqHp0n95p3kkdf2J9SPtsPhMHmr5RSp37yTrH9xL7N+SqTTvmM9pH7zTnLnP7+fVqf28wFSv3knWfpMY8p+StRO1k/hcJgEAgGiKIr2+sClCVK/eSep37yTTIhySp0GL4W0zwbDEpN+SqbHin/cTeo37yQHzgyk1Wnh07tI/eadpKNvhMiyTPbv308AkNbWVsIK7DeMYoSamhoAqkVWW1urvd7X1zfJOotHQ0MDli5dqv297bA6w1QVRlwT3WEFRtper9dQm7phgXF1tuE4TvsMz0erlXme1/axryzM1X5L/xl9bCRRu6ioKEbnZLJXFkUyXKMTaXWiMbHKwpwY2fWfSaVTujaVPVr6EU6pq9frRYh4tftEr2O3nxLpVFuaB0CN9aTTTyu+jdup1Eg7lewlJSUxr5fmeeEVOIiy6urPKvHHfF7f7h0YAaBWxtNEkd1+StauKsxF78iEdh+S6TQaJlpWvLY0DzzPX177ic2fPx81NTXYvXu39lo4HMbevXuxevXqlN+dlJ3UslvOpZ4Bc4WAdmQSRRFvvfVW2uwkoMsEmpHJwcAwoAvsp5FJFEXsa2nLjEwFKtkbScz0RNw7GrNigUR9ynGc4Uxuz7AqU00R+8Np41FlMLhPZSrL9yHHE41nskZWLbFLly7h5MmT2t8dHR04ePAgysrKMHfuXGzatAlbt27FwoULsXDhQmzduhV5eXl44IEHUl43PmuX6cFppEL+oo10uMfjwdq1aw0df2WmdCDjJJZGJo/Hg6LqucC5LtQUOytTkV/dIjwsKei/NIHZEcssEXodIIxkfVpZlIsLwyEtLpZUpsj71ZkgsbiEgxmZnNgUMasktn//fnz5y1/W/n7iiScAABs3bsSrr76KJ598EsFgEI888ggCgQBWrlyJxsZGFBYWGv4NRdHtseTw4KwwY/XYTIcbPb9Psw4NkFhPhgYCJbHRiNWTqk7u4iXVMnHawqBWT9dQEH2jaUgsMnhritnKlKhPjZZZ9Ayr72fCEqukCYc0MlESq2FosSZCVt3JNWvWaGli/b9XX30VgPpgbdmyBd3d3QiFQti7dy8aGhrSXld/tt1wUIQUWXPk1B5ZFNrSozSFgIpCtFnMykDQZ9nSwYwlplkYjAdnPApzPMiJHIySSi5JknD8XC+AzFgY0dIPY4TBUqZkfaoVvKYjjMjzVO1w3wE6dzKNdUgnRf3z5J47aRB6k5XeSL1f7hToLNibxsweHA9DlAk4LvpAmIHH48GGDRsMWWPVkUEwOiFhbCI56anEmpnZnOM4jQB6UwwEj8eDCV79XCZIrNqkm8TanUzUp9URq4fGl5LKlMGYGP2NHgsurrvHvgVkykUCdJ07HNKKEhPKFHngyvNz4LW4ltNogLQw14uCHHVgpHro+scmICkEPOfs2jsKOjtfSDE4JVnRXHOnrUMAqC1Ws38XhsxbGCyQqE/rSuh9ChqUyVnXTZVJvU/d6e5Thoh1RpKY3mSNzlDOdy41/SckRTv6LBF6bT5wkiShsbHRMJHRwZZqNu8djlZ7O7VIXo9aTabkg7NneBwKUReNOx3PBKKE0Z1CJlFWtAQIa3cyUZ9qhJHOEsvgZE1LPQbGwikzuT0Rt7zadSfNQ2+SOzVrJkKuV9Cq9lNZPT023RGv14t77703plYoFShhpBoIdmUyCyNWz8C4+sBXFuQw2cfeqEypLIyLoxMgRF0GxXIf+2R9SknswlAwqXWvZlTV5FUm+q/I79HW1nYNJSf8RG630YSUGcxIEtN3diZnKP3vpLZ67MlECMHIyEhKl1WPqJubwurJ8H2qNWAdUnmrM2BFA8ZcN61GrDCH6bmcyfqU3qfxsIzhYGLrnsbwvALn2H55enAcF0OuiRASo+tL9c+U0WfWDGYkielN1kwWAQK6wemgJSZJEj788EPD7qQRS8wusZpFVKbkhHEhoK67s5L8sCaTOjB7R0JQkpyrqN0nB+Jhifo01ytoFl8yq5U+41WFuY5UxCdCOhKjFlqeT4g5Q8J1Jw0i1p2c7Jc7CSOWmF2ZvF4v7r77bsPuZE1kcKaWKXNuN6Bz3VLI1B9Z1lKnW27jJKoKc8BzgCiTpKsuuh2aFFP1aS21EJMQxvmA+vqcsszcJwCYVar+VlcSYu0cVCeguWV5McTqupMGQbcCAZxJh6eCETfJbjpcURQMDg7G6GlEppSWWKbdycjAvHhpIumus9RKY7m8JxU8Aq/pnyxr2hmxDueUJS+GtYJUfVqnEX5iEjsXIYw5KQp0WWNWGkuMklh80bDRZ9YMZjSJTej2fcoUiRmpobEbf5JlGS0tLYZN8xoDLq5TFkYylOX54BN4EJK8LosOhFkZsg4BHeEnHZzU6mFLGKn6lFqiRqyeTKEujXXYmcQ6dEnMIKjJSiuvfR4eJSbPdrSK6jSW2HhY0gK0Vl03r9eLdevWmc5ODiZJiRNCMj4QeJ5LW/pBB8L8SuPLzOyiViOM1BbGnFK2rluqPk1X+qFZYpkksWJj9yn+eXLdSYOgbK+3LjIV8KzVijgTp8TpTF6U60Gx3xqxKoqCvr4+w7Nasd8Lf2R9YiKX8uLoBCYkBQLPaW5eJkDvFY3p6BESZfRGJqFZGZRpdoTEEslECNHcSdZkn6pPqUt2dmA84XejMbHMkRj9rQtDQYgJjt5L5uK6lphB0BsVnaEyF/CknTYakhIWvFKZ5pZbf+AURUF7e7vhB4LjONSX04EwllSmupJcyysIrGBeeT4A4EwCmc5HyCJXAIpznV0uFiNTRXKZBsbCGA/L4LhoYJsVUvXp/IhMHf1jkybGsKRoJSGZfM5rinLh9woQ5agVr0dnkufcJTGDoCarRhhl+Rn7bb9P0EoCzibo3HMM3DaPx4M77rjDlGkeJTFnZLKC+gr19870TyYMarHOryoy7DazACXWjgQy0ftUU5TLfB1uqj6lMg0HRS3GS6EWwaqHuzh5pF08eJ7DgkpVrlMXY+/V8LiIkZBaKjI7juxdd9IgNEssMptmfHCmsHo6GcQvFEVBV1eXqVktldWTjewWAMynhJGCWCv9nCOzdzLQgXk+EJyUNWXRd8mQqk/9PkHLBsaTq77vMhUyoVhQWQAAOH3xUszrZwdVGSsKfMjzxZKWa4kZRLw7mXkSUwfCuRSDs96GdagoCk6dOmXqgaAyJbTEBjIfGAZ0rlsKqyefjGeUxKoKc5DnEyAr0fgXRaeDZJ+uT6lLeTrO6jmbpYkaAK7QLLFYEjvWox5msqh6ckLGJTGDiLqTqkuScRKL/J6T7uRtt91myjSfF7EOU1li2bJYh4MiAnFuEpVp1fWLHHFBkoHjuGgMKo4wOvojE5CNeGYypOtTzXXrjyWMoxHCuKomcxncqEzUEou9T8e6VZkW1xRN+o7rThqEoigYm5C0qms7QXQroL8Xb4kpCptSBkVRcPbsWVOzGpWpc3AcctySmmyRWJ7Po62LjCdX6qLkSpcyaokBUQsx3nU72q0exuEEYaTr0wVJiJXKtLh2MmE4jeSWGJXJtcQsQ1EUzRUo9nstlzJYhea6DcY+cH2MShmsxMRqi/3wCTxEmcQUKI6ERG0zRCcsjHRIFKsLhmWNQPLFoYyTGCWM0zoSC0sKTvSpFsY1DhBGuj6dH7F69IShKATHe6hMWbDEKgrAcUBgXNQKlgkhGrFencASc0nMIDwej2YFZSNWQN3J3pEJBMPR4tKTfeoDOLvUb6uUwePxYPXq1aZMc4HntBS8fnAevaA+cHXFuSjJc34HhHhQN+lEb3RwHu8dhULUwPCGL38po+4kAFxZpRIGHYyASh6iTFCY65mUcWOBdH16dYSkTvePYSSklu6cGxzHeFhGjofXJoNMwu8TsKhKlevA2QAAteYwMC6C54CF1QWTvuO6kwYhyzJORAiDugaZREmeV9sdlZrWAHDkwjAA4No6ezO5LMs4efKk6R0BqMvR3jWsvfZ5ZKBeU1dsSyaraJil/u5n54e01z6/QGfyQpw6dcqRnQ9SYcmcUgBqf9EVDnrrwoksYLo+rSrMxdyyPBACtJ0bipFpUXVhRjayTITl89V71dyhkhh9nuZX5Cc8AMbdxcIgCCEaYTTYJAwr4DhOG5yHdYRxJDI4r7VJGIQQBAIB03sz3TBb/d1DOsKgMl2ThfsEADfOKQEAHOoc1ra/+bxbvWdX1xZa0tMu5pT5UVHggygT7f5oJOaQ22akT5fVq4TRemYQQLTvnJLJCJbPKwMAtERk2vdFPwDgxshEEA93PzGD8Hg8aO9SO5iSSaZxPSWx83oSU9t2CcPj8WD58uWmTfPrZ5cAAA7pZPpcI9bskNhV1YXwewWMTkhavEeTaVaJJT3tguM4LJmrDsK2c6qF8dl5SqzO3CcjfaqRWESmfzvWBwC4KUIk2cCK+epvH7kwjEsTEho/7wEArL22OuHnXXfSIIbHJ7SMW7YGZ7wlNh6WtFgUC3fy2LFjpk3z62YVg+fU9ZN9oyHHg9VG4BF4XBe5V22dQwiGZc0lWVxdYElPFlgytwQAcOBcAP2XJrA/Yml86coKR37PSJ/eNI8S6xCO9YzgaPcIBJ7DXVcnJoxMoLbYjzllfigEeO6dYzgfCCLXy+O2hZUJP++6kwZByWJWiT8rwWogavWc6LuEkCjjaPcoCFEP4qgqtL+gORhMffpNIuTneLSg9WedwzhwLgBRJijJ8zoSrDaKGyOE0dwxiD3H+hASFcwu9eOKynxLerIAdZP2fdGP/72/EwoBrp9d7GhBcDpdF1UVYk6ZH+NhGX/6kyYAwKoF5SjNwJbUqfDw6vkAgF9+chYAcOvCSvh9mVvvOi1I7Cc/+Qnmz5+P3NxcLFu2DB9++GHCz128eBEA0H5W/b9hVnasC0DdF76iIAeyQnDgXAD7vlBlonEpO+jr68Nbb72Fvr4+09+lLsm77T146+AFAMBdV1dnfMmKHncurgIA/J/PLmB70xkAwD031OHixYuW9bSLZXNLcVV1IS5NSHj+3eMAgA3X1Tr2e0b6lOc5bLpzEQBgLJL1Xn9djWMyGcWDN9drBcLFfi/+7o6FST87OKhatHSsssCUJ7Ff//rX2LRpE55++mm0tbXh1ltvxfr163Hu3LlJn+3vV4OKn55Wb9TSuYmDi5kAx3Ha4Px1Syd+13YegDo47eL8+fP4h3/4B5w/f970d//ipjkAgDcPnMevmtV7eN+SWbZlsoMV88tw/exiTEgKmiNu2z3X19nS0y54nsPjd16p/e33Cvjq9c6RmFFd71syCzfMLgbHAQ+tqsdfRvozm/B5ePzPjTfhe3cuxHubbsN1KSZqStJ0rLLAlCexF154Ad/85jfxrW99C1dffTVefPFFzJkzBy+99FLS73QMS+A54N4bszs4v3HzXADAWwcvoHMwiHyfgLXXZHfmXDK3FDdEMoKAulbw5gXl2RMIKuF/9/YrtL/XXlOd1YwbxfqGWjywci7uvbEOv3tk9aStlrMBgefwq7+9Gc0/+Aqeubcha6UV8biisgDfv2tRxs5o0COzaR+TCIfDaG1txVNPPRXz+tq1a9HU1JTyu7ctqszKDdXj+tklaJhVpGVK776+lkmsgB4Fb/VI+CfuWoS//cV+zCnLwxN3LcrImY7psP66Wryy8SYU+71YVl8KjuNs62kXAs9h659cl5nfMqFrns8zaXeI6QKeZ0+6U/pO9Pf3Q5ZlVFfHZl+qq6vR09Mz6fMTE+ryGWngHOaMFOGXv1RjGVVVVSgrUwO1giBAkiRtkEiSBJ7nwfO84bYgCOA4TmsDatZF3/Z4PCCE4BsLROyeuITSPC++UnkJBw4cgKIoUBQFHo8naVuWZRBCtDaVXZZlHD16FADQ3t6u/a4ZnQp5Hr+4pwyCIIAXu9Hc3GlKJ9o2oodRnQCgVBAgX5Kx/6L6+uHDhyEIAo4cOeJ4PzmlU3w7WT8dPnwYPM+n1XU66ZSoffr06ZixygJTmsQo4oPOhJCEgejxcbWson/nC/jhzoyIZgovML7exo0bGV9xauKhhx7KtggZw+WiKx2rLDClSayiogKCIEyyuvr6+iZZZwDwV3/1VwCAvLw85OREd7msqKhAZWXiuhUXLlxkDsFgEGfOnMG6deuYXZMjmV7TYRIrV67EsmXL8JOf/ER77ZprrsG9996LZ599NouSuXDhYipgSltiAPDEE0/gwQcfxE033YRVq1bh5Zdfxrlz5/Cd73wn26K5cOFiCmDKk9hf/uVfYmBgAM888wy6u7vR0NCAXbt2ob6+PtuiuXDhYgpgahSZpMEjjzyCM2fOYGJiAt/85jexcePGtNX7FHv37sWyZcuQm5uLBQsW4Kc//WmGpLYHo6sUAOCDDz4Ax3GT/h07diyDEpvHvn37cM8996Curg4cx+H3v/992u9Mx/40q+d07c9nn30Wy5cvR2FhIaqqqnDffffh+PHjab9nt0+nBYlRmKneB4COjg5s2LABt956K9ra2vCDH/wAf/d3f4c333wzw5Kbg1k9KY4fP47u7m7t38KFyZd/TAWMjY3hhhtuwLZt2wx9frr2p1k9KaZbf+7duxePPvooPvnkE+zevRuSJGHt2rUYG5t8rgMFkz4l0wgrVqwg3/nOd2JeW7x4MXnqqacSfv7JJ58kixcvjnnt29/+Nrn55psdk5EFzOr5/vvvEwAkEAhkQDpnAIDs2LEj5Wema3/qYUTPmdCfhBDS19dHAJC9e/cm/QyLPp02lhit3l+7dm3M66mq9z/++ONJn1+3bh32798PUZx8OvdUgBU9KZYsWYLa2lrceeedeP/9950UMyuYjv1pB9O9P4eH1W2oaKF5IrDo02lDYmar9wGgp6cn4eclSWK6AJUlrOhZW1uLl19+GW+++SZ+97vf4aqrrsKdd96Jffv2ZULkjGE69qcVzIT+JITgiSeewC233IKGhoakn2PRp1M+OxkPo9X7qT6f6PWpBjN6XnXVVbjqqqu0v1etWoXOzk788z//M2677TZH5cw0pmt/msFM6M/HHnsMhw4dwh//+Me0n7Xbp9PGEjNbvQ8ANTU1CT/v8XhQXp7dnRuSwYqeiXDzzTfjxIkTrMXLKqZjf7LCdOrPxx9/HH/4wx/w/vvvY/bs2Sk/y6JPpw2J+Xw+LFu2DLt37455fffu3Vi9enXC76xatWrS5xsbG3HTTTfB683sWZRGYUXPRGhra0NtrXP7X2UD07E/WWE69CchBI899hh+97vfYc+ePZg/f37a7zDpU/M5h+zhjTfeIF6vl7zyyivk888/J5s2bSL5+fnkzJkzhBBCnnrqKfLggw9qnz99+jTJy8sj3//+98nnn39OXnnlFeL1eslvf/vbbKlgCGb1/NGPfkR27NhBvvjiC9Le3k6eeuopAoC8+eab2VLBEEZHR0lbWxtpa2sjAMgLL7xA2trayNmzZwkhM6c/zeo5Xfvzu9/9LikuLiYffPAB6e7u1v6Nj49rn3GiT6cViRFCyI9//GNSX19PfD4fWbp0aUz6duPGjeT222+P+fwHH3xAlixZQnw+H5k3bx556aWXMiyxNZjR87nnniNXXHEFyc3NJaWlpeSWW24hb7/9dhakNgdaShD/b+PGjYSQmdOfZvWcrv2ZSEcA5Oc//7n2GSf6dMovAHfhwoWLVJg2MTEXLly4SASXxFy4cDGt4ZKYCxcupjVcEnPhwsW0hktiLly4mNZwScyFCxfTGi6JuXDhYlrDJTEXLlxMa7gk5sKFi2kNl8RcTFmsWbMGmzZtyrYYLqY4XBJz4cLFtIa7dtLFlMTDDz+M7du3x7zW0dGBefPmZUcgF1MWLom5mJIYHh7G+vXr0dDQgGeeeQYAUFlZCUEQsiyZi6mGabc9tYvLA8XFxfD5fMjLy0NNTU22xXExheHGxFy4cDGt4ZKYCxcupjVcEnMxZeHz+SDLcrbFcDHF4ZKYiymLefPm4dNPP8WZM2fQ398PRVGyLZKLKQiXxFxMWfz93/89BEHANddcg8rKSpw7dy7bIrmYgnBLLFy4cDGt4VpiLly4mNZwScyFCxfTGi6JuXDhYlrDJTEXLlxMa7gk5sKFi2kNl8RcuHAxreGSmAsXLqY1XBJz4cLFtIZLYi5cuJjWcEnMhQsX0xouiblw4WJawyUxFy5cTGv8/xwCKHzO97CvAAAAAElFTkSuQmCC", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "kp0 = 2.9 # 比例ゲイン\n", "K = tf([0, kp0], [0, 1]) # P制御\n", "Gyr = feedback(Pdelay*K, 1) # 閉ループ系\n", "y,t = step(Gyr, np.arange(0, 2, 0.01)) # ステップ応答\n", "\n", "fig, ax = plt.subplots(figsize=(3, 2.3))\n", "ax.plot(t, y*ref)\n", "\n", "ax.axhline(ref, color='k', linewidth=0.5)\n", "ax.set_xlim(0, 2)\n", "ax.set_ylim(0, 50)\n", "plot_set(ax, 't', 'y')\n", "\n", "# fig.savefig(\"tune_zn.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Classic\n", "kP= 1.74\n", "kI= 11.6\n", "kD= 0.06525\n", "------------------\n", "No Overshoot\n", "kP= 0.58\n", "kI= 3.8666666666666667\n", "kD= 0.05742\n", "------------------\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "kp = [0, 0]\n", "ki = [0, 0]\n", "kd = [0, 0]\n", "Rule = ['', '']\n", "\n", "T0 = 0.3 # 周期\n", "# Classic ZN\n", "Rule[0] = 'Classic'\n", "kp[0] = 0.6 * kp0\n", "ki[0] = kp[0] / (0.5 * T0)\n", "kd[0] = kp[0] * (0.125 * T0)\n", "\n", "# No overshoot\n", "Rule[1] = 'No Overshoot'\n", "kp[1] = 0.2 * kp0\n", "ki[1] = kp[1] / (0.5 * T0)\n", "kd[1] = kp[1] * (0.33 * T0)\n", "\n", "LS = linestyle_generator()\n", "fig, ax = plt.subplots(figsize=(3, 2.3))\n", "\n", "for i in range(2):\n", " K = tf([kd[i], kp[i], ki[i]], [1, 0])\n", " Gyr = feedback(Pdelay*K, 1)\n", " y, t = step(Gyr, np.arange(0, 2, 0.01))\n", "\n", " ax.plot(t, y*ref, ls=next(LS), label=Rule[i])\n", "\n", " print(Rule[i])\n", " print('kP=', kp[i])\n", " print('kI=', ki[i])\n", " print('kD=', kd[i])\n", " print('------------------')\n", "\n", "ax.axhline(ref, color=\"k\", linewidth=0.5)\n", "ax.set_xlim(0, 2)\n", "ax.set_ylim(0, 50)\n", "plot_set(ax, 't', 'y', 'best')\n", "\n", "# fig.savefig(\"tune_zn_result.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# モデルマッチング" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "閉ループ系Gyrの逆数のマクローリン展開" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/latex": [ "$\\displaystyle 1 + s^{2} \\left(- \\frac{Mgl k_{p}}{k_{i}^{2}} + \\frac{k_{d}}{k_{i}} + \\frac{\\mu}{k_{i}}\\right) + s^{3} \\left(\\frac{J}{k_{i}} + \\frac{Mgl k_{p}^{2}}{k_{i}^{3}} - \\frac{k_{d} k_{p}}{k_{i}^{2}} - \\frac{k_{p} \\mu}{k_{i}^{2}}\\right) + \\frac{Mgl s}{k_{i}} + O\\left(s^{4}\\right)$" ], "text/plain": [ " ⎛ 2 ⎞ \n", " 2 ⎛ Mgl⋅kₚ k_d μ ⎞ 3 ⎜J Mgl⋅kₚ k_d⋅kₚ kₚ⋅μ⎟ Mgl⋅s ⎛ \n", "1 + s ⋅⎜- ────── + ─── + ──⎟ + s ⋅⎜── + ─────── - ────── - ────⎟ + ───── + O⎝s\n", " ⎜ 2 kᵢ kᵢ⎟ ⎜kᵢ 3 2 2 ⎟ kᵢ \n", " ⎝ kᵢ ⎠ ⎝ kᵢ kᵢ kᵢ ⎠ \n", "\n", " \n", "4⎞\n", " ⎠\n", " \n", " " ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import sympy as sp\n", "s = sp.Symbol('s')\n", "kp, kd, ki = sp.symbols('k_p k_d k_i')\n", "Mgl, mu, J = sp.symbols('Mgl mu J')\n", "sp.init_printing()\n", "\n", "G = (kp*s+ki)/(J*s**3 +(mu+kd)*s**2 + (Mgl + kp)*s + ki)\n", "sp.series(1/G, s, 0, 4)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "規範モデルMの逆数のマクローリン展開と比較し,PIDゲインを決定する" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/latex": [ "$\\displaystyle \\left[ \\left( J \\omega_{n}^{2}, \\ 2 J \\omega_{n} \\zeta + \\frac{Mgl}{2 \\omega_{n} \\zeta} - \\mu, \\ \\frac{Mgl \\omega_{n}}{2 \\zeta}\\right)\\right]$" ], "text/plain": [ "⎡⎛ 2 Mgl Mgl⋅ωₙ⎞⎤\n", "⎢⎜J⋅ωₙ , 2⋅J⋅ωₙ⋅ζ + ────── - μ, ──────⎟⎥\n", "⎣⎝ 2⋅ωₙ⋅ζ 2⋅ζ ⎠⎦" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import sympy as sp\n", "z, wn = sp.symbols('zeta omega_n')\n", "kp, kd, ki = sp.symbols('k_p k_d k_i')\n", "Mgl,mu,J = sp.symbols('Mgl mu J')\n", "sp.init_printing()\n", "\n", "f1 = Mgl/ki-2*z/wn\n", "f2 = (mu+kd)/ki-Mgl*kp/(ki**2)-1/(wn**2)\n", "f3 = J/ki-kp*(mu+kd)/(ki**2)+Mgl*kp**2/(ki**3)\n", "sp.solve([f1, f2, f3],[kp, kd, ki])\n" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "from control.matlab import tf, step\n", "\n", "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": [ "2次の規範モデル" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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dg1edREdHq/taorCwkD179pCTk0NOTg6lpaXIsqxOyGa3211s569fS7bNZnOxnTdfnbYQookNuNiKorjYzl+klmxZll1sp7+yLCOEoGvXrggh2q1JURRVR3O2EKKJ7dTUkn3lTAyesMERsCVJQgjR4mIhX3/9tdua3nrrLbp06dLE9379+rF27Vqva3JXa2s6nPZzzz3HiBEjfH6cWrKbO/c0FcRKSkp49NFH+etf/9rqGD535nq6mvnz55OUlMTYsWMZO3Ysr732Gvv27aOoqAiA/Px8iouLAcdYrpKSEsAxBUtpaSkAmZmZ6iDX7du3U1VVBUB6erp6T27Lli3U19djt9vZsmULdrud+vp6tmzZAjhm40xPTwegqqqK7du3A1BRUUFmZibgmBLY2bIsKSkhOzsbcLRE8/PzASgqKlJX9SksLKSgoIDNmzezd+/eNmuqrKwEHDOjOoPexYsX1ZPN+YTsyqdlThscF4/TlmVZ/S7sdrtq22w2dW73xsZGampqAMcsFLW1tYBjfJ1zCp36+nrq6+sBx1J0TrumpkZNsZz+3n777RQVFXHixAl15R3nLBbV1dXX1OSs+2pNzrId1XThwoVWNdXW1tLQ0KDqc84ndunSJVVrdXW1+gPWnCYhBOfPn8dJc8fpStvbx+lqTc4f6/z8/CbXk1du9QgfsWnTJgEIs9ms/gFCkiRhNpvFkSNHBCD27Nnj8r7vf//7Yv78+c3WmZeXJwCxYcMGkZeXJ7Kzs0V2drY4c+aMsNvtwm63CyGEsNlsLrYsy63ajY2NLraiKC62oihNbCGEiy3Lsotts9late12u4vt9Ne5/cKFC010uKOppqZGHDx4UNTU1Kg6ZFluYiuK0sR2amrJdtbhKdv5fTi3paamijlz5riUycjIEIAoLy8Xn332mQBEZWWl6nt+fr4AxLFjx8T27dsF4PL33HPPialTpzbZ7vTliy++EJMnTxZBQUGid+/eYsmSJaK6ulr9/Pj4eLFixQqRmpoqIiIixPz588XcuXPFww8/rJZ55JFHBCAKCgrUcyIsLEz8+9//FoqiiPr6erF48WLRo0cPERgYKCZOnCh2796tfgdOv7ds2SKSkpKE1WoVf/zjH5v4/NZbbwlZlgUgXn/9dTFnzhwRHBwsEhISxKZNm7x2nK62a2trxcGDB0V1dXWT8zA3N1cAIi8vT3gKnwWxixcviv3797v8jR49WvzXf/2X2L9/v1AURcTExIhVq1ap72loaBCRkZHiD3/4Q7N1OoOYJ78grVFXVycOHjwo6urqXHc0XGr5r7EtZWvdK9sOnEHMSXV1tVi4cKFISEgQsiyLzz//XA1iTpxBrLi4WDQ0NIi1a9eKiIgIUVpaKkpLS0V1dbU4d+6c6N27t1ixYoW6XQgh9u3bJ8LCwsTLL78svvnmG/Hll1+KkSNHigULFqj1x8fHi4iICPHiiy+KoqIiUVRUJF555RWRmJiolhkxYoTo3r27+P3vfy+EECIrK0tYLBZRXV0thHAEubi4OLFlyxZx4MABkZqaKqKiosS5c+eEEELVNWzYMJGeni6OHDkiTp06JZ544glx8803qz7X1jq+e0D07t1bbNy4URQVFYlHHnlEhIWFqfV5mxbPMeGda9RnPfbDw8ObLHIaGhpKt27d1O1Lly5l5cqVDBw4kIEDB7Jy5UpCQkKYN29eq3Xr4enkli1bmDVrludmPlgZ1/K+gSlwz/vfvX4xAWy1zZeNnwT3bf7u9dqhUHuuabm0C9d0yZm6RkREqPdS2rtYCEBAQACRkZFIktRk0Quz2Ux4eLjL9hdffJF58+apfRcHDhzIK6+8wtSpU1m/fr16G2TatGkuc4MlJyfz6KOPUlFRgdls5sCBAzz33HPs2LGDRYsWsWPHDpKSkggLC6Ompob169fz1ltvMX78eCIiInjjjTfYtm0bb775Jk899ZRa74oVK5g+fbr62rmIR3MLeCxYsICf/OQnAKxcuZLf/e53ZGdnc/vtt1/ze/ImupvZddmyZdTV1bFo0SIqKysZN24c6enphIeHt/o+rT+1s1gspKSkdIpFYr2JJElEREQ0WSxk/fr1AJw/f55XX32VmTNnqvcSPUleXh5HjhzhnXfeUbeJyzfJi4uL1SmsR48e7fK+xMREunXrRkZGBlarleHDh/P973+fV155BXCsh+lcfeno0aPYbDYmTZqkarVarYwdO7bJYiVXf05rXNnnMjQ0lPDwcHVxFF+i+Tn2d+zY4fLauVhnZ1yw09d4PID94kzL+6SrTrynjrRS9qoW0dL97fepGVpbLMTZHUdc8cSvI33pFEVh4cKFPPLII0329e3b18WnK5EkiSlTprBjxw4CAgJITk4mMTERWZbZv38/WVlZauvO6as7D7Cu/pzWuLqFfuViIVpDkx2qtL7u5JVPQz1GQGjLf9agNpQNdq+sGwg3xhNeuVhIjx49ANQnYoC6GrjqTkBAs+dHc9tHjRrFgQMHSEhIaPJ3rcHaycnJ7Nixgx07dpCcnIwkSUyePJmXXnqJuro6dZk4Z107d+5UtdpsNnJzc6+5WElLWjozxrqTbqKHdHLWrFm6TCedi4WUlZVRWFjIkiVL1MVCEhIS6NOnD2lpaXzzzTds3ryZ3/zmNy519uvXj0uXLvHZZ59RUVGhdiXo168fmZmZnD59Wu1a8/TTT/PVV1/x8MMPq91ZPvroI5YsWXJN353jfPfv38/kyZPVbe+88w6jRo0iIiICcLSuHnroIZ5++mmysrIoLCzkpz/9KbW1tdx///2tfka/fv0oLi5m7969VFRUqN0cOjPeuDY1GcT0gNYfXrSEc7GQ2NhYxo0bR05OjrpYiNVq5d133+XQoUMMHz6cVatWNVmPcsKECTz44IP8+Mc/pkePHqxevRpw3DQ/fvw4AwYMUFt0w4YNIyMjg6KiIiZPnszIkSN59tln1cVKWiMxMZHu3bszfPhwNWBNnToVWZbV+2FOfv3rXzN37lxSU1NJSkriyJEjbN261WUYXnP88Ic/5Pbbb+fWW2+lR48evPvuu25/j1rCWCjED+nI00l/WiikuaeTWkVLWq/3QiGazEe0nmZZrVbmzJnjaze8jslkokuXLr5247qgF63euDb9O+S3gIYal83izg1vLSAujw3Vuk7Qj1Zv6NNkEPO3JzZtxW63s3PnTs3fFxM6WTwD9KPVG9emJvMuPaSTd9xxh6/d8Dp6SbFAP1qNdNJNtNqpz4miKJw/f17zOoUQ2O12zbdOQD9avXHOGkHMD5FlmZycnA41zf3hOxJCUFNTo/kLG7SltbVzyxvnnSbzLj2kkzNmzGjXewMCAjCZTJw5c4YePXoQEBDQqWdODQwMVOfc0jr+rlUIQWNjI2fPnsVkMjU7qsEb16Ymr3Z/aGV0BEVRqKiooHv37m3uU2Qymejfvz+lpaWcOdPKeMlOgHOwtclk6tSB1hNoSWtISAh9+/Zt9tw0WmJuoocgVlBQwJQpU9rVMTIgIIC+ffu6TGndGbHb7eTm5jJ69GjNt661otVsNmOxWFoMxEYQcxN/PgncwWKxMG3atA7V4ZzyxWPzkXmJ5ORkX7tw3dCDVuPppJvooSV2+vRpQ6eG0ItW4+mkm+jhRDh69KihU0PoRauRTrqJHtLJKVOm+NoNr6MXnaAfrUY66SZ6+DU7ceKEoVND6EWrkU66iR5OBL3cP9GDTtCPViOddBM9pJMTJkzwtRteRy86QT9ajXTSTTpz3ydPIMsyR44cMXRqCL1oNebYdxMtjD9rDSEElZWVhk4NoRet3tCnybxLD+nkmDFjfO2G19GLTtCPViOddBOfNcmFAOWKz264BGX7obGF1bLbiSzLHDp0SBephx50gn60GpMidlYqj8Pu16DgQ0j5JQy727H97CH4422ABF36Qp+xED8B4idB94HQgYG+dXV1HnG9s6MXnaAvrZ7Epy2x9evXM2zYMCIiIoiIiGD8+PH8+9//VvcLIUhLSyMuLo7g4GB1Lb9rcd3WnZTtsP1X8LvRsOtVuFQGJ7/6br8kQXAUIKDqBOx/Hz5+DH4/Bl4aCPv+r10fazabGTlypObX19SLTtCPVs2tO9m7d29+/etfk5ubS25uLtOmTWPOnDlqoFq9ejVr1qxh3bp15OTkEBMTw/Tp06murm613uvSJK+/CH+5CzJfBMUGNyTDvP+DGS98V6ZXEjx9HJ46CvP/CVOfgX6TwRIENWchuOt3ZY9/AR88AHkboKIIWulPI8syBQUFukg99KAT9KNVc+nk7NmzXV4///zzrF+/nl27djFkyBDWrl3L8uXLmTt3LgAbNmwgOjqajRs3snDhQl+47KCxBv46F07lQEA4fP8VSJzbcvnQ7o4gd0Oy47W9AU7lQtyI78oUpTtaavvfd7y2hkJMIsQMhW4JMPRuCO3mJUEGBv5Lp7knJssy77//PjU1NYwfP57i4mLKyspISUlRywQGBjJ16lSysrJaDWKHDh3CbDarUb9379707NkTcDRn7XY7kiSptslkwmQytWjbbDbMZrNqWwr/hXQqBxEcBf+1CeJGYLfZ1Ccvdrsdq9WqzptutVpRFAVZlh22yYrSexwWiwVFUVAUBcuQuxAmKxTvRCrbB7YaKNnt+APkgbcjB0ZRWVOPNeN5bjz8AbWfRVFv6UKjORgbFmxSAHYpgJ19FlJtiqRREfQr/5y+l/YhUEARgOMRtyIUJCHY2j2VC1I4IDG0eieDL+1CQjgeUqBgQiAJgYTCh10f4JylJ0IRjKnbydhL29V9IJAQjvII3uuykNLAfgghSKrdSXL1ZvWzr+b/utzPiYCBSJLE0NrdpFRvctl/8OPv7E2R91IUMBgJicENe7nj4t9w3lkU4rvbjELA5oi7KQwehVAUBjYe5AcX/9qkjNP+JPQH7A8dB0IQ3/ANd19821EGvqv/sr099A5yQyYiSSbiGouZV/Ua0hXqrrS/CE3hq5BbAYi2lzK/8hWXMlfWvTs4mdXZtyOEQld7BQ9UrmnR39ygCXwe7mgEhNqreKhydfNfgiSxL2gMW8PuQjKZCJRrWXJuRTOqHHZh0Ag+Dv8xILCg8NjZZ5s9ZgBHAgbzjy7zEUIBJJ44+/8wITdb93HrAP7e5X4GWStarK+9+DyI7d+/n/Hjx1NfX09YWBibNm1iyJAhZGVlARAdHe1SPjo6mhMnTrRa5/z5811eP/fcc8yZM4fg4GAGDRpEfn4+UVFRJCQkkJ2dTa9evYiPjycrK4sBAwbQq1cvMjMzSUxMpGfPnmzfvp0xY8bQtWtX0tPTmTx5FhFzXuWLg6cZ3XUQFrtdXZHbbreTnp7OnDlzqK6uZufOndxxxx1UVVWRk5PDjBkzqKiooKCggGnTplFaWsrRo0eZMmUKh+uiyG2YSvDwvpQc3E3QuYP0EqWE1pxk8csHqLUfBOA31q/5obmUgJpSwpvRn3psGuVEObRbdjDRsrXF7+rZsokcF7EADLLkMtmypcWyK85/j4OXr87B5kMkWb9osWxa1SzyRAgA/c3FJFrzWiz765Mz+EJx+BtrLmZoK2V/d3EKOxXHD1KU6TjDAlou+8fTt5Cp9AEg2HSSoa2Ufad6JJnyDQBMNp1qteym6iHslAcBkCSdZlhgy2U/qR7ATnkoAEOuUTbzUm8yS88C0F8qY2grZXMu9SCzzBEQojnPsKDcFssWXApnZ9k5ACKo4Y2glus9VhPIzsv1WrHzdiv1ltUIMsvPqq/fCszDKjWfLlbVNJB5toLQGM8+qQeQhI971zU2NnLy5Emqqqr44IMP+OMf/0hGRgZVVVVMnDiRM2fOEBsbq5b/6U9/SklJCZ988kmTuvbs2UNSUhJ/+tOfGDp0qPdaYpdnrrRd1fpyuyV22S6rtvHV0Qp2HztH3skqTpyvxZ2jER94iX7mCvoE1RNtrSHUZCNIshEsyQRJNnb2+DHmwDACLWYGXdhJfM0+kBy3PyVJQpJMjt9IycTB+Huos0RiMZvpVZVDj8p8TCYLwvlrbrIAEooQnOw9m/rAbghFpvulQ0RVFqAAJpMZR3tMwiSZUYAz3SdgD+mJEILwi0fpWl0IQiAEmEyS2ulRkiTKuo2lIagnJpOJkOpiulbuw2QyoSgyFy9cILJLFxCOshXdx1ATGI3JJBFae5qoijwkk4SEhKIoLvb57knUhfZGlmVCG8rpfi4XoShIl2fDFZengxbAucibqYu4ASEEAbVlxJzPRSAQirhc5ju7MnIwF0JvwGw2Ya07S8/yLEcZoVzW9J19sctgqsISAAi0X6RnaQaS5NCiKAKTBEgSsiJz3NYNyw2TEAIC5Brivv3cMWW14w2XbRNIcCEkngtdhzs+z3aJPmXbAUcL22QygfjOvhTal4rIoY6b6nIjvU79G5NJAiFQLh8Pp10f1puzUSMRAswmQe+Sj9XjdOUxE0JQFxTDuZ7jkGUFSYL405sv+8hlf7/TVxvQjYqeE2gsO8K8O6eRl5fHqFGjrn2yu4HPg9jVfO9732PAgAE8/fTTDBgwgD179jBy5Eh1/5w5c+jSpQsbNmxo8l5nEPPkF+RC3ga4aRaE9Wh3FUXfVvOvr8/w8f5Sjp2tabK/e1gAN0aHc0OPUGIjg4mNDCImMoiYiCC6hQUSFmjBbPLvOdgN9Is3rlGfp5NXI4SgoaGB/v37ExMTw7Zt29Qg1tjYSEZGBqtWrWq1Dq+sjF2SA/96BNKfhaVfX+464R6yIth2sIy3vzzO7uLz6naLSWJY70jG3dCNcf27MrRXJN3CAq9Zn91uJz8/n5EjR2p6dIJedIJ+tHrj2vTpt/WLX/yCmTNn0qdPH6qrq3nvvffYsWMHn3zyCZIksXTpUlauXMnAgQMZOHAgK1euJCQkhHnz5rVar1dWi/n8ecf/wbPdDmBCCHZ8c5ZV/z7EoTJHtxCzSeLWm3py57BYbhvck/Cgts9xL0kSUVFRfr8qzrXQi07Qj1Zv6PNpEPv222+59957KS0tJTIykmHDhvHJJ58wffp0AJYtW0ZdXR2LFi2isrKScePGkZ6eTnh4c7ezv8PjHerO7IVjn4NkhqnL3HpL2YV6nvlwHzsOO258hgdZmD8+nv+6JZ7YyOAOuWM2m0lISOhQHf6AXnSCfrR6o7OrT4PYm2++2ep+SZJIS0sjLS2tTfV6vMma9TvH/8S5EBV/zeIffX2G/7dpPxfr7QSYTaROiOfhWxPoEtJ0MdH2YLfbyc7OZuzYsZpPPfSgE/SjVXPppLdoz1qMLXLpLBz8p8OesKTVoooiWL31MH/IOArAsN6RrLl7OAk9W285thWTyUSvXr08q7MTohedoB+t3tBnBLFr8fVGx7CiXkkQO7zFYvU2mSfe/5rN+0oBWJQ8gMem34jV7PmDZjKZiI+/dovQ39GLTtCPVm8EMU2GfY82WRuqHWMdR6W2/HmywuKNe9i8rxSrWeKlHw1n2e2DvBLAwKEvMzPTO09hOxF60Qn60Wqkk27i0Wg/7f/B+MVgab7rg6IInv5gP58WlhNoMfFm6hgmDezuuc9vBpPJxIABA3SReuhBJ+hHq5FOuonHv6jgLi3uWr31MB/sOYXZJLFu3iivBzD47v6J1tGLTtCPViOddBOPNFkVBc5+02qRbQe/VW/ir/rhMKYPiW61vKew2+1s375dF6mHHnSCfrR6Q58mg5hHov2ZPY7JC9+cQXMDGs9U1fHU378G4L8n9uc/knp3/DPdxGQykZiYqIvUQw86QT9ajXTSTTzyRR2+PMNseEyTaaRlRfDoe/lU1doY1juSZ2YO6vjntQGTyaQOaNcyetEJ+tHaKdLJBQsWkJmZ6XFHPIlHmqzfXJ4l46aZTXZtzD5JzvFKwgIt/O4nIwmwXN9fT5vNxtatW7HZbNf1c683etEJ+tHaKdLJ6upqUlJS1LGMp0+f9rhTHaXD0b6qBL4tcExfMzDFZde5Sw28tPUwAE/NuIn4bqEd+6x2YDabGTNmjC7mY9eDTtCP1k7REvvggw84ffo0ixcv5v3336dfv37MnDmTv//9753mV6TDX9SRTx3/e4+FkK4uu1Z/cpgLdTYGx0Zwz7i+HfucdmIymejatasu7p/oQSfoR2unCGIA3bp149FHHyU/P5/s7GwSEhK49957iYuL47HHHqOoqMjTfraJDjdZj33u+D9gmsvmvSVV/C23BIBfzrkZi5c6s14Lm83G5s2bO82PhrfQi07Qj9ZOkU5eSWlpKenp6aSnp2M2m5k1axYHDhxgyJAhvPzyy57ysc10qEmuyFB8+Z6fc2GPy6zZ5uhyMXdkL0b364qvsFgsTJ48WdMDhUE/OkE/WjvFLBY2m42PPvqIt99+m/T0dIYNG8Zjjz3GPffco06R89577/HQQw/x2GOPedxhd+jQnEVCwOxX4PhOx3jJy+wtqSLzm7OYTRJLv3ejB7xsP5IkERER4VMfrgd60Qn60eqN+cTa3BKLjY3lpz/9KfHx8WRnZ5Obm8uDDz7oMsfXjBkz6NKliyf9bBMdarKaLTDk+zDrRYd9mXXbHSnyXSN60bdbSEdd7BA2m41//vOfmk899KIT9KO1U4ydfPnll/nRj35EUFBQi2WioqIoLi7ukGMdwdNN1gNnLvBpYTmSBItuHeDRutuDxWIhJSVF86mHXnSCfrR2ihXA77333lYDmF+jyPDFy3D8S4d9mVd3OIYW3TksjgE9wnzlnQtaP9md6EUn6EurJ9Hk89x2L5VefhA+TYONd6tDjcov1vNJQRngmCOsM2C/vM6lHsbZ6UEn6Edru6/NVtBkEGt3k/XEV47/fcap98P+L7cEWREkxUcxOLZz3Hi1WCzMmjVL87/cetEJ+tHaKdJJTVOyy/G/73jAMUby3WxHv7B5Y33TsbUltP6L7UQvOkFfWj2JJoNYu5uspy8v7957NACZRWc5XVVHZLCVO4bFtvLG64vdbic9PV3zJ71edIJ+tHojndRk27VdTfLa81B53GHHORbrfXf3SQDmjupFkLXzjGmzWq3MmTPH1254Hb3oBP1o9Ua6rMmWmGhm/q9rcnqP43/XARDchbPVDXx2qBzofKmkEIKLFy+2T6cfoRedoB+t3tCnySDWribrmctB7HIv/U8KSpEVwfDekQyM9uySax3Fbrezc+dOzaceetEJ+tGquaeTL7zwAmPGjCE8PJyePXty1113cfjwYZcyQgjS0tKIi4sjODiY5ORkDhw40Gq97WqyTlwKP/0cJj4KwMeXl167c1hc2+vyMlarlTvuuAOr1eprV7yKXnSCfrRqLp3MyMjg4YcfZteuXWzbtg273U5KSgo1NTVqmdWrV7NmzRrWrVtHTk4OMTExTJ8+nerq6hbrVRSl7c5YAqDXKIhJpPxiPdnHzwMwc2hM2+vyMoqicP78+fbp9CP0ohP0o9Ub+nwaxD755BMWLFjAzTffzPDhw3n77bc5efIkeXmOp4RCCNauXcvy5cuZO3cuiYmJbNiwgdraWjZu3NhivR39oj45UIYQMKJPF3pH+XacZHPIskxOTo5XmuadCb3oBP1o1VwQu5oLFy4A0LWrY5qb4uJiysrKSEn5bnbVwMBApk6dSlZWVov1tLnJeiwDPnoEDm0GrkwlO0+3iiuxWq3MmDFD86mHXnSCfrRqLp28EiEEjz/+OJMmTSIxMRGAsjLHcJ/oaNel0KKjo9V9zVFQUMCePXvIyckhJyeH0tJSZFlWf+XsdruLLY58Bns2oBzeSllVLTmXU8kZNzs+12azqb8gNptNfcLitIUQTWynJqetKIqL7byB25Ity7KL7fRXlmVsNhvl5eXYbLYWNTn9bcnubJqasxsbGykrK1Pr0IKmlo5TS1r9WVNztqZbYosXL2bfvn28++67TfZdPQeREKLVeYlSU1NJSkpi7NixjB07ltdee419+/apM87m5+ers2xkZ2fTcMzRqjtSF877XxUhBAyIlAi0O+7Nbd++naqqKgDS09PV+3Fbtmyhvr7eZdxbfX09W7ZsARzrEaSnpwNQVVXF9u3bAaioqFAXWyktLVVblSUlJWRnZwOOVmh+fj4ARUVF7Nu3D4DCwkIKCwspKChg//79LWoqKXGMNMjKyqK01NGyzMzMpKKiotNqApocp71796IoiqY0NXecvvrqK77++msURdGMpuaOk1fu+YlOwOLFi0Xv3r3FsWPHXLYfPXpUAGLPnj0u27///e+L+fPnN6knLy9PAOLPf/6zyMvLE9nZ2SI7O1ucOXNG2O12YbfbhRBC2Gy27+zGRqGs7C3EcxHCVrJHLHhrt4h/+mPxu08PC1mWhRBCNDY2utiKorjYiqI0sYUQLrYsyy62zWZr1bbb7S6209+WbBdNNpvqb0u2ocnQ5AtNzms0Ly9PeAqf9tgXQrBkyRI2bdrEjh076N+/v8v+/v37ExMTw7Zt2xg50tGLvrGxkYyMDFatWtVivYMHD2bUqFEt7r8yL7dcOgMNF8Fkxd59ELuOZQAwbXCMuqjBlfcp2mJLkqTaJpNJrc8d+8qBslfbiqJw+vRpYmNj1fIumtywO5um5myTyURpaSmxsbGa0dSS7y1p9WdNzdmaSycffvhh/vrXv7Jx40bCw8MpKyujrKyMuro6wHEgli5dysqVK9m0aRMFBQUsWLCAkJAQ5s2b12K9bfqivr3c56zHTeSUXKLOJtMzPJDBsZ2rg+uVKIrC0aNHdfE4Xg86QT9avaHPpy2x9evXA5CcnOyy/e2332bBggUALFu2jLq6OhYtWkRlZSXjxo0jPT3dZTrsq2nTExBnEIu+mYzDZwGYemMPr8wF7iksFgtTpkzxtRteRy86QT9avfF00ufp5LWQJIm0tDTS0tLcrrdN0f7i5cV/oxPZsdsRxJJv6tzLySuKQklJCX369NH0OoV60Qn60aq5dNJbtOmLmr0Wnj7B6QE/4kj5JcwmiUkDu3vNN0/gvCemh9RDDzpBP1o1l056izY3WYO7sGOfo6PtyD5diAzu3B0OLRYLEyZM8LUbXkcvOkE/WjXd2dWTtGfohvN+WPJNPTztjseRZZkjR45ofoiKXnSCfrRqbhYLb+HOvTYA9v8dNsxGyXmL3cWOXvqTBnb+ICaEoLKyUhdzT+lBJ+hHqzf06TudPJUDxZlUht3EhbpoQgPMJMZ1jsVAWsNisTBmzBhfu+F19KIT9KPVSCfdxO0m6+XuFQeVPgAk9euKxdz5vxJZljl06JAuUg896AT9aDXSSU8iBHxbAEDmBcdA73H9u/rSozbh7BCsdfSiE/Sl1ZNoMp10a2276lKoq0RIZv51xtFx9pYb/COImc1mdRiWltGLTtCPVmPdSTdxq8n67UEAGrvcQFktBFlNDO3VxbuOeQhZlikoKNBF6qEHnaAfrUY66UnOHgKgLKAfAKP6RhFg0e/XYWDgr+g3nVTsENKdAzbH7K3j+nfzsleew2w2qxNHahm96AT9aDXSSTdxq8k6aSniqSOsuHgnAOP85H4YOPTl5+frIvXQg07Qj1YjnfQwJ8/XUnbJToDZxIg+XXztTpsIDg72tQvXBb3oBH1p9ST6TSeB/JNVANzcK4Igq+ebud7CbDYzaNAgX7vhdfSiE/Sj1Ugn3eSaqygXZ8LaofT+4ucAftcKs9vt5OTkaH61aL3oBP1o9YY+TbbErjmhYfkhqDqJHOC4qT+yb9R18MpzSJJEVFRUp5640RPoRSfoR6s39GkyiF2zyXq5e0V+naOn/kg/a4mZzWYSEhJ87YbX0YtO0I9WI510k2s2Wc8eBuAbOY7uYYH0jvKvG6p2u52srCxdpB560An60eoNfZoMYtec3rfCEcSKRG9G9u3id014k8lEr169ND2NMehHJ+hHqzf0afIba/WLqjkHNY4JEI+KOEb27XJ9nPIgJpOJ+Ph4XZzwetAJ+tFqBDE3abXJerkVVkZ3agliZB//uqkPDn2ZmZm6SD30oBP0o9V4OukmrUZ7odAYm0TuKSsmCYb1jrx+jnkIk8nEgAEDdPGrrQedoB+tRkvMTVr9ovpNYvvEjSy2PcKN0eGEBvpfHNfT/RM96AT9aDWCmJtcq8n69akqwP86uTqx2+1s375dF6mHHnSCfrQaTyfdpNVob2+k4LRjebahfphKgkNfYmKiLn619aAT9KNVcy2xzMxMZs+eTVxcHJIk8Y9//MNlvxCCtLQ04uLiCA4OJjk5mQMHDlyz3ha/qPqLiOdj+GVJKoE0MsxPJkG8GpPJRM+ePXVxwutBJ+hHq+aCWE1NDcOHD2fdunXN7l+9ejVr1qxh3bp15OTkEBMTw/Tp06murm613habrBXfIAmZYFGHYg7kxpiwjkrwCTabja1bt2Kz2XztilfRi07Qj1bNPZ2cOXMmM2fObHafEIK1a9eyfPly5s6dC8CGDRuIjo5m48aNLFy4sMV6W4z2l3vqFym9GBQTQaDFf2auuBKz2cyYMWO8MoSjM6EXnaAfrZpribVGcXExZWVlpKSkqNsCAwOZOnUqWVlZrb63sLCQPXv2kJOTQ05ODqWlpciyjFJeCDh66t8c51gcxG63oyhKq7bNZnOxnQuAOm0hRBMbcLEVRXGxnb9ILdmyLLvYzsnkZFlGCEHXrl0RQqjb7Xa7i+1vmpqzFUUhMjISk8mkGU0tHSdFUejSpUsTrf6sqTlbV0GsrKwMgOjoaJft0dHR6r6WmD9/PklJSYwdO5axY8fy2muvsW/fPmpP7AEcPfVjAh0HNTs7m5KSEgCysrIoLS0FHPfrKioqANi+fTtVVVUApKenq+nsli1bqK+vx263s2XLFux2O/X19WzZsgWA6upq0tPTAaiqqmL79u0AVFRUkJmZCUBpaakalEtKSsjOzgYcQTw/Px+AoqIi9u3bBzgCdEFBAZs3b2bv3r0UFRUBkJ+fT3Fxsd9qKix0/MDs27dP1ZSXl8eWLVuw2Wya0dTScfryyy/ZvHkzNptNM5qaO05eefoqOgmA2LRpk/r6yy+/FIA4c+aMS7kHHnhAzJgxo9k68vLyBCA2bNgg8vLyRHZ2tsjOzhZnzpwRdrtdKC8PE+K5CHH3My+KvSfOCSGEsNlsQpblVu3GxkYXW1EUF1tRlCa2EMLFlmXZxbbZbK3adrvdxbbb7S7bL1y4IGw2m7r9atvfNDVnNzY2isrKSqEoimY0tXScWtLqz5qas3NzcwUg8vLyhKfotD09Y2JiAEeLLDY2Vt1eXl7epHV2NYmJiYwaNcp1Y2MtouoEAMdNfRgc1wVwXVa9JdtqtbbLliRJtU0mk9qUdse+8t5Ic3ZERISLPHd0dHZNV9tWq5UuXbpoSlNrvjen1Z81NWd7Y7KFTptO9u/fn5iYGLZt26Zua2xsJCMjgwkTJrT63mabrLZaTve5kyx5CNGxvfx6eTabzcY///lPzT/J0otO0I9WzT2dvHTpEkeOHFFfFxcXs3fvXrp27Urfvn1ZunQpK1euZODAgQwcOJCVK1cSEhLCvHnzWq232Sc8od35S9xyXis6xrxe/tnJ1YnFYiElJcXll06L6EUn6EerN56++vQby83N5dZbb1VfP/744wCkpqbypz/9iWXLllFXV8eiRYuorKxk3LhxpKenEx4e3q7P23/K0VN/mJ8HMUDzJ7sTvegEfWn1JD7NqZKTk9VHw1f+/elPfwIc+XNaWhqlpaXU19eTkZHh1gKjza1tJ6rLKDx9HoBEPw9iVz6R0jJ60Qn60WqsO+kmzTVZ7W/dwS5xL7dYirgxun0tuc6CxWJh1qxZmv/l1otO0I9WY4799mKrx1xVTKBkJ7hHP7++qe9E67/YTvSiE/Sl1ZP4/9XcDE2arBXfYBIyVSKUuD43+MYpD2K320lPT9f8Sa8XnaAfrd5IJzXZdm3SJC8/CMBh0YdhfjqH2JVYrVbmzJnjaze8jl50gn60eiNd1mRLTFweX6a+/vZyEFP6+P1NfXDou3jxYhOdWkMvOkE/Wr2hT5NB7Ooma+2p/QAclfr6/U19cKQeO3fu1HzqoRedoB+tRjrpJlc3WaXL6aSt2yCsZv+P21arlTvuuMPXbngdvegE/Wg10kk3cU7/cfkFu6Jms1keS0TfYb5zyoMoisL58+dddWoQvegE/Wj1hj7tBzGTiXXyD3jYtpSb+vf2nVMeRJZlcnJyvNI070zoRSfoR6s3gpjm00mbrHDgzEUAhvXu4iOPPIvVamXGjBm+dsPr6EUn6EerkU66yZXR/kRhLj3kbwkPMtO/W6gPvfIciqJQXl6ui9RDDzpBP1qNdNJNrvyiIrY/wxeBj/JQVB4mk+fnMvIFiqJQUFCgixNeDzpBP1qNdNJN1CarEIRd+AaA4N5DfeiRZ7FYLEybNs3XbngdvegE/Wg10kk3UaN9dSkhcjV2YSIuYbhvnfIgiqJw+vRpXfxq60En6EerkU66ifOLajz1NQDFIpah8T196ZJHURSFo0eP6uKE14NO0I9WI4i5ibPJWvHNVwB8Y04gNjLIly55FIvFwpQpUzQ/bYtedIJ+tBrppJuo6/SdzAOguttQryxQ4CsUReHEiRO6+NXWg07Qj1ajJeYmiqKAEERVFQAQ3G+Mjz3yLHq6f6IHnaAfrcbTSTexWCwosswvlftIsH/DLTff4muXPIrFYrnmik9aQC86QT9ajXTSTWRZ5si5Ot6vH8NaaT5D+mrnpj5c1nfkiOaHqOhFJ+hHqzHHvpsIIdh97BwAI/p00cTMFVcihKCyslIXc0/pQSfoR6sxn5ibWCwWzDmvM04qZMoA/58E8WosFgtjxozRxZMsPegE/Wg10kk3qav6lnnnf8+7Ab/i1v7BvnbH48iyzKFDh3SReuhBJ+hHq5FOuklZoaN/WJHUj5v6x/vYG+9QV1fnaxeuC3rRCfrS6kn8Ioi9+uqr9O/fn6CgIJKSkti5c2ez5c6ePQtAw5EMAMq6jdFU/zAn5eXl/POf/6S8vNzXrngVvegE/Wg9f96xgLXzWvUEnT6I/e1vf2Pp0qUsX76c/Px8Jk+ezMyZMzl58mSTshUVFQDcUOMYbhQ+Zt519fV6cerUKf73f/+XU6dO+doVr6IXnaAfrc4g7bxWPUGnD2Jr1qzh/vvv54EHHmDw4MGsXbuWPn36sH79+hbfEyDZOWLqx4gxU6+jpwYGBr6gUwexxsZG8vLySElJcdmekpJCVlZWq+/9dsCPMGmsa4UT51Lw3lgSvjOhF52gH60mk+evyU79PLeiogJZlomOjnbZHh0dTVlZWZPyDQ0NAGyuiKWvrTfH/vIXAHr27EnXrl0Bx0lit9uRJEm1TSYTJpPJbdtsNiNJkmqD46nLlbbFYkEIodqKoqAoitu2LMsIIVTb6bssyxQWFgJQUFCgfq6/a2rO3r9/P2azmQMHDmhGU0vHaf/+/ZhMpmtq9SdNzdnHjh1zuVY9QacOYk6uvjkvhGj2hn1tbS0A//PhEfjwvuvimy9JTU31tQvXhfnz5/vaheuGXrQ6r1VP0KmDWPfu3TGbzU1aXeXl5U1aZwD/+Z//CUBISAiBgYEu9fTo0cO7zhoYGFyTuro6jh8/7tFFUSTRycc5jBs3jqSkJF599VV125AhQ5gzZw4vvPCCDz0zMDDoDHTqlhjA448/zr333svo0aMZP348r7/+OidPnuTBBx/0tWsGBgadgE4fxH784x9z7tw5VqxYQWlpKYmJiWzZsoX4eG32xDcwMGgbftEHYdGiRRw/fpyGhgbuv/9+UlNTr9l730lGRgZJSUkEBQVxww038Ic//OE6ed0x3B2lALBjxw4kSWryd+jQoevocdvJzMxk9uzZxMXFIUkS//jHP675Hn88nm3V6a/H84UXXmDMmDGEh4fTs2dP7rrrLg4fPnzN93X0mPpFEHPSlt77AMXFxcyaNYvJkyeTn5/PL37xCx555BE++OCD6+x522irTieHDx+mtLRU/Rs4cOB18rh91NTUMHz4cNatW+dWeX89nm3V6cTfjmdGRgYPP/wwu3btYtu2bdjtdlJSUqipqWnxPR45psKPGDt2rHjwwQddtg0aNEg888wzzZZftmyZGDRokMu2hQsXiltuucVrPnqCtur8/PPPBSAqKyuvg3feARCbNm1qtYy/Hs8rcUenFo6nEEKUl5cLQGRkZLRYxhPH1G9aYu3pvf/VV181KT9jxgxyc3Ox2Wxe87UjdGSUwsiRI4mNjeW2227j888/96abPsEfj2dH8PfjeeHCBQC1o3lzeOKY+k0Qa2vvfYCysrJmy9vtdo8OQPUk7dEZGxvL66+/zgcffMCHH37ITTfdxG233UZmZub1cPm64Y/Hsz1o4XgKIXj88ceZNGkSiYmJLZbzxDHt9E8nr8bd3vutlW9ue2ejLTpvuukmbrrpJvX1+PHjKSkp4aWXXmLKlCle9fN646/Hsy1o4XguXryYffv28cUXX1yzbEePqd+0xNraex8gJiam2fIWi4Vu3bp5zdeO0B6dzXHLLbdQVFTkafd8ij8eT0/hT8dzyZIlfPTRR3z++ef07t271bKeOKZ+E8QCAgJISkpi27ZtLtu3bdvW4lJX48ePb1I+PT2d0aNHY7VaveZrR2iPzubIz88nNjbW0+75FH88np7CH46nEILFixfz4Ycfsn37dvr373/N93jkmLb9mYPveO+994TVahVvvvmmOHjwoFi6dKkIDQ0Vx48fF0II8cwzz4h7771XLX/s2DEREhIiHnvsMXHw4EHx5ptvCqvVKv7+97/7SoJbtFXnyy+/LDZt2iS++eYbUVBQIJ555hkBiA8++MBXEtyiurpa5Ofni/z8fAGINWvWiPz8fHHixAkhhHaOZ1t1+uvxfOihh0RkZKTYsWOHKC0tVf9qa2vVMt44pn4VxIQQ4ve//72Ij48XAQEBYtSoUS6Pb1NTU8XUqVNdyu/YsUOMHDlSBAQEiH79+on169dfZ4/bR1t0rlq1SgwYMEAEBQWJqKgoMWnSJLF582YfeN02nF0Jrv5LTU0VQmjneLZVp78ez+Y0AuLtt99Wy3jjmHb6AeAGBgYGreE398QMDAwMmsMIYgYGBn6NEcQMDAz8GiOIGRgY+DVGEDMwMPBrjCBmYGDg1xhBzMDAwK8xgpiBgYFfYwQxAwMDv8YIYgadluTkZJYuXeprNww6OUYQMzAw8GuMsZMGnZIFCxawYcMGl23FxcX069fPNw4ZdFqMIGbQKblw4QIzZ84kMTGRFStWANCjRw/MZrOPPTPobPjd9NQG+iAyMpKAgABCQkKIiYnxtTsGnRjjnpiBgYFfYwQxAwMDv8YIYgadloCAAGRZ9rUbBp0cI4gZdFr69evH7t27OX78OBUVFSiK4muXDDohRhAz6LQ8+eSTmM1mhgwZQo8ePTh58qSvXTLohBhdLAwMDPwaoyVmYGDg1xhBzMDAwK8xgpiBgYFfYwQxAwMDv8YIYgYGBn6NEcQMDAz8GiOIGRgY+DVGEDMwMPBrjCBmYGDg1xhBzMDAwK8xgpiBgYFfYwQxAwMDv+b/A6f4pKN3ETnYAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "omega_n = 15\n", "zeta = (1, 1/np.sqrt(2))\n", "Label = ('Binomial coeff.', 'Butterworth')\n", "\n", "LS = linestyle_generator()\n", "fig, ax = plt.subplots(figsize=(3, 2.3))\n", "\n", "for i in range(2):\n", " Msys = tf([0,omega_n**2], [1,2*zeta[i]*omega_n,omega_n**2])\n", " y, t = step(Msys, np.arange(0, 2, 0.01))\n", "\n", " ax.plot(t, y*ref, ls=next(LS), label=Label[i])\n", "\n", "ax.set_xlim(0, 2)\n", "ax.set_ylim(0, 50)\n", "plot_set(ax, 't', 'y', 'best')\n", "\n", "# fig.savefig(\"ref_model_2nd.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "モデルマッチングで求めたPIDゲインを用いたときのステップ応答\n", "\n", "この例の場合は,規範モデルの応答に完全に一致させることができる" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "kP= 2.25\n", "kI= 10.406647807637908\n", "kD= 0.2433517680339462\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "omega_n = 15\n", "zeta = 0.707\n", "\n", "Msys = tf([0,omega_n**2], [1,2*zeta*omega_n,omega_n**2])\n", "\n", "kp = omega_n**2*J\n", "ki = omega_n*M*g*l/(2*zeta)\n", "kd = 2*zeta*omega_n*J + M*g*l/(2*zeta*omega_n) - mu\n", "\n", "print('kP=', kp)\n", "print('kI=', ki)\n", "print('kD=', kd)\n", "\n", "Gyr = tf([kp,ki], [J, mu+kd, M*g*l+kp, ki])\n", "\n", "yM, tM = step(Msys, np.arange(0, 2, 0.01))\n", "y, t = step(Gyr, np.arange(0, 2, 0.01))\n", "\n", "fig, ax = plt.subplots(figsize=(3, 2.3))\n", "\n", "ax.plot(tM, yM*ref, label='M', ls = '-.')\n", "ax.plot(t, y*ref, label='Gyr')\n", "\n", "ax.set_xlim(0, 2)\n", "ax.set_ylim(0, 50)\n", "plot_set(ax, 't', 'y', 'best')\n", "\n", "# fig.savefig(\"model_match.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "3次の規範モデル" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "alpha1 = (3, 2, 2.15)\n", "alpha2 = (3, 2, 1.75)\n", "omega_n = 15\n", "Label = ('Binomial coeff.', 'Butterworth', 'ITAE')\n", "\n", "LS = linestyle_generator()\n", "fig, ax = plt.subplots(figsize=(3, 2.3))\n", "\n", "for i in range(3):\n", " Msys = tf([0, omega_n**3], [1, alpha2[i]*omega_n, alpha1[i]*omega_n**2, omega_n**3])\n", " y,t = step(Msys, np.arange(0, 2, 0.01))\n", "\n", " ax.plot(t, y*ref, ls=next(LS), label=Label[i])\n", "\n", "ax.set_xlim(0, 2)\n", "ax.set_ylim(0, 50)\n", "plot_set(ax, 't', 'y', 'best')\n", "\n", "# fig.savefig(\"ref_model_3rd.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 練習問題" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "kP= 3.519\n", "kI= 33.75\n", "kD= 0.285\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "alpha1 = 2\n", "alpha2 = 2\n", "omega_n = 15\n", "\n", "Msys = tf([0, omega_n**3], [1, alpha2*omega_n, alpha1*omega_n**2, omega_n**3])\n", "\n", "kp = J*alpha1*omega_n**2 - M*g*l\n", "ki = J*omega_n**3\n", "kd = J*alpha2*omega_n - mu\n", "\n", "print('kP=', kp)\n", "print('kI=', ki)\n", "print('kD=', kd)\n", "\n", "Gyr = tf([0, ki], [J, mu+kd, M*g*l+kp, ki])\n", "\n", "yM, tM = step(Msys, np.arange(0, 2, 0.01))\n", "y, t = step(Gyr, np.arange(0, 2, 0.01))\n", "\n", "fig, ax = plt.subplots(figsize=(3, 2.3))\n", "\n", "ax.plot(tM, yM*ref, label='M', ls = '-.')\n", "ax.plot(t, y*ref, label='Gyr')\n", "\n", "ax.set_xlim(0, 2)\n", "ax.set_ylim(0, 50)\n", "plot_set(ax, 't', 'y', 'best')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 状態フィードバック" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 極配置" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ ": sys[241]\n", "Inputs (1): ['u[0]']\n", "Outputs (2): ['y[0]', 'y[1]']\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", " [0. 1.]]\n", "\n", "D = [[0.]\n", " [0.]]\n", "\n" ] } ], "source": [ "from control.matlab import ss, acker, initial, lqr, care\n", "\n", "# A = '0 1; -4 5'\n", "# B = '0; 1'\n", "# C = '1 0 ; 0 1'\n", "# D = '0; 0'\n", "\n", "A = [[0, 1], [-4, 5]]\n", "B = [[0], [1]]\n", "C = [[1, 0], [0, 1]]\n", "D = [[0], [0]]\n", "P = ss(A, B, C, D)\n", "print(P)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A行列の固有値は不安定" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([1., 4.])" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.linalg.eigvals(P.A)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "極配置で設計する。A+BFの固有値が指摘極polesになるように,ackerの結果に負号をつけています" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "matrix([[ 3., -7.]])" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "regulator_poles = [-1, -1]\n", "F = -acker(P.A, P.B, regulator_poles)\n", "F\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A+BFの固有値が指摘した極になっています" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([-1., -1.])" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.linalg.eigvals(P.A+P.B@F)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "matrix形式の場合は,P.A+P.B*F で計算できますが,ndarray形式の場合は,P.A+P.B@F とします。\n", "\n", "ちなみに,1入力1出力の場合は,ndarray形式であっても,P.A+P.B*F の結果は,P.A+P.B@F と同じになります。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "初期値応答を可視化" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Acl = P.A + P.B@F\n", "# Acl = P.A + P.B*F # 型がMatrixの場合\n", "Pfb = ss(Acl, P.B, P.C, P.D)\n", "\n", "Td = np.arange(0, 5, 0.01)\n", "X0 = [-0.3, 0.4]\n", "x, t = initial(Pfb, Td, X0) #ゼロ入力応答\n", "\n", "fig, ax = plt.subplots(figsize=(3, 2.3))\n", "ax.plot(t, x[:,0], label = '$x_1$')\n", "ax.plot(t, x[:,1], ls = '-.', label = '$x_2$')\n", "\n", "plot_set(ax, 't', 'x', 'best')\n", "\n", "# fig.savefig(\"sf_pole.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 最適レギュレータ" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "--- フィードバックゲイン ---\n", "[[ -6.77032961 -11.28813639]]\n", "[[ -6.77032961 -11.28813639]]\n", "--- 閉ループ極 ---\n", "[-3.1440682+0.94083196j -3.1440682-0.94083196j]\n", "[-3.14406819+0.94083198j -3.14406819-0.94083198j]\n" ] } ], "source": [ "Q = np.diag( [100, 1] )\n", "R = 1\n", "\n", "F, X, E = lqr(P.A, P.B, Q, R)\n", "F = -F\n", "\n", "print('--- フィードバックゲイン ---')\n", "print(F)\n", "print(-(1/R)*P.B.T@X)\n", "print('--- 閉ループ極 ---')\n", "print(E)\n", "print(np.linalg.eigvals(P.A+P.B@F))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "リッカチ方程式の解Xを用いてフィードバックゲインを求めてもよいです" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "matrix([[ -6.77032961, -11.28813639]])" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "FF = - (1/R)*(P.B.T)@X\n", "FF\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "care関数でリッカチ方程式を解く" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "--- フィードバックゲイン ---\n", "[[ -6.77032961 -11.28813639]]\n", "--- 閉ループ極 ---\n", "[-3.1440682+0.94083196j -3.1440682-0.94083196j]\n" ] } ], "source": [ "X, E, F = care(P.A, P.B, Q, R)\n", "F = -F\n", "print('--- フィードバックゲイン ---')\n", "print(F)\n", "print('--- 閉ループ極 ---')\n", "print(E)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "最適レギュレータを用いたときの応答" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Acl = P.A + P.B@F\n", "Pfb = ss(Acl, P.B, P.C, P.D)\n", "\n", "tdata = np.arange(0, 5, 0.01)\n", "xini, tini = initial(Pfb, tdata, [-0.3, 0.4]) #ゼロ入力応答\n", "\n", "fig, ax = plt.subplots(figsize=(3, 2.3))\n", "\n", "ax.plot(tini, xini[:,0], label = '$x_1$')\n", "ax.plot(tini, xini[:,1], ls = '-.', label = '$x_2$')\n", "\n", "ax.set_xlabel('t')\n", "ax.set_ylabel('x')\n", "ax.grid(ls=':')\n", "ax.legend()\n", "\n", "# fig.savefig(\"sf_lqr.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 円条件(最適レギュレータのロバスト性)" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ ": sys[245]\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 = [[ 6.77032961 11.28813639]]\n", "\n", "D = [[0.]]\n", "\n" ] } ], "source": [ "from control.matlab import ss, nyquist, logspace\n", "\n", "# A = '0 1; -4 5'\n", "# B = '0; 1'\n", "# C = '1 0 ; 0 1'\n", "# D = '0; 0'\n", "\n", "A = [[0, 1], [-4, 5]]\n", "B = [[0], [1]]\n", "C = [[1, 0], [0, 1]]\n", "D = [[0], [0]]\n", "P = ss(A, B, C, D)\n", "L = ss(P.A, P.B, -F, 0)\n", "\n", "print(L)" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.patches as patches\n", "\n", "fig, ax = plt.subplots(figsize=(3, 3))\n", "x, y, w = nyquist(L, logspace(-2,3,1000), plot=False)\n", "ax.plot(x, y)\n", "ax.plot(x, -y, ls='--')\n", "ax.scatter(-1, 0, color='k')\n", "\n", "ax.grid(ls=':')\n", "ax.set_xlim(-2.5, 2.5)\n", "ax.set_ylim(-2.5, 2.5)\n", "\n", "c = patches.Circle(xy=(-1, 0), radius=1, fill=False, ec='k')\n", "ax.add_patch(c)\n", "\n", "fig.tight_layout()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "開ループ系のナイキスト軌跡が (-1, 0j) を中心とする単位円の中に入りません\n", "\n", "これにより,位相余裕が 60 [deg] 以上であることが保証されます" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### ハミルトン行列" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "最適レギュレータを用いたときの閉ループ極は,ハミルトン行列の安定固有値に等しいです" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-3.14406819+0.94083198j -3.14406819-0.94083198j 3.14406819+0.94083198j\n", " 3.14406819-0.94083198j]\n", "--- ハミルトン行列の安定固有値 ---\n", "[(-3.1440681937792814+0.9408319760374388j), (-3.1440681937792814-0.9408319760374388j)]\n", "--- フィードバックゲイン ---\n", "[[ -6.77032961 -11.28813639]]\n" ] } ], "source": [ "# H1 = np.c_[P.A, -P.B*(1/R)*P.B.T]\n", "# H2 = np.c_[ Q, P.A.T]\n", "# H = np.r_[H1, -H2]\n", "\n", "H = np.block( [ [P.A, -P.B*(1/R)@P.B.T], [-Q, -P.A.T]])\n", "eigH = np.linalg.eigvals(H)\n", "print(eigH)\n", "\n", "print('--- ハミルトン行列の安定固有値 ---')\n", "eigH_stable = [ i for i in eigH if i < 0]\n", "print(eigH_stable)\n", "\n", "F = -acker(P.A, P.B, eigH_stable)\n", "print('--- フィードバックゲイン ---')\n", "print(F)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 積分サーボ系" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [], "source": [ "from control.matlab import ss, acker, lsim\n" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ ": sys[252]\n", "Inputs (1): ['u[0]']\n", "Outputs (2): ['y[0]', 'y[1]']\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", " [0. 1.]]\n", "\n", "D = [[0.]\n", " [0.]]\n", "\n" ] } ], "source": [ "# A = '0 1; -4 5'\n", "# B = '0; 1'\n", "# C = '1 0 ; 0 1'\n", "# D = '0; 0'\n", "\n", "A = [[0, 1], [-4, 5]]\n", "B = [[0], [1]]\n", "C = [[1, 0], [0, 1]]\n", "D = [[0], [0]]\n", "P = ss(A, B, C, D)\n", "print(P)" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "matrix([[ 3., -7.]])" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Pole = [-1, -1]\n", "F = -acker(P.A, P.B, Pole)\n", "F\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "一定値の外乱がはいると,状態が0に収束しなくなります" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Acl = P.A + P.B@F\n", "Pfb = ss(Acl, P.B, P.C, P.D)\n", "\n", "Td = np.arange(0, 8, 0.01)\n", "Ud = 0.2 * (Td>=0)\n", "x, t, _ = lsim(Pfb, Ud, Td, [-0.3, 0.4])\n", "\n", "fig, ax = plt.subplots(figsize=(3, 2.3))\n", "\n", "ax.plot(t, x[:,0], label = '$x_1$')\n", "ax.plot(t, x[:,1], ls = '-.', label = '$x_2$')\n", "plot_set(ax, 't', 'x', 'best')\n", "\n", "# fig.savefig(\"sf_dis.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "拡大偏差系を構成し,積分型サーボ系を設計します" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ ": sys[254]\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)\n", "\n", "# 拡大系\n", "Abar = np.block([ [P.A, np.zeros((2,1))], [-P.C, 0] ])\n", "Bbar = np.block([ [P.B], [0] ])\n", "Cbar = np.block([ P.C, 0 ])\n", "\n", "# Abar = np.r_[ np.c_[P.A, np.zeros((2,1))], -np.c_[ P.C, 0 ] ]\n", "# Bbar = np.c_[ P.B.T, 0 ].T\n", "# Cbar = np.c_[ P.C, 0 ]" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "matrix([[ -7., -12., 5.]])" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Pole = [-1, -1, -5]\n", "F = -acker(Abar, Bbar, Pole)\n", "F\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "積分型サーボ系を用いると,一定値の外乱がはいっても,状態が0に収束します" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Acl = P.A + P.B*F[0,0:2]\n", "Acl = Abar + Bbar@F\n", "Pfb = ss(Acl, Bbar, np.eye(3), np.zeros((3,1)))\n", "\n", "Td = np.arange(0, 8, 0.01)\n", "Ud = 0.2 * (Td>=0)\n", "x, t, _ = lsim(Pfb, Ud, Td, [-0.3, 0.4, 0])\n", "\n", "fig, ax = plt.subplots(figsize=(3, 2.3))\n", "ax.plot(t, x[:,0], label = '$x_1$')\n", "ax.plot(t, x[:,1], ls = '-.',label = '$x_2$')\n", "# ax.plot(t, Ud, c='k')\n", "plot_set(ax, 't', 'x', 'best')\n", "\n", "# fig.savefig(\"servo.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 可制御性,可観測性" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [], "source": [ "from control.matlab import ss, ctrb, obsv\n" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ ": sys[256]\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", "\n", "A = [[0, 1], [-4, 5]]\n", "B = [[0], [1]]\n", "C = [1, 0]\n", "P = ss(A, B, C, 0)\n", "print(P)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "可制御性行列をもとめ,それが正則であれば,システムは可制御となります" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Uc=\n", " [[0. 1.]\n", " [1. 5.]]\n", "det(Uc)= -1.0\n", "rank(Uc)= 2\n" ] } ], "source": [ "Uc = ctrb(P.A, P.B)\n", "print('Uc=\\n',Uc)\n", "print('det(Uc)=', np.linalg.det(Uc))\n", "print('rank(Uc)=', np.linalg.matrix_rank(Uc))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "可観測性行列をもとめ,それが正則であれば,システムは可観測となります" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Uo=\n", " [[1. 0.]\n", " [0. 1.]]\n", "det(Uo)= 1.0\n", "rank(Uo)= 2\n" ] } ], "source": [ "Uo = obsv(P.A, P.C)\n", "print('Uo=\\n', Uo)\n", "print('det(Uo)=', np.linalg.det(Uo))\n", "print('rank(Uo)=', np.linalg.matrix_rank(Uo))\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 }