{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapter 7" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "ライブラリの読み込みと関数の定義" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "plt.rcParams['font.family'] ='sans-serif' #使用するフォント\n", "plt.rcParams['xtick.direction'] = 'in' #x軸の目盛線が内向き('in')か外向き('out')か双方向か('inout')\n", "plt.rcParams['ytick.direction'] = 'in' #y軸の目盛線が内向き('in')か外向き('out')か双方向か('inout')\n", "plt.rcParams['xtick.major.width'] = 1.0 #x軸主目盛り線の線幅\n", "plt.rcParams['ytick.major.width'] = 1.0 #y軸主目盛り線の線幅\n", "plt.rcParams['font.size'] = 10 #フォントの大きさ\n", "plt.rcParams['axes.linewidth'] = 1.0 # 軸の線幅edge linewidth。囲みの太さ\n", "plt.rcParams['mathtext.default'] = 'regular'\n", "plt.rcParams['axes.xmargin'] = '0' #'.05'\n", "plt.rcParams['axes.ymargin'] = '0.05'\n", "plt.rcParams['savefig.facecolor'] = 'None'\n", "plt.rcParams['savefig.edgecolor'] = 'None'\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# 線種を変更するジェネレータ\n", "def linestyle_generator():\n", " linestyle = ['-', '--', '-.', ':']\n", " lineID = 0\n", " while True:\n", " yield linestyle[lineID]\n", " lineID = (lineID + 1) % len(linestyle)\n", "\n", "# 時間応答のグラフを整える関数\n", "def plot_set(fig_ax, *args):\n", " fig_ax.set_xlabel(args[0])\n", " fig_ax.set_ylabel(args[1])\n", " fig_ax.grid(ls=':')\n", " if len(args)==3:\n", " fig_ax.legend(loc=args[2])\n", "\n", "# ボード線図を整える関数\n", "def bodeplot_set(fig_ax, *args):\n", " fig_ax[0].grid(which='both', ls=':')\n", " fig_ax[0].set_ylabel('Gain [dB]')\n", "\n", " fig_ax[1].grid(which='both', ls=':')\n", " fig_ax[1].set_xlabel('$\\\\omega$ [rad/s]')\n", " fig_ax[1].set_ylabel('Phase [deg]')\n", "\n", " if len(args) > 0:\n", " fig_ax[1].legend(loc=args[0])\n", " if len(args) > 1:\n", " fig_ax[0].legend(loc=args[1])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## オブザーバ" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "from control.matlab import ss, acker, lsim\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ ": sys[2]\n", "Inputs (1): ['u[0]']\n", "Outputs (1): ['y[0]']\n", "States (2): ['x[0]', 'x[1]']\n", "\n", "A = [[ 0. 1.]\n", " [-4. -5.]]\n", "\n", "B = [[0.]\n", " [1.]]\n", "\n", "C = [[1. 0.]]\n", "\n", "D = [[0.]]\n", "\n" ] } ], "source": [ "# A = '0 1; -4 -5'\n", "# B = '0; 1'\n", "# C = '1 0'\n", "# D = '0'\n", "\n", "A = [[0, 1], [-4, -5]]\n", "B = [[0], [1]]\n", "C = [1, 0]\n", "D = [0]\n", "P = ss(A, B, C, D)\n", "print(P)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### オブザーバゲインの設計(極配置)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "acker関数を用いてオブザーバゲインを設計するために,A行列とC行列の転置をとったものを用いる\n", "\n", "得られるゲインの転置をとることでオブザーバゲインが得られる" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-15.]\n", " [-46.]]\n" ] } ], "source": [ "# オブザーバ極\n", "observer_poles=[-10+5j,-10-5j]\n", "\n", "# オブザーバゲインの設計(状態フィードバックの双対)\n", "L = -acker(P.A.T, P.C.T, observer_poles).T\n", "print(L)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A+LCの固有値が指定極になっている" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([-10.+5.j, -10.-5.j])" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.linalg.eigvals(P.A + L @ P.C)\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "G = ss(P.A, P.B, np.eye(2), [[0],[0]])\n", "Obs = ss(P.A + L@P.C, np.c_[P.B, -L], np.eye(2), [[0,0],[0,0]] )\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,2, figsize=(6, 2.3))\n", "\n", "Td = np.arange(0, 3, 0.01)\n", "X0 = [-1, 0.5]\n", "# 入力 u = Fx\n", "u = np.zeros_like(Td)\n", "# u = 10*np.sin(10*T)\n", "\n", "x, t, _ = lsim(G, u, Td, X0)\n", "ax[0].plot(t, x[:, 0], ls='-.', label='${x}_1$')\n", "ax[1].plot(t, x[:, 1], ls='-.', label='${x}_2$')\n", "\n", "# 出力 y = Cx\n", "y = x[:, 0]\n", "# オブザーバで推定した状態の振る舞い\n", "xhat, t, _ = lsim(Obs, np.c_[u, y], Td, [0, 0])\n", "ax[0].plot(t, xhat[:, 0], label='$\\\\hat{x}_1$')\n", "ax[1].plot(t, xhat[:, 1], label='$\\\\hat{x}_2$')\n", "\n", "for i in [0, 1]:\n", " plot_set(ax[i], 't', '', 'best')\n", " ax[i].set_xlim([0, 3])\n", "\n", "ax[0].set_ylim([-2, 1])\n", "ax[1].set_ylim([-3, 1])\n", "ax[0].set_ylabel('$x_1, \\\\hat{x}_1$')\n", "ax[1].set_ylabel('$x_2, \\\\hat{x}_2$')\n", "\n", "fig.tight_layout()\n", "# fig.savefig(\"obs.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 出力フィードバック" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "オブザーバ併合レギュレータを設計します" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-25. -5.]]\n" ] } ], "source": [ "from control.matlab import tf, feedback, initial\n", "\n", "# レギュレータ極\n", "regulator_poles = [-5+2j, -5-2j]\n", "# 極配置\n", "F = -acker(P.A, P.B, regulator_poles)\n", "print(F)\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "K:\n", " : sys[5]\n", "Inputs (1): ['u[0]']\n", "Outputs (1): ['y[0]']\n", "States (2): ['x[0]', 'x[1]']\n", "\n", "A = [[-15. 1.]\n", " [-75. -10.]]\n", "\n", "B = [[15.]\n", " [46.]]\n", "\n", "C = [[-25. -5.]]\n", "\n", "D = [[0.]]\n", "\n", "----------------\n", "K(s)= \n", " -605 s - 2725\n", "----------------\n", "s^2 + 25 s + 225\n", "\n" ] } ], "source": [ "# 出力フィードバック(オブザーバ+状態フィードバック)\n", "K = ss(P.A+P.B@F+L@P.C, -L, F, 0)\n", "print('K:\\n', K)\n", "print('----------------')\n", "print('K(s)=', tf(K))\n", "\n", "# フィードバック系\n", "Gfb = feedback(P, K, sign=1)\n" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(-1.5, 0.5)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(3, 2.3))\n", "Td = np.arange(0, 3, 0.01)\n", "\n", "y, t = initial(P, Td, [-1, 0.5])\n", "ax.plot(t,y, ls='-.', label='w/o controller')\n", "\n", "y, t = initial(Gfb, Td, [-1, 0.5, 0, 0])\n", "ax.plot(t,y, label='w/ controller')\n", "\n", "plot_set(ax, 't', 'y', 'best')\n", "ax.set_xlim([0, 3])\n", "ax.set_ylim([-1.5, 0.5])\n", "\n", "# fig.savefig(\"obs2.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 外乱オブザーバ" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "出力に0.5の定値外乱が加わるとすると,推定がうまくいきまんせん" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,2, figsize=(6, 2.3))\n", "\n", "Td = np.arange(0, 3, 0.01)\n", "X0 = [-1, 0.5]\n", "d = 0.5*(Td>=1.5)\n", "\n", "G = ss(P.A, P.B, np.eye(2), [[0],[0]])\n", "x, t = initial(G, Td, X0)\n", "ax[0].plot(t, x[:, 0], ls='-.', label='${x}_1$')\n", "ax[1].plot(t, x[:, 1], ls='-.', label='${x}_2$')\n", "\n", "# 入力 u\n", "u = np.zeros_like(Td)\n", "# 出力 y = Cx+d\n", "y = x[:, 0]+d\n", "Obs = ss(P.A + L@P.C, np.c_[P.B, -L], np.eye(2), [[0,0],[0,0]] )\n", "\n", "xhat, t, _ = lsim(Obs, np.c_[u, y], Td, [0, 0])\n", "ax[0].plot(t, xhat[:, 0], label='$\\\\hat{x}_1$')\n", "ax[1].plot(t, xhat[:, 1], label='$\\\\hat{x}_2$')\n", "\n", "for i in [0, 1]:\n", " ax[i].grid(ls=':')\n", " ax[i].set_xlim([0, 3])\n", " ax[i].set_xlabel('t')\n", " ax[i].legend()\n", "\n", "ax[0].set_ylim([-2, 2])\n", "ax[0].set_ylabel('$x_1, \\\\hat{x}_1$')\n", "ax[1].set_ylabel('$x_2, \\\\hat{x}_2$')\n", "\n", "fig.tight_layout()\n", "# fig.savefig(\"dis_obs.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "拡大系を構成し,外乱もオブザーバで推定できるようにする" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 75.75]\n", " [-91. ]\n", " [-93.75]]\n" ] } ], "source": [ "# オブザーバ極\n", "observer_poles=[-10+5j,-10-5j, -3]\n", "\n", "# オブザーバゲインの設計(状態フィードバックの双対)\n", "\n", "Abar = np.block( [ [P.A, np.zeros([2,1])], [np.zeros((1,3))] ])\n", "Bbar = np.block( [ [P.B], [0] ])\n", "Cbar = np.block( [ P.C, 1 ] )\n", "\n", "Lbar = -acker(Abar.T, Cbar.T, observer_poles).T\n", "print(Lbar)\n", "\n", "Aob = Abar + Lbar@Cbar\n", "Bob = np.block([Bbar, -Lbar])\n", "Obs = ss(Aob, Bob, np.eye(3), np.zeros([3,2]) )\n" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([-10.+5.j, -10.-5.j, -3.+0.j])" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Obs.poles()\n" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(-0.5, 2.0)" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,2, figsize=(6, 2.3))\n", "\n", "Td = np.arange(0, 3, 0.01)\n", "X0 = [-1, 0.5]\n", "d = 0.5*(Td>=1.5)\n", "x, t = initial(G, Td, X0)\n", "ax[0].plot(t, x[:, 0], ls='-.', label='${x}_1$')\n", "ax[1].plot(t, x[:, 1], ls='-.', label='${x}_2$')\n", "\n", "\n", "# 入力 u = Fx\n", "u = np.zeros_like(Td)\n", "# 出力 y = Cx+d\n", "y = x[:, 0]+d\n", "xhat, t, _ = lsim(Obs, np.c_[u, y], Td, [0, 0, 0])\n", "#xhat, t, x0 = lsim(Obs, x[:, 0]+d, T, [0, 0, 0])\n", "ax[0].plot(t, xhat[:, 0], label='$\\\\hat{x}_1$')\n", "ax[1].plot(t, xhat[:, 1], label='$\\\\hat{x}_2$')\n", "\n", "for i in [0, 1]:\n", " ax[i].grid(ls=':')\n", " ax[i].set_xlim([0, 3])\n", " ax[i].set_xlabel('t')\n", " ax[i].legend()\n", "\n", "ax[0].set_ylabel('$x_1, \\\\hat{x}_1$')\n", "ax[1].set_ylabel('$x_2, \\\\hat{x}_2$')\n", "\n", "fig.tight_layout()\n", "# fig.savefig(\"dis_obs2.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n", "\n", "fig, ax = plt.subplots(figsize=(3, 2.3))\n", "ax.plot(t, xhat[:, 2], label='$\\\\hat{x}_2$', color='k')\n", "ax.grid(ls=':')\n", "ax.set_xlabel('t')\n", "ax.set_ylabel('$\\\\hat{d}$')\n", "ax.set_ylim([-0.5, 2])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "外乱 0.5 が推定できていて,状態推定もできています" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 定常カルマンフィルタ" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "from control.matlab import ss, lqe, lsim\n" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ ": sys[12]\n", "Inputs (1): ['u[0]']\n", "Outputs (1): ['y[0]']\n", "States (2): ['x[0]', 'x[1]']\n", "\n", "A = [[ 0. 1.]\n", " [-4. -5.]]\n", "\n", "B = [[0.]\n", " [1.]]\n", "\n", "C = [[1. 0.]]\n", "\n", "D = [[0.]]\n", "\n" ] } ], "source": [ "# A = '0 1; -4 -5'\n", "# B = '0; 1'\n", "# C = '1 0'\n", "# D = '0'\n", "\n", "A = [[0, 1], [-4, -5]]\n", "B = [[0], [1]]\n", "C = [1, 0]\n", "D = [0]\n", "P = ss(A, B, C, D)\n", "print(P)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-0.0245608 ]\n", " [-0.00030162]]\n" ] } ], "source": [ "QN = 1\n", "RN = 1\n", "L, _, _ = lqe(P.A, P.B, P.C, QN, RN)\n", "L = -L\n", "print(L)\n" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.9890062381774168\n", "0.03954331794165088\n", "[[-0.0245608 ]\n", " [-0.00030162]]\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Td = np.arange(0, 6, 0.01)\n", "u = 0.5 * np.sin(6*Td) + 0.5 * np.cos(8*Td)\n", "\n", "QN, RN = 1, 1\n", "w = np.random.normal(loc=0, scale=np.sqrt(QN), size=len(Td))\n", "v = np.random.normal(loc=0, scale=np.sqrt(RN), size=len(Td))\n", "\n", "print(np.var(w))\n", "print(np.mean(w))\n", "\n", "L, _, _ = lqe(P.A, P.B, P.C, QN, RN)\n", "L = -L\n", "print(L)\n", "# L = np.matrix([[-1], [-1]])\n", "Obs = ss(P.A + L@P.C, np.block([P.B, -L]), np.eye(2), np.zeros([2,2]))\n", "\n", "X0 = [-0.3, 0.2]\n", "_, t, x = lsim(P, u+w, Td, X0)\n", "_, t, xorg = lsim(P, u, Td, X0)\n", "\n", "# 出力 y = Cx\n", "y = x[:, 0]+v\n", "\n", "fig, ax = plt.subplots(2,2, figsize=(6, 4.6))\n", "ax[0,1].plot(t, y, ls='-.', label='$y$', c='gray', lw=0.5)\n", "ax[1,0].plot(t, xorg[:,0], ls='--', label='$x_1$', c='k')\n", "ax[1,1].plot(t, xorg[:,1], ls='--', label='$x_2$', c='k')\n", "ax[0,0].plot(t, u+w, ls='-.', label='$u+w$', c='gray', lw=0.5)\n", "\n", "# 入力 u = Fx\n", "#u = [ [F[0,0]*x[i,0]+F[0,1]*x[i,1]] for i in range(len(x))]\n", "#u = np.sin(T)\n", "#u = 0*(T>0)\n", "\n", "# オブザーバで推定した状態の振る舞い\n", "xhat, t, _ = lsim(Obs, np.c_[u, y], Td, [0, 0])\n", "ax[1,0].plot(t, xhat[:, 0], label='$\\\\hat{x}_1$', c='k')\n", "ax[1,1].plot(t, xhat[:, 1], label='$\\\\hat{x}_2$', c='k')\n", "ax[0,0].plot(t, u, label='$u$', c='k', ls='--')\n", "\n", "for i in [0, 1]:\n", " for j in [0, 1]:\n", " plot_set(ax[i,j], '$t$', '', 'best')\n", " ax[i,j].set_xlim([0, 6])\n", "\n", "ax[0,1].set_ylim([-4, 4])\n", "ax[0,1].set_ylabel('$y$')\n", "ax[0,0].set_ylabel('$u$')\n", "ax[0,0].set_ylim([-4, 4])\n", "ax[1,0].set_ylim([-0.4, 0.4])\n", "ax[1,0].set_ylabel('$x_1$')\n", "ax[1,1].set_ylim([-0.4, 0.4])\n", "ax[1,1].set_ylabel('$x_2$')\n", "\n", "\n", "fig.tight_layout()\n", "# fig.savefig(\"ex_kalman.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## ロバスト制御" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "from control.matlab import tf, bode, logspace, mag2db, ss2tf, step, feedback\n" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "g = 9.81 # 重力加速度[m/s^2]\n", "l = 0.2 # アームの長さ[m]\n", "M = 0.5 # アームの質量[kg]\n", "mu = 1.5e-2 # 粘性摩擦係数\n", "J = 1.0e-2 # 慣性モーメント\n", "\n", "P = tf( [0,1], [J, mu, M*g*l] )\n", "\n", "ref = 30 # 目標角度 [deg]\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 乗法的不確かさ" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# 垂直駆動アームのノミナルモデル\n", "Pn = tf( [0,1], [J, mu, M*g*l] )\n", "\n", "# Pn = tf( [0, 1], [1, 1])\n", "# 不確かさ\n", "delta = np.arange(-1, 1 , 0.1)\n", "WT = tf( [10, 0], [1, 150])\n", "\n", "fig, ax = plt.subplots(1, 2, figsize=(6,2.3))\n", "# fig, ax = plt.subplots(1, 2)\n", "\n", "for i in range(len(delta)):\n", " # 不確かさをもつ制御対象\n", " P = (1 + WT*delta[i])*Pn\n", " mag, _, w = bode(P, logspace(-3,3), plot=False)\n", "\n", " ax[0].semilogx(w, mag2db(mag), color = 'k', lw = 0.3)\n", "\n", " # 乗法的不確かさ\n", " DT = (P - Pn)/Pn\n", " mag, _, w = bode(DT, logspace(-3,3), plot=False)\n", "\n", " ax[1].semilogx(w, mag2db(mag), color = 'k', lw = 0.3)\n", "\n", "mag, _, w = bode(Pn, logspace(-3,3), plot=False)\n", "ax[0].semilogx(w, mag2db(mag), lw =2, color='k')\n", "\n", "mag, _, w = bode(WT, logspace(-3,3), plot=False)\n", "ax[1].semilogx(w, mag2db(mag), lw =2, color='k')\n", "\n", "ax[0].set_ylim(-100, 50)\n", "ax[1].set_ylim(-100, 50)\n", "bodeplot_set(ax)\n", "ax[0].set_xlabel('$\\\\omega$ [rad/s]')\n", "ax[0].set_ylabel('Gain of $P$ [dB]')\n", "ax[1].set_ylabel('Gain of $\\\\Delta W_T$ [dB]')\n", "#ax.grid(which=\"both\", ls=':')\n", "#ax.set_ylabel('Gain [dB]')\n", "#ax.set_xlabel('$\\omega$ [rad/s]')\n", "\n", "fig.tight_layout()\n", "# fig.savefig(\"robust_plant.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 混合感度問題" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "K= \n", " 7.21 s^4 + 1098 s^3 + 3259 s^2 + 1.081e+05 s + 9.032e+04\n", "---------------------------------------------------------------\n", "s^5 + 165.1 s^4 + 2448 s^3 + 2.449e+04 s^2 + 2.273e+04 s + 5540\n", "\n", "gamma = 0.9527651218302327\n" ] }, { "data": { "image/png": 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ICAjAn3/+WWbetAS9Powx5OXl2Vz3HMdxOH/+fKUW/tRoNLh79y7dM8WwRz3Eikn2qGVZWKLfjR8/HtnZ2QgODsbz588lscESdbEExNTDaipNp06dwpQpU3Dx4kUcPXoUarUawcHBepvQLl68GN988w1Wr16N2NhYKJVKBAUFITMzs9S8ba1yIAS25oT5+flITEyEk5MTqlatWuF8GGNIT0+ne6YY9qiHWDHJHrUsC0v0u0aNGuHYsWN4/PgxwsLCyvydEQNL1MUSEFUPZqWkpKQwAOzUqVOMMca0Wi1TKpXsv//9L39OXl4e8/T0ZOvWrTOaR1xcHAPA4uLiDN7Lzc1lN2/eZLm5ueIUQEROnTrFBg4cyGrVqsUAsD179hg9b9y4cez9999n3377LXNzc2MqlYp/LzMzkykUCtazZ0+9z5w+fZoBYLdv3y63XVJqum7dOubo6MiePn1q9mvbA6X5kr1Q2ZhEGlonly9fZh4eHuyLL76Q2hTi/xHTl6ympak4L1++BABUq1YNAJCQkIDk5GQEBwfz5zg5OcHf3x/nz58vNa8bN27gypUriI2NRWxsLJ48eQKNRsPXVhlj5UprtdpS04wxg7Quj5LS5bl+VlYW2rRpg9WrV/PvFT9Ho9Hg4MGDGDJkCAICApCVlYXLly/z1z127BiUSiViY2ORk5PD23vy5EnUrl0bTZo0qVCZimqhVqtLTWs0Gr20rvWrpLRardZL666bm5uL//73v3jttddQrVo1/rhKpdJL62zTpRljBmmNRoP4+Hjk5eXx9uoGzZuzTCWlK1Im3XdTtBzlLZOtThwoD0LFpJLikbXdE0Le5xqNBjdv3uRtsKQytWvXDufPn8f7779v9u+J4pH545FVVpoYY5g1axZ69uyJVq1aAQA/GK9mzZp659asWbPMgXrh4eHo2LEjunTpgi5dumD9+vW4ffs2/yXk5OTwiz1mZ2ejoKAAQGHlRPflZGZm8udnZmbyN1ZGRgZ/02RkZPA3R/E0UPjF69IajYZv7lWr1XxapVIhKysLAFBQUMB3BeTn5yMnJwcAEBgYiI8++gjDhg3jzwMKKw865zp+/DhkMhm6du2KunXronbt2jh58iSysrKgVqtx+vRphIaGolGjRjh//jxfppMnT6JHjx4VLpPu+mlpaTh9+jQA4MmTJ/yPyIMHDxATEwOg8Efn6tWrAIA7d+7g+vXrAID4+HjEx8cDAK5fv447d+4AAK5evYqEhAQAQExMDB48eACgcA+pxMREzJs3D6dPn+ZnvJw4cQIvXrwAAERFRfEaR0ZGIi8vD2q1GpGRkVCr1cjLy0NkZCRf5uPHjwMAXrx4wa8SbM4ynT9/np/2LESZMjMzERUVVeEyFR/LY28IGZOMxSNrvCeEvs8TExMttkyMMcjlcnz//fcYNWoUNBqN2b4nikdmjkflbZqyBCZPnswaNGjAHjx4wB87d+4cA8AeP36sd+748eNZSEiI0Xx0TXhbt25lcXFxLCYmhsXExLDHjx+zrKws9ueff7Lc3Fym1WqZVqtljDGT0hqNptS0Vqs1SOvyKCldnusXTQNgv/32m8Hx2bNns7feeos/Pnr0aBYcHMyf07lzZ7Zz5042adIkNm/ePKbRaFheXh5zcXFhGzZsqFCZcnJyeE01Gg3fHVhSWq1W66XVanWpaZVKpZfWaDRMrVazpk2bssGDB+sdZ4yxgoICvbSuTLq0Vqs1SOvKpEtrNBq9tDnKVFpaqjJdunTJrruWhIhJpcUja7wnbPE+L6tMO3fuZDKZjE2YMIEVFBTYRJms8XsSMx5Z3TzFadOmISIiAqdPn0bdunX540qlEkDh012tWrX44ykpKQZPesVp3rw5OnTooHcsLy+Pn1padOp9cnJymQub1a9fH97e3khLS0NSUhKf9507d/QGiRqjVatWcHR0REJCAjQaDZo0aaJ3/fKmi/5f9Pj+/fuxdOlS/nhAQABmzpwJjUaDnJwcXL16Fb1794ZWq8XKlSshk8lw6dIl5Obmom/fvnxen3/+OXbu3AmO4+Dk5IRff/0VDRs21LumsbRMJoNMJis1LZfLeXtNSRedZqpL//LLL/jrr7+wbds2g3McHBzKndY1h7do0cLkcghdptLSFSkTUPjd6NIVKZOtLU9RHoSOScbiUVGs5Z7QIcR9rtFocOvWLd7vLLVMI0aMQHZ2Nt588014eHhgyZIlJpWvomWieGT+eGQ1lSbGGKZNm4Y9e/bg5MmTaNiwod77DRs2hFKpxNGjR9G+fXsAhd1Sp06dwldffSWYHevXr8enn35a6jkbN27E+PHjsXfvXkyYMIHvxw0PDy9z36IHDx6gbt26eP/995GRkYEjR44IZruO+Ph4PHz4EP369eOPBQYGIjs7G7GxsXj+/DmaNGkCHx8f+Pv7Y+zYscjOzsbJkydRv359NGrUCEBhk+zJkydx7do1KBQKPHz4EFWqVBHc3oqi1Wrx+eefIyQkBJ07d5baHMLGsJSYRFgW4eHhyMzMxPTp06FUKjFnzhypTSIExGoqTVOmTMH27duxb98+uLu782MCPD094eLiAo7jMGPGDHz55Zdo0qQJmjRpgi+//BKurq4YPXp0qXkXrUmXxcSJEzF48OBSz6lfvz4AYOjQoXpPjJs3by6zpcnHxwcA8NVXX4k27T8iIgJBQUFwcXHhj/n5+aFu3bqIjo5Geno6AgICwHEclEolGjZsiHPnziE6Ohp9+vThP5OcnIyqVavyTxZFn7ItgYiICPzxxx9Yu3atYHnK5XJ+zArxN+XxIVtBrJhkj1qWhbX53bRp0wAAQUFBol7H2nQxF6L6kOAdfiIBwOhr06ZN/DlarZYtWLCAKZVK5uTkxHr37s1u3LhRYp66MQQxMTEG71nzkgNFgZElB7p168a+//57g3PHjh3LgoKCWKdOndjWrVv5/ucJEyawWbNmMWdnZ7Zlyxb+/IyMDNaqVSvWvHlzNn36dKM6FsXcmr7++ussICBA0DzVajW7cuUK369PFBITE2N3Y5qEjkmlxSN7x5r9LjMzkx08eFCUvK1ZFzERMx5ZTUsTM2GxKo7jsHDhQixcuFB8gyyYrKws3L17l/8/ISEB165dQ7Vq1eDs7IzY2Fjs3bvX4HOBgYGYMmUKVCoVevXqxR/39/fHO++8g7y8PAQGBvLH3d3dcfXqVURHR+PYsWMICgrCzp079aZYS8m2bdvw7NkzwfMt2kJH2C8Uk8yLtfrd+vXrMXfuXOzYsQMjRowQPH9r1cVaManSpJu6Xh7WrVvHdzVZOrbWHH758mW9ys2sWbMAAOPGjUOvXr3QtWtXo99NYGAgcnNz0bx5c/j6+vLH/f39kZmZicaNG6NevXp6n1EoFAgKCkJQUBC8vb0REREheaWJMYb4+Hi0bNkSNWrUEDRvuVyO5s2bC5qnLWBuH7LlmGRr8UgIrNnvZs6ciatXr2LMmDGoUqUKwsLCBMvbmnUREzF9yKR1mvbu3QtHR0d4enqa9Dp48CC/lpA1oFtfyVYICAjg10sq+tq8eTP27dtX4pgsX19fMMZw8+ZNZGdn80/SdevWBWNMr/UKAG7fvo179+4BKKyo/Pnnn2jQoIG4hTOBY8eO4ZVXXsG1a9cEz1utViM2Ntbm7pnKYm49bDkm0b1liDX7nUwmw6ZNmxAWFobhw4fj1KlTguVtzbqIiZh6mNw9t3LlSpOf0nbt2lVhg6TAnqZL9+zZE6+//nqZ55lSU8/KysLUqVP5xSs7duyIqVOnVtrGyhIYGIiIiAi0bdtW8Lw5jkPVqlXt6p4xBSn0sNWYRPeWIdbudw4ODtixYwcGDRqEy5cvw9/fX5B8rV0XsZB8yYHo6Gh+awBTOHToEOrUqVNho8yNPTWHz507t8xzOI6Ds7Nzmed17NgRFy5cEMIswVCpVHBwcMCgQYNEyV8ul8PPz0+UvK0Zc/uQLccke4pHpmILfufs7IxDhw7xs40zMzPh7u5eqTxtQRcxkLx7zt/fX2/BqrLo2bMnnJycKmyUuaGmTX0YY8jKyrK6nbMZY+jbty/+85//iHYNtVqN8+fP0z1TDHPrYcsxie4tQ2zF73T37I4dO9C8eXODIQ/lxVZ0ERox9ajU3nOMMZw4cQIHDx5Eenq6UDaZHd1KosTfFF2l1VqIjo7GmTNn0KlTJ9GuIZPJUKdOHbpnimEpethCTLIULS0JW/O7Pn36wN3dHf369eP3b6sItqaLUIiph8k5v3jxAuPGjUPr1q0xYcIEZGRkoFevXujXrx8GDRqE5s2b85v9WRt0w+mj2xLFmvrJGWNYsGABOnbsiNDQUNGuI5PJ0KBBA7pniiGFHrYak+jeMsTW/M7HxwdHjx4FYwxBQUFISUmpUD62potQWESlac6cObhw4QL++c9/4saNG+jfvz80Gg0uXLiAS5cuoWXLlvjoo49EM1RMqGlTH8YYMjMzrap77ujRozh79iz+85//iFrZU6vVOH36NN0zxZBCD1uNSXRvGWKLflevXj0cP34cL1++xOzZsyuUhy3qIgQWMXvu0KFD2L59O/z9/fHmm2+iXr16OHHiBLp27QqgcNuPsrYXsVRKq5VaU8VBSMQY/yGWlowxfPLJJ+jatauorUxA4b3SuHFjerIrhhR62GpMonvLEFv1Oz8/P0RHR5e5qXxJ2KoulcUiWpqePn2Kpk2bAgDq1KkDZ2dnvYUO69evj9TUVOEtNAPGBNaN6cnJyTG3OZLDcRwcHR0Fb7HRaSn0eKnIyEjExMTgs88+E71LkcYQGEcKPWw1JtG9ZYgt+13z5s1RtWpVJCYmYvz48cjLyzP5s7asS2UQUw+TW5q0Wq3eND65XK73A2VN41+KY6wpTy6Xw8vLi+9rdnV1teoylgfGGLKzs1GlShVByswYQ05ODlJSUuDl5SXodFDGGObPn8+PZREbXXN47969yzV7y9aRonvAVmMSdbUYYg9+l5SUhJ9++glpaWn49ddfTXq4tAddKoJFdM8BwHfffQc3NzcAhUZt3rwZ3t7eAArXnLBWSqqVKpVKAKjwID1rhTEGrVYLmUwm6A+Pl5cXr6lQHD9+HFeuXEF0dLRZfiRlMhlatWpFT3bFkEoPW4xJdG8ZYg9+17t3b+zevRtDhgzBm2++ia1bt5ZZXnvQpSJYREtT/fr1sXHjRv5/pVKJH3/80eAca6QkgTmOQ61ateDj4wOVSmVmq2wLBwcHURYc69u3L86ePYsePXoInrcxZDKZVexfZm6kCNq2GpPoB9AQe/G7sLAwbN++HaNGjULVqlWxatWqUs+3F13Ki0VUmhITE0UzQmrKasqTy+V2tUqvSqXCiRMn0KdPH4ter+nFixfw8vIyW4UJsB5tzI0UXUq2GpOoe84Qe/K7ESNGIDs7G9WrVy/zXHvSpTxY7OKWtgI92ekjl8vRuXNni64oqtVqdO/eHfPnzzfrda1BGykgHxIO0tIQe/O78PBwDBo0CIwxHDt2rMTz7E0XU5G8pWnlypUmZzh9+vQKGyMVFKT0kclk5drXSwrkcjn+85//mH3fJWvQRgrM7UO2HJMoHhlir3538OBBDBo0CCtWrDB6H9urLmUheaVp2bJlev+npqYiJycHXl5eAAq7SVxdXeHj42N1AQqg5vDiqFQqREVFITg42CKbfBlj4DgO//jHP8x+bUvXRirM7UO2HJMoHhlir343YMAAzJkzB++++y7c3d3x5ptv6r1vr7qUheTdcwkJCfzriy++QLt27RAfH4/nz5/j+fPniI+PR4cOHfDZZ5+JZqiYUNOmPgqFAr169bLYKayLFy/GiBEjJFl41NK1kQpz+5AtxySKR4bYq99xHIfFixfj3//+N8aPH49ff/1V73171aUsxPShcrdhffLJJ1i1ahWaNWvGH2vWrBmWLVuGjz/+WFDjzIW1ruciFhzHwcPDwyJ1ef78ORYtWgSlUimJfZasjZRIqYetxSS6twyxZ7/jOA5r167FqFGjsGfPHoP37FWX0hBTj3JXmp48eWJ0+r1Go8HTp08FMcrcUHO4PiqVCvv27bPIZRYWLVoEjUaDTz75RJLrW7I2UiKlD9laTKJ4ZIi9+51cLsfmzZuxdetWAOBXDbd3XUpC8u65ovTt2xcTJkzA5cuX+e6Ry5cvY+LEiWZZkVkMqDlcH4VCgeDgYItr8k1KSsKqVaswZ84cs61NotVqcfToUWzYsAGLFy/G/PnzcfDgQaxatYp+3IogpQ/ZWkyieGSIpcYkc+Lg4ACFQoG4uDg0btwYMTExpEsJiOlD5Vb6hx9+wLhx49ClSxd+4JlarUZISAi+++47wQ0kpMESnXDBggXw9PTErFmzzHI9lUqF4cOHY//+/Ubfv3r1KjZv3kw/chJDMck+sMSYJAXNmjWDr68v+vfvj5MnT6JFixZSm2RXlPsurFGjBiIjI3Hnzh3Ex8eDMYYWLVrwG2daIxqNRmoTLAq1Wo3IyEiEhYVZzIyM33//HVu2bMGqVavg7u4u+vUYY5gwYUKJFSYA2LZtGxQKBb7//nu7nyYupQ/ZWkyieGSIJcYkqXBzc8PBgwcRGBiI4OBgLFiwAOPHj7d7XYoipg9VuOrepEkTNGnSREhbJINaCvRRKBQICwuzmCc7xhimTZuGZs2aYcKECWa55ocffogtW7YAABwdHfHVV1+hXr168PT0REJCAiZPnszvdaZQKLB+/Xq7rjhZgg/ZSkyyBC0tDUuLSVLj5eWFqKgo9O7dGxs3bsTEiROlNsmikHz23KxZs5CdnW1yph9++CGeP39eYaMI6bGk8TqnT5/GmTNnsHLlSjg6Oop+veXLl+Orr74CUDgLY/v27ZgxYwaGDx+Ovn374l//+hd+/vln3jG/++47TJkyRZIlEOwVikn2hyXFJEugRo0aOHr0KL777juaPWdGTKo0rVixAjk5OSZnumbNGrx48aKiNpkdag7XR61WIyoqymKClL+/P+Li4hAUFCT6tX7++WfMnDmT/3/NmjUYPnw4/79OmyFDhmD79u1869K6desQEhKCv/76S3QbLRFz+5AtxySKR4ZYWkyyFGrWrIkHDx7g5cuXmDp1Kp49eya1SRaB5N1zjDE0bdrU5NpseZ4ALQFq8tXHwcEBQ4YMkdoMAMCff/6Jli1bokOHDqJf6/jx4xg3bhz///z58/HOO+/onVNUm5EjR0KtVmPs2LH8LLtWrVrhvffew7x581ClShXRbbYUzO1DthyTKB4ZYkkxyZLQ6XLnzh388ssvuHTpEo4fPw4PDw+pTZMUMX3IpJw3bdpU7oxr1qxZ7s8Ixdq1a7FkyRI8efIEr7zyCpYvX45evXqVeD51q+jDGENmZibc3d0lbfZ99OgR2rdvj/Xr1xtsHyA0165dw2uvvcavd/Lvf/8bCxcuNDivuDajR4+Gl5cX3nnnHSQlJUGlUuHLL7/Etm3bMGnSJHTt2hWdOnWy+SBmbh+ypphE8ajyWEpMsjR0uvj5+SEqKgqBgYEYOHAgDh8+DFdXV6nNkwwxfcikSlPRp29L55dffsGMGTOwdu1a9OjRA+vXr0doaChu3ryJ+vXrG/0MNYfro1arcebMGcn3M6pTpw4OHDhQ6g+MECQmJiI0NBSZmZkAgMGDB2PNmjVGg7MxbcLCwhAfH48vv/wSS5YsQUFBAZKSkjBv3jwAheOiWrRogWbNmqFq1aqoVq0aqlatCg8PDzg6OsLBwYH/K5PJ9F46G4raUtwuS/gRuX37tlmvZy0xieKRMFhKTDIHWq0WKSkpePToER49eoTHjx8jPz8fQKGvcxyHWrVqYdiwYdBoNLwu7du3x6FDhxAUFIRhw4bhwIEDdttqKaYPcczGHmu6du2KDh064Ntvv+WPtWjRAkOHDsWiRYv0zr1y5Qo6duyIrVu34pVXXuGFrlu3Lr94olwuh1qtBsdxfFr3g1ZSWqVSQS6X82mFQgGO4/g0UBgEiqYdHBzAGOPTWq0WGo2GT2u1WigUihLTGo0GjDE+rbO9pLSll+np06d8y4CYZXrx4gV69erF/+i/+uqrOHz4MN8yVN4y3bp1CzNnzkRUVFRlb2WrJC4uzixdqdZCReLR5MmTUa9ePWi1WgBAtWrV4OnpCaBw93aNRgOO40xOF7//5XI5OI7j00Dhj0zRtEKhAGOMTxf3UcYY5HK5XloXg4of15VDJpOVmNbZy3GcQTmMnaPz9aKxCQCf1tnOcZxeWqvV8p9Vq9X8GCmNRgO1Ws2/r1KpwBiDSqUqMa1Wq/nPaTQaPhboylU0rdNDFzt05+ryyc7O1nvpPlca7733HhYvXmwQj44dO4bLly/j/fff538T7OV3Q1eOuLg4dO3aVZx4xGyI/Px8JpfL2W+//aZ3fPr06ax3794G58fFxTEABq8FCxawK1eusPj4eMYYYzExMezOnTuMMcbOnTvHEhMTGWOMnTp1ij18+JAxxtjx48fZ06dPGWOMHT58mD179owxxtiBAwfYy5cvGWOM7d27l+Xk5LCCggK2d+9eVlBQwHJyctjevXsZY4y9fPmSHThwgDHG2LNnz9jhw4cZY4w9ffqUHT9+nDHG2MOHD9mpU6cYY4wlJiayc+fOMcYYu3PnDouJiWGMMRYfH8+uXLnCGGPsxo0b7MaNG4wxZnKZHjx4wJ49e8aOHTsmSZkOHTrEatWqxWbOnClYmYx9T3v37mVdunThv3c/Pz+Wmppaapk0Gg1LSkoqs0ynTp1iH374IXvnnXdYq1atmFwuN3qv2dorLi6uuJvZLULFI3rRy9iL4zh2/PjxUuPRsmXLmFqtNsvvhiX9Fm7ZsoUB4sQjm2ppevz4MerUqYNz586he/fu/PEvv/wSW7ZsMehC0D3Zbdq0CW3atKGWpv8vh0ajwcmTJ9G7d284OTmZvUxjxozB4cOH8fvvv6N27dqiPAWp1WoMGTIEhw8fBgAolUqcO3cOjRo1KrVMQOGA8d69e8PV1dXkMuXm5iI9PR1paWlIT0/Hy5cv8fLlS/5JMz8/HwUFBfwTcPEn1KJP5ronZl23nC6te0rXdesZS+vOL5rWPZmXlNZdv6S0VqvFo0ePsHHjRmppKkJF4xFhP8jlcigUClSpUoV/ubm5wcfHB3Xr1kWdOnVQs2ZNeHh48C1msbGxWLVqFQCgXr16+OabbxAWFmYQj/73v/+hWbNmCA8Px7p164y2OtlqS1NMTAy6d+8uSjyyyQ7P4mM8GGOljvto06ZNqcIW7Rc2JV20z708aY7j+LTupjM1XXQxL1PSpZVDoVAgJCRETwNzlem3337Djh07sG3bNr0xH5UtU9G0RqPB2LFj+QqTu7s7IiMj0ahRI5PK1L9/f/6Yqd+TLiDWrVsXtsiVK1ewceNGqc2wSMobj2bNmoV69eqJbZZZqMh4O2OfKWscX9Gxf7q07oFB9yo+VlAul/M/6Lq/uvine0/3v+5Y8f+Lv3R56a5X9Lo6O4qeWxF9Ro8ejRs3buDkyZN48OABfvvtN/zjH//gy6yLO40aNcJ3332H8PBwVKlSBcuWLTM4R8jfDWNpqX4LnZycissmGDZVafL29oZcLkdycrLe8ZSUlFJnzpjSf2xPaLVapKWlwdvb26yrXD99+hTvvPMOhg0bhtGjR4tyDcYYJk2ahJ07dwIAnJ2dceDAAbRv396kz0uljaVDPmRIRePR66+/jk6dOoltnlVBfvc3crkcW7duRevWrfHy5Uv8/PPPCAsLw7/+9S+Dc8eNG4ecnBxMnjwZVapUwRdffCGBxeZHzHhU7rsvOzsbn3zyCbp37w4/Pz80atRI7yUljo6O6NixI44ePap3/OjRo3rN48WhgK+PVqvFH3/8YVZddJUZjuPw7bffijIjjDGGOXPm8Ju4KhQK7N69G7179zY5Dym0sQak1MNSYxLFI+Egv9OnXr16WLduHf//1KlTcf/+faPnvvPOO1iyZAn2799vVeuVVQYx75NytzSNHz8ep06dwtixY1GrVi2LmO5clFmzZmHs2LHo1KkTunXrhg0bNiApKQmTJk0q8TP2Oi2zJBQKBfr06WPWa27btg179+7Fb7/9xo8nE5rPP/8c33zzDYDC5t+ffvoJYWFh5cpDCm2sASl9yJJjEsUjYSC/M2TUqFE4cOAAfvrpJ7x8+RLTpk1DRESE0XPnzJmDKVOmwMXFBbm5uXBxcTGzteZFVB8q78hxT09Pdvbs2UqNPhebNWvWsAYNGjBHR0fWoUMHfoR9cXSzVWJjY81soWWj0WjYw4cPmUajMcv1bty4wapUqcLGjh0r2jWWL1+uN/Nk48aNFcrH3NpYC7GxsaLNVikLS49JFI8qD/mdcZ49e8Zq1qzJADC5XM7PVCuJ9PR01rRpU7ZmzRozWSgNYsajcnfP6Rbns2QmT56MxMRE5OfnIy4urszuF2ry1Uer1eLevXtm06V+/fqYOHGi3lo2QvLDDz9gxowZ/P9Lly7F+PHjK5SXubWxFqTUw9JjEsWjykN+ZxwPDw/4+/sDKFwXKjIystTzPT09ERYWhilTpuCHH34wh4mSYFFjmj777DPMnz+/XJtlWjrUHK6PQqFA7969RdclLy8PCQkJ8PDwwNdffy3KXm07d+7EhAkT+P8XLFiA2bNnVzg/c2ljbUiph63FJLq3DCG/M45CocCUKVP4/0vqntPBcRy++eYbTJo0CePHj8e2bdvENlESJN97rihff/017t27h5o1a8LX19dgSfsrV64IZpy5oKcXfbRaLR48eIB69eqJOlNlwYIF+Omnn3D37l04OzsLnn9kZCTGjBnDf78zZ87EggULKpWnubSxNqT0IVuLSRSPDCG/M45Wq0WdOnVQvXp1PHv2DIcOHUJ+fn6pU+45jsOaNWuQn5+P8ePHIzAwEHXq1DGj1eJjUQPBhw4dKoIZ0kJBSh/dYoV16tQRNUB98MEHCA4OFqXCdPr0aQwfPpxfkHL8+PH4+uuvKz1I2FzaWBtS+pCtxSSKR4aQ3xlHt+VUaGgotm3bhqysLERHR+utJWcMmUyGjRs3YuLEiTZXYQIsrNJU2Sd1S4SafPVRKBSlTomuLGvXrkVYWBh8fX3Rt29fwfO/cuUKBg0ahLy8PADAP//5T6xbt06QWVVia2OtSOlDthaTKB4ZQn5nHJ0uycnJfFdbREREmZUmoHC9p65du4Ixhg8//BDdunXDkCFDxDbZLIjpQ1RlB+0qXhyNRoO7d+8KrotWq8Xs2bMxZcoU7Nu3T9C8ddy+fRv9+/dHRkYGACA0NBRbt27VW9W2MoiljbVDeggHaWkI+Z1xdLr07duX75KLiIgAK8fuaLpB9iNGjMCBAwfEMtWsiHmfmFRpqlatGtLS0gD8PVOlpJc1Up4bzB5gjCE9PV1QXQoKCjB27FgsW7YMK1euxLvvvitY3joePHiAoKAgpKamAgB69OiBXbt2wdHRUbBriKGNLWBuPWw5JtG9ZQj5nXF0ulSpUgX9+vUDADx69AhxcXEm5yGXy7F9+3YMHDgQw4YNw/79+8Uy12yIeZ+Y1Ia1bNkyuLu7AwCWL18umjFSQc3h+igUCnTu3Fmw/DIyMvCPf/wDp06dwi+//IIRI0YIlreO1NRUBAUF4cGDBwCAdu3a4cCBA3B1dRX0OkJrYyuY24dsOSZRPDKE/M44RXUZPHgwDh48CKCwtak8W/E4ODjgl19+weuvv47hw4fj5MmTVt0dalGLW9oSusXkYmJipDbFolCr1Sw+Pp6p1epK57Vnzx5Wp04d5uHhwU6cOCGAdYZkZmayzp078wtXNmnShCUnJ4tyLSG1sSViYmIkW9zSVqB4VDLkd8Ypqsvjx4/5GNimTZsK5VdQUMCWLFnC8vLyBLbUvIgZjyo1pik3NxcZGRl6L8I2yM3NrdTnGWMYOXIkXnvtNbRv3x7Xr19HYGCgQNb9TUFBAYYNG4bY2FgAQO3atXH06NFSN0StLJXVhhAPikm2C/mdcXS61KpVC127dgUAXL9+HQkJCeXOy8HBAXPmzIGTkxMuX76MPXv2CGqrLVChDXunTp0KHx8fuLm5oWrVqnova0SoQcK2glwuR/v27SukS1paGjIyMsBxHDp16oRff/0VERERaNCggeB2arVavPHGG/yGqF5eXjhy5Igo19JRGW1sGSn1sLWYRPeWIeR3ximuS9HZb5Udm/Tdd99hxIgR+PHHHyuVjxSIeZ+Uu+Nv7ty5iI6Oxtq1a/HGG29gzZo1ePToEdavX4///ve/YtgoOjQjQx+NRoP4+Hi0aNGiXDdfTk4OGjdujPnz52P27NmYO3euaDYyxvDuu+/il19+AQC4uLjgwIEDaNWqlWjXBCquja0jpQ/ZWkwqS0uNRgOVSmUmaywDjUaDe/fuoXHjxoL5nYODg9X7cPF4NHjwYMybNw8AsG/fPkyfPr3Cea9ZswZqtRpvvPEGsrKy8M477whltuiIGY/KXWnav38/tm7dioCAALz11lvo1asX/Pz80KBBA/z0008YM2aMGHYSFkZGRgbOnDmD6OhoxMTE4MiRI3B1dcW2bdvQrVs30a//xRdfYPXq1QAKnyp+/fVX9OjRQ/TrEpaHvcQkxhiSk5Px4sULqU0xO4wxMMZw//59QdZb0+Hl5QWlUilonlLSsmVLNG7cGPfu3cOpU6eQnp5e4dZWuVyOjRs3wt3dHZMnT4Zarca0adMEttj6KHel6fnz52jYsCGAws0Cnz9/DgDo2bOnVdVEi2LtTxtCI5fL9VpsHjx4gBs3buDWrVu4ffs2rl27hri4OGg0GtSpUwd9+vTB8+fPUadOHQwaNEh0+7777jt88skn/P/ff/89BgwYIPp1AUNtiEKk9CFbi0klaamrMPn4+MDV1dVmfuilgDGGnJwcpKSkACgcD2SNFI9HHMdh8ODBWLZsGTQaDY4ePYqRI0dWOH/dXnU1atSwqtl0FtU916hRIyQmJqJBgwZo2bIldu7ciS5dumD//v3w8vISwUTxuX//Pjw9PY2+V6VKFSiVSqjVaty/fx9KpRJVqlRBeno6H5xLwtvbG56ensjIyEBqaioaNWoEjuPw8OFDfrVqHazYuhK6PbQeP34MjUaDevXqQavV4vbt2/xTF2MMWq1WL+3o6Mg70cWLF1G3bl3UrVsXT548weXLl1FQUID8/Hzk5eUhLy8Pubm5yMzMRGZmJnr06MEPqh41ahSOHj2KRo0a4YMPPsD27dvh4uKCZs2aoWXLlnj77bcRGBgIPz8/swbviIgITJw4kf//q6++wrhx48x2fY1Gg+vXr6NNmzZU2S6ClN1zthaTjGmp0Wj4ClP16tUlsEpaGGPIzc2Fi4uLYPHGxcUFAJCSkgIfHx+r9Gdj8Sg0NBTLli0DABw6dKhSlSagsOKk6/LLz8/HypUrMWPGDIM9Hi0JUeNReafbffPNN2zFihWMMcZOnDjBXFxcmKOjI5PJZGz58uVCzOgzG7opvqW9XnvtNcYY46dzHjhwgDHG2GeffVbmZ9etW8cYY2zTpk0MAD9dtkePHmV+NiEhgTHG2KhRo1jfvn0ZY4xlZWWV+bmmTZvy5fPy8mKLFy9mjDG2e/dug3MdHByYu7s7q127NmvevDn76quvGGOM/e9//2Njx45l9+/fZ4wxdu/ePXb//n2m0WhE/kZK5+zZs8zZ2Zm3f+bMmUyr1ZrVBpr6bBwplxywlZhU2pIDubm57ObNmywnJ0cCy6RHq9WynJwcwf09JyeH3bx5k+Xm5gqar7kwFo/y8vKYq6srA8CUSqWgcfv06dPMwcGBBQUFsZcvXwqWr9CIGY84xiq3dGZSUhIuX76Mxo0bo23btpXJyuxcuXIFHTt2xLp169C0aVOj53h7e6N169bIz8/H+fPn0bp1a3h7eyMxMVFvSqexp5+mTZuidu3aSE5Oxq1bt+Dv7w+O43D16lWjU6GL5tGlSxc4Ozvj1q1bUKlUaN26NTQaDS5dusSfy3EcZDKZ3l8XFxe0aNECAHDnzh1Ur14d1apV46diOzo6wtnZGU5OTla18eXNmzfRs2dPpKenAwBGjx6NH3/80arKYMvofCkuLg4dOnSQ1BZrjUmlaZiXl4eEhAQ0bNhQlA2u7RVb1XXQoEH8lihXr15Fu3btBMs7Ojoar732Gho0aICDBw+ibt26guUtFGLGo0ovm1m/fn3Ur19fCFsko3379ujSpUup5zg5OemtM+Tr6wtfX1+T8lcqlVAqlXrXM5XmzZvzablcXq5+5SZNmvBpFxcXvjm6LNRqNa5evYr27dtbxOrESUlJCAkJ4StMQUFB2LRpkyQVJkvTxlJQq9VSm8Bj7THJkrS0FNj/j0GisVz6lBSPQkND+UrToUOHBK00BQYG4ty5cwgNDcWrr76KGzduWNzSHmL6kMlRPzc3F8ePH8fAgQMBAB9++CHy8/P59+VyOT777DOrrK2TE+rDcRyqVq1qEbqkpqYiODgYDx8+BAB06NABu3fvFnQ/ufJgSdpYElLoYasxie4t41jjmCOxKSkehYaG8ulDhw7hww8/FPS6r7zyCi5evIiff/7Z4ipMgLg+ZHKlaevWrThw4AAfoFavXo1XXnmFb724desWateujZkzZ4pjqYiQM+ojl8vh5+cntRnIzMxEWFgYbt++DaCw5ezQoUP8nmNSYCnaWBpS+JCtxiSKR4ZwHGd1lV9zUFI8atiwIZo1a4bbt2/j/PnzePHiheCTImrXro3Zs2cDADZt2oQzZ85gzZo1JvdoiImYPmRy/8ZPP/2Et956S+/Y9u3bER0djejoaCxZsgQ7d+4U3EBzQM3h+qjVapw/f15SXfLz8/Haa6/h8uXLAAodNCoqCj4+PpLZBFiGNpaIFHrYakyytXtLN/6ypFd4eHiZeTDGkJWVJeru9dZIafFI19qk0Whw7NgxUe1wdHTEjh070K1bN9y5c0fUa5mCmD5kcqXpr7/+0hss7ezsrDempEuXLrh586aw1pkJGkysj0wmQ506dSTTRa1W41//+heOHz8OAKhatSqOHDli8hgyMZFaG0tFCj1sNSbZ2r315MkT/rV8+XJ4eHjoHVuxYoVJ+VjyFHepKC0e9e/fn08fOnRIVDvGjBmDixcvIjs7G23btsXXX38t6TIkYvqQyd1zL1++1Btolpqaqve+VqvVG09gTdhakKosMplM1P3bSkOj0SA8PBy7du0CYL7tUUxFSm0sGSl8yFZjkq3Fo6KTYDw9PcFxnN4xU+A4Dk5OTkKbZvWUFo/8/f3h4uKC3NxcHD58GIwxUcf6tGnTBlevXsXHH3+MPXv2YMaMGaJdqywsotJUt25d/PHHH2jWrJnR969fv26RUw9NwdaawyuLrsm3e/fuZp0hptFo8NZbb+Gnn34CUPhkuXv3botaiVYqbSwdKXzIVmNSebTs1KkTkpOTRbTGOEqlku86Nwe67jk3NzcaKF+E0uKRs7MzAgMDERkZicePH+P69euiL8Hh5uaG5cuXQ6VSQS6X49y5c9i/fz/mzp2LatWqiXrtoljE7LmwsDDMnz8fAwYMMBiQl5ubi08//dRsW1kIja092VUWmUyGxo0bm1UXrVaLf//739i6dSsAQKFQYNeuXXqzQCwBKbSxBqTQw1ZjUnm0TE5OxqNHj0S0xnKgliZDyopHoaGhiIyMBFDYRWeudct0Xak3b97EypUrsXbtWkyfPh0zZ840y4r2FtHSNG/ePOzcuRPNmjXD1KlT0bRpU3Ach1u3bmH16tVQq9X8UuvWBv0A6qPrJzcXWq0W77zzDn744QcAhTMfdu7cicGDB5vNBlMxtzbWghQ+ZKsxqTxalrebSyjMfV2O4yRbZsSSKSseFV964IMPPjCHWTwTJkzA4MGDsXTpUixbtgwrVqzAvn370KdPH1GvK2o8Ks/y4f/73/9YSEgIk8lkjOM4xnEck8lkLCQkhN27d0/w5crFRrdtwaVLl6Q2xaJQqVTs+PHjTKVSiX6t/Px8NmbMGH5rFLlcznbu3Cn6dSuKObWxJi5duiTJNiq2FJNKi0e6bVSsdbsPHZs2bWKenp7l/pxWq2UvX74UfBsVa9fVlHjUpEkTBoApFAr24sULM1qnz9OnT9lHH33E27B06VK2Zs0alpqaKvi1xIxH5aqONWzYEIcPH0ZqaiouXryIixcvIjU1FYcPH0ajRo0Er9DpSExMxNtvv42GDRvCxcUFjRs3xoIFC1BQUKB3XlJSEgYNGoQqVarA29sb06dPNzjHGNTSpI9MJkOrVq1E1+XFixfo378/P4ZJJpNh27ZtGDFihKjXrQzm0sbakEoPW4xJdG8ZxxLW/7E0TIlHull0arWan5EsBT4+Pvj888/h6ekJoHB7l+nTp6NWrVro3bs35s2bhwcPHghyLYvonitKtWrVytx2REhu3boFrVaL9evXw8/PD3/88QcmTJiA7OxsLF26FEDhIOIBAwagRo0aOHv2LJ49e4Zx48aBMYZVq1aVmj8FKX1kMpno6yE9ePAAoaGh+PPPPwEUBsSff/4ZQ4YMEfW6lcUc2lgjUvuQLcUkqbW0RDiOoyUHjGBKPAoLC+Pvt4MHD2LYsGHmMK1Mtm3bhmXLlmHXrl04fvw4fvjhB7z55psAgP/85z+4du0amjZtiqZNm6JJkyZo3rw5atSoYVLeFtM9Z0ksXryYNWzYkP8/MjKSyWQy9ujRI/7Yzz//zJycnErcjVnXHL5p0yYWFxfHYmJiWExMDHv8+DFTq9X8ztEqlUovrds1uqR0QUGBXlrXpKxLa7VagzRjTC+t0Wj00rrm15LSarVaL62zt6R0aWXKy8tjhw8fZjk5OaKU6fLly6x27dp8l5y3tzc7e/asqGUS6nsqKChghw4dYtnZ2ZJ/T5Z0750/f16S7jlLorIxqbR4lJWVxf7880+Wm5vLf3eMMZPSGo2m1LRWqzVI6/IoKV2e6xdN//DDD3z3XHk+q9Fo2IsXL3gbhCpTdnY2u3nzJsvOzrZK3zUlHuXk5DAXFxcGgCmVSqZSqSyyTBqNhuXn5zPGGFu+fDkLCgpivr6+jOM4BoB98803TKPRsN27dzNfX1/Wvn171rt3bzZw4ED24Ycf8uV477332FtvvWUZ3XOWxMuXL/WmMF64cAGtWrVC7dq1+WMhISHIz89HXFxcqXm9+eab6NixI7p06YIuXbpg/fr1uH79Or+y6dWrV5GQkAAAiImJ4ZsQz58/jydPngAATp8+jbS0NADAiRMn8OLFCwBAVFQUMjMzAQCRkZHIy8uDWq1GZGQk1Go18vLy+NkNmZmZiIqKAlDYdXXixAkAQFpaGk6fPg2gcKG48+fPAyhsrYmJiQEAJCQk4OrVqwCAO3fu4Pr16wCA+Ph4xMfHA4DJZUpNTUXnzp1x/vx5QcuUlpaGf//733j11Vfx+PFjAICfnx/27NnDL4QmVpmE+p7kcjleeeUVREdHS/49WdK9ZwmrAEuNUDHJWDy6ffs2P406JyeHX38qOzub7+7LysqCSqUCUPh96s7PzMzk/SsjIwNarZZPM8bAGDNIA4UTNHRpjUbD30tqtZpPq1QqZGVlAQAKCgqQnZ0NoHBF/5ycHABAXl4ecnNzAQCjRo3i79vc3Fzk5eWZVCbd6uG6cghVJp296enpVum7psQjFxcX9OzZE0DhbMvDhw9bZJny8/P5RTjffPNNvPvuu0hISMDDhw+xfv16jB49GmlpaXj27BlGjRqFVq1a8ZMDnjx5gpiYGGg0GuzcuRN79uyBaAheDTMDd+/eZR4eHmzjxo38sQkTJrCgoCCDcx0dHdn27duN5qN7stu6dSu1NIlcprt377Ju3brxrUsAWNeuXVlKSorVlskWv6eKlkmqgeCWghAxqbR4ZCstTUKlqaWpfL67du1aPu4uWLDAJsokVTyStKVp4cKFZe5LVHwBtcePH6N///4YMWIExo8fr/eesUXPmAmroDZr1gwdOnRA586d0blzZ9SqVQtyuZzf9E+hUOildf2lJaUdHBz00rrr69K6/vmiaZ39urRMJtNL6xYuKyktl8v10jp7S0qXViaNRoODBw+CMVbpMhUUFGDdunVo27YtLly4wNs9b948nD59GjVq1DBLmYT6nlQqFd86I/X3ZEn3nq1gCTGppHik+4zODlPTMpms1DTHcQZpXR4lpStqS0XTWq0WL1++5PeeE7pM1uq7psajQYMG8edERkZadJl0342lxiNJlzSeOnUqRo0aVeo5Rfcbe/z4MQIDA9GtWzds2LBB7zylUolLly7pHUtPT4dKpULNmjVLvYYtBX0hUCgU6NWrV6VWvM7Pz8emTZvw5Zdf6s2IaNSoEX788UeLWuW7PAihjS1iKz5kCTHJVrQUEo7j4O7uTquBF8PUeFS3bl20bdsWv//+O2JjY5GcnCzZGl/mQEwfkjTye3t7w9vb26RzHz16hMDAQHTs2BGbNm0yGB3frVs3fPHFF3jy5Alq1aoFoLAP1cnJCR07diw1b3JEfTiOg4eHR4U+m5aWhh07dmDx4sUG00cnTJiAb775Bm5ubkKYKQmV0caWsRUfsoSYZCtaCgnHcVSZNEJ54tHAgQPx+++/Ayhc6FI3U80WEdOHrGIg+OPHjxEQEIB69eph6dKlSE1NRXJyst6eS8HBwWjZsiXGjh2Lq1ev4vjx45gzZw4mTJhQ5k1Fe8/po1KpsG/fPn5QaVmkpaVh48aNCA4OhlKpxLRp0/QqTAMHDkRMTAw2bNhg1RUmoPza2Av25kNixiR709IUtFotXrx4wQ/4JgopTzwquqXQwYMHxTRLcixi7zkpiYqKwt27d3H37l2DDTh1fdxyuRwHDx7E5MmT0aNHD7i4uGD06NH8mimlQU8w+igUCgQHBxtt8s3JycGtW7cQGxuLmJgYxMbG4s8//zQazAYOHIgFCxagU6dO5jDbLJSmjT1jbz4kZkyyNy1NQdeiQq1w+pQnHnXp0gXe3t5IS0tDVFQUCgoKbHZrGpvtnjOV8PBwhIeHl3le/fr1ceDAAfENsnIYY1CpVCgoKEBeXh6ys7P1Xs+ePUNqairS09Px/PlzPHz4EImJiUhISMDTp09LzdvX1xcjR47E6NGjzbY5pLmhChNBMYmwFEyNR3K5HKGhofjxxx+RmZmJM2fOoG/fviJbZ3tQ9Efh2iFVqlQRLD/dk2ZlPqP739jf4mmtVquXLvrSaDRQq9VQq9XQaDRQqVT8eihCIJfL0bp1awQFBWHkyJHo2LGjTT8N6tYVCQsLoxWKi6BbM4eoPKSlIez/11qi1iZ9yhuPBgwYgB9//BEAcODAAZutNInpQ1RpAnD37l2pTbAKateuDV9fXzRq1IhffK9du3ZwdXWV2jSzoVAoEBYWRq1NxaAuJeEgLQ2h7jnjlDcehYSEQC6X88vKLFu2TGQLpcHuu+fExtHRUfT9nkxx9uLnFF2rpPhfY+uS6GaYyGQy/rhCoeDX1tClnZyc4OTkBEdHRzg5OaFKlSp6Ly8vL3h6ekKpVMLb2xs1a9ZEgwYN4OzsLKQkVotaraZKE0EQFkF54pGXlxd69uyJU6dO4c6dO/jrr7/QtGlTkS20LSjyAzhz5oxZN/u0dHQLplEXlCFqtRpRUVGkTTGoS0k4bFHL06dPY8mSJYiLi8OTJ0+wZ88eDB061OC88PBwKJVK+Pr64r333kN6ejoUCgUYY3j8+DEaNmyIV199FWfOnOE/c+bMGfTu3Ru3b9+2uwpAReLRgAEDcOrUKQCFs+hsUTMxfcgqlhwQG2o10MfBwQFDhgyhSoERSBvjkA8Jhy1qmZ2djbZt22L16tUlnqPVanHw4EEMGTIEgYGByMrK4ldfl8lkuHHjBpRKJWJjY/l97QDg5MmTqF27tk3++JdFReLRwIED+bStTlIQ04eo0oSKDdy2ZViRzS4JfUgb45AewmGLWoaGhuLzzz/HsGHDSjzn3LlzkMlk6Nq1K5o1a4batWvj5MmTAAo1OXHiBAYPHozGjRvzG+oChZWmwMBAsYtgkVQkHjVv3hyNGjUCUNgC+PLlS7HMkwwxfYgqTbDN5vDKoFarcebMGVpkzwikjXHIh4TDXrWMiIjAoEGD+PGlAQEBiI6OBvB3pcnf3x/+/v788YKCAly4cMFuK00ViUccx/F70anVahw+fFgs8ySDZs+JjC02h1cGBwcHvdVjib8hbYxDPiQc5dXyyZMnePLkid6xqlWromHDhsjLy8PNmzcNPtOhQwcAwO3bt5Gdna33nq+vL6pVq4bU1FSDrZDc3d3RpEmTctlnKhEREXoLfwYEBGDmzJlQq9XIzc3F9evXERAQAMYYVq5cCQC4ePEicnNzERgYCI1Gw29Pk5ycDIVCAW9vb7i7u+uNgbIlKhqPBg8ejBUrVgAo1P2f//yn0KZJipjxiCIdQEvzF0O3ZYGXl5foswqtDdLGOORDwlFeLdevX49PP/1U79iYMWOwbds2PHz40Og+d7rui/DwcFy8eFHvvR9//BH/+te/sHPnTkydOlXvveDgYBw5cqRc9plCfHw8Hj58iH79+vHHAgMDkZ2djdjYWDx//hxNmzZFjRo14O/vj7FjxyI7OxsnT55E/fr1+e6ma9euAQAWLlwIb29vA/ttjYrGo169esHT0xMvX75EZGQkVCqVTY3TFDMeUaUJFPCLo9FoEBsbiz59+lDFoBikjXHIh4SjvFpOnDgRgwcP1jtWtWpVAIW728fFxZX42c2bNxttaQKAkSNHolu3bnrvubu7l8s2U4mIiEBQUBBcXFz4Y35+fqhbty6io6Px/PlzdOvWDYwxKJVKNGzYEOfOnUN0dDT69Okjik3WQEXjkYODA0JDQ7Fjxw68ePEC586dQ0BAgHiGmhmqNIkMdS3o4+DggJCQEKnNsEhIG+OQDwlHebWsVasWatWqZfQ9Z2dnvivOGM2aNSvxvRo1aqBGjRrlsqWi7Nu3D+PHjzc4HhgYiJMnTyI9PR3vvfceXzHw9/fHkSNHcPHiRbz55ptmsdESqUw8GjRoEHbs2AEA2L9/v01Vmmj2nMjQU7I+Wq0WKSkppIsRSBvjkB7CYYtaZmVl4dq1a3z3WUJCAq5du4akpCSkpKQgNjZWbyq8jsDAQJw9exbXrl1D9+7d+W5Ff39/bNy4EXl5eXY7CByoXDwKDQ3lV86OiIiwqVmbYvoQVZpgm0GqMmi1Wvzxxx+kixFIG+OQHsJhi1pevnwZ7du3R/v27QEAs2bNQvv27TF//nzs378fXbt2hY+Pj8HnAgMDkZubCz8/P3h4ePDH/f39kZmZicaNG6NevXpmK4elUZl4VLVqVfTq1QtA4VZit2/fFto8yaDuOZGhrgV9FAqFXY8TKA3SxjjkQ8Jhi1rqZr0ZY/DgwQZjsnT4+voa/VzdunVtqmWkolQ2Hg0ePJhfCysiIgLNmzcXyDJpoe45kbHFJ7vKoNVq8ejRI9LFCKSNcUgP4bA3LXv27InXX3+91HMYYygoKKCKUjEqG4906zUBheOabAVqaRIZewtSZaHVanHv3j3UrFmTZogVg7QxDvmQcNiblnPnzjXpvPz8fJOnxS9cuLASFlkPlY1Hfn5+aNGiBeLj43H+/HmkpaXB29tbBEvNC41pEhlbbA6vDAqFAr179yZdjEDaGIf0EA7S0hCO4+Du7g6O46Q2xaIQIh7pWpu0Wi0iIyOFMk1SqHtOZOztya4stFot7t+/T7oYgbQxDukhHKSlIYwx5OfnU/dcMYSIR0XHk0VERAhhluRQS5PIUJDSh8btlAxpYxzSQzhIS+OoVCqpTbA4hIhHr776Kt8ld+TIEeTn5wtlnmRQpUlkqDlcH4VCge7du5MuRiBtjEN6CAdpaQjHcXBzc6PuuWIIEY/kcjm/f11WVha/GbI1Q91zImOvu4qXhEajwd27d0kXI5A2xiE9hKM0Le21e4oxhry8PMHLb+16ChWPinbR7du3r7JmSY6Y8YgqTbB+xxEaxhjS09NJFyOQNsYhPYTDmJa6WWM5OTnmNsdiEOOHUKentW5WK1Q8Cg4OhpOTE4DCcU3W3kUsZjyidmBQc3hxFAoFOnfuLLUZFglpYxzyIeEwpqVcLoeXlxdSUlIAAK6urnbXVSWXywUbb8MYQ05ODlJSUuDl5cVvJ2JtCBWP3Nzc0K9fPxw8eBCPHz9GXFycVcc5MeMRRTpQ10JxNBoN7ty5gyZNmlhtMBEL0sY45EPCUZKWSqUSAPiKkz3BGINarYZCoRC0sujl5cXrao0IGY+GDBmCgwcPAihsbbLmSpOY8YgqTYRRcnNzpTbBYiFtCCngOA61atWCj4+P3c0k02g0uH37Nho3bizYw4qDg4NNPPgIFY+Krg6+b98+fPbZZ4Lka2vYdaUpNTUVAPD8+XOJLbEsUlJSsG/fPiiVStSqVUtqcywK0sY4Oh/S+RRRfkyNR3K53CZ+7MvDkydPEBERgYkTJ5LfFUHIeKRUKtG1a1dcunQJN27cQEJCAho2bCiQpeZFzHhkdQPB8/Pz0a5dO3Ach2vXrum9l5SUhEGDBqFKlSrw9vbG9OnTUVBQUGJeaWlpAOyzubs0Hj58iE8//RQPHz6U2hSLg7Qxjs6HdD5lTwgVkygelQz5nXGE1mXIkCF82ppn0YkZj6yu0jR37lzUrl3b4LhGo8GAAQOQnZ2Ns2fPYseOHdi9ezdmz54tgZUEQdgLFJMIW8FWKk1iYlWVpkOHDiEqKgpLly41eC8qKgo3b97Etm3b0L59e/Tr1w9ff/01Nm7ciIyMjFLzpY1X9dE1/dtbF4ApkDbGsVcfEiMm2auWpUF+ZxyhdWnRogX8/PwAAGfOnLHaoSti+pDVjGl6+vQpJkyYgL1798LV1dXg/QsXLqBVq1Z6T3whISHIz89HXFwcAgMDDT6jm7565swZAH8vve7j44Nq1aoBKLwZ1Wo1OI7j0zKZDDKZzOS0XC4Hx3F8Gih8Ci2aVigUYIzxaa1WC61Wa3Jao9GAMcandbaXlC6tTLdu3QIA3LhxA1qt1ibKJNT3dPv2bXAchxs3bvD3jLWXSYjv6e7du3o+ZQ8IHZMoHpVcpvj4eDg6OuKPP/4AAJsok6XGo1dffZVfMHPNmjXo37+/1d17YsYjq6g0McYQHh6OSZMmoVOnTkhMTDQ4Jzk5GTVr1tQ7VrVqVTg6OiI5OdlovrqFzdavX4/169cLbre1Ex4eLrUJFgtpYxx7WXxRjJhE8ahsxo0bJ7UJFolY8Wj+/PmYP3++KHmbAzHikaSVpoULF+LTTz8t9ZzY2FicP38eGRkZ+PDDD0s919j6HYyxEtf1GDVqFIDCheJ0q6ECgLe3N2rUqFGW+QRB/D+5ublITExESEiI1KZUCiljEsUjghAGMeMRxyTc/yAtLa3M0e2+vr4YNWoU9u/frxdodE16Y8aMwZYtWzB//nzs27cPv//+O39Oeno6qlWrhhMnThjtniMIgigKxSSCIEpD0kqTqSQlJekNnHz8+DFCQkKwa9cudO3aFXXr1sWhQ4cwcOBAPHz4kF+v4pdffsG4ceOQkpICDw8PqcwnCMLGoJhEEPaJVVSaipOYmIiGDRvi6tWraNeuHYDCp7x27dqhZs2aWLJkCZ4/f47w8HAMHToUq1atktZggiBsGopJBGEf2MzcVrlcjoMHD8LZ2Rk9evTAyJEjMXToUKNTgQmCIMSGYhJB2B5W2dJEEARBEARhbmympUlMMjMz0blzZ7Rr1w6tW7fGxo0bpTbJonjttddQtWpV/OMf/5DaFEkhHQwh3xEH0rVkyA//hrQwpLK+Qy1NJqDRaJCfnw9XV1fk5OSgVatWiI2NRfXq1aU2zSKIjo5GVlYWtmzZgl27dkltjmSQDoaQ74gD6Voy5Id/Q1oYUlnfoZYmE5DL5fyKv3l5efwqqkQhgYGBcHd3l9oMySEdDCHfEQfStWTID/+GtDCksr5jE5Wm06dPY9CgQahduzY4jsPevXsNzlm7di0aNmwIZ2dndOzYkd+qwFRevHiBtm3bom7dupg7dy68vb0Fsl5czKGNLUA6GUcIXazVdyoDxSTjkJ+ZDmllHKljkk1UmrKzs9G2bVusXr3a6Pu//PILZsyYgY8++ghXr15Fr169EBoaiqSkJP6cjh07olWrVgavx48fAwC8vLzw+++/IyEhAdu3b8fTp0/NUrbKYg5tbAEhdLJFhNDFWn2nMlBMMg7FI9OhmGQcyWMSszEAsD179ugd69KlC5s0aZLesebNm7MPPvigQteYNGkS27lzZ0VNlAwxtYmOjmbDhw+vrIkWQWV0siUdiiPE/WOtvlMZKCYZh+KR6VBMMo4UMckmWppKo6CgAHFxcQgODtY7HhwcjPPnz5uUx9OnT/nVfzMyMnD69Gk0a9ZMcFvNjRDa2AOkk3FM0cVWfacyUEwyDvmZ6ZBWxjFHTJJ0w15zkJaWBo1GY7DbeM2aNY3uNG6Mhw8f4u233wZjDIwxTJ06FW3atBHDXLMihDYAEBISgitXriA7Oxt169bFnj170LlzZ6HNlQxTdbJ1HYpjii626juVgWKScSgemQ7FJOOYIybZfKVJR/FdxVkJO40bo2PHjrh27ZoIVlkGldEGAI4cOSK0SRZJWTrZiw7FKU0XW/edykAxyTgUj0yHYpJxxIxJNt895+3tDblcbvCkkpKSYlAbtTdIG9MgnYxDulQM0s04pIvpkFbGMYcuNl9pcnR0RMeOHXH06FG940ePHkX37t0lssoyIG1Mg3QyDulSMUg345AupkNaGcccuthE91xWVhbu3r3L/5+QkIBr166hWrVqqF+/PmbNmoWxY8eiU6dO6NatGzZs2ICkpCRMmjRJQqvNA2ljGqSTcUiXikG6GYd0MR3SyjiS62LyPDsLJjo6mgEweI0bN44/Z82aNaxBgwbM0dGRdejQgZ06dUo6g80IaWMapJNxSJeKQboZh3QxHdLKOFLrQnvPEQRBEARBmIDNj2kiCIIgCIIQAqo0EQRBEARBmABVmgiCIAiCIEyAKk0EQRAEQRAmQJUmgiAIgiAIE6BKE0EQBEEQhAlQpYkgCIIgCMIEqNJEEARBEARhAlRpIgiCIAiCMAGqNBEEQRAEQZgAVZoIsxIQEACO48BxHK5duyZK/jNmzKjw58PDw3n79u7dK5hdBEFYHhSPiPJClSbC7EyYMAFPnjxBq1atzHbN8PBwfPDBB2Wet2LFCjx58sQMFhEEYQlQPCLKg0JqAwj7w9XVFUqlssT3CwoK4OjoKNj1tFotDh48iIiIiDLP9fT0hKenp2DXJgjCsqF4RJQHamkiysWePXvg5OSE1NRUg/fmzJmD9u3blzvPgIAATJ06FbNmzYK3tzeCgoIAAIcPH0bPnj3h5eWF6tWrY+DAgbh37x7/uezsbLzxxhtwc3NDrVq18PXXXxvN/9y5c5DJZOjatSsAYNeuXWjdujVcXFxQvXp19OvXD9nZ2eW2myAIaaF4RJgbqjQR5WLLli0IDQ1FjRo1DN4bPXo0rl27huvXr1coX4VCgXPnzmH9+vUACoPQrFmzEBsbi+PHj0Mmk+G1116DVqsFALz33nuIjo7Gnj17EBUVhZMnTyIuLs4g74iICAwaNAgymQxPnjzB66+/jrfeegvx8fE4efIkhg0bBsZYuW0mCEJaKB4RZocRhIloNBrm7u7OVq9eXeI5np6ebOnSpSW+7+/vz959912DY+3atSvz+ikpKQwAu3HjBsvMzGSOjo5sx44d/PvPnj1jLi4uBvk3bdqURUREMMYYi4uLYwBYYmJiqdcCwPbs2VOmTQRBSAPFI0IKqKWJMJmUlBRkZmbCz8+PPzZ27Fjs2rWL/79x48a4c+dOufPu1KmTwbF79+5h9OjRaNSoETw8PNCwYUMAQFJSEu7du4eCggJ069aNP79atWpo1qyZXh7x8fF4+PAh+vXrBwBo27Yt+vbti9atW2PEiBHYuHEj0tPTy20vQRDSQvGIkAKqNBHlRq1W8+lr164hKSmJ/18mk4HjuHLnWaVKFYNjgwYNwrNnz7Bx40ZcunQJly5dAlA4MJOZ2HwdERGBoKAguLi4AADkcjmOHj2KQ4cOoWXLlli1ahWaNWuGhISEcttMEIT0UDwizAlVmgiT8fHxgaurK/766y8AQH5+Pu7cuYObN28CKJwVkpCQAF9f30pf69mzZ4iPj8fHH3+Mvn37okWLFnpPYH5+fnBwcMDFixf5Y+np6bxtOvbt24fBgwfrHeM4Dj169MCnn36Kq1evwtHREXv27Km0zQRBmA+KR4QU0JIDhMnIZDIMGTIEq1evhr+/P3bv3o0+ffpgz549ePvttxEdHY3nz59j0KBBlb5W1apVUb16dWzYsAG1atVCUlKS3rombm5uePvtt/Hee++hevXqqFmzJj766CPIZH8/B6SkpCA2NlZvUbhLly7h+PHjCA4Oho+PDy5duoTU1FS0aNGi0jYTBGE+KB4RUkCVJqJcrFixAm+88Qa6d++Opk2bYteuXThw4ABCQ0Ph7OyMb7/9Fi1btqz0dWQyGXbs2IHp06ejVatWaNasGVauXImAgAD+nCVLliArKwuDBw+Gu7s7Zs+ejZcvX/Lv79+/H127doWPjw9/zMPDA6dPn8by5cuRkZGBBg0a4Ouvv0ZoaGilbSYIwrxQPCLMDcdM7YwlCAEICAhAu3btsHz5ctGvNXjwYPTs2RNz584t92c5jsOePXswdOhQ4Q0jCMIioHhElBca00SYnbVr18LNzQ03btwQ9To9e/bE66+/Xq7PTJo0CW5ubiJZRBCEpUHxiCgP1NJEmJVHjx4hNzcXAFC/fn1BtycQgpSUFGRkZAAAatWqZXQWDUEQtgHFI6K8UKWJIAiCIAjCBKh7jiAIgiAIwgSo0kQQBEEQBGECVGkiCIIgCIIwAao0EQRBEARBmABVmgiCIAiCIEyAKk0EQRAEQRAmQJUmgiAIgiAIE6BKE0EQBEEQhAlQpYkgCIIgCMIE/g8iBx1PvcIt0AAAAABJRU5ErkJggg==", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from control import mixsyn\n", "\n", "WS = tf( [0, 1], [1, 1, 0.25]) # 感度関数に対する重み関数\n", "WU = tf(1,1)\n", "WT = tf( [10, 0], [1, 150]) # 相補感度関数に対する重み関数\n", "\n", "# 混合感度問題\n", "K, _, info = mixsyn(Pn, w1=WS , w2=WU, w3=WT)\n", "\n", "print('K=', ss2tf(K))\n", "print('gamma =', info[0])\n", "\n", "fig, ax = plt.subplots(1, 2, figsize=(6,2.3))\n", "\n", "# 感度関数\n", "Ssys = feedback(1, Pn*K)\n", "mag, _, w = bode(Ssys, logspace(-3,3), plot=False)\n", "ax[0].semilogx(w, mag2db(mag), ls= '-', lw =2, label='$S$', color='k')\n", "\n", "mag, _, w = bode(1/WS, logspace(-3,3), plot=False)\n", "ax[0].semilogx(w, mag2db(mag), ls= '-.', lw =1, label='$1/W_S$', color='k')\n", "\n", "# 相補感度関数\n", "Tsys = feedback(Pn*K, 1)\n", "mag, _, w = bode(Tsys, logspace(-3,3), plot=False)\n", "ax[1].semilogx(w, mag2db(mag), ls = '-', lw =2, label='$T$', color='k')\n", "\n", "mag, _, w = bode(1/WT, logspace(-3,3), plot=False)\n", "ax[1].semilogx(w, mag2db(mag), ls= '--', lw =1, label='$1/W_T$', color='k')\n", "\n", "for i in range(2):\n", " ax[i].set_ylim(-40, 40)\n", " ax[i].legend()\n", " ax[i].grid(which=\"both\", ls=':')\n", " ax[i].set_ylabel('Gain [dB]')\n", " ax[i].set_xlabel('$\\\\omega$ [rad/s]')\n", "\n", "fig.tight_layout()\n", "# fig.savefig(\"robust_design.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "設計したコントローラのボード線図とノミナルモデルのボード線図" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(6,2.3))\n", "\n", "mag, _, w = bode(K, logspace(-1,3,1000), plot=False)\n", "ax.semilogx(w, mag2db(mag), ls= '-', lw =2, label='$K$', color='k')\n", "\n", "mag, _, w = bode(Pn, logspace(-1,3,1000), plot=False)\n", "ax.semilogx(w, mag2db(mag), ls= '-.', lw =1, label='$Pn$', color='k')\n", "\n", "ax.legend()\n", "ax.grid(ls=':')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "ステップ応答" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.0, 60.0)" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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xxRdZvXo1BoOh2uP+XB1FFMU7VkwZP3480dHR9OjRgx49erBs2TKOHDlCeno6ACkpKZw7dw6AxMREsrKyANi3bx/Z2dkA0mgHIC4ujoKCAgC2b98uzTvFxsZSXl5eKStneXk5sbGxABQVFbF9+3YACgoKpJFRXl4eCQkJAGRnZ0sjy6ysLBITE4GKkWhKSgoA6enpfPbZZ4SHh3Py5ElatGhBamoq//rXv/j3v//Np59+yuzZs/n3v//NwYMHJU3Dhg0jLy+P5cuXA9C0aVPWrFmDxWKpF5psDvXEiROcOHEC4JZ+soVYDaWfaqKpqu/e/v37JYftLJqq6ie7hMuig9i4caMIiBqNRvoDRJVKJWo0GvHMmTMiICYnJ1d63UMPPSSOGzeuynMeOnRIBMRVq1aJhw4dEhMTE8XExETx8uXLosViES0WiyiKomg2myvZVqv1trbJZKpkC4JQyRYE4RZbFMVKttVqrWSbzebb2haLRbK3bNkibt26VXzvvfdEo9EoLl26VFyxYoVYUlJSSYfZbBZ37dol/t///Z94/vx56fH169eLe/bsEc1ms5iVlSV+9tlnDtd0c39UZze0flI03VmT7Ro9dOiQWFs4zIkVFhaKaWlplf66desmPvXUU2JaWpooCIIYHBwszp8/X3qN0WgUvby8xM8++6zKc9o+oMTExLqSYXcEQRDfffdd8e233xYLCgrE//73v2JGRoaYnp4ufXH+jMViEZcsWSLu2rVLemz58uXi8ePHRVEUxdWrV4unTp2qk/bfCxaL5bY6nQm5aE1MTKx1J+awcNLDw4OoqKhKf+7u7vj5+REVFSWtGZs3bx4bN27k6NGjTJgwATc3N8aOHXvbc4tOlJNp+/btuLu7ExMTw8cff8yMGTNo2rQpSUlJLF26lMWLF7N48WK++eYbKQTRaDRMmTKFkpISNm/eDMDEiRNZv3495eXljB07lu+//77ef06iKJKfn1/v21kbyEWrPfTV61shs2bNoqysjKlTp5Kfn0/Pnj3Zvn07Hh4et32dM93hSU5ORqPRkJiYyLPPPktOTg6fffYZ0dHRPProo+h0OgCuX7/Or7/+ypUrV3jqqacICQlh5MiR/PLLL2zevJnhw4czbdo0Pv30U1555RUefvhhNm3aVK+ziWq1Wrp37+7oZtQJctHqdHcn/8yePXv46KOPpP+rVCrmzp1LdnY25eXlxMfHExUVdcfzOEsmgNTUVK5evUrjxo2Jjo7mjz/+IDk5mddee42wsLBK21N8fX0ZN24cM2fO5Oeff+aXX34BYOTIkZjNZuLj4/Hx8aFnz55s2bKFqKgoTp8+jdFodJS8O2K1Wjl58qTT9OftkItWpWSbzIiNjSUwMJBr166RlZWFr68vTz75JFevXuXHH3/k008/ZfHixaxYsYILFy4AFcsrJk+ejLe3N8uXL0cURUaPHs3Ro0fJzMykb9++nDp1ihs3bjB+/HhWrlzpYJW3p6yszNFNqDPkpLU2cUon1lA3PN9Mfn4+J0+elNLrBAYG0rp1axYsWMCOHTuYPn06L7zwAtOnT+eRRx4hKSmJBQsW8McffwBw//3306tXLxYuXIgoikyZMoVVq1ZRWlrKc889xxdffEFgYCCiKEpzafUNjUZDly5dnKI/74RctCp1J2uIMwzJv/vuO7y8vAgLCyM/Px+tVsu6det46aWXePLJJ7l06ZKk09PTk0ceeYRZs2ZRUFDAwoULMZlMREVFMWbMGD7++GPUajUzZ85k0aJFuLu707FjR/bv38+4ceNYvXq1g9VWjW2RrzP0552Qi1YlnJQJgiDw22+/4ebmxsWLF/H39+fGjRtMnz6dU6dOsXjxYtasWcOSJUv45JNP+Pbbb7lx4wYAQ4cOZdy4ccybN4/Lly8TERFBTEwMK1aswNPTk4EDB7Jp0yaGDBnCnj170Gq1eHl53XEXhIJCfcV5buPdREMfkickJGA0GtFoNLRt2xar1Urbtm2ZN28e0dHRTJ8+vZJG2xxZYWEhTz/9NAEBAfy///f/+PDDDxk+fDidO3emoKCAX3/9lREjRrBkyRKys7MZN24c3377LWPHjmXx4sW88sorDlR9KxqNpkY3cpwBuWhVwska0tCH5OvXr8fd3R1fX1+uXr0qbbuZPXs2Q4cORRRF9u3bJ+1vCwgI4Nlnn2XatGl8//33bN68GY1GwyuvvML27ds5fvw4MTEx5OXlcfLkSSZNmsTy5csJDQ2ltLSU0tJSAgMDpe0i9QWr1UpKSkqD78+aIBetSjgpA4xGI0eOHEGv11NUVISrqysBAQEMGzaMZcuWsWjRIpYuXcru3btZsmQJixYtYvHixVy8eBG9Xs/06dPx8/Pjvffew2Kx8MILL7Bz505OnTrF+PHjpQWvjzzyCOvXr2fChAmsWLGCf/zjH6xdu9bR8m/BWeoF1AQ5aa1NlHCynvHNN98AFYsCmzRpQmRkJOfPn+fYsWM89dRTNGrU6JbXmEwm1q1bR3Z2Ns8++yy9evUiMjKSt99+m1deeYUZM2Ywf/58Jk6cyMyZM/n444+ZPXs2u3fvpqysjKZNm5KRkSH927x587qWXSUajYY2bdo4uhl1gly0KuFkDWnIVZS///57vL29CQkJwcPDg4SEBLp168aECRP47bffWLx4MYsWLeK1117jq6++IjMzExcXF8aOHcvkyZP5+uuv2bRpEwEBAcyaNYsPPviAa9eu8corr7BkyRLUajXDhw9n/fr1PPPMM3z55Zc8+uijrF+/nscee4x169Y5+iOQsFgsJCUlNej+rCly0WoPfU7pxO6Uqqe+UlBQQGZmJj4+PqjVak6ePMmECRPYvXs3X3zxBREREUybNo1p06bx/PPPM3r0aFJSUnj//feJjY3Fzc2NF198kcDAQBYuXIhOp2POnDl8+umnFBUV8fLLL/PBBx/QsWNH8vPzuXLlCr169SI+Pp6BAwcSFxdHs2bNyMjIcPRHAVT0o4+PT4Ptz7tBLlrtoc8pnVhDDSfff/99DAYDarUas9nMwIEDWblyJY8//jhTp05FpVKRkJDAgQMH0Ov1+Pj48PDDD/Pqq68SGhrKu+++y8GDB+nVqxdPPvkkb7/9NiUlJbzxxhssWrQIURR57LHHWLFiBc888wxff/01ffr0ITExkU6dOnHw4EFGjx7N+vXrHf1RABX92KJFiwbbn3eDXLTaQ59KdKJt88nJydIewx49eji6OXdN+/bt8fHxoVevXnTq1AlRFOnZsyebN29Gp9PRqlUrQkNDMRqN7Ny5E51Oh1qt5oEHHpCKrGzatImLFy8yadIkLBYLCxYsYNKkSXh5eTF//nzefPNNtm/fjre3N+Hh4cTGxvLYY4+xZs0ahg8fzv79+1Gr1fTq1YtmzZo59POwWCwkJibSo0cPp9rUXxVy0ZqYmEjPnj05dOgQXbt2rZVzOuVIrCHW7cvPzyc7O5vAwED8/PzQarXk5+eTlpbGzJkzmTp1KtHR0QQFBdGhQweeeOIJXnrpJV544QWys7OZN28ex44d46GHHuLhhx/m7bffpqCggDfffJMVK1Zw5coVZsyYwfvvv8/w4cM5dOgQGo0Gf39/zp8/j7+/PxaLhStXrvDggw/Wi7kxtVpN48aNG2R/3i1y0WoPfU45EqtNL19XPPXUU+zZs4cHHniALl26UFBQwDPPPMPOnTs5e/YsJSUluLu74+HhgYuLC2q1GrVaTf/+/enYsSOiKPLzzz9z9uxZpkyZgouLCx9//DEDBgygc+fOLFiwgCeffBKTycS2bduYNGkSb731FnPmzGHBggW88sorfPDBB0yePJkffvgBLy8v+vbtS1hYmKM/GgUnwh7XqFOOWxviHZ6tW7fSokULPDw8uHHjBhqNhkcffZQzZ85w/fr1SseqVCpatWrFiBEj2LdvH1u3biU6OppRo0ZRWFjIokWLiImJ4ZVXXmHNmjVcvXqVWbNm8c477zBx4kS6du3K+vXrmTp1Kp988gnPP/88n3/+OaNGjSIhIQGtVktMTAzfffedQ1fxWywW9u3bx3333efUIRbIR6s9rk2n/LQa2pD8+vXrFBUV4efnh8ViYc2aNZw+fbra40VR5NSpU5w6dQqAfv36oVKp2LdvH48//jhvvPEGmzZtYuXKlYwbN44tW7awYcMG3njjDebNm8fzzz/P1atXOX78OD179uTAgQO0aNGC4uJizp8/z1NPPcXKlSsJCgoiKyuLpk2b1tVHUQm1Wk1kZGSD68+/gly02kOf4sTqAaNHj8ZgMFBcXMxXX31VqVq3h4cHXbt2pXHjxvj4+FBeXs7Bgwc5fPiwdExCQgIJCQn07NkTi8VCUFAQkyZN4vTp07z77rvMnDmTgwcPsmrVKmbPns28efOYPn0669ato3///hw/fpwHHniAH374gYkTJ/LNN98QHh5OmzZt+OGHHxw2GrPNEzkaURQ5ceIECQkJWCwWaZmAbSZGpVJJVXwCAgIYMGDALaUG70R90WpvFCdWQxpaOHngwAECAwOlUlpQUbl7yJAhxMTE0Lp1a1xdXcnNzeXixYu0a9eO48eP4+fnx6ZNmzh58iQAf/zxB3/88Qdjxozh3LlzTJ48malTp/Lee+8xYcIEPDw8+Oyzz5g1axbvvvsuL7/8MkuWLGHixIksXbpUKrobGRlJeHg4v/zyC02aNOHSpUsOucAsFgsJCQkOKyqbk5PDunXrsFgstG/fnokTJ+Li4nLb11y5coW4uDhyc3PR6XSMHDmyRiNZR2utK+xxbTrlxH5SUhLdunVzdHNqxOnTp2ndunWlx3r06MGqVau4cOEC586dw2w24+7uTuPGjenQoQOBgYHk5ORw9OhRDh8+zLVr1/j11185duyYdA5fX19GjRrF4MGD+fvf/86SJUvo0aMHPj4+bNq0ieeff57333+fl19+mYULF0pJE6Ojo9FoNPz222/07dsXURRJSUnh5ZdfruuPBkEQyMvLw9/fv05H15cuXeK7774jICCA9u3bk5aWRklJifS8SqWqNAoTRZHw8HC6dOlCkyZNpOPKysr45ZdfOH/+PF27dmXgwIHVLvZ0lNa65uDBg3Tv3r1WJ/Yd6sSWLl3K0qVLyczMBCrWSf373/9m2LBhQMVw/b///S+ff/65VCjk008/pX379lWeryHenfTw8KC4uFj6/+OPP063bt3w9fWld+/eREZG4uLiQnFxMZcuXSI1NZWcnBxEUeSBBx6gQ4cOZGRk8MMPP3Dp0iW+/fZb8vPzpfP16NGDvn37MnfuXLZt24ZaraZbt26sXr2a559/nk8++YQpU6bw5ZdfMmjQILKyssjIyGDw4MGcOHGCzMxMQkNDGTJkCCEhIY74iOoMo9HIF198wfnz5wkODkan09G+fXu6deuGVqulvLwcvV6PwWCoNFoSRZHz58+TnJzMpUuXEASBVq1aMWjQIKmQy8GDB9mzZw/h4eGMGTPG6Re1Voc9rtG7dmITJkxg4sSJ9OvX757f/JdffpFWKgOsXLmS9957j5SUFNq3b8/8+fN5++23+frrr2nVqhVvvfUWCQkJnDp1qsqKRw1tseuhQ4cqjRgfeOABXnrpJa5evUpRURFqtVqab7F1U6tWrbjvvvvYu3cvoihy/PhxmjdvzujRozl+/Dhr164lKSmJHTt2SOd1dXVl4MCB/Oc//8FisXDo0CHGjBnD8uXLeeaZZ/jqq6/4+9//zu7du3F1daV9+/bExcXh5uZGdHQ0Fy5c4PLly7z00kt1+vmYzWbi4uIYOHCg5AzsxYEDB1iwYAHNmjXD398fDw8PadSkUqlwd3fHYDBgMpkoKyuTwiJbv0RGRhIdHU1gYCAAJ0+eZOfOnZhMJrp06UJMTAwqlYqMjAzWrVtH+/btefDBB6X3qEutjsQei13v2ok98sgjbN68maZNm/LPf/6T8ePH1+p8ia+vL++99x4TJ04kNDSUmTNn8vrrrwMVv5RBQUHMnz+f559//pbXNqRwsri4mNDQUKksfXR0NI888gihoaH06tWLgoICysvLEQSBpk2bEhYWhk6n4+TJk+zevZvr16/ToUMHhg8fzrlz5/j5558JCQnh73//O7///jsrV65k586dXLx4UXrPVq1aMWHCBJ544gm++eYb/vnPf7J8+XKeeuopfvzxR/r27UteXh5Hjx6ld+/elJaWcurUKVQqFV5eXowcOZLg4OA6+4wEQaCgoABvb2+7hVgWi4Wnn36ajIwMevfujcFgwNvbW8oWcvMk/s12QEAAbdq0oWXLlhgMBs6ePcvBgwfJzc0FoF27dvTr1w8XFxeSk5OJj4/Hw8ODRx99FB8fHw4fPkxsbCz9+vWjT58+daK1PlBvwslr166xevVqvv76a44ePcqgQYN45plnGDVq1F/+FbFarfz444+MHz+elJQUDAYDkZGRJCcn06VLF+m4UaNG4e3tXWWVHpsTW7VqFe3bt5cSsDVp0kT6hdRoNNIdJpttWzhanW02m9FoNJKt1WpRqVSSDRUXw822TqdDFEXJFgQBq9Uq2S+++CKLFy8GIDAwkBdffBGDwQAgOS29Xo9OpyMzM5MLFy5gMpkQBIGOHTsyYMAATp06xdatW9Hr9TzyyCOUl5ezfv16AgMDeeSRR1i1ahWrV6/mt99+kz4jnU5H//79Wbx4Md99953k0B599FHi4uIIDg4mKCiIAwcO4OLiQrNmzXB3d5fm5l588cVqNQmCgFarrda2Wq2IoijZtv6ozrZnP9mmKpYsWULLli1p0aIFnp6eBAUF4enpKR0vCAJqtRpRFNFoNERERNC0aVMMBgOXL1/m5MmTlJSUoFar0ev1REdH06VLF44dO0ZCQgJms5nIyEgGDx6MyWTihx9+oKCggL/97W+0bduWvXv3cuDAAR566CHatm1bJ989R/ZTampqrYeTf8nl+/n58eKLL5KSkkJiYiItWrTg6aefJjQ0lJdeeon09PQanystLY1GjRqh1+uZPHkyGzdupF27dlLO9z/fqg4KCrpjPvhx48YRHR1Njx496NGjB8uWLePIkSNSu1JSUjh37hxQMby1ZTTdt28f2dnZQMWyBVsVoLi4OAoKCoCKity20VNsbCzl5eVYLBZiY2OxWCyUl5cTGxsLQFFREdu3bwcqMlTExcUBsGXLFsmBqdVqunfvjru7O8XFxVy8eJHc3Fy2bt3KmjVr2L17N/v37yc7O5sBAwYwcOBArl69yuTJk1m+fDnNmzdn3LhxfPLJJyxbtozRo0fj5ubGW2+9hZ+fH7NmzWL8+PHSCMpsNrNz50769OlDQEAAsbGxeHl58f3339OzZ092795NamoqHTt25OLFi5w8eZKkpCRSU1PRarVkZGRUqSkvL0+6u5qdnc2+ffsAyMrKIjExEYBz586RkpICQHp6OkeOHAHgxIkTnDhxAqBSPx06dIjY2FjMZnOt9dPKlSv529/+ho+PD++99x69evWiTZs2Ul41W/YQURQpKiqS2nLjxg2p/ulvv/3G559/TkpKCllZWVy8eJFmzZoRFhZGamoqS5YsYc2aNRQUFPDII48gCALz5s3jq6++ory8nOHDh3P58mVmzpzJ2bNnefXVV1m3bh3PPvss2dnZdv3u2aOf7uZ6qnd3J7Ozs1m1ahVfffUVly5d4pFHHiE7O5vdu3ezYMGCGs2hmEwmLly4QEFBAevXr2f58uXEx8dTUFBAnz59uHz5cqUJ5eeee46srCy2bt16y7lsI7GVK1cSFRVVL0digiDQpUsX6cvQvXt3hg8fTkBAAB4eHly7dk06HqB58+a0adMGf39/kpOTSU1NRRAEWrduzYABA9i7dy/Hjh3D19eXkSNHEh8fT3p6Ov379ycgIIB169bRunVrmjVrxowZM9i/f790bo1Gw+DBgxk9ejSenp5kZmbSunVrzp07R0lJCUFBQbi6ulJeXo7RaKS8vBydTse0adPq5BfebDZTUlKCl5eX9Pjly5fJyMggNzeX3NxcLl++zJUrVygpKaG4uJjy8nLKysooKytDo9FQVlZGbm4uN27cwGKxSCMqg8FAQEAAbm5uuLm5YTAY0Ov1aLVaXF1d8fX1xd/fXwotBUGgsLAQjUYj6XF3d0cQBDQaDb6+vpSVlVFYWIharcbFxYXWrVtLNUNFUaR9+/Z4eXlx4MABRFGU7hZv27YNg8HAgAED2LNnDwDjx4/H1dXV6UZiKSkpdOvWzbHhpNlsZtOmTaxYsYLt27fTsWNHnn32WZ588klpsn3t2rVMmTKl0l2ymjJo0CAiIyN5/fXX/3I4WZ/vTr7//vu89tprQEX21ilTphAWFoa/vz8GgwEXFxf0ej2+vr5ERkZSVFTEsWPHyMzMRBRFgoKC+Nvf/sb58+eJj4/HarXSu3dvmjdvzsaNGykpKeH++++ntLSUpKQkWrduTUREBJs3b6Zjx46cOnWKd999lytXrkhtcnNz44knnqBp06b4+/vTqFEjLl68iNFoxNXVVboobF/GiRMnEhAQYLfPSBAEMjIy2L9/P4mJiZw4cYKzZ89y6dKlSguB6wKtVouLiwsGg0FydjqdDo1GI9VB8Pb2xmw2IwgCnp6ehIaG4unpSWlpKYIg4Ofnh1qtlkbbAAaDAU9PT7Kzs9FqtfTu3ZvU1FQKCwvp1asX+/fvp3nz5jz88MN/OQeXKIqSA7vTHyA5HNsNpars2z2nUqnu2NZ6sXcyJCQEQRB44oknSExMpHPnzrccM3ToULy9vf9Sg0RRxGg0EhERQXBwMDt27JCcmMlkIj4+nvnz59/2HPV1sWtBQQHz5s2T/t++fXtCQkJQq9WUlpbi7e2Nh4eHdGds586dUlhhMBjo3bs3vr6+/Pjjjxw4cID77ruPESNGkJGRwZo1a9BoNAwbNozc3FwOHTqEn58fQUFBbNu2DT8/P+mXfd68eWzYsIGtW7ditVopLS3lyy+/xM/Pj759+9K/f3/0ej1Go1EKX6DiS67T6fjuu+944YUXqtRoNps5deoUqamppKamcvToUS5evEhJSQllZWUYjUZpRGQbmdr+RFHkHgIDu2CxWLBYLJSWlt6yh/VOqNVqaeSkVqulZRU2x2gbFdp+HEwmE66urqhUKml0M2nSJFxdXdHr9ZVG8zVxTI74LKtzYvZsy107sQ8//JDHHntMmoSuCh8fHylGvh1vvvkmw4YNo2nTphQVFbF27Vr27NnD1q1bUalUzJw5k3nz5tGyZUtatmzJvHnzcHNzY+zYsbc9b31dg/Pee+9Jo1O1Wi0tfiwpKcHX11dah3T+/HmuXLkiXdjh4eFER0eTnp7O7t27EQSBgQMH0rt3b3bu3MnVq1dxdXVlwIABnDlzhlOnTtGoUSN69OjB/v37UalU+Pv7k56eLl1YAwcOpHPnzmzevJnU1FSg4obNzz//zI4dO+jUqROtWrXC29tb+gLqdDopxEtPTyctLY3NmzeTkZHB9evXpcpJUPGl1el0GAwGGjVqhLu7O3q9Hjc3N4qKisjPz6ekpITr169XWidXHWq1Gl9fXxo1aiSFgTqdDk9PT6xWK+7u7gCUl5dX+tf2Hu7u7uTk5ODt7U1ZWRkmkwmj0YjJZMJisWA2m6WL/2aHei8XnyAImEymu3qNbf6roeIQx+nIxa7PPPMMu3btIjs7Gy8vLzp27Mjrr7/O4MGDgf9/seuyZcsqLXatrj6fbah68OBBoqOj61LKHcnOzqZZs2bSlzowMJB//etf+Pj4EB4eDlRceNnZ2RQWFiIIAiqVitatWxMaGiqtzBdFkVatWhEeHs4ff/zBjRs30Ol0dOvWjcuXL5OZmYlGo6F58+bk5+eTn5+PIAh4eHhQVFQkOc3S0lIpnMnPz2fXrl2VlmPY8Pb2Jjg4GI1Gw40bNyQHYHvOtvjTNp+k1+txcXHBy8sLs9nMjRs3MBqNXLt2jdzcXAoLC+/4RTcYDISGhtK8eXNCQkLw8/OjSZMmeHl5YTQaMRqN+Pr6cu3aNdzd3QkJCeHEiRO0a9eO1NRUHnroIbZs2UKfPn3YtWsXjz76KJs3b+b111+/p/TI5eXl0mean59PQUFBpf9X9XhJSQlms1lylH+2bUs3bl5WcTsHWlUoZwvjqrJtx978etsI0DYi1Gg0UuhpsViwWq2VRo620ahtJK5Wq6XR4M3H2Y6Fih+dRo0aScfa/kpLS8nKynL8Eov6Sn1e7Dpx4kRWrFgBVMxBTZo0iQ8//PC2rxEEgVOnTnHgwAGKiooQRZHmzZvj5+fHmjVrpNX8nTt3pqSkhBMnTkgTrJ6enhQWFmK1WlGpVOTl5VFSUoKHhwcajYbc3FyuX7+OVquluLiYwsJCLl++zPnz5+84MtJoNGg0Gry8vHB3d0ej0VRatHnjxg2Ki4trFNbrdDqaNm1KkyZNCA8PJzw8nI4dO5KXl0dpaSk5OTn069eP06dP4+HhQYsWLTh06BBNmjShWbNm7Nmzhz59+pCWlkZAQACtWrUiNjaWhx9+mHXr1vH000/z7bffMnv27Hq5/srmxMxmM7GxsTz44INVLlOyWCzs3LmTxYsXk5qaSllZGY0aNaJly5Z4e3vj4uJS6YaNVquV/vR6Pa6urri6ukrzejcvIbGNPI1GI4Ig4ObmJjlDb29vfH19uX79uhRFaDQa2rVrh4+PD0lJSZSUlKDT6ejduzedOnW67edcLxa71mfq60js5MmTtG3bFqj4JYyIiODjjz9mxIgRd3UeURTJyMhg79695Ofno1KpCAsLQxRFrly5IjksQRAoKyujoKBAulkgiiLXr18nLy+PgoICioqKKCgokMJA2wWg1WoJCQnB09OTixcvkpGRUWshglqtJiQkRJoesFV1CgkJoVWrViQlJVFWVkaTJk1o3749u3btoqysjJiYGK5du0ZaWhqdOnWiadOm/PTTT3Tr1g1XV1d+++03Jk6cKK2Za9OmDXFxcTz55JMsW7aM2bNn1/tN1ba7ibY5tDshCALr1q3jq6++4saNG3h5edGsWTOCg4Px9/eXzmkbdd38Pn8+v5+fH82aNcPLy4vCwkKOHz9eaa9oaGgoPXv2RK/Xs2fPHi5dugRU3DkfMGBAlWUEq8O2S0VxYtVQH53YlStXCAsLk0IwT09PWrVqRVxcXJVbp2qCKIrS/FlWVhZpaWmcP39eCkEBCgsLuXHjBoWFhZhMJmki3baFxs3NjebNm9OvXz9pkWVVXL16lR07drB//35SUlJIS0ujsLDwtu3TarX4+vri5+dHaGgoYWFhBAQEEBQUhE6nw8vLi86dO5ObmyttWg8LC6Nnz57SzYzw8HAGDhzIhg0buH79OkOHDsXHx4e1a9cSGRlJTEwMX375JV26dKFbt2588sknPPbYY1y+fJkLFy4watQoFi1axJtvvtkgtvHY+tRgMNx1yFteXs6OHTtITEwkNzcXDw8PmjRpIt1VhppVGfLz86N58+a0a9cOd3d3MjMzOXToEJcvX5ae79+/f6VN7neL4sTuQH0LJwsLC+nYsSMXLlyQvkwtWrSgffv2/PTTT3/5vHcKPexNUVER8fHxPProo4iiSExMDB4eHri5uREUFERAQACNGjXC09MTT09PAgICKCsrIzMzU/qFd3V1pWfPngQGBrJjxw6uXr2Kh4cHo0aNwmKxsGHDBsxmM15eXgwePJgffviBwMBAHn/8cTZv3kxmZiaTJk3iyJEj7N27l+nTp/Prr7/i6upK//79+eCDD3jjjTduewOqPlFbfWqxWEhOTiY5ORmTyYRKpUKn00kjXl9fX2kniG1tXVFREdnZ2ZWW3QDSDaXQ0NB7lSehhJN3oD6tE7NYLAwaNIiUlBRp5GIbhQ0ePLjSUouGitlspnHjxqhUKsaOHUujRo3Q6XQEBARIv/yNGjXC29ubZs2aERoayrVr16RMHFarlcDAQAYPHoyXlxexsbFkZGQQEhLCqFGjKC0tZfXq1Xh6ejJ27FiuXr3KypUrGTFiBB07dmT58uUEBwczcuRIPvvsMzp37kzHjh1ZsGABr7/+Om5ubg7+hOoHZrOZnJwcsrOzuX79OkajUUrv5OHhId0cCQoKsnvdy3qxTqwhUB/88htvvMHFixcpKyuTHgsKCkKv199zBhDblpibMy04Ap1OJ1Vo2r9/P0OGDJFGPrZ1SgUFBdy4cYPMzEz0ej1hYWH07duXkJAQcnNzSUhI4Ntvv0Wr1TJs2DBGjx5Neno6y5Ytw8PDgyeeeAJvb29WrVqFVqtl9uzZ5OXl8b///Y/x48fTpEkT5s+fz5gxYwgLC+Pdd9/ltddea3AOzJ59art54qg04zdjj2vTKZ2YbQWyo9i5c6eUyti2wtwWXrm7u9O3b997Or/FYmHv3r0MGTLE4fM9Go2Gc+fOERkZSXp6Om3btsXT07PSRmvbZLLJZOLMmTOkp6dLmSD69u1LkyZNMJlMbN++nY0bN9KiRQtmzJiBIAj83//9H+7u7vzzn/8kKChIGq3NmTOHsrIy3n77baZOnYq3tzfvvPMOL7300l1NNNcX6lOf2hN7XJtO6cQceSeqrKyMDz74AKi8cDEoKAiDwSBt67kXdDodw4cPv6dz1Caenp58++23vPjiiwQFBUmjCQ8PD/r37y9trL4Z29aiuLg48vPz0Wq1DBo0iBEjRiCKIrt27SIpKYnHH3+cqKgoSkpKWLBgAX379mX69OlkZmbyzTff8Prrr6PT6aS6AV5eXg76FO6N+tan9sIe16ZTOjHbcgFH8O6770prum7cuAEgzRO5urrSqlWre36P+ph7asiQITz88MMcO3aMwMBA3Nzc6NGjB4cPH+bXX3+VRmO2f1UqFc2aNeOhhx6StqgVFxfz7bffcvHiRQYNGsTrr79OQUEB27Zt48iRI0yePBlPT08OHDjAwYMHmTNnDoIg8M477zB58mT8/Pwc+yHcA/WxT+2BPa5NxYnVIidOnCAxMRGtViutpQEIDg6WFhjed9999/w+VquVpKQkBg4cWK++8G+99Rb//Oc/ycvLo02bNvzxxx9cu3aNxo0b07NnT8LDwyvN9wiCQGZmJj///DP5+fm4urry0EMPSVlLbJvVJ06cKG2aX7t2LRqNhunTp2M2myUHZstS0lCpr31a2yhOrIY4Kpy05QjTaDRSHiWoSAWk0WjQ6XS14sR0Oh1Dhw695/PUNmq1mvfee4/XX38dq9XK+fPnGTNmDP7+/iQlJfHLL79ICQZto7GwsDApM4mNc+fOsX79epo2bcry5cvRaDSUlJTw8ccfM3z4cDp16oTJZOKdd95h6tSpds2oUVfU1z6tbZRwsoY4YiQWHx/PxYsXpT2GRqMRQJoD02g0+Pn5SRuV74X6XBknMDCQGTNm8NNPP9G4cWMyMzPZsmULHTp04Lnnnqt23db169fZtWsX58+fp1mzZrzwwgtotVry8vI4ffq0tBbM09OTsrIy5s+fz4wZMxp0CHkz9blPaxNlJFZD6tqJiaLImjVrUKlUaLVaaYUzVIzCDAYDoijSsmXLWnk/QRA4evQo/fr1q5df+K5du3LhwgUKCwtJTU1l0qRJ5OXlsWrVKsrLy2/ZBmO1WvHx8WHAgAE89thj0nNXrlzhP//5D6NGjWL27NlARWbSxYsX89JLLzXYSfyqqO99WlsoTqyG1HU4aSvcodFoMBqN0spnnU5HcHAwZrMZNzc3evbsWSvvZ0ulU58ZPXo0a9eupUePHqxfvx5PT08mTpxYo77Jz8/nu+++Q6PRsHDhQmnN16lTp1i/fj1vvvnmHYvYNjQaQp/WBko4WUPqciQmiiIbNmyQ0hZfvnxZev/w8PBKa6V69+5dK+8pCALZ2dlSQsX6yj/+8Q++//57qRDHJ598Is0LduzYUfpCi6JIZmYmBw8eJCsrCx8fHylTcHZ2NgaDgQ0bNlBcXMzs2bMdusDXXjSUPr1XlJFYDalLJ7Z///5KKW9sRRKgYlOzLU2NLZFfbSAIAmfPniUoKKjef+Eff/xxYmNjiYuLY+bMmZjNZv744w+WL19eKVVPeHg4ffr0qbRPz1YjMy0tjWHDhjl8K5k9aUh9ei8oTqyG1GU4uXnzZoxGIyqVitLSUimddKNGjfDz85MuVFuB4NpAq9XWSvHiuuLBBx/kzJkzvPXWWzz22GPcf//93H///bd9TXl5Od999x1ms5lXX30VvV5fR611DA2tT/8qSjhZQ+pqJGbLt2VbNnDzKKxVq1ZSLnk3Nze6d+9ea+8rCAJZWVlVroSvr7Ro0YJ//etfbNy4kV9++YWOHTsSExNTyTkJgsDhw4eJj49Hp9MxevRoqWKPs9MQ+/SvoIzEakhdObG1a9dK6XlVKhUXLlyQnrt5s63ZbKZXr1619r6CIHDp0iUaN27coL7wKpWKMWPGIIoiJ0+e5Ouvv8ZsNldayd+hQwemT5+OVqvFYrGQmJjY4HT+FRpqn94tTufE3nnnHTZs2MDJkydxdXXlvvvuY/78+bRu3Vo6xpZn//PPP6+UZ799+/bVnrcuwsny8nIOHz6Mi4sLarWaK1euSNuM/P39pVqJtpJdtZnXqrZW/jsKlUpF27ZtpWy31dHQdd4NctFqj2vToS4/Pj6eadOmceDAAXbs2IHFYmHIkCGVUuMuWLCAhQsXsnjxYpKSkggODmbw4MGVSon9mbrIYrFx40ZcXV0RBAGj0VipyEZERAQlJSWUl5cjCAIRERG1+t5Wq5UzZ844PFuHvZGLTpCPVnvoc6gT27p1KxMmTKB9+/Z06tSJFStWcOHCBQ4dOgRUjMI++ugj5syZw5gxY4iKimLlypWUlpayZs2aas9bF/nEUlNTMZlMUoXmm51YeHg4Op0OFxcX3Nzc6NatW62+tyiK5Ofn14u8afZELjpBPlrtoa9eBd+2cMzX1xeo2EOXk5PDkCFDpGP0ej39+/dn37591Z7H3uFkRkYG2dnZWK1WDAYDJpOJa9euAf9/KGkr9V5aWlpri1xtaLVaunfvXu+LX9wrctEJ8tHqdOHkzYiiyMsvv0zfvn2lupI5OTlARS6umwkKCpKeq4q0tDSSk5NJSkoiKSlJcji2oayttp7Ntk02VmfbStTb7E2bNkkOzDZJbSMsLIyioiKpbH1oaKhUvdmWINFW3+92ttVqrWTb2mu1WjGZTJw8eRKTyVRrmmy/kDZbFMVbbFs/3ayjtjRVZZtMJo4fPy69zhk0VddPRqOREydO3KK1IWuqyna6cPJmpk+fzpEjR/juu+9uee7PK7SrKjt1MxMmTCA6OpoePXrQo0cPli1bxpEjR0hPTwcgJSVFqlCemJgoLY3Yt2+flH0iISFBWvMVFxcnJTjcunUrBw8exMPDg3PnzmE0Giul3WnZsiVXr14FKhIk2mo4FhQUEBcXB1Ts/0tISAAqiuraRpVZWVkkJiYCFaPQlJQUANLT0zly5AhQke7n5MmTlJWVcfTo0VrRtH37dmmOMTY2lvLyciwWC7GxsVgsFsrLy4mNjQUqioRs37691jWdOHECoFI/paamSp+ls2iqrp8OHDjA9evXnUpTdf1U29SLQiG2rAcJCQmVJsEzMjKIjIwkOTmZLl26SI/bUresXLmy0nlsRQhWrVpF+/btJa/fpEkTKd+URqPBYrFIRWZtlY3VanW1tm3eS61Ws23bNjZu3Ehpaal03LfffgtUlLQaNWoUJSUlUgHbxx9/nJiYGOlXSKfTSQVLtVpttbYtR73NtrW9OvteNJnNZqneoc0GpBTTNttWAsxmK5oUTXerKTU11bkKhYiiyIwZM9i4cSN79uy55S5eREQEwcHB7NixQ3JiJpOJ+Ph45s+fX+1527Rpc9sP6Oa4vCb2zYstk5KSJAfm7u5OUlKS9FzTpk0RRREfHx9MJhNFRUXSbfOby8nXxL4508OfbavVytGjR2nbtq303L1ouhvbVgKstjVVZatUKk6cOEHbtm2dRlN1bVepVBw/fvwWrQ1ZU1W20+XYnzZtGmvWrOHnn3/Gw8NDmufy8vLC1dUVlUrFzJkzmTdvnlQ1et68ebi5uTF27Ng6b29ZWRnp6elSgdOSkpJKdyU7duyIIAgUFRVhMBgICwtzumwLCgr1DYc6saVLlwIQExNT6fEVK1YwYcIEAGbNmkVZWRlTp06VFrtu3779ttWzb/6VqE22bNmCwWBAEARKS0txc3OTYn4fHx/p18bV1RWz2VyrRUdvRqPRSDc/nBm56AT5aLXHtenQiX3bHZU//9kcGFQMi+fOnUt2djbl5eXEx8ffsbPttWDw8OHDlJeXo1Kp8Pb2Ji0tTXouLCwMd3d3NBoNhYWFuLq62i3rgtVqJSUlRRYLI+WgE+Sj1anvTtZ3ioqKOHv2LFqtFoPBQGlpaaVQsnPnzhQUFKDRaPD396ewsLBWN33/GVdXV7uduz4hF50gL621iVOurLPHkPXXX3/F3d0dlUpFQUEB7u7u0tIKLy8vtFot7u7ulJaWYjabiYiIsFv2BY1GQ5s2bexy7vqEXHSCfLQ6XThpL25OtldbHDt2DJPJBFQUi01LS5MWHoaHh+Pt7U1hYSEGgwE3Nze7lhCzWCwkJSXZRWd9Qi46QT5a7aHPKZ1YbacvLigo4MKFC6hUKlxdXSkpKamUOywqKopr164REBBAcXExarWa6OjoWm3DzahUKnx8fJwyTfPNyEUnyEerPfQp4WQN2LJlC56enhiNRq5fv467u7vkxDw8PPD29kav15OXl0dgYCB5eXl2TaWs0WhqNVNsfUUuOkE+WpVwsobU9pD19OnTFBYWolar8fDw4NixY1IoGRkZiYuLCyUlJfj5+XH9+nUiIyPtmo3UYrGwb98+WYQectAJ8tGqhJM1pDYzY5aWlnLmzBm0Wm2VoWRkZCSCIODm5kZhYSEBAQH4+PjU2vtXhVqtdvoMoCAfnSAfrfbQ55SfWG1+ULaFtSqVivz8fNzd3Tl//jwA7u7uNG/eHLPZjFqtRq/XU1JSUuv5w/6MWq0mPDxcFl94OegE+WhVnFgNqc0h69GjRykqKkKj0dCoUSOOHj0qpRdp06YNJSUleHp6UlpaSqNGjTCZTJU2q9sDi8VCQkKCLEIPOegE+WhVwskaUlve3mQycfr06UoLXG9Ou9OkSRN8fHwoKCjA19eX/Px8IiIi7J7YTq1WExkZKYtfbTnoBPloVUZiNaS2Pqg9e/ZIBW9v3LiBp6enlDfJ1dWVDh06cPXqVYKCgrhy5QrBwcF4e3vXynvfDjnNn8hBJ8hHq+LEakhtDVmTk5MpLCxEp9NJoaRt71fbtm3Jy8sjNDSUK1euEBoaSl5eHr17966V974dFouFuLg4WYQectAJ8tGqhJM1pDa8vdVq5cSJE1LBj5KSkkqhZGhoKCEhIVy5cgV/f39KSkrQarV1kolArVYTFRUli19tOegE+WhVRmI1pDY+qAMHDkgZMouKivD29ubs2bMAGAwGunbtytWrV/H29sZsNmM2mwkLC6uTFddqtZrAwEBZfOHloBPko1VxYjWkNoas+/bto7S0FBcXFzw8PDh+/Lh03rZt21JQUICHhwdWqxWj0UhQUJDd14fZMJvNbNu2TSr+4KzIRSfIR6sSTtaQe/X2tgpGOp0OvV5PcXHxLaGkj48PFosFo9FIYGAgOTk59O/f/16bXiM0Gg3du3e3W/LH+oJcdIJ8tNpjJOaUeyfv9YNKS0uTSlIVFxfj6+srVXbR6/V07dqV4uJiBEEgJCSECxcu4OfnV+uVvqtDrVZLtTmdGbnoBPloVcLJGnKvQ9a4uDjKy8vR6/XSXknbML9t27aUlJSgUqnw8/MjNzcXLy8v/P39a6PpNcJsNrN582anDz3kohPko9Ue4aRTjsTudUhuuyup0+luKQYSFhaGXq/HYDCQm5uLt7c3Wq3WrvnD/oxWq+X++++XRbVoOegE+Wh1uiwWCQkJjBw5ktDQUFQqFT/99FOl50VRZO7cuYSGhuLq6kpMTAzHjh2743nv5Q7huXPnKCoqkoqBeHp6VgolO3TogEajIT8/n4CAAADy8/MZMGDAX37Pu0WlUuHp6SmL3FNy0Any0WoPfQ51YiUlJXTq1InFixdX+fyCBQtYuHAhixcvJikpieDgYAYPHixVQa6OexmybtmyBavViouLi7TA1Xa+9u3bYzabKS0tJTg4mPLycgoLCwkMDCQoKOgvv+fdYjab+fnnn50+9JCLTpCPVqcLJ4cNG8awYcOqfE4URT766CPmzJnDmDFjAFi5ciVBQUGsWbOG559/vtrz3suQ9dixY+h0OrRa7S17JSMiIhBFkcDAQG7cuIHRaCQ0NLTOa0tqtVqGDBni9KGHXHSCfLQ6XTh5O86dO0dOTg5DhgyRHtPr9fTv3599+/bd9rXHjh0jOTmZpKQkkpKSyM7Olu42QsWvwc22LSvF5cuXuXLlChaLRcpKcebMGaBigWvr1q3x8PDg2rVrAAQEBFBYWEhkZCRms1kqOWf7Nb3ZFgShkm37RarOtlqtlWxbe222rcT8nTRVZ5vN5kq2Lcnjn3XUpaY/2xaLRQo/nElTdf1ku3PnTJqqsmubeuvEbNXA/xymBQUFSc9Vx/jx44mOjqZHjx706NGDZcuWceTIEWluKyUlRdrInZiYKCU5XLRoEWVlZeh0OkpLSyvVAWzbtq30Wp1Oh5eXF0lJSZSUlHD//fcTGxuLxWKhvLyc2NhYoKLM2/bt24GKPP1xcXEA5OXlkZCQAEB2drbklLOyskhMTAQqnHhKSgoA6enpHDlyBKi46XDs2DFiY2M5fPjwHTXt27dPKvCbkJBAXl4eUHEHtqCgAKjImWYL0WNjYykvL8disdSpphMnTgBU6qfk5GS2bduGxWJxGk2366etW7dKKXmcRdOf+8kedSdVos21OxiVSsXGjRsZPXo0UPEB9OnTh8uXLxMSEiId99xzz5GVlcXWrVtvOUdycjLR0dGsXLmSqKgo6QNr0qSJdPdQo9FIv/A2W61Wo1armT59OgUFBbi4uCAIAvv27ZM66tFHHyUiIgJvb29MJhNGo1Fa2/Pyyy9jsVikUMBisUhblmy2IAhYrVbJFgQBrVZbrW21WhFFUbJtbbc9LooiKpWqko6qNFVnm81mNBqNZGu1WlQqlWTbdNSVpqpss9mM1WpFr9djtVqdQlN1/WQbcbm4uFTS2pA1VWWnpKTQrVs3Dh06VGt1KOptAB4cHAxUjMhudmK5ubl3nERv3779bT+gm+cdbHZRUREXL17E1dUVi8WCu7s7GRkZALi5udGiRQu8vLwoKChApVLh5eUlJUpUqVSVcurb7Jsft3VmTe2b5w7+bIuiSHl5OQaDQQq3qtJ0O7uq9tbEtpemqmytViuFNc6kqTq7vLzc6TRVZdc29TacjIiIIDg4mB07dkiPmUwm4uPjue+++2772r8yZN2yZYsUs3t5eXHy5EnpPFFRUbi4uHD16lVcXV3x8/PDaDSSn59PTEzMXb/XvWKxWNi+fbss0rbIQSfIR6s9wkmHjsSKi4uliXOoiMVTU1Px9fUlLCyMmTNnMm/ePFq2bEnLli2ZN28ebm5ujB079rbn/Stef//+/bi5uaHX6ykqKpJGYVDhUM1mM4GBgVitVvLz86V1Pa1atbrr97pXdDodo0aNqvP3rWvkohPko9UeIzKHOrGDBw9WWiT68ssvAxUT819//TWzZs2irKyMqVOnkp+fT8+ePaXCHbfjbqf5TCYTZ86cwc3NDYvFgkaj4cKFC0BFte/WrVtLRUBEUcRgMEhhpCMWJ9rSA9kKmDgrctEJ8tFqjyl4h4aTMTEx0iT1zX9ff/01UBHXz507l+zsbMrLy4mPj69R0sG7HbJu27ZNek2jRo04efKk9Fz37t0xmUwUFxej0+nw9vbGxcWF4uJiWrZseVfvU1tYLBb27t3r9KGHXHSCfLQ6XThpL+52yLp7925cXFwwGAyYzWZOnz4tPdesWTM0Go10V7KkpASomAity61GN6PT6Rg+fLhD3rsukYtOkI9We4ST9XZi/164m0V1ZWVlpKenS7f0c3NzpXU5TZo0oVmzZri6ukor9F1cXHBzc8Pd3V0qIlLXCILA9evX7bZ4sL4gF50gH6320Cd7J7Z582asVqu0RsZWGBega9euGI1GysrKMBgMeHt7S+t16nKv5J+xWq0kJSXZZWhen5CLTpCPVns4MdmHk7t27UKr1aLX63FxcZHmw7RaLZGRkbi6uqLRaBAEgfLycgRBQKVS8eCDD9qr+XdEp9MxdOhQh71/XSEXnSAfrUo4WUNq6u2Li4s5e/YsarUag8FQKflhp06d8PHxwWw2YzQagYobDQaDAVdX1zqpL1kdgiCQm5sri9BDDjpBPlqVcLKG1PSD2rhxo7TFw2KxcOrUKem5Ll26UFpaik6nw93dHb1ej1arRRRFvLy87NX0GiEIAkePHpXFF14OOkE+WpVwsobUdMi6Y8cOtFotarWa3Nxc8vPzgYoJ/aZNm6LT6VCr1ZhMJml9GODQUBIq9A0cONChbagL5KIT5KNVCSdrSE28/blz58jKypJyh928c6B79+7SeWzrdnQ6nbS41bav01EIgsClS5dk8astB50gH61KOFlDavJBrVixAo1Gg1arxWw2k5mZCYC7uztt2rSRnJtt0l+lUiEIAn5+fnZu/Z0RBIGzZ8/K4gsvB50gH61KOFlD7jRktVqtUh4lFxcXUlNTpe0QPXv2xGAwIAgCarUaFxeXSqlH6sP+Nq1WS79+/RzdDLsjF50gH61KOFlD7uTtf/31V4qKinBxccFoNFbK3tqtWzdUKpU0V2ar8C0IQr2Y1IcKfefPn5fFr7YcdIJ8tCrhZA250wf17bffotfr0ev1HD16VBqF3Xfffbi7u2MwGDAYDLi7u6NWq/H29sbLy4t27drVRfPviJzmT+SgE+SjVQkna8jthqznzp0jPT1dyglmS6trMBjo0qULarVaWthqWx9WWFiIWq1m8ODBddL+O6HVau+YU80ZkItOkI9WJZysIbfbujF//nxpQv/IkSOV5sJsGSr0ej3u7u40atQIDw8PXFxcUKvVdqnU8lewWq2cOXPG6beoyEUnyEerPfQ5pROrLmfRtWvX2L9/P3q9nvz8fKkcm7u7Oz179kQURaxWK2VlZZSVlUlVZNzd3Rk5cmRdSrgtoiiSn59vl9xM9Qm56AT5aLWHPlmFk//617+wWq2oVCrS0tKkxwcNGoS3tzcGg0FamQ8VyRLLysooLS2lefPmddL2mqDVaqW1bM6MXHSCfLQq4WQNqWrImpOTw65du3BxcSEjI4OysjIAwsLCpMreJSUlXLt2jevXr2M0GvHw8CAiIoLo6Oi6lnBbrFZrpRoAzopcdIJ8tCpJEe+BZ555RsrZZKuF5+LiwkMPPSTdjbTNgWm1WgoLC8nNzeXKlSu89tprDm79rdicsLMjF50gL621SYMYiS1ZsoSIiAgMBgPR0dHs3bu3yuOuXr0KwPXr1ys9/uOPP5KcnExZWVmlfGEPPfQQTZs2xcfHB29vb6xWK+fPnyczMxOdTkfHjh3p0KFDvct5npuby88//0xubq6jm2JX5KIT5KPVdm3artXaoN47se+//56ZM2cyZ84cUlJSuP/++xk2bJhUyONmbFWTb/4iZGdnM336dEpKSrh8+bL0eJ8+fejatSt6vR6j0cjly5cxmUy0bt2aDh06UFpaSnJyMn/729/sL/IuuXjxIv/973+5ePGio5tiV+SiE+Sj1XZt2q7V2qDeO7GFCxfyzDPP8Oyzz9K2bVs++ugjmjZtytKlS+/42lOnTtG6dWvy8vKk8u8AnTt3ZuDAgVIFo8LCQiIiImjRogVZWVmkpaURFhbGAw88UO9GYQoKCpWp107MZDJx6NAhhgwZUunxIUOGSHsfq+K1117Dw8ODNm3aUFRUJK0SVqlU9OzZk/79+0tZKYxGI23btsVgMJCcnEx4eDi9e/fm5MmT9OjRw676/iq29Wr1Zd2avZCLTpCPVluV8dqkXk/s5+XlYbVab8lnHxQURE5Ozi3H21bYX7ly5Zbn3N3d6dChA0FBQZSVlZGTk4OLiwtarZaLFy+Snp5O165dOXLkCPn5+YwePZqDBw9KCRNtZd5tdSlVKpVkQ8Vdl5ttWwJFmy0IgpTHvya21WpFFEXJBqSN6CdOnADg6NGj0vtaLBZUKpVk39zemtiO1lSVnZaWhkaj4dixY06jqbp+SktLQ61W31FrQ9JUlW0rSm27VmuDeu3EbPw5pBNFscowr7S0tNpzlJSUcODAgRq/56JFi2reQAcxfvx4RzehThg3bpyjm1BnyEXr7a7Vu6VeOzF/f380Gs0to67c3Nwqqw394x//AMDNzQ29Xl/pPAEBAfZtrIKCwh0pKysjMzOzVouiqMR6vs+hZ8+eREdHs2TJEumxdu3aMWrUKN555x0HtkxBQaE+UK9HYgAvv/wyTz/9NN26daN37958/vnnXLhwgcmTJzu6aQoKCvWAeu/EHn/8ca5du8b//vc/srOziYqKIjY2lvDwcEc3TUFBoR5Qr5dY2Jg6dSqZmZkYjUaeeeYZxo8ff8fV+zbi4+OJjo7GYDDQvHlzPvvsszpq9b1R010KAHv27JGKmNz8ZysEXF9JSEhg5MiRhIaGolKp+Omnn+74mobYn3ers6H25zvvvEP37t3x8PAgMDCQ0aNHVyqDWB332qcNwonZuJvV+1CRAPHBBx/k/vvvJyUlhTfffJMXXniB9evX13HL74671Wnj1KlTZGdnS38tW7asoxb/NUpKSujUqROLFy+u0fENtT/vVqeNhtaf8fHxTJs2jQMHDrBjxw4sFgtDhgyhpKSk2tfUSp+KDYgePXqIkydPrvRYmzZtxDfeeKPK42fNmiW2adOm0mPPP/+82KtXL7u1sTa4W527d+8WATE/P78OWmcfAHHjxo23Paah9ufN1ESnM/SnKIpibm6uCIjx8fHVHlMbfdpgRmJ/ZfX+/v37bzl+6NChHDx4ELPZbLe23gt/dZcCVFQtDwkJ4YEHHmD37t32bKZDaIj9eS809P68ceMGAL6+vtUeUxt92mCc2N2u3oeKHGJVHW+xWGp1A2pt8ld0hoSE8Pnnn7N+/Xo2bNhA69ateeCBB0hISKiLJtcZDbE//wrO0J+iKPLyyy/Tt29foqKiqj2uNvq03t+d/DM1Xb1/u+Orery+cTc6W7duTevWraX/9+7dm6ysLN5//32nq2XYUPvzbnCG/pw+fTpHjhzht99+u+Ox99qnDWYkdrer9wGCg4OrPF6r1daLSt5V8Vd0VkWvXr1IT0+v7eY5lIbYn7VFQ+rPGTNmsGnTJnbv3k2TJk1ue2xt9GmDcWIuLi5ER0ezY8eOSo/v2LGj2lJXvXv3vuX47du3061bN3Q6nd3aei/8FZ1VkZKSQkhISG03z6E0xP6sLRpCf4qiyPTp09mwYQNxcXFERETc8TW10qd3f8/Bcaxdu1bU6XTil19+KR4/flycOXOm6O7uLmZmZoqiKIpvvPGG+PTTT0vHZ2RkiG5ubuJLL70kHj9+XPzyyy9FnU4nrlu3zlESasTd6vzwww/FjRs3iqdPnxaPHj0qvvHGGyIgrl+/3lESakRRUZGYkpIipqSkiIC4cOFCMSUlRTx//rwois7Tn3ers6H255QpU0QvLy9xz549YnZ2tvRXWloqHWOPPm1QTkwURfHTTz8Vw8PDRRcXF7Fr166Vbt+OHz9e7N+/f6Xj9+zZI3bp0kV0cXERmzVrJi5durSOW/zXuBud8+fPFyMjI0WDwSD6+PiIffv2FTdv3uyAVt8dtqUEf/4bP368KIrO0593q7Oh9mdVGgFxxYoV0jH26NN6vwFcQUFB4XY0mDkxBQUFhapQnJiCgkKDRnFiCgoKDRrFiSkoKDRoFCemoKDQoFGcmIKCQoNGcWIKCgoNGsWJKSgoNGgUJ6agoNCgUZyYQr0lJiaGmTNnOroZCvUcxYkpKCg0aJS9kwr1kgkTJrBy5cpKj507d45mzZo5pkEK9RbFiSnUS27cuMGwYcOIiorif//7HwABAQFoNBoHt0yhvtHg0lMryAMvLy9cXFxwc3MjODjY0c1RqMcoc2IKCgoNGsWJKSgoNGgUJ6ZQb3FxccFqtTq6GQr1HMWJKdRbmjVrxh9//EFmZiZ5eXkIguDoJinUQxQnplBvefXVV9FoNLRr146AgAAuXLjg6CYp1EOUJRYKCgoNGmUkpqCg0KBRnJiCgkKDRnFiCgoKDRrFiSkoKDRoFCemoKDQoFGcmIKCQoNGcWIKCgoNGsWJKSgoNGgUJ6agoNCgUZyYgoJCg0ZxYgoKCg0axYkpKCg0aP4/QDgc0nR6pvUAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(3, 2.3))\n", "\n", "for i in range(len(delta)):\n", " P = (1 + WT*delta[i])*Pn\n", " Gyr = feedback(P*K, 1)\n", "\n", " y, t = step(Gyr, np.arange(0,5,0.01))\n", "\n", " ax.plot(t, y*ref, color ='k', lw =0.3)\n", "\n", "Gyr = feedback(Pn*K, 1)\n", "y, t = step(Gyr, np.arange(0,5,0.01))\n", "ax.plot(t, y*ref, lw =2, color='k')\n", "\n", "plot_set(ax, 't', 'y')\n", "ax.set_xlim(0, 2)\n", "ax.set_ylim(0, 60)\n", "\n", "# fig.savefig(\"robust_step.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### PID制御との比較" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "ステップ応答" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "kp = 2\n", "kd = 0.1\n", "ki = 10\n", "\n", "# fig, ax = plt.subplots()\n", "fig, ax = plt.subplots(figsize=(3,2.3))\n", "\n", "for i in range(len(delta)):\n", " Kpid = tf([kd, kp, ki], [1, 0])\n", "\n", " P = (1 + WT*delta[i])*Pn\n", " Gyr = feedback(P*Kpid, 1)\n", " y, t = step(Gyr, np.arange(0,5,0.01))\n", " ax.plot(t, y*ref, color ='k', lw =0.3)\n", "\n", "ax.set_xlim(0, 2)\n", "ax.set_ylim(0, 60)\n", "plot_set(ax, 't', 'y')\n", "\n", "# fig.savefig(\"robust_comp.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "ナイキスト線図で不確かさの影響を確認する" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "from control.matlab import nyquist\n" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/minami/opt/anaconda3/envs/bookpython/lib/python3.11/site-packages/control/freqplot.py:943: UserWarning: number of encirclements was a non-integer value; this can happen is contour is not closed, possibly based on a frequency range that does not include zero.\n", " warnings.warn(\n", "/Users/minami/opt/anaconda3/envs/bookpython/lib/python3.11/site-packages/control/matlab/wrappers.py:113: UserWarning: number of encirclements does not match Nyquist criterion; check frequency range and indent radius/direction\n", " _, contour = nyquist_plot(syslist, omega, *args, **kwargs)\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,2, figsize=(6, 3))\n", "\n", "for i in range(len(delta)):\n", "# ロバスト制御:閉ループ系が安定になる\n", "\n", " P = (1 + WT*delta[i])*Pn\n", "\n", " x, y, _ = nyquist(P*K, logspace(-3,5,1000), plot=False)\n", " ax[0].plot(x, y, lw = 0.5, color='k')\n", " #ax[0].plot(x, -y, ls='--', color='k')\n", " ax[0].scatter(-1, 0, color='k')\n", " plot_set(ax[0], 'Re', 'Im')\n", "\n", "# PID制御:閉ループ系が不安定になる\n", " xpid, ypid, _ = nyquist(P*Kpid, logspace(-3,5,1000), plot=False)\n", " ax[1].plot(xpid, ypid, lw = 0.5, color='k')\n", " #ax[1].plot(xpid, -ypid, ls='--', color='k')\n", " ax[1].scatter(-1, 0, color='k')\n", " plot_set(ax[1], 'Re', 'Im')\n", "\n", "x, y, _ = nyquist(Pn*K, logspace(-3,5,1000), plot=False)\n", "ax[0].plot(x, y, lw = 2, color='k')\n", "ax[0].set_xlim(-1.2, 1.2)\n", "ax[0].set_ylim(-1.2, 1.2)\n", "\n", "xpid, ypid, _ = nyquist(Pn*Kpid, logspace(-3,5,1000), plot=False)\n", "ax[1].plot(xpid, ypid, lw = 2, color='k')\n", "ax[1].set_xlim(-1.2, 0.5)\n", "ax[1].set_ylim(-1.2, 0.5)\n", "fig.tight_layout()\n", "\n", "# fig.savefig(\"nyquist_robust.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "左:ロバスト制御,右:PID制御" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### おまけ" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "from control import augw, hinfsyn\n", "G = augw(P, w1=WS, w2=WU, w3=WT)\n" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\frac{5.264 s^5 + 1592 s^4 + 1.227 \\times 10^{5} s^3 + 4.366 \\times 10^{5} s^2 + 1.19 \\times 10^{7} s + 9.958 \\times 10^{6}}{s^6 + 320.4 s^5 + 2.892 \\times 10^{4} s^4 + 3.768 \\times 10^{5} s^3 + 2.799 \\times 10^{6} s^2 + 2.53 \\times 10^{6} s + 6.109 \\times 10^{5}}$$" ], "text/plain": [ "TransferFunction(array([5.26385918e+00, 1.59156522e+03, 1.22682223e+05, 4.36556203e+05,\n", " 1.19037009e+07, 9.95839882e+06]), array([1.00000000e+00, 3.20437726e+02, 2.89216312e+04, 3.76842182e+05,\n", " 2.79873805e+06, 2.53046728e+06, 6.10856797e+05]))" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "k, cl, gam, ro= hinfsyn(G, 1, 1)\n", "ss2tf(k)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## ディジタル実装" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "from control.matlab import tf, c2d, step, lsim\n" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "連続時間システム \n", " 1\n", "---------\n", "0.5 s + 1\n", "\n" ] } ], "source": [ "P = tf([0, 1], [0.5, 1])\n", "print('連続時間システム',P)\n" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "離散時間システム(zoh) \n", " 0.3297\n", "----------\n", "z - 0.6703\n", "\n", "dt = 0.2\n", "\n", "離散時間システム(tustin) \n", "0.1667 z + 0.1667\n", "-----------------\n", " z - 0.6667\n", "\n", "dt = 0.2\n", "\n" ] } ], "source": [ "ts = 0.2\n", "\n", "Pd1 = c2d(P, ts, method='zoh')\n", "print('離散時間システム(zoh)', Pd1)\n", "\n", "Pd2 = c2d(P, ts, method='tustin')\n", "print('離散時間システム(tustin)',Pd2)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "ステップ応答" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,2, figsize=(6, 2.3))\n", "\n", "Tc = np.arange(0, 3, 0.01)\n", "y, t = step(P, Tc)\n", "ax[0].plot(t, y, ls='-.')\n", "ax[1].plot(t, y, ls='-.')\n", "\n", "\n", "Td = np.arange(0, 3, ts)\n", "y, t = step(Pd1, Td)\n", "ax[0].plot(t, y, ls='', marker='o', label='zoh')\n", "\n", "y, t = step(Pd2, Td)\n", "ax[1].plot(t, y, ls='', marker='o', label='tustin')\n", "\n", "for i in [0, 1]:\n", " plot_set(ax[i], 't', 'y', 'best')\n", " ax[i].set_xlim([0, 3])\n", "\n", "fig.tight_layout()\n", "# fig.savefig(\"c2d_step.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "特定の周波数の信号を印加したときの応答" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/minami/opt/anaconda3/envs/bookpython/lib/python3.11/site-packages/control/timeresp.py:940: UserWarning: return_x specified for a transfer function system. Internal conversion to state space used; results may meaningless.\n", " warnings.warn(\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,2, figsize=(6, 2.3))\n", "\n", "Tc = np.arange(0, 3, 0.01)\n", "Uc = 0.5 * np.sin(6*Tc) + 0.5 * np.cos(8*Tc)\n", "\n", "y, t, x0 = lsim(P, Uc, Tc)\n", "ax[0].plot(t, y, ls='-.')\n", "ax[1].plot(t, y, ls='-.')\n", "\n", "\n", "T = np.arange(0, 3, ts)\n", "U = 0.5 * np.sin(6*T) + 0.5 * np.cos(8*T)\n", "\n", "y, t, x0 = lsim(Pd1, U, T)\n", "ax[0].plot(t, y, ls='', marker='o', label='zoh')\n", "\n", "y, t, x0 = lsim(Pd2, U, T)\n", "ax[1].plot(t, y, ls='', marker='o', label='tustin')\n", "\n", "for i in [0, 1]:\n", " plot_set(ax[i], 't', 'y', 'best')\n", " ax[i].set_xlim([0, 3])\n", " ax[i].set_ylim([-0.3, 0.3])\n", "\n", "fig.tight_layout()\n", "# fig.savefig(\"c2d_time.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [], "source": [ "from control.matlab import bode, logspace, linspace, mag2db\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "ボード線図" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(2, 1, figsize=(4, 3.5))\n", "\n", "mag, phase, w = bode(P, logspace(-2,2), plot=False)\n", "ax[0].semilogx(w, mag2db(mag), ls = '-.', label='continuous')\n", "ax[1].semilogx(w, np.rad2deg(phase), ls = '-.', label='continuous')\n", "\n", "# 離散時間システム (0次ホールドによる離散化)\n", "mag, phase, w = bode(Pd1, linspace(0.01, np.pi/ts-0.001, 1000), plot=False)\n", "ax[0].semilogx(w, mag2db(mag), ls = '--', label = 'zoh')\n", "ax[1].semilogx(w, np.rad2deg(phase), ls = '--', label= 'zoh')\n", "\n", "# 離散時間システム (双一次変換による離散化)\n", "mag, phase, w = bode(Pd2, linspace(0.01, np.pi/ts-0.001, 1000), plot=False)\n", "ax[0].semilogx(w, mag2db(mag), ls = '-', label = 'tustin')\n", "ax[1].semilogx(w, np.rad2deg(phase), ls = '-', label = 'tustin')\n", "\n", "bodeplot_set(ax, 3)\n", "\n", "# ナイキスト周波数 w = pi/ts のところに線を引く\n", "ax[0].axvline(np.pi/ts, lw = 0.5, c ='k')\n", "ax[1].axvline(np.pi/ts, lw = 0.5, c ='k')\n", "\n", "ax[0].set_ylim([-43, 3])\n", "# ax[0].set_xlim([0.01, np.pi/ts])\n", "# ax[1].set_xlim([0.01, np.pi/ts])\n", "\n", "fig.tight_layout()\n", "# fig.savefig(\"c2d_bode.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "サンプリング周期を0.05にしたときのボード線図" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "離散時間システム(zoh) \n", " 0.09516\n", "----------\n", "z - 0.9048\n", "\n", "dt = 0.05\n", "\n", "離散時間システム(tustin) \n", "0.04762 z + 0.04762\n", "-------------------\n", " z - 0.9048\n", "\n", "dt = 0.05\n", "\n" ] }, { "data": { "image/png": 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xJPmrVmPR9ffj8MJfsGL8F+hD9wOhKBz1NGLp6Q/w2BfjsP/Iz07VKyUeUmRiMZSLrjaW3ImylCSCspSk0FXZe2wnNqW8i3SPegCAmhBMN/vjhVvfQ1jktI5t3DWEspR0FeOOaW1iYqLT01qxMkI2fDpHcnuZUN4VX6SixEkcV2NEaj2w/h978dmo9zHa5AuaovCXrgmz9v0T/056BdUt1YL1SomHFJlYDOWiq40ld6KcGCTijmltdHS009NasTJCNnw6R3J7mVDeFV+kosRJnMuN0fTRM/HtosNYM+otTFT5wkxR2FK0A7G/zsKGC0fRoHf0Mgpp8ZAiE4uhXHS1seROlKUkEZSlJIVrjeRzB/B+6scoajwNAOhjIXguchZumrYClEZ5UE5ulKWkqxi5p25msxnx8fHcS1PkKiNkw6dzJLeXCeVd8UUqSpzEkTtGk3tPxW9zfsZdvZfCl9agVEPhmXN/4pFN45F6eB1w8VpSSjykyMRiKBddaSy5eykJREGQ9PR0AoCkpqbKWi9N06SmpobQNC1rGSEbPp0jub1MKO+KL1JR4iSOO2NUWn6GrPrfQjJ2w3ASvTGajNwwnDy3dgIpLDgqKR5SZGIxlIvOOpZmz57t0FYon5qaSgCQ9PR0yb44g2xLSXfffbfTZb744gvu9ZidFWUpSUEBKK85ibd3/BPJOA8ACLbQuFM1Ck889C08tcpenJdDl15K+uOPP6DT6RAQECDp788//0Rzc7Nch3c77lhK+vPPP52e1oqVEbLh0zmS28uE8q74IhUlTuJciRiFhQzBugV/4c3BL6GXWY1ajRrfqLIx8Zu78F3GYcF6xWRiMZSLrjSWrpqlJIqiyPnz5yXb+/r6ksLCQrkO7zbYpaS0tDRZ62UYhjQ0NBCGYWQtI2TDp3Mkt5cJ5V3xRSpKnMS50jEymgzkzZ+fJNHfjCHRG6PJ8A0jyd0bHyMlp9MkxcheJhZDueisY4ldSnJmLKWlpV0dS0n79+/HlClToNFIm1YePHgQ48ePh4eHhxyHdxvKUpKCgmNO1ZTgqfi3UW5OAQD0NFvwkHYC5s39HBoP7w5u3dVDl15KmjZtmuSTAgBcf/31nf6kYI07lpK2bdvm9LRWrIyQDZ/OkdxeJpR3xRepKHESpyNiBAD9/HvhSZ85eGHYcoRaVKjUavAhMvDs+nFIO/C9YD1CcelKcXLXWHL3UpLbn2MghGDv3r3Q6/WYPHkygoKC3Hk42WHPzGlpaYiJ4X8jlrMQQmAwGODp6Sn5bUxSygjZ8Okcye1lQnkATvsiFSVO8vjrShkxG2t9i6kFr/3+T+wzpIOhKATSNB6yROKxBzcDPiGCcQMgGEO56Kxj6Y477sD27dudGksZGRkYN25c558xAEB9fT0WLFiAESNGYNGiRWhsbMTUqVNxyy23YPbs2Rg6dCiysrLkPORVjTMzLGfKCNnw6RzJ7WVCeVd8kYoSJ3E6IkbWel8PX3w6dxP+e/1ahFs8Ua9WY41HKR7/birOnd0nGjexGMpFVxpL7kTWE8Pzzz+Pw4cP4/7778eJEydw2223gaZpHD58GEePHkVUVBRee+01OQ95xaBpWtb6LBYL4uLinN63RayMkA2fzpHcXiaUd8UXqShxEqcjYsSnnxgxCY+FvIIHu82EjgCHPTS4+9CLeOy711Fe3+SwrFgM5aIrjSW5v4/aIecv2WFhYWTfvn2EEELOnTtHKIoie/fu5fRHjx4lPXr0kPOQbseddyWZTCan75AQKyNkw6dzJLeXCeVd8UUqSpzE6YgY8emtZWdrT5P/2/Egid4Y3fZw3BezSPrOFYRYTIJx6UpxkjKWrO9KkjqW3H1XkqwzhvPnz2Pw4MEAgPDwcHh6eqJPnz6cvm/fvrhw4YKch7yqceWKSEoZsasbqXJHVzl8eXf+GKbESZyOiBGfnpVFBA3A13/bgieGvwiKeIDxPIvHK37A1m8mgynLEIxLV4qTu8aSO5H1xMAwDNRqNZdXq9U2P7jI/cPklcQdS0kJCQlOT2vFygjZ8Okcye1lQnlXfJGKEidxOiJGfHp7GUVRWDRqLpb6LcEYrwgYVCq8rzPg0T8fwK4v5sPc2igaQ7noSmPJ3UtJst6VpFKpsHLlSvj6+gIAXnrpJbzwwgsIDQ0FADQ1NeHNN990//qYjCjPMSgoyANDGPyU9Q0+PrYaejDwYhg8Wg/MvvlT9Bp5S0c3r8PojM8xyPoTd9++ffHVV19x+Z49e+Lbb79tZ3M1IuP5k6uvqakJfn5+Tt06J1ZGyIZP50huLxPKA3DaF6kocZLHX1fKiNlIiYe9bO6oRzGlfyyWbFuEMyjD6mAgJfkJzD5+D2Y9+C7UapVL/sjlsytlLncs8dkK5eX+PrJH1qWks2fPoqioSPTvasQdS0kHDhxwelorVkbIhk/nSG4vE8q74otUlDiJ0xEx4tNLkfXx64Of7tuGWzSx0BIKR7088bp5N/72zScoqWnpUnFy11i6qpaSuiLKUpKCgvsoqj+Lf+58FqWm0wAA0jwSH/QYi9jb/w8qn+AObt2VoUsvJX322WeSbZ9++mm5DnvFYBhG9vrq6+sRGBgo+TV9UsoI2fDpHMntZUJ5AE77IhUlTvL460oZMRsp8RCTRQT2xbZ7f8L7B1fjp7ObQPlm4cOGDKjX/Bejb3wf3Sfe50pIXPbZlTKXO5b4bIXycn8f2SPb6Pzkk09s/l599VU888wzeOutt/DWW2/hmWeewauvvopVq1bJdcgritwdQdM0UlNTnZoSSikjZMOncyS3lwnlXfFFKkqcxOmIGPHpXZIRYIJxOL6N3Yxu6m6o0mjwXE8fbDj6Ak59fhdIU6Vkv4ToSmPJ3ScGt7zBbevWrWTKlCkkPz+fk+Xn55OpU6eSLVu2uOOQboN9wM1dD5IoKChcotXcSl5KfJ17KO7OLweTjHf6ksYjmwhxwwOUnQH2ATdncPf3klve+fzGG29g9erVGDJkCCcbMmQIPvnkE7z++uvuOKTbccdSUlVVlVP1SikjZMOncyS3lwnlXfFFKkqcxOmIGPHpXZFZp700Xnh32ttYGfMOfFW+OK3T4ZEwP/x66FUwvz4q2T9XfXalTEeNJXfilhNDRUWFwy1oaZrG+fPn3XFIt+OOD3N2drbTg1SsjJANn86R3F4mlHfFF6kocRKnI2LEp3dF5ihmflW+2HbXNkzsfj3MFIWPQoKwiDqP8qZKVDUZJPvprM+ulOmoseRO3HJX0uzZs1FSUoKvv/4aMTExoCgKaWlpWLRoEfr06eP0L/AdiXJXkoJCx0EIwe+nf8f7R9+DnjbAU+UPQ/m9+HJcP0waFQWEDuroJl42nfGuJLfMGL755huEh4djwoQJ8PT0hIeHByZOnIhevXph/fr17jik23HHVV5ZWZnTVy9iZYRs+HSO5PYyobwrvkhFiZM4HREjPr0rMqGYURSFuwfdjZ9m/4whQUNhYBqBnl9jf/5LMH8+BTjwEUBLe/FOVxtL7sQtJ4Zu3bohLi4OJ0+exM8//4yffvoJeXl5iIuLQ/fu3d1xSLfjjg9zYWGh04NUrIyQDZ/OkdxeJpR3xRepKHESpyNixKd3RSYWQwCIDIjE1plbMHfIAwCArb5aPNwjEKX734Fl3XSg4rgsPrtSpqPGkjtRHnATQVlKUlDoXCSWJOKNQ2+g0dQIX4ZgeXUNbm0xwjLpKXjc9Aqg9ezoJjpFl15KWrZsGVpaWiTbv/LKK6itrZXr8G7HHVd5xcXFTl+9iJURsuHTOZLby4TyrvgiFSVO4nREjPj0rsjEYmjPTX1vwi+zf8GY7mPQrKLwQvdQ/Cs0AMyRT9G6ehJgaHTZZ1fKdNRYcieynRg+/fRTtLa2Srb/73//i/r6erkO73bc8WHuSuudym8Mym8MrsrEYuiIXr698E3sN3hs5GOgQOFXP1/cHxaGLc3d8FZCKfSm9g+bdbWx5E5kW0pSqVQICAiQvGthQ0MDCgoK0L9/fzkO7zaUpSQFhc7N0YqjeCnpZdQYqgFaB33FfejrORGfzeyFaE0pMLBzb+ndpZeSNmzYgFWrVrXbGoPv75tvvkGPHj3kOjzOnj2LRx55BP369YOXlxcGDBiA5cuXw2Qy2diVlJRg9uzZ8PHxQWhoKJ5++ul2No5wxzYGp0+fdvrxfLEyQjZ8Okdye5lQ3hVfpKLESZyOiBGf3hWZWAzFmNhrIn6e/RPGdh8LqE3w6r0FZdRPOPfdYmDLPWB+exxore1yY8mdyLaJ3oIFC+SqyiXy8/PBMAzWrVuHgQMHIjs7G4sWLUJLSws+/PBDAG2BnTlzJrp164aDBw+ipqYGCxYsACEEq1evFqxf7t/oCSGoq6tDZGSkrGWEbPh0juT2MrG8s75IRYmTOB0RIz69qzKhmEmhm3c3rI9dj88yPsPGnI3QhRzAKi9vjL2gRvesH2Ap+AvU3z5Anb53lxhL7r5nqEvflfTBBx/g888/x5kzZwAAO3fuxKxZs1BaWoqwsDAAwA8//ICFCxeiqqoK/v7+7epQlpIUFK4udhfvxhuH3kCLuQUaixfeOt+MO0xlAAAyKBbU3z4AgiI6uJWX6NJLSZ2RhoYGBAdf2tP98OHDiI6O5k4KABAbGwuj0Yj09HTBuk6cOIGMjAykpqYiNTUVFRUVNlM665dnWCwW7schvrTRaEReXh5omobZbOauANg0IaRdmqZp5OXlwWBo2xKAYRhu6xGGYbg25OXlwWg02sgBwGQyITc3l2s3215HcpqmkZubyy2zWbfXYrHAbDYjPz8fRqPRJs36J9UnADZpe5+MRiPy8/NhNps5P6x9YtvDph213VE/sTbssYT6hpUbDIZ2fWaxWJCTkwOLxQJCCAwGA/Lz87kYWfeHUN+I+SSUtu4/KWPPbDZzfWYwGHj7yWKx2Iw3+35y1Ddms5lri/WYtO8Pk8mE/Px8mEwmm7Sj/pPqE5u+MexGfPe37zAwcCAsGj1eD9PiMZ/JMBI1qIJ4kP9OhOX0PtGxJ/Z5YuMtNN7s+4aVW48xQggYhmk3Ju3HocVi4frMHS/FsqbLnhgKCwuxevVqLF68mJNVVla2+10jKCgIOp0OlZXCW/suXLgQMTExmDBhAiZMmIB169YhKysLBQUFAIDMzEzu7XQpKSkoLS0FACQnJ6OiogIAkJSUhOrqagDAvn370NDQAABISEhAU1MTACAuLo7r+Li4OFgsFhgMBsTFxQEAGhsbsWfPHgBte/snJiYCAKqrq5GUlAQAqK2txZEjRwAApaWlSElJAQAUFxfj3LlzAICCggJkZWUBaFuGY/239uncuXMoLi4GAKSnp3NtT05ORmVlJfR6PQ4ePIjq6mro9Xrs27ePu9PMGZ+ampqQkJDg0KeDBw9Cr9ejsrISycnJ7XwqKipCZmZmO58qKyuRn5/fzifrfiotLeXiYd1PBw8eRF1dHQAgMTGR82nPnj1obGxs59Pp06c5n+Lj46HX69Hc3Mz51NDQgH379gFoWzI5ePAggLY9xZzxKS8vD3l5ee18OnbsGC5cuABA2thLTExEQ0MD9Ho99uzZI9hPzc3NiI+Pd9hP+/btg16vtxl7lZWV3Jix9unChQs4duwY51N2djb0ej3y8/ORn58PvV6P7Oxsh2NPqk/WYy9UFYqtf9uKkdqRAMXgcPdzmN3zVtQGjwTx6YZdJ6pEx57Y58m6n86fP4/s7Ox2/ZSdnc3tD2c99qw/T7W1tZxPZ8+e5f2OaG5uhl6vR3x8vKTfRS8LObZodSfLly8nAAT/UlNTbcqUlZWRgQMHkkceecRGvmjRIjJjxox2x9BqteT77793eHx2e9vNmzeT9PR0kpKSQlJSUkh5eTmxWCzEYrEQQggxm802aZqmBdMmk8kmzVzcUphNMwzTLk0IsUnTNG2TNpvNgmmLxWKTZtvLl1Z8Uny62n0yGo3kmxPfkBEbR5DojdFkQdwCUn0+m9Q0tpJXfssiVfXNxLLnXUKaqzvMp1mzZjndT2lpaVfftttysmTJEu4MzPcXHR3N2ZeXl2P69OmYNGkSvvzyS5u6evbs2W5mUFdXB7PZLHqH1NChQzF27FiMHz8e48ePR69evaBWq6FWqwEAGo3GJs2+rYkvrVKpuCmmVqvlbvNl0xRFtUvTNI2cnBybOrRaLZfWaDTcdJStj5Wz5Ofng6Zpm7YD4KasrJymae6KGwAoiuLaq9FoQAhBdnY295Ly7OxsqFQqrm1SfWLrtvbDOk1RFLKzs0EI4fyw9kmtVtuk2bazV2zWcut+Yv0jF5dRrPvG2letVmsT75ycHJs+YxgGJ0+eBMO07eujUqm4HTDZPsvNzYVKpRLsGzGfhNIURXH9J2XsabVamz7j6yeGYWzGm30/sb5a9w0hhBtj1mMyLy+POw7bbvYK2zrtaOxJ9cnR2NPpdPi/6P/DmpvXwFfri/SqdDyYtAyv79yD746W4Nev3oE66X1gTQxUx7ZCe7FtUj5PbD8JjTcANn1j3WfsGGPHjf2YtP+OYBiG6zN3P8cg211J1rS0tOD999/Hnj17HO5Fzv4YLIXQ0FCEhoZKsi0rK8P06dMRExODDRs2tHvN3qRJk/DOO++goqICvXr1AtA2RfPw8EBMTIzkNikoKFxd3ND7BmyK3YQndz+J8pZy1KhXILLPw7hh/M1A2j6gKgfYvgRI3wDc/h+g97iObnKH4pa7kh544AHs378f8+fPR69evdo99LZ06VK5D4ny8nJMmzYNffv2xebNm23O2D179gTQ9qPQ6NGj0aNHD3zwwQeora3FwoULceedd/LerqrclaSg0HWoN9Tj+f3P42jlUVCg8NKElzBv8H3Akc9hTnwPWvri7g0j5wK3LAf8w4QrlIHOeFeSW35jCAgIIAcPHnRH1bxs2LCB9zcIa4qLi8nMmTOJl5cXCQ4OJkuWLCEGg4G3XvY3hpSUFFnba7FYSEZGBrfmKFcZIRs+nSO5vUwo74ovUlHiJE5HxIhP74pMLIZywdarN+nJ28lvc68P/Sj1I3LqfAO5/vWt5KfXZxGy3L/tb/OdV2Qssa/2dGYspaSkuPU3BrcsJQUFBdncJnolWLhwIRYuXChq17dvX+zYscP9DZKAl5eXW8oI2fDpHMntZUJ5V3yRihIncToiRnx6V2RiMZQLLy8vaFVavHHdG+jl0wufZX6GDTkbcK6pAhNG3I8XMhbjW8uteNf7e/iMeg592baY9QDlDagc/yzbEWPJnbhlKWnLli3Ytm0bNm3aBG9vb7mrv6IoS0kKCl2X7YXbsfzQcliIBRN6TsDsnq9gxfYi1LYYoVOr8dyMwXh0an+od78OnNkH3PQGMDgWkLgnnBQ641KSW+5K+uijjxAfH48ePXpgxIgRGDt2rM3f1YjcD5RYLBakpqY6Va+UMkI2fDpHcnuZUN4VX6SixEmcjogRn94VmVgM5cJRvXMGzMF/b/kvfLQ+SKlMwdaSV/DjEyNwy7AeMNEM3tuZj7s/2gH62I/A+Wzg+/uBb2KBswcF6xXTyTGW3IlblpLuvPNOd1TboUjdNdaZ+oKCgpyqV0oZIRs+nSO5vUws76wvUlHiJE5HxIhP76pMKGZywVfv5LDJ2HjbRjy++3Hk1+bjhYOL8eXfv8QtOT2wYkcujtcAUz3exzcDkzGk+DtQpUeBjTOByKnA9c+Cipx2xceSOz5rNu1zx1JSV0JZSlJQuDYoaijCowmPoqq1ChH+EVg/Yz2MBj8899NxpBW3PQl/3xA1VgTuhOeJLQBz8ap9xkpg8lMuH/eaWUrqirhjWpucnOz09F+sjJANn86R3F4mlHfFF6kocRKnI2LEp3dFJhZDuRCrt19AP2y8bSPCfcNR3FiMBTsXgKgu4JmRBM/fOghaNYWfTtK4Pmc2js5OBK57EvAMhGXYnZfqrcoHGstFjynHWHInsp0YgoODuT0+2LuS+P6uRuwflpOjvvDwcKfqlVJGyIZP50huLxPKu+KLVJQ4idMRMeLTuyITi6FcSKm3j18fbLxtIyL8I1DeUo7H9zwOr1BPPDl9IP745xQM7uGL6mYjTL5hwG3vAc+dhCog/FK9u14GPokGvn8AOPELVOZmt40ldyLbUtKmTZswd+5ceHh4YNOmTYK2Hf3uBmdQlpIUFK49LrRewMJdC1HSVIJI/0hsvG0jQrxCYDDT2H/qAmKH9+RsG1rNCPDWAhYTsOVu4OyBSxWpdUD/6UD/G4H+04Aew9sdqzMuJXX6TfQ6GvYBt6NHj8par9lsJvv37+c24ZKrjJANn86R3F4mlHfFF6kocRKnI2LEp3dFJhZDuXC23vKmcnLLT7eQ6I3R5K4/7iL1hvp2NiU1LWTE8l1kyZcJpNVgbBNW5RPy1wpCPht76WG55f6EfPfApba01JPKtXOIJXUj94CbM2Pp6NGjV/cmenq9Ho2NjTZ/VyPumNYOGDDA6em/WBkhGz6dI7m9TCjvii9SUeIkTkfEiE/vikwshnLhbL29fHvhy1u/RJAuCAX1Bfjnnn/CYDHY2Px5ogKNBguKW7XQsNvwdBsC3PwGsCQNzOJDaBi/DGTgLcCgS++eVulr0OP8PqjKUnnbJzaW3Ilb7kpqaWnBSy+9hJ9++gk1NTXt9O5+X6mcKEtJCgrXNgV1BViwawGaTE2IjYzFf274D1TUpS/muBMViA4LQN+Qtod5TRYGGhUFlUrgltKWGiDzW6DHcMx5bnWnW0pyy2nnxRdfRGJiItauXQsPDw+sX78eb7/9NsLCwrB582Z3HNLtuOMOicTERKfvJBErI2TDp3Mkt5cJ5V3xRSpKnMTpiBjx6V2RicVQLlyNU2lmKT6+4WNoVBrEn43HZxmf2djMGNYNp48f4ep9f2c+Hv4mBRUNev6x5BGARNNIWPpN522f2FhyK+5Yn+rTpw/Zu3cvIYQQPz8/UlBQQAghZPPmzeT22293xyHdBvsbg/3LgC4XmqbJ+fPnuRdxyFVGyIZP50huLxPKu+KLVJQ4idMRMeLTuyITi6FcXG6ctp3exm2899up3xzanG/Uk6Gv7yQRL+0gI5bvIn9klIqOJfY3BmfGUmpqqlt/Y3DLUpKvry9ycnIQERGB3r1747fffsOECRNQVFSEESNGoLm5We5Dug1lKUlBQYFl7bG1+Pz459CpdNj8t80YHtL+LqPCC81Y9uMxHD/X9lrOOaPC8K87otvuXHJAZ7wryS1LSf3798fZs2cBAFFRUfjpp58AAP/73/8QGBjojkO6HbmnbmazGfHx8dyLv+UqI2TDp3Mkt5cJ5V3xRSpKnMTpiBjx6V2RicVQLuSI0+JRi3FjnxthYkxYtncZ6g317WwGdPPFL09MxjO3DIJaRWH78XLMWLUfBwuqBdvizFi6KpeSPv74Y/Lpp58SQghJTEwkXl5eRKfTEZVKRVatWuWOQ7oNdy4l1dTUOD2tFSsjZMOncyS3lwnlXfFFKkqcxOmIGPHpXZGJxVAu5IpTg7GB3P7r7SR6YzR5fPfjxGwx89abcbaGTH3/LxLx0g4S8dIO8tb2bKI3WWzqtV5KkjqWrsqlJHtKSkqQlpaGAQMGYNSoUe4+nKwoS0kKCgr2nKw9iYfiHoKBNuDlCS9j3rB5vLatJgvei8vHt0eKAQADu/ti1f2jER0eAOAaWkqyp2/fvrj77ruvupOCNe5YSvrzzz+dntaKlRGy4dM5ktvLhPKu+CIVJU7idESM+PSuyMRiKBdyxmlI8BAsG7cMAPBJ+ifYsG0D71jauzseb84cgg3/Nx7d/DxwuqoZd/73EJ76/E8YjCbeYwnl3b2UJOuMQa/XY8+ePZg1axYA4JVXXoHRaOT0arUa//rXv+Dp6SnXId0Oe2ZOS0tDTEyMbPUSQtDU1AQ/Pz/JW+hKKSNkw6dzJLeXCeUBOO2LVJQ4yeOvK2XEbKTEQ4oMgGAM5ULuOBFC8Pjux3G44jCGBA7Bd7O+g06tEyxf22LCa7+fwM7sSgDAvIl9cWLDa9i+fbtTYykjIwPjxo27OmYMmzdvxrp167j8mjVrkJycjMzMTGRmZmLLli34/PPP5TzkFcMde8P7+/s7vYe+WBkhGz6dI7m9TCjvii9SUeIkTkfEiE/vikwshnIhd5woisK/pvwLfjo/nKw/ia15W0XLB/vosHbeWHx83yh08/PA/02J5LUVG0vuRNYTw9atW/GPf/zDRvbdd99h79692Lt3Lz744APuDqWrDXcsJW3bts3paa1YGSEbPp0jub1MKO+KL1JR4iROR8SIT++KTCyGcuGOOPXw6YFlY9qWlD4//jkqWypFy1MUhdkjeuClqBZEBF1aPfktvQRbfpE2lq6qu5J69OhBsrOzuXxoaCgpKiri8idPniT+/v5yHtLtsHclpaWlyVovwzCktbWVMAwjaxkhGz6dI7m9TCjvii9SUeIkTkfEiE/vikwshnLhrjhZaAuZt2Meid4YTZ7d+6yk8tby2bNnk7SzNaTfyzvImLfjyfkGvcOy1vm0tLSrZxO9hoYGaDSX3hZ64cIFREZGcnmGYWx+c7jWsY6VnGWEbPh0juT2MqG8K75IRYmTOB0RIz69KzKxGMqFO+KkolR4ZfwrUFNq7C7ejcPlhyWVt5b7eGgwqIcfpg0ORTc/D96y7vycWSPriaF3797Izs7m1WdlZaF3795yHvKKQcu88Z/FYkFcXJzT+7aIlRGy4dM5ktvLhPKu+CIVJU7idESM+PSuyMRiKBfujNPpw6dx36D7AACfZnwKcvGeHqljaWhPf/z6+ERM0pVyssr6Fvz3R8dxkfv7qB1yTj+efvppEhUVRfR6fTtda2sriYqKIk8//bSch3Q77lxKMplMTk9rxcoI2fDpHMntZUJ5V3yRihIncToiRnx6V2RiMZQLd8fpQssFMn7LeBK9MZrsPrtbsLy1nH3AzT4m//fNUdLv5R3k3zvziNFM2+ivqqWkV199FbW1tRgyZAg++OADbNu2Ddu3b8d//vMfDBkyBHV1dXj11VflPORVjStXRFLKiF3dSJU7usrhy7vzxzAlTuJ0RIz49K7IxGIoF+6MU4hXCOZHzQcArM5cDZqhBcsLxcREMwjw1oEhwNp9hbj780M4XdXs/h+dLyLriaFHjx5ITk7GsGHD8PLLL+Ouu+7CnXfeiVdeeQVRUVE4ePAgevToIechrxjuWEpKSEhwelorVkbIhk/nSG4vE8q74otUlDiJ0xEx4tO7IhOLoVxciTgtHL4Q/jp/nGk4gz0le1weSx4aNf5z93AsHEwj0EuL7LJGzFp9EK9t2g2Tyez2pSS3bYlRW1uL06dPAwAGDhyI4OBgdxzG7ShbYigoKDjDmsw1WJe1DiNDR2LL37aIPnMgtiXG+UYDXvglC0mnLgAArh8YivmDaNx245Sr4wE3a4KDgzFhwgRMmDDhqj0pWCP3+ZMQgsbGRqfqlVJGyIZP50huLxPKu+KLVJQ4idMRMeLTuyITi6FcXKk4zR06FzqVDlnVWcisyrzssdTdzwOb/m88VswZDk+NCgdPV2PJdxnOuO40V2SvpK6AO5aSDhw44PS0VqyMkA2fzpHcXiaUd8UXqShxEqcjYsSnd0UmFkO5uFJxCvUKxewBswEAm3I2yTKWKIrCA+PD8eIoBiPD/dFsvEqXkroKylKSgoKCs5yuO427tt8FDaXB7nt3I9QrlNfW2d1VzTSDV7/ajg+fuOvqW0rqajAMI3t9tbW1TtUrpYyQDZ/OkdxeJpR3xRepKHESpyNixKd3RSYWQ7m4knEaGDQQI0NHwkIs+Dn7Z1nHkpoC7h/n3ufBlBODROQepDRNIzU11aklKillhGz4dI7k9jKhvCu+SEWJkzgdESM+vSsysRjKxZWO0x0D7wAA/Hrq13ZLSZc7ltxxEWaNspQkgrKUpKCg4ApNpiZM/2k6jLQRP8z8AcND278fGriGX9TTFXDHtLaqqsrpaa1YGSEbPp0jub1MKO+KL1JR4iROR8SIT++KTCyGcnGl4+Sn88O03tMAALuLd4uWcXYsuRPlxCARdwzS7OxspwepWBkhGz6dI7m9TCjvii9SUeIkTkfEiE/vikwshnLREXGa3ns6AOCv4r9sbk2VYyy5E2UpSQRlKUlBQcFVmk3NuOHHG2BmzPjjjj8wIHBAOxtlKekqxh1XL2VlZU5fvYiVEbLh0zmS28uE8q74IhUlTuJ0RIz49K7IxGIoFx0RJ2+NN0YHjQYA7C3dK1jG2bHkTpQTg0TcMUgLCwudHqRiZYRs+HSO5PYyobwrvkhFiZM4HREjPr0rMrEYykVHjaVIRAIAjpQfESzj7FhyJ8pSkgjKUpKCgsLlUNRQhDl/zIFWpcWhBw7BS+Nlo1eWkq5i3HH1Ulxc7PTVi1gZIRs+nSO5vUwo74ovUlHiJE5HxIhP74pMLIZy0VFjiaqj0MO7B8yMGZlVmbxlnB1L7qRLnhiMRiNGjx4NiqJw7NgxG11JSQlmz54NHx8fhIaG4umnn4bJZBKt0x2DVFk7F0eJkzgdESM+vSsysRjKRUeNpfLyckzsOREAkFaZxlvG2bHkVlx5u09n5+mnnya33347AUAyMzM5ucViIdHR0WT69OkkIyOD7N69m4SFhZElS5bw1sW+wc1db0pSUFDo+vx88mcSvTGaPBL/SDsd+wY3Z3D391KXmzHs3LkTCQkJ+PDDD9vpEhISkJubiy1btmDMmDG45ZZb8NFHH+Grr75CY2OjYL3ueDz/9OnTTj+eL1ZGyIZP50huLxPKu+KLVJQ4idMRMeLTuyITi6FcdORYig6OBgBkV2eDZhyPBWfHkjvpUieG8+fPY9GiRfj222/h7e3dTn/48GFER0cjLCyMk8XGxsJoNCI9PV2w7tzcXGRkZCA1NRWpqamoqKiw6SCLxWKTZqd6fGmz2Yza2loQQmA2m7mHX9i0tdw6XVtbyy19MQwDs9nMpS0WC2djL2ePX1NTA0JIu7azbWHlhBDU1NRwZa3by/paV1cHs9lsk7b2T4pPAGzS9j6ZzWbU1dWBpmmuLdY+Wcut215bW9tObt1PrH+O+sy+b1i5yWRq12cMw6CmpgYMw4AQApPJhLq6Oq7t1v0h1DdiPgmlrftP6thj+8xkMvH2E8MwNuPNUT/Z9w1N09wYsx+T9v7V1dVx226zaUdjT6pPYmOP7T/rMSY09sQ+T6wfYuOttrYW/fz7wVvjjRZzC840nLEZY2ys7Meko3Fo32fuosucGAghWLhwIRYvXoxx48Y5tKmsrGz3atGgoCDodDpUVlYK1r9w4ULExMRwLx9at24dsrKyUFBQAADIzMxEUVERACAlJQWlpaUAgOTkZFRUVAAAkpKSUF1dDQDYv38/Bg4cCI1Gg4SEBDQ1NQEA4uLiYDAYYLFYEBcXB4vFAoPBgLi4OGg0GgwdOhSJiYkAgPr6ei5dXV2NpKQkaDQahIeHIyUlBQBQWlpqk1apVNBoNCgoKEBWVhYAoKCgAN7e3tBoNJxPGo0GKpWK8yMjIwM9evSARqNBcnIyLly4gPHjxyM5ORn19fUYP3489u/fj/r6egCQ7BMANDU1ISEhwaFPycnJGD9+PC5cuIDk5OR2PhUVFSEzM5PzIysrCxqNBt7e3lzfOOonjUYDmqa5vrHup+TkZERGRkKj0SAxMZHzKTExEUOHDoVGo+F8YscVABgMBiQkJGD8+PHQ6/VISEiARqPBwIEDsX//fmg0GkRGRnJ+VFRUSPYJAPLy8pCXl9fOp6ysLAQHB0Oj0Ugae4mJiWhubsb48eORmJjI208AMGLECK5v7Ptp//79GD9+POrr65GUlAQAuHDhAoxGIzQaDeeTRqNBcHCwzXjLzc3F+PHjUVBQgIKCAowfPx65ubkOx55Un8TGXkJCAsaMGWPjn9DYE/s8sf2k0Wjg7++P3Nzcdv2Um5sLf39/eOg8EKGLaOuvC1k2n6fa2lpUVFRAo9GgpaWF88P+O0Kv12P8+PFue42uDe5Yn5KT5cuXEwCCf6mpqeTTTz8lkydPJhaLhRBCSFFRUbvfGBYtWkRmzJjR7hharZZ8//33Do/PruVt3LiRpKenk5SUFJKSkkLKy8uJxWLhjmc2m23SNE0Lpg0GA8nNzSUWi4WYTCbCMAwhhHBphmHapS0WC8nNzSV6vZ4QQghN08RkMnFptg25ubnEYDDYyAkhxGg0kpycHK7dbHsdyS0WC8nJySFGo7Fde81mMzGZTCQvL48YDAabNOufVJ8IITZpe58MBgPJy8sjJpOJ88PaJ7Y9bNpR2x31E2vDHkuob1i5Xq9v12dms5lkZ2cTs9lMGIYher2e5OXlcTGy7g+hvhHzSSht3X9Sxp7JZOL6TK/X8/aT2Wy2GW/2/eSob0wmE9cW6zFp3x9Go5Hk5eURo9Fok3bUf1J9Eht7bP+xfSM29sQ+T2y8hcabdd98cPQDEr0xmqw8vNJmjM2aNYvQNN1uTNqPQ7PZzPXZ0aNH3fobg8a9p53LZ8mSJZg7d66gTWRkJFauXIkjR47Aw8PDRjdu3DjMmzcPmzZtQs+ePXH06FEbPbsEYj+TsCcqKkrwfmGNRuN0mr3i1Gq1nFwoTdM0DAYDJ1epVFCpVDZp1oY9lrWNWq2G0Wjk0iyO5DRNw2g0cnnr9rJX23q9njsOm2aPJdUnAKAoitcnjUYDvV4PlUrFtcXeJ2s/HLXd2oZtL2vD1iO1b+zlFEXBZDKBoijOD71eD4qiuDhZ9wdf34j5JJZm+0/K2GPHkl6vh1ar5d5JLDbe7PuJr2/YtliPSUf9odfr26XVarXDsSfFJylpg8HA9Y0jn5z9PAHC4826b4aEDAEAFNQX2IwxiqJs4mQ9Jq3Hm6M+cxtuOd10AMXFxeTEiRPcX3x8PAFAfvnlF1JaWkoIISQuLo6oVCpSXl7Olfvhhx+Ih4cHaWhocFjvrl27CACya9euK+LH1Uh5eTlZvny5TVwV2qPESRpdNU55NXkkemM0mfzdZG5GQ4hrdyW5+3upy/zG0LdvX0RHR3N/gwcPBgAMGDAAvXu3ve1oxowZiIqKwvz585GZmYk9e/bg+eefx6JFi+Dv7++wXnYNs6qqStb20jSN7Oxsp++QECsjZMOncyS3lwnlz507h7fffhvnzp2T7ItUlDiJ0xEx4tO7IrPXd6U4Wev6B/SHmlKj0dSIiuaKyxpL7PcR+/0kN13mxCAFtVqNP//8E56enpgyZQruu+8+3HnnnQ5vbb0SfP/9924pI2TDp3Mkt5eJ5d2FEidxOiJGfHpXZNfCWNKpdejj1wcAUNxY3GnHEoCus5TkLrZs2UIAkC1btshe97Bhw9xSRsiGT+dIbi/jy7v7YRslTuJ0RIz49K7IrNNdLU7Wunu330uiN0aTA+cOcHLrpSSpY8md30uEXAU/Pnc07A9HZ86cQUZGhmz10jSNhoYGpKam2vxYdbllhGz4dI7k9jKhfH5+PgAgJyfHlVBcts+ulOlKceqIGPHpXZEBsNGz8ekKcbLX1RfWQ9+gR96xPE5eX1+PjIwMp8bSmTNnAFz6fpIbZXdVEdasWYOnnnqqo5uhoKCg0I7Vq1djyZIlsterzBhEmDt3LoKCghAZGQkvLy/xAgoKCgpuRq/X4+zZs4iNjXVL/cqMQUFBQUHBhmvqriQFBQUFBXGUE4OCgoKCgg3KiUFBQUFBwQblxKCgoKCgYINyYpCJ0tJS3HjjjYiKisLIkSPx888/d3STOi133XUXgoKC8Pe//72jm9Jp2LFjB4YMGYJBgwZh/fr1Hd2cTosydsSR47tIuStJJioqKnD+/HmMHj0aVVVVGDt2LE6ePAkfH5+OblqnY+/evWhubsamTZvwyy+/dHRzOhyLxYKoqCjs3bsX/v7+GDt2LI4ePYrg4OCOblqnQxk74sjxXaTMGGSiV69eGD16NACge/fuCA4ORm1tbcc2qpMyffp0+Pn5dXQzOg0pKSkYPnw4wsPD4efnh7/97W+Ij4/v6GZ1SpSxI44c30XXzIkhKSkJs2fPRlhYGCiKwh9//NHOZu3atejXrx88PT0RExODAwcOuHSstLQ0MAyDPn36XGarrzxXMk5dhcuNWXl5OcLDw7l87969UVZWdiWafkVRxpY05IyTq99F18yJoaWlBaNGjcKaNWsc6n/88Uc888wzeO2115CZmYmpU6fi9ttvR0lJCWcTExNjs7U3+1deXs7Z1NTU4OGHH8aXX37pdp/cwZWKU1ficmPmaDXX7S9i6QDkGFvXAnLF6bK+i9yyNV8nBwD5/fffbWQTJkwgixcvtpENHTqUvPzyy5LrNRgMZOrUqWTz5s1yNLPDcVecCCFk79695J577rncJnY6XInZoUOHyJ133snpnn76abJ161a3t7UjuZyx1VXHjiNcjdPlfhddMzMGIUwmE9LT0zFjxgwb+YwZM7iXtYtBCMHChQtx0003Yf78+e5oZocjR5yuNaTEbMKECcjOzkZZWRmampoQFxfntj1wOivK2JKGlDjJ8V2knBjQ9hYkmqbbvfe5R48eqKyslFTHoUOH8OOPP+KPP/7A6NGjMXr0aJw4ccIdze0w5IgTAMTGxuLee+9FXFwcevfuzW293BWREjONRoOPPvoI06dPx5gxY/DCCy8gJCSkI5rbYUgdW9fS2HGElDjJ8V2k7K5qhf26LiFE8lrv9ddfD4Zh3NGsTsflxAnANXnHjVjM5syZgzlz5lzpZnU6xOJ0LY4dRwjFSY7vImXGACA0NBRqtbrdVW9VVVW7M/O1jBIn51FiJg0lTtK4UnFSTgwAdDodYmJisHv3bhv57t27MXny5A5qVedDiZPzKDGThhInaVypOF0zS0nNzc04ffo0ly8qKsKxY8cQHByMvn37YtmyZZg/fz7GjRuHSZMm4csvv0RJSQkWL17cga2+8ihxch4lZtJQ4iSNThEnl+5lugrZu3cvAdDub8GCBZzNf//7XxIREUF0Oh0ZO3Ys2b9/f8c1uINQ4uQ8SsykocRJGp0hTspeSQoKCgoKNii/MSgoKCgo2KCcGBQUFBQUbFBODAoKCgoKNignBgUFBQUFG5QTg4KCgoKCDcqJQUFBQUHBBuXEoKCgoKBgg3JiUFBQUFCwQTkxKCgoKCjYoJwYFBQUFBRsUE4MCgoKCgo2KCcGBQUFBQUblBODgoKCgoINyolBQUFBQcEG5cSgoKCgoGCDcmJQUFBQULBBOTEoKCgoKNhwzbzz2VWqq6sRHx+PyMhIeHl5dXRzFBQUFKDX63H27FnExsYiNDRU/gPI+qLQq4j//ve/JDIyknh4eJCxY8eSpKQkh3Zbtmxx+P5V5U/5U/6Uv47+27Jli1u+H6/JGcOPP/6IZ555BmvXrsWUKVOwbt063H777cjNzUXfvn1tbCMjIwEAW7ZswbBhwzqgtQoKCl2ZZ555BqtWrXKqTF5eHh566CHu+0l23HK66eRMmDCBLF682EY2dOhQ8vLLL7ezTU9PJwBISkqKrG2wWCykoKCAWCwWWcsI2fDpHMntZUJ5V3yRihIncToiRnx6V2RiMZSLzjqWZs+e7dBWKJ+SkkIAkPT0dMm+OMM19+OzyWRCeno6ZsyYYSOfMWMGkpOT+cuZaZgsDMw0A5ohYBgCQojL7SCEoK6uzqk6pJQRsuHTOZLby4TyrvgiFSVO4nREjPj0rsjEYigXXW0suROKuPsInYzy8nKEh4fj0KFDmDx5Mid/9913sWnTJpw8edLGPiMjAzExMei5YBU8eg5sVx9FASqKAgVARQEURUFFUch+61ao1WpYLBa8+kcO9uRV4fkZg3D/+L5QqVRIPXMBz/1yAmqVChQINGoVVBQFFQVoVCqoVBTUFKBRq6BRtcm1GjU+vm8UfLQUtFotfk0vRXJhNWKH98Itw7qDYRg0GGh8c7AIahXgodVAq6KgUQGeOi3UKgKdSgUvDw00FKDTquGt00CjAgZ194WPpw40TcNoYaBWq6AiDFQqFeeHSqWCSqXiTZvNZqjVai6t0WhAURSXBgCLxWKT1mq1IIRwaYZhQNM0l2YYBhqNhjdN0zQIIVwaANRqNW/aYrGAoijFJ8WnTuPT7NmzsW3bNqd8ysrKwrhx45Ceno6xY8dK+epzimvyNwag7QvcGkJIO5kUCAFom3NrW/rcuXOIiIhAcnIyqupUqGkxITf/FKr7eaN79+5ITklDSS3j9PFOZGej8UIFZs6cicMF5/HrsfPoE+yD0d1UyM7ORs+hY/HffYVO1/vuVG/cf9sNyMrKwm8n9fj2WB2mhavx+m0DMGjQIOw9dARvH2xGSIAvzPpmBPv5QKtiQBv1oEIKoTFmws/Yim5B4Qj274WqiiaMGD4OowcOR9qBFMyaMQtarRZxcXH429/+BovFgoSEBNxxxx1oamrCgQMHMHPmTNTX1yM1NRWxsbGorq7GiRMnEB4eDh8fHxQVFeGGG25AaWkpysrKMHnyZBQVFaGurg7jx49HQUEB9Ho9Ro4ciUOHDiEwMBAjR45EVlYWvLy8MHToUGRmZiIoKAj9+vXD3r17MXDgQPTr1w/JyckYMGAAwsPDsX//fgQGBmL06NFITEzE+PHjERwcjISEBPTu3RvR0dGIi4vDjBkzQFEU4uPjERsbC0IIEhISMGTIEPTs2ROHDh3CbbfdhqysLFRVVeGWW27BsWPHUF9fj5tvvhkVFRUoLCyU5NOYMWOQl5cHAIiOjrbxKSMjAxaLBRMnTkRKSgrCw8O5scf6lJSUhOjoaHTv3h2JiYmIiYlBdXU1CgsLMXXqVPj7+3M+aTQaxMXFITY2FgUFBThz5gxvP0VERCAgIAB5eXm46aabUFZWhtzcXNxyyy04d+4cysrKMHHiRBw9ehQajQYTJkxAQUEBWltb4e3tDZPJBADQ6XScbNCgQdi/fz/69u2LQYMGSfbJup/4fBo4cCAiIiKwZ88e0bGXnZ2NadOmISMjA62trZg2bZrDfho7diwOHz4Mb29vjB071qafjh8/jtbWVkyaNIkbewMHDkRKSgrKTeUwdDOg5EIJKioq0LNnT+zevRujR49Gr169kJiYiO7du2PkyJFISEjAlClTUFlZiZMnTyIkJMTpz7gzXHMzBpPJBG9vb/z888+46667OPnSpUtx7Ngx7N+/38aenTF8sX4DooZHw0LTIAB69QpDSGjoxROKCiaLBQAFUBTMZgsiQn25K4DKRiOaTTRCvDUI8fWESqVCdUMLdh89gf4DBsLC0AClAkMAk9kCAgo0AcxmCwilAs0wMJlpMATop6rGqBHD4enpif0nz+PEuQZMHBCKmL6BYBgG5xuNeOe3FPgHBoEBBaOFgclCw8IABpMFdQ1N8PD2hsnCtP3RBAYzjTen+GHGlBgAwH/iT2JdUhFmDfLGx/OnQKfT4WxVA278+KDDmHqGb4HWP1sw7mpKBZ3KB0ajB3ppgP5aIEjrhxCvEFQ1esLfswdCAyPRM3QA+oaEY0j3cHiotTCbzcjNzUV0dDQoipJ01QYAx48fR3R0NHQ6ncOrNgA4duwYRo4cCa1Wa3OlZjQakZOTg1GjRoFhGO6qzWAwIDc3l5Ozxzx+/DhGjRoFtVoNo9GIvLw8jBgxAoQQqFQqHD9+HMOHD4dGo+HSHh4esl2JmkwmZGdnY9SoUdwxxa6uASA7OxvDhg2Dh4eHw6triqKQlZWFqKgoeHp6tru6dtQ37NXs6NGjQVEUGIYBRVHt+oOmaeTk5GD48OEAwKXVajXXNyNGjIBOp5NtxmA0GpGbm4uRI0eCECJpxsC23VGfsf3kyD++vmFnDEajEZ/s/wRbK7aidV0rCg4WgBBiMybtxyFFUThx4gSGDRuGrKwsTJw40W0zhmvuxAAAEydORExMDNauXcvJoqKicMcdd+C9996zsWVPDO7qgM6ImWagN9NQUxR8PNo+VAYzjYySOrQaabSYLGg10WgxWtBipHGiIQFU/Z9Qm89DT5mhp2i0UAya1RQaVSpYXJiJAQBoXwQxOvQkFPw1IQjyCke3gP7o22M4xkUORb/AMKhVahk9V1C4cnx+7HOsPb4W5vVm5B/Id6qsu7+XrsmlpGXLlmH+/PkYN24cJk2ahC+//BIlJSVYvHgxbxnrq1E5oGkaeXl5GDZsGHeVJEcZIRs+nb1cq1ZBBWIrUwH++kpMvJi3LgMsRl7etPbHpM0g+noYWqrQ5BuK4vpaFNZcgK7qEKjWU6gx1OCCvgHl+gY0wYxGFY1atQrVag0oigDqZtSpgToAQA1gPAVU7QWqAJwAtATo7d8XvppwGFqDMCY0DDcPHo3eAf1QX1KP4VHD3RonRzKhPACn+1wKHTGW+PSuyAAIxlAuOttn7kzFGQCAhtI4tBXKy/19ZM81eWK4//77UVNTgxUrVqCiooJbM46IiOjopnUt1FpQvt3g5dsNXgC6+/TA+PBhAG5wbE8IYGyCWeuDs3UXcLK6FDX5v+JCZTqa0Ix60ow6lQlVahXOa9QwUxSKmkoAlAAACsqAn8raqtIRIPioD0JUvdDLfzgGh1+HG/qPwrBu4VCprrmb8RQ6Ia10KwBAo+p8X8PX5FKSM1yLS0mdGkIAfR3ourM4X52H4m79sbcwF5kVpxHc9BcqmCac02pg5lu+on3gr4rEIJ9+GBM2AbGDJ2Jot7Ar64OCAoCnEp/CvtJ98NjkgbTENKfKuvt7Sbl0kog7lpIyMzOdqldKGSEbPp0jub1MKO+KL1JpVzdFAd7BUIePRdioeZgUNgmvTn0EP9/3Htb9IwXbHziAI1PXYK3HzXiVDMLDLTrc3GJAuJmAEApQt6CRykF66w6sP/0m7o2LxZSvx+HODXdh2Y6PcPx8LswW81UVp44YS3x6V2RiMZSLzvaZq6itAHBpxuDsWHInnW8Ocw3hyqZ8UsoI2fDpHMntZUJ5d24wKLluigJ8u0HtNRXdzD0xedCgtnVdhgZaqlGn9sFfhVlILs2Ermg18nXAGZ0WjRojGnEahTWnsXvXRgSoPDAkYBT6N0/AxF4TMb3/CO5H7s4ap44YS3x6V2RiMZSLzvSZ0zN6ALZLSc6MJXeiLCWJoCwldVFoM1CVi5rCJKQWJqKg8SRyNCZkeHpAb/cbRIDKGzf1vh439L8dk8ImwUfr00GNVuhK3PLzLTjfeh6h34di7669TpVVlpI6CRaLRfb6UlNTnapXShkhGz6dI7m9TCjvii9ScVucCIXUcyYEXPcEblvwO55akoMv7t+NQyOWYdOwJ3Bnt7vhxwwHGC0amFb8XpKAZ/c9iylbJ+HGr2fi6T9X4UTl2U4Rp44YS3x6V2RiMZSLzvaZq9fXA7g0Y3B2LLkTZSlJIq48FS1WX1BQkFP1SikjZMOncyS3l4nlnfVFKlcsThQFBPeDNvgRjKJp+BcV4a3YftCXpSPrrxdwoLkYSd6eKNFqUaMpwd7qr7E3/mv4W/pgsO/1eLpXCMb07t8hceqIscSnd1UmFDO56EyfOQuxwEiMAC6dGJz5zLnjs2bTbmUpSRhlKUkBANBSDRQkID/rVxyuScc+by0yPTxArD6gXvRATAu/Dcsm3Yte/sEd2FiFzk6toRbTfpwGAIj8JRL/+9//nCqvLCV1EtwxrU1OTnZ6WitWRsiGT+dIbi8Tyrvii1Q6TZx8QmGJvg+1A5/D/MePY9Pk97BDPQw3Bz0MnakfAECvPo1dlWtw26/TccvmR7E+LR4Go9HtceqIGPHpXZGJjTW56DRjCUBda9tjm75aX+7q39nPnDtRlpIkIvdDUSqVCuHhzj1sJaWMkA2fzpHcXiaWd9YXqXTKOHn6ASP+jr4j/o6PGQalpfehQcvg0G93IsHDgNM6Hc6To/g05yj+e9wfseG3Y6BxIEK9Qt0Sp46IEZ/eVZnQ2JKLzjSWmsxNAAB/nT+vrVDe3Q9pSlpKCg52blpMURQyMjK6xJPEylKSgmRqCsFkfIusrK3YoTMjzscHTeq2D7CGUuPWyBmYFXEvru8Tozx9fY1zqOwQFv+1GEOChsC03oTt27c7Vb5TLCXV19fjrbfewieffCL69/HHH0Ov17v9AYwrjTumtUlJSU5Pa8XKCNnw6RzJ7WVCeVd8kcpVFaeQAWCmv46mmHV45abP8Jd6EN6vqsZogxEWQmNn0U78c98/MH7jLHyV+SNMtEmyT5frrytlxGykjBspMrGxJhedaSzV6duWkvx0fry2Yp85dyJ5KWnu3Lno3r27JNunnnrK5QZ1VtwxrR0wYIDT01qxMkI2fDpHcnuZWN5ZX6RyNcap/6AhoHr1gvfwObi9Kh/T9n6C4qjp+KIiE3vLEmBSl+KzrJX4vuALzI96GH8f9Hf4efjBVToiRnx6V2VCY0suOtNYajY3A2hbSqpBjUNboXynWEq6llGWkhTkpLDmPLbvXIQdxgJUXXxPgJp4YpjP7Xh7+mIMDlX2bboWWH9iPT7N+BR3DrwTx/99/OpcSlJwz1JSYmKi09NasTJCNnw6R3J7mVDeFV+k0tXiVHw8B08Puxc7mzRYcaEGkSYzaMqA7Nbfcc///oY53z+LzPIiyb5K9deVMmI2UuIhRSYWQ7noTGOJfbjNV+PLays2ltyJ03cl8Z3ZKIqCp6cn96rEroY7prXR0dFOT2vFygjZ8Okcye1lYnlnfZFKV4wTFXojdKMfwF3Zv2LOgQ+wr+4cvgnwR5anB4pMf2F+/F5EetyEd6Yvxahe4jdwdESMpMZDqkwoZnLRmcYSe1dSgEcAr61QvtMtJalUKlAUBftirIyiKFx//fX4448/EBQUJGtjOwJlKUnBrTAMkLcNTOJKpLeU4l8hA1Gka/vSIIwGAz1vwTs3LcXwHr07uKEKcrJs3zLsLt6NVya8gh9e+uHqX0ravXs3xo8fj927d6OhoQENDQ3YvXs3JkyYgB07diApKQk1NTV4/vnnZW9sRyL31M1sNiM+Pp57/65cZYRs+HSO5PYyobwrvkily8dJpQKG3wXVk0cxPvZjbH/wf3hh5CfwZgaBUllQaNqF++Nm464fXkT+hbJOEyOp8ZAiE4uhXHSmsdRgaAAA+Kh9eG2F8u5eSgJxkuHDh5NDhw61kx88eJBERUURQgjZvXs36dOnj7NVd0rS09MJAJKamiprvTRNk5qaGkLTtKxlhGz4dI7k9jKhvCu+SOVajRND02T3F9PIQ18MItEbo0n0xmgy/JuxZO7Py8m5+hqn/XXGf6k2UuIhRSYWQ7noTGPp3u33kuiN0WRfyT4ye/Zsh7ZC+dTUVAKApKenS/bFGZyeMRQWFsLf37+d3N/fH2fOtL3DdNCgQaiurr7cc1anwh3rncHBwU6vd4qVEbLh0zmS28uE8q74IpVrNU4UCG4Zchs2VTdhXWUVRhiMoFQmZLf8inv/nI1NOZtgpI2S/XXGf6k2UuIhRSYWQ7noTGOp0dQIoP1vDM6MJXfidO0xMTF44YUXcOHCBU524cIFvPjiixg/fjwAoKCgAL17d601UXcsJf35559OT2vFygjZ8Okcye1lQnlXfJHKNRsnlRq48WWonkrH5CH3YEtFFVadv4B+ZguazI34MO1DzPxtJt4/sAkNLS1XPEZS4yFFJhZDuehMY6nJ1PY7kpfKi9dWKN/plpLy8/PJkCFDiE6nIwMGDCADBw4kOp2ODB06lJw8eZIQQsjvv/9ONm/eLPv0RoyIiAgCwObvpZdesrEpLi4ms2bNIt7e3iQkJIQ89dRTxGg08tbJLiWlpaXJ2laGYUhDQwNhGEbWMkI2fDpHcnuZUN4VX6SixOkiZZmEfHM7MS/3J7990IvcsnUSt8Q0cv1N5Kes35xaIrncGPHpXZGJxVAuOstYohmajNg4gkRvjCZVLVXcUpIzYyktLc2tS0kuPeBGCEF8fDxOnToFQgiGDh2KW2+91e3TGzEiIyPxyCOPYNGiRZzM19cXvr5t9wrTNI3Ro0ejW7du+Oijj1BTU4MFCxbg7rvvxurVqx3WqdyVpNBpIATI3wFkboXx719j5aGN+KPoW0DdAgCIDonG0piluK7XdR3cUAUhGk2NmPL9FABA2kNpuPeue6/+u5KAtltTb7vtNjz22GN4+umnERsb2+EnBRY/Pz/07NmT+2NPCgCQkJCA3NxcbNmyBWPGjMEtt9yCjz76CF999RUaGxsF63XHUtK2bducntaKlRGy4dM5ktvLhPKu+CIVJU5WUBQwbDbw4A/w0PngX9P/iT33bMdjesCTUMiuycaihEWYtOE+/HLisGBVlxsjPr0rMrEYykVnGUvsMpIGGqgYFa+tUL7TLSXRNE1WrFhBwsLCiFqtJoWFhYQQQl5//XWyfv16WaczzhIREUF69uxJgoODyahRo8jKlSttloneeOMNMnLkSJsytbW1BABJTEx0WKc7l5JaW1udntaKlRGy4dM5ktvLhPKu+CIVJU4inEogzPIAUv12IHl3dX8yasMIbonpho0LSPypTIfFLjdGfHpXZGIxlIvOMpZyq3NJ9MZocuMPNxKGYWyWkqSOJXcvJTl9mb9y5Ups3LgR//nPf6DT6Tj5iBEjsH79evnOWC6wdOlS/PDDD9i7dy+WLFmCVatW4cknn+T0lZWV6NGjh02ZoKAg6HQ6VFZWCtadk5ODjIwMpKamIjU1FRUVFaBpmttF1mKx2KQZhhFNs7Mss9nMPTDIpgkh7dIAoFaruTTDMDZp9ipCpVJxaWs5TdPcS0Gs284npyjKxie2vawfGo3GYdpZn6zTjnzSaDQ2ftj7ZJ121Ha+fmLrEusba5/UanU7n6z/zGYzNBqNjU/W/cHXN1J8cpgedCssj+xBUPhEvFJdjR3nziG2xQIQoBbpWHboYdzy7WNIKsy28YPtM7F+sh5v9v3E1zfWsWXlFEW180mj0ThMOxp7Yp8n+37i80mtVjs19oT6zLqf+Mab9WeLHXvsHUnsuxgIIe3i5mgcEkLa9Zm7cPrEsHnzZnz55ZeYN28e9yEBgJEjRyI/P1/WxgHAW2+9xb3jlO8vLS0NAPDss89i2rRpGDlyJB599FF88cUX+Prrr1FTU8PV5+hdqeTiE9tCLFiwADExMZgwYQImTJiAdevWISsrCwUFBQCAzMxMFBW17XGTkpKC0tJSAEBycjIqKioAAElJSdxtvImJidi1axcsFgsSEhLQ1NQ2vYyLi4PBYIDFYkFcXBwsFgsMBgOX3rlzJ3bv3g2gbTv0xMREAEB1dTW3Je+uXbuQnJwMACgtLUVKSgqAtluN4+PjYbFYUFBQgKysLABtJz1WzvpksVgQHx+PwsJCzie2vcnJySgrK0NcXBySkpJw/vx5xMXFITExEfX19QAg2ScAaGpqQkJCAq9PcXFxKCsrc+hTUVERMjMzAYDziW17Tk4OADjsJzbuxcXFDvuJ9dXap927d2Pnzp2cHwaDAQaDAbt37+bSO3fuRFxcHOrr65GQkMD1B7vHza5du5CUlAQAqKiokOwTAOTl5SEvL6+dTxnlFvwvZDEsd3+DUE0IPqwqxx9l5biuVQWKIjjPHMaTB+Yh9tt/IqPsDBITE1FTU4O4uDjs3r2bt59Yf3bu3MnbT3FxcTh//jznU1lZGec36xPbHxkZGZxPx48fR1xcHHJycpCTk4O4uDgcP36cd+xJ+TyJjT3Wl+bmZsljT+jzxPYT297jx4+366fjx49zny127LEnBktL255HtbW1qKio4Mbk+fPnOZ+svyPq6+sRFxeHnTt3orW1Fe7E6R+fvby8kJ+fj4iICPj5+eH48ePo378/cnNzMWHCBDQ3N8vawOrqatFnIiIjI+Hp6dlOXlZWht69e+PIkSOYOHEi3nzzTWzbto3rQACoq6tDcHAwEhMTMX369HZ1sD/ybNq0CdHR0dyVQO/evbltyNVqNSwWCyiK4tLsvcZ8afYKR6fTcVdeFEVxV5wAOLl1mr2i0el0YBgGNE1Dq9WCYRgwDAO1Wg2TyQSVSmUjZ6/oLRYLPDw8uKsStr32cpVKBaPRCI1Gwx2XbS97FWRta10f658Un7RaLQghXNreJzbeKpWKu2Ky9ommaU5ubWvddlZu3U8qlQoGgwE6na5dn9n3DeuTydT2/gStVsv5QQiBwWCAp6cn5ys7DtgrYbY/rNP2fSPmE1ufo7TZbAZN0/Dw8ABtaIYq5XOoDq4CEzEFO8Y+h/+krEYD1XZyIYwa/T1uxr+mPYWo7uEghECr1TrsJzYu7Hhz1E/2fUPTNEwmEzw9PbkrYbVaDaPRCLVaDa1Wy/lnfUHGptm+se4/qZ8nsbHHfnbYdoqNPbHPE+sH6x/feGM/W+znZtuZbVievBzXh12PtbesxZw5c7Bt2zZQFGUzJh2NQ/aYWVlZGD9+vNt+fHZ6E73hw4fjwIED7d7O9vPPP2PMmDGyNYwlNDQUoaGhLpVlr7p69eoFAJg0aRLeeecdVFRUcLKEhAR4eHggJiZGsK7hw4cLdgA7+JxJGwwGAG1fNCxCaUIIaJrmToLWD7qwafbDyC7zWdtYLwtYz/YcydkPLpu3bi/7hch+AQDg0uwHXapPQNssjk3b+8R+WKzrtvfJ2g9Hbbe2YfuAvR5i65HaNwaDAVqt1kZuPXtlbTQaDddn1v3B1zdiPgml2S9PANB4+QHTXgTGzIeKMWNOYF/MiboOP6f+D5uOf4hibS2KzAmYl7AX/XQ3Y8WN/8SY8EiHvtqPN/t+4usbFusxyZ442LZbn1AB2NTjaOzZ9599Wup4s+8/obEn5fMECI83688W295GY9uMwU/rx7WBPZZ1DO3HIXsSs463u3B6KWn58uVYsmQJ/v3vf4NhGPz2229YtGgR3n33Xbz55pvuaKMkDh8+jE8++QTHjh1DUVERfvrpJzz++OOYM2cO+vbtCwCYMWMGoqKiMH/+fGRmZmLPnj14/vnnsWjRIodPc1tjvS4tB+z00NktgMXKCNnw6RzJ7WVCeVd8kYoSJ3Ec1uvfCwjsy2XvrdiNHeeOYW09QTdLN1AqM85admHB7ruw4vAKlDaVSqtXRO+KTCyGctFZxhK7lFRXUefyWJL7+6gdrvxivWvXLnLDDTcQHx8f4uXlRaZMmULi4+NdqUo20tPTycSJE0lAQADx9PQkQ4YMIcuXLyctLS02dsXFxWTmzJnEy8uLBAcHkyVLlhCDwSBYL9z467+CwhXh+E+EfDiEkOX+hFnuT+LX3UBu+Po27g6mUZtGkWcTXyRxeRkd3dIuz78O/4tEb4wmqzNWE0IId1eSM7j7e8nppSQAiI2NRWxsrLxnqMtk7NixOHLkiKhd3759sWPHDqfrJzLfBUAIQVNTE/z8/CRPC6WUEbLh0zmS28uE8gCc9kUqSpzk8Rcj7wWG/g04uApU8meYUX4Mt1IqpI+Yg/XeGhw6n4LdJXHYXRKHj9PH4d2bn0RM9xg0Nzfz1islHlJk9nFxpc9li5MLZZwdS+yMQUd0Nt8rzowlub+P7OkcT6VdBbhjKenAgQNOT2vFygjZ8Okcye1lQnlXfJGKEidxJNer8wFueg1Ykgpm2B2gCINxWX/gC1Uv/DjrR4RrJ4IQCpWWNPwj/h+493/34j/xH+NCU4Pk47oiE4uhXHSWscSeGCqKKlweS+5eSpJ0V1JQUJDkM2xtbe1lN6ozoWyJodBlKU4G9v8b+PsGwDsYAJBSlIGdFTvwZ9EO6C36NjvaB0N9ZuDZiQswOXJABza4azAvbh6yLmRh1fRVuLnvzZgzZ06n2xJD0lLSqlWruHRNTQ1WrlyJ2NhYTJo0CUDbD7/x8fF44403ZG9gZ8H6ARRHOvZWRmfqa2xshL+/v+TtRKSUEbLh0zmS28uE8gCc9kUqnS1Ora2tNlshMwyD+vp6BAYGcnHhywOw0cmF/TEll/EbisCHfr9UhhBM2P8mJmg88MxNn+PXmuNYnbYJFnUt8g2/47F9f8CHHo6/9bsDz0y6A34eHu2O66gtYjL7uLjij1vjJFJGyMaRjr0riTJQNt8rzowloe8jOZB0YliwYAGXvueee7BixQosWbKEkz399NNYs2YN/vrrLzz77LPyt7ITwNcRJpMJRUVFTncUuXi7Xm1trVPrnWJlhGz4dI7k9jKhPACnfZFKZ4tTa2srDAYDwsPDuaddU1NTcdNNN0GlUgnmAdjo5ML+mC6XuXASKDkCMGYEFO7FgnGPICz0n8gNBn49/RMaqZNo1WTjl9Js/HJ2Ffp7TsN4Kgov3P0APDx0vPWKyezj4oo/VzROTtg40rFLScWnikH3o3lthfLuPjE4/YCbr68vjh07hoEDB9rICwoKMGbMGNkfcOtohKZshBCUlJTAbDYjLCys02wkqOAe2BNDVVUVAgMDuWdhuhQ1hUDCG8DJP9vyXsHAtJeAcf+HzAsl+OTIVhyr2w2ivrTppMrUGyOCpuGR0XfixgFD3H6P/dUMIQRjt4yFhbEg4Z4E9PLtdfUuJVkTEhKC33//HS+88IKN/I8//kBISIhsDetsODpDWywWtLa2IiwsDN7e3k7VRy4+rMI+oSlXGSEbPp0jub1MKM/GwhlfpNLZ4sQ+3HfhwgV0794dFEWhuroaoaGh3HSfLw/ARicX9se8rDIhA4AHvgMK94LsehnUhXxg10tA8mqMWbAdm+96C0bLq/g6fSd+OfUrqujjYHTncLxlK54+tBWafZF4YPAMPDTmHoT5hfEeSygurvhzxeMk0cZeZ6ANsDBtPyYbG41gvBleW6G8u2cMTkf97bffxssvv4yZM2di5cqVWLlyJWbNmoVXXnkFb7/9tjva2Clw1BHsnQHWmwk6g16vd0sZIRs+nSO5vUwo74ovUulscWIvAtgtC7KzL21QJ5S318mFK/WKlhkwHfSi/cgfuBjErxeg8wYC23Y78NDo8OTEO5DwwDdY0XMF7ur9NAKoYSCEgkV7Ft8WfYnY32Jx7//uxZNx72J9yj6kHjvebj2dLy5XVZxEbOx17O8LakqNwrxC3piI5TvdUhIAHD16FJ999hny8vJACEFUVBSefvppTJw40R1t7FCEpmwGgwFFRUXo16+fw72aFLom11y/mw1AwzkgdOCl/A8PAjEL294PcXFWdba+Ar/kxSGrfj+OVR0DwaWvFn9tMG6OmIaJvSZieNBY9AnoCbXq2ltyKqgrwN3b70agRyAOzD0AAF1jKQkAJk6ciK1bt8rdlk6N3GdocnG7X3YDM7nKCNnw6RzJ7WVCeQCSfNm4cSOeeeYZbhdMuXx2pczlxMn6WophGG7vLXa6z5cHYKOTC/tjylXGxibU6jfFjM1A4R6gcA9MoVHQ3PwaVEP+hsjAXlg28f9QUXEbPII8kFhyAN9k/Ily03E0mmvx++nf8fvp39vqMPVAqGoYrgufhDuHXo9eahV6h4c5jKFcXJE4OVhKstaxL+nx1/mjrKzM5ncqZ8ZSp1hKEnu7mT3slrddCXd0hNFodEsZIRs+nSO5vUwob6+LjIy0uc0ZAO6//36cOnWKt218dOY4MQyDwsJCm+k+X95eJxeu1CulDK/NyPuAG14E0flAV50L1Y/zgHVTgezfwFjMKCwsRKAuEPcNvQu7HlyPow8k4ameT+HhYQ9jWPAwgFCA7jyqNfuw4/x7eHT/TPxt18O4YcNi/OO3z/BNyiEczT559cfJgY69I8lP59eujLNjyZ1IWkpSq9WoqKjgtpkWw9/fH8eOHUP//v0vu4EdjbKU5BqRkZF45pln8Mwzz3R0U2RH6feLtNQAh9cAKV8BF6+EEToEWJQIePjyFqtprcNveUlILE7G6cZMGKiKdjaE1kFt6YNQXT/09x+M2cNicNvg0dCpXfs9r7OwvXA7Xjv4Gib1moQvZ3wJoHMuJUmaMRBCsH79enz22WeS/tzx7t+Oxh1LSUaj0ak9T6SUEbKx1jEMg3//+98YOHAgPDw80KdPH6xcuRIAcOLECdx0003w8vJCSEgIHnvsMTQ1NXFlFy5ciDvvvBPvv/8+evXqhZCQECxevJh7yO/GG29EcXExnn32WW47aqBtKYl9oAloewnT6NGj8e233yIyMhIBAQGYO3euzYwzMjISH374oY0/o0ePxltvvcXlS0pKcMcdd8DX1xf+/v647777UFJSwpVh22vN0qVLccMNN3A2v/zyC0aMGMH5fNNNN7W79dpRbBmGQXFxsc1VHV/eXicXrtQrpYyYDeMVhOJBC8EsPQ7c+ArgGQASFIniyppLZS6ONet6QryD8MiY2Xg/5kkcfXgXEv++D4sjX8WUkPsRqo4GRTxBqU1gPApRRf2FI01r8VrKI5i4dSLu3n43noh/HrO/fRuvxW9FYX0hTLS0h0s7Ik72OnYpyU/n166Ms2PJnUj6jaFv37746quvJFfas2dPm33QuwLOdESrSXwvFkIIWloM8EHbvvY6tQoa9cVXZ9IMTDQDFUXBU3tpb/dWk8WmDIu3zrYbzWYz751SrO6VV17BV199hU8++QRTpkzBmTNnUFxcjNbWVtx222247rrrsH//fjQ1NWHRokV46qmnsGbNGq7evXv3IjQ0FImJiTh9+jTmzp2LsWPH4rHHHsNvv/2GUaNG4bHHHsOiRYsE41BYWIg//vgDO3bsQF1dHe677z68//77eOeddzgboX1hCCG488474ePjg/3798NiseDJJ5/EvHnzuLeKCZUF2tb9H3jgAfznP//BXXfdhcbGRuzZs8fhydX69Z5A27goKytDeHg4tw7Mlwdgo5ML+2PKVUbM5pJ+AlQ3vgxc9yTollqUnbxYpqkc2DQbZMJilJuH2NRjXXeQRwDGaCPw+G33QqPRwGgy4uekbajyNuFEdT7ONhbAoCpFs7kJBXUFKEDbm+vOVgLbtwEqSoXevr1xvsYPXlQvdPMMQ2+/cAwI6ovh3SLQLzQIPf094aF2Pv6XGyd7nfW7GKzHhSNboXynODGcPXvWrY24GrB+KYgYUW/GO13/fx8ci5kj236Iis85j39+l4GJ/YLx4+OTOJup/9mH2pb2V0dn35/JpSmKgq+v42k8q2tqasKnn36KNWvWcE+1sw8sfvXVV9Dr9di8eTN8fHwAAGvWrMHs2bPx73//m6s7KCgI69atg1qtxrBhwzBz5kwkJibiscceQ3BwMNRqNfz8/NCzZ09BvxmGwcaNG7ldNufPn489e/bYnBg8PDx4f0T+66+/kJWVhaKiIvTp0wcA8O2332L48OFIS0vD+PHjeWOhVqtBURT3WsW7776bewHVyJEjeePHvjwFaBsXkydPlpy3TsuF/THkKiNm007v6Q+Npz8mT45sy6d8BdSegXrXi5jk2wNQLQHG/QPw8BWMi4fOAw/dcp/NsQghON96Hvm1+UguPYGM8lNoIeWoM5ehxdyCkqYSQAcYkYN6GiioB/bWAygCGIsviDkIajoY3uruCMrfj1Cvbujl0x1/Hx2FseER0Kq1aDKYYbQwCPLWcXdMXW6c7HXsbwwBngGYHDNZ0FYo78z3kSu4t/YuhNtfjCET7HKHoy9TVpebmwuj0Yibb765XZm8vDyMGjUK3t7eMBgM8PDwwJQpU8AwDE6cOMH9zjR8+HCYzWbuCqlbt27ce26dITIykjspAG1v26uqqrKxYe8EcnRyyMvLQ58+fbiTAgAMGzYMgYGByM3N5T0xsMtphBCMGjUKN998M0aMGIHY2FjceuutmD17Nnr27NnuriT7pSSaprnfG9hXL/LlAdjo5ML+mHKVEbNxpLeR3fgy4B8OcmgVqMYyYPcbwMGPgYlPgB73KIoq6xzGxVG9FEWhp09P9PTpiRv73Mi1gRCCan01CuoKcbT0JArqClHWXI4aQyWa6SrQlB4qTTOgaQZQilYArQDKTMBxE7Brb1s9QR5B0CAAFTU6hPn2wB0jhiLIMwgB2gCs21OGHn49EeoTgm5ewQjy9oafpwZ+nlr4eWrgo1Wh7kIlhgyIhL+3Dj46DXdisfeF+/FZ64fTp09z/juyFcq7+/tIOTFIxJnfAnJXiL+rom17BT28vb24pSSW2OE9kLsiFiq7L8IDL95oU4YPoUFD0zS8vLx4y1h/AdvXYz19Zd/dy6eXiv2So/W7pAHb90mzWP+GxXfCsJZbvzbRug5WplarsXv3biQnJyMhIQFr1qzBa6+9hqNHj7a7gYKmaZvlAkII6urqEBkZKSlvnZYL+2PIVUbMxpHeRqb1AiY+Bnr0Qyj980NEnvsDVG0hsO9dqNK+Rv3UjSAO4uKMPxRFoZt3N3Tz7obJ4de10zeaGlHWVIbC+lLkXyjC8eIcGLVG1Bpr0GSugQn1sBAL6ox1AOqg8QWqcApfnThwqRIvoMQCoKHtj9A6ENoXhPYBsfi0/ad9QPZ5g9DeIBYfvDRjLG4a3A++al/szC7DX7sqMWlAKBo9Lp0YPtpbgh65BpyuasanfxVApwaqKsvRv0oNLw8tNBTBuZJKDDX6wMtDCxUIWiprEBkZ6fb3MSgnBok4M3WzX/Pnw8fD8e8wGqvfG+zt+cqwUBTFLQHx6QYPHgwvLy/s2bMHjz76qE2ZqKgobNq0Ca2trZzs0KFDUKlUGDVqlM2XsPVx7L/gdTqdLFc13bp1Q01NzaWXnDQ2oqioiNNHRUWhpKQEpaWl3KwhLy8PDQ0NiIqK4urIzs62qff48eM2zylQFIUpU6ZgypQpePPNNxEREYE//vgDy5Yt48qwcbJfSrKelYjl+WYwl4P9MeQqI2bjSO9Q5uGNfne/CTCvATm/Awc+BjVgOsZNvLRMMn5oX+DiZ8wVf/jw1/nDP8Qfw0KGYdYAAHbnDkIIGowNqNJX4ULrBVS2nEdlSxUaTLWoM9ShWl+LkvoqNFsaoKcbQUCDUptAqWsB8L9i4LO8b/GZ1QSaeHugrMq/bfaCtqWk+DN6MIXFqKppwSd/Wd3GfTzXtrIjGVzy07mjodFolKWkzoLcUzd2B09nXuwtpYyQjbXupZdewosvvgidTofJkyejrKwMBQUFmDdvHpYvX44FCxbg5ZdfRmNjI5566inMnz8f/v7+Nlcqer2eu13T/iUlkZGRSEpKwty5c+Hh4cHtieMs06dPx8aNGzFr1iwEBwfjjTfesFnWuOWWWzBy5EjMmzcPq1at4n58njp1KmJiYgAAN910Ez744ANs3rwZkyZNwpYtW5CdnY1Ro0aBEIKUlBTs2bMHM2bMQPfu3XHkyBFcuHABQ4cOdRg/a2iaRkFBAQYNGsRN9/nyAGx0cmF/TLnKiNk40ovKRvwdGH43aFMrCvLz2+JSchiqb+8AGTkXqqnLQAdGXrE4URSFQM9ABHoGYnDQYMEyKpUKjaZG1BnqUG+sR62h7eRRo6/BmcozoLwo1BsbUGuoR5O5Hg3GBjSZmkBAQKmNMOICcPFj0tunD+aNaoCPfyA27PXG3RP6Qm+yoLa+ATovH5hpAoOZRmNzC1RaD1hoAhNNo7G6EjTdU1lK6sq4Mh2UUkbsdlYAeOONN6DRaPDmm2+ivLwcPXv2xOLFi+Ht7Y34+HgsXboUU6dOhbe3N+655x589NFH7eq1fy2hNStWrMDjjz+OAQMGOH1brjWvvPIKTp8+jdmzZyMgIAD/+te/bGYMFEXhjz/+wFNPPYUbbrgBKpUKt912G/79739zNrGxsXjjjTfw4osvwmAw4B//+Afmz5+PrKwsAG3P3SQlJWHVqlVobGxEREQE3nvvPdx+++0O42d/wu0Me0p1xH5SfHpRmUoFaL04GVWwGxRjAXVsC3D8O1BRd4F0nwlcPJnKyeXEiaIoBHgEIMAjwEZP0zSymCyMHDmy3YnMZDbhyLEjCB8QjiZLE+qN9QjwCMCwkKG4e0gWRo4cguQv/PDe3SPa6sm6VA9f/opAXCApKYnMmzePXHfddeTcuXOEEEI2b95MDhw44Ep1kli5ciWZNGkS8fLyIgEBAQ5tiouLyaxZs4i3tzcJCQkhTz31FDEajTY2WVlZ5IYbbiCenp4kLCyMvP3224RhGN7jCr10W6/Xk9zcXKLX6y/LN4WrC6Xf3UDxEUK2/J2Q5f6X/r57gJBzaR3dMrcze/Zsp8sIfS/JgdM3U//666+IjY2Fl5cXMjMzuS0Cmpqa8O6778p82rqEyWTCvffeiyeeeMKhnqZpzJw5Ey0tLTh48CB++OEH/Prrr3juuec4m8bGRtx6660ICwtDamoqVq9ejQ8//BAff/yx6PHdsZSk1+udfsBNrIyQDZ/OkdxeJpR3xRepdPY40TSN7OxsbnwI5e11cuFKvVLKiNk40rsio2ka2Y0+oOf+ADyeBDJsDgiotndC/PIIINM9+x0RJz6dlDiJjSV34vRS0sqVK/HFF1/g4Ycfxg8//MDJJ0+ejBUrVsjaOGvYLb03btzoUJ+QkIDc3FyUlpYiLKxtH/iPPvoICxcuxDvvvAN/f39s3boVBoMBGzduhIeHB6Kjo3Hq1Cl8/PHHWLZsmfKCEQWFjqbXKDB/34gzR3diQOX/oOo3tW3pCQAsRuDsQWDATdyOrgpuwtkphpeXFykqKiKEEOLr60sKCwsJIYQUFhYSDw8Pp6cszrJhwwaHS0lvvPEGGTlypI2straWACCJiYmEEELmz59P5syZY2OTkZFBAJAzZ844PJ6ylKRgj9LvHUTahrYlpi+mEpLzByE03dEtkoUusZTUq1cvnD59up384MGDHbppXmVlJXr06GEjCwoKgk6nQ2VlJa8Nm2dt+Dhx4gQyMjKQmpqK1NRUVFRUgKZpm6UVZ9IMw6ClpcXmQStWzto5Sre0tHD39bNy67od2Tg6ppjcvh57G4Zh0Nrayu3bwqbt/RDzyZEf9mn7usXiKxQDZ+Nk74d9nCwWC9LT02GxWLi7ljIzM2GxWGA2m0HTNDIyMmA0Gm3SbH3s3VzWaZqmbdLWSwmO0iaTCRkZGVw51ie+tNlshtlsRmZmJgwGA+cf+2wHIW3bi1ssFmRkZHB3YrFytr1GoxGZmZmcLVtHeno6aJrmfGL9ZvfSomkaJpMJmZmZMJlMNmnWr/T0dM6ea7uxCUTrDVQcB356GGTdDWAK/gIutsvaP0c+GQwGZGRkcH3jyCfrtHXbHfUZG29H/vH1DSs3Go2cnB1nrN9sG6xt2BizfWZ/F6DcOH1iePzxx7F06VIcPXoUFEWhvLwcW7duxfPPP48nn3zSqbreeustbpM1vr+0tDTJ9Yk96OTIhh1AYstICxcuRExMDCZMmIAJEyZg3bp1OHnyJNdBra2t3OBpaWnhBklzczPX0U1NTZx9U1OTzb353La8jY3cQLZPs+1k0zRNcxvOWSwWm83nWlpaALQNTOs0OzANBgN3t4XBYOCOr9fruS8C9gPM+sfGqrm5GRaLBRRF2aSbmpq4+p3xiWEYXp+am5tBURSXtvfJaDSitbW1nU8Mw3B+WPtk3U/sB86+n6w3z7P3ie0zvV4Po9EIi8WCc+fOwWKxwGAwID4+Hl5eXmhubkZCQgLXZ/v27QPQNt4OHjwIoG2PpuTkZABAaWkpUlJSALQ9BZyZmQmg7fZW9k6UvLw87unyrKwsFBS07Rl07Ngxzr+UlBSUlpYCAJKTk1FR0bZzaVJSEqqrqwEAiYmJaGho4J5lYeMdFxfHfenExcXBYrFAq9UiPj6eiwXrU319Pfbt2wcvLy9UV1dz+1JVVlZyx7H2yWAw4NixY5xP2dnZ8PLyQn5+PvLz8+Hl5YXs7GzOp/r6ehQXF9v6NPkpHJ74JRrHPAF4+IM6fwKqrfcAm+9A2vavuPd8JCQkOPQpPj4eHh4eMBgMiIuLc+hTYmIiANj4RNM0jhw5IthPra2t3LMy1v2UnZ3Njc/MzEzujjrrE19tbS3XT1VVVVz89u3bx423hIQENDc3w8vLC/Hx8VxZt+HsFIMQQl599VXi5eVFKIoiFEURT09P8vrrrztdz4ULF0heXp7gn/10vaOWkjZv3kzS09NJSkoKSUlJIeXl5aS5uZnk5OQQvV5PGIbh7m6SkqZpWjDNMEy7NFsHX9qZ47sjfa34pNfrSU5ODmltbSUMwxCTycSVMZlMXB1smqZpm7TZbBZMWywWm7TFYhFMm81mmzQbP760yWSySbP+2fvRqX1qriZ03EuEWRFKyHJ/Qn/zt6vWp1mzZjndT2lpaW5dSnLpxEAIIS0tLSQ1NZUcPXqUNDU1ydkmQfhODHFxcUSlUpHy8nJO9sMPPxAPDw/S0NBACCFk7dq1JDAw0OYW1vfff5+EhYXx3rLKnhiOHj3aTnc5a80Mw5Dm5mbBW2VdKSNkw6dzJLeXCeVd8UUqnTFOra2tXL+bzWaSkpLCfUEI5e11cuFKvVLKiNk40rsiE4uhIHXFhPz6GCGlVre1GpoI0de75LMrZYRs+HTWcvY3BmfG0tGjRzvXbwws3t7eGDduHIYOHYq//vrLpQ3UnKGkpATHjh1DSUkJaJrGsWPHcOzYMW7aP2PGDERFRWH+/PnIzMzEnj178Pzzz2PRokXw9/cHADz44IPw8PDAwoULkZ2djd9//x3vvvuupDuS3HHHkitPdUopI2TDp3Mkt5cJ5eV8QlWsHXKVkSNOFEUhKCjIZmsNvry9Ti5cqVdKGTEbR3pXZGIxFCSwL3D3OqB3zCXZ/veB1TFA5habW107Ik58OilxEhtLbsXZM8m9995LVq9eTQghpLW1lQwePJhotVqi0WjIL7/8IvuZi2XBggUEQLu/vXv3cjbFxcVk5syZxMvLiwQHB5MlS5YQg8FgU09WVhaZOnUq8fDwID179iRvvfWW8oCbglMo/d6JsZgI+e+kSw/JfTmdkNLUjm6VIF3irqSkpCRMnToVAPD777+DYRjU19fjs88+494A5g42btzY7q4ZQghuvPFGzqZv377YsWMHWltbUVNTg9WrV8PDw8OmnhEjRiApKQkGgwEVFRVYvny5pLOv3HcBEELQ3Nzs9INbYmWEbPh0juT2Mut8ZGQkPvnkEy7vii9S6exxslgsSE5O5saHUN5eJxeu1CuljJiNI70rMrEYOoVaCzy2D5ixEtD5AWXpwPqbgT+fg6Wl9orHiU8nJU5iY8mdOH1iaGhoQHBwMABg165duOeee+Dt7Y2ZM2dydxR0ReR84xaLK2+5k1JGyIZP50huLxPKu/ONfZ05TiqVyubNXUJ5e51cuFKvlDJiNo70rsjEYug0Gh0w+SngqXRg1ANtstT1UK+bgn7a6isaJz6dlDiJjSV34nTtffr0weHDh9HS0oJdu3ZhxowZANr2U+/KL0aXuyMoihJ8M5mrZYRs+HSO5PYyobwrvkils8dJpVIhIiLC5sPLl7fXyYUr9UopI2bjSO+KTCyGLuPXA7jrC+DhbUBQJChDE3oNjrmiceLTSYmT2FhyJ07X/swzz2DevHno3bs3wsLCuKWcpKQkjBgxQu72dRrcsZTU1NTk9BKJWBkhG1ZXVFTk8JkRti9//fVXDB8+HB4eHoiMjOR2VrWut6WlBfPnz4efnx/69u2Lzz77zG1LSR0VJ0dLSfZyi8WCpKQkm+k+X95eJxeu1CuljJiNI70rMrEYXjb9bwSeOAzLAz8h6XjhpXovnBQterlx4tNJiZPYWHInTp8YnnzySRw5cgTffPMNDh48yJ25+vfv79bfGDoap87Qphb+P/Ol/fw9PDxEbPXt6vWgLO3t7LD/XcVe16dPH1RUVHB/GRkZCAkJwdSpU5Geno777rsP999/P9LT07F8+XK88cYb3P5SLB9//DHGjx+PjIwMPPHEE3j22WeRn58vPUZOIOTP5ZQRi5MUuUqlwoABA2yu6vjy9jq5cKVeKWXEbBzpXZGJxVAWdN5QRVx3qd6C3cB/JwB/Pt/+cybiozM2fDopcRIbS+6EIu64zOtCZGRkICYmBunp6Rg7dqyNzmAwcO9gtVlGeysAvAyaAcz7+VL+nV6AudWxbcT1wP/9eSn/n/5Aa017u7caJHjiGIPBgBtvvBHdunXDtm3bMH/+fFy4cIF7GhQAXnzxRfz555/IyckB0PYSnqlTp+Lbb78F0HYl3bNnT7z99ttYvHixy225WuDtd4Wrh/3/Afa+05YOHQLcsx7oNbJDmjJnzhxs377dqTJC30ty4NJp59y5c1i7di1efvllLFu2zOavq+KOpaTGxkY4c1aWYsvVy7NEYq975JFH0NTUhC+++AIURSEvLw9TpkyxsZ0yZQoKCgpQV1fHlR0xYoRNXd27d8f58+ed8EYaQv5cThln48Qnt1gsSExMtJnu8+XtdXLhSr1SyojZONK7IhOLoVzY1DvtReChXwHfHkD1SWD9LUDGt5J8dMaGTyclTmJjyZ04ve32nj17MGfOHPTr1w8nT55EdHQ0zp49C0KIW85cnQWnpm6vlvPrqEsPSHl5eQHPF/BvIUzZHXNpFswWCzQajeAPq15eXpJ0K1euxK5du3D06FF0794dgO3eUqwt+0VoXVar1drkVSoVtzeS3Aj5czllpMbJXm79oVSpVIiOjraZ7gvlrdNyYX8MucqI2TjSuyoTiplctKt34C3AE4eBP54ACuKB7UuAcynA7R8AWk/JbRGy4dNJiYlQvtP9+PzKK6/gueeeQ3Z2Njw9PfHrr7+itLQU06ZNw7333uuONnYKnOoInQ//38UBR1FU28voPXwFbG2/nCgPX2h9AtuXsbZh6+W524bV/frrr1ixYgV++uknDBw4kJNHRUXh4MGDNrbJyckYPHiwzXukrfXWf3Ij5M/llJEaJzG5SqVC9+7dbT68fHl7nVy4Uq+UMmI2jvSuyMRiKBcO6/UJAR74AZj+OgAKyNgMnN4tXEZKvSI6KXESG0vuxOna8/LysGDBAgCARqOBXq+Hr68vVqxYYfOe3a6G3FM3hmHQ0NDg1FW2lDJCNqwuKysLDz/8MF566SUMHz4c5eXlOHXqFKqrq/Hcc89hz549WLFiBdLT07FhwwasWbMGy5Yts6mXEMLlmYtbBrvj56qOjJO9zpHcbDYjPj6e25lVKG+vkwtX6pVSRszGkd4VmVgM5YK3XpUKmPZC29LS9c8Cw2aLl5FSr4BOSpyE8u5eSnJ6S4wePXqQnJwcQgghUVFRZNu2bYQQQo4dO0Z8fHycra7Twz56npra/rH6y91Ez2w2O705nFgZIRtW98033zjcXmTatGmEEEJ++eUXEhUVRbRaLenbty/54IMPbOqNiIggH3/8MZdnGIaMHDmSvPnmm07HQQ6fXSkjJU6ONtEzm802m+jRNE1qamq4XTCF8vY6uXClXillxGwc6V2RicVQLpyut6WG0Lk7LitOfDprObslhjNjKTU1tXPtrnrHHXeQL7/8khBCyAsvvEAGDhxIVq5cScaOHUtuvvlm2RvY0Sh7JSnYo/T7NYDZSMiGmW37LSV9RIgbdg5m6RJ7JX388ceYOHEigLYX7dx666348ccfERERga+//lquiUynwx1LSfX19U4vkYiVEbLh0zmS28uE8q74IpXOHiez2Yw///zTZrrPl7fXyYUr9UopI2bjSO+KTCyGcuFUvSo10GN4W3rP26D/fMFmp1ap9fLppMRJKN/plpKuNdgzc1paWjvd5S4lWSwWp5dIxMoI2fDpHMntZUJ5V3yRSmeMk/VSEsMwpKGhwSYufHl7nVy4Uq+UMmI2jvSuyMRiKBcuxenw54RZHtA2c/jtcUIs7d+5IFQvn85azs4YnBlL7n5Rj9O3q7KYTCZUVVW1u6rq27fvZZ6qOifu2EPf2fcMSCkjZMOncyS3l4nl3fU+hs4YJ/s9pdj3fUjJW6flwv4YcpURs3Gkd1UmFDO5cClO1y0GvILabmk9/j1gbAL+/g2gufQEvFC9fDopMRHKu/t9DE4vJZ06dQpTp06Fl5cXIiIi0K9fP/Tr1w+RkZHo16+fO9rYKVCWkpSlJL6lpG3bttlM9/ny9jq5cKVeKWXEbBzpXZGJxVAuXI7TWU9Y/r4RUHsA+TuAbf+UXC+fTkqchPLuXkpyekuMKVOmQKPR4OWXX0avXr3anblGjRolawM7GvbR87S0NMTExNjoLmdrBHLxPQbO3P8vpYyQDZ/OkdxeJpRn7d3xLENnjJPRaMTZs2fRr18/7uXy7DMehBDePAAbnVzYH1OuMmI2jvSuyAAIxlAuLjtORUnA/5YCc78DekRJqpdPZy2/4447sH37dsGxY5/PyMjAuHHj3LYlhtNLSceOHUN6ejqGDh0qe2MUFK5GNBqN5Ly9zl1tkKuMmI0jvSsysRjKxWXFqf80YElq28uAnKiXTyclTlcqLvY4vZQUFRWF6upqd7SlU0PTtKz1kU6+B5C9TCjvii9S6exxslgsiIuLs9nPhi9vr5MLV+qVUkbMxpHeFZlYDOVCljhZnxSKkoDtT8FiNvHWy3dMKXESysv9fWSPpKWkxsZGLp2WlobXX38d7777LkaMGNHujVbu+NGoI1GWkpSlJHu5/VKSxWr/KkIIbx6AjU4u7I8pVxkxG0d6V2QABGMoF7LGSV8HrBoJGBtBJj4Byy3/clgvX3lrufVSktSx5O6lJEkzhsDAQAQFBSEoKAi33norjhw5gptvvhndu3fn5KyNu3jnnXcwefJkeHt7IzAw0KEN+0G2/vviiy9sbE6cOIFp06bBy8sL4eHhWLFihVuudBWuHRxdDfLl3fWjoSv1SikjZsN3leysTCyGciFbnLyCgFmfAACoo58DyWucPqaUOF2puNgj6cSwd+9eJCYmcn/2eWuZuzCZTLj33nvxxBNPCNpt2LDB5iU07L5OQNvM59Zbb0VYWBhSU1OxevVqfPjhh/j4449Fj68sJTm/lBQZGYlVq1ZJ9s9Zfy6njJxLSQkJCTbTfb68vU4uXKlXShkxG0d6V2RiMZQL2eM04u/ArSsAANq9b4HO+rmdCV95KXESyrt7KQnkKmPDhg0kICDAoQ4A+f3333nLrl27lgQEBBCDwcDJ3nvvPRIWFsb70EtX3BJj2rRpZOnSpbLVx9cnVVVVpKWlRbbjdBau1n5XcAMMQ8ifL7Q9ALcilJDiw05XcVVvidHa2op//vOfCA8PR/fu3fHggw92yh+hlyxZgtDQUIwfPx5ffPGFzT3nhw8fxrRp02xezxgbG4vy8nKcPXtWsN7s7GxkZGQgNTUVqampqKiosNlRlFy8cpaaZhgGFosFhBAwDGMjZ+0cpS0Wi80Op9Zp9s/exvr47NWHI7l1HdYy+/ayfzRNO2w7mw4NDYW3t7egT478sE+zcZYaX/u2O2sj1Df2MWAYBrW1tZydyWRCY2MjGIaB2WwGIQT19fXt0tb12adpmrZJs1eHfGmz2Yz6+vp2fc+XNpvNoGkajY2NMJlMnH9sGwkhMJvN3G6yJpOJi5F1281mMxobG9u1l32hk3W8rP1m7RsbG7kZA5tm+7qurs7mSlmKT9ZpRz6ZTCZud1y2LY58su9rvj6jaRoWmgaJfRemAbEAbQJ+nA+6rpTrG4vFYtM3jvrMepzV1tY6tGH9Y/vMHc8MWSP5xLB8+XJs3LgRM2fOxNy5c7F7927RZZ0rzb/+9S/8/PPP+OuvvzB37lw899xzePfddzl9ZWUlevToYVOGzVdWVgrWvWDBAsTExGDChAmYMGEC1q1bh5MnT3KDpLW1FUajEQDQ0tLCfZiam5u5QdXU1MTZNzU1obm5mVueYDva0fKMdbq5uZm7GYCmaTQ1NQFoG4Dsi+qbm5vR0tL2LmiTycSljUYjHn74Yezfvx+fffYZVCoVKIrCl19+iZCQEBBCoNfrYTAY8Pvvv0Or1XI+HT16FNOnT4e/vz8CAgIQExODpKQk7Ny5E//4xz/Q0NAAtVoNlUqFt956C42NjejXrx9WrVrFtV2lUmHNmjW466674OPjg0GDBmH79u3cgHfkU3NzM5qammAymdDc3OzQp9bWtlejGgwG6PV6LgZ6fdu7fFmfrPuJtXHUT83NzVzfNDU1cR/UxsZGTq7X62E0GmEwGHDgwAEYDAYYDAbs3LkTBw4cQH19PTftP3jwIPfmrQMHDiApKQkAUFFRgeTkZABAaWkpUlJSAABFRUXIzMwEABQUFCArKwtA25b3eXl5AICsrCwUFBQAaLtB4sCBA7BYLEhJSUFpaSkAIDk5GRUVFQCApKQk7kIuMTERNTU1OHDgAHbv3s3FOy4uDgaDgbv7hfVt586d3JhlX/laX1+PxMREHDhwAOfPn+d8Kisr415Yz/rE+p2RkcH5dPz4cRw4cAA5OTnIycnBgQMHcPz4cRQUFHD2hYWFACDZp/r6egBAQkKCQ5/YvmlubkZcXByvTwBQXV3N+XHgwAHBfrIwBLt9/45W//5AvxuQX3ye66fjx49z9WRmZqKoqIjzie2z2tpaVFRUcMdi34SYmJiIgwcPcktI9fX1XH+wY95tCE8oLtG/f3/y/fffc/mjR48SjUZDLBaL1CrasXz5cofbP1v/2W93LbSUZM+HH35I/P39ufytt95KHnvsMRubc+fOEQDk8GHHU0B2yrZ582aSnp5OUlJSSEpKCikvLyfNzc0kJyeH2zOHpmnSYmohzcZm0mxsFkw3GZoE083G5nZptg5HaZqmbfZU4UvX1dWRSZMmkUcffZSUl5eTiooK8tVXX3ExZe1///13AoArO3z4cPLQQw+RvLw8cvLkSfLjjz+SY8eOEYPBQD755BPi7+9PysrKSHl5OWlqaiI0TZOIiAjyySefcG0DQHr37k22bt1KTp06RZ566ini6+tLqqurua2F2TiK+XGl0tZxZdN6vZ7k5OSQ1tZWwjAMMZlMXBmTycTVwaZpmrZJm81mwbTFYrFJs58xvrTZbLZJs/HjS5tMJps065+9H4pPTvrUVE3Ixf20nPFp1qxZTvvUafZKKi0txdSpU7n8hAkToNFoUF5ejj59+rh0UlqyZAnmzp0raBMZGelS3QBw3XXXobGxEefPn0ePHj3Qs2fPdjODqqoqAGg3k7Bn2LBh7W4LMxgM3C1oFEVBb9Fj4ncTXW7v5XD0waPw1npzSzzsXj/2t8/5+vpCp9PBx8cHvXr1AnBpnyNCbG8/taakpATLli3DkCFDQFEUBg0axB0nICAAFEU5fBIesH373cKFC/Hggw8CAN577z2sWbMGqampuO2227j2WseUXJyCW+9RZL9XkX1aKAZSbABwOuu2UxTFLXVY37bb1NSEwMBAqFQqqNVq1NbWIjAwEFqtlttGIzAw0CbNxsX67Vxsmm8PKr60SqXi6uV7aMw6zbaLbSfru/Wt5/ZtZ/1nbdi2snVY19/Y2MjFg33la0NDA1ePWq22Ob51Paw9W4eQH/Y+iaXVajXq6uq4vnHkk31/CPUZ2weX/AsCqIv7bBECVGaD6h7lsG+s+4yiKId+q9VqzobtD7b99p9PuZG8lETTNHQ6nY1Mo9Fc1p0DoaGhGDp0qOCfs88HWJOZmQlPT08u0JMmTUJSUhK3fAC0TTvDwsJET0DuXtOTC0IIWlpaeO+2YZdg7OXsn7XM+v+zzz6Lxx9/HLfeeivef/99nD59mjuOo/J8jBw5kkv7+PjAz8+POzk768/llJESJ3udIzlN00hNTbVZ++fL2+vkwpV6pZQRs3Gkd0UmFkO5uGJxMrUCPzwIfDUddNkxh+WlxEko7+7vI8kzBkIIFi5caPPDrcFgwOLFi+Hjc+m9w7/99pu8LbxISUkJamtrUVJSApqmcezYMQDAwIED4evri//973+orKzEpEmT4OXlhb179+K1117DY489xrX5wQcfxNtvv42FCxfi1VdfRUFBAd599128+eabog+8SHkU3UvjhaMPHr1sX13BS9P2fmiVSoWAgACHNnw61jfrq2N2MLKyt99+G/PmzcOff/6JnTt3Yvny5fjhhx9w1113cb9VSHkPrf0DkRRFCQ5yIX8up4wrcWLl7O8VQJs/sbGxkvPWabmwP4ZcZcRsHOldlQnFTC6uWJy0Xm0zBtoE7R+LEPvYPsBu3EuJiVDe3VtjSJ4xLFiwAN27d0dAQAD399BDDyEsLMxG5i7efPNNjBkzBsuXL0dzczPGjBmDMWPGIC0tDUBb0NauXYtJkyZh5MiR+PTTT7FixQp89NFHXB0BAQHYvXs3zp07h3HjxuHJJ5/EsmXLsGzZMtHjSzlDUxQFb623pD8vjRe00MJL4yVLGeslEuu7MqxhdTqdzuZKJTQ0lPsxnIX98dN65tCvXz8888wzSEhIwN13342vv/4ahBBotVq3vfNZyJ/LKSMlTo5mDPZyhmFstp8Xytvr5MKVeqWUEbNxpHdFJhZDubhicaIo4M61gH84UHMahl//CcZuxiAlTmJjyZ1IPjFs2LBB0p+72LhxY7tlC0IIbrzxRgDAbbfdhszMTDQ1NaGlpQUnTpzA0qVL251ZR4wYgaSkJBgMBlRUVGD58uWSHo93R0ewd83IXUbIRq/XIyIiAkePHsXZs2dRXV2NiRMnwtvbG6+++ipOnz6N7777Dps2bbIps2TJEiQkJKC4uBiHDh1CamoqBg4cCKDtd6Dm5mbs2bMH1dXVst8x0VFxkiJnGAbZ2dk2H16+vL1OLlypV0oZMRtHeldkYjGUiysaJ+9g4J71IJQKnqe2gWT9KFrG2bHkVuT8Jbsr0hUfcDt58iS57rrriJeXFwFAioqKyO+//04GDhxIPD09yaxZs8iXX35J2OFhNBrJ3LlzSZ8+fYhOpyNhYWFkyZIlNn4vXryYhISEEABk+fLlhBDC3ZXEAgcPIAYEBJANGza42WN5uVr7XaED2Pfvtoff3u1DSEOZQ5PO+ICbcmIQge0A+9tmCbn8V3sajUanX8coVkbIhk/nSG4vE8q74otUOmOcrF/tSdM0OXfuHHdboVDeXicXrtQrpYyYjSO9KzKxGMpFR8SJNhuJcc2UtpPDlnsdlmFPDM6MpdTU1M7x5PO1jjumbuzDY3KXEbLh0zmS28uE8q74IpXOHCeGYVBYWGgz3efL2+vkwpV6pZQRs3Gkd0UmFkO56Ig4MVDheP8nQLoNA6YuEyzj7FhyJ06/we1ag91229H2tpez7bbC1YvS7wpOwzAAz117c+bMwfbt252qTuh7SQ6UGYNE5D5DE0K4rRnkLCNkw6dzJLeXCeVd8UUqnT1ODMOguLjY5qqOL2+vkwtX6pVSRszGkd4VmVgM5aIj4sTprIWN5WBoWjROYmPJnSgnBom4oyNcedm5lDJiL3iXKnf0AnO+vNwvbhc6rlxl5IgTwzAoKyuz+fDy5e11cuFKvVLKiNk40rsiE4uhXHREnNrpjnwBfDYWJPs30TiJjSV3oiwliaAsJSnYo/S7gsvsex/Y9x7gF9b2/mgPX2Up6WpG6JF4V86thBAYDAanl0jEygjZ8Okcye1lQnlXfJFKZ4yT9dUaTdM4ffq0zbYFfHl7nVy4Uq+UMmI2jvSuyMRiKBcdEad2uilLgcAIoKkcddtfFYyT2FhyJ8qJQSKOvkDYTbSs915yBlc6V0oZsUEsVe5ofxe+vDsHameLE/sAn1arBSGEe/8AAMG8vU4uXKlXShkxG0d6V2RiMZSLjohTO53WC7j93wCAgNytINWneG3FxpI7UZaSRBCashFCUFJSArPZjLCwMEl7BSlcvRBC0NraiqqqKgQGBnK70yooOM3W+4CCeKD/dMz5hel0S0nu3YmpC+HoCpLdarqoqAjFxcVO1UdI23bSGo1G0pYcUssI2fDpHMntZUJ5AE77IpXOFiez2YzQ0FD07NkTQNu4KCgowKBBg6BWqwXzAGx0cmF/TLnK/H97dxvT1NnGAfzf6rqhvIxWi51MUFFGBa1gNDrM6huGZXS+zGSawIjEhA/OGDYWE5csfniyZBuJTuYynB8wLpsZSxk6x0a0zoVlHUPJdDKngKlAXQ06FeJGKOf5YOzjoW+n7SmnD/3/EhLPfZ9zn6tXbs/FOS13g+3jqz+cNgABcygXJfLkr89d9B+ous5A3W0Dhow+9w20He1HSSwMEdJoNJg3b17Ij5PcbjeuXLmCuXPnhjRJgx0TaB9/fb7ax7YF2gYQ8muRKhbzNGPGDFHBGLt+UqDtcNZ9kkKJ9aT89YfTFiyHcomZdbe0c+DMqYAhcz7Q3uh33/HKixeBAmpubhYACM3NzUqHErP6+/uFd955R+jv71c6lJjGPEkTb3kKZ62kaF+X+FA8iEffKRvoy2TC4Xa7cenSpZA/IRHsmED7+Ovz1T62LdB2b28v9u3bh97eXsmvRSrmKTglcuSvP5y2sf0TKU/RmkuPrkePrk9yY2FQ0Oeffx6VYwLt46/PV/vYtmDb0cI8BadEjvz1h9PGueS7Tan/c3yUFMSxY8cEAMKxY8dkHzsnJycqxwTax1+fr/axbf62o70EMPMUnBI58tcfTtvj/55oeQo2lx5/lCR1LkXzuiQIgsA3n4N4tJpmd3c3zp8/L9u4brcbd+/eRVtbW0hvqgY7JtA+/vp8tY9tC7T9xx9/AAB+//33cFIR8WsO55iJlCclcuSvP5w2AKL+R/mZCHmSMpf+/vtvnD9/PqS51N3dDSB6qxrz7xiCqK2txeuvv650GEREXg4ePIidO3fKPi7vGIJ49dVXkZqaiszMTCQkJCgdDhERHjx4gOvXr2P9+vVRGZ93DEREJMJPJRERkQgLAxERibAwEBGRCAuDTG7cuAGz2Qyj0YiFCxfiyy+/VDqkmLVx40akpqbilVdeUTqUmHHy5ElkZ2dj3rx5+PTTT5UOJ2Zx7gQnx7WIbz7LxOl04q+//oLJZILL5UJ+fj6uXLmCqVOnKh1azLHZbBgcHER9fT0aGhqUDkdxIyMjMBqNsNlsSE5ORn5+Pux2O7RardKhxRzOneDkuBbxjkEmBoMBJpMJAKDX66HVanH79m1lg4pRq1atQlJSktJhxIxffvkFCxYswMyZM5GUlIQXX3wR3333ndJhxSTOneDkuBbFTWE4d+4cSkpK8Mwzz0ClUqGxsdFrn0OHDnm+x7egoAA//vhjWOf69ddfMTo6imeffTbCqMffeOZpoog0Z/39/Zg5c6ZnOz09HX19feMR+rji3JJGzjyFey2Km8IwNDSERYsWoba21mf/8ePHsXv3buzduxcXLlzAypUrUVxcDIfD4dmnoKAAubm5Xj/9/f2efQYGBlBWVoa6urqov6ZoGK88TSSR5szX01y5v/AoFsgxt+KBXHmK6FoUlRWYYhwAwWq1itqWLl0qVFZWitqee+45Yc+ePZLH/eeff4SVK1cKR48elSNMxUUrT4IgCDabTdi8eXOkIcaccHLW2toqbNiwwdO3a9cu4bPPPot6rEqKZG5N1LnjS7h5ivRaFDd3DIEMDw+jvb0dRUVFovaioiL89NNPksYQBAHl5eVYvXo1SktLoxGm4uTIU7yRkrOlS5fi0qVL6Ovrw/3793Hq1KmoLXUQqzi3pJGSJzmuRSwMePhlF263G2lpaaL2tLQ03Lx5U9IYra2tOH78OBobG2EymWAymXDx4sVohKsYOfIEAOvXr8eWLVtw6tQppKene1bYnIik5Gzy5MmoqanBqlWrsHjxYlRXV0On0ykRrmKkzq14mju+SMmTHNciLqL3GF9fCi/1WW9hYSFGR0ejEVbMiSRPAOLyEzfBcmaxWGCxWMY7rJgTLE/xOHd8CZQnOa5FvGMAMG3aNEyaNMnrt16Xy+VVmeMZ8xQ65kwa5kma8coTCwMAjUaDgoICtLS0iNpbWlqwYsUKhaKKPcxT6JgzaZgnacYrT3HzKGlwcBDXrl3zbPf09KCjowNarRazZs1CVVUVSktLsWTJEixfvhx1dXVwOByorKxUMOrxxzyFjjmThnmSJibyFNZnmf4P2Ww2AYDXz2uvvebZ56OPPhIyMjIEjUYj5OfnCz/88INyASuEeQodcyYN8yRNLOSJayUREZEI32MgIiIRFgYiIhJhYSAiIhEWBiIiEmFhICIiERYGIiISYWEgIiIRFgYiIhJhYSAiIhEWBiIiEmFhIAqT2WyGSqWCSqVCR0dHVMbfvXt32MeXl5d74vP1hfJE/rAwEEVgx44dcDqdyM3NHbdzlpeXY8+ePUH3O3DgAJxO5zhERBNN3Cy7TRQNU6ZMwYwZM/z2Dw8PQ6PRyHa+0dFRfPPNN2hqagq6b0pKClJSUmQ7N8UP3jFQ3LJarXjyySdx69Ytr74333wTixcvDnlMs9mMnTt3oqqqCtOmTcO6desAAM3NzSgsLMTTTz8NnU6Hl156CV1dXZ7jhoaGUFZWhsTERBgMBtTU1Pgcv7W1FWq1GsuWLQMANDQ0IC8vDwkJCdDpdFi7di2GhoZCjpvocSwMFLfq6+tRXFyM6dOne/Vt27YNHR0d+O2338Iad/LkyWhtbcUnn3wC4OGFv6qqCm1tbTh9+jTUajU2btzo+W7e6upq2Gw2WK1WfP/99zh79iza29u9xm5qakJJSQnUajWcTie2bt2K7du3o7OzE2fPnsWmTZvAlfQpUnyURHFpdHQUZ86cwbvvvuuzPz8/HykpKWhpacHChQtDGjsrKwvvvfeeqG3z5s2i7SNHjkCv1+Py5cvIzMzEkSNHcPToUc8dRn19PdLT073GbmpqwgcffAAAcDqdGBkZwaZNm5CRkQEAyMvLCylWIl94x0BxyeVy4f79+8jKyvK0lZaWoqGhwbM9d+5cXL16NeSxlyxZ4tXW1dWFbdu2Yc6cOUhOTsbs2bMBAA6HA11dXRgeHsby5cs9+2u1WmRnZ4vG6OzsRG9vL9auXQsAWLRoEdasWYO8vDxs2bIFhw8fxp07d0KOl2gsFgaKayMjI55/d3R0wOFweLbVajVUKlXIY06dOtWrraSkBAMDAzh8+DDsdjvsdjuAh29OS33009TUhHXr1iEhIQEAMGnSJLS0tODbb7+F0WjEwYMHkZ2djZ6enpBjJnocCwPFJb1ejylTpuDPP/8EAPz777+4evUqLl++DODho6aenh5kZmZGfK6BgQF0dnbi7bffxpo1a5CTkyP6zT4rKwtPPPEEfv75Z0/bnTt3PLE98vXXX8NisYjaVCoVnn/+eezbtw8XLlyARqOB1WqNOGaKb3yPgeKSWq3Gyy+/jNraWrzwwgv46quvsHr1alitVlRUVMBms+H27dsoKSmJ+FypqanQ6XSoq6uDwWCAw+EQ/R1CYmIiKioqUF1dDZ1Oh7S0NOzduxdq9f9+b3O5XGhraxP9oZrdbsfp06dRVFQEvV4Pu92OW7duIScnJ+KYKb6xMFDcOnDgAMrKyrBixQrMnz8fDQ0NOHnyJIqLi/HUU0/h448/htFojPg8arUaX3zxBXbt2oXc3FxkZ2fjww8/hNls9uzz/vvvY3BwEBaLBUlJSXjjjTdw9+5dT/+JEyewbNky6PV6T1tycjLOnTuH/fv34969e8jIyEBNTQ2Ki4sjjpnim0rgZ9uIwmI2m2EymbB///6on8tisaCwsBBvvfVWyMeqVCpYrVZs2LBB/sBoQuJ7DEQROHToEBITE3Hx4sWonqewsBBbt24N6ZjKykokJiZGKSKayHjHQBSmvr4+PHjwAAAwa9YsWZe+kIPL5cK9e/cAAAaDweenpYh8YWEgIiIRPkoiIiIRFgYiIhJhYSAiIhEWBiIiEmFhICIiERYGIiISYWEgIiIRFgYiIhJhYSAiIhEWBiIiEvkvkNUbDtOrA3sAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ts = 0.05\n", "\n", "Pd1 = c2d(P, ts, method='zoh')\n", "print('離散時間システム(zoh)', Pd1)\n", "\n", "Pd2 = c2d(P, ts, method='tustin')\n", "print('離散時間システム(tustin)',Pd2)\n", "\n", "fig, ax = plt.subplots(2, 1, figsize=(4, 3.5))\n", "\n", "mag, phase, w = bode(P, np.logspace(-2,2), plot=False)\n", "pltargs = {'ls': '-.', 'label': 'continuous'}\n", "ax[0].semilogx(w, mag2db(mag), **pltargs)\n", "ax[1].semilogx(w, np.rad2deg(phase), **pltargs)\n", "\n", "# gain, phase, w = bode(Pd1, np.logspace(-2,2), plot=False)\n", "mag, phase, w = bode(Pd1, plot=False)\n", "pltargs = {'ls': '--', 'label': 'zoh'}\n", "ax[0].semilogx(w, mag2db(mag), **pltargs)\n", "ax[1].semilogx(w, np.rad2deg(phase), **pltargs)\n", "\n", "\n", "# gain, phase, w = bode(Pd2, np.logspace(-2,2), plot=False)\n", "mag, phase, w = bode(Pd2, plot=False)\n", "pltargs = {'ls': '-', 'label': 'tustin'}\n", "ax[0].semilogx(w, mag2db(mag), **pltargs)\n", "ax[1].semilogx(w, np.rad2deg(phase), **pltargs)\n", "\n", "bodeplot_set(ax, 3)\n", "\n", "# 周波数が w = pi/ts のところに線を引く\n", "ax[0].axvline(np.pi/ts, lw = 0.5, c ='k')\n", "ax[1].axvline(np.pi/ts, lw = 0.5, c ='k')\n", "\n", "ax[0].set_ylim([-43, 3])\n", "# ax[0].set_xlim([0.01, np.pi/ts])\n", "# ax[1].set_xlim([0.01, np.pi/ts])\n", "\n", "fig.tight_layout()\n", "# fig.savefig(\"c2d_bode2.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### プログラム実装(おまけ)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "離散時間システム(コントローラ)プログラムに実装する方法" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [], "source": [ "from control.matlab import tf, tfdata, c2d, step\n" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [], "source": [ "zeta, omega_n = 0.2, 10\n", "P = tf([omega_n**2], [1, 2*zeta*omega_n, omega_n**2])\n", "\n", "ts = 0.2\n", "Pd = c2d(P, ts, method='zoh')\n", "[[[b]], [[a]]] = tfdata(Pd) # 分子・分母多項式の係数を取得\n", "\n", "b1, b2 = b\n", "a1, a2 = a[1:]\n" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.0, 3.0)" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(3, 2.3))\n", "\n", "Tc = np.arange(0, 3, 0.01)\n", "y, t = step(P, Tc)\n", "ax.plot(t, y, ls='-.', label='continuous', color='k')\n", "\n", "Td = np.arange(0, 3, ts)\n", "y, t = step(Pd, Td)\n", "ax.plot(t, y, ls='', marker='o', label='zoh', color='k')\n", "\n", "plot_set(ax, 't', 'y', 'best')\n", "ax.set_xlim([0, 3])\n" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.0, 3.0)" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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mzUJ2djY2bNgAoHLiZFZWllMYLqBSV/Wxc1BDR6FQwNXVlYWNMmDGSwKWuKdVQ0apD6ZKpcKiRYsAVL6ycu/ePbPLtzUcxyEqKoqFjTKhKssvM6TBwkYJWGLh9carR48esvJ5e3uL763p1553BpRKJXr37s08LzNwtHdCHR1LnrFGM0nVEiXpN7eQa7wA4I033jA7r71QKpVo06aNvcVwOqouh82QBjNeErDEPdWv9vrAAw/Izvv888+bXa690Ol0iIqKwrhx41hjlIEgCCgpKUHTpk2Z1yoRFjZKwNyHiYhw5coVAMaXLmmIqFQqDB482OGndDgaCoUCTZo0sVqHfWhoqFMt6WwOrMNeAuYq6c6dO+Jed506dTLrGsnJyfj222/F6zg6SqUSLVu2ZN6DTBQKhdk74gQGBmLTpk0Gx+bOnWv05e+GBDNeEjDXPdXP72rfvr3ZnbGPP/44/t//+39ISUkxK7+t0el0OHjwoLjhKUMagiCgqKjIol2gq+Lh4dHg+x5Z2CgBc0Mga4SMEyZMwKRJkxxmbay6UKvVGDlypNPIawsEQcDHH3+MoKAguLm5oWPHjvjggw8AAGfPnsW4cePQpEkTdOnSBS+88IK46zRQuVv7jBkzsGHDBvj6+qJVq1Z46aWXxB+HMWPG4OrVq1i+fLnBHofVw8Z3330X/fr1w/bt2xEYGIjmzZvjiSeeMNh12pgH169fP4M15nJycjB9+nR4eXmhWbNmmDNnDm7evFlD3qosW7bMYCWUvXv34sEHH4SHhwdatWqFCRMmiLtry4EtRigBc/sh2rdvj6effhrdu3c3u+zvv//e7Lz2QKFQoFmzZjYt05wH383NTTSwHMehoqICSqXSwEM2dt2qC/1JZdWqVfj++++xceNGjBgxAvn5+bhw4QLKysrwj3/8A0OHDkVSUhIKCgrw7LPPYsmSJQgNDRXzR0dHw9fXF9HR0bh06RLmzp2Lfv364bnnnkN4eDj69u2L559/Hs8991ytcly+fBn79+/HgQMHcPfuXcyZMwcfffSRaEjrgogwY8YMNGnSBLGxseA4DosXL8bcuXMRExMj6Rr5+fl48skn8cknn2DmzJkoKSlBfHy8WfPbLOoftOh1cSfAlkviNBS0Wi3t37+ftFqtVa9b2+oCkLAaR/XPnj17xPx79uwhADR69GiD67Zu3bpGPrkUFxeTm5sbff/99zW+27JlC3l7e9P9+/eJ53m6e/cu/fe//yWlUkk3btwgIqKQkBAKCAgwWLrn8ccfp7lz54r/V999iIjoxx9/pObNm4v/r127ljw9Pam4uFg8tmLFCnrooYdqvU7fvn1p7dq1REQUGRlJKpWKcnJyxO/PnTtHACgxMVGUd/r06QbXWLp0qahbfZvKzs42rrBq1NeSOCxstCGFhYVO0Y+kVqudKsytbzIyMlBRUWF0h/SMjAz07dtXHGVs1qwZRowYAUEQcPHiRfG8Xr16GTyDvr6+KCgokC1LYGAgmjZtavZ1MjIy4O/vb7CSas+ePdGiRQtxPmNd9O3bF+PHj8eDDz6Ixx9/HN9//z3u3r0rvRJVYGFjPXL16lW0b9/e4vlOQ4YMQVJSEk6ePImhQ4daSbr6w9aGq2ofkVSqvgQ9c+ZM3L9/v8boVXZ2tqWi1TpQQ0S1LoGkp/rzo1AozOrYr+s6SqWyRvhW9QfTlLxVj9d1DZVKhSNHjiAhIQGRkZH48ssvsWbNGpw6dcrsEXlzaDSelznrxmu1WnTq1AkeHh419tWTS+vWrQE4x2tCHMchIiLCpu82NmnSRPanqoFVq9Vo0qRJDUNjLJ9cunbtCg8PDxw7dqzGdz179sTp06dRWloqvtt4/PhxKJVKWZOaXV1drbK3gY+Pj8H2b8XFxcjKyjKQNycnB7m5ueKx8+fP4969e+JbINWvAVTuelQVhUKBhx9+GO+99x7S0tLg6uqKffv2yZbXkjo3GuNljnt6/fp1uLm5wd3dHa1atbKo/P79+wNwDuOlVqsxZcoUFjb+D3d3d7zxxhtYuXKluG3YH3/8ga1bt+Kpp56Cu7s7QkJCcO7cOaSkpGDp0qWYP3++pBVI9AQGBiIuLg55eXkW/VCOGzcO27dvR3x8PNLT0xESEmLw7E+YMAF9+vTBU089hdTUVCQmJmLBggUYPXq0uN3auHHjkJycjG3btiEzMxNr165Fenq6eI1Tp05h/fr1SE5ORk5ODsLDw3Hr1i2zXoGzJGxsNMbLHAIDA1FaWoorV65YPGtab7yq/4I5KmxFCUPefvttvPbaa3jnnXfQo0cPzJ07FwUFBfD09MThw4dx584dDBkyBHPmzMG4cePw73//W9b1161bh+zsbHTp0gU+Pj5my7lq1SqMGjUKU6dOxZQpUzBjxgx06dJF/F6hUGD//v3w9vbGqFGjMGHCBHTu3Bm//PKLeM7kyZPx9ttvY+XKlRg8eDBKSkqwYMEC8ftmzZohLi4OU6ZMwQMPPIC33noLn332GYKDg82W2xwUVD24bWCkpqZi4MCBOHXqlLhrsT24dOkSunbtCnd3d5SUlDisV8PzPKKjo3Ho0CEEBwdj7NixVhvs0Gg0yMrKQqdOneDu7m6VazoSgiCguLgYzZo1Y28nVKG2+56YmIiHHnoIKSkpGDBggKzrNhoNyzUWPM8jJiYGu3btQkxMjMX9EZ07d0bTpk2h0Whw4cIFi65VX4SHhyMwMBATJ07E559/jokTJzrVTt/2RqlUokWLFsxwycCSH/FGo2U5Dqa+EY8dOxbz5s3D2LFjLW7ESqUSffv2BeB4/V4cxyE8PByzZ8+use+kfqdvZsDqhojA8zxbjFAGluiq0RgvqZ5TfTZiR+v3KigowLx58zBnzhwsXbrU6INETrTTt70htgGHbNhoowSkuKc8z9drI3a0EcfExETs2rULBw4ckLzTN8M0LGyUDwsbJSBlQmB8fHy9NuJ+/foBqDRejvDrPHXqVGzevNngpd3aqD73h2EIEYHjOIe4t86CJStwMONVBamN09xG3KtXL7i4uKCoqAg5OTlmXcNSeJ6HRqMR/3/llVcwfPhwSXl9fX2tIoO1loxxNIhInKzK+Jva7rclz4JjjtfXA1LcU6mN09xG7Orqil69euH06dNIS0tDQECAWdexhE8//RR79uzB3r17xWV+9Dt95+XlmWx4rVu3tninb1dXVyiVSly/fh0+Pj4NcpswNzc3aLVae4vhEBARtFotbt26BaVSCVdX1xrnWBI2NhrjJcXC19WIFQoF/Pz8LGrE/fr1w+nTp5Genl5jzaT6Ji8vD++//z5KS0sRHx8vGi/9Tt+zZ8+GQqEwWvfS0lJcvXrVonXNlEolOnXqhPz8fFy/ft3s6zgqRARBEKBUKhucUbYET09PdOzY0WhfIPO8JCBFSVUbcXX0D+OmTZssmrT5zjvv4L333jN4q99WvPHGGygtLcXw4cMNZkwDf+/0vXTpUoN+Pz8/PzRt2hQZGRmYN28e4uPjLXpJ3dXVFR07dgTHcQ1u9JLjOCQnJ2PQoEEOOwnZ1qhUqlqXxraoC0H2IjpOhn7tITnrBYWFhZGXl5fBGlD+/v4UFhZWj5LWL3/++ScBIIVCQcnJySbP4ziOoqOjaefOnRQdHU0cx9HVq1epefPmBIDeeustG0otD2OyMxwbc9qnnkZjvJKSkmTle+yxxwgALViwoEE0hCeeeIIAGCyAZwqe5+natWvE87x47JdffhGNX3x8fH2KahZhYWHk5+dn8IPj5+dn0x8cY3pj1E5SUhJbjLAu5Lqn+tBpxowZGDNmjFUXM/zmm28wc+ZMJCQkWO2atZGZmYk9e/YAAFavXl3n+YIg4PLlywY6mzNnDhYuXAgiQkhIiFnrb9UXjvJ2gDG9MWqHTZWQgNw+CH2HcocOHawuy7Fjx7B//36bGa8NGzZAEARMnToVffr0qfN8tVqNUaNG1dDZ5s2b0bFjR1y5cgUHDhyoL3FlUd8Ti+VgSm91Ye33aJ0JNtooATkWXhAEcS6XteY2VSUkJAQPP/wwJk2aZPVrV6eoqAg7duwAAKxYsUJSHkEQkJubC39/f4MRombNmmH79u3QaDQ2kb02iAjR0dE4d+6cpInFGzduxCuvvGJ0uN5amNJbbYSHhxsdJNm8eTNmzZol6Ro8zyM+Ph75+fnw9fXFyJEjbbbsuaVlO22HfWxsLE2dOpV8fX0JAO3bt6/OPDExMTRgwAByc3OjTp060TfffFPr+eZswKHRaOjNN9+k+fPnU0VFheR8jsimTZsIAPXu3ZsEQZCUR6fT0YkTJ0in09WzdPLheZ62bdtG3bt3JwDUv39/yRt2tGrVil5++WVKTk6uoQtrdPbL1VtYWBgpFIoacioUClIoFJL66yzt67Ok3tboZ7RkAw67Gq+IiAhas2YNhYWFSTJeV65cIU9PT1q6dCmdP3+evv/+e3JxcaG9e/eazGPJaIazw/M8PfDAAwSAvv76a6tfPzs7mz766COrX9cU8fHxNGDAALGhNG3alGbOnCnJcHl7exv8/+CDD9IXX3xBd+7csUojlGsEOI6rUWb1T7t27SgnJ4dKSkqM/vBYavwsqbc1DC9RAxltlGK8Vq5cSd27dzc49sILL9DQoUNN5tErR7+tk6Nw4cIF2r59O2VlZdVbGTExMQSAvLy8DLbLqguO4ygzM7PWBnj37l3RIFTdgqw+4DiO3n77bbGxNG3alD788EO6d++eaASMNSR9Y/L396eKigr6/fff6YknniA3Nzfxe1dXV5P56tP72bZtm2SPEQAplUpq0aIFde/encaNG0dPP/00NW3a1OT5+nqbuoeWGB8phtfHx4ciIiLo999/p0OHDtGhQ4coMjKSYmJi6OLFi+K1EhMTG4fxGjlyJL3yyisGx8LDw0mtVpvcY1BvvEJDQyklJYUSExMpMTGRrl+/ThzHiTdXp9OJ6evXr9OVK1dIo9GQTqcTh76rprVarUFa/8uoTwuCUCNNRGJ60qRJBIC++uorIqr0kvThhqk0x3EGab28ptKLFi0iALRo0SKT9TBWJ51OR3/88Ycos6k6rVq1ioYPH05//fWXeC7P8wZpOXWqqKigo0eP0s6dO+no0aNUUVFB169fp9GjR4uNYsGCBXT9+nUD2fUNsXpj1B/79ddfDepx584d2rRpEz344IO1NkC9AdBqtSbrtGfPHpOGEwCtWLGCVq1aRf/4xz/ou+++E+/Nxx9/LMlo1XZtKZ+oqCjSarW0bds2+uSTT+irr74S95qsLZ+Xlxft2bNHrOuVK1eod+/e1LdvXzp69KhFMs2fP1+8f3/88UfjMF5du3alDz74wODYiRMnCID4QFdHb7yqf9auXUupqamUkZFBRJW/AJmZmURE9NxzzxEAeuaZZyg2NpauXbtGRETHjh2jmzdvEhHR77//Trdv3yYiogMHDtC9e/eIiGj//v1UVlZmsHFrWVkZ7d+/n4iI7t27RwcOHKA33niDANCUKVOIiOjmzZt07NgxIiK6du0axcbGElFlaHbixAkiIsrMzBQ9yIyMDEpNTSUiorNnz9LZs2eJiCg1NZXS09MpOjqaXnzxRZo4cSLFxcXRiRMnxE1CrVWnvXv3EsdxYp2IiAoKCujjjz+mnTt3Unh4OEVGRkqqU1hYGLVr187gHrVo0UKcHOvp6Uk///yzwX2qWqd//etfYt+p/uPv709vvfWWyTodOnRIUmPbtWsXHTp0qMZ9unr1Kvn4+EhutI888oh4n7766itJeX755Re6f/8+7dmzh+Lj4+nYsWO0YsUKmjVrlqT8oaGhtH//fho+fLhsIxMcHCzep/j4eAJAarWaPv30U0n527dvT/369aMHHniAevXqRX369KGOHTvSkiVLxGfvyJEjjcd4rV+/3uDY8ePHCQDl5+cbzWOO57V69Wpyc3Ojt99+u948r927dxMAGjx4MBFZz/P69ddfjYYwe/bskex5cRxH6enpYllS6/TZZ5+ZDJ9qq1Nd3ktAQACdO3euxn2qXg+tVkvR0dG0fft2OnbsGHEcV+t9+vnnnyU1wlatWpGXlxdduHBBlP3DDz+kLl26SDYCX3/9NaWmpoqyV1RU1Bnu+vn5iTqufp+OHTsmqWy95/XBBx/Q/Pnzadq0aZIHOVasWCHep7KyMjp06BCdPHlSNDh1fY4ePVrr86bT6Zy3w74qUoyXJWGj3D4vQRDqdaTx4sWLBIDc3d2tNqpnrU5UjuMMGlpdCIJg0hOoq2wp/ScdOnSolzccoqOjJTVCvU6LiorEvEuXLpXswezcudNo+XWFu1L6nerq6zOmN6n1jo6OtnrZ1Wk0fV4rV66kHj16GBx78cUXJXXYO9poI8/zYofrn3/+afH16jICch4oc8o2t/PY0oZkqdxSGmFJSYlBJzNRZagutd+qNtmNdfZLfY/WXONnDeNjieGtitOONpaUlFBaWhqlpaURAPr8888pLS2Nrl69SkQkzrXSo58qsXz5cjp//jxt3bpV8lQJRxttJCIaN24cAaAtW7ZYfC1rGgGO4+js2bOSDZ0lZe/cudMi78VS7OX9VL+ONedaSTF+1jA+lhhePU7reZl66ENCQoiIKCQkhEaPHm2QJyYmhvr370+urq4UGBgoeZKqVOPF8zwNHz6cZs6caRAm1AerV68moHI00FKsaQTkGi9Lyt6yZYvdPC899vB+rIm5xs8axsfSyb1Oa7xsgVy39ObNm+LDZ6ofzVr897//JQA1QmFzsGf4Jbfs8vJyMW9eXl6tnfX1Ge5WxR7ejyNg72WEnDZstAVyPa/Tp08TAGrTpk09S1Y5rUD/sN+9e9eia1mzE1Vuh31dZes/Pj4+1LJlSwoKCjLI/95774ky2st7sRSO4+jo0aO0fv16Onr0qNMvoWQrLPG8Gs2qElLRrybRvn37ei/Lx8cHXbp0AVC5DZklqFQqbNq0yeTy1YC8VWA9PDxklb1582aDsoxx69Yt3LlzB5cuXUJubq54/J133kFYWFiNFTz8/Pywd+9eyS8o2xOVSoUxY8Zg5syZVl9CiWGcRmO8pD5MtjReADB06FAAwMmTJy2+ln5p6eoGRK4RUKlU6N69u6wGqF9GuroB8vf3R1hYGO7cuYO0tDSkp6fj9u3bNZbBnjVrFrKzsxEdHY2dO3ciOjoaWVlZTmG49Jijt8aOJbpqNEvicBwn6bz6XArHGMOGDcPPP/+M48ePW3yt7du3AwCeeOIJPP/882YvU8JxHNLS0tC/f39Z6y3NmjUL06dPN7lEire3d6359d6Ls2Ku3hozUtulMRqNhqXu5mJrz2vMmDHo0qULevbsadF1dDoddu/eDQBYsGCBRUZAoVDA29vbrB1wnN0AWYIlemusWKKrRmO8HDVs7NWrFy5dumTxdSIjI1FYWIi2bdtiwoQJFl1LpVIhKCjIYpkaG0xv8rEkbGw0fV5S3VO98bJV2Ggttm3bBqAyZLQ0ZOE4DgkJCRa59I0Rpjf5WKKrRmO8pC7Lq+/zspXnpYfjOFy4cMGsvHfu3MH+/fsBAAsXLrRYFqVSiQ4dOkjWGaMSpjf5WKKrRhM2SlFS1bXrbWm8rl+/jh49eqCiogJFRUVwd3eXlX/37t3QarXo27cv+vXrZ7E8SqUSAQEBFl+nscH0Jh9LjFej+YmQ4p7eunULPM9DoVCgbdu2NpCqEl9fXzRp0gReXl64cuWK7Pw//vgjAOCf//ynVeThOA5xcXEs/JEJ05t82GijBKRYeL3X1aZNG5sOdSsUCsTFxSEwMFB2uenp6UhOToZarca8efOsIo9SqUSXLl1Y+CMTpjf5sLBRAlKU5O3tjVWrVtlljo65o1ShoaEAgGnTpsHHx8cqsuj7bhjyYHqTDzNeEpDingYEBGD9+vU2kMY0RISKigpJ/V4ajUYcZbRGR70effhjzgaqjRmmN/mw0UYJOIMr/8MPP6Bjx4748MMPJZ0fHR2NW7duwc/PD8HBwVaTQ6lUonfv3k6hM0eC6U0+rMNeAlKUdOXKFWRlZaGiosIGEtXE1dUV165dw65du4y+YF2d4OBgpKen44cffoCLi4vV5FAqlWjTpg1rhDJhepMPM14SkOKeLl++HJ07dxZH72zNzJkz4eXlhczMTGzcuBG7du1CTEwMeJ43madXr16YPHmyVeXQ6XQ4fPgwdDqdVa/b0GF6k49Nw8aFCxciLi7O7ALthRQLr1Qq4e7ubrfZ9U2bNsXDDz8MAHjttdcwb948jB07FoGBgQgPDxfPIyJkZWXVmxwqlQqDBw9mqyPIhOlNPjb1vEpKSjBp0iR07doV69evR15entmF2xIpStq3bx/Kysowbdo0G0hUk/DwcBw+fLjG8by8PMyePVs0YBEREejatSuWLVtWL3IolUq0bNmShT8yYXqTj02NV1hYGPLy8rBkyRL8+uuvCAwMRHBwMPbu3evQ7rJU91ShUNjl4eN5HkuXLjX6nb7/a9myZeB5HtHR0eB5Hm5ubvUii06nw8GDBx36fjoiTG/ysfloY6tWrbB06VKkpaUhMTERQUFBmD9/Ptq3b4/ly5cjMzPTbIHqC0d35ePj43Ht2jWT3xMRcnNzER8fjw0bNiA+Ph5vvvlmvciiVqsxcuRINtwvE6Y3+dhtVYn8/HxERkYiMjISKpUKU6ZMwblz59CzZ09s3LjRkktbnbrWDTp37hweeughPPPMMzaSyBD97H6p540YMaLOxf3MRaFQoFmzZmxdKpkwvcnHEl3JNl46nQ5hYWGYOnUqAgIC8Ouvv2L58uXIz8/HTz/9hMjISGzfvh3r1q0zW6j6oC739OrVq0hMTMTp06dtI1A1pA4SeHp61rMklff4t99+Y+GPTJje5GPTdxt9fX0hCAKefPJJJCYmGl3FYPLkyWjRooXZQtUHdbmn9l7Ha+TIkfDz80NeXl6tc7yKi4vrXRa1Wo1Jkyax8EcmTG/yseka9hs3bsTjjz9e6+sr3t7e9TqUXx/YegXV6uh34Jk9ezYUCoVRA/bDDz9g/vz5NpGHNUDzYHqzHbLDxvnz58teb8oRqG2iJ2D7jTeMUdcOPLbqj+M4DhEREWxpF5kwvcmnrnZZG43mZ0Jq2Ggvz0tPXTvw2AK1Wo0pU6YwL0ImTG/yYVufWQFHMV6AY+zAw3Eca4RmwPRmOxrNVOC63FN7d9g7EhzHITIykoU/MmF6kw8LGyVQ268hz/O4efMmAMfwvOyNi4sLpk+fbm8xnA6mN/lY4qU2Gs+rtukH+rXr9UuaNHaICMXFxZKW5WH8DdObfCzRVaMxXrW5p/qQ0dZr1zsqHMchPj6ehT8yYXqTDwsbJVCbUbLXXo2OiouLCx555BF7i+F0ML3Jh4WNEhAEweR3rLPeEEEQcOfOnVp1xqgJ05t8LNEVM14A+vXrhzVr1uDxxx+3oUSOC8/zSEpKssilb4wwvcnHEuPFwkYAgwcPxuDBg20ojWPj4uJi9aWlGwNMb/JhYaMEmCsvHUEQUFBQwHQmE6Y3+bCwUQK1KSktLQ2XL19mS5n8D0EQkJ6ezhqhTJje5MOMlwRqc0+nTp2KoKAgnDlzxoYSOS5qtRrjxo1j00ZkwvQmHxY2SsCUhScieHl5wcPDg402/g9BEJCXl8c8CJkwvcmHeV4SMKUkhUKBixcvorS0lBmv/yEIAi5fvswaoUyY3uTDRhslUJd7ytYd/xu1Wo1Ro0bZWwyng+lNPixslAD7NZSOIAi4evUq05lMmN7k49Rh49dff41OnTrB3d0dAwcORHx8vMlzY2JioFAoanwuXLhQZzmmlPTzzz9j0KBBWL9+vdl1aGiwvhvzYHqTj9Mar19++QXLli3DmjVrkJaWhpEjRyI4OBg5OTm15rt48SLy8/PFT9euXessy5R7evHiRaSkpCA3N9esOjRE1Go1hg8fzkbNZML0Jh+nDRs///xzPPPMM3j22WfRo0cPbNq0Cf7+/vjmm29qzdemTRu0a9dO/EhZStbUKxv69xqrrxvfmOF5HpcuXWKvuciE6U0+lujKbsZLq9UiJSUFkyZNMjg+adIkJCQk1Jq3f//+8PX1xfjx4xEdHS2pvPPnzyM1NRVJSUlISkpCfn4+eJ4Xd6lu27atqEiO40R31lRap9MZpPXrEunTRFQjDcAgLQiCQVq/lIqpNM/zBmm9vKbSHMeZVSciwu3bt2vUz5nrZIv7pNPpcPfuXXAc12DqZKv7ZA52M16FhYXgeR5t27Y1ON62bVvcuHHDaB5fX19s2bIFYWFhCA8PR7du3TB+/HjExcXVWd7ChQsxcOBADBkyBEOGDMF3332HM2fOiFu0lZeXi+nExEQxjExISBCXzImLi0NhYSEAICoqCkVFRQCAyMhIlJSUAAAiIiKg0WgMdpLRaDSIiIgAAJSUlCAyMhIAUFRUhKioKFEf+nrk5+eLBjw3NxeJiYkAgKysLKSlpQEAMjMzxUm1GRkZyMjIAACcOXMGmZmZACrfHDCnTmq1GoWFhSgvL28wdbLFfUpNTcXgwYORm5vbYOpU3/dJL7tZkJ3Iy8sjAJSQkGBw/P3336du3bpJvs7UqVNp2rRpJr9PSUkhABQaGkopKSmUmJhIiYmJdP36deI4jlq2bEkAKC0tjTiOIyIinU5HPM/XmtZqtQZpQRAM0oIg1EgTkUGa53mDtE6nqzXNcZxBWi+vqbROpzOrThzHUXp6ulhWQ6iTLe6TRqOhjIwMqqioaDB1qu/7dOrUKQJAKSkpJBe79Sy2bt0aKpWqhpdVUFBQwxurjaFDh2LHjh11ntezZ08MGDDA4JhGo8GdO3cAAB07dhT7zqp2IppKu7i4mJVWKBRiWqlUQqlUSk5X7duTkpZSD2N14nkeWq1WnPvWEOokN21OndRqNcrLy6FSqUSZnb1O9X2fLJlfabew0dXVFQMHDsSRI0cMjh85cgTDhw+XfJ20tDRJM+ONderrO+vd3d3h7e0tucyGjkqlQv/+/W26V2RDgOlNPk67b+Orr76K+fPnY9CgQRg2bBi2bNmCnJwcvPjiiwCAVatWIS8vD9u2bQMAbNq0CYGBgejVqxe0Wi127NiBsLAwhIWF1VmWsVGNvLw8AJUjjWyG/d/wPI+MjAz06NGDNUQZML3Jx2nXsJ87dy5u376NdevWIT8/H71790ZERAQCAgIAVHYeVp3zpdVq8frrryMvLw8eHh7o1asXDh48iClTpphVviNtNMtgMORh99l0ixcvxuLFi41+FxoaavD/ypUrsXLlSrPKMfZLWNXzYvyNSqVC79697S2G08H0Jh9LPFS7vx5kK2oLG5nnZQjP80hLS2OTLWXC9CYfp5yk6giw2fWm8fDwsLcITgnTm+2we9hoK4y5p08++SSCgoIwYsQIO0jkuKhUKnTv3t3eYjgdTG/ycdrRRltibBfjRx99FI8++qgdpHFsOI5DWloa+vfvz14ylgHTm3ws2V280YSNbCqEdBQKBby9vZnOZML0Jh+nnKRqa6q7pxqNBrGxsbh06ZKdJHJcVCoVgoKC2FwlmTC9yYeNNkqgunuamZmJMWPGYOjQoXaSyHHhOA4JCQkWufSNEaY3+Viiq0YTmOvf0dJTXl6Orl27olWrVnaSyHFRKpXo0KFDDZ0xaofpTT6W6KrRGq8hQ4bgr7/+spM0jo1SqRTfcmBIh+lNPpYYr0bzE8FceelwHIe4uDimM5kwvcmHjTZKgLny0lEqlejSpQvTmUyY3uTDPC8JVFfSvHnzMGjQIHE1ScbfsL4b82B6kw8zXhKo7p6mpaUhJSXFTtI4NhzHISoqioU/MmF6kw8LGyVQ1cITEa5evQqgcgVVhiFKpRK9e/dmHoRMmN7kw0YbJVBVSbdv3xY3l/D397eXSA6LUqlEmzZt7C2G08H0Jh8WNkqgqnuq97p8fX3h5uZmL5EcFp1Oh8OHD4tbYzGkwfQmHxY2SqCqhWchY+2oVCoMHjyYveYiE6Y3+bCwUQLGjBebUGgcpVKJli1b2lsMp4PpTT4sbJSAsbCRGS/j6HQ6HDx4kIU/MmF6kw8LGyVQ1ZXXb+rBwkbjqNVqjBw5kq1JJROmN/mwxQglUHXdIOZ51Y5CoUCzZs3sLYbTwfQmH7aelwRY2CgdnU6H3377jYU/MmF6kw8LGyWgd09LS0tx+/ZtACxsNIVarcakSZNY+CMTpjf5sMUIZXD58mUAgLe3N1q0aGFfYRwY1gDNg+nNdjQa46XfH87X1xdbt27FunXr7CyR48JxHCIiItg7ejJhepOPJfs2NpqfCb176uPjg0WLFtlZGsdGrVZjypQpzIuQCdObfFjYyLA6zHswD6Y329FojJfePf3Pf/6D2NhYlJaW2lkix4XjOERGRrKGKBOmN/lYEjY2GuOld+WfffZZjBkzhq1fXwsuLi6YPn06XFxc7C2KU8H0Jh9LQuxGY7yICFqtFoMGDULnzp0RFBRkb5EcFiJCcXExiMjeojgVTG/ysURXjcZ48TwPV1dXRERE4PLly2jatKm9RXJYOI5DfHw8C39kwvQmHzbaKAE2AiQdFxcXPPLII/YWw+lgepMPCxslIAgCe21DIoIg4M6dOxAEwd6iOBVMb/KxRFeNynjNnz8fPj4+2LFjh73FcWh4nkdSUpJFLn1jhOlNPpYYr0YTS6nVavz5558oLCyEj4+PvcVxaFxcXDB58mR7i+F0ML3Jh4WNEigrKxOnR/Tt29fO0jg2giCgoKCAhT8yYXqTDwsbJZCZmQlBENCmTRu0a9fO3uI4NIIgID09nTVCmTC9yYeFjRK4dOkSAOZ1SUGtVmPcuHH2FsPpYHqTDwsbJXD69GkAwNChQ+0riBMgCALy8vKYByETpjf5sLBRAmfOnAEAPPzww3aWxPERBAGXL19mjVAmTG/yYWGjBK5duwaFQsE8Lwmo1WqMGjXK3mI4HUxv8mFho0T69++P5s2b21sMh0cQBFy9epV5EDJhepOPU4eNX3/9NTp16gR3d3cMHDgQ8fHxtZ4fGxuLgQMHwt3dHZ07d8a3334ruaxLly4hPDzcUpEbPKzvxjyY3uTjtMbrl19+wbJly7BmzRqkpaVh5MiRCA4OFvdVrE5WVhamTJmCkSNHIi0tDatXr8Yrr7yCsLAwSeUVFxdj9uzZzIDVgVqtxvDhw9n7oDJhepOPRboiOzJkyBB68cUXDY51796d3nzzTaPnr1y5krp3725w7IUXXqChQ4eaLCMlJYUAiB+FQkH+/v7EcZzlFWigcBxHmZmZTEcyYXqTT2JiIgGglJQU2Xnt5nlptVqkpKRg0qRJBscnTZqEhIQEo3lOnjxZ4/zJkycjOTlZ8kvXRITc3Fzs378fPM+L76FxHGeQ1ruzptI6nc4gTf9bl0ifJqIaaX35+nTVl8UFQRCXUjGV5nneIK2X11Ta3DoREW7fvl2jfs5cJ1vcJ51Oh7t374LjuAZTJ1vdJ3Owm/EqLCwEz/No27atwfG2bdvixo0bRvPcuHHD6Pkcx6GwsFBW+Tt37sSZM2eQmZkJAEhLS0NWVhYAIDExEbm5uQCAhIQE5OfnAwDi4uLEcqKiolBUVAQAiIyMRElJCQAgIiICGo3GYCcZjUaDiIgIAEBJSQkiIyMBAEVFRYiKihL1ERcXBwDIz88XDXhubi4SExMBVIbNaWlpACrfGNBP/8jIyEBGRgYAWKVOarUahYWFKC8vbzB1ssV9Sk1NxeDBg5Gbm9tg6lTf90kvu1mY7/BZRl5eHgGghIQEg+Pvv/8+devWzWierl270vr16w2OHT9+nABQfn6+0TzVw0b9Z+/evcRxnOji63Q6gzTP87WmtVqtQVoQBIO0IAg10kRkkOZ53iCt0+lqTXMcZ5DWy2sqbW6dOI6j9PR0sayGUCdb3CeNRkMZGRlUUVHRYOpU3/fp1KlTZoeNdutZbN26NVQqVQ0vq6CgoIZ3paddu3ZGz1er1WjVqpWkchUKBfz8/DBjxgyDbZeqdhxKSVddp1xOWqFQiGmlUgmlUik5XVVeKWlz68TzPLRaLRQKRYOpk9y0OXVSq9UoLy+HSqUSZXb2OtX3fdI/Y+Zgt7DR1dUVAwcOxJEjRwyOHzlyBMOHDzeaZ9iwYTXOj4yMxKBBg0xuenDr1i0xrVfUpk2bLNovrqFTUFCA3377DQUFBfYWxalgepPPnTt3ABi2U8nI9tWsyO7du8nFxYW2bt1K58+fp2XLllGTJk0oOzubiIjefPNNmj9/vnj+lStXyNPTk5YvX07nz5+nrVu3kouLC+3du9dkGTt27BBDRX9/fwoLC6v3ejk7+hGgxMREe4viVDC9yWfbtm0EgHbs2CE7r10npMydOxe3b9/GunXrkJ+fj969eyMiIgIBAQEAKjsPq8756tSpEyIiIrB8+XJ89dVXaN++Pb744gs89thjdZa1atUq/Otf/2IeF4PRQLD7bLrFixdj8eLFRr8LDQ2tcWz06NFITU2VXU6vXr2Y4ZKIsf4aRt0wvclH36dmDnY3XvVNRUUFAODKlStmGb3GyLlz5wz+MqTB9CafK1euAPi7ncqiHsJYh+LLL780OlWCfdiHfRzn8+WXX8pu2w3e83riiSfg7e2NwMBAeHh42FscBoNRhfLycmRnZ5u1cYmCiO1NzmAwnA+7L4nDYDAY5sCMF4PBcEqY8WIwGE5JgzZecldpbezExcVh2rRpaN++PRQKBfbv329vkRyeDz/8EIMHD0bTpk3Rpk0bzJgxAxcvXrS3WA7PN998gz59+qBZs2Zo1qwZhg0bhkOHDsm6RoM1XnJXaWUApaWl6Nu3L/7973/bWxSnITY2Fi+99BL++OMPHDlyBBzHYdKkSSgtLbW3aA6Nn58fPvroIyQnJyM5ORnjxo3D9OnT5c2Rs/rEKgdB7iqtDEMA0L59++wthtNRUFBAACg2Ntbeojgd3t7e9MMPP0g+v0F6Xuas0spgWIN79+4BAFq2bGlnSZwHnuexe/dulJaWYtiwYZLzNchJquas0spgWAoR4dVXX8WIESPQu3dve4vj8Jw9exbDhg2DRqOBl5cX9u3bh549e0rO3yCNl57qC50RkUWLnzEYtbFkyRKcOXMGx48ft7coTkG3bt1w+vRpFBUVISwsDCEhIYiNjZVswBqk8TJnlVYGwxJefvll/Oc//0FcXBz8/PzsLY5T4OrqiqCgIADAoEGDkJSUhM2bN+O7776TlL9B9nmZs0org2EORIQlS5YgPDwcUVFR6NSpk71FclqISNbqEg3S8wKAV199FfPnz8egQYMwbNgwbNmyBTk5OXjxxRftLZrDcv/+fVy6dEn8PysrC6dPn0bLli3RsWNHO0rmuLz00kvYuXMnfvvtNzRt2lT09ps3b84WAqiF1atXIzg4GP7+/igpKcHu3bsRExOD33//XfpF6mnU0yH46quvKCAggFxdXWnAgAFs+LoOoqOjjS5XEhISYm/RHBZj+gJAP/74o71Fc2gWLVoktk0fHx8aP348RUZGyroGW1WCwWA4JQ2yz4vBYDR8mPFiMBhOCTNeDAbDKWHGi8FgOCXMeDEYDKeEGS8Gg+GUMOPFYDCcEma8GAyGU8KMF4PBcEqY8WI4DWPGjMGyZcvsLQbDQWDGi8FgOCXs3UaGU7Bw4UL89NNPBseysrIQGBhoH4EYdocZL4ZTcO/ePQQHB6N3795Yt24dAMDHxwcqlcrOkjHsRYNdz4vRsGjevDlcXV3h6emJdu3a2VschgPA+rwYDIZTwowXg8FwSpjxYjgNrq6u4Hne3mIwHARmvBhOQ2BgIE6dOoXs7GwUFhZCEAR7i8SwI8x4MZyG119/HSqVCj179oSPjw9ycnLsLRLDjrCpEgwGwylhnheDwXBKmPFiMBhOCTNeDAbDKWHGi8FgOCXMeDEYDKeEGS8Gg+GUMOPFYDCcEma8GAyGU8KMF4PBcEqY8WIwGE4JM14MBsMp+f8Jmw4BiZY8IAAAAABJRU5ErkJggg==", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(3, 2.3))\n", "\n", "# 離散時間システムのステップ応答\n", "uold, uold2 = 0.0, 0.0\n", "yold, yold2 = 0.0, 0.0\n", "\n", "Td = np.arange(0, 3, ts)\n", "u = 1.0*(Td>=0) # 単位ステップ入力\n", "\n", "# プログラム ===============\n", "for k in range(len(Td)):\n", " y[k] = b1*uold + b2*uold2 - a1*yold - a2*yold2\n", "\n", " yold2 = yold\n", " yold = y[k]\n", " uold2 = uold\n", " uold = u[k]\n", "# ========================\n", "\n", "ax.plot(Td, y, ls='', marker='o', label='discrete', color='k')\n", "\n", "#連続時間システムのステップ応答\n", "yc, t = step(P, np.arange(0, 3, 0.01))\n", "ax.plot(t, yc, ls='-.', label='continuous', color='k')\n", "\n", "plot_set(ax, 't', 'y', 'best')\n", "ax.set_xlim([0, 3])\n", "\n", "# fig.savefig(\"c7_system2program_plot.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.0, 3.0)" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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ZKBQKlohQJtZ8x9rNt9PaEOjs2bMAYDZPvUqlwubNmwE07og0/H/Tpk0O35fEcRySk5NZ2CgTIkJlZaVFkzXbK2y0UQLWWHitVov8/HwA5o0XAMybNw979+7FHXfcYXQ8MDAQe/fudYp5XkqlEn369GGelwW05ZUXLQHzvCRgjZJ+//13CIIAX19fSSNI8+bNQ2FhIT788EMAQPfu3VFQUOAUhguo01VL7BzU1lEoFHB1dWVhowyY8ZKANe5p/ZBR6hdTpVJh6dKlAOp2zLl586bF929tOI5DfHw8CxtlQvXSLzOkwcJGCVhj4Q3GS+48Fl9fX/Tu3RsAxNzzzoBSqURYWBjzvCyArQmVhzXfsXazttEaJRk2t7BkEt6LL75ocV17oVQq0bVrV3uL4XTUT4fNkAYzXhKwxj29cOECAMha7mHgb3/7m8X3tRd6vR7x8fGYMmUKexllIAgCKisr4e3tzbxWibCwUQKWfpmICBcvXgQAMQRs66hUKowcOdLhp3TYm0mTJmHVqlUA6pb3bN68GR06dGAd9jJgnpcELFVSeXm5uNddr169LLpGRkYGMjIysHDhQvj4+Fh0jdZEqVTCz8/P3mKYhOd5pKSkoKSkxGFypaWnpzfKdNGaJCYmYvLkybhx44ZTbdrBRhslYKl7apjf1aNHD4s7Yx9++GH8z//8DzIzMy2q39ro9XocPHjQKA2KoxATE4OQkBBMnjwZCxcuxOTJkxESEmL3VEP+/v5wd3dHRUWFVbtAN4SI2vSoLwsbJWDpL7MtQsb77rsP4eHhdvtVlotarcb48eMdTt6YmBjMnz+/UeaO1siVVlVVhcWLF8PLywsBAQH46KOPjP5uCBu9vb2hUCjwxhtvoGfPnnBzc0OPHj2wYsUK8dza2lqsWbMGQUFBcHNzQ9++fbF161YAdR6UQqHA4cOHMWLECLi5uSElJQVEhPfffx+9e/eGh4cHBg8eLO4fWlhYKG5kY0hltGTJEgAwW88RsMZjdqxvZwtiaT9Ejx498MQTT1iVWdSQVdVZUCgUDhfeNpcrTaFQYNWqVZg9e3aLhJAvvPACEhISsG/fPnTv3h3r1q1DZmYmhgwZIp6jUCigUqmwd+9ebNy4Ebt27cKgQYNw7do1/Pbbb+J5ixcvxokTJ/DJJ59g8ODBKCgoaJQGZ82aNfjwww/Ru3dvdOrUCa+88gpiYmLw5Zdfom/fvkhOTsYTTzwBf39/jBs3DtHR0XjooYdw/vx5+Pj4iFGCuXoTJ060uZ7kYlX/oOVrxZ0DQ1aJkydP2lsUp0Gn09H+/fvF3W1shTVZJeyZsaOyspJcXV1p165d4rHr16+Th4cHrVy5kojqdu35+OOP6caNG/Thhx/SnXfe2aT+zp8/TwDoyJEjZtu5f/9+8djt27fJ3d2dUlNTjc598skn6bHHHjOqd+PGDVn1WgNzz/3kyZMWZ5VoN56XvTt0AaCsrAwdO3Z0+OkHarXa4cJce+ZKy8/Ph06nw5gxY8Rjfn5+6NevX6NzfXx88PDDD2Pz5s3o3bs3HnjgAURERGDmzJlQq9XIzs6GSqVq1usxJAYE6iZJa7Va3H///Ubn6HQ6DB061OQ1LK3XmrCwsQW5dOkSevToYbXBGTVqFNLT03HixAmMHj3aRtK1HI5kuIC6jSZseZ4cSOZyn6CgIJw/fx5HjhzB0aNHsWzZMnzwwQdISkqSPOhTP9e+YQDg4MGDjRb8m1sIbmk9Z6HddNhbkh9cp9OhV69e8PDwsCo1LwB06dIFgHMsE+I4DrGxsQ41ymXPXGmhoaFwcXHBr7/+Kh67ceMGfv/990bnGtY2enh4YNasWfjkk0+QmJiIEydO4PTp07jrrrsgCAKSkpIk33/gwIFwc3PD5cuXERoaavQx7ALk6uoKwPh7LqWevWH7NkrAEvf06tWrcHNzg0qlQufOna26/9ChQ3Ho0CGnMF5qtRoREREO5X0ZcqXNnz8fCoXCyBtq6VxpXl5eePLJJ/HCCy+gc+fO6NatG15++eUm5yj5+Pjgu+++gyAIuOeee+Dp6Ynt27fDw8MDwcHB6Ny5MyIjI7F06VKxw/7SpUsoLS3FI4880uT9vb298fzzz2P16tUQBAHjxo3DrVu3kJqaCi8vL0RGRiI4OBgKhQIHDhxAREQEPDw8JNWzN1Y9L6t74xwcQ4d9RkaGRfV5nqc//vjDajn27NlDAGjkyJFWX6ulEQSBqqurbZ7O2BZpoKOjoykwMNCokz4oKIiio6NtKGljKisr6YknniBPT0/q1q0bvf/++zRx4sRGHfY8z1NMTAzdc8895OPjQx06dKDRo0fT0aNHxWvV1NTQ6tWrKSAggFxdXSk0NJT+93//l4ia7ngnqnsmmzdvpn79+pGLiwv5+/vTtGnTKCkpSTxn/fr11L17d1IoFBQZGSm5Xktj7rlnZGRY3GGvIGrb+TuysrIwfPhwnDx5EqNGjbKbHBcuXEDfvn3h7u6OyspKh/Jq6sPzPBISEnDo0CFMnz4dkydPtpk3o9VqUVBQgF69esHd3d0qGR1thj1Q18d069Yt+Pj4sLWN9TD33NPS0nDPPfcgMzMTw4YNk3Vdx3yDWgC5xsLWL0jv3r3h7e2NyspKnDt3DmFhYRZfq6WIiYnBypUrxUmgH3/8sUPu9K1SqTBp0iR7i9EIpVLpVEtzHAFrfsTbzc+DHAezJZagKJVKDB48GIDjddpzHGfX2ettBSICz/MsGaEMrNFVuzFeUkc1WvIlNsytabj7sL0oLS3FwoUL8cgjj7SJnb7tDbENOGRjzXeq3RgvKe5pc0tQAOteYoPxchTPKy0tDT/88AMOHDjQJnb6tjeGsJH1d0mHhY0SkLLSPyUlpUVfYsM6OI1G4xC/zjNmzMDmzZvxxhtvSDrf0Xf6tjf0nwwQjvBsnQVrMnAw41WPll6CMmjQILi4uKCiogKXL1+26BrWwvM8tFqt+P8VK1Zg7Nixkuraava6LVPGOBJEhKqqKma8GmDueVvzXWCjjfVo6SUorq6uGDRoELKzs6HRaBAcHGzRdazhgw8+wO7du7F3714xzY9h9npxcbHJF69Lly5Wz153dXWFUqnE1atX4e/v3ya3CXNzc4NOp7O3GA4BEUGn0+HPP/+EUqkUVwHUx5qwsd0YLykWvrmXWKFQIDAw0KqXeMiQIcjOzkZOTg7mzJlj8XUsobi4GG+99RaqqqqQkpIiGi9zs9cN3L59G5cuXbIqr5lSqUSvXr1QUlKCq1evWnwdR4WIIAgClEplmzPK1uDp6YmePXs22RfIPC8JSFFS/Ze4IbZagvLaa6/hzTfftMvashdffBFVVVUYO3YsFi9ebPQ3w07f9ed5AXU7fXt5eeHcuXNYuHAhUlJSrFqk7urqip49e4LjuDY3eslxHDIyMjBixAiHnYTc2qhUKqjVapPG3KouBNlz8p0Mw/IgOcsPoqOjycvLq9WXoLQkv/32GwEghUJhdqkUx3GUkJBAO3fupISEBOI4ji5dukQdO3YkAPTKK6+0otTyaEp2hmNjyftpoN0Yr/T0dFn1HnroIQJAixcvbhMvwqOPPkoAaMGCBc2ey/M8XblyhXieF4/9+OOPovFLSUlpSVEtoqk1j4GBga36g9OU3hjmSU9Pt9h4sdFGExhCpzlz5mDSpEk2XTv35ZdfYu7cuUhNTbXZNc2Rl5eH3bt3AwDWrVvX7PmCICA/P99IZ4888giWLFkCIkJkZCRu377dYvLKxVFWBzSlN4Z52FQJCcjtgzB0KDdM4mYLjh07hv3797ea8frwww8hCAJmzJiBu+++u9nz1Wo1JkyY0EhnmzdvRs+ePXHx4kUcOHCgpcSVRUtPLJaDKb01B8/zSExMxA8//IDExMQ21xdoDjbaKAE5Fl4QBHEuV0tk5oyMjMS9996L8PBwm1+7IRUVFdixYweAuk0kpCAIAoqKihAUFGQ0QuTj44Pt27dDq9W2iuzmICIkJCTgzJkzkiYWb9y4EStWrGhyuN5WmNKbORouhgcgezG8PbNsWHtvp+2wT0pKohkzZlBAQAABoH379jVbJzExkYYNG0Zubm7Uq1cv+vLLL82eb8kGHFqtll566SVatGgR1dbWSq7niGzatIkAUFhYmOT8XHq9no4fP056vb6FpZMPz/O0bds26t+/PwGgIUOGSNqYAwB17tyZ/vGPf1BGRkYjXdiis1+u3qKjo0mhUDSSU6FQkEKhkNRfZ21fnzXttkU/ozUbcNjVeMXGxtLLL79M0dHRkozXxYsXydPTk1auXElnz56lr7/+mlxcXGjv3r0m61gzmuHs8DxPd955JwGgL774wubXLywspHfffdfm1zVFSkoKDRs2THxRvL29ae7cuZIMl6+vr9H/77rrLvrkk0+ovLzcJi+hXCPAcVyjezY0YAEBAXT58mWqrKxs8ofHWuNnTbttYXiJ2shooxTjtWbNGurfv7/RsaeffppGjx5tso5BOWlpabYQ02acO3eOtm/fTgUFBS12j8TERAJAXl5edOvWLcn1OI6jvLw8sy/gjRs3RIOwe/duW4hrVp5XX31VfFm8vb3pnXfeoZs3b4pGoKkXyfAyBQUFUW1tLf3888/06KOPkpubm/h3FxcXk/Va0vvZtm2bZI8RACmVSurUqRP179+fpkyZQo8//jh5e3ubNX5BQUEmn6E1xqc5wwuA/P39KTY2ln7++Wc6dOgQHTp0iOLi4igxMZHOnz8vXistLa19GK/x48fTihUrjI7FxMSQWq02ucegwXhFRUVRZmYmpaWlUVpaGl29epU4jhMfrl6vF8tXr16lixcvklarJb1eLw591y/rdDqjsuGX0VAWBKFRmYjEcnh4OAGgzz//nIjqvCRDuGGqzHGcUdkgr6ny0qVLCQAtXbrUZDuaapNer6dff/1VlNlUm9auXUtjx46l33//XTyX53mjspw21dbW0tGjR2nnzp109OhRqq2tpatXr9LEiRPFl2Lx4sV09epVI9kNL2LDl9FwbM+ePUbtKC8vp02bNtFdd91l9gU0GACdTmeyTbt37zZrBF544QVau3YtPfDAA/TVV1+Jz+bdd9+VZLRMGWWpn/j4eNLpdLRt2zZ6//336fPPP6ctW7Y08kQbfry8vOjHH38U23rx4kUKCwujwYMH09GjR62SadGiReLz+/XXX9uH8erbty+9/fbbRseOHz9OAMQvdEMMxqvh5/XXX6esrCzKzc0lorpfgLy8PCIieuqppwgAPfnkk5SUlERXrlwhIqJjx46J+ex//vlnun79OhERHThwgG7evElERPv376fq6mqjjVurq6vFTURv3rxJBw4coBdffJEAUEREBBER/fHHH3Ts2DEiIrpy5YqYY7ywsJCOHz9ORER5eXmiB5mbm0tZWVlERHT69Gk6ffo0ERFlZWVRTk4OJSQk0DPPPEP3338/JScn0/Hjx6mwsJCIyGZt2rt3L3EcJ7aJiKi0tJTee+892rlzJ8XExFBcXJykNkVHR1P37t2NnpGvry/5+PgQAPL09KTvv//e6DnVb9M///lPse/U8AkKCqJXXnnFZJsOHTok6WX74Ycf6NChQ42e06VLl8jf31/yS/vggw+Kz+nzzz+XVGf37t10+/Zt2r17N6WkpNCxY8fohRdeoHnz5kmqHxUVRfv376exY8fKNjLTp08Xn1NKSgoBILVaTR988IGk+j169KAhQ4bQnXfeSYMGDaK7776bevbsScuXLxe/e0eOHGk/xmvDhg1Gx3755RcCQCUlJU3WscTzWrduHbm5udGrr77aYp7Xrl27CPjvhhy28rz27NnTZAize/duyZ4Xx3GUk5Mj3ktqmz766COT4ZO5NpnyXgyf4OBgOnPmTKPn1LAdOp2OEhISaPv27XTs2DHiOM7sc/r+++8lvYR+fn7k5eVF586dE2V/5513qE+fPpKNwBdffEFZWVmi7LW1tc2Gu4GBgaKOGz6nY8eOSbq3wfN6++23adGiRTRz5kwaOnSopLovvPCC+Jyqq6vp0KFDdOLECcmel2HTEXNev9N22NdHivGyJmyU2+clCEKLjjQatn13d3e32aierTpROY4zetGaQxAEk55Ac/eW0n8SGBjYIiscDDv1SP1UVFSIdVeuXCm53s6dO5u8f3PhrpR+p+b6+prSm9R2JyQk2PzeDWk3fV5r1qyhAQMGGB175plnJHXYO9poI8/zYofrb7/9ZvX1pIxeSf1CWXJvSzuPrX2RrJVbyktYWVlp1MlMVBeqv/fee1bLbs1WbpYaP1sYH2sMb32cdrSxsrKSNBoNaTQaAkAff/wxaTQaunTpEhGRONfKgGGqxOrVq+ns2bO0detWyVMlHG20kYhoypQpBIC2bNli9bVsaQQ4jqPTp09LNnTW3Hvnzp1WeS/WYi/vp+F1bDnXSorxs4XxscUemk7reZn60hs2zIyMjKSJEyca1UlMTKShQ4eSq6srhYSESJ6kKtV48TxPY8eOpblz5xqFCS3BunXrCKgbDbQWWxoBucbLmntv2bLFbp6XAXt4P7bEUuNnC+Nj7eRepzVerYFct/SPP/4Qv3ym+tFsxf/93/8RgEahsCXYM/ySe+/6OycXFxeb7axvyXC3PvbwfhwBe6cRctqwsTWQ63llZ2cTAOratWsLS1Y3rcDwZW+4vbtcbNmJKrfDvrl7Gz5dunQhPz8/Cg0NNar/5ptv2t17sRaO4+jo0aO0YcMGOnr0qNOnUGotrPG82k1WCakYskn06NGjxe/l7++PPn36AKjbhswaVCoVNm3aZDJ9NSAvC6yHh4ese2/evNnoXk1RVlaG8vJyXLhwAUVFReLx1157DXv37m2UwSMwMBB79+51qN26TWHYxXvu3Lk2T6HEaJp2Y7ykfpla03gBwOjRowEAJ06csPpaplJLyzUCKpUK/fv3l/UCGtJINzRAQUFBiI6ORnl5OTQaDXJycnD9+vVGss6bNw+FhYVISEjAzp07kZCQgIKCAqcwXAYs0Vt7xxpdtZuUOBzHSTqvJVPhNMWYMWPw/fff45dffrH6Wtu3bwcAPProo3j66actTlPCcRw0Gg2GDh0qK9/SvHnzMHv2bJMpUnx9fc3WN3gvzoqlemvPSH0vm6LdaFjqbi6t7XlNmjQJffr0wcCBA626jl6vx65duwDU5QuzxggoFAr4+vpatAOOsxsga7BGb+0Va3TVboyXo4aNgwYNwoULF6y+TlxcHMrKytCtWzfcd999Vl1LpVIhNDTUapnaG0xv8rEmbGw3fV5S3VOD8WqtsNFWbNu2DUBdyGhtyMJxHFJTU61y6dsjTG/ysUZX7cZ4SU3La+jzai3PywDHcTh37pxFdcvLy7F//34AwJIlS6yWRalU4o477pCsM0YdTG/ysUZX7SZslKKk+rnrW9N4Xb16FQMGDEBtbS0qKirg7u4uq/6uXbug0+kwePBgDBkyxGp5lEolgoODrb5Oe4PpTT7WGK928xMhxT39888/wfM8FAoFunXr1gpS1REQEIAOHTrAy8sLFy9elF3/22+/BQD85S9/sYk8HMchOTmZhT8yYXqTDxttlIAUC2/wurp27dqqQ90KhQLJyckICQmRfd+cnBxkZGRArVZj4cKFNpFHqVSiT58+LPyRCdObfFjYKAEpSvL19cXatWvtMkfH0lGqqKgoAMDMmTPh7+9vE1kMfTcMeTC9yYcZLwlIcU+Dg4OxYcOGVpDGNESE2tpaSf1eWq1WHGW0RUe9AUP4Y8kGqu0Zpjf5sNFGCTiDK//NN9+gZ8+eeOeddySdn5CQgD///BOBgYGYPn26zeRQKpUICwtzCp05Ekxv8mEd9hKQoqSLFy+ioKAAtbW1rSBRY1xdXXHlyhX88MMPTS6wbsj06dORk5ODb775Bi4uLjaTQ6lUomvXruwllAnTm3yY8ZKAFPd09erV6N27tzh619rMnTsXXl5eyMvLw8aNG/HDDz8gMTERPM+brDNo0CBMmzbNpnLo9XocPnwYer3eptdt6zC9yadVw8YlS5YgOTnZ4hvaCykWXqlUwt3d3W6z6729vXHvvfcCAJ577jksXLgQkydPRkhICGJiYsTziAgFBQUtJodKpcLIkSNZdgSZML3Jp1U9r8rKSoSHh6Nv377YsGEDiouLLb55ayJFSfv27UN1dTVmzpzZChI1JiYmBnFxcY2OFxcXY/78+aIBi42NRd++fbFq1aoWkUOpVMLPz4+FPzJhepNPqxqv6OhoFBcXY/ny5dizZw9CQkIwffp07N2716HdZanuqUKhsMuXj+d5rFy5ssm+LsOxVatWged5JCQkgOd5uLm5tYgser0eBw8edOjn6Ygwvcmn1UcbO3fujJUrV0Kj0SAtLQ2hoaFYtGgRevTogdWrVyMvL89igVoKR3flU1JScOXKFZN/JyIUFRUhJSUFH374IVJSUvDSSy+1iCxqtRrjx49nw/0yYXqTj92ySpSUlCAuLg5xcXFQqVSIiIjAmTNnMHDgQGzcuNGaS9uc5vIGnTlzBvfccw+efPLJVpLIGMPsfqnnjRs3rtnkfpaiUCjg4+PD8lLJhOlNPtboSrbx0uv1iI6OxowZMxAcHIw9e/Zg9erVKCkpwXfffYe4uDhs374d69evt1iolqA59/TSpUtIS0tDdnZ26wjUAKmDBJ6eni0sSd0z/umnn1j4IxOmN/m06trGgIAACIKAxx57DGlpaU1mMZg2bRo6depksVAtQXPuqb3zeI0fPx6BgYEoLi42O8fr1q1bLS6LWq1GeHg4C39kwvQmn1bNYb9x40Y8/PDDZpev+Pr6tuhQfkvQ2hlUG2LYgWf+/PlQKBRNGrBvvvkGixYtahV52AtoGUxvrYfssHHRokWy8005AuYmegKtv/FGUzS3A09r9cdxHIfY2FiW2kUmTG/yae69NEe7+ZmQGjbay/My0NwOPK2BWq1GREQE8yJkwvQmH7b1mQ1wFOMFOMYOPBzHsZfQApjeWo92MxW4OffU3h32jgTHcYiLi2Phj0yY3uTDwkYJmPs15Hkef/zxBwDH8LzsjYuLC2bPnm1vMZwOpjf5WOOlthvPy9z0A0PuekNKk/YOEeHWrVuS0vIw/gvTm3ys0VW7MV7m3FNDyNjauesdFY7jkJKSwsIfmTC9yYeFjRIwZ5TstVejo+Li4oIHH3zQ3mI4HUxv8mFhowQEQTD5N9ZZb4wgCCgvLzerM0ZjmN7kY42umPECMGTIELz88st4+OGHW1Eix4XneaSnp1vl0rdHmN7kY43xYmEjgJEjR2LkyJGtKI1j4+LiYvPU0u0Bpjf5sLBRAsyVl44gCCgtLWU6kwnTm3xY2CgBc0rSaDTIz89nqUz+gyAIyMnJYS+hTJje5MOMlwTMuaczZsxAaGgoTp061YoSOS5qtRpTpkxh00ZkwvQmHxY2SsCUhScieHl5wcPDg402/gdBEFBcXMw8CJkwvcmHeV4SMKUkhUKB8+fPo6qqihmv/yAIAvLz89lLKBOmN/mw0UYJNOeesrzj/0WtVmPChAn2FsPpYHqTDwsbJcB+DaUjCAIuXbrEdCYTpjf5OHXY+MUXX6BXr15wd3fH8OHDkZKSYvLcxMREKBSKRp9z5841ex9TSvr+++8xYsQIbNiwweI2tDVY341lML3Jx2mN148//ohVq1bh5Zdfhkajwfjx4zF9+nRcvnzZbL3z58+jpKRE/PTt27fZe5lyT8+fP4/MzEwUFRVZ1Ia2iFqtxtixY9momUyY3uTjtGHjxx9/jCeffBJ//etfMWDAAGzatAlBQUH48ssvzdbr2rUrunfvLn6kpJI1tWTDsK6xYd749gzP87hw4QJb5iITpjf5WKMruxkvnU6HzMxMhIeHGx0PDw9Hamqq2bpDhw5FQEAApk6dioSEBEn3O3v2LLKyspCeno709HSUlJSA53lxl+pu3bqJiuQ4TnRnTZX1er1R2ZCXyFAmokZlAEZlQRCMyoZUKqbKPM8blQ3ymipzHGdRm4gI169fb9Q+Z25TazwnvV6PGzdugOO4NtOm1npOlmA341VWVgae59GtWzej4926dcO1a9earBMQEIAtW7YgOjoaMTEx6NevH6ZOnYrk5ORm77dkyRIMHz4co0aNwqhRo/DVV1/h1KlT4hZtNTU1YjktLU0MI1NTU8WUOcnJySgrKwMAxMfHo6KiAgAQFxeHyspKAEBsbCy0Wq3RTjJarRaxsbEAgMrKSsTFxQEAKioqEB8fL+rD0I6SkhLRgBcVFSEtLQ0AUFBQAI1GAwDIy8sTJ9Xm5uYiNzcXAHDq1Cnk5eUBqFs5YEmb1Go1ysrKUFNT02ba1BrPKSsrCyNHjkRRUVGbaVNLPyeD7BZBdqK4uJgAUGpqqtHxt956i/r16yf5OjNmzKCZM2ea/HtmZiYBoKioKMrMzKS0tDRKS0ujq1evEsdx5OfnRwBIo9EQx3FERKTX64nnebNlnU5nVBYEwagsCEKjMhEZlXmeNyrr9XqzZY7jjMoGeU2V9Xq9RW3iOI5ycnLEe7WFNrXGc9JqtZSbm0u1tbVtpk0t/ZxOnjxJACgzM5PkYreexS5dukClUjXyskpLSxt5Y+YYPXo0duzY0ex5AwcOxLBhw4yOabValJeXAwB69uwp9p3V70Q0VXZxcbGorFAoxLJSqYRSqZRcrt+3J6UspR1NtYnneeh0OnHuW1tok9yyJW1Sq9WoqamBSqUSZXb2NrX0c7JmfqXdwkZXV1cMHz4cR44cMTp+5MgRjB07VvJ1NBqNpJnxTXXqGzrr3d3d4evrK/mebR2VSoWhQ4e26l6RbQGmN/k47b6Nzz77LBYtWoQRI0ZgzJgx2LJlCy5fvoxnnnkGALB27VoUFxdj27ZtAIBNmzYhJCQEgwYNgk6nw44dOxAdHY3o6Ohm79XUqEZxcTGAupFGNsP+v/A8j9zcXAwYMIC9iDJgepOP0+awX7BgAa5fv47169ejpKQEYWFhiI2NRXBwMIC6zsP6c750Oh2ef/55FBcXw8PDA4MGDcLBgwcRERFh0f0daaNZBoMhD7vPplu2bBmWLVvW5N+ioqKM/r9mzRqsWbPGovs09UtY3/Ni/BeVSoWwsDB7i+F0ML3JxxoP1e7Lg1oLc2Ej87yM4XkeGo2GTbaUCdObfJxykqojwGbXm8bDw8PeIjglTG+th93DxtaiKff0scceQ2hoKMaNG2cHiRwXlUqF/v3721sMp4PpTT5OO9rYmjS1i/GsWbMwa9YsO0jj2HAcB41Gg6FDh7JFxjJgepOPNbuLt5uwkU2FkI5CoYCvry/TmUyY3uTjlJNUW5uG7qlWq0VSUhIuXLhgJ4kcF5VKhdDQUDZXSSZMb/Jho40SaOie5uXlYdKkSRg9erSdJHJcOI5DamqqVS59e4TpTT7W6KrdBOaGNVoGampq0LdvX3Tu3NlOEjkuSqUSd9xxRyOdMczD9CYfa3TVbo3XqFGj8Pvvv9tJGsdGqVSKqxwY0mF6k481xqvd/EQwV146HMchOTmZ6UwmTG/yYaONEmCuvHSUSiX69OnDdCYTpjf5MM9LAg2VtHDhQowYMULMJsn4L6zvxjKY3uTDjJcEGrqnGo0GmZmZdpLGseE4DvHx8Sz8kQnTm3xY2CiB+haeiHDp0iUAdRlUGcYolUqEhYUxD0ImTG/yYaONEqivpOvXr4ubSwQFBdlLJIdFqVSia9eu9hbD6WB6kw8LGyVQ3z01eF0BAQFwc3Ozl0gOi16vx+HDh8WtsRjSYHqTDwsbJVDfwrOQ0TwqlQojR45ky1xkwvQmHxY2SqAp48UmFDaNUqmEn5+fvcVwOpje5MPCRgk0FTYy49U0er0eBw8eZOGPTJje5MPCRgnUd+UNm3qwsLFp1Go1xo8fz3JSyYTpTT4sGaEE6ucNYp6XeRQKBXx8fOwthtPB9CYfls9LAixslI5er8dPP/3Ewh+ZML3Jh4WNEjC4p1VVVbh+/ToAFjaaQq1WIzw8nIU/MmF6kw9LRiiD/Px8AICvry86depkX2EcGPYCWgbTW+vRboyXYX+4gIAAbN26FevXr7ezRI4Lx3GIjY1la/RkwvQmH2v2bWw3PxMG99Tf3x9Lly61szSOjVqtRkREBPMiZML0Jh8WNjJsDvMeLIPprfVoN8bL4J7++9//RlJSEqqqquwskePCcRzi4uLYiygTpjf5WBM2thvjZXDl//rXv2LSpEksf70ZXFxcMHv2bLi4uNhbFKeC6U0+1oTY7cZ4ERF0Oh1GjBiB3r17IzQ01N4iOSxEhFu3boGI7C2KU8H0Jh9rdNVujBfP83B1dUVsbCzy8/Ph7e1tb5EcFo7jkJKSwsIfmTC9yYeNNkqAjQBJx8XFBQ8++KC9xXA6mN7kw8JGCQiCwJZtSEQQBJSXl0MQBHuL4lQwvcnHGl21K+O1aNEi+Pv7Y8eOHfYWx6HheR7p6elWufTtEaY3+VhjvNpNLKVWq/Hbb7+hrKwM/v7+9hbHoXFxccG0adPsLYbTwfQmHxY2SqC6ulqcHjF48GA7S+PYCIKA0tJSFv7IhOlNPixslEBeXh4EQUDXrl3RvXt3e4vj0AiCgJycHPYSyoTpTT4sbJTAhQsXADCvSwpqtRpTpkyxtxhOB9ObfFjYKIHs7GwAwOjRo+0riBMgCAKKi4uZByETpjf5sLBRAqdOnQIA3HvvvXaWxPERBAH5+fnsJZQJ05t8WNgogStXrkChUDDPSwJqtRoTJkywtxhOB9ObfFjYKJEhQ4agY8eO9hbD4REEAZcuXWIehEyY3uTj1GHjF198gV69esHd3R3Dhw9HSkqK2fOTkpIwfPhwuLu7o3fv3vjXv/4l+V75+fmIiYmxVuQ2D+u7sQymN/k4rfH68ccfsWrVKrz88svQaDQYP348pk+fLu6r2JCCggJERERg/Pjx0Gg0WLduHVasWIHo6GhJ96usrMT8+fOZAWsGtVqNsWPHsvWgMmF6k49VuiI7MmrUKHrmmWeMjvXv359eeumlJs9fs2YN9e/f3+jY008/TaNHjzZ5j8zMTAIgfhQKBQUFBRHHcdY3oI3CcRzl5eUxHcmE6U0+aWlpBIAyMzNl17Wb56XT6ZCZmYnw8HCj4+Hh4UhNTW2yzokTJxqdP23aNGRkZEhedE1EKCoqwv79+8HzvLgOjeM4o7LBnTVV1uv1RmX6T14iQ5mIGpUN9zeU6y8WFwRBTKViqszzvFHZIK+psqVtIiJcv369UfucuU2t8Zz0ej1u3LgBjuPaTJta6zlZgt2MV1lZGXieR7du3YyOd+vWDdeuXWuyzrVr15o8n+M4lJWVybr/zp07cerUKeTl5QEANBoNCgoKAABpaWkoKioCAKSmpqKkpAQAkJycLN4nPj4eFRUVAIC4uDhUVlYCAGJjY6HVao12ktFqtYiNjQVQF7rGxcUBACoqKhAfHy/qIzk5GQBQUlIiGvCioiKkpaUBqAubNRoNgLoVA4bpH7m5ucjNzQUAm7RJrVajrKwMNTU1baZNrfGcsrKyMHLkSBQVFbWZNrX0czLIbhGWO3zWUVxcTAAoNTXV6Phbb71F/fr1a7JO3759acOGDUbHfvnlFwJAJSUlTdZpGDYaPnv37iWO40QXX6/XG5V5njdb1ul0RmVBEIzKgiA0KhORUZnneaOyXq83W+Y4zqhskNdU2dI2cRxHOTk54r3aQpta4zlptVrKzc2l2traNtOmln5OJ0+etDhstFvPYpcuXaBSqRp5WaWlpY28KwPdu3dv8ny1Wo3OnTtLuq9CoUBgYCDmzJljtO1S/Y5DKeX6ecrllBUKhVhWKpVQKpWSy/XllVK2tE08z0On00GhULSZNsktW9ImtVqNmpoaqFQqUWZnb1NLPyfDd8wS7BY2urq6Yvjw4Thy5IjR8SNHjmDs2LFN1hkzZkyj8+Pi4jBixAiTmx78+eefYtmgqE2bNlm1X1xbp7S0FD/99BNKS0vtLYpTwfQmn/LycgDG76lkZPtqNmTXrl3k4uJCW7dupbNnz9KqVauoQ4cOVFhYSEREL730Ei1atEg8/+LFi+Tp6UmrV6+ms2fP0tatW8nFxYX27t1r8h47duwQQ8WgoCCKjo5u8XY5O4YRoLS0NHuL4lQwvcln27ZtBIB27Nghu65dJ6QsWLAA169fx/r161FSUoKwsDDExsYiODgYQF3nYf05X7169UJsbCxWr16Nzz//HD169MAnn3yChx56qNl7rV27Fv/85z+Zx8VgtBHsPptu2bJlWLZsWZN/i4qKanRs4sSJyMrKkn2fQYMGMcMlkab6axjNw/QmH0OfmiXY3Xi1NLW1tQCAixcvWmT02iNnzpwx+pchDaY3+Vy8eBHAf99TWbRAGOtQfPrpp01OlWAf9mEfx/l8+umnst/tNu95Pfroo/D19UVISAg8PDzsLQ6DwahHTU0NCgsLLdq4REHE9iZnMBjOh91T4jAYDIYlMOPFYDCcEma8GAyGU9KmjZfcLK3tneTkZMycORM9evSAQqHA/v377S2Sw/POO+9g5MiR8Pb2RteuXTFnzhycP3/e3mI5PF9++SXuvvtu+Pj4wMfHB2PGjMGhQ4dkXaPNGi+5WVoZQFVVFQYPHozPPvvM3qI4DUlJSfj73/+OX3/9FUeOHAHHcQgPD0dVVZW9RXNoAgMD8e677yIjIwMZGRmYMmUKZs+eLW+OnM0nVjkIcrO0MowBQPv27bO3GE5HaWkpAaCkpCR7i+J0+Pr60jfffCP5/DbpeVmSpZXBsAU3b94EAPj5+dlZEueB53ns2rULVVVVGDNmjOR6bXKSqiVZWhkMayEiPPvssxg3bhzCwsLsLY7Dc/r0aYwZMwZarRZeXl7Yt28fBg4cKLl+mzReBhomOiMiq5KfMRjmWL58OU6dOoVffvnF3qI4Bf369UN2djYqKioQHR2NyMhIJCUlSTZgbdJ4WZKllcGwhn/84x/497//jeTkZAQGBtpbHKfA1dUVoaGhAIARI0YgPT0dmzdvxldffSWpfpvs87IkSyuDYQlEhOXLlyMmJgbx8fHo1auXvUVyWohIVnaJNul5AcCzzz6LRYsWYcSIERgzZgy2bNmCy5cv45lnnrG3aA7L7du3ceHCBfH/BQUFyM7Ohp+fH3r27GlHyRyXv//979i5cyd++ukneHt7i95+x44dWSIAM6xbtw7Tp09HUFAQKisrsWvXLiQmJuLnn3+WfpEWGvV0CD7//HMKDg4mV1dXGjZsGBu+boaEhIQm05VERkbaWzSHpSl9AaBvv/3W3qI5NEuXLhXfTX9/f5o6dSrFxcXJugbLKsFgMJySNtnnxWAw2j7MeDEYDKeEGS8Gg+GUMOPFYDCcEma8GAyGU8KMF4PBcEqY8WIwGE4JM14MBsMpYcaLwWA4Jcx4MZyGSZMmYdWqVfYWg+EgMOPFYDCcEra2keEULFmyBN99953RsYKCAoSEhNhHIIbdYcaL4RTcvHkT06dPR1hYGNavXw8A8Pf3h0qlsrNkDHvRZvN5MdoWHTt2hKurKzw9PdG9e3d7i8NwAFifF4PBcEqY8WIwGE4JM14Mp8HV1RU8z9tbDIaDwIwXw2kICQnByZMnUVhYiLKyMgiCYG+RGHaEGS+G0/D8889DpVJh4MCB8Pf3x+XLl+0tEsOOsKkSDAbDKWGeF4PBcEqY8WIwGE4JM14MBsMpYcaLwWA4Jcx4MRgMp4QZLwaD4ZQw48VgMJwSZrwYDIZTwowXg8FwSpjxYjAYTgkzXgwGwyn5f5n4QqoIBHaAAAAAAElFTkSuQmCC", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(3, 2.3))\n", "\n", "Tc = np.arange(0, 3, 0.01)\n", "yc, t = step(P, Tc)\n", "ax.plot(t, yc, ls='-.', label='continuous', c='k')\n", "\n", "xold, xold2 = 0.0, 0.0\n", "\n", "Td = np.arange(0, 3, ts)\n", "u = 1.0*(Td>=0)\n", "\n", "# プログラム ================\n", "for k in range(len(Td)):\n", " x = u[k] - a1*xold - a2*xold2\n", " y[k] = b1*xold + b2*xold2\n", "\n", " xold2 = xold\n", " xold = x\n", "# ========================\n", "\n", "ax.plot(Td, y, ls='', marker='o', label='discrete', c='k')\n", "\n", "plot_set(ax, 't', 'y', 'best')\n", "ax.set_xlim([0, 3])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 最適制御" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [], "source": [ "import control as ct\n", "import control.optimal as obc\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 有限時間最適制御" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "1次系" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1.+0.j]\n" ] } ], "source": [ "P = ct.ss(1, 1, 1, 0) # システム dxdt=x+u,y=x の記述\n", "sys = ct.ss2io(P) # 状態空間モデルを入出力モデル変換\n", "print(sys.poles())\n" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [], "source": [ "xf = 0 # 基準状態,終端状態\n", "uf = 0 # 基準入力\n", "Q = 50 # 状態に関する重み\n", "R = 0.1 # 入力に関する重み\n", "\n", "# 評価関数の設定\n", "cost = obc.quadratic_cost(sys, Q, R, x0=xf, u0=uf)\n", "\n", "# traj_cost = obc.quadratic_cost(sys, R, R, x0=xf, u0=uf)\n", "# term_cost = obc.quadratic_cost(sys, Q, None, x0=xf)\n", "\n", "# P = 100\n", "# term_cost = opt.quadratic_cost(sys, P, 0, x0=xf)\n", "\n", "# 制約条件の設定\n", "umin, umax = -4, 4\n", "constraints = [ obc.input_range_constraint(sys, [umin], [umax]) ]\n", "terminal = [ obc.state_range_constraint(sys, [xf], [xf]) ]\n" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Summary statistics:\n", "* Cost function calls: 3535\n", "* Constraint calls: 3672\n", "* Eqconst calls: 3672\n", "* System simulations: 1\n", "* Final cost: 5.585715123369499\n", "最適化成功: True\n" ] } ], "source": [ "Td = np.arange(0, 0.5, 0.01) # シミュレーション時間\n", "x0 = 1 # 初期状態\n", "\n", "# 最適制御問題を解く\n", "result = obc.solve_ocp(sys, Td, x0, cost=cost,\n", " constraints=constraints, terminal_constraints=terminal)\n", "# result = obc.solve_ocp(sys, Td, x0, cost=traj_cost, terminal_cost=term_cost,\n", "# constraints=constraints)\n", "print('最適化成功:', result.success)\n" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Final_computed_state: [0.]\n" ] } ], "source": [ "print(\"Final_computed_state:\",result.states[:,-1]) # 終端状態\n" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Final_simulated_state: [0.00570882]\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "resp = ct.input_output_response(sys, Td, result.inputs, x0)\n", "# t, y = ct.initial_response(sys, Td, x0)\n", "\n", "print(\"Final_simulated_state:\", resp.states[:,-1]) # 終端状態\n", "\n", "fig, ax = plt.subplots(1, 2, figsize=(6, 2.3))\n", "ax[0].plot(resp.time, resp.outputs, c='k')\n", "ax[1].plot(resp.time, resp.inputs, c='k')\n", "# ax[0].plot(t, y)\n", "\n", "ax[0].set_xlim([0,0.5])\n", "# ax[0].set_ylim([0,1])\n", "ax[1].set_xlim([0,0.5])\n", "ax[1].set_ylim([-5,1])\n", "plot_set(ax[0], 't', 'x')\n", "plot_set(ax[1], 't', 'u')\n", "plt.tight_layout()\n", "# fig.savefig(\"c7_obc.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "2次系" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [], "source": [ "A = [ [0, 1], [-4, -5] ]\n", "B = [ [0], [1] ]\n", "C = np.eye(2)\n", "D = np.zeros([2,1])\n", "P = ct.ss(A, B, C, D)\n", "sys = ct.ss2io(P)\n" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [], "source": [ "xf = [0, 0]\n", "uf = 0\n", "Q = np.diag([100, 1])\n", "R = 0.1\n", "cost = obc.quadratic_cost(sys, Q, R, x0=xf, u0=uf)\n", "\n", "constraints = [obc.input_range_constraint(sys, [-15], [15])]\n" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Summary statistics:\n", "* Cost function calls: 15351\n", "* Constraint calls: 15704\n", "* System simulations: 1\n", "* Final cost: 29.16562957646857\n", "最適化成功: True\n" ] } ], "source": [ "Td = np.arange(0, 1, 0.01)\n", "x0 = [1, 0]\n", "result = obc.solve_ocp(sys, Td, x0, cost=cost, constraints=constraints)\n", "print('最適化成功:', result.success)\n" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "resp = ct.input_output_response(sys, Td, result.inputs, x0)\n", "\n", "fig, ax = plt.subplots(1, 2, figsize=(6, 2.3))\n", "ax[0].plot(resp.time, resp.outputs[0], label='x1')\n", "ax[0].plot(resp.time, resp.outputs[1], label='x2')\n", "ax[1].plot(resp.time, resp.inputs[0])\n", "\n", "ax[0].set_xlim([0,1])\n", "ax[1].set_xlim([0,1])\n", "# ax[1].set_ylim([-5,1])\n", "plot_set(ax[0], 't', 'x', 'best')\n", "plot_set(ax[1], 't', 'u')\n", "plt.tight_layout()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### モデル予測制御" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [], "source": [ "A = [ [0, 1], [-4, -5] ]\n", "B = [ [0], [1] ]\n", "C = np.eye(2)\n", "D = np.zeros([2,1])\n", "P = ct.ss(A, B, C, D)\n", "# 離散時間モデル\n", "Pd = ct.c2d(P, 0.1, name='plant')\n", "sys = ct.ss2io(Pd)\n" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [], "source": [ "xf = [0, 0] # 基準状態\n", "uf = 0 # 基準入力\n", "Q = np.diag([100, 1]) # 状態に関する重み\n", "R = 0.1 # 入力に関する重み\n", "\n", "# 評価関数\n", "cost = obc.quadratic_cost(sys, Q, R, x0=xf, u0=uf)\n", "\n", "# constraints = [opt.input_range_constraint(sys, [-10], [10])]\n", "# constraints = opt.state_range_constraint(sys, [-1.5, -2], [1.5, 1.5])\n", "\n", "# 制約条件\n", "xmin, xmax = -1.5, 1.5\n", "umin, umax = -8, 8\n", "constraints = [obc.input_range_constraint(sys, [umin], [umax]),\n", " obc.state_range_constraint(sys, [xmin, xmin], [xmax, xmax]) ]\n" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [], "source": [ "# MPC制御器の設計\n", "N = 5 # 予測ホライズン\n", "ctrl = obc.create_mpc_iosystem(sys, np.arange(0, N)*0.1,\n", " cost, constraints, name='controller')\n", "\n", "# print(ctrl)\n", "# print(sys)\n" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [], "source": [ "# 閉ループ系の定義\n", "loop = ct.interconnect(\n", " [sys, ctrl], #制御対象と制御器の結合\n", " connections=[ #信号の接続\n", " ['plant.u[0]', 'controller.u[0]'],\n", " ['controller.x[0]', 'plant.y[0]'],\n", " ['controller.x[1]', 'plant.y[1]']\n", " ],\n", " outlist=['plant.y[0]', 'plant.y[1]', 'controller.u[0]']\n", ")\n", "\n", "# Define an I/O system implementing model predictive control\n", "# loop = ct.feedback(sys, ctrl, 1)\n", "# print(loop)\n" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [], "source": [ "# シミュレーション\n", "Td = np.arange(0, 2.1, 0.1) #シミュレーション時間\n", "X0 = [1, 0, 0, 0, 0, 0, 0] # 初期状態 [1,0]+予測ホライズンの初期値\n", "resp = ct.input_output_response(loop, Td, 0, X0)\n" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "image/png": 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fTlpaGq+88gpbtmxxry/kanGaP38+06ZN41e/+pX72a5anCoqKggLC+vQ4lRUVMQdd9xBQUGBu9woeo6rjtqyZQtZWVmBNsdnyNrtI6sukFdbXl4es2bN8nkdJb3jtHXrVjIyMgJtjs8QQri7fmQaVBpMulpbWykrK2P06NFERET0+X3i9GJvrpkk/uQnP/kJ7733Ht988w0DBw7kkksuITo6mg8++ADA7fT88Ic/ZMKECfzkJz8hLCyMyZMnd/q+7uKioKCAmTNnKsfJS1QdFVrIqgvk1eavOkquDs3zBFcGlw1ZdfUXGzZs4MUXX2T9+vXuGTIrVqzgggsu4LXXXuPee+91twaCs1J5++23SU1N9d9CcYrzElnLsqy6QG5tvkb6dZz8uex6IHA4HOTm5ko3E0dWXeD8NVdfX9/twGJfsHDhQux2OxdffLH73MiRI6mtreXee+9123L24a3TJFvZChSyxaOsZVlWXSCvNn+VLendS9k8aKvVyvXXXx9oM3yOrLrAORYqJiYm0Gb4HNnKVqCQLR5lLcuy6gJ5tfmrbMlVYjtBtiFcQggaGhr6ZSXq/kRWXeDUZhgGJpNJKm2yla1AcfYEi1CfwGIYBk1NTe6NrWWZwCKEwGw2M336dBwOR0AnsLQnOTmZ5ORk6uvrPRZoBedEkilTpgDOffXOblEaP348AwcOpKKigrKyMo/NyOPj4xk5ciTNzc3s2bPH4zmTycSFF14IwO7duztMcBkzZgwxMTEcO3aMo0ePelyLiYlhzJgx2Gw2ioqKOmi98MILMZlM7Nu3j8bGRo9rI0eOJD4+nurqag4dOuRxbeDAgYwfP95jAsvZae8zfDpHL4hQe9WFFsGkS9a96rxB7VXnP9SSKaG3ZEpWVpaw2WwBXzKl/bF06VIhhBAff/xxh2tpaWnu98bHx3e4vnnzZiGEEA8//HCHa/fdd1+X+TQ6Otr93smTJ3e4vmbNGiGEEM8880yHa9/97neFEEJUVFR0qrW1tVUIIcSCBQs6XHv99deFEEK8/vrrHa4tWLBACNE/S6ZIP6tOzfhR9BZfz6oLZbqLC1XG+oYr/t566y13iw2EfovT2V8psrQ4AQwePJi0tLSAL9LbHl+0OB0+fJiqqiqPa7K0ON16661qOYKe4qqU8vPzmTlzZqDN8RmGYVBbW0tMTIx7M0UZCCZd/liOQNd1zGZzyHXVdRcXW7duJTMzUzlOXqLqqNBCVl0grzZ/1VHyxFAXnL14YKij6zr5+fnSzcSRVRc4HaempibpxgTJVrYChWzxKGtZllUXyKvNX2VL+sHhMs5YWbRoUaDN8Dmy6gJns/bgwYMDbYbPka1sBQrZ4lHWsiyrLpBXm7/KlmpxCjEMw6CqqkrpCiGEENjtdtXipOgU2eJR1rIsqy6QV5u/9CjHKcQwDIOioiKlK8Q4ewCqDMiaVv2NbPEoa1mWVRfIq0111XmJbM3gFouFSy+9NNBm+BxZdYFzFo9rCxSZkK1sBQrZ4lHWsiyrLpBXm+qqAzZt2sR1113HsGHD0DSN999//5zPyOhBHzlyROkKIYQQ2Gy2gHfV/eMf/+CKK64gISGBQYMGMWfOHNauXev1+2RMq0AgWzzKWpZl1QXyalNddUBTUxPTp0/n1Vdf7fEzMmaE0tJSpSvEaGtrC7QJbNq0iSuuuIKcnBwKCgq45JJLuO666ygsLPTqfbKmVX8jWzzKWpZl1QXyalNddcBVV13FVVdd1atnZGwGnz9/fqDN8Dmy6gJnV110dLTfP+fEiRNMmzaNhx56iMcffxyALVu2MG/ePD744ANefPFFj/ufeeYZ1qxZw7/+9S/3goC9QbayFShki0dZy7KsukBebaqrzku2H6qhttkWaDN8hmEYHDx4UMpfBkGrSwiwNXl9iLZG2hpOIdoae/98L7r3EhISeOONN3jyySfZunUrjY2N3Hrrrdx3331kZ2d3uN8wDBoaGoiNjfUqWoIyrUIQ2eIxqMtyH5BVF8irTbU4eclP3y/i6a9biYs0kTrYwrQRQ8hIG8qkodGMSRyEMHQ0TcNsNuNwODCZTJhMpi7Ddrsds9nsDlssFjRNc4cBHA6HR9hqtSKEcIcNw0DXdXfYMAwsFkuXYV3XEUJgsViw2+0cPnyYlJQU95gZs9nsXrjMpSOUNOm6jsPh4MiRIwwdOhSLxRJQTa6tHYRrc15HCzwzzOs8qAHhXj4r/vsIhDk33jQMA03TugwDXHnllfzwhz/klltuYebMmURERPDss8+6NxkWQiCEwGQy8dxzz9HU1MT3vvc9d17SNK1D2PV/+/RwpZmi78j4ZXXkyBFSUlKkWoVaVl0grzY1xslLHA3OvZFOthhsO2bjzfzjPLTyG6548QumLl3Llc9/xoN/+YpPdh/n6y1b3Ps7bd68mcrKSsA5NqS6uhqAdevWUVtbC0Bubq57P6KcnBxaW1txOBzk5OTgcDhobW0lJycHgIaGBnJzcwGora1l3bp1AFRXV7Np0yYAKisr2bx5MwAVFRXk5eUBUFZW5h6HUlZWRlRUFBaLheLiYvc+TDt27HDv9VRYWOjeTyovLy/oNZWUlLB7927mzp1LSUlJwDV9+eWXgNNROHu/qf6mobHR7aA0NDS4nZf6+np3pVBfX+92cOrr6/n1r3+Nw+Hgb3/7G3/9618JCwujvr4eOKPpnXfe4amnnuKNN94gMTERu93u3hfKZrO590Cz2WzYbM4W25KSEnbs2AE494A6e68ohXfI2FU3d+5cpSuEkFWbv/SE7F51mqaxevVqbrjhhk6vu/aBWr58OWMmTKGspo2DdQ6qHeGU1zrYe7yBVrunNzoyNpK3fziL4bEDgrZ1xmazUV5eTlpamttuGVqcdF3n0KFDjBw5ErPZHFBNjY2NHD58mFGjRhEeHo5J0xC2Jne+6651prOwYRjYbDbCw8+0O/X4PZZI6KaV6ewWJyEEu3fvJjMzE7vdzurVq7n22mvdrUxCCFauXMnixYtZtWoV11xzTbef39LSQllZGWPGjMFqtXrkt61btzJ79my1V52XuOqovLw8MjMzA22Oz9B13b2/odlsDrQ5PkNWXSCvtvz8fLKysnxeR8nlXnbCpEmTyMqaybyzzuuGoPxkE8WV9Ww7WMt7BRVYzSaGxUQBTk+11a4TYfL0Wl1fHr0Na5rmDru+3Hsabp+RTSYTdXV1bqfDRft72p/vSTjQmsxmM0IIampqGDVqlPtaoDVpmua2Vwsf6L63/Ta9PQoLga43Q1iUxya/vX1P+yb0rsJ2u51bb72V73//+0ycOJHFixezc+dOkpKSAFi5ciU/+MEPeOedd7j22mvPfE57u84Ku/4/O81CbcNif/Pkk0/y1FNPeZxLSkri2LFj3T4Xor9du6R9WZYJWXWBvNr8VbZCynFqbGxk//797v/LysrYvn07sbGxjBw5stNnumqqM5s00hIGkpYwkGsvGMZ/ZY/nSG0LJpPzy6DVrjP/V+uZkxbHU9+aQkxUmO8FeYHFYpHq16kLWXWB0/kYMGBAv3zWT3/6U+rq6nj55ZcZOHAgH330EYsXL+aDDz7gnXfe4fbbb+ell15i9uzZ7i/0yMhIr/bSk61Z3xdMmTKFTz/91P1/T369yxaPspZlWXWBvNrUrDpg69atpKenu6dOP/roo6Snp/PEE090+UxPd3seEG5hfNKZKeMb952gqqGNgoM1DAwPnopN13X27Nkj3S7WsuoC56+elpYWv7csbNiwgRdffJEVK1YwaNAgTCYTK1as4IsvvuC1115j2bJlOBwO7r//fpKTk93Hww8/7NXnyZhWfcVisTB06FD3kZCQcM5nZItHWcuyrLpAXm3+0hM8HkEPWLhwYb81ay+aMpQPHryYk002LGanf2lzGNz6xy38W0YK/zZjuPt8fyPjvmcgry7on+6YhQsXumcEuhg5cqR7kPy9997rdxvOd0pKShg2bBjh4eHMmjWLZ555hjFjxnT7zO7duz3G9A0fPpzExEQgdMcsuiYXnD0TM5Q16bpOS0uLVJra62hubu6QZqGuSc2q85K+DHSbmjKYBePP/GLM2VlJXvkp/t/fd3LlS5+zdtexfh+fYDabSU9Pl2oAH8irC5xddVFRUdKNCZIxrfrCrFmz+Mtf/sLatWt5/fXXOXbsGHPnzuXkyZPdPnfnnXeSkZFBVlYWWVlZLFu2LKRnyR44cACTyYTZbJZq5u+uXbtIT09n37590mhyzZLdt28fYWFhmM1maTQVFxdz8OBB/EHIzqo7F/6YsdJsc/D2lkP8dv1+apqdv+xnjIxhyVWTyBrt3SKCvUXXdYqLi5k0aZJUX1zBpKu1tdU9wyQiIqLP7xNC0NraSkRERMg5T93Fhb9mrMhCU1MTaWlpPPbYYzz66KMdrref+Ttt2jRpWpxsNht79uxhypQpbq0ytM7ous6+ffsYP358wGf++rp1pqs0C2VN/pz5G1JddYEmKszCD+eN4XuZI/jDxgP86Ysyth2q5XvLvuKyiYk8duVEJgz1/9YaCoUi+BkwYADTpk1z/3rvismTJ3dbqYfiLNmuzoeypvbhYJn560tNnd0jiyZfo7rqvGBQhJUfL5rAxp8s5JZZIzGbND7bU8WVL23iv1Z9w+GaZp9/pguz2czUqVMD3irja2TVBc5KITIyMuRam86FjGnlS9ra2iguLiY5Obnb+2SLR1nLsqy6QF5t/tIjvePkz1kCiYMi+Pm3p/HJj+ZzzbRkhIC/bzvMpc9t5Gcf7Kamyfd75Om6TmFhoZSzH2TUBc6uuubmZunW65ExrfrCj3/8YzZu3EhZWRlbtmzhu9/9LvX19dxxxx3dPidbPMpalmXVBfJq85ce6R2n/mBMwkB+e8sM1tx/EXPGxGHTDf74RRlXvrQJm8P3o/ojIyN9/s5gINh0+dLRCdXWJtmcPX9y+PBh/v3f/50JEybwne98h7CwML7++mtSU1MDbVq/E2xl2VfIqgvk1uZrpB/j1J9Nj9NHxPD2XbPYVFLNLz/aw+WTkwiznPFNdUNgNvXtC9RsNjNx4sS+mhp0BJMuV197c3OzTyoTV1ddKOKaotx+XIIL2Zr1+8rKlSu9ek62eAymsuxLZNUF8mrzV9mS3nHq7x3cNU1jwfgE5o2Nx95uDYmvSk/yP+/vZMlVk7hicpLX73c4HBQWFpKeni7VisPBpMtsNhMTE0NVVRVAn5cScC2AGUrjnFzdi1VVVcTExHRaAfV32ZIV2eIxmMqyL5FVF8irzV9lS54Y6oJAfVGZTBrhpjNfNr/fWErpiSY27TvRJ8dJ0zSGDBkSMl/APSXYdA0dOhTA7Tz1BddUW9fU3FAiJibGHRdnE2paghXZ4jHYyrKvkFUXyKvNX3qkd5yCpRn8lZvTeX3TAW6fM8p97sCJRgwhGJvY8yUMzGYzY8eO9YOFgSXYdGmaRnJyMomJiR1W4z5fsFqt3ZafYClboY5s8RhsZdlXyKoL5NWmuuq8JFiawQdFWPmv7Ake557+YDeb9p3gezNH8Mjl4xk6+NyLLTocDvLy8sjKypKuSTUYdbVfs8VbglVbXwmWshXqyBaPMud3GXWBvNr8Vbakn1XnrwWw+kqrXSfMbMIQsDK/goXPrefZj4qpbe5+CQOTyURKSkrQ6vIWWXWBvNpk0xMoZItHmfO7jLpAXm1qAUwvCdaMEGE184fbZ/L3e+cwM3UIrXaDZRsPMO9X63l1XQlNbZ17yiaTidTU1KDV5S2y6gJ5tcmmJ1DIFo8y53cZdYG82pTj5CXB3gyekRrL3+6Zwxt3zmTi0GgaWh08l7uPBb9ez5+/LKPN4bmAl8PhYNOmTUGvq7fIqgvk1SabnkAhWzzKnN9l1AXyalNddV4SCh60pmlcOjGJnIfm8dJNFzIqLorqRhtP/Ws3lz63kVVbK3DozqUNTCYTaWlpIaGrN8iqC+TVJpueQCFbPMqc32XUBfJqUy1OXhJKGcFk0rj+whQ+eXQBz3x7GkmDwjlS28Jj7+1g0Yub2HLgpNR90TLqAnm1yaYnUMgWjzLndxl1gbzalOPkJaHY9Gg1m7h51kg2/uQSfnr1JIZEWSk90URkmBmHw8G6detCUld3yKoL5NUmm55AIVs8ypzfZdQF8mpTC2B6SSh70BFWM3fNH8NNWSNYt6eKC4bHYBgGU6dOZdnnZQwfEsU105KxmENXowuTycTUqVNDOr26QlZtsukJFLLFo8z5XUZdIK82f+lRjlMIEB1h5foLU4DTeiIG8dKnBdh0gxGxUcwYOSTAFvYdk8lEYmJioM3wC7Jqk6FsBQOyxaPM+V1GXSCvNtVV5yWyNT3a7Xa+3LSBexeMJntykofTtH5PFdWNbQG0znvsdjtr166VcpVuWbXJVrYChWzxKGt+l1UXyKtNddV5iWy/5sxmMwvmZnF9TIyHtpomG/f9dRuGENw4czh3zRtDatyAAFraO8xmM5mZmdJtPwHyapOtbAUK2eJR1vwuqy6QV5tqcfIS2Solk8lEbGxsB13VjW2MTxpIm8Pgra8PcclzG7j/r9soOFiDECJA1vacrnTJgKzaZNMTKGSLR5nzu4y6QF5tynHyEhmbwT/88MMOTarjkqJ5//6LeOeu2VwyIQFDwIc7K/m31zZzyXMb+M0n+zhwojFAVp+brnTJgKzaZCtbgUK2eJQ1v8uqC+TVprrqvES2pkeLxcK8efM63YhR0zTmpMUxJy2OPcfqeX1TGTk7Kyk/2czLn5Xw8mclXDB8MNdfmMJ105NJjD73psL9RXe6Qh1ZtclWtgKFbPEoa36XVRfIq81fZUv6FidN0wJtgk/RNI1BgwadU9fEoYN4/nvT2fo/l/PC96ezcEICZpPGjsN1/N8Hu5n9zGe8+Om+frL63PRUVygiqzbZ9AQK2eJR5vwuoy6QV5u/9EjvOMnYDL5mzZoeN6kOCLfw7fThLP+PLLY8fhlPfWsK6SNjMASMS4x231dZ18K/vjnKiYbAzMrrra5QQlZtspWtQCFbPMqa32XVBfJqU111XiJjM3h2drZXTarxA8O5Y+4o7pg7ioMnm0gadKar7r2th3n+k31cPW0ov7slAwAhBNWNNhKiw31mf1f0RVewI6s22cpWoJAtHmXN77LqAnm1+atsyRVL5wm+yNxnL1UQFW5hcvIg5qbFu8+VVTdx6fMbSUsYwOwxccweE8esMbF+GxslW6Ftj8zaFIqzkTW/y6oL5Nbma0Kuq+53v/sdo0ePJiIigoyMDD7//PNu79d1vZ8s6x8cDgc5OTk+b4JcfPFoch6exy2zRrrP7a6sR9Og9EQTf91yiAffKSTr559x2fMbeGRlIb9dv5+Pi45ReqIRh2706fP9pSsYkFWbbGXLV6g6Ss78LqsukFebv8pWSLmY7777Lo888gi/+93vuOiii1i2bBlXXXUVu3fvZuTIkZ0+I2Mz+NVXX+23XwftB9Nde8EwLh4bT17ZKb4+cIqvD5yk+Fg9pSeaKD3R5PGc1awxKm4AU4YN4sWb0t3ndUNgNp17gJ6/dQUSWbXJVrZ8gaqjgje/t9h0TjS0caKxjRMNbVSf/lvTbMOuC4QQGEJgCDCEQJz+awgwDIEuBMIYxmfv7STMYibMYiLMbCLcaiLcbHL+f/pcmMVMhNVEpNVMRJiZSOvpI8zzb4TV3KP60d8Ea5r1laDpqvv000+5/PLLO722bNky7r777j4b1RW/+c1vWLx4MT/84Q8BePHFF1m7di2vvfYazz77rN8+N9hwOBz9lsFjosLInjKU7ClDAahttrG1vIa9xxvYX9XI/qpGSk800mzTKalqxHTWLIZv/+5LjtS08PodM93bw2yvqKXgYA0J0eEkRoeTEB1O/MAwrKL/dHmNYYC9CdoaQW8DQz99OECc/nv2Od2BYbNBeARo2unDBJz+q2meYc0EJguYzM6/mhlMpnZh1zVzu/9dR8g1IkuFqqOc9Gcd1Z6q+lbyyk+x7WAtlXUtHg5Sky04W/bCLKZuHauoduciTt8XbjURYTERbnU6aOGnHbUIi/Oa6/9wixmr2YTVrBFmMWE1Ox07UyfOWqDSLBTpdSxdc801PPDAAzz77LOEhYUBcOLECX7wgx/w5Zdf+s1xstlsFBQUsGTJEo/z2dnZbN68ucvnZGwGz83N5eqrr8Zqtfb758dEhXH55CQun5zkPmcYgsr6VkqON6AbwuN8yfFGWuw60eFnstqmfSf4zScdl0KwaIJBUWEMDLcyINzCgDAzA8ItDAy3kBoXxWNXTnTf+89vjtLY6uDyyYnuMVeHTjaz/0QDFpPJXVlYzSbMJs3pj+D8a9JO/7W3ENFSyXDTSag7DHWHaao9jmhtIMJoxuJogrYG9NYGRFsDmq0Jk70Jjd6txK4B/h9efwZhsqBjRmhmDK39XxMC598z500ITBiahSEDI7CYnU5ZfZtBQ5vBgMgwYqLCQTPjQKOipu30e0wcqqjrR1VnePrpp7u9/sQTT/STJZ6oOspJf9VRQggqTrWwpewk+eWnyCs7RfnJ5m6fCbeYSHD/WHP+jRsQhtVswqQ5W9xNmoZJ43S94QybNA1h6BTt2sX4iZNxCLA5jDOHbtBmd/61OQzaHAZtDp02u0GLXafZ5qD1dLjFptNiP5PmrnfUtfTfjDaLqZ0jZTFhNWnYWlsYFD0Aq9nZCmYxa1hMGhaTyeN/s8mE2eSME5NJw+yKI3f49HnXPad/TLvr3dPx7KqTTa7fkrjOcfrHpDPs+i3ucb3d+e4o33PQ11EHeOE4bdq0idtuu41PP/2Ut99+m/Lycn7wgx8wefJkvvnmG3/YCEB1dTW6rpOUlORxPikpiWPHjnX53L7inVgsFnflNHz4cPcu0GazGYfDgaZp7rDJZMJkMnUZttvtmM1md9hisaBpmjsMnp67w+HAarUihHCHDcNA13V32DAMLBZLl2Fd1xFCYLFYMJlMXHvttZjNZrems8OB0JQ8KJzEARYPTWazmc8fW8ixuhZGxkW5z49NHMg104ae/jVoo6qhjcY2Bw6hcarJzqmmjhXIpORo/uuKcW5Nz+fu5eDJZsYmZBE/IAyTycTHRUd55qO97mc0DMZqRxmnHWaYdpIUrZph2kmGnf4bpzV0+JzOdvfrrLFXFxpthOHAhI4ZHdOZQ5jRNTOp8dFoJgtCM3G4poXGNjvJg8IYHGFBA5rabByra8WE4awgEJgQmDQDMwZmdMwYWDAwceac1STQRNdjyjTDgQUvxiq0W1h+0OmDdr6RBRjd7va6usB84a9evdrjf7vdTllZGRaLhbS0tIA5Tt7WUXv37lV1VA80aZqJAyeb2bz/BNsO1ZJXVsOx+laPuNQ0mDR0EBmpMYxNjCZ+YBhDIi0kDxlAbJSFSItGWFhYrzW5bb84zSeaNE2jsaUNmwFtDkF9cxsOAS12g4aWNuw6NNt0mtrs2HThDrc5oNXuoMWuY9MFrTadVruOTXc6ZW12p9PWaneet+sCm254/KAFcBgCh00H2pdhjeq27h3PUKPtWIVf3ttrx2nWrFkUFhZyzz33kJGRgWEY/OxnP+MnP/lJvyyedfZnCCG6/dzX/uduNh8+kzmWLl3K9ddfT2RkJBMnTqSwsJAhQ4YwduxY8vLySElJITU1lc2bN5OWlkZKSgqbNm1i6tSpJCYmsm7dOjIzM4mNjSU3N5d58+YxaNAgcnJy3NM5c3JyuPrqq92/vK6//noaGhr4/PPPueaaa6itrSU/P59FixZRXV1NUVERl156KZWVlZSWljJ//nwqKio4cuQIc+fOpaysjJqaGjIzM9m3bx8NDQ1kZmZSXFwMwNSpU9mxY0dQamqrP8mpA6WED5/PwYMHOXLkCFfPncv4yKbTmuayZ88eahuaGJw0gv3lFbTqgsSUVHbtKcGhWRgUm0B1ZQVlZWVuTRckhTM+KZqyPbtICR9HSkoKTeWF3Bl7gAn6fsa27WISZQyk+4qgmUgi4kdywhZO0rgM3tvTRmm9xvWzJjI8bhD7Dh6lNXEKL22qpF63YrcOotEIp1mYCQsLRxg6wtAJDw9H1x0IwyAiIhx0By9fnEB6ejpFO3fy26+rKWs0cX2alUvHxzJx4kRWf7yZFbtaiIiIoKmxgYjwcCLCw2morycyMoKIiHBqa2qJjh5IeFgYp06eZHDMIP70H7NZn/sx8y6aw/s7T7Bm807+Y+EkFk1K4LNP1jIxfRa/31hCzYnjDEuKB3sbdTUnGZoQh25vo6GuhqS4GBy2Npob64iPjcHe1sKs2DZmTZ9MVdUxtpQco45IkiN0Rg1wkDYqlQOHKvi8tJbogVG0NDVysKES+Iv3hdlLCgsLO5yrr6/nzjvv5Nvf/na/23M2va2jbr/9do//VR3lqWnA4FiW/uVTNh43c6LR80eVWRNcMDyGzFFD4EQpd3/ncqKsmlPT3Oupr6/n888/Z+4113Dq1CnWe6mppKSElpYW0tLSOHjwIJqm9bne3fz5RjIzMxkWG0vhl+tOp1MMa9as6TadXJquOa3JlU5VVVVuTUeOHHFrOnjwIBWHDzMzazZ7SvZTfaqWqdOmU7yvhMbmFsaOn8juvftos9kZM3Y8e/eVYLGGkZySwp69JUREDSA+MYk9e/YyKGYIg4fEsnffPuLiEogeNIi9+0pIHDqUqKgB7Nm7j2EpKYRHRLJn7z5GjBhBWHg4e/buY/To0aBplJYeYNTo0RiGQVn5QcaMSaO1rY0jR48yKjWVltZWqqqqGDFiJM0tzZw6eYphKSk0NjVRX1fP0ORkGhoaaGpuYmhSEnV19bS1tZGYmEBtbS0Oh058fBynTtVwwhKJ588s36AJL3aA3bZtGzfffDMOh4OjR49y00038corrzBgQGe/132DzWYjKiqKv/3tbx6V48MPP8z27dvZuHFjBxszMjJY+79XEn/Dz6X5Ndfa2sqnn37KokWL3BsYBkOLU1806bqO3W7ns88+47LLLsNqtZ5bk3BgOr4L/dDXmI4WoB0pgJryjhnHGoWROAVtSCra4OHoA4dhih0Jg4fjGJCMZUAsaJpfNLls7yrNQjGd2ue3vLw85s6dS0FBATNmzPCqXPuSoqIirr32WsrLywPy+d7WUX/+85+54IILVB11lo6axhbe2lLBG1+WU9PsdJgirCbSR8Qwa3QcWWNimTp0INFR4X7X5FUdFeTppOoo7+m14/SLX/yCpUuX8p//+Z/8+te/prS0lFtvvZX6+nreeust5syZ4zPjzmbWrFlkZGTwu9/9zn1u8uTJXH/99R0GXroqpYJHxzDjuf096xBVBDf2FtibAztWQel65+Dss4mfAMMzYXiG82/CJDCrAY/+wF3GgsRx+uKLL7juuuuoqakJmA1e1VFBEn/BwqkmG3/+sozlm8tpaHV2OafGRXHfwjRuSE8h3CLXLESF//BXGev1N8pLL73E+++/z1VXXQXAlClTyMvL4/HHH2fhwoW0tflvy45HH32U2267jZkzZzJnzhz+8Ic/cOjQIe65556uH2o8DlW7IWmK3+zqTwzDoLa2lpiYGPcvAxnoUpdhwMEvYcdK2P1PaKs/cy1yyGknKROGz4RhMyAypt9tPxcyp1kgePnllz3+F0JQWVnJihUruPLKKwNikwtv6qhAxaO/8Da/VzW08sfPy3jr64M0n54BNy5xIPdfMpZrL0jGYg5s2ZG1HIO82vxVtnrtOO3cuZP4+HiPc1arlV//+tdce+21PjOsM77//e9z8uRJnn76aSorK5k6dSo5OTmkpqZ2/+C+j6VxnHRdJz8/n0svvVSqDN5B14m98M1K2Pk3qGs3wG/wCLjgezDtRkiYGBItibKmWaC+8F944QWP/00mEwkJCdxxxx3893//d0BscuFNHSWb49Tb/H60toVlG0t5J78Cm8MZF1OGDeLBS8eSPXlop1PnA4Gs5Rjk1eavsuXVGKdQwN1E958DmJE1FxbnBtokxbloPAFF7zkdpsrtZ86HD4LJ18P0m2DkXLVWUZCgupr6xvkef20OnWc+LObtvEPYdefXUPrIGB66dBwLJyT0y2QjhdwETVddSFKRB00nYUBcoC3pM4ZhUF1dTXx8vDy/DBqOI9b/HArfQhOnZ0CaLDD2Cpj+fRh/JVgjA2tjH5AyzZCvpSRQyBaPPcnvp5ps3L1iK/nlzvFoc8bE8eClY5mTFhe0DpOs5Rjk1eavsiVPDHWBiE0DBOz/JNCm+ATDMCgqKpKjsrU1wcZfwcvpaNveRBM6YtgMuOrX8F974eaVMOXbIe00gWRp1g7Z9AQK2eLxXPl9f1UjN/z2S/LLa4iOsPDn/8jknf+czdyx8UHrNIG85Rjk1RY0Y5xCDS11Lhwrd45zmn5ToM3pMxaLhUsvvTTQZvQNQ3d2x637P2iodJ5LmQmLfo42cnZgbfMDUqRZJ6jtGXyDbPHYXX7/cn81975VQH2rg5GxUbxx50zGJkb3s4XeIWs5Bnm1+atsSd/iZIw4/UW8/zPQ+29Je39hGAZHjhwJ3V8Gpeth2QJYc5/TaYoZCd99A+MHuRwxjwhdXd0Q8mnWBbLpCRSyxWNX+f2dvEPc8UYe9a0OZqYOYfV9c0PGaQJ5yzHIq0111XmJET8BouKd09gPfRVoc/qMYRiUlpaGXgavKoa/3ggrboDjOyF8MFzxf/DAVpj6bxhChKauHhCyaXYOZNMTKGSLx7Pzu2EIns0p5r//sROHIbj+wmG89cNZxA3szx0c+46s5Rjk1aa66rzEYg2Dcdnwzduwby2Mnh9ok/qExWJh/vwQ0tBYBeufgW1vgjCcg74zfwjzH/MYrB9yunqBrNpk62IKFLLFY/v83mxz8MjK7eTuPg7Ajy4fz0OXjQ3qsUxdIWs5Bnm1qa46LzEMA8Yvcv6zb21gjfEBhmFw8ODB0Phl8M1KeDkdCv7sdJomXgv358FVv+wwwzGkdPUSWbXJpidQyBaPrvx+tKaZ7y37itzdxwmzmHjppgt5+PJxIek0gbzlGOTVprrqvMQwDEi71NnScbIETpYG2qQ+ERJ90Q4bfPhfsPpusDXCsHS4Mwdu+ivEpXX6SEjo8hJZtcmmJ1DIFo+GYfDl7oN8+7XNFB2pJ25AGO/cNYvrL0wJtGl9QtZyDPJqU111XmKxWCBiEKReBGUbna1Oc+4LtFleY7FYmDt3bqDN6Jr6o7Dqdjic7/x/wf9zHqbu95cKel19QFZtsnUxBQrZ4nHT/pP87Ktmmm06YxMH8uc7MxkRGxVos/qMrOUY5NWmuuq8xLVb8pnuuo8DZ4wP0HWd/fv3n9EVTJR9DsvmO52miMHw7+/CJY+f02mCINfVR2TVJpueQCFTPO45Vs+9b22j2aZz8dg4/n7vXCmcJpC3HIO82vylR3rHyb2jzPjTm38e/BJa67t+IMgRQlBTU0NQ7ZQjBHz5Mvzlemg6AUnT4D83wISeb7galLp8hKzaZNMTKGSJx2abg/v/uo02h8GFSWG8ftsMBkdaA22Wz5C1HIO82vylR3rHyd1UF5cGcWPBcEDpusAa1QcsFguZmZnB07zf1gB/uwM++V8QOlxwk3NfwNgxvXpN0OnyIbJqk01PoJAlHpeu2UXpiSaSBoXzp7vmExkeFmiTfIqs5Rjk1aa66rzEo6nO1eoUwrPrdF1nz549wdGkemIfvH4p7F4DJitc/Rx8+/cQ1vum+aDS5WNk1SabnkAhQzyuLjzM3woOY9Lghe9N58ThMil0tUfWcgzyalNddb7ANc6pJNe57UeI0tLSEmgTnM7S65dA9T6ITob/yIGsu6APU42DQpefkFmb4vzmwIlGfrq6CICHLhvHrNGx0uZ3WXWB3Np8jVztcp1gNrcbmDxyDoQPguZqOLINRmQGzjAvMZvNpKenB84AQ4dPn4TNLzv/HzUPvvsGDEzs02sDrsuPyKrNo2wpvCaU47HVrnP/24U023Rmj4nlwUvHYTZp0uZ3GXWBvNr8Vbakb3HyaKozW2HsZc5wiM6u03WdoqKiwDSpGjqsuf+M0zT3Ibjt/T47TRBgXX5GVm2y6QkUoRyPz+QUU1zpXKvppZvSMZs0qfO7jLpAXm2qq85XSDDOKSC4nKZv3gHNDN/5I2T/H5ilb7RUKBSd8HFRJX/56iAAz39vOkmDIgJskULRP0j/rdehqW7sFYDm3Gi27ggMDq3VbM1mM1OnTu3fDzV0eP8+2LHS6TR99w2YcoNPPyIguvoJWbWFchdTMBGK8VhxqpmfvLcDgLsXjGHhhDOtzjLndxl1gbzaVFedl3RoqhsQByOynOGS0Gt10nWdwsLC/mtS7QenCQKgqx+RVZtsegJFqMWjXTd48J1CGlodpI+M4cfZEzyuy5zfZdQF8mpTXXW+JMQ3/Y2MjOyfDzrbabrxz35xmlz0m64AILM2xfnFc2v3sr2ilkERFl6+KR2ruePXiKz5XVZdILc2XyO949RpU51rnNOBDWBr7ld7+orZbGbixIn+b943dHj/XqfTZLI4nabJ1/vt4/pNVwCQVZtsegJFKMXj+r1VLNt0AIBfffeCTrdTkTm/y6gL5NWmuuq8xOFwdDyZOBkGjwBHK5R/3v9G9QGHw0F+fn7nunyF22l61+k0ffcNvzpN0E+6AoSs2mTTEyhCJR6P17fyX6u+AeD2OalcOTW50/tkzu8y6gJ5tflLj/SOk9bZgoyaFrKb/mqaxpAhQzrX5QsMHVbf085p8m9Lkwu/6wogsmqTTU9fGTVqFJqmeRxLliw553OhEI+6IXh4ZSGnmmxMTh7E41dP6vJemfO7jLpAXm3+0nP+zapzMW4R5P/ROc5JiD6teN2fmM1mxo4d65+Xu5ymnavaOU3f8s9nnYVfdQUYWbXJ1qzvC55++mnuuusu9/8DBw485zO+jMfN+6t5aOV2RsZGMjctnrlpccxIHUKEtfefYRiCPccayCs7yWd7qvj6wCmiwsy8enN6t++TOb/LqAvk1eavOkp6x6nLprrR88ASCfVH4HgRDJ3Wv4Z5icPhIC8vj6ysLN9uYGjosPpu2Pm302OalsOk63z3/nPgN11BgKzaZGvW9wXR0dEMHTq0V8/4Kh4NQ/DUv3ZT3dhGdWMb2w7V8ur6/YRZTMwYGeN2pC4YHkOYpWNng103KDpSR17ZKfLKTpFffor6Vk/bfv7tqYxJ6N4ZlDm/y6gL5NXmrzpKnhjqApOpi95IaySMWQj7PnJ214WI42QymUhJSelalze4W5oC4zSBn3QFCbJqk02PL/jlL3/J//3f/zFixAhuvPFGfvKTnxAWFtbtM3v27MFisbinTg8fPpzEROe6SGazGYfDgaZp7rDJZMJkMnUIf7zrOHuPNzAw3MLjV08kv7yGzfurOd7QxtcHTvH1gVP85hOItJqZmRrD3LHxTEiKZsfhWgoO1VJwsIZmm+f07QFhZjJShzAzdQiXTkpicnI0DocDi8WCYRgYhuG2XQiBxWJBCEFycjImk8mtyWw2e4R7qskVttvtmM1md9hisaBpmjsMuO1yha1WK0IId9gwDHRdd4ddtncVbq/JFU5JSUEIga7rUmhy2d5VmoWyJn8urSB9zddt5R6CyxKYTCZSU1N996UlBHy85Ez3XACcJvCDriBCVm2y6ekrDz/8MCtXrmT9+vU88MADvPjii9x3333nfO6OO+4gIyODrKwssrKyWLZsGTt27KCkpASAwsJCysrKAMjLy6OiogKAzZs3U1lZCcCGjRt5PncPAAuTDa4cF80L37+Q/53exj/vzuBnN0zlwjiDIVFWWuw6n+8/yS8/3ssP3tzKi5/t5/OSapptOgMscMXkJB69JJX/zjDzzdJsnrtuNFNNh5maMpjKyko2b94MQEVFBXl5eQCUlZVRWFgIQGlpKbW1tZhMJoqLiykuLgbotaZNmzZRXV0NwLp166itrQUgNzeXhoYGAHJycmhtbcXhcJCTk4PD4aC1tZWcnBwAGhoayM3NBaC2tpZ169YBUF1dzaZNmwB6pKmkpISioiJSU1PZu3evNJp27HAuYrp3716ampowmUzSaCouLqa8vBy/ICSloKBAAGLLli1d31R3RIilg4RYOliIxhP9ZltfsNvtYuPGjcJut/vmhZuePxMHO9/zzTu9wOe6gghZtW3ZskUAoqCgINCm+I2lS5cKoNsjPz+/02ffe+89AYjq6upOr7vqqOXLl4uCggKRl5cn8vLyxNGjR4XD4RAOh0MI4cw/7cO6rncIry44JFL/3wdi2tKPxcn6Jvd5m80mDMNwhx0OXew+Wiv+sLFELF6eJy55br24b8VW8ZfNZaL4aJ1obW0TQgih67qw2WzusCvvdhV2OBzucGtrq9iwYYPbbpftvdXUPmyz2brUZBiGMAyjQ1gI4RHuiyaHwyFaW1vFxo0bRWtrqzSaXPZ2lWahrMnhcIivvvrKL3VUyHTV/fznP+fDDz9k+/bthIWFub3ac9Htr+JBw2DoBXBsB5R8Ahf+u2+M9SMmk4m0tDTf/Nov/Ct89pQzfOUvYOq/9f2dXuJTXUGGrNpk09MZDzzwADfddFO394waNarT87NnzwZg//79xMXFdfn8lClTmDFjRpfX24856SysG4JX1pcC8MN5Y4iNPrO2ktVq7RCelDyYScmDuWt+lx/p7nrpabj9IFyr1crYsWM9rp99z7k0nR3uTEdPwpqmucN90WQ2m9E0jbS0NKxWa6f3hKKm9u/uLM1CWZPZbPbbeK2QcZxsNhs33ngjc+bM4U9/+lOPnztn5T7+SqfjtPfDkHGcUlJ8sL9eySfwzwed4Ysehtn39P2dfcBnuoIQWbWdD45TfHw88fHxXj3r6j5ITu58vSMXfY3HD3YcpfREE4MjrfzHRaP69C5fIHN+l1EXyKvNX3VUyNR8Tz31FD/60Y+YNq13g7jPOap+0rXOv3ty4GSpl9b1Hw6Hg3Xr1vVttsDhAlh1OwgdLrgJLnvSZ/Z5i090BSmyapNNT1/46quveOGFF9i+fTtlZWWsWrWKu+++m29961uMHDmy22f7Eo8O3eClT53jUe6aN5roCOs5nvA/Mud3GXWBvNrUApheck6PM3k6jMt2OhEbftE/RvUBk8nE1KlTvfekT5bC2zeCvRnSLoPrX4UgaDnos64gRlZtsunpC+Hh4bz77rssXLiQyZMn88QTT3DXXXfxzjvvnPPZvsTjP785yoHqJmKirNx50Wiv3+NLZM7vMuoCebX5S0/IdNV5S3FxsccUy06n+i5YgrkkF7Hzb4iLHsE0dErQTrcUQhAXF+fdVN/aI5hXfBut+SQi+ULEjcsxma0B1+SyPTExEV3XpZzq21mahbIm13mFkxkzZvD111979ay3lbtDN3j5M2dr03/OH8PA8OCozk0mk7uOlQlZdYG82qTsqnvyySc7bFFw9rF169Y+fcbtt99+7qm+rYNh0nVoCFo+egII3umWe/bs4aOPPsJut/duqm9rPS1/vBat9iAMGc0XqQ9TXd8aFJpKSkrYvn07a9eupaioSLqpvkVFRe40k0VTcXExpaXB37UdCnjbnfD+9qOUn2wmdkAYd8wZ5Vuj+oDdbmft2rXY7fZAm+JTZNUF8mrzV1edJgL4s7G6utr9pdAVo0aNIiIiwv3/8uXLeeSRR845q27btm1kZGTw5ptvMnXq1HMvLle9F/HaXDQE/OdGHIlTg/JXv91up7a2lri4OPcv/nO2zggHpne+Dwc2IAYkoC3OxTFoZNBo0nUdwzBoaGggOjoak8kkVYuT3W6nrq6O2NhYjzQLZU26rlNQUMCsWbMoKCjodlaYonNcdVR+fj4zZ87s1bMO3eCy32zk4Mlmllw1kXsWpPnJyt5jGAa1tbXExMRI1fUjqy6QV9vWrVvJzMz0eR0V0LbdvsxY6SlTp07t2VTfpMlo077rXD17/TNYblnV8R4CP93SarWSkJDQQUeX02JNJlj9ABzYANYBaLf8DWLHeCR8oDWZzWbMZjOxsbE90xRi02KtVmun+TyUNflzqu/5hjdfVP8oPMLBk83EDQjj9jmpfrDKe0wmU4eyLAOy6gJ5tUnZVdcbDh06xPbt2zl06BC6rrN9+3a2b99OY2Njt8/1qqluwRLQzFCyFiry+mixf7Db7Xz44Yc9b1L95H/PbKXy/RUwLN2/BnpJr3WFELJqk20GTqDobTzadYNX1jm7e+9ZkEZUWHA5sLLmd1l1gbzazvtZdU888QTp6eksXbqUxsZG0tPTSU9PP+cYqF7tjhw/9sxaTut+1gdr/YfFYmHevHk9+7W/+VX46lVn+PrfwtjL/GtcH+iVrhBDVm3+2nn8fKO38fj3gsNUnGohfmA4t84OrtYmkDe/y6oL5NXmrzoqZByn5cuXI4TocCxcuLDb5zRN690HzX8MTFYo2whlm7w32E9omsagQYPOreur30LuT53hK56G6d2vfhxoeqwrBJFVm2x6AkVv4tHmMHhl3X4A7lkwhsiw4HNeZc7vMuoCebX5S0/IOE7e0uumuiGpkHGHM7zu585NcIMIu93OmjVrum9S3fRrWPu4M3zxozD3of4xrg/0SFeIIqs21VXnG3oTj+8VHOZIbQsJ0cHZ2gTy5ndZdYG82s77rjpv8aqpbt6PwRIBFV/D/s98b1QfsFgsZGdnd96kKoSzi9HVzXjJT+GyJyAEfkV0qyvEkVWb6qrzDT2NxzaHzm/XO1ub7l2QRoQ1OONf1vwuqy6QV9t531XXrwxKhswfOsPrfxZ0rU5dOk25/+NsbQJn99yCx0LCaXIhW6Ftj8zaFP3Dqq3O1qakQeHcPKv7bVwCjaz5XVZdILc2XyO94+Rae6bXXPQIWAfA0ULYm+NTm/pC+0UO3RgG5PzkzEDwq37l3Lg3hOhUlyTIqs3rsqXwoCfx2ObQ+d3p1qb7Fo4N2tYmkDe/y6oL5NXmrzpKesfJ66a6gQkw+x5neN3Pnc5JEGCxWLj66qvP/DowdPjXQ5D/OqDBdS/BrLsDaqM3dNAlEbJqU111vqEn8fhufgWVda0MHRTB9zNH9INV3iNrfpdVF8irzV91lFyx5GvmPgh5f4SqXbB7NUz9t0BbBLRbHVp3wPv3ws5VoJnghteCfvZcd7Rf9Vo2ZNam6Bt/21rB1/WDu73nzc3lANx/SfCObWqPrPldVl0gtzZfI30s9ampLnIIzH0A1v8c1j8Lk64Hc2CjzOFwkJuby9WLLse65h4o/qdzcct/+yNM+XZAbesLbl1XX+2x+rUMyKpNddX5hj9+8AXWuIPu/00RA7HGDEU4bNiqD7nPJwwMZ5w5ERgFwN69e2lqavJ416hRo4iNjeXEiRPuvQ9dREdHM27cOHRd55tvvulgx7Rp07BarZSWllJXV+dxLSUlhaSkJGpqatz7K7qIjIxk0qRJgHP/RbvdzhdffMHFF1+MxWJh0qRJREZGcvDgQU6ePOnxbFJSEikpKTQ0NLj3cHRhtVqZNm0aADt37uww42vcuHFER0dz5MgRjh8/7nEtLi6O1NRUWlpa3HtfutA0jfR050LAxcXFtLS0eFwfPXo0Q4YM4fjx4xw5csR93uFwsG3bNhYvXuy26WymT5+O2WympKTEvZekixEjRpCQkMCpU6coLy/3uDZgwAAmTJgAOLfiOZvJkycTERFBWVkZNTU1HteSk5NJTk6mvr6e/fv3e1wLDw9nypQpgHPvz7O74saPH8/AgQMpLy9n9erV7jQD584eI0eOpLm5mT179ng8ZzKZuPDCCwHYvXs3ra2tHtfHjBlDTEwMx44d4+jRox7XYmJiGDNmDDabjaKiog5aL7zwQkwmE/v27euwwPXIkSOJj4+nurqaQ4cOeVwbOHAg48ePxzAMtm/fDsCuXbs6vN8nCEkpKCgQgCgoKOjbi1rqhPjFKCGWDhKi8K++Ma6v2FqE+Ov3nDY9HS9E8YeBtkhxHuKzMnae4oq/s4/J864Wj/3tG3HXy//q9LqL2bNnd7i2YsUKIYQQr776aodr2dnZQggh6urqOn1vVVWVEEKI6667rsO1559/XgghxKpVqzpcS09Pd9sUFhbW4XpRUZEQQojFixd3uLZkyRIhhBDr16/vcC0lJcX93pSUlA7X169fL4QQYsmSJR2uLV68WAghRFFRUYdrYWFh7vemp6d3uL5q1SohhBDPP/98h2vXXXedEEKIqqqqTuOwrq5OCCFEdnZ2h2uvvvqqEEKIFStWdLg2e/Zst02dvbekpEQIIcQtt9zS4drSpUuFEEJ8/PHHHa6lpaW53xsfH9/h+ubNm4UQQvzoRz/qcO2+++7rMp9GR0e73zt58uQO19esWSOEEOKZZ57pcO273/2uEEKIioqKTrW2trYKIYRYsGBBh2uvv/66EEKI119/vcO1BQsWCCGEaG1t7XDN13VUQDf59SeuDTS3bt1KRkZG31725UvwyRMQkwoPbAVLmG+M9AJha0L/6/exHPzcuWTCTX+FsZcHzB5fIYRwb/Ir2yJssmorKChg5syZapNfL3HVUW+99Za7xQZgyJAhjB49mtbWVnbv3t3hOVdcB2uLk2EYNDU1MWDAADRNk6bFSQiB2Wxm+vTpOBwOqVqcKioqKCsrc6cZyNHiVFxczK233urzOkp6x2nLli1kZWX17WW2ZnhpOjRVwbUvwMwf+MbIntJa59ykd/+niH25aI3HENYBaDevhNHz+9cWP2G328nNzSU7O1uq7iyQV1teXh6zZs1SjpOX+LSOCiJkze+y6gJ5tfmrjpJ+jJNPBruFRcH8H8NHj8HGX8P0m8Ea0ff3doVhwPGdUPKJcwHOii0gnONJNIDIWLR/fwdGzvafDf2M1WrlmmuuCbQZfkFWbWogqW+QLR5lze+y6gJ5tfmrbMlVYjvB8NUyAhl3wpcvQ/1heP0SiBkJUfEQFQsD4k+H406H45xHeHTPF6BsPgWl65yO0v5Pna1b7YkbB+OuwBhzKbUxU4iJHyrVWhKGYVBbW0tMTAwmk0zK5NXms7J1niNbPMqc32XUBfJq81fZkt5x2r17t0dG6NP4gRkPEbvhMU6UFVFR79m/HR0G4+LM6Ibgm+OnE0szO5cJAKYlWbCaNUpP6dS1eiZmyiAzSZF2aloEZbWnr1kiIWUGkWMvZtIVt8GQUc4ZK7V28nL/QVZWlnQzVnbt2sWtt96KrutSjR84ePAgH374oTvNQI7xA52VH0Xvkc1x0nWd/Px8Lr30Uqm+hGXVBfJq81vZ8ulQ8yCiqxkrt9xyixBCiJKSkk6vu+h0xspf/iLEkULx6v/c0+Fa9rREIX4/X9Q9M6nT91b9eKAQSweJ68ZbOlx7PjtciKWDxKrF4zpcUzNW1IyVs6/LPmPlfEHNSlQo/Iu/ypj0g8NXrFjB5MmT3ef7bcaKvQVaG3B+t8C0KROdM1bKyqmr82wtSRk2lKSUVGratHPOWNF13aNJVZYWJ8MwMAyDmTNnStfidOjQIfbt2+fRDC5Li9Ntt92mBod7iauOys/PZ+bMmYE2x2cYhkF1dTXx8fHStV7IqAvk1bZ161YyMzN9X0f51A0LIlye5pYtWwJtik+x2+3is88+E3a7PdCm+BRZdQkhr7YtW7acNy0mP/vZz8ScOXNEZGSkGDx4cKf3HDx4UFx77bUiKipKxMXFiQcffFC0tbV1+U5VR4UWsuoSQl5t/qqjpB/jJNuMFYvFwqWXXhpoM3yOrLpAXm2yla3usNls3HjjjcyZM4c//elPHa7rus4111xDQkICX3zxBSdPnuSOO+5ACMErr7zS7btli0eZ87uMukBebf4qW/K0yXWBbAMvDcPgyJEjSlcIIas22fR0x1NPPcWPfvQjd/f22eTm5rJ7927eeust0tPTufzyy3n++ed5/fXXqa+v7/bdssWjzPldRl0grzZ/6VGOU4hhGAalpaVKVwghqzbZ9PSFr776iqlTpzJs2DD3uUWLFtHW1kZBQUG3z8oWjzLndxl1gbzalOPkJTI2g8+fP1/pCiFk1Sabnr5w7NgxkpKSPM4NGTKEsLAwjh071u2ze/fuZdu2beTn55Ofn09lZSW6rrs3UXY4HB5h15dBV2G73e4RFqfn/7jCQogOYcAjbBiGR9g18aGrsK7r7rCmaVx00UVYLBYPHaGsSdd1NE1j/vz5aJomjSaXvV2lWShrcqWZP5DecZLRgz548KDSFULIqi3U9Tz55JNomtbtsXXr1h6/r7NKWghxzsr79ttvJyMjg6ysLLKysli2bBk7duxwz4QtLCx0z7bNy8tzz+jdvHkzlZWVAGzatInq6moA1q1bR21tLeDsQnTNQM3JyaG1tRWHw0FOTg4Oh4PW1lZycnIAaGhoIDc3F4Da2lrWrVsHQHV1NZs2bQKgsrKSzZs3A1BRUUFeXh4AZWVlFBYWArBv3z42b96MYRgUFxe7Z96GsqaSkhJ27NjBwYMH2b17t1SawDlDdsuWLRiGIY2m4uJiDhw4gD+QfjkC2faBcjgc5OXleSymKAOy6gJ5tYX6XnXV1dXuCr8rRo0aRUTEme2Vli9fziOPPOL+cnDxxBNPsGbNGo/Nc2tqaoiNjWXdunVccsklHd7tqqOWL1/OtGnT3L+Uhw8fTmJiIgBmsxmHw4Gmae6wyWTCZDJ1Gbbb7ZjNZnfYYrGgaZo7DM482T5stVoRQrjDhmGg67o7bBgGFouly7Cu6wghsFgstLW1sXXrVmbNmuV2Gs1ms1tfKGpytWoUFBSQkZGBxWKRQpPL9q7SLJQ1uRb1nDNnjtqrrrfI9EUFTj1z584NtBk+R1ZdIK+2UC9b8fHxxMfH++Rdc+bM4ec//zmVlZUkJycDzl/c4eHhZGRkdPvstGnTuq3U28dzT8LtN2ntTVjTNHfY9UXY07DZbHa/Lzw8nIsuuqiDjvb3hJoms9mM2WzuUI5DXZOLrtIslDWZzWbCwsI6aPIF0nfVuTxQWdB1nf379ytdIYSs2mTT0x2HDh1i+/btHDp0CF3X2b59O9u3b3cvIpqdnc3kyZO57bbbKCws5LPPPuPHP/4xd911F4MGDer23bLFo8z5XUZdIK82f+mR3nGSrSdSCEFNTY3SFULIqk02Pd3xxBNPkJ6eztKlS2lsbCQ9PZ309HT3GCiz2cyHH35IREQEF110Ed/73ve44YYbeO655875btniUeb8LqMukFebv/SEdlt7Dwj17oSzsVgsZGZmBtoMnyOrLpBXm2xlqzuWL1/O8uXLu71n5MiRfPDBB71+t2zxKHN+l1EXyKtNLYDpJTI2Pe7Zs0fpCiFk1SabnkAhWzzKnN9l1AXyalNddQo3Z2+cKwuy6gK5tSkUZyNrfpdVF8itzdeEhONUXl7O4sWLGT16NJGRkaSlpbF06VJsNluXz5w4cQKAU6dO9ZeZ/UJVVRVr1qyhqqoq0Kb4FFl1gbzaXGXLVdYUvUPVUaGFrLpAXm3+qqNCwnHas2cPhmGwbNkydu3axQsvvMDvf/97Hn/88S6fca3PIltGOHz4ME899RSHDx8OtCk+RVZdIK82V9k611pIis5RdVRoIasukFebv+qokBiVeOWVV3LllVe6/x8zZgx79+7ltdde69GsFYVCoVAoFApfEBItTp1RV1dHbGzsOe9zLZIlC64Fvtov9CUDsuoCebXJVrYChWzxKGt+l1UXyKvNX2UrJFqczqa0tJRXXnmF559/vst72traAPj888+BM/tqJSYmuh0ub5aUPztsNpvRNM0dBudI/vZhi8WCEMId7sky8l0tKV9UVITFYmHXrl0dlpcPVU26rrv3fioqKnJ/VqhrctneVZqFsiZd1yktLfUoa4re4Yq3AwcOsG3btgBb4zt27drl8VcWZNUF8mpz7VXn8zpKBJClS5cKoNsjPz/f45kjR46IsWPHisWLF3f77ldeeeWc71aHOtTR9+OVV17xZzUhLaqOUoc6+ufwdR0V0E1+e7vJ5tGjR7nkkkuYNWsWy5cv77YZrrq6mpUrVxIVFUV4eLj7fHx8PAkJCb4RoFCcx7S0tFBeXs6iRYt8tufb+UR1dTVr165l1KhRREZGBtochUI6/FVHBdRx6g1HjhzhkksuISMjg7feeku6vliFQqFQKBTBT0g4TkePHmXBggWMHDmSv/zlLx5O09ChQwNomUKhUCgUivOJkBgcnpuby/79+9m/fz/Dhw/3uBYCfp9CoVAoFApJCIl5sHfeeSdCiA7Hb3/7W0aPHk1ERAQZGRnuGXRdsXHjRjIyMoiIiGDMmDH8/ve/7ycFveN3v/tdj3Vt2LABTdM6HHv27OlHi8/Npk2buO666xg2bBiapvH++++f85lQSK/e6gqV9Hr22WfJzMwkOjqaxMREbrjhBvbu3XvO50IhzfqT3pRlCJ34U3WUk1BIL1VHeeKLNAsJx6kz3n33XR555BF++tOfUlhYyLx587jqqqs4dOhQp/eXlZVx9dVXM2/ePAoLC3n88cd56KGH+Pvf/97PlndPb3W52Lt3L5WVle5j3Lhx/WRxz2hqamL69Om8+uqrPbo/VNKrt7pcBHt6bdy4kfvvv5+vv/6aTz75BIfDQXZ2Nk1NTV0+Eypp1l+oOsqTYM/zqo7yJNjTK6B1lE/n6PUjWVlZ4p577vE4N3HiRLFkyZJO73/sscfExIkTPc7dfffdYvbs2X6z0Rt6q2v9+vUCEDU1Nf1gnW8AxOrVq7u9J1TSqz090RWK6SWEEFVVVQIQGzdu7PKeUEwzf6LqKCehmOdVHRVa6SVE/9ZRIdniZLPZKCgoIDs72+N8dnY2mzdv7vSZr776qsP9ixYtYuvWrdjtdr/Z2hu80eUiPT2d5ORkLrvsMtavX+9PM/uFUEivvhBq6VVXVwfQ7Wr9sqdZb1B1VEdCLc+fi1BIr74QaunVn3VUSDpO1dXV6LpOUlKSx/mkpCSOHTvW6TPHjh3r9H6HwxE0m5R6oys5OZk//OEP/P3vf+cf//gHEyZM4LLLLmPTpk39YbLfCIX08oZQTC8hBI8++igXX3wxU6dO7fI+WdPMG1QddYZQzPM9IRTSyxtCMb36u44KiVl1XaFpmsf/QogO5851f2fnA01vdE2YMIEJEya4/58zZw4VFRU899xzzJ8/3692+ptQSa/eEIrp9cADD7Bjxw6++OKLc94rY5r1BVVHhWae7ymhkl69IRTTq7/rqJBscYqPj8dsNnf4hVNVVdXBm3QxdOjQTu+3WCzExcX5zdbe4I2uzpg9ezYlJSW+Nq9fCYX08hXBnF4PPvgg//znP1m/fn2HpUDO5nxKs3Oh6qjuCeY831NCIb18RTCnVyDqqJB0nMLCwsjIyOCTTz7xOP/JJ58wd+7cTp+ZM2dOh/tzc3OZOXMmVqvVb7b2Bm90dUZhYSHJycm+Nq9fCYX08hXBmF5CCB544AH+8Y9/sG7dOkaPHn3OZ86nNDsXqo7qnmDM870lFNLLVwRjegW0jurVUPIgYuXKlcJqtYo//elPYvfu3eKRRx4RAwYMEOXl5UIIIZYsWSJuu+029/0HDhwQUVFR4kc/+pHYvXu3+NOf/iSsVqt47733AiWhU3qr64UXXhCrV68W+/btE0VFRWLJkiUCEH//+98DJaFTGhoaRGFhoSgsLBSA+M1vfiMKCwvFwYMHhRChm1691RUq6XXvvfeKwYMHiw0bNojKykr30dzc7L4nVNOsv1B1lJNQyfOqjnISKukVyDoqZB0nIYT47W9/K1JTU0VYWJiYMWOGxzTEO+64QyxYsMDj/g0bNoj09HQRFhYmRo0aJV577bV+trhn9EbXL3/5S5GWliYiIiLEkCFDxMUXXyw+/PDDAFjdPa4prmcfd9xxhxAidNOrt7pCJb060wSIP//5z+57QjXN+hNVR4VOnld1lJNQSa9A1lEhsVedQqFQKBQKRTAQkmOcFAqFQqFQKAKBcpwUCoVCoVAoeohynBQKhUKhUCh6iHKcFAqFQqFQKHqIcpwUCoVCoVAoeohynBQKhUKhUCh6iHKcFAqFQqFQKHqIcpwUCoVCoVAoeohynBQKhUKhUCh6iHKcFEHBwoULeeSRRwJthkKhUHSKqqMULpTjpFAoFAqFQtFD1F51ioBz55138uabb3qcKysrY9SoUYExSKFQKNqh6ihFe5TjpAg4dXV1XHXVVUydOpWnn34agISEBMxmc4AtUygUClVHKTyxBNoAhWLw4MGEhYURFRXF0KFDA22OQqFQeKDqKEV71BgnhUKhUCgUih6iHCeFQqFQKBSKHqIcJ0VQEBYWhq7rgTZDoVAoOkXVUQoXynFSBAWjRo1iy5YtlJeXU11djWEYgTZJoVAo3Kg6SuFCOU6KoODHP/4xZrOZyZMnk5CQwKFDhwJtkkKhULhRdZTChVqOQKFQKBQKhaKHqBYnhUKhUCgUih6iHCeFQqFQKBSKHqIcJ4VCoVAoFIoeohwnhUKhUCgUih6iHCeFQqFQKBSKHqIcJ4VCoVAoFIoeohwnhUKhUCgUih6iHCeFQqFQKBSKHqIcJ4VCoVAoFIoeohwnhUKhUCgUih6iHCeFQqFQKBSKHqIcJ4VCoVAoFIoe8v8BEu/dACa+B7wAAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 2, figsize=(6, 2.3))\n", "ax[0].plot(resp.time, resp.outputs[0], label='x1', ls='-.') # 状態のグラフ\n", "ax[0].plot(resp.time, resp.outputs[1], label='x2', ) # 状態のグラフ\n", "ax[1].plot(resp.time, resp.outputs[2]) # 制御入力のグラフ\n", "\n", "ax[0].set_xlim([0,2])\n", "ax[1].set_xlim([0,2])\n", "ax[0].set_ylim([-2,2])\n", "ax[1].set_ylim([-12,12])\n", "# 制約条件をプロット\n", "ax[0].hlines(xmin, 0, 2, colors='black', linestyle='dashed', lw=1)\n", "ax[0].hlines(xmax, 0, 2, colors='black', linestyle='dashed', lw=1)\n", "ax[1].hlines(umin, 0, 2, colors='black', linestyle='dashed', lw=1)\n", "ax[1].hlines(umax, 0, 2, colors='black', linestyle='dashed', lw=1)\n", "plot_set(ax[0], 't', 'x', 'best')\n", "plot_set(ax[1], 't', 'u')\n", "plt.tight_layout()\n", "\n", "# fig.savefig(\"c7_mpc.pdf\", transparent=True, bbox_inches=\"tight\", pad_inches=0.0)\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.3" } }, "nbformat": 4, "nbformat_minor": 4 }