{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Describing function analysis\n", "Richard M. Murray, 27 Jan 2021\n", "\n", "This Jupyter notebook shows how to use the `descfcn` module of the Python Control Toolbox to perform describing function analysis of a nonlinear system. A brief introduction to describing functions can be found in [Feedback Systems](https://fbsbook.org), Section 10.5 (Generalized Notions of Gain and Phase)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import control as ct\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import math" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Built-in describing functions\n", "The Python Control Toobox has a number of built-in functions that provide describing functions for some standard nonlinearities. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Saturation nonlinearity\n", "\n", "A saturation nonlinearity can be obtained using the `ct.saturation_nonlinearity` function. This function takes the saturation level as an argument." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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claQpVqDs/Qto/kKrSL169crcXwBU9hkArc+c2rlzJ+7fv4+IiAhltQaAxtPKNXF2dsayZcuwbNkyJCUlYdeuXZgzZw4yMjIQGRmJ8+fP4+zZs9i4cSPGjx+vXO7KlStarb+Uru8LTePfsmULxo0bp5xvViozMxN16tTRKZ5Sj/8tPXmW2ZN/S9Whbt26sLCw0Om9Ut1Kt186l64scrkcv/32G+bPn485c+Yo20vn72mijzMGmzZtikGDBuHrr7/GoEGDsGvXLixYsACWlpZPvW5TwsoQ6UVERIRKRSE3Nxe7d+9Gjx49lH903t7eyMjIUP4nBQAFBQXYt2+f2vrK+u9y+/btGDp0qMpp1QEBAbCzs1ObtJmSkoKDBw+ib9++yjZvb29cvnxZ5YsoKysLx44dU9s+UP5/k6X/aZX66aefUFRUpHIxN29vb5w7d06l38GDB9WqZU/736uuJBIJpFKpyodteno6fv31V439Dxw4oLLfiouLsW3bNjRp0qRSp2b37dsX8fHx+Pvvv1XaN23aBIlEgt69e+u8TuB/Xx6Pvz+EEPj22291XlejRo0wdepU9O/fXxmnpvUDwNq1a9WWL2+favu+KI9EIlGLY8+ePUhNTdU6jif16dMHANT+lk6ePIkLFy6o/C1VB3t7e3Tp0gUREREq8SsUCmzZsgUNGzZE8+bNqzWmJw0YMABWVla4evUqOnbsqPEBlOwvIYTaPlu3bt1TTyWoqBo3Y8YMnDt3DuPHj4elpSUmT578VNszRawMkV5YWlqif//+mD17NhQKBRYvXoycnBwsWLBA2WfUqFH46KOPMHr0aLz77rvIy8vDihUrNH4QtG7dGtHR0di9ezfc3d3h4OAAZ2dnHD58GD/++KNK3zp16mDevHn44IMPMG7cOLzyyivIysrCggULYGtri/nz5yv7BgcHY+3atXj11VcxefJkZGVlYcmSJXB0dFRZp4ODA7y8vPDrr7+ib9++cHJygrOzM7y9vZV9IiIiYGVlhf79++Pff//FvHnz0KZNG4wcOVJle/PmzcNHH32Enj17Ij4+HqtWrYJMJlPZXqtWrQAA33zzDRwcHGBrawsfH59KVV20MXToUERERODtt9/GSy+9hOTkZHz88cdwd3fXePads7Mz+vTpg3nz5sHe3h5hYWG4ePGi2r7Q1qxZs7Bp0yYMGTIECxcuhJeXF/bs2YOwsDC89dZblf6C69+/P6RSKV555RW89957yMvLw+rVq5GdnV3hsnK5HL1798aYMWPg6+sLBwcHnDx5EpGRkXjhhRcAAL6+vmjSpAnmzJkDIQScnJywe/duREVFqa2vdevWAIDly5dj/PjxsLa2RosWLeDg4KD1+6I8Q4cOxcaNG+Hr6wt/f3+cPn0an3/+uVpy2qRJE9jZ2SE8PBx+fn6oXbs2PDw8lIeZHteiRQu88cYbWLlypfKM0MTERMybNw+enp4GuWDmokWL0L9/f/Tu3RvvvPMOpFIpwsLCcP78eWzdutXgV9D29vbGwoUL8eGHH+LatWsYOHAg6tati1u3buHEiROwt7fHggUL4OjoiGeffRaff/658rPk8OHDWL9+faUreaVat26NiIgIrF69Gh06dICFhYUyCQNK/i5atmyJQ4cO4dVXX4WLi8tTjtoEGXT6NtUI5V1n6ElPnn3y+HVgFixYoLw+S7t27cS+ffvUlt+7d69o27atsLOzE40bNxarVq3SeDbZmTNnRLdu3UStWrWU1xlat26dqFWrlrh//77Gcaxbt074+/sLqVQqZDKZeP7558W///6r1u/7778Xfn5+wtbWVrRs2VJs27ZN45luf/zxh2jXrp2wsbHReJ2h06dPi+eee07Url1bODg4iFdeeUXcunVLZR35+fnivffeE56ensLOzk707NlTnDlzRu2sISFKzpLz8fERlpaWWl9n6PFr2whR9n4rvSbM4z777DPh7e0tbGxshJ+fn/j222817gs8uh5MWFiYaNKkibC2tha+vr4iPDy8zPgep+lsMiFKrjM0ZswYUa9ePWFtbS1atGghPv/8c43XGfr888+12pYQQuzevVu0adNG2NraigYNGoh3331X/P777xWerZeXlydCQkKEv7+/cHR0FHZ2dqJFixZi/vz5Ku+5+Ph40b9/f+Hg4CDq1q0rXn75ZZGUlKTxDLG5c+cKDw8PYWFhobJ9bd8Xmv42S2VnZ4uJEycKFxcXUatWLdG9e3dx9OhRjWdKbd26Vfj6+gpra2utrzPUvHlzYW1tLZydncWrr75a5nWGnlTWWaNPKn1fPUnT30bpdYbs7e2FnZ2d6Nq1q9r1iMr6XZVea+nxfa/L2WTarE8IIXbu3Cl69+4tHB0dhY2NjfDy8hIvvfSSyvXWUlJSxIsvvijq1q0rHBwcxMCBA8X58+d12u+azia7c+eOeOmll0SdOnWERCJR26dCCBEaGioAiNjYWLXXSAiJEEJUT9pFpigxMRE+Pj74/PPP8c4771TptgYPHgw7Ozts3769SrdTkdDQUCxYsAC3b982+HyF6iCRSDBlyhSsWrXK0KEQUSV17NgREokEJ0+eNHQoNRIPk5HR2Lt3r6FDICIyGjk5OTh//jx+++03nD59Gjt27DB0SDUWkyEiIiIT9Pfff6N3796oV68e5s+fr7f7A5oiHiYjIiIis8ZT64mIiMisMRkiIiIis8ZkiIiIiMwaJ1BXQKFQ4ObNm3BwcDD4xb2IiIhIO0II5ObmwsPDAxYW5dd+mAxV4ObNm/D09DR0GERERFQJycnJFd42yOiSobCwMHz++edIS0vDM888g2XLlqFHjx5l9g8PD8eSJUuQkJAAmUyGgQMH4osvvtD6NgcODg4ASn6ZT96ygYiIiGqmnJwceHp6Kr/Hy2NUydC2bdswc+ZMhIWFoVu3bli7di0GDRqE+Ph4NGrUSK3/n3/+iXHjxmHp0qV47rnnkJqaipCQEEyaNEnri0+VHhpzdHRkMkRERGRktJniYlQTqL/66itMnDgRkyZNgp+fH5YtWwZPT0+sXr1aY//Y2Fh4e3tj+vTp8PHxQffu3fHmm2/i1KlT1Rw5ERER1VRGkwwVFBTg9OnTCAoKUmkPCgrCsWPHNC4TGBiIlJQU7N27F0II3Lp1C7/88guGDBlSHSETERGRETCaZCgzMxPFxcVwdXVVaXd1dUV6errGZQIDAxEeHo5Ro0ZBKpXCzc0NderUwcqVK8vcTn5+PnJyclQeREREZLqMJhkq9eSxPyFEmccD4+PjMX36dHz00Uc4ffo0IiMjcf36dYSEhJS5/kWLFkEmkykfPJOMiIjItBnNvckKCgpQq1Yt/PzzzxgxYoSyfcaMGThz5gwOHz6stkxwcDDy8vLw888/K9v+/PNP9OjRAzdv3oS7u7vaMvn5+cjPz1c+L52NLpfLOYGaiIjISOTk5EAmk2n1/W00lSGpVIoOHTogKipKpT0qKgqBgYEal3nw4IHahZYsLS0BlFSUNLGxsVGeOcYzyIiIiEyf0SRDADB79mysW7cO3333HS5cuIBZs2YhKSlJedhr7ty5GDdunLL/c889h4iICKxevRrXrl3DX3/9henTp6Nz587w8PAw1DCIiIioBjGq6wyNGjUKWVlZWLhwIdLS0tCqVSvs3bsXXl5eAIC0tDQkJSUp+0+YMAG5ublYtWoV/vOf/6BOnTro06cPFi9ebKghEBERUQ1jNHOGDEWXY45ERERUM5jknCEiIiKiqsBkiIiIiMwakyEiIiIya0Y1gZqIiIyDEAK3c/NRUKwwdChkBBxsrCGrZW2w7TMZIiIivfsq6jJWHrxi6DDISLzdqwneG+hrsO0zGSIiIr06cvm2MhGyseJsDKqYlYXm22pV2/YNunUiIjIpGbl5mP3TGQBAcFcvfDy8lWEDItICU3YiItILhULgPz+dRea9Avi6OeDDIX6GDolIK0yGiIhIL745eg1HEzJha22BVWPawdba0tAhEWmFyRARET21uKRsfLHvEgBgwbBn0NTFwcAREWmPyRARET0V+cNCTNsahyKFwFB/d4zs6GnokIh0wmSIiIgqTQiBD3b8g5Tsh/B0ssOnL7SGRGLYM4OIdMVkiIiIKm3byWTsOZcGKwsJVr7SHo62hrtwHlFlMRkiIqJKSbiVi9Dd/wIA3hnQAm096xg2IKJKYjJEREQ6yyssxtQf4pBXqECPZs54o0djQ4dEVGlMhoiISGef7InHpVu5cK5tg69GtoWFga8gTPQ0mAwREZFOIs+nYUtsEgBg6ag2qO9gY+CIiJ4OkyEiItJaXmEx5u8qmScU0rMJejSrb+CIiJ4ekyEiItLa1hNJuJWTDw+ZLWb1b2bocIj0gskQERFpJa+wGGHRVwEAU/o0hY0Vb7dBpoHJEBERaSX8eBJu5+ajQR07vNyBV5km08FkiIiIKvSwoBirH1WFpvZpCqkVvz7IdPDdTEREFQo/fgOZ9/LRsK4dXmzf0NDhEOkVkyEiIirXw4JirDl8DQAwtTerQmR6+I4mIqJybYktqQp5OtnhxQ6sCpHpYTJERERlelBQhDWHS+YKTevdDNaW/Nog08N3NRERlWlzzA1k3S9AI6daGNG+gaHDIaoSTIaIiEij+/lFWHukZK7QtD5NWRUik8V3NhERabQ59gbu3C+AV71aGNGOVSEyXUyGiIhIzf38InyjrAo1gxWrQmTC+O4mIiI138ck4s79Avg422N4Ww9Dh0NUpZgMERGRinsqVaGmrAqRyeM7nIiIVHx/LBF3HxSisbM9hrVhVYhMH5MhIiJSys0rxLdHH1WF+rIqRObB6N7lYWFh8PHxga2tLTp06ICjR4+W2z8/Px8ffvghvLy8YGNjgyZNmuC7776rpmiJiIyLsipU3x7D2vAMMjIPVoYOQBfbtm3DzJkzERYWhm7dumHt2rUYNGgQ4uPj0ahRI43LjBw5Erdu3cL69evRtGlTZGRkoKioqJojJyKq+UqqQtcBADP6NoOlhcTAERFVD4kQQhg6CG116dIF7du3x+rVq5Vtfn5+GD58OBYtWqTWPzIyEqNHj8a1a9fg5ORUqW3m5ORAJpNBLpfD0dGx0rETEdV0Kw4k4Kuoy2hS3x77Z/VkMkRGTZfvb6M5TFZQUIDTp08jKChIpT0oKAjHjh3TuMyuXbvQsWNHLFmyBA0aNEDz5s3xzjvv4OHDh9URMhGR0ZA/LMS6R3OFZvRrzkSIzIrRHCbLzMxEcXExXF1dVdpdXV2Rnp6ucZlr167hzz//hK2tLXbs2IHMzEy8/fbbuHPnTpnzhvLz85Gfn698npOTo79BEBHVUBv+uo6cvCI0damNIa3dDR0OUbUymspQKYlE9b8VIYRaWymFQgGJRILw8HB07twZgwcPxldffYWNGzeWWR1atGgRZDKZ8uHp6an3MRAR1STyh4VY/yfnCpH5MppkyNnZGZaWlmpVoIyMDLVqUSl3d3c0aNAAMplM2ebn5wchBFJSUjQuM3fuXMjlcuUjOTlZf4MgIqqBvvvzOnLzitDclVUhMk9GkwxJpVJ06NABUVFRKu1RUVEIDAzUuEy3bt1w8+ZN3Lt3T9l2+fJlWFhYoGHDhhqXsbGxgaOjo8qDiMhUyR8U4jtlVag5LFgVIjNkNMkQAMyePRvr1q3Dd999hwsXLmDWrFlISkpCSEgIgJKqzrhx45T9x4wZg3r16uG1115DfHw8jhw5gnfffRevv/467OzsDDUMIqIaY/2f15CbXwRfNwcMauVm6HCIDMJoJlADwKhRo5CVlYWFCxciLS0NrVq1wt69e+Hl5QUASEtLQ1JSkrJ/7dq1ERUVhWnTpqFjx46oV68eRo4ciU8++cRQQyAiqjHuPijAd38lAiiZK8SqEJkro7rOkCHwOkNEZKq+2HcJqw5dga+bA/ZO78FkiEyKSV5niIiI9Cf7fgE2/FUyV2hmP1aFyLwxGSIiMkPr/ryG+wXF8HN3RFBLzhUi88ZkiIjIzNy5X4CNj+YKsSpExGSIiMjsfHu0pCrU0t0RQS01X6eNyJwwGSIiMiNZ9/Lx/bFEACVVobKu4E9kTpgMERGZkW+OXsODgmK0auCI/qwKEQFgMkREZDYy7+Vj07EbAICZfZuzKkT0CJMhIiIz8e2Ra3hYWAz/hjL09XMxdDhENQaTISIiM5B5Lx+bYh5VhThXiEgFkyEiIjOw9vBVPCwsRpuGMvRuwaoQ0eOYDBERmbiM3Dxsji2tCnGuENGTmAwREZm4tYevIa9QgbaeddCrRX1Dh0NU4zAZIiIyYRm5edgSy7lCROVhMkREZMLWRF9DfpEC7RrVQc/mrAoRacJkiIjIRGXk5CH8eElVaBbnChGVickQEZGJCou+ivwiBTp41UWPZs6GDoeoxmIyRERkgtLlefjhRBIAzhUiqgiTISIiE7Tm8FUUFCnQ0asuujdlVYioPEyGiIhMzONVoVn9OVeIqCJMhoiITExY9BUUFCnQ2dsJgU3qGTocohqPyRARkQm5efchfjyRDACY2Z9zhYi0wWSIiMiEhEVfQUGxAl18nBDYhHOFiLTBZIiIyETcvPsQ204+qgr1a27gaIiMB5MhIiIT8fWhKygsFuja2AkBnCtEpDUmQ0REJiAl+wF+OlVSFZrFqhCRTpgMERGZgK8PXUVhsUBgk3ro0phVISJdMBkiIjJyKdkP8HNpVag/q0JEumIyRERk5L4+dAVFCoHuTZ3RydvJ0OEQGR0mQ0RERiz5zgP8fCoFADCrfzMDR0NknJgMEREZsVUHS6pCPZo5o4MXq0JElcFkiIjISCVlPcAvf5dUhXhdIaLKYzJERGSkVh5MQLFC4Nnm9dHBq66hwyEyWkyGiIiMUGLmfUTEpQIAZvXjXCGip8FkiIjICK08eAXFCoFeLeqjXSNWhYiehtElQ2FhYfDx8YGtrS06dOiAo0eParXcX3/9BSsrK7Rt27ZqAyQiqmKJmfex80xJVYhzhYienlElQ9u2bcPMmTPx4YcfIi4uDj169MCgQYOQlJRU7nJyuRzjxo1D3759qylSIqKqs+LRXKE+vi5o61nH0OEQGT2jSoa++uorTJw4EZMmTYKfnx+WLVsGT09PrF69utzl3nzzTYwZMwYBAQHVFCkRUdW4dvsedj6aKzSjL+cKEemD0SRDBQUFOH36NIKCglTag4KCcOzYsTKX27BhA65evYr58+drtZ38/Hzk5OSoPIiIaoqVB69AIYC+vi5ow6oQkV4YTTKUmZmJ4uJiuLq6qrS7uroiPT1d4zIJCQmYM2cOwsPDYWVlpdV2Fi1aBJlMpnx4eno+dexERPpw9fY9/Mq5QkR6ZzTJUCmJRKLyXAih1gYAxcXFGDNmDBYsWIDmzbX/0Jg7dy7kcrnykZyc/NQxExHpw4oDCVAIoJ+fK1o3lBk6HCKToV25pAZwdnaGpaWlWhUoIyNDrVoEALm5uTh16hTi4uIwdepUAIBCoYAQAlZWVti/fz/69OmjtpyNjQ1sbGyqZhBERJV0JeMedp29CQCYyesKEemV0VSGpFIpOnTogKioKJX2qKgoBAYGqvV3dHTEP//8gzNnzigfISEhaNGiBc6cOYMuXbpUV+hERE9txYEECAEEtXRFqwasChHpk9FUhgBg9uzZCA4ORseOHREQEIBvvvkGSUlJCAkJAVByiCs1NRWbNm2ChYUFWrVqpbK8i4sLbG1t1dqJiGqyhFu52H2upCo0g1UhIr0zqmRo1KhRyMrKwsKFC5GWloZWrVph79698PLyAgCkpaVVeM0hIiJjs/xRVWjAM654xoNVISJ9kwghhKGDqMlycnIgk8kgl8vh6Oho6HCIyMxcvpWLAcuOQAjg9xk94OfOzyEibejy/W00c4aIiMzR8j9KqkKDWrkxESKqIkyGiIhqqIvpOdjzTxoAzhUiqkpMhoiIaqgVBxIAAENau8PXjVUhoqrCZIiIqAa6kJaDvf+kQyIBpvMeZERViskQEVENtPyPkqrQ4NbuaOHmYOBoiEwbkyEiohrm35tyRP5bUhWayaoQUZVjMkREVMOUVoWG+nugmSurQkRVjckQEVENcj5Vjv3xtyCRADP6NjV0OERmgckQEVENsvzRGWTP+XugqQurQkTVgckQEVENcT5Vjqj4W7DgGWRE1YrJEBFRDbHsj8sAgGFtPNDUpbaBoyEyH0yGiIhqgHMpd/HHhQxWhYgMgMkQEVENsOzRGWTD2zZA4/qsChFVJyZDREQGdib5Lg5eLKkKTe3DM8iIqhuTISIiAyudKzS8HatCRIbAZIiIyIDikrIRfek2LC0kmN6Hc4WIDIHJEBGRAZXOFRrRrgG8ne0NHA2ReWIyRERkIKdvZOPw5ZKq0DTOFSIyGCZDREQGUjpX6IV2DeBVj1UhIkNhMkREZACnb9zB0YRMWFlIMI1zhYgMiskQEZEBLI0qmSv0YvuGaFSvloGjITJvTIaIiKrZycQ7+PNKSVWI1xUiMjwrXTpfunQJW7duxdGjR5GYmIgHDx6gfv36aNeuHQYMGIAXX3wRNjY2VRUrEZFJKJ0r9HLHhvB0YlWIyNC0qgzFxcWhf//+aNOmDY4cOYJOnTph5syZ+Pjjj/Hqq69CCIEPP/wQHh4eWLx4MfLz86s6biIio3Ti+h38dSULVhYSTOnNqhBRTaBVZWj48OF49913sW3bNjg5OZXZLyYmBkuXLsWXX36JDz74QG9BEhGZiqVRpVUhTzSsy6oQUU2gVTKUkJAAqVRaYb+AgAAEBASgoKDgqQMjIjI1sdeyEHMtC9aWnCtEVJNodZhMm0QIAB48eKBTfyIic1JaFRrZ0RMN6tgZOBoiKqXz2WS9evVCSkqKWvvx48fRtm1bfcRERGRyjl3NxPHrdyC1tOBcIaIaRudkyNHREf7+/vjxxx8BAAqFAqGhoXj22WcxbNgwvQdIRGTshBDKe5CN6uQJD1aFiGoUnU6tB4Bdu3ZhzZo1mDRpEnbt2oXExEQkJSVhz5496NevX1XESERk1GKuZuHEo6rQ272bGDocInqCzskQAISEhODGjRtYvHgxrKysEB0djcDAQH3HRkRk9IQQWProukKjO3vCXcaqEFFNo/NhsuzsbLz44otYvXo11q5di5EjRyIoKAhhYWFVER8RkVH760oWTiZmQ2plgbd7ca4QUU2kc2WoVatW8PHxQVxcHHx8fDB58mRs27YNb7/9Nvbs2YM9e/ZURZxEREbn8arQmM6N4CazNXBERKSJzpWhkJAQHDlyBD4+Psq2UaNG4ezZs7y+EBHRY44mZOL0jWzYWFngrV6cK0RUU+mcDM2bNw8WFuqLNWzYEFFRUXoJqjxhYWHw8fGBra0tOnTogKNHj5bZNyIiAv3790f9+vXh6OiIgIAA7Nu3r8pjJCJSqQp1aQRXR1aFiGoqrZKhpKQknVaamppaqWAqsm3bNsycORMffvgh4uLi0KNHDwwaNKjM+I4cOYL+/ftj7969OH36NHr37o3nnnsOcXFxVRIfEVGpIwmZiEu6W1IV6smqEFFNplUy1KlTJ0yePBknTpwos49cLse3336LVq1aISIiQm8BPu6rr77CxIkTMWnSJPj5+WHZsmXw9PTE6tWrNfZftmwZ3nvvPXTq1AnNmjXDp59+imbNmmH37t1VEh8REfCoKvToatOvdvWCC6tCRDWaVhOoL1y4gE8//RQDBw6EtbU1OnbsCA8PD9ja2iI7Oxvx8fH4999/0bFjR3z++ecYNGiQ3gMtKCjA6dOnMWfOHJX2oKAgHDt2TKt1KBQK5Obmlnuz2fz8fOTn5yuf5+TkVC5gIjJb0Zdv40zyXdhaW+DNno0NHQ4RVUCrypCTkxO++OIL3Lx5E6tXr0bz5s2RmZmJhISSK6qOHTsWp0+fxl9//VUliRAAZGZmori4GK6urirtrq6uSE9P12odX375Je7fv4+RI0eW2WfRokWQyWTKh6en51PFTUTmRQiBZaVVoS5ecHFgVYioptPp1HpbW1u88MILeOGFF6oqngpJJBKV50IItTZNtm7ditDQUPz6669wcXEps9/cuXMxe/Zs5fOcnBwmRESktUOXMnA2Rf6oKsS5QkTGQOezyV5//XXk5uaqtd+/fx+vv/66XoLSxNnZGZaWlmpVoIyMDLVq0ZO2bduGiRMn4qeffqrwliE2NjZwdHRUeRARaePxe5CNC/BGfQcbA0dERNrQORn6/vvv8fDhQ7X2hw8fYtOmTXoJShOpVIoOHTqonb4fFRVV7q1Atm7digkTJuCHH37AkCFDqiw+IqKDFzNwLkUOO2tLvPEs5woRGQutD5Pl5ORACAEhBHJzc2Fr+7/j4MXFxdi7d2+5h5/0Yfbs2QgODkbHjh0REBCAb775BklJSQgJCQFQcogrNTVVmZRt3boV48aNw/Lly9G1a1dlVcnOzg4ymaxKYyUi86JSFQr0gnNtVoWIjIXWyVCdOnUgkUggkUjQvHlztdclEgkWLFig1+CeNGrUKGRlZWHhwoVIS0tDq1atsHfvXnh5eQEA0tLSVK45tHbtWhQVFWHKlCmYMmWKsn38+PHYuHFjlcZKRObljwsZ+CdVjlpSS7zRg1UhImMiEUIIbToePnwYQgj06dMH27dvVzk9XSqVwsvLCx4eHlUWqKHk5ORAJpNBLpdz/hARaSSEwNCVf+LfmzkI6dkEcwb5GjokIrOny/e31pWhnj17AgCuX78OT09PjbfkICIyR1Hxt/DvzRzYSzlXiMgY6XzX+tJDUg8ePEBSUpLazVn9/f31ExkRkRF4fK7Q+EBvONlLDRwREelK52To9u3beO211/D7779rfL24uPipgyIiMhb7/r2F+LQc1LaxwmTOFSIySjof65o5cyays7MRGxsLOzs7REZG4vvvv0ezZs2wa9euqoiRiKhGUigElj26M/2EQG/UZVWIyCjpXBk6ePAgfv31V3Tq1AkWFhbw8vJC//794ejoiEWLFvFaPkRkNvb9m46L6bmobWOFST18DB0OEVWSzpWh+/fvK68n5OTkhNu3bwMAWrdujb///lu/0RER1VAKhcDyAyVzhV7r5o06tVgVIjJWOidDLVq0wKVLlwAAbdu2xdq1a5Gamoo1a9bA3d1d7wESEdVEkY+qQg42VpjUnXOFiIyZzofJZs6cibS0NADA/PnzMWDAAISHh0MqlfJChkRkFhQKgeWPziB7rbsPZLWsDRwRET0NnZOhsWPHKn9u164dEhMTcfHiRTRq1AjOzs56DY6IqCbaez4Nl27lwsHWChO7c64QkbF76isn2tjYwMLCApaWlvqIh4ioRnu8KjSxuw9kdqwKERm7Sp1av379egAl1xR69tln0b59e3h6eiI6Olrf8RER1Sh7/klDQsY9ONpa4bVurAoRmQKdk6FffvkFbdq0AQDs3r1beZhs5syZ+PDDD/UeIBFRTVH82Blkk3o0ZlWIyETonAxlZmbCzc0NALB37168/PLLaN68OSZOnIh//vlH7wESEdUUv527iSuPqkITunkbOhwi0hOdkyFXV1fEx8ejuLgYkZGR6NevH4CSe5Vx3hARmapihcCKR1WhyT0aw9GWVSEiU6Hz2WSvvfYaRo4cCXd3d0gkEvTv3x8AcPz4cfj6+uo9QCKimmD32Zu4evs+6tSyZlWIyMTonAyFhoaiVatWSE5OxssvvwwbGxsAgKWlJebMmaP3AImIDO3JqpADq0JEJkXnZAgAXnrpJbW28ePHP3UwREQ10a6zqbiWWVIVGh/obehwiEjPnvo6Q0REpqyoWIEVB64AAN54tjFq21Tqf0giqsGYDBERlePXMzdxPfM+6tayxrgAb0OHQ0RVgMkQEVEZiooVWHmwZK7QG882YVWIyEQxGSIiKsOOuFQkZj2Ak70U4wK8DB0OEVURJkNERBoUFSuw6lDJXKE3n20Me1aFiExWpZKh1q1bIzk5We1nIiJTERGXihtZD+BcW4pgVoWITFqlkqHExEQUFhaq/UxEZAoKH5sr9OazTVBLyqoQkSnjYTIioidE/J2C5DsP4VxbirFdGxk6HCKqYkyGiIgeU1CkwMqDJXOFQnqyKkRkDpgMERE9ZvvfKUjJfgjn2jYY24VzhYjMAZMhIqJHCooUWPWoKvRWryawk1oaOCIiqg5MhoiIHvnldApS7z6Ei4MNxnbhXCEic8FkiIgIJVWhrw/9rypka82qEJG5qFQy5OXlBWtra7WfiYiM1U+nkpVVoVc6sypEZE4qdZrE+fPnNf5MRGSM8ouKlVWht1kVIjI7PExGRGbvp5PJSJPnwc3RFqNZFSIyO0yGiMislVSFrgIA3u7NqhCROTK6ZCgsLAw+Pj6wtbVFhw4dcPTo0XL7Hz58GB06dICtrS0aN26MNWvWVFOkRGQMtp1MRnpOHtxlthjVydPQ4RCRARhVMrRt2zbMnDkTH374IeLi4tCjRw8MGjQISUlJGvtfv34dgwcPRo8ePRAXF4cPPvgA06dPx/bt26s5ciKqifIKH5sr1LspbKxYFSIyRxIhhDB0ENrq0qUL2rdvj9WrVyvb/Pz8MHz4cCxatEit//vvv49du3bhwoULyraQkBCcPXsWMTExWm0zJycHMpkMcrkcjo6OTz8IIqoxNv51HaG74+Ehs8Whd3sxGSIyIbp8f+tcGZowYQKOHDlS6eAqq6CgAKdPn0ZQUJBKe1BQEI4dO6ZxmZiYGLX+AwYMwKlTp1BYWKhxmfz8fOTk5Kg8iMj05BUWIyy6dK4Qq0JE5kznZCg3NxdBQUFo1qwZPv30U6SmplZFXGoyMzNRXFwMV1dXlXZXV1ekp6drXCY9PV1j/6KiImRmZmpcZtGiRZDJZMqHpyfnEBCZoh+OJyEjNx8N6thhZEf+nROZM52Toe3btyM1NRVTp07Fzz//DG9vbwwaNAi//PJLmdUWfZJIJCrPhRBqbRX119Reau7cuZDL5cpHcnLyU0ZMRDVNXmExVh8uqQpN6d0UUiujmj5JRHpWqU+AevXqYcaMGYiLi8OJEyfQtGlTBAcHw8PDA7NmzUJCQoK+44SzszMsLS3VqkAZGRlq1Z9Sbm5uGvtbWVmhXr16GpexsbGBo6OjyoOITEv48STcflQVeqlDQ0OHQ0QG9lT/DqWlpWH//v3Yv38/LC0tMXjwYPz7779o2bIlli5dqq8YAQBSqRQdOnRAVFSUSntUVBQCAwM1LhMQEKDWf//+/ejYsSNvIUJkph4WFGP1o7lC0/qwKkRElUiGCgsLsX37dgwdOhReXl74+eefMWvWLKSlpeH777/H/v37sXnzZixcuFDvwc6ePRvr1q3Dd999hwsXLmDWrFlISkpCSEgIgJJDXOPGjVP2DwkJwY0bNzB79mxcuHAB3333HdavX4933nlH77ERkXEIP34Dmffy0bCuHV5kVYiIUIl7k7m7u0OhUOCVV17BiRMn0LZtW7U+AwYMQJ06dfQQnqpRo0YhKysLCxcuRFpaGlq1aoW9e/fCy8sLQEml6vFrDvn4+GDv3r2YNWsWvv76a3h4eGDFihV48cUX9R4bEdV8DwqKsObw/6pC1pasChFRJa4ztHnzZrz88suwtbWtqphqFF5niMh0fHPkKj7dexGNnGrhwH96MhkiMmG6fH/rXBkKDg6udGBERIbyoKAIaw9fAwBMZVWIiB7DTwMiMgubY24g634BvOrVwgvtGhg6HCKqQZgMEZHJu59fhLVHHlWFejeFFatCRPQYfiIQkcnbFHMDd+4XwLteLYxgVYiInsBkiIhM2r38InxzpPQMsmasChGRGr1+Khw5cgRyuVyfqyQieiqbYhKR/aAQPs72eL6th6HDIaIaSK/JUK9evdC4cWN8+eWX+lwtEVGllFSFSuYKTe/LuUJEpJlePxmuX7+O7du3l3lHeCKi6vT9sUTcfVCIxs72GNaGc4WISDOdrzNUHi8vL3h5eaFXr176XC0Rkc5y8wofqwo1g6WFxMAREVFNpXNlqHHjxsjKylJrv3v3Lho3bqyXoIiIntbGvxIhf1iIJvXt8VwbzhUiorLpnAwlJiaiuLhYrT0/Px+pqal6CYqI6Gnk5BXi26OsChGRdrQ+TLZr1y7lz/v27YNMJlM+Ly4uxoEDB+Dt7a3X4IiIKmPjX4nIyStCU5faGOrPqhARlU/rZGj48OEAAIlEgvHjx6u8Zm1tDW9vb55FRkQGJ39YiHWPqkIzWBUiIi1onQwpFAoAgI+PD06ePAlnZ+cqC4qIqLI2/HUdOXlFaOZSG4Nbuxs6HCIyAjqfTXb9+vWqiIOI6KnJHxZi/Z8ln1Ez+rEqRETa0TkZWrhwYbmvf/TRR5UOhojoaaz/8zpy84rQwtUBg1uxKkRE2tE5GdqxY4fK88LCQly/fh1WVlZo0qQJkyEiMgj5g0JseKwqZMGqEBFpSedkKC4uTq0tJycHEyZMwIgRI/QSFBGRrtb9eQ25+UXwdXPAwGfcDB0OERkRvdyOw9HREQsXLsS8efP0sToiIp3cfVCADX8lAig5g4xVISLShd7uTXb37l3esZ6IDOLbo9dw71FVaACrQkSkI50Pk61YsULluRACaWlp2Lx5MwYOHKi3wIiItJF9vwAbH1WFZvZrzqoQEelM52Ro6dKlKs8tLCxQv359jB8/HnPnztVbYERE2vj26DXcLyhGS3dHDHjG1dDhEJER4nWGiMho3blfgO+PJQIoOYNMImFViIh091RzhpKTk5GSkqKvWIiIdPLNkZKq0DMejghqyaoQEVWOzslQUVER5s2bB5lMBm9vb3h5eUEmk+H//u//UFhYWBUxEhGpybqXj00xiQBK5gqxKkRElaXzYbKpU6dix44dWLJkCQICAgAAMTExCA0NRWZmJtasWaP3IImInvTNkWt4UFCM1g1k6OfnYuhwiMiI6ZwMbd26FT/++CMGDRqkbPP390ejRo0wevRoJkNEVOUy7+VjU8wNAMBMzhUioqek82EyW1tbeHt7q7V7e3tDKpXqIyYionJ9c+QaHhYWo01DGfr4sipERE9H52RoypQp+Pjjj5Gfn69sy8/Px3//+19MnTpVr8ERET3pdi7nChGRflXq3mQHDhxAw4YN0aZNGwDA2bNnUVBQgL59++KFF15Q9o2IiNBfpEREANYevoq8QgXaeNZBrxb1DR0OEZkAnZOhOnXq4MUXX1Rp8/T01FtARERlycjNw5bjnCtERPqlczK0YcOGqoiDiKhCa6KvIa9QgbaeddCrOatCRKQfOs8Z6tOnD+7evavWnpOTgz59+ugjJiIiNRk5eQh/VBWa1Z9zhYhIf3ROhqKjo1FQUKDWnpeXh6NHj+olKE2ys7MRHBwMmUwGmUyG4OBgjUlZqcLCQrz//vto3bo17O3t4eHhgXHjxuHmzZtVFiMRVZ3Vh68iv0iB9o3q4NlmzoYOh4hMiNaHyc6dO6f8OT4+Hunp6crnxcXFiIyMRIMGDfQb3WPGjBmDlJQUREZGAgDeeOMNBAcHY/fu3Rr7P3jwAH///TfmzZuHNm3aIDs7GzNnzsSwYcNw6tSpKouTiPTvVk4ewo8nAWBViIj0T+tkqG3btpBIJJBIJBoPh9nZ2WHlypV6Da7UhQsXEBkZidjYWHTp0gUA8O233yIgIACXLl1CixYt1JaRyWSIiopSaVu5ciU6d+6MpKQkNGrUqEpiJSL9Wx19FQVFCnTwqovuTVkVIiL90joZun79OoQQaNy4MU6cOIH69f83eVEqlcLFxQWWlpZVEmRMTAxkMpkyEQKArl27QiaT4dixYxqTIU3kcjkkEgnq1KlTJXESkf6ly/Pww4lHVSFeV4iIqoDWyZCXlxcAQKFQVFkwZUlPT4eLi/pVZl1cXFQO15UnLy8Pc+bMwZgxY+Do6Fhmv/z8fJULSubk5OgeMBHpTVj0FRQUKdDJuy66Na1n6HCIyATpfGr9pk2byn193LhxWq8rNDQUCxYsKLfPyZMnAUDjf4NCCK3+SywsLMTo0aOhUCgQFhZWbt9FixZVGBMRVY80+UP8eCIZAKtCRFR1JEIIocsCdevWVXleWFiIBw8eQCqVolatWrhz547W68rMzERmZma5fby9vfHDDz9g9uzZameP1alTB0uXLsVrr71W5vKFhYUYOXIkrl27hoMHD6JevfL/s9RUGfL09IRcLi+3okRE+jdv53lsjr2Bzj5O2PZGVyZDRKS1nJwcyGQyrb6/da4MZWdnq7UlJCTgrbfewrvvvqvTupydneHsXPFkyICAAMjlcpw4cQKdO3cGABw/fhxyuRyBgYFlLleaCCUkJODQoUMVJkIAYGNjAxsbG+0HQURV4ubdh9h2klUhIqp6Ol9nSJNmzZrhs88+w4wZM/SxOjV+fn4YOHAgJk+ejNjYWMTGxmLy5MkYOnSoyuRpX19f7NixAwBQVFSEl156CadOnUJ4eDiKi4uRnp6O9PR0jddJIqKa5etDV1BQrEDXxk4IaMK5QkRUdfSSDAGApaVllV7QMDw8HK1bt0ZQUBCCgoLg7++PzZs3q/S5dOkS5HI5ACAlJQW7du1CSkoK2rZtC3d3d+Xj2LFjVRYnET29lOwH+OlUSVVoZr/mBo6GiEydzofJdu3apfJcCIG0tDSsWrUK3bp101tgT3JycsKWLVvK7fP49Cdvb2/oOB2KiGqIrw9dRWGxQEDjeujamFUhIqpaOidDw4cPV3kukUhQv3599OnTB19++aW+4iIiM5WS/QA/P6oKzerPqhARVT2dkyFDXGeIiMzH14euoEgh0K1pPXT2cTJ0OERkBio9ZygzMxNZWVn6jIWIzFzynQf4+VQKgJIzyIiIqoNOydDdu3cxZcoUODs7w9XVFS4uLnB2dsbUqVPLvYM8EZE2Vh0sqQr1aOaMjt6sChFR9dD6MNmdO3cQEBCA1NRUjB07Fn5+fhBC4MKFC9i4cSMOHDiAY8eOqV2UkYhIG0lZD/DL3yVVoZn9mhk4GiIyJ1onQwsXLoRUKsXVq1fh6uqq9lpQUBAWLlyIpUuX6j1IIjJ9qw4loPhRVaiDF6tCRFR9tD5MtnPnTnzxxRdqiRAAuLm5YcmSJcoLHhIR6eJG1n1s/zsVAM8gI6Lqp3UylJaWhmeeeabM11u1aqX1HeSJiB638uAVFCsEejavj/aNeKidiKqX1smQs7MzEhMTy3z9+vXrWt37i4jocYmZ97EjjlUhIjIcrZOhgQMH4sMPP9R4X6/8/HzMmzcPAwcO1GtwRGT6VhwsmSvUu0V9tPWsY+hwiMgMaT2BesGCBejYsSOaNWuGKVOmwNfXFwAQHx+PsLAw5Ofnq90rjIioPNcz72Pno6oQ70FGRIaidTLUsGFDxMTE4O2338bcuXOV9/2SSCTo378/Vq1aBU9PzyoLlIhMz8oDCVAIoI+vC9qwKkREBqLT7Th8fHzw+++/Izs7GwkJCQCApk2bwsmJp8ESkW6u3b6HnWdKq0K8rhARGY7O9yYDgLp166Jz5876joWIzMiKR1Whfn4u8G9Yx9DhEJEZq/S9yYiIKutKxj3sOnsTAOcKEZHhMRkiompXWhXq39IVrRrIDB0OEZk5JkNEVK2uZORi97nSqhDnChGR4TEZIqJqtfzAFQgBDHjGFc94sCpERIbHZIiIqs3lW7n47VFVaEZfzhUiopqByRARVZvlBxIgBDDwGTe09HA0dDhERACYDBFRNbmUnou9/6QBAGZwrhAR1SBMhoioWiw/cBlCAINbu8HPnVUhIqo5mAwRUZW7mJ6Dvf+kQyLhXCEiqnmYDBFRlVv+R8ntewa3dkcLNwcDR0NEpIrJEBFVqfibOfj9fGlViHOFiKjmYTJERFVq+YHLAIAhrd3R3JVVISKqeZgMEVGV+femHPv+vcWqEBHVaEyGiKjKLHs0V+g5fw80Y1WIiGooJkNEVCXOp8oRFX8LFhJgOqtCRFSDMRkioipRWhUa1sYDTV1qGzgaIqKyMRkiIr37J0WOPy6UVIWmsSpERDUckyEi0rtlf5ScQfZ82wZoUp9VISKq2ZgMEZFenU2+iwMXM0qqQn2aGjocIqIKMRkiIr0qrQoNb9cAjVkVIiIjYDTJUHZ2NoKDgyGTySCTyRAcHIy7d+9qvfybb74JiUSCZcuWVVmMROYuLikbhy7dhqWFBNP7cK4QERkHo0mGxowZgzNnziAyMhKRkZE4c+YMgoODtVp2586dOH78ODw8PKo4SiLztvxAyRlkI9o1gLezvYGjISLSjpWhA9DGhQsXEBkZidjYWHTp0gUA8O233yIgIACXLl1CixYtylw2NTUVU6dOxb59+zBkyJDqCpnI7PydlI3oR1UhzhUiImNiFJWhmJgYyGQyZSIEAF27doVMJsOxY8fKXE6hUCA4OBjvvvsunnnmmeoIlchslV5X6IV2DeBVj1UhIjIeRlEZSk9Ph4uLi1q7i4sL0tPTy1xu8eLFsLKywvTp07XeVn5+PvLz85XPc3JydAuWyAydvpGNI5dvw8pCgmmcK0RERsaglaHQ0FBIJJJyH6dOnQIASCQSteWFEBrbAeD06dNYvnw5Nm7cWGYfTRYtWqScpC2TyeDp6Vm5wRGZkdIzyF5s3xCN6tUycDRERLoxaGVo6tSpGD16dLl9vL29ce7cOdy6dUvttdu3b8PV1VXjckePHkVGRgYaNWqkbCsuLsZ//vMfLFu2DImJiRqXmzt3LmbPnq18npOTw4SIqBynEu/gaEImrCwkmMq5QkRkhAyaDDk7O8PZ2bnCfgEBAZDL5Thx4gQ6d+4MADh+/DjkcjkCAwM1LhMcHIx+/fqptA0YMADBwcF47bXXytyWjY0NbGxsdBgFkXlb+qgq9FKHhvB0YlWIiIyPUcwZ8vPzw8CBAzF58mSsXbsWAPDGG29g6NChKmeS+fr6YtGiRRgxYgTq1auHevXqqazH2toabm5u5Z59RkTaO3H9Dv66kgUrCwmm9GZViIiMk1GcTQYA4eHhaN26NYKCghAUFAR/f39s3rxZpc+lS5cgl8sNFCGR+SmdK/RyR09WhYjIaBlFZQgAnJycsGXLlnL7CCHKfb2seUJEpLvj17Jw7GoWrC05V4iIjJvRVIaIqGYpnSs0sqMnGtSxM3A0RESVx2SIiHQWczULsdfuwNpSgrc5V4iIjByTISLSiRBCWRUa1YlVISIyfkyGiEgnMdeycOL6HUgtLXgGGRGZBCZDRKQ1IQSWRZXcg2x0Z0+4y1gVIiLjx2SIiLR27GoWTiSWVIXe7sWqEBGZBiZDRKQVIQSWRpXMFXqlsyfcZLYGjoiISD+YDBGRVv68kolTN7IhtbLgGWREZFKYDBFRhR6vCo3p3AiujqwKEZHpYDJERBU6mpCJv5PuwsbKAm/3amLocIiI9IrJEBGV6/HrCo3t4gUXVoWIyMQwGSKich2+fBtxj6pCIb0aGzocIiK9YzJERGUqqQqVXFfo1a5ecHFgVYiITA+TISIqU/Sl2zibfBe21hYI6cm5QkRkmpgMEZFGQggsezRXKLirF+o72Bg4IiKiqsFkiIg0OnQpA2dT5LCztsSbrAoRkQljMkREakqqQiVzhcYFeMG5NqtCRGS6mAwRkZoDFzJwLkWOWlJLvPEszyAjItPGZIiIVAghsOxAyVyhcQHeqMeqEBGZOCZDRKTijwsZOJ+aw6oQEZkNJkNEpPT4GWTjA73hZC81cERERFWPyRARKe2Pv4V/b+bAXmqJN3qwKkRE5oHJEBEBABSK/51BNqGbN+qyKkREZoLJEBEBAPbHp+NCWg5q21hhUndWhYjIfDAZIiKVqtBrrAoRkZlhMkRE2PdvOi6m58LBxgoTu/sYOhwiomrFZIjIzD1ZFapTi1UhIjIvTIaIzNzv59Nx6VYuHGytMJFzhYjIDDEZIjJjCoXA8kdXm369mw9ktawNHBERUfVjMkRkxvaeT8PlW/fgYGuF1zlXiIjMFJMhIjNVrBBY/miu0KTujSGzY1WIiMwTkyEiM7XnnzQkZNyDo60VXuvubehwiIgMhskQkRkqqQqVzBWa1KMxHG1ZFSIi88VkiMgM/XbuJq7evg+ZnTVe6+Zt6HCIiAzKaJKh7OxsBAcHQyaTQSaTITg4GHfv3q1wuQsXLmDYsGGQyWRwcHBA165dkZSUVPUBE9VQxQqB5QdK5gpN7uEDB1aFiMjMGU0yNGbMGJw5cwaRkZGIjIzEmTNnEBwcXO4yV69eRffu3eHr64vo6GicPXsW8+bNg62tbTVFTVTz7D57E9du30edWtYYH+ht6HCIiAxOIoQQhg6iIhcuXEDLli0RGxuLLl26AABiY2MREBCAixcvokWLFhqXGz16NKytrbF58+ZKbzsnJwcymQxyuRyOjo6VXg9RTVBUrEDQ0iO4lnkf7w5ogSm9mxo6JCKiKqHL97dRVIZiYmIgk8mUiRAAdO3aFTKZDMeOHdO4jEKhwJ49e9C8eXMMGDAALi4u6NKlC3bu3FnutvLz85GTk6PyIDIVu87exLXM+6jLqhARkZJRJEPp6elwcXFRa3dxcUF6errGZTIyMnDv3j189tlnGDhwIPbv348RI0bghRdewOHDh8vc1qJFi5TzkmQyGTw9PfU2DiJDKipWYEXpXKFnG6O2jZWBIyIiqhkMmgyFhoZCIpGU+zh16hQAQCKRqC0vhNDYDpRUhgDg+eefx6xZs9C2bVvMmTMHQ4cOxZo1a8qMae7cuZDL5cpHcnKyHkZKZHg7z9xEYtYDONlLMT7A29DhEBHVGAb913Dq1KkYPXp0uX28vb1x7tw53Lp1S+2127dvw9XVVeNyzs7OsLKyQsuWLVXa/fz88Oeff5a5PRsbG9jY2GgRPZHxKCpWYOXBkqrQG882hj2rQkRESgb9RHR2doazs3OF/QICAiCXy3HixAl07twZAHD8+HHI5XIEBgZqXEYqlaJTp064dOmSSvvly5fh5eX19METGZEdcam48agqNC6A738ioscZxZwhPz8/DBw4EJMnT0ZsbCxiY2MxefJkDB06VOVMMl9fX+zYsUP5/N1338W2bdvw7bff4sqVK1i1ahV2796Nt99+2xDDIDKIwmIFVh68AgB489nGqCVlVYiI6HFGkQwBQHh4OFq3bo2goCAEBQXB399f7ZT5S5cuQS6XK5+PGDECa9aswZIlS9C6dWusW7cO27dvR/fu3as7fCKD2fF3KpLuPIBzbSmCWRUiIlJjFNcZMiReZ4iMWWGxAn2+jEbynYf4cLAfJj/b2NAhERFVC5O7zhARVc720ylIvvMQzrVt8GpXVoWIiDRhMkRkogqKFFh1qGSuUEjPxrCTWho4IiKimonJEJGJ2v53ClKyH6K+A6tCRETlYTJEZIIKihRYdbC0KtQEttasChERlYXJEJEJ+vl0MlLvPoSLgw3Gdmlk6HCIiGo0JkNEJia/qBhfP6oKvdWLVSEiooowGSIyMT+dSsFNeR5cHW3wSmdWhYiIKsJkiMiE5BcVI+zRGWRv92rKqhARkRaYDBGZkJ9OJiNNngc3R1uM6uRp6HCIiIwCkyEiE5FXWIyvD10FAEzpzblCRETaYjJEZCK2nUxGek4e3GW2GMmqEBGR1pgMEZmAvMJihEU/mivUuylsrFgVIiLSFpMhIhOw9UQSbuXkw0Nmi5EdGxo6HCIio8JkiMjIPSwoxuroR3OF+rAqRESkKyZDREbu4z3xyMjNR4M6dni5A+cKERHpiskQkRHbcy4NPxxPgkQCLH7RH1Ir/kkTEemKn5xERir5zgPMiTgHAHirZxN0b+Zs4IiIiIwTkyEiI1RYrMCMH+OQm1eEdo3qYFb/5oYOiYjIaDEZIjJCS6Mu4++ku3CwtcKK0e1gbck/ZSKiyuInKJGR+TMhE6sPl5w9tvhFf3g61TJwRERExo3JEJERybyXj1k/nYEQwCudG2Fwa3dDh0REZPSYDBEZCYVC4D8/ncXt3Hw0d62Nj4a2NHRIREQmgckQkZFY/+d1HL58GzZWFlg1pj3spLy4IhGRPjAZIjICZ5PvYnHkRQDAR8+1RHNXBwNHRERkOpgMEdVwuXmFmLY1DkUKgcGt3TCmcyNDh0REZFKsDB2AucrJK0TOw0JDh0FGYHHkJSTdeYAGdeyw6AV/SCQSQ4dERGRSmAwZyJbYG1gSecnQYZCRsLSQYMUr7SCzszZ0KEREJofJkIFYWUhgw/tIkRasLCR4Z0ALdPCqa+hQiIhMkkQIIQwdRE2Wk5MDmUwGuVwOR0dHQ4dDREREWtDl+5ulCSIiIjJrTIaIiIjIrDEZIiIiIrPGZIiIiIjMGpMhIiIiMmtGkwxlZ2cjODgYMpkMMpkMwcHBuHv3brnL3Lt3D1OnTkXDhg1hZ2cHPz8/rF69unoCJiIiIqNgNMnQmDFjcObMGURGRiIyMhJnzpxBcHBwucvMmjULkZGR2LJlCy5cuIBZs2Zh2rRp+PXXX6spaiIiIqrpjCIZunDhAiIjI7Fu3ToEBAQgICAA3377LX777TdculT2VZxjYmIwfvx49OrVC97e3njjjTfQpk0bnDp1qhqjJyIioprMKJKhmJgYyGQydOnSRdnWtWtXyGQyHDt2rMzlunfvjl27diE1NRVCCBw6dAiXL1/GgAEDylwmPz8fOTk5Kg8iIiIyXUaRDKWnp8PFxUWt3cXFBenp6WUut2LFCrRs2RINGzaEVCrFwIEDERYWhu7du5e5zKJFi5TzkmQyGTw9PfUyBiIiIqqZDJoMhYaGQiKRlPsoPaSl6U7dQohy7+C9YsUKxMbGYteuXTh9+jS+/PJLvP322/jjjz/KXGbu3LmQy+XKR3Jy8tMPlIiIiGosg96oderUqRg9enS5fby9vXHu3DncunVL7bXbt2/D1dVV43IPHz7EBx98gB07dmDIkCEAAH9/f5w5cwZffPEF+vXrp3E5Gxsb2NjY6DgSIiIiMlYGTYacnZ3h7OxcYb+AgADI5XKcOHECnTt3BgAcP34ccrkcgYGBGpcpLCxEYWEhLCxUi1+WlpZQKBRPHzwRERGZBKOYM+Tn54eBAwdi8uTJiI2NRWxsLCZPnoyhQ4eiRYsWyn6+vr7YsWMHAMDR0RE9e/bEu+++i+joaFy/fh0bN27Epk2bMGLECEMNhYiIiGoYg1aGdBEeHo7p06cjKCgIADBs2DCsWrVKpc+lS5cgl8uVz3/88UfMnTsXY8eOxZ07d+Dl5YX//ve/CAkJ0Xq7QggA4FllRERERqT0e7v0e7w8EqFNLzOWkpLCM8qIiIiMVHJyMho2bFhuHyZDFVAoFLh58yYcHBzKPXOtMnJycuDp6Ynk5GQ4Ojrqdd01Acdn/Ex9jByf8TP1MXJ8lSeEQG5uLjw8PNTmDz/JaA6TGYqFhUWFGeXTcnR0NMk3eSmOz/iZ+hg5PuNn6mPk+CpHJpNp1c8oJlATERERVRUmQ0RERGTWmAwZkI2NDebPn2+yF3nk+IyfqY+R4zN+pj5Gjq96cAI1ERERmTVWhoiIiMisMRkiIiIis8ZkiIiIiMwakyEiIiIya0yGqkliYiImTpwIHx8f2NnZoUmTJpg/fz4KCgrKXU4IgdDQUHh4eMDOzg69evXCv//+W01R6+6///0vAgMDUatWLdSpU0erZSZMmACJRKLy6Nq1a9UGWkmVGZ8x7cPs7GwEBwdDJpNBJpMhODgYd+/eLXeZmr7/wsLC4OPjA1tbW3To0AFHjx4tt//hw4fRoUMH2NraonHjxlizZk01RVo5uowvOjpabV9JJBJcvHixGiPW3pEjR/Dcc8/Bw8MDEokEO3furHAZY9t/uo7RmPbhokWL0KlTJzg4OMDFxQXDhw/HpUuXKlzOEPuQyVA1uXjxIhQKBdauXYt///0XS5cuxZo1a/DBBx+Uu9ySJUvw1VdfYdWqVTh58iTc3NzQv39/5ObmVlPkuikoKMDLL7+Mt956S6flBg4ciLS0NOVj7969VRTh06nM+IxpH44ZMwZnzpxBZGQkIiMjcebMGQQHB1e4XE3df9u2bcPMmTPx4YcfIi4uDj169MCgQYOQlJSksf/169cxePBg9OjRA3Fxcfjggw8wffp0bN++vZoj146u4yt16dIllf3VrFmzaopYN/fv30ebNm3UbspdFmPbf4DuYyxlDPvw8OHDmDJlCmJjYxEVFYWioiIEBQXh/v37ZS5jsH0oyGCWLFkifHx8ynxdoVAINzc38dlnnynb8vLyhEwmE2vWrKmOECttw4YNQiaTadV3/Pjx4vnnn6/SePRN2/EZ0z6Mj48XAERsbKyyLSYmRgAQFy9eLHO5mrz/OnfuLEJCQlTafH19xZw5czT2f++994Svr69K25tvvim6du1aZTE+DV3Hd+jQIQFAZGdnV0N0+gVA7Nixo9w+xrb/nqTNGI15H2ZkZAgA4vDhw2X2MdQ+ZGXIgORyOZycnMp8/fr160hPT0dQUJCyzcbGBj179sSxY8eqI8RqEx0dDRcXFzRv3hyTJ09GRkaGoUPSC2PahzExMZDJZOjSpYuyrWvXrpDJZBXGWhP3X0FBAU6fPq3yuweAoKCgMscTExOj1n/AgAE4deoUCgsLqyzWyqjM+Eq1a9cO7u7u6Nu3Lw4dOlSVYVYrY9p/T8sY96FcLgeAcr/3DLUPmQwZyNWrV7Fy5UqEhISU2Sc9PR0A4OrqqtLu6uqqfM0UDBo0COHh4Th48CC+/PJLnDx5En369EF+fr6hQ3tqxrQP09PT4eLiotbu4uJSbqw1df9lZmaiuLhYp999enq6xv5FRUXIzMysslgrozLjc3d3xzfffIPt27cjIiICLVq0QN++fXHkyJHqCLnKGdP+qyxj3YdCCMyePRvdu3dHq1atyuxnqH3IZOgphYaGapzM9vjj1KlTKsvcvHkTAwcOxMsvv4xJkyZVuA2JRKLyXAih1laVKjNGXYwaNQpDhgxBq1at8Nxzz+H333/H5cuXsWfPHj2OomxVPT7AsPtQl/FpiqmiWA29/yqi6+9eU39N7TWFLuNr0aIFJk+ejPbt2yMgIABhYWEYMmQIvvjii+oItVoY2/7TlbHuw6lTp+LcuXPYunVrhX0NsQ+tqmzNZmLq1KkYPXp0uX28vb2VP9+8eRO9e/dGQEAAvvnmm3KXc3NzA1CSKbu7uyvbMzIy1DLnqqTrGJ+Wu7s7vLy8kJCQoLd1lqcqx1cT9qG24zt37hxu3bql9trt27d1irW6919ZnJ2dYWlpqVYlKe937+bmprG/lZUV6tWrV2WxVkZlxqdJ165dsWXLFn2HZxDGtP/0qabvw2nTpmHXrl04cuQIGjZsWG5fQ+1DJkNPydnZGc7Ozlr1TU1NRe/evdGhQwds2LABFhblF+Z8fHzg5uaGqKgotGvXDkDJPIHDhw9j8eLFTx27tnQZoz5kZWUhOTlZJXmoSlU5vpqwD7UdX0BAAORyOU6cOIHOnTsDAI4fPw65XI7AwECtt1fd+68sUqkUHTp0QFRUFEaMGKFsj4qKwvPPP69xmYCAAOzevVulbf/+/ejYsSOsra2rNF5dVWZ8msTFxRl8X+mLMe0/faqp+1AIgWnTpmHHjh2Ijo6Gj49PhcsYbB9W6fRsUkpNTRVNmzYVffr0ESkpKSItLU35eFyLFi1ERESE8vlnn30mZDKZiIiIEP/884945ZVXhLu7u8jJyanuIWjlxo0bIi4uTixYsEDUrl1bxMXFibi4OJGbm6vs8/gYc3NzxX/+8x9x7Ngxcf36dXHo0CEREBAgGjRoUCPHqOv4hDCufThw4EDh7+8vYmJiRExMjGjdurUYOnSoSh9j2n8//vijsLa2FuvXrxfx8fFi5syZwt7eXiQmJgohhJgzZ44IDg5W9r927ZqoVauWmDVrloiPjxfr168X1tbW4pdffjHUEMql6/iWLl0qduzYIS5fvizOnz8v5syZIwCI7du3G2oI5crNzVX+jQEQX331lYiLixM3btwQQhj//hNC9zEa0z586623hEwmE9HR0SrfeQ8ePFD2qSn7kMlQNdmwYYMAoPHxOABiw4YNyucKhULMnz9fuLm5CRsbG/Hss8+Kf/75p5qj19748eM1jvHQoUPKPo+P8cGDByIoKEjUr19fWFtbi0aNGonx48eLpKQkwwygArqOTwjj2odZWVli7NixwsHBQTg4OIixY8eqncJrbPvv66+/Fl5eXkIqlYr27durnNY7fvx40bNnT5X+0dHRol27dkIqlQpvb2+xevXqao5YN7qMb/HixaJJkybC1tZW1K1bV3Tv3l3s2bPHAFFrp/Q08icf48ePF0KYxv7TdYzGtA/L+s57/POxpuxDyaOAiYiIiMwSzyYjIiIis8ZkiIiIiMwakyEiIiIya0yGiIiIyKwxGSIiIiKzxmSIiIiIzBqTISIiIjJrTIaIiIjIrDEZIqIaa8KECRg+fHi1b3fjxo2oU6dOtW+XiAyDyRARERGZNSZDRGQ0evXqhenTp+O9996Dk5MT3NzcEBoaqtJHIpFg9erVGDRoEOzs7ODj44Off/5Z+Xp0dDQkEgnu3r2rbDtz5gwkEgkSExMRHR2N1157DXK5HBKJBBKJRG0bZdm0aRNq166NhIQEZdu0adPQvHlz3L9//2mGTkRViMkQERmV77//Hvb29jh+/DiWLFmChQsXIioqSqXPvHnz8OKLL+Ls2bN49dVX8corr+DChQtarT8wMBDLli2Do6Mj0tLSkJaWhnfeeUerZceNG4fBgwdj7NixKCoqQmRkJNauXYvw8HDY29vrPFYiqh5MhojIqPj7+2P+/Plo1qwZxo0bh44dO+LAgQMqfV5++WVMmjQJzZs3x8cff4yOHTti5cqVWq1fKpVCJpNBIpHAzc0Nbm5uqF27ttbxrV27FmlpaZg+fTomTJiA+fPno1OnTjqNkYiql5WhAyAi0oW/v7/Kc3d3d2RkZKi0BQQEqD0/c+ZMVYcGAKhbty7Wr1+PAQMGIDAwEHPmzKmW7RJR5bEyRERGxdraWuW5RCKBQqGocDmJRAIAsLAo+dgTQihfKyws1GOEwJEjR2BpaYmbN29yrhCREWAyREQmJzY2Vu25r68vAKB+/foAgLS0NOXrT1aNpFIpiouLK7XtY8eOYcmSJdi9ezccHR0xbdq0Sq2HiKoPD5MRkcn5+eef0bFjR3Tv3h3h4eE4ceIE1q9fDwBo2rQpPD09ERoaik8++QQJCQn48ssvVZb39vbGvXv3cODAAbRp0wa1atVCrVq1Ktxubm4ugoODMW3aNAwaNAiNGjVCx44dMXToULz88stVMlYienqsDBGRyVmwYAF+/PFH+Pv74/vvv0d4eDhatmwJoOQw29atW3Hx4kW0adMGixcvxieffKKyfGBgIEJCQjBq1CjUr18fS5YsAQCEhobC29u7zO3OmDED9vb2+PTTTwEAzzzzDBYvXoyQkBCkpqZWzWCJ6KlJxOMHzomIjJxEIsGOHTuq5MrVEyZMAFByhWoiMh08TEZEpKXDhw/jyJEjhg6DiPSMyRARkZauX79u6BCIqAowGSIik8Ij/0SkK06gJiIiIrPGZIiIiIjMGpMhIiIiMmtMhoiIiMisMRkiIiIis8ZkiIiIiMwakyEiIiIya0yGiIiIyKwxGSIiIiKz9v9rOAnVaAbJ3wAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "saturation=ct.saturation_nonlinearity(0.75)\n", "x = np.linspace(-2, 2, 50)\n", "plt.plot(x, saturation(x))\n", "plt.xlabel(\"Input, x\")\n", "plt.ylabel(\"Output, y = sat(x)\")\n", "plt.title(\"Input/output map for a saturation nonlinearity\");" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/murray/anaconda3/envs/python3.10-slycot/lib/python3.10/site-packages/matplotlib/cbook/__init__.py:1298: ComplexWarning: Casting complex values to real discards the imaginary part\n", " return np.asarray(x, float)\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "amp_range = np.linspace(0, 2, 50)\n", "plt.plot(amp_range, ct.describing_function(saturation, amp_range))\n", "plt.xlabel(\"Amplitude A\")\n", "plt.ylabel(\"Describing function, N(A)\")\n", "plt.title(\"Describing function for a saturation nonlinearity\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Backlash nonlinearity\n", "A friction-dominated backlash nonlinearity can be obtained using the `ct.friction_backlash_nonlinearity` function. This function takes as is argument the size of the backlash region." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "backlash = ct.friction_backlash_nonlinearity(0.5)\n", "theta = np.linspace(0, 2*np.pi, 50)\n", "x = np.sin(theta)\n", "plt.plot(x, [backlash(z) for z in x])\n", "plt.xlabel(\"Input, x\")\n", "plt.ylabel(\"Output, y = backlash(x)\")\n", "plt.title(\"Input/output map for a friction-dominated backlash nonlinearity\");" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "amp_range = np.linspace(0, 2, 50)\n", "N_a = ct.describing_function(backlash, amp_range)\n", "\n", "plt.figure()\n", "plt.plot(amp_range, abs(N_a))\n", "plt.xlabel(\"Amplitude A\")\n", "plt.ylabel(\"Amplitude of describing function, N(A)\")\n", "plt.title(\"Describing function for a backlash nonlinearity\")\n", "\n", "plt.figure()\n", "plt.plot(amp_range, np.angle(N_a))\n", "plt.xlabel(\"Amplitude A\")\n", "plt.ylabel(\"Phase of describing function, N(A)\")\n", "plt.title(\"Describing function for a backlash nonlinearity\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### User-defined, static nonlinearities\n", "\n", "In addition to pre-defined nonlinearies, it is possible to computing describing functions for static nonlinearities. The describing function for any suitable nonlinear function can be computed numerically using the `describing_function` function." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Define a saturation nonlinearity as a simple function\n", "def my_saturation(x):\n", " if abs(x) >= 1:\n", " return math.copysign(1, x)\n", " else:\n", " return x\n", "\n", "amp_range = np.linspace(0, 2, 50)\n", "plt.plot(amp_range, ct.describing_function(my_saturation, amp_range).real)\n", "plt.xlabel(\"Amplitude A\")\n", "plt.ylabel(\"Describing function, N(A)\")\n", "plt.title(\"Describing function for a saturation nonlinearity\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Stability analysis using describing functions\n", "Describing functions can be used to assess stability of closed loop systems consisting of a linear system and a static nonlinear using a Nyquist plot." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Limit cycle position for a third order system with saturation nonlinearity\n", "\n", "Consider a nonlinear feedback system consisting of a third-order linear system with transfer function $H(s)$ and a saturation nonlinearity having describing function $N(a)$. Stability can be assessed by looking for points at which \n", "\n", "$$\n", "H(j\\omega) N(a) = -1$$\n", "\n", "The `describing_function_plot` function plots $H(j\\omega)$ and $-1/N(a)$ and prints out the the amplitudes and frequencies corresponding to intersections of these curves. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[(3.343977839541308, 1.4142156916816762)]" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Linear dynamics\n", "H_simple = ct.tf([8], [1, 2, 2, 1])\n", "omega = np.logspace(-3, 3, 500)\n", "\n", "# Nonlinearity\n", "F_saturation = ct.saturation_nonlinearity(1)\n", "amp = np.linspace(00, 5, 50)\n", "\n", "# Describing function plot (return value = amp, freq)\n", "ct.describing_function_plot(H_simple, F_saturation, amp, omega)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The intersection occurs at amplitude 3.3 and frequency 1.4 rad/sec (= 0.2 Hz) and thus we predict a limit cycle with amplitude 3.3 and period of approximately 5 seconds." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Create an I/O system simulation to see what happens\n", "io_saturation = ct.NonlinearIOSystem(\n", " None,\n", " lambda t, x, u, params: F_saturation(u),\n", " inputs=1, outputs=1\n", ")\n", "\n", "sys = ct.feedback(ct.ss(H_simple), io_saturation)\n", "T = np.linspace(0, 30, 200)\n", "t, y = ct.input_output_response(sys, T, 0.1, 0)\n", "plt.plot(t, y);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Limit cycle prediction with for a time-delay system with backlash\n", "\n", "This example demonstrates a more complicated interaction between a (non-static) nonlinearity and a higher order transfer function, resulting in multiple intersection points." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[(0.6260158833534124, 0.3102619497970334),\n", " (0.8741930326860968, 1.2156410944770426)]" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Linear dynamics\n", "H_simple = ct.tf([1], [1, 2, 2, 1])\n", "H_multiple = H_simple * ct.tf(*ct.pade(5, 4)) * 4\n", "omega = np.logspace(-3, 3, 500)\n", "\n", "# Nonlinearity\n", "F_backlash = ct.friction_backlash_nonlinearity(1)\n", "amp = np.linspace(0.6, 5, 50)\n", "\n", "# Describing function plot\n", "ct.describing_function_plot(H_multiple, F_backlash, amp, omega, mirror_style=False)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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": "3.10.6" } }, "nbformat": 4, "nbformat_minor": 4 }