{ "cells": [ { "cell_type": "markdown", "id": "270ad328-df02-497f-90ef-6407b88fa5c8", "metadata": {}, "source": [ "# Control theory. Course introduction.\n", "\n", "## TP1. System modeling. State-space representation of dynamical systems.\n", "\n", "## Study load\n", "\n", "Course grade breakdown:\n", "\n", " Labs - 40%\n", " \n", " Final project presentation 30%\n", "\n", " Final test 30%\n", " \n", "File name for lab submission: yourname_labnumber.ipynb (example: elenavanneaux_TP1.ipynb) \n", "\n", "The completed notebooks should be sent to your tutor (elena.vanneaux@ensta.fr or adnane.saood@ensta.fr) before the beginning of the next session. Please add [APM_4AUT2_TA] to the topic of e-mail.\n", "\n", "## Prerequisites for practice\n", "### Math\n", "During the course, we will cover the following areas of mathematics:\n", " \n", " 1. Linear Algebra\n", "\n", " 2. Calculus\n", "\n", " 3. Differential equations\n", "\n", " 4. Dynamics (Mechanics and Physics)\n", "\n", "### Python programming\n", "In the labs we will use a Python programming language and the following libraries:\n", "\n", " 1. NumPy https://numpy.org/doc/stable/\n", "\n", " 2. SciPy https://docs.scipy.org/doc/scipy/\n", "\n", " 3. Matplotlib https://matplotlib.org/stable/tutorials/index\n", "\n", " 4. SymPy https://docs.sympy.org/latest/tutorials/intro-tutorial/intro.html\n", "\n", "### Jupyter Notebook Markdown Cells Documentation\n", "\n", "Please check on Markdown cells documentation, to provide a fancy look for your notebooks!\n", "\n", "https://jupyter-notebook.readthedocs.io/en/stable/examples/Notebook/Working%20With%20Markdown%20Cells.html" ] }, { "attachments": { "6f14898e-e45b-4904-b40e-f138432b0f95.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "3e68a5e9-25d8-4044-9d5d-9b0a2f9f3658", "metadata": {}, "source": [ "## Ex.1: Vehicle Suspension System\n", "\n", "Vehicle Suspension System\n", "\n", "![Suspension.png](attachment:6f14898e-e45b-4904-b40e-f138432b0f95.png)\n", "\n", "with the following system parameters:\n", "\n", " (m) mass 1.0 kg\n", "\n", " (k) spring constant 5.0 N/m\n", "\n", " $(c)$ damping constant 2 Ns/m\n", "\n", "### **Equation of Motion:**\n", "\n", "For a mass-spring-damper system, the equation of motion can be derived using Newton's second law or by applying the principles of dynamics. The general form of the equation is:\n", "\n", "$$\n", "m \\frac{d^2x}{dt^2} + c \\frac{dx}{dt} + kx = u + w\n", "$$\n", "\n", "### **State-Space Representation:**\n", "\n", "To convert the second-order differential equation into a system of first-order differential equations, we introduce the following state variables:\n", "- Let $ x_1 = x $ (position),\n", "- Let $ x_2 = \\dot x $ (velocity).\n", "\n", "The system becomes:\n", "\n", "$$\\dot x = Ax+Bu+Dw$$\n", "\n", "where\n", "state vector $x = (position, velocity)$, and state and control matrices are the following:\n", "$$ A = \\begin{pmatrix} 0&1\\\\ -\\frac{k}{m}&-\\frac{c}{m}\\end{pmatrix},\\ B = \\begin{pmatrix} 0\\\\ \\frac{1}{m} \n", "\\end{pmatrix},\\ D =\\begin{pmatrix} 0\\\\ \\frac{1}{m} \n", "\\end{pmatrix}$$\n", "\n", "## TODO\n", "\n", "Today we will study the dynamic of a passive suspension system, i.e. we assume that there is no active control ($u =0,$ for all $t>0$). \n", "\n", "1. Check on the code below, what kind of situation does it model?\n", "\n", "Modify the code below to analyse how the suspension system will work on different roads.\n", "\n", "2. Let disturbance input $w(t)$ is given by a step function\n", " $$w = \\left\\{\\begin{aligned}\n", " &0, \\quad t <3.0\\\\\n", " &1.0, \\quad 3.0 \\leq t < 7.0\\\\\n", " &0, \\quad t \\geq 7\n", " \\end{aligned}\\right.$$\n", " How will it affect the behavior of the system? What kind of road scenario is modeled with step function disturbance?\n", "3. How the system behavior will change additionally assume that there is no damper in the system (i.e., c=0)?\n", "4. Let now assume that the system is disturbed by a sinusoidal input\n", " $$w = sin(t)$$\n", " How will it affect the behavior of the system? What kind of road profile does a sinusoidal input model?" ] }, { "cell_type": "code", "execution_count": 15, "id": "cc3aa850-445d-45cd-b290-1e557ab026c9", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from scipy.integrate import odeint\n", "import matplotlib.pyplot as plt\n", "\n", "# x is a state vecot, t is a current time, A is a dynamic matrix, B is a control matrix, D is a disturbance matrix, \n", "# u_func(t) is a control input, w_func(t) is a disturbance input \n", "def StateSpace(x, t, A, B, D, u_func, w_func):\n", " w = w_func(t)\n", " u = u_func(t)\n", " # Flatten u and w for proper matrix operations\n", " return np.dot(A, x) + np.dot(B, u).flatten() + np.dot(D, w).flatten()\n", "\n", "# OpenLoopInputOutputSystem with time-dependent w(t)\n", "def OpenLoopInputOutputSystem(A, B, D, C, R, u_func, w_func, T, x0):\n", " # Solve the ODE system with odeint, passing the time-dependent w function\n", " solution = odeint(StateSpace, x0, T, args=(A, B, D, u_func, w_func))\n", " # Output calculation using C and the solution\n", " return (C @ solution.T) " ] }, { "cell_type": "code", "execution_count": 14, "id": "e48f85a4-b5c9-4b28-b4b1-e5c0cc882330", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# System parameters\n", "m = 1\n", "k = 5\n", "c = 2\n", "g = 9.8\n", "\n", "A = np.array([[0, 1],\n", " [-k/m, -c/m]]) # Corrected c instead of rho\n", "\n", "B = np.array([[0],\n", " [1/m]]) # Reshaped to column vector\n", "\n", "D = np.array([[0],\n", " [1/m]]) # Reshaped to column vector\n", "\n", "C = np.array([[1, 0],[0,1]]) # Output matrix\n", "\n", "R = np.array([0])\n", "\n", "# flatten() to convert to 1D array since scipy.integrate.odeint requires the state vector (x) to have shape (n,), not (n,1).\n", "x0 = np.array([0, 0]).flatten() # Initial state\n", "\n", "# Time settings\n", "t0 = 0 # Initial time \n", "tf = 10 # Final time\n", "T = np.linspace(t0, tf, 1000) # Time vector\n", "\n", "def w_func(t):\n", " return 0.0 # Disturbance input\n", " \n", "def u_func(t):\n", " return 0.0 # Control input\n", "\n", "# Compute system response\n", "y = OpenLoopInputOutputSystem(A, B, D, C, R, u_func, w_func, T, x0)\n", "\n", "# Plot the response\n", "plt.plot(T, y[0,:], linewidth=2.0, color='red')\n", "plt.grid(color='black', linestyle='--', linewidth=1.0, alpha=0.7)\n", "plt.xlim([t0, tf])\n", "plt.ylabel(r'Position (m)')\n", "plt.xlabel('Time (s)')\n", "plt.title('Passive Suspension System ')\n", "plt.show()\n", "\n", "plt.plot(T, y[1,:], linewidth=2.0, color='red')\n", "plt.grid(color='black', linestyle='--', linewidth=1.0, alpha=0.7)\n", "plt.xlim([t0, tf])\n", "plt.ylabel(r'Velocity (m/s)')\n", "plt.xlabel('Time (s)')\n", "plt.title('Passive Suspension System ')\n", "plt.show()" ] }, { "attachments": { "088d06d6-d3f2-4eb0-b59e-26c1eae022e8.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "2c556998-dcec-4db7-a62d-ab23cbed0974", "metadata": {}, "source": [ "## Ex.2: DC Motor Speed: System Modeling\n", "\n", "A common actuator in control systems is the DC motor. It directly provides rotary motion and, coupled with wheels or drums and cables, can provide translational motion. The electric equivalent circuit of the armature and the free-body diagram of the rotor are shown in the following figure.\n", "\n", "![motor.png](attachment:088d06d6-d3f2-4eb0-b59e-26c1eae022e8.png)\n", "\n", "For this example, we will assume that the input of the system is the voltage source ($V$) applied to the motor's armature, while the output is the rotational speed of the shaft $\\dot{\\theta}$. The rotor and shaft are assumed to be rigid. We further assume a viscous friction model, that is, the friction torque is proportional to shaft angular velocity. We will assume that the magnetic field is constant and, therefore, that the motor torque is proportional (with constant $K_t$) to only the armature current. Let us remark that in SI units the motor torque and back emf constants are equal, that is, $K_t = K_e$.\n", "\n", "The physical parameters for our example are:\n", "\n", " (J) moment of inertia of the rotor 0.01 kg.m^2\n", "\n", " (b) motor viscous friction constant 0.1 N.m.s\n", "\n", " (Ke) electromotive force constant 0.01 V/rad/sec\n", "\n", " (Kt) motor torque constant 0.01 N.m/Amp\n", "\n", " (R) electric resistance 1 Ohm\n", "\n", " (L) electric inductance 0.5 H\n", "\n", "## TODO\n", "1. Let us assume that the state vector is $x = (w,i)$ where $w = \\dot\\theta$ is an angular velocity of the motor. Derive the state space equations of the system. Is the system linear?\n", "2. Rewrite the system equations in canonical first order ODE system form.\n", "3. Simulate the output of the system corresponding to uncontrolled system (i.e V = 0) and a random initial position.\n", "4. Let's assume that the motor is off. How will the system's behavior change if we apply 15 volts as an input?\n" ] }, { "cell_type": "code", "execution_count": null, "id": "bca05712-67db-4e0b-b21b-403eba888b46", "metadata": {}, "outputs": [], "source": [] }, { "attachments": { "07d2d484-1bdd-424d-a286-f484bdacbf16.png": { "image/png": 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IDg7Gxo0btXkSPD098f7776e4TyLC06dPTdJERUWlOcARQkCv12PmzJkYPXo05s6di6lTp3JwwbKcWvKW0n3PWE6Wtqczy7PUB2F6H4aKomD69OkICAiAoihQFAXt2rWDnZ1dqvu8deuWyd+ppU+Oev7Tp0/HyJEjMWnSJEyaNIkDC5Zl1EBWUZQ0B8eM5RR8ZzOLqHXB6cnU1VKHRYsWgRL1/OjRo0eKdcxqhv/kyROT5Rl5IKvBxdy5c/Hhhx/i559/xrRp07jkgmUZ9V7LyH3MWHbGdzaziJrppvdhuGXLFkRGRmqBRYUKFVCvXr0UAxUiQmxsLO7du2ey3MHBQauaSQ9h7C0yd+5cjBw5EhMmTMAvv/xinoyxTMElFiy34zubWSS9dcJqQLJ69WqTB2nPnj3h4OCQ6j6jo6Px6tUrk23d3d0zXLoghIAkSZg1axbee+89jBkzBtOnT+eSC5YlZFnmwILlWnxnM4uoVRZpfRgSEU6fPo1Lly7BYDBACAFbW1v06tUr1aBCCIGAgACEhYVpxycilC5dOs3nkRRhbNC5cuVKjBw5EpMnT8avv/4KJAqIGLM2NXjV6XTmqxjLFTL+dGZ5QnrbWAghsGbNGhgMBm1ZwYIFUaZMGe0Bm9wLAC5cuIDY2FiQsQolX7588PLyskpgoRJCYN68eRgwYADGjBmDefPmccmFBfgapQ9xrxCWy1nv6cxytfT0CiEiGAwGHD58WNuOiODp6QlXV1dtf8m9YGyboRJCoFKlSihSpEiaziM1QgjY2Njgt99+Q8+ePfH1119j7ty5AJdcJEsN9IRxmHe+TpZTAwtrBseMZSc8bTpLFRHh77//xsiRI/HgwQMUK1bMoociESEgIABVq1ZFZGSkVurh5eWFVq1aWZQZ/f3334iKigKM1TCff/45Zs2aZdXAQkVESEhIwMcff4wVK1Zg9uzZGDVqFJCOkprcSs0UlyxZgqNHj0KWZfj4+ODDDz+Era2teXJmRlEUREZGokaNGujZsydmzJhh0XeJsRyFGEuFoii0cuVKcnBwoMDAQFIUxTxJkmRZplWrVpEQgoQQBCDdL3UfK1assPj46aEoCsXExFDv3r1JkiSaP38+ybKcqcfMKWRZpjt37lDdunVJp9NR6dKlqVKlSmRjY0NDhgwhg8FgvgkzI8syhYeHk4eHB33zzTcky7J5EsZyPC6xYBYJCQnBlStX0LRpU4t+YalF5UOHDsWKFSu0VvClSpXCsmXLEBsbm2wpABHBxsYGS5Yswdq1awFjaYVOp8OpU6dQq1Yti84hvYgIMTExGDx4MHbu3Ik5c+Zg+PDhyZ5vXqAoCu7cuYOOHTvi4cOHGDJkCGbMmAE7Ozt8/PHH2LlzJy5evIiSJUtm6meTW5w7dw6lSpVC0aJFzVcxluNxYMEyBREhOjoa5cuXR1BQkBZovPfee1i1ahWQQvWCmrZ79+7Yvn271r6jWLFiuH79OpydnTM98yLjGBojRozA6tWrsXjxYgwdOjTZc87NiAihoaFo0aIFrl27hkqVKuH48eMoUKAAiAjbt29H//79ceLECdSqVStPXiPG2P+XuU9nlmcREZ4/f44XL16YLGvWrJnW6C85QggoioILFy6YLO/fv3+WBBUwnoO9vT0WLlyIVq1aYfjw4VrJS16KxYkIsizjgw8+wI0bN5AvXz7s3LnTZJp7R0dHKIqC8PBw880ZY3lQ5j+hWZ4VGBio/V8NJKpUqZJqxkxEOHXqlMksqI6Ojvjf//6XYkBibUIIODg4YOfOnejevTs++eQTrFu3zjxZrrd27Vps3rwZsizjnXfeQbly5bR1kiQhOjoawtgVmDHGOLBgmebVq1cmfwshUK5cuVQDC7XXgZpOCIE6deqgePHi5kkznRACdnZ2WLZsGdq1a4dBgwZh9erVqb6H3ICIEBYWhqlTp0Kn08HR0RFfffWVVlUF4/V5+PAhdDodnJ2d88R1YYyljAMLlimEEFo3UVX58uXh5uZmssycoigICQnBzp07tWVEhJ49e5pkaFlJCIH8+fNj+fLlaNSoEYYMGYLNmzdDUZRcm5Gq13rixIm4ffs2AKBz584mDWfV937t2jXY29vDycnJZB+MsbyJAwuWKRIHFmScybFu3bpwcHBIsY2EEAK3bt3S6uuFEChatCj69etnnjRLqUX9O3fuxDvvvIOhQ4di48aN5slyladPn2LVqlUQxnlVRowYYRLYqf8/efIkypQpg0KFCqX42TLG8gZ+CrBMExcXp/2fjCNuWvILf+vWrUhISAAZ51P49ttvUbBgwbdSWpGYWnKxZMkS1KtXD++//z42bdqkDfyV2yxevBjBwcEAgCJFiqB27dom6xVFwalTp/DgwQP07t2bB8hijAEcWLDMZG9vDxgzZCJCpUqVUgwOFEXBkydP8Ndff2lF8QUKFED37t0tCkiygnpOGzZsQMOGDTFkyBDs3bs3V/UWURQFr169wqxZs7RlgwYNgpOTk/b5qZ/PsmXLYGNjgx49euSa988YyxgOLJhFyDiUs6WIyKTOXafTpTrHhxACf/31F8LDw7VM6uOPP0bRokWzVRG7JElwdXXF5s2b0axZM/Tq1Qvbtm0D5ZI5M4QQ2L59O6KioiCEgJOTU5IDhD19+hQbN25Ey5Yt4enp+cZ6lrzc3D6HsezztGbZWnR0NAICAswXJ4uITBpqqhlUcsg4XsLmzZshjHX6devWxffff58tMywhBFxdXfH333+jYsWKGDBgAPbt25fjgwu1JGL9+vXada9WrRrKlCnzxuewYcMGhIaG4v3339e6BbPUkXEOncRVhYzlJhxYsFQREZYtW4YGDRpoU5hbwrx7aEJCgsnfiRERZsyYgVu3bmmlI5MmTQISNRLMbnQ6HQoVKoT9+/ejXr166N+/P44dO2bx9cmOiAgPHz7EmTNnIIwDlTVt2hRI9DkoioKAgADMmDEDHh4eaN++fbb9jLIbRVHw+vVr1KlTBytWrMjR9wpjyeHAglkkNDQUoaGhkGXZfFWShBAoW7YsXFxcAACyLOPVq1dJPkiJCHfu3MGPP/4IMjbYHD9+PDp06JCtqkCSIoSAm5sb1q1bB29vb3To0AG7du1K8n3mBEII/Pnnn4iIiNBKL3x9fbVqMDL28Jk9ezZCQ0Mxb948k7YXLGVknEE3NDQUkZGR5qsZyxWy91ObZRtqUXdaMhAnJycMGDAAkiSBiHD37t0kM1wiwtSpU5GQkABFUVCvXj1MmDAhTW063iYhBNzd3bFu3ToUL14cffr0wX///Zfj6tHJOPna33//rX3e7u7uqFatmsn7CAwMxF9//YWaNWuidevWabon2P9dZzVAYyw34jubWUTNWCx9GKqZzRdffAEHBwfodDocOXJEe6giUYPQmTNnarOY1qtXDxs3boStra3Fx8oO1GqR06dPo3bt2ujevTtOnjyZ4wKLe/fuITw8XAsimzZtikKFCkGn04GIEB4eDl9fXwDAvHnzYGtry4FFGqnfAZ1OZ76KsVwh5zy52Vullh6kNRMpW7asVpS+e/duk1KLhIQE7NixAz/99BOICFWqVMG6detQrFixNB8nO5AkCQULFsTq1atRpkwZdOrUCYcOHcoxwYUQAn5+flpbGCJC7969TdYvXrwYV65cwVdffYV69erlyM8pO1AUJUcFzoylBd/ZzCJkrG9PS0aipl2wYAHKlCkDGxsbDBs2DIGBgQgICMCHH36Id999F2FhYXjnnXfg5+eXZO+DnESSJJQsWRI7duyAu7s7evfujStXruSY4GLv3r1ahpcvXz4teJBlGUeOHMG4ceNQrlw5fPHFFznmPWU3aS39Yyyn4TubWURttJnW4EL9Fb937168++67uHr1KsqUKYOyZcti3bp1aN68OdasWYN169bBzs4uVzxsJUlC4cKFcejQIXh6eqJt27Y4ceJEts6IFUVBVFQUTp48qbWvKFSoENzc3KAoCoKDg/HRRx+hUKFC2Lt3LxwdHXPFZ/U2cGDBcju+s5lF0lNioRJCoEKFCvjnn39w9+5dHDx4EPv27cPt27dx4MAB9O7dG3Z2dunad3alllysXbsWBQoUQNeuXbUGndnVs2fP8OzZM63RaZUqVeDo6IjIyEj07t0b9+/fx7Rp01ChQgXOFDNA/S5xGwuWW/HTgVkko3XCatDg7u6Oxo0bo1mzZihWrFiGApbsTpIklC5dGocPH0aRIkXQq1cv3L17N9sGFxcvXtT+L4RAixYtYGNjg2+++QZHjx7F119/jffff99kG5Z+Gfk+MZad8Z3NLCLLslUehDqdzuSVGwOKxHQ6HYoWLYodO3agcOHCaNSoEU6fPp3tqkWEELh48aIW6EmShIYNG2LixIlYtGgRfH19MWbMmDzxmWU2rgphuR3f2cxinKGkjyRJ8PDwwObNm6HT6dCtWzdcu3Yt25RckLH74507dwDj51ykSBEEBARg2rRpaNiwIXbv3g1nZ2e+B6yAAwuW2/GdzSyS0nDcLHWSJKFcuXK4ePEi3N3d0alTJ9y5cydbBRchISGAsdrr5cuX+PDDD1GpUiX8888/WkkGy7jcXP3HGDiwYJZq3rw5+vTpww3OMkAIgWLFimHDhg2wt7dH8+bN4efn99aDC/UXdFRUlLbMYDCgRIkS2LVrF0qVKsWZoJWovaTatWuH6tWr83VluZKg7FbZy7Il/sVqPUSEx48fw9vbG05OTjhz5gyKFy/+1orGFUWBoiioXbs2rl27BiEEihcvjgsXLqBgwYJv7bwYYzkTPzGYRYQQ2a7BYU4lhEDp0qXh5+cHV1dXNGvWDDdv3nyr15eIEBsbC51OB0VRMGHCBLi7u3NQkUne5mfNWGbjpwazGJdYWI8QAuXLl8c///wDg8GADh064OrVqxbPHmtNRIQzZ84gKChIy/DKlCljnoxZEX+XWG7GgQVjb4kkSfD29sbhw4cRFxeHHj164PXr11n+a3b79u1o27YtwsPDtfYe+fLle+ttPxhjORMHFoy9RUIIlCtXDvv27YNOp4OPj0+WVIsQEWRZxtKlSzF06FCUKlUKxYsX19arw3ozxlhacWDB2FsmSRKqV6+ODRs2ICQkBF27dsX9+/cztVpElmX8888/+Pjjj1GqVCn4+fmhdevW2vro6OhUAwsiQkJCApdsMMZMcGDBWDagBhenTp1CbGwsunXrhvDw8EwpuTAYDNi/fz+GDx8OT09P7Ny5E05OTvDy8tLSREZGmmxjjojw8uVLtGrVChs3bjRfzRjLwziwYCybEELA09MTGzZsQFRUFHx8fHD79m2rlwhIkoRq1arhww8/xO7du1GqVCkAQNu2bSFJEoQQuHfvnvlmGkVRcPfuXXTt2hXnzp2Dg4NDpgRAjLGcicexYCybISJcv34dDRo0QJkyZXDkyBEUKlQoU7p+knF8EvXfVq1a4cSJE2jbti127twJJOrBQMahvx89eoQWLVogKCgIa9euRefOnTPl3HIz9Xozlhvx04CxbEYIgapVq+LMmTOIioqCr68vXr58afVSgcSZmxpcfPnllwCAI0eO4PDhw9oxiQhxcXGYPn06atWqBUVRsGPHDnTq1IkzSMaYCQ4sWKqICEuWLMH48eOtnrmxpKnBxcqVK/HixQt06NABDx8+tOr1Nw8IhBBo27YtBg8eDIPBgH79+uGff/7BwYMH8fvvv6N+/fqYPHkyateujf3796N169Y822kaKYqCFy9eoF27dvD397fq58lYdsFVISxVRIR+/frhypUruHr1Khd7Z7Hr16+jUaNGKF++PP777z/Y29tnWmauVnf88ccfGD9+PKKjo7V1jRo1wuTJk9G8eXMInkQrXRRFwaVLl9CwYUPs3bsXLVu2NE/CWI7HOQSzGP86fTu8vLywe/duvH79Gk2bNkVAQIDVG3SqhBCQJAmffPIJ/P39cf78eZw5cwb+/v44dOgQWrRooTXwZOmj/pbT6/XmqxjLFTiwYBZRFIVLKt4SIQR8fHywbNky+Pv7o0+fPggKCsq04ALGYxYsWBDe3t6oXbs2SpYsCRsbGw4orED93Pj7xHIrvrOZRTiweLuEscfGvn37cOvWLfTo0QOKomRqHb0kSdqLS6usR/3M+PvEciu+s5lFOLB4+4QQqFOnDv755x88ePAAjRo1wvPnzzM1uGDWp/bG4e8Ty634zmYWUR+G7O0SQqBdu3ZYuXIlrl+/jn79+iEiIoKDixxErQrR6XTmqxjLFTiwYBaRZZkfhNmEWi2yf/9+XL9+HZ07d0ZsbCwHFzkEV4Ww3I7vbGYRdbZLLrXIHiRJgo+PDxYvXowbN26gQ4cOCAwMzNQGncw6uPEmy+34zmYW4TYW2Y8QAl27dsU///yD06dPY8CAAdo4FCz74hILltvxnc0sQkT8IMyG1GqR9evX49KlS/D19c20WVGZdXAbC5bbcU7BLCLLMgcW2ZROp0Pnzp3x559/4uzZs3jvvffw+vVrDi6yKa5WZLkd5xTMIvnz54eTk5P5YpZNCCHQq1cvrFu3DkeOHEH//v0hjBOLsexFHZJdp9Px58NyJZ4rhFkkICAABoMBZcqUMV/FsgkigqIoWLNmDT755BM0bNgQ//zzDwoUKMC/jrORhIQEnD59Gg0aNICtra35asZyPA4smEXU24QzqOyPiLB27VoMHToU7du3x/Lly+Hk5MRVWdkIN4ZmuRkHFozlQrIsY+fOnejfvz9atGiB7du3c70+YyxLcMjMWC4kSRI6deqE2bNn48iRI+jevTuCg4N5nAvGWKbjEgvGcjEiwpo1azBo0CB0794dK1euhK2tLZdcMMYyDZdYMJbL9e7dG8uXL8euXbvQp08fxMTEcG8Exlim4cCCsVxM7db43nvvYerUqdi3bx9GjhyJsLAwrhZhjGUKrgphLI9QFAX//PMPhgwZgt69e2P16tXmSRhjLMO4xIKxPEIIgT59+mDOnDnYsmUL+vbty1OuJ4GM862oL3UZY8wyuokTJ040X8iYOUVRQETc6C8HE0JAkiTUq1cPDg4O+OOPP/DixQu0atUKNjY2/Nka7/OYmBjcuXMHhw8fxokTJxAZGQm9Xo/8+fMDVhjLRQ1YMrofxrIrrgphFrlw4QJcXFxQvnx581UsB0pISMCyZcvwySefYMCAAViyZAlghUwzpztz5gxGjBiBe/fuIS4uDkQEvV4PJycnTJw4EaNGjcrQ5GFEhKioKGzevBl9+/blkTdZrsRVISxVRISRI0di8uTJ5qtYDqXX6zFkyBD8+OOPWLt2LYYNG5Znq0WICGFhYRgzZgzatGmDW7duoW/fvjh58iRu376N33//HQaDAWPHjsWiRYvMN08TIQQOHDiATz75BE+fPs2T15vlfhxYMIvEx8cjPj7efDHLoYQQsLGxwdixYzFx4kSsWLEC33//PeLj4/NUZkdEiImJwYgRI/DLL78gJiYGY8aMwV9//YV69eqhXLlyGD58OHr16oXY2FiMGjUKV69ezVCPmoSEBJP2G4zlNhxYMIvIspzni8lzq88//xyzZ8/GwoUL8dlnn0GW5TyR6alBRe/evbFx40YAwKBBgzB+/HjAOHqpTqeDLMvo2LEjYAzI5s2bB5GBmWPVadMZy604sGAW4UmTcichBGxtbfHJJ59g7NixWLFiBb7++mtERUWlO+PMKRRFwU8//YR9+/YBADw8PDBt2jRtWnMVEcHDw0MLNI4fP46EhIREe0obtbSDgwuWW3FOwSxCRBxY5FJqb5GJEydiwoQJmDdvHn744QetJ1BupCgKNm/ejClTpsBgMEAIgblz56JQoUJvZPhCCBQuXBj58uWDoii4c+cO7ty5Y5ImLbjEguV2nFMwi8iyzIFFLieEwOjRozFx4kT8+eefGD16NOLi4jLUniA7IiKEh4dj3LhxWgbfqVMnvPPOO0ne42qpjo2NjbZs9+7dJmnSQg3WOLhgudWb3yLGksAlFnmDnZ0dvvvuO/zvf//DokWLMHXqVK3bZW6RkJCAjz/+GA8ePNAaUX788cegFMaWkCTJZN2xY8dM1qcFl1iw3I5zCmYRbmORN6gZ3uTJkzFu3DhMmzYNP/74I0QGGitmJ0SECxcuYP369Vqw3LJlS7Ru3do8qYaIEBcXp/XmAAB/f38tKEkrLrFguR3nFMwi/Csr7xDGicvGjh2LL774AnPmzMG4ceNyfMmFeu5z5szRqnd0Oh0mT54MIUSK93dYWBiioqK0v2NiYtLd/Vr9LqV0PMZyMg4smMW4xCLvEELAzs4OM2bMwEcffYRffvkFv/76a4Z6Q7xtRIRz585h3bp1WmBRqlQpVKtWzTypCUVREBQUBFmWtWUZCQpycnDGmCU4p2AW48Aib1Ezz2nTpmHMmDH44YcfMHny5HRXAbxN6jlPmzbNZHnXrl3h7OxsssycTqdDYGCgyTLzNhdpQca2HOndnrHsjnMKlir1AajX63NchsIyRi25+OGHHzBixAjMmjULP//8c44cofPJkyc4duyYFhTY2dmhb9++qVbzSZKEa9eumQRUai+RlLZLjhpYMJZbcWDBUkVE+OSTT9CtWzfzVSwPEMbhv3/77TcMHToU48aNw4IFC3JUN1Qiwpo1axAeHq41RC5fvjzq1q2b4qRiaiBx584dkxK7okWLpis4ICI0adIEHTt2RMGCBdO1D8ayOw4sWKqEEPjiiy/QsmVLfhDmUern/vPPP2PUqFH45ptv8PPPP+eI4b/JOKPorFmztHYSsizD19c31ftZXX/z5k2T5dWrVzf521JCCFSqVAkrVqxAvnz5zFczlitwYMEsIrhOOM8TQsDR0RG///47BgwYgMmTJ2PBggUwGAzZOrggIpw9exavX782uY+bN2+uVW+k9AoNDcX9+/dN3mPz5s0THSFt+LvEcjsOLBhjFhPG8SwWLlyI/v3745NPPsGiRYuydUYphMCePXsAsx4Z3t7eJl0/k3opioIdO3Zoc6cIIeDg4IAGDRokOgJjLDFB2fmnBmMsWyJj9cJnn32GdevWYerUqfj0008z1FsiM6iPt8aNG+PcuXMwGAwAAAcHB4wcORJ6vT7F3k5CCBw4cAAXLlwAEUGn06FKlSq4fPkylzwwlgwOLBhj6aI+OgYPHox169bhzz//xKBBg7JVcEFEePnyJSpWrIjw8HDtnCVJSlfjUyEEOnXqhO3bt2slGIwxUxxYMMbSjYgQHx+PYcOGYf369ZgzZw5GjRqVbTJdRVGwf/9+dOjQQTsnnU6HBQsWpDp+BQA8fPgQ3377rUk7kokTJ+KHH34wT8oYM+LAgjGWIUSE6OhofPDBB/j3338xZ84cDBw4EDqd7q0HF0SE0aNHY968eVpgUbp0ady+fRt6vT7F8xNCYO3atRgwYIBJ6caxY8fQuHHjFKtQGMvL+JvBGMsQYewtsmbNGnTo0AEjRozA2rVrzZNlOSJCQkICzp8/r5U2CCHg4eGhta1I6QUA//77r8m2VapUQYMGDVIMSBjL6ziwYIxlmDD2Fvnrr7/QpUsXjBw5EosWLQK9xeG/iQgxMTF4/vy5ybLatWun2g5EURSEhYXhyJEjJuk++OCDVEs6LPG2rgljWYEDC8aYVQgh4OTkhPXr16N9+/YYM2YMNmzY8FYz0bi4OERHR5tUW9SqVctkQrGkKIqCU6dO4dmzZyDj9Or58+fHO++8k+GgIi4uziTYYSy34cCCMWY1auPIDRs2oGnTpujTpw82btxonixLEBEMBgMSEhIgjF1DJUlC5cqVzZO+Qa/XY/v27YBxP4qiwNPTE2XKlDFPmmYrVqyAj48PQkND32rQxVhm4cCCMWZVaia+YsUK+Pr6YsSIEVi5cmWWZ6LCOMCVOuy4EALu7u7w8vJKcX4QGEssjh07Bhj3AwDTp0+HnZ1dhkssXrx4gbi4OMTFxZmvYixX4MCCMWZ1QggUKFAAu3btQtOmTfHxxx9jx44dWRpcqO0+Eh+zcOHCsLe3TzE4ICJcvnwZ9+7dA4z7adWqFdq2bWueNF3U80npHBjLyTiwYIxlCrXkYuPGjahduza6d++OrVu3mifLNGopReIM3MPDwySNOTUQGTt2rNYOQ1EUDB8+PNXp1S2lnhdjuRUHFoyxTCOEgK2tLTZt2oRWrVph+PDh2Lx5c5aVXOh0Om08DSKCu7u7eZI3XLx4Efv379fGrqhZsyY6depktWBA3a+19sdYdsOBBWMsUwkh4Obmhl27dqFmzZro378/9u7dm+nBBRHB1tYW9vb2Wmbu4OBgnuwNK1as0DJ9Jycn/PXXX3B0dLRaIGCtkg/GsisOLBhjmU4IAb1ejw0bNqBWrVro2bNnpleLSJIEBwcHFCxYUAtiUupmKssyrl69isWLF2vL+vXrh1q1alk1EEg8oypjuREHFoyxLCGEgKurK/799180aNAAI0eOzNSSC2Gc4tzb21vLxMPCwsyTAcbSDVmWMX78eMTGxkIIgbp162Lq1KlWDwIy6/0yll1wYMEYyzJCCLi4uODff/9FhQoV0L59exw8eDBdM41agojQv39/LTh48OCBeRLNwYMHceDAAS0gWbRoEdzc3KwaVCAXllioDV7f1otlPzwJGWMsyxERXrx4gY4dO+Lhw4dYuXIl2rdvn+pQ22lFxkGy6tWrhxs3bsDV1RU3b95EgQIFtNE4DQYDrly5glatWiE6OhqOjo7YvHkzWrRokSkTjX3zzTdYvXo1Ll26lCmBS1YiIsTGxqZYxZRZJEmCo6Oj+WKWDXBgwRh7K4gIUVFR6NixI27evIn169ejefPmVs/MiQgLFy7ERx99BCEEFi5ciCFDhkCn04GIcP/+ffTr1w8XLlxAgQIFMG/ePLz33nuZluGPGTMGa9asweXLl1GgQIFMO05mUxQF48ePx8aNG1MtcUr8Hi3JcoSxF09KJElC165d8csvv+TYa5hbcWDBGHtrZFlGZGQkGjdujJs3b+LgwYNo1qyZVYMLtdSic+fOOHToEAoXLox9+/ahTJky2LdvHwYPHoyoqCi4uLjg4MGDqFGjRqZmVF9//TXWrVuHy5cvw9XVNVOPlVkURUFwcDBq1qyJFy9egIzzqciyDGEcOl39DM3fn8FgSDJo0Ol0SX7uZBxSXd23SgiBXr16YfXq1drfLHvgwIIx9lYREQICAtC1a1c8e/YMq1atQsuWLZPMZDIiJiYGU6dOxeHDh9/o8tmhQwd88MEHKFq0aKZnUL/99huWLVuG48ePW7Uba1YiIuzduxddunSBLMtQFAWVK1fG4MGD0bBhQxQqVAjOzs6ws7MzCRiICHv27MGAAQO04EIIgXbt2mHhwoVwcnIy+dxlWUZcXBxCQ0Px9OlTLFy4EFu2bAGMJRbTp0/Hl19+meoQ7SxrcWDBGHvrFOM05b6+vrh79y527twJHx8fq2a6qT3q1F/dmYmIkJCQgOjoaLi6upqvzjFkWcbgwYOxZs0a2NjYYOjQoZg2bRpcXFy060xJNK4kIowbNw6zZ8/Wqk8kScLRo0fRqFEjk7Qq9R4QQiA+Ph6DBw/G+vXrIYTAgQMHrF7CxTKOAwvGWLYgyzJevXoFHx8fBAYGYs+ePWjcuHGuyzTUDDenvi8iQmBgIEqVKgVFUfD1119j+vTpgDFISA4ZG3qqDWmJCDqdDiVLlsTNmzdTncMFxn08f/4cVapUgaIoePnypVUmhmPWlfxdwBhjWUin06Fw4cI4dOgQKleujP79++PMmTOpNgzMadQ2CDnZ/v37IcsyvL29MWbMGCCVoALGUqlnz57hxo0bJsu9vb0tGhEVxsDCwcEB+fPnh5ubG+zt7c2TsGwg5TuBMcaykBACJUuWxK5du+Dq6op27drBz88v1wUXObWgmIwTqO3atQs2Njb45ZdfULBgwVSDChgDR39/f+29CyEgyzLq1aun/W0JSZKg0+lQtGhR81Usm0j9bmCMsSyk0+ng7u6OLVu2wNXVFd26dcuRwYXak8E8iIiJiUFsbOwby3OKiIgInDp1CqVLl0a9evXS9LmcPXsWMAusatWqlaZxMNQGnRxYZF8cWDDGsh1JkuDh4YGTJ0+icOHC6N27N65cuZKmTCwrkLErpPnfanuRW7du4dChQ1iyZAnGjh0LX19feHh4oF27doiPj8+RwcW///6Lx48f45NPPkH+/PktKq2A8docPHhQK5kgIuj1etSsWdPifQghEBsbi9jYWHh6emrLWPbCjTcZY9mWoih4+vQpmjZtilevXuHkyZPw9va2OCPKTGqX1fj4eMTExODVq1c4c+YMjh07hosXL8Lf3x8hISHQ6/WwsbGBra0tihYtinfffReDBw+Gh4eH+S6zPVmW4ePjA39/fzx9+hS2trYWZexEhNDQUHh6eiIkJES7dnXr1sXp06ct/jyJCOfOnUOLFi3w22+/YdiwYeZJWDZg2afJGGNvgSRJKFmyJPbs2YMCBQqgZ8+euHr16lv7pa8oCsjYq+O///7D6NGj4ePjAy8vL3h5eeH999/HwYMHUbJkSQwfPhxLlizB0aNHcf78edy6dQtXr17FpEmTULZsWfNdZ3uKouDRo0e4ffs2fH1909QbQ5ZlHD16VAsqYPxs+/XrZ/E+YAwsrl27htjYWHh4eMBgMJgnYdkABxaMsWxNkiRUqlQJx48fh4ODA7p06YJr165lebUIESEkJAQrVqxA7dq10aZNG+zYsQPFixfHiBEjsH37djx+/BjXrl3Dpk2bMG3aNAwaNAgNGjSAp6cn3N3dodPpIHLoBGSSJCE0NBSOjo7o16+fxcEdGbuVHj16VNtGCAFbW1s0b97cPHmqJEmCl5cXKlWqZHFJB8taXBXCGMsRFEXB48ePUbNmTSiKgnPnzsHT0zNLMhciwpUrV9CuXTsEBQWhUqVK+P3339GiRQvo9Xrz5LlaQkICbGxszBcni4yDgjVp0gTnz5+HoijQ6XQoXrw4rl69mqZ2Gioy9k5h2VPaPk3GGHtLJElC6dKlcfz4cRQoUAA9evTA3bt3Lf7lnF6KomDWrFlo0qQJPDw8sHPnTly9ehWtWrXSJjJLix07dmDmzJlZXuJiDWRscJlW0dHRCAgI0K6VLMsoW7YsHBwcOEDIhTiwYIzlGJIkoWrVqtizZw/i4uLQsmVL3Lp1K1MyaSJCfHw85s2bh2+//RZdunTBvn370KFDB9jY2EAyTvFuacaoZqpbtmzBokWLcmSX07S838QePnyIoKAg7W8hBBo0aAAbG5t07S8927Csw4EFYyxHUdtcbNmyRZtfxN/fP1OCi61bt2Ls2LEYMmQI/v777zcmyUqPzDjP7IyIsGbNmjfG9OjatWuOC6yYZTL2DWGMsbdALbk4ceIEdDodevTogYCAAKtl2oqi4Nq1a/j444/RqlUrTJ06FXq93iq/lNWultbYV3anlvocOHBAe7+SJKFo0aKoXr16nrgGeREHFoyxHEmSJHh7e2Pjxo148eIF6tSpgwcPHmT4V7DaMPCLL76Ao6Mj1q5dCzc3N6tlghk9v5xEURQEBATgwoUL2vuWJAkNGjSAs7Oz1a4py144sGCM5Vg6nQ41a9bE9u3bERoaim7duuHp06cZyryJCBs2bMCRI0cwefJkODk5WTUDzEslFpIk4fr169rfQggYDAY0bNjQJB3LXTiwYIwxxpjVcGDBGMvRdDod6tWrh1OnTiE8PBydO3fGkydP0tXegojw/PlzfPbZZ3jnnXfQv3//DDfWNJeR0pScRgiB06dPA2bvu169ennqOuQ11v3GMMbYWyBJEmrUqIE1a9bg9u3baNy4MZ4/f57m4EIIgQ0bNuDly5cYM2ZMplRZ5JWqEDVwOHPmjPZe1WWenp65/v3nZRxYMMZyBb1ej4YNG2Lv3r0ICwtDjx498PLlS4t/GRMRXr9+jT/++AMdOnRA3bp1MyXzs/R8coPw8HBcv35du45CCHh5eaFYsWLmSVkuwoEFYyzXkCQJTZo0wc6dO/HkyRO0a9fOZMTHlCiKgoULFyIoKAizZs2yWvdSc2ktRcmpFEXB0aNHTYI7IQSGDBmizZnCcicOLBhjuYokSWjcuDHWrl2LK1euoHXr1nj9+nWKGToRISoqCkuXLkWzZs1QqVKlTMv48kJVCBFBkiQcOHBA+1sYJx5r3769eXKWy3BgwRjLdXQ6HZo0aYIDBw7g5cuX6NmzJ0JDQ5MtuSAibNu2DY8ePcL//vc/LfPPDMmdQ24TGxuLgwcPau9XkiQUL14cXl5e5klZLsOBBWMsV5IkCS1btsSaNWtw7do1NG/ePMkGnUSEsLAwTJkyBb6+vmjdunWmBRVINGV4bvfq1SsEBgZqf8uyjAoVKli9lw2Mn2HiF3u7rP8JM8ZYNiFJEtq2bYu1a9fi2rVr6N69O8LCwiDLspZGCIF///0XDx8+xDfffKMV21ubus9vv/0WCxYsSPcEXDmBEAKPHz9GeHi4yXK1m6k13reiKNr8I0IIKIpiUtIky/IbQSTLGhxYMMZyNUmS0Lp1a+zevRv+/v7o2bMnwsPDTX7dLlmyBJUrV0aNGjXMN7e6WrVqoVGjRlbJXLMrRVGwa9cuk4nHhBBo2bKledJ0ISJERkZi1apVGDhwIOrWrYvKlSvDy8sLderUwYABA7Bx48Y3Jj5jWUMQX3XGWB4gyzL+/fdf9OvXD56enjhw4ACcnZ1x8OBBdO7cGWvWrEH37t2h0+nMN2VpQERQFAVNmjTBuXPnIMsyhBBwcXHB3bt34ebmlqHqEEVRcOPGDfTv3x9XrlyBs7MzOnfujK5duyIiIgIHDhzAtm3bEBMTg8aNG2PDhg0oUqRIrg7kshsOLBhjeYaiKNi7dy+6dOmCpk2bYsOGDWjdujXs7Oxw8uRJ7gZpBbIs4+HDh/Dy8kJCQgKICHq9Hu+88w42b96c4aDi8OHD6Nu3L0JCQlCwYEHs2bMH3t7eWhoiwunTp9GjRw+EhobCx8cHu3fvhr29PX+2WST9nzBjjOUwkiShffv2WL9+Pa5cuYImTZrgxo0b+PzzzzmosBJJknDp0iUkJCQAxioQRVHQtGnTDF1fIsK1a9fQq1cvhISEwNXVFUePHkWNGjUgSRJ0Op32aty4Mb7//nskJCTg2LFjmD17NleJZCEOLBhjeYoQAl26dMGiRYtw584duLi4oE2bNtzQz0qEEDhy5IhJGxa9Xo9mzZqZJ7WYup9JkyZpjW87dOiAypUrQ5iNCaIGMt26ddPW/fPPP9yYMwtxYMEYy3N0Oh26d++O9evXIyYmBsOGDUNcXBxnPBZS21EoiqIFEIlfR48eNcns7e3tUaRIEW29uq36Sg0R4d69e9i7dy9gDB569uyJ+Ph4KMbeIYlfAFCkSBE0bdoUkiThxYsXCAsLy1CJCbMcBxaMsTyre/fuWLBgAY4fP44ePXogLCyMi8wtEBwcjIcPH8Lf3x93797FzZs3cf78eWzbtg2tW7fG1atXtetIRIiJicGmTZtw7tw53LhxA/fu3YO/vz8ePHiAly9fmu/+DUIIbNq0CdHR0SAi6HQ6FC5cGMHBwcm+QkND4enpCUVREBkZiYCAAPPdskzCjTcZY3maoijYvHkzevfujXbt2mH79u3Q6/UZamSYW5FxzIhGjRrh+vXrWndOtRTCYDBof5sTQkCv12ttWYQQkCQJJUqUwMWLF1NtXNmjRw9s3bpVO4d8+fK9UQ1iLjY2VmvrsW/fPrRq1Yo/1yzAgQVjLM8jImzYsAHDhw9H27Zt8c8//+TqAazSS80uRowYgbt370Kn08HGxgY2NjZa0KDT6SBJkpaBq20b1MAjISFB+1eWZXh7e2Pu3LkpBglEhMaNG+PUqVMQQqBgwYL4888/4eDgkOw2SHS+Op0OLVq0gIODg3kSlgk4sGCMMWMmtHjxYnzxxRdo0aIF1qxZAycnpxQzrvR48eIF9Ho9ChYsaL4qR7FW1mHp9e3Xrx/Wrl0LIQQKFSqEq1evolChQlwCkQ3xJ8IYY0YffPABFi9ejH///RdDhw61ak+CxL/2P/74Yx4VMg2ICA0aNND+//r1awQGBlrts2HWxYEFY4wZfzkLIdCnTx8sXboU+/btw8CBAxEXF2fVACAsLAzBwcFW3efboF6vjL4sQUTo27cvChYsCEmSoCgKzpw5k2ppBREhJCQE06dPx4sXL3L8Nc8pUv5UGGMsDxHGBoVDhgzBzz//jI0bN+L9999HfHy81TIlMvZqYJYTQqBw4cLo2rWrVkqxcuVKCCGS/VzI2KB00aJFmDBhAu7fv59sWmZdHFgwxpgZIsLw4cOxcOFCbN++HSNGjAAl09shrYgo1V/azJRasjFp0iSULFkSkiTh9OnTmDVrlhZAJKZ+VoGBgfjjjz/g7e2NunXrWlxCwjKG727GGDOjllwMHDgQM2fOxNatWzF06FBtHIWMUBSFhw9PByEEihcvjkOHDqFy5cqQZRljx47F5MmTtfYWapARGRmJ/fv3o3HjxoiNjcXs2bOh1+v5mmcR7hXCGGNJICI8e/ZMm5Z7xowZGDhwIJYvXw4yjqWQFuo2jRs3hru7OzZt2gRJktK8n+wsPdclrYgIcXFx6N27N3bs2AFhHNPC19cXtWrVQmBgILZu3YqAgADY29vj1KlTqFGjhvluWCbiwIIxxswoioLbt2+jV69eeP36NY4dO4b9+/fjyy+/xMCBA7FgwQIgDV0lkSjT9fHxQdGiRbFhw4ZcFVgQEV6+fImCBQtmehsSNbjw8/PDv//+i//++w+PHz9GREQEChUqhEqVKsHX1xfvvvsud0l9CziwYIyxRNSSCl9fX4SHh2PPnj2oXLkyiAhTp07FTz/9hMGDB2PmzJnIly+f+ebJUgOLRo0aoWTJkli7dm2uCSyICPfv38fnn3+OTZs2wc7OLtPfl3nWpQ64ZWNjYxLYZPZ5sDdxGMcYY0ZEhIcPH6JOnTp48eIFdu7ciUqVKkEyTsv97bffYurUqViwYAHGjh37RuZmCUVRctUvaCLCq1ev4Ovri6CgoEwvrVAJs26rtra2cHBw0NpSqC+W9XLP3c0YYxmgKAru3r2LHj16QFEUbN26FdWqVTPJKCVJwqhRo/DTTz9hyZIl+Oyzz7T5McxRojk01H+joqJgMBhgMBgQHx9vki6pfWR3RAQ/Pz/UqVMHjx49gqOjY64Kmlj6cFUIYyzPI2P1R/PmzREdHY0TJ06gbNmySWaSahDw/fffY+bMmfjss88wZcoU2Nvbm6QzGAx48eIFjh8/jiNHjuDAgQN48uQJEhISIISAvb09GjRogDZt2qB169aoUqUKnJ2dTfaRnSmKgjt37qBNmzYIDAyELMvw9fXFrl27uLQgj+PAgjGWpymKAn9/f7Rv3x6hoaH4999/Ua9evSSDChURISEhAb/++ivGjRuHL774AjNnzgQZ21FcvnwZEydOxKlTp/Dq1SttG/PHrZoB29nZoWzZsujVqxe++uqrTJmjxJqICNeuXUOHDh3w/PlzKIoCIQQGDhyIZcuWAdy2IU/TTZw4caL5QsYYywsURcGjR4/Qu3dvhISEYMuWLWjYsGGKQQUSjXNRr149yLKMuXPnIiIiAjVq1MCUKVMwdOhQ3LhxA9HR0UASDQ0TIyLIsoxXr17h6NGj2L17N8qWLYuyZctmy1/+iqLg8OHD6Nq1q8kw2UII+Pr6om3bttnunFnW4hILxlieJMsyXrx4gfr16yM+Ph4nT56Eh4dHmhofqiUUY8aMwaxZsyBJEmRZ1tapEu8zcUas/p145Eg1qBk1alS2G9jJYDDg8uXLaNu2LcLCwkzOWwiBWbNmYfTo0SbbsLyHAwvGWJ6jKAru37+Pnj174unTp9i+fTt8fHxSLalIiqIoOH78ONq0aQODwWCyTggBAlCidAnUrFMTlatXgb29PQhA4NPnuHbpKi6fv4T4ONO5SIQQ0Ol06NOnD1atWqUFMG8TEWHfvn3o379/kpOoSZKEv//+G/369UtTcMZyHw4sGGN5iqIoePbsGTp37oygoCBs2bIF9erVS1fGTUQICAhAixYt4O/v/0YpRZ1GdfHugN5o3LIJ7OzstG2QqH1FwOMn2LZhG3Zu3IGg56YzcEqShI8++gizZs2Cra1tus7RGmRZxvbt2zFo0CBERka+EVTAeK47duxA27ZtYWNjY76a5SEcWDDG8gxZlvH8+XPUqFFDK2moXLky9Hq9edJUERFiY2NRq1Yt3LlzxyRgsLG1wfczJqJj13cQGxebYkkIEUGv0yEiIhJjR32F86f9APr/1Sw2NjbYtm0bfH1930pgQUQ4fPgwunTpkuxcKcI4y+h///2HevXqpet6stwj+budMcZyEUVR8ODBA3Tv3h2yLGPLli3w8vLKUCa4YsUK3L17V/tbCIEixYti4ZrFaNepHeLi41IMKmDcRlYUOOZzxB8r56NL727aOjL2Pvnoo4/w9OnTJDP1zEREiI6OxsaNG7XqjaSCG2HsPuvq6prkepa3pHzHM8ZYLqAoCl68eIHu3bsjICAAhw8fRrNmzVLN9FMSFhaGCRMmgIzdSIUQ0Ov1+G7696jiXRWKkvZ2EQaDjG+nfY+2ndpp50ZEePToEX777TetZCCrCOMEX3/++SfOnDmDgQMHolChQkm+LycnJxQoUCDJdSxvSf+3ijHGcgBZlvH48WPUr18fjx8/xubNm1G9evUMBRWyLGPJkiV4+fKlSUY/ZNRQ1G/SMN2ZvyRJMBgM+HLC18jv4gwY82hJkvDvv/+aJ89SFStWxJIlS3Du3DkUK1ZMu36Scb6TfPnycWDBAA4sGGO5GRHhyZMn6Nu3LyIjI7Ft2zbUr18/Q9UfZBx3YuPGjVomKoRA0eJFMWDEwDd6hqSVEALOri4Y+b8PIYyRhSzLuHXr1lsNLtQAYvny5QgLC8Pu3bsxdepUeHp6AsYSC1tbW/PNWB7EgQVjLFdSqz/atm2LBw8e4PDhw2jatGmGSipUERERuHfvnsmypm2awcaKPTe69+uJwkULa/sjIm10z7dBHaF01qxZ6Nu3L9q2bYtx48bhwoUL+P3331GpUiUgmTYYLG/J+DeMMcayGVmW8ejRI7Rp0wZBQUFYt24dqlevbrXxFR48eICQkBBtgCghBDq/29U8WYbY29ujTqN6Jstu3br1RnfPrAo0hHEALFmW8fnnn2vtShwcHDBixAisWrWKgwoGcGDBGMttiAiBgYHo378/goKCsG3bNjRr1sxqQQUAHD582CSocHFzRdkK5cyTZUhCQgIqVCr/f4GDMcN+/fo1Xrx4YTLipdp4VDHOopoZiAhr1qzB0qVL8f3336NatWpayY8wDm9uPgkby7s4sGCM5RpqJtuzZ0+cPXsWu3btslr1R2IPHz7U/i+EQOkypazeviAhIQFlypUFxP+1tBDGHiHqWBJEhJcvX6Jbt24YNGgQ/vrrL7x8+RKyLGsBRuIAJL3I2OX1m2++QZ06dfD555+bJwG4CoQlYt1vG2OMvUXCOJrltGnT4Orqiq+//hqhoaFWyWCzIyEE8ufPj+vXr+Orr76Ch4cHqlSpgm7duuGPP/7A9evXTQINNSCxFBHh8ePHqFu3LiRJwqpVq97qCKAsZ+DAgjGWqwgh0KpVKyxcuBCXLl1Cr169EBQUlKYMNTXm1SpxcfEmf1uDEALxcXFAoqBAXa7+W6hQIaxatQp+fn64cuUK/v77bzRr1gyPHz/GDz/8gIYNG6JBgwaYMmUKTp48iWfPniEuLk6rNknpJcsybty4gXfffRcBAQH4+++/4eHhYfXSH5b78JDejLFcSVEUnD59Gr6+vqhRowZOnDgBssJkXkSEZcuW4YMPPvi/zF4IODjYY8/Z/bA1zgdiDTY2Npg/6w8s+W0xYAwkdDod7t27h5IlS74xY6qiKFp7h7i4OISHh2PPnj1Ys2YN9u3bB0mS4ODggGrVqqFjx47o1KkTvLy8kpzX4+nTp5g1axaWLVuGfPny4ejRoxxUMItxYMEYy7UURcHu3bsxZMgQeHp6YuPGjShatGiGggsiwu3bt1GjRg3Ex/9fSYUQAr8umYcGTRuaJ083O3s7fDHscxw7cFQLGkqXLo1bt27Bzs4uxfegBlBqwPHixQtcvHgR586dw8mTJ3Ht2jUEBwcjf/78KFWqFFxdXWFjYwMhBB4/fownT54gX7586NWrF/73v/+hfPnyKR6PscQ4sGCM5Xq7du1Cnz59ULNmTWzduhVubm7pziiJCJGRkfDy8sKzZ8+0TL+Fb0tM/32G9ndGhYeFo3vzzoiJjtEChb59+2L16tUZ3n9ISAju3r2LU6dO4dSpUwgMDERCQgIURUHVqlXRsmVLvPPOO3BxccnwsVjew4EFYyzXUxQFZ86cwTvvvINKlSrh2LFj0Ov16co01fYH3bp1w65du7RM36WAC9bsXg9XtwLmm6SdAGZNnIFNqzdq+7exscHFixdRpUqVdJ13YmobC2Fs7KqWbiQu6YBxtE3G0orvGsZYridJEho2bIgVK1bg/v37aNasGQICArQMNC3UjHjQoEHaMiJCWEgYpo6bkuHxJIQQuHvjNv7dvNNkWZ06deDl5WWSNr0kSYJOp9OG6YbxGOrfkiRxUMHSje8cxlieIIRAp06dsH79ely+fBm9e/dGTMz/VTOklU6nQ69evVCzZk0tAyYQThw+hg0r10Gv16drv4qiIDo6GhNGf4fYmFhtH0SE/v37ayUKjGVnHFgwxvKUZs2aYf/+/bh//z5atmyJ0NDQdAcBM2fO1EowQAAIWPTrAvw9fylsbCwPLogIkk5CbGws/jfkUzx+8NikOqJNmzYYMmSI+WaMZUscWDDG8hRJkuDj44MlS5bgwYMH6NSpU7qqRSRJQosWLTBkyBCTaoOY6BgsnD0fE7+cgKDAF9Dp/n+1gtqOQX2p1Q6kEI7uO4JebXrg6oUr2oBeQgg4Oztj1qxZcHBw4NIKK1GvP8sc3HiTMZYnERH8/PzQsmVLVKlSBadPnzZpc2AJNYOqWbMmbt68aTJluiRJsLO3Q0vfVhj19ScoXrIE7B3stQxNCCAsNBzn/juDOVNm48H9ByDl/z+O1fNYs2YNevXqxW0eWI7BgQVjLM9SFAVHjx5Fv379ULx4cezcudPicS4URUFwcDD69u0LPz8/eHt74+TJkya/htVqEjt7OxQuWgSFihTSBqQKDwvHy+dBeP3qNYgAgvJ/1SnGoISI8Ndff2Hw4MFZGlSoJSm5VUBAAIYNG4aQkBBERETAxsYGly9fNk/GMoADC8ZYnkZEOHDgAPr06YOKFSti06ZNKF68eIqZKxEhODgYQ4YMwf79+7FgwQJ069YNH3/8MbZu3YqoqCjzTbRgQX3kmv+dmIeHB+bNm4eOHTsCiUovMpssywgODoa7u7v5qlwjPDwc69atw969e7F582a4uLggJCTEPBnLAA4sGGNWR2ZDTGd3RIRLly6hTZs2KFeuHE6fPg2dTpdkhk5EiI+PR9u2bXHhwgVs2bIFrVq1giRJkGUZx48fR+/evfHq1StIkqS1l0iJWrKhKAo++OADzJgxAy4uLll+7e7evYtBgwbh5MmTSb733CI+Ph7Xr19H7dq14erqyoGFlWXtXcsYy7XUX9/q5FXHjh3DtWvXTKb5zq6EEKhZsybWr1+P58+fo1atWnj06NEb50xECAgIQJs2bXDt2jUsWbIEbdq00dpm6PV6tGjRAvfu3cPy5cvh6+sLvV6vHUPNrNWAS/27TJky+Oyzz3DixAnMnz8fBQoUyPKgAgBevnyJsLCwN953bqPT6bTPhVkfl1gwlklkWdb+n9ZGgTmNLMuIiYnBjh078MMPP+D+/fvQ6/UwGAxwd3fHb7/9hi5dumT7KbeJCKdOnYKvry88PT2xZ88eFCxYEDqdDoqiIDw8HJ06dcKVK1ewadMmtGnTJsn3oz5WhRB49eoVDh06hCNHjuDp06c4ePAgihcvDm9vb9SpUwetWrVCnTp1YGNjA1mW35g5NasQEX744Qds3rwZV65ceSuBTVZRg19vb28uscgEHFgwlgmICC9evMD58+dRrFgxeHt759pfSESEJ0+eoE+fPrhw4QKICJMnT0azZs1w9epVfP3110hISMA333yD77//PsmMOLtQH4dXr16Fr68vihcvjoMHD8LFxQXBwcFo164dHj9+jB07dqBevXoWBwHqaJySJMHT0xN9+/bFjz/+qC0TxmG0U7o2ZCz1UdtmqNRt1PXm1AAhqfVqKYrBYEBgYCBq166NwoUL4/LlyyalK0mdV+I5UYSxGsc8beL3rS433y5xOmFWdaYGWonfe3ISX7+krk9iHFhkLg4sGLMyIsLy5cvx6aefIioqCpIk4YMPPsAvv/wCJycn8+Q5mqIoOHToEAYMGIBXr16hYsWKWL16NWrWrAkYr8XPP/+Mb7/9FgCwZcsWdO7cOcUMIrs4dOgQBg4ciIIFC+K3337Dl19+iadPn2L58uVo27YtkEymlRw146tQoQL69u2LKVOmmGSGKSEivHr1CgcPHsTly5cRGxuLChUqoE2bNqhYsSKEEHjx4gWeP38OOzs7kLFKiojg5eUFvV6Ply9fIiAgALa2tiBjOxEPDw/Y2tri6tWrmDBhAvbu3QsPDw/8888/EMZgp0iRIihbtqzJ+SiKglu3buHAgQN4+PAh9Ho96tatizZt2qBAgQIQQiAuLg5+fn4ICwtDVFQU9Ho9unbtilu3buH8+fOwsbFB+/bt4ejoiPPnzyM0NBRRUVEICwtD7969IYTAwYMHERgYCAcHB1SqVAm1a9dOcpp3Mga3+/btw/3795GQkIDq1aujXbt2KFKkyBv3GwcWmYwYY1ZjMBjo9u3bpNfrSZIkgnE8RiEE/fHHHyTLsvkmOZYsy3TlyhVydnYmSZJIr9fTf//9RwaDwSTNw4cPSa/Xk06no9atWxMRkaIoifaUfV25coWKFClCQghyc3Ojq1evpvvc1e3Kly9P3333ncmylBgMBrpw4QIVL16c8ufPT7Nnz6a1a9dSuXLlyMHBgY4cOUJERLNnzyY7OzvS6XTaPefg4ECXL18mIqLvv/9eux8lSSJbW1v666+/aP78+WRvb0+2trbadvb29trrk08+ITKeq/qaOXMmCSHIx8eH1q9fTzNmzCAXFxeqUaMGRUVFkaIo5O/vT4ULFyYbGxvS6XRUv3592rdvH9na2lLt2rUJANWpU4eePHlCBQoUIBsbG+3Yd+/eJW9vb6pVqxZ9+OGH5OnpSQBo7NixJtdG9d9//1G+fPmoV69etG7dOpo1axa5ubmRra2tdn0SMxgMdOXKFQJArq6u5qtZBnFgwZgVGQwG2rNnDwkhSAihPcgB0DfffGOePEfz9/enUqVKkU6nI1tbW1q6dGmSGaXBYKBy5cqRJElkb29P/v7+SabLbhRFodu3b1OJEiWoTJkydP78eZJlOd3nnp7AQj2HokWLUoUKFejx48dkMBjIYDBQSEgI1alTh4oUKUL+/v4UERFBjx49olWrVpGTkxMBoNmzZ1NCQgLJskxPnjyhcuXKUcGCBWnRokV05coVioiIoMjISHr8+DGtWLGCAFClSpUoICCAnj9/Ts+ePaOwsDDtXBRFoSlTppCtrS316NGDoqKiSJZlSkhIoN27d5NOp6OWLVtSZGQkJSQk0NOnT2n9+vUkhKDy5ctTnTp16Pr16zR16lQSQpBer6cXL17Q06dP6cyZM+Ts7EyOjo5Uo0YN+uOPPyg+Pp4MBgMFBARQkSJFyMXFhe7evatdN1mWKSQkhCpXrkxFixalK1eukCzLZDAY6NSpUyRJErm7u9O1a9dMgnoOLDIXBxaMWZHBYKAbN26Qg4ODFlioQcZvv/2WK0osFEWh0NBQatGihfbeGjVqRJGRkclmlD169CBJkkgIQV9//bVJqUZ2pCgKXblyhapUqUIlS5ak06dPmydJs7QGFoqiUHR0NDVp0oQA0NSpU03SK8aSAwA0btw4LUNVFIX+/PNPkiSJqlSpQk+fPtUCXjc3Nzpx4oQWJKiv2NhY2rp1KwEgLy8vLRhJHEjJskzXrl0jJycncnZ2pqdPn2r3s7qf1q1bEwA6cuQIKYpCcXFxdPfuXe178PnnnxMZg9IPP/yQVq5cSWT83hgMBvL09CSdTkcDBw7U9qkeu169egSAFi5cqN0/CQkJdPXqVe0+nD59uvHq/N827du310o6El87DiwyV/av6GQsB9HpdKhUqRLGjx+vLRPGKa+HDRtmUX16dieEwJQpU3D06FEIIeDo6Ii///47xbksXFxctHUnT57U6v+zI0VREBQUhM6dOyMiIgJnz55F/fr1zZNlOlmWce7cOW1MiTZt2miNHMk4TkiDBg0AY9sVIYTWmHTkyJHo1asX7ty5g169eiEyMhIjRozAmjVr0KBBAwhjI0v1Zd4GQTJOm5640aUQAtu2bUNcXBzq1KmDEiVKQBjbYaiaNm0KALh48aK2X/UYANC/f38oioKyZcvizz//RP/+/bXjJT6fwYMHm2wnSRIKFiwIAAgODtaOqdPpULFiRXTr1g0lS5ZEy5YtTXpjNWrUCAAQGBioLWOZjwMLxqxMkiR89dVX2LlzJ2bNmoWVK1di7969KWa8OQUR4fbt21i6dKn2Xnr37q01IEwKEcHe3l77+/79+4iIiMiWgQUR4fz586hduzby5cuH3bt3o0iRIsm+t8yk1+tx584d7TqtWLECEydOxIQJEzBhwgT88MMPWLVqFYQQCA0N1WZpVTPkZcuWoVatWjh37hyqVauGkSNHom3btunqnaTu99SpUyAiPH/+HN9//712Lur5nDlzBkIIPHny5I3t9Xo9ihcvDiRq9JrUdZUkCQUKFHhjYDE1beLlQgjY2tpi3bp1uH79OkqUKIGNGzdizJgx+OCDD7Bly5Y3tmGZjwMLxjKBnZ0dOnbsiC+++AL9+vVDgQIFzJPkOESEmJgY9OvXz2Sq8WHDhpl0ITQnhNCGuBZCIDY2FjExMdkusDAYDDh//jy6desGSZKwZcsWeHl5vfFrPiu9evUKMGa2lSpVQrFixVC8eHEUL14cJUqUQM2aNbFw4UL8+uuvyJ8/v7admuH+/vvvUBQFAQEBqFKlSrquubqNoih4+fIlAKBw4cIoVaqUyfkUK1YMXbt2xcKFC9GvXz/ALHBwdXWFo6Oj9ndy9wuM6yw9VzJ27R47diy8vb3xww8/AAB69OiB2rVrv5GWZQHzuhHGGEvO7t27tfpsnU5HPXv21Or1U+Lr60uSJJEkSeTk5GTSAC87kGWZzp8/T0WLFqWqVavSy5cvrX5+6v4sbWNBRLR06VICQDqdjl68eKG1RTB/xcfHm29KREQ///wz5c+fn2xtbalEiRIm7SISi4+PN2ljkbhtxS+//KL9v3v37mRjY0Pvv/8+KYryxnkkfpGxLcO9e/cIABUpUoSCg4OTPL6iKCTLMlWsWJFsbW3p0qVL2j5UHTp0IBjbmiQkJBAZP7e7d+9S6dKlCQB9//33FBYWRoqiUEJCAv30008E4I02GwZuY5Gp3l4ozhjLMchYpz9v3jxtmU6nwyeffGJSD58UIjIp0leXZRdEhIMHD8LX11crSlfHYnibZFlGhQoVAGNpwZ07dyCM7SjUl2Scn8TPz8+kbQER4ezZs1i3bh0OHz6MUaNG4dmzZ+jVqxfCw8NTvP6J37csy1i7di3I2K6jTp06ICL4+/u/cS7q+YSHh+PBgwcm+8wMZBww68cff8TTp0/RtGlTjBkzBvny5QOMpTzqNVHf79y5c/Hy5csU3z/LOA4sWI6lPuxY5lMUBQcOHMCePXu0ZSVLlkTt2rVT/AyICKGhoXj+/Ln5qmzBYDDAz88P7777LpydnbFjxw54enpaPKJmZpIkCY0bN0aNGjVARNi3b98bVQREhHv37qF3796IiYmBoiiQZRn37t1D48aNMWXKFNSuXRuzZ89G27ZtcebMGUyePBkGg+GNz83Ozg4AEB0drbVJUIdqh/Ee6NGjB+zt7XHx4kU8ePDgjX3IsoypU6di6dKlQBoDyNTSquvN3//FixdBROjbty8cHR2hM04epygKrl+/brLN/v37ER4erm3PMgcHFjmc+ZcxpUZKZPzVaS655Ykll0YxtlLPCEVRLN534odLQkKCVldvni6tEh9f3V/i/Sa1LCnqgz2pc09JWrajZD6L5JZnlLrfGTNmaH8DQMuWLZE/f/4U2yAoioLbt28jLi5O206SJNjY2KT6PjObYgyWfH194e3tjZMnT6Jo0aLZIqiAseRACIE1a9bA3d0dixcvxvXr103uybCwMIwaNQpTp07VfqmfOHEC3bt3R4MGDdC6dWst7ezZs2Fra4u5c+fijz/+0JbDWPpUvnx5ODg44PHjx7h//z5kWcZ///0HV1dX7Vw8PT0xfvx4REdHY8CAASYTlhER/Pz8MH/+fAwYMEBbnpCQABgDloSEhGQ/d0VREBUVBSKCwWAwKTkhIkRGRgKJ9qdSJ2y7ceOGFngRES5fvoxt27ZBr9drjYXDwsLg7OwMMrYXgjG4zI5tfnIy3cSJEyeaL2TZn/olePLkCY4dOwY/Pz8EBwfDxsZGGzZa/WKqaRVFwbNnz3Dx4kVcuHAB58+fh7+/P2JjY5EvXz7tF4v5FxoAYmNjcfv2bZw/fx7nzp3D7du3ERgYCCEEnJ2dtQdPWqgPgNjYWPj7++P8+fO4cOECLl26hCdPniAuLg758+eHXq/XzuPRo0dYtWoVxo8fjylTpmDu3Lk4ceIE6tWrl67ia/UcXr9+jbNnz2Lz5s1YtWoVVq9ejVWrVmHv3r24f/8+JElCoUKFEB8fjx9//BEnT55EkyZNTN53QkICQkJCEBYWhhcvXuDJkye4d+8ebt68iXPnzsHJyUl7SCcmy7K2XVBQEJ48eYL79+/j5s2b8PPz046dOP3Dhw9x/vx5+Pn54erVq3j69ClCQkLg4OCg9cAwP05GBAYG4vvvv0dcXBxgDA5mzJiBsmXLpngcMlYzbN++HTCek729PT777DPky5cvxaAks6j30tatW9G/f39Uq1YNq1ev1rpPZiYhBObNm4fq1aujVatW2rLkCCFQqFAh1KlTB8ePH8fcuXPh4OCA6OhonD17Fl999RWqVq2K0aNHY926dfjiiy8wffp0BAYGIigoCK1atUKZMmUghMCiRYtw5MgRyLKMI0eO4OzZs7hx4waaNGkCnU4HNzc3RERE4PTp03jx4gWcnZ0xZswYDB06FHXq1NGqvNT0e/fuxaFDh5AvXz4EBQVh48aNmDJlChYsWAAfHx+8fv0a3377LRYsWIAnT54gPj4ex48fh5+fH4QQqFixopbZjx07FnPnzsWVK1e0qp0rV66gVatWWLp0KWbNmoVDhw7BYDDg6tWruHnzJnQ6HSpXrgw3NzecOHECBw8e1EosTpw4gR9//BG//PIL7ty5g0uXLmlDhnfq1Anjxo3DsmXL8PTpU8THx+PUqVM4deoUfHx8YGdnl+JnwlLHc4XkUESEmzdvolmzZnj9+rX2RcifPz9WrlyJzp07QyQqNg0LC8Onn36KdevWISEhQUtPxm5kJUuWxKZNm1C3bl1tnaIokCQJZ8+exccffww/Pz/ArMW2EAIjRozA/Pnz0/RlVLe/dOkShgwZgsuXL5snAQBUrlwZixYtQtOmTXHw4EF0794dkZGRqFOnDjp06ICff/4ZiqKga9eu2Lhxo/Z+LKGew9q1a/H555/j5cuXEEKgadOmqFq1KhTjfAjHjx8HEaFRo0aQJAknTpxA9erVcebMGdjZ2WmZ47Fjx9CqVSuTuu7E/vrrLwwZMuSNzPT27duoX79+kl0wJUnCt99+i0mTJoGIEB0djcGDB2Pr1q2QZdnks4Cx5f20adPw4YcfAqlkWpaSZRlz5szB119/DSKCTqdDuXLlcPny5RS70KqfxZdffonZs2cDxvMpVqwYrl27BhcXlzeuRWZTr9XRo0fRoUMHVKlSBUePHs2SIEe9HhUqVMB7772HyZMnW3y/KooCg8GALVu2YPPmzbh27RoqV66MMWPGaGNsXLp0CTdu3ICDgwMMBgMiIiLQoUMHrYvnvn37EBgYCHt7e+iMs7USEXr27Km9d0VRsGnTJixZsgQBAQH45ptvMGDAAJNzSfxMmT9/Pvbv34/Xr1+jXbt2GDt2LNzc3CBJEiIiIrBx40bY2dnB1tYWknHytIiICHh7e2vVaNHR0Vi/fj1sbW21HzcGgwHx8fHo168fTp8+jXv37mlBg8FgQHh4OHx8fFC1alUQEaKiovDXX39h//79uH//Pnx8fPDdd9+hdOnSCAoK0ubpGT16NHQ6HdatWwcnJydt3pHY2FgoioI+ffpk+xl4cwTz1pws+5Nlma5evUru7u5UrVo1OnLkCF27do3q1KlDkiSRjY0NrV+/XmsFPWvWLCpUqBAVLVqURo8eTQcPHqSrV6/SrVu3aOnSpeTi4kI6nY7y589vst2LFy+oW7du5ODgQI0aNaLFixfTyZMn6datW3TixAl69913td4BrVu3poiICPNTTZKiKBQeHk4jRozQ5gcoXbo0LVq0iE6fPk1+fn60YcMGqlOnDgkhyNbWlho2bEg2NjbUq1cvOn/+PMXFxdHmzZsJxhbz5cuX1/ZtCbUV+ieffEJ6vZ4qVqxIW7dupdevX5u0RjcYDBQUFERLliyhwoULk06nIyEEVa9enaKjo01auB8+fJicnJzIxsZGG2Uy8Wvp0qVJtoi/ceMGFSpUiOzt7bWeE8I4aqckSTRhwgRSFIUOHDhAJUqUoJIlS9LUqVPpv//+o9u3b9OlS5do3rx5VLBgQZIkiXQ6HfXv358oDdcjOYqiUGRkJFWsWFGb+0QIobWyT4m6vk2bNibzVzRu3Jji4uJS3d7a1Pt6xYoV5ODgQJ07d6YXL15k2Xmox0lLr5DE1HtWMfZ4UP9WycaRMtWXway3jros8fqk7kd1vXqM5KjXM3Fa8/Tmx0zqvCjRyJtJnZsl+1CPnfjaqOsTr1OXJd6Xuj/zXigs/TiwyKE++OADypcvH/n5+WlfpilTppAQgiRJorp161JcXBx9/fXXpNfrqU2bNnT//v03vtBEROPGjdMysapVq1JcXBw9ePCA6tevTy4uLvTTTz+9sZ0sy/T48WOToasXLFjwRjpziqJQVFQUdenSRctAy5UrR9evX9ceJGTcf0BAAFWsWFHLmAsVKkTPnj3THgYXLlygAgUKkCRJ5Ovra3Kc1BgMBvrll19IGCc9unjxYornrigKHTt2THu/SQUWcXFx9Pz5c3rw4AGtXr2aXFxctGsDgJYsWWKSXpWQkECBgYH06NEjOnLkCHl7e5sEFt9//z1duHCBSpQoQU2bNqWnT5++ca6yLNO8efO0zFsIQfPnz0/yeGmhKAr9999/2n7V97JixQpSEmV0Sb1kWab4+HgqW7asSVAyevToLH+IK8aukUuXLiV7e3tq2bJlpnQpTYl6rPQGFozlFBxY5DCKolBYWBi5ubmRr6+v1p/bYDDQggULtEwlX7589Nlnn5Fer6dPPvmE4uLiksxkZFmmI0eOaAGJJEn033//UbNmzahAgQJ06dKlZH+5KIpCzZs3145ZoUKFNzJbc4qi0G+//UY6nU4rXTl48GCS2yiKQqdOndIyc0mSaPz48dq5KIpCt27dojVr1lBQUFCS55gUxTg3QpUqVUiv11Pv3r2TPL45g8FAQ4cOJQBJBhZq5mUwjivw2WefaRlqSoEFJfrFFh8fT/v27dO2kSSJvvnmGypXrhy1bNmSYmJiksyUDcaJmlxdXbVjFi1alEJCQiy+LsmZNm2adj7qa+HChXT06FE6duxYii91AqrE2x46dCjZ65AZ1CBnxYoVZG9vT506dXrjs8sKHFiwvIIDixxGlmWaNGkS6XQ6OnHihPZwlGWZJk6caPIQF0LQ+++/TxEREck+RA0GA128eFELDoQQVLFiRcqfPz9t2bIl2e3I+FAcPHiwtp2DgwM9fPgwyYyPjOf49OlTKlSokHaebm5uyQYFsixTWFgYeXp6apll/vz56e7du9p5qZlGUtun5PHjx9oU07Nnz7Zoe1mW6ebNm+To6Eje3t4pZk4JCQk0Z84ciwMLlWychTLxZ+jh4UEuLi508eLFFLdXFIU6duyolQTZ2dnRpUuXUtwmJYqx5KFbt25v3FdqEJray3w7Nzc3io6ONj9UplHfw7x580in09H7779PISEh6b4mGcGBBcsrMre1ErMqMnaR2r59Ozw9PVGvXj2t8Z4QAlevXtXSCmPXsDlz5qTYME2SJISEhGh/k7Ff/FdffYWuXbsmu50qKChI+39MTIzWJSwpQggcOXIEr1+/1s65WLFiyQ53LYwTXFWqVElrMBYZGYktW7Zof4tEEx1ZSn2P8fHxUBQFO3bsSLJfvzkhBCpXrozSpUtb1CVRbRimsvQcE29HRHj48CGGDBkCb2/vVD8PT09P7X3IsoyXL1+muk1KZFnGzZs3TfZRunRpNGnSJNVXw4YNTealkCQJlStXhoODg7YssxkMBsydOxdffvklOnbsiPnz58PZ2TlD14QxljL+duUgZOwW6e/vD29vb5MMSDGOzKdmspIk4ffff0+ye2NiQggEBASYZNTOzs4YNWpUihktGfuaX7x4UVtmZ2en9aVPihr8JN5vkSJFkn3Iq++jcOHCJssT91dPr8SzbR4+fBjz588HjO8rtbEgsro3g62tLT766COLjunu7q5dFzIOTpXe60REuHv3Lh4/fgzFOBeIJEmYNWsWDh8+jKNHjyb7OnToEJYvXw69Xq9dZ0VRUK9ePW3f1pLUvsjYjfiXX37B2LFjMWTIEGzYsAGOjo4WXUfGWPrxNywHkSQJT58+RVRUFFq2bAkk+hX8+vVrPHnyBGQsCWjbti3atm1r0UP0/PnzgPFhLITAzz//jIIFC6a4LRHh6dOn2iRJQgiUKFEixUABwBuj3qUW+JCxe2Piv4ODg03SpJUQAh4eHnBxcdH+/uqrr9C9e3ds27YNjx49Mt/EJPOaMmUKZsyYAXt7+xTfqzVIkgR3d3eTgCElanc9GM85Pj7eZH1anT9/XhvcSggBV1dXtG3bNsXPDMYBl/z9/bXjq4Fghw4dtG6y1nD37l1tUCWV+v+pU6diwoQJGDZsmDY4lLWOyxhLXuY+FZnVeXl5YdasWejbt6/J8uPHjyMsLAyKcRTLZs2amaxPivoAPnfunPZrtFChQnjvvffMk75BCAF/f38YDAbAuK9GjRqlOrhM0aJFTf5OauwGFRnnAoiNjdWWCSEyPI01ESF//vyoW7eu9ndCQgJ27NiB7t27o0qVKqhZsya+++47/Pfff3j58qXJiIGtWrVCixYtMnQOaZEvXz7Y2tome51SklrpS3LUa3/69GntuESEkiVLmsyimRwiwrFjx7T/A0Dx4sXRokULqwRjRARZltGnTx9888032tgh6vLx48fjhx9+wKBBgzBv3jw4Ojpm2efFWF6X8W84y1Kurq746KOPTIryAWDRokVAohKM+vXrW5SphIeH4+7du9ovylKlSlmUccA4IJS6HQAMGjQoxYc3EaFWrVoQxtEqiQi3b99+Y4jexNRRKROrXbu2VjSfHmoQ9eeff8LDw0MrEVH3mZCQgGvXruGnn35C8+bNUaVKFTRu3Bg//fSTNv23NTJHS9na2lrUpiMp6QlGVLIs4+7du9rfRKSNtJnatRdCYOvWrdo9KITARx99ZNVSg8OHD+PSpUuYP38+PvvsM+29jh8/HjNnzsTYsWMxf/58be4IxljWyLqnI7OaxA9KMlYNnDp1Sltvb29v0ogvOYqi4NixY3j16hXIWCdds2ZNwIKGhoqi4NChQ1omXahQIXh7e5snM0FEaNy4McqVK6dlTiEhIXj27Jl5UsCYPioqCjdv3gSM51SsWDF07949wxm7EALly5fHtm3bULNmTZP9qb96ZVmGwWBAcHAwzp8/j++++w5eXl44cuRIqtfWWrLqOElRFEWrXlNVrVrVJE1SZFnG2bNncfv2bcAYhDk5OaFHjx7mSdNNGIeohvE8Fy5ciHHjxmH06NGYN28evv76a0yaNMmkjQdjLGtk7OnM3jr1V2VERIS2zNvbGyVLlkzxVy4Z2y4cOHBA+xsAGjZsmGpmphgnljp58iRkWQYRoVixYnBxcUlxW0mS4Obmhj/++EPLyCMjI7Fr1y7zpIAx87h69SoeP36sLfvxxx9RuHBhq2QWQgh4eXnh9OnTWLRoEYoUKaIFWJIkQTI2hFWXkbFdia+vL/bu3WtRiVBOZjAYTEqThBBaaVFKJEnCxo0btXuDiFC/fn14enqaJ00XRVFw48YNbf4RddmMGTMwb948fPvtt5g6dSoHFYy9JRxY5HB6vR5XrlwxWTZ48GCLHqgxMTHYs2ePSTDQpEmTVDMOIQRWrlxpsqx79+6wsbGxqCShRYsWGDFihFZqMWnSJBw+fNgkAydjHX2fPn20+vOhQ4e+0bYkI9T3rdPpMGzYMNy/fx9+fn5Yvnw5Pv/8c7Rs2RJubm6A8T0L41TMsixj2LBhCAwMNNtj7qIkMeush4fHG8sSI2NvIXWKbxiv76RJk6xSJUHG9jDjxo1DfHy8yb2r/j8iIkK7ZxhjWS/1XIBla0SEM2fOaKUT9vb2aN++vXmyJL169Uobh0KSJFSvXl2bCTE5iqIgLi4Ou3fvBowZrp2dHfr162cSVCSVKcF4vkIIPHz4EM7OzihSpAhCQkLQpUsXfPvtt9i6dSu2bduGr776Ch07dsTLly/h6uqKb7/9FosXL7ZaIzyDwaBNDa3uz9HREbVq1cLAgQMxa9Ys7N+/H0+ePMGmTZvQvHlzrasiEeH58+eYP3++ScaW26jBlPp/BwcHFCxYMNXrf+XKFdy6dQtkLBXr1KkTfHx8LAo6LfHo0SMcPXo0yfMgIsyZMwe//vqrNhMrYyxrWeebzt4aRVFw4sQJkLH4vkSJEm+M+5AUIQQCAwO1Aa2EEGjevLnJbJ1JEULg6dOn8Pf31zKeJk2awNPT0+RBHxkZiQcPHphsC+P29+/fx+HDhzF+/HhcuHABY8aMgbOzM3766Sf07t0bvXr1wuzZs+Hs7Ixhw4bBz88PP/zwg7Z9RhERzp07h7p16+LgwYNaACSM7UVUambatWtX7N69G5s3bzaZWn7dunWIjo5OMoDKDXQ6nRawCiHg5uYGZ2fnZD8DMo4BMmrUKK2bqSzLGDFihFWv0R9//IHw8PBk92kwGDB+/HjMmTMnVwd+jGVXyecgLNsj49Tp9+7d00oIypUrZzKWQXKICLt37zYpMm7Xrl2ymUZiixYtQmRkJMhYZdGzZ0+T7WRZxtChQ9GlSxfArAEiEWHdunWIjY1F8+bNUbhwYUydOhW3b9/G+fPnsX//fhw8eBAXL17ErVu3MH/+fJQrV84qxeiJhYaGIiIiAlu3bjVfBZgFMDqdDnZ2dmjbti0WLVqkDUwWEBCAly9f5trMS6/Xa1NuCyFgb28PW1tb82QaIsLJkydx9uxZbVnPnj3RqlWrFINVS8myjNu3b+Pvv/82X6VRPzdbW1vcunUL0dHR5kkYY5ks49929tYoioKdO3eaZGyNGjXSGh0mR/1leeDAAS2d+dDZSSEihISEaK3xYaxCad68uRagKIqCkJAQnDp1CuXLl0+09f8hIpw/fx5kHJ5c5eTkBG9vbzRt2hSNGzdG9erV4ezsrK1P6f2kl5oRyrKc7K9flXr8AQMGoGrVqpAkCTExMYiNjU3xmuVUaulN9erV03TtE3fvLFGiBP76668Ug5G00Ol0+Ouvv94Y+0QIoZWsFChQAIMGDYK/vz+WLVuW4kiwjLHMwYFFDqWWFvz3338my5s2bZpqRqcYuxGeO3cOiqKAiODs7IxixYqlmIkQEc6ePYuwsDBtWf369VGhQgWTIvMzZ87g5cuXeOedd0DGNhWJxcfHQwiBHTt2QCSa60Qteldf5ttZmxACjx49wpMnT9J0rMKFC0NRFLi6uqZYNZDTKYqCVq1aae8vNjY22ZE8ZVnGnj17sHnzZi1QmzBhAvLnz2+166MoCjZs2GCyTC0JKVeuHBYvXoyLFy9i8eLFbwzExhjLOhxY5FBEhOjoaG3eDCEEChYsiMaNG6da7CxJEs6dO2cyVHPTpk1T/XUnSZI2NgGMGfOPP/6oTTSlntOPP/4IV1dXdOrUKcmSAA8PD0iShKVLl2Lz5s2Ijo5OMRgiYwmLGkyllDYtiAiRkZGYNGlSmnoRREREQKfToXr16ihWrFiq11tl6Xlbmi4p5ttmJFMXQqBRo0YoWLAgYGzsm9TcI2Qcb2T8+PEwGAzQ6XT48MMP8cEHH1h8bVIjyzImTZqEJ0+eAMZ70dHREa1bt8by5cvh5+eHYcOGoVSpUtr9mJH3zhhLP+t861mWE0Lg1atXWh2/JElo2rQpHBwcUn2gCiFw9OhRLYMQQqBnz55akJESNQMWQsDd3R2NGzfW1imKgk2bNuHcuXMYO3YsihcvrpVkqCRJQv/+/SGEQGhoKN59911UqlQJ3bp1w7vvvovevXujd+/e6Nu3LwYMGICRI0fixx9/xPLly3Hp0iXExMSAjANYmWdw6UFEWLFiBY4ePZpqcKEoCu7evYsrV65AURR8+umnWlCnUoMgRVHeqN+PioqCwWDQgqTEEm+nju4J43VW06vrE29LxkBLXW5+TLVLZuLAzFJCCBQuXBhNmzaFYuwNlNQ8KrIs49tvv9W6PVeqVAk///wzYKXMXVEUPH/+HDNmzIBOp4OtrS06deqEy5cvY9++fRgwYIBWcmSN4zHGMsh8HnWWMyiKQlu3biVJkggACSFo5syZpCiKeVIT6voWLVqQEIIkSSI3Nzd69uxZqtvKskxbtmwhAKTX66lixYoky7K27uHDh+Tp6UleXl70+vXrJPenKApFRERQw4YNSQiR6kuSJO1lZ2dHxYoVo3feeYc2bNhAcXFxSR4jNYqi0K5du0gIQQAIAJUpU4ZOnz6d7P4URaHnz59TzZo1SZIkatCgAYWFhb2RXlEUiouLo8ePH1ONGjW0YwghqEOHDhQSEkJxcXHadUu8XUJCAoWGhtJHH32knZcQgpycnOjff/+lqKgokmX5jWPKskyxsbF0/fp1KleunHZMSZKoefPmdPfuXYqJiSGDwfDGtqlRFIX27Nmjnctnn31msl6WZZo7d672GbVq1YpevXr1xvvLqN9//51KlChB06ZNo5s3b1JCQgIpipLm9/M2qedavnx5+u6770yWMZabcGCRQymKQiNGjDDJeI8dO5bqg0pdX7p0aW07Hx8fix7SsixTUFAQlS9fnnQ6Hbm5udHt27fp9evXdODAAfLw8KDixYuTn59fshmLmoFevnyZihQpYnL+yb0SBxk6nU77u0ePHvT8+fNUz9uckiiwkCSJmjZtSsWKFSNXV1eaNWsWXb16lV6/fk1RUVEUEhJCd+7coX/++YeqVKlCkiRR/fr16cGDB28cd8WKFVS7dm2qVq0aubq6vhEkCSHIxcWFvL29qVWrVhQZGUmKotC9e/eoYcOGVLNmTSpevPgb2wghSKfTUfny5al27drUtWtXiomJISKi77//nmrVqkVVq1alfPnyvbEdAHJwcKDKlSuTt7c3zZgxI9nPJimKopDBYKAPP/yQ7OzsqGjRonT27FkKDw+nBw8e0KRJk8jW1pZsbW2pT58+FBQUlKb9pyY4OJgCAwNp165dFBUVRYqiWHX/WYkDC5ZXcGCRQymKQiNHjtQy3mLFilFoaGiqD131QVayZEnS6XQEgObNm2eeLFmKotDDhw+pZMmSBIAcHR3J2dmZbG1tqWzZsnThwoVkH5ayLJMsyzR//nwqVKiQFiRUrVqVunbtqr3eeecdateuHbVs2ZIaNmxIZcuWJRsbG+1Xs5SolKZRo0YUHR2d7DGTkjiwqF+/PkVHR9P9+/epbdu2pNPpyN7enpydncnV1ZWcnZ3JwcGBdDodOTk50cSJEyk8PPyN66woCv3888/aedna2pKTkxMVLFiQ3N3dydnZmezs7AgA6XQ6KlmypLafy5cvU758+bRAytHRkVxdXcnd3Z3c3d3JxcWF7OzstACjSpUqFBsbS0REQ4cO1Uo3zI/p5uZGTk5OJtdu5MiRZDAYTM49NYqxFGb48OHae3NxcSFHR0eSJImKFi1KGzdu1EoRrEWWZRo+fDh5eHiQv78/JSQkmCfJUbJTYPG2jsvyBkFpqXRl2crz58+xcOFCwDiMd2qjZib277//4tChQ6hcuTLee+895MuXz+JtFUVBQEAADhw4oDUe9fb2RocOHeDm5pbifkaMGIGlS5cCALp164YJEyagfPnybzQcVdsEyLKMmJgYhIWF4fHjxzh06BCWLVuGhw8fQggBGxsbLFq0CAMHDkzxuOYCAwMxb948fPTRRyhRogSEcVbTy5cv4+LFi7h79y5iY2Ph4uKCggULokqVKvDy8kLJkiWTrcsPDQ1FSEgI9Hq91rNF7fqr9pSQjZObERFKly4NSZIQHx+PgIAAkx4xknGuEhivhbqdLMvQ6/UoUaIEACA4OBhhYWFJHlNtWyEbJ1OTZRn58+dHoUKFzM48dWr7jjNnzsDPzw+PHj1CgQIFUK1aNTRq1AhFihQBrNSmQkVEuHXrFjp37gw7Ozvs3LlTm101JyJjG6YKFSrgvffew+TJk7VlWW3fvn2oVq1aqj3BGEsPDixysMQPJUVR0tQCP/G26Xm4JXW8pJapZFnG9OnT8cMPP0AIgbZt22Lbtm0WTRSlNjoUxrEVHj9+jNatW+PevXuQJAmVKlXCpUuXYGNjk+q+zJlfBzI2hDWX0jpV4oaVKZ2HmiZxw9bEjWJTYr6teszUtkOi95rSe0hJUu/NkuuSEYqi4PLly+jSpQtkWcaBAwdQpUoVi95vdqNe/+wQWHTr1g1ffvklfHx83mhgzVhGZc7TgGWJxA+ktD7YE2+bngdbUsdLahmMD9Tnz59j5syZAAAXFxf89ttv0Ov12q/rlF6SJGm/xAGgZMmS2LdvnzZvxe3bt3H9+vVUe3Ukxfw6JPceUlqnUs8zcYlDUi81TWKWbJfUtuoy83RJvRJfw/RQPw/zZRnZZ2okSUKNGjWwc+dOxMbGolu3bvD394eSRDdmZrk7d+5AlwVjxbC8KfOeCIwl8uTJE228iiJFimjVD+lVrlw5eHh4QBiL/IODgzO0P5Z9SZIEb29vbeKxjh074tatWxxcpBEZZ549cOCANgGfWuKklkYlhRJ1dVZf5tR9qOvV/aW0jSqp7dTl5n8ntz/z4yfHfB8ppWXpx4EFyxLpKU1ITeJf7jY2Nik+HFnOJoSAl5cX1q9fj+DgYLRt21abI4dZhowDmX377bcwGAwmy5P77qiZb0xMDCIiIhATE5NkhiyM460oigKDwQCDwaDtMyEhQQtizKnLDQYDEhIStIxfXZf4uWG+/8TU7WRZ1vaTnISEBERGRiIiIgLx8fFQkhhXhmUMBxYsS5QsWVJrAxEQEIAnT56k+8tMRLh//z6uXbsGIkKBAgVQvnz5TC2SZ2+fzjjaqTrHTbdu3fDgwYM3MjmWtJkzZ6JZs2baXD1TpkzBkCFDMGjQILz//vsIDAzUvpNqsHHlyhW89957qF+/Pnr06IEWLVrA19cXhw8fNkl78+ZNdOvWDS1atICPjw+mT5+O4OBg9OvXD40aNUKbNm1w7do17VzUQODEiRMYOHAgfHx84OPjg3fffRfXr18HAMyZMwebNm0CANy6dQtdunRBq1at0KxZMwwYMEDbR3h4OIYMGYI2bdqgWbNmaNmy5RvPF/X/v/76K3x8fNC6dWu0adMGPj4+mDdvnpaOWQc/iVmmE0KgVKlSGDlyJGAcgXLIkCEICgrSHmCWUNMGBQXh3XffRXR0NCRJwrhx41C8eHEOLPIAtVpk165diI+PR6tWrXDz5k2L76G8LCQkBO3bt9eGaHd2dkahQoXg7u6OwoULv9HuZ9u2bWjZsiUURcGePXuwd+9e7Ny5EzVq1EDPnj0xbdo0bSRcGxsblC5dGhERETh//jzu3r2Lvn37onbt2ihbtixOnTqFH3/8UfsOx8TEYOLEiWjbti1u3bqF77//Hps2bULz5s3RokUL7Ny5E7/99htCQkIA42y1Hh4eCAkJwblz53Dr1i3tPCVJQvHixZEvXz6cP38eV69eNZkckIyTJ3bp0gUTJkzAe++9h0OHDuHQoUPo1asXvvnmG3z33Xfa/pgVmPc/ZSwzKMYBuNq1a6eNRVGtWjUKDQ0lxTjoUXJ969XxL9QxNDw9PcnGxoYkSaL27dunewROlnMlJCTQ9evXyd7enkqWLKkNnpWdve1xLGTjCK01atQgnU5Hx44d00ZjTXwesizTsWPHSAhBTZo0IcU4qJ0sy1r64cOHk06no40bN2rbKYpCBw4c0AayGzlyJCmKQp988glJkkQjRozQxn/55ptvSAhBjo6OFBAQQAkJCdoxDh8+rH2///zzT+3cZFmm9evXEwCqXr26yXmr/y9Tpgw5OTnRnTt3tGMpikJffvklSZJE//vf/7T3kZCQQLGxseTj40P29vYUGBiYpZ9HbsY/8ViWUHsUrFu3DjNmzICjoyOuX7+OMmXKYNCgQdi5cydev36t/aJRX4qi4PXr19ixYwfef/991KxZE/fu3YMQAlOnTsX69evT1c2U5Wx6vR6VK1fGhQsXMG7cONja2vI9kIqkro/6vUy8TpIkzJw5E5Ik4eOPPwaM11vtWURE6N+/P2RZxueff44XL15o1VHqd9HR0RGffvopiAg//fQTzp07h19//RVCCISEhGDJkiXQ6/VYuHAhihUrBr1er3U9b9y4MWrVqpVkKZSTk5P5Io0QAra2tibLZFnGrVu3sGDBAiiKgp49e0JRFIhEvc18fX0RGxuLL774IsljsrTjwIJlKRcXF3z55Ze4ePEiRo0ahQIFCmDLli3o3r07vLy80LBhQ/Tu3RvDhw9H79694ePjAy8vL3Tv3h1bt26Fm5sbhg0bhtu3b2Ps2LFwcnJK8oHJcj9JklC5cmV89NFH2oymLGPUqsYDBw7AxsYGVapUMU8CIQSqVasGSZLw7NkzHD582DwJSpcuDS8vLwghkC9fPtSsWROOjo4gIsyfPx/BwcEoXLgwOnXq9EZmrtfrUbVq1TeWI5ngKDHz9UII7N69G9HR0dDpdHB3d0doaKjJq379+gCAy5cvaz9oWMZwYMGylPrryMPDA/PmzcPly5dx+vRpLF68GB07dkT+/Plx48YNbN++HVeuXIFOp0O3bt2wYMECnDp1ChcvXsSCBQtQqlSpN35psbyH7wHrSFxKeO7cOcTFxUGSJNjY2CTZONbe3h758uUDEeHOnTuQJMkkQ3Z3dzdJr64XQuD48eOAsY2HeQmD+nk6OjqaLE8P9Xh37twBjKUXjRs3RpUqVVCpUiVUqlQJVapUwXvvvQchBGJjYxEfH2++G5YOHFiwt0IyDtqUP39+eHl5YfDgwVi2bBn279+PK1euICAgANevX8fx48exaNEifPDBB6hWrRry58//xiBRjLGMiY2NRVhYGAAgOjpaC9YsaRAdHR1tvkgbot886CMixMXFQVEUODg4QDIOkGcuqWVplXgfRAR7e3vcuXMH/v7+ePDggfZ68uQJwsPDce3aNTg4OFjl2Hld6ncNY5lI/YWiPmCEENDpdLCxsTEZmTPxesaY9ciyjLlz52LJkiWQjEPkC+O4FPHx8Ul+5+Lj4xEREQEhBIoWLWq+OknCOJhduXLloNPpEBYWluqYE2mVkJBgvgjly5eHMM4FlJCQACcnpzde+fLl4x8rVsSBBWOM5XGhoaHaYFReXl6oXLkyEhIStIbSiZFxcjiVj48PDAbDG+mSIkkSPv30UwDA69evERQU9EbJAhEhMjIy0Vb/n42NjfkiTXh4uFbqoiIitGvXDvb29pBlGffv33+jakdRFNy5cwf9+/dHfHy8VQOdvIoDC8YYyyN0Oh3c3NwgyzKePXumZbI3b96Em5sbiAg6nQ7Dhw8HEWH58uUmo1OqPSq2bNkCIQQGDx6MevXqaY1n1UzZ/N/EatasiebNmyMiIgK//PKLtm/1FRISgmPHjiVZDePs7AwAiIuLe2NI8r///huhoaHa3zAGMjVq1MD7778PIQRWr16t9WxR348kSVi+fDmEEBZNisgsYN7/lDHGcgNFUSgmJoamT59Ojx49IoPBYJ4kS73tcSzIOBbEnDlzSAhBNWrUoOjoaHr8+DHlz5+f/Pz8tPFiZFmmvn37kiRJNHbsWIqNjSWDwUBxcXG0fv16sre3p0qVKtHr16+1cS5CQ0Np3rx5JIQgT09PCggIoJCQEEpISDA5B4PBQDdu3KCCBQsSANq0aRMZDAYyGAwUGhpKTZs2JVtbWwJgMo6FoigUERFBRYsWJZ1OR6dOndLGv7h27Rq5ublRwYIFSa/X08KFCyk4OFgbAycoKIhKly5NQgiaPXu2yftZtmwZeXp6pjiWDksbDiwYY7mSLMsUHBxMHh4eVKVKFbp79642aNLbkB0CC0VRKCoqij799FMSQlC9evWoatWq9NNPP70RAMTHx9OKFSuoRo0a5OXlRS1btqRatWqRu7s7/fjjj/Tq1SstCDlx4gQVLVqUihQpQqVKldJehQoVoh07drzxPhVFofv379OHH35I7u7u1LJlS+revTt5e3vT7Nmz6d13330jsFBduXKFatSoQcWKFaNevXpR69atqWbNmnTmzBmqW7cuSZJEer2eihUrRvfu3dMChuDgYJo2bRoVKVKEqlevTq1btyZvb2/q1q0b3bt3z+QYLGMEJVVWxRhjuQAR4erVq3j33XcRGRmJvXv3wsvL66001CNj98cKFSrgvffew+TJk7VlWUl95Pv7++PGjRsoUaIEatasCWHWOFpNZzAY8ODBA9y+fRsFCxZEnTp1tG6iSaVXqY01k3t/avrXr1/jypUrSEhIQN26dVGgQAG8//77+Oeff/Dnn3/iww8/fOM4RITr16/j/v37cHFxQYMGDeDo6Ijjx49Dr9drQ5W7urq+cbyYmBjcuHEDz58/R4UKFVCpUiXAwh4wzDIcWDDGcjVFUXDz5k3UqVMHbm5uOHnyJEqVKpXlg2pll8BCRYnaTKSWqaYlbVqpgQISBSMpBRaJtzM/J7XNiJo+qe2QKB04oMgUfEUZY7maJEnw8vLChQsX4ODggI4dO/KsqMZMV6fTWZSxpiVtWqmBgWQ2yJYqceCRWFLnpO5HpNI1XU2XGe+HcWDBGMsDhBCoXLkytmzZgri4OPj4+ODGjRtaF0uWPQQHB+PRo0d4+PAhAOD06dN49OjRG91IWfbGgQVjLE+QJAnVqlXD9u3bER8fj86dO+PRo0d5vuQiO1BLJX788UfUr19fK11at24d6tSpgzlz5vDnlINwGwvGWJ6itrno0aMHAGDz5s3ahFmZKbu1sciOXrx4gdDQUNjY2ECSJMiyjISEBBQuXBhubm7myVk2xSUWjLE8RTLOirpp0yZERkaiZcuWuHPnDv8izgbc3d1RoUIFlC1bFqVLl0a5cuXg6emJAgUKmCdl2RgHFoyxPEen08HLywv79u2Dra0tVq5cyQ35sgFJkrQGmepLp9NxqU4Ow98kxlieJBl7i5w/fx5jxowxX80YSycOLBhjeZYQAu7u7sifP7/5KsZYOnFgwRjL09RxDxhj1sGBBWOMMcashgMLxhhjjFkNBxaMMZYCdU4KxphlOLBgjLEUGAwGREZGJjlfBWPsTRxYMMZYMmRZxq+//opmzZrh3r17XHLBmAU4sGCMsWRIkoQePXogLi4Obdu2xfXr1zm4YCwVHFgwxlgyhBAoV64cNm/ejIiICLRp0wa3b9/mWVEZSwEHFowxlgKdTodKlSrh2LFjcHR0RLdu3fDgwQOLSy7UmTvVNhpCCEiSpP2deB1juQHPbsoYYxaQZRm3bt1Cz549ER4ejl27dsHb2zvFOUb++ecfbN26VQscbG1tsX37dpQqVQpVq1YFjIEGAMybNw9FihThwbpYjseBBWOMWUiWZdy7dw/e3t7/r727D4rqOsMA/py7ywKCfA3Lx0qqwQYLNjZuSSR21jSVOCSGJtWm7USb9MOMsXEyxDYzSdqZNjpN6j+NsV9j2xknSVvbqRbbjtZYrTbWWA3GhIgRBA0oQUVACSwuu/e8/aO7d3aXZQFdMwM8vxkm7OWce9fMynl8z7nnIjs7GwcOHEBxcTFsNlt0U2itsW/fPlRWVsJms1nhQmsNpZQVIOx2OxYsWIDdu3cDYUGDaLwaPmoTEVEEm82GW265BceOHUNGRgaqq6tx+vTpmFMZSimUl5cjNzcXWmvrC2F7Y4gIAoEAvv71r1t9iMY7BgsiojEwDAOzZs1CbW0t/H4/KioqUF9fPyRcKKWQkZGBZ599Nu50SWpqKjweT/RhonGLUyFERNfANE00NTXh9ttvR15enlXFCK86iAi8Xi9mzJiB7u7uIQs+lVK4//77UVtby4eh0YQxfIwmIqJhhe4WOXr0KKqrqyPWTYSbMmUK5s6dGzNUJCcn43vf+96wfYnGI1YsiIiug4hAKWX9N5qIYPPmzVixYkXEdIlhGJg9e7Y1jRKrL9F4xIoFEdF1CAWC4YKBiKC6uhoFBQURbbTWWLx4MRCnL9F4xGBBRHQDGYaB3NxcfPnLX7YWcYamPpYsWTJkioRovGOwICL6GDz88MPWAk3DMODxeFBeXs5qBU04DBZERB+D0tJSOJ1OIFixeOKJJ6zviSYSBgsiohtMRDB16lR85zvfgWEYyM7O5t4VNGExWBAR3WD/+Mc/0NHRgccffxw5OTlwu91W9YJoomGwICK6QUJbd7/44ov4/Oc/j0uXLuGuu+7CU089xb0raMJisCAiukFC4eHXv/41RAQejwf33HMPFi5cGHebb6LxjBtkERHdYFprNDY2YsGCBUhNTcX+/ftx8803s2JBExIjMxHRDRZ6cNmBAwdQUlKCd999d8hDy4gmClYsiIg+Jty6myYDViyIiD4mKvhMEaKJjMGCiOhjxIoFTXQMFkRERJQwDBZERESUMFy8SUQ0yUUPA5yuoevBigURUZCIRAyy8R5pLiIwTTP68LDHw4V25IymtR4yyI/VcOeOdTz0WikFn8+Hrq6uIf8PiMaKFQsiouDA29bWhu3bt6OtrQ3FxcVwu92YN2/ekO23Q782m5ubUVdXh9OnT6O7uxtpaWmYM2cO3G43ZsyYMWw/n8+Huro6HDt2DB9++CGUUnC5XCgrK8Odd96JlJSUMVcNQuceGBhAQ0MD6urqcP78efT19SEnJwdlZWWoqKhAQUEBJHjb65kzZ7B582bs3LkTbW1t8Pv9yM/PxwsvvIAlS5aM+T0QAf//MBIRTWpaa2loaJCioiJJT0+XoqIiSUpKErvdLqtWrZK+vj6rbSAQkJaWFlm+fLmkpqZKWlqa5OfnS1FRkUydOlUAyJQpU+TFF1+U/v5+0Vpb17h69ars3r1bKioqJCkpSbKyssTlconT6RS73S5KKbnjjjukvr5eTNMMe4fxhc79xhtvSHl5uSilxDAMycnJkfz8fElPTxellGRnZ8sPf/hDuXDhgvzzn/8Up9Mp2dnZct9998mvfvUrcblckpKSIgsXLrTOSzRWDBZENKlpraWtrU2cTqcUFRXJ22+/LV1dXbJy5UoxDEMMw5Ann3xStNaitZaNGzdKVlaW5OTkyNq1a6WxsVE6Ojqkq6tLGhsbpayszOr3xBNPiNZaTNOU7u5uWbx4sTgcDpk3b55s375dzpw5I52dnXLu3DnZuHGjGIYhdrtdCgsLpaGhYVQDu9ZaAoGAfPvb37bCUEFBgWzdulU++OAD6ejokKamJvnWt74lSilRSonL5RKHwyEPPPCAnD59Wnw+n9TV1YnNZhOHwyGVlZXWuYnGisGCiCa9H/3oR5KcnCw7d+4U0zTF5/PJ66+/HvEv/7a2NqvdvffeKydPnrRCQyh0mKYp27ZtEwCilJLMzExpbW2VDz74QBYsWCDp6emyfv16GRwcjOhrmqZ4vV654447rFBy//33y+DgYPRbjaC1Fq/XK48++qgVGoqKiqSurm7I+X0+n6xatco6v91ulzfeeEMCgYBoraWnp0cqKirE4XDI0qVLrfMTjRWDBRFNWlpr8fv9UlJSIp/61KfE6/Vaxw4ePGgFBADy0EMPSXJysixfvlwkOCUSTWst7e3tAkAAiGEY8txzz0lVVZWkp6fLv//9bzFNM+Y0RyAQkPXr11vXAyCnTp2K2TZEay1///vfJSkpSQzDEKWUvPLKKzEDgdZaOjs7pbCwUJRSYrfbZf78+VawEBEZGBiQN998Uy5fvhzzHESjwbtCiGjS0lpjx44daGlpQU1NDZKTk60Fix0dHRFbcG/btg2LFi3Cz372M2itYbPZos72f1OmTLHOobXGL3/5S+zbtw8///nPMX/+fBiGEfOR6UqpiIWVAHD27NnoZhYRgc/nw5o1axAIBIDgtefPnx/d1JKVlQW32w0ACAQCOHToEP74xz9aP09OTsa8efOQkZHBhZt0zYZ+uomIJoHQAP7qq68iMzMTX/ziF60gYbfbceTIEatt6K6NTZs2ITMzM2YwQPCcoVs2Q3p7e7FixQo88sgjsNvtEe3DiQja29sjwkxfX1/EucKJCI4cOYJTp04hWH1GUlISsrOzY/ZRSsFms2H+/PlWaBAR1NbWWv2VUjAMg6GCrkvsvx1ERJNAb28vDh8+jFtuuQWFhYXWcRHB22+/HdH2+eefR15eXtxBV0Rw7tw567UK3m66Zs2aIXtIhBMRGIaBo0ePRpw/Kysrol04rTWam5utawBASkpK3PBimiZcLlfEsdbWVqviQZQIDBZENCmFqgsfffQR7r77biBsx0kRQVNTEwDAZrPh1ltvxbJly4atVIQYhoH6+nog7FyrVq3C9OnTh506QfB6V65cwYEDByKqDTNnzhz2mkopDAwMRBxLS0uLex0E32O4wcHBmBUOomsV+xNLRDTBGYaBm266Ca+++irWrFkTMbg2NTXh/PnzQLAy8NnPfhYOhyOs91Ch/ocOHbJCRVJSElavXj1kMI+mlMLZs2fR1dVlvZ47dy7y8vKim0YIrckIXbu/vz9u9cEwDPT29kYcy8rKGjGMEI1F/E87EdEE5nA48MADD8DpdFphQGuN1157zRqgRQQejwcYxTM0lFJ4//33rYG6oKAAJSUlo+pXX19vbeltGIZVIRmur2EYuP32262fK6Xg9XrR398f3dSilLICU4jb7YbNZhv2OkRjxWBBRBQkIvD7/di5c6f1GgA+85nPjGq6oLW1FY2NjTBNE0opK1SM1FdEsGPHDiAYGFJSUlBZWRl3sFdKoaioCN/4xjdgGAZEBAMDA2hubo5ZIRERDA4OYt++fZDgQs2srCysWLEiuinRdRn66SMimqREBBcvXsQ777xjhYHs7GyUlpbGHeRD9uzZg6tXr1rTE+Xl5dFNhpDgWo+9e/da13A6nZg+ffqIgUQphbVr1yI/Px8I3kK6ceNG+P3+mH2bm5tRX19vXaempgZlZWWj+rMRjRaDBRFRkGEYaGxstF7bbDZ89atfHfVDwbZt2xbx+nOf+xwCgUDcvqFqRWdnJ7TW0FqjoqICGRkZMSsP4ZRSKCwsxG9/+1vr2N/+9jesW7fOCjehr0OHDmHRokXwer0QEXzlK1/B008/HXE+okSI/6klIppk6urqrO+VUqiqqor5r/9wWmtcvnwZJ06csKYZMjIyMHfu3LjhIDTob9261TqmlMI3v/nNiHaI8wh3rTX+8pe/ICcnBwsWLAAAvPDCC6iqqsKPf/xjvPzyy1i5ciXuvfdenD9/Hk6nE9///vexZcsWpKamxg09RNeCj00nIgoSESxatAj/+te/oJRCZmYmmpubkZWVFXcA1lqjpaUF5eXl6OvrAwBUVFTgP//5T9x+CO6lMWvWLFy4cAGGYaCkpATHjh2Dw+Gw+nq9Xhw7dixicysE96Vob2/H3LlzsXz5crz00kvYtWsXnn/+eRw/fhx+vx8IhpX8/Hw8+OCDWLduHXfWpBtq+ChNRDSJaK3R3d2N48ePW68LCgqQkpIyYsVCKYV33nkH/f39EBForbFkyZLoZkNorbFt2zZ0dnZa/aqrqyNChdYaa9euxYMPPoje3t6I92IYBt566y1cuXIFFRUVAICqqiocPHgQzc3NOH78ON577z2cOnUKJ06cwIYNG5CZmWn1J7oRGCyIiILVisOHD+PChQvWFEVZWRmSk5PjTmeE7Nu3z/re4XDgzjvvjFsVkOAdKBs3brSmT0QEixcvtsKD1hperxc7duzAjBkzhoQCEcHp06dhmia6urpgBJ9DYrPZUFBQgJkzZ+KTn/wkioqKkJaWZv054r0vous18t8WIqJJwDAMKxyEBvqFCxeOOAiLCEzTRG1tLbTWUEohPT0d06dPH3ZdBIL9Tp06hXfffdcKEpmZmSgvL7euqZTCuXPncObMGVRWVlrHwpmmiaSkJPz1r38Fwt67Cj4bxGazxd0PgyjRGCyIaNILVQ8OHDgABAfvpKQk3HXXXRFTD7GICOrq6iIqHcXFxcjJyYk7mBuGgbNnz1rnV0rhueeei7gDxTRNPPPMMwgEAnj44YeHBBWlFIqLiyEi2L9/P1auXIkPP/wQpmlCBzfbCn2FCz8e/TOi68XFm0Q06YkIenp6cOutt6KjowOGYeDTn/40jhw5gqSkpLgBwTRN/OIXv0BNTQ0kuGvmU089hfXr14+4Vfbrr7+OqqoqGIaB5ORkHD58GLNnz4ZhGAgEAtizZw/uu+8+PPnkk9iwYUN0d2itrcWbPT09EBGkpKRgzpw51iPgw6sXDocDubm5yMvLQ2lpKdxuNz7xiU8gOzsbiFENIboWDBZENOmJCE6ePAm32w2fzwcVvOXzN7/5TdzBVoLTDo888ghee+01qOBjx998802Ul5fHXZuhtUZTUxNKS0ths9kwdepUNDU1ITc3FwBw5coVeDweXLx4EUePHoXL5Yp5vkAggGeeeQY//elPrepDrHbhVHA9R3JyMpxOJ5YuXYpnn30Wubm5cf+8RKMR/9NHRDQJSHAqwefzAcFB/wtf+EJ0s2E1Nzdbz9uYMWPGiKECwcF95syZeOyxx4DgLaVbt25Fe3s7amtr4fF40N3djT/96U+YNm1azPOFKiQ1NTWYM2fOqNZSSPDuE6UUfD4fzp49iw0bNsDj8WD//v2cGqHrxooFEU16IoI///nPWLZsGbTWyMjIwPHjx+FyueIO1KGKxT333GM9g+O73/0u1q9fD4xyasHn82Hp0qXYu3cvfD4fRAR2ux3Tp0/H7373O+s20mgSXBfyhz/8AatXr0Z/fz+mTp2K2bNnw+12W9fWWmNwcBB+vx8+nw8dHR1obW1FT09PxO2xhmEgLy8Pb7311rDVEaLRYLAgIgLg9/uxa9cuXLp0CZWVlbjpppuimwyrtbUVe/fuRWFhITweD9LT06ObxDUwMID3338fDQ0N8Hq9KCkpgdvtHnYjq9Cv7ccffxybN29GIBBAdXU1XnrpJUybNi3iEe/h/UUEgUAAPp8PPT09aGhowIYNG7B7926r7UMPPYQtW7bEvC7RaDBYEBGFDdah9QdjGVjD24+1L6KuHRKqIsQiInjllVfw2GOPQWuN8vJy7Nq1ywoiI10//HperxdPP/00Nm3aBK01bDYbTp48ieLi4mGvTxQPgwUR0TgiIujt7UVZWRk6OjqQkpKC//73v5gzZ05001EJBSG3223tqbF582YsW7YMdrs9ujnRiBhHiYjGEa01Ll68iMuXL8NmsyEnJwfTpk0bssfFWJWWllrfX7lyZcRbZYmGw2BBRDTOhE+7BAIB+P3+Eac/RjI4OGh9n5aWdt1BhSYvBgsionHEMAy4XC7k5+dDa43Ozk7s378/utmoSdiuoxLciTP8rhKisWKwICIaR5RSSE1NxaZNm5Ceng6lFFavXm3tQTHaZXOhLb9Dd8F0dnZCKYWamhrcdtttXLhJ14yfHCKicUYF9874wQ9+gJSUFFy+fBlLly7F1q1b0dfXB631sFMZEty3wjRNnDhxAosXL8bBgwehlILH48G6deuiuxCNCe8KISIapwKBAI4cOYJHH30ULS0tMAwDpaWl+NrXvoYvfelLmDVr1pBFmBcvXsTu3bvx+9//HgcPHsRHH30EpRR+8pOfYNWqVVYVhOhaMVgQEY1jWmv09fVh+/bt2LJlCxoaGnD+/HnYbDbk5eXB5XIhIyMDV69exaVLl9De3o7e3l5kZGSgpKQEd999N1auXImbb76ZgYISgsGCiGgC8Xq9eO+997Bnzx60tLSgvb0dHR0dSE9Ph9PpxKxZs+DxeHDbbbeNaXdRotFisCAimiBCv85Dm16F35aKsF1FQz8PHSNKJAYLIiIiShjeFUJEREQJw2BBRERECcNgQURERAnDYEFEREQJw2BBRERECcNgQURERAnDYEFEREQJw2BBRERECcNgQURERAnDYEFEREQJw2BBRERECcNgQURERAnDYEFEREQJw2BBRERECcNgQURERAnDYEFEREQJw2BBRERECcNgQURERAnDYEFEREQJw2BBRERECcNgQURERAnzP11Gc32hKgE0AAAAAElFTkSuQmCC" } }, "cell_type": "markdown", "id": "e8e35402-d698-4428-a9c6-6c69b00cce26", "metadata": {}, "source": [ "## Ex.3: Pendulum\n", "\n", "Let us now consider the pendulum example from the lecture.\n", "\n", "![pendulum.png](attachment:07d2d484-1bdd-424d-a286-f484bdacbf16.png)\n", "\n", "Using the free body diagram we can derive the following equation of motion.\n", "$$ml^2*\\ddot \\theta = -m*g*\\sin(\\theta)*l +T_e$$\n", "\n", "we then rewrite it in the canonical form\n", "$$\n", "\\begin{aligned}\n", "&\\dot\\theta_1 = \\theta_2\\\\\n", "&\\dot\\theta_2 = -\\frac{g}{l}*\\sin(\\theta_1) + \\frac{T_e}{m*l^2}\n", "\\end{aligned}\n", "$$\n", "where we use the notation $\\theta_1 = \\theta, \\theta_2 = \\dot\\theta_1$.\n", "\n", "We then linearise the system around an equilibrium point ($\\theta_1, \\theta_2, T_e$) = (0,0,0), with a help of symbolic calculus (see the code below) and get a linear time invariant model\n", "$$\n", "\\begin{aligned}\n", "&\\dot\\theta_1 = \\theta_2\\\\\n", "&\\dot\\theta_2 = -\\frac{g}{l} + \\frac{T_e}{m*l^2}\n", "\\end{aligned}\n", "$$\n", "\n", "## TODO\n", "1. Let fisrt consider the system without control ($T_e = 0$). Plot the trajectories of linear and nonlinear systems for\n", " $\\theta^0 = (0.1, 0)$ and $\\theta^0 = (1, 0).$ What kind of conclusion could you make when analyzing the simulation's result?\n", "2. Let $\\theta^0 = (0, 0)$, play with different control inputs, and look at how they affect linear and nonlinear systems correspondingly. What kind of conclusion can you make from this?" ] }, { "cell_type": "code", "execution_count": 33, "id": "80217e8f-fcf3-45ab-ad4a-2ef52216fa87", "metadata": {}, "outputs": [], "source": [ "#profite from symbolic calculus do easy the math part\n", "import sympy as sp\n", "m, l, g, Te = sp.symbols('m l g Te')\n", "theta1, theta2, dottheta2 = sp.symbols('theta1 theta2 dottheta2')\n", "\n", "# Define the differential equations of the system\n", "eq1 = m*l*l* dottheta2 + m*g*sp.sin(theta1)*l - Te\n", "\n", "# Solve for the first derivative of theta1 (angular velocity)\n", "dotthet2_sol = sp.solve(eq1, dottheta2)[0]\n", "\n", "# Solve for the first derivative of y1 (linear velocity)\n", "dottheta2_sol = sp.simplify(sp.solve(eq1, dottheta2)[0])\n", "\n", "# Define the state-space representation of the system dynamics\n", "f1 = theta2\n", "f2 = dotthet2_sol\n", "f = sp.Matrix([f1, f2])\n", "\n", "# Define state and control variables\n", "variables_x = sp.Matrix([theta1,theta2])\n", "variables_u = sp.Matrix([Te])\n", "\n", "# Compute the Jacobian matrices of the system\n", "jacobian_A = sp.simplify(f.jacobian(variables_x).subs([(theta1,0), (theta2,0)]))\n", "jacobian_B = sp.simplify(f.jacobian(variables_u).subs([(theta1,0), (theta2,0)]))" ] }, { "cell_type": "code", "execution_count": 10, "id": "acb531bc-eee6-401b-b8dd-3632d4b90631", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}0\\\\\\frac{1}{l^{2} m}\\end{matrix}\\right]$" ], "text/plain": [ "Matrix([\n", "[ 0],\n", "[1/(l**2*m)]])" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "jacobian_B" ] }, { "cell_type": "code", "execution_count": 9, "id": "acca14c1-f886-486f-b30d-28d0c19d1e9f", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}0 & 1\\\\- \\frac{g}{l} & 0\\end{matrix}\\right]$" ], "text/plain": [ "Matrix([\n", "[ 0, 1],\n", "[-g/l, 0]])" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "jacobian_A" ] }, { "cell_type": "code", "execution_count": 38, "id": "7dee8747-3a98-41a3-9204-519da9274f04", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from scipy.integrate import odeint\n", "import matplotlib.pyplot as plt\n", "\n", "def PendulumNonlinear(theta,t,m,l,g,Te):\n", " dth1 = theta[1]\n", " dth2 = -g/l*np.sin(theta[0]) +1/(m*l*l)*Te(t)\n", " return [dth1, dth2]\n", "\n", "m = 0.1;\n", "l = 1;\n", "g = 9.8;\n", "\n", "A = np.array([[0,1],[-g/l, 0]])\n", "B = np.array([[0],\n", " [1]])\n", "D = np.array([0])\n", "C = np.array([[1,0],[0,1]])\n", "R = np.array([0])\n", "\n", "t0 = 0 # Initial time \n", "tf = 10 # Final time\n", "T = np.linspace(t0, tf, 1000) # Time vector\n", "\n", "def w_func(t):\n", " return 0.0 # Disturbance input\n", " \n", "def u_func(t):\n", " return 0.0 # Control input\n", "\n", "x0 = np.array([0, 0]).flatten() # Initial state\n", "\n", "# Compute system response\n", "y = OpenLoopInputOutputSystem(A, B, D, C, R, u_func, w_func, T, x0)\n", "\n", "y1 = odeint(PendulumNonlinear, x0, T, args=(m,l,g, u_func))\n", "\n", "# Plot the response\n", "plt.plot(T, y[0,:], linewidth=2.0, color='red')\n", "plt.plot(T, y1[:,0], linewidth=2.0, linestyle='--',color='green')\n", "plt.grid(color='black', linestyle='--', linewidth=1.0, alpha=0.7)\n", "plt.xlim([t0, tf])\n", "plt.ylabel(r'Angle (rad)')\n", "plt.xlabel('Time (s)')\n", "plt.title('Pendulum')\n", "plt.show()\n", "\n", "plt.plot(T, y[1,:], linewidth=2.0, color='red')\n", "plt.plot(T, y1[:,1], linewidth=2.0, linestyle='--',color='green')\n", "plt.grid(color='black', linestyle='--', linewidth=1.0, alpha=0.7)\n", "plt.xlim([t0, tf])\n", "plt.ylabel(r'Angular velocity (rad/s)')\n", "plt.xlabel('Time (s)')\n", "plt.title('Pendulum')\n", "plt.show()" ] }, { "attachments": { "71664055-85e2-408b-9f36-29162fd4184c.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "adff30a4-0fdf-46a5-a55c-792665747d8f", "metadata": {}, "source": [ "## Ex 4. Dynamic modeling of an inverted pendulum on the cart\n", "\n", "The system in this example consists of an inverted pendulum mounted to a motorized cart. The inverted pendulum system is an example commonly found in control system textbooks and research literature. Its popularity derives in part from the fact that it is unstable without control, that is, the pendulum will simply fall over if the cart isn't moved to balance it. Additionally, the dynamics of the system are nonlinear. The objective of the control system is to balance the inverted pendulum by applying a force to the cart that the pendulum is attached to. A real-world example that relates directly to this inverted pendulum system is the attitude control of a booster rocket at takeoff.\n", "\n", "![inverted_pendulum.png](attachment:71664055-85e2-408b-9f36-29162fd4184c.png)\n", "\n", "Let us consider the system with the following system parameters\n", " \n", " (M) mass of the cart 0.5 kg\n", " \n", " (m) mass of the pendulum 0.2 kg\n", " \n", " (l) length to pendulum center of mass 0.3 m\n", " \n", " (b) coefficient of friction for cart 0.1 N/m/sec\n", " \n", " (I) mass moment of inertia of the pendulum 0.006 kg.m^2\n", " \n", " (F) force applied to the cart\n", " \n", " (y) cart position coordinates\n", " \n", " (theta) angle between the pendulum and the vertical axis\n", "\n", "## TODO\n", "1) Show that the inverted pendulum on the cart can be modeled as follows\n", "\n", "$$(M+m)\\ddot{y} + b\\dot{y} + ml\\ddot{\\theta}\\cos\\theta -ml\\dot\\theta^2\\sin(\\theta) = F$$\n", "$$ml\\cos(\\theta)\\ddot{y} + (I+ml^2)\\ddot{\\theta} - mgl\\sin\\theta = 0$$\n", "\n", "If you find it difficult to derive the equations yourself, please, watch the following video: \n", "https://www.youtube.com/watch?v=kXLjs5aW2uE\n", "\n", "or, alternatively, check the following tutorial https://ctms.engin.umich.edu/CTMS/index.php?example=InvertedPendulum§ion=SystemModeling\n", "\n", "2) Rewrite the system equation in a canonical form $\\dot x = f(x,u),$ where state vector $x = (y,\\theta,\\dot y,\\dot\\theta)$.\n", "\n", "3) Find an equlibrium point. Linearise the system equations by finding the Jacobian matrix.\n", "\n", "4) Simulate trajectories of the uncontrolled nonlinear system and its linear approximation for different initial vectors. What can you say about system dynamics?\n" ] }, { "cell_type": "code", "execution_count": null, "id": "96e6879b-3501-47ed-95c9-fead52c31e20", "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": "3.13.1" } }, "nbformat": 4, "nbformat_minor": 5 }