From f93949c707d2e659c6f81ad14e26b8a25c1a3004 Mon Sep 17 00:00:00 2001 From: Mohammadmehdi Karami Date: Thu, 11 Jul 2024 13:45:07 +0330 Subject: [PATCH] Update@20240711 --- Chapter3/Active_s.ipynb | 235 +++++++++++++++++++++ Chapter3/Active_s.py | 57 ++++++ Chapter3/DCmotor.ipynb | 167 +++++++++++++++ Chapter3/DCmotor.py | 39 ++++ Chapter3/DCmotor_transfun.ipynb | 235 +++++++++++++++++++++ Chapter3/DCmotor_transfun.py | 36 ++++ Chapter3/Invpend_solver.ipynb | 159 ++++++++++++++ Chapter3/Invpend_solver.py | 44 ++++ Chapter3/inverted_pendulum.ipynb | 74 +++++++ Chapter3/inverted_pendulum.py | 22 ++ Chapter3/robot_model.ipynb | 95 +++++++++ Chapter3/robot_model.py | 43 ++++ Chapter3/robot_solver.ipynb | 180 ++++++++++++++++ Chapter3/robot_solver.py | 65 ++++++ Chapter3/tank_model.ipynb | 67 ++++++ Chapter3/tank_model.py | 15 ++ Chapter3/tank_solver.ipynb | 150 ++++++++++++++ Chapter3/tank_solver.py | 35 ++++ Chapter3/train.ipynb | 241 ++++++++++++++++++++++ Chapter3/train.py | 63 ++++++ Chapter3/train_linear.ipynb | 242 ++++++++++++++++++++++ Chapter3/train_linear.py | 64 ++++++ Chapter4/DCmotor_jordan.ipynb | 156 ++++++++++++++ Chapter4/DCmotor_jordan.py | 35 ++++ Chapter4/ex3_1.ipynb | 169 +++++++++++++++ Chapter4/ex3_1.py | 35 ++++ Chapter4/ex3_2.ipynb | 310 ++++++++++++++++++++++++++++ Chapter4/ex3_2.py | 37 ++++ Chapter4/ex3_3.ipynb | 159 ++++++++++++++ Chapter4/ex3_3.py | 15 ++ Chapter4/ex3_8.ipynb | 159 ++++++++++++++ Chapter4/ex3_8.py | 29 +++ Chapter4/jordan_forms.ipynb | 242 ++++++++++++++++++++++ Chapter4/jordan_forms.py | 49 +++++ Chapter5_6/ex4_3.ipynb | 147 +++++++++++++ Chapter5_6/ex4_3.py | 26 +++ Chapter5_6/ex4_9.ipynb | 147 +++++++++++++ Chapter5_6/ex4_9.py | 26 +++ Chapter5_6/ex5_1.ipynb | 342 +++++++++++++++++++++++++++++++ Chapter5_6/ex5_1.py | 75 +++++++ Chapter5_6/ex5_2.ipynb | 125 +++++++++++ Chapter5_6/ex5_2.py | 25 +++ 42 files changed, 4636 insertions(+) create mode 100644 Chapter3/Active_s.ipynb create mode 100644 Chapter3/Active_s.py create mode 100644 Chapter3/DCmotor.ipynb create mode 100644 Chapter3/DCmotor.py create mode 100644 Chapter3/DCmotor_transfun.ipynb create mode 100644 Chapter3/DCmotor_transfun.py create mode 100644 Chapter3/Invpend_solver.ipynb create mode 100644 Chapter3/Invpend_solver.py create mode 100644 Chapter3/inverted_pendulum.ipynb create mode 100644 Chapter3/inverted_pendulum.py create mode 100644 Chapter3/robot_model.ipynb create mode 100644 Chapter3/robot_model.py create mode 100644 Chapter3/robot_solver.ipynb create mode 100644 Chapter3/robot_solver.py create mode 100644 Chapter3/tank_model.ipynb create mode 100644 Chapter3/tank_model.py create mode 100644 Chapter3/tank_solver.ipynb create mode 100644 Chapter3/tank_solver.py create mode 100644 Chapter3/train.ipynb create mode 100644 Chapter3/train.py create mode 100644 Chapter3/train_linear.ipynb create mode 100644 Chapter3/train_linear.py create mode 100644 Chapter4/DCmotor_jordan.ipynb create mode 100644 Chapter4/DCmotor_jordan.py create mode 100644 Chapter4/ex3_1.ipynb create mode 100644 Chapter4/ex3_1.py create mode 100644 Chapter4/ex3_2.ipynb create mode 100644 Chapter4/ex3_2.py create mode 100644 Chapter4/ex3_3.ipynb create mode 100644 Chapter4/ex3_3.py create mode 100644 Chapter4/ex3_8.ipynb create mode 100644 Chapter4/ex3_8.py create mode 100644 Chapter4/jordan_forms.ipynb create mode 100644 Chapter4/jordan_forms.py create mode 100644 Chapter5_6/ex4_3.ipynb create mode 100644 Chapter5_6/ex4_3.py create mode 100644 Chapter5_6/ex4_9.ipynb create mode 100644 Chapter5_6/ex4_9.py create mode 100644 Chapter5_6/ex5_1.ipynb create mode 100644 Chapter5_6/ex5_1.py create mode 100644 Chapter5_6/ex5_2.ipynb create mode 100644 Chapter5_6/ex5_2.py diff --git a/Chapter3/Active_s.ipynb b/Chapter3/Active_s.ipynb new file mode 100644 index 0000000..6a856be --- /dev/null +++ b/Chapter3/Active_s.ipynb @@ -0,0 +1,235 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Import necessary libraries" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy import signal" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the system matrices" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "A = np.array([[0.0, 0.0, 1.0, 0.0],\n", + " [0.0, 0.0, 0.0, 1.0],\n", + " [-10.0, 10.0, -2.0, 2.0],\n", + " [60.0, -660.0, 12.0, -12.0]])\n", + "b1 = np.array([[0.0], [0.0], [0.0033], [-0.02]])\n", + "b2 = np.array([[0.0], [0.0], [0.0], [600.0]])\n", + "B = np.hstack((b1, b2))\n", + "C = np.array([[1.0, 0.0, 0.0, 0.0]])\n", + "D = np.array([[0.0]])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Create the state space model of the active suspension system" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "active_suspension = signal.StateSpace(A, b2, C, D) # Note only Second input is used" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the time vector" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "t = np.arange(0.0, 7.0, 0.01)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Initial condition" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "x0 = np.array([0.2, 0.0, 0.0, 0.0])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Simulate initial response" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "t, y, x = signal.lsim(active_suspension, U=np.zeros_like(t), T=t, X0=x0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Plot initial response" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(10, 6))\n", + "plt.plot(t, x[:, 0], 'k', label='x1')\n", + "plt.plot(t, x[:, 1], 'k-.', label='x2')\n", + "plt.grid()\n", + "plt.xlabel('Time (sec)')\n", + "plt.ylabel('State variables')\n", + "plt.legend()\n", + "plt.setp(plt.gca().get_lines(), linewidth=2)\n", + "plt.title('Initial Response of Active Suspension System')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define input u" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "u = 0.1 * (np.sin(5.0 * t) + np.sin(9.0 * t) + np.sin(13.0 * t) + np.sin(17.0 * t) + np.sin(21.0 * t))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Simulate the system with input u and initial condition x0=0" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "t, y, x = signal.lsim(active_suspension, U=u, T=t, X0=np.zeros_like(x0))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Plot the result" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(10, 6))\n", + "plt.plot(t, x[:, 0], 'k', label='x1')\n", + "plt.plot(t, x[:, 1], 'k-.', label='x2')\n", + "plt.grid()\n", + "plt.xlabel('Time (sec)')\n", + "plt.ylabel('State variables')\n", + "plt.legend()\n", + "plt.setp(plt.gca().get_lines(), linewidth=2)\n", + "plt.title('Response of Active Suspension System with Input (Initial x0=0)')\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.12.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Chapter3/Active_s.py b/Chapter3/Active_s.py new file mode 100644 index 0000000..f5bf8ae --- /dev/null +++ b/Chapter3/Active_s.py @@ -0,0 +1,57 @@ +# Import necessary libraries +import numpy as np +import matplotlib.pyplot as plt +from scipy import signal + +# Define the system matrices +A = np.array([[0.0, 0.0, 1.0, 0.0], + [0.0, 0.0, 0.0, 1.0], + [-10.0, 10.0, -2.0, 2.0], + [60.0, -660.0, 12.0, -12.0]]) +b1 = np.array([[0.0], [0.0], [0.0033], [-0.02]]) +b2 = np.array([[0.0], [0.0], [0.0], [600.0]]) +B = np.hstack((b1, b2)) +C = np.array([[1.0, 0.0, 0.0, 0.0]]) +D = np.array([[0.0]]) + +# Create the state space model of the active suspension system +active_suspension = signal.StateSpace(A, b2, C, D) # Note only Second input is used + +# Define the time vector +t = np.arange(0.0, 7.0, 0.01) + +# Initial condition +x0 = np.array([0.2, 0.0, 0.0, 0.0]) + +# Simulate initial response +t, y, x = signal.lsim(active_suspension, U=np.zeros_like(t), T=t, X0=x0) + +# Plot initial response +plt.figure(figsize=(10, 6)) +plt.plot(t, x[:, 0], 'k', label='x1') +plt.plot(t, x[:, 1], 'k-.', label='x2') +plt.grid() +plt.xlabel('Time (sec)') +plt.ylabel('State variables') +plt.legend() +plt.setp(plt.gca().get_lines(), linewidth=2) +plt.title('Initial Response of Active Suspension System') +plt.show() + +# Define input u +u = 0.1 * (np.sin(5.0 * t) + np.sin(9.0 * t) + np.sin(13.0 * t) + np.sin(17.0 * t) + np.sin(21.0 * t)) + +# Simulate the system with input u and initial condition x0=0 +t, y, x = signal.lsim(active_suspension, U=u, T=t, X0=np.zeros_like(x0)) + +# Plot the result +plt.figure(figsize=(10, 6)) +plt.plot(t, x[:, 0], 'k', label='x1') +plt.plot(t, x[:, 1], 'k-.', label='x2') +plt.grid() +plt.xlabel('Time (sec)') +plt.ylabel('State variables') +plt.legend() +plt.setp(plt.gca().get_lines(), linewidth=2) +plt.title('Response of Active Suspension System with Input (Initial x0=0)') +plt.show() diff --git a/Chapter3/DCmotor.ipynb b/Chapter3/DCmotor.ipynb new file mode 100644 index 0000000..0841c6c --- /dev/null +++ b/Chapter3/DCmotor.ipynb @@ -0,0 +1,167 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Import necessary libraries" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy import signal" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the system matrices" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "A = np.array([[0, 1, 0],\n", + " [0, 0, 4.438],\n", + " [0, -12, -24]])\n", + "b1 = np.array([[0], [0], [20]])\n", + "b2 = np.array([[0], [-7.396], [0]])\n", + "B = np.hstack((b1, b2))\n", + "C = np.array([[1, 0, 0],\n", + " [0, 1, 0]])\n", + "D = np.array([[0], [0]])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Create the state space model of the DC motor" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "DC_motor = signal.StateSpace(A, b1, C, D) # Note only first input is used" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the time vector" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "t = np.arange(0.0, 4.0, 0.01)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Generate input signal u" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "u = 6 * signal.square(2 * np.pi * 0.25 * t) - 3" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Simulate the system" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "t, y, x = signal.lsim(DC_motor, u, t)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Plot the result" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(10, 6))\n", + "plt.plot(t, x[:, 0], 'k', label='theta')\n", + "plt.plot(t, x[:, 1], 'k-.', label='omega')\n", + "plt.plot(t, x[:, 2], 'k:', label='i')\n", + "plt.grid()\n", + "plt.xlabel('Time (sec)')\n", + "plt.ylabel('State variables')\n", + "plt.legend()\n", + "plt.title('Simulation of DC Motor')\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.12.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Chapter3/DCmotor.py b/Chapter3/DCmotor.py new file mode 100644 index 0000000..6b246d9 --- /dev/null +++ b/Chapter3/DCmotor.py @@ -0,0 +1,39 @@ +# Import necessary libraries +import numpy as np +import matplotlib.pyplot as plt +from scipy import signal + +# Define the system matrices +A = np.array([[0, 1, 0], + [0, 0, 4.438], + [0, -12, -24]]) +b1 = np.array([[0], [0], [20]]) +b2 = np.array([[0], [-7.396], [0]]) +B = np.hstack((b1, b2)) +C = np.array([[1, 0, 0], + [0, 1, 0]]) +D = np.array([[0], [0]]) + +# Create the state space model of the DC motor +DC_motor = signal.StateSpace(A, b1, C, D) # Note only first input is used + +# Define the time vector +t = np.arange(0.0, 4.0, 0.01) + +# Generate input signal u +u = 6 * signal.square(2 * np.pi * 0.25 * t) - 3 + +# Simulate the system +t, y, x = signal.lsim(DC_motor, u, t) + +# Plot the result +plt.figure(figsize=(10, 6)) +plt.plot(t, x[:, 0], 'k', label='theta') +plt.plot(t, x[:, 1], 'k-.', label='omega') +plt.plot(t, x[:, 2], 'k:', label='i') +plt.grid() +plt.xlabel('Time (sec)') +plt.ylabel('State variables') +plt.legend() +plt.title('Simulation of DC Motor') +plt.show() diff --git a/Chapter3/DCmotor_transfun.ipynb b/Chapter3/DCmotor_transfun.ipynb new file mode 100644 index 0000000..05ef01e --- /dev/null +++ b/Chapter3/DCmotor_transfun.ipynb @@ -0,0 +1,235 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Import necessary libraries" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import sympy as sp" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define symbolic variables" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "s = sp.symbols('s')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the system matrices (DC motor example)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "A = sp.Matrix([[0, 1, 0],\n", + " [0, 0, 4.438],\n", + " [0, -12, -24]])\n", + "b1 = sp.Matrix([[0], [0], [20]])\n", + "b2 = sp.Matrix([[0], [-7.396], [0]])\n", + "B = sp.Matrix.hstack(b1, b2)\n", + "C = sp.Matrix([[1, 0, 0]]) # Only theta is used as output\n", + "D = sp.Matrix([[0, 0]]) # Two inputs, so D is 1x2 matrix" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Calculate (sI - A)^(-1)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "sI_A_inv = (s*sp.eye(A.shape[0]) - A).inv()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Calculate the transfer function G(s) = C(sI - A)^(-1)B + D" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "G = C*sI_A_inv*B + D" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Simplify expressions" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "sI_A_inv_simp = sp.simplify(sI_A_inv)\n", + "G_simp = sp.simplify(G)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Print the results" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(sI - A)^(-1) =\n", + "⎡1.0 1.0⋅s + 24.0 4.438 ⎤\n", + "⎢─── ──────────────────────────── ────────────────────────────⎥\n", + "⎢ s ⎛ 2 ⎞ ⎛ 2 ⎞⎥\n", + "⎢ s⋅⎝1.0⋅s + 24.0⋅s + 53.256⎠ s⋅⎝1.0⋅s + 24.0⋅s + 53.256⎠⎥\n", + "⎢ ⎥\n", + "⎢ 1.0⋅s + 24.0 4.438 ⎥\n", + "⎢ 0 ──────────────────────── ──────────────────────── ⎥\n", + "⎢ 2 2 ⎥\n", + "⎢ 1.0⋅s + 24.0⋅s + 53.256 1.0⋅s + 24.0⋅s + 53.256 ⎥\n", + "⎢ ⎥\n", + "⎢ -12.0 1.0⋅s ⎥\n", + "⎢ 0 ──────────────────────── ──────────────────────── ⎥\n", + "⎢ 2 2 ⎥\n", + "⎣ 1.0⋅s + 24.0⋅s + 53.256 1.0⋅s + 24.0⋅s + 53.256 ⎦\n", + "\n", + "G(s) =\n", + "⎡ 88.76 -7.396⋅s - 177.504 ⎤\n", + "⎢──────────────────────────── ────────────────────────────⎥\n", + "⎢ ⎛ 2 ⎞ ⎛ 2 ⎞⎥\n", + "⎣s⋅⎝1.0⋅s + 24.0⋅s + 53.256⎠ s⋅⎝1.0⋅s + 24.0⋅s + 53.256⎠⎦\n" + ] + } + ], + "source": [ + "print(\"(sI - A)^(-1) =\")\n", + "sp.pprint(sI_A_inv_simp)\n", + "print(\"\\nG(s) =\")\n", + "sp.pprint(G_simp)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Print the LaTeX formatted output" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "LaTeX formatted output:\n", + "$G(s) = $ \\left[\\begin{matrix}\\frac{88.76}{s \\left(1.0 s^{2} + 24.0 s + 53.256\\right)} & \\frac{- 7.396 s - 177.504}{s \\left(1.0 s^{2} + 24.0 s + 53.256\\right)}\\end{matrix}\\right]\n", + "$[sI - A]^{-1} = $ \\left[\\begin{matrix}\\frac{1.0}{s} & \\frac{1.0 s + 24.0}{s \\left(1.0 s^{2} + 24.0 s + 53.256\\right)} & \\frac{4.438}{s \\left(1.0 s^{2} + 24.0 s + 53.256\\right)}\\\\0 & \\frac{1.0 s + 24.0}{1.0 s^{2} + 24.0 s + 53.256} & \\frac{4.438}{1.0 s^{2} + 24.0 s + 53.256}\\\\0 & - \\frac{12.0}{1.0 s^{2} + 24.0 s + 53.256} & \\frac{1.0 s}{1.0 s^{2} + 24.0 s + 53.256}\\end{matrix}\\right]\n" + ] + } + ], + "source": [ + "print(\"\\nLaTeX formatted output:\")\n", + "print(\"$G(s) = $\", sp.latex(G_simp))\n", + "print(\"$[sI - A]^{-1} = $\", sp.latex(sI_A_inv_simp))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Convert the LaTeX formatted output to an image and display it" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\left[\\begin{matrix}\\frac{88.76}{s \\left(1.0 s^{2} + 24.0 s + 53.256\\right)} & \\frac{- 7.396 s - 177.504}{s \\left(1.0 s^{2} + 24.0 s + 53.256\\right)}\\end{matrix}\\right]$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from IPython.display import display, Latex\n", + "display(Latex(\"$\" + sp.latex(G_simp) + \"$\"))" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Chapter3/DCmotor_transfun.py b/Chapter3/DCmotor_transfun.py new file mode 100644 index 0000000..4f4bceb --- /dev/null +++ b/Chapter3/DCmotor_transfun.py @@ -0,0 +1,36 @@ +# Import necessary libraries +import sympy as sp + +# Define symbolic variables +s = sp.symbols('s') + +# Define the system matrices (DC motor example) +A = sp.Matrix([[0, 1, 0], + [0, 0, 4.438], + [0, -12, -24]]) +b1 = sp.Matrix([[0], [0], [20]]) +b2 = sp.Matrix([[0], [-7.396], [0]]) +B = sp.Matrix.hstack(b1, b2) +C = sp.Matrix([[1, 0, 0]]) # Only theta is used as output +D = sp.Matrix([[0, 0]]) # Two inputs, so D is 1x2 matrix + +# Calculate (sI - A)^(-1) +sI_A_inv = (s*sp.eye(A.shape[0]) - A).inv() + +# Calculate the transfer function G(s) = C(sI - A)^(-1)B + D +G = C*sI_A_inv*B + D + +# Simplify expressions +sI_A_inv_simp = sp.simplify(sI_A_inv) +G_simp = sp.simplify(G) + +# Print the results +print("(sI - A)^(-1) =") +sp.pprint(sI_A_inv_simp) +print("\nG(s) =") +sp.pprint(G_simp) + +# Print the LaTeX formatted output +print("\nLaTeX formatted output:") +print("$G(s) = $", sp.latex(G_simp)) +print("$[sI - A]^{-1} = $", sp.latex(sI_A_inv_simp)) diff --git a/Chapter3/Invpend_solver.ipynb b/Chapter3/Invpend_solver.ipynb new file mode 100644 index 0000000..c2d108d --- /dev/null +++ b/Chapter3/Invpend_solver.ipynb @@ -0,0 +1,159 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Import necessary libraries" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from scipy.integrate import odeint\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the model of the inverted pendulum" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "def inverted_pendulum(x, t):\n", + " g = 9.8\n", + " l = 1.0\n", + " m = 1.0\n", + " M = 1.0\n", + " \n", + " d1 = M + m * (1 - np.cos(x[1])**2)\n", + " d2 = l * d1\n", + " \n", + " F = 0 # No input\n", + " \n", + " xp = np.zeros(4)\n", + " xp[0] = x[2]\n", + " xp[1] = x[3]\n", + " xp[2] = (F + m * l * x[3]**2 * np.sin(x[1]) - m * g * np.sin(x[1]) * np.cos(x[1])) / d1\n", + " xp[3] = (-F * np.cos(x[1]) - m * l * x[3]**2 * np.sin(x[1]) * np.cos(x[1]) + (M + m) * g * np.sin(x[1])) / d2\n", + " \n", + " return xp" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Initial conditions: [x, theta, v, omega]" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "x0 = [0, 0.1, 0, 0] # Initial state" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Time vector for the simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "tspan = np.linspace(0, 1, 100) # From 0 to 1 second, 100 points" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Solve the system of ODEs" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "x = odeint(inverted_pendulum, x0, tspan)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Plot state variables" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(10, 6))\n", + "plt.plot(tspan, x[:, 0], 'k', linewidth=2, label='x (m)')\n", + "plt.plot(tspan, x[:, 1], '-.k', linewidth=2, label=r'$\\theta$ (rad)')\n", + "plt.grid(True)\n", + "plt.xlabel('Time (sec)')\n", + "plt.ylabel('State Variables')\n", + "plt.legend()\n", + "plt.title('Inverted Pendulum Simulation')\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.12.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Chapter3/Invpend_solver.py b/Chapter3/Invpend_solver.py new file mode 100644 index 0000000..58ea699 --- /dev/null +++ b/Chapter3/Invpend_solver.py @@ -0,0 +1,44 @@ +# Import necessary libraries +import numpy as np +from scipy.integrate import odeint +import matplotlib.pyplot as plt + +# Define the model of the inverted pendulum +def inverted_pendulum(x, t): + g = 9.8 + l = 1.0 + m = 1.0 + M = 1.0 + + d1 = M + m * (1 - np.cos(x[1])**2) + d2 = l * d1 + + F = 0 # No input + + xp = np.zeros(4) + xp[0] = x[2] + xp[1] = x[3] + xp[2] = (F + m * l * x[3]**2 * np.sin(x[1]) - m * g * np.sin(x[1]) * np.cos(x[1])) / d1 + xp[3] = (-F * np.cos(x[1]) - m * l * x[3]**2 * np.sin(x[1]) * np.cos(x[1]) + (M + m) * g * np.sin(x[1])) / d2 + + return xp + +# Initial conditions: [x, theta, v, omega] +x0 = [0, 0.1, 0, 0] # Initial state + +# Time vector for the simulation +tspan = np.linspace(0, 1, 100) # From 0 to 1 second, 100 points + +# Solve the system of ODEs +x = odeint(inverted_pendulum, x0, tspan) + +# Plot state variables +plt.figure(figsize=(10, 6)) +plt.plot(tspan, x[:, 0], 'k', linewidth=2, label='x (m)') +plt.plot(tspan, x[:, 1], '-.k', linewidth=2, label=r'$\theta$ (rad)') +plt.grid(True) +plt.xlabel('Time (sec)') +plt.ylabel('State Variables') +plt.legend() +plt.title('Inverted Pendulum Simulation') +plt.show() diff --git a/Chapter3/inverted_pendulum.ipynb b/Chapter3/inverted_pendulum.ipynb new file mode 100644 index 0000000..b01feb8 --- /dev/null +++ b/Chapter3/inverted_pendulum.ipynb @@ -0,0 +1,74 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Import necessary libraries" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the model of the inverted pendulum" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "def inverted_pendulum(x, t):\n", + " g = 9.8\n", + " l = 1.0\n", + " m = 1.0\n", + " M = 1.0\n", + " \n", + " d1 = M + m * (1 - np.cos(x[1])**2)\n", + " d2 = l * d1\n", + " \n", + " F = 0 # No input\n", + " \n", + " xp = np.zeros(4)\n", + " xp[0] = x[2]\n", + " xp[1] = x[3]\n", + " xp[2] = (F + m * l * x[3]**2 * np.sin(x[1]) - m * g * np.sin(x[1]) * np.cos(x[1])) / d1\n", + " xp[3] = (-F * np.cos(x[1]) - m * l * x[3]**2 * np.sin(x[1]) * np.cos(x[1]) + (M + m) * g * np.sin(x[1])) / d2\n", + " \n", + " return xp\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.12.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Chapter3/inverted_pendulum.py b/Chapter3/inverted_pendulum.py new file mode 100644 index 0000000..60756d1 --- /dev/null +++ b/Chapter3/inverted_pendulum.py @@ -0,0 +1,22 @@ +# Import necessary libraries +import numpy as np + +# Define the model of the inverted pendulum +def inverted_pendulum(x, t): + g = 9.8 + l = 1.0 + m = 1.0 + M = 1.0 + + d1 = M + m * (1 - np.cos(x[1])**2) + d2 = l * d1 + + F = 0 # No input + + xp = np.zeros(4) + xp[0] = x[2] + xp[1] = x[3] + xp[2] = (F + m * l * x[3]**2 * np.sin(x[1]) - m * g * np.sin(x[1]) * np.cos(x[1])) / d1 + xp[3] = (-F * np.cos(x[1]) - m * l * x[3]**2 * np.sin(x[1]) * np.cos(x[1]) + (M + m) * g * np.sin(x[1])) / d2 + + return xp diff --git a/Chapter3/robot_model.ipynb b/Chapter3/robot_model.ipynb new file mode 100644 index 0000000..07f9053 --- /dev/null +++ b/Chapter3/robot_model.ipynb @@ -0,0 +1,95 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Import necessary libraries" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the model of the 2R Robot" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "def robot_model(x, t):\n", + " g = 9.81\n", + " l1 = 1.0\n", + " l2 = 0.5\n", + " m1 = 2.0\n", + " m2 = 1.0\n", + " I1 = 1e-2\n", + " I2 = 5e-3\n", + " D = 2.0\n", + "\n", + " # Define the state variables\n", + " theta1, theta2, omega1, omega2 = x\n", + "\n", + " M = np.zeros((2, 2))\n", + " M[0, 0] = m1 * (l1 / 2) ** 2 + m2 * (l1 ** 2 + (l2 / 2) ** 2) + m2 * l1 * l2 * np.cos(theta2) + I1 + I2\n", + " M[0, 1] = m2 * (l2 / 2) ** 2 + 0.5 * m2 * l1 * l2 * np.cos(theta2) + I2\n", + " M[1, 0] = M[0, 1]\n", + " M[1, 1] = m2 * (l2 / 2) ** 2 + I2\n", + "\n", + " V = np.zeros((2, 1))\n", + " V[0, 0] = -m2 * l1 * l2 * np.sin(theta2) * omega1 * omega2 - 0.5 * m2 * l1 * l2 * np.sin(theta2) * omega2 ** 2\n", + " V[1, 0] = -0.5 * m2 * l1 * l2 * np.sin(theta2) * omega1 * omega2\n", + "\n", + " G = np.zeros((2, 1))\n", + " G[0, 0] = (m1 * l1 / 2 + m2 * l1) * g * np.cos(theta1) + m2 * g * l2 / 2 * np.cos(theta1 + theta2)\n", + " G[1, 0] = m2 * g * l2 / 2 * np.cos(theta1 + theta2)\n", + "\n", + " Q = np.zeros((2, 1)) # No input\n", + " Q = Q - D * np.array([[omega1], [omega2]])\n", + "\n", + " xy = np.linalg.pinv(M) @ (Q - V - G)\n", + "\n", + " xp = np.zeros(4)\n", + " xp[0] = omega1\n", + " xp[1] = omega2\n", + " xp[2] = xy[0, 0]\n", + " xp[3] = xy[1, 0]\n", + "\n", + " return xp" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.12.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Chapter3/robot_model.py b/Chapter3/robot_model.py new file mode 100644 index 0000000..98c8f37 --- /dev/null +++ b/Chapter3/robot_model.py @@ -0,0 +1,43 @@ +# Import necessary libraries +import numpy as np + +# Define the model of the 2R Robot +def robot_model(x, t): + g = 9.81 + l1 = 1.0 + l2 = 0.5 + m1 = 2.0 + m2 = 1.0 + I1 = 1e-2 + I2 = 5e-3 + D = 2.0 + + # Define the state variables + theta1, theta2, omega1, omega2 = x + + M = np.zeros((2, 2)) + M[0, 0] = m1 * (l1 / 2) ** 2 + m2 * (l1 ** 2 + (l2 / 2) ** 2) + m2 * l1 * l2 * np.cos(theta2) + I1 + I2 + M[0, 1] = m2 * (l2 / 2) ** 2 + 0.5 * m2 * l1 * l2 * np.cos(theta2) + I2 + M[1, 0] = M[0, 1] + M[1, 1] = m2 * (l2 / 2) ** 2 + I2 + + V = np.zeros((2, 1)) + V[0, 0] = -m2 * l1 * l2 * np.sin(theta2) * omega1 * omega2 - 0.5 * m2 * l1 * l2 * np.sin(theta2) * omega2 ** 2 + V[1, 0] = -0.5 * m2 * l1 * l2 * np.sin(theta2) * omega1 * omega2 + + G = np.zeros((2, 1)) + G[0, 0] = (m1 * l1 / 2 + m2 * l1) * g * np.cos(theta1) + m2 * g * l2 / 2 * np.cos(theta1 + theta2) + G[1, 0] = m2 * g * l2 / 2 * np.cos(theta1 + theta2) + + Q = np.zeros((2, 1)) # No input + Q = Q - D * np.array([[omega1], [omega2]]) + + xy = np.linalg.pinv(M) @ (Q - V - G) + + xp = np.zeros(4) + xp[0] = omega1 + xp[1] = omega2 + xp[2] = xy[0, 0] + xp[3] = xy[1, 0] + + return xp diff --git a/Chapter3/robot_solver.ipynb b/Chapter3/robot_solver.ipynb new file mode 100644 index 0000000..8bdc9fb --- /dev/null +++ b/Chapter3/robot_solver.ipynb @@ -0,0 +1,180 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Import necessary libraries" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from scipy.integrate import odeint\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the model of the 2R Robot" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "def robot_model(x, t):\n", + " g = 9.81\n", + " l1 = 1.0\n", + " l2 = 0.5\n", + " m1 = 2.0\n", + " m2 = 1.0\n", + " I1 = 1e-2\n", + " I2 = 5e-3\n", + " D = 2.0\n", + "\n", + " # Define the state variables\n", + " theta1, theta2, omega1, omega2 = x\n", + "\n", + " M = np.zeros((2, 2))\n", + " M[0, 0] = m1 * (l1 / 2) ** 2 + m2 * (l1 ** 2 + (l2 / 2) ** 2) + m2 * l1 * l2 * np.cos(theta2) + I1 + I2\n", + " M[0, 1] = m2 * (l2 / 2) ** 2 + 0.5 * m2 * l1 * l2 * np.cos(theta2) + I2\n", + " M[1, 0] = M[0, 1]\n", + " M[1, 1] = m2 * (l2 / 2) ** 2 + I2\n", + "\n", + " V = np.zeros((2, 1))\n", + " V[0, 0] = -m2 * l1 * l2 * np.sin(theta2) * omega1 * omega2 - 0.5 * m2 * l1 * l2 * np.sin(theta2) * omega2 ** 2\n", + " V[1, 0] = -0.5 * m2 * l1 * l2 * np.sin(theta2) * omega1 * omega2\n", + "\n", + " G = np.zeros((2, 1))\n", + " G[0, 0] = (m1 * l1 / 2 + m2 * l1) * g * np.cos(theta1) + m2 * g * l2 / 2 * np.cos(theta1 + theta2)\n", + " G[1, 0] = m2 * g * l2 / 2 * np.cos(theta1 + theta2)\n", + "\n", + " Q = np.zeros((2, 1)) # No input\n", + " Q = Q - D * np.array([[omega1], [omega2]])\n", + "\n", + " xy = np.linalg.pinv(M) @ (Q - V - G)\n", + "\n", + " xp = np.zeros(4)\n", + " xp[0] = omega1\n", + " xp[1] = omega2\n", + " xp[2] = xy[0, 0]\n", + " xp[3] = xy[1, 0]\n", + "\n", + " return xp" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Initial conditions: [theta1, theta2, omega1, omega2]" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "x0 = [-np.pi/3, np.pi/3, 0, 0] # Initial state" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Time vector for the simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "tspan = np.linspace(0, 5, 500) # From 0 to 5 seconds, 500 points" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Solve the system of ODEs" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "x = odeint(robot_model, x0, tspan)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Plot state variables in degrees" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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xzJCiOGZIUUVxzOTlEiRurkFERERERFTImHgREREREREVMiZeREREREREhYzXeBERERFRiScIAjIzM5GVlaXsUOgLZDIZNDQ0kJaW9k1+X1KpFOrq6l/dDxMvIiIiIirRMjIy8OzZM6SkpCg7FMoDQRBgYWGBmJiYb3JfXYlEgnLlykFfX/+r+mHiRUREREQlVnZ2NqKioqCurg4rKytoamp+ky/zlH/Z2dlISkqCvr7+F29a/LUEQUBcXBweP36MypUrf9XMFxMvIiIiIiqxMjIykJ2djfLly0NXV1fZ4VAeZGdnIyMjA9ra2oWeeAGAqakpHj58CJlM9lWJFzfXICIiIqIS71t8gafiqaBmQDnCiIiIiIiIChkTLyIiIiIiokLGxIuIiIiIiKiQMfEiIiIiIiIqZEy8iIiIiIiKMUEQ4O/vD1tbW+jq6sLHxwcJCQn56uvVq1cwMzPDw4cPP9mmSZMmGDlyZP6CLYJ++OEHLFq0qNDPw8SLiIiIiKgYGzt2LFasWIENGzYgJCQEV65cwfTp0/PV16xZs9C+fXtUqFChQGMsyiZPnoxZs2blO1nNKyZeRERERETF1IULF+Dv74/t27ejUaNGcHNzw48//ojAwECF+0pJScGaNWswYMCAQohUcRkZGd/kPE5OTqhYsSI2bdpUqOdh4kVEREREVEwtXLgQzZs3h6urq1hmbm6Oly9fKtxXYGAgtLS04O7uLpYlJyejd+/e0NfXh6WlZa5L8rKzszFnzhzY2tpCR0cHNWrUwM6dO+XavH37Fj169ICenh4sLS2xePHiHEsWmzRpgp9//hkjR46EiYkJWrZsmae+v9Rm586dcHZ2ho6ODoyNjdGiRQskJyfL9eHl5YVt27Yp/JkpQqNQe6dCd/LkSaxatQoxMTFo1aoVKlWqpOyQiIiIiIq9WrVqITY29pue08LCApcvX85z+/T0dBw8eBALFy6UK09LS0OpUqUUPn9ISAjc3NzkysaOHYuTJ09i7969MDMzw8SJE3H16lXUrFlTbDNnzhxs2rQJK1euROXKlXHq1Cn07NkTpqamaNy4MQDA19cXZ86cwb59+2Bubo6pU6fm6AcANmzYgKFDh+LMmTOf7Lt3794ICAhA69atv3j+KlWqoFu3bpg/fz6+//57vH37FiEhIRAEQe68derUwaxZs5Ceng4tLS2FP7s8EUghCQkJAgAhISFB2aEIgiAIM2fOFACIj3r16gn//POPkJqaquzQqAjKyMgQ9uzZI2RkZCg7FComOGZIURwzpChlj5nU1FQhLCwsx3ensmXLyn3H+haPsmXLKhT72bNnBQCCtra2oKenJz40NTWFli1bCoIgCD4+PoKRkZHQsWPHL/bXvn17oX///uLx27dvBU1NTWHHjh1i2atXrwQdHR1hxIgRgiAIQlpamqCrqyucPXtWrq8BAwYI3bp1EwRBEBITEwWpVCr8+++/Yn18fLygq6sr9iMIgtC4cWPBxcVFPP5U3/379xc6duwoZGVlffH8V65cEQAIDx8+/Ox7v3HjxifbfWqMCIJiuQFnvIq5J0+eyB2fPXsWZ8+eha+vL8aPH4+ffvoJOjo6SoqOiIiIqHiysLAo8ue8e/cu9PT0cP36dbnytm3bon79+gCAESNGoH///tiwYcMX+0tNTYW2trZ4/ODBA2RkZKBu3bpiWZkyZVC1alXx+P79+0hJSYGHh4dcXxkZGXBxcQEAREZGQiaToU6dOmJ9qVKl5Pp578MZt8/1Xb169Tydv0aNGmjevDmcnZ3RsmVLeHp6olOnTihdurRc+/ffl1NSUj7zCX0dJl7F3OTJk2FtbY3s7Gxs27YNoaGhAIC4uDiMGTMGixcvxtSpU9GvXz9IpVIlR0tERERUPCiy5E9ZEhMTYWJiInepyaNHj3Dv3j107NgRwLvrpk6cOJGn/kxMTPDmzRuFYkhKSgIAHDx4EGXLlpWry8+SPT09vS/2nZ2dLW688aXzq6urIzg4GGfPnkVQUBCWLl2KSZMm4cKFC7C1tRXbvn79GgBgamqqcMx5xc01ijkzMzM4Ojpi3LhxuHnzJkJCQtClSxdIJBIA72bEBg8eDAcHB+zcuTPHelYiIiIiKp5MTEyQkJAg9/1u1qxZaNOmDRwdHRXuz8XFBWFhYeJxxYoVIZVKceHCBbHszZs3uHv3rnjs6OgILS0tREdHo1KlSnKP8uXLAwDs7OwglUpx6dIl8XUJCQly/eTmc32XK1cuz+eXSCSoX78+/Pz8cO3aNWhqamL37t1y5woNDUW5cuVgYmKi8OeWV5zxUiESiQQNGjRAgwYNMHnyZEyZMgV79+4F8G6quHPnzmjSpAl+//13cXqWiIiIiIqnZs2aIS0tDXPnzsUPP/yAzZs3Y//+/bh48WK++mvZsiUmTJiAN2/eoHTp0tDX18eAAQMwduxYGBsbw8zMDJMmTYKa2v/mbgwMDDBmzBiMGjUK2dnZaNCgARISEnDmzBkYGhqiT58+MDAwQJ8+fTB27FiUKVMGZmZmmDZtGtTU1MTJgtx8qu/Tp09DKpVi8ODBXzy/vb09jh49Ck9PT5iZmeHChQuIi4uDg4OD3LlCQkLg6emZr88tr5h4qShnZ2fs2bMH58+fx8SJE3H8+HEAwIkTJ+Di4oJBgwZh5syZhZrVExEREVHhMTc3x/r16zF27FjMnDkTzZo1w+nTp8WZHkU5OzvD1dUVO3bswODBgwEACxYsQFJSEry8vGBgYIDRo0fnuNHwzJkzYWpqijlz5iAyMhJGRkZwdXXFxIkTxTb+/v4YMmQI2rVrB0NDQ4wbNw4xMTFy15TlJre+XVxc8Msvv+Tp/IaGhjh16hSWLFmCxMRE2NjYYNGiReKOiMC7XSD37NmDw4cP5+tzy7Mvbr9BcoraroZ52QkoOztb2Lt3r1CxYkW5nXOMjIyE33//XZDJZN8wYlImZe8cRcUPxwwpimOGFKXsMfO5HetUxfHjx/O0q6EgCMKBAwcEBwcHISsrq1BjSkpKEkqVKiWsXr1a4ddmZWUJb968KbAYly9fLnh4eHyyvqB2NeQ1XiWARCKBt7c3bt++jblz50JfXx8AEB8fj8WLF3+zu4ITERER0bfVokULdO7cGYGBgShXrhzOnTv32fZt27bFoEGDcuyc/bWuXbuGrVu34sGDB7h69Sp69OgBAGjfvn2Bnic/pFIpli5dWujn4VLDEkRLSwvjx49H7969MXHiRKxfvx5Lly6Frq6uskMjIiIiokJw5MgRhV8zcuTIgg8EwMKFCxEREQFNTU24ubkhJCSkSFz2MnDgwG9yHiZeJZClpSXWrVuH8ePHw97eXq7u/v37OHfuHHr27PnZix2JiIiIiPLKxcUFV65cUXYYSsWlhiXYx0mXIAgYNmwYevfujWbNmuHx48dKioyIiIiISLUw8SLRmTNnEBQUBODd9vNGRkbKDYiIiIiISEUw8SJRgwYNEBgYCFtbW/zxxx/iJhxERERERPR1mHiRnNatWyM8PDzHDjMxMTH45Zdfcty3gYiIiIiIvoyJF+WgpaUlt7GGIAgYPHgwli5dimrVquHAgQNKjI6IiIiIqPhh4kVf9ODBA4SEhAAAnjx5Ai8vL3Tv3h1xcXFKjoyIiIiIqHhg4kVfVKlSJYSGhqJVq1Zi2datW+Ho6Ijt27crMTIiIiIiouKBiRfliY2NDQIDA7Fx40aUKVMGAPDy5Uv88MMP6Nq1K169eqXkCImIiIiIii4mXpRnEokEvXr1QlhYGDp37iyW79ixA05OTjh48KASoyMiIiIiKrqYeJHCzM3NsWPHDmzfvl2c/YqNjUW7du0wcOBAJCYmKjlCIiIiIqKihYkX5VuXLl0QGhqKNm3aiGVr1qxB9erVceLECeUFRkRERFSCCIIAf39/2NraQldXFz4+Pvm+BdCrV69gZmaGhw8ffrJNkyZNMHLkyPwFWwT98MMPWLRoUaGfR6USr+nTp0Mikcg97O3txfq0tDQMGzYMxsbG0NfXR8eOHfH8+XMlRlz8WVpa4sCBA1i1apV4w+VHjx6hadOm8PX1RXp6upIjJCIiIlJtY8eOxYoVK7BhwwaEhITgypUrmD59er76mjVrFtq3b48KFSoUaIxF2eTJkzFr1qxCv1+tSiVeAFCtWjU8e/ZMfJw+fVqsGzVqFPbv349///0XJ0+exNOnT9GhQwclRqsaJBIJBg4ciJs3b6JRo0Zi+eLFi1G3bl2Eh4crMToiIiIi1XXhwgX4+/tj+/btaNSoEdzc3PDjjz8iMDBQ4b5SUlKwZs0aDBgwoBAiVVxGRsY3OY+TkxMqVqyITZs2Fep5VC7x0tDQgIWFhfgwMTEBACQkJGDNmjXw9/dHs2bN4ObmhnXr1uHs2bM4f/68kqNWDba2tjh+/DgWLVoETU1NAMCNGzfy/RcXIiIiIvq8hQsXonnz5nB1dRXLzM3N8fLlS4X7CgwMhJaWFtzd3cWy5ORk9O7dG/r6+rC0tMx1SV52djbmzJkDW1tb6OjooEaNGti5c6dcm7dv36JHjx7Q09ODpaUlFi9enGPJYpMmTfDzzz9j5MiRMDExQcuWLfPU95fa7Ny5E87OztDR0YGxsTFatGiB5ORkuT68vLywbds2hT8zRWgUau9KcO/ePVhZWUFbWxvfffcd5syZA2tra1y5cgUymQwtWrQQ29rb28Pa2hrnzp2TG2AfSk9Pl1su937jCJlMBplMVrhvJg/ex1AUYnlv+PDhaNSoEXr16oWEhAQsWbKkSMVXkhXF8UJFG8cMKYpjhhSl7DEjk8kgCAKys7ORnZ0tV7d48WIsXrz4q8+xceNGNGnSRDw+ceIEevfuDeDdiqxRo0blq9/09HQcPHgQCxYskIs9NTUVpUqVyvF+vuTUqVNwdXWVe92YMWNw8uRJ7N69G2ZmZpg0aRKuXr2KGjVqiO1mz56NzZs3Y/ny5ahcuTJOnTqFnj17wtjYGI0bNxbf55kzZ7Bnzx6Ym5tj2rRpOfoBgA0bNmDIkCEICQn5ZN+9e/dGQEAAWrVqhezs7M+ev0qVKujWrRvmzZsHHx8fvH37FqdPn0ZWVpbceWvVqoVZs2YhNTUVWlpacp9LdnY2BEGATCaDurq6XJ0i41alEq+6deti/fr1qFq1Kp49ewY/Pz80bNgQoaGhiI2NhaamJoyMjOReY25ujtjY2E/2OWfOHPj5+eUoDwoKgq6ubkG/hXwLDg5Wdgg5+Pn5ITY2FhcvXpQrT01NhY6OjpKiIqBojhcq2jhmSFEcM6QoZY2Z96ulkpKScixti4uLw5MnT776HG/evJHb9fnNmzdiv3FxcfneEfrixYtITU3FmDFjMH78eLFcJpOhYcOGCAsLw5AhQ/Dy5Uuoq6tj7Nix8PHx+WR/Dx48gKmpqRhPUlIS1q5di7/++gu1a9cGACxduhTVqlVDRkYGEhMTkZ6ejjlz5mD37t2oU6cOAKBDhw44ceIE/vzzT7i4uODt27fYuHEjVq1aJfazZMkSODo6iv0AQGZmJuzs7DBp0iQA+Gzf69atQ/369b94/uHDhyMzMxMtWrRAmTJlUKZMGdjY2CA7O1vuczc0NERGRgbu3bsHa2truc8lIyMDqampOHXqFDIzM+XqUlJS8vz7UqnEq3Xr1uLz6tWro27durCxscGOHTvy/UV/woQJ8PX1FY8TExNRvnx5eHp6wtDQ8Ktj/loymQzBwcHw8PCAVCpVdjhf9OLFC9SpUwe9evXCtGnToKGhUkOwyCtu44WUj2OGFMUxQ4pS9phJS0tDTEwM9PX1oa2tLVdnamqKsmXLfvU5SpcuLfe9sXTp0mK/pqam+f5O+eTJE+jp6eHq1aty5V5eXmjUqBFKly6NP/74AzVr1kRsbCxq166Njh07Qk9PL9f+ZDIZDAwMxHiioqKQkZGBJk2aiGWGhoaoWrUqNDU1YWhoiNu3byMlJSXHvgkZGRlwcXGBoaEhoqKiIJPJ0Lhx40/2A7xLgmvXri0ef67v6tWrw8DAADExMZ89f7169dC8eXM0aNAAnp6e8PDwQKdOnVC6dGm59qampgAAdXX1HL+PtLQ06OjooFGjRjnGiCJJs0p/6zUyMkKVKlVw//59eHh4ICMjA/Hx8XKzXs+fP4eFhcUn+9DS0sox3QgAUqm0SP2DUtTiyY0gCBg8eDCePn2KefPmISsrCwsWLFB2WCVScRgvVLRwzJCiOGZIUcoaM1lZWZBIJFBTU4Oamvz2B6NHj8bo0aML/JzNmjXD48ePv7qfpKQkmJiYoEqVKmLZo0ePcO/ePXTq1Ally5YVEzwrKyuYmJggPj4eBgYGufZnamqK+Ph48XP48OfHn837z+z9jM/BgwdzJKlaWlpyr/1cP+/p6+uLx5/qOzs7GxkZGZBIJF88v1QqRXBwMM6ePYugoCD8+eefmDJlCi5cuABbW1uxbXx8PIB3q+E+jlFNTQ0SiSTXMarImFW5zTU+lJSUhAcPHsDS0hJubm6QSqU4evSoWB8REYHo6Gh89913Soyy5BAEAQ0bNoSGhgbMzc0L5X9kRERERCWFiYkJEhISIAiCWDZr1iy0adMGjo6Ocm2vXLmCrKwslC9f/pP9ubi4ICwsTDyuWLEipFIpLly4IJa9efMGd+/eFY8dHR2hpaWF6OhoVKpUSe7x/lx2dnaQSqW4dOmS+LqEhAS5fnLzub7LlSuX5/NLJBLUr18ffn5+uHbtGjQ1NbF79265c4WGhqJcuXLixnyFQaVmvMaMGQMvLy/Y2Njg6dOnmDZtGtTV1dGtWzeUKlUKAwYMgK+vL8qUKQNDQ0MMHz4c33333Sc31qCCpaamhvHjx6Nhw4aQyWSfnWkkIiIios9r1qwZ0tLSMHfuXPzwww/YvHkz9u/fn+P6+tevX6N3795YtWrVZ/tr2bIlJkyYgDdv3qB06dLQ19fHgAEDMHbsWBgbG4uba3w4I2RgYIAxY8Zg1KhRyM7ORoMGDZCQkIAzZ87A0NAQffr0gYGBAfr06YOxY8eiTJkyMDMzw7Rp08SZpE/5VN+nT5+GVCrF4MGDv3h+e3t7HD16FJ6enjAzM8OFCxcQFxcHBwcHuXOFhITA09MzH7+FvFOpxOvx48fo1q0bXr16BVNTUzRo0ADnz58X12wuXrwYampq6NixI9LT09GyZUssX75cyVGXPPXq1ctR9vr1a4waNQrz5s1jQkZERESUB+bm5li/fj3Gjh2LmTNnolmzZjh9+rTcrFZ6ejp8fHzw66+/5vod7EPOzs5wdXXFjh07MHjwYADAggULkJSUBC8vLxgYGGD06NE5bjQ8c+ZMmJqaYs6cOYiMjISRkRFcXV0xceJEsY2/vz+GDBmCdu3awdDQEOPGjUNMTEyOa6Y+llvfLi4u+OWXX/J0fkNDQ5w6dQpLlixBYmIibGxssGjRIrm9IdLS0rBnzx4cPnz4yx/6V5AIH85N0hclJiaiVKlSSEhIKDKbawQGBqJNmzbFdi29IAho37499u/fDwsLC2zZsgVNmzZVdlgqSRXGC31bHDOkKI4ZUpSyx0xaWhqioqJga2v7xSSguBEEAd27d0fVqlXzfF/VgwcPYuzYsQgNDc1xrVNBSk5ORtmyZbFo0SKFb9j8fkdCQ0PDAolxxYoV2L17N4KCgnKt/9wYUSQ3UOlrvKh4iImJwZUrVwAAsbGxaNGiBX777TeF7z1BRERERP9z5swZbN++HXv27EHNmjVRs2ZN3Lp167Ovadu2LQYNGlQg2+h/6Nq1a9i6dSsePHiAq1evokePHgCA9u3bF+h58kMqlWLp0qWFfh6VWmpIxZO1tTWuXbuGnj17Ijg4GNnZ2ZgyZQrOnTuHTZs25djuk4iIiIi+rEGDBvn6Q/bIkSMLPhgACxcuREREBDQ1NeHm5oaQkJBC3cwirwYOHPhNzsMZLyoSzMzMcOjQIcyYMUO8yDIwMBC1atXCzZs3lRwdEREREX0NFxcXXLlyBUlJSXj9+jWCg4Ph7Oys7LC+KSZeVGSoq6tjypQpCAoKgrGxMQAgMjIS7u7u2LJli5KjIyIiIiLKPyZeVOS0aNECV65cgZubGwAgNTUVPXr0wMiRIyGTyZQcHRERERGR4ph4UZFkY2OD06dPo1+/fmLZ77//jubNmyM2NlaJkRERERERKY6JFxVZ2traWLNmDVauXCluLxsSEgI3NzecO3dOydERERGRKuEdluhTCmpsMPGiIk0ikWDw4ME4deoUrKysAABPnz5F48aNsWLFCv5PkoiIiL7K+z/upqSkKDkSKqoyMjIAvNuP4GtwO3kqFtzd3XH16lV06dIFp06dgkwmw08//YSLFy9ixYoVKnfDQyIiIvo21NXVYWRkhBcvXgAAdHV1xR2WqWjKzs5GRkYG0tLSCvUmz+/PFRcXB11dXWhofF3qxMSLig1zc3McOXIE48aNw5IlSwAAe/fuxdSpU2Fra6vc4IiIiKjYsrCwAAAx+aKiTRAEpKamQkdH55skyWpqarC2tv7qczHxomJFKpVi8eLFqFOnDgYPHowdO3Yw6SIiIqKvIpFIYGlpCTMzM+6gXAzIZDKcOnUKjRo1EpeKFiZNTc0CmVlj4kXFUrdu3dCqVSuULl1arjwrK+ur198SERFRyaSurs7vEcWAuro6MjMzoa2t/U0Sr4LCzTWo2Po46RIEAb169cIvv/zCv1YRERERUZHCGS9SGQsXLsTWrVsBAI8ePcLevXuVHBERERER0Tuc8SKVYWxsLE43f3jjZSIiIiIiZeOMF6mM/v37w97eHhcuXICPj4+ywyEiIiIiEnHGi1RKvXr1MGrUqBzl+/btQ3Z2thIiIiIiIiJi4kUlwMqVK9G+fXv4+PggMTFR2eEQERERUQnExItUWmxsrDgDtn//fri7u+PevXtKjoqIiIiIShomXqTSLCwssG/fPnHr+fDwcNSpUwf//fefkiMjIiIiopKEiRepPA8PD1y8eBGOjo4AgPj4eLRp0wYLFiyAIAhKjo6IiIiISgImXlQiVKpUCefPnxd3O8zOzsa4cePQs2dPpKamKjc4IiIiIlJ5TLyoxDAwMEBAQACmTZsmlm3ZsgUNGzZEdHS0EiMjIiIiIlXHxItKFDU1NUyfPh0BAQHQ09MDAFy5cgW1atXCyZMnlRwdEREREakqJl5UInXo0AHnzp2DnZ0dACAuLg7NmzfHH3/8weu+iIiIiKjAMfGiEsvZ2RmXLl2Cp6cnACArKwsjRoxA3759ed0XERERERUoJl5UopUpUwaBgYEYP368WLZx40Y0bNgQMTExSoyMiIiIiFQJEy8q8dTV1TF37lxs374durq6AN5d9+Xm5oYXL14oOToiIiIiUgVMvIj+X5cuXXDu3DnY2toCALp37w4zMzMlR0VEREREqoCJF9EHqlevjsuXL2PChAlYsGCBssMhIiIiIhXBxIvoI2XKlMHs2bMhlUrlyg8dOsTrvoiIiIgoX5h4EeXB9evX0bFjR7i5ufF+X0RERESkMCZeRHkwevRopKamIi4uDps3b1Z2OERERERUzGgoOwCi4mDHjh3o1q0bEhIS8Mcffyg7HCIiIiIqZph4EeWBsbExDh06hPj4eGhra8vVpaamQkdHR0mREREREVFxwKWGRHmkrq4OY2NjubKwsDDY2tpi69atSoqKiIiIiIoDJl5E+ZSUlIROnTrh+fPn6N69O4YNG4b09HRlh0VERERERRATL6J8UldXh7u7u3i8fPlyNGrUCI8ePVJiVERERERUFDHxIsonHR0drF27FqtXr4aWlhYA4OLFi3B1dcXhw4eVHB0RERERFSVMvIi+0oABA3Du3DnY2dkBAF6/fo02bdpg4sSJkMlkSo6OiIiIiIoCJl5EBcDFxQVXrlyBt7c3AEAQBMyZMweNGzfm0kMiIiIiYuJFVFCMjIywZ88eLFiwABoa7+7UcO7cOdSsWRMBAQFKjo6IiIiIlImJF1EBkkgkGDNmDM6cOQNbW1sAQHx8PDp16oSffvoJqampSo6QiIiIiJSBiRdRIahTpw6uXbuGLl26iGUrVqxA3bp1ER4ersTIiIiIiEgZmHgRFZJSpUph27ZtWLVqFXR0dAAAt27dgpubG1auXAlBEJQcIRERERF9K0y8iAqRRCLBwIEDcenSJVSrVg0AkJqaiqFDh2L16tVKjo6IiIiIvhUmXkTfQLVq1XDx4kUMGTIEAODk5IRevXopOSoiIiIi+lY0lB0AUUmhq6uLFStWoF27dihXrhy0tbXl6rOzs6Gmxr+FEBEREakifssj+sbatm2LGjVqyJWFhYXByckJp06dUlJURERERFSYmHgRKVlGRgZ69uyJ8PBwNGnSBIcOHVJ2SERERERUwFQq8ZozZw5q164NAwMDmJmZwcfHBxEREXJtmjRpAolEIvd4f90NkTIkJCRAX18fAODg4IBmzZopOSIiIiIiKmgqdY3XyZMnMWzYMNSuXRuZmZmYOHEiPD09ERYWBj09PbHdjz/+iBkzZojHurq6ygiXCABgamqK48ePw9/fHw0bNoSWlpZcfVZWFtTV1ZUUHREREREVBJVKvA4fPix3vH79epiZmeHKlSto1KiRWK6rqwsLC4s89Zmeno709HTxODExEQAgk8kgk8kKIOqv8z6GohALfZ2RI0cCkP9d3r59G506dcLixYvRqlWrrz4HxwspimOGFMUxQ4rimCFFFaUxo0gMEkGF7+J6//59VK5cGbdu3YKTkxOAd0sNb9++DUEQYGFhAS8vL0yZMuWTs17Tp0+Hn59fjvItW7ZwpowKVVZWFn799Vfcu3cPwLux279/fxgaGio5MiIiIiICgJSUFHTv3h0JCQlf/I6msolXdnY2vL29ER8fj9OnT4vlf//9N2xsbGBlZYWbN29i/PjxqFOnDnbt2pVrP7nNeJUvXx4vX74sEl+AZTIZgoOD4eHhAalUquxwqAC9fv0aPXv2xJEjR8QyY2NjzJkzB717987X1vMcL6QojhlSFMcMKYpjhhRVlMZMYmIiTExM8pR4qdRSww8NGzYMoaGhckkXAAwaNEh87uzsDEtLSzRv3hwPHjxAxYoVc/SjpaWV45obAJBKpUr/RX+oqMVDX8/c3BxBQUFYt24dfH19kZCQgFevXmHQoEHYsGEDVqxYAWdn53z1zfFCiuKYIUVxzJCiOGZIUUVhzChyfpXa1fC9n3/+GQcOHMDx48dRrly5z7atW7cugHfLEomKGolEgv79+yMsLAxdu3YVy8+cOQMXFxeMHTsWSUlJSoyQiIiIiPJCpRIvQRDw888/Y/fu3Th27BhsbW2/+Jrr168DACwtLQs5OqL8s7KywrZt2xAUFITKlSsDeHcN2MKFC+Hg4IAtW7ZARVcNExEREakElUq8hg0bhk2bNmHLli0wMDBAbGwsYmNjkZqaCgB48OABZs6ciStXruDhw4fYt28fevfujUaNGqF69epKjp7oyzw8PHDz5k34+fmJS2AfP36MHj16oH79+rh06ZKSIyQiIiKi3KhU4rVixQokJCSgSZMmsLS0FB/bt28HAGhqauLIkSPw9PSEvb09Ro8ejY4dO2L//v1Kjpwo77S1tTF16lSEhoaiTZs2Yvm5c+dQp04d9O3bF0+fPlVihERERET0MZXaXONLS63Kly+PkydPfqNoiApXpUqVcPDgQRw6dAi+vr64c+cOAGDDhg3YuXMnfv31V4waNUru5uFEREREpBwqNeNFVBK1bt0aN2/exJIlS2BkZAQASE5Ohp+fH54/f67c4IiIiIgIABMvIpUglUoxYsQI3Lt3Dz/99BPU1dUxePBg2NnZKTs0IiIiIgITLyKVYmJigj///BO3b9/G1KlT5epSU1Ph4+ODy5cvcwdEIiIiom9Mpa7xIqJ3qlatmqNs2bJlCAwMRGBgIDIyMjBv3jwlREZERERUMnHGi6gEEAQB//33H4B3N2Xu1q2bkiMiIiIiKlmYeBGVABKJBEFBQfj333/RqVMnVKtWTa5+586d2LRpE2QymZIiJCIiIlJtTLyISgg1NTW0b98ePXr0kCvPysrC+PHj0atXL1SsWBH+/v5ITExUUpREREREqomJF1EJd+TIEURGRgIAYmJiMHr0aFhbW2P8+PF4/PixkqMjIiIiUg1MvIhKOE9PT5w8eRLt2rUTyxISEjB//nxUqFABHTt2xNGjR7kTIhEREdFXYOJFVMJJJBI0atQI+/fvR1hYGAYMGABNTU0A75Yh7tq1Cy1atICjoyOWLl2KhIQEJUdMREREVPww8SIikYODA1avXo2HDx9i6tSpsLCwEOvu3LmDX375BWXLlkXfvn1x8uRJzoIRERER5RETLyLKwdLSEn5+foiOjsb27dvRqFEjsS45ORkbNmxAkyZNUKlSJcycORPR0dFKjJaIiIio6GPiRUSfJJVK0aVLF5w8eRK3bt3C0KFDYWhoKNZHRkZi6tSpaN26tRKjJCIiIir6mHgRUZ44OTlh+fLliI2NxebNm9GiRQtIJBIAQO/eveXaCoKAf//9F/Hx8UqIlIiIiKjoYeJFRArR0dFB9+7dERwcjIcPH2LGjBno1auXXJtbt26hS5cuMDc3x9SpU5UUKREREVHRwcSLiPLN2toaU6ZMgZWVlVz59u3bAQAZGRmwtLSUq5PJZLhy5Qqys7O/WZxEREREyqah7ACISPV07NgRycnJ2LVrF7y8vOTqzpw5g6ZNm8LY2BjNmzeHh4cHPDw8YGNjo6RoiYiIiAofEy8iKnCurq5wdXXF4sWLxevA3tu3bx8A4NWrV9ixYwd27NgBAKhUqRKaNm2KBg0aoH79+rCzs8vxWiIiIqLiiokXERWa3BInd3d3+Pj44NixY0hMTBTL79+/j/v372PVqlUAAHNzc9SvXx/169dHgwYNULNmTfHGzkRERETFDRMvIvqmunTpgi5duiAzMxOXL19GcHAwgoODce7cOWRmZortnj9/jl27dmHXrl0AAE1NTTg5OYmzab1794aenp6y3gYRERGRQph4EZFSaGhowN3dHe7u7pgyZQqSk5Nx8eJFnDlzBqdPn8a5c+fkZsQyMjJw9epVXL16FRoaGujXr59cf8ePH8fLly9hb28Pe3t7SKXSb/2WiIiIiD6JiRcRFQl6enpo2rQpmjZtCgDIysrC7du3cebMGZw5cwZXrlxBREQEBEGAo6MjtLW15V6/bNkycXbs3r17qFSpklgXGhqKR48ewdbWFhUqVICuru63e2NEREREYOJFREWUuro6qlevjurVq2Po0KEAgKSkJNy8eROpqak52t+5cwfAuyWJtra2cnX//PMP5s+fLx6bm5vD1tYWNjY2KFu2LCwtLWFlZSX30NfXL8R3R0RERCUNEy8iKjb09fVRr169XOvmzJmDW7duITExEerq6nJ1UVFRcsfPnz/H8+fPcf78+U+ey8DAAJaWljA1NYWxsTFMTEzw22+/yd2XLC4uDq9evYKxsTFKly4NDQ3+L5WIiIhyx28JRKQSvL294e3tnWtdr169ULVqVURFRYmPZ8+efba/t2/f4u3bt7h7965Y5ufnJ9dm8+bNGDVqFABgx44d6Ny5s1h369YtjBgxAqVKlYKhoWGOn+8fBgYGcj8NDQ2hpaWV34+BiIiIiigmXkSk8ry8vHLcyDk1NRVPnz794iMpKUl8jbGxsVwfr169Ep8bGhrK1T179gzHjx/PV7xSqVRMxkaMGIGRI0eKdTKZDL/++isMDQ3h4OCALl26yL32/v370NDQEBM5bjJCRERUNDDxIqISSUdHBxUrVkTFihU/2y49PR2vX7/Gy5cvoaOjI1dXo0YN9OrVC69fv0a5cuXk6j7ckVFRMpkMr169wqtXr5CSkiJX9/btW/j7+wMAWrdunSPx8vLyEq93AwBtbe0cs2qlSpUSl09+/PP9w9TUNN/xExERUU5MvIiIPkNLSwuWlpZy13a916lTJ3Tq1CnX13Xs2BFJSUlISEhAYmKi+PP984SEBHE5Y2Jiovjzw+dv375FmTJl5Pr9MKH7eJbt43oASEtLQ1paGuLi4vL8nkuXLo3Xr1/Lla1duxZhYWGwtLTEjz/+mGP2j4iIiD6PiRcRUSGQSCTQ09ODnp4erKysCqxfc3NzhISE4O3btzAxMclR37FjR7x48SLXJC4hIUHuJtWfklu/Bw8exP79+wG8u2buQ8uXL8ecOXNgZWWFcuXKwdraGjY2NrC2thafm5iYQCKR5PNdExERFX9MvIiIihEdHR00aNDgk/V//PHHJ+sEQUB6ejri4+Px6tUrvHz5MtefuSVesbGxAN4llObm5nJ10dHRePz4MR4/foyLFy9+Mu73iZi1tTXs7OxQqVIlVKpUCRUrVkSpUqXy8vaJiIiKLSZeREQlhEQigba2NiwsLGBhYaHQa7du3Yrnz5/j5cuXObbNl0qlMDMzQ1xcHARByPX1qampiIiIQERERK71JiYm2L9/P9zd3cWyt2/fIi0tjbNlRESkEph4ERHRF1lbW39yI5KZM2di5syZkMlkePr0KR49eoTo6GhER0fneJ6cnJxrHy9fvoSZmZlc2c6dO9G/f38YGRlh2bJl6NGjh1iXlZUFADnu2UZERFRUKZR4xcfHY/fu3QgJCcGjR4+QkpICU1NTuLi4oGXLlp+8sSkREak+qVQKGxsb2NjY5FovCALevHmDhw8fIjIyEvfv38f9+/fx4MEDPHz4ENbW1nLt79+/D+Ddvz2lS5eWq7t8+TIaNWqEKlWqwMHBAQ4ODrC3t4ejoyPs7e15LzQiIipy8pR4PX36FFOnTsXmzZthZWWFOnXqoGbNmtDR0cHr169x/PhxLFy4EDY2Npg2bRq6du1a2HETEVExI5FIUKZMGZQpUwaurq5fbF+xYkV4eHggIiIC9vb2cnV37txBRkYGQkNDERoaKlenrq6OKlWqwNnZWe5RoUIFqKmpFeh7IiIiyqs8JV4uLi7o06cPrly5AkdHx1zbpKamYs+ePViyZAliYmIwZsyYAg2UiIhKlv79+6N///651qmrq8PR0RH37t2DTCaTq8vKykJ4eDjCw8OxY8cOsVxPTw9OTk5wdnYWf9aqVSvXbfmJiIgKWp4Sr7CwsC/es0VHRwfdunVDt27d8OrVqwIJjoiIKDc9e/ZEz549IZPJEBUVJSZat2/fxq1btxAeHo6MjAy51yQnJ+PChQu4cOGCWLZz50507NhRPH6/FNLR0ZHLFYmIqEDlKfFS9EaZvLEmERF9C1KpFFWqVEGVKlXQvn17sVwmk+HevXsIDQ3FrVu3xEdkZKTc652dneWOg4OD0bVrV6irq+OPP/7ATz/9JNa937GROywSEVF+KLyr4YYNG2BiYoK2bdsCAMaNG4e///4bjo6O2Lp16ycvqiYiIvpWpFIpHB0d4ejoiC5duojlSUlJ4qzY7du3c+zUePPmTQDvliuWLVtWri40NBRNmjRB9erVUaNGDVSvXh3Vq1dHtWrVoKOjU/hvioiIijWFE6/Zs2djxYoVAIBz587hzz//xOLFi3HgwAGMGjUKu3btKvAgiYiICoK+vj7q1q2LunXr5lpfq1Yt9OrVCzdv3kSNGjXk6m7cuIHXr1/jxIkTOHHihFiupqaGypUryyVj1atXh7W1NWfHiIhIpHDiFRMTg0qVKgEA9uzZg44dO2LQoEGoX78+mjRpUtDxERERfTM+Pj7w8fHJtS4tLQ1WVlZ4+vSpXHl2drZ4c+gPN/MoVaoUnJ2d5RIyJycn6OvrF+ZbICKiIkrhxEtfXx+vXr2CtbU1goKC4OvrCwDQ1tZGampqgQdIRERUFAwcOBADBw7Ey5cvcfPmTblHaGgo0tPT5donJCTg9OnTOH36tFz5nj175K5Hy8zMhJqaGre6JyJScQonXh4eHhg4cCBcXFxw9+5dtGnTBgBw+/ZtVKhQoaDjIyIiKlJMTEzQrFkzNGvWTCzLzMzEvXv3ciRk0dHROV5fuXJlueP9+/ejV69ecHZ2xoQJE+Dt7V3o74GIiL49hROvP//8E5MnT0ZMTAwCAgLEHQyvXLmCbt26FXiARERERZ2GhgYcHBzg4OCArl27iuVv3rzBrVu3xEQsLCwMVapUkXvtjRs3kJycjPPnz+e4J9n9+/fh6+srLlWsUaMGKlWqBHV19W/yvoiIqOAonHgZGRlh2bJlOcr9/PwKJCAiIiJVUbp0aTRq1AiNGjX6ZBsdHR3Y2toiKioK1atXl6u7cuUK9u/fj/3794tl2tracHR0hL29PapWrSr+rFy5MnR1dQvtvRAR0ddROPECgJCQEPz111+IjIzEv//+i7Jly+Kff/6Bra0tGjRoUNAxEhERqazx48dj/PjxSExMzLHxxu3bt3O0T0tLw9WrV3H16tUcdTY2NqhatapcQla1alVYWVnxGjIiIiVTOPEKCAhAr1690KNHD1y9elW8mDghIQGzZ89GYGBggQdJRESk6gwNDXOUTZ8+Hf369cPNmzdx48YN8WdkZCSys7NztH/06BEePXqEoKAgufKAgAB06NBBPI6NjcWFCxdgZ2cHOzs76OnpFfwbIiIiOQonXr/99htWrlyJ3r17Y9u2bWJ5/fr18dtvvxVocERERCWZmpoabG1tYWtrK7cTYlpaGu7fvy9uYx8REYE7d+4gIiICCQkJOfr5+EbRISEh4o2l58yZg19//VWse/v2Lf755x+UK1dOfJiamvKeZEREX0nhxCsiIiLXteqlSpVCfHx8QcREREREn6GtrQ0nJyc4OTnJlQuCgBcvXsglYnfv3oWtra1cu8jISPG5nZ2dXN2DBw8wbNgwuTJNTU25RKxcuXKwsLCAubk5zMzMxJ8mJiYF/E6pMGRmZiI1NRVpaWkK/UxPT8fgwYPFjdUA4OzZs/j333+RmZmJHj16wN3dXax79OgRxo0bh8zMTGRmZuaI430yn52djRcvXmDt2rXiktgPE/3mzZvnGJOjR49GRkYGrKysMGHCBLm67du34+HDh9DU1ISWlha0tbXFx4fHn6vT0NDgHxuowCmceFlYWOD+/fs5to4/ffp0jv95ExER0bcjkUhgbm4Oc3Pzz27o0bhxY0yfPh2RkZFwdnaWq3v8+HGO9hkZGYiMjJRL2D51fhMTE+jo6CA6OhrDhw8X6zIzM7Fx40YYGRmhQoUKcHV1VfDdqRZBECCTyXIkOHlNgmxtbdGzZ0+5PocOHYqoqChoaWlh7969cnU//fQT/vnnH6SmpiIrKyvfcXfo0EEu8QoNDcWSJUsAAC4uLnKJV2JiotxNxfOrTJkyOcpWrVqFt2/fwtHRMUfitXbt2hzLbRWlpqaG58+fy/0xYePGjVi/fj309PQwbdo01KpVS6x79OgRdu3aBT09Pejp6UFXV1d8rqenB319ffGhq6vLay5LKIUTrx9//BEjRozA2rVrIZFI8PTpU5w7dw5jxozBlClTCiPGQvHnn39iwYIFiI2NRY0aNbB06VLUqVNH2WEREREVOnd3d7kvyB+qUaMG1qxZg8ePH4uPmJgYPH78+IsrWwRBQFxcHIB3X7o/9ObNGwwYMAAA0KZNGxw8eDDHeZ8/f57jy+qHx7q6utDU1IRUKs31p5GRUY5b25w/fx7Pnj0DALRu3Rra2tpi3b179xAWFgbg3azL+5kZmUwmPv/UQyaTIT09HWlpaRgyZAgcHR3Ffi9evIixY8ciPT0d/fv3x6BBg8S6hIQEWFhYIC0t7bOf5Zd4enrmSLxOnTqFsLCwHJu0AIBMJkNSUtJXnRNAjpkrDY3/fZX8OKH7sO5r5NbP+zg+V/c1srOzc+wSevfuXRw/fhwAMGLECLm6sLAw+Pr65rl/XV1dcXy/T8j09PTQt29f9OjRQ2yXkZGB33//Hfr6+qhUqRI8PDzk+nn8+DGkUqn43wcTuqJN4f8ifv31V2RnZ6N58+ZISUlBo0aNoKWlhTFjxsj9Zaso2759O3x9fbFy5UrUrVsXS5YsQcuWLREREQEzMzNlh0dERKQ05cuXR//+/XOtS0pKwpMnT/D48WM8f/4cL168yPXns2fPcvx7+ubNG/F56dKlc/T9/PlzPH/+/Ktit7GxyZF4zZkzB/v27RPP8WHiFRAQkGO2JD88PT3lEq+kpCScOnUKAORutA0AWlpaX510Aci1j/fvLbe6cuXKwdHRETo6OtDW1lb45/uleNbW1nL9tm3bFmfPnoWGhkaO1VCVKlXCw4cPoaGhAXV19RxL9wRBAPAuKTx69CiaN2+eI5ESBAE6Ojo53s+5c+cgk8mgqamZo27mzJkYPnw40tPTxeQ4LS1N7nlejj8+b0pKivj846QsOTk5Rxyfk5KSItffe82bN5c7TkhIwLhx4wAA7dq1y5F4NWvWDPfu3ROPP55hy8vz0qVLy91/EABevnyJ7Oxs6OvrQ0dHh8suC4jCiZdEIsGkSZMwduxY3L9/H0lJSXB0dMz1rytFlb+/P3788Uf069cPALBy5UocPHgQa9eulbvAmIiIiP5HX19f3KL+U2QyGQ4ePIhWrVrJlZuYmGDlypV48+YNHBwccrzO2toa2traSE5ORnJyMlJTUxWOTyqVKvyagvBxovNhcvfx7IuWlhaqV68OLS0taGlpQUdHR6Hk5/1zc3PzHHEEBQVBXV1d7vzvTZs2DdOmTSugd/w/75e25kYqlcLGxuaLfchkMpQuXRoWFhZ5/h3WqFHjk3X16tXLUx+KWrhwIWbMmIGUlBQYGRnJ1dWtWxfbtm0Tx29KSor4PDk5GUlJSUhKSvrk8/fj/eMdRj+cpcztu/bHs5jvz/fixYs8vy9LS8scidfw4cPFTfQiIyPlrhPdunUrli1b9sXETldXF1paWuK1dh8/t7W1ldvNNSsrC5mZmdDU1FTZRC/fc8DR0dGIiYlBo0aNoKOjA0EQisWHlJGRgStXrsj9hUtNTQ0tWrTAuXPncrR//9eS994vnZDJZJDJZIUf8Be8j6EoxEJFH8cLKYpjhhQlk8kgkUiQnZ0tN24MDAzkZtI+HlNnzpyRO87Kysrx5TU1NVX89zcjIwMZGRnic5lMBl1d3Rz9frjhg6amplz9+x2ZBUGAuro6NDQ0FHq834yhUqVKcv26urri7du34hfIj2O6fPlyPj9deR/3++GX2OL032xx+v/M+6QBkI/XwsJC7pYNino/3jU0NOT6LVWqFLZt24akpCRYW1vn+Ixat26NFy9eICUlRUziPnyel9lVPT29HP1+uFRYS0tLrv7Bgwc4e/Zsft+qaOfOnfD29haPT506hRYtWgAAxo4di1mzZol16enpcHJyEmdPNTQ0MHny5CIxZhSJQeHE69WrV+jSpQuOHz8OiUSCe/fuwc7ODgMGDEDp0qWxaNEiRbv8pl6+fImsrKwcf50xNzfHnTt3crSfM2cO/Pz8cpQHBQXlmGZWpuDgYGWHQMUIxwspimOGFPUtxoy6unqOGZ6P7yeqpaUlLgM8efJkjj4+3hkyL7Kzs8XE7+3bt+J1bfR1+P+Z3L2f7UxJSckxvj9MXHKTlZUlLqF8vzPlhxu5pKWlQSqV5ujXyMgItWvXRlpaGk6fPi0mm8C7DVUKwo0bN+SWll6/fl18/vDhQ7mYUlNT8ejRI7nXSySSIjFmclsy+ikKJ16jRo2CVCpFdHS03FKBrl27wtfXt8gnXoqaMGGC3MWSiYmJKF++PDw9PXO92eW3JpPJEBwcDA8PD6UtsaDig+OFFMUxQ4rimCFFccwUPW3atPls3bp16+SWSn44y/bhDHV6ejoyMjLEFWTvN6VJT09Hx44d5a6NNDY2xtGjR5Geno7mzZvLxZCYmAgLCwu5jW/U1NSKxJj5eCOhz1E48QoKCsJ///2HcuXKyZVXrlw5RyZaFJmYmEBdXT3HBbzPnz+HhYVFjvYfTil/SCqVKv0X/aGiFg8VbRwvpCiOGVIUxwwpimOm+JBKpdDR0SnQe/c1aNBA3JTmY8bGxuLupMC7ZD0wMLBIjBlFzq/wnpPJycm5LrF7/fp1rglKUaOpqQk3NzccPXpULMvOzsbRo0fx3XffKTEyIiIiIiJSVQonXg0bNsTGjRvF4/cX0M6fPx9NmzYt0OAKi6+vL1atWoUNGzYgPDwcQ4cORXJysrjLIRERERERUUFSeKnh/Pnz0bx5c1y+fBkZGRkYN24cbt++jdevX+fYkaio6tq1K+Li4jB16lTExsaiZs2aOHz48Ce3QyUiIiIiIvoaCideTk5OuHv3LpYtWwYDAwMkJSWhQ4cOGDZsGCwtLQsjxkLx888/4+eff1Z2GEREREREVAIolHjJZDK0atUKK1euxKRJkworJiIiIiIiIpWi0DVeUqkUN2/eLKxYiIiIiIiIVJLCm2v07NkTa9asKYxYiIiIiIiIVJLC13hlZmZi7dq1OHLkCNzc3KCnpydX7+/vX2DBERERERERqQKFE6/Q0FC4uroCAO7evStXJ5FICiYqIiIiIiIiFaJw4nX8+PHCiIOIiIiIiEhlKXyNFxERERERESlG4Rmv77//PtclhRKJBNra2qhUqRK6d++OqlWrFkiARERERERExZ3CM16lSpXCsWPHcPXqVUgkEkgkEly7dg3Hjh1DZmYmtm/fjho1auDMmTOFES8REREREVGxo/CMl4WFBbp3745ly5ZBTe1d3padnY0RI0bAwMAA27Ztw5AhQzB+/HicPn26wAMmIiIiIiIqbhSe8VqzZg1GjhwpJl0AoKamhuHDh+Pvv/+GRCLBzz//jNDQ0AINlIiIiIiIqLhSOPHKzMzEnTt3cpTfuXMHWVlZAABtbW1uLU9ERERERPT/FF5q2KtXLwwYMAATJ05E7dq1AQCXLl3C7Nmz0bt3bwDAyZMnUa1atYKNlIiIiIiIqJhSOPFavHgxzM3NMX/+fDx//hwAYG5ujlGjRmH8+PEAAE9PT7Rq1apgIyUiIiIiIiqmFE681NXVMWnSJEyaNAmJiYkAAENDQ7k21tbWBRMdERERERGRCsjXDZQzMzNx5MgRbN26VbyW6+nTp0hKSirQ4IiIiIiIiFSBwjNejx49QqtWrRAdHY309HR4eHjAwMAA8+bNQ3p6OlauXFkYcRIRERERERVbCs94jRgxArVq1cKbN2+go6Mjln///fc4evRogQZHRERERESkChSe8QoJCcHZs2ehqakpV16hQgU8efKkwAIjIiIiIiJSFQrPeGVnZ4v36/rQ48ePYWBgUCBBERERERERqRKFEy9PT08sWbJEPJZIJEhKSsK0adPQpk2bgoyNiIiIiIhIJSi81HDRokVo2bIlHB0dkZaWhu7du+PevXswMTHB1q1bCyNGIiIiIiKiYk3hxKtcuXK4ceMGtm3bhps3byIpKQkDBgxAjx495DbbICIiIiIioncUTrwAQENDAz179izoWIiIiIiIiFRSnhKvffv25blDb2/vfAdDRERERESkivKUePn4+MgdSyQSCIKQowxArjseEhERERERlWR52tUwOztbfAQFBaFmzZo4dOgQ4uPjER8fj0OHDsHV1RWHDx8u7HiJiIiIiIiKHYWv8Ro5ciRWrlyJBg0aiGUtW7aErq4uBg0ahPDw8AINkIiIiIiIqLhT+D5eDx48gJGRUY7yUqVK4eHDhwUQEhERERERkWpROPGqXbs2fH198fz5c7Hs+fPnGDt2LOrUqVOgwREREREREakChROvtWvX4tmzZ7C2tkalSpVQqVIlWFtb48mTJ1izZk1hxEhERERERFSsKXyNV6VKlXDz5k0EBwfjzp07AAAHBwe0aNFC3NmQiIiIiIiI/idfN1CWSCTw9PSEp6dnQcdDRERERESkcvK01HDbtm157jAmJgZnzpzJd0BERERERESqJk+J14oVK+Dg4ID58+fnul18QkICAgMD0b17d7i6uuLVq1cFHigREREREVFxlaelhidPnsS+ffuwdOlSTJgwAXp6ejA3N4e2tjbevHmD2NhYmJiYoG/fvggNDYW5uXlhx01ERERERFRs5PkaL29vb3h7e+Ply5c4ffo0Hj16hNTUVJiYmMDFxQUuLi5QU1N4k0QiIiIiIiKVp/DmGiYmJvDx8SmEUIiIiIiIiFQTp6iIiIiIiIgKGRMvIiIiIiKiQsbEi4iIiIiIqJAx8SIiIiIiIipkX514ZWVl4fr163jz5k1BxENERERERKRyFE68Ro4ciTVr1gB4l3Q1btwYrq6uKF++PE6cOFHQ8RERERERERV7CideO3fuRI0aNQAA+/fvR1RUFO7cuYNRo0Zh0qRJBR4gERERERFRcadw4vXy5UtYWFgAAAIDA9G5c2dUqVIF/fv3x61btwo8QCIiIiIiouJO4cTL3NwcYWFhyMrKwuHDh+Hh4QEASElJgbq6eoEHSEREREREVNxpKPqCfv36oUuXLrC0tIREIkGLFi0AABcuXIC9vX2BB0hERERERFTcKZx4TZ8+HU5OToiJiUHnzp2hpaUFAFBXV8evv/5a4AESEREREREVdwonXgDQqVMnAEBaWppY1qdPn4KJiIiIiIiISMUofI1XVlYWZs6cibJly0JfXx+RkZEAgClTpojbzCvDw4cPMWDAANja2kJHRwcVK1bEtGnTkJGRIddGIpHkeJw/f15pcRMRERERkepTOPGaNWsW1q9fj/nz50NTU1Msd3JywurVqws0OEXcuXMH2dnZ+Ouvv3D79m0sXrwYK1euxMSJE3O0PXLkCJ49eyY+3NzclBAxERERERGVFAovNdy4cSP+/vtvNG/eHEOGDBHLa9SogTt37hRocIpo1aoVWrVqJR7b2dkhIiICK1aswMKFC+XaGhsbi1viExERERERFTaFE68nT56gUqVKOcqzs7Mhk8kKJKiCkpCQgDJlyuQo9/b2RlpaGqpUqYJx48bB29v7k32kp6cjPT1dPE5MTAQAyGSyIvF+38dQFGKhoo/jhRTFMUOK4pghRXHMkKKK0phRJAaFEy9HR0eEhITAxsZGrnznzp1wcXFRtLtCc//+fSxdulRutktfXx+LFi1C/fr1oaamhoCAAPj4+GDPnj2fTL7mzJkDPz+/HOVBQUHQ1dUttPgVFRwcrOwQqBjheCFFccyQojhmSFEcM6SoojBmUlJS8txWIgiCoEjne/fuRZ8+fTBhwgTMmDEDfn5+iIiIwMaNG3HgwAHxhsoF5ddff8W8efM+2yY8PFzuHmJPnjxB48aN0aRJky9ed9a7d29ERUUhJCQk1/rcZrzKly+Ply9fwtDQUIF3UjhkMhmCg4Ph4eEBqVSq7HCoiON4IUVxzJCiOGZIURwzpKiiNGYSExNhYmKChISEL+YGCs94tW/fHvv378eMGTOgp6eHqVOnwtXVFfv37y/wpAsARo8ejb59+362jZ2dnfj86dOnaNq0KerVq4e///77i/3XrVv3s9mylpaWeK+yD0mlUqX/oj9U1OKhoo3jhRTFMUOK4pghRXHMkKKKwphR5Pz5uo9Xw4YNv9nUnqmpKUxNTfPU9smTJ2jatCnc3Nywbt06qKl9edPG69evw9LS8mvDJCIiIiIi+qR8JV5F0ZMnT9CkSRPY2Nhg4cKFiIuLE+ve72C4YcMGaGpqitei7dq1C2vXrlXqNvhERERERKT68pR4lS5dGhKJJE8dvn79+qsCyq/g4GDcv38f9+/fR7ly5eTqPryMbebMmXj06BE0NDRgb2+P7du3o1OnTt86XCIiIiIiKkHylHgtWbKkkMP4en379v3itWB9+vRBnz59vk1ARERERERE/y9PiReTFSIiIiIiovzL1zVeWVlZ2L17N8LDwwG8u7dX+/btoaGhMpeMERERERERFRiFM6Xbt2/D29sbsbGxqFq1KgBg3rx5MDU1xf79++Hk5FTgQRIRERERERVnX95v/SMDBw5EtWrV8PjxY1y9ehVXr15FTEwMqlevjkGDBhVGjERERERERMWawjNe169fx+XLl1G6dGmxrHTp0pg1axZq165doMERERERERGpAoVnvKpUqYLnz5/nKH/x4gUqVapUIEERERERERGpkjwlXomJieJjzpw5+OWXX7Bz5048fvwYjx8/xs6dOzFy5EjMmzevsOMlIiIiIiIqdvK01NDIyEjuBsqCIKBLly5i2fsbFHt5eSErK6sQwiQiIiIiIiq+8pR4HT9+vLDjICIiIiIiUll5SrwaN25c2HEQERERERGprHzf8TglJQXR0dHIyMiQK69evfpXB0VERERERKRKFE684uLi0K9fPxw6dCjXel7jRUREREREJE/h7eRHjhyJ+Ph4XLhwATo6Ojh8+DA2bNiAypUrY9++fYURIxERERERUbGm8IzXsWPHsHfvXtSqVQtqamqwsbGBh4cHDA0NMWfOHLRt27Yw4iQiIiIiIiq2FJ7xSk5OhpmZGQCgdOnSiIuLAwA4Ozvj6tWrBRsdERERERGRClA48apatSoiIiIAADVq1MBff/2FJ0+eYOXKlbC0tCzwAImIiIiIiIo7hZcajhgxAs+ePQMATJs2Da1atcLmzZuhqamJ9evXF3R8RERERERExZ7CiVfPnj3F525ubnj06BHu3LkDa2trmJiYFGhwREREREREqiDf9/F6T1dXF66urgURCxERERERkUrKU+Ll6+uLmTNnQk9PD76+vp9t6+/vXyCBERERERERqYo8JV7Xrl2DTCYDAFy9ehUSiSTXdp8qJyIiIiIiKsnylHgdP35cfH7ixInCioWIiIiIiEglKbSdvEwmg4aGBkJDQwsrHiIiIiIiIpWjUOIllUphbW2NrKyswoqHiIiIiIhI5Sh8A+VJkyZh4sSJeP36dWHEQ0REREREpHIU3k5+2bJluH//PqysrGBjYwM9PT25+qtXrxZYcERERERERKpA4cTLx8enEMIgIiIiIiJSXQonXtOmTSuMOIiIiIiIiFSWwtd4ERERERERkWIUnvHKysrC4sWLsWPHDkRHRyMjI0OunptuEBERERERyVN4xsvPzw/+/v7o2rUrEhIS4Ovriw4dOkBNTQ3Tp08vhBCJiIiIiIiKN4UTr82bN2PVqlUYPXo0NDQ00K1bN6xevRpTp07F+fPnCyNGIiIiIiKiYk3hxCs2NhbOzs4AAH19fSQkJAAA2rVrh4MHDxZsdERERERERCpA4cSrXLlyePbsGQCgYsWKCAoKAgBcunQJWlpaBRsdERERERGRClA48fr+++9x9OhRAMDw4cMxZcoUVK5cGb1790b//v0LPEAiIiIiIqLiLs+7Gi5btgw9e/bE3LlzxbKuXbvC2toa586dQ+XKleHl5VUoQRIRERERERVneZ7xmjRpEqysrNCjRw8cO3ZMLP/uu+/g6+vLpIuIiIiIiOgT8px4xcbGYuXKlXj69Ck8PDxga2uLmTNnIiYmpjDjIyIiIiIiKvbynHjp6Oigd+/eOH78OO7du4devXphzZo1sLW1RatWrfDvv/9CJpMVZqxERERERETFksKbawCAnZ0dZsyYgaioKBw6dAjGxsbo27cvypYtW9DxERERERERFXv5Srzek0gk0NDQgEQigSAInPEiIiIiIiLKRb4Sr5iYGMyYMQN2dnbw8PDA06dPsWrVKvH+XkRERERERPQ/ed5OPiMjA7t27cLatWtx7NgxWFpaok+fPujfvz/s7OwKM0YiIiIiIqJiLc+Jl4WFBVJSUtCuXTvs378fLVu2hJraV61UJCIiIiIiKhHynHhNnjwZvXr1gqmpaWHGQ0REREREpHLynHj5+voWZhxEREREREQqi2sFiYiIiIiIChkTLyIiIiIiokLGxIuIiIiIiKiQ5TvxysjIQEREBDIzMwsynq9SoUIFSCQSucfcuXPl2ty8eRMNGzaEtrY2ypcvj/nz5yspWiIiIiIiKikUTrxSUlIwYMAA6Orqolq1aoiOjgYADB8+PEeSowwzZszAs2fPxMfw4cPFusTERHh6esLGxgZXrlzBggULMH36dPz9999KjJiIiIiIiFSdwonXhAkTcOPGDZw4cQLa2tpieYsWLbB9+/YCDS4/DAwMYGFhIT709PTEus2bNyMjIwNr165FtWrV8MMPP+CXX36Bv7+/EiMmIiIiIiJVl+ft5N/bs2cPtm/fDnd3d0gkErG8WrVqePDgQYEGlx9z587FzJkzYW1tje7du2PUqFHQ0Hj3Ns+dO4dGjRpBU1NTbN+yZUvMmzcPb968QenSpXP0l56ejvT0dPE4MTERACCTySCTyQr53XzZ+xiKQixU9HG8kKI4ZkhRHDOkKI4ZUlRRGjOKxKBw4hUXFwczM7Mc5cnJyXKJmDL88ssvcHV1RZkyZXD27FlMmDABz549E2e0YmNjYWtrK/cac3NzsS63xGvOnDnw8/PLUR4UFARdXd1CeBf5ExwcrOwQqBjheCFFccyQojhmSFEcM6SoojBmUlJS8txW4cSrVq1aOHjwoHjt1Ptka/Xq1fjuu+8U7e6Lfv31V8ybN++zbcLDw2Fvby93k+fq1atDU1MTgwcPxpw5c6ClpZWv80+YMEGu38TERJQvXx6enp4wNDTMV58FSSaTITg4GB4eHpBKpcoOh4o4jhdSFMcMKYpjhhTFMUOKKkpj5v1quLxQOPGaPXs2WrdujbCwMGRmZuL3339HWFgYzp49i5MnTyra3ReNHj0affv2/WwbOzu7XMvr1q2LzMxMPHz4EFWrVoWFhQWeP38u1+b9sYWFRa59aGlp5Zq0SaVSpf+iP1TU4qGijeOFFMUxQ4rimCFFccyQoorCmFHk/AonXg0aNMD169cxd+5cODs7IygoCK6urjh37hycnZ0V7e6LTE1NYWpqmq/XXr9+HWpqauLSyO+++w6TJk2CTCYTP6Tg4GBUrVo112WGREREREREBUHhxAsAKlasiFWrVhV0LF/l3LlzuHDhApo2bQoDAwOcO3cOo0aNQs+ePcWkqnv37vDz88OAAQMwfvx4hIaG4vfff8fixYuVHD0REREREakyhRMvdXV1PHv2LMcGG69evYKZmRmysrIKLDhFaGlpYdu2bZg+fTrS09Nha2uLUaNGyV2fVapUKQQFBWHYsGFwc3ODiYkJpk6dikGDBiklZiIiIiIiKhkUTrwEQci1PD09XW6b9m/N1dUV58+f/2K76tWrIyQk5BtERERERERE9E6eE68//vgDwLtdDFevXg19fX2xLisrC6dOnYK9vX3BR0hERERERFTM5Tnxen8dlCAIWLlyJdTV1cU6TU1NVKhQAStXriz4CImIiIiIiIq5PCdeUVFRAICmTZti165d3AWQiIiIiIgojxS+xuv48eOFEQcREREREZHKytd28o8fP8a+ffsQHR2NjIwMuTp/f/8CCYyIiIiIiEhVKJx4HT16FN7e3rCzs8OdO3fg5OSEhw8fQhAEuLq6FkaMRERERERExZqaoi+YMGECxowZg1u3bkFbWxsBAQGIiYlB48aN0blz58KIkYiIiIiIqFhTOPEKDw9H7969AQAaGhpITU2Fvr4+ZsyYgXnz5hV4gERERERERMWdwomXnp6eeF2XpaUlHjx4INa9fPmy4CIjIiIiIiJSEQpf4+Xu7o7Tp0/DwcEBbdq0wejRo3Hr1i3s2rUL7u7uhREjERERERFRsaZw4uXv74+kpCQAgJ+fH5KSkrB9+3ZUrlyZOxoSERERERHlQuHEy87OTnyup6eHlStXFmhAREREREREqkbha7zs7Ozw6tWrHOXx8fFySRkRERERERG9o3Di9fDhQ2RlZeUoT09Px5MnTwokKCIiIiIiIlWS56WG+/btE5//999/KFWqlHiclZWFo0ePokKFCgUaHBERERERkSrIc+Ll4+MDAJBIJOjTp49cnVQqRYUKFbBo0aICDY4+Lzo6GgCQkpKCrKwsSKVSJUdERERERES5yXPilZ2dDQCwtbXFpUuXYGJiUmhBUd60aNEC9+7dE48NDAxQsWJFVK1aFU5OTmjWrBlq167NhIyIiIiISMkUvsYrKiqKSVcR8X5b//fevn2L69evY/v27ZgyZQrq168PY2NjdOrUCfv370dmZqaSIiUiIiIiKtnynHidO3cOBw4ckCvbuHEjbG1tYWZmhkGDBiE9Pb3AA6RP8/Lygre3N2rUqAF3d3dUrFgR6urqcm3evn2LgIAAeHt7o3z58pg6dWquu1ISEREREVHhyXPiNWPGDNy+fVs8vnXrFgYMGIAWLVrg119/xf79+zFnzpxCCZJy99dff2Hnzp3w8/PDqVOncP/+faSkpCAsLAxr1qxBt27d5GYnY2NjMXPmTFSoUAETJ05kAkZERERE9I3kOfG6fv06mjdvLh5v27YNdevWxapVq+Dr64s//vgDO3bsKJQgKe80NTXh4OCA/v37Y8uWLXj27BkOHDiADh06QEPj3SV9SUlJmDNnDqpUqYJVq1aJ1+8REREREVHhyHPi9ebNG5ibm4vHJ0+eROvWrcXj2rVrIyYmpmCjo6+moaGBtm3bIiAgAA8ePMDQoUOhqakJAHj9+jUGDRqEevXq4datW0qOlIiIiIhIdeU58TI3N0dUVBQAICMjA1evXoW7u7tY//btW+6eV8RZW1tj+fLluH//Pnr06CGWX7hwAbVr18bvv//O2S8iIiIiokKQ58SrTZs2+PXXXxESEoIJEyZAV1cXDRs2FOtv3ryJihUrFkqQVLDKly+PTZs24dixY3BwcAAApKenY+TIkWjdujWeP3+u5AiJiIiIiFRLnhOvmTNnQkNDA40bN8aqVauwatUqcckaAKxduxaenp6FEiQVjqZNm+LatWvw9fUVy4KCglCrVi1cvnxZiZEREREREamWPN9A2cTEBKdOnUJCQgL09fVzbFv+77//Ql9fv8ADpMKlpaWFRYsWoVWrVujduzdiY2Px+PFjNGzYEKtXr5ZbkkhERERERPmj8A2US5UqlSPpAoAyZcrIzYBR8eLh4YFr166hXr16AIC0tDT07NkTM2bMgCAISo6OiIiIiKh4UzjxItVlYWGBY8eOYeDAgWLZtGnT8NNPPyErK0uJkRERERERFW9MvEiOlpYW/v77byxatEgsW7lyJbp27Yr09HQlRkZEREREVHwx8aIcJBIJfH19sWnTJvGmywEBAejUqROTLyIiIiKifGDiRZ/Uo0cPHDhwADo6OgCAAwcOoEOHDkhLS1NyZERERERExQsTL/qsli1bIjAwELq6ugCAwMBAdOjQgTNfREREREQKYOJFX9SkSRMcOnQIenp6AIBDhw6hV69e3HCDiIiIiCiPmHhRnjRq1AiBgYHissN///0XQ4YM4VbzRERERER5wMSL8qxRo0YICAgQN9xYvXo1JkyYoOSoiIiIiIiKPiZepJDWrVtj06ZNkEgkAIB58+bhr7/+UnJURERERERFGxMvUljXrl3x559/isfDhg3Df//9p8SIiIiIiIiKNiZelC9Dhw7F6NGjAQBZWVno3Lkzbt26peSoiIiIiIiKJiZelG/z58/H999/DwB4+/Yt2rZti2fPnik5KiIiIiKiooeJF+WbmpoaNm3ahNq1awMAYmJi4OXlhZSUFCVHRkRERERUtDDxoq+iq6uLffv2wdraGgBw5coVDB48mNvMExERERF9gIkXfTULCwscOHBAvMHypk2bsHTpUiVHRURERERUdDDxogLh7OyMtWvXise+vr44deqUEiMiIiIiIio6mHhRgenSpQvGjRsH4H87HT5+/FjJURERERERKR8TLypQs2bNQosWLQAAL168QMeOHZGenq7kqIiIiIiIlIuJFxUoDQ0NbNu2DTY2NgCAixcvYsyYMUqOioiIiIhIuZh4UYEzNjbG7t27oaWlBQBYtmwZAgIClBwVEREREZHyMPGiQuHi4oIlS5aIxwMGDEBkZKTyAiIiIiIiUiImXlRoBg8ejC5dugAAEhIS8MMPPyAjI0PJURERERERfXtMvKjQSCQSrFq1ChUrVgQAXLp0Cb/++quSoyIiIiIi+vZUJvE6ceIEJBJJro9Lly4BAB4+fJhr/fnz55UcveoyNDTEjh07oKmpCQBYvHgx9u3bp+SoiIiIiIi+LZVJvOrVq4dnz57JPQYOHAhbW1vUqlVLru2RI0fk2rm5uSkp6pLB1dUV/v7+4nH//v3x7NkzJUZERERERPRtqUzipampCQsLC/FhbGyMvXv3ol+/fpBIJHJtjY2N5dpKpVIlRV1y/PTTT/Dx8QEAvHr1Cv369UN2drZygyIiIiIi+kY0lB1AYdm3b5/4Bf9j3t7eSEtLQ5UqVTBu3Dh4e3t/sp/09HS5GwAnJiYCAGQyGWQyWcEHrqD3MRSFWL5k+fLluHDhAp49e4b//vsPv//+O37++Wdlh1WiFKfxQkUDxwwpimOGFMUxQ4oqSmNGkRgkgiAIhRiL0rRp0wYAEBgYKJa9fPkSGzduRP369aGmpoaAgADMnz8fe/bs+WTyNX36dPj5+eUo37JlC3R1dQsneBV27do18fOUSqVYuHCheLNlIiIiIqLiJCUlBd27d0dCQgIMDQ0/27bIJ16//vor5s2b99k24eHhsLe3F48fP34MGxsb7NixAx07dvzsa3v37o2oqCiEhITkWp/bjFf58uXx8uXLL36434JMJkNwcDA8PDyKzZLJ0aNHY+nSpQAAZ2dnnD17VrzZMhWu4jheSLk4ZkhRHDOkKI4ZUlRRGjOJiYkwMTHJU+JV5Jcajh49Gn379v1sGzs7O7njdevWwdjY+LNLCN+rW7cugoODP1mvpaWVa1IglUqV/ov+UFGL53Pmz5+P48ePIzQ0FLdu3cK0adOwaNEiZYdVohSn8UJFA8cMKYpjhhTFMUOKKgpjRpHzF/nEy9TUFKampnluLwgC1q1bh969e+fpg7h+/TosLS2/JkRSkLa2NjZv3ozatWsjIyMD/v7+aN26NVq0aKHs0IiIiIiICkWRT7wUdezYMURFRWHgwIE56jZs2ABNTU24uLgAAHbt2oW1a9di9erV3zrMEq969eqYO3cufH19AQB9+vTBrVu3UKZMGSVHRkRERERU8FRmO/n31qxZg3r16sld8/WhmTNnws3NDXXr1sXevXuxffv2XHc+pMI3YsQIcZbr6dOnGD58uJIjIiIiIiIqHCo347Vly5ZP1vXp0wd9+vT5htHQ56ipqWH9+vVwcnJCfHw8tmzZgg4dOnxxQxQiyr+srCxERkYiIiICz549Q2xsLGJjY/H8+XMkJycjIyMDMpkMGRkZkEgk0NPTQ1JSEnbs2AEjIyOULVsW5cuXR7ly5VC+fHlUqFABGhoq908JERFRgeO/lqRUZcuWxbJly9CzZ08AwJAhQ9CwYUOYmZkpOTKi4i8zMxPXrl1DSEgILl++jNu3byMiIkJup9a8unDhQq7lWlpacHBwgLOzM5ydncUVBXp6el8bPhERkUph4kVK1717dwQEBGD37t14+fIlhg4dip07d0IikSg7NKJiRRAEhIWFYd++fTh27BjOnTuH5OTkQj1neno6rl+/juvXr4tl6urqcHV1Rf369dG4cWM0b94cBgYGhRoHERFRUcfEi5ROIpFg5cqVCAkJwcuXL7Fr1y5s3boV3bt3V3ZoREWeIAg4e/Ysdu/ejb179+L+/fufbKuuro7KlSujWrVqcHBwgLW1NczNzWFhYQFzc3MYGhpCU1MTmpqa0NDQQHZ2NhISErB37164u7sjMTERT548wePHjxETE4OHDx8iNDQUd+/eRXZ2tnierKwsXLp0CZcuXcKSJUsglUrRsGFDtGnTBm3atIGDg8O3+GiIiIiKFCZeVCSYmZlhxYoV6Ny5MwBg2LBhaNKkCaysrJQcGVHR9OTJE2zYsAHr1q37ZLJVtmxZNGzYEA0aNECDBg3g4OAATU3NPJ9DXV0dBgYGKFOmDCpVqvTJW3SkpaXhzp07uHHjBs6ePYszZ87g9u3bYr1MJsOxY8dw7NgxjBkzBo6OjujatSu6du2KqlWrKvbGiYiIiikmXlRkdOrUCd26dcPWrVsRHx+PH3/8EQcOHOCSQ6L/JwgCDh8+jGXLluHw4cNys0zAuw1rGjVqhPbt26Ndu3aoWLHiN/nvR1tbGzVr1kTNmjXFDYxev36NM2fOICgoCAcPHkRUVJTYPiwsDNOmTcO0adNQo0YN9OrVC7169eK1nUREpNJUbjt5Kt6WLVsGCwsLAEBgYCDWrl2r5IiIlC89PR3r1q2Ds7Mz2rRpg8DAQLmkq1mzZli3bh1evHiB48ePY+TIkahUqZJS/2hRpkwZeHl5YenSpXjw4AHu3LmDRYsWoX79+nLtbty4gTFjxqBs2bLo2LEjAgMDkZWVpaSoiYiICg8TLypSypQpg1WrVonHo0aNwqNHj5QYEZHypKamYuHChahQoQL69+8vt3zP2toa06ZNQ2RkJI4ePYq+ffvC2NhYidF+mkQiQdWqVeHr64vTp08jOjoaixYtQp06dcQ2mZmZ2LVrF9q2bQs7OzssWLAAb968UWLUREREBYuJFxU57dq1E29q/fbtW/Tv3z/HkioiVZaRkYHly5ejYsWKGDt2LGJjY8W6+vXrY/fu3YiMjMT06dNha2urxEjzp3z58vD19cWFCxdw584djBs3Dubm5mJ9dHQ0xo0bh3LlymHo0KEIDw9XYrREREQFg4kXFUmLFy9G+fLlAQDHjh3DihUrlBwRUeHLzs7Gpk2bULVqVQwbNgzPnj0D8G7GqEOHDjh79ixOnz4NHx8fqKurKznaglG1alXMmzcPMTEx2Lt3L9q0aSPWpaSkYOXKlXB0dETLli1x5MgRCIKgxGiJiIjyj4kXFUmlSpXCmjVrxONx48YhMjJSiRERFa7Lly+jfv366NWrFx4+fCiW+/j44ObNmwgICMB3332nvAALmVQqhbe3Nw4ePIiIiAj8/PPP0NfXF+uDgoLg4eEBd3d37N27l7PgRERU7DDxoiLLw8MDgwcPBvDuL99cckiq6MWLFxg4cCDq1KmD8+fPi+Wenp64ePEidu/eDScnJyVG+O1VqVIFS5cuxePHj7F48WLY2dmJdRcvXoSPjw9q1KiBLVu2IDMzU4mREhER5R0TLyrSFixYABsbGwDAyZMn8eeffyo5IqKCIQgC1qxZgypVqmDNmjXiEjoHBwcEBQXhv//+Q+3atZUcpXKVKlUKI0eOxN27d7F9+3bUqFFDrAsNDUWPHj3g4OCATZs2cSdEIiIq8ph4UZFmYGAgt6X8+PHjP3mzWKLiIjIyEh4eHhg4cCASEhIAAIaGhvD398eNGzfg4eGh5AiLFnV1dXTp0gXXrl3DgQMH5JZc3r9/H7169UL16tUREBDAWXEiIiqymHhRkdesWTP89NNPAN5tr92vXz9+uaJiKSsrC0uWLIGzszOOHj0qlvfs2RMREREYNWoUpFKpEiMs2iQSCdq2bYszZ87g+PHjaN68uVgXFhaGTp06oVatWggMDOQmHEREVOQw8aJiYd68eeK22adPn8Yff/yh5IiIFBMdHY1mzZph1KhRSElJAfDuXlyHDh3CP//8I944nL5MIpGgSZMmOHLkCI4fP4569eqJddeuXUPbtm3RoEEDHD9+XIlREhERydNQdgBEeaGvr49169ahSZMmAIAJEyagTZs2qFKlinIDI8qDrVu3YujQoeKyQgAYNmwY5syZAwMDAyVGVvw1adIEp0+fxuHDhzF58mRcvXoVAHD27Fk0a9YMrVu3xvz580vcBiVE30pmZiaSk5ORnJyMpKQkJCcnIz09HdnZ2eJDEARkZ2dDQ0MD2tra0NLSgpaWFrS1taGtrQ1dXV1lvw2ib4KJFxUbjRs3xvDhw7F06VKkpaWhX79+OHXqlMrcz4hUT0JCAn7++Wds2rRJLLO2tsbGjRvRuHFjJUamWiQSCVq3bo1WrVph9+7dmDJlCsLCwgAAhw4dwn///Ye+fftixowZKFu2rJKjJSr6MjMz8eTJE0RHR+PRo0eIjo7G8+fPERcXJ/d49eoV0tPTC+ScmpqaKFOmDIyMjGBkZARjY2NYWFjA0tISVlZWsLS0FB8WFhbQ1NQskPMSfUtMvKhYmTNnDgIDA/HgwQOcPXsWS5YswejRo5UdFlEO169fR6dOnfDgwQOxrHv37vjzzz9hZGSkvMBU2PsbTbdv3x5btmzB5MmTER0djezsbKxduxZbt26Fr68vxo0bB0NDQ2WHS6RU2dnZePz4Me7cuSP3ePDgAZ48efLNdwrNyMhAbGwsYmNjv9hWIpGgfPnysLOzy/GoWLEiTExMvkHERIpj4kXFip6eHtatW4fGjRtDEARMmjQJbdu2hb29vbJDIxKtW7cOP/30E9LS0gC827Fw+fLl6NGjh5IjKxnU1dXRq1cvdO7cGX/88Qdmz56NhIQEpKamYtasWfj7778xffp0/Pjjj9zMhEqE9PR03L59G1evXsW1a9dw7do13Lx5E8nJyfnqTyqVwtTUFMbGxjAwMIC+vj709PTEh7a2NtTV1aGmpgaJRCL+zMzMRFpaGtLT08WfKSkpSEhIEP9IEh8fj7dv3372/IIgIDo6GtHR0Thx4kSOehMTEzg6OsLBwQGOjo7icysrK0gkkny9Z6KCwMSLip2GDRtixIgRWLJkCdLT09G3b1+cOXOGSw5J6VJTUzF8+HCsWbNGLKtVqxZ27Nghbg5D3462tjbGjRuHAQMG4LfffsOff/4JmUyGuLg4DBs2DL///jvmzp0LHx8ffhkjlSEIAh49eoSzZ8+Kj1u3buX5ZuPGxsaoUKECrK2tYWNjAxsbG1hbW8PKygomJiYwNTWFoaFhgf43I5PJEBgYiDZt2kAqlSIzMxOvXr3Cs2fPcjyePn2KmJgYREZG4vXr17n29/LlS5w6dQqnTp2SKy9VqhRq1KiBmjVrwsXFBTVr1oSjoyOXLdI3w8SLiqVZs2bh4MGDuHfvHi5cuIBFixZh3Lhxyg6LSrDIyEh06tQJ165dE8uGDBmCJUuWQEtLS4mRkbGxMRYvXoyff/4ZEydOxI4dOwAAd+/eRYcOHVC/fn0sWrQIdevWVXKkRIoTBAFhYWE4evQoQkJCcPbsWTx9+vSLr7O1tYWTkxPs7e3FR9WqVWFsbPwNov48DQ0NmJubw9zcHDVr1vxku4SEBERFRSEyMlJ8REREIDw8HM+ePcu1/ccJmVQqRbVq1cREzM3NDa6urtDR0SmMt0YlHBMvKpZ0dXWxfv16NGjQAIIgYOrUqWjXrh0cHR2VHRqVQIcPH0a3bt0QHx8PANDR0cHff/+Nnj17KjcwklOxYkVs374dvr6+GDNmDE6fPg0AOHPmDNzd3dG1a1fMnj0bdnZ2So6U6POio6Nx9OhR8fG566IkEgkcHBzg6uoKV1dXMcFQhWtNS5UqhZo1a+aanMXHxyM8PBxhYWEICwtDeHg4bt68iSdPnsi1k8lkuH79Oq5fvy6Wqauro3r16qhTp474cHBw4Moa+mpMvKjYqlevHnx9fbFo0SJxyeHZs2ehocFhTd+GIAj4/fffMXr0aPGm3lWqVEFAQAC3Ly/C6tati1OnTmHfvn0YP348IiIiAADbt2/Hrl27MHz4cEyaNAllypRRcqRE76SlpeHEiRM4cOAA/vvvP9y/f/+TbQ0MDODu7o569eqhfv36qFu3boncTMbIyAjfffcdvvvuO7nyuLg43LhxA9evX8e1a9dw/fp13LlzR/x/OPDuZvfvr4X766+/ALy7rU2tWrXkkrFy5cpxmTIphN9QqVibOXMmDhw4gIiICFy6dAkLFizAhAkTlB0WlQAZGRkYNmwYVq9eLZZ9//33WL9+fYn8klPcSCQStG/fHm3atMHq1asxbdo0xMXFQSaTwd/fH+vWrcPkyZMxbNgwLhUlpXj69CkCAwNx4MABBAcHizde/5ienh4aNWqE5s2bo1mzZqhevTpnZj7D1NQULVq0QIsWLcSy1NRU3Lp1C9euXcOlS5dw4cIF3L59G4IgiG2SkpJw4sQJuc08LC0t4e7ujrp168Ld3R21atWCnp7et3w7VMww8aJiTUdHB+vXr0f9+vWRnZ2N6dOnw8vLi7MNVKhevnyJjh07yl0nMHnyZPj5+UFNTU2JkZGipFIphg4dih49emDevHnw9/dHWloa3rx5g9GjR2PZsmWYO3cuOnfuzL9sU6ELCwvDzp07sW/fPly5ciXXNlKpFO7u7mjevDmaN2+OOnXqcHOIr6SjoyPOYg0ePBgA8PbtW1y9ehUXL17ExYsXceHCBcTExMi97tmzZ9i9ezd2794N4N0SRWdnZzERc3d3R5UqVfjvAomYeFGx5+7ujjFjxmD+/PnIyMhA3759ce7cOW4TTYXi9u3b8PLyQlRUFABAS0sL69atQ7du3ZQcGX0NQ0NDzJo1C0OGDMHkyZPxzz//QBAEREVFoWvXrvD398fChQvRoEEDZYdKKkQQBNy8eRM7d+5EQEAAwsPDc21nZmaGtm3bol27dvDw8ICBgcE3jrTkMTAwQOPGjeVudv/s2TNcunRJTMQuXbqEhIQEsT4rK0u8Xuz9EkUjIyPUqVNHTMTq1KlTJDYwIeVg4kUqwc/PD/v370d4eDiuXLmCefPmYfLkycoOi1TM0aNH8f3334v3mLGwsMDevXtRp04dJUdGBaV8+fLYsGEDRo4ciTFjxuDYsWMAgAsXLqBhw4bo0KED5s6di8qVKys5UiquBEHA1atXsXPnTuzcufOT12u5uLigXbt2aNeuHWrVqsVZkyLA0tIS3t7e8Pb2BvDuJtQRERE4f/68+AgNDZW7Xiw+Ph5BQUEICgoSyypXriwmYu7u7nB2duYfi0sIJl6kErS1tbFhwwZ89913yMrKwowZM+Dt7Y3q1asrOzRSEZs3b0a/fv0gk8kAAK6urti7dy/KlSun5MioMLi4uODIkSM4dOgQxo4di7CwMADArl27sG/fPgwdOhRTp06FiYmJkiOl4uL27dvYvHkztm7diocPH+aol0gkaNCgATp27IgOHTqgfPny3z5IUoiamhocHBzg4OCAfv36AXh3Ldjly5flkrHnz5/Lve7evXu4d+8e/vnnHwDvvsPUqlVLTMTq1q3Lf1tUFBMvUhm1a9fGuHHjMGfOHMhkMvTp0wcXL17kX5HoqwiCgHnz5slt2uLt7Y0tW7bwImoVJ5FI0KZNG3h6emLdunWYMmUKnj9/jszMTCxduhQbNmzApEmT8Msvv0BbW1vZ4VIR9OTJE2zduhWbNm3CjRs3ctSrqamhcePG6NSpE77//ntYWloqIUoqSPr6+mjSpAmaNGkC4N2/IdHR0WISduHCBVy5cgUZGRnia9LS0nD69GnxFhcAULZsWblEzM3NDbq6ut/67VABY+JFKmXatGnYt28fbt++jevXr2P27NmYNm2assOiYiorKwsjRozAn3/+KZYNGTIES5cu5W0LShANDQ38+OOP6NatGxYsWICFCxciJSUFiYmJGD9+PP7880/MmjUL3bp1425yhISEBAQEBGDz5s04fvy43M54wLsNGJo1a4bOnTvDx8cHpqamSoqUvgWJRAIbGxvY2Niga9euAID09HTcuHFDTMTOnz+PyMhIudc9efIEAQEBCAgIAPBu3NSoUQN169ZFrVq1ULNmTTg6OvKPPsUMvzmQStHS0sKGDRtQt25dZGVl4bfffkP79u1zvbki0eekpqaiR48e4m5VADBr1ixMmDCBu9uVUPr6+vDz88PgwYMxdepUrF27Vvxrdq9evTB37lzMnDkTPj4+HCMlTEZGBg4dOoRNmzZh//79SE9Pz9GmTp066NmzJ7p27QozMzMlRElFhZaWlriL4nsvXrwQk7ALFy7g4sWL4vXEwLs/BF69ehVXr14Vy9TV1eHg4ICaNWuiRo0a4k8m80UXEy9SOW5ubpgwYQJ+++03ZGZmok+fPrh06RK326U8e/XqFby9vXH27FkA72Y81qxZg969eys5MioKrKyssHr1aowYMQLjxo3D4cOHAby7hqdDhw5wc3PDb7/9hpYtWzIBU2HZ2dk4c+YMNm3ahH///Rdv3rzJ0aZSpUro0aMHevTowQ1Z6LPMzMzg5eUFLy8vAO8SrfDwcLlZsY/vLZaVlYXQ0FCEhoZi06ZNYrmVlRVq1KiBatWqwcHBAfb29nBwcEDp0qW/+fsieUy8SCVNmTIF+/btw82bN3Hz5k389ttvmDFjhrLDomIgOjoanp6eiIiIAPBuliMgIACenp5KjoyKGmdnZxw6dAhHjx7FpEmTcOHCBQDAlStX0Lp1azRo0ACzZs1Co0aNlBwpFaT3m2Rs3rwZ0dHROepNTU3xww8/oGfPnqhduzaTb8oXdXV1ODk5wcnJCQMHDgQAJCYm4sqVK+KW9devX0dYWBgyMzPlXvv06VM8ffoUhw4dkis3MzMTkzB7e3tUrVoVtra2qFChApcsfiNMvEglaWpqYv369ahTpw4yMzMxe/ZseHl5oXbt2soOjYqwu3fvokWLFuJNMi0sLBAYGAgXFxclR0ZFWfPmzdGsWTMcPHgQkydPFjdROH36NBo3bowWLVpgypQpTMCKsfebZGzevBnXr1/PUa+rq4vvv/8ePXr0QIsWLbipExUKQ0NDNG3aFE2bNhXL0tPTER4ejhs3buD69eviz9xmYF+8eIEXL17g1KlTOeqsrKxgZ2cHW1tb2NnZwcbGBmXLloWVlRXKli0LIyMj/hGhADDxIpXl4uKCSZMmwc/PD1lZWejZsyeuXr3KnegoVzdv3oSHhwdevHgB4N0SoeDgYFSoUEG5gVGxIJFI0K5dO7Rp0wYBAQGYOnUq7ty5AwA4cuQIjhw5goYNG2LSpEnw9PTkF5hi4P0mGZs2bcKJEydy3STD09MTPXr0QPv27aGvr6+kSKkk09LSQs2aNVGzZk306dMHwLudFJ88eYLw8HDcuXMH4eHh4vPY2Nhc+3k/S/bhzoof0tbWFpMwCwsLGBsb5/ooXbo09PX1oaenBz09vUL5I4QgCMjIyEBSUhJSU1OL1R86mHiRSps0aRICAwNx6dIl3L17F6NHj8bKlSuVHRYVMefPn0fr1q0RHx8PAKhevTqCgoJgbm6u3MCo2FFTU0Pnzp3x/fffY8uWLZg+fTqioqIAACEhIWjVqhVq1aqFyZMnw8vLizfFLWLS09MRGBiIzZs348CBA5/dJKNLly78fwQVSRKJBOXKlUO5cuXg4eEhV/fmzRtEREQgPDwc9+/fR1RUFCIjIxEVFSX+4TE3aWlpiIyMzLH74pdoampCT08P+vr60NXVhYaGhvhQV1cXn6upqSErK0vukZmZiaysLMhkMqSmpiI1NRUpKSlISUkRb1K9bNkyDBs2TPEPSUmYeJFKk0ql2LRpE1xcXJCSkoK//voLbdq0Ee86T3T06FG0b98eycnJAAB3d3cEBgbyImT6KhoaGujduze6d++OrVu3Yvbs2eIM2OXLl+Hj4wMHBweMGjUKPXv2hI6OjpIjLrmys7Nx6tQpbN68GTt37hT/APMhbpJBqqJ06dLi/cE+lpSUhIcPHyIyMhIxMTF48uSJOBP2/nlu/318TkZGBjIyMnJd+lgQUlJSCqXfwsLEi1RelSpVsGTJEgwaNAgAMGDAANy6dQsWFhZKjoyUbe/evejSpYt4I8tmzZph7969XDJEBUZDQwO9evVC9+7dsXv3bvz222/iNWDh4eEYNGgQJk6ciKFDh+Knn37i/5e+kf9r796joq4T/48/B1QEuZXinRQyUPMCKioqiaCiqatlrXm3cjdNbY3K9Nt+tbVW8Lgdaysvx3W9raSu39RSDBE1UfAKk9clr0uWIObKXUGY3x8e57dkmRTDZwZfj3PmCO/5zMxr6H2C13w+n/fHYrFw7Ngx4uLi+OSTT6zndf63hg0b8txzzzF69GgtkiEPBHd3d+uCHj+lqKiI7Oxsrl27xvfff3/X7fr16xQWFlJQUFDh38LCQoqKiqx7su7cfoqTk1OFvWJubm64urpa/3V1daWwsJDmzZvb4kdhMype8kCYOHEi27ZtY8uWLVy9epUXXniBbdu26RfpA2zt2rWMHz+esrIyAH7zm9+wfv16rewkNuHs7MwzzzzD8OHDiY+PZ/78+SQnJwNw9epV3nnnHebPn8+oUaN4+eWX6dKli/7/VMUsFgtms5mNGzfyz3/+kzNnzty1Tb169Xj66acZPXo0kZGRulC6yA+4ubnh5+eHn5/fr34ui8VCeXm59ZBCZ2dn6+3n/v9XWlpKfHw8Tz755K/OUZ10cLk8EEwmE8uWLbN+mrx9+3YWLVpkcCoxyuLFixk7dqy1dI0ePZqNGzeqdInNmUwmBg0axN69ezl8+DCjRo3C2dkZuH1Izp3VWDt16sSSJUvIy8szOLFjs1gsHD16lJkzZ/LYY4/RqVMn5s2bV6F01apVi0GDBhEXF0d2djarV68mKipKpUvExkwmE87Ozri4uODm5oaLiwu1atWq0R86qXjJA8PHx4cVK1ZYv3/99dc5deqUgYnECLGxsbz88svWFcomTZrE6tWrHWpVJKkZunTpwtq1a7lw4QIzZszAy8vLep/ZbGby5Mk0adKEiRMnkpqaeteqevLjysrKSElJYcaMGTz66KN06dKF+fPnc+7cOes2Tk5O9OnTh0WLFnH58mW2bt3KyJEjteqtiNiUipc8UAYMGMC0adOA2yv0jBo1ihs3bhicSqqDxWJh1qxZzJo1yzr25ptvsmjRIq0sJ4by9fVl/vz5XLp0ib/97W907drVel9RURHLly+nR48etGrVirfeeouTJ08amNY+5ebmsmHDBsaNG0ejRo3o2bMnCxYssK4oCbfLVkREBIsXL+a7775j165dTJ48mQYNGhiYXEQeJPprQx448+fPp23btgB89dVXREdHG5xIbK28vJypU6cSGxtrHYuJiSE2NrZGH9IgjsXd3Z0XX3yRgwcPkp6ezuTJk/Hw8LDef/78eebNm0e7du3o0KEDsbGxP3qe0oPAYrFw8uRJFi5cSEREBA0aNGDEiBGsWbOG77//3rqds7Mzffv2ZenSpWRlZZGUlMSkSZO0DLyIGELFSx44rq6urFu3zno+z+LFi9mwYYPBqcRWbt26xfjx4yuc0/fxxx8zc+ZMA1OJ3FtQUJD1MLgVK1bQr1+/Cntmjx8/zqxZswgICKB169bMmDGD5OTke64S5uguXrzI8uXLGTVqFE2aNKFdu3ZER0eze/fuCu/b3d2d4cOH8/e//52srCwSExP5/e9/j4+Pj4HpRUS0qqE8oNq3b8+HH37I7373O+D2qoedO3fm0UcfNTiZVKUbN27w3HPPsWXLFuD2p98rV65kzJgxBicTuT/16tVjwoQJTJgwgaysLDZs2MAnn3zCgQMHrNtkZGSwYMECFixYgJeXF+Hh4URGRhIREUHbtm0dcq/urVu3OH78OKmpqaSmprJ///4Khw3+kL+/P0OGDGHw4MGEhYXh4uJSjWlFRO6Pipc8sF588UV2795NXFwc+fn5/Pa3vyUlJUW/sGuIgoIChg0bRlJSEgB16tRh/fr1DBs2zNhgIr9Q48aNeeWVV3jllVc4f/48Gzdu5PPPPyclJYXy8nLg9rlOW7ZssX7Y4OPjQ/fu3enWrRvdu3cnJCQET09PI9/GXUpKSsjIyODYsWMcO3aMw4cPc+jQIetFzX+Mu7s7vXv3JjIykoEDBxIYGOiQBVNEHiwqXvLAMplMLFmyhCNHjvD111+TlpbGG2+8wV//+lejo8mv9J///IdBgwaRmpoK3L7uyJYtW+jbt6/ByUSqhr+/PzNmzGDGjBlcvXqV+Ph4tm7dyq5duyqc45STk8Pnn3/O559/bh1r2bKl9SKp7dq149FHH8XPz4+GDRvarLxYLBays7M5f/689XbmzBmOHz/OqVOnKC0tvefj69atS7du3YiMjCQyMpKQkBCtRCoiDkfFSx5oHh4ebNiwgW7dunHz5k0+/PBDwsPDefrpp42OJr9QdnY2UVFRfPXVVwB4e3sTHx9PaGiowclEbKNBgwaMGzeOcePGUV5ezvHjx0lKSiIpKYnU1FT+85//VNj+4sWLXLx4ka1bt1YYd3V1pWXLljRt2hQfHx98fHxo2LAh3t7euLm54ebmhqurKy4uLtYLn1osFsrKyigsLKSgoICCggKuX7/O0aNHWbNmDTk5OWRnZ5OZmUlxcfF9vydfX1969OhBaGgooaGhBAUFUadOnSr5eYmIGEXFSx54HTt25P3332fy5MkAvPDCCwQHB1fJVdmlemVmZtKvXz++/vprABo2bMiOHTvo2LGjwclEqoeTkxMdO3akY8eOREdHY7FYOHPmDAcPHuTAgQOkp6dz4sQJ8vPz73pscXExp0+f5vTp09WW19nZmdatW9OhQwfrLSgoiKZNm1ZbBhGR6uIwxevPf/4z27Ztw2w2U6dOHa5fv37XNpmZmUyePJndu3fj7u7O+PHjiYmJqXD1+T179hAdHc3Jkyfx9fXlj3/8IxMmTKi+NyJ26aWXXmL37t1s2LCB3Nxchg8fzv79+3F1dTU6mtynjIwM+vXrxzfffAPc/sR8586dBAQEGJxMxDgmk4mAgAACAgIYO3YscPuwv8zMTE6cOMGpU6e4cOGC9Xbx4kVu3rxZpRnc3d1p1qwZjz76KP7+/vj7++Pn54e/vz8BAQHWFWZFRGo6hyleJSUlPPvss4SGhrJ8+fK77i8rK2PQoEE0btyYlJQULl++zLhx46hduzbz5s0D4MKFCwwaNIhJkyaxdu1akpKSmDhxIk2aNCEqKqq635LYEZPJxLJly0hLS+Ps2bOkp6fz0ksvsWrVKp2w7QDS09OJiooiJycHgMcee4zExERatGhhcDIR+2MymWjRogUtWrRg0KBBFe6zWCzk5+dz5coVcnJyyMnJIS8vj6KiIuutpKQEk8mEyWTCyckJJycn3N3dcXd3p169etStW5evv/6aYcOG0axZM9zc3Ax6pyIi9sVhitef/vQnAFauXPmj9+/YsYNTp06xc+dOGjVqRFBQEO+88w5vvvkmb7/9NnXq1GHJkiX4+fnx3nvvAdCmTRv27dvHwoULVbwET09PNm3aRPfu3SksLGTNmjWEhIQwbdo0o6PJPSQnJzN48GDy8vKA24eOJiQk6AKpIr+AyWTC09MTT09PWrVq9Yue485CGS1bttQCGCIi/8VhitfPSU1NpX379hX+2IqKimLy5MmcPHmS4OBgUlNT71rVLCoqiunTp//k8968ebPCYRd3/rgrLS392VWYqsOdDPaQpSYIDAxk2bJljBo1CoDo6Ggef/xxwsLCDE5WNWrafPniiy8YMWKE9aT9Hj16sHnzZry9vWvMezRaTZszYnuaM1JZmjNSWfY0ZyqTocYUr6ysrLs+4b7zfVZW1j23ycvLo7i4+EfP54mJibHubftvO3bssKvDJxITE42OUGO4ubnx1FNPsWnTJm7dusXTTz/Ne++9R4MGDYyOVmVqwny5s7e6rKwMgODgYF555RVSUlIMTlYz1YQ5I9VLc0YqS3NGKsse5kxRUdF9b2to8Zo5cybz58+/5zanT5+mdevW1ZTobrNmzSI6Otr6fV5eHr6+vvTv398uLkJZWlpKYmIi/fr10yEdVah///4MGTKEpKQkcnNzWbx4MUlJSXZVtn+JmjJfli9fznvvvYfFYgFg+PDhrFq1SstN20BNmTNSfTRnpLI0Z6Sy7GnO3Dka7n4YWrxee+21n11R0N/f/76eq3Hjxhw6dKjCWHZ2tvW+O//eGfvvbTw9PX9y9ToXFxdcXFzuGq9du7bh/6H/m73lcXS1a9dm/fr1dOnShYsXL3L06FFeeOEF/vnPf+Lk5GR0vF/NkefLggULmDFjhvX7F198kaVLl+Ls7GxgqprPkeeMGENzRipLc0Yqyx7mTGVe39DidecCjVUhNDSUP//5z1y5coWGDRsCt3c/enp60rZtW+s28fHxFR6XmJioC6vKj6pfvz6fffYZPXv2JD8/n08//ZS33nqLmJgYo6M9kCwWC7Nmzaqwl/y1115jwYIFWnlSRERE7J7DfHSfmZmJ2WwmMzOTsrIyzGYzZrOZgoIC4PahYW3btmXs2LF89dVXJCQk8Mc//pEpU6ZY91hNmjSJ8+fPM2PGDP71r3+xaNEiNmzYwKuvvmrkWxM71r59e9avX2/dyxUbG8uKFSsMTvXgKS0tZfz48RVK17vvvqvSJSIiIg7DYYrX7NmzCQ4OZs6cORQUFBAcHExwcDBHjhwBwNnZma1bt+Ls7ExoaChjxoxh3LhxzJ071/ocfn5+bNu2jcTERDp27Mh7773H3/72Ny0lL/c0cOBAPvjgA+v3v//979mzZ49xgR4w+fn5DB48mDVr1gC3l7tetGgRb731lkqXiIiIOAyHWdVw5cqVP3kNrztatGhx16GEPxQeHk56enoVJpMHwdSpU8nIyOCjjz7i1q1bPPXUU+zdu5f27dsbHa1Gy87O5sknnyQtLQ2AunXrEhcXx1NPPWVwMhEREZHKcZg9XiJGW7hwIQMHDgTg+vXrREVFceHCBYNT1VxnzpyhR48e1tL10EMPsXPnTpUuERERcUgqXiL3qVatWqxfv56QkBAALl++TP/+/e9aKVN+vZSUFHr27Mn58+cB8PX1Zd++ffTs2dPgZCIiIiK/jIqXSCV4eHgQHx9PYGAgAGfPnmXgwIHk5uYanKzmWLt2LX369CEnJwe4vcBJamqqdXVSEREREUek4iVSSQ0aNGDHjh00b94cgPT0dIYNG0ZxcbHByRxbeXk5s2fPZsyYMZSUlAAQGRnJ3r17adasmcHpRERERH4dFS+RX+CRRx5hx44d1K9fH4A9e/bwm9/8hqKiIoOTOabi4mJGjhzJO++8Yx176aWX2L59O97e3sYFExEREakiKl4iv1CbNm2Ij4/Hw8MDgJ07dzJkyBCVr0rKysoiPDycDRs2ALeXi1+4cCGLFy82/Gr0IiIiIlVFxUvkV+jatSsJCQnW8rVr1y4GDx5MYWGhwckcw4EDB+jSpQuHDh0CwN3dnc8++4zp06frGl0iIiJSo6h4ifxKoaGh7NixA09PTwB2797N4MGDKSgoMDiZ/bJYLCxdupQnnniCb7/9Fri9cuH+/fsZPHiwwelEREREqp6Kl0gV6N69O4mJiXh5eQG3z/mKiIjgypUrBiezPzdu3GDixIlMmjSJ0tJSAMLCwjh06BAdOnQwOJ2IiIiIbah4iVSRrl27kpiYaF0M4vDhw/To0YOzZ88aG8yOnD17ll69evH3v//dOvaHP/yBpKQkGjdubGAyEREREdtS8RKpQiEhISQnJ1uXPz937hw9evSwnsP0IFu7di3BwcEcPXoUAFdXV/7xj3/w/vvvaxENERERqfFUvESqWLt27Thw4ADt2rUDICcnhz59+vDZZ58ZnMwYBQUFTJgwgTFjxljPe2vVqhWpqamMHj3a4HQiIiIi1UPFS8QGmjdvTnJyMr179wagqKiIoUOHMnfuXMrLyw1OV30OHDhA586dWbVqlXVs3LhxpKWl0bFjRwOTiYiIiFQvFS8RG/H29iYhIYHnnnvOOjZnzhyGDx9Obm6ugclsr7i4mDfeeIOePXvy9ddfA7eXil+zZg2rVq2yLr8vIiIi8qBQ8RKxIRcXF+Li4oiNjbVel2rz5s0EBwdz8OBBg9PZRkpKCkFBQfzlL3+x7t0LCQkhLS2NMWPGGJxORERExBgqXiI2ZjKZePPNN4mPj7eueHjhwgV69epFbGwsZWVlxgasIt9//z0vv/wyvXr1su7lqlOnDrGxsaSkpPDYY48ZnFBERETEOCpeItVkwIABpKen0717dwBu3brFrFmz6NmzJ6dOnTI43S9XVlbGkiVLCAgIYPHixVgsFgC6detGeno6b775JrVq1TI4pYiIiIixVLxEqlHLli3Zu3cvb731lvXQw4MHDxIcHMzcuXO5ceOGwQkrZ8+ePYSEhDB58mSuXbsG3D6Xa8GCBezfv5+2bdsanFBERETEPqh4iVSz2rVr8+6777J3714CAgIAKCkpYc6cObRp04ZPP/3UutfIXu3fv5/IyEj69OlDenq6dXz06NFkZGTw+uuv4+zsbGBCEREREfui4iVikF69emE2m5k5c6a1pFy8eJHhw4fTu3dvdu/ebVcFzGKxkJKSQlRUFL169WLXrl3W+4KCgkhOTuYf//gHTZs2NTCliIiIiH1S8RIxkKurKzExMZjNZiIjI63jycnJREREEB4eTnx8vKHX/iopKSEuLo7u3bvTs2dPduzYYb2vVatWrFmzhiNHjtCrVy/DMoqIiIjYOxUvETvQrl07EhMT2bx5M4GBgdbxvXv3MmjQIAIDA1m4cCE5OTnVksdisWA2m5k+fTrNmjVj9OjRHDp0yHq/n58fK1as4PTp04wZM0aHFYqIiIj8DBUvETthMpkYOnQoJ0+eZO3atRUK2NmzZ4mOjqZJkyZERUWxfPlyvv322yp9/dLSUvbt28cbb7xBYGAgwcHBfPDBB1y9etW6TVBQECtWrCAjI4MJEyZotUIRERGR+6S/mkTsjLOzM6NGjWLEiBFs3bqVjz76iJ07dwK3l27fsWOH9XC/Nm3aEB4eTqdOnQgODqZ169bUq1fvZ1/j1q1bXLhwgePHj3Ps2DH2799PamoqRUVFd23r4uLCsGHDePnllwkLC7OuxigiIiIi90/FS8ROOTs7M3ToUIYOHcrp06dZvXo169at4+LFi9ZtTp8+zenTpys87uGHH8bX1xdvb2/c3NyoW7cuJSUlFBcXk5uby/nz58nNzb3neWPOzs6EhYUxYsQIRowYwUMPPWSrtykiIiLyQFDxEnEAbdq0ISYmhnnz5nHw4EHi4+NJTEzk0KFDdxWoa9euWa+pVRm+vr707t2bvn37MnjwYOrXr19V8UVEREQeeCpeIg7EZDLRvXt3unfvzty5c8nNzSU9PZ309HTMZjMXL14kMzOTS5cucevWrbse7+TkhJeXF/7+/rRs2ZL27dvTvn17OnXqRMuWLav/DYmIiIg8IFS8RByYl5cX4eHhhIeHVxi3WCzcvHmTwsJCbty4gYuLC66urjg7O5OQkMCTTz5J7dq1jQktIiIi8gBS8RKpgUwmE3Xr1qVu3boVxktLSw1KJCIiIvJg03LyIiIiIiIiNqbiJSIiIiIiYmMqXiIiIiIiIjam4iUiIiIiImJjKl4iIiIiIiI2puIlIiIiIiJiYypeIiIiIiIiNqbiJSIiIiIiYmMqXiIiIiIiIjam4iUiIiIiImJjKl4iIiIiIiI2puIlIiIiIiJiYypeIiIiIiIiNqbiJSIiIiIiYmMqXiIiIiIiIjam4iUiIiIiImJjKl4iIiIiIiI2VsvoAI7GYrEAkJeXZ3CS20pLSykqKiIvL4/atWsbHUfsnOaLVJbmjFSW5oxUluaMVJY9zZk7neBOR7gXFa9Kys/PB8DX19fgJCIiIiIiYg/y8/Px8vK65zYmy/3UM7EqLy/nu+++w8PDA5PJZHQc8vLy8PX15ZtvvsHT09PoOGLnNF+ksjRnpLI0Z6SyNGeksuxpzlgsFvLz82natClOTvc+i0t7vCrJycmJ5s2bGx3jLp6enoZPPHEcmi9SWZozUlmaM1JZmjNSWfYyZ35uT9cdWlxDRERERETExlS8REREREREbEzFy8G5uLgwZ84cXFxcjI4iDkDzRSpLc0YqS3NGKktzRirLUeeMFtcQERERERGxMe3xEhERERERsTEVLxERERERERtT8RIREREREbExFS8REREREREbU/FyYB9//DEtW7akbt26dOvWjUOHDhkdSezY3r17GTJkCE2bNsVkMrF582ajI4kdi4mJISQkBA8PDxo2bMiwYcPIyMgwOpbYscWLF9OhQwfrBU1DQ0PZvn270bHEQcTGxmIymZg+fbrRUcSOvf3225hMpgq31q1bGx3rvql4Oaj169cTHR3NnDlzSEtLo2PHjkRFRXHlyhWjo4mdKiwspGPHjnz88cdGRxEH8OWXXzJlyhQOHDhAYmIipaWl9O/fn8LCQqOjiZ1q3rw5sbGxHD16lCNHjhAREcHQoUM5efKk0dHEzh0+fJilS5fSoUMHo6OIA3j88ce5fPmy9bZv3z6jI903LSfvoLp160ZISAgfffQRAOXl5fj6+jJt2jRmzpxpcDqxdyaTiU2bNjFs2DCjo4iDyMnJoWHDhnz55Zc88cQTRscRB/Hwww+zYMECXnzxRaOjiJ0qKCigU6dOLFq0iHfffZegoCDef/99o2OJnXr77bfZvHkzZrPZ6Ci/iPZ4OaCSkhKOHj1K3759rWNOTk707duX1NRUA5OJSE2Vm5sL3P5DWuTnlJWVsW7dOgoLCwkNDTU6jtixKVOmMGjQoAp/04jcy5kzZ2jatCn+/v6MHj2azMxMoyPdt1pGB5DKu3r1KmVlZTRq1KjCeKNGjfjXv/5lUCoRqanKy8uZPn06PXv2pF27dkbHETt2/PhxQkNDuXHjBu7u7mzatIm2bdsaHUvs1Lp160hLS+Pw4cNGRxEH0a1bN1auXElgYCCXL1/mT3/6E2FhYZw4cQIPDw+j4/0sFS8REbmnKVOmcOLECYc6jl6MERgYiNlsJjc3l40bNzJ+/Hi+/PJLlS+5yzfffMMf/vAHEhMTqVu3rtFxxEEMHDjQ+nWHDh3o1q0bLVq0YMOGDQ5xSLOKlwNq0KABzs7OZGdnVxjPzs6mcePGBqUSkZpo6tSpbN26lb1799K8eXOj44idq1OnDq1atQKgc+fOHD58mA8++IClS5canEzszdGjR7ly5QqdOnWyjpWVlbF3714++ugjbt68ibOzs4EJxRF4e3sTEBDA2bNnjY5yX3SOlwOqU6cOnTt3JikpyTpWXl5OUlKSjqUXkSphsViYOnUqmzZtYteuXfj5+RkdSRxQeXk5N2/eNDqG2KHIyEiOHz+O2Wy23rp06cLo0aMxm80qXXJfCgoKOHfuHE2aNDE6yn3RHi8HFR0dzfjx4+nSpQtdu3bl/fffp7CwkOeff97oaGKnCgoKKnwidOHCBcxmMw8//DCPPPKIgcnEHk2ZMoW4uDi2bNmCh4cHWVlZAHh5eeHq6mpwOrFHs2bNYuDAgTzyyCPk5+cTFxfHnj17SEhIMDqa2CEPD4+7zhmtV68e9evX17mk8pNef/11hgwZQosWLfjuu++YM2cOzs7OjBw50uho90XFy0GNGDGCnJwcZs+eTVZWFkFBQXzxxRd3LbghcseRI0fo06eP9fvo6GgAxo8fz8qVKw1KJfZq8eLFAISHh1cYX7FiBRMmTKj+QGL3rly5wrhx47h8+TJeXl506NCBhIQE+vXrZ3Q0EakhLl26xMiRI/n+++/x8fGhV69eHDhwAB8fH6Oj3Rddx0tERERERMTGdI6XiIiIiIiIjal4iYiIiIiI2JiKl4iIiIiIiI2peImIiIiIiNiYipeIiIiIiIiNqXiJiIiIiIjYmIqXiIiIiIiIjal4iYiIiIiI2JiKl4iI1CgTJkxg2LBhhr3+2LFjmTdvXrW81syZM5k2bVq1vJaIiPw6JovFYjE6hIiIyP0wmUz3vH/OnDm8+uqrWCwWvL29qyfUf/nqq6+IiIjg3//+N+7u7jZ/vatXr+Lv74/ZbMbf39/mryciIr+cipeIiDiMrKws69fr169n9uzZZGRkWMfc3d2rpfD8lIkTJ1KrVi2WLFlSba/57LPP0rJlSxYsWFBtrykiIpWnQw1FRMRhNG7c2Hrz8vLCZDJVGHN3d7/rUMPw8HCmTZvG9OnTeeihh2jUqBHLli2jsLCQ559/Hg8PD1q1asX27dsrvNaJEycYOHAg7u7uNGrUiLFjx3L16tWfzFZWVsbGjRsZMmRIhfFFixbx2GOPUbduXRo1asQzzzxjva+8vJyYmBj8/PxwdXWlY8eObNy4scLjT548yeDBg/H09MTDw4OwsDDOnTtnvX/IkCGsW7ful/w4RUSkGql4iYhIjbdq1SoaNGjAoUOHmDZtGpMnT+bZZ5+lR48epKWl0b9/f8aOHUtRUREA169fJyIiguDgYI4cOcIXX3xBdnY2v/3tb3/yNY4dO0Zubi5dunSxjh05coRXXnmFuXPnkpGRwRdffMETTzxhvT8mJobVq1ezZMkSTp48yauvvsqYMWP48ssvAfj222954okncHFxYdeuXRw9epQXXniBW7duWZ+ja9euXLp0iYsXL1bxT01ERKqSDjUUERGHtHLlSqZPn87169crjE+YMIHr16+zefNm4PYer7KyMpKTk4Hbe6a8vLx4+umnWb16NXD7EMYmTZqQmppK9+7deffdd0lOTiYhIcH6vJcuXcLX15eMjAwCAgLuyrN582aeeeYZSktLreeiffrppzz//PNcunQJDw+PCtvfvHmThx9+mJ07dxIaGmodnzhxIkVFRcTFxfE///M/rFu3joyMDGrXrv2jP4e8vDy8vLzYs2cPvXv3rtwPUUREqk0towOIiIjYWocOHaxfOzs7U79+fdq3b28da9SoEQBXrlwBbi+SsXv37h89X+zcuXM/WryKi4txcXGpsABIv379aNGiBf7+/gwYMIABAwbw1FNP4ebmxtmzZykqKqJfv34VnqekpITg4GAAzGYzYWFhP1m6AFxdXQGse+tERMQ+qXiJiEiN98PiYjKZKozdKUvl5eUAFBQUMGTIEObPn3/XczVp0uRHX6NBgwYUFRVRUlJCnTp1APDw8CAtLY09e/awY8cOZs+ezdtvv83hw4cpKCgAYNu2bTRr1qzCc7m4uAD/v1Tdy7Vr1wDw8fH52W1FRMQ4Kl4iIiI/0KlTJ/7v//6Pli1bUqvW/f2qDAoKAuDUqVPWrwFq1apF37596du3L3PmzMHb25tdu3bRr18/XFxcyMzM/MlDBDt06MCqVasoLS39yb1eJ06coHbt2jz++OOVeo8iIlK9tLiGiIjID0yZMoVr164xcuRIDh8+zLlz50hISOD555+nrKzsRx/j4+NDp06d2Ldvn3Vs69at/PWvf8VsNvPvf/+b1atXU15eTmBgIB4eHrz++uu8+uqrrFq1inPnzpGWlsaHH37IqlWrAJg6dSp5eXk899xzHDlyhDNnzrBmzZoKS+gnJycTFhZ2X3vHRETEOCpeIiIiP9C0aVP2799PWVkZ/fv3p3379kyfPh1vb2+cnH76V+fEiRNZu3at9Xtvb28+/fRTIiIiaNOmDUuWLOGTTz6x7p165513+N///V9iYmJo06YNAwYMYNu2bfj5+QFQv359du3aRUFBAb1796Zz584sW7aswt6vdevW8bvf/c5GPwkREakqWtVQRESkihQXFxMYGMj69esrrFRoK9u3b+e1117j2LFj931IpIiIGEN7vERERKqIq6srq1evvueFlqtSYWEhK1asUOkSEXEA2uMlIiIiIiJiY9rjJSIiIiIiYmMqXiIiIiIiIjam4iUiIiIiImJjKl4iIiIiIiI2puIlIiIiIiJiYypeIiIiIiIiNqbiJSIiIiIiYmMqXiIiIiIiIjam4iUiIiIiImJj/w+JCm/T/tVWaAAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(10, 6))\n", + "plt.plot(tspan, np.degrees(x[:, 0]), 'k', linewidth=2, label=r'$\\theta_1$ (degrees)')\n", + "plt.plot(tspan, np.degrees(x[:, 1]), '-.k', linewidth=2, label=r'$\\theta_2$ (degrees)')\n", + "plt.grid(True)\n", + "plt.xlabel('Time (sec)')\n", + "plt.ylabel('State Variables (degrees)')\n", + "plt.legend()\n", + "plt.title('2R Robot Simulation')\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.12.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Chapter3/robot_solver.py b/Chapter3/robot_solver.py new file mode 100644 index 0000000..aa9b3f4 --- /dev/null +++ b/Chapter3/robot_solver.py @@ -0,0 +1,65 @@ +# Import necessary libraries +import numpy as np +from scipy.integrate import odeint +import matplotlib.pyplot as plt + +# Define the model of the 2R Robot +def robot_model(x, t): + g = 9.81 + l1 = 1.0 + l2 = 0.5 + m1 = 2.0 + m2 = 1.0 + I1 = 1e-2 + I2 = 5e-3 + D = 2.0 + + # Define the state variables + theta1, theta2, omega1, omega2 = x + + M = np.zeros((2, 2)) + M[0, 0] = m1 * (l1 / 2) ** 2 + m2 * (l1 ** 2 + (l2 / 2) ** 2) + m2 * l1 * l2 * np.cos(theta2) + I1 + I2 + M[0, 1] = m2 * (l2 / 2) ** 2 + 0.5 * m2 * l1 * l2 * np.cos(theta2) + I2 + M[1, 0] = M[0, 1] + M[1, 1] = m2 * (l2 / 2) ** 2 + I2 + + V = np.zeros((2, 1)) + V[0, 0] = -m2 * l1 * l2 * np.sin(theta2) * omega1 * omega2 - 0.5 * m2 * l1 * l2 * np.sin(theta2) * omega2 ** 2 + V[1, 0] = -0.5 * m2 * l1 * l2 * np.sin(theta2) * omega1 * omega2 + + G = np.zeros((2, 1)) + G[0, 0] = (m1 * l1 / 2 + m2 * l1) * g * np.cos(theta1) + m2 * g * l2 / 2 * np.cos(theta1 + theta2) + G[1, 0] = m2 * g * l2 / 2 * np.cos(theta1 + theta2) + + Q = np.zeros((2, 1)) # No input + Q = Q - D * np.array([[omega1], [omega2]]) + + xy = np.linalg.pinv(M) @ (Q - V - G) + + xp = np.zeros(4) + xp[0] = omega1 + xp[1] = omega2 + xp[2] = xy[0, 0] + xp[3] = xy[1, 0] + + return xp + +# Initial conditions: [theta1, theta2, omega1, omega2] +x0 = [-np.pi/3, np.pi/3, 0, 0] # Initial state + +# Time vector for the simulation +tspan = np.linspace(0, 5, 500) # From 0 to 5 seconds, 500 points + +# Solve the system of ODEs +x = odeint(robot_model, x0, tspan) + +# Plot state variables in degrees +plt.figure(figsize=(10, 6)) +plt.plot(tspan, np.degrees(x[:, 0]), 'k', linewidth=2, label=r'$\theta_1$ (degrees)') +plt.plot(tspan, np.degrees(x[:, 1]), '-.k', linewidth=2, label=r'$\theta_2$ (degrees)') +plt.grid(True) +plt.xlabel('Time (sec)') +plt.ylabel('State Variables (degrees)') +plt.legend() +plt.title('2R Robot Simulation') +plt.show() diff --git a/Chapter3/tank_model.ipynb b/Chapter3/tank_model.ipynb new file mode 100644 index 0000000..618a2c6 --- /dev/null +++ b/Chapter3/tank_model.ipynb @@ -0,0 +1,67 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Import necessary libraries" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the model of the tank" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "def tank_model(x, t):\n", + " A = 1.0\n", + " C = 2.0\n", + " F_in = 0.0 # No disturbance input\n", + " u = 0.1 # Constant opening for valve\n", + " \n", + " x = np.maximum(x, 0) # Ensure tank level is non-negative\n", + " \n", + " xp = (F_in - C * u * np.sqrt(x)) / A\n", + " \n", + " return xp" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.12.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Chapter3/tank_model.py b/Chapter3/tank_model.py new file mode 100644 index 0000000..f83f972 --- /dev/null +++ b/Chapter3/tank_model.py @@ -0,0 +1,15 @@ +# Import necessary libraries +import numpy as np + +# Define the model of the tank +def tank_model(x, t): + A = 1.0 + C = 2.0 + F_in = 0.0 # No disturbance input + u = 0.1 # Constant opening for valve + + x = np.maximum(x, 0) # Ensure tank level is non-negative + + xp = (F_in - C * u * np.sqrt(x)) / A + + return xp \ No newline at end of file diff --git a/Chapter3/tank_solver.ipynb b/Chapter3/tank_solver.ipynb new file mode 100644 index 0000000..84ea55d --- /dev/null +++ b/Chapter3/tank_solver.ipynb @@ -0,0 +1,150 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Import necessary libraries" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from scipy.integrate import odeint\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the model of the tank" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "def tank_model(x, t):\n", + " A = 1.0\n", + " C = 2.0\n", + " F_in = 0.0 # No disturbance input\n", + " u = 0.1 # Constant opening for valve\n", + " \n", + " x = np.maximum(x, 0) # Ensure tank level is non-negative\n", + " \n", + " xp = (F_in - C * u * np.sqrt(x)) / A\n", + " \n", + " return xp" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Initial condition: Tank level" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "x0 = [100.0] # Initial level of the tank" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Time vector for the simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "tspan = np.linspace(0, 100, 1000) # From 0 to 100 seconds, 1000 points" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Solve the system of ODEs" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "x = odeint(tank_model, x0, tspan)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Plot the results" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(10, 6))\n", + "plt.plot(tspan, x, 'k', linewidth=2)\n", + "plt.grid(True)\n", + "plt.xlabel('Time (sec)')\n", + "plt.ylabel('Tank Level (m)')\n", + "plt.title('Tank Model Simulation')\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.12.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Chapter3/tank_solver.py b/Chapter3/tank_solver.py new file mode 100644 index 0000000..d6a1caa --- /dev/null +++ b/Chapter3/tank_solver.py @@ -0,0 +1,35 @@ +# Import necessary libraries +import numpy as np +from scipy.integrate import odeint +import matplotlib.pyplot as plt + +# Define the model of the tank +def tank_model(x, t): + A = 1.0 + C = 2.0 + F_in = 0.0 # No disturbance input + u = 0.1 # Constant opening for valve + + x = np.maximum(x, 0) # Ensure tank level is non-negative + + xp = (F_in - C * u * np.sqrt(x)) / A + + return xp + +# Initial condition: Tank level +x0 = [100.0] # Initial level of the tank + +# Time vector for the simulation +tspan = np.linspace(0, 100, 1000) # From 0 to 100 seconds, 1000 points + +# Solve the system of ODEs +x = odeint(tank_model, x0, tspan) + +# Plot the results +plt.figure(figsize=(10, 6)) +plt.plot(tspan, x, 'k', linewidth=2) +plt.grid(True) +plt.xlabel('Time (sec)') +plt.ylabel('Tank Level (m)') +plt.title('Tank Model Simulation') +plt.show() diff --git a/Chapter3/train.ipynb b/Chapter3/train.ipynb new file mode 100644 index 0000000..c29487d --- /dev/null +++ b/Chapter3/train.ipynb @@ -0,0 +1,241 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Import necessary libraries" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy import signal" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the state-space matrices" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "A = np.array([\n", + " [0, 0, 0, 0, 0, 1, 0, 0, 0, 0],\n", + " [0, 0, 0, 0, 0, 1, -1, 0, 0, 0],\n", + " [0, 0, 0, 0, 0, 0, 1, -1, 0, 0],\n", + " [0, 0, 0, 0, 0, 0, 0, 1, -1, 0],\n", + " [0, 0, 0, 0, 0, 0, 0, 0, 1, -1],\n", + " [0, -12.5, 0, 0, 0, -0.75, 0.75, 0, 0, 0],\n", + " [0, 62.5, -62.5, 0, 0, 3.75, -7.5, 3.75, 0, 0],\n", + " [0, 0, 62.5, -62.5, 0, 0, 3.75, -7.5, 3.75, 0],\n", + " [0, 0, 0, 62.5, -62.5, 0, 0, 3.75, -7.5, 3.75],\n", + " [0, 0, 0, 0, 62.5, 0, 0, 0, 3.75, -3.75]\n", + "])\n", + "b1 = np.array([0, 0, 0, 0, 0.005, 0, 0, 0, 0, 0]).reshape(-1, 1)\n", + "b2 = np.array([0, 0, 0, 0, 250, 0, 0, 0, 0, -1250]).reshape(-1, 1)\n", + "B = np.hstack((b1, b2))\n", + "C = np.array([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]).reshape(1, -1)\n", + "D = np.array([0])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Create the state-space model using signal.StateSpace" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "train_model = signal.StateSpace(A, b1, C, D) # Note only first input is used" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Time vector for simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "t = np.arange(0, 7, 0.01)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Initial conditions for simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "x0 = np.array([20, 20, 20, 20, 20, 0, 0, 0, 0, 0])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Simulate the initial response using initial_response method" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "t_initial, y_initial, x_initial = signal.lsim(train_model, U=np.zeros_like(t), T=t, X0=x0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Plot initial response" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(10, 6))\n", + "plt.plot(t_initial, x_initial[:, 0], 'k', label='x1')\n", + "plt.plot(t_initial, x_initial[:, 4], '-.k', label='x5')\n", + "plt.grid(True)\n", + "plt.xlabel('Time (sec)')\n", + "plt.ylabel('State Variables')\n", + "plt.legend()\n", + "plt.title('Initial Response of Train Model')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Generate input signal u(t)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "u = 0.1 * (np.sin(5 * t) + np.sin(9 * t) + np.sin(13 * t) + np.sin(17 * t) + np.sin(21 * t))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Simulate the system response to input signal using lsim function" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "t_response, y_response, x_response = signal.lsim(train_model, U=u, T=t, X0=np.zeros_like(x0))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Plot the response to input signal" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(10, 6))\n", + "plt.plot(t_response, x_response[:, 0], 'k', label='x1')\n", + "plt.plot(t_response, x_response[:, 1], '-.k', label='x2')\n", + "plt.grid(True)\n", + "plt.xlabel('Time (sec)')\n", + "plt.ylabel('State Variables')\n", + "plt.legend()\n", + "plt.title('Response of Train Model to Input Signal')\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.12.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Chapter3/train.py b/Chapter3/train.py new file mode 100644 index 0000000..9500a6b --- /dev/null +++ b/Chapter3/train.py @@ -0,0 +1,63 @@ +# Import necessary libraries +import numpy as np +import matplotlib.pyplot as plt +from scipy import signal + +# Define the state-space matrices +A = np.array([ + [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 1, -1, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 1, -1, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 1, -1, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 1, -1], + [0, -12.5, 0, 0, 0, -0.75, 0.75, 0, 0, 0], + [0, 62.5, -62.5, 0, 0, 3.75, -7.5, 3.75, 0, 0], + [0, 0, 62.5, -62.5, 0, 0, 3.75, -7.5, 3.75, 0], + [0, 0, 0, 62.5, -62.5, 0, 0, 3.75, -7.5, 3.75], + [0, 0, 0, 0, 62.5, 0, 0, 0, 3.75, -3.75] +]) +b1 = np.array([0, 0, 0, 0, 0.005, 0, 0, 0, 0, 0]).reshape(-1, 1) +b2 = np.array([0, 0, 0, 0, 250, 0, 0, 0, 0, -1250]).reshape(-1, 1) +B = np.hstack((b1, b2)) +C = np.array([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]).reshape(1, -1) +D = np.array([0]) + +# Create the state-space model using signal.StateSpace +train_model = signal.StateSpace(A, b1, C, D) # Note only first input is used + +# Time vector for simulation +t = np.arange(0, 7, 0.01) + +# Initial conditions for simulation +x0 = np.array([20, 20, 20, 20, 20, 0, 0, 0, 0, 0]) + +# Simulate the initial response using initial_response method +t_initial, y_initial, x_initial = signal.lsim(train_model, U=np.zeros_like(t), T=t, X0=x0) + +# Plot initial response +plt.figure(figsize=(10, 6)) +plt.plot(t_initial, x_initial[:, 0], 'k', label='x1') +plt.plot(t_initial, x_initial[:, 4], '-.k', label='x5') +plt.grid(True) +plt.xlabel('Time (sec)') +plt.ylabel('State Variables') +plt.legend() +plt.title('Initial Response of Train Model') +plt.show() + +# Generate input signal u(t) +u = 0.1 * (np.sin(5 * t) + np.sin(9 * t) + np.sin(13 * t) + np.sin(17 * t) + np.sin(21 * t)) + +# Simulate the system response to input signal using lsim function +t_response, y_response, x_response = signal.lsim(train_model, U=u, T=t, X0=np.zeros_like(x0)) + +# Plot the response to input signal +plt.figure(figsize=(10, 6)) +plt.plot(t_response, x_response[:, 0], 'k', label='x1') +plt.plot(t_response, x_response[:, 1], '-.k', label='x2') +plt.grid(True) +plt.xlabel('Time (sec)') +plt.ylabel('State Variables') +plt.legend() +plt.title('Response of Train Model to Input Signal') +plt.show() diff --git a/Chapter3/train_linear.ipynb b/Chapter3/train_linear.ipynb new file mode 100644 index 0000000..d9f5192 --- /dev/null +++ b/Chapter3/train_linear.ipynb @@ -0,0 +1,242 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Import necessary libraries" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy import signal" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the state-space matrices" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "A = np.array([\n", + " [0, 0, 0, 0, 0, 1, 0, 0, 0, 0],\n", + " [0, 0, 0, 0, 0, 1, -1, 0, 0, 0],\n", + " [0, 0, 0, 0, 0, 0, 1, -1, 0, 0],\n", + " [0, 0, 0, 0, 0, 0, 0, 1, -1, 0],\n", + " [0, 0, 0, 0, 0, 0, 0, 0, 1, -1],\n", + " [0, -12.5, 0, 0, 0, -0.75, 0.75, 0, 0, 0],\n", + " [0, 62.5, -62.5, 0, 0, 3.75, -7.5, 3.75, 0, 0],\n", + " [0, 0, 62.5, -62.5, 0, 0, 3.75, -7.5, 3.75, 0],\n", + " [0, 0, 0, 62.5, -62.5, 0, 0, 3.75, -7.5, 3.75],\n", + " [0, 0, 0, 0, 62.5, 0, 0, 0, 3.75, -3.75]\n", + "])\n", + "b1 = np.array([0, 0, 0, 0, 0, 0.005, 0, 0, 0, 0]).reshape(-1, 1)\n", + "b2 = np.array([0, 0, 0, 0, 0, 250, 0, 0, 0, -1250]).reshape(-1, 1)\n", + "C = np.array([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]).reshape(1, -1)\n", + "D = np.array([0])\n", + "u = 750 # Constant input\n", + "b = u*b1 + b2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Create the state-space model using signal.StateSpace" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "train_model = signal.StateSpace(A, b2, C, D)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Time vector for simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "t = np.arange(0, 7, 0.001)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Initial conditions for simulation" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "x0 = np.array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Simulate the forced response using lsim function" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "t_initial, y_initial, x_initial = signal.lsim(train_model, U=np.ones_like(t), T=t, X0=x0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Plot initial response" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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8QFZWltT1tWrVgoqKSo5SywEBAVJDAiMjI3H69Gm4u7tDKBRCKBTC3d0dp0+fRkREBLffly9fcODAATRp0oQbephf379/zxG/JFmVxNezZ0+IRCIsWLAgx+2zsrJyLUMtIYvniCxJeoGy32fGGNauXavQOCQWLlyIOXPmYOzYsXnu07p1a6irq2PdunVScW/fvh0JCQlo3749AKB+/fowNjbG5s2bkZGRwe23a9euHG3Us2dPREVFwcfHJ8f5UlNTkZycXMR7RggpragniRBCACxfvhxt27aFi4sLhg4dypV3NjAwwNy5c397+8qVK2PWrFlYsGABmjZtim7dukFDQwMPHz6Eubk5Fi9eDH19fWzatAn9+/dHvXr10Lt3bxgbG+PDhw84f/48GjdujA0bNgAAFi9ejPbt26NJkyYYMmQIvn37hvXr16NGjRpISkoq9P20t7dHu3btsG3bNsyePRu2trZYuHAhZs6ciYiICHTp0gV6enoIDw/HyZMnMWLECEyZMgVXr17FmDFj0KNHD1StWhVZWVnYu3cvhEIhunfvLnWOmjVrwsPDQ6oEOPCzRLrEwoUL4efnhyZNmuDPP/+EqqoqtmzZgvT0dCxbtqzA92v37t3w9vZG165dYWtri8TERPj4+EBfX59LYJo3b46RI0di8eLFCA4Ohru7O9TU1PDmzRscPXoUa9euxR9//JHnOYr6HJGl6tWrw9bWFlOmTEFUVBT09fVx/PjxAs8nkpXmzZtz60PlxdjYGDNnzsS8efPQpk0bdOrUCaGhofD29oaTkxO38LGamhoWLlyIkSNHomXLlujVqxfCw8Oxc+fOHHOS+vfvjyNHjmDUqFG4du0aGjduDJFIhFevXuHIkSO4fPmyXBaQJoSUAvwU1SOEEMWRlJH+VXloxhjz9/dnjRs3ZlpaWkxfX5917NiRvXjxQmofSTnl2NjYXI+xY8cOVrduXaahocGMjIxY8+bNmZ+fn9Q+165dYx4eHszAwIBpamoyW1tbNmjQIKmy2Ywxdvz4cWZnZ8c0NDSYvb09O3HiBBs4cGC+S4DXqFEj1+uuX7/OALA5c+ZInatJkyZMR0eH6ejosOrVqzMvLy8WGhrKGGPs3bt3bMiQIczW1pZpamqyMmXKsBYtWjB/f3+pYwNgXl5ebN++faxKlSpMQ0OD1a1bl127di1HHI8fP2YeHh5MV1eXaWtrsxYtWrC7d+9K7ZNX20nKbEuO+/jxY9anTx9mZWXFNDQ0WPny5VmHDh1yPKaM/Swl7ejoyLS0tJienh6rVasWmzZtGvv06dPvHtZ8PUdkXQI8exnt7F68eMFat27NdHV1Wbly5djw4cO5Mt47d+7k9surBLiXl1eOY+anTHb2EuC/klfsGzZsYNWrV2dqamrMxMSEjR49mn3//j3Hft7e3szGxoZpaGiw+vXrs5s3b7LmzZtLlQBn7GfJ8KVLl7IaNWpwrztHR0c2b948lpCQUKD7RgghEgLGCjhDkxBCCMmDQCCAl5cX1yNGCCGEFEc0J4kQQgghhBBCsqEkiRBCCCGEEEKyoSSJEEIIIYQQQrKh6naEEEJkhqa5EkIIKQmoJ4kQQgghhBBCsqEkiRBCCCGEEEKyKfHD7cRiMT59+gQ9PT0IBAK+wyGEEEIIIYTwhDGGxMREmJubQ0Ul7/6iEp8kffr0CZaWlnyHQQghhBBCCFESkZGRsLCwyPP6Ep8k6enpAfj5QOjr6/MaS2ZmJnx9feHu7g41NTVeYyE/UZsoF2oP5UNtonyoTZQLtYfyoTZRPsrUJj9+/IClpSWXI+SlxCdJkiF2+vr6SpEkaWtrQ19fn/cnCPmJ2kS5UHsoH2oT5UNtolyoPZQPtYnyUcY2+d00HCrcQAghhBBCCCHZUJJECCGEEEIIIdlQkkQIIYQQQggh2ZT4OUmEEEIIIYSUFowxZGVlQSQS8R0KJzMzE6qqqkhLS5N7XEKhEKqqqkVe+oeSJEIIIYQQQkqAjIwMfP78GSkpKXyHIoUxBlNTU0RGRipk3VJtbW2YmZlBXV290MegJIkQQgghhJBiTiwWIzw8HEKhEObm5lBXV1dIQpIfYrEYSUlJ0NXV/eUCrkXFGENGRgZiY2MRHh6OKlWqFPp8lCQRQgghhBBSzGVkZEAsFsPS0hLa2tp8hyNFLBYjIyMDmpqack2SAEBLSwtqamp4//49d87CoMINhBBCCCGElBDyTkKKA1k8BvQoEkIIIYQQQkg2lCQRQgghhBBCSDaUJBFCCCGEEEJINpQkEUIIIYQQQpTSiRMn4ObmBmNjY+jr68PFxQWXL1+W+3kpSSKEEEIIIYQopZs3b8LNzQ0XLlxAYGAgWrRogY4dOyIoKEiu56US4IQQQgghhJRAjDFeFpbV1tbO9xpNsbGxqFWrFsaNG4e//voLAHD37l24urri4sWLWLNmjdT+//77L06fPo2zZ8+ibt26sg6dQ0kSIYQQQgghJVBKSgp0dXUVft6kpCTo6Ojka19jY2Ps2LEDXbp0gbu7O6pVq4b+/ftjzJgxaNWqVY79xWIxEhMTUaZMGVmHLYWSJEIIIYQQQghv2rVrh+HDh8PT0xP169eHjo4OFi9enOu+K1asQFJSEnr27CnXmChJIiVCXFwcgoKCoKKignr16sHIyIjvkAghhBBCeKWtrY2kpCRezltQK1asQM2aNXH06FEEBgZCQ0Mjxz4HDhzAvHnzcPr0aZQvX14WoeaJkiRSrMXHx2PKlCnYvXs3srKyAABqamoYNGgQlixZIveuWEIIIYQQZSUQCPI97I1vYWFh+PTpE8RiMSIiIlCrVi2p6w8dOoRhw4bh6NGjaN26tdzjoSSJFFsfP35EixYt8PbtWwBA1apVIRaL8fbtW/j4+MDf3x8XL15EtWrVeI6UEEIIIYTkJSMjA/369UOvXr1QrVo1DBs2DM+ePeN6iw4ePIghQ4bg0KFDaN++vUJiohLgpFiKj49Hq1at8PbtW1hbW+PmzZsIDQ3FmzdvcPPmTVSqVAnh4eFo2bIlIiMj+Q6XEEIIIYTkYdasWUhISMC6deswffp0VK1aFUOGDAHwc4jdgAEDsHLlSjRo0ADR0dGIjo5GQkKCXGOiJIkUO4wxDB8+HK9fv4aVlRVu3ryJpk2bctc3bdoUAQEBsLe3x6dPn9CpUyekp6fzGDEhhBBCCMnN9evXsWbNGuzduxf6+vpQUVHB3r17cevWLWzatAlbt25FVlYWvLy8YGZmxl3Gjx8v17houB0pdk6cOIFjx45BTU0NR48ehZWVVY59ypcvj4sXL8LR0RHBwcH4+++/sXz5ch6iJYQQQggheXF1dUVmZqbUtooVK3I9RaNHj+YjLOpJIsVLSkoKJk2aBACYPn06nJ2d89zXysoK27dvBwCsXLkSDx8+VEiMhBBCCCGkeKMkiRQrmzZtwocPH2BpaYmZM2f+dv9OnTrB09MTjDGMGzcOYrFYAVESQgghhJDijJIkUmykpaVh5cqVAIA5c+bkuwb/smXLoKuri3v37uHw4cPyDJEQQgghhJQAlCSRYmP37t34/PkzLCws0L9//3zfztzcHNOnTwcAzJ8/HyKRSF4hEkIIIYSQEoCSJFIsMMawbt06AMCUKVOgrq5eoNuPGzcORkZGePXqFY4ePSqPEAkhhBBCSAlBSRIpFgICAvDixQtoaWlh0KBBBb69vr4+Jk6cCABYuHAhGGMyjpAQQgghhJQUlCSRYsHHxwcA0LNnTxgYGBTqGOPGjYOuri6eP3+OK1euyDI8QgghhBBSglCSRJReYmIijhw5AgAYPnx4oY9jYGDA9UKtX79eFqERQgghhJASiJIkovTOnTuHlJQUVKlSBY0aNSrSscaMGQMAOHv2LN69eyeL8AghhBBCSAlDSRJRepJCCz169IBAICjSsapVqwYPDw8wxrBlyxZZhEcIIYQQQkoYSpKIUktKSsLFixcB/EySZGHkyJEAgL179yIrK0smxySEEEIIIbJ3/fp1CASCHJfo6Gi5nldVrkcnpIjOnTuHtLQ0VK5cGbVr15bJMdu3b4+yZcvi8+fP8Pf3l8kxCSGEEEKI/ISGhkJfX5/7u3z58nI9H/UkEaV26tQpAMAff/xR5KF2Eurq6vD09AQA7NmzRybHJIQQQghRVsnJyQW+ZB9tk5WVheTkZKSmpv72uAUVGxsLU1NT/Pvvv9y2u3fvQl1dXaoacfny5WFqaspdVFTkm8ZQkkSUVlZWFnx9fQEAHTt2lOmxJVXuzpw5g6SkJJkemxBCCCFEmejq6hb4cvLkSe72J0+ehK6uLtq2bSt13IoVK+a4XUEZGxtjx44dmDt3Lh49eoTExET0798fY8aMQatWrbj96tSpAzMzM7i5ueHOnTuFfzDyiZIkorQePHiA79+/w8jICA0aNJDpsevUqQMHBwdkZGTg7t27Mj02IYQQQgjJv3bt2mH48OHw9PTEqFGjoKOjg8WLFwMAzMzMsHnzZhw/fhzHjx+HpaUlXF1d8fjxY7nGRHOSiNKSFGxwd3eHUCiU6bEFAgF69+6Np0+fKuTXCEIIIYQQvhRm1IyGhgb3/65duyIpKSnHELeIiIiihsZZsWIFatasiaNHjyIwMJA7f7Vq1VCtWjVuv0aNGiEsLAyrV6/G3r17ZXb+/6KeJKK0JElSmzZt5HJ8SbW8Z8+eIS4uTi7nIIQQQgjhm46OToEvqqr/60tRVVWFjo4OtLS0fnvcwgoLC8OnT58gFot/m3w5Ozvj7du3hT5XfvCaJG3atAkODg7Q19eHvr4+XFxcuC/GAODq6pqj3N+oUaN4jJgoypcvXxAYGAhAfkmSpGKeWCzGmTNn5HIOQgghhBDyaxkZGejXrx969eqFBQsWYNiwYYiJiclz/+DgYJiZmck1Jl6H21lYWGDJkiWoUqUKGGPYvXs3OnfujKCgINSoUQMAMHz4cMyfP5+7jba2Nl/hEgW6du0aAKB27dowNTWV23m6d++OJ0+e4Pjx49z6SYQQQgghRHFmzZqFhIQErFu3Drq6urhw4QKGDBmCc+fOYc2aNbCxsUGNGjWQlpaGbdu24erVq1xxL3nhNUn6b8WyRYsWYdOmTbh37x6XJGlra8v1SzJRTjdu3ADwszdRnrp3745//vkHV69exdevX1G2bFm5no8QQgghhPzP9evXsWbNGly7do1bB2nv3r2oXbs2Nm3ahIyMDEyePBlRUVHQ1taGg4MD/P390aJFC7nGpTSFG0QiEY4ePYrk5GS4uLhw2/fv3499+/bB1NQUHTt2xOzZs3/Zm5Seno709HTu7x8/fgAAMjMzkZmZKb87kA+S8/MdR3Fw/fp1AEDjxo3l+nhVrFgRFStWREREBE6ePImBAwfK7Vzk9+g1onyoTZQPtYlyofZQPqW1TTIzM8EYg1gshlgs5jscKYwx7t//xtasWTPuu7vkOisrK3z//p3bZ8qUKTmO+av7KBaLwRhDZmZmjuJf+X1e8J4kPXv2DC4uLkhLS+Nqstvb2wMA+vbtC2tra5ibm+Pp06eYPn06QkNDceLEiTyPt3jxYsybNy/Hdl9fX6UZqufn58d3CEotPj4er169AgCkpaXhwoULcj1fgwYNEBERge3bt8PY2Fiu5yL5Q68R5UNtonyoTZQLtYfyKW1toqqqClNTUyQlJSEjI4PvcHKVmJiokPNkZGQgNTUVN2/elFoUFwBSUlLydQwBk6R2PMnIyMCHDx+QkJCAY8eOYdu2bbhx4waXKGV39epVtGrVCm/fvoWtrW2ux8utJ8nS0hJxcXFcFx5fMjMz4efnBzc3N6ipqfEaizI7fvw4+vTpgxo1aiAoKEiu58rMzMSmTZswZcoU6Orq4vPnz1IlL4li0WtE+VCbKB9qE+VC7aF8SmubpKWlITIyEhUrVoSmpibf4UhhjCExMRF6enoQCARyP19aWhoiIiJgaWmZ47H48eMHypUrh4SEhF/mBrz3JKmrq6Ny5coAAEdHRzx8+BBr167Fli1bcuwrWVD0V0mShoZGrl9y1dTUlOaFokyxKCPJukWurq4KeZwqVaoEMzMzfP78GXfv3oW7u7vcz0l+jV4jyofaRPlQmygXag/lU9raRCQSQSAQQEVFJcd6RnyTDI2TxCdvKioqEAgEuT4H8vucUK5HED8fxOw9QdkFBwcDgNxL/hF+Kapog4SKigratm0LADh37pxCzkkIIYQQQpQXr0nSzJkzcfPmTURERODZs2eYOXMmrl+/Dk9PT4SFhWHBggUIDAxEREQEzpw5gwEDBqBZs2ZwcHDgM2wiRz9+/EBISAgAoEmTJgo7b/v27QEAZ8+eBc8jUAkhhBBCCo2+x8jmMeB1uF1MTAwGDBiAz58/w8DAAA4ODrh8+TLc3NwQGRkJf39/rFmzBsnJybC0tET37t3x999/8xkykbOHDx+CMQZra2uFln5v2bIlNDQ0EBERgRcvXnAl6AkhhBBCigPJMLKUlBRoaWnxHA2/JMUZijLcktckafv27XleZ2lpyQ27IqXH/fv3AQANGzZU6Hl1dHTQqlUrXLhwAWfPnqUkiRBCCCHFilAohKGhIWJiYgD8XGtUEUUS8kMsFiMjIwNpaWlynZPEGENKSgpiYmJgaGiYo/x3QfBeuIGQ7CRJkqRIhyK1a9cOFy5cgK+vL2bMmKHw8xNCCCGEFIVkFI4kUVIWjDGkpqZCS0tLIYmboaFhkUckUZJElAZjDPfu3QPAT5IkqWp3+/ZtJCcnQ0dHR+ExEEIIIYQUlkAggJmZGcqXL69Ui+lmZmbi5s2baNasmdwrDqqpqRWpB0mCkiSiNN6/f4+YmBioqqqibt26Cj9/5cqVYW1tjffv3+PmzZtcxTtCCCGEkOJEKBTKJFGQFaFQiKysLGhqahabsuxKVwKclF6SoXa1a9fmZcKhQCDgepN8fX0Vfn5CCCGEEKIcKEkiSoOvog3Zubm5AQD8/Px4i4EQQgghhPCLkiSiNPgs2iDRsmVLCAQCPH/+HFFRUbzFQQghhBBC+ENJElEKIpEIwcHBAID69evzFkfZsmW58/v7+/MWByGEEEII4Q8lSUQpvH79GikpKdDW1kbVqlV5jUUy5I7mJRFCCCGElE6UJBGlIOlFcnBw4L0ai6R4g7+/PxhjvMZCCCGEEEIUj5IkohSCgoIAgJfS3//l4uICLS0txMTE4OXLl3yHQwghhBBCFIySJKIUlClJUldXR6NGjQAA169f5zcYQgghhBCicJQkEd4xxpQqSQIAV1dXAJQkEUIIIYSURpQkEd5FRUXh69evEAqFqFmzJt/hAJBOkmheEiGEEEJI6UJJEuGdpBfJzs4OmpqaPEfzk5OTE7S0tBAbG0vzkgghhBBCShlKkgjvlG2oHQBoaGhw85Ju3LjBczSEEEIIIUSRKEkivFPGJAmgeUmEEEIIIaUVJUmEd0+ePAEA1KlTh99A/oPmJRFCCCGElE6UJBFeJSUlITw8HABQq1YtnqOR5uTkBE1NTcTExODVq1d8h0MIIYQQQhSEkiTCK0lRBBMTE5QrV47naKRln5dEQ+4IIYQQQkoPSpIIr0JCQgBAaUp//xfNSyKEEEIIKX0oSSK8kiRJNWrU4DmS3DVr1gwAcOfOHZqXRAghhBBSSlCSRHj1/PlzAMrbk+Tk5ARVVVVERUXhw4cPfIdDCCGEEEIUgJIkwitlH26nra2NevXqAQBu377NczSEEEIIIUQRKEkivImPj0dUVBQAwN7enudo8ta4cWMAP4fcEUIIIYSQko+SJMIbyVA7S0tLGBgY8BxN3ihJIoQQQggpXShJIrxR9qF2EpIk6dmzZ0hISOA5GkIIIYQQIm+UJBHeSHqSlLWynYSpqSlsbW3BGENAQADf4RBCCCGEEDmjJInwprj0JAE05I4QQgghpDShJInwhpIkQgghhBCijChJIryIi4tDbGwsBAIB7Ozs+A7nt5o0aQIAuH//PjIzM3mOhhBCCCGEyBMlSYQXr169AgBYWVlBW1ub52h+r3r16jAyMkJKSgqCg4P5DocQQgghhMgRJUmEF6GhoQB+Jh/FgYqKCho1agSAhtwRQgghhJR0lCQRXkh6kqpVq8ZzJPlH85IIIYQQQkoHSpIILyQ9ScUpSZL0JN27d4/nSAghhBBCiDxRkkR4URyTpPr160NFRQUfP35EVFQU3+EQQgghhBA5oSSJKFxGRgbCwsIAFJ85SQCgo6ODWrVqAfhZ5Y4QQgghhJRMlCQRhXv37h1EIhF0dXVhbm7OdzgF0rBhQwA05I4QQgghpCSjJIkonKRoQ9WqVSEQCHiOpmAaNGgAgHqSCCGEEEJKMkqSiMIVt/Lf2Ul6kh49eoSsrCyeoyGEEEIIIfJASRJRuOJYtEGiWrVqMDAwQEpKCkJCQvgOhxBCCCGEyAElSUThiuMaSRIqKipwdnYGQPOSCCGEEEJKKkqSiMIV5+F2AM1LIoQQQggp6ShJIgoVFxeHb9++AQCqVKnCczSFQxXuCCGEEEJKNkqSiEJJhtpZWVlBW1ub52gKRzLc7tWrV4iPj+c3GEIIIYQQInOUJBGFKs5FGySMjY1ha2sLAHjw4AHP0RBCCCGEEFnjNUnatGkTHBwcoK+vD319fbi4uODixYvc9WlpafDy8kLZsmWhq6uL7t2748uXLzxGTIrq9evXAIp3kgTQvCRCCCGEkJKM1yTJwsICS5YsQWBgIB49eoSWLVuic+fOeP78OQBg4sSJOHv2LI4ePYobN27g06dP6NatG58hkyIKCwsDAFSuXJnnSIqG5iURQgghhJRcqnyevGPHjlJ/L1q0CJs2bcK9e/dgYWGB7du348CBA2jZsiUAYOfOnbCzs8O9e/e4L6mkeHn79i2A4p8kZe9JYoxBIBDwHBEhhBBCCJEVXpOk7EQiEY4ePYrk5GS4uLggMDAQmZmZaN26NbdP9erVYWVlhYCAgDyTpPT0dKSnp3N///jxAwCQmZmJzMxM+d6J35Ccn+84+MIY45Ika2trpXgcCtsmNWrUgIaGBr5+/YpXr14V+6RPWZT214gyojZRPtQmyoXaQ/lQmygfZWqT/MbAe5L07NkzuLi4IC0tDbq6ujh58iTs7e0RHBwMdXV1GBoaSu1vYmKC6OjoPI+3ePFizJs3L8d2X19fpamm5ufnx3cIvPj+/TuSk5OhoqKCV69ecUPvlEFh2sTa2hqvX7/Gtm3b0KxZMzlEVXqV1teIMqM2UT7UJsqF2kP5UJsoH2Vok5SUlHztx3uSVK1aNQQHByMhIQHHjh3DwIEDcePGjUIfb+bMmZg0aRL3948fP2BpaQl3d3fo6+vLIuRCy8zMhJ+fH9zc3KCmpsZrLHy4c+cOgJ/lvzt37sxzND8VpU18fX3x+vVriEQitGvXTk4Rli6l/TWijKhNlA+1iXKh9lA+1CbKR5naRDLK7Hd4T5LU1dW5oUqOjo54+PAh1q5di169eiEjIwPx8fFSvUlfvnyBqalpnsfT0NCAhoZGju1qamq8N4qEMsWiSBEREQB+zkdStvtfmDZxdnaGt7c3AgMDle7+FHel9TWizKhNlA+1iXKh9lA+1CbKRxnaJL/nV7p1ksRiMdLT0+Ho6Ag1NTVcuXKFuy40NBQfPnyAi4sLjxGSwiopRRsknJycAACPHz+GSCTiORpCCCGEECIrvPYkzZw5E23btoWVlRUSExNx4MABXL9+HZcvX4aBgQGGDh2KSZMmoUyZMtDX18fYsWPh4uJCle2KqZKWJFWrVg06OjpITk7Gy5cvUbNmTb5DIoQQQgghMsBrkhQTE4MBAwbg8+fPMDAwgIODAy5fvgw3NzcAwOrVq6GiooLu3bsjPT0dHh4e8Pb25jNkUgQlLUkSCoVwdHTEzZs38ejRI0qSCCGEEEJKCF6TpO3bt//yek1NTWzcuBEbN25UUEREXrKX/y4pSRLwc8jdzZs38fDhQwwaNIjvcAghhBBCiAwo3ZwkUjJ9+/YNCQkJAIBKlSrxHI3s1K9fHwDw6NEjniMhhBBCCCGyQkkSUQhJL5KFhQW0tLR4jkZ2JMUbgoODkZGRwXM0hBBCCCFEFihJIgpREofaAT97xYyMjJCRkYGQkBC+wyGEEEIIITJASRJRiJKaJAkEAm7I3cOHD3mOhhBCCCGEyAIlSUQhSmqSBNC8JEIIIYSQkoaSJKIQJTlJksxLop4kQgghhJCSgZIkohCSJMnW1pbnSGRP0pMUEhKC1NRUnqMhhBBCCCFFRUkSkbuEhATExcUBKJlJkoWFBUxMTCASiRAcHMx3OIQQQgghpIgoSSJyFxYWBgAoX7489PT0eI5G9rIXb6B5SYQQQgghxR8lSUTu3r17B6Bk9iJJ0LwkQgghhJCSQ5XvAEjJFx4eDgCwsbHhORL5oZ4kImtZWVkIDg7GkydP8PXrV2hra8Pa2hqNGjVC2bJl+Q6PEEIIKdEoSSJyV5qSpFevXiExMbFEDiskivH582esXr0aO3fu5ObyZScQCNC6dWuMHTsWHTp0gEAg4CFKQgghpGSj4XZE7kpDkmRiYgJLS0swxhAYGMh3OKQYEovFWLlyJapWrYrly5cjLi4OBgYGcHd3x4ABA/DHH3/Azs4OjDH4+fmhU6dOcHV1xcuXL/kOnRBCCClxKEkiclcakiTgf/OSKEkiBfX161d06NABU6ZMQVJSEpydnXH69GnExcXh8uXL2L17N44ePYoXL17g3bt3mDZtGrS0tHDz5k04Ojpi+/btfN8FQgghpEShJInIlVgsRkREBICSnyTVq1cPAPD48WOeIyHFSVRUFJo0aYKLFy9CS0sLW7duRUBAADp16gRV1Zwjom1sbLB06VKEhobCzc0NqampGDZsGKZPnw6xWMzDPSCEEEJKHkqSiFxFR0cjPT0dQqEQlpaWfIcjV5QkkYL6+PEjmjZtilevXsHS0hL37t3D8OHDoaLy+7dmS0tLXLp0CfPnzwcALFu2DMOHD6dEiRBCCJEBSpKIXEmG2llaWub6q3hJIkmSQkNDkZiYyHM0RNklJCSgXbt2CA8Ph62tLW7dugUHB4cCHUNFRQWzZ8/Gzp07IRQKsWPHDkyZMgWMMTlFTQghhJQOlCQRuZKskVTSh9oBP4s3VKhQAYwxPHnyhO9wiBITiUTo2bMnnj17BlNTU1y5cgXW1taFPt6gQYOwY8cOAMDq1auxYsUKWYVKCCGElEqUJBG5Ki1FGyRoyB3Jj3///Re+vr7Q1tbGuXPnipQgSQwYMABr1qwBAMyYMQO+vr5FPiYhhBBSWlGSRORKkiRVqlSJ50gUw9HREQAlSSRvN27cwNy5cwEAmzdv5p4zsjB+/HgMGzYMYrEYvXv35l5/hBBCCCkYSpKIXJXWniQqA05yk5SUhAEDBkAsFmPgwIHo37+/zM+xYcMGODs74/v37/D09ERWVpbMz0EIIYSUdJQkEbkqrUnSixcvkJKSwnM0RNn8/fff+PDhAypWrIgNGzbI5RwaGho4cuQI9PX1ERAQgGXLlsnlPIQQQkhJRkkSkZvMzEx8/PgRQOlJkszNzVG+fHmIxWI8e/aM73CIErl//z7WrVsHANiyZQt0dXXldi5ra2usX78eADBnzhwEBQXJ7VyEEEJISURJEpGbDx8+QCwWQ0tLCyYmJnyHoxACgYDmJZEcxGIx/vzzTzDG0L9/f7i7u8v9nP3790f37t2RlZWF4cOHQyQSyf2chBBCSElBSRKRG8lQu4oVK0IgEPAcjeLQvCTyX3v37sXjx4+hr6+PlStXKuScAoEAGzduhIGBAQIDA7Fp0yaFnJcQQggpCShJInJT2uYjSVAZcJJdSkoKZs2aBQCYNWsWjI2NFXZuExMTLF68mDv358+fFXZuQgghpDijJInITWlaSDY7yXC7kJAQpKen8xwN4duqVasQFRWFihUrYty4cQo//4gRI+Dk5IQfP35g6tSpCj8/IYQQUhxRkkTkprT2JFlZWaFMmTLIzMzE8+fP+Q6H8Cg+Ph4rVqwAACxevBiampoKj0EoFHJD7fbv30/DQAkhhJB8oCSJyI0yJUmTJ09Gr1698PLlS25bVlaWXNaQEQgENC+JAADWrVuHhIQE1KxZEz179uQtDkdHR3h6egIApk6dCsYYb7EQQgghxQElSURuJElSpUqVFHrejIwMPHr0SGqbv78/jhw5gsjISG7b6dOnUalSJezfvx/fv3+XaQw0L4kkJCRg9erVAIDZs2dDRYXft9tFixZBQ0MD165dw4ULF3iNhRBCCFF2lCQRuUhKSkJsbCwAxfUkMcZw6NAh2NraokWLFlKJz8yZM7Fu3TpUrVqV23b8+HFER0fj6NGjqFq1Kry9vWX2CzuVAScbNmxAfHw87Ozs0L17d77DgbW1NcaPHw8AmDZtGpUEJ4QQQn6BkiQiFxEREQAAIyMjGBgYyP18Hz9+hIeHB/r06YOPHz9CT08PoaGh3PW9e/fG2LFjUbFiRW7brl27cOjQIVhZWSEhIQFeXl5o06YN4uLiihyPpCfpyZMnyMzMLPLxSPGSkpIi1YskFAp5juinmTNnwsjICC9evMCRI0f4DocQQghRWpQkEblQ5HykCxcuoE6dOvDz84OmpibmzZuHd+/eoWHDhr+8nbq6Orp164bVq1dj1apV0NTUhK+vLxo2bIjXr18XKaZKlSpBX18f6enpUvOgSOmwZ88efP36FTY2NrzORfovQ0NDTJ48GQAwf/586k0ihBBC8kBJEpELRSRJjDEsXboU7du3x9evX1GvXj08ffoU//zzT4GqiAmFQowZMwaPHj1CxYoVERYWhsaNGyMkJKTQsamoqNC8pFJKLBZjzZo1AIDx48crTS+SxNixY2FkZIRXr15RbxIhhBCSB0qSiFxIhttlH94mSyKRCGPGjMGMGTMAAH/++Sfu3r2LKlWqFPqYNWrUwL179+Do6Ii4uDi0bt1aasheQVGSVDpdunQJoaGh0NfXx5AhQ/gOJwd9fX3qTSKEEEJ+g5IkIhfv378HIJ8kKSsrC/369YO3tzcEAgFWr16NjRs3QkNDo8jHNjExga+vL2rXro0vX76gXbt2hZ6jRGXASyfJXKRhw4ZBT0+P52hyR71JhBBCyK9RkkTkQpIkWVlZyfS4IpEIgwcPxqFDh6CmpobDhw9jwoQJMj1HmTJl4OfnBxsbG7x79w5//PEHMjIyCnwcSZIUHBxMv9aXEiEhIfD394eKigrGjh3Ldzh50tfXx8SJEwEAS5cupXWTCCGEkP+gJInIxYcPHwD8LDssK2KxGMOHD8e+ffugqqqKI0eOoEePHjI7fnbGxsY4e/Ys9PT0cOPGDZw7d67Ax6hatSp0dHSQkpJS5EIQpHjYunUrAKBz585yG2oqK15eXtDR0cGTJ0/g7+/PdziEEEKIUqEkichcSkoKt0aSLHuSRCIRGGMQCoU4cOAAunTpIrNj56ZGjRo4dOgQzp49i27duhX49kKhEHXq1AFA85JKg5SUFOzduxcAMGrUKJ6j+b0yZcpg6NChAIDly5fzHA0hhBCiXChJIjIXGRkJANDT04OhoaHMjqumpoYdO3bg0aNHcutB+q927dqhQ4cOhb49zUsqPY4dO4b4+HhUrFgRrVu35jucfJk4cSKEQiH8/PwQFBTEdziEEEKI0qAkichc9vlIAoGgyMd78eIFN6dHIBBwvTOKFhkZiZUrVxboNo6OjgCoJ6k0kAy1GzZsGFRUisdba8WKFbkfHFasWMFzNIQQQojyKB6f5KRYkeV8pLdv36JRo0bo1q0bUlJSiny8wkpISEDt2rUxZcoUnD17Nt+3q1u3LgAgKCgIYrFYXuERnj1//hx37tyBUCjE4MGD+Q6nQKZOnQoAOHz4MPcDByGEEFLaUZJEZE7yRUsWSVJISAjS0tIQFxfH66KcBgYGGD58OFxcXFCpUqV8387Ozg4aGhr48eMHt8AuKXl8fHwAAB07doS5uTnP0RRMvXr10KpVK4hEImzatInvcAghhBClQEkSkTlZlv/u0qUL7t69iyNHjshkHaSiWLBgAW7fvo0aNWrk+zZqampwcHAAQEPuSqrMzEzs27cPwM+hdsXRuHHjAADbtm1Damoqz9EQQggh/KMkicicLIbbZWVlcf+vV68eKlSoUOS4ikpdXV1qrkl+15aRFG+gJKlkunz5Mr5+/QoTExN4eHjwHU6htG/fHtbW1vj69SsOHTrEdziEEEII7yhJIjJX1J6kx48fw87ODg8fPpRlWDITHx+PKVOmoF+/fvnaXzIviZKkkklS9rtPnz5QVVXlOZrCEQqF+PPPPwEA69evp8VlCSGElHq8JkmLFy+Gk5MT9PT0UL58eXTp0gWhoaFS+7i6ukIgEEhdisMaJKWVSCTCx48fARSuJyklJQV9+/bF27dvlbbaVmRkJFavXo0DBw7g9u3bv91f0pMUFBREXz5LmISEBJw5cwYA8p00K6uhQ4dCU1MTQUFBuHfvHt/hEEIIIbziNUm6ceMGvLy8cO/ePfj5+SEzMxPu7u5ITk6W2m/48OH4/Pkzd1m2bBlPEZPf+fz5M7KysqCqqgozM7MC337SpEkIDQ2Fubk5vL295RBh0dWqVYubezJjxozfJj61atWCUChEbGwsoqKiFBEiUZATJ04gLS0NdnZ2XDJcXJUtWxZ9+vQBAGzYsIHnaAghhBB+8ZokXbp0CYMGDUKNGjVQu3Zt7Nq1Cx8+fMix8Ka2tjZMTU25i76+Pk8Rk9+RDLWzsLAocDW606dPY8uWLRAIBNizZw/Kli0rjxBlYs6cOdDU1MSdO3fg6+v7y301NTW5Yg805K5kkQy169evn0zWBOPbmDFjAABHjx5FdHQ0z9EQQggh/FGqAfQJCQkAgDJlykht379/P/bt2wdTU1N07NgRs2fPhra2dq7HSE9PR3p6Ovf3jx8/APysQJWZmSmnyPNHcn6+45Cnd+/eAfg5H6kg9/PTp08YOnQoAGDixIlo1qyZQh6nwraJsbExRo4cibVr12L27Nlo0aLFL78k165dG0+fPsXDhw/Rtm3bIsVckhWn10hkZCSuX78OAOjZs2exiPl3atWqBRcXFwQEBGDLli3466+/ilWblBbUJsqF2kP5UJsoH2Vqk/zGoDRJklgsxoQJE9C4cWPUrFmT2963b19YW1vD3NwcT58+xfTp0xEaGooTJ07kepzFixdj3rx5Obb7+vrmmVgpmp+fH98hyI3kvqmoqODChQv5ug1jDAsWLMDXr19RqVIluLi45Pu2slKYNqlbty40NDTw8OFDLFiwAPXr189zX0n5cl9f31/uR34qDq+RkydPgjGGGjVq4Pnz53j+/DnfIcmEs7MzAgIC4O3tDQcHB66iY3Fok9KG2kS5UHsoH2oT5aMMbZKSkpKv/QRMSWaSjx49GhcvXsTt27dhYWGR535Xr15Fq1at8PbtW9ja2ua4PreeJEtLS8TFxfE+TC8zMxN+fn5wc3ODmpoar7HIy9ixY7FlyxbMnDkz12Q1N3v27MGwYcOgoaGBBw8ewM7OTs5R/k9R22TmzJlYuXIl6tati3v37uXZm3Tnzh20aNECFhYWXG8byak4vUZcXFwQGBiIDRs2YMSIEXyHIzOpqamwtrZGfHw8zp8/D1dX12LTJqVFcXqdlAbUHsqH2kT5KFOb/PjxA+XKlUNCQsIvcwOl6EkaM2YMzp07h5s3b/4yQQKABg0aAECeSZKGhkaui46qqanx3igSyhSLrEVGRgIAbGxs8nUfo6KiMHnyZADA/PnzuYVXFa2wbTJjxgxs3rwZQUFBuHbtWp7r5Dg6OkIgEODjx4/4/v07ypcvX9SQSzRlf42Eh4cjMDAQKioq6NGjh1LHWlBqamro168fNmzYgJ07d8LNzY3bXpLuZ0lAbaJcqD2UD7WJ8lGGNsnv+Xkt3MAYw5gxY3Dy5ElcvXoVNjY2v71NcHAwABSqchqRv4IsJMsYw8iRI5GQkABnZ2dMmjRJ3uHJXLly5bhehKVLl+a5n56eHqpWrQrgZylwUrwdP34cANC8efMSmfAOHz4cwM9iKjExMTxHQwghhCger0mSl5cX9u3bhwMHDkBPTw/R0dGIjo5GamoqACAsLAwLFixAYGAgIiIicObMGQwYMADNmjXjrceB5I0xVqCFZPfu3Yvz589DXV0dO3fuLLYLcU6YMAGqqqq4du3aLxfAlSwqS0lS8Xf06FEAQI8ePXiORD4cHBzg7OyMzMxMroIfIYQQUprwmiRt2rQJCQkJcHV1hZmZGXc5fPgwAEBdXR3+/v5wd3dH9erVMXnyZHTv3h1nz57lM2ySh/j4eCQmJgL4fZIUHR2N8ePHAwDmzp0Le3t7uccnL1ZWVtz6MsuXL89zP8k6OlQGvHh7//49Hjx4AIFAgK5du/IdjtxIepN27NhBiyATQggpdXj96f53H7yWlpa4ceOGgqIhRSUZamdsbPzbSoLlypXD9OnTce7cOUydOlUR4cnV1KlTsXfvXhw/fhxv375F5cqVc+xDSVLJIBlq16xZM5iamvIcjfz07t0bEydOxJs3b/D8+XO0b9+e75BIMcUYw6dPn/D48WO8f/8esbGxEIlE0NTUhJmZGapUqYK6detCT0+P71AJIYRTPMc3EaVUkKF2qqqqmDFjBqZNm8aVGC7OatWqhQkTJqBevXp5zseSDLcLCwtDfHw8DA0NFRghkZWSPtROQldXF3369IGPjw/8/Pwwbdo0vkMixczDhw9x8OBBnDp1CuHh4b/cVygUwtnZGZ06dUK/fv1+W8SJEELkjZIkIjP5KdqQnJwMNTU1qKurA0CJSJAkVq9e/cvry5QpA2tra7x//x7BwcFwdXVVTGBEZiIjI7lS7926deM7HLkbPnw4fHx8cPfuXcTHx8PY2JjvkIiSY4zh9OnTWLZsGQICArjtKioqsLe3R7Vq1VC+fHmoqakhJSUFHz58wMuXLxEZGYmAgAAEBATgr7/+QqdOnTBr1iw4OTnxeG8IIaVZyfmGSniXn56kadOmoW7durh//76iwlIqkiF3VLyheJIsYt2kSZNSUWGzfv36qFGjBjIzM3Hs2DG+wyFK7tGjR2jWrBm6du2KgIAAqKuro2/fvjhx4gQSEhLw7NkzHDt2DN7e3li7di18fHxw+fJlfPjwAREREdiyZQuaNm3KJVrOzs7o0KED3rx5w/ddI4SUQpQkEZmRJEl59SQlJCTg+PHjePHiRb5XOy5uUlJSsGbNGnh4eEAsFue4nuYlFW9nzpwBgBJdsCE7gUCA/v37AwBVuSN5ysjIwMyZM9GgQQPcvn0bWlpa+Ouvv/D+/Xvs378fXbt2ha6u7i+PYW1tjREjRuDmzZt4+fIlBg4cCKFQiPPnz6NmzZqYPXs2MjIyFHSPCCGEkiQiQ5Lhdnn1JBkYGODFixfYsWMHWrRoocjQFIYxhnnz5sHX1xcXL17McT0lScXX9+/fuUIynTp14jkaxenTpw9UVFQQEBCA169f8x0OUTLv3r1DgwYNsGTJEojFYvTp0wevX7/GokWLCl3YpHr16ti1axdevHgBDw8PZGRkYOHChWjYsCFevnwp43tACCG5oySJyMzvepKAn/NyBg8erKiQFE5HRwdz587F5s2bc51zJCne8OrVqxLbm1ZSXbp0CSKRCDVq1ICtra1Cz/3mzRvs2rULly9fVuh5gZ8Ld0uet3v27FH4+Ynyunr1KpycnBAcHIyyZcvi+PHjOHDggMyKLlStWhUXL17EsWPHULZsWQQFBcHR0RH79u2TyfEJIeRXKEkiMpGeno7o6GgAOZOkiIgIHD58uNSstTJ+/HiMHDkSOjo6Oa4zMzODqakpxGIxnj59ykN0pLAkQ+3k1YuUlZWFixcvwsvLC5UrV8b58+e560JCQjB48GD8888/UrdZuHAhdu/ejR8/fsglJomWLVsC+Jkk5TaMlJQ+u3fvhru7O759+wYnJyc8efJELsVMBAIBunfvjqdPn8Ld3R2pqano378/pk2bBpFIJPPzEUKIBCVJRCYiIyMBAFpaWihbtiy3nTEGLy8v9O7dG7Nnz+YrPKVCQ+6Kn4yMDG74pKyTpNjYWMyZMwfW1tZo164dvL29ERYWJpVE29raom3btnBxceG2paWlYeHChRg0aBBMTU3h6emJwMBAmcYm4eTkBENDQ0RGRuLatWtyOQcpPjZu3IhBgwZBJBLB09MTN27cQIUKFeR6TnNzc1y8eBGzZs0C8HPh7i5dulCPPCFEbihJIjKRvfy3QCDgth87dgwXLlyAuro6+vXrx1d4CpeRkQFvb2+0aNECaWlpUtdRklT83Lp1CwkJCShfvjycnZ1lcsyEhAT8/fffsLGxwfz58/Hp0ycYGxtj5MiROHPmDEaPHs3t6+DggAsXLmDNmjXctrS0NEydOhXVqlVDamoqDhw4gPr168PNzQ0PHz6USYwS6urq6NmzJwBg165dMj02KV5WrVqFMWPGAAAmTJiAvXv3QktLSyHnVlFRwcKFC3Hw4EFoamri3LlzaNOmDRISEhRyfkJI6UJJEpGJ3Mp/JyQkYPz48QCAmTNnonr16rzExgehUIilS5fi+vXrOH78uNR1kvkdlCQVH5Khdh07dpTJ2l4nTpyAnZ0dFi1ahOTkZDg6OuLQoUOIjIzE5s2b0bFjx98uNmxoaIgFCxbg5cuXePDgAfr37w+hUAh/f384Oztj4MCB+PTpU5FjlRgwYAAA4Pjx43If3keU0/bt2zF58mQAwN9//41Vq1ZJ/SimKL1794afnx/09fVx69YttGjRArGxsQqPgxBSslGSRGQit6INs2fPxufPn1G1alXMmDGDr9B4IRQKMXToUACAj4+P1HWSnqSQkBAqaVsMMMZkNh8pPj4ePXr0QPfu3fH582dUqVIFJ06cwMOHD9GrVy9oaGgU+JgCgQBOTk7Ys2cP3r59yyUze/bsgb29Pfbs2SOT+YBOTk5crxWtmVT6nDhxAiNGjAAATJ8+HQsWLOAlQZJo0qQJrl+/DmNjYwQFBaF169b49u0bb/EQQkoeSpKITPy3/HdQUBA2btwIAPD29oampiZvsfFlyJAhUFFRwY0bNxAaGsptt7a2hpGRETIzM/H8+XMeIyT58ezZM0REREBTUxOtW7cu9HECAwNRr149HDt2DKqqqpg1axaePn2Krl27yuzLZsWKFbF79248ePAAzs7OSEhIwMCBA9G1a1fExcUV6dgCgQADBw4E8HPSPik97ty5gz59+kAsFmPo0KFYvHgx3yEB+Nkrf+vWLZiamuLp06fw8PCgoXeEEJmhJInIRPaeJLFYDC8vL4jFYvTq1QutWrXiOTp+WFhYoF27dgCAbdu2cdsFAgHNSypGJL1Ibm5u0NbWLvRxZsyYgfDwcFSsWBEBAQFYuHCh3H48cHJywp07d/Dvv/9CTU0Np0+fRr169RAeHl6k4/bv3x8CgQA3b97Eu3fvZBQtUWaRkZHo1q0bMjIy0KVLF2zevJnXHqT/qlatGq5cuYJy5crh0aNHaN++PZKTk/kOixBSAlCSRGQie+GGXbt2ISAgALq6uli5ciXPkfFLMjxl165dSE9P57bTvKTiQ1KKu2PHjkU6zu7duzF48GA8fvwY9evXl0Vov6SqqoqZM2fi4cOHqFKlCmxtbWFpaVmkY1pYWHA/ehw4cEAWYRIllpKSgi5duiAmJga1a9fGvn37oKqqyndYOdjb28PX1xeGhoa4c+cOevfujaysLL7DIoQUczJJkuLj42VxGFJMicViLknS19fH9OnTAQBz586Ve1lYZde2bVuYm5sjLi4Op0+f5rZTT1Lx8PXrVzx48ADAz7YsCLFYDF9fX+5vc3Nz7NixA0ZGRjKN8Xdq166Nhw8f4siRI9wXXLFYXOj1jiRVKvfv319q1j4rjRhjGD58OB4/foxy5crh9OnTua79pizq1q2LCxcucFXvxo8fT89PQkiRFDhJWrp0KQ4fPsz93bNnT5QtWxYVKlTAkydPZBocKR6+fPmCjIwMqKioYNOmTYiLi0ONGjUwbtw4vkPjnaqqaq4FHCRJ0pMnT2hBRCXm5+cHsViMmjVrwsLCIt+3Y4xhzJgx8PDwUIqS2QYGBjA2Nub+njx5MgYMGFCowiFdu3aFpqYmXr16RUl+CbZ9+3YcOHAAQqEQx44dy7FIuDJycXHBvn37IBAI4O3tXepHMhBCiqbASdLmzZu5IRt+fn7w8/PDxYsX0bZtW0ydOlXmARLlJ+lFKleuHJcIbNy4EWpqanyGpTSGDh0KgUAAf39/REREAACqVKkCXV1dpKamShV1IMpFsoBsQXuRAEBbWxsCgUAmJcNl6cWLF9iwYQP279+PGzduFPj2+vr66Ny5MwBg3759sg6PKIEXL15wP3ItWrQIzZs35zmi/OvevTtWrVoFAJg6dSpVYiSEFFqBP72jo6O5JOncuXPo2bMn3N3dMW3aNJkvYEiKB0nRhoyMDDDG4OnpWaw+VOXN2tqam8exZ88eAD8XRaxduzYAGnKnrMRiMS5fvgyg4EmSQCDA8uXLcf/+fa4kt7Kwt7fH+fPnsWbNGri5uRXqGJ6engCAQ4cO0dyPEiY1NRW9evVCamoq3N3di+WPnxMmTOCSvIEDB+LZs2c8R0QIKY4KnCQZGRkhMjISAHDp0iWuJC5jjIYNlVKSnqQWLVpg5MiRWL58Oc8RKZ9BgwYB+FnAQTIXhOYlKbfg4GB8+fIFurq6aNy4cb5uc/nyZW4Im2T9ImXk7u7OLfQMAHFxcQVaINbDwwNly5ZFdHQ0rl69Ko8QCU+mTp2KkJAQmJiYYM+ePUrXE5pfK1euROvWrbniE7SGEiGkoAr87tetWzf07dsXbm5u+Pr1K/cLa1BQECpXrizzAInyk/QkVatWDZs3b4aZmRnPESmfrl27Qk9PD+Hh4bh9+zaA/yVJQUFBfIZG8iAZateqVSuoq6v/dv9jx46hbdu2aNeuHdLS0uQdnsx8+/YNrVu3hoeHBxITE/N1G3V1dfTs2RPAzwIOpGS4evUqt77dnj17YGJiwnNEhaeqqopDhw7BxsYG7969Q58+feiHXEJIgRQ4SVq9ejXGjBkDe3t7+Pn5QVdXFwDw+fNn/PnnnzIPkCg/yVCG4jCxly/a2tpckZOoqCgA0j1Jha00RuTn0qVLAPI31C4gIAD9+vUDYwxVq1aFhoaGvMOTmY8fPyIyMhL37t1Dly5d8p3gSarcnThxAikpKfIMkShAYmIihgwZAgAYPXo03N3deY6o6MqWLYuTJ09CW1sbvr6+mDlzJt8hEUKKkQInSWpqapgyZQrWrl3LrfUCABMnTsSwYcNkGhxRfgEBAdzk79Je7vt3lixZgk+fPqFPnz4AADs7O2hoaODHjx9FXuSTyFZ8fDwCAgIAAG3atPnlvp8+fUL37t2Rnp6Ojh07Yv369Uq12ObvODg44NKlS9DV1cXVq1fRp0+ffM0zcnFxgY2NDZKSkrgFd0nxNX36dLx//x7W1tZYunQp3+HITO3atbFz504AwPLly6WWYiCEkF8p1GDjvXv3okmTJjA3N+eGWq1Zs4befEqh7EPFKlWqxGMkyq9cuXJSw7bU1NRQq1YtADQvSdn4+flBJBLBzs7ulz2k6enp+OOPP/D582fY29tj//79EAqFCoxUNpycnHD27FloaGjg1KlTGDp06G97NwUCAVfAgarcFW9Xr17Fpk2bAAA7duyAnp4ezxHJVs+ePTFp0iQAP+eHSqqMEkLIrxQ4Sdq0aRMmTZqEtm3bIj4+nhvja2hoiDVr1sg6PqLkJENuAMDKyorHSIoPsVjMJZc0L0k55bf097hx4xAQEAADAwOcOnWqWH+5dHV1xZEjRyAUCrFnzx5Mmzbtt7eRJEmXL19GbGysvEMkcpCamorhw4cD+DnMrmXLljxHJB+LFy9GgwYNEB8fj969exdqjTBSukVHR+P8+fNYuHAhhg4dCnd3d9SqVQuVK1eGpaUlLC0tYW9vjwYNGqBz586YOHEiNmzYgNu3b9OQ5GJKtaA3WL9+PXx8fNClSxcsWbKE216/fn1MmTJFpsER5SepbGdkZFSsvyAqSkpKChwcHBAWFobw8HCqcKeEGGP5mo+0a9cubN26FQKBAAcPHkSVKlUUFaLcdOrUCTt37sSAAQOwcuVKVKpUifsCnZvq1avD0dERgYGBOHLkCLy8vBQYLZGFJUuW4N27dzA3N5f6TC9p1NXVcejQIdStWxf379/HzJkzabFZ8kspKSnw9/fHxYsXcenSpSL1QAqFQjg4OMDNzQ3t27dHo0aNoKpa4K/gRMEK3ELh4eFSc5EkNDQ0kJycLJOgiPLz9vaGi4sLPn/+DIB6kfJLW1sb1tbWiImJwbNnz6SSJMZYsZrLUlI9e/YMnz9/hra2Npo2bZrrPq9eveISgvnz5xdqsVll1b9/f0RGRmLWrFkYO3bsb+caenp6IjAwEPv376ckqZh58+YNlxitWbMG+vr6PEckXxUrVsSuXbvQpUsXrFq1Cs2bN0enTp34DosoEcYYbt68iT179uDo0aNSFT9VVFRQvXp11K1bF9WqVYOlpSXMzc2ho6MDTU1NAD8LoCQkJCAqKgrv3r3D69ev8ejRI3z+/BlBQUEICgrCsmXLYGRkhB49emDAgAFo1KgRffYrqQInSTY2NggODs4xTv/SpUuws7OTWWBEeYWEhGDcuHFgjGH27NkAqLJdQWzbtg0mJibQ1tZGWloahEIhYmNjERUVBQsLC77DK/V8fX0B/Bx+lluVurS0NPTu3RspKSlo2bJliayYNXPmTLx79w7bt2+Hp6cnFixYkOe+vXv3xpQpUxAQEICwsDDY2toqMFJSWIwxeHl5ISMjAx4eHvjjjz/kcp60tDQcOXIEnz59woQJE7gvk7t374avry/09fWhr68PMzMz2NjYoFKlSqhSpQq3n6x17twZEyZMwJo1azBo0CA8efIElpaWcjkXKT7S09Nx8OBBrFy5EiEhIdx2a2trdOzYEW3atEHz5s25is4FwRjDx48fcevWLVy4cAGXLl3C169fsXXrVmzduhW2trb4888/MXToUBgYGMjybpGiYgXk4+PDKlSowA4dOsR0dHTYwYMH2cKFC7n/K5uEhAQGgCUkJPAdCsvIyGCnTp1iGRkZfIdSaGKxmLVq1YoBYF27dmUzZsxgANjYsWP5Dq1QlKFNatWqxQCwM2fO8BaDslCG9vDw8GAA2OrVq3O9fty4cQwAK1euHIuKilJscAqUkZHBWrduzQAwIyMjFhYWlue+bm5uDACbP3++AiMsvWTxOjl8+DADwDQ0NNibN2+KHJNYLGZv375lW7ZsYbt27eK2Z2ZmMg0NDQZA6jk0bdo0BiDXi6qqKqtbty4bPnw42717N/v06VOR48suPT2dOTk5MQDM1dWVZWVlFel4yvC+RaTlt00yMjLYxo0bmZmZGff809XVZcOHD2e3bt1iYrFY5rFlZWWxK1eusIEDBzIdHR3uvHp6emz8+PHs/fv3Mj+nMlCm10l+c4MCJ0mMMbZv3z5WuXJlJhAImEAgYBUqVGDbtm0rVKDyRkmSbJ08eZL7YA0LC2N9+vRhANjy5cv5Dq1Q+GwTsVjMIiIi2MCBAxkANnfuXIXHoGz4fo2kpaUxLS0tBoA9e/Ysx/VnzpzhPtDOnz/PQ4SKFR8fz+zt7RkA5uHhked+u3fvZgBY1apV5fKlgkgr6uskMTGRmZubMwBs3rx5RYolJCSEzZ49m1WrVo17bdSoUUNqn1GjRrEBAwawiIgIbtu9e/fYqlWr2Ny5c9nEiRNZjx49WP369ZmRkVGuiZODgwNbtmxZkWLN7vXr19wX1KVLlxbpWHy/b5GcftcmYrGYHT58mFWuXJl7jlWoUIEtW7aMff/+XWFxJiUlsS1btjA7OzsuDnV1debl5VXifoRTpteJXJMkieTkZPbly5eiHELuKEmSndTUVGZjY8MAsL/++osxxlijRo0YAHbkyBGeoyscvtokKiqK2dnZMT09PbZ8+XIGgHXq1EmhMSgjvl8jV69eZQCYqalprl/2Hz16xOzt7dmECRN4iI4fb968YfXr12fh4eF57vPjxw8uuXzw4IHigiulivo6+fvvvxkAZmtry1JTUwt8++TkZLZ9+3ZWr149qURGTU2NNWvWjM2dO5eJRKJCxSYWi9n79+/ZsWPH2LRp05ijoyN3/FGjRkntFx0dXahzSPj4+HBxBwYGFvo4fL9vkZx+1SavXr1izZs3555X5cuXZxs3bmTp6ek8RPqTWCxmly5dYq6urlxcmpqabMqUKQpN2uRJmV4nCkmSigNKkmTn33//ZQCYubk5S0xMZIwxZmFhwQCwe/fu8Rxd4fDVJiKRiEs4JV9YLCwsFBqDMuL7NfLXX38xAKxfv3557pOamsrS0tIUGBW/8tsmvXv3ZgDY+PHjFRNYKVaU18n79++ZpqYmA8BOnDhRoNvGxMSw6dOnS/X2qKmpsY4dO7J9+/bJ7XM2JiaG7du3jz19+pTbFhAQwIRCIfP09Cx076VYLGZdu3ZlAFj16tVZcnJyoY7D9/sWySm3NklLS2Nz585l6urqDADT0tJic+bMYT9+/OAx0pyuXLnC/QANgBkbG7OtW7cWeVgo35TpdZLf3CBf6yTVrVsX9erVy9eFlEyxsbFYvHgxAGDp0qXQ1dVFZmYmPn36BIAKNxSUiooKBgwYAAC4c+cOAODjx4+01gzP/P39AQCtW7eW2p6amsr9X1NTM9eCDqXF0aNHcfbs2RzbJWumHTp0CFlZWYoOi+TTjBkzkJaWhubNm6NLly75uk1MTAymTZuGihUrYunSpfj+/TtsbGywbNkyfPr0CWfOnIGnp6fcquMZGxvD09OTW3wbAK5cuQKRSARVVVWpymC/WwQ5O4FAAB8fH5iZmeHVq1eYOnWqTOMmyuP58+do0KAB5s6di4yMDLRp0wbPnz/H3LlzlW75kpYtW+L27ds4f/48qlevjtjYWIwYMQJOTk7c9wWiGPmqbpffN1JSci1YsACJiYlwdHRE3759AQBRUVEQi8VQV1dH+fLleY6w+BkwYADmzZuH69evw8bGBuHh4QgKCoK7uzvfoZVK379/x6NHjwBIJ0nR0dGoV68exo4di6lTp5bqtS3OnTuHnj17QldXF8HBwVKV7Nzd3VGuXDl8+fIFV65cgYeHB4+Rktzcu3cPBw8ehEAgwOrVq/NVdjgrKwvOzs54//49gJ9rIs6ePRvt27eHUCiUd8h5mjVrFjp37ixVBe/58+fo0qULpk2bhgEDBuTrx4yyZcti9+7dcHd3h7e3N9q2bYsOHTrIM3SiQIwxbNiwAVOnTkVaWhrKlSuHDRs2oGfPnkpddlsgEKBdu3Zwc3ODt7c35syZg6CgIDRp0gSjR4/GkiVLSnzJfqWgmI4t/tBwu6J78+YNU1VVZQDYlStXuO3Xr19nAFjlypV5jK5o+G6Tpk2bcpOSAbDFixfzEoey4LM9jh8/zgAwOzs7qe2LFy9mAFidOnWK3WtXFrK3SUZGBnN1dWWTJ09mmZmZOfb18vL67XBFUnSFeZ2IxWLWsGFDBoANHjz4t/tmH8Lm7e3N6tevz86fP6/UhTlGjBjBDVGqWLEi27NnT76HKE2YMIEb2lTQuU58f46QnDIyMti+fftYu3btuOdEmzZt2OfPn/kOrVBiYmLY0KFDpYpMFLeKuMr0OpHpcLvcPHr0CHv37sXevXsRGBhYhDSNKLtZs2YhKysLbdq0QcuWLbntkl8Waahd4Q0cOBAAuEV5Hz9+zGc4pVpeQ+2mT5+O3bt3Y/fu3VBTU+MjNKWhpqaGy5cvY8WKFbn2qHl6egIATp48SYuLK5lDhw7h3r170NHRwaJFi/Lc78OHD2jfvj1OnjzJbRsxYgTu37+Pdu3aKfWv76tWrcLq1athZmaGiIgIDBgwAPXq1cOFCxfAGPvlbRcvXoxatWohNjYWQ4cO/e3+RLk9e/YMU6ZMwYULF6ChoYF169bhwoULMDU15Tu0QjE2Nsa2bdtw9epV2NraIioqCp06dULv3r3x9etXvsMrsQqcJH38+BFNmzaFs7Mzxo8fj/Hjx8PJyQlNmjTBx48f5REj4dH9+/dx5MgRCAQCLF26VOq6Dx8+AACsrKz4CK1E6NGjB7S0tLi5SJQk8SevJEkgEGDAgAFwcHDgIyylo66uzv0/IyMDJ06c4P5u2LAhKlWqhOTkZJw+fZqP8Egu0tPTuUWPZ8yYATMzszz33bRpEy5evIi///6bSxSEQiFUVAr9m6rC6OjoYMKECXj79i0WL14MAwMDPH36FO3bt0erVq2kFgn9L01NTRw4cADq6uo4f/48tm7dqsDIiSwdOnQITZs2RXR0NCpWrIiAgACMHTtWqRP8/GrRogWePXuG6dOnQygU4vDhw6hVqxYuXbrEd2glUoHf9YYNG4bMzEy8fPkS3759w7dv3/Dy5UuIxWIMGzZMHjESHs2YMQMAcv2SSD1JRaevr4+uXbtyf4eFhSEhIYHHiEqn9+/f482bNxAKhXB1dQUA7N69G9+/f+c3MCWWmZmJVq1aoXv37jhw4ACAnwmlpIDDvn37+AyPZLNlyxa8f/8e5ubmmDRp0i/3nT17Nvr27YsTJ04U2y+V2tramDFjBt69e4cpU6ZAQ0MD165dQ506dTB+/HjEx8fneruaNWtiyZIlAIBJkybh9evXCoyaFBVjDLNmzUKfPn2QkpKC2rVrIyAgAHXr1pXLubL7/v07Pn36hKSkJJmf67+0tLSwZMkS3L9/H3Z2dvj8+TPatm0LLy8vpKSkyP38pUpBx/Fpamqyx48f59j+6NEjpqWlVdDDyR3NSSqa+/fvs06dOuW6ArS7uzsDwHbs2MFDZLKhDG1y+fJlBoCpqKgwAOz69eu8xcI3vtpj27ZtDABr1KgRY4wxf39/BoCZmZkpxXsHn37VJpKS6Zqamtw6M6GhoQwAEwqFSr+OXnFVkNfJjx8/mLGxMQPAtmzZkuP648ePs65duxb78sK/Eh4ezrp16yZVUnnbtm25ruUkEolYq1atGADm5OSUr8dYGT5HSru0tDTWt29fro2nTJnCjh8/Xug2iYmJYdevX2fe3t5s+vTpzNPTkzVr1ozZ2tqyMmXKMA0NDan5eX369GEA2Jo1a7htgYGBzMTEhNWsWZN5eHiwoUOHsn/++Ydt376d3blzh339+rXI9zslJYWNGzeOu99Vq1Zl9+/fL/Jx5UGZXidyWyepSpUquTbA/fv3ma2tbUEPJ3eUJMmPZIX17MUcihtlaJOsrCxWoUIF7k1u1apVvMXCN77aQ7LGzz///MNSU1O5Vdj//PNPhcahjH7VJllZWdzEaCsrKxYTE8MYY8zJyYkBYOvWrVN0uKVCQV4n8+fP5wrsZN8/JSWFjRo1invf2bp1qzxDVgp+fn7Mzs6Ou88DBw7Mdb/IyEhmaGjIvSf8jjJ8jpRmX79+Zc2aNWMAmKqqKtuxY0eB2iQ+Pp6dOnWKTZ8+nbVo0YL7UeF3F8l6kYwx1q9fP6aqqir1nif5se1Xl/Lly7NmzZqx8ePHs3379rHQ0NBCLcTs6+vLzM3NuR+oFi9eXOgFneVFmV4nckuSTp06xZydndnDhw+5bQ8fPmQNGzZkJ0+eLHCg8kZJUuH8roKRWCxmWlpaDAB78+aNgqKSPWVpk+nTp3NvmqW5Mhgf7SESiVi5cuUYAHbr1i1ucV8zMzMWHx+vsDiU1e/a5Pv376xKlSoMAHN1dWUZGRlszZo1DABzdnZWcLSlQ35fJ7GxsUxPT48BYIcOHeK2h4aGspo1a3LvOdOmTWPp6enyDlspZGRksFWrVjFDQ0N29+7dPPc7dOgQ18P/q/0kx1SGz5HSKDw8nPvBVl9fn/n5+THGft0m3759k6pgePXq1VwTGBsbG9a+fXs2duxYtmzZMnbgwAF28+ZN9uLFC/bx48ffJiGJiYksKCiIXb58me3YsYPNnz+fjRw5krm5uTFLS8s8E6fsnzuRkZH5Xrz869evrFevXtxx3NzcClypUZ6U6XUi0yTJ0NCQGRkZcRd1dXWmoqLC1NXVpf5vZGQkk+BliZKkghOLxczd3Z2NHz+e+2X4v2JiYrgXYn5fwMpIWdrk+fPn3ONZrVo1XmPhEx/tERQUxAAwXV1dFhwczNTU1BgAduzYMYXFoMzy0yYvXrzgvoyPGzeORUdHM6FQyACw169fKzDa0iG/r5PJkydz5eslX+jOnj3L9PX1GQBmYmLCLl++rIiQlc6PHz+k/t6yZQvz9fWV2ubp6ckAMFtbW6leg/9Sls+R0ubFixdc74mFhQV7+vQpd11ebbJw4UKmoqLCJk+ezG1LTExkNWvWZEOHDmU+Pj7s4cOHLCkpSe7xJyYmskePHrHdu3ezsWPHsoYNG7I6depI7ePq6sq0tLTY6dOn83VMsVjMtm/fzv2IbWJiwiWOfFOm10l+c4N8rYq4Zs2a/OxGSogHDx7A19cXN27cyHMFcknRBjMzs3wt2Ed+zd7eHh4eHrh8+TJev36NlJQUaGtr8x1WqSCpatesWTN4eXkhMzMTHTt2RLdu3XiOrPiws7PD3r170aVLF6xbtw5169aFm5sbLl26hP3792Pu3Ll8h1jqREZGYsOGDQB+lrcGgHnz5nFt0aRJExw9erTYlkQuKj09Pe7/b968wbhx45Ceno7bt2+jcePGAIANGzbg1q1bCAsLw8SJE+Hj48NXuOQ/JAuvx8XFwd7eHr6+vqhQoQJ3PWMMHz58wIIFC9CvXz9UrVoVAGBrawuxWIywsDBuX11dXTx79kzh90FXVxeOjo5wdHTEgAEDuLglRCIR3r17h9TUVFSrVo3bfvjwYZw/fx7t27eHu7s7jIyMuOsEAgGGDBmChg0bolevXggJCYG7uztmzJiBefPmlfplLApMISkbj6gnqeDEYjHz8/Nj69evz3MfycKbDRo0UGBksqdsbWJiYsIAsICAAL5D4QUf7dG2bVsGgJuXpKOjk2uhktKqIG0yd+5cBoBpaGhw/69cubJSL0BaHOWnTYYNG8YAsGbNmrHv37+zTp06cb3VXl5epWZ4XX78+PGDjRs3jrVr1y7Hc/X69etMIBAwAHlOKVC2z5GS7vbt28zAwIABYI6Ojiw2Npa77suXL2zlypVSw0nnzZvHXZ+YmFis3t/FYjF78eKF1PMyexESoVDImjRpwlasWMHCwsKkbpuSksJGjhzJ7duoUSMWERGh6LvAUabXidzmJGWXmprKEhISpC7KhpIk+Vi1ahUDwHr27Ml3KEWibG0i+cK+ceNGvkPhhaLbIyMjg+nq6jIAzMjIiAFgK1asUMi5i4uCtIlIJGKdO3dmAJi5uTk35OPevXsKiLT0+F2bvHr1iquWeeLECVajRg0ueS3O1UjlLXuFv2/fvrFevXqxN2/esKlTpzIArFy5cuzz5885bqdsnyMlma+vL9PW1mYAWJMmTVh8fDz3+Hfu3JmpqqpySYGqqipr164dO3v2LN9hy9StW7fYlClTmL29fY75THXq1GHz589nISEhXGJ15MgRboitoaEhO3HiBC9xK9PrJL+5QYHXSUpOTsaYMWNQvnx56OjowMjISOpCireMjIx87UcLycpHnTp1AABHjhzhN5BSIjAwEElJSdDQ0MD3799RvXp1jB07lu+wii0VFRXs2bMHdnZ2+PTpE3R1dQHQmkmKtmDBAojFYjRv3hxjx47F8+fPYWZmhlu3bmHw4MF8h6e0hEIh9/9Zs2ZxC3Xq6+vDwcEBcXFxGDp0aI41cohiXLhwAR06dEBKSgo8PDxw8OBBbNy4EdbW1ujSpQtOnz6NrKwsODs7Y/369di1axdOnTqFDh068B26TDVp0gTLly/H8+fPER4ejvXr16Nly5YQCoUIDg7GP//8g5o1a6J69eqYOXMmKlasiKCgIDg7OyM+Ph7dunWDl5cXUlNT+b4rSq/ASdK0adNw9epVbNq0CRoaGti2bRvmzZsHc3Nz7Nmzp0DHWrx4MZycnKCnp4fy5cujS5cuCA0NldonLS0NXl5eKFu2LHR1ddG9e3d8+fKloGGTfPj48SMqVKiAGTNmQCQS/XJfWkhWPiQfvnfu3EFWVhbP0ZR8169fB/C/HwfWrVsHdXV1HiMq/vT19XHq1CkYGBggNjYWwM8x9JmZmTxHVjq8evUKBw8eBPDzPT0qKgr29va4d+8enJyceI6u+Jg8eTJat26NtLQ0zJ49G+np6VBTU8OFCxewefNmvsMrdS5evIiuXbsiIyMDbm5usLGxQbVq1TBr1ix8/vwZJiYmmDJlCkJCQnD//n2MHDmS+5GmJKtYsSLGjBmDK1euIDo6Gjt27ECHDh2grq6O169fY8mSJXB2dsajR49w+/Ztbp65t7c3GjRogJcvX/J8D5RcQbuoLC0t2bVr1xhjjOnp6XHln/fs2cPatm1boGN5eHiwnTt3spCQEBYcHMzatWvHrKyspKqKjBo1illaWrIrV66wR48esYYNG3ILPuYHDbfLP8mQAldX19/uW69ePQYg3xVXlJWytcmrV6+4srN5VRYsyRTdHm5ubtwwhW7duinknMVNYdvk/PnzzN7enhvGeP78eTlFWPr8qk0kFdk6d+7Mnj59yjp27Mi+ffvGQ5TFn1gsZrt372ZlypRhALi5SZqamuzVq1fcfsr2OVLSXLp0iWloaDAArGXLllw74P+Hl+3duzfHHLvS3iYJCQns0KFDrGfPnqxMmTJSZcXHjh3LNDU1GQCmpaXFfHx8FDJvVJnaRG5zkrJPaq5QoQK3sOy7d++Yjo5OIUL9H0lZ6Rs3bjDGfi7wpaamxo4ePcrt8/LlywJNbKckKX+Sk5O5xfPyM35Xsq5McHCwAqKTH2VrE7FYzE1Iffz4Md/hKJwi2yMjI4P74NXQ0GDh4eFyP2dxVJQ2yczMZGPHjmUAWJ8+feQQXemUV5u8ePGC+wJZGt8/5CUmJoZLPiWX7IvzKtvnSEly8eJFblmGLl26sLS0NFarVi3Wrl07duXKlTy/3FOb/E9mZqbU3/Xr12cApBZW7tatm9zXVFKmNpFpCfDsKlWqhPDwcFhZWaF69eo4cuQInJ2dcfbsWRgaGhaiL+t/EhISAABlypQB8HO+QGZmJlq3bs3tU716dVhZWSEgIAANGzbMcYz09HSkp6dzf//48QMAkJmZyftwD8n5+Y4jNwcPHkR8fDxsbGzg5ub2yxhTUlIQFxcHADA3N1fK+5Nfytgm9erVw7Vr1/Dw4UPUrFmT73AUSpHtERAQgPT0dOjq6mLu3LmoUKGCUj0PlEVR26R3795Yv349jh8/jpCQEKlStqRwcmsTkUiEzp07gzGGRo0aoWbNmvR8lhFDQ0Ps3LkTffr0wahRo/Dx40e8ffsWtWvXhp+fHzcfmx5v2dq/fz83h65NmzbYt28fVFRUcOvWLW6JjLyGpSvjZzufsj8O8+bNw8mTJzF79mzs378f//zzD06cOIGTJ0+iZcuWGDp0KNq0aSPz4YrK1Cb5jaHASdLgwYPx5MkTNG/eHDNmzEDHjh2xYcMGZGZmYtWqVQUOVEIsFmPChAlo3Lgx98UwOjoa6urqOZIvExMTREdH53qcxYsXY968eTm2+/r6Ks26M35+fnyHkMOyZcsA/JwQeOnSpV/u+/HjRwCAlpYW7ty5A4FAIPf45E2Z2sTAwAAAsGPHDsTExKBWrVo8R6R4imiPo0ePAgBq1aqFypUr48KFC3I/Z3FW2DZhjMHQ0BDx8fFo3bo11q9fT/O+ZCR7m3z48AFv3rwB8HP9Ono+y8eKFSuwYsUKPHr0CC9fvkSVKlUwbNgwtGzZUqk+R4qr9PR0aGho4OnTp1iwYAEAQFVVFc2bN+fWtCsIapPcdejQAUFBQbC3t8e///7Lzbu7cuUKrly5AnV1ddStWxcuLi6oX7++TBMmZWiTlJSUfO0nYKxoZVrev3+PwMBAVK5cGQ4ODoU+zujRo3Hx4kXcvn0bFhYWAIADBw5g8ODBUj1DAODs7IwWLVpg6dKlOY6TW0+SpaUl4uLioK+vX+j4ZCEzMxN+fn5wc3NTqgW9goKC0KBBA6ipqeHdu3cwMTH55f6+vr7o0KEDatSogaCgIAVFKR/K2CaHDh3iFpZr2LAhbt68yXNEiqOo9oiOjkb//v1x48YNrF27FqNHj5bbuYo7WbTJpEmTsGHDBpiZmSE0NBSampoyjrJ0ya1NBg4ciIMHD6JBgwa4desWzxGWfJ06dZL6QfGvv/7CrFmzlOZzpLgJDAzE6tWrERAQgM2bN+OPP/5AamoqmjRpghMnThR4pJIyfrYrs+/fv6NPnz64evVqjuvU1NTQvHlzuLu7w93dHXZ2doX6cVyZ2uTHjx8oV64cEhISfpkbFLgn6b+sra2LXOFszJgxOHfuHG7evMklSABgamqKjIwMxMfHS71Avnz5kucq4RoaGtDQ0MixXU1NjfdGkVCmWICfPRYA0K1bN6nHPy9RUVEAflZVUab7URTK1CbZK1Ddu3cP4eHh3GrhpYW822PkyJG4ceMGAKBVq1ZK0/bKrChtMn78eGzYsAHR0dFITk6Gnp6ejKMrnT5+/Ii9e/fC09MThw8fBvCzahU9n+Xv0KFDcHBwwIcPH2BhYQEnJyfuNcIYKxEjLORNJBLh3LlzWLlypVRi361bN6Snp6NNmzY4efJkkX5UUabPdmVWvnx5+Pv7Y8eOHRgzZgzS0tKgqamJsmXLIioqCv7+/vD398e0adNgaWmJNm3a4M8//+SWLSkIZWiT/J4/XyXA161bh7S0NO7/v7oUBGMMY8aMwcmTJ3H16lXY2NhIXe/o6Ag1NTVcuXKF2xYaGooPHz7AxcWlQOciuUtJScH+/fsB/PzimB+0RpJ8ValSBTo6OtzfBS2tT34tLi4OT548AQAYGRnB3t6e54hKvsqVK6NBgwZgjOHQoUMQi8UICwvjO6xi7e3bt2jWrBkWLlyIvn37QiwWo1OnTqhXrx7foZUKBgYG2LdvHwQCAT5+/Ij79+8D+PkLdf369bF//35aTykPycnJ8Pb2RvXq1dGlSxfcunULqqqqaNu2LbS1tZGeng43N7ciJ0ikYAQCAYYOHYrHjx+jXr16SEtLQ1RUFNq0aYMFCxbAw8MDGhoaiIyMhI+PDz5//szd9vnz5zh16hQ3X73EyE8ViIoVK7K4uDju/3ldbGxsClRdYvTo0czAwIBdv36dff78mbukpKRw+4waNYpZWVmxq1evskePHjEXFxfm4uKS73NQdbtfO3DgAAPAbGxs8l0Csl+/fgwAW7JkiZyjkz9lbBPGGGvcuDFXdcbKyoqJRCK+Q1IIRbXH7NmzGQDWo0cPuZ6nJJBVm6xfv54BYHXr1mUdOnRg5cqV4yqlkoI5e/YsV8K3WrVqXEW7wMBAvkMrdaZPn84AMD09Pfb+/Xu2YMECBoBVrVo1R1nq0u7Tp0/sr7/+4kqqA2CGhoZsxowZ7PLly1yF3ebNm7Pk5OQinUtZP9uLi4yMDDZ37lymqqrKALDy5cuzU6dOseTkZHbx4kU2fvx4qTaaNm0aA8CGDh3KbUtLS2P3799nqamp3DGVpU3kVgJclpCtnGb2y86dO7l9UlNT2Z9//smMjIyYtrY269q1K/v8+XO+z0FJ0q+1a9eOAWCzZ8/O922aNm3KALCDBw/KMTLFUMY2YYxxZZMlJaqvXr3Kd0gKoaj2aNmyJQPAvL295XqekkBWbRITE8OEQqFU6dl69epJrYtHfm/Hjh3c49iyZUvWs2dPBoB16tSJ79BKpfT0dFa7dm0GgLVp04alpKSwf//9l128eJHbJyUlhVtTsjR69OgR69evH1fKGwCrVKkSW7duHUtMTGQhISHcsiIuLi4sMTGxyOdU1s/24ubRo0esRo0aXLv17ds311Lhy5cvZ/b29mzPnj3ctoCAAAaAqaqqstq1a7MZM2YoTZvIJUnKyMhglSpVYi9evChScIpESVLevnz5wn3YZl8Y73esrKwYAHbnzh05RqcYytYmEjt27GAAmJmZGQPABg4cyHdICiHP9vjw4QPbsGEDS0pK4n6Ff/nypczPU9LIsk0kP8qMGTOG+1LUoUOHHOt4kJzEYjGbN28e92WlefPm7PHjx0xFRYV6kXgWHBzM1NXVGQC2cuXKHNevXLmSCYVCNnz4cPbhwwceIuSPZLSK5NKoUSN2/PhxlpWVxRhjLDQ0lJmYmDAArH79+lKLnhaFsn62F0dpaWls+vTp3HuNoaEh27JlS64jXLKPSDp9+jT3Po//X4tJWdokv7lBvuYkSaipqXFzk0jxd/jwYYhEIjg5OeV77ZKsrCyucENRC3aQvEnmFUjWDjt27BiSkpL4DKnYmzJlCsaMGYNevXohLS0NpqamtGaPgvXv3x8AcPr0aZw4cQKampo4d+4cvLy8aP7GL2RlZWHkyJGYM2cOAGDq1KmYMGECVqxYQXORlIC9vT23ns/06dNx584dqeufPHkCkUgEHx8fVKlSBRMmTEBkZCQfocpdbGwsgoODub/bt2+PsmXLwtPTEw8ePMCdO3fQrVs3CIVCvHv3Di1btsSXL1/g4OCAy5cvc0tgEOWhoaGBJUuW4P79+6hXrx7i4+MxcuRINGnSBE+fPpXaN3vBkk6dOiEmJgYfPnzAyZMn8eeffyo69CIrUJIEAF5eXli6dGmeC3iR4sPExASOjo7o169fvm/z6dMniEQiqKmpwczMTI7RlW729vZQV1dHSkoKKlasiOTkZJw4cYLvsIqta9eu4ciRI1BRUeEqOLq6ulIFKgXr0qULDA0NERkZibS0NBw4cAACgQBbt27FokWL+A5PKSUnJ6Nr167w8fGBiooKNm7ciEWLFuHTp084dOgQAOCff/7hOUrSpk0b9OrVC1lZWejVqxdiYmK463bv3o3bt2+jWbNmSE9Px9q1a1GpUiUMGjQIz58/5zFq2Tp37hwqVKiAIUOGcNv09fXx4cMH7Nu3T6pya2RkJFq1aoWoqCjY2dnBz88PZcqU4SNskk/169fH/fv3sWbNGujq6iIgIAD16tXD6NGj8eXLl1xvIxAIYGlpiS5duqBZs2YKjrjoCpwkPXz4ECdOnICVlRU8PDzQrVs3qQspPnr27IlHjx5hzJgx+b7N+/fvAQAWFhZQUSnw04fkk5qaGrfuWMOGDQH8/KAlBZeVlYWxY8cCAEaNGoVXr14B+JkkEcXS1NREnz59AAA7d+5E165dsX79egDA7NmzsWvXLh6jUz7R0dFo3rw5zp07B01NTZw4cYL7NfbIkSMQi8Xo2LEjHB0deY6UCAQCbNq0CXZ2doiKioKnpydEIhF3fePGjXH9+nVcvnwZrq6uyMrKwu7du1GzZk106NAB58+fl9q/OIiIiEBgYCD3t4uLCwQCAYRCIeLj47nt2traUrf7/PkzWrZsiYiICFSuXBn+/v4oX768osImRaCqqorx48fj1atX+OOPPyASibB582ZUrlwZixYtyvcircVFgb/lGhoaonv37vDw8IC5uTkMDAykLqT4KUiyIyn/TUPt5K9u3boAwP26du3aNS5JJfm3ceNGPH/+HGXLlsWsWbNw7949AECLFi14jqx0kgxLOnnyJOLj4+Hl5YUZM2YAAIYNG4YLFy7wGZ7SePnyJVxcXBAYGIhy5crh6tWr6Ny5MwDg9evX3LoykiF4hH+6uro4duwYtLW14e/vjwULFkhdLxAI4O7ujmvXruHevXvo3r07BAIBzp8/jw4dOsDGxgbz58/Hx48feboHvxcTE4ONGzeicePGsLGxwbhx47jrypYtizdv3uDhw4d5Lv4aExODVq1a4e3bt7C2tsaVK1dgbm6uoOiJrFSoUAFHjx7FjRs3UL9+fSQlJeHvv/9G1apVsWHDhpIzNUcxU6T4Q4Ubcnfp0iX2/fv3At9u0aJFJaqQgDK1yX9t2rSJAWAeHh5cNbaCVCEsjmTdHl++fGEGBgYMANuyZQu7evUqA8DMzc3zXfK+tJN1m4jFYq5a0qZNm7ht/fv3ZwCYpqYmu3LlikzOVZzdvHmTqaurs8qVK+eojObp6ckAsPbt2/MUHcnuv6+Rffv2MQBMIBBIVbnLzevXr9nEiROlymJXr15dEWHni1gsZi9evGDLli1jzZs354o9Se5fq1atWFpaWr6O9fXrV+bg4MAAsAoVKrCwsDC5xa3Mn+0ljUgkYvv37+eKegFgpqambOXKlVLVS5WpTeRSuIGUDDExMWjbti3Kly+P2NjYAt1W0pNBPUnyJ5mI/fjxY4wYMQIAsGvXLojFYj7DKlZmzpyJhIQE1KtXD0OHDsX169cB0HwkPgkEAq43aefOndy27du3o3PnzkhLS0OnTp1yTH4vbZo2bYqzZ88iICAAlStX5ra/fv0aBw8eBPBziCJRPp6enhg5ciQYY+jTpw9ev36d575VqlTBqlWrEBUVhX379qFZs2bo0aMHd31ycjKaNGmCv//+GxkZGYoIHx8+fMD+/fsxcuRIVK5cGfb29pg2bRpu3LjBFXtavXo1Pn78CH9/f2hoaPz2mF+/fkWrVq3w9OlTmJiY4OrVq6hUqZIC7g2RNxUVFfTt2xehoaHw9vaGlZUVoqOjMXnyZFhaWmLKlCnFd/HwwmRgR48eZT169GANGjRgdevWlbooG+pJyunRo0fM3t6eOTo6Fvi2bdq0YQDYtm3b5BCZ4ilLm+QmJSWF+9Xu3bt3bOHChSW+fKws2+PevXvcr1p3795ljP1vjS8fH58iH7+0kMdrJDo6mntuP3/+nNuelpbG3N3dGQBmbW1dqhbjFIvFbMWKFezp06e/3E/S4+bk5KSU71ulUW6vkbS0NNaoUSNuYdlv377l+3jZe7kvXLjAvR6yb1+/fj3bs2cPe/ToUaFGhTD2cx3KuLg47u/o6Gip3gDJRV1dnXl4eLD169ezd+/eFfg8sbGx3FpS5cuXZyEhIYWKtyCU+bO9pEtPT2c+Pj6sUqVKUr2Obdu2ZTNmzFCK93W5LSa7du1apqury8aMGcPU1dXZyJEjWevWrZmBgQH766+/Ch2wvFCSlLfCrEcgWQTSz89PDhEpnrK1yX/VrFmTAWBnzpzhOxSFkFV7iEQi5uTkJDU0NDk5mVvMsDQv7FhQ8nqNdOrUiQFgU6ZMkdqenJzM/vjjD/b48WOZnk/ZrVixggFgFhYWeb43h4aGcmuVrFixQmnft0qbvF4j0dHRzNLSkgFg7u7uhVoPLDY2lu3cuVPqhx2RSMT09fWlEpkyZcqwOnXqsFatWrEePXqwESNGsD///JONGTOGjRs3jg0fPpwFBQVxx/Dx8eHWrsl+XB0dHSYUCpmTkxObNGkSO3XqVJEWd42NjeWG2JmYmEj9KCJPyv7ZXhpkZWWxs2fPcj+uA2BVqlRRijbJb26gWtCeJ29vb2zduhV9+vTBrl27MG3aNFSqVAn//PMPvn37VtDDER4VtNAGY4yG2ylYvXr1EBISgsePH6Njx47cdsYYDRf7hZ07d+Lhw4fQ09PDkiVLAAABAQHIzMyEhYUFbG1teY6QDB48GGfOnMHevXvx77//Qk1NDcDPSlhHjx6V2jc5ORk6Ojp8hKkwQ4YMwY4dO+Dl5ZXne/PChQshFovRrl07qSF4RDmZmJjgzJkzaNy4MXx9fTFlyhSsWbOmQMcoV64cBg0aJLUtNTUVgwcPRmBgIN68eYMvX77g27dvv/0O1qpVK9SpU4eLDYBU6WYVFRVcv34d1atXh66uboHizE1sbCxatWqFZ8+ewdTUFNeuXUP16tWLfFxSPAiFQnTo0AEdOnTA27dvsWnTpmK3Hl6Bk6QPHz6gUaNGAAAtLS0kJiYC+LlIYMOGDbFhwwbZRkhk6tu3b9DR0cnXGOLcbisp72hpaSnr0Egu6tWrhz179uDx48cAgLt372LhwoVwdHTMUTmJ/PT9+3fMnDkTADB37lyYmpoC+FkdEKD5SMqiffv2MDY2xpcvX3Dp0iWpHwGyCwgIQJcuXbB37164u7srOEr5evfuHWxsbCAQCGBkZISgoCCoq6vnuu+bN2+wf/9+AD/nIuW1LglRLnXq1MGePXvwxx9/YO3atahSpQq8vLyKdEwdHR2pZCspKQlhYWH49OkTvn79im/fviE+Ph4ikQhisRgikQhaWlqoUaMGd5vWrVsjLi4ux9pE9evXL1JsEpIqdiEhIZQgEVSuXBlLliwpdtVLC1y4wdTUlPu1wsrKiiunGx4eXuwyxNJo/vz5KFOmDLc2SUFIepFMTEygqakp69BILiTFG4KCggD8XDfl4sWL2LZtW7FbU0NRVqxYgdjYWNjZ2XHrIwHgijZQ6W/loKamxi1kLSngkJv169cjJiYGGzZsKDGfMYwxbNmyBXZ2dvD29ua255UgAf/rRerQoQOti1TMdO/enftRa+zYsTh27JhMj6+rq4vatWujbdu26NevH8aNG4d//vkH8+bNw4IFC/Dvv/9i9uzZqFmzJncbLS0tlC1bVi4/GL1//x5NmjRBSEgIzMzMuN4pQoqbAidJLVu2xJkzZwD8HC4xceJEuLm5oVevXujatavMAySydenSJaSkpKBChQoFvi0NtVO82rVrA/i5OnlsbCw6duyI2bNn49atWxAKhTxHp5xmzpyJmTNnYv369dwQruTkZDx48AAAJUnKZMiQIQCAs2fPIjo6Otd9du3ahblz5+LgwYMlogcwMTERffv2xahRo5CRkYHr16//Nvl78+YN9u3bB4DWRSquZs2axVW88/T05H60KWlevnyJxo0b482bN7C2tsaNGzdQrVo1vsMipFAKnCRt3boVs2bNAgB4eXlhx44dsLOzw/z587Fp0yaZB0hkJzw8HKGhoRAKhWjVqlWBby9ZSNbKykrWoZE86Ovro0qVKgB+9iapqalh/vz5NB/hF3R1dfHvv/9KPcfv3LmDzMxMWFlZoWLFivwFR6TUrFkTDRo0QFZWVp69Serq6pgzZw43J4kxhl27diEzM1ORocrE06dPUb9+fRw6dAhCoRDLli3D4cOHf5v8SXqR2rdvL7PhUESxBAIBNm7ciK5duyIjIwOdO3fGkydP+A5Lph49eoSmTZsiKioKdnZ2uH37Nvf5RUhxVOAkSUVFBaqq/5vK1Lt3b6xbtw5jx4795VABwr/Lly8DABo1alTgog0A9STxJft6Sf9VUoYfyUJERESea0hlH2pXEnojSpJRo0YB+PkDXH7WAFuyZAkGDx6M1q1b49OnT/IOTyZEIhFWrlwJZ2dnvH79GhYWFrh58yamTp0KFZVffwy/ffuWm4tEvUjFm1AoxIEDB9C0aVP8+PEDrVu3RkhICN9hycSVK1fQokULfP36FU5OTrh58yYsLCz4DouQIilwklS5cmXMnTv3l4ujEeUkSZI8PDwKdXtKkviRW5L07NkzdOvWDX/++SdfYSmVxMRENG7cGI0aNeJ6PLPLXrSBKJeePXvCwMAAERER8PX1/e3+Dg4O0NXVxc2bN1G3bl1cuXJFAVEWXlhYGFxdXTFlyhSkp6ejffv2CAoK4gog/c7ChQshEonQrl07ODk5yTlaIm+ampo4c+YMHB0dERcXh5YtWxb7RGn79u1o06YNkpKS0LJlS1y5cgXlypXjOyxCiqzASZKXlxfOnz8POzs7ODk5Ye3atXmOJSfKQyQScb+mu7m5FeoYki+flCQpVt26dQH8r3gDAMTHx+PkyZPYtWsXvn79yldoSiMoKAiJiYmIi4uDsbGx1HVJSUl4+PAhAJqPpIy0tbUxcOBAAMCWLVt+u3/79u0RGBgIBwcHxMTEwM3NDX///TfS09PlHWqBZGVlYfXq1XBwcMDt27ehq6sLHx8fnD17Nt9fIN++fUtzkUogQ0ND+Pn5oV69eoiNjUXLli3x/PlzvsMqMLFYjBkzZmDYsGHIyspC3759cf78eejp6fEdGiEyUeAkaeLEiXj48CFevnyJdu3aYePGjbC0tIS7uzv27NkjjxiJDDx79gzx8fHQ09PjeiYKStKTRHOSFEuSJL19+xYJCQkAgCZNmqBu3bpIS0vD1q1b+QxPKTRr1gwvX77E4cOHoaWlJXXd7du3IRKJYGNjQwm+kho5ciSAnwUcoqKifrt/1apVce/ePQwbNgyMMSxatAiOjo5ccQ6+3bp1C/Xq1cOkSZOQkpKCFi1a4NmzZxg2bFiBhnsuWrSI60VydnaWY8RE0YyMjODn54e6desiNjYWzZo1w927d/kOK9+SkpLQs2dPLF26FMDPJH7fvn1U+ZaUKAVOkiSqVq2KefPm4fXr17h16xZiY2MxePBgWcZGZEjSi9S4cWOpOWX5lZKSgtjYWADUk6Ro5cqV4xJTyZA7gUCACRMmAAA2btxYLCexy1qFChVyLY0see7TUDvlZW9vj6ZNm0IkEmH79u35uo2WlhZ8fHxw9OhRGBsb4/nz53BxccHYsWN57V3NysrC4MGD8ezZM5QtWxbbtm2Dv79/gQuGvH37Fnv37gVAvUglVZkyZeDv748GDRrg27dvaNWqFU6fPs13WL/16tUrODs74/jx41BXV8e+ffswd+5cmu9JSpxCJ0kA8ODBA0yYMAFdu3bF69ev0aNHD1nFRWTsxo0bAIDmzZsX6vaRkZEAAD09PRgaGsoqLJJPkrkIkmFjANCrVy+YmJggKioKJ06c4Cs0Xh0+fPi381gk85FoqJ1yk/Qm+fj4ICsrK9+3++OPP/DixQv07dsXYrEYGzZsQOXKlbFy5Upu8Wt5e/v2LdLS0gAAqqqqWLt2LUaNGoXXr19j6NChvy3OkBtJL1Lbtm2pF6kEK1OmDK5cuYL27dsjLS0N3bp1w/r165W2KM+RI0fg5OSEly9fwtzcHNeuXYOnpyffYREiFwV+5379+jXmzJmDqlWronHjxnj58iWWLl2KL1++4NChQ/KIkRSRWCzGzZs3ART+1/TsQ+3o1yLFk3xJyj6cSENDg6sMln319dLiy5cvGDlyJDw8PPJcxfvHjx8IDAwEQD1Jyq579+4oW7YsPn78iIsXLxbotuXKlcP+/fvh7++P2rVrIz4+HlOmTIG1tTWePn0qp4h/mjhxIqpWrSo17LV9+/bYtGkTypQpU6hjvnnzhnqRShEdHR2cOnUKQ4cOhVgsxrhx4zBo0CCkpqbyHRonMTERI0aMQK9evZCUlIQWLVrg8ePH+S5AQkhxVOAkqXr16rh06RK8vLzw8eNHXL58GQMGDICurq484iMy8Pz5c3z79g06OjqFXqmdKtvxS5IkZe9JAn6WT9bQ0MC9e/dw69YtPkLjzeTJk5GQkABHR8c8KzZK5iPZ2trC0tJSwRGSgtDU1MSgQYMAAN7e3oU6RqtWrRAYGIjt27fDxsYGmpqaqF69Onf9y5cvi/TFkzGG4OBgfP/+ndtmZ2fHbZeVOXPmcHORGjRoILPjEuWlqqoKHx8frFixAkKhEHv27EGjRo2UopLwzZs3Ubt2bfj4+EAgEGDGjBnw9fWFiYkJ36ERIlcFTpJCQ0Nx//59jB8/nl4gxYRkqF2jRo2gpqZWqGNQksQvR0dHCAQCfPjwQaqapKmpKffFcvHixTxFp3j+/v7Yv38/VFRUsHnzZgiFwlz3o9LfxcuoUaMgEAhw6dIlhIaGFuoYQqEQQ4YMwevXr3HlyhVu/T6RSITWrVvDyMhIqncpKSkJGRkZOY4jEokQHR2Nq1evYu3atejTpw9MTU1Rt25dHDx4kNuvX79+ePXqFXbs2FGoeP/r2bNn3KiMhQsXyuSYpHgQCASYPHky/Pz8YGxsjODgYNSpUwfr1q3L1xpisvb161eMGjUKrq6uCA8Ph7W1Na5du4bFixcXam4zIcVNgZMkWj25+ImKioKamlqh5yMB/yv/TZXt+KGnpwd7e3sAOXuTJAtSXrx4Uaa/ZiurpKQkDB8+HMDPJQnq16+f577ZF5Elyq9y5cro0KEDAGD9+vVFOpaqqiqqVq3K/f3u3TuoqKhATU1NqndpzJgx0NDQQNmyZWFhYQELCwuUL18eampqMDMzQ6tWrTBhwgQcOnQIMTEx0NbWllrEVltbG9WqVStSrNnNnj0bjDH07NmTq2xJShfJULbWrVsjNTUV48ePR4sWLfDkyROFnD8rKwtbt25FtWrVsGXLFjDGMGTIEDx9+rRI3yMIKW6KVLiBFA+LFy/Gjx8/MG7cuEIfg3qS+JfbvCQAsLW1Ra9evQAAS5YsUXhcijZr1ixERETA2toaixYtynO/hIQErhog9SQVH5Kqjbt27UJ8fLzMjlulShV8+PABL1++5HqXAHDr03z79g1RUVGIiopCbGwsGGMQCASoVKkSOnfujDlz5uDGjRv4/v273Hp47t+/j9OnT0NFRQXz5s2TyzlI8WBhYQFfX194e3tDR0eHWzx5xIgR+SqTXxgikQj79u2DnZ0dRo4cia9fv6JWrVq4ceMGtm/fDn19fbmclxBlRUlSKaGpqVmkBd4oSeJfXkkSAMyYMQMAcPTo0f9r787Dqqzz/48/D4uIggu4ooiaG7nivm+5l2aLM5qlqdVULqNOX0drxi3LyZzGnBpp1FzGTFtGMy333VBRBtdSQcUVcUNEDBDO7w/nnB+MG3AO3PfhvB7XxXXJzX0+90s+oLz5bMTExBRoroK0a9cu+wjD3LlzH/o1vWPHDjIzM6lZsyaVKlUqqIjioE6dOlGvXj1u3bqV4+3Ac8pisVC5cuVs1/bs2cOVK1c4fPgwUVFR7N+/n4MHDxIfH09aWhqxsbGsXLmSyZMn0759+2wFlrP96U9/AmDw4MHZRrvEPVksFt544w2OHDnCb3/7W6xWK3PnzqVatWoMGzbMaQfQXrlyhRkzZlCzZk1eeuklYmJiKFOmDLNmzSIqKor27ds75TkirkZFkjxSRkYG586dA1QkGcm2DfjevXvv2R62QYMGPPnkk2RmZtoP9ytsbt++zdChQ+1TP7p27frQ+3U+kmvKegbY3//+91xtB54XHh4eBAYGUrduXcLCwmjcuDH169enfPnyBbruYsuWLWzcuBFvb28mTpxYYM8V8wsJCWHZsmXs2LGDdu3akZ6ezueff069evVo1qwZs2bN4ueff87VtuEXLlxgwYIFPPXUU1SqVIk//vGPnDp1ioCAAKZPn86pU6f4/e9/r7VH4tby/NWflpbGqVOneOyxx/RNZGLvvPMOa9eu5a233mLAgAF5auPChQtkZGTg5eVFhQoVnJxQcqp+/fr4+PiQmJhITEzMPesD3377bdLT03nttdcMSpi/bIdXV6xYkb/+9a+PvF/nI7muF154gT/+8Y/ExcWxatUqnn32WaMj5Sur1co777wD3D0vKrcHz4p7aNu2Ldu3byciIoIPP/yQ77//nn379rFv3z4AgoKCaNy4MY8//jjBwcGUKlUKX19fbt++zc2bN4mLi+PkyZPs3bvXPjvEpnHjxgwfPpz+/ftTrFgxI/56IqaT6+omJSWFkSNHsmjRIuDuuUnVq1dn5MiRVKpUyT7tR8xh586dREVF2Q86zAvbP6bBwcEP3EVM8l+RIkUICwtj9+7dREZG3lMktW7dmnXr1hmULn/t3buXmTNnAhAeHv7IA40TExP5z3/+A2gkyRX5+vry+uuv89577zFr1qxCXyStXr2aiIgIfH197cWSyIO0atWKf//731y+fJlly5bx3XffsXPnTi5cuMCFCxdYvXr1I9vw8PCgUaNG9O3bl2effZbHH39cZyCK/I9cF0kTJkzgwIEDbN26lR49etivd+nShcmTJ6tIMpklS5awe/du2rRpk+c2bDvbaaqd8Zo3b87u3bvZu3cvL7zwwkPvtS08d3XJyckMHDiQjIwMXnjhBfr06fPI12zfvh2r1Urt2rWpWLFiAaQUZ3vzzTeZMWMGO3bsICIiglatWhkdKV/cuXOHP/7xjwCMGjVKo/WSY2XLlmXkyJGMHDmS27dvExkZyZEjRzh69Cjx8fEkJiZy+/ZtfH19KVasGFWqVKFatWo0aNCAFi1aOLROWcQd5LpIWrlyJcuXL6dly5bZfgCrW7cusbGxTg0njgsODnb4EE3bSJK2/zbewzZvsLl8+TLvvfcely9f5osvviioaPkmOjqa+Ph4KleuzCeffJKj12g9kusLCgripZde4vPPP2f69OmsWrXK6Ej5Yv78+fz8888EBgYyYcIEo+OIi/L19aV9+/baZEHEiXK9ccPly5cpV67cPddv3bpVKH5rLfc6ffo0gObJm4CtSIqKiiI9Pf2+9yQkJDB79myWLl1qitPaHdW2bVsOHDjAN998Q+nSpXP0Gq1HKhzGjRuHxWLh+++/5/Dhw0bHcbqbN2/aN2mYNGkSJUuWNDiRiIjY5LpIatq0KWvWrLG/byuM5s2bV2inQ7iqv//977z//vsObwltK5KqVavmhFTiiBo1alCqVClSU1M5dOjQfe+pW7cukyZNYsOGDdkO03Rl1atXp0WLFjm699q1a/ZDF3XwoWurXbs2zz33HFA4zwCbMWMGCQkJ1KxZk9/97ndGxxERkSxyXSS9//77vP3227zxxhvcuXOHjz/+mG7durFgwYKHHuwoBW/evHm88847Dv8G9tSpU4BGkszAYrHkaMrdpEmT6NKlS0HFcrrMzEyGDRvG5s2bc/1a23qk0NBQre8oBGxT0JYtW2b/t6gwOH/+vH2Xxg8++CBfz18SEZHcy3WR1LZtW6Kjo7lz5w7169dn/fr1lCtXjoiICJo0aZIfGSUPUlNTOXr0KHB3a8+8yszMtK9JUpFkDrbzkiIjI3N0/8WLF0lJScnPSE43d+5cPv/8c/r06UNCQkKuXqv1SIVL48aN6datGxkZGXz44YdGx3GaP//5z9y+fZu2bdvSt29fo+OIiMj/yNNhso899hhz585l7969HD16lCVLllC/fn1nZxMHHD58mDt37hAQEODQxg0XL14kLS0NT0/Pe06qF2PkZCTJZt68edSqVcu+fbarGDRoEEOHDuWTTz657xrIh7GtR1KRVHi8/fbbwN1NDmy7bbqyffv2sXDhQgBmzpyp9bwiIiaU6yLJ09Pzvr/ZvXr1qs7QMRHbGTFhYWEO/QdsW48UHBysQ4NNwjaSdOTIEW7evPnQe/39/UlOTmb69OkOr00rSL6+vsyfP5+XX345V6+7evUqBw8eBFQkFSbt27enY8eOpKWl8e677xodxyGZmZmMGDECq9XKwIEDc7zWTkREClauiySr1Xrf66mpqZpTbSJZiyRHaNMG86lYsSLBwcFYrVaioqIeeu9vfvMbunbtyq+//sqrr776wO9fM0hNTSU8PJyMjIw8t7F9+3YAHn/88VyPQIl5WSwW+5rXBQsWcOLECYMT5d2CBQvYs2cP/v7+hWr6oIhIYZPjoYHZs2cDd/+zmjdvHn5+fvaPZWRksH37durUqeP8hJInziqStGmDOTVv3pyzZ8+yZ8+eh+7gZrFY+Oyzz6hXrx5bt25l3rx5vPrqqwWYNGesViu/+93vWLRoEZ06daJ37955akdbfxderVu3plevXvzwww9MmTKFJUuWGB0p165fv24/cH3y5Mk66FhExMRyXCT97W9/A+7+MBMeHp5tal2RIkWoWrUq4eHhzk8ouZaRkWHfAtmRTRtAZySZVcuWLfn222+JiIh45L3VqlXjvffeY8yYMbz11lt0797ddAcDz5w5k0WLFuHp6enQtt3atKFwe/fdd/nhhx9YunQp48ePp169ekZHypU///nPXLlyhccff5yRI0caHUdERB4ix9PtTp06xalTp+jQoQMHDhywv3/q1CmOHTvGunXrNLfaJE6cOEFKSgrFihWjZs2aDrVlG0nSdDtzad26NQA//fRTjqbQjRw5kpYtW5KUlMTAgQO5c+dOfkfMsZUrV/LHP/4RgI8++ohGjRrlqZ3Lly/bz47S+UiFU+PGjXnuueewWq32ERlXsX//fubMmQPAJ598gre3t8GJRETkYXK9JmnLli05PvVejGGbatewYUOHN9PQSJI5NW7cGG9vbxISEnJ0doynpydffPEFJUqUYOfOnUydOrUAUj7a1q1b6d+/P1arlTfeeIM33ngjz23Z1iPVq1ePsmXLOiuimMx7772Hl5cXa9asYf369UbHyZH09HSGDh1KZmYmAwYM0HRQEREXkKftys6dO8eqVas4c+YMaWlp2T720UcfOSWY5F10dDTg+HqkjIwM+3a7KpLMpWjRojRp0oTdu3fz008/Ub169Ue+pnr16nz22WcMGDCAadOm0b59e0MPnN2/fz99+vQhNTWVvn37Mnv2bIc2ltB6JPdQu3ZtRowYwaxZsxgzZgwHDhww/c6bM2bM4ODBgwQGBvLxxx8bHUdERHIg1yNJmzZtonbt2syZM4e//vWvbNmyhQULFvD555/bfzgXYx0+fBjA4bOrzp8/z507d/D29iYoKMgZ0cSJWrVqBZCjdUk2/fv3Z9iwYVitVvr168exY8fyK95DHTx4kB49enDz5k06derEl19+6fAPulqP5D4mTpxIYGAgR48e5bPPPjM6zkP9/PPP9pHbjz/+WKOcIiIuItdF0oQJE3jrrbc4dOgQRYsW5dtvv+Xs2bN06NCBfv365UdGySVbkeToombbVLsqVaroDCwTsq1Lyk2RBHfXQ7Ru3ZrExER69+7NtWvX8iPeA0VGRtKxY0euXLlC06ZN+e677yhatKhDbSYkJHDkyBFA65HcQenSpe2Fx8SJE7ly5YrBie4vIyODV155hbS0NHr16sULL7xgdCQREcmhXBdJP//8M4MGDQLAy8uL27dv4+fnx9SpU/nggw+cHlByJzMzk/79+9OrVy/q1q3rUFvatMHcbCNJBw4cIDk5OcevK1q0KCtWrCAkJISYmBj7Wp6CsH37dp544gmuX79Oy5Yt2bBhA/7+/g63u23bNgAaNGhAYGCgw+2J+b322mvUr1+fa9euMXbsWKPj3Nf06dP56aef8Pf3Z86cOQ4d7C0iIgUr10VS8eLF7euQKlasSGxsrP1jZv1tnjvx8PDggw8+YM2aNQ5vsKFNG8ytUqVKBAcHk5mZSWRkZK5eW65cOdasWcMXX3xB37598yfg/1i2bBldunTh5s2bdOzYkfXr11OqVCmntL1582ZAU+3ciZeXF3PnzsVisfCvf/2LdevWGR0pmz179jB58mQAPv30U9Ntuy8iIg+X6yKpZcuW7Ny5E4BevXrxhz/8gffee4+hQ4fSsmXLXLW1fft2evfuTVBQEBaLhZUrV2b7+Msvv4zFYsn21qNHj9xGljxSkWR+WbcCz626desyYMAA+/unT5/m4sWLTsv2v2rUqIGXlxfPP/88a9asccoIks2mTZsAeOKJJ5zWpphfixYtGDVqFAC/+93vcjWimp9u3rzJwIEDycjIoH///rz44otGRxIRkVzKdZH00Ucf2c9DmjJlCk888QTLly+natWqzJ8/P1dt3bp1i4YNG/Lpp58+8J4ePXpw8eJF+9uXX36Z28huJSYmhsuXLzulLU23M7+8bN5wP9evX6dnz560bNmSX375xRnRAEhKSrL/uWnTpuzZs4fly5dTrFgxpz3jzJkznDhxwuGDaMU1TZs2jZCQEOLi4hg3bpzRcbBarbz++uvExsZSpUoVTbMTEXFRud5OKutWw8WLFyc8PDzPD+/Zsyc9e/Z86D0+Pj5UqFAhx22mpqaSmppqf9/2Q1p6ejrp6el5C+oktufnZ47f/e53bN68mc8//9zh317aRpIqV65s+OcuvxREn+Sn5s2bA3eLpLS0tDz/MHblyhUyMjLIyMigdOnSDn8+rFYrM2bMYObMmfzwww80a9YMgDp16tifcz956Q/bWTlNmzalWLFiLtuXZmX27xEfHx/mzJlDr169mDNnDp07d+bpp582LM/s2bNZunQpnp6eLFy4kOLFizv9c2f2PnE36g/zUZ+Yj5n6JKcZ8lQkRUZG3rM4OjExkcaNG3Py5MncNvlQW7dupVy5cpQuXZrOnTszbdq0hy7Mnj59OlOmTLnn+vr1653622tHbNiwId/avnDhAhaLhatXr/LDDz/kuZ07d+5w9uxZAGJjY7l+/bqzIppSfvZJfkpPT6dIkSJcu3aNefPmUalSpTy3NWnSJBISEti9ezdwd2euo0ePUq9evTwVX5s3b+bGjRtMmjSJESNG5Oq1uemPJUuWAHd3YXTka14ezuzfI3379mXlypUMHTqUv/3tb5QpU6bAMxw6dIhJkyYBMGTIEJKSkvL1a9LsfeJu1B/moz4xHzP0SUpKSo7us1hzeXqjh4cH8fHxlCtXLtv1S5cuUaVKlWyjOLlhsVhYsWJFtkXky5Yto1ixYlSrVo3Y2Fjefvtt/Pz8iIiIeOCW1PcbSQoODubKlSuUKFEiT9mcJT09nQ0bNtC1a1e8vb3z7TkpKSkUKVLEoXNnTp06Re3atfHx8eHGjRt4eOR6ZqZLKKg+yU+dO3dm586dzJs3z77zpDMsWrSIV199ldDQUIYMGULPnj2pVavWPQVTSkoKkZGRrFixgmeeecY+5e3SpUts3ryZ/v3757jIym1/WK1WQkJCiI+PZ/369dq4IR+4yvdIWloa7du3JyoqilatWrF+/Xp8fHwK7PkxMTG0b9+eK1eu8MILL7BgwYJ8m2bnKn3iLtQf5qM+MR8z9UlSUhJlypThxo0bD60NcvxT9KpVq+x/XrduHSVLlrS/n5GRwaZNm5y+wL9///72P9evX58GDRrw2GOPsXXr1gcu0Pbx8bnvf4ze3t6Gd4pNfmfJ2jd5df78eQBCQkIK9AcNo5jp6yO3Wrduzc6dO9mzZw/Dhg1zWrtXrlyhePHi/Pzzz4wbN45x48ZRqlQpatasiZ+fH5mZmVy8eJGTJ09y584dAJKTk+nSpQtwd5pmXou2nPbH0aNHiY+Pp2jRorRr185l+9AVmP17xNvbm+XLl9O0aVMiIiIYNWoU8+fPL5D1QJcuXeKpp57iypUrNGnShLlz51KkSJF8f67Z+8TdqD/MR31iPmbok5w+P8dFkm2Ex2KxMHjw4HseVrVqVf7617/mPGEeVK9enTJlyhATE6NdrPKZNm1wHXk9VPZRxo8fzxtvvMGSJUtYuXIl27dvJzEx8b7bjQcFBdG5c2deeuklp2Z4lI0bNwLQrl07hw+kFddXo0YNvvrqK3r27MmCBQsIDQ3l//7v//L1mTdu3KBXr16cPHmS6tWrs2bNGtNM7RYRkbzLcZGUmZkJ3P2hOTIy0pD53ufOnePq1atUrFixwJ/tCiZMmMCuXbsYO3asw2ffaPtv12Hb4e7IkSMkJiY67ewhuDsqOXz4cIYPH86vv/7KiRMnOHnyJLdv3wbunpVWrVo1goODDdnBS1t/y//q1q0bf/vb3/j973/PuHHjKFmyJK+99lq+POv69et069aNqKgoypQpw9q1aylfvny+PEtERApWrhet2EYYnCE5OZmYmJhsbUdHRxMQEEBAQABTpkzhueeeo0KFCsTGxjJu3Dhq1KhB9+7dnZahMNm7dy87duxg6NChDrelkSTXUa5cOWrWrMmJEyfYtWsXTz75ZL48p2jRotSvX5/69evnS/u5defOHbZu3QqoSJLsRo4cydmzZ5k5cyavv/46RYoU4eWXX3bqMy5dukSPHj2Ijo4mMDCQDRs2ULNmTac+Q0REjJPj1fgRERGsXr0627XFixdTrVo1ypUrx2uvvZbrTRv27dtHWFgYYWFhAIwdO5awsDAmTpyIp6cnBw8epE+fPtSqVYthw4bRpEkTduzY4RZrZPLi2LFjANSuXdvhtjSS5Frat28PwI4dOwxOUnD2799PUlISpUqVsv8bIgJ3p4XPmDGDESNGYLVaGTJkCO+//z653KfogaKjo2nWrBnR0dGUL1+erVu30qhRI6e0LSIi5pDjImnq1KkcOXLE/v6hQ4cYNmwYXbp0Yfz48Xz//fdMnz49Vw/v2LEjVqv1nreFCxfi6+vLunXrSEhIIC0tjdOnT/PPf/5TUxkeIDk52b7ZgjOKJNtW7iqSXEO7du0A2L59u8FJCo5tPVKnTp0euNuluC+LxcLHH3/MH/7wBwDeeecdBg8ezM2bN/PcptVqZf78+bRp04azZ89Sq1YtduzYQb169ZwVW0RETCLHRVJ0dHS2KS3Lli2jRYsWzJ07l7FjxzJ79my++uqrfAkpj3b8+HEAypQpQ0BAgENt3b59mwsXLgDw2GOPOZxN8p9tJCkyMjLH+/+7Ott6JNtueiL/y8PDg5kzZ/LJJ5/g4eHBv/71L8LCwtiyZUuu24qNjaVPnz688sorpKSk0LVrV3bv3q0pdiIihVSOi6Tr169nG8XZtm0bPXv2tL/frFkz++GjUvCcOdXOth6pRIkSDz24V8yjatWqVK5cmTt37tgPgy3Mbt++zU8//QRoPZI82vDhw9myZQtVqlQhNjaWzp0706dPH7Zv3/7IKXhHjx7lzTffJDQ0lNWrV1OkSBE+/PBDfvzxR0qXLl1AfwMRESloOd64oXz58pw6dYrg4GDS0tKIiopiypQp9o/fvHnT8H3P3Zkzi6TY2Fjg7iiSETuWSe5ZLBbatWvHl19+yY4dO+jcubPRkfLVrl27SE1NpVKlStSqVcvoOOIC2rdvz4EDB/jTn/5EeHg433//Pd9//719M6BGjRpRqVIlLBYLly5d4siRI2zcuJH//Oc/9jZ69OjBzJkzqVu3roF/ExERKQg5LpJ69erF+PHj+eCDD1i5ciXFihWzr4MAOHjwoKZmGciZRZJtPVL16tUdbksKTvv27fnyyy/dYl1S1q2/VchLTpUqVYpPPvmEESNG8NFHH/HFF18QExOTbZfV/+Xh4UGfPn0YNWoUnTp1KsC0IiJipBwXSe+++y7PPvssHTp0wM/Pj0WLFmU7Ufzzzz+nW7du+RJSHi2/RpLEddjWJUVERJCWlpbt+7OwWbduHaD1SJI3derU4Z///CczZ85k8+bNbNmyhRMnThAfHw9AQEAANWrUoF27dnTp0kUbBomIuKEcF0llypRh+/bt3LhxAz8/v3t2k/r666/x8/NzekB5NKvVat+4oU6dOg63pyLJNYWGhhIYGMjVq1fZv3+//ZDZwubSpUv2KVD6xYw4okSJEvTt29fhw7dFRKTwyfHGDTYlS5a873a7AQEBhfo312Z2/vx5bt26hZeXl1OmyGm6nWuyrUuCwn1e0oYNGwAICwvTb/hFREQkX+S6SBLzsU21q169usObZ2RmZtp3t9NIkuuxTbkrzOuSbFPtunfvbnASERERKaxUJBUCzlyPdP78eVJTU/Hy8iI4ONjh9qRg2YqknTt3kpGRYXAa58vMzFSRJCIiIvkux2uSxLw6derE7NmznVLU2KbahYSE4OWlLw9X07BhQ/z8/Lhx4wYHDx4kLCzM6EhOFR0dzeXLl/Hz86N169ZGxxEREZFCSj8FFwKhoaGEhoY6pS1t2uDavLy8aNu2LWvXrmXLli2FrkiyjSJ17txZayBFREQk32i6nWRjK5K0aYPreuKJJ4D/f5ZQYaKpdiIiIlIQVCS5uIyMDJYuXcqePXucsgbFNt1OI0muy1Ykbd++nfT0dIPTOM/NmzfZtWsXoCJJRERE8peKJBd39uxZBg4caF+w7yiNJLm+hg0bEhgYSHJyMpGRkUbHcZotW7Zw584datSooSJeRERE8pWKJBd3+/Zt2rdvT6tWre57flVuaSTJ9Xl4eNCpUyegcE25W7t2LaBRJBEREcl/KpJcXGhoKNu2bWPr1q0Ot3Xjxg2uXr0KaCTJ1XXu3BkoXEWS1iOJiIhIQVGRJHa2qXZly5bF39/f4DTiCNu6pIiICFJSUgxO47jjx49z8uRJvL297aNkIiIiIvlFRZKLc+aBoZpqV3jUrFmTypUrk5aWxs6dO42O47DVq1cD0LFjR/z8/AxOIyIiIoWdiiQX17x5c6pUqUJERITDbWnThsLDYrEUqq3Av//+ewCeeuopg5OIiIiIO1CR5MKsVivHjx/n7NmzlC5d2uH2dJBs4VJYiqTExER27NgBqEgSERGRgqEiyYVdvnyZ5ORkLBYL1apVc7g9jSQVLrYiKSoqimvXrhmcJu/WrVtHRkYGjz/+uL42RUREpECoSHJhtqKmcuXK+Pj4ONzeiRMngLvrWcT1BQUFERoaitVqZePGjUbHyTPbeiSNIomIiEhBUZHkwpw5Pe727ducPXsWgFq1ajncnphDz549Afjxxx8NTpI3d+7c4YcffgBUJImIiEjBUZHkwpxZJNnaKlmyJGXKlHG4PTEHW5G0du1aMjMzDU6Te7t37+batWuULl2aVq1aGR1HRERE3ISKJBcWExMDQI0aNRxu6/jx48DdUSSLxeJwe2IO7dq1o3jx4sTHx3PgwAGj4+Sabapdz5498fLyMjiNiIiIuAsVSS7MmSNJWo9UOPn4+NC5c2fANafcaetvERERMYKKJBemIklywlXXJR0/fpyjR4/i5eVFjx49jI4jIiIibkRFkou6desWCQkJAE7Z/jvrdDspXGxFUkREBImJicaGyYUVK1YA0KlTJ6ecAyYiIiKSUyqSXJRtJzp/f39KlSrlcHsaSSq8qlatSmhoKBkZGWzYsMHoODn27bffAvDcc88ZnERERETcjYokF3XmzBkAQkJCHN5oISkpifj4eEBFUmFlG02ybadtdmfOnCEyMhKLxcLTTz9tdBwRERFxMyqSXFRcXBwAVapUcbgt2y55ZcuWdcqolJhPr169gLtFUkZGhsFpHm3VqlUAtGnThgoVKhicRkRERNyN9tR1UU8++SSrVq3C39/f4bZsU+20Hqnwat++PSVLliQhIYHdu3fTpk0boyM9lG09kqbaiYiIiBE0kuSigoKC6N27Nx07dnS4LdumDZpqV3h5e3vbt9G2FSBmlZiYyM6dOwF45plnDE4jIiIi7khFkmjTBjdhKzhWrlyJ1Wo1OM2D7d27F6vVSpMmTQgJCTE6joiIiLghFUkuKjw8nOXLl5OUlORwW5pu5x66d++Oj48PsbGxHD582Og4D2QbRdJUOxERETGKiiQXlJGRwahRo+jfv79Tzr3RdDv34OfnR7du3YC7o0lmdPHiRQ4dOgRA//79DU4jIiIi7kpFkgu6ffs2v/3tb+nQoQNBQUEOtXXt2jWuXbsGQI0aNZwRT0ysb9++gHnXJX399ddYrVZatmzplEOSRURERPJCu9u5ID8/P/71r385pS3bVLtKlSpRvHhxp7Qp5tW7d288PDz4z3/+w+nTp6latarRkbJZvnw5oFEkERERMZZGktycptq5l7Jly9KhQwcAvvrqK4PTZBcTE0NkZCQeHh5ajyQiIiKGUpHkgpKTk0lPT3dKWz///DMAderUcUp7Yn62UZovv/zS4CTZ2fI0aNCA8uXLG5xGRERE3JmKJBc0fvx4ihYtyvTp0x1u65dffgEgNDTU4bbENTz33HN4e3sTHR1tL5KNZrVaWbp0KXD34FsRERERI6lIckFnzpwhMzOTgIAAh9uy/ZCsIsl9BAYG0r17d8A8o0l79uzhl19+wdfXl5YtWxodR0RERNyciiQXdObMGQCqVKniUDvp6enExMQAmm7nbgYMGADA0qVLTXGw7Pz58wF49tlnKVasmMFpRERExN2pSHJBcXFxAISEhDjUTmxsLHfu3MHPz4/KlSs7I5q4iD59+lCsWDFiY2PZt2+foVmSk5NZtmwZAEOGDDE0i4iIiAioSHI5SUlJ9gNkg4ODHWor66YNFovF0WjiQvz8/Hj66acBWLRokaFZvv76a5KTk6lRowbt2rUzNIuIiIgIGFwkbd++nd69exMUFITFYmHlypXZPm61Wpk4cSIVK1bE19eXLl262M/1cVdnz54FoHTp0vj7+zvUlna2c2+2UZsvvviC27dvG5bDNtVu6NChKtZFRETEFAwtkm7dukXDhg359NNP7/vxGTNmMHv2bMLDw9mzZw/Fixene/fu/PrrrwWc1DxsU+0cXY8E2tnO3T3xxBOEhISQmJjIt99+a0iGo0ePsmvXLjw8PBg8eLAhGURERET+l6FFUs+ePZk2bRrPPPPMPR+zWq3MmjWLP/3pTzz99NM0aNCAxYsXc+HChXtGnNyJbdMGR9cjgXa2c3ceHh4MGzYMgHnz5hmS4ZNPPgGwjyiLiIiImIGX0QEe5NSpU8THx9OlSxf7tZIlS9KiRQsiIiLsB2L+r9TUVFJTU+3vJyUlAXd3cnPWAax5ZXu+IzlOnToFQOXKlR1qx2q12keSHnvsMcM/N0ZxRp+4shdffJHJkyezbds2jhw5Qq1atQrs2YmJifb1UMOHD8/2Pequ/WFG6hPzUZ+Yi/rDfNQn5mOmPslpBtMWSfHx8QCUL18+2/Xy5cvbP3Y/06dPZ8qUKfdcX79+vWm2Ft6wYUOeX7t7927g7lTFH374Ic/tXL58meTkZDw9PTlx4oS9+HJXjvSJq2vcuDH79u3jnXfeKdDd5b777jtSUlKoUqXKPV/P7twfZqU+MR/1ibmoP8xHfWI+ZuiTlJSUHN1n2iIpryZMmMDYsWPt7yclJREcHEy3bt0oUaKEgcnuVq4bNmyga9eueHt756mNDz/8EIBu3brRq1evPGfZuHEjADVq1KBPnz55bsfVOaNPXJ3VauWZZ55h69atLFiwAD8/v3x/ZkZGBmPGjAHufs8++eSTgPrDjNQn5qM+MRf1h/moT8zHTH1im2X2KKYtkipUqADApUuXqFixov36pUuXaNSo0QNf5+Pjg4+Pzz3Xvb29De8UG0ey2NYkVa9e3aG/j22XwNDQUNN8Xoxkpq+PgtanTx9q1arF8ePHWbJkCSNHjsz3Z3733XecOnWK0qVLM2jQoHs+9+7cH2alPjEf9Ym5qD/MR31iPmbok5w+37TnJFWrVo0KFSqwadMm+7WkpCT27NlDq1atDExmnDt37nD+/HnA8d3ttGmD2Hh4eDB69GgAZs2aRUZGRr4+z2q1Mm3aNABGjhxpmmmwIiIiIjaGFknJyclER0cTHR0N3N2UIDo6mjNnzmCxWBg9ejTTpk1j1apVHDp0iEGDBhEUFETfvn2NjG0Yi8VCVFQU3333nX2kLa+0/bdkNWjQIAICAjh58iTfffddvj5rzZo1HDhwAD8/P0aNGpWvzxIRERHJC0OLpH379hEWFkZYWBgAY8eOJSwsjIkTJwIwbtw4Ro4cyWuvvUazZs1ITk5m7dq1FC1a1MjYhvH09KRhw4b06dMHDw/Huu7o0aOADpKVu4oXL84bb7wBwNSpU8nMzMyX52QdRXrzzTcJDAzMl+eIiIiIOMLQIqljx45YrdZ73hYuXAjcHTmZOnUq8fHx/Prrr2zcuLFAtygurBISEkhISMBisfD4448bHUdMYsyYMfj7+3PgwIF8O4ts9erV7Nmzh6JFi2bbYEVERETETEy7JknutX79ej788EP27NnjUDuHDx8G7m7+ULx4cWdEk0IgMDDQvjZp0qRJTh9NunPnDuPGjQPg97///T3b+4uIiIiYhYokF7JixQrGjRvHmjVrHGrHViTVq1fPGbGkEBkzZgwlS5bk8OHDLFmyxKltf/755/zyyy8EBgYyYcIEp7YtIiIi4kwqklxIy5YtGThwIM2bN3eoHVuRVL9+fWfEkkKkdOnS9gJm3LhxOT5L4FGuXr3Kn/70JwAmTpxIyZIlndKuiIiISH5QkeRCBg8ezJIlS3jqqaccaufQoUOARpLk/kaPHk3NmjW5dOkSU6ZMcUqbf/jDH7h8+TJ169bl9ddfd0qbIiIiIvlFRZKbsVqtGkmSh/Lx8eHjjz8G4OOPP3Z4Ddz69etZtGgRFouFuXPnUqRIEWfEFBEREck3KpJcRFpaGqdPnyY9Pd2hduLi4khOTsbb25uaNWs6KZ0UNj179mTAgAFkZGTw4osvkpycnKd24uPjGTRoEADDhw9324OgRURExLWoSHIRP//8M9WqVSM4ONihdmyjSKGhoXh7ezsjmhRSn376KcHBwcTExPDqq69itVpz9fq0tDReeOEFLl26RP369ZkxY0Y+JRURERFxLhVJLuLMmTMAVK5c2aF2tB5Jcqp06dIsWbIELy8vli1bxuTJk3P8WqvVyrBhw9iyZQvFixfnq6++wtfXN//CioiIiDiRiiQXYSuSqlSp4lA72v5bcqN9+/aEh4cDMHXqVKZOnfrIEaX09HSGDBnCkiVL8PT05JtvvqFOnToFEVdERETEKVQkuYi4uDgAQkJCHGrHNpKkTRskp4YNG8a0adOAu4fMvvjiiyQmJt733ri4OLp06cKiRYvw9PRk4cKF9OjRowDTioiIiDjOy+gAkjPOGElKT0/nl19+ATSSJLnzzjvvULJkSUaPHs3SpUtZu3Ytb775Jt27d6dMmTKcOXOGlStXsmDBAn799VeKFy/Ol19+Se/evY2OLiIiIpJrKpJchDOKpOPHj5Oeno6fn5/DI1LifkaMGEGTJk0YMmQIx44dY9q0afYRpqw6dOjA/PnzeeyxxwxIKSIiIuI4FUkuwhnT7Q4ePAjcHUWyWCxOySXupVWrVhw5coSvv/6ar7/+mv3793P9+nXKlStH27ZtefHFF+ncubO+vkRERMSlqUhyAWlpaVy8eBFwbCQpOjoagLCwMGfEEjfl6elJ//796d+/v9FRRERERPKFNm5wAefOncNqteLj40PZsmXz3M5//vMfABo1auSkZCIiIiIihY+KJBeQdT1SXqcxWa1We5GkkSQRERERkQdTkeQCbEWSI+uRLly4wJUrV/D09NTOdiIiIiIiD6EiyQXYNm1wZD2SbRSpTp06+Pr6OiWXiIiIiEhhpCLJBThj+29NtRMRERERyRntbucCPvzwQ4YPH05gYGCe29DOdiIiIiIiOaMiyQWUKlXK4R3ptLOdiIiIiEjOaLqdG0hMTOTUqVOAiiQRERERkUdRkWRy169fZ8SIEcycOROr1ZqnNg4cOADc3R0vICDAmfFERERERAodFUkmd/LkST799FM++uijPJ+RpKl2IiIiIiI5pzVJJhcQEMCECRPw9vbOcxtRUVGANm0QEREREckJFUkmV61aNd5//32H2oiMjASgadOmzogkIiIiIlKoabpdIXfjxg2OHTsGQLNmzQxOIyIiIiJifiqSTO7nn38mLi6OO3fu5On1+/fvx2q1UrVqVcqVK+fkdCIiIiIihY+KJJMbNGgQVatWZc2aNXl6vW2qnUaRRERERERyRkWSyZ05cwaAKlWq5On1e/fuBaB58+ZOyyQiIiIiUpipSDKx27dvk5CQANw94ygvNJIkIiIiIpI7KpJM7OzZswAUL16c0qVL5/r18fHxnD17Fg8PD5o0aeLseCIiIiIihZKKJBPLOtUuLwfJ2kaRQkND8fPzc2o2EREREZHCSkWSidmKpLxOtdN6JBERERGR3FORZGKObtqg9UgiIiIiIrmnIsnE4uLigLyNJGVmZtpHklQkiYiIiIjknIokE3NkJOmXX37h+vXr+Pr60rBhQ2dHExEREREptFQkmZgjRdJPP/0E3F2P5O3t7dRcIiIiIiKFmYokk8rMzHRo44Zdu3YB0KZNG6fmEhEREREp7FQkmVRCQgJpaWl4eHgQFBSU69erSBIRERERyRsVSSZlG0UKCgrK9XS5hIQETpw4AUCrVq2cnk1EREREpDDzMjqA3F+zZs24evUqV69ezfVrbeuR6tatS+nSpZ0dTURERESkUFORZFIWi4WAgAACAgJy/VrbVLvWrVs7O5aIiIiISKGn6XaFkG0kSeuRRERERERyT0WSSb3//vuMHDmS6OjoXL3u119/Zd++fYCKJBERERGRvDB1kTR58mQsFku2tzp16hgdq0B8/fXXfPLJJ5w7dy5Xr9u3bx9paWmUK1eOxx57LJ/SiYiIiIgUXqZfk1S3bl02btxof9/Ly/SRnWLMmDH88ssv1K9fP1ev27p1KwDt27fHYrHkQzIRERERkcLN9BWHl5cXFSpUMDpGgRs0aFCeXrdlyxYAOnbs6MQ0IiIiIiLuw/RF0okTJwgKCqJo0aK0atWK6dOnU6VKlQfen5qaSmpqqv39pKQkANLT00lPT8/3vA9je35+5UhNTbVv2tC2bVvD/76uIL/7RHJH/WE+6hPzUZ+Yi/rDfNQn5mOmPslpBovVarXmc5Y8+/HHH0lOTqZ27dpcvHiRKVOmcP78eQ4fPoy/v/99XzN58mSmTJlyz/WlS5dSrFix/I7sFFevXiU+Pp6KFSvmagvwI0eO8M4771CqVCkWLFig6XYiIiIiIlmkpKTwwgsvcOPGDUqUKPHA+0xdJP2vxMREQkJC+Oijjxg2bNh977nfSFJwcDBXrlx56CeiIKSnp7Nhwwa6du2Kt7f3A+8LDw9n1KhRPPXUU/z73//Ocfvvvvsu7777Lv369eOLL75wRuRCL6d9IgVD/WE+6hPzUZ+Yi/rDfNQn5mOmPklKSqJMmTKPLJJMP90uq1KlSlGrVi1iYmIeeI+Pjw8+Pj73XPf29ja8U2welcW2o121atVylXnHjh0AdO7c2TR/V1dhpq8PUX+YkfrEfNQn5qL+MB/1ifmYoU9y+nxTbwH+v5KTk4mNjaVixYpGR8lXcXFxAFStWjXHr/n111+JiIgAoFOnTvkRS0RERETELZi6SHrrrbfYtm0bp0+f5qeffuKZZ57B09OTAQMGGB0tX9mKpJCQkBy/JiIigtTUVCpWrEitWrXyK5qIiIiISKFn6ul2586dY8CAAVy9epWyZcvStm1bdu/eTdmyZY2Olq/yUiTZzkfq2LGjNmwQEREREXGAqYukZcuWGR2hwKWmpnLx4kUgd0WS7cBdTbUTEREREXGMqafbuaOzZ88C4OvrS5kyZXL0msTERPbs2QNA9+7d8y2biIiIiIg7UJFkMlmn2uV02tymTZvIyMigTp06Dz1oV0REREREHk1FksnkZT3SunXrAI0iiYiIiIg4g4okk8ltkWS1WlUkiYiIiIg4kYokk8ntGUnHjh3jzJkz+Pj40KFDh3xMJiIiIiLiHlQkmczp06eBnI8k2UaR2rVrR7FixfIrloiIiIiI21CRZDJXrlwBcl8kaaqdiIiIiIhzmPqcJHd06NAhrl+/jp+f3yPv/fXXX+2HyKpIEhERERFxDhVJJmOxWAgICMjRvZs3b+b27dtUqlSJevXq5XMyERERERH3oOl2LmzVqlUA9OnTJ8dnKomIiIiIyMOpSDKRVatW0adPH8LDwx95b2ZmJt9//z1wt0gSERERERHn0HQ7E4mMjOT777+nUqVKj7w3KiqKCxcu4OfnR6dOnQognYiIiIiIe1CRZCL9+vWjUqVK1KlT55H32qbade/eHR8fn/yOJiIiIiLiNlQkmUiDBg1o0KBBju7Nuh5JREREREScR2uSXFBcXBwHDhzAw8ODXr16GR1HRERERKRQUZFkEikpKSxevJhdu3ZhtVofeq9tFKlNmzaUKVOmIOKJiIiIiLgNTbcziRMnTjB48GACAwO5cuXKQ+/95ptvAOjbt28BJBMRERERcS8aSTKJkydPAlC9evWH3nfx4kV27NgBwPPPP5/vuURERERE3I2KJJOwFUmPPfbYQ+/79ttvsVqttGzZkipVqhRENBERERERt6IiySRiY2OBR48kff311wD85je/yfdMIiIiIiLuSEWSSeRkJElT7URERERE8p+KJJOwjSRVq1btgffYptq1atWK4ODggoomIiIiIuJWVCSZQFpaGqdOnQKgVq1aD7zPNtWuX79+BZJLRERERMQdqUgygdjYWDIyMvDz8yMoKOi+98TFxbF9+3YsFoum2omIiIiI5CMVSSZw7Ngx4O4oksViue89S5YsAaBTp06aaiciIiIiko9UJJmArUiqXbv2fT9utVpZvHgxAIMGDSqwXCIiIiIi7khFkgk8qkjau3cvx48fp1ixYjz77LMFGU1ERERExO2oSDKBRxVJixYtAuDZZ5/F39+/wHKJiIiIiLgjFUkm4OvrS7Fixe5bJKWmprJs2TJAU+1ERERERAqCl9EBBDZu3EhmZuZ9P7Zy5UquX79OUFAQnTt3LuBkIiIiIiLuR0WSSXh43H9QLzw8HIBhw4bh6elZkJFERERERNySptuZ2C+//MLWrVvx8PDg1VdfNTqOiIiIiIhbUJFksLFjx9KgQQOWLl16z8c+++wzAJ566imdjSQiIiIiUkBUJBls//79HDp0iIyMjGzXU1JSWLhwIQCvv/66AclERERERNyT1iQZbMmSJRw4cIAmTZpku7506VISExOpWrUq3bt3NyidiIiIiIj7UZFksODg4Hum0mVmZjJz5kwARo4c+cBNHURERERExPn007cJrV69mmPHjlGyZElt2CAiIiIiUsA0kmSgb7/9lsOHD9OrVy+aNWtmvz5jxgzg7lokf39/o+KJiIiIiLglFUkGWrx4MatWraJEiRL2Imnnzp3s2rULb29vRo0aZXBCERERERH3o+l2BrFarezZsweAFi1a2K+9/fbbAAwZMoSgoCDD8omIiIiIuCsVSQaJi4vj0qVLeHt7ExYWBsD69evZsWMHPj4+/PnPfzY4oYiIiIiIe1KRZJDdu3cD0LBhQ3x9fcnIyLCPIg0fPpzKlSsbGU9ERERExG2pSDLI9u3bAWjVqhUA8+bNIyoqCn9/f8aPH29kNBERERERt6YiySAbNmwAoEuXLly+fJkJEyYAMG3aNMqWLWtkNBERERERt6bd7Qxw+vRpYmJi8PT0pEOHDgwZMoTr16/TqFEj3nzzTaPjiYiIiIi4NY0kGWDVqlUAtG7dmqVLl7JixQq8vb2ZN28eXl6qW0VEREREjOQSRdKnn35K1apVKVq0KC1atGDv3r1GR3LI8uXLAahXrx4jR44EYPr06TRp0sTIWCIiIiIiggsUScuXL2fs2LFMmjSJqKgoGjZsSPfu3UlISDA6Wp4cP36cyMhIPDw8mD9/PhkZGbz44ouMGTPG6GgiIiIiIoILFEkfffQRr776KkOGDOHxxx8nPDycYsWK8fnnnxsdLVcyMzNZt24dM2fOtL+flpbG008/zfz58/HwMH1XiIiIiIi4BVMvgElLS2P//v32nd8APDw86NKlCxEREfd9TWpqKqmpqfb3k5KSAEhPTyc9PT1/Az+E1Wqlf//+3Lp1C7j793jrrbeYMmUKFovF0GzuzPZ51+ffHNQf5qM+MR/1ibmoP8xHfWI+ZuqTnGawWK1Waz5nybMLFy5QqVIlfvrpJ/t5QgDjxo1j27Zt7Nmz557XTJ48mSlTptxzfenSpRQrVixf8z7Ke++9x7lz56hduzbPP/+8DowVERERESlAKSkpvPDCC9y4cYMSJUo88D5TjyTlxYQJExg7dqz9/aSkJIKDg+nWrdtDPxEFoWvXrmzYsIGuXbvi7e1taBa5Kz09XX1iIuoP81GfmI/6xFzUH+ajPjEfM/WJbZbZo5i6SCpTpgyenp5cunQp2/VLly5RoUKF+77Gx8cHHx+fe657e3sb3ik2Zsoid6lPzEX9YT7qE/NRn5iL+sN81CfmY4Y+yenzTb1bQJEiRWjSpAmbNm2yX8vMzGTTpk3Zpt+JiIiIiIg4i6lHkgDGjh3L4MGDadq0Kc2bN2fWrFncunWLIUOGGB1NREREREQKIdMXSb/97W+5fPkyEydOJD4+nkaNGrF27VrKly9vdDQRERERESmETF8kAYwYMYIRI0YYHUNERERERNyAqdckiYiIiIiIFDQVSSIiIiIiIlmoSBIREREREclCRZKIiIiIiEgWKpJERERERESyUJEkIiIiIiKShYokERERERGRLFQkiYiIiIiIZKEiSUREREREJAsVSSIiIiIiIlmoSBIREREREclCRZKIiIiIiEgWKpJERERERESy8DI6QH6zWq0AJCUlGZwE0tPTSUlJISkpCW9vb6PjCOoTs1F/mI/6xHzUJ+ai/jAf9Yn5mKlPbDWBrUZ4kEJfJN28eROA4OBgg5OIiIiIiIgZ3Lx5k5IlSz7w4xbro8ooF5eZmcmFCxfw9/fHYrEYmiUpKYng4GDOnj1LiRIlDM0id6lPzEX9YT7qE/NRn5iL+sN81CfmY6Y+sVqt3Lx5k6CgIDw8HrzyqNCPJHl4eFC5cmWjY2RTokQJw79AJDv1ibmoP8xHfWI+6hNzUX+Yj/rEfMzSJw8bQbLRxg0iIiIiIiJZqEgSERERERHJQkVSAfLx8WHSpEn4+PgYHUX+S31iLuoP81GfmI/6xFzUH+ajPjEfV+yTQr9xg4iIiIiISG5oJElERERERCQLFUkiIiIiIiJZqEgSERERERHJQkWSiIiIiIhIFiqSCtCnn35K1apVKVq0KC1atGDv3r1GR3Jb27dvp3fv3gQFBWGxWFi5cqXRkdza9OnTadasGf7+/pQrV46+ffty7Ngxo2O5tTlz5tCgQQP7wX+tWrXixx9/NDqW/Ndf/vIXLBYLo0ePNjqK25o8eTIWiyXbW506dYyO5fbOnz/Piy++SGBgIL6+vtSvX599+/YZHcttVa1a9Z7vE4vFwvDhw42O9kgqkgrI8uXLGTt2LJMmTSIqKoqGDRvSvXt3EhISjI7mlm7dukXDhg359NNPjY4iwLZt2xg+fDi7d+9mw4YNpKen061bN27dumV0NLdVuXJl/vKXv7B//3727dtH586defrppzly5IjR0dxeZGQkn332GQ0aNDA6iturW7cuFy9etL/t3LnT6Ehu7fr167Rp0wZvb29+/PFHjh49yl//+ldKly5tdDS3FRkZme17ZMOGDQD069fP4GSPpi3AC0iLFi1o1qwZn3zyCQCZmZkEBwczcuRIxo8fb3A692axWFixYgV9+/Y1Oor81+XLlylXrhzbtm2jffv2RseR/woICODDDz9k2LBhRkdxW8nJyTRu3Jh//OMfTJs2jUaNGjFr1iyjY7mlyZMns3LlSqKjo42OIv81fvx4du3axY4dO4yOIg8wevRoVq9ezYkTJ7BYLEbHeSiNJBWAtLQ09u/fT5cuXezXPDw86NKlCxEREQYmEzGnGzduAHd/KBfjZWRksGzZMm7dukWrVq2MjuPWhg8fzpNPPpnt/xMxzokTJwgKCqJ69eoMHDiQM2fOGB3Jra1atYqmTZvSr18/ypUrR1hYGHPnzjU6lvxXWloaS5YsYejQoaYvkEBFUoG4cuUKGRkZlC9fPtv18uXLEx8fb1AqEXPKzMxk9OjRtGnThnr16hkdx60dOnQIPz8/fHx8eP3111mxYgWPP/640bHc1rJly4iKimL69OlGRxHuzhBZuHAha9euZc6cOZw6dYp27dpx8+ZNo6O5rZMnTzJnzhxq1qzJunXreOONNxg1ahSLFi0yOpoAK1euJDExkZdfftnoKDniZXQAEZGshg8fzuHDhzW33wRq165NdHQ0N27c4JtvvmHw4MFs27ZNhZIBzp49y+9//3s2bNhA0aJFjY4jQM+ePe1/btCgAS1atCAkJISvvvpKU1INkpmZSdOmTXn//fcBCAsL4/Dhw4SHhzN48GCD08n8+fPp2bMnQUFBRkfJEY0kFYAyZcrg6enJpUuXsl2/dOkSFSpUMCiViPmMGDGC1atXs2XLFipXrmx0HLdXpEgRatSoQZMmTZg+fToNGzbk448/NjqWW9q/fz8JCQk0btwYLy8vvLy82LZtG7Nnz8bLy4uMjAyjI7q9UqVKUatWLWJiYoyO4rYqVqx4zy9xQkNDNQ3SBOLi4ti4cSOvvPKK0VFyTEVSAShSpAhNmjRh06ZN9muZmZls2rRJ8/tFAKvVyogRI1ixYgWbN2+mWrVqRkeS+8jMzCQ1NdXoGG7piSee4NChQ0RHR9vfmjZtysCBA4mOjsbT09PoiG4vOTmZ2NhYKlasaHQUt9WmTZt7jo84fvw4ISEhBiUSmwULFlCuXDmefPJJo6PkmKbbFZCxY8cyePBgmjZtSvPmzZk1axa3bt1iyJAhRkdzS8nJydl+23fq1Cmio6MJCAigSpUqBiZzT8OHD2fp0qV89913+Pv729fqlSxZEl9fX4PTuacJEybQs2dPqlSpws2bN1m6dClbt25l3bp1RkdzS/7+/ves0StevDiBgYFau2eQt956i969exMSEsKFCxeYNGkSnp6eDBgwwOhobmvMmDG0bt2a999/n9/85jfs3buXf/7zn/zzn/80Oppby8zMZMGCBQwePBgvL9cpPVwnqYv77W9/y+XLl5k4cSLx8fE0atSItWvX3rOZgxSMffv20alTJ/v7Y8eOBWDw4MEsXLjQoFTua86cOQB07Ngx2/UFCxa4zALPwiYhIYFBgwZx8eJFSpYsSYMGDVi3bh1du3Y1OpqIKZw7d44BAwZw9epVypYtS9u2bdm9ezdly5Y1OprbatasGStWrGDChAlMnTqVatWqMWvWLAYOHGh0NLe2ceNGzpw5w9ChQ42Okis6J0lERERERCQLrUkSERERERHJQkWSiIiIiIhIFiqSREREREREslCRJCIiIiIikoWKJBERERERkSxUJImIiIiIiGShIklERERERCQLFUkiIiIiIiJZqEgSERHDvPzyy/Tt29ew57/00ku8//77BfKs8ePHM3LkyAJ5loiIOMZitVqtRocQEZHCx2KxPPTjkyZNYsyYMVitVkqVKlUwobI4cOAAnTt3Ji4uDj8/v3x/3pUrV6hevTrR0dFUr149358nIiJ5pyJJRETyRXx8vP3Py5cvZ+LEiRw7dsx+zc/Pr0CKkwd55ZVX8PLyIjw8vMCe2a9fP6pWrcqHH35YYM8UEZHc03Q7ERHJFxUqVLC/lSxZEovFku2an5/fPdPtOnbsyMiRIxk9ejSlS5emfPnyzJ07l1u3bjFkyBD8/f2pUaMGP/74Y7ZnHT58mJ49e+Ln50f58uV56aWXuHLlygOzZWRk8M0339C7d+9s1//xj39Qs2ZNihYtSvny5Xn++eftH8vMzGT69OlUq1YNX19fGjZsyDfffJPt9UeOHOGpp56iRIkS+Pv7065dO2JjY+0f7927N8uWLcvLp1NERAqQiiQRETGVRYsWUaZMGfbu3cvIkSN544036NevH61btyYqKopu3brx0ksvkZKSAkBiYiKdO3cmLCyMffv2sXbtWi5dusRvfvObBz7j4MGD3Lhxg6ZNm9qv7du3j1GjRjF16lSOHTvG2rVrad++vf3j06dPZ/HixYSHh3PkyBHGjBnDiy++yLZt2wA4f/487du3x8fHh82bN7N//36GDh3KnTt37G00b96cc+fOcfr0aSd/1kRExJk03U5ERPLdwoULGT16NImJidmuv/zyyyQmJrJy5Urg7khSRkYGO3bsAO6O+JQsWZJnn32WxYsXA3en8VWsWJGIiAhatmzJtGnT2LFjB+vWrbO3e+7cOYKDgzl27Bi1atW6J8/KlSt5/vnnSU9Pt6+d+ve//82QIUM4d+4c/v7+2e5PTU0lICCAjRs30qpVK/v1V155hZSUFJYuXcrbb7/NsmXLOHbsGN7e3vf9PCQlJVGyZEm2bt1Khw4dcvdJFBGRAuNldAAREZGsGjRoYP+zp6cngYGB1K9f336tfPnyACQkJAB3N2DYsmXLfdc3xcbG3rdIun37Nj4+Ptk2l+jatSshISFUr16dHj160KNHD5555hmKFStGTEwMKSkpdO3aNVs7aWlphIWFARAdHU27du0eWCAB+Pr6AthHwURExJxUJImIiKn8b5FhsViyXbMVNpmZmQAkJyfTu3dvPvjgg3vaqlix4n2fUaZMGVJSUkhLS6NIkSIA+Pv7ExUVxdatW1m/fj0TJ05k8uTJREZGkpycDMCaNWuoVKlStrZ8fHyA/18APcy1a9cAKFu27CPvFRER46hIEhERl9a4cWO+/fZbqlatipdXzv5ba9SoEQBHjx61/xnAy8uLLl260KVLFyZNmkSpUqXYvHkzXbt2xcfHhzNnzjxwmlyDBg1YtGgR6enpDxxNOnz4MN7e3tStWzdXf0cRESlY2rhBRERc2vDhw7l27RoDBgwgMjKS2NhY1q1bx5AhQ8jIyLjva8qWLUvjxo3ZuXOn/drq1auZPXs20dHRxMXFsXjxYjIzM6lduzb+/v689dZbjBkzhkWLFhEbG0tUVBR///vfWbRoEQAjRowgKSmJ/v37s2/fPk6cOMG//vWvbNue79ixg3bt2uVo1ElERIyjIklERFxaUFAQu3btIiMjg27dulG/fn1Gjx5NqVKl8PB48H9zr7zyCl988YX9/VKlSvHvf/+bzp07ExoaSnh4OF9++aV91Ofdd9/lz3/+M9OnTyc0NJQePXqwZs0aqlWrBkBgYCCbN28mOTmZDh060KRJE+bOnZttVGnZsmW8+uqr+fSZEBERZ9HudiIi4pZu375N7dq1Wb58ebYd6/LLjz/+yB/+8AcOHjyY42mBIiJiDI0kiYiIW/L19WXx4sUPPXTWmW7dusWCBQtUIImIuACNJImIiIiIiGShkSQREREREZEsVCSJiIiIiIhkoSJJREREREQkCxVJIiIiIiIiWahIEhERERERyUJFkoiIiIiISBYqkkRERERERLJQkSQiIiIiIpKFiiQREREREZEs/h/xeOedpJgRyAAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(10, 6))\n", + "plt.plot(t_initial, x_initial[:, 1], 'k', label='x2')\n", + "plt.plot(t_initial, x_initial[:, 4], '-.k', label='x5')\n", + "plt.grid(True)\n", + "plt.xlabel('Time (sec)')\n", + "plt.ylabel('State variables')\n", + "plt.legend()\n", + "plt.title('Forced Response of Train Model')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Generate input signal u(t)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "u = 0.1 * (np.sin(5 * t) + np.sin(9 * t) + np.sin(13 * t) + np.sin(17 * t) + np.sin(21 * t))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Simulate the system response to input signal using lsim function" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "t_response, y_response, x_response = signal.lsim(train_model, U=u, T=t, X0=x0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Plot the response to input signal" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(10, 6))\n", + "plt.plot(t_response, x_response[:, 0], 'k', label='x1')\n", + "plt.plot(t_response, x_response[:, 1], '-.k', label='x2')\n", + "plt.grid(True)\n", + "plt.xlabel('Time (sec)')\n", + "plt.ylabel('State variables')\n", + "plt.legend()\n", + "plt.title('Response of Train Model to Input Signal')\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.12.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Chapter3/train_linear.py b/Chapter3/train_linear.py new file mode 100644 index 0000000..b3d2c30 --- /dev/null +++ b/Chapter3/train_linear.py @@ -0,0 +1,64 @@ +# Import necessary libraries +import numpy as np +import matplotlib.pyplot as plt +from scipy import signal + +# Define the state-space matrices +A = np.array([ + [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 1, -1, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 1, -1, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 1, -1, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 1, -1], + [0, -12.5, 0, 0, 0, -0.75, 0.75, 0, 0, 0], + [0, 62.5, -62.5, 0, 0, 3.75, -7.5, 3.75, 0, 0], + [0, 0, 62.5, -62.5, 0, 0, 3.75, -7.5, 3.75, 0], + [0, 0, 0, 62.5, -62.5, 0, 0, 3.75, -7.5, 3.75], + [0, 0, 0, 0, 62.5, 0, 0, 0, 3.75, -3.75] +]) +b1 = np.array([0, 0, 0, 0, 0, 0.005, 0, 0, 0, 0]).reshape(-1, 1) +b2 = np.array([0, 0, 0, 0, 0, 250, 0, 0, 0, -1250]).reshape(-1, 1) +C = np.array([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]).reshape(1, -1) +D = np.array([0]) +u = 750 # Constant input +b = u*b1 + b2 + +# Create the state-space model using signal.StateSpace +train_model = signal.StateSpace(A, b2, C, D) + +# Time vector for simulation +t = np.arange(0, 7, 0.001) + +# Initial conditions for simulation +x0 = np.array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) + +# Simulate the forced response using lsim function +t_initial, y_initial, x_initial = signal.lsim(train_model, U=np.ones_like(t), T=t, X0=x0) + +# Plot initial response +plt.figure(figsize=(10, 6)) +plt.plot(t_initial, x_initial[:, 1], 'k', label='x2') +plt.plot(t_initial, x_initial[:, 4], '-.k', label='x5') +plt.grid(True) +plt.xlabel('Time (sec)') +plt.ylabel('State variables') +plt.legend() +plt.title('Forced Response of Train Model') +plt.show() + +# Generate input signal u(t) +u = 0.1 * (np.sin(5 * t) + np.sin(9 * t) + np.sin(13 * t) + np.sin(17 * t) + np.sin(21 * t)) + +# Simulate the system response to input signal using lsim function +t_response, y_response, x_response = signal.lsim(train_model, U=u, T=t, X0=x0) + +# Plot the response to input signal +plt.figure(figsize=(10, 6)) +plt.plot(t_response, x_response[:, 0], 'k', label='x1') +plt.plot(t_response, x_response[:, 1], '-.k', label='x2') +plt.grid(True) +plt.xlabel('Time (sec)') +plt.ylabel('State variables') +plt.legend() +plt.title('Response of Train Model to Input Signal') +plt.show() diff --git a/Chapter4/DCmotor_jordan.ipynb b/Chapter4/DCmotor_jordan.ipynb new file mode 100644 index 0000000..abb22d7 --- /dev/null +++ b/Chapter4/DCmotor_jordan.ipynb @@ -0,0 +1,156 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Import necessary libraries" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from scipy import signal" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the state-space matrices" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "A = np.array([\n", + " [0, 1, 0],\n", + " [0, 0, 4.438],\n", + " [0, -12, -24]\n", + "])\n", + "b1 = np.array([0, 0, 20]).reshape(-1, 1)\n", + "b2 = np.array([0, -7.396, 0]).reshape(-1, 1)\n", + "B = np.hstack((b1, b2))\n", + "C = np.array([\n", + " [1, 0, 0],\n", + " [0, 1, 0]\n", + "])\n", + "D = np.array([[0], [0]])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Create the state-space model using signal.StateSpace" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [], + "source": [ + "DC_motor = signal.StateSpace(A, b1, C, D) # Note only first input is used" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Calculate the eigenvalues and right eigenvectors of A" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "eigenvalues, right_eigenvectors = np.linalg.eig(A)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Calculate the left eigenvectors of A" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [], + "source": [ + "_, left_eigenvectors = np.linalg.eig(A.T)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Display the results" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Right Eigenvectors (V):\n", + "[[ 1. -0.33290784 0.00938002]\n", + " [ 0. 0.82362581 -0.20191394]\n", + " [ 0. -0.45914364 0.97935835]]\n", + "Eigenvalues (Lambda):\n", + "[ 0. -2.47403548 -21.52596452]\n", + "Left Eigenvectors (W):\n", + "[[ 0. 0. 0.90907852]\n", + " [-0.48691774 -0.97940144 0.40967937]\n", + " [-0.87344783 -0.20192283 0.07575654]]\n" + ] + } + ], + "source": [ + "print(\"Right Eigenvectors (V):\")\n", + "print(right_eigenvectors)\n", + "print(\"Eigenvalues (Lambda):\")\n", + "print(eigenvalues)\n", + "print(\"Left Eigenvectors (W):\")\n", + "print(left_eigenvectors)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.12.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Chapter4/DCmotor_jordan.py b/Chapter4/DCmotor_jordan.py new file mode 100644 index 0000000..49e3e51 --- /dev/null +++ b/Chapter4/DCmotor_jordan.py @@ -0,0 +1,35 @@ +# Import necessary libraries +import numpy as np +from scipy import signal + +# Define the state-space matrices +A = np.array([ + [0, 1, 0], + [0, 0, 4.438], + [0, -12, -24] +]) +b1 = np.array([0, 0, 20]).reshape(-1, 1) +b2 = np.array([0, -7.396, 0]).reshape(-1, 1) +B = np.hstack((b1, b2)) +C = np.array([ + [1, 0, 0], + [0, 1, 0] +]) +D = np.array([[0], [0]]) + +# Create the state-space model using signal.StateSpace +DC_motor = signal.StateSpace(A, b1, C, D) # Note only first input is used + +# Calculate the eigenvalues and right eigenvectors of A +eigenvalues, right_eigenvectors = np.linalg.eig(A) + +# Calculate the left eigenvectors of A +_, left_eigenvectors = np.linalg.eig(A.T) + +# Display the results +print("Right Eigenvectors (V):") +print(right_eigenvectors) +print("Eigenvalues (Lambda):") +print(eigenvalues) +print("Left Eigenvectors (W):") +print(left_eigenvectors) diff --git a/Chapter4/ex3_1.ipynb b/Chapter4/ex3_1.ipynb new file mode 100644 index 0000000..31b2b72 --- /dev/null +++ b/Chapter4/ex3_1.ipynb @@ -0,0 +1,169 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Import necessary libraries" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from scipy.linalg import null_space" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the state-space matrices" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "A = np.array([\n", + " [-3/2, 1/2],\n", + " [1/2, -3/2]\n", + "])\n", + "C = np.array([[1, -1]])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Function to compute the observability matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "def observability_matrix(A, C):\n", + " n = A.shape[0]\n", + " O = C\n", + " for i in range(1, n):\n", + " O = np.vstack((O, np.dot(C, np.linalg.matrix_power(A, i))))\n", + " return O" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Calculate the observability matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "O = observability_matrix(A, C)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Calculate the rank of the observability matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "rank_O = np.linalg.matrix_rank(O)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Calculate the null space of the observability matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "null_O = null_space(O)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Display the results" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Observability Matrix (O):\n", + "[[ 1. -1.]\n", + " [-2. 2.]]\n", + "\n", + "Rank of Observability Matrix:\n", + "1\n", + "\n", + "Null Space of Observability Matrix:\n", + "[[0.70710678]\n", + " [0.70710678]]\n" + ] + } + ], + "source": [ + "print(\"Observability Matrix (O):\")\n", + "print(O)\n", + "print(\"\\nRank of Observability Matrix:\")\n", + "print(rank_O)\n", + "print(\"\\nNull Space of Observability Matrix:\")\n", + "print(null_O)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.12.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Chapter4/ex3_1.py b/Chapter4/ex3_1.py new file mode 100644 index 0000000..8460744 --- /dev/null +++ b/Chapter4/ex3_1.py @@ -0,0 +1,35 @@ +# Import necessary libraries +import numpy as np +from scipy.linalg import null_space + +# Define the state-space matrices +A = np.array([ + [-3/2, 1/2], + [1/2, -3/2] +]) +C = np.array([[1, -1]]) + +# Function to compute the observability matrix +def observability_matrix(A, C): + n = A.shape[0] + O = C + for i in range(1, n): + O = np.vstack((O, np.dot(C, np.linalg.matrix_power(A, i)))) + return O + +# Calculate the observability matrix +O = observability_matrix(A, C) + +# Calculate the rank of the observability matrix +rank_O = np.linalg.matrix_rank(O) + +# Calculate the null space of the observability matrix +null_O = null_space(O) + +# Display the results +print("Observability Matrix (O):") +print(O) +print("\nRank of Observability Matrix:") +print(rank_O) +print("\nNull Space of Observability Matrix:") +print(null_O) diff --git a/Chapter4/ex3_2.ipynb b/Chapter4/ex3_2.ipynb new file mode 100644 index 0000000..a1f38b8 --- /dev/null +++ b/Chapter4/ex3_2.ipynb @@ -0,0 +1,310 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Import necessary libraries" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import sympy as sp" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the state-space matrices" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "A = sp.Matrix([[1, 0], [1, 1]])\n", + "B = sp.Matrix([[1], [1]])\n", + "u = 1 # Step input\n", + "x0 = sp.Matrix([[1], [1]])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the symbolic variable for time" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "t = sp.symbols('t')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Calculate the state transition matrix (phi)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "phi = sp.exp(A * t)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Calculate the zero-state response" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "x1 = sp.exp(-A * t) * B * u\n", + "x_zs = sp.integrate(x1, (t))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Calculate the zero-input response" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "x_zi = phi * x0" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Calculate the total response" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "x = x_zi + x_zs" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Display the results" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "State Transition Matrix (phi):\n", + "Matrix([[exp(t), 0], [t*exp(t), exp(t)]])\n", + "\n", + "Zero-State Response (x_zs):\n", + "Matrix([[-exp(-t)], [t*exp(-t)]])\n", + "\n", + "Zero-Input Response (x_zi):\n", + "Matrix([[exp(t)], [t*exp(t) + exp(t)]])\n", + "\n", + "Total Response (x):\n", + "Matrix([[exp(t) - exp(-t)], [t*exp(t) + t*exp(-t) + exp(t)]])\n" + ] + } + ], + "source": [ + "print(\"State Transition Matrix (phi):\")\n", + "print(phi)\n", + "\n", + "print(\"\\nZero-State Response (x_zs):\")\n", + "print(x_zs)\n", + "\n", + "print(\"\\nZero-Input Response (x_zi):\")\n", + "print(x_zi)\n", + "\n", + "print(\"\\nTotal Response (x):\")\n", + "print(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Display the results using latex" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\text{State Transition Matrix (phi):}$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}e^{t} & 0\\\\t e^{t} & e^{t}\\end{matrix}\\right]$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle \\text{Zero-State Response (x\\_zs):}$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}- e^{- t}\\\\t e^{- t}\\end{matrix}\\right]$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle \\text{Zero-Input Response (x\\_zi):}$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}e^{t}\\\\t e^{t} + e^{t}\\end{matrix}\\right]$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle \\text{Total Response (x):}$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}e^{t} - e^{- t}\\\\t e^{t} + t e^{- t} + e^{t}\\end{matrix}\\right]$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from IPython.display import display, Math\n", + "\n", + "display(Math(r\"\\text{State Transition Matrix (phi):}\"))\n", + "display(Math(sp.latex(phi)))\n", + "\n", + "display(Math(r\"\\text{Zero-State Response (x\\_zs):}\"))\n", + "display(Math(sp.latex(x_zs)))\n", + "\n", + "display(Math(r\"\\text{Zero-Input Response (x\\_zi):}\"))\n", + "display(Math(sp.latex(x_zi)))\n", + "\n", + "display(Math(r\"\\text{Total Response (x):}\"))\n", + "display(Math(sp.latex(x)))" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.12.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Chapter4/ex3_2.py b/Chapter4/ex3_2.py new file mode 100644 index 0000000..99f2512 --- /dev/null +++ b/Chapter4/ex3_2.py @@ -0,0 +1,37 @@ +# Import necessary libraries +import sympy as sp + +# Define the state-space matrices +A = sp.Matrix([[1, 0], [1, 1]]) +B = sp.Matrix([[1], [1]]) +u = 1 # Step input +x0 = sp.Matrix([[1], [1]]) + +# Define the symbolic variable for time +t = sp.symbols('t') + +# Calculate the state transition matrix (phi) +phi = sp.exp(A * t) + +# Calculate the zero-state response +x1 = sp.exp(-A * t) * B * u +x_zs = sp.integrate(x1, (t)) + +# Calculate the zero-input response +x_zi = phi * x0 + +# Calculate the total response +x = x_zi + x_zs + +# Display the results +print("State Transition Matrix (phi):") +print(phi) + +print("\nZero-State Response (x_zs):") +print(x_zs) + +print("\nZero-Input Response (x_zi):") +print(x_zi) + +print("\nTotal Response (x):") +print(x) diff --git a/Chapter4/ex3_3.ipynb b/Chapter4/ex3_3.ipynb new file mode 100644 index 0000000..c96d101 --- /dev/null +++ b/Chapter4/ex3_3.ipynb @@ -0,0 +1,159 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Import necessary libraries" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import sympy as sp" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the state-space matrix A" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "A = sp.Matrix([[0, 6], [-1, -5]])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the symbolic variables" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "t = sp.symbols('t')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Calculate the matrix exponential exp(A*t)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "expm_A_t = sp.exp(A * t)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Display the result" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Matrix Exponential (exp(A*t)):\n", + "Matrix([[3*exp(-2*t) - 2*exp(-3*t), 6*exp(-2*t) - 6*exp(-3*t)], [-exp(-2*t) + exp(-3*t), -2*exp(-2*t) + 3*exp(-3*t)]])\n" + ] + } + ], + "source": [ + "print(\"Matrix Exponential (exp(A*t)):\")\n", + "print(expm_A_t)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Display the results using latex" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\text{Matrix Exponential (exp(A*t)):}$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}3 e^{- 2 t} - 2 e^{- 3 t} & 6 e^{- 2 t} - 6 e^{- 3 t}\\\\- e^{- 2 t} + e^{- 3 t} & - 2 e^{- 2 t} + 3 e^{- 3 t}\\end{matrix}\\right]$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from IPython.display import display, Math\n", + "\n", + "display(Math(r\"\\text{Matrix Exponential (exp(A*t)):}\"))\n", + "display(Math(sp.latex(expm_A_t)))" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.12.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Chapter4/ex3_3.py b/Chapter4/ex3_3.py new file mode 100644 index 0000000..92dd932 --- /dev/null +++ b/Chapter4/ex3_3.py @@ -0,0 +1,15 @@ +# Import necessary libraries +import sympy as sp + +# Define the state-space matrix A +A = sp.Matrix([[0, 6], [-1, -5]]) + +# Define the symbolic variables +t = sp.symbols('t') + +# Calculate the matrix exponential exp(A*t) +expm_A_t = sp.exp(A * t) + +# Display the result +print("Matrix Exponential (exp(A*t)):") +print(expm_A_t) diff --git a/Chapter4/ex3_8.ipynb b/Chapter4/ex3_8.ipynb new file mode 100644 index 0000000..a315370 --- /dev/null +++ b/Chapter4/ex3_8.ipynb @@ -0,0 +1,159 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Import necessary libraries" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import scipy.signal as signal" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the state-space matrices" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "A = np.array([[0, 1], [-2, -3]])\n", + "B = np.array([[1], [1]])\n", + "C = np.array([[1, 0]])\n", + "D = np.array([[0]])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Create the state-space system" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "sys = signal.StateSpace(A, B, C, D)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Compute eigenvalues of A" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "eigs = np.linalg.eigvals(A)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Compute poles and zeros of the system" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "c:\\Users\\User\\AppData\\Local\\Programs\\Python\\Python312\\Lib\\site-packages\\scipy\\signal\\_filter_design.py:1101: BadCoefficients: Badly conditioned filter coefficients (numerator): the results may be meaningless\n", + " b, a = normalize(b, a)\n", + "c:\\Users\\User\\AppData\\Local\\Programs\\Python\\Python312\\Lib\\site-packages\\scipy\\signal\\_ltisys.py:600: BadCoefficients: Badly conditioned filter coefficients (numerator): the results may be meaningless\n", + " self.num, self.den = normalize(*system)\n" + ] + } + ], + "source": [ + "poles = sys.poles\n", + "zeros = signal.TransferFunction(*signal.ss2tf(A, B, C, D)).zeros" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Display the results" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Eigenvalues of A:\n", + "[-1. -2.]\n", + "\n", + "Poles of the system:\n", + "[-2. -1.]\n", + "\n", + "Zeros of the system:\n", + "[-4.]\n" + ] + } + ], + "source": [ + "print(\"Eigenvalues of A:\")\n", + "print(eigs)\n", + "\n", + "print(\"\\nPoles of the system:\")\n", + "print(poles)\n", + "\n", + "print(\"\\nZeros of the system:\")\n", + "print(zeros)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.12.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Chapter4/ex3_8.py b/Chapter4/ex3_8.py new file mode 100644 index 0000000..b666264 --- /dev/null +++ b/Chapter4/ex3_8.py @@ -0,0 +1,29 @@ +# Import necessary libraries +import numpy as np +import scipy.signal as signal + +# Define the state-space matrices +A = np.array([[0, 1], [-2, -3]]) +B = np.array([[1], [1]]) +C = np.array([[1, 0]]) +D = np.array([[0]]) + +# Create the state-space system +sys = signal.StateSpace(A, B, C, D) + +# Compute eigenvalues of A +eigs = np.linalg.eigvals(A) + +# Compute poles and zeros of the system +poles = sys.poles +zeros = signal.TransferFunction(*signal.ss2tf(A, B, C, D)).zeros + +# Display the results +print("Eigenvalues of A:") +print(eigs) + +print("\nPoles of the system:") +print(poles) + +print("\nZeros of the system:") +print(zeros) diff --git a/Chapter4/jordan_forms.ipynb b/Chapter4/jordan_forms.ipynb new file mode 100644 index 0000000..88bc54a --- /dev/null +++ b/Chapter4/jordan_forms.ipynb @@ -0,0 +1,242 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Import necessary libraries" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import sympy as sp" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the matrices for Inverted Pendulum" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "A1 = sp.Matrix([\n", + " [0, 1, 0, 0],\n", + " [0, 0, -9.8, 0],\n", + " [0, 0, 0, 1],\n", + " [0, 0, 19.6, 0]\n", + "])\n", + "B1 = sp.Matrix([0, 1, 0, 1])\n", + "C1 = sp.Matrix([\n", + " [1, 0, 0, 0],\n", + " [0, 0, 1, 0]\n", + "])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Compute the Jordan form" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "T1, J1 = A1.jordan_form()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Compute transformed B and C" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "Bn1 = T1.inv() * B1\n", + "Cn1 = C1 * T1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Display the results" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Inverted Pendulum Jordan Form:\n", + "⎡0 1.0 0 0 ⎤\n", + "⎢ ⎥\n", + "⎢0 0 0 0 ⎥\n", + "⎢ ⎥\n", + "⎢0 0 -4.42718872423573 0 ⎥\n", + "⎢ ⎥\n", + "⎣0 0 0 4.42718872423573⎦\n", + "\n", + "Transformation Matrix T:\n", + "⎡1.0 0 0.112938487863156 -0.112938487863156⎤\n", + "⎢ ⎥\n", + "⎢ 0 1.0 -0.5 -0.5 ⎥\n", + "⎢ ⎥\n", + "⎢ 0 0 -0.225876975726313 0.225876975726313 ⎥\n", + "⎢ ⎥\n", + "⎣ 0 0 1.0 1.0 ⎦\n", + "\n", + "Transformed B (Bn):\n", + "⎡ 0 ⎤\n", + "⎢ ⎥\n", + "⎢1.5⎥\n", + "⎢ ⎥\n", + "⎢0.5⎥\n", + "⎢ ⎥\n", + "⎣0.5⎦\n", + "\n", + "Transformed C (Cn):\n", + "⎡1.0 0 0.112938487863156 -0.112938487863156⎤\n", + "⎢ ⎥\n", + "⎣ 0 0 -0.225876975726313 0.225876975726313 ⎦\n" + ] + } + ], + "source": [ + "print(\"Inverted Pendulum Jordan Form:\")\n", + "sp.pretty_print(J1)\n", + "print(\"\\nTransformation Matrix T:\")\n", + "sp.pretty_print(T1)\n", + "print(\"\\nTransformed B (Bn):\")\n", + "sp.pretty_print(Bn1)\n", + "print(\"\\nTransformed C (Cn):\")\n", + "sp.pretty_print(Cn1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the matrices for Example 3-13" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "A2 = sp.Matrix([\n", + " [0, 1, 0, 3],\n", + " [0, -1, 1, 10],\n", + " [0, 0, 0, 1],\n", + " [0, 0, -1, -2]\n", + "])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Compute the Jordan form" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "T2, J2 = A2.jordan_form()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Display the results" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Example 3-13 Jordan Form:\n", + "⎡-1 1 0 0⎤\n", + "⎢ ⎥\n", + "⎢0 -1 1 0⎥\n", + "⎢ ⎥\n", + "⎢0 0 -1 0⎥\n", + "⎢ ⎥\n", + "⎣0 0 0 0⎦\n", + "\n", + "Transformation Matrix T:\n", + "⎡9 11 11 1⎤\n", + "⎢ ⎥\n", + "⎢-9 1 0 0⎥\n", + "⎢ ⎥\n", + "⎢0 1 1 0⎥\n", + "⎢ ⎥\n", + "⎣0 -1 0 0⎦\n" + ] + } + ], + "source": [ + "print(\"\\nExample 3-13 Jordan Form:\")\n", + "sp.pretty_print(J2)\n", + "print(\"\\nTransformation Matrix T:\")\n", + "sp.pretty_print(T2)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.12.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Chapter4/jordan_forms.py b/Chapter4/jordan_forms.py new file mode 100644 index 0000000..03ac307 --- /dev/null +++ b/Chapter4/jordan_forms.py @@ -0,0 +1,49 @@ +# Import necessary libraries +import sympy as sp + +# Define the matrices for Inverted Pendulum +A1 = sp.Matrix([ + [0, 1, 0, 0], + [0, 0, -9.8, 0], + [0, 0, 0, 1], + [0, 0, 19.6, 0] +]) +B1 = sp.Matrix([0, 1, 0, 1]) +C1 = sp.Matrix([ + [1, 0, 0, 0], + [0, 0, 1, 0] +]) + +# Compute the Jordan form +T1, J1 = A1.jordan_form() + +# Compute transformed B and C +Bn1 = T1.inv() * B1 +Cn1 = C1 * T1 + +# Display the results +print("Inverted Pendulum Jordan Form:") +sp.pretty_print(J1) +print("\nTransformation Matrix T:") +sp.pretty_print(T1) +print("\nTransformed B (Bn):") +sp.pretty_print(Bn1) +print("\nTransformed C (Cn):") +sp.pretty_print(Cn1) + +# Define the matrices for Example 3-13 +A2 = sp.Matrix([ + [0, 1, 0, 3], + [0, -1, 1, 10], + [0, 0, 0, 1], + [0, 0, -1, -2] +]) + +# Compute the Jordan form +T2, J2 = A2.jordan_form() + +# Display the results +print("\nExample 3-13 Jordan Form:") +sp.pretty_print(J2) +print("\nTransformation Matrix T:") +sp.pretty_print(T2) diff --git a/Chapter5_6/ex4_3.ipynb b/Chapter5_6/ex4_3.ipynb new file mode 100644 index 0000000..311e2de --- /dev/null +++ b/Chapter5_6/ex4_3.ipynb @@ -0,0 +1,147 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Import necessary libraries" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from scipy.linalg import null_space" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the matrices" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "A = np.array([[-3/2, 1/2], [1/2, -3/2]])\n", + "C = np.array([[1, -1]])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Compute the observability matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "O = np.vstack([C, C @ A])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Compute the rank of the observability matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "rank_O = np.linalg.matrix_rank(O)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Compute the null space of the observability matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "null_O = null_space(O)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Display the results" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Observability Matrix (O):\n", + "[[ 1. -1.]\n", + " [-2. 2.]]\n", + "\n", + "Rank of Observability Matrix (O):\n", + "1\n", + "\n", + "Null Space of Observability Matrix (O):\n", + "[[0.70710678]\n", + " [0.70710678]]\n" + ] + } + ], + "source": [ + "print(\"Observability Matrix (O):\")\n", + "print(O)\n", + "\n", + "print(\"\\nRank of Observability Matrix (O):\")\n", + "print(rank_O)\n", + "\n", + "print(\"\\nNull Space of Observability Matrix (O):\")\n", + "print(null_O)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.12.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Chapter5_6/ex4_3.py b/Chapter5_6/ex4_3.py new file mode 100644 index 0000000..188a7ad --- /dev/null +++ b/Chapter5_6/ex4_3.py @@ -0,0 +1,26 @@ +# Import necessary libraries +import numpy as np +from scipy.linalg import null_space + +# Define the matrices +A = np.array([[-3/2, 1/2], [1/2, -3/2]]) +C = np.array([[1, -1]]) + +# Compute the observability matrix +O = np.vstack([C, C @ A]) + +# Compute the rank of the observability matrix +rank_O = np.linalg.matrix_rank(O) + +# Compute the null space of the observability matrix +null_O = null_space(O) + +# Display the results +print("Observability Matrix (O):") +print(O) + +print("\nRank of Observability Matrix (O):") +print(rank_O) + +print("\nNull Space of Observability Matrix (O):") +print(null_O) diff --git a/Chapter5_6/ex4_9.ipynb b/Chapter5_6/ex4_9.ipynb new file mode 100644 index 0000000..4ab7475 --- /dev/null +++ b/Chapter5_6/ex4_9.ipynb @@ -0,0 +1,147 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Import necessary libraries" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from scipy.linalg import null_space" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the matrices" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "A = np.array([[-3/2, 1/2], [1/2, -3/2]])\n", + "B = np.array([[1/2], [1/2]])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Compute the controllability matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "C = np.hstack([B, A @ B])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Compute the rank of the controllability matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "rank_C = np.linalg.matrix_rank(C)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Compute the null space of the controllability matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "null_C = null_space(C)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Display the results" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Controllability Matrix (C):\n", + "[[ 0.5 -0.5]\n", + " [ 0.5 -0.5]]\n", + "\n", + "Rank of Controllability Matrix (C):\n", + "1\n", + "\n", + "Null Space of Controllability Matrix (C):\n", + "[[0.70710678]\n", + " [0.70710678]]\n" + ] + } + ], + "source": [ + "print(\"Controllability Matrix (C):\")\n", + "print(C)\n", + "\n", + "print(\"\\nRank of Controllability Matrix (C):\")\n", + "print(rank_C)\n", + "\n", + "print(\"\\nNull Space of Controllability Matrix (C):\")\n", + "print(null_C)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.12.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Chapter5_6/ex4_9.py b/Chapter5_6/ex4_9.py new file mode 100644 index 0000000..5f9fa7b --- /dev/null +++ b/Chapter5_6/ex4_9.py @@ -0,0 +1,26 @@ +# Import necessary libraries +import numpy as np +from scipy.linalg import null_space + +# Define the matrices +A = np.array([[-3/2, 1/2], [1/2, -3/2]]) +B = np.array([[1/2], [1/2]]) + +# Compute the controllability matrix +C = np.hstack([B, A @ B]) + +# Compute the rank of the controllability matrix +rank_C = np.linalg.matrix_rank(C) + +# Compute the null space of the controllability matrix +null_C = null_space(C) + +# Display the results +print("Controllability Matrix (C):") +print(C) + +print("\nRank of Controllability Matrix (C):") +print(rank_C) + +print("\nNull Space of Controllability Matrix (C):") +print(null_C) diff --git a/Chapter5_6/ex5_1.ipynb b/Chapter5_6/ex5_1.ipynb new file mode 100644 index 0000000..9aa3a74 --- /dev/null +++ b/Chapter5_6/ex5_1.ipynb @@ -0,0 +1,342 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Import necessary libraries" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import control" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the first state-space system" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Transfer Function (sys1):\n", + ": sys[1]\n", + "Inputs (1): ['u[0]']\n", + "Outputs (1): ['y[0]']\n", + "\n", + "\n", + "s^2 - 8.882e-15 s + 1\n", + "----------------------\n", + "s^3 + 6 s^2 + 11 s + 5\n", + "\n" + ] + } + ], + "source": [ + "A1 = np.array([[0, 1, 0], [0, 0, 1], [-5, -11, -6]])\n", + "B1 = np.array([[0], [0], [1]])\n", + "C1 = np.array([[1, 0, 1]])\n", + "D1 = np.array([[0]])\n", + "sys1 = control.ss(A1, B1, C1, D1)\n", + "tf1 = control.ss2tf(sys1)\n", + "\n", + "print(\"Transfer Function (sys1):\")\n", + "print(tf1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the second state-space system" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Transfer Function (sys2):\n", + ": sys[3]\n", + "Inputs (1): ['u[0]']\n", + "Outputs (1): ['y[0]']\n", + "\n", + "\n", + "s^2 - 8.882e-15 s + 1\n", + "----------------------\n", + "s^3 + 6 s^2 + 11 s + 5\n", + "\n" + ] + } + ], + "source": [ + "A2 = np.array([[0, 0, -5], [1, 0, -11], [0, 1, -6]])\n", + "B2 = np.array([[1], [0], [1]])\n", + "C2 = np.array([[0, 0, 1]])\n", + "D2 = np.array([[0]])\n", + "sys2 = control.ss(A2, B2, C2, D2)\n", + "tf2 = control.ss2tf(sys2)\n", + "\n", + "print(\"\\nTransfer Function (sys2):\")\n", + "print(tf2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the third state-space system" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Transfer Function (sys3):\n", + ": sys[5]\n", + "Inputs (1): ['u[0]']\n", + "Outputs (1): ['y[0]']\n", + "\n", + "\n", + "s^2 - 3.375e-14 s + 1\n", + "----------------------\n", + "s^3 + 6 s^2 + 11 s + 5\n", + "\n" + ] + } + ], + "source": [ + "A3 = np.array([[0, 1, 0], [0, 0, 1], [-5, -11, -6]])\n", + "B3 = np.array([[1], [-6], [26]])\n", + "C3 = np.array([[1, 0, 0]])\n", + "D3 = np.array([[0]])\n", + "sys3 = control.ss(A3, B3, C3, D3)\n", + "tf3 = control.ss2tf(sys3)\n", + "\n", + "print(\"\\nTransfer Function (sys3):\")\n", + "print(tf3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Observability matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Observability Matrix (sys3):\n", + "[[1. 0. 0.]\n", + " [0. 1. 0.]\n", + " [0. 0. 1.]]\n", + "Rank of Observability Matrix (sys3): 3\n" + ] + } + ], + "source": [ + "O3 = control.obsv(A3, C3)\n", + "rank_O3 = np.linalg.matrix_rank(O3)\n", + "print(\"\\nObservability Matrix (sys3):\")\n", + "print(O3)\n", + "print(\"Rank of Observability Matrix (sys3):\", rank_O3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the fourth state-space system" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Transfer Function (sys4):\n", + ": sys[7]\n", + "Inputs (1): ['u[0]']\n", + "Outputs (1): ['y[0]']\n", + "\n", + "\n", + "s^2 + 5.329e-15 s + 1\n", + "----------------------\n", + "s^3 + 6 s^2 + 11 s + 5\n", + "\n" + ] + } + ], + "source": [ + "A4 = np.array([[0, 0, -5], [1, 0, -11], [0, 1, -6]])\n", + "B4 = np.array([[1], [0], [0]])\n", + "C4 = np.array([[1, -6, 26]])\n", + "D4 = np.array([[0]])\n", + "sys4 = control.ss(A4, B4, C4, D4)\n", + "tf4 = control.ss2tf(sys4)\n", + "\n", + "print(\"\\nTransfer Function (sys4):\")\n", + "print(tf4)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Controllability matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Controllability Matrix (sys4):\n", + "[[1. 0. 0.]\n", + " [0. 1. 0.]\n", + " [0. 0. 1.]]\n", + "Rank of Controllability Matrix (sys4): 3\n" + ] + } + ], + "source": [ + "C4 = control.ctrb(A4, B4)\n", + "rank_C4 = np.linalg.matrix_rank(C4)\n", + "print(\"\\nControllability Matrix (sys4):\")\n", + "print(C4)\n", + "print(\"Rank of Controllability Matrix (sys4):\", rank_C4)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Transfer function to state-space" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "State-Space Representation from Transfer Function:\n", + "A matrix:\n", + " [[ -6. -11. -5.]\n", + " [ 1. 0. 0.]\n", + " [ 0. 1. 0.]]\n", + "B matrix:\n", + " [[1.]\n", + " [0.]\n", + " [0.]]\n", + "C matrix:\n", + " [[1. 0. 1.]]\n", + "D matrix:\n", + " [[0.]]\n", + "\n", + "State-Space Representation from Transfer Function:\n", + "A matrix:\n", + " [[ -6. -11. -5.]\n", + " [ 1. 0. 0.]\n", + " [ 0. 1. 0.]]\n", + "B matrix:\n", + " [[1.]\n", + " [0.]\n", + " [0.]]\n", + "C matrix:\n", + " [[1. 0. 1.]]\n", + "D matrix:\n", + " [[0.]]\n" + ] + } + ], + "source": [ + "num = [1, 0, 1]\n", + "den = [1, 6, 11, 5]\n", + "sys_tf = control.tf(num, den)\n", + "sys5 = control.tf2ss(num, den)\n", + "sys_ss = control.ss(sys_tf)\n", + "\n", + "print(\"\\nState-Space Representation from Transfer Function:\")\n", + "print(\"A matrix:\\n\", sys5.A)\n", + "print(\"B matrix:\\n\", sys5.B)\n", + "print(\"C matrix:\\n\", sys5.C)\n", + "print(\"D matrix:\\n\", sys5.D)\n", + "\n", + "print(\"\\nState-Space Representation from Transfer Function:\")\n", + "print(\"A matrix:\\n\", sys_ss.A)\n", + "print(\"B matrix:\\n\", sys_ss.B)\n", + "print(\"C matrix:\\n\", sys_ss.C)\n", + "print(\"D matrix:\\n\", sys_ss.D)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.12.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Chapter5_6/ex5_1.py b/Chapter5_6/ex5_1.py new file mode 100644 index 0000000..c998f6d --- /dev/null +++ b/Chapter5_6/ex5_1.py @@ -0,0 +1,75 @@ +# Import necessary libraries +import numpy as np +import control + +# Define the first state-space system +A1 = np.array([[0, 1, 0], [0, 0, 1], [-5, -11, -6]]) +B1 = np.array([[0], [0], [1]]) +C1 = np.array([[1, 0, 1]]) +D1 = np.array([[0]]) +sys1 = control.ss(A1, B1, C1, D1) +tf1 = control.ss2tf(sys1) + +print("Transfer Function (sys1):") +print(tf1) + +# Define the second state-space system +A2 = np.array([[0, 0, -5], [1, 0, -11], [0, 1, -6]]) +B2 = np.array([[1], [0], [1]]) +C2 = np.array([[0, 0, 1]]) +D2 = np.array([[0]]) +sys2 = control.ss(A2, B2, C2, D2) +tf2 = control.ss2tf(sys2) + +print("\nTransfer Function (sys2):") +print(tf2) + +# Define the third state-space system +A3 = np.array([[0, 1, 0], [0, 0, 1], [-5, -11, -6]]) +B3 = np.array([[1], [-6], [26]]) +C3 = np.array([[1, 0, 0]]) +D3 = np.array([[0]]) +sys3 = control.ss(A3, B3, C3, D3) +tf3 = control.ss2tf(sys3) + +print("\nTransfer Function (sys3):") +print(tf3) + +# Observability matrix +O3 = control.obsv(A3, C3) +rank_O3 = np.linalg.matrix_rank(O3) +print("\nObservability Matrix (sys3):") +print(O3) +print("Rank of Observability Matrix (sys3):", rank_O3) + +# Define the fourth state-space system +A4 = np.array([[0, 0, -5], [1, 0, -11], [0, 1, -6]]) +B4 = np.array([[1], [0], [0]]) +C4 = np.array([[1, -6, 26]]) +D4 = np.array([[0]]) +sys4 = control.ss(A4, B4, C4, D4) +tf4 = control.ss2tf(sys4) + +print("\nTransfer Function (sys4):") +print(tf4) + +# Controllability matrix +C4 = control.ctrb(A4, B4) +rank_C4 = np.linalg.matrix_rank(C4) +print("\nControllability Matrix (sys4):") +print(C4) +print("Rank of Controllability Matrix (sys4):", rank_C4) + +# Transfer function to state-space +num = [1, 0, 1] +den = [1, 6, 11, 5] +sys_tf = control.tf(num, den) +print(control.tf2ss(num, den)) +sys5 = control.tf2ss(num, den) +sys_ss = control.ss(sys_tf) + +print("\nState-Space Representation from Transfer Function:") +print("A matrix:\n", sys5.A) +print("B matrix:\n", sys5.B) +print("C matrix:\n", sys5.C) +print("D matrix:\n", sys5.D) diff --git a/Chapter5_6/ex5_2.ipynb b/Chapter5_6/ex5_2.ipynb new file mode 100644 index 0000000..cf57fec --- /dev/null +++ b/Chapter5_6/ex5_2.ipynb @@ -0,0 +1,125 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Import necessary libraries" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import control" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the first state-space system" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Transfer Function (sys1):\n", + ": sys[1]\n", + "Inputs (1): ['u[0]']\n", + "Outputs (1): ['y[0]']\n", + "\n", + "\n", + " s^2 - 2 s + 1\n", + "---------------------\n", + "s^3 + 4 s^2 + 5 s + 2\n", + "\n" + ] + } + ], + "source": [ + "A1 = np.array([[-1, 1, 0], [0, -1, 0], [0, 0, -2]])\n", + "B1 = np.array([[0], [1], [1]])\n", + "C1 = np.array([[4, -8, 9]])\n", + "D1 = np.array([[0]])\n", + "sys1 = control.ss(A1, B1, C1, D1)\n", + "tf1 = control.ss2tf(sys1)\n", + "\n", + "print(\"Transfer Function (sys1):\")\n", + "print(tf1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define the second state-space system" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Transfer Function (sys2):\n", + ": sys[3]\n", + "Inputs (1): ['u[0]']\n", + "Outputs (1): ['y[0]']\n", + "\n", + "\n", + " s^2 - 2 s + 1\n", + "---------------------\n", + "s^3 + 4 s^2 + 5 s + 2\n", + "\n" + ] + } + ], + "source": [ + "A2 = np.array([[-1, 0, 0], [1, -1, 0], [0, 0, -2]])\n", + "B2 = np.array([[4], [-8], [9]])\n", + "C2 = np.array([[0, 1, 1]])\n", + "D2 = np.array([[0]])\n", + "sys2 = control.ss(A2, B2, C2, D2)\n", + "tf2 = control.ss2tf(sys2)\n", + "\n", + "print(\"\\nTransfer Function (sys2):\")\n", + "print(tf2)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.12.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/Chapter5_6/ex5_2.py b/Chapter5_6/ex5_2.py new file mode 100644 index 0000000..60982a3 --- /dev/null +++ b/Chapter5_6/ex5_2.py @@ -0,0 +1,25 @@ +# Import necessary libraries +import numpy as np +import control + +# Define the first state-space system +A1 = np.array([[-1, 1, 0], [0, -1, 0], [0, 0, -2]]) +B1 = np.array([[0], [1], [1]]) +C1 = np.array([[4, -8, 9]]) +D1 = np.array([[0]]) +sys1 = control.ss(A1, B1, C1, D1) +tf1 = control.ss2tf(sys1) + +print("Transfer Function (sys1):") +print(tf1) + +# Define the second state-space system +A2 = np.array([[-1, 0, 0], [1, -1, 0], [0, 0, -2]]) +B2 = np.array([[4], [-8], [9]]) +C2 = np.array([[0, 1, 1]]) +D2 = np.array([[0]]) +sys2 = control.ss(A2, B2, C2, D2) +tf2 = control.ss2tf(sys2) + +print("\nTransfer Function (sys2):") +print(tf2)