control_systems.ipynb

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  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "The Python Control Environment"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This notebook uses SymPy and the python-control libraries. \n",
      "\n",
      "SymPy provides symbolic mathematics whilst python-control contains tools to help design and analyse control systems. It implements some of the features available in the MATLAB control systems toolbox. Links for each library are below:\n",
      "\n",
      "* http://sympy.org/en/index.html\n",
      "* https://www.cds.caltech.edu/~murray/wiki/Control_Systems_Library_for_Python"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Basics of SymPy and python-control"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This example comes from http://www.jairusmartin.com/2013/02/control-systems-in-python-part-1.html.\n",
      "\n",
      "First, some basics to test the use of the control library."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import sympy\n",
      "from sympy import *\n",
      "sympy.init_printing()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Create a symbol s:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "s = Symbol(\"s\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can now use our symbol to define a transfer function:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "G1 = 1 / (s + 1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "And it prints in a nice way using $\\LaTeX$:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "G1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{1}{s + 1}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "  1  \n",
        "\u2500\u2500\u2500\u2500\u2500\n",
        "s + 1"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "G2 = 10 * s / (s + 10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "G2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{10 s}{s + 10}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        " 10\u22c5s \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "s + 10"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "G = G1 * G2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "G"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{10 s}{\\left(s + 1\\right) \\left(s + 10\\right)}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "      10\u22c5s      \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "(s + 1)\u22c5(s + 10)"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's try simplifying:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "G.simplify()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{10 s}{\\left(s + 1\\right) \\left(s + 10\\right)}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "      10\u22c5s      \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "(s + 1)\u22c5(s + 10)"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Nothing to be done then, it seems."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "G = 0.3 * (s + 0.05) * (s ** 2 + 1600.0) / ((s ** 2 + 0.05 * s + 16.0) * (s + 70.0))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "G"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{\\left(0.3 s + 0.015\\right) \\left(s^{2} + 1600.0\\right)}{\\left(s + 70.0\\right) \\left(s^{2} + 0.05 s + 16.0\\right)}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "                 \u239b 2         \u239e \n",
        " (0.3\u22c5s + 0.015)\u22c5\u239ds  + 1600.0\u23a0 \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "           \u239b 2                \u239e\n",
        "(s + 70.0)\u22c5\u239ds  + 0.05\u22c5s + 16.0\u23a0"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "G.simplify()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{\\left(0.3 s + 0.015\\right) \\left(s^{2} + 1600.0\\right)}{\\left(s + 70.0\\right) \\left(s^{2} + 0.05 s + 16.0\\right)}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "                 \u239b 2         \u239e \n",
        " (0.3\u22c5s + 0.015)\u22c5\u239ds  + 1600.0\u23a0 \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "           \u239b 2                \u239e\n",
        "(s + 70.0)\u22c5\u239ds  + 0.05\u22c5s + 16.0\u23a0"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Again, simplifying doesn't do anything."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "factor(G)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{0.3 \\left(20.0 s + 1.0\\right) \\left(1.0 s^{2} + 1600.0\\right)}{\\left(1.0 s + 70.0\\right) \\left(20.0 s^{2} + 1.0 s + 320.0\\right)}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "                     \u239b     2         \u239e  \n",
        "  0.3\u22c5(20.0\u22c5s + 1.0)\u22c5\u239d1.0\u22c5s  + 1600.0\u23a0  \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "               \u239b      2                \u239e\n",
        "(1.0\u22c5s + 70.0)\u22c5\u239d20.0\u22c5s  + 1.0\u22c5s + 320.0\u23a0"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now a system in feedback form:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "H = 50"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "G1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{1}{s + 1}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "  1  \n",
        "\u2500\u2500\u2500\u2500\u2500\n",
        "s + 1"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "G2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{10 s}{s + 10}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        " 10\u22c5s \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "s + 10"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Ts = G1 * G2 / (1 + H * G1 * G2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Ts"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{10 s}{\\left(s + 1\\right) \\left(s + 10\\right) \\left(\\frac{500 s}{\\left(s + 1\\right) \\left(s + 10\\right)} + 1\\right)}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "                  10\u22c5s                 \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                 \u239b     500\u22c5s          \u239e\n",
        "(s + 1)\u22c5(s + 10)\u22c5\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + 1\u239f\n",
        "                 \u239d(s + 1)\u22c5(s + 10)    \u23a0"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Ts.simplify()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{10 s}{s^{2} + 511 s + 10}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "      10\u22c5s     \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        " 2             \n",
        "s  + 511\u22c5s + 10"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Simplify works with this one!"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Step Response Plots"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's import the control library."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from control import matlab"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.pyplot as plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A quick helper function:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def step_response(Ts, *args, **kwargs):\n",
      "    num = Poly(Ts.as_numer_denom()[0], s).all_coeffs()\n",
      "    den = Poly(Ts.as_numer_denom()[1], s).all_coeffs()\n",
      "    tf = matlab.tf([float(i) for i in num], [float(i) for i in den])\n",
      "    y, t = matlab.step(tf, *args, **kwargs)  # Doesn't work if passed as a list (as used in example).\n",
      "    plt.plot(t, y)\n",
      "    plt.title(\"Step Response\")\n",
      "    plt.grid()\n",
      "    plt.xlabel(\"Time (s)\")\n",
      "    plt.ylabel(\"y(t)\")\n",
      "    info = \"OS: {:f}{:s}\".format(round((y.max() / y[-1] - 1) * 100, 2), \"%\")\n",
      "    try:\n",
      "        i10 = next(i for i in range(0, len(y) - 1) if y[i] >= y[-1] * 0.1)\n",
      "        Tr = round(t[next(i for i in range(i10, len(y) - 1) if y[i] * 0.9)] - t[i10], 2)\n",
      "    except StopIteration:\n",
      "        Tr = \"unknown\"\n",
      "    try:\n",
      "        Ts = round(t[next(len(y) - i for i in range(2, len(y) - 1) if abs(y[-i] / y[-1]) > 1.02)] - t[0], 2)\n",
      "    except StopIteration:\n",
      "        Ts = \"unknown\"\n",
      "        \n",
      "    info += \"\\nTr: {}\".format(Tr)\n",
      "    info += \"\\nTs: {}\".format(Ts)\n",
      "    print(info)\n",
      "    plt.legend([info], loc=4)\n",
      "    plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "step_response(G)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "OS: 5268.130000%\n",
        "Tr: 0.0\n",
        "Ts: 265.86\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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30N1dfJ5PPy3a2duLh31pqfh7zM0Vdt6/L96z1NSKh7elpWjj5yf+bm1tgeRk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\nYRiGMRgWD4ZhGMZgWDwYhmEYg/n/fPkpMfCfQbIAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f9cfe987c10>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Note that `map()` returns an iterator in Python 3, so I used list comprehension to convert the numerator and denominators to floats. Also the example code sent `tf` as a list to the step function, but that failed."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "step_response(G1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "OS: 0.000000%\n",
        "Tr: 0.0\n",
        "Ts: unknown\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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r8PBwlZycXOz6gwcPVkuXLi1ymaVi5ucr1aCBUtu2WWTzJgkJCZZ9AQszcn4j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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f9ce3860c50>"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Bode, Magnitude/Phase Plots"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Firstly I don't yet understand these &ndash; control theory was banished from my brain several years ago..."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def freq_response(Ts, *args, **kwargs):\n",
      "    num = Poly(Ts.as_numer_denom()[0], s).all_coeffs()\n",
      "    den = Poly(Ts.as_numer_denom()[1], s).all_coeffs()\n",
      "    tf = matlab.tf([float(i) for i in num], [float(i) for i in den])\n",
      "    matlab.bode([tf], *args, **kwargs)  # tf needs to be passed as a list here for some reason.\n",
      "    plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So as before, we can send the function a transfer function such as G1:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "G1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{1}{s + 1}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "  1  \n",
        "\u2500\u2500\u2500\u2500\u2500\n",
        "s + 1"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "freq_response(G1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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hw4fzwQcfoJTCZDJx5swZxo0bx/79+12qWGZmJtOmTePPP/9k5cqVxSsvQ1WCIJQjCteM\nFA5p7dwJZvNV30jDhrbJcZmPY+nSpbz77rv88MMPRYamatSoQVxcHAMHDnS4UXu4//77xXAIgiAU\nQ06OFpRx3Tpt46pbb9UMSL9+2oytCiWMKTn97iwtJsnHH3/sVEyT+Ph4Vb9+fXXbbbcVOb5hwwYV\nFhamQkND1auvvlpi/fvuu6/Eczao7zVIrCrn6kusKtchsaqck+GuWFW5uUqlpCj15JNKBQWlqIAA\npcaOVWrtWqXOny9a1tl3Z4nrOJYtW8aIESPIysritddeu9bQYDKZePLJJ20yTPHx8UyaNIkHH3zQ\neiw/P5+JEyeyadMmAgMD6dChA/379+eHH35gx44dPP300zS09ZtLEARBwM9PG7Yym7UvjoYNteGs\n117TFh3ecYd2vG9f59sq0Tl+4a9IXWfPni022Uq3bt2sm0AVkpqaSmhoKMHBwfj5+TFkyBDWrFnD\niBEjmDNnDg0bNiQnJ4dx48aRlpbGzJkzS5QfFxdHQkICCQkJzJ07t8hsAovF4jV5819h4d3ZfuEx\nPeVfL9td9e25f9eGmXZG3vU6u+P+GpG35X65Il94zJPkXS9L7/tnq/zS+qfZbOb4cQtt21pISYHl\nyy2cPRvHzJlxhIYm4CxuCXKYlZVFv379SE9PB+Djjz/miy++4K233gLg/fffZ+vWrbzxxht2yRUf\nhyAIgn3k5YGfn4vXcZw6dYpp06YxduxY4uPjiY+PZ9SoUQ43CFgXFApXuf6/DW9t01mZjta3p54t\nZfUoY8QzdQVGXYfe7eohzxEZevdNW8r93Xk9giyWKuLee+/ljjvuIDo6mgp/ueidffEHBgaSnZ1t\nzWdnZxMUFOSQrLi4ONkB0MF8Wlqa7vLT0tIMrW9LvhBX3z9X3F8j8oV4e//UQ54j/bMQT+j/hTsA\nOkupQ1WRkZHWG+4o1w9V5eXlERYWxpdffknDhg2JiooiMTGRFnZG+ZKhKkEQBPtxeciRvn37sn79\neocbGDp0KJ07dyYjI4NGjRqxZMkSfH19mT9/PjExMYSHhzN48GC7jUYhcXFxVstqccDZJXnJS17y\n5SU/d+5cEhIScJrS5utWq1ZNmUwmValSJVW9enVVvXp1VaNGDafmAOuFDep7DbKOw7n6so7Ddcg6\nDudklMU9x0v1cZw7d8556yQIgiCUGUo1HDt27LjhWM2aNWncuDG+HrAHYllxjhuhf+ExT3OmOlJf\n7/tni7zCY+6+v+UlX3jM0+RdK0vP67VHfmn9s6TzbnOOd+zYke3bt9OqVSsA0tPTadmyJX/++ScL\nFy4kJibGaSUcRZzjgiAI9uNy53jDhg1JS0tj+/btbN++nbS0NG699VaSk5N55plnHG5YKMr1/214\na5vOynS0vj31bCmrRxkjnqkrMOo69G5XD3mOyNC7b9pSztXPrFTDceDAAVq2bGnNh4eHs3//fkJC\nQmQhnyAIQjmkVCdFy5YtGT9+PEOGDEEpxUcffUR4eDiXL1/Gz8/PHTr+LeLjMH7MV+8xYEfq633/\nbJFXeMzd97e85AuPeZq8a2Xpeb32yC+tf5Z03m0+jgsXLrBgwQL+97//AdClSxcmTJhA5cqVOX/+\nPDVq1HBaCUcRH4cgCIL9uNzHUbVqVSZPnszq1atZvXo1kydPpmrVqlSoUMFQo1HWuP6/DW9t01mZ\njta3p54tZfUoY8QzdQVGXYfe7eohzxEZevdNW8q5+pmVOlSVkZHB888/z969e7n41wa3JpOJn376\nyaWKCYIgCJ5JqV8c8fHxjBs3Dl9fX1JSUhg5ciTDhw93h242UVZCjhSOSbqz/cJjesq/Xra76ttz\n/64d83VG3vU6u+P+GpG35X65Il94zJPkXS9L7/tnq/zS+mdJ5/UKOVKqj6Nt27bs2LGDiIgIa5DC\nwmNGIz4OQRAE+3G5j6Ny5crk5+cTGhrK/Pnz+eSTTzh//rzDDQrFc/1/G97aprMyHa1vTz1byupR\nxohn6gqMug6929VDniMy9O6btpRz9TMr1ccxd+5cLly4wLx583jxxRc5c+YM7777rkuVEgRBEDwX\nt2wd6ypkqEoQBMF+nH13lvjF0a9fvxKFm0wm1q5d63CjelJWFgBKXvKSl7yr83otACwxKHu9evVU\nZGSkmjlzprJYLMpisaiUlBSVkpKiLBaLU7Hc9eJv1Pc6ZD8O5+rLfhyuQ/bjcE5GudqP48SJEyQn\nJ5OYmEhiYiJ9+vRh6NChReJWCYIgCOUPm3wcly9fJjExkcmTJ5OQkMDEiRPdoVupiI9DEATBflzm\n4wC4dOkS69ev58MPPyQrK4vHHnuMAQMGONyYIAiC4P2UuI5jxIgRdO7cmZ07d/LSSy+xbds2Xnzx\nRQIDA92pX7mh0JHl7W06K9PR+vbUs6WsHmWMeKauwKjr0LtdPeQ5IkPvvmlLOVc/sxK/OJYvX061\natV4/fXXef3114ucM5lMnDlzxqWK2YrMqnI8n5aWprv8tLQ0Q+vbki/E1ffPFffXiHwh3t4/9ZDn\nSP8sxBP6v9vCqnsy4uMQBEGwH5eHHBEEQRCEaxHD4SFc/1nrrW06K9PR+vbUs6WsHmWMeKauwKjr\n0LtdPeQ5IkPvvmlLOVc/MzEcgiAIgl2Ij0MQBKGcIT4OQRAEwa2I4fAQxMfhXH3xcbgO8XE4J0N8\nHIIgCEK5x+sNh+w57ni+8Jie8q+X7a769ty/axdEOSPvep3dcX+NyNtyv1yRLzzmSfKul6X3/bNV\nfmn9s6Tzbttz3JMR57ggCIL9iHO8jHD9fxve2qazMh2tb089W8rqUcaIZ+oKjLoOvdvVQ54jMvTu\nm7aUc/UzE8MhCIIg2IUMVQmCIJQzZKhKEARBcCtiODwE8XE4V198HK5DfBzOyRAfhyAIglDuER+H\nIAhCOUN8HIIgCIJbEcPhIYiPw7n64uNwHeLjcE6G+DjcyJo1a3jooYcYMmQIycnJRqsjCHZTuMe1\nIJQ1PN7H8ccffzB58mTefvvtG86Jj0PwZBISEnSJCyQIeuPxPo5Ro0bh7+9PREREkeNJSUk0b96c\npk2bMnPmzBLrv/LKK0ycONHVahqODFU5V98Th6rKCjJU5ZwMGapygPj4eJKSkoocy8/PZ+LEiSQl\nJbF3714SExPZt28fy5Yt44knnuD48eMopXj22Wfp3bs3kZGRrlbTcJYuXVom2nRWpqP17alnS1k9\nymRlZdmkj6djRN90Rbt6yHNEht5905ZyLn9myg1kZmaq2267zZr/7rvvVExMjDU/Y8YMNWPGjCJ1\nXn/9ddWuXTs1btw49eabbxYrNyQkRAGSJEmSJMmOFBIS4tQ73RcDOHbsGI0aNbLmg4KC2Lp1a5Ey\njz76KI8++ujfyjl06JBL9BMEQRBKxpBZVSaTyYhmBUEQBB0wxHAEBgaSnZ1tzWdnZxMUFGSEKoIg\nCIKdGGI42rdvz8GDB8nKyiI3N5cVK1bQv39/I1QRBEEQ7MTlhmPo0KF07tyZjIwMGjVqxJIlS/D1\n9WX+/PnExMQQHh7O4MGDadGihatVEQRBEHTA4xcACoIgCJ6Fx4YccYbMzEzGjBnD/fffb7QqggDA\n+fPnGTlyJA899BAffPCB0eoIQhHsfWeWScPRpEmTYkOUCIJRfPLJJ8TGxrJo0SLWrl1rtDqCUAR7\n35kebTicDVciCK7Env557dolHx8ft+sqlD9c+f70aMPhaLgSQXAH9vTPoKAg6xT0goICI9QVyhn2\n9E978WjD0a1bN2rXrl3kWGpqKqGhoQQHB+Pn58eQIUNYs2YNI0aMYM6cOTRs2JCcnBzGjRtHWlqa\nfJEILsOe/jlw4EBWrVrFhAkTZOq54Bbs6Z/2vjMNCTniDLaEK6lTpw5vvvmmu1UThBL7Z9WqVVm8\neLGBmglCyf3T3nemR39xFIeEKxE8GemfgiejV//0OsMh4UoET0b6p+DJ6NU/vc5wSLgSwZOR/il4\nMnr1T482HGazmdDQUPbs2UPNmjUlXIngUUg4HcGTcWX/9NiQI/n5+YSFhbFp0yYCAwPp0KEDiYmJ\n8kcoCIJgMB77xVHStDFBEATBWDzWcBQ3bezYsWMGaiQIgiCAB6/jsGXaWGBgoKwUFwRBsJOQkBCn\ntt722C8OW6aNHT9+HKVUmUgjR44sE206K9PR+vbUs6WsHmWMeKauSEZdh97t6iHPERl6901bypV2\n/vDhw069nz3WcJS3aY2RkZFlok1nZTpa3556tpTVq0xZwKjr1LtdPeQ5IkPvvmlLOVc/M4+dVQWw\nYcMGHn/8cfLz8xk9ejRTpkwpct5kMuHB6gvlnISEBBISEoxWQxBuwNl3p0cbjtIQwyF4MhaLBbPZ\nbLQagnADzr47PXaoqrxhsVjKRJvOynS0vj31bCmrV5mygFHXqXe7eshzRIbefdOWcq5+Zh47q8pW\nZs2CBg3A31/72aAB1K0LsleOIAiCa/D6oaonn1T88gucPIn15x9/wM03Q8OGEBCg/SxMAQEQGAiN\nGmkGRoKZCoJQ3vBqH8fKlStJSEhg//79bNu2jbZt21rPzZgxg8WLF+Pj48O8efPo1avXDfVLuvgr\nVzQjcuIEHD9+9efx43DsmJaOHoWLFyEo6Gpq1AhuuQUaN76aqlVz6S0QBEFwO077h5WB7Nu3Tx04\ncECZzWa1fft26/Eff/xRtW7dWuXm5qrMzEwVEhKi8vPzb6jvrPrnzim1f79SmzYptXSpUi+/rNTY\nsUr16qVUWJhSVaooVbeuUm3bKjVggFJPPaXU//2fUp9/rtW7dMmp5ouQkpKinzAD23RWpqP17aln\nS1k9yhjxTF2BUdehd7t6yHNEht5905ZypZ139t1pqI+jefPmxR5fs2YNQ4cOxc/Pj+DgYEJDQ0lN\nTaVjx466tl+tGoSFaak4lILTp+HnnyErCzIzYfdu+PRT+OknyM6G+vXh1luhadOrqVkzCAmBKlV0\nVVcQBMEj8Agfx5133sns2bOtQ1WTJk2iY8eODB8+HIAxY8bQu3dvBg0aVKSe0dNx8/K0Ia/Dh+Hg\nwaIpM1MzKs2aQfPm0KLF1Z8BAeJbEQTBOJx9d7r8iyM6OpqTJ0/ecHz69On069fPZjklxa6Ki4sj\nODgYgFq1ahEZGWmdO184Jc1V+W+/1fI9e5rp2bPo+fx8+OgjC9nZULGimfR0WLTIws8/g1JmmjeH\n2rUtNGkC//iHmYgIOHDAgsnkOn0lL3nJl8+8xWJh6dKlANb3pVM4NdClE+brfBwzZsxQM2bMsOZj\nYmLUli1bbqjnIerbza+/KvXtt0otWqTUo48q1aOHUrVqpajatZXq1k2p8eOVevNNpbZsUer8edfp\nIT4O15YRH4dntSs+jqs4++70mHUc6prPpv79+zNs2DCefPJJjh07xsGDB4mKijJQO32pWxe6dNFS\nIRYLhIfDjz9Cejps2waLFsG+fdrsrsjIq6ldO6hXzzD1BUEo5xjq41i9ejWPPvoov/76KzVr1qRN\nmzZs2LAB0IayFi9ejK+vL6+//joxMTE31Dfax+EOrlyB/fshLU1LO3fCjh1Quza0bw8dOmg/27WD\nmjWN1lYQBG/Aq9dxOEt5MBzFUVAAhw5pXyU//KD9TEvTFjZ27AidOmmpZUvw9ZhvSkEQPAWJVVVG\nKHRk2UKFCtpsreHDYc4c+PZbbbX8ypXa8NfWrTB4MNSpAz16wAsvwPr18PvvjrdpK87KdLS+PfVs\nKatHGVfcXyMw6jr0blcPeY7I0Ltv2lLO1c9M/h8tI/j6QqtWWnroIe1YTg5s2QLffw+vvQZDhmjr\nS7p1gzvukHhegiA4hqFDVU8//TSfffYZFStWJCQkhCVLllDzr4F6Z0KOCMWTm6v5RzZvhm++0b5U\nbr4ZunfXvkx69NCCRQqCULbxah9HcnIyPXv2pEKFCjz33HMAvPrqq+zdu5dhw4axbds2jh07xl13\n3UVGRgYVKhQdWRPD4Rz5+bBnjzaj66uv4OuvtZhdPXtqqXt3cbgLQlnEq30c0dHRVmNw++23c/To\nUaDkkCNlGSPGkb/5xkLr1vDYY7BmDfz6KyxerK1sf+MNzYh06gRTp2p+k/z80mWKj8M+Gd6A+Dic\nk1EWfRyfYHYqAAAgAElEQVQe4xxfvHgx99xzDwDHjx8nKCjIei4oKIhjx44ZpVq5wdcXoqLguecg\nOVmL0/XKK3DuHIwdqw1jDR0K776rRRwWBKF84hEhR6ZNm0bFihUZNmxYiXI8MeSInvnCsADubL/w\nWEnnt2yx4OMDs2aZmTULVq60sG0brF9v5oknoG5dC507w6RJZtq2hc2bLVyLo/o5Ul/v+2eLvMJj\njp6X/N/nC495mrxrZel5vfbIL61/Xn/eonPIEZt8HKdOnWLlypVs3ryZrKwsTCYTjRs35o477uD+\n+++nfv36DiuwdOlS3nrrLb788ksqV64MaH4OwOr3uPvuu5k6dSq33357UeXFx2EYeXnw3Xewbp2W\nzp6FPn2gXz/NP1K1qtEaCoJQEi73cYwePZrY2FjOnTvHuHHjePfdd1myZAkPP/wwZ8+eJTY2ljFj\nxjjUeFJSErNmzWLNmjVWowFayJEPP/yQ3NxcMjMzy1zIkeK4/r8NT2/T11eb0jtrlray3WLRov++\n+KKFBg1gwABYtkxbX+IOneypZ0tZPcoY8UxdgVHXoXe7eshzRIbefdOWcq5+ZqUOVT322GO0atXq\nhuMtWrSgR48ePPfcc+zatcuhxidNmkRubi7R0dEAdOrUiQULFhAeHk5sbCzh4eH4+vqyYMGCEoeq\nBM+gaVN48klo2xZat9a+Qlatgkcegc6dYdAguPdeLdS8IAjejYQcEVzKuXPw+efwySeQlKQFaYyN\nhfvuEyMiCEbhtnUcERERNzRWs2ZNOnTowD//+U/q1q3rsBKOIobDu7h0CTZuhBUrtBAoUVFaaJSB\nA7WgjYIguAe3reO4++676dOnDx988AHLly+nX79+tG/fHn9/f+Li4hxWQNDwNh+HIzIrV4b+/WH5\ncjh+XAuNsmEDBAdrTvXly2HDBsd0Eh+H6xAfh3MyyqWPo5BNmzaxc+dOa75Vq1a0adOGnTt3EhER\n4VDjL774ImvXrsVkMlG3bl2WLl1Ko0aNANtCjgjeS9Wq2nDVffdpM7LWroUPPtBWrw8YACNGaLOz\nJJ6WIHggtu74FBERUWQXvq1bt6pWrVoppZSKjIx0ZBMpdebMGevv8+bNU6NHj1ZKKfXjjz+q1q1b\nq9zcXJWZmalCQkJUfn7+DfXtUF/wEk6eVGruXKXat1cqIECpp55SKi3NaK0EoWzh7LvT5qGqd955\nh9GjRxMcHExwcDCjR4/mrbfe4vz580yZMsUho1WjRg3r7+fOnaPeX9valceQI4KGv78WAmXbNvjy\nS6hUSRveat0a5s7VVrMLgmAsNhuODh06sGfPHnbt2kVaWhrp6elERUVRrVo1YmNjHVbghRde4JZb\nbmHp0qVWA1QeQ46UBx+HvfVbtIBp0yAzUzMaO3Zo037vu0+bqZWX51i74uOwD/FxOCejXPs4Tp48\nyQsvvMCxY8dISkpi7969fP/994wePfpv65UWcmTatGlMmzaNV199lccff5wlS5YUK6eshxwxIp+W\nlqa7/LS0NJfUv/NOMJksxMbC8eNm/vUvePBBC716wdSp9rVXiKvvnyvurxH5Qry9f+ohz5H+XYg7\n/n5KylssBoQcAW1WVXx8PNOmTWP37t1cuXKFNm3asGfPHqeVADhy5Aj33HMPe/bskZAjgk3s3atF\n8122TNsm9+GH4R//0Ia3BEEoGbdNx/31118ZPHgwPn9Nc/Hz88PXyQ2tDx48aP19zZo1tGnTBiif\nIUcE+wkPh//8B44cgXHj4K23oFEjePppyMgwWjtBKLvYbDiqV6/Ob7/9Zs1v2bLFulufo0yZMoWI\niAgiIyOxWCzMnj0boEjIkd69e5eLkCPXf9Z6a5vOynSkfqVKUL++hU2btMCLFSpo2+Peeae22DA3\n1/429ChjxDN1BUZdh97t6iHPERn21LG1rNF9z+ZPhtmzZ9OvXz9++uknOnfuzOnTp/n444+davzv\n6j///PM8//zzTskXyh+hoTBzJrz8Mnz6Kbz5Jjz+OIwZoy04/GuZkCAITmBXrKorV65w4MABAMLC\nwvDz83OZYrYgPg7BFvbuhYULtZXp3btrgRd79NC+TAShPOLyWFWrVq2yNlLccNHAgQMdbtxZxHAI\n9nDunGY8FizQ4mZNmABxcbKvulD+cLlzfN26daxbt47FixczevRoli9fzvLlyxkzZgyLFy92uOFr\nmT17NhUqVCAnJ8d6bMaMGTRt2pTmzZuzceNGXdrxZMTH4Vx9W+pVr67NvJo718I778D330OTJjBx\noraniL3yjB5ndhfi43BORrn0cRTO/Y2Ojmbv3r0EBAQAcOLECUaOHOm0AtnZ2SQnJ9O4cWPrsb17\n97JixQr27t3LsWPHuOuuu8jIyKCCjC0IOmAyQdeuWjp2TPODdO+uhXyfNAnuucdoDQXBs7HZx9G8\neXP27dtnHa4qKCggPDyc/df/q2Yn999/Py+++CL33nsv27dvp06dOsyYMYMKFSrw7LPPAto6joSE\nBDp27FhUeRmqEnTi0iX46COYN0/btXDiRBg1Cm66yWjNBEF/3LaO46677iImJoalS5eyZMkS7rnn\nHuvOfY6yZs0agoKCbthhsDyGHBGMpXJlePBBLUbWsmWwZYsW7v3xx+HwYaO1EwTPwmbD8cYbbzBu\n3Dh27drF7t27efjhh3njjTdKrRcdHU1ERMQNae3atcyYMYOpU6day/6dBZR1HN7Rpif7OGwpazJB\np04wbpyFXbs0g9Kxo7btbUoKXNtFjR5ndhfi43BORrn0cRTOpjKZTAwcOLDYWVQlzbgCSE5OLvb4\nnj17yMzMpHXr1gAcPXqUdu3asXXrVgIDA8nOzraWPXr0KIGBgcXKkVhVnhMLyOLCWFV65gsprfzh\nwxbuvhtefNHM++9DXJwFX18tP3SoxKrytv4psaqWAm6KVdW9e3f69u3LvffeS7NmzYqcO3DgAJ9+\n+inr169n8+bNTinSpEkTq49j7969DBs2jNTUVKtz/NChQzcYJ/FxCO5EKW3r2zlzYNcuGD9eSzff\nbLRmgmAfLvdxbNy4kbp16/LII48QEBBAs2bNaNq0KQEBAUycOBF/f382bdrksAKFXGsUymPIEcHz\nMZkgJgaSkmDTJsjOhmbNtFXpP/5otHaC4Ebs2fUpLy9PnTx5Up08eVLl5eU5tYOUHtipvkeTkpJS\nJtp0Vqaj9e2pZ0tZW8ucOqXUv/6lVIMGSvXqpVRSklIFBfbr5MkYdR16t6uHPEdk6N03bSlX2nln\n3512LYzw8fHB398ff39/a5RcQSjP3HwzvPgiZGXB0KHwzDNw223w9ttw+bLR2gmCa7ArVpWnIT4O\nwdNQCr76SvODbNumhXufMEHbElcQPAW3reMQBKF0TCbo2RM++wy+/hpOnYLmzbXFhOnpRmsnCPpg\nl+HIysqyOsIvXLjAmTNnnGo8ISGBoKAg2rRpQ5s2bdiwYYP1nMSq8s42nZXpaH176tlSVo8yJ09a\nWLgQDh7Uwr3HxMBdd8H69VBQYJuunoARfdMV7eohzxEZevdNW8q5+pnZbDgWLVrE/fffz8MPPwxo\naysGDBjgVOMmk4knn3ySnTt3snPnTnr37g0UjVWVlJTEhAkTKPCmvzRBuIZ69eD55zU/yMiRmk8k\nPFyLkXXhgtHaCYL92OzjaN26NampqXTs2JGdO3cCEBERQboT399Tp06levXqPPXUU0WOS6wqoSyj\nlDaMNWeOtmPhmDHaHiHXRNkRBJfiNh9HpUqVqFSpkjWfl5eny9qKN954g9atWzN69Gj++OMPQGJV\nCWUbkwnMZlizRjMc589Dq1barKytW43WThBKx+atY7t37860adO4cOECycnJLFiwgH79+pVaLzo6\nmpMnT95wfNq0aYwfP56XXnoJgBdffJGnnnqKd955p1g5JRmpshJy5NoxSXe1P3fuXN3vV1paGo8/\n/rjb69tz/66v46i80u6frfd33jwzL78Mzz9v4d57ITjYzOOPQ716WogTo/unLffLFXm9+6ce8hzp\nn4XH9JRfWv8srm09Q47YvAokLy9P/fe//1WDBg1SgwYNUosWLVIFhSuddCAzM1PddtttSimlZsyY\noWbMmGE9FxMTo7Zs2XJDHTvU93hkAaBz9Y1aAOisjOvJy1Nq9WqlundXKihIqWnTlDp1ym4xuiIL\nAJ2TURYXADq0jiMnJ4fs7GxrgEJHOXHihHVjqDlz5rBt2zY++OADiVUlCEBaGrzxBnzyCfzjH9om\nU23bGq2VUBZwm4+je/funDlzhpycHNq1a8fYsWN54oknHG4Y4Nlnn6VVq1a0bt2ar7/+mjlz5gAS\nq0oQQNuR8J13tOm8YWGa8ejaFVasgCtXjNZOKNfY+mnSunVrpZRSb731lnrppZeUUso6tGQUdqjv\n8chQlXP1y8pQ1d9x5YpSH3+sDWMFBio1dapSx4/r2kSxyFCVczLK4lCVzV8c+fn5nDhxgo8++og+\nffoAZX9zJUHwJHx9YdAgsFjg88/hxAltPUhsrHZMRm0Fd2Gzj2PlypW8/PLLdOnShYULF3L48GGe\neeYZVq1a5WodS0R8HEJ558wZbavbBQs0wzFhAowYATVrGq2Z4Mk4++40PMjhG2+8wYIFC/Dx8aFP\nnz7MnDkT0BYBLl68GB8fH+bNm0evXr1uqCuGQxA0lILNmzUDsnGj9mXy8MPQvr22bkQQrsVtzvGL\nFy8yf/58JkyYQHx8PPHx8YwaNcrhhgFSUlJYu3Ytu3fvZs+ePUyePBkonyFHrp137c1tOivT0fr2\n1LOlrB5l3PlMTSbo3l1znO/bp8XGGjJEm4W1cCH8+afjso3om65oVw95jsjQu2/aUs7Vz8xmwzFi\nxAh++eUXkpKSMJvNHD16lOrVqzvV+MKFC5kyZQp+fn4A3PzXHpxr1qxh6NCh+Pn5ERwcTGhoKKmp\nqU61JQjlhQYN4LnntNlYs2ZpYd6Dg7XQJlu3ii9EcB6bh6oiIyNJS0ujVatW7N69mytXrtC1a1e2\nOhEjoU2bNtx7770kJSVRuXJl/vOf/9C+fXsmTZpEx44dGT58OABjxoyhd+/eDBo0qKjyMlQlCDbx\nyy+wdKm2wVTFilqY9wcekH1CyivOvjttDjlSsWJFAGrWrEl6ejoNGjTg9OnTpdb7u5AjeXl5/P77\n72zZsoVt27YRGxvLTz/9VKycsh5yRPKSd2Xe3x9uv91CVBT4+ppZvBhCQixERsIzz5jp3Rv+9z/P\n0Vfy+uYtRoUcWbRokfrtt9+UxWJRwcHBql69emrhwoVOzQW+++67lcViseZDQkLU6dOnJeSIF7cp\n6zjsk2EkZ84o9c47SnXpopS/v1JPPaVUWtqN5WQdh3MyyvU6jrFjx1KnTh26d+9OZmYmp0+fZty4\ncU4ZrX/84x989dVXAGRkZJCbm0u9evXo378/H374Ibm5uWRmZnLw4EGioqKcaksQhKLUqKENWX37\nrRbmvVIl6N9fi9Q7axZIQGqhJGz2cVy6dIlVq1aRlZVFfn4+SilMJpM1uq0jXLlyhVGjRpGWlkbF\nihWZPXu29TNr+vTpLF68GF9fX15//XViYmJuVF58HIKgKwUF8M038P77sGqVNitrxAgYOFAzNELZ\nwG3rOGJiYqhVqxbt2rXDx8fHajiu34TJnYjhEATXcekSrFunLTD8+muIjobBg6FPH6ha1WjtBGdw\n+t1p65hWy5YtnRoTcwV2qO/xiI/Dufri43AdKSkpKidH84dERytVs6ZSw4YptWaNUpcuubZdT5Mn\nPg4Nm30cnTt3Zvfu3Y5bKEEQvJbatTV/yMaNkJEBXbrA7NkQEAAPPqjtZnjxotFaCu6i1KGqiIgI\nQAtyePDgQZo0aWLdQtZkMjllTIYMGcKBAwcA+OOPP6hVq5Z1P3MJOSIIns+xY7B6tbZnyI4d0KuX\n5g/p00d8Ip6My30cWVlZ1jUUxRXVZU4wMHnyZGrVqsU///lP60ZO27Zts27klJGRQYUKRT+QxHAI\ngudw+jSsXasZkW++0UKg9O8PfftqXyaC5+DyWFX+/v588skn/Pvf/+aLL74gKCiI4OBga9IDpRQf\nffQRQ4cOBcpnyJHCxTre3qazMh2tb089W8rqUcaIZ+oKbL2Om2+G0aNh/XrIzoahQ7VwJy1bQlQU\nvPyytquhre8rve+fHvIckaF337SlnKv7XqmGY+TIkWzfvp2IiAg+//xzl8yi+uabb/D39yckJASA\n48ePExQUZD0fFBTEMZlULgheQ82aMGwYJCZq4U5efRVycuC++6BxYxg/Xvs6OXvWaE0FRyg15Mi+\nfftIT08HtJhRHTp0sKuBkkKOTJ8+nX79+gGQmJjIsGHD/lZOWQ85UhgWwJ3tFx7TW/61st1VX+/7\nZ4u8wmPuvr/emO/RAypUsNC/PzRoYOazz2DqVAuDB0OnTmbuvhvq1rVw661w551a/UIZntbfr5Wl\n1/2xV35p/fP68xadQ46U6uNo06aN1WFdXN5Z8vLyCAoKYseOHTRs2BCAV199FYDnnnsOgLvvvpup\nU6dy++23F1VefByC4NWcOwcWCyQlwRdfwPnzmoO9Z0/o0QMCA43WsGzich/H7t27qVGjhjWlp6db\nf7/pppscbriQTZs20aJFC6vRAMplyJHr/9vw1jadlelofXvq2VJWjzJGPFNX4MrrqF5dc57Pn6+F\ngd+8GW6/XZve26KFhebNtV0NV62C335zri09rsMRGXr3TVvKubrvlTpUlZ+f71IFVqxYYXWKFxIe\nHk5sbCzh4eH4+vqyYMEC2d9cEMoBoaFaGj9ec6zXrg1ffgnvvAPx8XDrrXDHHVrq1k3CwhuF4VvH\nOoMMVQlC+SE3F7Zv16b6bt6sBWf0979qSLp0gSZNZKtcW/D6PcedQQyHIJRf8vMhPf2qIfnuO8jL\ng06drqb27SWuVnG4bc9xwbWIj8O5+uLjcB1GXUdp7fr4QGQkTJoEK1fC0aOwbZu2fuTECXj6aW1t\nSfv2mp/kmWcspKdrxsVVOjlbp8z4OARBELwBkwluuUVLgwdrxy5d0kKhbNsGn32mrR05elQzOO3b\na6lNGwgLA195G9qMoUNVqampTJw4kStXrlid4IXrRCRWlSAIruDPP68akx9+0FazHzumrXCPjLya\nWrXSZn2VRbzax2E2m5kyZQoxMTFs2LCBf//736SkpEisKkEQ3MrZs5q/JC3tavrxR2jQAG67rWgK\nC4OKFY3W2Dm82scREBDAn3/+CWjRcQP/Wu0jsaq8t03xcdgnwxvwVB+HnvJq1IDOnTVfyKJFkJoK\nZ87Ahg0wcqRmKD75BPr0sVCzJoSHw6BB8M9/arslbt+uLWZ09jrEx2EDr776Kl27dmXy5MkUFBTw\n/fffA1qsqo4dO1rLSawqQRDcjY8PNGumpYEDtWMWC3TsCAcOwP79sG+f5juZNUtbwFivnvZF0rTp\n1ZSTo00l9vavlGtxueEoKVbVtGnTmDdvHvPmzWPAgAGsXLmSUaNGkZycXKwciVWlf77wmBGxdvSu\nr/f9s0Ve4TF339/yki885mnyKleG1q3h998t+PtDQoJ2/ssvLfzyC9SpYyYjA1JSLCQmwm+/mRk7\nVovFFRgI7dubufVWuHDBQsOGEBtrpmbNMharypXcdNNNnDlzBtBCq9eqVYs///xTYlUJglCmyM2F\nzEw4fBh++unGVKmSFjW4MAUHF83XqaPvwkav9nGEhoby9ddfA/DVV1/RrFkzQGJVeXObzsp0tL49\n9Wwpq0cZI56pKzDqOvRuVw95jsiwWCxUrKgNYd1zD0ycCK+9Bp9+Crt3a475ffvgv/+FyEgLjRpp\nxmTpUm273tBQqFZNGzLr0UPbqveBBywsXAjr1mn+lRMntAWRel7r32Goj2PRokU88sgjXL58mSpV\nqrBo0SJAYlUJglB+MJmgfn0tnT8P14ysWTl3Tlt/Upg2b9Zmfq1bpxmN48fh99+1BY8NG2r+lIgI\nbVaYv/+NP53WWUKOCIIgeD9XrmibZh0/ftWY/PILnDyppWt/v3TJi9dxOIsYDkEQBPtQCipU8GIf\nh3AV8XE4V198HK5DfBzOydC7b9pS7u/O6zHqb6jh2LVrF506daJVq1b079+fs9dsQDxjxgyaNm1K\n8+bN2bhxo4FaCoJjpKWlGa2CILgEQ4eqOnTowGuvvUa3bt1YsmQJmZmZ/Otf/5KQI0KZICEhgYSE\nBKPVEIQb8OrpuAcPHqRbt24A3HXXXaxatQqQkCPe3KYMVZU9ZKjKORmeNlSlB4YajpYtW7JmzRoA\nVq5cSXZ2NqCFHAkKCrKWKw8hRwpXdXp7m87KdLS+PfVsKatHmaysLJv08XSM6JuuaFcPeY7I0Ltv\n2lLO1c/M5UNVJYUcmT59Os2aNePRRx/lt99+o3///sybN49ff/2VSZMm0bFjR4YPHw7AmDFjuOee\nexhYGDDmL0JDQzl8+LAr1RcEQShzhISEcOjQIYfru3wBYEmxpwr54osvAMjIyGD9+vUABAYGWr8+\nAI4ePWqNnHstzly4IAiC4BiGDlWdPn0agIKCAl555RXGjx8PlM+QI4IgCN6CoYYjMTGRsLAwWrRo\nQVBQEHFxcUDRkCO9e/eWkCOCIAgehFevHBcEQRDcj6wcFwRBEOxCDIcgCIJgF2XScGRmZjJmzBju\nv/9+o1URBADOnz/PyJEjeeihh/jggw+MVkcQimDvO7NMGo4mTZrw9ttvG62GIFj55JNPiI2NZdGi\nRaxdu9ZodQShCPa+Mz3acIwaNQp/f38iIiKKHE9KSqJ58+Y0bdqUmTNnGqSdUN6xp38eO3aMRo0a\nAeDj4+N2XYXyhyvfnx5tOOLj40lKSipyLD8/n4kTJ5KUlMTevXtJTExk3759LFu2jCeeeILjx48b\npK1Q3rCnfwYFBVkXtRYUFBihrlDOsKd/2otHG45u3bpRu3btIsdSU1MJDQ0lODgYPz8/hgwZwpo1\naxgxYgRz5syhYcOG5OTkMG7cONLS0uSLRHAZ9vTPgQMHsmrVKiZMmED//v0N0lgoT9jTP+19Zxq6\n57gjXPvJD1oAxK1btxYpU6dOHd588013qyYIJfbPqlWrsnjxYgM1E4SS+6e970yP/uIoDllBLngy\n0j8FT0av/ul1huP6AIjZ2dlFQrALgpFI/xQ8Gb36p9cZjvbt23Pw4EGysrLIzc1lxYoVMmYseAzS\nPwVPRq/+6dGGY+jQoXTu3JmMjAwaNWrEkiVL8PX1Zf78+cTExBAeHs7gwYNp0aKF0aoK5RDpn4In\n48r+KUEOBUEQBLvw6C8OQRAEwfMQwyEIgiDYhRgOQRAEwS7EcAiCIAh2IYZDEARBsAsxHIIgCIJd\niOEQBEEQ7EIMh+CR+Pj40KZNG2s6cuSI0SrpRnp6OqNGjXJKRlxcHKtWrbLmP/zwQ6ZPn+6sagDM\nmzePZcuW6SJLKJt4XXRcoXxQtWpVdu7cWey5wjWr3hpQcNasWUyaNOmG43l5efj62vYnef21JyUl\n8dhjj+miX3x8PD179mTEiBG6yBPKHvLFIXgFWVlZhIWFMXLkSCIiIsjOzmbWrFlERUXRunVrEhIS\nrGWnTZtGWFgY3bp1Y9iwYcyePRsAs9nM9u3bAfj1119p0qQJoG1u8/TTT1tlLVq0CACLxYLZbOb+\n+++nRYsWPPDAA9Y2tm3bRpcuXYiMjKRjx46cO3eO7t27s2vXLmuZrl27kp6eXuQ6Ll++zJYtW+jQ\noQMACQkJjBgxgq5duzJy5Eh+/vln7rjjDtq1a0e7du34/vvvAc1YTpw4kebNmxMdHc2pU6esMpVS\npKWl0aZNG77++mvrV1rbtm05f/48QIn36r333qN169ZERkby4IMPAlCjRg3q1q3Ljz/+6PgDE8o0\n8sUheCQXL16kTZs2ANx666289tprHDp0iGXLlhEVFcXGjRs5dOgQqampFBQUcO+99/LNN99QtWpV\nVqxYwa5du7hy5Qpt27alffv2gPZfenFfKe+88w61atUiNTWVy5cv07VrV3r16gVAWloae/fuJSAg\ngC5duvDdd9/Rvn17hgwZwkcffUS7du04d+4cVapUYfTo0SxdupQ5c+aQkZHB5cuXb9i2c+fOnYSF\nhRU5tn//fr799lsqVarExYsXSU5OplKlShw8eJBhw4axbds2Vq9eTUZGBvv27ePkyZOEh4czevRo\nq8zIyEgAZs+ezYIFC+jUqRMXLlygUqVKJd6rOnXqMG3aNL7//nvq1KnD77//btUpKiqKzZs307Jl\nS52eqFCWEMMheCRVqlQpMlSVlZVF48aNiYqKAmDjxo1s3LjRalzOnz/PwYMHOXv2LAMHDqRy5cpU\nrlzZpsifGzduJD09nY8//hiAM2fOcOjQIfz8/IiKiqJhw4YAREZGkpmZSY0aNQgICKBdu3YAVK9e\nHYD77ruPl19+mVmzZrF48WLi4+NvaOvnn38mICDAmjeZTPTv359KlSoBkJuby8SJE9m1axc+Pj4c\nPHgQgM2bNzNs2DBMJhMBAQH06NHDKiMpKYnevXsD0KVLF5544gmGDx/OwIEDCQwMLPZeHTp0iPPn\nzxMbG0udOnUAiuwW17BhQ3766adS751QPhHDIXgN1apVK5KfMmUKDz30UJFjr7/+OtfG7bz2d19f\nX+t+35cuXSpSb/78+URHRxc5ZrFYrC900Bz2eXl5JfpWqlatSnR0NJ9++ikrV65kx44dN5QxmUxc\nH1e0atWq1t/nzJlDQEAAy5YtIz8/n8qVK5dYr5Dk5GTGjx8PwLPPPkvfvn1Zv349Xbp04YsvvgCK\nv1fz588vUaZSymt9SILrER+H4JXExMSwePFi6xj+sWPHOH36NHfccQeffvoply5d4uzZs3z22WfW\nOsHBwfzwww8A1q+LQlkLFiwgLy8PgIyMDC5cuFBsuyaTibCwME6cOGGVdfbsWfLz8wEYM2YMjz76\nKA6sxxEAAAH/SURBVFFRUdSsWfOG+o0bN+bkyZMlXteZM2do0KABoPkfCuXecccdrFixgoKCAk6c\nOEFKSgoAf/75J3l5edavhcOHD9OyZUueeeYZOnTowIEDB0q8Vz169GDlypXk5OQAWH8CnDhxguDg\n4BL1FMo38sUheCTF/bd77bHo6Gj27dtHp06dAM2h+/7779OmTRsGDx5M69atqV+/Ph06dLD+Vz15\n8mRiY2NZtGgRffr0scobM2YMWVlZtG3bFqUU9evXZ/Xq1SX6RPz8/FixYgWTJk3i4sWLVK1aleTk\nZKpVq0bbtm2pWbNmscNUAK1bt+bAgQMlXteECRMYNGgQ7733Hnfffbd1GGzAgAF89dVXhIeHc8st\nt9C5c2eUUiQnJxf5Unr99ddJSUmhQoUK3HbbbfTu3Rs/P79i71V4eDgvvPAC3bt3x8fHh7Zt21r3\nRU9NTeU///lPKU9JKK/IfhxCmWbq1KlUr16dp556yi3tHT9+nDvvvPMG43AtcXFxjB8/nttvv93p\n9saOHcvYsWOtvh89OHPmDD179mTbtm26yRTKFjJUJZR53DVW/95779GxY8dSF+JNnjyZN998U5c2\n33rrLV2NBsDSpUt1WxMilE3ki0MQBEGwC/niEARBEOxCDIcgCIJgF2I4BEEQBLsQwyEIgiDYhRgO\nQRAEwS7+P9ufLpzEeFczAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f9cfe99e490>"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Arguments can also be passed through to `matlab.bode` like this:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "freq_response(G, dB=True, Hz=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Uny5DGAuOtWTJEixZsgQRERGYPn06NmoGrZfBksGxNHn6ykuWlS1PTEzE9OnT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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f9cfe987f50>"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can smooth this out by passing your own omega values to the function:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "freq_response(G, omega=logspace(-3, 3, 500), dB=True, Hz=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ZBBkTBwcH9OnTB+vXr8fx48fh6emJ4OBgfPnll1YTRhCE8qlTh88Vp53njai8\nCJ5OJT8/H7t378amTZuQmpqKfv36YdSoUQad4hUF+UwIQj4cOgQEB/NwvV99JbUawhiS+EyGDx+O\nCxcu4JVXXsEnn3wCPz8/wQIIgqi8aMeWaJu5iMqLoGauH3/8EVeuXMHSpUvRpUsX1KlTR7fUrVvX\n2horBLm0W5LPxLJ80i9v/Rcv8nXymViuzZwycvKZCKqZ0JxYBEGYgzYCJ/lMKj80BT1BEDZDo+EB\nsZYuBSZPlloNYQxJp6AnCIIwht0/b5iiIml1ELaHjMk/yKXdknwmluWTfnnr164XFpberiw+h5Lr\nStRvTZ8JGROCIGzOkydSKyBsDflMCIKwKZ06AYsWAV26SK2EMAbFgC8DGROCIAjLIQe8lZBLuyX5\nTCzLJ/3y1m/oWiqLz6HkuhL1V3qfyfLly9G6dWv4+vpi2rRpuvT58+fDy8sLrVq1wr59+yRUaDvK\nxntQEkrWDpB+qSH9CkdU0F8b8Mcff7AePXqwwsJCxhhjmZmZjDHGLly4wPz9/VlhYSFLSUlhHh4e\nrLi4uNz+Mrwki5g1a5bUEgSjZO2MkX6pIf3SIvbdKbuayddff40ZM2bA0dERANCwYUMAPDb80KFD\n4ejoCHd3d3h6eiIuLs5q51V6VVMOzSxiIP2G05Ss35JmLqHIpZlLKEp/92iRnTG5cuUKDh06hE6d\nOiEkJATx8fEAgJs3b8LNzU1Xzs3NDenp6VY7rzlhhw2VKZtubFvfesm01NRUkzos0WYqX1+6UP1C\ntRvTZyqf9Mtbv6Fr0VfGVs++sTJif7sl15Wo35Jw6yaxUg3JInr06MF8fX3LLTt27GC+vr5s8uTJ\njDHG4uLiWPPmzRljjE2cOJH98MMPumNERESwrVu3lju2h4cHA0ALLbTQQosFi4eHh6j3uqCJHsWy\nf/9+g3lff/01BgwYAADo2LEj7OzscPfuXbi6uiItLU1X7saNG3pjpyQnJ1tfMEEQBGEU2TVzvf76\n6/jjjz8AAElJSSgsLESDBg3Qr18/bNq0CYWFhUhJScGVK1cQFBQksVqCIAgCEDgFvS0ZNWoURo0a\nBT8/P1SrVg3r168HAPj4+GDw4MHw8fGBg4MDVqxYAZVKJbFagiAIAqiEI+AJgiCIikd2zVwEQRCE\n8iBjQhAEQYimyhiTvLw8dOzYEbt375ZaisVcunQJEyZMwODBg7F69Wqp5VjMjh07MHbsWISFhRnt\nySdXUlIL9OD4AAAgAElEQVRSMHr0aAwaNEhqKRaRl5eH8PBwjB07Fj/99JPUcixGqfddi5Kfe0Hv\nHFEdixXEJ598whYsWMB27doltRTBFBcXs0GDBkktQzD3799nERERUssQzMCBA6WWYBHr16/XPe9D\nhgyRWI1wlHbfy6Lk596Sd46iaiajRo2Cs7Mz/Pz8SqXHxMSgVatW8PLyQlRUVLn99u/fDx8fH93U\nLFIhVD8A7Ny5E6+++irCwsIqQqpexOgHgDlz5mDixIm2lmkQsfrlgCXXkJ6ejqZNmwIA7O3tK1yr\nPpT+HQjRL/Vzr8VS7Ra/c2xs2KzKoUOH2KlTp5ivr68uraioiHl4eLCUlBRWWFjI/P39WWJiIlu/\nfj2bMmUKS09PZ//73//YlClTWM+ePVn//v2ZRqNRlP6S9OvXr6Jl6xCqX6PRsKlTp7IDBw5Ipp0x\n8fdfDv+QLbmGDRs26GomYWFhUkkuhSX6tcjhvmuxRL9cnnstQu49Y+a/c2Q3zsQYL774Yrn5b+Li\n4uDp6Ql3d3cAQFhYGHbs2IHp06dj+PDhAPg/AwBYt24dGjZsKNn4FKH6Dx48iF9++QX5+fno1q1b\nBat+ilD9y5Ytw++//47s7GwkJydj3LhxFaycI1R/VlYWPvroIyQkJCAqKqpUWISKxpJrmDx5MiZO\nnIjdu3ejX79+FS9WD5bod3Z2ls1912KJ/gMHDsjiuddiifbMzEyL3zmKMib6KFmVB/gEkCdOnNBb\nNjw8vKJkmY05+oODgxEcHFzR0szCHP2TJ0/G5MmTK1qaWZij38nJCStXrqxoaWZj6Bpq1qyJNWvW\nSKjMPAzpl/t912JI//LlyzFp0iQJlZnGkHYh7xxF+Uz0ofRR8KRfWpSuH1D+NZB+6bCmdsUbk7IT\nQKalpZWaql7ukH5pUbp+QPnXQPqlw5raFW9MOnTogCtXriA1NRWFhYWIjo6WTfuwOZB+aVG6fkD5\n10D6pcOq2q3aXcBCRo4cyRo1alSqd8G9e/dYjx49mJeXFwsNDWX379/X5bVt25bZ29szAKxBgwZs\nzZo1jDHG9uzZw1q2bMk8PDzYvHnzKvw6zCUsLIw1adKEVatWjbm5uZH+Ckbp+hlT/jWQfumwtXZJ\nJ3o8fPgwateujbfffhvnzp0DAEydOhUNGjTA1KlTERUVhfv37yMyMhKJiYkYNmwY/vrrL6Snp6NH\njx5ISkqCnZ3iK1cEQRCKR9I38Ysvvohnn322VNqvv/6q63UVHh6O7du3A7B9DHiCIAhCOLL7W3/7\n9m04OzsDAJydnXH79m0Ato8BTxAEQQhH1uNMVCqV0a5r+vJcXV1x8+ZNW8oiCIKodHh4eIgKey67\nmomzszNu3boFAMjIyECjRo0AlO/CZigG/M2bN8EYs3gJDw8XXKZsurFtfeuG8q2p31ztYvQL1U76\nK69+Q9di6ndgTe2W6Lf03itdf8m0v//+W9S7W3bGpF+/fli3bh0APv3J66+/rku3ZQz4du3aCS5T\nNt3Ytr51c84tVJupfH3ppN9ySL/+NEPXYqyMpUj52zX3/EK0mVNGDu8eHUxCtF3VHB0ddV3V7t27\nx7p37663a/DcuXOZh4cH8/b2ZjExMXqPKfEliWbWrFlSSxCMkrUzRvqlhvRLi9h3Z6WLAa9SqaDk\nS1Kr1QgJCZFahiCUrB0g/VJD+qVF7LtTds1cUqFWqwWXKZtubFvfujnnFqrNVL6+9KqunzHg0SPg\n5k0gMRE4ehTYvx/49Vdg82Zg3Tpg5UpgyRJg/nxg9mwgPFyNjz8GZs4EPvoImDEDmD4dmDoVmDYN\nGD5cjTlzgM8/B5Yu5fuvXQt89pkahw4BFy4At2/zc1em+2/oWoyVsRQpf7vmnl+INnPKyOHdo0XW\nvbkIwlowBty7B1y6BGRnA7ducSMRHQ2cOwcUFwNpaUBhIfDgAWBvD9Svz5d69YDatYEaNYDq1fln\nyfVnngFUKsDREbCz4+sq1dN1xoDMTODxY+DhQ6CggC/5+UByMvDbb1zb3bs8zdUVeOUVYNQowNdX\n6jtHEOZBzVxEpeLBA+D8eb5cuQKkpABXr/LFzg5o3py/rBs3Bpo04Z/apUGDp8ajenVp9N+/z2tD\nv/0GfPMNEBUFjBghjRaiaiH23UnGhFAsGRnA8ePAiRPA2bO8hvHgAdCmDV+8vYEWLfjSvDlQZrIF\n2XPpEtClC5CaCtStK7UaorJDPhMrIZd2S6FtmHLwOYhpfzW1b2ysGpcvA199BQwZAjRrxpuAoqLU\nqFkTGD8eOHSINyNFRqqxejX3VwwcCGRnq3WGRCr9Qu5/q1ZAcDC/Hn3l5a5fX76xZ95Wz76xMtb0\nmShRP/lMiCrBw4dATAywbx+wcydQrRoQGgq8+iowZw7g6QkcPAgouAONSVq35o55gpA71MxFyIo7\nd3ivqa1bgSNHgBdfBHr35kbE25s7tKsSX33F/T9ffy21EqKyI/bdSTUTQnIKCnjNY+1abkB69gTe\nfhvYtIl8Ba6u3BlPEHKHfCb/IJd2y6rkM7lwAZg4kb8w585VY/Bg4MYNPpYjLKy0IZGjflM6zMk3\npd/VFbh0Sa03Twn6yWdiGrm8e8RCNROiQtFogD17+MC9c+eAceOA+HjeY6ky+z6E4uLCx58QhNwh\nnwlRITx+DKxZw0eN16sHvPceMHgwH/BHGCYnh4+Hyc2VWglR2am0PhN3d3fUrVsX9vb2cHR0RFxc\nHLKysjBkyBBcu3YN7u7u2Lx5M+rXry+1VMIIeXl88N0XXwAdO3K/SJcuVc+RLhQ7O16bUzKzZ/MZ\nBd57j3xglRnZ+kxUKhXUajVOnz6tC88bGRmJ0NBQJCUloXv37oiMjLTa+eTSbllZfCa5uXz0dosW\nfNqSPXuAHTuArl31GxK56bcUW+m3tweePFHrzVOCfrVajdhYYO9e3pV77Fg1cnMrj8+h5LoS9VvT\nZyJbYwKgXJXLUHx4Qj48ecInMfTyAk6dAn7/Hfj5Z8CaYROqEvb2yq+ZaDT8j8XBg3wuMg8PPida\nfr7UyghrIlufSYsWLVCvXj3Y29tj3LhxGDNmDJ599lncv38fADc0Tk5Oum0t5DORBsaA7dv5TLlu\nbnx23MBAqVUpH42GGxQlP9JduwILFvDmTYB3vJg5EzhzBpg7Fxg6lDfnEdJSaX0mf/75J5o0aYI7\nd+4gNDQUrVq1KpVvKj48UXH8+SefuiQ3l/fS6tWLfCLWQvuSZUy591SjKW0s/Px4k+ehQ8CHHwKL\nFnFj8/LL0mkkxCNbY9KkSRMAQMOGDfHGG28gLi5OFx++cePGpeLDl2XEiBFwd3cHANSvXx/t2rXT\nBa3RthGW3damGcovmVc2PyEhAVOmTDFre8mSJTo92uMZyjem11L9hvL1nc9c/evXq7FqFXDhQgKW\nLp0CV1c17O21U5zIX3/Z+2/o+5VaP5CA4uIpcHBQnv4lS5bgwYN2sLMrXV57jMhINb7/PgGjR09B\no0ZqjBvHJ+W0RH/5+yVcv7Htsv4FbZrY+y+VfoD7oRs3bqx7X4pCVJxGG5GXl8eys7MZY4zl5uay\nLl26sN9++419+OGHLDIykjHG2Pz589m0adPK7Sv0kmJjYwWXKZtubFvfuqF8SzC1n7na9aWV1Xfz\nJmPjxjFWt24s+/xzxn77LdYsDUL0mcoXor/sur7vwVJsqd/ePpbl55fPU4L+2NhY1qEDY3/9VTqv\nbJn8fMbefTeWNWzI2OjRjKWnW0+7sTJif7sl12312zVWxprvHrHmwKjPJDMzE1u2bMGhQ4eQmpoK\nlUqFZs2a4aWXXsKgQYMM1gzEkpKSgjfeeAMAUFRUhLfeegszZsxAVlYWBg8ejOvXrxvsGkw+E9uR\nm8u7+C5fDowcySMKOjlJraryU6MGD55Vs6bUSoQRGAh8+y3Qvr3psg8e8OiV330HvPMObwaj7sQV\ng83imURERODvv/9Gnz59EBQUhCZNmoAxhoyMDMTFxSEmJgaenp747rvvBJ/cFpAxsT5FRfzH/emn\nQPfufMZea9SKCfOoXZtHhqxdW2olwggIAL7/3rIefdevA598wmeNnjkTGDuWzxpN2A7R705DVZYz\nZ86YrNYkJCSIqhbZAiOXZBS5VDXl1Myl0TC2fTtjTZvGspdfZiw+XnnNLGW3lai/Zs1Y9uBB+Twl\n6I+NjWVt2zKmfZ0Ye+b1HSshgbFevRjz9GRsyxb+TFqq3RL91MwlHIMd8tq2bWvSEPn7+wu3YoSs\niY3l07/PnAm8+y5w4AB19ZUKlYrHqFcqZXtzWYK/P6+dfP01MG8e0Lkz7+BByA+T40z8/PzKVX/q\n1auHjh07YubMmXjuuedsLtISqJlLHIcOAbNmAWlpvJnhrbf4OAdCOho0AC5eBBo2lFqJMNq0AbZs\nAXx8xB1HowE2bgQ+/pg3s86axSNREtbB5uNMevfuDQcHBwwbNgyMMWzatAmPHj2Cs7MzRowYgZ07\ndwo+OSEPGOP/9ubMAa5e5Ubk3/8GHGTbcbxqYW9fdWsmJbGz439uBg8GfvgBiIjgA2RnzeIzTit1\nHE6lwVQ7WLt27Qym+fr6impjswVmXJJe5NJuWZE+kydPGPv4Y951s2VLxr77jrHCwsrnc1C6fien\nWF1XWaXpj42NZS1bMnb5cuk8a/gcnjxhbN06xlxdY9nzzzO2aRNPE6OffCbCMfl/obi4GCdOnNBt\nx8XFQfPPZEEO9NdVkdy/z6eC9/TkI5E/+YQ3o0REAI6OUqsjymJnp+yaSXGxbaZLcXDgETnXrQOm\nTQNWrOATi37+OX/GiYrFpM/kr7/+wsiRI5H7T0CFOnXqYPXq1WjTpg12796NwYMHV4hQcyGfiX4Y\n4yFxV63iIXJfeQWYMgUICpJaGWGKZs14M6RSu2O3aME7cLRoYftznTzJp/TZuRPo3x8YNYp3JKEm\nMNPYbJxJWR4+fAjGmOzjh5AxKU1SEp+h9ccf+b/DMWOA4cO5U5dQBi1aAPv389l2lYi7O6BWV6wx\nzMzkfpXVq4HCQmDECGDIEF4bJ/Qj9t1psvJ569YtREREYMiQIahfvz4SExOxevVqwSeUK+bM62+o\nTNl0Y9v61g3lW4J2P8Z4k1VUFB9xHBzMw75OmqTGhQvA+++XNiT6zidUv1Dt5uxr7r3Xl6Z0/QUF\nat009ErTr1arSzngjT3zYp/9kjRqBPznP8D58/yPVFycGi+8wAdQzpvH/2Tp29fSZ8dW+s0tY813\nj1hMGpMRI0agZ8+euHnzJgDAy8sLixcvtpoAQjx5ecCxY3z6iRYtgN69eUz1hQuBGzd4tb9NG6rq\nKxXqzSUclYo35b7/PpCezn2FN2/y3l+ensDixdxvmJMjjb7KhMlmrg4dOiA+Ph4BAQE4ffo0AKBd\nu3ZISEioEIGWUhWaue7d4/6PI0eAw4f5v6+gIKBPH+4L8fEhw1GZ8PHh4zTatJFaiTBcXID4eP4p\nFxjjcVV++40vJ04Abdvy2Ctdu/LBkTaaelC22HycSe3atXHv3j3d9vHjx1GvXj3BJyQsIyMDOH26\n9HL3LtCpE3csRkVxQ1KjhtRKCVtBNRPro1Jx49G2LZ9MUlu7P3qUj7YPD+eDRAMD+Sj8tm35p6sr\n/VEzhMmveOHChejbty+uXr2KLl26YPjw4Vi2bFlFaNNLTEwMWrVqBS8vL0RFRVntuFK1WzIG7Nql\nxpkz/N9nRIQa4eH8n9Fzz/FAQosXAw8fAm++CezaBWRl8X9TM2dyn0iNGuRzMJamdP2PH6t1xkRp\n+qXymZhbRpteqxbQowfw0ktqxMTw2v+2bUCLFmrcu8ebx3x91WjQgP+J691bjblzgc2bgVWr1MjO\nJp+JyZpJYGAgDh48iMuXLwMAvL294SjRYITi4mJMnDgRBw4cgKurKzp27Ih+/fqhdevWkugxRnEx\n7+t+5w5w9iw3AHfv8n8+P/zApyu5dImnFxXxnjotWwLVq/OHeswYvt2wIf0TqurY2Sk7Drwcayam\nsLcHfH2Bnj25fwXg89W1agVcvgzs3s39LNHRQEIC98moVLzHmqsrH5mv/WzShP+OGzXin7VrV87f\ntEGfydatW3VtaPrC4w4YMMDm4spy7NgxfPrpp4iJiQHAo4QBwPTp03VlhLT7FRcD+fnGl0eP+MOT\nnc0/S66X/NQakAcPgHr1eM+phg2ffjZuDDRt+nRxc+PlKuPDRViHoCDgyy+VOybIyQlITq7csW8Y\n47/99HTe6aXk561bvKtyZiaPCXTnjtRq9WMzn8nOnTuhUqmQmZmJo0eP4uV/AjTHxsaiS5cukhiT\n9PR0NG3aVLft5uZWanS+ORQX80FgWiNRUMDTatTgtQLt8swzpbdr1OBBeurUefrZrBn/LJn27LPc\naDg50dxWhHVQ+gh4JdZMLEWl4r95JyfeNF0VMfi6W7t2LQAgNDQUiYmJupjsGRkZCA8PrxBxZdFX\nQ9KHsRjwhw+rsWgR0K1bCKpXB06c4HHLVSpxMeCHDHkaw3n//qoRA76sfkP3h/SL03/7No8Br0T9\nS5YsQWGh4RjwJcsL1U8x4BUSA97b25tpSkSkKS4uZt7e3qImBBPKsWPHWK9evXTb8+bN08WE12LG\nJelFLpOtVeREj4bSK9tEiUrX7+cXyw4eLJ+nBP2xsbGsVi3GcnJK51WWiRJLritRvzUnejQ5zmTi\nxIlISkrSTUEfHR0NLy8vLF++XLwls5CioiJ4e3vj999/h4uLC4KCgrBx48ZSDviqMM6EqFp068Yn\n4+zWTWolwqhZk3c+UWoM+6qCzceZLF++HNu2bcPhw4cBAOPGjcMbb7wh+IRicHBwwJdffolevXqh\nuLgYERERsuzJRRDWhMaZEIrAUJVFoy/YsoAyFY2RSzKKXKqa1MxlWX5V0B8YGMtiYsrnKUF/bGws\nc3RkrKCgdF5laSYqua5E/dZs5jL4fyEkJAQLFixAknZGtBJcvnwZUVFRCKaYmQRhc+xonAmhAAz6\nTAoKCvDjjz9i48aNOH/+POrUqQPGGHJzc+Hr64u33noLw4YNQ7Vq1Spas1HIZ0JUNl57DRg/nn8q\nETs7PjCXDIq8qZB4JsXFxbh79y4AoEGDBrC3txd8QltDxoSobGiDPPXvL7USy2Hsac2KBubKG5vH\nMwEAe3t7ODs7w9nZWdaGRAzmzFFjqEzZdGPb+tYN5VuCqf3M1a4vzVz9QrWbs29V1p+Vpdy5uWJj\n1VCpnhoSY8+8rZ59Y2XE/nZLritRv5hnpixU8SQImWOn4BHw2poJUfkxO2yvUqBmLqKyMWQIMGAA\n/1QahYV8YsPCQqmVEKaokGau1NRUHDhwAADw6NEjZGdnCz4hQRCWoeRxJtSTq+pg8mtetWoVBg0a\nhHHjxgEAbty4IdmgRVsil3ZL8plYll8V9N+5o1yfiVqtLmVMyGdivjZzyijKZ/LVV1/hyJEjqFu3\nLgCgZcuWyMzMtJoAgiCMQz4TQgmY9JkEBQUhLi5OFwO+qKgI7du3x9mzZytKo0WQz4SobIwaBbzw\nAv9UGtnZPGYPtYzLH5v7TIKDgzF37lw8evQI+/fvx6BBg9C3b1/BJyQIwjLIZ0IoAZNfc2RkJBo2\nbAg/Pz988803eOWVVzBnzhybCZo9ezbc3NwQEBCAgIAA7N27V5c3f/58eHl5oVWrVti3b59VzyuX\ndkvymViWXxX0376tXJ/JoUPkMxGqzZwycvKZmJw12N7eHmPHjsXYsWORlZWFtLQ0s4NUCUGlUuE/\n//kP/vOf/5RKT0xMRHR0NBITE5Geno4ePXogKSkJdvS3h6jkkM+EUAImfSbBwcHYuXMnioqKEBgY\niIYNG6Jr165YvHixTQR9+umnqF27Nj744INS6fPnz4ednR2mTZsGAOjduzdmz56NTp06lSpHPhOi\nsjFpEtCyJf9UGpmZgK8v/yTkjc19Jg8fPkTdunXxyy+/4O2330ZcXJxuzImtWL58Ofz9/REREYEH\nDx4AAG7evAk3NzddGTc3N6Snp9tUB0HIAfKZEErAZDNXcXExMjIysHnzZp2vRGwzV2hoKG7dulUu\nfe7cuZgwYQI++eQTAMDHH3+MDz74AKtXr9Z7HEM6jMWA17YRWhoDu2wMZXNjjpfdphjwpF+I/qZN\nlan/m2+W4MmTdgBKly95PKXGUFe6fqCCY8Bv3ryZ+fn5sfHjxzPGGEtOTmYDBgwQFUTFXFJSUpiv\nry9jjLH58+ez+fPn6/J69erFjh8/Xm4fMy5JL3IJUEPBsSzLrwr6hwyJZVFR5fOUoH/z5ljm6lo+\nr7IElyq5rkT91gyOJbu5uTIyMtCkSRMAwOLFi/HXX3/hp59+QmJiIoYNG4a4uDidAz45Oblc7YR8\nJkRlY8YMoG5d/qk0rl/nY2SuX5daCWEKm8eAf/z4MVavXo3ExEQ8fvxYd9I1a9YIPqkxpk2bhoSE\nBKhUKjRv3hzffPMNAMDHxweDBw+Gj48PHBwcsGLFCpv2KiMIuWCn4EiL5DOpOpj8mocPH47bt28j\nJiYGISEhuHHjBmrXrm0zQevXr8fZs2dx5swZbN++Hc7Ozrq8jz76CMnJybh06RJ69epl1fPqa080\nt0zZdGPb+tYN5VuCqf3M1a4vzVz9QrWbs29V1p+WptxxJkeP0jgTodrMKWPNd49YTBqT5ORkfPbZ\nZ6hduzbCw8OxZ88enDhxwmoCCIIwjp2Cx5lQzaTqYPbcXC+++CJWrFiBxo0b4/nnn8fVq1crSqNF\nkM+EqGzMmQPk5/NPpXH5MtC3L5CUJLUSwhQ295mMGTMGWVlZmDNnDvr164fc3Fx89tlngk9IEIRl\n1KoF3L0rtQphUM2k6mDyax4zZgycnJwQHByMlJQU3LlzB+PHj68IbRWKXNotyWdiWX5V0J+Zqca9\ne+XzlKD/+HHymQjVZk4ZOflMTNZM8vPzsXXrVqSmpqK4uBiMMahUKt3AQoIgbEvdutAZE6VBc3NV\nHUz6THr16oX69esjMDAQ9vb2OmNSdu4suUA+E6Kycfw4MHkyEBcntRLLOXMGGD4ckGn4I6IENveZ\npKen47fffhN8AoIgxNGggXJrJuQzqTqY/Jq7dOki26iK1kQu7ZbkM7Esvyrov3hRuT6TuDjymQjV\nZk4ZRfhM/Pz8APCJHr///ns0b94czzzzDABeHaoKBoYg5ECtWkBeHvDkidRKLId8JlUHgz6T1NRU\n3XQl+opYZZZJG0A+E6Iy0rgxcOwY0Ly51Eos48QJHodFif6eqobNfCbOzs5YuXIlkpOT0bZtW0RE\nRMDBwaSLhSAIG/Daa0B0NDB9utRKLIN8JlUHg19zeHg4Tp48CT8/P+zZs8eqvbe2bNmCNm3awN7e\nHqdOnSqVZyjOu1aLl5cX3nvvPatp0SKXdkvymViWX1X0v/cesHAh8NFH5efpkrP++HjymQjVZk4Z\nRfhMLl68iHPnzgEARo8ejY4dO1rtpH5+fti2bRvGjRtXKl1fnPcrV65ApVJhwoQJWL16NYKCgvDK\nK68gJiYGvXv3tpomgpAzfn7Arl1ARASwahXQrdvT8SfZ2UCZ6NWygXwmVQeDPpOAgACcPn3a4LY1\n6NatGxYuXIj27dsDMBznvVmzZnj55Zdx8eJFAMCmTZugVquxcuXK8hdEPhOiknPjBhAbC1y4AFy6\nxJfUVKBRI8DTky8eHqXXbTjRt1EOHgQ+/hg4dEia8xPmYzOfydmzZ1GnTh3d9uPHj3XbKpUK2dnZ\ngk9qiJs3b6JTib9Y2jjvjo6OpeK/u7q6Uvx3osri5sYHApakuBhISwOSk58ux47xz6tXgXr1nhoX\n7eLnB3h78xjztoJ8JlUHg19zcXExcnJydEtRUZFu3RxDEhoaCj8/v3LLzp07rXoB1kIu7ZbkM7Es\nn/TzT3t7IDVVjR49gPHjgS++ALZvB86fB3Jzgb/+Aj77DOjaFcjJATZvBvr350amSxfgjTfUWLMG\nSEzkTVPW0n/qFPlMhGozp4wifCZi2b9/v8X7uLq6Ii0tTbd948YNuLm5wdXVFTdu3CiV7urqavA4\nI0aM0HVdrl+/Ptq1a4eQkBAAT29e2W0thvKNbSckJJi9nZCQYHR/ffnmbJvSbyjflB5L9Qu5f6S/\nYvTzyr0anp5AZCTP37VLjeRk4MoV4I8/gJkz1cjLA7p1C8FLLwG1aqnh5fW0dmGp/uTkBDx8CACl\ny5e8H2Lvvzn7lzyfMf2mtvUdT6n61Wo1IiMjsXbtWusM9RAVQV4kISEhLD4+Xrd94cIF5u/vzwoK\nCtjVq1dZixYtmEajYYwxFhQUxI4fP840Gg3r06cP27t3r95jSnxJBKF4btxgbONGxiZMYKxVK8Ya\nNmTs7bcZ27SJsfv3LTtWTAxjoaG20UlYF7HvTklaM7dt24amTZvi+PHjePXVV9GnTx8ApeO89+nT\np1Sc9xUrVmD06NHw8vKCp6cn9eQiCBvh6gqEhQErVgAXL/KBh0FBwPr1wL/+BXTvDnz7rXnzhZHP\npAphJaMmG4ReUmxsrOAyZdONbetbN5RvCab2M1e7vjRz9QvVbs6+pN/wekXqz8tjbOtWxgYNYqxu\nXcY6dYplP/3EWH6+/mPNmxfL+vQpn2fqd2BN7cbKiP3tllxXov6SaWLNAf1nIAjCbGrWBAYM4A78\nGzeAl18G1qzhPcw++IB3Uy4JY7btLUbIB5PxTJQGjTMhiIrn77+B774Dvv8e8PHhhqVPH2DnTm5s\nduyQWiFhCrHvTjImBEFYjcJC4Oefedfkx4+Bjh15V+Rt26RWRphC7LuTmrn+wZz+1obKGOq+p29b\n37qhfEswtZ+52vWlmatfqHZz9iX9htflpL9aNcDFRY2TJ4GvvgIuX1bjX/8qX97U78ASpPztllxX\non4xz0xZaBpggiCsjkrF/SlRUcA/QxyISg41cxEEQRDUzEUQBEFIDxmTf5BLuyX5TCzLJ/3y1m/o\nWpe6NHIAAAq0SURBVCqLz6HkuhL1W9NnQsaEIAiCEA35TAiCIAjymRAEQRDSI4kxMRQDPjU1FTVq\n1EBAQAACAgLwzjvv6PIoBrwwbabyK3ubfdlt0m+ZPlP55DNRtn7F+0y0MeBfeumlcnmenp44ffo0\nTp8+jRUrVujStTHgr1y5gitXriAmJqYiJVcYZeM9KAklawdIv9SQfoUjappIkYSEhLCTJ0/qtlNS\nUpivr2+5cjdv3mStWrXSbW/cuJGNGzdO7zElviTRzJo1S2oJglGydsZIv9SQfmkR++6Unc8kJSUF\nAQEBCAkJwZEjRwAA6enpNo8Br/SqphyaWcRA+g2nKVm/Jc1cQpFLM5dQlP7u0WIzYyIkBryLiwvS\n0tJw+vRpLFq0CMOGDUNOTo6tJJZi7dq1gsuUTTe2rW+9ZFpqaqpJHZZoM5WvL12ofqHajekzlU/6\n5a3f0LXoK2OrZ99YGbG/3ZLrStRvzrnNxko1JEGUbeYylF+2meunn34y2Mzl4eHBANBCCy200GLB\n4uHhIep9LvlEj6xEv+a7d+/i2Wefhb29Pa5evYorV66gRYsWqF+/PurWrYsTJ04gKCgIGzZswOTJ\nk/UeLzk5uaKkEwRBEP8gqxjwBw8ehL+/PwICAjBo0CB88803qF+/PgCKAU8QBCFnKt0IeIIgCKLi\nkV1vLoIgCEJ5kDEhCIIgRFNljEleXh46duyI3bt3Sy3FYi5duoQJEyZg8ODBWL16tdRyLGbHjh0Y\nO3YswsLCsH//fqnlWExKSgpGjx6NQYMGSS3FIvLy8hAeHo6xY8fip59+klqOxSj1vmtR8nMv6J0j\nqi+Ygvjkk0/YggUL2K5du6SWIpji4mI2aNAgqWUI5v79+ywiIkJqGYIZOHCg1BIsYv369brnfciQ\nIRKrEY7S7ntZlPzcW/LOUVTNZNSoUXB2doafn1+p9JiYGLRq1QpeXl6Iiooqt9/+/fvh4+ODhg0b\nVpRUvQjVDwA7d+7Eq6++irCwsIqQqhcx+gFgzpw5mDhxoq1lGkSsfjlgyTWkp6ejadOmAAB7e/sK\n16oPpX8HQvRL/dxrsVS7xe8cGxs2q3Lo0CF26tSpUvN3FRUVMQ8PD5aSksIKCwuZv78/S0xMZOvX\nr2dTpkxh6enp7H//+x+bMmUK69mzJ+vfvz/TaDSK0l+Sfv36VbRsHUL1azQaNnXqVHbgwAHJtDMm\n/v7L4R+yJdewYcMGXc0kLCxMKsmlsES/Fjncdy2W6JfLc69FyL1nzPx3juSDFi3hxRdfLDdlQVxc\nHDw9PeHu7g4ACAsLw44dOzB9+nQMHz4cAP9nAADr1q1Dw4YNoVKpKlK2DqH6Dx48iF9++QX5+fno\n1q1bBat+ilD9y5Ytw++//47s7GwkJydj3LhxFaycI1R/VlYWPvroIyQkJCAqKgrTpk2rYOVPseQa\nJk+ejIkTJ2L37t3o169fxYvVgyX6nZ2dZXPftVii/8CBA7J47rVYoj0zM9Pid46ijIk+SlblAcDN\nzQ0nTpzQWzY8PLyiZJmNOfqDg4MRHBxc0dLMwhz9kydPNjhjgdSYo9/JyQkrV66saGlmY+gaatas\niTVr1kiozDwM6Zf7fddiSP/y5csxadIkCZWZxpB2Ie8cRflM9CFVLcNakH5pUbp+QPnXQPqlw5ra\nFW9MXF1dkZaWpttOS0srNV293CH90qJ0/YDyr4H0S4c1tSvemHTo0AFXrlxBamoqCgsLER0dLZv2\nYXMg/dKidP2A8q+B9EuHVbVbtbuAjQkLC2NNmjRh1apVY25ubmzNmjWMMcb27NnDWrZsyTw8PNi8\nefMkVmkY0i8tStfPmPKvgfRLh62100SPBEEQhGgU38xFEARBSA8ZE4IgCEI0ZEwIgiAI0ZAxIQiC\nIERDxoQgCIIQDRkTgiAIQjRkTAiCIAjRkDEhKi329vYICAjQLdevX5daktU4d+4cRo0aBQBYu3Zt\nuQkFQ0JCcPLkSYP7Dx48GCkpKTbVSFQtFD9rMEEYombNmjh9+rTePO1YXaVO0rdgwQKdAdF3DSqV\nyui1jRkzBosXL8ayZctsppGoWlDNhKgypKamwtvbG+Hh4fDz80NaWhoWLFiAoKAg+Pv7Y/bs2bqy\nc+fOhbe3N1588UUMGzYMCxcuBFD6H//du3fRvHlzAEBxcTE+/PBD3bFWrVoFAFCr1QgJCcGgQYPQ\nunVr/Pvf/9ad46+//kLXrl3Rrl07dOrUCbm5uQgODsaZM2d0ZV544QWcO3eu1HUUFBTg+PHj6Nix\no9HrZYxh586dupqZt7c3WrRoobuOPXv2CLyTBFEeqpkQlZbHjx8jICAAANCiRQssWrQIycnJ2LBh\nA4KCgrBv3z4kJycjLi4OGo0G/fv3x+HDh1GzZk1ER0fjzJkzePLkCdq3b48OHToAMPyPf/Xq1ahf\nvz7i4uJQUFCAF154AT179gQAJCQkIDExEU2aNEHXrl1x9OhRdOjQAWFhYdi8eTMCAwORm5uLGjVq\nICIiAmvXrsXixYuRlJSEgoKCcmFWT58+DW9vb902YwzR0dE4cuSILi05ORkqlQp9+/ZF3759AQBD\nhgxBSEgIAMDR0RGurq64ePEiWrdubb2bTlRZyJgQlZYaNWqUauZKTU1Fs2bNEBQUBADYt28f9u3b\npzM4eXl5uHLlCnJycjBgwABUr14d1atXN2sW1X379uHcuXP4+eefAUAXXc/R0RFBQUFwcXEBALRr\n1w4pKSmoU6cOmjRpgsDAQABA7dq1AQADBw7EZ599hgULFmDNmjUYOXJkuXNdu3YNTZo00W2rVCqE\nhYWVarIqGx3v888/R82aNTFhwgRdmouLC1JTU8mYEFaBjAlRpahVq1ap7RkzZmDs2LGl0pYuXYqS\n85+WXHdwcIBGowEA5Ofnl9rvyy+/RGhoaKk0tVqNZ555Rrdtb2+PoqIig/6MmjVrIjQ0FNu3b8eW\nLVtw6tSpcmVUKhXKzs9qbL7WAwcOYOvWrTh06FC5fezsqKWbsA70JBFVll69emHNmjXIy8sDwEOY\n3rlzBy+99BK2b9+O/Px85OTkYNeuXbp93N3dER8fDwC6Woj2WCtWrEBRUREAICkpCY8ePdJ7XpVK\nBW9vb2RkZOiOlZOTg+LiYgDA6NGjMXnyZAQFBaFevXrl9m/WrBlu3bql2zZmSK5du4Z3330Xmzdv\nLmXUACAjIwPNmjUzfIMIwgKoZkJUWgz1ctISGhqKixcvonPnzgCAOnXq4IcffkBAQACGDBkCf39/\nNGrUCB07dtS9sP/73/9i8ODBWLVqFV599VXd8UaPHo3U1FS0b98ejDE0atQI27ZtM+hjcXR0RHR0\nNCZNmoTHjx+jZs2a2L9/P2rVqoX27dujXr16epu4AMDf3x+XL18udU36zsEYw7p165CVlYXXX38d\nAI+st2vXLjx58gQ3btxAq1atzL2dBGEUimdCECb49NNPUbt2bXzwwQcVcr6bN2+iW7dupQxGWUaM\nGIEJEybg+eefF3SOffv2Yffu3Vi6dKlQmQRRCmrmIggzqKjxKOvXr0enTp0wb948o+X++9//YuXK\nlYLP89133+H9998XvD9BlIVqJgRBEIRoqGZCEARBiIaMCUEQBCEaMiYEQRCEaMiYEARBEKIhY0IQ\nBEGIhowJQRAEIZr/B2yIUifQpDtDAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f9ce3791150>"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Solving a Problem"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This example of sorts is taken from http://www.jairusmartin.com/2013/02/control-systems-in-python-part-2.html, stated to be DP 9.11 from *Modern Control Systems* by Dorf and Bishop."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Ki = Symbol(\"Ki\")\n",
      "Kp = Symbol(\"Kp\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The controller is:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Gc = (Ki + Kp * s) / s\n",
      "Gc"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{1}{s} \\left(Ki + Kp s\\right)$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 31,
       "text": [
        "Ki + Kp\u22c5s\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "    s    "
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "And the system is:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "G = exp(-0.4 * s) / (0.2 * s + 1.0)\n",
      "G"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{e^{- 0.4 s}}{0.2 s + 1.0}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 32,
       "text": [
        "   -0.4\u22c5s  \n",
        "  \u212f        \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "0.2\u22c5s + 1.0"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The exponential term is approximated as a second order polynomial using `matlab.pade`:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "matlab.pade(0.4, 2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\begin{pmatrix}\\begin{bmatrix}1.0, & -14.999999999999998, & 74.99999999999999\\end{bmatrix}, & \\begin{bmatrix}1.0, & 14.999999999999998, & 74.99999999999999\\end{bmatrix}\\end{pmatrix}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 33,
       "text": [
        "([1.0, -14.999999999999998, 74.99999999999999], [1.0, 14.999999999999998, 74.9\n",
        "9999999999999])"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "And so the system can be approximated as:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Gapprox = (s ** 2 - 15 * s + 75) / ((0.2 * s + 1) * (s ** 2 + 15 * s + 75))\n",
      "Gapprox"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{s^{2} - 15 s + 75}{\\left(0.2 s + 1\\right) \\left(s^{2} + 15 s + 75\\right)}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 34,
       "text": [
        "        2                   \n",
        "       s  - 15\u22c5s + 75       \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "            \u239b 2            \u239e\n",
        "(0.2\u22c5s + 1)\u22c5\u239ds  + 15\u22c5s + 75\u23a0"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      ">*Using frequency response methods, design the controller so that the overshoot of the system is P.O. &lt;= From this we determine 0.59. When we plot the poles and zeros of the system we see that there are 3 poles in the LHP and two zeros in the RHP. The controller adds another pole at 0, so the zero of our controller should be somewhere to the left of the -5 pole on the real axis.*\n",
      "\n",
      ">*Thus Ki/Kp &gt; 5. If Ki/Kp = 6. Using a Routh Hurwitz table we can see that 0&gt;Kp&gt;0.66 makes the system stable.*"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def routh_hurwitz(Ts, *args):\n",
      "    den = Poly(Ts.as_numer_denom()[1], s).all_coeffs()\n",
      "    n = len(den) - 1\n",
      "    if n < 2:\n",
      "        return None\n",
      "    m = matrices.zeros(n + 1)\n",
      "    \n",
      "    # Insert the first two rows.\n",
      "    c = [den[i] for i in range(0, n + 1, 2)]\n",
      "    for i in range(0, len(c)):\n",
      "        m[0, i] = c[i]\n",
      "    c = [den[i] for i in range(1, n + 1, 2)]\n",
      "    for i in range(0, len(c)):\n",
      "        m[1, i] = c[i]\n",
      "        \n",
      "    # Compute the rest of the entries\n",
      "    for i in range(2, n + 1):\n",
      "        for j in range(1, n):\n",
      "            if m[i - 1, j] == 0:\n",
      "                m[i, j - 1] = m[i - 2, j]\n",
      "            elif m[i -1, 0] != 0:\n",
      "                m[i, j - 1] = ((m[i - 1, 0] * m[i - 2, j] - m[i - 2, 0] * m[i - 1, j]) / m[i - 1, 0]).together().simplify()\n",
      "    \n",
      "    m = m.col_insert(0, Matrix(([s ** (n - 1) for i in range(0, n + 1)])))\n",
      "    return m"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "routh_hurwitz(Gapprox.subs(Ki, Kp*6))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "AttributeError",
       "evalue": "'module' object has no attribute 'zeros'",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
        "\u001b[1;32m<ipython-input-36-1b2e77ee00da>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mrouth_hurwitz\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mGapprox\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msubs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mKi\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mKp\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;36m6\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
        "\u001b[1;32m<ipython-input-35-0d069c4712e5>\u001b[0m in \u001b[0;36mrouth_hurwitz\u001b[1;34m(Ts, *args)\u001b[0m\n\u001b[0;32m      4\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mn\u001b[0m \u001b[1;33m<\u001b[0m \u001b[1;36m2\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m         \u001b[1;32mreturn\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 6\u001b[1;33m     \u001b[0mm\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmatrices\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mzeros\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      7\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      8\u001b[0m     \u001b[1;31m# Insert the first two rows.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;31mAttributeError\u001b[0m: 'module' object has no attribute 'zeros'"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I don't know what is causing this error..."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "SymPy Tutorial"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Roots are left unevaluated by default:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sympy.sqrt(3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "But simplification is possible:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sympy.sqrt(8)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Symbols"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Symbols must be defined before being used, just like any other Python variable."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x, y = symbols(\"x y\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "expr = x + 2 * y\n",
      "expr"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "expr + 1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "expr - x"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x * expr"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Note that the expression has not been automatically expanded. However, the `expand` function can do that:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "expanded_expr = expand(x * expr)\n",
      "expanded_expr"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "And `factor` can be used to factor:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "factor(expanded_expr)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x, t, z, nu = symbols(\"x t z nu\")\n",
      "nu"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Note that greek characters are supported.\n",
      "\n",
      "Now we can take the derivative of $\\sin(x)e^x$ with respect to $x$:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "diff(sin(x) * exp(x), x)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Similarly we can integrate:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "integrate(exp(x) * sin(x) + exp(x) * cos(x), x)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can even calculate definite integrals (declaring infinity using `oo`):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "integrate(sin(x ** 2), (x, -oo, oo))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Limits:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "limit(sin(x) / x, x, 0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Solutions:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "solve(x ** 2 - 2, x)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Differential equations:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y = Function(\"y\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dsolve(Eq(y(t).diff(t, t) - y(t), exp(t)), y(t))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Eigenvalues:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Matrix([[1, 2], [2, 2]]).eigenvals()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Rewriting the Bessel function in terms of the spherical Bessel function:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "besselj(nu, z).rewrite(jn)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Outputting as raw $\\LaTeX$:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "latex(Integral(cos(x) ** 2, (x, 0, pi)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So it seems pretty powerful..."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}