python_Bode_examples.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generating Bode Plots in Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Big Ideas:\n",
    "\n",
    "- you have some transfer function $G(s)$ you want to analyze\n",
    "- evaluate $G(s)$ at $s = j \\omega$\n",
    "    - $\\omega$ is a vector of frequencies\n",
    "    - $\\omega$ typically spans a large range\n",
    "- find the magnitude and phase of $G(j \\omega)$\n",
    "- plot magnitude and phase vs. frequency\n",
    "    - usually with a logarithmic axis for frequency, using the `semilogx` command\n",
    "- it is usually helpful to also use a logarithmic scale for magnitude as well\n",
    "    - decibels are used for historic reasons"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Steps:\n",
    "\n",
    "- create a frequency vector and ultimately an $s$ vector:\n",
    "    - `f = np.logspace(-2,3,1000)` (Hz)\n",
    "    - `w = 2*np.pi*f`\n",
    "    - `s = 1.0j*w`\n",
    "- evaluate $G(s)$ at $s = j \\omega$\n",
    "- find the dB magnitude and phase and plot them"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import time\n",
    "plt.rcParams['font.size'] = 14\n",
    "#import pylab_util as PU\n",
    "import os\n",
    "import control"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create the frequency and s vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "f = np.logspace(-2,4,1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.01"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f.min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10000.0"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1000"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "w = 2*np.pi*f\n",
    "s = 1.0j*w"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1\n",
    "\n",
    "$$G(s) = \\frac{p_1 p_2}{(s+p_1)(s+p_2)}$$\n",
    "\n",
    "### Without the Python-Control Module"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "p1 = 1.0*2*np.pi\n",
    "p2 = 100.0*2*np.pi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Substitute `s` into the transfer function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Gjw = p1*p2/((s+p1)*(s+p2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$G(j\\omega)$ is a vector of complex numbers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "        -1.11686081e-06 -1.19218851e-08j,\n",
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       "        -1.02793799e-06 -1.05267605e-08j,  -9.99899000e-07 -1.00989900e-08j])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Gjw"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Find the dB magnitude and phase:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "db_mag = 20*np.log10(np.abs(Gjw))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "phase = np.arctan2(np.imag(Gjw),np.real(Gjw))*180/np.pi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generate the Bode plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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HqKPKH56ccsCTk3PFa+VKm7vvnnvgzDPh97+HTTeNOqr484lfnXMui5o0gWHD4JNP7Abe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\n5OSccy52PDk555yLnf8HoYJj0Lqn0P4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113a67f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.subplot(211)\n",
    "plt.semilogx(f,db_mag)\n",
    "plt.ylabel('dB Mag.')\n",
    "plt.ylim([-120,5])\n",
    "plt.subplot(212)\n",
    "plt.semilogx(f,phase)\n",
    "plt.xlabel('Freq. (Hz)')\n",
    "plt.ylabel('Phase (deg.)')\n",
    "plt.ylim([-185,10])\n",
    "out = plt.yticks(np.arange(-180,5,45))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### With Python-Control"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "        3948\n",
       "--------------------\n",
       "s^2 + 634.6 s + 3948"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "part1 = control.TransferFunction(p1,[1,p1])\n",
    "part2 = control.TransferFunction(p2,[1,p2])\n",
    "G = part1*part2\n",
    "G"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3947.8417604357433"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p1*p2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-71.927194734324601"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "20*np.log10(1/(p1*p2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "634.6017160251382"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p1+p2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  9.99899000e-01 -1.00989900e-02j,\n",
       "         9.99896168e-01 -1.02395938e-02j,\n",
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       "         9.99890263e-01 -1.05266990e-02j,\n",
       "         9.99887186e-01 -1.06732550e-02j,\n",
       "         9.99884022e-01 -1.08218505e-02j,\n",
       "         9.99880770e-01 -1.09725139e-02j,\n",
       "         9.99877427e-01 -1.11252738e-02j,\n",
       "         9.99873990e-01 -1.12801593e-02j,\n",
       "         9.99870456e-01 -1.14372001e-02j,\n",
       "         9.99866824e-01 -1.15964261e-02j,\n",
       "         9.99863089e-01 -1.17578676e-02j,\n",
       "         9.99859250e-01 -1.19215554e-02j,\n",
       "         9.99855303e-01 -1.20875206e-02j,\n",
       "         9.99851246e-01 -1.22557950e-02j,\n",
       "         9.99847075e-01 -1.24264107e-02j,\n",
       "         9.99842787e-01 -1.25994000e-02j,\n",
       "         9.99838379e-01 -1.27747960e-02j,\n",
       "         9.99833847e-01 -1.29526321e-02j,\n",
       "         9.99829188e-01 -1.31329422e-02j,\n",
       "         9.99824398e-01 -1.33157606e-02j,\n",
       "         9.99819474e-01 -1.35011222e-02j,\n",
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       "         9.99597476e-01 -2.01580518e-02j,\n",
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       "         9.99537804e-01 -2.15999585e-02j,\n",
       "         9.99524848e-01 -2.19004657e-02j,\n",
       "         9.99511529e-01 -2.22051456e-02j,\n",
       "         9.99497837e-01 -2.25140559e-02j,\n",
       "         9.99483761e-01 -2.28272550e-02j,\n",
       "         9.99469291e-01 -2.31448021e-02j,\n",
       "         9.99454415e-01 -2.34667571e-02j,\n",
       "         9.99439123e-01 -2.37931808e-02j,\n",
       "         9.99423402e-01 -2.41241348e-02j,\n",
       "         9.99407241e-01 -2.44596816e-02j,\n",
       "         9.99390627e-01 -2.47998845e-02j,\n",
       "         9.99373548e-01 -2.51448075e-02j,\n",
       "         9.99355991e-01 -2.54945157e-02j,\n",
       "         9.99337941e-01 -2.58490750e-02j,\n",
       "         9.99319387e-01 -2.62085521e-02j,\n",
       "         9.99300312e-01 -2.65730147e-02j,\n",
       "         9.99280704e-01 -2.69425313e-02j,\n",
       "         9.99260546e-01 -2.73171714e-02j,\n",
       "         9.99239824e-01 -2.76970055e-02j,\n",
       "         9.99218521e-01 -2.80821048e-02j,\n",
       "         9.99196622e-01 -2.84725418e-02j,\n",
       "         9.99174110e-01 -2.88683895e-02j,\n",
       "         9.99150968e-01 -2.92697224e-02j,\n",
       "         9.99127178e-01 -2.96766156e-02j,\n",
       "         9.99102721e-01 -3.00891453e-02j,\n",
       "         9.99077580e-01 -3.05073888e-02j,\n",
       "         9.99051736e-01 -3.09314244e-02j,\n",
       "         9.99025167e-01 -3.13613313e-02j,\n",
       "         9.98997856e-01 -3.17971900e-02j,\n",
       "         9.98969779e-01 -3.22390817e-02j,\n",
       "         9.98940917e-01 -3.26870890e-02j,\n",
       "         9.98911248e-01 -3.31412954e-02j,\n",
       "         9.98880748e-01 -3.36017856e-02j,\n",
       "         9.98849395e-01 -3.40686454e-02j,\n",
       "         9.98817164e-01 -3.45419616e-02j,\n",
       "         9.98784031e-01 -3.50218222e-02j,\n",
       "         9.98749972e-01 -3.55083165e-02j,\n",
       "         9.98714960e-01 -3.60015346e-02j,\n",
       "         9.98678969e-01 -3.65015682e-02j,\n",
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       "        -1.64491723e-06 -2.13095485e-08j,\n",
       "        -1.60005167e-06 -2.04436378e-08j,\n",
       "        -1.55640963e-06 -1.96129109e-08j,\n",
       "        -1.51395777e-06 -1.88159384e-08j,\n",
       "        -1.47266363e-06 -1.80513488e-08j,\n",
       "        -1.43249565e-06 -1.73178265e-08j,\n",
       "        -1.39342312e-06 -1.66141093e-08j,\n",
       "        -1.35541619e-06 -1.59389863e-08j,\n",
       "        -1.31844579e-06 -1.52912956e-08j,\n",
       "        -1.28248367e-06 -1.46699228e-08j,\n",
       "        -1.24750233e-06 -1.40737986e-08j,\n",
       "        -1.21347504e-06 -1.35018970e-08j,\n",
       "        -1.18037578e-06 -1.29532340e-08j,\n",
       "        -1.14817924e-06 -1.24268653e-08j,\n",
       "        -1.11686081e-06 -1.19218851e-08j,\n",
       "        -1.08639654e-06 -1.14374245e-08j,\n",
       "        -1.05676316e-06 -1.09726495e-08j,\n",
       "        -1.02793799e-06 -1.05267605e-08j,  -9.99899000e-07 -1.00989900e-08j])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Gjw = G(s)\n",
    "Gjw"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "z = 2*2*np.pi\n",
    "wn = 200*2*np.pi\n",
    "zeta = 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "          s + 12.57\n",
       "-----------------------------\n",
       "s^3 + 251.3 s^2 + 1.579e+06 s"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G2 = control.TransferFunction([1,z],[1,2*zeta*wn,wn**2,0])\n",
    "G2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Gjw2 = G2(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "db2 = 20*np.log10(np.abs(Gjw2))\n",
    "phase2 = np.angle(Gjw2,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Zj1tvba2e1Na+fbxj1NasgSOPtMu3d9zhLaioFTo51QKfYZ0gslLVnO47hdXYkhkichpw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\nIZEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113a9ce10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.subplot(211)\n",
    "plt.semilogx(f,db2)\n",
    "plt.ylabel('dB Mag.')\n",
    "#plt.ylim([-120,5])\n",
    "plt.subplot(212)\n",
    "plt.semilogx(f,phase2)\n",
    "plt.xlabel('Freq. (Hz)')\n",
    "plt.ylabel('Phase (deg.)')\n",
    "plt.ylim([-185,10])\n",
    "out = plt.yticks(np.arange(-180,5,45))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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RU6ioMG/AiRMryxZb2BJg795wwAEWlsm5rjviPP00XHihvZnv5fkNL1lib+RPPGF/M478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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113584f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "out = control.bode_plot(G2,w,dB=1,Hz=1,deg=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the second input to `control.bode_plot` is $\\omega$ in radians/second regardless of requesting Hz on the $x$-axis of the plot.  Also note that compared to my previous examples, the second input is $\\omega$, not $s=j \\omega$, i.e. the code will multiply by $j$ for you."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### My bode_utils module"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import bode_utils"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function bode_plot in module bode_utils:\n",
      "\n",
      "bode_plot(freq, dB_mag, phase, fig=None, fignum=1, clear=True, xlim=None, label=None, fmt='-', grid=True, figsize=None, **kwargs)\n",
      "    This function plots a very nice Bode plot.  freq is a vector in\n",
      "    Hz.  dB_mag and phase are vectors with the same length as freq.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(bode_utils.bode_plot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function bode_plot2 in module bode_utils:\n",
      "\n",
      "bode_plot2(freq, Gjw, *args, **kwargs)\n",
      "    calculate dB_mag and phase from Gjw and then plot a Bode plot\n",
      "    using the bode_plot function, passing in\n",
      "    bode_plot(freq,dB_mag,phase,*args,**kwargs).\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(bode_utils.bode_plot2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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7df2qOpfZXl29quP6kiv9smlLsn5V6Rr2VFC+9Ivi2WV7Pf/u1dwe1fNLERvj\nJCIlwNVY2KHyoLkdlmwwk6+pSIeR95QZhfwHFEaQxkI2TnHWLxvjFCf96vJyy5d+Ub2866tfIb9b\nQifMQH3ZFCy1RXk1ZR3QJ+MzzYBxwGtAo7T2S4DPK7nHTODPwfG9wKuV9FkDHFOFjOrFixcvXmpX\nwrQVBZ8yQ0SaAaMxo3W4qq5O67cAqCSQBm2oSIdR65QZYbpDOo7jOLUn78ZJVRcDi7PpKyLNMcOk\nwK9UdWVGl3eB5iLSO7XuJCJ7AU2xiOWpPpeJSIe0daeDscSEH9ZLGcdxHCcnFOwm3MAwvQI0BwYA\n6V51i1MRxUXkRWBz4HQsrca9wCxVHRCcbwBMxNamLgRaAQ8DT6rqH/OijOM4jlMrCtk47Qe8ntmM\njaJ+SuMebLi9E+gf9HkWOEcrMuPWOmWG4ziOEy0Fa5wcx3Gc4iU2ruSFhIh0FJE3RGSqiEwSkaNr\n/lS8EJGnRWSxiPwralnCQkQOE5FPRGSGiPwuannCJonPLEXSv3Mi0kJExovIBBGZIiJnRy1T2IhI\nExGZLSJ/y6q/j5xqj4i0A9qo6mQRaYs5VnRW1R8iFi00RKQPsDEwSFV/G7U89UVEGgLTgP2w9csJ\nwB6quiRSwUIkac8snaR/50REgMaqukpEmmB/q7uramX7OGOJiFwLbAt8paoX19TfR051QFUXqOrk\n4HghsAhoWf2n4kWwppek0E67A1OCZ/c98ALmtZkYEvjMfiLp3zk1VgXVJpg38apqPhIrRGQ7oAvm\nfZ0VbpzqiYjsAjRQ1f9FLYtTLR2A9Gf0P8zL04kZSf3OBVN7k7B9nneq6vKoZQqRm7CgCVnvIU28\ncRKRfUXkWRGZKyLlInJSJX3OEpFZIvKDiPxXRPbJ8totgeHAaWHLnS251K9QSLqOrl/2+hXCdy6T\nsPRT1e9UtSewNfAHEdk2H/JXRxi6iUh/YIaqfp5qyubeiTdO2D6pj4FzqQgY+xMicgxwG3Atlnrj\nHWB04H6e6nOWiEwMFisbB22NgGeA61X1/dyrUSU50a/AqLeOwDwgvb550FYIhKFfIROKfgX0ncsk\n1OcXrDOVBX2jJgzdegPHisgsbAR1qohcXuOd8x1bL8oCLAdOymh7D7gno+1T4LoarvU4cGXUOuVK\nv6BfKfDvqPUKQ0csXNUMoH3whZsObBq1PmE/w0J8ZmHpV4jfubD0w0KuNQ+OWwCTge2j1iesZ5d2\nbhDwt2yxHZQ4AAAgAElEQVTuVwwjpyoRkQ2xtBmvZJx6mYx4fBmf2xv4DTAgbcTRPXeS1o266hd8\n9hXgCeAQsSzEe+RGyvqRrY6qug64APuPdAJwk8bAU682zzAuzyydbPWLy3cuk1o8v62wPHQTgTeA\nG1X10/xIWTfq837JhoJNNpgnUgFgF2a0LwQOqOpDajmj4vC7q5N+AKp6UK6ECpmsdVTVUcCoPMkV\nFrXRLy7PLJ2s9IvRdy6TbPUbD+ycR7nCoNbvF1Udnu3Fi23ktCFwU2rhDnMvdhzHcQqMojFOwcJd\nY+A5KhbuHsFScbTN6N6WKtJpxIxUUsWk6gfJ19H1izdJ1i+nuhWNcQLOxxIMjlXVGap6LjAfy5qb\nOR1yEPB2nuULHbXAth+SUP0g+Tq6fvEmyfrlWrc4zuHWCrFkhV2xhbt1wJYi0gPLKfUy5t00WETG\nY7/QMzGPrnsjEbiWBPpth+0daECafqr6FXALMCKu+kHydXT9XL9CJVLdonZPzIP7435Y+nfFjFOq\n/AO4AnMpPgOYhaXTGA/sHbXcddBvXaZ+aX1iq18x6Oj6uX6FWqLUrSgCv4pIeyxcTR9VfSut/Qrg\nOFXtFplwjuM4zs9I/LReQK0W7kQk+RbbcRwnZFQ169h5NVEUDhFah4W7+gxHhwwZUu9+VZ3LbK+u\nXtnxoEGD6j3czpV+2bQlWb+qdE1vj5N+tX12+dQviu9eGPoV8rslbIpl5AR5XJQsLS2td7+qzmW2\nV1ev7LhTp05ZyVYdudIvm7Yk61eVruntYem3fDnMmwcLFsCSJbB06frlu+/gyy9LGTAAfvxx/VJe\nDitWlPLii9CgQUVZubKUiROheXMrS5aUcvXV0KYNtGsHbdqUMns2dOhQtd75en5RfPeg/voV8rsl\nbIpizSmFiJwBXIwZpSnAH9V2nmf206T+Xq666iquuuqqqMXIGa4fqML8+TBzppVZs+znV19Z+/z5\n1qdDBzMaLVtCScn6pUULaNIEGjf+eWnY0AxUelGFVavg++/XL0uXwtdfmxFcsAAWLrTSsSNsvz10\n6QK9esGee8K228LQof784oqIoCFO6xXTyAlVvQe4J2o5oqSkpCRqEXJKsem3aBFMngwff2xl8mSY\nNg2aNrWXfaocfDBsuaUZpPbtYeONQUJ7jdSO1avhiy9gxgz45BN4/nm49FIzbltsUUK3bvCrX5mM\nSSPpf59hEmvjJCKbAkOxtaOtMMeHUcDlqro4rV8JcCdweND0HHCOqn6XX4mjp2fPQojCnzuSrN+a\nNdCkSU/uvhvefdfKokWw006w446w665w8snwi1/YyKdQadTIRkxdukD//hXtX30Ft97ak4cfhjPP\nhGOPhfPOs35JIcl/n2ET62m9ICrxUOAhbL/S5sDfgbmq+su0fqOxXD6/wzaTPQjMVNUjqrhuYqf1\nnPigaiOLV16xMnYsbLEF9O5t02B77gldu9p6T9KYNw/uvReGDYPf/AauvdamH53CJexpvVgbp8oQ\nkUOA54ESVf1eRLoC04C9VPW9oM/ewDigi6p+Vsk13Dg5kbBmDZSVwVNPwQsvmOE56CArBxwArVpF\nLWF++fZbuPJKGDUKHn8c9qp3IgYnV4RtnGr9P5eINA/r5jmiBfAjFVkb9wSWpwwT/BR+fwUh5ByJ\nG2VlZVGLkFPiqN/atfDiizB4sDkoXHGFrRO9+irMng0PPADHHGOGKY761YZM/TbbDO6+28qAATB6\ndDRyhUXSn1+Y1LjmJCL7AQOxMBbbAg1FZB0wExgLPKaqb+ZUyiwJ1pauBu5T1fKguR3wTSXdvw7O\nOU4kTJ8ODz0EI0fC1lvDwIFwzTU2deesz2GHwbPPwhFH2M8994xaIifXVDmtJyL9gesxt+uXgA+A\nOcAyYBPMAWF3oB8W3fsSVX0+FKFErgEuq6aLAvur6ti0zzQL5FwNHKKqq4P2S4Dfqep2GfeYiRmx\nGyq5v0/rOTlh9Wr417/grrvMAeDEE23E1LVr1JLFg1GjzFli8mTYdNOopXHSyduaU5CM73rgebUI\nC1X12xDoD/xFVXcLRSiRlliWxeqYo6qrgv7NgNFYgMJfqWpqSg8RORm4TVXX818SkeXA2VpJZkYR\n0UGDBv20Ya6kpISePXv+tNksNTT3utezrS9dClOmlDJsGLRvX8avfw0XX1zKBhsUhnxxqh9xRBmq\n8NxzhSFPsdZTx7NnzwZg+PDhoRqneocKiboAzTHnhrFA00rOd8Xi6vVOa9sraOtcxTU1qbzxxhtR\ni5BTCk2/L79UPfNM1ZIS1d/9TnXy5Ppdr9D0C5ts9FuyRLV1a9Vp03IvT9gk+fkF783Q3u2xdkIN\nnDNeAUqAk4GNRaRtUDYEUNVPgDHAvSLSW0T2xDbiPq+VeOo5ThjMmWPTTz17wiab2IbTBx6w/UhO\n/SgpgXPOgRtvjFoSJ5fUy5VcRI4AWqjqiPBEqtX99wNez2wmY01KRFpgm3BTW/6exTbhLqviulqf\n34tTvCxcCEOHwhNPwO9/DxdcUHzu3/lg8WLYZhv4/HP//RYKBbXPSUSmA9urasOwBCoE3Dg5teWH\nH+CWW+DWW2HQILjkEn9p5prjjoN99oGzzopaEgcKYJ9TBgcA24QhSBiIyGgRKReRozLaS0RkpIgs\nDcqIYDRVdKQvZiaRfOtXXg6PPGIhdiZNgvffh5tvzp1h8udXwcCB5vkYJ5L+/MKkXrH1VHVeWILU\nFxG5EFiLTell8jgWvuhgKsIXjQAqDV/kONkwbRqcdppton38cdh776glKi769rXR07Jltq7nJIus\npvVEZMsqTimwSlUr2+SaN0RkN+BJYBdsc+3Rqvp0cM7DFzmhsno1/N//wZ13wtVXw+mnJzO+XRw4\n+GCb1hswIGpJnKhSZsym8hEJACKyDAu+erGqrg1BrqwRkY2BR4HTVHWR/DwPQKXhi0QkFb7IPfac\nrHnvPTj1VIvoMHGi5SVyomPffeHtt904JZFs/987FvgKuBxLT3FQcDwHi/R9FXAicEX4ItbI34EX\nVfXlKs57+KI0kj7nnSv9vv8e/vhHOPJIi3333HPRGCZ/fuuz5572D0NcSPrzC5NsR05nAH9KTZUF\nvC4iM4DzVHU/EfkaS18xpL5CZRu+CAuh1AObznOcnDBmDJxxBvTpA1OmWDBSpzDYfXeYMMHW/TaI\ndXY6J5Ns15x+AHbKXJ8Rke2BSaraVEQ6AdNUtWm9hcoufNFXwDBsxJauREMsjNE7qtrHwxd5va71\nHXcs5fzz4eWXy/jTnyzcUCHJ53Wrb755GX/9K5x0UmHIUyz11HGuwhdla5w+wSIqXJTRfiNwuKp2\nDZwSnlHVvE12iEh7IDP84xTgj8Bzqjo7cIiYCuyd5hCxF+YQ0dUdIpxMVG0T7fnnWzbWa66B5oWe\nKKaIOeIIC6B79NFRS1LcRLXP6QLgHBGZKiIPB2UKcDbwp6DPbkBedx2o6nxVnZZeglNzVXV20MfD\nF6WR/l9PEqmvfl99ZanDr7sO/vMf21RbSIbJn9/P6d4dpk4NX5ZckPTnFyZZGSdVfQHYHngOS5ex\nSXDcRVVfDPoMU9U/VX2VvFHZkGcg8BGWUmM0MBE4KZ9COYVNebmlBO/Vy9YxPvwQ9tgjaqmcbOje\n3facOckicWnaw8Cn9YqLTz6xzbTl5XD//bDDDlFL5NSG99+HP/wB/vvfqCUpbiILXyQiO4rIXSLy\nYrDWg4gMEJGdwxLGcfLJmjU2fbfPPpYGfdw4N0xxZOutLZ29kyyyMk4icjAwHtgci6fXJDi1LSG4\njtcXEdldRF4WkeUiskxE3go8/lLnPbZeQNLnvLPV7733YJddbAPnhAlw9tnxiPLgz+/ntG4Nq1bB\n8uXhyxM2SX9+YZLt1/EabJ/TkVga9BRlWKr2yBCRPTCHh9cDWXoBNwHp2XsfB3pisfX6BX0iSfPh\nRMuyZWaIjjoKLr0UXngBtqwqOJcTC0SgUyf44ouoJXHCJFtX8hVA98A1eznQQ1VnicjWwHRV3SjX\nglYj29vAa6p6ZRXnPbaeA8Azz1iSukMOgRtugJYta/6MEw8OO8zWDY/wUM6REdWa02JsSi+TXsDc\nsISpLSLSGoudt1BExonIQhEZKyJ907pVGlsPSMXWcxLOF19Y7LVLLoHHHjOnBzdMyWKLLWBuZG8i\nJxdka5weA24UkY6Yq/YGQRbam4h2eiyVS+oq4AFs2m4cMEZEUgmxPbZeGkmf807Xb8UKi4O3225W\nPvrIQhDFmWJ6frWhQweYPz9cWXJB0p9fmGRrnC4HvgC+BJpj02SvA28B14UtlIhcEyQNrKqsE5E+\nafLfo6rDVfUjVb0Mc944I2y5nHigaiOkrl1h1ixLAnjZZdC4cdSSObmifXuYVzDZ5ZwwyCpUoqqu\nAY4XkSuBnTGjMDGHERZuBUbW0GcOFSOf6RnnpgGpZe4FQOtKPt8mOFcpgwcPTmRsvdLS0oKSJ/x6\nKd27l7F2Lfzzn6Xsvbed//zzQpHPn18u9Fu0CObPj17+XOlXiPXU8ewc+fHHfhOuiMwFHlTVIWlt\nY4HJqnq2x9YrDsaPt9HRzJmWAPDYY6Fhw6ilcvLFxIkweLBN3TrRkLdkgyLyj2wvoqqnhCNOnbgR\nuEpEPsbCEh0D7AH8IZDtExFJxdY7HUvTXtSx9VL/ASWBDz+0jbTvv2/rS9ttV8aBB5ZGLVbOSNrz\ny6Su+rVvH581pyQ/vzCpblovcyqsD5aK4uOg/gtsem9sDuTKGlW9XUQaYc4Zm2GjpF+q6sdp3QYC\nd2Kx9QCeBc7Jq6BOaKjCa69ZqvQZM+BPf4JHH4UmTcDXm4uT1q1hyRKL+rHhhlFL44RBtvucLsHW\nmk5W1RVBWzPgQeBjVQ3dKSJKfFqvMFm1Cp580iKF//ADXHwxHHccNGoUtWROIdC2rU3rtSs6H9zC\nIKp9TucCV6UME0BwfA0Rj0BEpL2IPCoi80VkhYhMEpHjMvp4+KIY89lncOGFtpdl5EgYMsQy0g4e\n7IbJqaBVK1i0KGopnLDI1jg1BzpU0t4eqHfm23ryKNAZOBzoju27Giki+6T18fBFAWUxmfdauhQe\nfBD69oW99zbnhvfes5Tp/ftXHQcvLvrVFdevauJgnJL+/MIkK1dy4CngIRG5CEhFWugN3AA8nQvB\nasFuWLr1VMD8W0TkXCzO3lsi0g0zSHup6gcAgWPEOBHpXIxOEYXK99/D6NG2R+n11+HAA+Gss+Dw\nw32PklMzrVrBN5Vtt3diSbZrTk2Am4FTgNRy41pszelCVV2ZMwlrlu0JbGR3IrAE6I+NpvZU1Y9F\n5GTgNlVtkfG55ZhRG17JNX3NKU/Mng2jRll55x3Yc09zAz/ySCgpiVo6J06ccQb06AFnnhm1JMVJ\n3lzJ01HVH4CzgpHTtkHzzPQ1qAgZjHnfLcIM5ipgYJq3nocvKiC+/hrefNO86srK7D/dQw+1oJ3/\n/jdsvHHUEjpxJQ7Tek721CqDjaquUNXJQcmZYapF+CKAR7C08X2BXbB9TyPTYus5aeRzznvNGvOe\nevBB+6+2e3fYfnsYMQK22QaGD7e9KQ89BL/+dTiGKelz+q5f1cTBOCX9+YVJdZtwHwKuU9XPa7qI\niHQGLlXVk0OSK6vwRUH0hyOBnVR1StD+cWC4zgF+j4cvykv9u++gZctSpk+H0aPLmDEDvvyylK22\ngo4dy9h+exg5spQePWDcOPv8rrsWjvxej3+9VatSxo8vHHmSXk8d5z18kYhcAfwJmAI8hwVTnQN8\nj63xbIk5I/THNuTelO/9TiKyA7YpeEdVnZbW/hIwV1VP9fBF4aAKixdb+onZs63MnAnTp8O0abB6\nNXTrZmnOd9gBdt0Vdt4ZNtkkasmdYuGll2wP3JgxUUtSnIS95lStQ4SIbIqt6RyLuV+nTwOWY+GC\nHgeGq+risITKFhFpiBmnr4GLgG+xkdQNQH9VfTHo9yKWjyoVvuheYJaqDqjiukVlnFasgAULKi/z\n58OXX5ox2mADyzi69dYVP3fYwYxS+/aWkdRxouK//4Xf/x4mTIhakuIkr8Yp48bNgK2x9Z3vgC+i\n9NJLEWTjvQHYB9gY+By4WVUfSevTAgtf1D9oehY4R1WXVXHNWBinNWvMsFRVvv/e9gstWVJRPvus\njIYNS9drUzXj0q7dz0vbtrDVVmaM4uA9V5bw2GWuX9XMnm35uubMCVWkUEny84vEWw9+iggxpcaO\neUZVvwB+W0Of74CTanPdd96BdetqLuXl2fVL9V271qbAVq+GH3+s/riytpUrK4xPeTk0a1Z9KSmB\nTTeFLbc0N9vOnWHffS0T7KabWmna1Ec9TvyJg0OEkz0FnTJDRE7DgrbuDLQAOqnqnIw+Jdio6PCg\n6TlsVPRdWp8tgGHA/sAPWGbfC1R1bRX31d69lYYNqbE0aFBzn/S+G2xgIXcaN17/Z7bHTZtWGJ5G\njdyoOE4KVQv+u3ixfU+c/BLZyCkimgJjgP9gHnyV8TjQEQtNJNjG4BHAEQAi0gB4EdvrtDfQiorQ\nRedVdeN3362/8I7j5A8Ri06+aJHNFDjxplb7nPKNqt6uqjcAb1d2PvDE6wecpqofqOr7mNPD4YF7\nO8H5bsAJQRr314CLgdNEpHnutSgs0t1Ak4jrF2/qq1+hT+0l/fmFSUEbpyzYE1iechEHUNW3gRXA\nXkFTb2C6qs5L+9wYYCNs067jOAnB4+slh1oZJxFpJSJ7iEihhOHMJjRRO2Bh+klVXQSsowjDFyXV\nUyiF6xdv6qtfoRunpD+/MMnKOInIxiLyL+yl/w62ZwgRuUdErqrNDWsZmshxHCdrUmtOTvzJ1iHi\nBswg9QLeSmsfBVwHXFWLe2YVmijLa2UTmmgBFVN8gI0AgYYUYfii9DnvQpDH9XP9wtSvdWsYP76M\nsrLC0Cds/QqpnjrOVfgiVLXGAswFdguOlwPbBMfbYms+WV2nrgVbG1oHbJnR3jVo753WtlfQ1jmo\n/xKLVt4hrc9xwEqgeRX306TyxhtvRC1CTnH94k199bvnHtVTTw1HllyQ5OcXvDdDe+9nm89pBRa/\nblaQB6lHcNwTKFPVnMQOEJG22LpQdyz6+KHAPGCOqi4J+lQbmihwJZ+IrU1diLmSPww8qap/rOK+\nms3vxXGcwuLppy3a/bPPRi1J8RH2PqdsHSLGUxH6ByD15j4dW4PKFWdghmVkcM9RwAQqNtyCbdL9\nCHgJGB30/ykahKqWY0ZtJTYl+TjwbywWn+M4CaJNm8J2iHCyJ1vjdClwjYjcj61T/UlEXseyz16e\nK+FUdaiqNlDVhhllRFqf71T1JFUtCcogzYiZp6pzVbW/qjZX1daqer6qrsmV3IVM+nxxEnH94k19\n9St045T05xcmWRknVX0HW8tpBMwEDsCm1/ZUVY8B7DhOQdC6tWVbduJPrGPrichWwBVYzLz2wHzg\nCeBqVV2V1q/WsfUK+ffiOE7lqFosyuXL7aeTPyJZcxKRHUSkS1r9IBF5REQuCXIq5YpUbL0hVKxz\npdMV0+F0YAfgbGy96bY0WVOx9ZphsfWOBY4Gbs6h3I7jRIBI4W/EdbIj2zWnf2Cjl9Qo5FmgJfAH\n4NrciFZzbD1VHaOqp6jqq6o6W1VHY/uufp3WzWPrpZH0OW/XL96EoV8hrzsl/fmFSbbGqSvmJQc2\n6nhfVX+FOUQMzIVg9aAFsCSt7rH1HKeI8HWnZJCtcWoIrA6OD8CmycCcI9qGLVRdCdagLgDuTmv2\n2HpppHZ5JxXXL96EoV+bNoVrnJL+/MIk2/BFU4AzRWQUZpwuCdo3B2oVyUpErgEuq6aLAvur6tha\nXrctts9pjKreXpvPVkZSwxd53etJr69dW8a4cXDiiYUhT1LrqeNchS/KNkJEHyzhXwtguKqeErT/\nFdheVX9d3eczrtUSi9JQHXMyvO12AT4AttaMTLjB+XbAa8DHwHHBxtvUuaHAUaq6Y1pbKyyI7f6q\n+mYl10ust15ZWdlPf2RJxPWLN2Hod/vt8PnncOed4cgUJkl+fpFkwlXVsSLSGtgkFTYo4F4s8kLW\nqOpiYHFtPlMdItIeeJ1KDFPAu8BlItIhbd3pYGAV8GFYcjiOUxh07AjudxB/Cn2fU7Wx9QLD9CYW\nmPYkID3qwzeqWu6x9RynuHj/fTj7bBg/PmpJiotIRk7BjffHPPO2xCJF/ISq9g1LoAzOoGKPUyq2\nHsDJwAhsBLRtUL5MiRr03RozYuUicii2CfctbBPuI5g7ueM4CaNjR5g7N2opnPqS7SbcwZizwcZA\nKTYK2RTL7zQtR7LVGFtPVYdXci7Vf07adTy2XkBZwuc7XL94E4Z+7drBt9/C6tU19803SX9+YZKt\nK/mFwNmqOhCbOrtEVXfGRiDf50o4ETlNRF4XkSVBltwtq+nbWEQ+Cvr1yji3hYg8LyLfi8g3InK7\niGQ9anQcJz40bGijpy+/rLmvU7hk6623EthBVWeLyCKgr6pOFpGuWD6nnOwXEpHzsM2yP2AZdCv1\n1gv63gl0An6FJUacELQ3wFJqfAOcj605jcDWnM6r4lq+5uQ4Mebgg+H88+GQQ6KWpHiIKp/Tt9iU\nHsD/gF8Ex5sBTcISJpOawhelEJEjsOnGC7E1p3Q8fJHjFBmdO8Nnn0UthVMfsjVO4zDnA4B/AXeI\nyENY4r5XciFYtohIR8zZYSDmHp6Jhy9KI+lz3q5fvAlLv+22s71OhUbSn1+YZLvucjb2Mgf4K7AW\ni/D9L3IY+LUmgim7R4AbVXVKEL4ok0rDF4lIUYYvcpxioHNneOmlqKVw6kPe9znVJXxRVREiROQK\nYB9V7RfUOwGzgF3T1pzuBbZV1QMz5FiDTfU9UYmMvubkODFmzhzYYw+YPz9qSYqHyPY5BTfvALQh\nYzqwltlwbwVG1tCnUqeHSugL7BMYmnTeE5EnVPVEYAGWxfcngvBFDYNzleKx9bzu9fjWVeHHH0tZ\nsAA++SR6eZJYTx3nKrYeqlpjwXI5TcUieZdnlHXZXKM+BVsbWgdsmdG+FZZkMFUODGQ6GugQ9Pkl\nNg3ZIe1zx2Fhl5pXcT9NKm+88UbUIuQU1y/ehKnf/vurvvRSaJcLhSQ/v+C9Gdp7P9uR033AV8Bp\nWPigvMx5pYUv6oJ54XUXkU0Jwhep6pcZ/VcEh7O0wgHiZcywjhCRVPiivwH3qWrO9mg5jhMtu+0G\n774L/fpFLYlTF7Ld57QC2FlVP829SOvddwiVp2g/WYMoERn9t8LWnH7a5xS0pzz6+pIWvkiriBLh\na06OE3/GjIHrroOxY2vu69SfsNecsjVO72Ev86J4zG6cHCf+rFgBbdvCwoXQrFnU0iSfvG3CFZGW\nqQJcCvxNRA4Ukbbp54LzOSHb8EUi0k9E3hGRFUHfVzPOe/iigPTFzCTi+sWbMPVr1gx69YK33grt\nkvUm6c8vTKp7QS9i/ek0wdZvMtsU83zLBU2xDbP/wbz8foaIDAD+gWXnfS2QpVfa+QZYWvlvsL1Z\nqfBFAJWGL3IcJxkceig89ZSvO8WRKqf1RGS/bC+ilWSTDZNq9jk1AL4AhqrqP6r47CHA85in37yg\n7XjgfqBNZU4RPq3nOMlg7lzYaSf43/+gSc4CrTmQx31OuTY4IbEL0BFYKyIfAh2AycCfVXVS0Kem\n8EVx0NNxnDrQsSPssgs88wwcd1zU0ji1odrYeiLSVETuEpG5wVrNY8EG1kJhG2xqcSgWRulXWFbc\nssANHaoIX4Ttmyq68EVJn/N2/eJNLvQ7/3z461+hvDz0S9eapD+/MKkp8OtQLOvsC1iQ14OBv9fn\nhiJyTeDcUFVZJyJ9srxcSv5rVfUZVZ0I/B74Dkvb7jhOkXPIIeYc8dhjUUvi1IZqXclFZCZwmar+\nM6jvjqWv2EhV19XphubdV9Poa46q/hRhvJo1p1LgdSy+3jtp7a9iU3nniMhQ4ChV3THtfCvgayyG\n38+m9UREBw0a5OGLvO71hNSnT4ehQ0uZPBmmTYteniTUU8ep8EXDhw/P3z4nEVmNGYT/pbX9AGyv\nql+FJURNVGOcNsaMzFmq+lDQJthG3LtV9SYR+SUwivUdIo4DHsAdIhynaLjsMosY8dJL0KhR1NIk\nj3wnG2wIrM5oW0stA8bWlWBPVQ/WD1/UIwhhhKouB+4BhorIwSKyPXAHUEJFcNn08EU9ReRAijh8\nUfp/PUnE9Ys3udTv6qthk03g2GNhVWWZ3/JA0p9fmNRkZAR4RER+TGvbCLg/SN0OgKr2z4VwwBlU\nhC9SbAQEtg6W2qt0IfAj8DC2L2oCUKqqCwPZykXkUCx80VukhS/KkcyO4xQgDRvCE0/AiSfCgQfa\nGtSWlW7rdwqBmqb1HsrmIqp6cmgSFQA+rec4yWXdOrjxRrjlFvjLX+APf4DGjaOWKv5EElsvKkTk\nNCz9+s5AC6BT+ppT0KcLNk23F9AYm8K7SlXHpPXZAhs57Y+NnB4DLlDVtVXc142T4yScadPgz3+G\nSZPgjDPg1FMtFp9TN/K95hQ1qfBFlUUmTzEa2BAzPD2xqbtnRWRrWC98UTMsfNGxWL6nm3MqeYGS\n9Dlv1y/e5FO/HXaA55+3Mns2bL897L8/3HEHTJmSm31RSX9+YVLQxklVb1fVGzD39Z8hIpsBnYAb\nVHWKqs4C/oKtpe0cdOsHdMNSsn+kqq9h602niUjzXOtQaEyaNKnmTjHG9Ys3UejXsyfcfz8sWGAb\ndidNggEDoHVrOPxwuPJK+Ne/YPp0WFvpXEv2JP35hUmsI3Or6rci8gFwooj8F5uyOx1YRoVB8/BF\naSxdujRqEXKK6xdvotSvSRPo398KwLx58M47MHkyPP64uaLPmQObbw6dOlWUjh2hTRubEmzTxkpV\ncfyS/vzCpKBHTlnSHxslLcO89q4EDkl56xFB+KJsh+7V9avqXGZ7dfWqjutLrvTLpi3J+lWla9hT\nQQ6GiLIAAAnPSURBVPnSL4pnl+31stGtQwc4+mhzQX/mGbj//jKWLbMkhpdcAi1blrFqlSUzHDYM\nTjihjH33hZISaNq0jG23tZQdPXuWMWAADBoEL74Il19uDhn33QePPgpPPw2jR8Obb8IHH8DHH8PM\nmWYclyyBH3+E1BJ40t8t6eTdOIUZvkhEGgLPAQuw9aTdgCeBp0Wkfe60qJ5C/gNK7eauD4VsnOKs\nXzbGKU761eXlli/96vrda9wYOneGgw6C5s3LuP56ePhhMzoDB5YxZ47toTr33DLGjLHpwh49yhg0\nyNazYDaNGlkCxPHj4YUXYORIuP12uOIK8xwcONCuv8susPXWsPHGsMEGNhrr16+MzTaDdu3MDX7b\nbaFrV9hxR+vfuzfsuy+cfHIZ/frZtORRR8Fvf2v7u44/3mQbNAhOOcWcQE4/Hc48Ey6+uIxzz7Wp\nzQsugEsvLeMvf4FLLzXZhgwp4+qr4dpr4ZpryrjhBjOy119fxi231P451UTevfVCDl+Uiv7QUlWX\npbV/CjysqtfXNXxR3bRzHMcpXvKSMiNXqOpiYHFIl0uN/DLj/JWnnXsXuExEOqStOx0MrAI+rELG\n0H7BjuM4Tu0p6DWnmsIXAe9gGXsfFpGdRKSziNwIbE1FNAkPX+Q4jhMzCto4YeGLJmJx8lLhiyYA\nhwOo6lLMVbwZ8CowHtgHOCKVbFBVy4FDgZXYHqjHgX8DF+VTEcdxHCd7CjpChOM4jlOcFPrIyXEc\nxylC3DjVARHpKCJviMhUEZkkIkdHLVPYiMjTIrJYRP4VtSxhISKHicgnIjJDRH4XtTxhk8RnliLp\n3zkRaSEi40VkgohMEZGzo5YpbESkiYjMFpG/ZdXfp/Vqj4i0wxIVThaRtpjXX2dV/SFi0UIj2Gu2\nMTBIVX8btTz1JdgTNw3YD/geW7vcQ1WXRCpYiCTtmaWT9O9ckCS1saquEpEm2N/q7qr6TcSihYaI\nXAtsC3ylqjWmLPKRUx1Q1QWqOjk4Xoh5DLaMVqpwUdWx2Es8KewOTAme3ffAC9iWgsSQwGf2E0n/\nzqmR2tvZBNvqElFKxPARke0wr+vR2X7GjVM9CTYIN0hPZe8UJB2A9Gf0P2DziGRx6kFSv3PB1N4k\nYA5wZ5DpOyncBFyCbQnKisQbJxHZV0SeFZG5QXikkyrpc5aIzBKRH0TkvyKyT5bXbgkMB04LW+5s\nyaV+hULSdXT9stevEL5zmYSln6p+p6o9sX2afxCRbfMhf3WEoZuI9AdmqOrnqaZs7p144wQ0Bz4G\nzsX2Oq2HiBwD3AZci+WDegcYLSId0/qcJSITg8XKxkFbI+AZ4HpVfT/3alRJTvQrMOqtIzAPSK9v\nHrQVAmHoV8iEol8BfecyCfX5BetMZUHfqAlDt97AsSIyCxtBnSoil9d4Z1UtmgIsB07KaHsPuCej\n7VPguhqu9ThwZdQ65Uq/oF8p8O+o9QpDR6AhMANoH3zhpgObRq1P2M+wEJ9ZWPoV4ncuLP2ANkDz\n4LgFMBnYPmp9wnp2aecGAX/L5n7FMHKqEhHZEMvp9ErGqZextO9VfW5v4DfAgLQRR/fcSVo36qpf\n8NlXgCeAQ0RkjojskRsp60e2OqrqOuAC7D/SCcBNGgNPvdo8w7g8s3Sy1S8u37lMavH8tgLGichE\n4A3gRlX9ND9S1o36vF+yIdbJBkOgFfYf9cKM9oXAAVV9SFXfJh6/uzrpB6CqB+VKqJDJWkdVHUVF\nzMW4UBv94vLM0slKvxh95zLJVr/xVGTvjgu1fr+o6vBsL17UIyfHcRynMCl245TKiNs2o70tlsAw\n7iRdP0i+jq5fvEmyfjnVraiNk6quwXaaZ06HHAS8nX+JwiXp+kHydXT94k2S9cu1bnGcw60VItIM\n2A7zrW8AbCmWI2qxqn4F3ILlehqP/ULPxDy67o1I5FqRdP0g+Tq6fq5foRKpblG7J+bB/XE/LDPu\nuozyj7Q+ZwCzgB+wnFB7Ry2361c8Orp+rl+hlih188CvjuM4TsFR1GtOjuM4TmHixslxnP9v715C\n66jiOI5/fxYfRG0RUZOFBDS+NlIKYlJBcNNetT5AULQgKihdSIML0YWILhRUBFFEkIpCQcVVfaAR\n0WKLVRRFRSilQTFKjamvaFVsSf8uzoy9HnPTmZt76xB+H7jcmTln/nOyyf+eOefMmDWOk5OZmTWO\nk5OZmTWOk5OZmTWOk5OZmTWOk5OZmTWOk5OZmTWOk5PZEiJpq6T1PY45KGmvpFN6GddsIU5OZhVI\nelbSQUlzxXe5ff7/3baSpBZwOvB827FvJG2cp+5dknZXiRsR08BLwOFfrW3WI05OZtW9BQy2fYaA\nL+arWLwl9Ei7Hdgc1Z9JVufZZZuBmyQdV79ZZvU5OZlV91dE7I2ImbbPQQBJ2yU9IelRSTOk18Ej\naYWkTZK+lzQr6R1J/3rjqaSbJX0taZ+kLZI2SjpQp2GSTgLWAq/U/aMkLct6heX3/rJORHxAerDn\nurrxzbrh5GTWOzcCB4CLgFskCZgATgZawCpgB/B2OX4jaTWwCXgSWAm8AdxLvV4NwOri2p9XrK9y\nIyLmONQTHASGgU+Brdk5H5GeUm3Wd0v+fU5mPXSppN/a9rdFxOVt+7sj4u5yR9Ia4Fzg4kgvZgO4\nR9JVwHrgMWAcmIiIh4vySUmjRXkdZwHTRaLJPSTpgezY0cBUuRMRM23tfhoYAK7NzpkCzq7ZLrOu\nODmZVfcucCuHeh1/ZuUfZ/urgBOBn1In6h/HAmcU2+eRJhu0e5/6yWk5sK9D2SPAc9mxDcDVeUVJ\n48A1wIURMZsV/wqsqNkus644OZlV90dEfLVA+e/Z/lHAHtKtMGVl+T/+xZoFTuhQ9kNEfNl+QNKP\neSVJa4EHgXURMTlPnOXAL4ttqFkVTk5m/fMJaQxnLiKmOtTZCYxmx8a6uNYkMCRpWYdbewuSdA7w\nAnBHRORjTaVhoNL0c7PF8oQIs/55E/gQ2CJpjaRhSWOS7i/GlQAeB1qS7pQ0ImkDcEV7EEmjknZK\nWrnAtXaQfmzWXnclaQB4FXgdeFnSacXn1KzqBcC2uvHNuuHkZNYb/5ldV6w3agHbgWeAXcCLwAjw\nXVHnPeA20hqlz4DLgPuyUMeTJiIMdLx4xM+kZHjl4do1jyHgTOB60m3IPUX7vi0rSBojjZW9ViGe\n2aKp+no9MzsSJF1HWkx7TM3zWqQp6SM1FuJWjf0UsD8ixnsZ16wT95zMloiImCBN976hl3ElDZJm\n8OXT0c36xhMizJaQiLikDzGngXz8yayvfFvPzMwax7f1zMyscZyczMyscZyczMyscZyczMyscZyc\nzMyscZyczMyscf4G1OBa2OaZr1cAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113949b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "out = bode_utils.bode_plot2(f,Gjw2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}