{ "cells": [ { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "# Post Run MICH Calibration" ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "This is a report of the post run calibration measurements done on 2016/4/28" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": true, "hide_input": false, "run_control": { "marked": false } }, "outputs": [], "source": [ "import numpy as np\n", "pi = np.pi\n", "import sympy as sp\n", "from sympy.abc import s\n", "sp.init_printing()\n", "import matplotlib.pyplot as plt\n", "import plotutils as plu\n", "%matplotlib inline\n", "from unit import *\n", "import ltiutils as ltu" ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "## 1. Optical Gain " ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "In order to measure the optical gain, MICH lock was first turned off. After adjusting the alignment to maximize the beam power coming back to REFL from the each arm, MICH was shaken sinusoidally by injecting a signal of amplitude 1000 count at 0.2Hz into the K1:LSC-MICH_CTRL_INJ_EXC channel. So this signal was directly sent to the MICH actuator. The observed fringes in REFL DC and also in REFL RF error signal are shown below." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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nKroZqbayfzCBbtZRZB1EK7HPjsm+A48lY//+/Th69CgCgQAopUIT1AcHB1FV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3j3Xdhpp9hppApUZPrHmcDMEu5/AzgrPXFEskzfvr5D1hdfxE4ikl4h+MLE/v2hptaai6Rd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\npIl3BJEKU1Etk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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "DC = np.loadtxt('data/Fringe/data/REFL-PDA1-DC.txt', comments='#')\n", "RF = np.loadtxt('data/Fringe/data/REFL-PDA1-RF17_Q_ERR.txt', comments='#')\n", "INJ = np.loadtxt('data/Fringe/data/InjectionSignal.txt', comments='#')\n", "\n", "t = DC[:,0]\n", "t = t - t[0]\n", "dc = DC[:,1]\n", "rf = RF[:,1]\n", "inj = INJ[:,1]\n", "\n", "data = [{'x':t, 'y':dc, 'title':'K1:LSC-REFL_PDA1_DC_OUT','ylabel':'count'},\n", " {'x':t, 'y':rf, 'title':'K1:LSC-REFL_PDA1_RF17_Q_ERR_DQ','ylabel':'count'},\n", " {'x':t, 'y':inj, 'title':'K1:LSC-REFL_MICH_CTRL_INJ_EXC','ylabel':'count','xlabel':'Time [sec]'}]\n", "ax=plu.multiPlots(data, size=(10,12), font_scale=0.7)" ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "#### Contrast" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false, "run_control": { "marked": false } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Contrast is 62.8%\n" ] } ], "source": [ "Pmax = 7000.\n", "Pmin = 1600.\n", "Contrast = (Pmax - Pmin)/(Pmax + Pmin)\n", "print(\"Contrast is {0:.3}%\".format(100*Contrast))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Optical gain from the error signal slope" ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "The amplitude of the DC signal Adc:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": true, "run_control": { "marked": false } }, "outputs": [], "source": [ "Adc = Pmax - Pmin" ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "The amplitude of the RF signal Arf:" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false, "run_control": { "marked": false } }, "outputs": [], "source": [ "Arf = np.max(rf)-np.min(rf)" ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "The slope of the signal at the middle fringe is $A/2\\cdot 2\\pi/\\lambda\\cdot 2\\Delta L=\\frac{2\\pi A}{\\lambda}\\Delta L$" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false, "run_control": { "marked": false } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Hdc=3.19e+10[cnt/m]\n", "Hrf=5.79e+10[cnt/m]\n" ] } ], "source": [ "wl = 1064*nm #Wave length\n", "Hdc = 2*pi*Adc/wl #Optical Gain measured by the DC signal [cnts/m]\n", "Hrf = 2*pi*Arf/wl #Optical Gain measured by the RF signal [cnts/m]\n", "print(\"Hdc={0:.3}[cnt/m]\\nHrf={1:.3}[cnt/m]\".format(Hdc, Hrf))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These numbers are consistent with the mid-run optical gain measurements\n", "\n", "Hdc=3.25e+10[cnt/m]
\n", "Hrf=5.66e+10[cnt/m]" ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "## Actuator Efficiency" ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "Now we locked the MICH using the DC signal at the middle frindge. \n", "An excitation signal is injected just before the LSC filter and the transfer function from tge input to the MICH actuator (just after the UGF servo) to the input to the filter (= the error signal) was measured. During this and most of the following measurements, the UGF servo was on hold otherwise noted." ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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HVq9eTdWqVXnuuee48sor6du3L7NmzeLEiROhDlMppZRSeZg2qlVEqVixIn36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\nVEdro3irj+stXerrqms9l+Jtc0qqE7J48cZJAKqp3pRWh6hPKv8Q6d1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4xjf8Dn1SvUL5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wWwHhhc5lyuWosXO7flllUfXrN58+Ylfo2333auf3/nHn447LVq6XvcY+O0j9K2UpveHp83b1Hk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\nvqtXw+bNo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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "TF=np.loadtxt('data/TFs/Data/DC-Lock-LBW-OPLG.txt', comments='#')\n", "f = TF[:,0]\n", "real = TF[:,3]\n", "imag = TF[:,4]\n", "mag = np.sqrt(real**2+imag**2)\n", "phase = rad2deg(np.angle(1j*imag+real))\n", "\n", "data = [{'x':f, 'y':20*np.log10(mag), 'plot_type':'semilogx', 'ylim':[-150,50], 'title':'K1:LSC-MICH_IN1_DQ/K1:LSC-MICH_CTRL_CAL_IN1','ylabel':'Magnitude'},\n", " {'x':f, 'y':phase, 'plot_type':'semilogx', 'ylim':[-180,180], 'xlabel':'Frequency [Hz]','ylabel':'Phase'}]\n", "ax=plu.multiPlots(data, size=(10,8), font_scale=0.9)" ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "The actuator efficiency at 100Hz is the following." ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false, "run_control": { "marked": false } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Transfer function magnitude at 100Hz is 0.00787\n", "Actuation efficiency at 100Hz is 2.47e-13[m/cnt]\n" ] } ], "source": [ "tf100=np.interp(100,f,mag) #Transfer function magnitude at 100Hz. This is in the unit of [cnt/cnt]\n", "print(\"Transfer function magnitude at 100Hz is {0:.3}\".format(tf100))\n", "#The actuator efficienty at 100Hz can be obtained by dividing tf100 with Hdc\n", "A100 = tf100/Hdc # in the unit of m/cnt\n", "print(\"Actuation efficiency at 100Hz is {0:.3}[m/cnt]\".format(A100))" ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "The slope of the actuator efficiency should be $\\propto 1/f^2$. The actuation efficiency above the resonant frequency of the pendulum ($\\simeq$1Hz) can be written $A=\\alpha/f^2$." ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false, "run_control": { "marked": false } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Actuation efficiency is 2.47e-09/f^2[m/cnt/Hz^2]\n" ] } ], "source": [ "alpha = A100*100**2 # [m*Hz^2/cnt]\n", "print(\"Actuation efficiency is {0:.3}/f^2[m/cnt/Hz^2]\".format(alpha))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is not so consistent with the previous calibration: 2.24e-09/f^2[m/cnt/Hz^2] on 2016/4/19. I will revisit this below." ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "## RF Optical Gain from actuation efficiency " ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "Now we have the actuator efficiency. We can measure the RF optical gain by locking the MICH with RF and making a transfer function measurement." ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false, "hide_input": false, "run_control": { "marked": false } }, "outputs": [ { "data": { "image/png": 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Kt2jWtXzzhjVyvK9j+Rac5Zv3dRI136z7h8lURISaNWtSs2ZNHnroIZKTk3n1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\nuPjbsccey5w5c+jTpw+77747Dz/8MH5/4az+5n2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gOHYTuKL45m/GmAuMMcOBrwO3iUgP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ip5ieoVKzJf16wU3qAfXhRFKSbGjYM//hEuuyy4OdvaYMMG/98rEyEgbkV1Y6NdMXZLOlH9f/8H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\nBl/6EjzySCgLmTIll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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "TF=np.loadtxt('data/TFs/Data/RF-Lock-OPLG.txt', comments='#')\n", "f = TF[:,0]\n", "real = TF[:,3]\n", "imag = TF[:,4]\n", "mag = np.sqrt(real**2+imag**2)\n", "phase = rad2deg(np.angle(1j*imag+real))\n", "\n", "data = [{'x':f, 'y':20*np.log10(mag), 'plot_type':'semilogx', 'ylim':[-150,50], 'title':'K1:LSC-MICH_IN1_DQ/K1:LSC-MICH_CTRL_CAL_IN1','ylabel':'Magnitude'},\n", " {'x':f, 'y':phase, 'plot_type':'semilogx', 'ylim':[-180,180], 'xlabel':'Frequency [Hz]','ylabel':'Phase'}]\n", "ax=plu.multiPlots(data, size=(10,8), font_scale=0.9)\n" ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "The magnitude of this transfer function at 100Hz can be divided by the actuation efficiency at 100Hz to give the RF optical gain." ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false, "run_control": { "marked": false } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Transfer function magnitude at 100Hz is 0.0134\n", "Hrf from the actuation efficiency = 5.43e+10[cnt/m]\n", "Hrf from fringe amplitude = 5.79e+10[cnt/m]\n" ] } ], "source": [ "tf100=np.interp(100,f,mag) #Transfer function magnitude at 100Hz. This is in the unit of [cnt/cnt]\n", "print(\"Transfer function magnitude at 100Hz is {0:.3}\".format(tf100))\n", "Hrf2 = tf100/A100\n", "print(\"Hrf from the actuation efficiency = {0:.3}[cnt/m]\\nHrf from fringe amplitude = {1:.3}[cnt/m]\".format(Hrf2,Hrf))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There is a noticeable discrepancy." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Actuation efficiency from the RF lock" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here I will try to calculate the actuation efficiency from the RF fringe calibration and the transfer function measurement with RF lock." ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Actuation efficiency from the RF calibration = 2.31e-09/f^2[m/cnt/Hz^2]\n" ] } ], "source": [ "alpha = tf100/Hrf*100**2\n", "print(\"Actuation efficiency from the RF calibration = {0:.3}/f^2[m/cnt/Hz^2]\".format(alpha))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The above number is much closer to the number we got on 4/19: 2.24e-09/f^2[m/cnt/Hz^2].\n", "\n", "It seems that there was something wrong with the DC lock transfer function measurement. It is not only different from the previous measurement but self inconsistent within the measurements done this time between RF and DC. It is unlikely that the actuation efficiency changes by a large amount during the run. From the RF measurement, we got a similar actuation efficiency as before. For this reason, I will use the actuation efficiency obtained from the RF measurement in the following analysis." ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "## Open Loop Gain Model" ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "Now we try to make a theoretical model of the open loop gain" ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "### Actuator" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false, "run_control": { "marked": false } }, "outputs": [ { "data": { "image/png": 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e+WSUE9NflwBrRWQ18B5wh6oecNt+C0wFNgEZGibsvWEYhh+ceeaZPPTQQ2zd\nupWrrrqK22+/nYsuuoj333+f48eP+y0vIfi+TyVe2PSXYRh+k5OTw+zZs5k4cSL79+/n/vvv56ab\nbqJChQp+SwtL3POplFTMqBiGERRUlX/9619MnDiRNWvWMHr0aO68806qVKnit7RfkIiAkkaMKK1z\nqLEmiJogmLpMkzf81iQidO/enXnz5jFv3jzWrFlDw4YNGTduHJmZmb5qCyXePhXDMAwjxpx//vlM\nmzaNl19+mSNHjtCmTRvuuOMOMjIy/JYWE2z6yzAMw0e+//57XnjhBV566SV69OjB2LFjueCCC3zT\nYz6VMJhRMQyjJHHkyBGmTJnCs88+S/PmzXn++ec555xzEq7DfColCL/ndQvCNHkniLpMkzdKgqZK\nlSpx9913s2XLFoYNG8YZZ5zhu6ZI8M2oiMh4EdnhxvhaLSK9Q9rGiUiGiKwXkV4h9e1FZK2IbBKR\nSf4oj5z09HS/JfwC0+SdIOoyTd4oSZrKlSvH0KFDYxIypbjE4j75/aTyrKq2d4/5ACLSGrgeaA30\nAV6UEzGmXwJGqGoLoIWIXO6L6gg5cOBA0Z0SjGnyThB1mSZvmCZvxEKT30aloHm7/sAMVc1W1W1A\nBtAxnqHvi/PIV1jfcEHiIqEsaSrutaM5L1z/WGoq7rklSVNBbabJe1tp+5wXhN9G5Xciki4iU0Sk\nqltXH/g2pM93bl3cQt8n6oO9bds20xSmLbQuXpoK6+/ljy3R9yqImgpqM03e24L+OS+OpnDEdfVX\nIaHvHwSW4+RnURGZANRR1VtF5AVgmapOd68xBZgHbAceV9Vebn1XYEy4DJQiYku/DMMwIiCa1V9h\n86nEAlW9rOheALwKzHVffwc0DGnLDYsfrj7c2KUz16dhGEaA8XP1V52Q4jXAV+7rOcAgESkvImfj\nhL5fURpC3xuGYZR24vqkUgRPikg7IAfYBtwBoKrrROQ9YB2QBYwK2cX4W+AN4DRgnoW+NwzDCBal\ndke9YRiGkXj8Xv1lGIZhlCLKlFERkbPd5cvv+a0FQEROF5E3RGSyiNzot55cgnafAESkv4i8IiLv\niIjXBSBxRURaichLIvKeiNzpt55c3M/VShHp67cWABHpLiL/cu/VJX7rARCHCSLyvIjc5LeeXESk\nq3ufXhWRT/zWAyAiDUVklvudMLao/mXKqKjqVlW91W8dIVwD/F1V7wAKXBrtBwG8T6jqbFW9HRiJ\nE3HBd1R2jsEDAAAgAElEQVR1g6qOBAYCXfzWE8JY4F2/RYSgwGGgAifvNfOT/jgrSI8RHE2o6ifu\nZ+qfwJt+63Fpi/M9dSvQrqjOJdKoiMhUEdktImvz1fcWkQ1ubLAiLWoAdDXgxEbPuCWwDuL9ikLT\nQ8Bfg6JJRPrhfAHMC4ImEfkNziKX7yk4YkXCNanqv1T1CuAB4NEgaAJaAp+q6n3AqHhoilBXLjcC\n0wOiaTlwq4gsAopeHKWqJe4AuuJYzLUhdUnAZqAxUA5IB1q5bTcBzwJ13fLfA6JrMNDXfT09KPcr\npE9c7lOkmoAngJ5B0hTS759B0ARMcD/rC4BZQdAU0qc88F4QNLl/e9e5r2cE6TOFsx9vclA0AX8A\nurqvi/xOKJFPKqr6CbA/X3VHIENVt6tqFjAD5xEXVf2bqt4LHBWRl4B28fjPvLi6gFnAdSLyV05s\n/ow5xdUlIjXieZ8i1HQX8Guc+3V7QDR1F5HnRORl4IMgaFLVh9zP+jScTcW+axKRq9179Cbwf0HQ\nBLwP9BaR54Cl8dAUoS6AEcDrAdI0HxjtfidsLer6fu5TiTX5Y4btwLlReajqPpw5+UQSVpeq/gjc\nkmA9uRSmy4/7VJSmF4AXAqZpKXH8QopEUy6q+lZCFRV+n2bh/AOVaArT9BPgl9+w0N+fqj6caEEU\nfq++BgZ4vVCJfFIxDMMwgklpMirfAY1CyoXGBksgpss7pskbpskbQdQEwdQVM00l2agIJ69uWQk0\nE5HGIlIeGIQTR8x0BVeXaTJNpV1TUHXFT1O8VhjE88BZarcTOAr8B7jZre8DbMRJ7PWA6QquLtNk\nmkq7pqDqircmX2N/iUgDnAyOtXECS76qqs+LSHWczVuNcYJNXq+qB91zxuE4t7OB0aq60A/thmEY\nxi/x26jUwUnOlS4ilYAvcJax3QzsVdUn3SWt1VX1ARFpg7NU8kKcOb9FQHP1800YhmEYefjqU1HV\nTFVNd18fAdbjGIv+nAhR8CYnctFfRQH56xMq2jAMwwhLYBz1ItIEZ5fncqC2qu4Gx/AAZ7ndwuWv\nNwzDMAJAIDY/ulNfM3F8JEfkl/nliz29VcA1DMMwDA9oFOnYfX9SEZFTcQzK31Q1Nz3wbhGp7bbX\nAfa49cXNU+/pGD9+fEz65m/LXx42bJhpCtMWWhcvTYX1L0qTH/cqiJoKajNN3tuC/jkfNmxY1N/p\nvhsV4DVgnao+F1I3Bxjuvh7GiVz0Beavj1ZAjx49YtI3f1v+cpMmTUxTmLbQunhpKqx/UZog8fcq\niJoKajNN3tuC/jkvjqawFMf6xfoALsYJ+Z4O/BtYDfQGauCs7NoILASqhZwzDiea5nqgVyHX1qAx\nfvx4vyX8AtPknSDqMk3eME3eGD9+vLrfnRF/r/vqU1HVT4FTwjT/Jsw5jwOPx01UHKlWrZrfEn5B\nWdV09OhR3n77bbKyshBxpo9FJO8oqLxp0ybefPNNT329tMWi7+7du1m0aBFJSUmceuqpUR1JSbGZ\nuCirn6niUlo1BcJRX1Zo167IpGkJp6xq+vrrrxk7dizXXXdd/ifcsOV9+/axePFiT33zl4vTtzjX\n2rdvHxkZGRw/fpzjx4+TnZ0d0ZGVlUW5cuWoWLFikccZZ5xBtWrVqFq1aoE/69evn3e9oFBWP+fF\nJRaafN38GE9EREvrezOi5/PPP+euu+5ixYqoXXKlAlXl2LFj/PTTT0UeR44c4eDBgxw8eJADBw6c\n9HP//v3s2bOHH374gSpVqlCnTh1q165NnTp1aNy4McnJyZx99tmcffbZNGrUKFCGx3AQETSK1V/2\npGKUSbKzszn1VPv45yIiVKhQgQoVKsRkCiQnJ4e9e/eSmZnJ7t272bVrF9u2bWPZsmVMnz6drVu3\nsmvXLurVq8c555xD27Zt845WrVqZsSnB2F9VAklLSyv2Ko54U1Y1ZWdnF/uLq6zeq+KSq6lWrVrU\nqlWLtm3bFtgvKyuLbdu28fXXX/Pll18ya9YsHn30UXbs2EGHDh3o3LkzXbp0oXPnztSqVSsmmoJE\nUDVFi+9GRUSmAlcCu1X1PLduPHAbJ/an/FFV57ttFlDSiBp7UvGfcuXK0bx5c5o3b05KSkpe/cGD\nB1mxYgWfffYZf/3rXxk6dCjJycn06dOH3r1707lzZ/vdBRjffSoi0hU4AryVz6gcVtVn8/VtjRO2\nuciAkuZTMQpjwYIFPPvssyxYsMBvKUYRZGVlsXz5cubPn8+HH37I1q1b6dOnD4MGDeLyyy+nQoUK\nfkssVUTrU/F986OqfgLsL6CpoDfVHwsoacQAe1IpOZQrV45u3brxl7/8hdWrV7N+/Xq6devGM888\nQ7169RgxYgSLFi0iJyfHb6kGATAqhfA7EUkXkSkiUtWtK9EBJWMxXxlryqqmrKysYhuVsnqviku8\nNdWpU4eRI0eydOlS1qxZwznnnMOYMWNo2rQpjz32GJmZmQnXFAmlVVNQ/1V7EXhUVVVEJgDPALcW\n9yLDhw/PCztQrVo12rVrl+cYy715iSynp6f7On5B5VyCoidR5TVr1rB//4kHZPv9ldzyvffeS/v2\n7dm4cSOrVq2idevWnHfeefTv35977rkHESE9PT0wenPLQfk8paWl8cYbbxArfPepAIhIY2Burk8l\nXJuIPIATQmCi2zYfGK+qnxdwnvlUjLDMmDGD1NRUZsyY4bcUI8YcOnSIadOm8cILL1C+fHnuuece\nBg0aZL4Xj5R4n4qLEOJDcSMT53IN8JX7Oi4BJY2yh/lUSi9VqlRh5MiRfPXVVzzxxBNMmzaNs88+\nmwkTJvDDDz/4La/U47tREZHpwGdACxH5j4jcDDwpImtFJB3oDtwDoKrrgPeAdcA8YFRJehzJP2UR\nBMqqpkiMSlm9V8UlKJqSkpLo3bs3CxcuZMKECWzdupXmzZtzxx13sH79er/lBeY+hRILTb4bFVW9\nUVXrqWoFVW2kqq+r6lBVPU9V26lqirpZIN3+j6tqM1VtbXtUjEiJxFFvlFySk5OZOnUqGzdupF69\nelx66aX07duXBQsW2KqxGBMIn0o8MJ+KURgvvfQSa9as4eWXX/ZbiuEDP//8M9OnT+eFF17g8OHD\njBw5kptvvpkaNWr4Lc13SotPxTASSiRhWozSw2mnncYtt9zC6tWrefvtt0lPT6dp06bccsstrFq1\nym95JRozKgmktM6hxhrzqXjHNHkjnCYR4aKLLuJvf/sbmzZtomXLllx33XW0a9eOJ598km+//bbA\n8+KpyU/i6lMRkfYejoIjxRUDEZkqIrtFZG1IXXURWSgiG0VkQcjmR0RknIhkiMh6EekV7fhG2cRW\nfxn5qVWrFmPHjmXLli1MmjSJzZs35+1te/nll/nuu+/8llgiCOtTEZHDwEoKDpeSy9mq2iQqAQXH\n/poI7FXVJ0VkLFBdVR8QkTbANCz2lxEljz/+OIcOHeLxx0tkElEjQRw9epT58+fz7rvvsmDBAho2\nbMgVV1xB37596dSpU6n8xySe+VRWqmrPIgZfHOnAuajqJ+4Gx1D64ywlBngTSAMeAK7Cjf0FbBOR\n3Nhfv9j8aBiFYau/DC9UqFC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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Actuator model\n", "Pend = ltu.lpf2(fc=0.93,Q=4.85) #Pendulum LTI model\n", "(w,h)=Pend.freqresp(w=2*pi*100) #Pendulum response at 100Hz\n", "Pend = ltu.ltiprod(Pend, alpha/100**2/np.abs(h)) #Correct the gain of the pendulum response\n", "\n", "#Coil inductance\n", "Rout = 73 #[Ohm] Coil driver's output resistance\n", "Lc = 10e-6 #[H] Coil inductance ** NEED TO CHECK THIS VALUE **\n", "fc = Rout/Lc/2/pi\n", "Coil = ltu.lpf1(fc=fc)\n", "\n", "Act = ltu.ltiprod(Pend, Coil)\n", "\n", "(w,h)=ltu.bode(Act)" ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "### Feedback Filters" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false, "run_control": { "marked": false } }, "outputs": [ { "data": { "image/png": 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BjThwcpCLhri6dPMB84IabIBlNxeqOti9rhtwOKjBBlgOvhftgRZAYVwFZjMU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\nVavqAatVZYwxoSmgZdWz0AsYJSK5gHN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oW7cuOXPmdDlyY4wJL7vjyIALFy4QFxfH8uXLWbJkCT/++CMxMTE0a9aMFi1a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\nffZZ1q1bR4kSgbySZbKScPR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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Feedback filters\n", "LagLead = ltu.ltiprod(ltu.zero(70),ltu.lpf1(fc=2000),ltu.lpf1(fc=2000))\n", "Boost = ltu.ltiprod(ltu.lpf1(fc=0.02),ltu.zero(0.2),10)\n", "\n", "MICH_GAIN = 50 #Gain in the K1:LSC-MICH filter bank\n", "UGF_SERVO_GAIN = 1/1.12 #Gain of the UGF Servo\n", "\n", "(w,h)=ltu.bode(LagLead)\n", "(w,h)=ltu.bode(Boost)" ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "### DGS filters" ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "The total transfer function of the digital system from the analog AA filter to the analog AI filter is reported [here](http://gwwiki.icrr.u-tokyo.ac.jp/JGWwiki/CLIO/Tasks/DigitalControl/Caltech_setup?action=AttachFile&do=view&target=analog_system_investigation.pdf)." ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false, "run_control": { "marked": false } }, "outputs": [ { "data": { "image/png": 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rIitFpF10Wm2M8cf74wbQpEkTvv76a+655x6mTZsW5ZaFlzeoLFu2LGr1iwhx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\n8d8jR46QkJCQKfCUKVOGMmX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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Time delay in the DGS\n", "Td=70e-6 + 3000.0/3e8 #70usec DGS delay + 3000m light travel time\n", "\n", "P0 = ltu.pole2(10.304784e3,1.0159584)\n", "P1 = ltu.pole(51.53319e3)\n", "P2 = ltu.pole(7.8430016e3)\n", "P3 = ltu.pole(346.96389e3)\n", "Z0 = ltu.zero2(67.205279e3,68.668973e6)\n", "\n", "AA = ltu.ltiprod(P0,P1,P2,P3,Z0)\n", "AI = ltu.ltiprod(P0,P1,P2,P3,Z0)\n", "\n", "P0 = ltu.pole2(2.9126274e3,1.1663357)\n", "Z0 = ltu.zero2(8.7381935e3, 3.7254539e6)\n", "P2 = ltu.pole2(5.3800106e3,8.3770775)\n", "Z2 = ltu.zero2(8.7381935e3, 5.5411258e6)\n", "\n", "DAA = ltu.ltiprod(P0,Z0,P2,Z2)\n", "DAI = ltu.ltiprod(P0,Z0,P2,Z2)\n", "\n", "DGS = ltu.ltiprod(AA,DAA,DAI,AI)\n", "\n", "f = np.logspace(2,4,1000)\n", "a=ltu.bode(DGS, w=f)" ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "### Open Loop Gain" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false, "run_control": { "marked": false } }, "outputs": [ { "data": { "image/png": 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iOzOJ91s9zplX2P4DDooxxpjAhP3Nj86ZSjdVTS1L6XtjjDHlL2yv/vKj+LrG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\nHwIJhd2QEsr7VHJycjhw4AC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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Open Loop Gain\n", "OPLG = ltu.ltiprod(Act, LagLead, Boost,Hrf,MICH_GAIN,UGF_SERVO_GAIN,DGS) #Open Loop Gain\n", "f = np.logspace(-1,3,1000)\n", "(w,h)=ltu.bode(OPLG,f)" ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "The theoretical open loop transfer function G has the following form." ] }, { "cell_type": "code", "execution_count": 66, "metadata": { "collapsed": false, "hide_input": true, "run_control": { "marked": false } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Open Loop Gain: G(s) =\n" ] }, { "data": { "image/png": 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BgU+ffsvP41+c9rcP9ah0Zfjwzf9i4i1basg239chEQompzHcRa8Vs6aJNO9z4e7aBoXN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\nRK5CYII=\n", "text/latex": [ "$$\\frac{6.92990366438969 \\cdot 10^{44} s^{14} + 3.05706600992631 \\cdot 10^{47} s^{13} + 2.55484839781279 \\cdot 10^{56} s^{12} + 1.12703265685184 \\cdot 10^{59} s^{11} + 2.50498992776018 \\cdot 10^{67} s^{10} + 1.10502155922032 \\cdot 10^{70} s^{9} + 2.79207686636597 \\cdot 10^{77} s^{8} + 1.23163048633873 \\cdot 10^{80} s^{7} + 1.22834013491393 \\cdot 10^{87} s^{6} + 5.41825821452829 \\cdot 10^{89} s^{5} + 2.43436177901796 \\cdot 10^{96} s^{4} + 1.07377690777736 \\cdot 10^{99} s^{3} + 1.81916778268998 \\cdot 10^{105} s^{2} + 8.02397214248258 \\cdot 10^{107} s + 1.00544936492533 \\cdot 10^{108}}{1.0 s^{24} + 12598265.6365121 s^{23} + 47860168587311.8 s^{22} + 7.30402802408645 \\cdot 10^{19} s^{21} + 4.57507583781277 \\cdot 10^{25} s^{20} + 1.4291578374472 \\cdot 10^{31} s^{19} + 2.60544916903589 \\cdot 10^{36} s^{18} + 3.29003901334975 \\cdot 10^{41} s^{17} + 3.09169274290079 \\cdot 10^{46} s^{16} + 2.26640330059425 \\cdot 10^{51} s^{15} + 1.33737880755041 \\cdot 10^{56} s^{14} + 6.48171496352864 \\cdot 10^{60} s^{13} + 2.62093056193966 \\cdot 10^{65} s^{12} + 8.88366107348671 \\cdot 10^{69} s^{11} + 2.52229652640252 \\cdot 10^{74} s^{10} + 5.98360995385174 \\cdot 10^{78} s^{9} + 1.16505437391728 \\cdot 10^{83} s^{8} + 1.82993849828781 \\cdot 10^{87} s^{7} + 2.23583692847016 \\cdot 10^{91} s^{6} + 2.01709109542622 \\cdot 10^{95} s^{5} + 1.21424580672562 \\cdot 10^{99} s^{4} + 3.59179409500874 \\cdot 10^{102} s^{3} + 4.8182902571891 \\cdot 10^{102} s^{2} + 1.23134771745139 \\cdot 10^{104} s + 1.54046116422229 \\cdot 10^{103}}$$" ], "text/plain": [ " \n", " \n", "──────────────────────────────────────────────────────────────────────────────\n", " 24 23 22 \n", "1.0⋅s + 12598265.6365121⋅s + 47860168587311.8⋅s + 7.30402802408645e+19⋅s\n", "\n", " 14 \n", " 6.92990366438969e+44⋅s + 3.05706\n", "──────────────────────────────────────────────────────────────────────────────\n", "21 20 19 \n", " + 4.57507583781277e+25⋅s + 1.4291578374472e+31⋅s + 2.60544916903589e+36\n", "\n", " 13 12 11 \n", "600992631e+47⋅s + 2.55484839781279e+56⋅s + 1.12703265685184e+59⋅s + 2.50\n", "──────────────────────────────────────────────────────────────────────────────\n", " 18 17 16 \n", "⋅s + 3.29003901334975e+41⋅s + 3.09169274290079e+46⋅s + 2.26640330059425e\n", "\n", " 10 9 8 \n", "498992776018e+67⋅s + 1.10502155922032e+70⋅s + 2.79207686636597e+77⋅s + 1.2\n", "──────────────────────────────────────────────────────────────────────────────\n", " 15 14 13 \n", "+51⋅s + 1.33737880755041e+56⋅s + 6.48171496352864e+60⋅s + 2.620930561939\n", "\n", " 7 6 5 \n", "3163048633873e+80⋅s + 1.22834013491393e+87⋅s + 5.41825821452829e+89⋅s + 2.4\n", "──────────────────────────────────────────────────────────────────────────────\n", " 12 11 10 \n", "66e+65⋅s + 8.88366107348671e+69⋅s + 2.52229652640252e+74⋅s + 5.983609953\n", "\n", " 4 3 2 \n", "3436177901796e+96⋅s + 1.07377690777736e+99⋅s + 1.81916778268998e+105⋅s + 8.\n", "──────────────────────────────────────────────────────────────────────────────\n", " 9 8 7 \n", "85174e+78⋅s + 1.16505437391728e+83⋅s + 1.82993849828781e+87⋅s + 2.235836928\n", "\n", " \n", "02397214248258e+107⋅s + 1.00544936492533e+108 \n", "──────────────────────────────────────────────────────────────────────────────\n", " 6 5 4 \n", "47016e+91⋅s + 2.01709109542622e+95⋅s + 1.21424580672562e+99⋅s + 3.591794095\n", "\n", " \n", " \n", "──────────────────────────────────────────────────────────────────────────────\n", " 3 2 \n", "00874e+102⋅s + 4.8182902571891e+102⋅s + 1.23134771745139e+104⋅s + 1.54046116\n", "\n", " \n", " \n", "───────────\n", " \n", "422229e+103" ] }, "execution_count": 66, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#Open Loop Gain as Rational Function\n", "print('Open Loop Gain: G(s) =')\n", "sp.Poly(OPLG.num, s)/sp.Poly(OPLG.den, s)" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false, "hide_input": true, "run_control": { "marked": false } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Time delay is 80.0usec\n", "Multiply the above transfer function with the following to include the time delay.\n" ] }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGIAAAAXBAMAAAACZIdPAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n", "text/latex": [ "$$e^{- 8.0 \\cdot 10^{-5} i s}$$" ], "text/plain": [ " -8.0e-5⋅ⅈ⋅s\n", "ℯ " ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "print('Time delay is {:.5}usec'.format(Td/1e-6))\n", "print('Multiply the above transfer function with the following to include the time delay.')\n", "sp.exp(-Td*sp.I*s)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Saturation of the excitation signal" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It was found later that the excitation signal was too large and saturated the DAC. Here, we try to include this effect.\n", "\n", "The DAC saturates at $2^{16}/2 = 32768$ counts." ] }, { "cell_type": "code", "execution_count": 77, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 77, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Load the frequency points to calculate\n", "TF=np.loadtxt('data/TFs/Data/RF-Lock-OPLG.txt', comments='#')\n", "f = TF[:,0]\n", "\n", "#Open loop Gain from the excitation injection to DAC\n", "FBFLT = ltu.ltiprod(LagLead, Boost, MICH_GAIN, UGF_SERVO_GAIN)\n", "#Closed loop Gain from the excitation injection to DAC\n", "CLG = ltu.ltiprod(FBFLT, ltu.ltiinv(ltu.ltiadd(OPLG, 1)))\n", "#Excitation voltage (we used the envelope mode of DTT)\n", "excV = np.piecewise(f, [f <=1, (1 2**15], \n", " [lambda x: x,\n", " 2**15])\n", "#Ratio between saturated and non-saturated signals. This is the reduction factor for the measured OPLG.\n", "GainRatio = SatSig/DACSig\n", "\n", "#Frequency response of the Open Loop Gain Model\n", "(w, OPLGSat) = OPLG.freqresp(w=2*pi*f)\n", "#Multiply the OPLG with the gain ratio to get the saturated OPLG\n", "OPLGSat = OPLGSat*GainRatio\n", "\n", "plt.loglog(f,np.abs(OPLGSat))\n" ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "## Comparison with the measured Open Loop Gain" ] }, { "cell_type": "markdown", "metadata": { "hide_input": false, "run_control": { "marked": false } }, "source": [ "Below is the comparison of the model and the measured open loop gain. With the saturation effect taken into account, the model and the measurement agree well except for the phase" ] }, { "cell_type": "code", "execution_count": 79, "metadata": { "collapsed": false, "hide_input": false, "run_control": { "marked": false }, "scrolled": true }, "outputs": [ { "data": { "image/png": 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GG1p/joyM5Pnnn+f555//1b5jx45l7NixXe26x+poBH/KGDOpo51FJNbJ/VFK\n2SkoCAoKrMUiQBqQRmPjb6iqgtLSA0tJ9TbWbCnj2z1r+DJsDeE9ivFPeJ+G8DXUB6wnPrAHif4p\nFJYPoG9qT3rF9aRnrLXEhMS474sqpZTqVLsFnTHmn53tbE+MUqr7BQZCr17Wcvrp+9fGAoVAIXV1\n1qtXKiqsWTTWVO5jeU0Fy2pX8B9Ty7vhZYSl/QSxZdSHriHQL5C00J70jM2hb1oOBUk9yYnJISc2\nh6zoLI+YSUMppXxZR/fQhQB/ALYB04C7gN8Aa4CHjDGbu6WHSimni4yEfv2sxWI9kTtvXh1Dh57D\njh3W3Ljl5bBmjWF5xRZWbihjyY4yvm4sJzCpmMCkf9MSVU59YDVRAUn0CM8hLyGHWAlmRMBSsmOy\nyYnJIT0qXS/nKqWUi3U0yk4GGoFw4A5gKfAsMAJ4E/itqzvnC3S+RcdifXm+xe6cyzU6GgYPthbr\nUm6CbTmalhZYt+5AwVda1sSyympKNpbzza5ydviVMTX1a/wTymkKr2BvwEbiAtLIiMwmPymbgpRs\nsmOyyIrOIismi4yoDAL9A3UuVyfTscWxWF/PF+X92p3LVUSWGmP6i0gAUG2MSWmzbZExZlB3dbIr\ndC5XZS+dm9O5Ghqsy7llZbaCr7yBZWvXsmZLBTV7KmgIrSAsvQL/uEoawiqp919HdEASPSKzyE3I\nIi8pq7Xgy4zOJCM647Bfx+JMmi/KXjqXqzoUd8zl2gBgjGkSkdqDtjUfIr7biMgZwD8BP+A1Y8yj\nneyilOomQUGQm2sttjVAL9sCO3dahV5lpXUP35ryJlbW1FC2tZIZuyv5NKKS8LRi/OM/pCl8LbsD\nqgiQQFJCM8mMySAvMZOe8VahlxGVQUZ0BumR6Xofn1LKp3VU0PWwvYtO2vyM7XO6y3vWDhHxw7r0\neypQCxSJyMfGmJXu6pNSyn5RUQfeuWcJALJsC2zfbhV7lZXWFGpVaw1ltdso21LFql1rmd1QRUD8\nWkKSFyMx1TSGrqU+oJYwvxiSQzPIiOpBr8Qe9EzIICO6B+mR6aRHpZMemU54ULibvrVS3SsrK8un\nZknwJm2nKXOmjgq6P7X5ed5B2w7+3J2OBkqMMZUAIvIe1jvztKBT6ggQE2MtBwo+AeJsy2CMgc2b\nYe1aq+CrqYG11S2sWb+R8i1rWb2rmtkN1ZjItYQkLcIvpobmsBr2BtYSKCHEB6WTEp5OZkw6vZLS\nyYlPp0eaaYpmAAAgAElEQVRUOqmRqaRFppEUnqQPcSivV1FR4e4uqG7W0WtLOnwHnRulA2vbfK7G\nKvKUUj5ABBITrWXIkP1r/YAU2zIMsC7tVldDba31EEdtraF8w1bKN9dQU1fD93trmNZcQ0vEfILj\nP8Uvah1NYbU0+G8m3C+B+KA0UsJTyYxNo2dSKllxqaRGpLJtmz9JO5pIDk/Wy7xKKY/R0WtLpgHt\n3lFpjBnjkh450XXX3dH6c2HhcRQWDndjbw6trq6OyMhIj2+/K+04so+9sZ3FdbS9vW21tXXMm3fw\nbaKex9W54qxjdLUNZ+fL/pj9Z/z69Nm/xXpit66uJ5GRkezeLWza5Mfmzf5s2uTPxs0tlG1Yz+Z9\n29iwdwMrm9ZTx3okspjA2PWYiFrMNxtoDNpIoAknUlKIDUgkISSJ5IgE0qMTSAxNJC44kfjgROKC\nEokNjsdf/B3+nRwOHVsci9WxRccWe2OdlSvFxXMoLv7Rrn7Zo6OnXE+0/Xge1v/2vm37fDGwwRhz\nm9N64QARORa43xhzhu3zBMAc/GCEtzzlOm/ePIYOHerx7XelHUf2sTe2s7iOtre3zVueWnR1rjjr\nGF1tw9n54sxcMQZ27IANG2DWrM3ExCSwbn0LFRu2UrllPTU71rGhfh3bGjawy2wgKG49gTEbIGID\nTSHrafDbRphfHHFBySSGJZMalURmXDI9YpNIjkgiOTyZpPAkksKTSI5IJiQgxK7fw+F8f09pX8cW\n99OxxbFYV+QKuPApV2PMt7YDPGGMaXv0aSLiznvoioBcEckC1gEXYRWZSinlEiIH7u2rq2vAGo/9\nOPB+vv6tsc3N1j1+69YdWGrWNVG+YTNVW9ezvm4jRXs3MLNhI03BGwmOX0lgzEYI30hT8Ab2+m8k\n0C+Y6IBEEsKSSI1MokdcEqlRia1FX2JYIonhia1/BvkHuecXo5TyGPbc+RsuIj2NMWUAIpKD9bJh\ntzDGNIvIzcCXHHhtyQp39Ucppdry94fkZGuxXswM1lC7/x6/A+rrrbN+bZd16wxVG3dStXkjtTs2\nsWj3RmY1bMQ/ahNhCeUExv6MRGykJWQT+wI2sbtlM6EBYSSGJ5IccaDQa6lrYYTfCAoSCsiPzycx\nLFGfelTqCGZPQXcbMEtEyrAeN8sCrnNprzphjJkBFHQaqJRSHiw0FLKzreUAAaJtSx5gXfLdtu3A\nGb/aWtsrXaqgsspQuX47VVs2sT5kE/GZm4hO20RLaBmLy79nZ9CrbGhahZ+foSAhv7XAK4gvoCCh\ngIL4An24Q6kjQKcFnTFmhojkAb1tq1YaY/a5tltKKaX2E4G4OGs5MP9u61YgFohlx458qqqsQu/7\n7ysxu7KoqIDyCkP5+i0sDFxFVd5qfshYhYmfwp7QlWyjnB7hOQxO68/gtP70T+rPgKQB9Iztib9f\n9z7IoZTquo6ech1ijJkPYCvgFnUUo7pG51t0LNaX51vszrlc3dGGzuV6+KKjYcAAaznqqEAOfA1r\nPt7duxOorDyeigprlo6yMlhdto8VG1fx2d6lfJG2lOCMN2mMXcK+wI2kB/emb0J/js0ZwNFZAxiQ\nPIDUiFRERMeWLvbHE+nY4lisp+ZKR0+5LgJOwhoJ2vOVMeYoF/TrsHnLU67K/bzlSTTlGY7UfDHG\nupy7Zg2UlsKy0joW1iynZMcS1jUvgeQlmKQl+Psb0gL60yduIEdnD+DkvgMY0qM/EUER7v4KHudI\nzRXlGq6cyzUaKKbjgm5TVw+slFLKc4hAWpq1/OY3AJHAMcAxGAPr18OqVYaiFRv4uWIJK6qW8MPc\nOTwQ9hIkLiekKZVUvwEUxAxkWOZATuk3gOP75BLgr5dtleoOHb22JLsb+6GUUspDiUBqKqSmCied\ntP9p3ZEANDZC6Zpmvl1aypw1i1m6fgnPVb7Nw3MX0xyygdA9fUhhIPkxAxnecyBnFQ5kSO8E/Pzc\n+pWUOuLohIVKKaW6LDAQ+vT2p0/vAv4fBcAFrduqN9XxxYKlzC5dwqL1i/jXog+5f8ViaAwjau9A\nskMGMjh1ICf3HcjZx/QmIVbfp6dUV2lBp5RSyiV6JEZyzajjuGbUca3rjDEsXbuWz+YtZnbpYr7f\n8ClT1/2NvT+UE1iXR0LzQHLCBjI4dRAnFAxk+IAUevQQ9BV6SnVMT3q7WW2ta+f5c1b7XWnHkX3s\nje0srqPtrv5du1p39N8Zx+hqG87OF1/OFfDcsUVEGJCZyYTzfsu0u/7M97c+Sf3jy6m7dysfXPoG\nfzj6NAJi1/HfTY9x2ewBZD2XRMA1p5F0+e0c8//e5Ka/zuetKdXs3OncfvpyvujY4lisp+ZKpwWd\nWC4Tkf+zfc4UkaNd1iMf46mDrjPa0YLOuXTQdSzWl3MFvG9siQgJ5XdHF/LUFVfy7cSnqPnbVzT8\ndRPV9yzi/Vvv5A9np+CfN5OpDVcwdkUeMff0I+aaizn69kcY/9x0vp5XTXPzr99soGNL53RscSzW\nU3PFnkuuzwMtwCnAg0Ad8B9gmMt6pZRSyueJCGmRaZw/KI3zB53Run7Oz3MITA9j+rzFfLdqMVOr\nnuKZ6kWYfzcT0zCQnuEDGZA0kBG5A0n2a3TjN1Cq+9hT0B1jjBkiIgsAjDHbRETvXFVKKeUWQf5B\nDO0xmGE9Bv9i/bLKDXw4ezE/lC7iu4rveL/8WfaErcLv8wxi9w0kM3gg/RMHMjx3IKcMySIv10/v\nzVNHDHsKukYR8QcMgIgkYp2xU0oppTxGv6xk+mWNZP8rVQB+/PknGiIj+WrZYoqqFvPD9pf5YPEi\n9i3eif+W/qT6DaR/4gByo2KJScklt0eM+76AUofBnoLuaeAjIElEHgZ+D9zr0l4ppZRSThDoH8Bx\nfftxYt9+wMWt67fWb2XW8iXMWLCEoqpFfLd2Ic+8cD3+jbEkmQH0iRvIcT0HcGr/AQwvKHDfF1DK\nTp0WdMaYd0SkGDgVa9aIc4wxK1zeMx+hc7k6Fuupc+h1B51v0bFYX84V0LGls9i40DjOKzyR8wpP\nBKyb1ZOSU/h6fgWfFi3mp/LFvLj2I/4+5yFaoioI2dOT1KkDyY8ZQGFmf07pN4DfDMgiKNDP6/NF\nxxbHYj11bOloLte4jnY0xmx1SY+cROdyVfbS+RaVIzRffM/adXv5csEKZpcsYfGGpVTWL2Fb4BKa\nA3YQWT+A/glHcfaQozh90GD6J/UnJCAE0FxRjjncuVw7KujKse6bEyAT2Gb7OQaoMsbkdPWg3UEL\nOmUvHXSVIzRf1H7VW7by9szFfDJ3IQvXL6AlaSHNMavJjMxleM5RJDTlMGbYSQxNG0pkcKS7u6s8\nnMsKujYHeAX4yBgz3fb5TKzLrtd39aCddkrkPmAcsNG26s/GmBm2bROBq4Em4FZjzJfttKEFnbKL\n/gOtHKH5og6lpQXmzYP/fLyXf3+7nM0BC4jvX0RI9hKqGhbRP6k/J2efzEnZJ3F85vFEBEW4u8vK\nw3RHQbfEGDOgs3XOZCvo6owxTx60vg/wLtY78HoA/wPyDlW5aUGn7KX/QCtHaL4oe6xZA889t4MF\nC6IpWlhPcK+fiB44i31p37AlaD65kQMZmXcyZ/WxCrywwDB3d1m52eEWdPY85VorIvcCb9s+Xwp0\nx2uxD/Wlfge8Z4xpAipEpAQ4Gvi5G/qjlFJK2aVXL7jkkt08+WQ0xoRSXX0yy5adzPLlD7B4xR6K\n1v3IC1/O4tnMB2hJWkiK3wCOzxzO+cOGc0LOcFIjU939FZSXsWcu14uBRKxXl3wEJNH22W/XuVlE\nForIqyISbVuXDqxtE1NjW+e1vG16Hlfto9PzdE6n53Es1pdzBXRscTTWlfkiAhkZcMYZcPvt8OYr\nYSz79FTqpz9E5X0/8NHwDZzS8ghz/pfApf94g6zH+hP/UA6/feNSnp37HAvXL6Sppcmu79EVOrY4\nFuupY0unBZ0xZqsx5lZjzFG25VZnPOEqIjNFZHGbZYntz9FY0431NMYMBtYDTxzu8TyVDrqOxXrq\nX6TuoIOuY7G+nCugY4ujse7IFxFIS4MxZ4bz1kMnUj1lIhue+pTJ/Tdxcs3nzHn7VO7+5wJOfvYS\noh6O4/hXTuJPX/6JD5Z9QMX2Cpx1W5GOLY7FeurYYs89dN9gmyWiLWPMKa7q1EHHzwKmGWMGisgE\n69DmUdu2GcB9xphfXXIVETNu3O2tnwsLj6OwcHh3dNkhtbW1Ln0vjbPa70o7juxjb2xncR1tb29b\nbW0daWme/wSaq3PFWcfoahvOzhdX5Iq1TfPFme3r2NI+Y6Cy0p+ffw7h+3m7WbhpMRF5cwnJ/Zm6\nyGIkoJF+MYPpGzOIvtGD6BszmPjgRIePo2OLY7HOypXi4jkUF//Yuu2VV548rHvoMMZ0uACFbZbj\ngSeBxzrb73AWIKXNz7cB79p+7gssAIKAHKAUW1F6iDaMNygqKvKK9rvSjiP72BvbWVxH29vbVlRU\nY9ex3c3VueKsY3S1DWfniytyxdqm+eLM9nVssV9DgzGzZxvz4IPGnHiiMaHJ1ab3OR+Z4++baAr/\ndZqJeSTG9HiyhxkzZYx5YNYDZtqqaaZ2Z22n7erY4lisq8YWW93S5drJnpkiig9aNVtE5na5grTP\nYyIyGGvO2ArgeltflovI+8ByoBG40fZLUEoppY5ogYEwfLi1/OUvsGdPOj/8kM5XX53DV5OhucRw\n3EVlDM2fz7bG+Tz989MUrysmyD+IwtRChqQOoTC1kMK0QtIj0xHp+skg5Xk6LegOmjHCD+tMXXQ7\n4U5hjLmig21/B/7uyuMrpZRSni4sDEaNshaAjRuF117rxbM39CIj4wJuvhmm3WpYX1/F/HXzKV5X\nzIvFL1I8rRg/8aMwrZChqUOJ2hNFWl0aaZH6Oh5vZs9rS4o5MGNEE1AOXOPKTvkSnW/RsVhPnUOv\nO+h8i47F+nKugI4tjsYeCfmSlAQTJ8Kf/gTTpsGzz8LttwvXXZfFdddlcW6fcwHrVqvqndXMq51H\n8bpiPl3/KY+8+AgBfgEUphYyNG0ox2ccz7E9jnXaDBc6tjjeF0fZ81BEiDFm70Hrgo0x+1zWKyfQ\nFwsre+mLYpUjNF+UvTwhV5Yvh+efh3ffhdNOgxtvhGOOgdDQX8YZY6jaUUXxumKKaoqYvXY289fN\npyChgBEZIxiRaS36fjzX6Y6ZIuYbY4Z0ts7TaEGn7OUJg67yHpovyl6elCs7d8LkyfDaa7BihXU2\nLy8PcnOtP/f/3KsXhIRY++xr2kfxumJ+qPqBH6p+YPba2cSGxDIicwS/yfwNZ+adqZdpnchlBZ2I\npGC9tPdt4BIOzNwQBbxojOnd1YN2By3olL08adBVnk/zRdnLU3OluRmqqqCkxFpKSw/8XFkJ6enw\n5z/DVVeBX5u31baYFlZuXsn3ld8zq3IWX5R+Qa+4XozOH82YgjEMSh6kD1ocBlcWdGOBK4GhwLw2\nm+qAN40xH3b1oN1BCzplL08ddJVn0nxR9vLGXGlqgnnz4LbbrPfgPf88DGnnelxjcyOz187mk1Wf\n8MmqT2hobmB0/mhGF4zm5OyTCQ4I7t7Oe7nuuOR6vjHmP109gLtoQafs5Y2DrnIfzRdlL2/OlZYW\nePNN60zd+efDX/8KsbHtxxtjWLl5JdNWT+OTVZ+wdONSRvYayeUDL+fM3DMJ9A/str57q8Mt6Nqd\n+ktELrP9mC0itx+8dPWA6pd0eh7HYj11ypXuoNPzOBbry7kCOrY4GuvL+XKo/vv5wdVXWw9VAPTp\nA2+8YRV6hyIi9Ensw13H38UPV/9AyS0ljOo5ikdnP0rmPzO54aMbWL5pudP76ez9vHls6Wgu13Db\nnxFA5CEW5QQ66DoW66l/kbqDFnSOxfpyroCOLY7G+nK+dNT/uDh47jn47DN46SUYMQIWLOi4vX37\noGF7IiPjxzH76tnMGjuL+t31jHxrJMe8egwvznuR7Xu3O7WfztrPm8eWdt9DZ4x5yfbnAy47ulJK\nKaU8XmEhzJljnaU74ww480yIjoYtW2Dz5gPLli1WQZeQYJ3NS0mBK68s4NJ+43n1kleZuWYmbyx8\ngwn/m8BZeWdx9VFXc0rOKfhJR+eXlD3smSkiERgHZLeNN8Zc7bpuKaWUUsqT+PnBNdfAuedarz8J\nDIRhw6ziLT7e+jMhASIiQMQq6GbNsorAv/ylPyNHBnDVVWfy7rlnsqNhC1OWTuHOL+9kd+Nuri+8\nnqsGX0V8WLy7v6bXsmemiI+B74H/Ac2u7Y5SSimlPFlcnDUbRWf8/OCUU6xl1qzFlJYO4ZFH4Lrr\n4LLL4rnqqpu56fqb+Kn6J16Y9wK9nu7FmIIx3DD0Bo7tcay+AsVB9hR0YcaYu13eE6WUUkodkSIi\nWrj2Wrj2Wli1ynqCduRISEgQevc+jszM45iYsYVVW97koqlXEBUazk3H/D8uHXCp06YfO9LZU9B9\nKiJnGWOmu7w3PkjnW3Qs1lPn0OsOOperY7G+nCugY4ujsb6cL909thQUwN//br0KpagIysutFxpX\nrIhnQ9UdRFTeRilfccuPL3Bz1p/pWX8B913we0Zk5B/2sZ0R66m5Ys976OqwnnjdBzRizRhhjDFR\nLuuVE+h76JS9vPldUar7ab4oe2mudJ0xsG0bFK2s4R8z32LW+o8ISi3h3H5nc17fczm91+mEB4V3\n3pAXcfmLhb2VFnTKXjroKkdovih7aa44z6pVcOUtNayL/piUkz9i+Y6fOSXnFM7tfS6/zf/trx6m\naGxupK6hjp37drJz304WrthJlMnknJMz3fQNOne4BZ09T7keatKPHUClMaapqwdWSimllLJHQQHM\n+SKdN964kQkTbuSqq7YxoNenfLzqI/44449kRmeyt2lvawHX2NxIZFAUfo1R1G+Pork+gqbwShb1\nWEn/vCPznjx7Lrn+BAwBlthWDQCWAtHADcaYL13awy7SM3TKXvp/0coRmi/KXporrrFhA4wfD3Pn\nwosvwvEn7WHl5pVEBEUQ6hfFz99FMeWtUL76n3D22TB2LJx6Khzz9yvZVJFMxSuP4okP0Lps6q82\naoGjjDGFxphCYDBQBowEHuvqgUXk9yKyVESaDz4LKCITRaRERFaIyKg264eIyGIRWS0i/+zqsZVS\nSinlnZKTYcoUeOYZGDcOrr86jPqyIbz0t3yG9UnhqcfCOON0obIS3nkHRo0Cf3/46Ka/U5v8Gg89\nX+Lur+AS9hR0+caYZfs/GGOWA72NMWWHeewlwLnAt21Xikgf4EKgD3Am8LwceBnNC8A1xph8IF9E\nTj/MPridTs/jWKynTrnSHXTqL8difTlXQMcWR2N9OV+8dWw56yxYuhSSkqx5Z0ND4bvvYPZsq9CL\njv7lfhmxqdw69G7+Ou82Kiu73k9PzRV7CrplIvKCiJxoW54HlotIMNZTr11ijFlljCnBemq2rd8B\n7xljmowxFUAJcLSIpACRxpgiW9xk4JyuHt9T6KDrWKyn/kXqDt466LpiP28edLuLji2Oxfpyvnjz\n2BIRAU88YT008de/Qv4h3mzSdr+/jbmV6OwSzrlrOoe6K8ubxxZ7CrorgVJgvG0ps61rBE52QZ/S\ngbVtPtfY1qUD1W3WV9vWKaWUUkp1Ksg/iNf/8BQrMsfz0qsN7u6OU3X6lKsxph54wrYcbFdH+4rI\nTCC57SrAAPcYY6Y50M8uue66O1p/Liw8jsLC4a4+pMNqa60bZz29/a6048g+9sZ2FtfR9va21dbW\nufS/gbO4OlecdYyutuHsfHFFrljbNF+c2b6OLe7na2NLKoPpm5zFbVOfokfqlaSkNLcb25V+2Jsr\nxcVzKC7+0ZGv0jFjTIcLkAf8G1iOdXauDCjrbD97F+AbYEibzxOAu9t8ngEcA6QAK9qsvwh4oYN2\njTcoKiryiva70o4j+9gb21lcR9vb21ZUVGPXsd3N1bnirGN0tQ1n54srcsXapvnizPZ1bHE/Xxxb\nVm9ebcLujzcn/bbWtLQ4dgxXjS22uqXL9ZQ9l1zfwHoYoQnrEutk4G1nFJNttL2P7hPgIhEJEpEc\nIBeYa4xZD+wQkaNtD0lcAXzs5H4opZRS6giXF5/HDcdew+Kkibzxhrt74xz2FHShxpivsN5ZV2mM\nuR84+3APLCLniMha4Fis+WI/h9anaN/HOiM4HbjRVrkC3AS8BqwGSowxMw63H+6m8y06Fuupc+h1\nB53L1bFYX84V0LHF0VhfzhdfHVvuO+le/PNncvuTP1Ndbf8xPDVX7Hmx8BxgBNZl16+xHlJ4xBhT\n4LJeOYG+WFjZS1/+qRyh+aLspbni+SYvmsyf//ssA+f+xGef+rn1hcPd8WLhW4Ew4I9AIXA5MLar\nB1RKKaWU8gSXDbyMHun+LA2YxOTJ7u7N4em0oDPGFBljdhljqo0xVxljzjPG/NQdnVNKKaWUchU/\n8eOZM5+m/rh7uOOeHdTUuLtHXdfua0tE5JOOdjTGjHF+d5RSSimlus+w9GGM6XMmK659iEsu+Qef\nfw5hYe7uleM6eg/dcVgv+J0C/MyvZ3RQSimllPJ6fzv1b/Rf3Z/hudcyenRvpk3zvqKuo0uuKcCf\ngf7Av4CRwGZjzLfGmG872E85QKfncSzWU6dc6Q7ePD2Ps/fz5ul5uouOLY7F+nK+6NgCyRHJTDh+\nAvUjbiUtDcaMgfr6rrXncVN/GWOajTEzjDFjsV4tUgrMEpGbXdYbH6SDrmOxnvoXqTvooOtYrC/n\nCujY4misL+eLji2WG4fdSPGGedz52FJSUuB3vzt0UeepudLhQxEiEiwi52G9SPgm4GngI5f1Riml\nlFLKDUIDQ7ko+yKe+OkxJk2CxEQ455z2z9R5mnYLOhGZDPwIDAEeMMYMM8Y8ZIzx4mdAlFJKKaUO\n7fdZv+fT1Z9SXVfJpEkQFwfnngt797q7Z53r6AzdZVjzuN4KzBGRnbalTkR2dk/3lFJKKaW6R2Rg\nJNcOuZYnfnyCgAB46y2IifGOoq6je+j8jDGRtiWqzRJpjInqzk4qpZRSSnWH2469jbcXv82m3ZsI\nCIC334bISDjvPNi3z929a589M0UoF9L5Fh2L9dQ59LqDr8632NVYX84V0LHF0VhfzhcdW34ZmxqZ\nygV9L+CZuc8AEBAA77wD4eFw/vkQH++ZudLpXK7eSudyVfbS+RaVIzRflL00V7xX6dZSjnvtOMr+\nWEZkcCQAjY1w8cWQkwOPP+78Y3bHXK5KKaWUUj4jNy6XU3JO4ZX5r7SuCwyEKVPgnnvc2LEOaEGn\nlFJKKXWQu4+/myd/fJJ9TQdunAsMtB6S8ERa0CmllFJKHWRI6hD6JfXjnSXvuLsrdtGCTimllFLq\nECYcP4HHZj9Gc0uzu7vSKbcVdCLyexFZKiLNIjKkzfosEdkjIvNty/Nttg0RkcUislpE/umenjuX\nTs/jWKynTrnSHXR6HsdifTlXQMcWR2N9OV90bGk/9qTsk4gOiea/K/9rd3seOfWXiy0BzgW+PcS2\nUmPMENtyY5v1LwDXGGPygXwROb07OupKOug6Fuupf5G6gw66jsX6cq6Aji2OxvpyvujY0n6siDBx\nxEQemf0I+9+c4am54raCzhizyhhTAhzqEd1frRORFCDSGFNkWzUZOMeFXVRKKaWUjxtTMIZdDbv4\nuvxrd3elQ556D1227XLrNyIywrYuHahuE1NtW6eUUkop5RJ+4sfdx9/NI7MfcXdXOuTSFwuLyEwg\nue0qwAD3GGOm2WK+Ae4wxsy3fQ4EIowx22z31v0X6AsUAH83xoyyxY0A7jLGjGnn2GbcuNtbPxcW\nHkdh4XBnf8XDVltb69I3Rzur/a6048g+9sZ2FtfR9va21dbWkZYWaVc/3cnVueKsY3S1DWfniyty\nxdqm+eLM9nVscT8dWzqPbWxp4JxvhvN44WvE7El0Sq4UF8+huPjH1m2vvPLkYb1YGGOMWxfgG2BI\nZ9uBFGBFm/UXAS90sJ/xBkVFRV7RflfacWQfe2M7i+toe3vbiopq7Dq2u7k6V5x1jK624ex8cUWu\nWNs0X5zZvo4t7qdji32xT/34lPn9+7932dhiq1u6XE95yiXX1opURBJExM/2c08gFygzxqwHdojI\n0SIiwBXAx27prRPpfIuOxep8i55/DJ3L1TPo2OJYrC/ni44t9sVeO+RaZlXMoj6svsttHJFzuYrI\nOcAzQAKwHVhojDlTRM4DHgQagBbg/4wx0237FAJvAiHAdGPMrR20b9z13ZR30fkWlSM0X5S9NFeO\nPPfPup9t9dv415n/cnrbhzuXa4AzO+MIY8x/se6PO3j9h8CH7exTDAxwcdeUUkoppX7lzuF34i/+\n7u7GIbmtoFNKKaWU8iYRQRHu7kK7POUeOqWUUkop1UVa0CmllFJKeTkt6NxMp+dxLNZTp1zpDjo9\nj2OxvpwroGOLo7G+nC86tjgW66m5ogWdm+mg61isp/5F6g466DoW68u5Ajq2OBrry/miY4tjsZ6a\nK1rQKaWUUkp5OS3olFJKKaW8nBZ0SimllFJeTgs6pZRSSikvpwWdm+l8i47F6nyLnn8Md8+3aG/M\nkZwroGOLo7G+nC86tjgW66m54ra5XF1N53JV9tL5FpUjNF+UvTRXlCMOdy5XPUOnlFJKKeXltKBT\nSimllPJyWtAppZRSSnk5LeiUUkoppbycFnRuptPzOBbrqVOudAednsexWF/OFdCxxdFYX84XHVsc\ni/XUXHFbQScij4nIChFZKCL/EZGoNtsmikiJbfuoNuuHiMhiEVktIv90T8+dSwddx2I99S9Sd9BB\n17FYX84V0LHF0VhfzhcdWxyL9dRccecZui+BfsaYwUAJMBFARPoCFwJ9gDOB50Vk/2O8LwDXGGPy\ngXwROb37u62ONMXFc9zdBeVFNF+UvTRXVHdyW0FnjPmfMabF9vEnoIft5zHAe8aYJmNMBVaxd7SI\npLR8i7gAACAASURBVACRxpgiW9xk4Jzu7LM6MhUX/+juLigvovmi7KW5orqTp9xDdzUw3fZzOrC2\nzbYa27p0oLrN+mrbOq9WXFzsFe13pR1H9rE3trO4jra7+nftat3Rf2cco6ttODtffDlXQMcWR2N9\nOV90bHEs1lNzJcBlLQMiMhNIbrsKMMA9xphptph7gEZjzBRX9sVT6aDrWKyn/kXqDjroOhbry7kC\nOrY4GuvL+aJji2Oxnporbp36S0SuBMYBpxhj9tnWTQCMMeZR2+cZwH1AJfCNMaaPbf1FwInGmBva\naVvn/VJKKaWU1zicqb9ceoauIyJyBvAn4IT9xZzNJ8A7IvIU1iXVXGCuMcaIyA4RORooAq4Anm6v\n/cP5pSillFJKeRO3naETkRIgCNhiW/WTMeZG27aJwDVAI3CrMeZL2/pC4E0gBJhujLm1u/utlFJK\nKeVp3HrJVSmllFJKHT5PecpVKaWUUkp1kRZ0Sv1/9s47PK7iatzvqPfiJrkb3B0CxjLNQGxKjKkm\nQBJTQgngJCS/ND5/QBop35cQkpBGQigOJaGZ5KMGsCkJzdh4bYwNNrjbsmTJktVldZ3fH1drraTd\nu/fu3rt7pZ33efbR6t6ZM2d3R6OzZ+aco9FoNBrNICdhDDqlVJZS6iGl1L1KqSvirY/G2yiljlJK\nPaCUWhFvXTTeRim1WCl1n1LqcaXUZ+Otj8bbKKVmKKXuUUqtUEp9Nd76aLxNj+2yTil1Xti2iXKG\nTil1FVArIv9SSj0hIkvirZPG+yilVojIF+Kth8b7KKUKgF+JyI3x1kXjfXpKWj4sIlfHWxeNd1FK\n/QRoBLaIyItmbQeth04ptVwpVamU2tTv+iKl1MdKqW1KqVsCbo2jtwJFV8wU1XiCCOaLJkGJYq78\nAPhTbLTUeIVI5otS6kLgBXorJGkSALtzRSl1NrAFqMIozGDKoDXogAeBcwIvKKWSgLt7rn8KuFwp\nNaPndim99WJ1jrrEw+58OdIsNuppPITtuaKUugMjldLGWCqq8QS254uIPC8i5wNXxVJRTdyxO1cW\nACcBVwA3hBM+aA06EXkbqO13+URgu4jsFZEO4Algcc+9p4HLlFJ/Ap6PnaYaL2B3viilhiml7gFm\na89dYhHBXPl/wFkY68vSmCqriTsRzJf5SqnfK6X+Avwrttpq4onduSIiPxCR7wKPAveHkx+3ShEu\nMZbebVWA/RhvFiJyGPhyPJTSeBaz+VIDBC0rp0lIzObKH4E/xkMpjWcxmy9vAG/EQymNJwk5V/yI\nyCNWBA1aD51Go9FoNBqNxmCoGXRlwISA38f1XNNogqHni8Yqeq5o7KDni8Yqjs2VwW7QKfoeWl8H\nTFFKTVRKpQFLgOfiopnGi+j5orGKnisaO+j5orGKa3Nl0Bp0SqnHgNXANKXUPqXUdSLSBfw/YBXw\nEfCEiGyNp54ab6Dni8Yqeq5o7KDni8Yqbs+VhEksrNFoNBqNRjNUGbQeOo1Go9FoNBqNgTboNBqN\nRqPRaAY52qDTaDQajUajGeRog06j0Wg0Go1mkKMNOo1Go9FoNJpBjjboNBqNRqPRaAY52qDTaDQa\njUajGeRog06j0Wg0Go1mkKMNOo1Go9FoNJpBTlwNOqXUOKXU60qpj5RSm5VS3+y5XqiUWqWU+kQp\ntVIplR/Q5zal1Hal1Fal1ML4aa/RaDQajUbjDeJa+kspVQwUi8hGpVQOsB5YDFwHHBKRO5VStwCF\nInKrUmoW8ChwAjAOeBWYKrp+mUaj0Wg0mgQmrh46EakQkY09z5uArRiG2mLg4Z5mDwMX9zy/CKNw\nbaeI7AG2AyfGVGmNRqPRaDQaj+GZM3RKqUnAbGANUCQilWAYfcConmZjgdKAbmU91zQajUaj0WgS\nlpR4KwDQs936D+BbItKklOq/hWp7SzWIDI1Go9FoNBrPIiIq0r5x99AppVIwjLm/icizPZcrlVJF\nPfeLgYM918uA8QHdx/VcC4qIeP5x++23Dwr5kcix08dq23DtzO6Hunfjjd+N+zyI5Wfp9hiRynB6\nvrgxV0T0fHFavl5b4v/Qa4u9tm6tLdESd4MO+CuwRUR+H3DtOeDanufXAM8GXF+ilEpTSh0FTAHe\ni5WibnDMMccMCvmRyLHTx2rbcO3M7rv9XrtNLPR3YoxIZTg9XxJ5roBeW+y2TeT5otcWe229Olfi\nuuWqlDoVuBLYrJR6H2Nr9XvAL4EVSqkvA3uBLwCIyBal1ApgC9AB3CROmLVxZNKkSYNCfiRy7PSx\n2jZcO7P7br/XbhML/Z0YI1IZTs+XRJ4roNcWu20Teb7otcVeW6/OlbgadCLyDpAc4vbZIfr8AviF\na0ppEo6SklPirYJmEKHni8Yqeq5oYokXtlw1mrhSUjIv3ipoBhF6vmisoueKJpZog06j0Wg0Go1m\nkKMNOo1Go9FoNJ6kqQkeeCDeWgwOPJGHbjCzZg3s3w8NDdDY2PsI/D0vD/72t+D9x4wZ46p+kciv\nqoJ9+6CkJDo5Vvo88ABkZsIZZ1iTH06m2X2332u3iYX+TowRqQw7/ay0TeS5At5cW8zkdHZCWRlM\nnBjd2JsrN/PCthf4+olfJy89z7KeiTxfvLy2fPABfOc7cN113lhbtm+HqirzSRqvuRLXWq5uopRy\nPQC2qwsyMmDxYsjNNR55eb3P/Y/LLoO2NkgOFf7hMR56CJ55xni4zU03QU4O3Hmn+2OFwucrZ+7c\nwb0ga2KHni/usGoVLFoEl18OP/kJTJkSmZzfrfkdv3znl3RLN7eddhtfm/s10lPSnVXWInquRM//\n/R9ceils2QIzZ8ZbG/j1r40vHr/9rfOylVJIFImFtYcuCurqDGPkH/8wb5eXZ7QdPjw2ekVLba3x\niNVYHR2xGUuj0XiXqiq44ALjn/bJJxv/xH/4Qxg3zp6c2pZals5ZymWzLuP7r3+f3635HT9Z8BOu\nOvYqkpMGybdqzREqKoyf69d7w6ArK4OxHi04qs/QRUFtLQwbFr5dYWHsDCQniKVBV1c3uN4bjUbj\nDrW1MH48/OAHsG2bsW4edxzcfLNh7FmW01pLYWYhny76NM9d/hx/v+Tv3LfhPmbfO5vnP3nekYz8\nmthRWWnsdK1fH29NDLRBN0SprTUWnXBog858rLq62Iyl0Wi8S+B6OmwY3HEHfPihcVxlxgy4/Xao\nr7cgp7WWwozehfm0Cafx9nVv8/Mzf85tr93G6Q+eztv73nbpVWgCaetsi1pGRQUsXAg+nwMKOYA2\n6IYoNTXaoBtMY2k0Gu8SbD0dPRruvtv4Z753L0ydapxd6uwMLae2xfDQBaKU4sLpF/LBVz/gxjk3\ncuX/XcmlKy6lrCFkKXBNlDS2NTLmrjE0tTdFJaeyEs47DzZuNM6txxtt0A1RnNhyLS8vd1YpB+TX\n1kJzc9+zbZHIsdLHb9BZlR+undl9t99rt4mF/k6MEakMO/2stE3kuQLeXFvM5Jitp0cdZQRr/ec/\n8NJLcNxxHaxdG7xtTUtNHw9doJ7JSclcM/saPvnGJ3xq5KeYfe9s/vTen+jq7kro+eKG/hVNFdS0\n1LBq56qoxqioMDy0RUXw9tsHI5Lh1NoiAgcOAHhzrsTdoFNKLVdKVSqlNgVcu10ptV8ptaHnsSjg\n3m1Kqe1Kqa1KqYXx0drAiS1XLy66fl0DdXbDoBPRBp0dtEFnr20izxXw5tpiJsfKejprFqxcCZdf\nXsrFF8PXvz5wG7a2tZZhmb2WYTA9M1Iy+OkZP+WNa9/g8Q8f57QHT+PNj9+0pKfde4MBN/SvPlwN\nwLOfPBvVGJWVhjFXUgJvvBGZt8+ptaW62giErK315toSd4MOeBA4J8j1u0RkTs/jZQCl1EzgC8BM\n4Fzgz0qpiEN8o2Uob7kq5f7ZtuZmI5VLYyN0d7s7lkaj8TZWvyArBYsW1bBli7H1OmsWrFhhfEGE\n4FuuoZg1chZvXvcm182+jpvW3sT3XvseLR0tUbwKjZ+qw1UcV3Qc/9r2Lzq7TfbITRAxPHRFRTB3\nLmzdmu2wlvbw8nYreMCgE5G3gWDmTjBDbTHwhIh0isgeYDtwoovqmTKUo1zHjXNf59paI5VLTg40\nNel0AhpNImPVoPNTWAj33gtPPQU/+5lxzmrnThkQFBGOJJXE0pKlPHb6Y+ys3cmn7/k0r+56NYJX\noAmkqrmK40cfz6SCSREHoTQ2Gl/6c3IMD93WrVkOa2mPsjLwcg7puBt0JnxDKbVRKfWAUiq/59pY\noDSgTVnPtbgwFD10/m3Qo492X+e6OuO9KSyEhgZt0Gk0iUxNjbUvyP2ZNw82bIAFC+DEUw/T3aVI\nIdO2nBEZI3jysif5/aLfc8NzN3D101cf2TbU2KfqcBUjs0Zy8YyLeebjyLLUV1RAcbHxfM4c2L49\nK66BEV730Hk1sfCfgZ+KiCil/gf4DXCDXSFLl9585HlJySmUlMxzTkNg9+5CZsxowedrNW1XU5PB\nrl2Z+HwDLaTyciObuFvYld/aqlCqmLS0Vtavb2XEiJaI5Fjps2FDGqmpuaSnK3btSrEkP5xMs/uh\n7pWXN7r6GTiF23PFqTEilWGnn5W2bswV456eL07K98s5dKiY3bsrqagInycu2NhnnQUjjq7ka+8X\nMmtWBz/6UR0zZ3ZY1tPfrojjeeTkV7h326/41B8/zU9n/5GS4fP02mKTzbt2MyJ9FFNGnsKfN13L\nGdOvJFwwQX/efz+N7Ow8fD7DsM7PH8Y//3mIo4+2t4Xr1Nqybl0ujSm7eHvHJ0BoV53VubJ+/WrW\nr3/Xkl6WEJG4P4CJwKZw94BbgVsC7r0MnBSin7jN/Pkir78evt0rr4iceWbwe2VlZY7qFK38/ftF\nRo8W+epXRf70p8jlWOnzzDMiF15ovDePP17liEyz+6HurVvn7mfgFG7PFafGiFSGnX5W2roxV0T0\nfHFafllZmbS2iqSminR3Rzf2popNMutPs+TvfxcZNUrk1ltFdu60pmcwmS9vf1mKf10sP/73j2Vf\n6T7b+iTyXLn66avlrxv+Kt3d3XL074+WVZtW2ZaxYoXIJZf0/n7RRYfl4Yft6+LU2nL99SKX/eY3\ncv0/ro9Yhtm9HrslYlvKK1uuioAzc0qp4oB7lwAf9jx/DliilEpTSh0FTAHei5mW/XBiy9VrBbT9\n51j66xyJnuH61NZCQYExVnLyCEdk6gLa8R/DCwW0rbQZynMFvLe2mMnxrztWQ9xCje0/P3fllbBp\nk1FI/fzzx/CuBSdIMJnnTDmH9UvX88beN7jmtWsobwzudRns88UN/auaqxiZPRKlFIunL2b1odW2\nZfgjXP2cdlpmRBUjnFpbyspAsiqZUmReaDhea0vcDTql1GPAamCaUmqfUuo64E6l1Cal1EZgPvAd\nABHZAqwAtgAvAjf1WLVxYSgGRfgX1oKC2ARFBDMeNRpNYmH1y3E4AiNci4qMOts/+xlccgl897tw\n+LB9mWNyx/DKl15hwaQFlNxXwsodK6NXNAHwn6EDuHjGxUfSl9gh8AwdGJGu8SwBVlYGbakVFGUX\nhW8cB+Ju0InIFSIyRkTSRWSCiDwoIleLyLEiMltELhaRyoD2vxCRKSIyU0RWxVP3oRgUEUsjK9B4\n1OW/NJrExeqX43D0TyoMcNllsHkzHDwIxx4Lb7xhX25yUjI/mv8jnrj0CW54/gZuffVWOro6wndM\nYPweOoB54+dR2lDK3rq9tmT099DNmRN5xYg1+9fwlee/Yr9jAOXl0KwqKcrRBt2Qor3deOTkhG+b\nnw9NTd4oWxKOeBh0g8ng1Wg0zmM3ZUlIOf2SCvsZMQL+/ne46y648kojIXFjo3358yfNZ8PSDWyq\n3MT8h+bbNlASierD1Uc8dClJKVww7QLbXrr+Hrr8fKMc3Mcf29fng4oPWFe+zn7HHlpbjTlT215J\ncU5x+A5xQBt0EWLnzEdSEuTmWissHW9iaWQFpi3RBp1Gk7g4ZtC1mOegu+gi+PBDY+v1hBPgk0/s\njzEyeyQvXPECn5vxOU584ERe3P5iFBoPTVo6Wujo7iAnrdfjcfF0+9uu/qTCgUS67VraUEpFU4X9\njj2UlxvGZEWz3nIdctg98xHKaPFaeZ5QBp0bpb8Cxyovt5adPZHLOenSX/baJvJcAe+tLWZy7Bp0\nocaubR1YJaJ/24ICePBB+K//gtNPN2rDmskMJidJJbHs1GU8/cWnuf656/nFq7+wrrwHcXqu+M/P\nBRZyOibrGNaVraOmpcaynMrKvh668vJySkrA57OnT3l5OaUNpRxsPkhXt/lWWaj3oqwMxoztpvpw\nNZ0N5mlTErn016DE7pkPbdCZj3XwYLsjMofyP2lt0Nlrm8hzBby3tpjJsZtU2NSgyzA36PzccAM8\n/TRcfz3ceSeUldmfL/PGz+Pt697mLxv/wrJVy+iWwVnD0HGDLuD8nJ/ag7WcedSZ/GvbvyzJEBl4\nhs5v0Nn10JWXl1NaX0qXdHGo5VDYtsEoK4OREw6Rl55HVUVVRDLC3YsWbdBFSCRlagbDtmKgkeV2\noEJg2pKGBq/muNZoNG7j1JZrTUtN0DN0oTj1VFi71qgF+8MfHhVRFOzkYZNZPm85a8rWsOQfS3Qt\nWPpGuAZiJ9q1rg4yMiCzX9GPOXPggw+MOr52KG0oJSMlI+Jt17IyyB3t3fNzoA26iLH7jXKwGXR5\nedDc7G4gR6Dx2NioS39pNImKo2foMu0JGj8e3nrLOA99+ulQWhq+T38K0gp45UuvkJyUzNl/Ozvh\nS4ZVH64e4KEDuGDaBbyy6xVaO82rK8HAgAg/+flGPVU7gREiwv6G/RxffHxUBl3WKO+enwNt0EXM\nUPfQJSUZRp2bXrq+Bp320Gk0iYqTUa5mQRGhyMyEn/50N5dfDiedBG9HUEs+IyWDRy95lPkT53PK\n8lPYfmi7fSFDhKrmKkZkDkwWPyJrBLOLZ/PartfCyui/3RqI3cCIuvY6MlMymTxsMgcaD1jvGEBZ\nGaQWeDdlCWiDLmKcCorwGoELq5s6t7QYZyQyM41t16amZLoH5/ETjUYTJfH00PlRygiU+Otf4dJL\n4f777ctIUkn8/Kyf89/z/pvTHzydD2oiT5MxmKk6PPAMnZ/F0xfzzMfPhJURykMH2A6MqGytZHz+\neIqzi6Py0JFTSXG23nIdcjgVFOG18jz+c23QV2enS38Fpn1JSYHMTLGUFyqRyznp0l/22ibyXAHv\nrS1mcuweYQk2togE9dBZ1dPfbtEiYwv2rrvgRz+yJqf/vRtLbuThix9m2frrWfHRCkvjxxOn50pV\n88AzdP4xFk9fzHPbngsbbRrMQ+eXYTcwoiOzg/F54xmdOzqsQRfqvSgrg/a0Copyijy7tmiDLkKc\n2nL12qIbykPntEHnz0HnZ9iwJEveQK/+IcUCbdDZa5vIcwW8t7aYybG7ngYbu6m9ibTkNNJT0sO2\nDSdz2jTDqHv8ccNjF05OqDqwd5/0ODevupk/vfcnSzrEC6fnSnXLwDN0/jEmD5vMqOxRrC1bayoj\nmIfOL2POHKNWr9XAiOaUZsbnjac4p5iKZvsGnQgcOAAtSZUUZWuDLiRKqeVKqUql1KaAa4VKqVVK\nqU+UUiuVUvkB925TSm1XSm1VSi2Mj9ZDc8s1cBsU3K3n2n8B1+W/NJrExYkt10jPz4VixAj417/g\ne9+DV1+NTMa0vE/x1nVv8avVv+Je372O6eZ1qpqrGJE18Aydn4unXxx229XsDF1eHowdC1u3WtOn\ntL7U2HLNiWzL9dAhyMqC6lYd5RqOB4Fz+l27FXhVRKYDrwO3ASilZgFfAGYC5wJ/VspKrQbncWrL\n1Uv0r37hps79F/DB8P5oNBrnaenJ8tE/PYVdojk/F4pp04yUJldcAR99FJmMSQWTeO3q1/jft/6X\n5RuWO6qfVwmVtsTPxTMMg05EQrYxO0MH9rZdSxtKez10ERh0ZWWGAVnRVKGDIswQkbeB/v/KFwMP\n9zx/GLi45/lFwBMi0ikie4DtwImx0LM/Q9FDF0sjK/CsnttjaTQa72L3/FwonPbQ+fnMZ4zzdBdc\nYHiNImHysMm8dvVr3P6f23l448PhOwwCnnnG2NEJRrDEwoHMGT2Hls4WPq4OnXvEzEMH9iJdSxui\n89D5DbrK5kqdtiQCRolIJYCIVACjeq6PBQKzBJX1XIs5Q9lD50d76DQajdvEK6mwHa66Cq691qgF\nG0nyYYCpw6fy6tWv8r3Xv8ejmx51VL9Y09oKn/tc8Fq4HV0dNLQ1mH4WSqmw0a5WPHRWI11L6w0P\nXWFGIYc7DttO/hxY9mtU9qjwHeLEYEn+Fdova8LSpTcfeV5ScgolJfOcUUagpmY0u3YdMEKZLVBf\nr6iuLsLn6/vtoLGxkdzcXEf0CoYd+evWpZOUlI3PZ9Taa2jIYtu2VHy++oj0NOvz0Uc5dHYqfD4j\ntLWpKYNNm5Lx+Zojlhnufqh75eWN+HzeL/Xk9lxxaoxIZdjpZ6WtG3MF9HxxWv4773SSmlqEz2de\nkinc2O/v201Xc/qAz8aqnuHanX56I2vXjueCCxR33FFLUlL4vgPnSh53Hf93vv7iEvbuaWDhmMVh\n9YoFdj/LiookoJgHHqhnyZK+a/ahtiryUgvYsN78f91MdRp/2XAnn828ZoD87m44eHA0paUH+nhF\nA2WIKDZuLGLNmgpSTCyZLumirKGcyu1J1CYfoDB1BK+8u4kxWeODtg/2Xqxbl0tbcjXZybl88H6V\nY2vL+vWrWb/+3dDK20VE4v4AJgKbAn7fChT1PC8GtvY8vxW4JaDdy8BJIWSKWzQ1iWRk2OvT2SmS\nnCzS1dX3+rp165xTLAh25D/yiMiVV/b+/uSTIpdeal+OlbG/9S2R3/ym9/evfnW/fO970ckMdz/U\nvXXrysIP7AHcnitOjRGpDDv9rLR1Y64Y9/R8cVL+r3+9TS64IPqxf/XOr+Q7L3/HUlurMvvfb20V\n+cxnRJYts9Y31Fz5oOIDKfpVkfzjo39Y0s1t7H6WPp8IiJx//sB7mys3y8y7Z4Ydo62zTQruKJCy\nhoHvUVWVSGFheD2nTxf54ANzXcsaymTYz4cd+f2E+06Qd0vfDdk+2Htxww0iP/jDJpn1p1kh24ST\nYeVej90SsS3llS1X1fPw8xxwbc/za4BnA64vUUqlKaWOAqYA78VKST92t1sBkpMhJwfq693RyQmC\nbYO6FXnaP21Jbm6n3nLVaBKQxsYU55IKu3CGLpD0dHj6aXj2Wbg3iqDVY4uO5eWrXuamF2/i2Y+t\n1Tb1EgcPwgknwJtvQltb33vhzs/5SUtO47yp5/HcJ88NuBfu/JwfK4ERpfWlFGX2CrOSi64/ZWWQ\nNszb5+fAA2folFKPAauBaUqpfUqp64A7gM8qpT4Bzur5HRHZAqwAtgAvAjf1WLUxxW5AhB+vnxOL\n5xm6vLwuT783Go3GHRoaUpwLinA4yjUYw4YZ6Uxuvx1Wroxczuzi2bx4xYssfWEpL2x7wTkFY8DB\ngzBjBsycCatX970XLsI1kFDn6MKdn/NjyaBrKKUoo9cQi6RaRFkZqFxvpywBDxh0InKFiIwRkXQR\nmSAiD4pIrYicLSLTRWShiNQFtP+FiEwRkZkisioeOkfioQNt0JmNpT10Gk1i0tCQ7PmgiP5MmQL/\n/Cd86Uvw4YeRyykZU8JzS57jy89+mdd3v+6cgi5z8CCMGgULF8Kqfv+Fqw9XWzboFk1ZxDul79DQ\n1tDnulUP3dy54QMj+nvoIol0LSuDzowK7aEbikQalaUNur5jBaYt0R46jSYxaWx0xqBzK21JKE49\nFX75S7jySujoiDwd6knjTuLJy57k8n9ezvZD2x3U0D0OHoSRI4MbdOGSCgeSl57HqeNP5eUdL/e5\nbtVDd/zxsHmzecWIAR46mwZdWxs0NEAzlZ7OQQfaoIsIJ7dcvVSep79Bl58PjY1GxJFbtVz9TJ48\nXJf+CoMu/WWvbSLPFfDW2mJGZ2eu7fU02NihEgtHUvrL6v1rr4WJE+HJJ6dZGiMUZxx1Bj9d8FMu\nfPxC6lpjXzLH7mdZVWV46E4+GXbsMH4/cu9w8DN0ocZYPH0xz37S9xxhKA9dfxm5uTBhAmzZElrX\n0oZSZoyZceT34pxiDjQdCNm+/xjl5TB6NBw83Lvl6tW1RRt0EeDklquXFt3+RlZgIIfbBt306aMs\nBWB49Q8pFmiDzl7bRJ4r4K21xYyWlixnDLoQHjo3DTql4L774PHHc1m3ztIwIfnK3K+wcPJCvviP\nL9LZbbFIqUPY/Sz9W66pqbBgQd/SaKHO0IUa46LpF/HS9pfo6Oo4ci2Uhy6YjHD56ErrSzl24rFH\nfg/noes/Rp8qET1brl5dW7RBFwGJsuUK7ujc3m48cnL6jlNXFzrzuEajGZpE+gW5P7E8QxdIcTH8\n/veGt661NTpZd51zFwDfXfnd6BVzEb9BBwO3Xa1GufoZmzeWycMm89a+t45cs3qGDsIHRvirRPix\nu+V6pEpEk95yHZJEWqpmMBp0BQXO61xXZ8gNrMKblmZ822s2zyus0WiGGE5UiuiWbupb6ynIKAjf\n2AW++EUj4vP226OTk5KUwpOXPcmqnau41xdFXhSXCWbQ+b+M2wmK8LN4+uI+6VusnqED8xJgHV0d\nVDVXMSa31yvmN+isJsgILPulo1yHINpD5/w4bo2l0Wi8jRMGXWNbI5mpmaQmpzqjlE2UgnvugUce\ngXejTPxfkFHA85c/z4/+8yP+vfvfzijoICK9QRFgRPymp/eeY6s6bD0owo//HJ3fyLLjofMHRnR0\nDLxX3ljOqOxRpCT1lpLITM0kMyXT8lnFsjIYPaYrIkM11oQ06JRSDWEejUqpbbFU1isMxTx0bW1G\npFBWVt/r2qDTaDRuIeKMQRfrCNdgjBwJd99tbL1GWu/Vz9ThU3n80sdZ8s8l7KjZ4Yh+TtHUQmUl\nswAAIABJREFUBCkpvf8rlAr00gnVh6ttG3THjDqGJJXEpspNdHVBdXWvBzAcOTmhAyP6b7f6sbPt\nWlYGecWHyE/Pj9sXBquYeeh2ikieySMXSMgNMieDIsrL3a0JaVW+f1FV/aLv/TpHomeoPv1Tlvjb\nWjHowulhdt/t99ptYqG/E2NEKsNOPyttE3mugHfWFjOamyElpZv09OjGDhXhGqytVZl27vvvXXqp\ncabr+9+3NKQpZx51Jj+e/+OYRL7a+SwDt1v9+A26utY6slKzSE8Z+IGajaGUOuKlO3TIyLCQGsR2\nCiUjVD660vpSxuWNG9DPzKDr37asDDKG991u9eraYmbQXWqhv5U2Qw4nt1y9suiG85o5bdD1H0sb\ndOHRBp29tok8V8A7a4sZtbVGUvFoxzYLiIilQQfwxz/CihVGWaxo+doJX+Pso85myT+WuBr5Gq1B\nd+aZ8M47UFYbelsy3BiLZxgGndn5uVAyQgVGlDaUMj5vfNQGncrrGxDh1bUlpEEnIrvCdbbSZigy\nFLdczQw6p+u56i1XjUYDkRt0A+R4YMvVz/Dh8Je/wHXXweHDkScc9vPbRb+lW7r5r1X/5YB20RPM\noCsogGOOgdfX2otwDeS0Caexp24Pm/eVWj4/5+f442HjxoHX9zfsZ3xe8C1Xs1x0fkSMPHRdg6BK\nBFgIiug5K9f//FypUupppdTRbiqnlNqjlPpAKfW+Uuq9nmuFSqlVSqlPlFIrlVL5burQn+5uIy9b\nIhl0+gydRqNxg9pao0pM1HJavGPQAVx4IZx+Otx9d17UsvyRry/teIlHNz3qgHbREcygA2Pb9T/r\n7AdE+ElJSuG8qeexas9zliNc/Rx9NOzZM/B6tGfoamogMxPqOiqHhkEH/A5YBowFxgH/BTwGPAH8\n1T3VAOgGFojI8SJyYs+1W4FXRWQ68Dpwm8s69KGhwTgMmpISvm1/CgqM/t3dzusVLdqg02g0saam\nxkEPXYgzdPHid7+DN97I4LXXopdVmFnI45c+zrdXfpu9dXujFxgFVVW9Ea6BLFwIvi3BkwpbZfH0\nxbxb+6xtD92YMXDokBHcF0hpfWlID50Vg24wpSwBawbdRSJyr4g0ikiDiNwHnCMiTwJu/wUpBuq4\nGHi45/nDwMUu69CHaJJgJidDdrZh1HmNWBpZdXXBx3Ij551Go/EuTnro4pFU2IyCAvj+9+u4/npn\n1vw5o+dw8yk3c80z19DVHf17FimhPHQnnmikLMkicoPunMnnsKfrXfKL6m31S042jLrS0r7XQ3no\nRueMtmXQVTRVeD6pMFgz6A4rpb6glErqeXwB8OfDdjuvvwCvKKXWKaVu6LlWJCKVACJSAVgMbnaG\naEPs+xtIXinPE86gc7L0V7CxxowZY+m8nldLrsQCXfrLXttEnivgnbXFjNpaGD06I+qxa1pqQm65\nuln6K9y9efPaOO88uOKK4HnS7LJs3jK6pZu73r0remEB2PksQxl0KSkwbmo1NaXBDTorY+Sm5zLy\n8OlU5LxkW8bEibA3wHnZ1tlGbUstRdlFA/qZeegC2wZ66AK3XL26tljZOLwS+D3wZwwDaw1wlVIq\nE/iGa5oZnCoiB5RSI4FVSqlPGGhEhjQqly69+cjzkpJTKCmZF7VCa9emkZKSi893KKL+6ekjeeed\nOg4d6v3r9kI02scf51FU1IXP1zcTzf79yVRUDKe83LlI1337hlNZ2YjP197nenX1Ifbsycbnq7Et\n0+r9YPfKyxvx+QZHVKOOdLXX1o1oND1fnJO/ZUsuqakS0fsZOPauA+VMlNkh5cQ60rX3WiNXX13O\nsmXD+Nznurn99roBqaHs8l+Tf8U1b57H2LbZTMv7VHTCArD6Hu3YMZy6uiZ8vrYB99KHl/HRumlR\nfQ5pu87jvcIV+HyfsSUjJ6eAN95oIz+/BYD9zXsYkV7E+xsqB/Q71Ab768rD6rluXQ5KKXZX7adm\nXzK++vIBbUJhZa6sX7+a9eujzEQdQFiDrieS9cIQt992TJPgYx/o+VmllHoGOBGoVEoViUilUqoY\nOBiq/333/cZxnXbvNr4JzJ0bmZU9diyMHj2SuXMdVixK0tLg2GNh7ty+MSaTJhlJMiN9vcHo7IST\nT05nzpy+19va4KmnnB3LCj5feczH1Axe9HxxjowMo2TW3LlRBg9sbaVk1tHMneKtz8U/V1auhLPO\ngqeeyuLOO6OVOobf5d3Fz1d/B99SHxkp9j2c0dDaCqedls5xxw28N/z9ejatHEdJyZiIDdf0vZew\nfc4POfb4EaQlp1nud/zxkJSUxdy5hqe2ac82Ju+aFPRvtau7iMbX6znu+JGmyYLvuw9OOAFebK7h\njBOP6VNCzAnmzr0MuOzI7/ffH53n1UqU6zSl1GtKqQ97fj9WKfWDqEa1gFIqSymV0/M8G1gIbAae\nA67taXYN8GxQAS7h9JarVwj1ugoKjKheJwM5dFCERqOByOti98cssbAXyMqCF14wHr9xwM9w9XFX\nM2PEDL732veiF2aTUEERAM1SRTYj2bw5cvk1e8cwpXAab+61l8iv/5ZrqIAIgOSkZEZkjeBgc0h/\nEGBsuRYPkrJfYO0M3f0YkaQdACKyCVjiplI9FAFvK6Xex9jmfV5EVgG/BD7bs/16FnBHDHQ5QrQL\nkFeNllBGVkqKEbbd2Oj+WF59bzQajTs4UfYLzBMLe4Xhw2HlSvjDH+Bvf4tOllKKey+4lxUfreC1\nXQ6E0Vqku9soyzUiRGaSqsNVLDhhJKtWRSa/s9OYE5fMWsyzH9vz1Qww6BpCG3RgLdK1rAxyRh6i\nIKPA82W/wJpBlyUi7/W75l7K6h5EZLeIzO5JWfJpEbmj53qNiJwtItNFZKGIuFsTpR+J5qEDZ3Xu\n7DS2cPOC7LD4xxG3Q200Go0ncMqg81JiYTPGj4eXXoJly4yf0TA8azjLL1rOdc9eR21LbP6pGImg\njSM6wag+XM35Z0Ru0FVVGQ6Tz800qkaIjX8GQT10QSJc/Vg16FLyB0cOOrBm0FUrpSbTE3yglLoM\nCJ9ieYgSaZUIP/2NI68cWg5n0G3bZu6atjp2fb1hzCUlDWybkWFcb2mxJ9Pq/cFezkkHRNhrm8hz\nBbyztphRWwvt7ZVRjd0t3TS0NVCQURC2rVWZdu/beS9mzYKnn4arr4Y1ayx3C8o5U85h8fTF3PTi\nTVHJsap/qAhXgMMdh+nq7uLcs7J5992B67iVMfxlv2aNnEVachobK/qWfzCTMWEC7N/fezwo0EMX\nrF8og87ftq3N+H/VljYwZYlX1xYrBt3XgXuBGUqpMuDbwNdc08jjRJOHDgavQbdzp/1vgMHGDjWO\nv204b6BX/5BigTbo7LVN5LkC3llbzKipgdZW+/6BwLHrW+vJScshOSk5bFurMu3et/tenHIKPPQQ\nXHwxbN1qq+sAfvnZX7KxYiOPbX4sYhlOGHRVzUbZr4ICxXHHwVtv2R+jshKKiowt5cXTDS+dVRkZ\nGcb/j4oeGy0wB12wfqFy0fnbHjhgGJdVhwcmFfbq2hLWoBORXSJyNjASmCEip4nIHtc08jhDccu1\nvd3IkZSdHfx+YSE0NgZfLO0S7v3z4vuj0WicR8TIOxltYuHaVu8lFbbC+efDnXfCokUDE+LaISs1\ni0cveZRvv/xt9tXvc07BIBw8GDogoupwb5WIhQuJaNvV76EDWDxjoEEXjsBtV7OgCAi/5XokB13T\n4NlyDZm2RCn13RDXARARZzMbDhKGYlBEba0RzRoqzNww6CKodWYyVih0tQiNJjFobDQCrlJSojs0\na5ZU2OtcfbXhlVq0CP7zn9DGUjjmjJ7Dt0/+Ntc+cy2vXv0qScrK5pt9qqpCe+iqD1czMrvXoFu6\n1L58v4cOYN74eZTWl7K3bi8TCyZa6j9hgmHQHVvSTEtni2ld2eKcYt7a91bI+32qRAwSg87sU8/t\neczF2GId2/P4KjDHpN+QZih66Kx4zRoatIdOo9E4h2MBER5PWRKOZcvg85838qhFU/f1llNvobWz\nleUbljunXD/Cbbn6Dai5c43zbAds7qYHeuhSklI4f9r5PPfJc5b7+z10pQ2ljMsbd8QBFYzinGIO\nNIZWsE+ViEFQ9gtMDDoR+YmI/AQYB8wRkZtF5GagBJgQKwW9htNBEV7AipHlpIcu3Fjhyn9pNJrB\nT6JFuJrx4x/DX/9qeOxuuy2yMmHJScncfd7d/PDfP6Su1Z1F1NSgC9hyTUmBM8+EV16xJz/QQwcE\nPUdnxhGDLsx2K9jYcm0eeIbOq1jxyxYBgTWa2nuuJRxmKTes4sVarlaMrK4u+y862NihxvK3DWfw\nerWGXizQtVzttU3kuQLeWFvM8B9fibZOdG2LuUEXz1qudli4EN5/HzZtglNPhZ077cuYM3oOF067\nkJ+98TNb/azqHzYoIiD5bv9zdFbGCPTQASycvJC1ZWuPGKjhZAR66AJTlgTrF8qg87c1O0MX77kS\nCisG3SPAe0qpHyulfgysBR5yTSMPU1cH+fkDU27YoX/lBS8sulYMuvb2EBETNseuq9MGXaRog85e\n20SeK+CNtcUM/7oTrUEXLqnwYDHowDCWXngBrrwSTj45sgTE/3vW//LIpkf4uPpjy30cMegOVx05\nQweGQffKK715Ra2M0d9Dl5OWw/yJ83lx+4uWZEycCPv2DfTQBeuXm5ZLt3TT1N7U53p/g66iaWDa\nEi/MlWBYiXL9X+A6oLbncZ2I/MI1jTxMtNutYLiis7KcrbwQLbE816bP0Gk0GnB4y3UQn6Hrj1Lw\nrW/Bq6/Cz38OV10FDQ3W+4/KHsVtp93Gd1cGjWuMCrOyX/3LY02aZGRO2LLFuvz+Hjqwt+3q99Dt\nC1MlAowAT7Nt17IyKB7dxaGWQ4Oi7BdY89AhIhtE5Pc9j/fdVsqrRJuDzo/XjBZt0Gk0mljjaFDE\nID9DF4zjjoP16w2j6PjjYe1a632/ceI32FW7i39t+5ejOoXz0PWPKj3jDCN61wrt7YbhOnx43+sX\nTr+QVTtX0dEV/mBhfr7xc/ch8yoRfkbnBs9FJwLl5ZAxbPCU/QITg04ptSFcZytt3EAptUgp9bFS\naptS6pZYjevUAuQ1oyXc63IylUi4tCVee280Go07aA9deLKy4N57jXx1F15o3ahLS07jt+f8lu+s\n/A7tXe3hO1igo8MwuEI5NfyJhQNZsAD+/W9r8v057vofaSrOKeaogqNYsz98WQ2lDC/dnprwHjq/\n7GAGXU2Nkai4oXvwpCwBcw/dTKXUJpPHZiB0kheXUEolAXcD5wCfAi5XSs2IxdjR5qDz4zWjJZZG\nlvbQaTQacG49HQpRruG49FL47nfhwQet9zl36rlMGz6NP6z9gyM6VFcb3rNQZ8gDo1z9LFgAb7zR\ne2bcjP7n5wJZNGURL+2wVvx2wkThwGFrHrri7OCpS8rLYcwYIyBisES4grlBNwO40ORxATDPbQWD\ncCKwXUT2ikgH8ASwOBYDu+Gh80J5HmupRAQbdZJDjq1Lf0WOLv1lr20izxXwxtpihn8tiEROYJ9w\nQRFeLP0VCUuWwD//aS+lyV3n3MUdb98Rtgi9Ff3Ntls7ujpobGsc4CkdP97YBv3oo/BjBDs/5+fc\nKefy0o6XLOk5elI90g356flHroXqF8xDV15eHjYHnVfnilkeur0WHvtd0yw0Y4HAQin7e665jhNB\nETD4DLq0NEhJ6aa5OfqxtUEXOdqgs9c2kecKeGNtMcMpgy5cYuGhYtBNmgRTp9rL7TZt+DSum30d\n33/t+6btrOhvFhBxqOUQwzKHBa1QsWCBcY4u3BhmHrpTxp/Cnro9bNq1KayeueNKye4a3yepcKQG\nXagqEV6dK85ki/UoS5fefOR5SckplJRE51D8+OM8Ro7swuezadn0o60tj82bDTnl5eDzufcBW5Ff\nXj6S8vJafL7OkG2ys0fwn/9UUVxswXceYuzubmhoGM2OHQfYvTt425YWRU1NMT5f8Aze4V6P2f1Q\n98rLG139DJzC7bni1BiRyrDTz9q8dn6uGPf0fHFC/v79I6ioqKetzb6cwLGrm2vY83ErNan2P0s7\n7bywtpx6ajZ3353KqFHWEwefn3s9l22Yz/zsl5hVcFzQNlbeozVrMklJScfnGzj2joat5CQVBpUx\ncWIm//d/GUycaD7G+vU5iCh8vuApIEoKTuXF7asZkXGsqZ41nVugYWyfsUK9vsbKVD4p2zOg7Xvv\nNZCUpPhg504K04YP6OvUXFm/fjXr179r+npsISKD6gGcDLwc8PutwC1B2onTXHutyPLl0cv5n/8R\nue024/m6deuiF2iCFfnjxons2WPeZvLkZvngg+jGrq0Vycszb9vdLZKaKtLSYk2mnfuh7q1bV2Yq\n0yu4PVecGiNSGXb6WWnrxlwx7un54oT8o48W2b49Mjn+Pp1dnZL0kyTp6u4K29aqzEjux2ptqagQ\nyc8XaW6212/5huVyygOnSHd3d9D7Vt6j3/5W5JvfDH7vtV2vyfwH5we9t3+/yLBhImvXmo/xzW+K\n3HVX6PvLNyyXs+89O6ye//3kX2TEl6/vcy3U63tv/3sy5945A9ouXSry5z+LfOn/viQPvf/QgH5u\nrS09dkvE9pGltCVKqYlKqbN7nmcqpXKdMyltsw6Y0qNTGrAEsF7sLQqGclBEuK3kvLyuqHW2Mo5S\nuvyXRpMIOHEmua61jvz0fNeK0XuNoiI44QT4l81sJNfOvpb2rnYe2/xYxGOHrRKRHXw/duxYI5hi\n585MU/lmZ+jACIx4r/o9OrtD7yQBtKaX0lIRPiACQqctGYx1XMFCHjql1I3AP4B7ey6NA55xUykz\nRKQL+AawCvgIeEJEtsZi7KGYtqSjA1pbITeMiZ6b2+mIQWcWTevHS++PRqNxHuP4hbX1wIyalpoh\nm7IkFJdfDo/ZtMuSVBJ/OPcP3PLqLQMqI1jFzKDrn1S4PwsWgM9n/k/G7AwdwJjcMRRlFrF2v3nu\nltruUtqqxtPSYtoMMJIwVzVX0S19jxKFO0PnVax8rfk6cCrQACAi24EQH2tsEJGXRWS6iEwVkTti\nNa4bQRHxLs/jN7ICzo8Gpago3baR1X9sM4M4sK2ZQefVkiuxQJf+stc2kecKxH9tMaOhwUiYm5wc\nXekvKylLBlPpLytccgm89pr9XYx54+exYNIC7nh74L9MK/r788QFI1hS4UDOOAO2bDGvthDOQwdw\nzlHnhE1fsr+hlJHp49m3r/daqNeXlpxGXnoe1Yer+7QNrOMaLG2JV+eKFYOuTUSOZCZUSqUANhNY\nDA3cqBQR70XXqtdx7NgsbdDFGW3Q2WubyHMF4r+2mBG4FkRl0IWJcLUjf7DMl4ICOPNMePpp+33v\nOPsO/uL7C6X1pX2uW9G/qirMlquJh27+fFi7NtM0H104Dx3A54//fFiDrrShlAn51gw6GBjpOnz4\nGOrqYPiInrJfQbaSvTpXrBh0byilvgdkKqU+CzwFPO+aRh5mKG65Wn1NTugcy7E0Go130UmFo+Py\ny+Hxx+33G5c3ji8f/2V+vfrXtvuGK/sV6gwdGEl6R46ETSGyjrS2QnNz+P8Pp4w7hZ01O0Pm1RMR\n9jfsZ2rRePbuNZflp79Bd+CA4Smsaa2mIKOAlKTBkwzEikF3K1AFbAa+ArwI/MBNpbxIayt0dRml\nWKLFSwaLNug0Gk2scerLcbikwkOVCy+E994zvFp2+c7J3+Fvm/5GVXOVrX7RnKED87qulZWG7FBV\nKPykJqdy1tFnsXLHypB6ZKZkMmVCdsQGXXl5b0DEYKoSARYMOhHpFpH7ReTzwFJgbU94bULhX4DC\nnTWzQkGBcf7BC+9iLI2sujpt0Gk0GgfruLYkpocuKwvOPx+eesp+39G5o/nip77I79f+3nKfw4eN\nALpQwXPhPHRgXte1sjL8+Tk//qoRwShtMEp+TZhAxAZdWVlv2a/BFBAB1qJc/6OUylNKDQPWA/cr\npX7rvmrewqkFCCA1FTIzoTF4/sSYYvV1FRRoD51Go3EGxwy61vBn6IYqkW67Aiw7dRl/8f2FhrYG\nS+395+dCOTSqms2DIsAw6N5809jp6k9FRfjzc34WTVnEK7teoat7oKDS+lLG541n4sToDLojEa6D\nKGUJWNtyzReRBuAS4BEROQk4y121vIdTZz78+I2WeJfnsbqwdnVV2zay+o9tlrYksK2ZQefVkiux\nQJf+stc2kecKxH9tMSNwPY2m9JcVD91QKf3Vn4UL4ZNPrBsugRxdeDSLpizinnX3AOH1Nyv71S3d\nHGo5FNag6+4up7gYPvhg4D2rHrry8nLG5Y1jbO5Y3it7b8D90obgBp3Z6xud0zcX3SefNPVuuWYH\nV8qrc8WKQZeilBoNfAF4wTVNPI6THjoYfAZdW1uF7TD5YAZdqLEC25p5A736hxQLtEFnr20izxWI\n/9piRuBaEJVB11ob9gzdUDXo0tKMFCZPPBFZ/1tPu5Xfrf0dLR0tYfU3Oz9X11pHdmo2aclppjLK\ny8tDnqOz6qHz6xlq27W0vpRxeeMYP94IbvB7A81eX3FOMQeaektN7t7ddiRlSSgPnVfnihWD7qfA\nSmCHiKxTSh0NbHdNI4/iVA46P17ZVrR6ri1WlSLAO++NRqNxByeDIhJ1yxXgiisi33Y9ZtQxnDj2\nRB7c+GDYtmEDIsKcn/OzYEFwg87OGTqAc6eGMOh6ztClpcGIEUaAQzj6b7kePJjWWyViqJ2hE5Gn\nRORYEbmp5/ddInKp+6p5C6dy0PnxitFidWH1V4qIJpDDjkGnS39pNEMXR8/QJWBQhJ/TTze2Q7dG\nWCvpttNu48537gxbTitc2a9w261+5s+Ht94aeI7Ozhk6MJIkbz+0nYPNB/tc92+5ApbP0fU36Kqq\nUo+coRtyUa5KqQyl1NeVUn9WSv3V/4iFcl7CrS3XeGP1daWnC0lJWCqnEu1YXnlvNBqNOzga5ZrA\nHrrkZPjiFyP30p087mSOLjyaVeWrTNuFzUEXJmWJn6IiI4J048a+1+166NKS0zjjqDMGpC8prTc8\ndIDlSNfCzEKa25tp7WxFBKqq0gZlHVewtuX6N6AYOAd4A6OWq6vxmUqp25VS+5VSG3oeiwLu3aaU\n2q6U2qqUWuimHoG4FRQRb+wsrNHoLKLTlmg0GgOdWNg5/NGuke6e3HbabTy086EB9UwDMQuKCFcl\noj/B0pfY9dDBwHN03dJNeaMRNAHWPXRJKominCIqmyqprYXU1G6ys4do2hJgioj8EGgWkYeB84GT\n3FULgLtEZE7P42UApdRMjOCMmcC5wJ+VciIzXHjc8tDFuzyP1dc1ZswY24ZW4NhNTZCRYaRsCdc2\nJwfa2oy8R2btwsmx29fr6NJf9tom8lyB+K8tZjhR+qujq4OWjhby0vPCtrUqM9L78Zwvc+caxtz6\n9ZH1P/vos8nLyOO5T54L2caJM3T+9yhYYIRVD13g+3zulHNZtXPVkfQllU2VFGQUkJGSAfQ16MJ9\nPv5tVyMHndDVHbrslxV5Xi795f+3WqeUOgbIB0J8tI4SzFBbDDwhIp0isgcjOOPEGOjiWlBEvBfd\nWBl0ZilL+rdVKnSkq1f/kGKBNujstU3kuQLxX1vMcMKgq22tpSCjgHDf6Ye6QadUdDnplFL86Mwf\n8fO3fk6omgFObLn636PPfAbefhs6e47tHT5sfIHPzw+va+D7PD5/PMU5xfjKfUBvQISfiRM5Us81\n3OfjT11SXg4TJ6ZSfbiawozCkGW/vDpXrBh09ymlCoEfAs8BW4A7XdOol28opTYqpR5QSvk/6rFA\nYFXhsp5rrjMUgyI6O40/plDZv/sTjc52PZxeeH80Go3zdHUZHnsr/8DNSPTzc4Fcfjk8+SR0h941\nNeXiGRfT2N7I67tfD3o/nEFnNSgCDDnjxsH77xu/+71zkey1BW67+pMK+4kkufCHH8LUqYPz/BxA\n2KqzIvJAz9M3gKOdGlgp9QoQ+I4pQIDvA38GfioiopT6H+A3wA12x1i69OYjz0tKTqGkZF7E+h44\nMJKyslp8PvNoIKtUVaWzZ082Pl+NI/Iioa4uiZycUWzYELzQcX+6uwvYsKGNMWPsR0asX59Gamou\nPt8hS+3T0kawenU9jY1B9l0dpry8EZ9v8Ocd08QGPV+io65OkZ1dZHndCcXm2m2kdeV4+rOI5VzJ\nyhrJ/ffXU1LSHlH/JWO/yq0v3s49J8/sc10EKitHs2/fAQ4eHNhvx4H9zE1Pwtdp/XV+6lN5/P3v\nXSjVzKZNqeTm5uPzVdvW+ejuE/jTB3dwQc5S3tn9Iemtw468383Nit27i1i3riKssdjdkM36xm1s\neqqVyy47zJsbPiKzq8D1z279+tWsX/+uY/LCGnRKqXTgUmBSYHsR+Wk0A4vIZy02vR94vud5GTA+\n4N64nmtBue++30SmXBAOH4bPfGaU7YOboejshEcfhblz4+eq377dyNVjVYcpU6CgIIu5c+1/Ky4t\nhfHjrY81bhwUF49k7lzbQ9nG5yuP6+egGVzo+RIdO3bYW3dCUbX9A8ZXFnn6s4jlXPnyl+H990fw\nla9E1v+442/iwT/+lq7iUk4a13tMvqEB0tPhtNOCv472DQ3MO24Gc8daf51f+AIsXw5z5+azfz8c\nfXRk8+HYrou5deONTJyZijrUQMmYGX3kZGbCUUeNYUQYB+IcmcqGsk189FEGK1dm8NyeTqa1THT9\ns5s79zLgsiO/33//XVHJs7Ll+izG2bVOoDng4RpKqcDjkZcAH/Y8fw5YopRKU0odBUwBBtb/cBg7\nEZpW8cKWot1t0GjqucZyLI1G4110UmF3WLIE/vnP4MFkVkhNTmXZvGX84u1f9Llutt0K9hIL+5k/\nH955x3BsVFTYS1kSSFpyGmdMOoNVO1f1yUHnx2rqkuKcYrbsq2D2bOMowGBMKgzWDLo3WDD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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "TF=np.loadtxt('data/TFs/Data/RF-Lock-OPLG.txt', comments='#')\n", "f = TF[:,0]\n", "real = TF[:,1]\n", "imag = TF[:,2]\n", "mag1 = np.sqrt(real**2+imag**2)\n", "phase1 = rad2deg(np.angle(-1j*imag-real))\n", "\n", "mag2 = np.abs(OPLGSat)\n", "phase2 = rad2deg(np.angle(OPLGSat*np.exp(-2j*pi*f*Td))) #Time delay is explicitly introduced as a phase delay here.\n", "\n", "\n", "fig = plt.figure()\n", "ax1 = fig.add_subplot(2,1,1)\n", "ax2 = fig.add_subplot(2,1,2)\n", "ax1.set_axisbelow(True)\n", "ax2.set_axisbelow(True)\n", "\n", "ax1.semilogx(f, 20*np.log10(mag1))\n", "ax1.semilogx(f, 20*np.log10(mag2))\n", "ax2.semilogx(f,phase1)\n", "ax2.semilogx(f,phase2)\n", "\n", "ax1.grid(True, color=(0.6,0.6,0.8),ls='-')\n", "ax1.grid(True, which='minor', color=(0.6,0.6,0.6),ls='--')\n", "ax2.grid(True, color=(0.6,0.6,0.8),ls='-')\n", "ax2.grid(True, which='minor', color=(0.6,0.6,0.6),ls='--')\n", "\n", "ax1.set_ylabel('Magnitude [dB]')\n", "ax2.set_ylabel('Phase [deg]')\n", "ax2.set_xlabel('Frequency [Hz]')\n", "\n", "ax1.legend(['Measured','Model'])\n", "\n", "ax1.set_title('MICH Open Loop Gain')\n", "fig.set_size_inches(10,6,forward=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Extra time delay " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By adding extra time delay of $130\\mu \\mathrm{s}$, the phase difference can be accounted for. " ] }, { "cell_type": "code", "execution_count": 82, "metadata": { "collapsed": false, "hide_input": false, "run_control": { "marked": false }, "scrolled": true }, "outputs": [ { "data": { "image/png": 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GG1p/joyM5Pnnn+f555//1b5jx45l7NixXe26x+poBH/KGDOpo51FJNbJ/VFK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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "TdExtra = 130e-6\n", "\n", "TF=np.loadtxt('data/TFs/Data/RF-Lock-OPLG.txt', comments='#')\n", "f = TF[:,0]\n", "real = TF[:,1]\n", "imag = TF[:,2]\n", "mag1 = np.sqrt(real**2+imag**2)\n", "phase1 = rad2deg(np.angle(-1j*imag-real))\n", "\n", "mag2 = np.abs(OPLGSat)\n", "phase2 = rad2deg(np.angle(OPLGSat*np.exp(-2j*pi*f*(Td+TdExtra)))) #Time delay is explicitly introduced as a phase delay here.\n", "\n", "\n", "fig = plt.figure()\n", "ax1 = fig.add_subplot(2,1,1)\n", "ax2 = fig.add_subplot(2,1,2)\n", "ax1.set_axisbelow(True)\n", "ax2.set_axisbelow(True)\n", "\n", "ax1.semilogx(f, 20*np.log10(mag1))\n", "ax1.semilogx(f, 20*np.log10(mag2))\n", "ax2.semilogx(f,phase1)\n", "ax2.semilogx(f,phase2)\n", "\n", "ax1.grid(True, color=(0.6,0.6,0.8),ls='-')\n", "ax1.grid(True, which='minor', color=(0.6,0.6,0.6),ls='--')\n", "ax2.grid(True, color=(0.6,0.6,0.8),ls='-')\n", "ax2.grid(True, which='minor', color=(0.6,0.6,0.6),ls='--')\n", "\n", "ax1.set_ylabel('Magnitude [dB]')\n", "ax2.set_ylabel('Phase [deg]')\n", "ax2.set_xlabel('Frequency [Hz]')\n", "\n", "ax1.legend(['Measured','Model'])\n", "\n", "ax1.set_title('MICH Open Loop Gain')\n", "fig.set_size_inches(10,6,forward=True)" ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "## Generation of h(t)" ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "h(t) can be generated either from the error signal e(t) or from the feedback signal f(t).\n", "From the error signal, the calbration filter is \n", "$$h(t) = \\frac{1}{H}\\frac{1+G}{1}\\frac{e(t)}{L}$$\n", "\n", ",where $L$ is the arm length, $G$ is the open loop gain, $H$ is the optical gain.\n", "\n", "From the feedback signal, the calibration filter is\n", "\n", "$$h(t) = A\\frac{1+G}{G}\\frac{f(t)}{L}$$\n", "\n", ",where $A$ is the actuator efficiency." ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false, "run_control": { "marked": false } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/aso/anaconda2/lib/python2.7/site-packages/scipy/signal/filter_design.py:1057: BadCoefficients: Badly conditioned filter coefficients (numerator): the results may be meaningless\n", " \"results may be meaningless\", BadCoefficients)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "C_err(s) = \n" ] }, { "data": { "image/png": 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W4buBzxn/fR3wz4F/PF57G8Pbe1JsMz6jtM3SbmouWHV6JHDP8ecbgE9z+va82DVVS1Y9\nrTLV+TenRF9WmTk2JMZSX7G/pdhmfi40L636W32i3qdovYc9UjWUstPbSBss2w/2vEsR08xJ5v2Q\n1pA13mrbVA1ZZVp1qRmDLXFi1xSfJPUsKNdzDksNfSPDATEY3iL3iIwythmfSfkxISyd5NrfpW1I\nzeOc+ViyhqjXate6mC+mjEMIxU87mf38RIaALsDPk6ezUDnfxOlhxl/MvH9b8CwoTwiH+l7181P3\nxeqYmh8pnbdcO616gmb3cq7lomh5aTcV/23iZPazsmfZFjyrVMuKLnvsUaw1XF0L1HqqPkrq2pZ6\nWmgZ4IuBtwvPP1n8XlrOtvB5uXqusV2xOZDyK2HdPUjO2q7GbkL31fRLLiV6jsVpVNt8MvtZ9Ve2\nBc8rsc0xO1Jjmyz9bCP1UPfF6vrRY8/J7G+t91dzSm1zTM8tbPM3c5pAfT3wJRn3bxPX1b6qiY8r\nscka/2Si1I6qPkHreZ67n0ihxuk3wBsXfzspfHbsnlDZMbaZnyuNz9XEjFv72sz+VhL/hbz+WWpA\n9aOsurTSa6i+OZrdcKqpmpgFXKjZXjmliRJfIlauGp8C3ReN3dfLZ4bw/MjRhmLrSyjVq7WmnwjP\nX95T6kdvG33GwtJ5q1xf7n6m1CdQY37bwDOgbu2JlTlH/cJQ7H5rPEJaVnzWiZPMv1lsCz7bImac\n+8xWOk/VRdnvp+aOsue06mm1fVdxCQj7DkqubeJk9nOvnF3NOlYas1fzFWoMriYPuCVMjf2NPa9V\n/KGFXic25O+zeuXnlLmsxvTVtbPm3IGyf6+xtYodrjlvVkKtdtVzgPuUi0u1OfZcNdZV4/O29mvV\n+KC699uVzYWLY7tKnCBUToptwWchX7tqzKv23Fzpmt9DY6o9rvXfYd29GoT1puQplBjbtqB8tV9C\nX1aJjW2v2JGau1NyCKq/qtrcVBtyKdWttcafFDy3Rz4NtLWox3lEaP89gB7nb9T9f4+z36WUaNfS\n7Yb8/dmckvu2ievq9yN6jJ/6PQLVjqtn1VJzXTmbbNUzt8wULWyustfqnUMDzV8oyUmoZ9zXPnMO\nfc6XbQOfBX2ul1KiXSuWdSI8u0c+DcrPRNecPS89N5jaE20jdVTron6fEDR7WxuPyKXU5oa0q8YW\nYmwT12vzLyHboq6JStxBzRmoOlN9ITXusMuzjmvo82ApefvLMXEb8NHx52uAh5EOKL2T4e107xt/\n/4Lxv++dfeY7udh5sZ5lXbuO4a0pDwKeC/ws8NDx2sfG/14+e849gC8bf/5F4GYGob8K+IVFnUL1\nhMFYPJ9hgv6fwJdmPG8zawMME/QvuNAQWMTqUkNNnX4eeDHw7QwO8tsW168Hvgf4NuB549+eyfBm\nm9uAPwP+FPg3wO0MztivMYxHCzaUt83SbmouxDQB8C6GNwbBsIj9OKdaiV1TtWTV0ypTnX8Waj1z\nbEiuvkJ/a0loXlr13xDvE/U+61oM5Z45LW14yk7H5pZl+8GedxDWEIQ1c3eGQz4PZ3gD192pxxpv\ntW2qhqwyrbrUjIFlM2PXVFtkPQvK9TxRoqHfZBiPZzBsAt6dUe8cUn5MCEsnOfY3RGoep+ZjiA2a\n3bOu1a51MV9MGYccNsTbErJL/51hDJ7P0OdLnYU0GyrnvcC9ge9leMvgPhDqe9XPT90XIzU/Ujpv\nuXamUOxezjWVDfYatLSbj8f232L2N6Tn1J5lbRRd9tijWGu4uhao9dyg+Sipa6l5oJCqa2zvcVfg\nA5Eyc21zqpw1qbFdsTmQ8ith3T1Izdqu2NGaflHZENdzKE6T2lvnajnlr6xNzI5s0G2TpR8lnqje\nt/aec0LdX6lssMcqFneM2dQSP+PXgWcxjM1vA/9vbWPQ+6omPq7EJmv8kxQxO6r6BK3nubqfSJGq\nz/TMFzG8tf1JpONVJX7GsuxWlMYDamLGrX3tidL4L2i+qOpHWXXppVdIa3apKSVmAWHN9sopKcTG\neoMWnwLdF43d18tnhvD82JC2Z4qtryFVp9Ca3srG9spR9djzxtig6bl2P1Mai1V96pq1Z81xmNgQ\nH4+QllM+a66We+TJaik9x2GxQbfbVl2U/X5q7ih7TqueG+Jt31VcAsK+g5VrK/EleuXsatax0pi9\nmq9QY3A1ecAe9jf2vF7xhw3legV7nxXSbK/8nDKX1Zi+unbWnDtQ9u81tlaxwzXnzWrYUKZd5Rwg\nGfetyQa7zbG+VmNdNWtla79WjQ+qe79d2Vy4OLabihPEtLsveTc15lV7bq50ze+hMdUeb6jz33tg\n1QnCeivNIcP+5dliWGO7oU/sSM3dKTkE1V9VbW6qDSob7LEIrfFKzKxHPg20+b4h3mb1GrT/HkCP\n8zfWNWvO9jj7XcuGeFtivmnp/oyM+xTUM1kb2o+fVaZal4mQLVPPqqXmeo94TI9cxYZym6vs0fYp\nh6ainnHfsO6Zc+hzvkzZ8+3qTE4olqX4CtD3O1+lZ/lqzp6XPiu1J1LPmcXqon6fEDTbWBuPUNlg\n29yQdtXYgkqP/Iu6filxBzVnoOpsg+YLqXGHXZ51VPTpnCHegP1/go/xJuBnZr9fz6noTgi/kch6\n1vLacxjE/MTx9yuAvwQewPAWmJtnz7iOYWK/cvz9/sCvMDh4twFfm1nP6xjejgLDW1P+F8MLQKzn\nvRL4z4u2vHes/5zQm3By+uybSL8JZll2bp1KuRL44/Hn+wK/UVnekm3GZ1q0bandiZA+Y5qY+Arg\nR8Z777G4N3SthZaW9UzNB6t9OddUfaVsy3IceusL8jSWMy/hwvqX6DL3PkXrve1RiYZSuozNLcv2\nT8Tm3b5oaM58vGvaFiszZ8xDZVp1qamnZTNT9hTKfBKrPFXP+6Ihy4/JJbbWWdeWtiFnfUlptmQN\naWETS9c6Sys547BrP20ffLM5ofUlRqzvVT8/1x9K1TE0P2I6b712puqp2r1c3yal50PWMvT9P1fU\n6hLa7FFy1vDU85Q5Eqqn6qOkruX4E7vUMhy2bZ4otV2xOZDS5Np7kJy1Xd0rhe5T+2Xi2P0M6Gub\nQ3akxjZZ+lHiiTX3zem954T6uQruZ8wp2ffWxMehPDa5pMQ/mVDsqOITxK6p8zy3X9zPOCXHnoQo\njRn38LWV+O/0jJQvaq1XJX6UVZeStrv9PaXEl4iNdU18SvVFc+5r6TPH5keq7TW2fsJtbJ6dsbB0\n3irXl7ufKfUJVHvfIu/Q2t77Xu5CWsSMQRuXGrut6LUm96bsOa16Wm0viSG6LzGg+L4tYva5+Qo1\nBleTB+xhf63n5ZR5TL7ENuMzJXM5hBLTn8hdO2tjVaX79xpbq9rhCeW82cQx2dptwWdLfIRUm3P7\nOjfWVePztvZr1figuveb4zY3jJJ3g/yYV43tVNb8HhpT7XGLc0Gp8XGbW8byPmtse8aOlNxd7L4a\nnydWZo3NbXE27Zhtbm5Ored5xF7fA4A2529a7P9bnf2ec2zxsW3h562zu3N6jF9uP5b2f8yWtTir\nFpvrpWeTrXrmlnmWba7iL5TkJJbknnHfxZnzHufLas971uzPQvU9dJubG1+do+7XlXODqXFVz4vV\nxHmhnb2tiUfMOUSbu01cr43ZxmynsiYqcYcW3x0q0ZnqC9XEgVP1nNi1Ps8Ul+26AjvmfsDXUf6G\nmecxCPwHx98/H/g7DG9iVJ4Vunb7+N93jP/9OPDXwNOA1wFPBs4BVzMsZp8AbmUwsK9jePvKZxgm\nyL8DHgN8KlHP32eYYDBMoocBjwL+yHjePTldWCeuAD4SecZETp/BMJFvoextMLeLdUpxJ3AVw9vR\n3srQHyr3Z3h717yeTwDuNvv9Y8BPLO6rbdtSuxMxfVqaAPi98d8LGd6g+9UMWrWu1WgpVM87jTJT\n7UtdC5EzBqkyQ+PQUl+gaSx3Xi7rn6vLkvvunVnmHHV+9LDhKV3G5lbK9kN8bu2DhuaExhu0tlll\npsY8VKZVlw8Y11L1tGxmyp6W2qJYeR9G1/M+aMjyY85nPje21qWuLclZX1KaXaLavRybWGqnLNuX\nOw679tP2wTdTsPre0l1qXFJ6TRGbHyGdX2W0YaKl/wWa3cv1baBcz/uqZVhXzy102WqPkuNrWM9L\nUVJP1UdJ7aVS/gTsVstwuLZ5otR2WXPA0uR/ZN09iOpjldjROWq/zOfqMfkZsL6eY/sgxTZdgq0f\nJZ5IxX0Ta+w5a+MFE+5nDCgxOCiPj0+UxibnlPonMXI0pPgEsWs1PkhOv7ifcUppPADKY8Y9fG01\n/gt5vmiMUj/qvFGXnHjNhNtfDWvPpcSnVF80576WPrM1P6y219r6CbexdXamFFXPufuZJTWxWNWn\njrVhTmt7D76XU0nZEmVcVJ2relVzb282yjyPFhe22v45Rl2W89h9iYFS39fSUI0/GquLGoOryQP2\nsL/W83LKPFRfoubsFJSvyaDH9KFs7ayNVZXu363nWbb2o8a180b7UnrPXbsO1dauuUdLtTmnr0tz\nXFA+v3r4tWp8UN37TbjNbUtJzEu1ndb5BUsPPTSm2uMWZ1JTuM2twxrbnrEjJXcXu6/G57Hqqdjc\nXmfTjsXmlsz3nucRe3wPANqdv7HakLP/b3n2u+bcDhyPzS05k1Ubv6nZ25XUJZU7SNUTtNxzy3hM\nbpln1eauTckZ97XPnPc6X1YTO2m9P4PDtrnKWT51v66eG0yNq3JeTD13P9HS3lrPO5SzDJDWrqLP\nmpitRekY1cQdar47VKoz1Reqybml6jmxa306Z4gbgT8svOepnAr4bgxvGvkOBsH/0PjvVuD1DG8q\nyXlW6No1DBPpitnfbgVeNP48F/19gL9hWLCezmBA5/wE8IxEPR/HMKEnQ/sohgXzEYnnfS0Xbkgv\nG6998aIOy7ey5PRZLsuyc+tUyiXA3YFvBn4LeE1leUu2GZ+paVtIuxMhDVqaeBzwIU7f1PMl47Vv\nSVyDOi3F5lGszNR9qWug6csqMzYOvfUFaY3lzMtQ/XP6pPQ+Res97ZGioZgurbll2f6cubVrDU2E\nxrumbbEyrTG3yrTqotYzZTOtNRbKfBKrvBo974OGLD8mB2uts65B+K191jxOaTZUpmr3atee0DVL\nK7XjMKenn7YPvtmc3Lf3puap4udb9+XUMTQ/LJ33Wjtj9VTt3qHsOfbB/s4peRN1rS5b7lFSe+jU\n86Bsjlj1VH0U1dcooff++VBt80Sp7bLmgKXJtfcguWu7GrtZ3qf2Sylumy/GsiOqbbLGU40nqvdN\nrLXnrJ2ruZwVLZf2lRofV2OTE6Xr/pwSO1rjE7Se55C3n0hxFvyM3HhAiNKYcQ9fW43/5vqisfWq\n1I+y6gJt9Apnx/5CmS8RG2s1PqX6ojn3tfSZrflhtV219aUcu41tsee1dN4q15e7nynxCVR7X5t3\n6GHvc3H7ezE15zhiz1J1rupVzb2pe07Vbntc4pRt4rq6jtXG7EvzFTUxOGVf2cv+pvq6Nv5wSL7E\nNuMzNXO5NKY/Ubp21pw7UPbvqq2tif1BeS6nlEOytduCz5b4U6l4T6qvS2Ndqs/bw69V44PWtTVi\nvsdmc+eU7gVKY16q7VTX/B4aU+1x7bkgOFt7tW3BZ9V+Wd5njW2P2FFN7k7JIUwo/qpic1udTTtW\nm1uyFvU4j6iOuaqxiVJfvXb/3/LsdynHaHNTZ7KW9Bg/9XsEqh2vPasW208pZ5PXyFUcq80FzV8o\nyUlMlJ5xX/vMeY/zZTV7vlg9Szkmm5uzp12i7tdzn1XiN6fWUrUuqfMDLe1t6nmHcJYBNO1uE9dr\n8y/LNqtjVHN2VckZTJTqTPWF1LiDVc9SeuvTOUP8FPA7gb8/BfiywN+fBDyf4Q0sVzMYsesCnzsP\nfE3ms6xrvzXWBeC+DG8yuWb8/Rbgq8afXwX8i/HnRwNvXJTzGuBBiXo+ALhpdu2FizrFnncZgxF4\n4Pj7k4GbA89KObzzupSyLDu3TiVsGN5Wfvn4+w1oCX6LbcZnUm1TtRvSoKWJaxn0edfx96cCnwK+\nKHEN6rQUmyuxMlP3pa6Bpq9YmbFx2NBfX1C+UT3PhfMyVv9Unyj3KVr14G2cAAAgAElEQVTvaY8U\nDcV0mbK3Mdtvza0N+6Mhy94obbPKtMY8Vaa1xir1tMY1NeZQ5pPklDdxnjw9b9gPDaX8mNg6B7b2\ncny4kG2IzeOUvmJlqnavZu1JXZs4z6lWSvzJFL38tA374ZvNCWnI0uzEeS6cp6qfn/KHYnWMzY9c\nnYfaAG39r1q7l3MtxSFrGeoPN8S0XKPL1nsUsNd3dS1Q6qn6KKqvUULP/fOGw7fNpbYrNQcsTc45\nT989SO7arsZulve16pcUbpsv1rJlR1TbZI2nGk9U74N195xLzlM2V3M5K1oujcWDFh9XY5Ogrftz\nSuyo6hP0mOeQt59IcRb8jFQ/Kn5GTHc9fe2J8+TFf3N90dgcUPwoqw0t9Bqq77HaX8j3JayxVuNT\nqi+ac19Ln3nJeU7nR4k25veVxFZSHLuNTdmZnBhbyUHKmnhrzn6mxCdQ7X1N3qGXvc/F7W9ZzFgd\nl9q8QqguNfv92LWaPWesnqm2e1xiYJu4XuP7zjlPfsxezVeoMThlX9nD/ub4DLXxh0PyJbaZn7PG\nvXRvpp556XH2o2b/rtjaWjus5HJKOCRbuy34bImPYLU51ddqrEvxeXv5tUp8MHVtznnax3yP0eZO\nlGhXjXmpcf4558lb863npe5rbY9b+O9naa+2Lfisui8L3Rcb2x6xIzV3p+YQQPdXFZvb6mzasdrc\nkpxaj/OIvb4H0Pr8Te3+v/XZ7xKOzeZaY6v4uaCNn/o9AtWOp+qpaF49m2zVs1Wu4lhtLmj+QunL\nHZQz7mufOe9xvqxmzxerZynHZnPnnOdCmxTSbYuz56FnTZT4zTXnxay6KN8nrLG3LeIRKfbR5m4z\nPqPGbOHiNqtjVJPLqvnuUKnOanwhJe5g1bOUNb7HfWa4bNcV2DF3AO8J/P2FwDu48K0hDwbeAly5\n+Oy9Zj8/AHgJg0P1Coa3oLwl8Szr2o0MC9cjgIczOGkfHK+9Fngsw4J0BfD949//GPgN4GcYjMpd\ngf8CvD+jnjcD3wfcBXgY8A9n98SedyfwbcAPA28frz9rdt9zgSeMP78GeBvwCxl1ySFWdqpOCh9h\nMGDPAO4B3JOhT9Ym1TZVuyEN3kJcE+8A3sCwgH+GYRyeBrx3vG5dU7UUq6dVZuo+61qNvkJlWuPw\nGfZDXxOheflu4vW3+sRqt3WfovWe9kjRUEyX1tyCuO3/IPG5dQX7oaGUvVHapmooZaesNVapJ8TH\nNTXmUOaT5JRXqud9WedSfkyoP8DWSUqXlm2IzeOUvpQ1pMYmgmanIK6VlD+Zorefti+aBVtDMc1C\nvO9VP9/yh2J1tObHHdg6t9oAbf2vWru3z3uOQ9eyqsseexSIr+HqWqDWs8ZHUXyNHNbYPx+6nqHc\ndqXmgOVzwnp7kFQ91b1S7L7afknhtnkgpOWUjVFtkzWeSjwxZc/V9aP1nnNCnaspzpKWoWzfO6HE\nx1N6bu2fgG5HVZ+gxzxPxVctzpKfkerHUj8jtSfr5WuXxn/vwLbbqTlQ6kel2lCjV6u+x2h/S30J\na41W41OqL5qT72zpM0/EbHaq7Yqtz+Gs2NiUf2jZV0vnrXN9YPsnqk+g2Hs175Bae2rsfQq3vwNK\nzFgZl9q8gqJXNfem7jmtelpt97hEHjW+L5TH7FP+qJr3teqi7it72N+Uz6DGH47Zl7DGvXRvpp55\nSa2d6rkDdf+u2toaO6zkcnI4Vlur+AhWm62+rol1KT6vmjNUc39Wmalr0Cfme8w2t1S7NTEv1XZC\n+ZpvPY/EfT3sseq/+14tjLovs+6z9NIjdqTk7t6fuE/1eWryCz3Oph2zzYWynJrVZvWamlNS/Wqr\n3WobIL1XbH32O4djtLmpsVX8XNDGL1VmTf/HbJl6Vi3WhtT865GXTnHMNlfxF5SchHrGvYeNn2iZ\n05tQ4tuqrc7hGG3uRKyvQ7qtOXtuPUv1m5XzYqm6KN8nrLG3NfGIFIduc5WYbazN6hjVnF1Vcwag\n6Uz1hdS4Q6yeuayhT8dxnJ3x7F1XwDl6XGNOLa4hpxbXkHNIuF6dY8L17BwLrmXnmHA9O8eCa9k5\nFlzLzqHhmnUOCderc0y4np1jwbXs7CuuTedQce06h4jr1jlUXLvOIeK6dQ4V165ziLhunUPFtevs\nM65Px3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ec\nx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ec\nx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ec\nx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3Ecx3EOmkvG/352p7VwHMdxHMdxHMdxHMdxHMdxHMdx\nHMdxHMdxHMdxHMdxHMdxHMdxHMdxHMdxHMdxHMdxmnEp8GLgB8Z/c+4F/OTqNXIOkaWOrgTOAc8F\n/hVwl53VzDkUQrbIsk+O04NLgZ+d/X4Z8GrgRuDZBWWEdLss23F6EdPglzNo+tENyvox4AbgZVU1\ndZyBmN+o2M0WdtxxVGJavh54CYM9zWWp5bsw6PiZwAtqK+o4BSzjQi1s84OBlwJ3q6ua4xSx1HIL\n26yW4zgqoT2dGmtY3qfsFx2nhpDmWtlm8NyWsx4h3Spxs6WWPcfm7IKlnlX/YKlnz/U5a7PUshoj\nDvkZnutz1sKKn5X6uiHdep7PWZOQnpWch+f8nDUJaVTZp3l+z1mbkOaUvJzn8pw1ia3xyv7L83bO\nmsS0q8TUPE/nrEVItzV7Lc/HOWuSinGpuQjPyTk9yInJKpr1nJuzNiX5BfcLnH0gR7N7t/ZfD3zB\n+POvAY+dXfsu4I1rV8g5SJY6ugn46fH3PwAes4tKOQdFyBZZ9slxWnMv4OXAzbO/fSunwap/TV7S\nKqTbUNmO04uY7bwd+DPgeZVlfQPwqvFvrwMeWlNZx2HQ2dJvVOxmKzvuOCohLd8HePP4tzcB984o\nJ6Tlf8DpnurlwOfWVtZxMpnHhVrZ5q8GPgncAfwp8KvVtXScNHMtt7LNSjmOU8NyT6fGGkL3KftF\nx6lhqblWtnnCc1vOGoR0q8TNQloO7S8dpychPSv+QUzPnutz1iKkZSVGHNKy5/qcNbHiZyW+bki3\nnudz1iakZyXn4Tk/Z01CGlX2aZ7fc9YmpDklL+e5PGdNQmu8sv/yvJ2zNjH/VImpeZ7OWYuQbmv2\nWp6Pc9YiJ8b1YrRchOfknNbkxmSV/Jnn3Jw1Kc0vuF/g7JoS+xtd+y/tW8cgD+HUIf/fnBr6DXDb\nDurjHCZLHb2T4c0md2XQ9Xt3VC/ncAjZoph9cpwe3M7whqY7Zn97PPDB8eePkrdhD+k2VLbj9CJm\nO/8JcD/gDZVlXQf8j/Fv7wSeWFNZxwH+Exf7jYrdbGXHHUclpOUbgN8dr78A+MuMckJa/luG4MLd\nxn9/0abKjmOy4cK4UCvbfCVwBXAV8Cz8LdJOfzZcqOVWtlkpx3FqWO7p1FhD6D5lv+g4NSw118o2\ng+e2nPUI6VaJm4W0HNpfOk5PQnpW/IOQnj3X56xJSMtKjDikZc/1OWsSi59tKPN1Q7r1PJ+zNiE9\nKzkPz/k5axLSqLJP8/yeszYhzSl5Oc/lOWsSWuOV/Zfn7Zy1ifmnSkzN83TOWoR0q+61Nng+zlmP\nnBjXZWi5CM/JOa3Jjckq+TPPuTlrUpJf2OB+gbN7cjVrrv27eLnDL43/AB4F/N7482MYKu04OSx1\n9LsMbz79YeD7gU/sqF7O4RCyRTH75Dhr8RGGzT4Ma/Q1Gfe4bp1dY/l2TwNeUlnW/Thd1z8B3L+m\nso4DfIZ+fqNixx1HJaTlRwIPAp4CvLCi7BPgU8C7gT8cn+U4vekVF3oL8GmGA2EPAN7X4RmOM2ep\n5Va2uVU5jpOLsqfbh7IdJ8RScy1tque2nLUI6bZV3KxnrMRxQoT03Mo/8JyJsyYhLXuM2DlEYvGz\nFr6u5/mctQnp+YTynIfbc2dNTrhYo8o+LVSO4/TkhIs1p+TlPJfnrEmrNd7zds7axLSrxNQ8T+es\nRUi3qh32fJyza5YxrqvQchGek3PWIBSTVfJnnnNzdk0sv+B+gbOvhDRrrv27eLnDJ4GPMbx17beB\nW4HHAjfvoC4WX8GwWbgEuBp4nNdlb+oBYR19APhR4JXAfXdXtYNjn8Z1TUIaCv3NORvsyzz4D8DD\nxp+/lLxE6yHoVu3fHuOyL2N9TMQ0+IMMCdirgYdXlHUpw9v+Wfx8FnC99qOX36jY8X3kLGvv0Nq+\n1PJlDP9HiLcCDybf/i65BvivwM8Br2X4v6U4Z4NdzYE14kLfy2CnHacnIS23ss2tynHqWdtW7so2\nK3u6fSjbycfS1qH5xSmWmmtlU/cxt3VWOTbNhgjptmXczHNs5ZwF3fUipOdW/sEh5Eyc4yGk5WOJ\nES85FJvn9axjHj9r5ev2zPPtaz/2xnPoecz1rOQ8jsWe79NZDSdOTKOl+zTP7zlrY2lOycsdei7P\nbedh0GqN97zduvj8imtXial5ni7MoejsUOoJYd0qdnjf8nGHNAYKx94+lWWM66/QcxGek2uLa/Zi\nQjFZJX/mObfD4JjnQEjL++YXWBzz2DhhYjmx6Nq/fLnDlcCvAg/MfOC1wL8EbgR+GXho5n1XAU8G\nXjP+/nDga4FvGcu4LrOcXGLt+krgZcAW+E3gSbNr3wPcAtwJ/Hvgz2fX/h7weuBFDO2/dnbtC4EX\nA98FvBr48sznAXw78CPAC4BXZNbFIlbeE4FnA88H3sQwFi3qofSzdV+KuY4umf39Qwxt7MFPLsq+\nhSFAN/83vZnK0gLE+zk1r6z+ipVp1cUaV+s+q+0pjVltKNVDqp8tlrYo9rdarL6ysPox1/4uNWvd\nZ81Vq5/VMtV6qnPLep5qZydiui1dJ/+A4e3jTx3/+67M5/fQbQ7Lfoxh9a81P6z7rL5Vy7S0Zc3H\nmrVAWTut56n2JqdOVp8vNfgdwPPGn/+G4W2NuSzL+jPg7rNrHy4oK4Xqg8DF+rfGzPIdrXqoc6eH\nlq22W9esMnPXCAtFrz39RtWOp6jpK8XnzF0XS7SgzgOrDVaZVvuseaCuE6n25VCq55CWbwVuG/92\nB/AIoR5w2jc/B/wfwNeI5YRI7RVCqDbW0oGqEfV5EB9j63m5/VUy51RfKRfFNveOC10ylv/xhmUq\nWga7H9a2larPOaeVT6TOV6uetba5lZZb2eZW5YRQfA01zpm6NlESJ1DtqKo7NW5stU+NU+dSquea\nPV2KnmVD+T5P1Y8aG1X3cmpsTl331ZjMnNB+oWYfbt1v1SmkuVY2tacPk2MrLZb9r8aoUj5BzpiW\n7g+V3JalWTXubdXFal8upXoO6bZV3KxnrESNacT63ipP9bVVfyG1Rlv6iY2/Wk91XqWu5aDY5qWe\nn0pb/6BHzkTNR6rru5rPT11TxqsmJzxRui7F2tBiXYrRQsuPoF+MuCWKbVbXWvWaatfUelplzmmV\ne6+pZw5q7mQeP2vl6/bM8yn7ZfW8l2qXVf/Euma126qnem4I9P3CxFo+88RSz0rOo6c9V9crJT6s\n7u/VXGGPWIoaN1fz1DXn0FJ1ivV5SKPKPq1nfg/anulT/QB1z5Q7riUxDLV96nlMNbaTi2JzY5pT\n8nI9cnmqX2Xd1+OsgepnqDlAdT5Y+uxx5jmXUu22WuP3LW+njoE6rur6rJap+ibqPlDdy+ai9E9I\nu0rOrWeeTlmLWnzHpHTcY/epdjw1/5Q4V03uWNF1Dq10q9jhnvk45exPzXkBxR6rZxB62Fz1jIXq\nA1vty6XVdzxCMS4lF7HG995K+krdZ/TY7/WItao5hZqzwmvnKULEYrKKZnt+T6m0r9S9mvUsNc9l\naUvVnWoP1dhuTTwuhxZ6Dmm591njGMrcVvcxNeeylDxx6pqSP+uRO6zJK6boaX+z1/4XMDTus8Am\no9KXA+8HPm/8/e8Dv59xH8B3A58z/vu62d83wBszy7gh83Oxdl0B/LPZ789geHvWNePvW4a3oly9\nKO9eDB07bWbvx7CxmF6U8VOzz14C/Erm885xuthtgE8B90nUxcIq7yMMooKhHz8x1q+mHmo/l+pu\nzlxHNwP/ePz72xgmZQ65OoJh8nyI0yD01cDLgYcwOG8bhoXzc8frMS1AvJ9T88rqr1iZqbpsiY9r\n7L5U2y2NWW1Q9GC1LUXIFsXsU4yUhlJ9ZRHrx1z7u9SsdV9qrsb6uaZMpZ5WXcCeB7HngWZnJ2K6\nzR2nk9nP38TQBoBfLKhDTLcnwU+HKbGHEO7HGFvC/ZuaH7H7rL5VywRbW7H5WLMWKGun9bwae5Oq\nU0rPSw1+M6d9/HrgSwrqsCzrG4GXjtfeRF4yLEfPNT7IUv/WmKV8R6seW7S500PLE9bcL/GVctcI\nC1Wv/5y433hS8PzQPYodT+m1pq/OofmcW9LrYokWauZBrA1Wman2Wb7qlvJ1ItW+HBQ9h7T8RIY3\nOwL8PGUHCE5mP9/EaXDhWuAJmWXk2F+r/0OoNtbqO1UjNbqzdG71SU5/lcy5Gl8ph1rfeMPFcaET\noR7Le74YeHvB/T20DHY/rG0rVZ9zTiufSJ2vVj1rbXNLLbeyzUo5OVpWfI2aOKd1baI0TqDY0Zp1\nYosWN461T41T56Lo2drTnYj1mO5T94u99nmKftTYaM1eTonN1az7sWtqXBLq9uHW/ak6hTTXyjZP\nbGib2zpH2lZahPpfiVGlNJQzpqX7w3Noua0tYc2qce9UXWLty0XRc0i3Stxs4mT2sxUridHLz4B4\n31vl1fjaai5mS9yOxtoA8fFX61kzr6xrOai2eannV6HHk+Fi29w61wd6PlJZ30HP51vXlPGqyQlP\nlK5LsTa0WJditNLyI9BzfRD2M0J/i9HTNm8pX2vVazV2TalnqsyJlrl3tZ45qHqOxc825Pu6Eyez\nn1V/JUfPW8r2y+p5L9DssuqfpOq5Jd5uq57quSF1vzCxps88sdSzkvPokfMDfb1Sz4tt0fb3sfvm\nhMa2dSxFjZvX5KlrzqFZdbL6PKRRZZ/WM7/X8kyf6geoeyarLnNKYxjqOWH1PKYS28lFtbkxzZXm\n5ZR7ep2zSN3X+qxBqsxztM0BpuoyUXL+p9eZ5xwU7Vpr/EnBs9UYcw/tqmOgjqu6PteUuaXcN1H3\ngepeNhfV5oa0q+TclHt6+QotvmNSOu6x+0Cz46lxO0d5nKsmdxx7Xq12W+q2Jna2oSxG0evszxbt\nvIBij9UzCD1sbs0ZC9UHjrUvl5bf8QjFuEpzEdAvJzdR2lfqPqP1fq9HrLUmp6CeFd5FnmLiZPZz\nLCaraLZHzg3K+6pmr6ae3Z0o2R+puquxh1vKY7ugx+NyqNHzyexnK7+woTx3EaJnTHdL+T6m5lzW\nOcrzxKlrVpmxuvTIHdbkFVP0tr/Fa3+u0L4e+J+z3y9heGvqFybueybDWyo/AvwF8Mjx75cDPz2W\nmfMmuG3GZ+Ys2/Vo4DMMhg+Gt2F8lmFwrfKfPn7ustnfbgMeP/78Hk7bBMNbOVLPu5xBRA+a3ffg\n2c+xusRIlfdI4J7jzzcAn2Z4w0iLepT2c+y+FCEdPYfBcXhZQTnbzM9dxfD2lhNOjc3nceFC+Rzg\nq2a/x7Rg9XPuvAoZDGvsYnUBuw9i96XaHtPYHGvMS/Rgtc0ipKGYfbLYJq6n+soi1o85Oglp1rov\nNVdj/VxTplJPqy6peRB7HpTb2RBL3abacXeGRftDDI743YGHjX/7XvL0B2HdhspOsc18HsT7sbTs\n1PyI3Wf1rVom2PYkNh/VtWBOydppPa/G3qTqZPV5SIN3YdDg84HnFjw3VtbPMLT/1ZnlbAueWeqD\nhPRvjVnKd7TqsY3UoUZ3qpbBnvulvlKuj5hDqf0N+Y2K3Wxlx7eJ62pf1ficqTqVakGdB1YbrDJz\nNBDzVbfEic2t3PblUKLn2B7onzLY3+/OfGZIy38X+AGGt20+s6D+24zP5OwV5qg21uo7VSM1upsI\n2XurT1L9VTrnanylEkptM1wcF2plm2HQ0f9VUP9txmdKtQx2P6xtK1Wfk9nnW/lE6ny16tnKNrfQ\nMrSxzUo524zPKL6GGudU9+01a7sSW1F9pRzdlc4d63mllOg5tKdT7HLovnsGys5hW/DZkn2eoh81\nNlqzl1NiczXrfuyaGpecox4yj92fqlMsRtHKNrfObeXYSotY/ysxqtxYU2xMS31VNbcF8X5V4941\nseYSSvW81K0SNwtpWcmxbTM+o/gZVt9b5dX42mouZiu0Yc5y/NV6qvOq1t7MUfzmuZ7VeHJIzz1y\nfaDnI5X1HbR8vqq9Gn9CiVuAZn9r16UcarUMWow4pOVeuT413hwr2ypPvVbjLyj17LFXVfd5u8yd\nhOJnpb5uSLeKvwJ5es75zBz1vBdodln1T1L13EZbaNtl9dzQhLJf2IXPDBfrWcl59Mj5zVHXq9Lz\nYrE69coVto6lqHHzmjy16vctKdFuSKPKPq1nfm+ixZk+1Q9Q90xWXSaUHLfSPuu+HuePSim1uTHN\nlebllHu2GeUpflXqvtZnDawye+QAU3WZPl9y/qfXmecSSrQbWuPV/EdpjBn6aFcdA3Vc1fW5pswt\nNqX5NzUGucs9W0i7SkxNuWeb+TkoW4tqv2Oi5F1j94Fmx61xU+NcakxB1XUJLXSr7LWgPEYB/c7+\nxMrtsX9RzyD0sLk1ZyxUHxh2E1vIiXEpuQjol5MDra/UfUbr/V6PWGtNTqH2rPCaeYrcmKyi2V45\ntzm5fVWzV7OepeS5Wnyfp2WsdRsoP/U8qI/H5VCi55L8guIXxNgWfLZ0bqfKVs5Jxu5T88TWNTV/\n1iN32OL7Wil62V9z7b9s+YcCNsBHFw2YjPWfjH+7HvgC4GMMb+l5A0MALhSE+xTwfeO/NXgncB3D\nmzhgqCfAe8f/3pNh4/rXDIMxTfqPjdcvB+4cf74H8GXA7zC8Qe5m4LXAXwK/kPG86xjeWvIghrfX\nPhb4z7PPxuoSI1Xeu2affTrw42O7vrpxPVLtziGkIQjr6F304zsZxvJbZn+7bfbzNQybzfmbymJa\nsMZnQ3pehUiNeawuYI9r7L5U22Ma64HVNijXUGliIUWqryxi/bghrZOQZq373oI9V2P9XFOmUs8/\nMeqSmgex54Fm31Kk2vHXYxteO/vMe8Z/MUrW1WXZLYn1Y4xY/6bmR+y+DfG+/XWxTLDtSWw+zm1b\nyVpgYa2dVp/V2JsUG+J9bmkwRoltBnhFWXW7EtK/NWbTm+livqOFOnd6aBnsuV/qK9X6iBYbbPv7\nLi72G0M2eU5Is4odV1D7qsbnTK2LpVpI7aGUNlhlfjrRPstXVdYJtX05bIy2/DrhPdCPGOXlavmv\nGd4U2YPSvYJqYy0dXG1cszRSozsLq09S/VUz50p9pRo2pPsnFBeK2eaYLxGz539M2UHGHJR974Z4\nP6xtK38JzeecaOkTqfPV8v172eaNUR9Lyy1sc6ocFcXXUOOc6r59g762K7GV1Dqhxo1j7VPj1LVs\nsNu51J/iM8fu6xWvUFD0k9o/9YghKLG5mhiJEpOx4pI9SdXpbwlrLmZTS/2M1rmtHFtpEet/JUZV\nG2sq9VUvQ8ttQVyzKRvbI9ZcwwZbz0vd/i123CzXzwjFSlqg+BlW31vlXYvua6u5mJju1Hms1lOd\nV7X2xmJDer1Y6lmJJ4f0HIsx16LY0dR9ShzXyuerY7pB9yeUuAVo9rdnDiTGhnItK7m+mJ/RI9en\nxpuVtVa9ZsUQUv6CUs8ee9VUnlz1XWqw6vsnhONnlq9bouVeeb7S/bJ63gs0u7xB80/ea1z7nUS7\nLbusnhuKocYQa9mQts1LPf858ZxHzM/okfPrgXrmcEOfXGGvWEppnLcmT636fSk22D7XUqOpfVpI\nu5bWd4FyjtbyA1L2UbWBoOXblPZZdak5B9KLDbatiGkulpeL2VzrHhXVr0rd1/qsgVWm5WeoOcBU\nXaD8/M+GPmeea7Dq9OtcvMar+Y99ydtt0MZAHVd1fa4pU/FN1H2gupetZYM9jiH/NJb/gLhurXvW\nprY/lbxr7D7Q7PiG+Lg9EC3OpeaOVV3XsKFct0rsDPp910w5+1NzXiCEpQf1DMKG9jbXKjN1xkL1\ngWPtq2WTqG9ujMvKRcS03CsnB1pftc599Dg7psZaa3IKuzgrHGNDO72WarZXzk2hZq9moeS5enyf\np8YequfKWsfjctiQPquWk18ozV3sCmUfs0E7l9Vjj63mz3rkDtX1pedZ4Vz7a679NS93uA/wV4u/\n/Q2nb6i5EvgJhjdj3Bf4N+x2Qiz5LPD/zH7/IeBngT8cf/93wO+On/vw+PvDgf82fuYrGN4qch1w\nKXCv8b5/C3wlgyjvPpaRet5zZp95M/B/A7cwDPYtRl0+E2nbNYnyGOv/DQxC+unM+0rrkWp3in3R\n0PXAW4FPGp/58fHfnJgWrH5OzasYqbGL1QXscbXumwi1HcIa64FVx33R0ESsryxC/ZjSSUyz1n2p\nuRrr55oylXpadUnNA2su59i3b2JYiN8euD+EOp9j7Iuec2zikpz+Dc2P2H25fVtSZo7NS9m1krXA\nInfttGxKyt7sUs/7omWFmP6tMbsM23e0UOdODy1bc1/xlUp8xLNuf1V/usbntLSnaCG1h1LakCoz\npYHYPFDWidz2lWoZjtf+luwVamxsrO9y+jVUx1rdWVh9ErtWO+dKfaU57ksMlO57rX74Dda1lTU+\nZw+fqGa+hurZyzYfm58Bmq+hxjnVfbtqt61rVpmqr5TSnTJ3rOfVxCzIaGcJ+6DlGpR1eEKNjZbu\n5ZTYXOp5lrbUmIwSN1py1v2MnPxODKv/lRjVnNLYtuKrqrktsKgU8kkAAA/8SURBVPWsxL1rYs0T\nbps1PyPV97HyvpE6X1vJxcR0p87jHB+2dK9q1aWknmfdNoNuR5X1faI0n69qr8afiNUTtHUptw1K\nzhV8Dwh6vFlda5VrVgyh5kyLel6nR+5d7c8J9zMGSs8wqee9JkrtshoLTNUz1e6YXVbPDeVQmluc\n435GHapd7JUrhLaxFDXHaD1PPR81x+1wHso5WssPUPdMVl1Az7cp7UvVZaLV+aMlZ8nmqn5vzn0t\nzxpYZfbKASrzYc5Sn73OPE+cNZuraLdFe0vGVc1r15Sp+CY139tQ97lzzpLNVan5jomad1XPkSt5\numnsSuNcakxBja3POauxs9KzP+p5gRxKz74ocSvV5tacsVB94EOILYTYhZbVPH3r3EePs2MtztSU\n5hRqzwpb7Jte4TB8h5q9WgolzzVR832ekjJrvwsXoyYet+u9Woh907Kyj1HPZdWcNYqhnptJzdc1\n84pz9tH+Vr3c4XbgksXfrgA+Mv58J3AVw5sx3gqcq3jW/YGXLp73BOBus98/xjABFZ7H8JabH5z9\n7fcZxATDWzweBjwK+CPgyQztuRr4X8AngFsZBud1wHMZJtorGSbeY4DzxvNuH//7jvG/H2cwjE8b\ny7PqEiJVHsDvjf9eCPx3hre8tq7HklA/W7TUEGg6+nzg73Dh/5Vkyf2Ar2No34SlBaufU/MqhlXm\nm426nCc+ru9L3Bdr+0RIYx9PtKOU1JzbBw1NWH1lEZurMZ1Yms3V13KupvSslKnWU51b/9F4HuTZ\nt+cwOCC5C7k6n2Psw7qaYxNDpPo3Nj9i9+X0bWmZOTbPsmula8F58oitnZZNybE3u9TzPtnmEnL1\nvxyzO4n7jimUuZOju1ItW21XfaU5KR/R7e8pJf50jc8Z096H0bSgzoPU/iRW5j0T7YP4PFDXiZz2\nlWoZjtf+qnuFEhtr6eDexrVUHWt0Z2H1SejaVdTNuVJfabnvd19ioFTLVj+sbSvnlPicPXyi2vka\nqmduf7qfcSGlsbvQPZYmP2Bcs/btOf1eaketMlO6U+LG6txJPW/C/Yw6SvVj7Z9yyizdy33UuNYj\nRvJHxjU1LlnCWfczcvI7Iaz+r41Rlca21f2hmtuy9nJzW1ka947VJRVrnjgm27ymn5E7B0I+SI2v\nXeovgG0rc9qwRK2ntVdVfbNlPc+6bVbtqLq+T2WW5vNLxnROjT8Rq6cVt1Dt79QGNecKvgdcUrIH\nVNba3GeVxBBanGkp2cfW7lVDz0Os55xj8jNA13PpGSZLW2p+Tc3FWHVJ+QSpdofqeUmifTXnwWpi\niHC4fsbasYsYql3skSucaB1LUXPtqedB2T7x/Oy+Q7bDa2lXPUdbYx+h3AZ+Ci2GobYv575e54/g\n7NpcJfdh3df6rEGszB45QEtL1nyYCOmzx5nn+R72LNvcknhaTXtLx7Umr62WWeObQPn3NmL3WWUu\nOas2V6XEVqt519R9ih23xu1zxt9r4lwlMYUWuj7k2NmaZ3+U8wI5lJ59Ub+Lodpc9YyF6gMfSmwh\nxNpaVvP0PXIf8/tanR2bo8RaS3MKqfbVzHPYP72Crtl98xvUc8mlea6J2u/z5Jap+jA5sd2aeNyu\n92ohUlpeW7PKPqbm+6JQnie2aHFuplXu0Lp2KGeFs/kssMn43Ndy4US/jOHtE188/n4JwxuKvhn4\nLeA17aoIwLbw87F2PZVTo3e38TOPYxDcNDkfNd7/iPH3+cDch6Hdnw88nWGSz/kJ4BmJ513DsOhf\nMfvcrcCLMuoSIlXeh4AvHP/+JWN539KoHiX9nLqvt4YgraPvYHDGfmj8dyvweoa3tUzcyMVvLrS0\nYPVzal5NLPvLKtOqizWuOXoOtd3SmNWG3GtzUnXcBw1NhPrKwupHSyeWZnP0FZqrVj+rZar1VOeW\n9TzFzoZY6jZ3PueyD+tqjk1cktO/MVsSuy+nb0vLTNnKlF0rXQvmKGunZVNK7U2InnreJ9sM+WtO\njv5jYxbzHa16qHOnh5attqu+0kTKR8zhLNhfKO8r1ee0tFejBWUeWG2wyky1LzYPanzjnPblcOz2\nN3evEKLUxlp9p2pEfd6ckL23NBm7VjvnSn2lUlzLYXJiaRO9beVEqc/ZwydS56tVT+t5JZwVPwM0\nv6w0zqnu22vWdiW2ovpKENedOnfcNp+yLfhs7j5P1c+EGhst3cvVxuZK1301JpMbN8odnxjHruXU\n2h7D6v/aGFUq1rS8T/VV1dxWjq0sjXura1Yph6znbcFnS/yMnDkQKk/1tVV/wdJd7jyO5UZL62nd\np/pmpRyyliGt51w7WnKfGsdtMabKeJX6Peq6lNOG0nWpBN8DhlHX2pprqr+g1LPHXtV6Xm1/5nLs\ntlndLyvnvVS7XBMLtHwCay8Xq6d6bmhOyX7hrPrM24LPqutVSXxY3d+rucJesRQlbm49b6J0n1jK\nWdeueo4WdPuo2EA1hqG2Tz2PWRvbyeUYdav6VTE/rvVZA9XPAC0HWDMfIKzPHmeeSznr2lXHYEIZ\nV2V9ronfKb7JROk+0Lov51oux6hb0Nai0u+YqOOe8mUVO26NW22cqzSmUKvrHA4tdrZNXFfO/qjn\nBeaU7l+UMwg9bK56xkL1gQ8lthBibS2rfaXuM3rs93rGWktzCi3OCu9zniJES81uCz9f2lelezXr\nWWqea6Lm+zytYq1qbLdFPC6HQ7C/24LyS/Sq7mPUc1k1ZxRi12rPzbTOHVrXWmh2F/Y3qyIATwG+\nbPG3yxg6/oHj708Gbh5/3jD83yYuH3+/AS3gYrEt/HyoXU8Cns/wVo6rGSbvdcADgJtmn3sh8Duz\n328Bvmr8+VXAvxh/fjTwxsUzXgM8KPE8GIzGU8af78vwdo9rMuoSGhurvGvHa3cdrz2V4Y2rX1RZ\nj4mSfrbu29BfQ1Cuo/PA1yz+9lNc3BcpLcT62ZpXc0L9HCvTqos1rqk2QLjtKY1ZbbCuhbRu1XHD\nfmko1FcQn8NWP+bqBC7UbOq+2Fy1+lktU62nOres5+XatxRL3ZaMU4oN+7euwsU2MaTnnP4NzQ/r\nvpy+LS3T0laOXVPWggll7YzZlNS1XHrpecN+2WbIX3OWnOdC/VtjFvMdrXqoc6eHlpec52J/yLoW\nKzN3jUhxFuyv1VeWXhWfs2RdPE++FpR5APbaHivTap81D2p845z25XDs9jdlh2J6Vmys1XeqRtTn\nzVmOsfW83L0VlM+5Ul+pFNdyWMupfljTVkKdzzlxnnqfSJ2vqXq2sM1nwc8AzddQ4pypa3POkxcn\nUO2oqjs1bmy1D/Q4dQnHbpvn5O7zatdhNTZauperic3FnmdpqzYmM3Ge8H6h9SHzY9SyZStzYhZw\nYf/XxKgg7ROkxnReF7BtpZLbStlKJe5t1SXVvhIOWc/bzM8pfobV97HyVF9b9RdSusvRT2juKPW0\n7kvVJVfnKQ5Zy5DWc8pexLSsru9qPj91bUIZr5qcMJStS6k21K5LFr4H1HJ9VnnqNcWu1dSz9V7V\nel5NPUs4dtusnqVSznupdrkmFhi7ZrXbqqd6bmiOul+As+Mzbws+q+aoS+LD6v5ezRX2iqWocfPY\n80DfJ5Zw1rVbc45WsY+qDVxynrwYhto+9TxmbWwnl2PTrXrOInZfj7MGNfs/JQdYMx8grM8eZ55L\nOevarRkD0MZVWZ/VMmvOMan7QHUvW8Kx6Xai1M/N6c/SHIRybl2146lxU+NcakxB1XUuhxY72yau\nK2d/WpwXKN2/KGcQethc9YyF6gMvOc/+xRZCbNitHYa873eAvs/osd/rFWuF8pxCi7PC+5qnCLGh\nrWa3hZ8v8R2UvZr1rJrzuVD3fZ5WsVY1ttsiHpfDIdjfbcEzSvSq7mNqzmWpZxSsa+q5mR65QzWe\nmMva9vf/f8jEc4EnjD+/Bngb8Avj7y8E3sGFb5u4E/g24IeBtzMMwLPGax9hMCjPAO4B3BN4bevK\nZxJr14OBtwBXLj5/L+AOhs7+PuAuwMOAfzj7zGuBxzK0+Qrg+8e//zHwG8DPMIjirsB/Ad6feB4M\nb9e5ieENLA9nENgHx2tWXUJjY5X3QeANDAbqM2PfPA14b2U9lH627tsnDcFgVF/CMPlfwTDubxmv\n3QG8Z/F5Swtg93NsXoE9T60xt+oSG9dUG2Jtfwe2xqw2lNohq45XsF8aCvUVxOdwqh8tnUBcs7H7\nUjbR0oJSplrPmrllPc+ybyliurXWyVIOxSaG9HwL6f4NzQ/rvpy+LS3T0tb7sedj7HkpvaprZ+x5\nOddS9NbzPmm5dM2ZCOn/3dhjFvMdrXqoc6eHlq22vyXjWqjMHJ2nOCv2N9VXll4VnzNHe4oWlHmQ\nakOsTEsDKR9L9Y2t9uVwVuxvqv9Dek7NAUUHNRpRngfxMU49L2W3lTkH5b5SLq7lgZhtTvXDmray\n1uds6ROp8zVVzxrbfFb8DNB8jZo4p7pvV+22EluxxjllK1O6K507qTh1DmfFNkP5Pq92HVZio7H7\nUv6mEpuznmdpuTYmE5vH1vjkcJa0bNlKaw8I8f5XYlQTsbU2dZ/iq6q5rZhma+Le6pqVw1nRsxrT\niPW9VZ7qa6u5mJRPYOnHmjtqPZV5lbqWw1nRcmqdjmlZXd9TcVx1TGvGS/V7lHUppUt1XbLwPaBt\nmy2bZ5WnXgPdrin1TJUJ7XPvaj1zOCu2ObUWx2yzct6rxi6rscDYNavdKbusnBsCfb8A7jOHUHPU\nanxY2d/X5Ap7xFLUuHnseTX7xBxcuwM152gV+1hjA6E8hqG2L0djLc8f5XKMulVjEqnxa33WoMbP\nUHKAORosPf+j5slT7cvBtTtQMwagjauyPqtlqr5JKnetxCB9zxZH8XPV75hMKOMeu886R55ah61x\nU+JcNd9xUnSdw7HGzpSzPzXnBdT9tXIGwYpbWWWqeWLrmvqdpFT7clhDu0t2GTuL9ZWaw4j1X4/9\nnjUmNXYRynMKNWeF9z1PEeJQfIeavZp6dhfK90ckrvWItSqx3Zp4XA7HZn8VX7cmxqqey1LPKNTs\n20t98l3kFVPsyv4ePM/edQWco8B15NTiGnKOBdeyc0y4np1DwvXqHBOuZ+dYcC07x4Jr2TkmXM/O\nseBado4F17JzTLienWPBtewcE65n5xBx3TqHimvXOURct86h4tp1DhHXrXOouHadY8G17BwSrlfn\n0HDNOo7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7j\nOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7j\nOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7j\nOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOI7jOM4Z4f8DgbtCq85V0I4AAAAASUVORK5CYII=\n", "text/latex": [ "$$\\frac{7.2477698459014 \\cdot 10^{-8} s^{23} + 0.275339079771072 s^{22} + 420200.014779563 s^{21} + 263203663557.547 s^{20} + 8.2219310007748 \\cdot 10^{16} s^{19} + 1.49891234771544 \\cdot 10^{22} s^{18} + 1.89275621270335 \\cdot 10^{27} s^{17} + 1.77864779814186 \\cdot 10^{32} s^{16} + 1.30385959263247 \\cdot 10^{37} s^{15} + 7.69392714333039 \\cdot 10^{41} s^{14} + 3.7289242517829 \\cdot 10^{46} s^{13} + 1.5078187794043 \\cdot 10^{51} s^{12} + 5.11076148957251 \\cdot 10^{55} s^{11} + 1.45107486685406 \\cdot 10^{60} s^{10} + 3.4423649357237 \\cdot 10^{64} s^{9} + 6.70256339688575 \\cdot 10^{68} s^{8} + 1.05276189569947 \\cdot 10^{73} s^{7} + 1.28634969968071 \\cdot 10^{77} s^{6} + 1.16043383023948 \\cdot 10^{81} s^{5} + 7.00039027006795 \\cdot 10^{84} s^{4} + 2.06701046273143 \\cdot 10^{88} s^{3} + 1.11220007814567 \\cdot 10^{91} s^{2} + 4.89416594973199 \\cdot 10^{93} s + 6.13186937306687 \\cdot 10^{93}}{1.0 s^{24} + 12598265.6365121 s^{23} + 47860168587311.8 s^{22} + 7.30402802408645 \\cdot 10^{19} s^{21} + 4.57507583781277 \\cdot 10^{25} s^{20} + 1.4291578374472 \\cdot 10^{31} s^{19} + 2.60544916903589 \\cdot 10^{36} s^{18} + 3.29003901334975 \\cdot 10^{41} s^{17} + 3.09169274290079 \\cdot 10^{46} s^{16} + 2.26640330059425 \\cdot 10^{51} s^{15} + 1.33737880755041 \\cdot 10^{56} s^{14} + 6.48171496352864 \\cdot 10^{60} s^{13} + 2.62093056193966 \\cdot 10^{65} s^{12} + 8.88366107348671 \\cdot 10^{69} s^{11} + 2.52229652640252 \\cdot 10^{74} s^{10} + 5.98360995385174 \\cdot 10^{78} s^{9} + 1.16505437391728 \\cdot 10^{83} s^{8} + 1.82993849828781 \\cdot 10^{87} s^{7} + 2.23583692847016 \\cdot 10^{91} s^{6} + 2.01709109542622 \\cdot 10^{95} s^{5} + 1.21424580672562 \\cdot 10^{99} s^{4} + 3.59179409500874 \\cdot 10^{102} s^{3} + 4.8182902571891 \\cdot 10^{102} s^{2} + 1.23134771745139 \\cdot 10^{104} s + 1.54046116422229 \\cdot 10^{103}}$$" ], "text/plain": [ " 23 22 \n", " 7.2477698459014e-8⋅s + 0.275339079771072⋅s + 420200.014779563⋅s\n", "──────────────────────────────────────────────────────────────────────────────\n", " 24 23 22 \n", "1.0⋅s + 12598265.6365121⋅s + 47860168587311.8⋅s + 7.30402802408645e+19⋅s\n", "\n", "21 20 19 18\n", " + 263203663557.547⋅s + 8.2219310007748e+16⋅s + 1.49891234771544e+22⋅s \n", "──────────────────────────────────────────────────────────────────────────────\n", "21 20 19 \n", " + 4.57507583781277e+25⋅s + 1.4291578374472e+31⋅s + 2.60544916903589e+36\n", "\n", " 17 16 \n", " + 1.89275621270335e+27⋅s + 1.77864779814186e+32⋅s + 1.30385959263247e+37⋅\n", "──────────────────────────────────────────────────────────────────────────────\n", " 18 17 16 \n", "⋅s + 3.29003901334975e+41⋅s + 3.09169274290079e+46⋅s + 2.26640330059425e\n", "\n", " 15 14 13 \n", "s + 7.69392714333039e+41⋅s + 3.7289242517829e+46⋅s + 1.5078187794043e+51\n", "──────────────────────────────────────────────────────────────────────────────\n", " 15 14 13 \n", "+51⋅s + 1.33737880755041e+56⋅s + 6.48171496352864e+60⋅s + 2.620930561939\n", "\n", " 12 11 10 \n", "⋅s + 5.11076148957251e+55⋅s + 1.45107486685406e+60⋅s + 3.4423649357237e+\n", "──────────────────────────────────────────────────────────────────────────────\n", " 12 11 10 \n", "66e+65⋅s + 8.88366107348671e+69⋅s + 2.52229652640252e+74⋅s + 5.983609953\n", "\n", " 9 8 7 \n", "64⋅s + 6.70256339688575e+68⋅s + 1.05276189569947e+73⋅s + 1.28634969968071e+\n", "──────────────────────────────────────────────────────────────────────────────\n", " 9 8 7 \n", "85174e+78⋅s + 1.16505437391728e+83⋅s + 1.82993849828781e+87⋅s + 2.235836928\n", "\n", " 6 5 4 \n", "77⋅s + 1.16043383023948e+81⋅s + 7.00039027006795e+84⋅s + 2.06701046273143e+\n", "──────────────────────────────────────────────────────────────────────────────\n", " 6 5 4 \n", "47016e+91⋅s + 2.01709109542622e+95⋅s + 1.21424580672562e+99⋅s + 3.591794095\n", "\n", " 3 2 \n", "88⋅s + 1.11220007814567e+91⋅s + 4.89416594973199e+93⋅s + 6.13186937306687e+9\n", "──────────────────────────────────────────────────────────────────────────────\n", " 3 2 \n", "00874e+102⋅s + 4.8182902571891e+102⋅s + 1.23134771745139e+104⋅s + 1.54046116\n", "\n", " \n", "3 \n", "───────────\n", " \n", "422229e+103" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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xuM25Keg1Vb3a7VjcJCIPAvuBdar6SVn7RuWViohMFZFfRWR1sfLzRWSDMzbY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\n4LDP+mGObrYKhSdEZLWIZAC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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#The arm length\n", "L = 3000.\n", "\n", "#Calibration filter for the error signal\n", "C_err = ltu.ltiprod(ltu.ltiadd(OPLG,1),1/Hrf/L)\n", "\n", "f = np.logspace(-1,4,1000)\n", "a=ltu.bode(C_err,f)\n", "print(\"C_err(s) = \")\n", "sp.Poly(C_err.num, s)/sp.Poly(C_err.den, s)\n", "\n", "#print(\"Numerator = {0}\".format(C_err.num))\n", "#print(\"Denominator = {0}\".format(C_err.den))" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false, "run_control": { "marked": false } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "C_fb(s) = \n" ] }, { "data": { "image/png": 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y5Pzx14Jjj6LFntao85dzahkuz8+oRZ2PRuV6YpcLLTHWEX7zFrUf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\nVT8kmkeo2qdQ7tLeHZaz4Vv9Ke+sIVP3jHzkwh72OzpX77pkZT3haB9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/GXFvd8d8LLI5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\nAAAAAAAAAAAAAAAAAAAAAOCA/gefCP2lwKwpyQAAAABJRU5ErkJggg==\n", "text/latex": [ "$$\\frac{5.52589835948042 \\cdot 10^{-11} s^{42} + 0.000216961512657348 s^{41} + 354.790420312223 s^{40} + 260266274.536923 s^{39} + 105580723756812.0 s^{38} + 2.78004856933243 \\cdot 10^{19} s^{37} + 5.37867827220287 \\cdot 10^{24} s^{36} + 8.20432734885922 \\cdot 10^{29} s^{35} + 1.03083250710448 \\cdot 10^{35} s^{34} + 1.09796222632483 \\cdot 10^{40} s^{33} + 1.01105895054077 \\cdot 10^{45} s^{32} + 8.16333718601102 \\cdot 10^{49} s^{31} + 5.83972234439465 \\cdot 10^{54} s^{30} + 3.73095603895531 \\cdot 10^{59} s^{29} + 2.14219696085644 \\cdot 10^{64} s^{28} + 1.11077753396176 \\cdot 10^{69} s^{27} + 5.22105343580463 \\cdot 10^{73} s^{26} + 2.23085610896236 \\cdot 10^{78} s^{25} + 8.68189709324965 \\cdot 10^{82} s^{24} + 3.08098502476118 \\cdot 10^{87} s^{23} + 9.97395166832189 \\cdot 10^{91} s^{22} + 2.94436592305837 \\cdot 10^{96} s^{21} + 7.91721423016217 \\cdot 10^{100} s^{20} + 1.93537554615261 \\cdot 10^{105} s^{19} + 4.28887460205994 \\cdot 10^{109} s^{18} + 8.58313714037551 \\cdot 10^{113} s^{17} + 1.54351842543881 \\cdot 10^{118} s^{16} + 2.47840334029502 \\cdot 10^{122} s^{15} + 3.52450838428602 \\cdot 10^{126} s^{14} + 4.39301876098821 \\cdot 10^{130} s^{13} + 4.73426813026615 \\cdot 10^{134} s^{12} + 4.33155316116204 \\cdot 10^{138} s^{11} + 3.28010751019969 \\cdot 10^{142} s^{10} + 1.98055861296111 \\cdot 10^{146} s^{9} + 8.99019173723305 \\cdot 10^{149} s^{8} + 2.7661311978351 \\cdot 10^{153} s^{7} + 4.66808939754821 \\cdot 10^{156} s^{6} + 2.41860179983683 \\cdot 10^{159} s^{5} + 9.27762534878257 \\cdot 10^{161} s^{4} + 2.47031574817965 \\cdot 10^{162} s^{3} + 3.32538628068683 \\cdot 10^{163} s^{2} + 4.36703360574347 \\cdot 10^{163} s + 4.96732314532177 \\cdot 10^{162}}{1.0 s^{41} + 19898707.9825279 s^{40} + 140204979770383.0 s^{39} + 4.29817422086958 \\cdot 10^{20} s^{38} + 6.30721276002286 \\cdot 10^{26} s^{37} + 5.05003751525654 \\cdot 10^{32} s^{36} + 3.25651706408734 \\cdot 10^{38} s^{35} + 1.63167699669109 \\cdot 10^{44} s^{34} + 6.29118882689929 \\cdot 10^{49} s^{33} + 2.0148485075795 \\cdot 10^{55} s^{32} + 5.02132890886361 \\cdot 10^{60} s^{31} + 9.27721532289994 \\cdot 10^{65} s^{30} + 1.38650642951997 \\cdot 10^{71} s^{29} + 1.70800615744304 \\cdot 10^{76} s^{28} + 1.79971629549211 \\cdot 10^{81} s^{27} + 1.64394234357549 \\cdot 10^{86} s^{26} + 1.32251429513324 \\cdot 10^{91} s^{25} + 9.44888377329462 \\cdot 10^{95} s^{24} + 6.03435562142154 \\cdot 10^{100} s^{23} + 3.46159654412903 \\cdot 10^{105} s^{22} + 1.7864645595547 \\cdot 10^{110} s^{21} + 8.31127794472349 \\cdot 10^{114} s^{20} + 3.4808656234484 \\cdot 10^{119} s^{19} + 1.31080803669544 \\cdot 10^{124} s^{18} + 4.4240041681939 \\cdot 10^{128} s^{17} + 1.33050515721277 \\cdot 10^{133} s^{16} + 3.54865122212777 \\cdot 10^{137} s^{15} + 8.29093172869544 \\cdot 10^{141} s^{14} + 1.68197708212625 \\cdot 10^{146} s^{13} + 2.90000809661285 \\cdot 10^{150} s^{12} + 4.16001019850112 \\cdot 10^{154} s^{11} + 4.77987082985886 \\cdot 10^{158} s^{10} + 4.16424438219602 \\cdot 10^{162} s^{9} + 2.50306576003682 \\cdot 10^{166} s^{8} + 7.91304008790529 \\cdot 10^{169} s^{7} + 3.05609950237586 \\cdot 10^{172} s^{6} + 1.20534163037796 \\cdot 10^{173} s^{5} + 2.23008821434378 \\cdot 10^{174} s^{4} + 5.52032625910151 \\cdot 10^{174} s^{3} + 3.91817932795838 \\cdot 10^{175} s^{2} + 4.91734692984843 \\cdot 10^{175} s + 5.5709884075953 \\cdot 10^{174}}$$" ], "text/plain": [ " 42 41 40 \n", "5.52589835948042e-11⋅s + 0.000216961512657348⋅s + 354.790420312223⋅s + 2\n", "──────────────────────────────────────────────────────────────────────────────\n", " 41 40 39 \n", " 1.0⋅s + 19898707.9825279⋅s + 140204979770383.0⋅s + \n", "\n", " 39 38 37 \n", "60266274.536923⋅s + 105580723756812.0⋅s + 2.78004856933243e+19⋅s + 5.378\n", "──────────────────────────────────────────────────────────────────────────────\n", " 38 37 36\n", "4.29817422086958e+20⋅s + 6.30721276002286e+26⋅s + 5.05003751525654e+32⋅s \n", "\n", " 36 35 34 \n", "67827220287e+24⋅s + 8.20432734885922e+29⋅s + 1.03083250710448e+35⋅s + 1.\n", "──────────────────────────────────────────────────────────────────────────────\n", " 35 34 \n", " + 3.25651706408734e+38⋅s + 1.63167699669109e+44⋅s + 6.29118882689929e+49⋅\n", "\n", " 33 32 31 \n", "09796222632483e+40⋅s + 1.01105895054077e+45⋅s + 8.16333718601102e+49⋅s +\n", "──────────────────────────────────────────────────────────────────────────────\n", " 33 32 31 \n", "s + 2.0148485075795e+55⋅s + 5.02132890886361e+60⋅s + 9.27721532289994e+6\n", "\n", " 30 29 2\n", " 5.83972234439465e+54⋅s + 3.73095603895531e+59⋅s + 2.14219696085644e+64⋅s \n", "──────────────────────────────────────────────────────────────────────────────\n", " 30 29 28 \n", "5⋅s + 1.38650642951997e+71⋅s + 1.70800615744304e+76⋅s + 1.79971629549211\n", "\n", "8 27 26 \n", " + 1.11077753396176e+69⋅s + 5.22105343580463e+73⋅s + 2.23085610896236e+78\n", "──────────────────────────────────────────────────────────────────────────────\n", " 27 26 25 \n", "e+81⋅s + 1.64394234357549e+86⋅s + 1.32251429513324e+91⋅s + 9.44888377329\n", "\n", " 25 24 23 \n", "⋅s + 8.68189709324965e+82⋅s + 3.08098502476118e+87⋅s + 9.97395166832189e\n", "──────────────────────────────────────────────────────────────────────────────\n", " 24 23 22 \n", "462e+95⋅s + 6.03435562142154e+100⋅s + 3.46159654412903e+105⋅s + 1.786464\n", "\n", " 22 21 20 \n", "+91⋅s + 2.94436592305837e+96⋅s + 7.91721423016217e+100⋅s + 1.93537554615\n", "──────────────────────────────────────────────────────────────────────────────\n", " 21 20 19 \n", "5595547e+110⋅s + 8.31127794472349e+114⋅s + 3.4808656234484e+119⋅s + 1.31\n", "\n", " 19 18 17 \n", "261e+105⋅s + 4.28887460205994e+109⋅s + 8.58313714037551e+113⋅s + 1.54351\n", "──────────────────────────────────────────────────────────────────────────────\n", " 18 17 16 \n", "080803669544e+124⋅s + 4.4240041681939e+128⋅s + 1.33050515721277e+133⋅s +\n", "\n", " 16 15 14 \n", "842543881e+118⋅s + 2.47840334029502e+122⋅s + 3.52450838428602e+126⋅s + 4\n", "──────────────────────────────────────────────────────────────────────────────\n", " 15 14 \n", " 3.54865122212777e+137⋅s + 8.29093172869544e+141⋅s + 1.68197708212625e+146\n", "\n", " 13 12 \n", ".39301876098821e+130⋅s + 4.73426813026615e+134⋅s + 4.33155316116204e+138⋅s\n", "──────────────────────────────────────────────────────────────────────────────\n", " 13 12 11 \n", "⋅s + 2.90000809661285e+150⋅s + 4.16001019850112e+154⋅s + 4.7798708298588\n", "\n", "11 10 9 \n", " + 3.28010751019969e+142⋅s + 1.98055861296111e+146⋅s + 8.99019173723305e+\n", "──────────────────────────────────────────────────────────────────────────────\n", " 10 9 8 \n", "6e+158⋅s + 4.16424438219602e+162⋅s + 2.50306576003682e+166⋅s + 7.913040087\n", "\n", " 8 7 6 \n", "149⋅s + 2.7661311978351e+153⋅s + 4.66808939754821e+156⋅s + 2.41860179983683\n", "──────────────────────────────────────────────────────────────────────────────\n", " 7 6 5 \n", "90529e+169⋅s + 3.05609950237586e+172⋅s + 1.20534163037796e+173⋅s + 2.230088\n", "\n", " 5 4 3 \n", "e+159⋅s + 9.27762534878257e+161⋅s + 2.47031574817965e+162⋅s + 3.32538628068\n", "──────────────────────────────────────────────────────────────────────────────\n", " 4 3 2 \n", "21434378e+174⋅s + 5.52032625910151e+174⋅s + 3.91817932795838e+175⋅s + 4.917\n", "\n", " 2 \n", "683e+163⋅s + 4.36703360574347e+163⋅s + 4.96732314532177e+162\n", "─────────────────────────────────────────────────────────────\n", " \n", "34692984843e+175⋅s + 5.5709884075953e+174 " ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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G2qnqfhFZBPweWAxMBv4ZKKeKGRUvvn+BRRKXy8Xq1auZO3cuc+bMYc6cObhcLi666CIu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\naCSwQUTWAl1FZCNwuqoudvp9DAwEvo2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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Calibration filter for the error signal\n", "C_fb = ltu.ltiprod(ltu.ltiadd(OPLG,1),ltu.ltiinv(OPLG),Act,1/L)\n", "\n", "f = np.logspace(-1,4,1000)\n", "a=ltu.bode(C_fb,f)\n", "print(\"C_fb(s) = \")\n", "sp.Poly(C_fb.num, s)/sp.Poly(C_fb.den, s)" ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "## ETM individual actuation efficiency" ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "We also wanted to check the actuation efficiency of individual ETM. To do so, we first locked MICH with low UGF (around 10Hz). The open loop gain of this lock is shown below.Around 100Hz, the open loop gain is low enough that the feedback will not affect the actuation efficiency measurement." ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": false, "hide_input": false, "run_control": { "marked": false } }, "outputs": [ { "data": { "image/png": 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rFr2cC/yp+D13X5Bkx0REkrbmmmHaxyVLFlEYBbOSjz8OCyxNnx6S9BkzQpK+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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "TF=np.loadtxt('data/TFs/Data/RF-Lock-LBW-OPLG.txt', comments='#')\n", "f = TF[:,0]\n", "real = TF[:,1]\n", "imag = TF[:,2]\n", "mag = np.sqrt(real**2+imag**2)\n", "phase = rad2deg(np.angle(1j*imag+real))\n", "\n", "fig = plt.figure()\n", "ax1 = fig.add_subplot(2,1,1)\n", "ax2 = fig.add_subplot(2,1,2)\n", "ax1.set_axisbelow(True)\n", "ax2.set_axisbelow(True)\n", "\n", "ax1.semilogx(f, 20*np.log10(mag))\n", "ax2.semilogx(f,phase)\n", "\n", "ax1.grid(True, color=(0.6,0.6,0.8),ls='-')\n", "ax1.grid(True, which='minor', color=(0.6,0.6,0.6),ls='--')\n", "ax2.grid(True, color=(0.6,0.6,0.8),ls='-')\n", "ax2.grid(True, which='minor', color=(0.6,0.6,0.6),ls='--')\n", "\n", "ax1.set_ylabel('Magnitude [dB]')\n", "ax2.set_ylabel('Phase [deg]')\n", "ax2.set_xlabel('Frequency [Hz]')\n", "\n", "\n", "ax1.set_title('K1:LSC-MICH_IN1_DQ/K1:LSC-MICH_IN2_DQ')\n", "fig.set_size_inches(12,8,forward=True)" ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "Now we injected a signal to ETMX and measured the transfer function to the MICH RF signal output. By dividing this with the RF optical gain, we can compute the actuation efficiency of ETMX. Note that this calculation does not take into account the open loop gain. So the values at low frequencies (below 10Hz) is inaccurate. " ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "collapsed": false, "hide_input": false, "run_control": { "marked": false } }, "outputs": [ { "data": { "image/png": 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BvPTS0tx5Zy/mz6/hgguW4KCDYIkl4rFH8pUnP3bseGpr55SMPZKXfCHlE0Ou\nI0eOzKuHLtOA7m133zDl2n/dfWCuFUeNhlxFNVBKQ1Hu8MILcPnl8MkncOaZcPTR0KlT3JaJcqeU\n/FyIqCjKkGsLcpkuqBBCVAFmQTqxF1+EMWPguedg1VWD7U5+/DFu64QQorLJNCirN7NrgZvD898B\nBdg0JVoqeZVrY2Njq6tmorYnkZeu1PUn2ilbe8aPH8+cOdkN8UycOLFZrr589Cff49aGXIuxyjVb\n+c02g8cfh//9Lwjo+vWbz667fssBB3zDiivOaSbfkv7U/IfF/j7m6j/F1p/r96WmpoYBA7Ibsk/+\nWwj9yfe4JfsrfZWrnufV/Twv9j50XYArgHqCdF2XAV3y2S8l6gPtQ1fW9Wvfosran+vTT93PPNO9\nRw/3PfcMsk8sWNB2Ofl5tHrk56WB/DxaPeXi5+S5D12rQ65mdq6ZDXT3me5+jrtv7O6buPt57j6z\ntbJCCJFglVXgqqvg889ht93g5JNh/fVhxIhgGxQhhBD50dYcuk+AU8zsv2Z2p5kdaGbdi2GYEKLy\n6NIFhg6Fd9+F66+Hp56ClVeGs84Kgj0hhBC50eocOnd/AHgAwMwGArsAj5hZe4K8rv9w97citzJH\nKnkOXdzyjY3K/ZdOf6Xkci2GfLducOutvfnll97cfDNstBFssw2ccgqsvnojU6Y0b9NSsr+U5HP9\nviiXq+QT53qeN9dfkblcUw9gKWBfYEQ+471RHmgOXVnXrzkX1Te3qKnJ/ZZb3Pv3dx8wwP2OO9xf\neaU+Vpvk5/mVkZ9nhp7n0eopFz+nGLlcwx653YFVSOrVc/eh+YeUIhda+qVcKfUXSn+uenIpl02Z\nTGTjvsfFpmtXOOEEOO64YD+7G26AN97YkOOPD+bcLb988W2Sn+dXRn6eGXG3gfw8vzKl4ueZbiz8\nNPAL8C6QSO7j7n5JhLblhTYWFtVApW+4OmkSXHcd3H8/7L8/nH46rLVW3FaJYlPpfi4E5L+xcKb7\n0PVx9+abCQkhRISssQbccgv84Q9w002w1Vbw618HWSi22CJu64QQonTINKB7xsx2cvfnIrWmwGhR\nhOQrXb6cF0VkKz94MBx22Ir84x+9OPRQ6N07COwGD4avvy59+yWfu7wWRUi+kuULtSgi0yHXvYF7\nCLY5mQsYwZDrUnlbEBEachXVQLUORc2bB488EuxtN2MGnHEGHHooLLlk3JaJKKhWPxfVRbFyuV4L\nbA50dvejbA1vAAAgAElEQVSl3L22lIM5IURl06EDHHAAjBsHt94KDz8M/frB5ZfD9OlxWyeEEMUn\n04DuS+B/6vIqHdJ171ZS/YXSn6ueXMplUyYT2bjvcSnQVhuYwaBB8Mwz8NxzMGECrLYanHZaYTYq\nlp/nV0Z+nhlxt4H8PL8ypeLnmQZ0nwAvhanAhieOKA0TraMHQLR6quUBUOpk0wbrrw933QXvvAPt\n28PAgfCb38CTTwZDtFHXH6d++Xl5E3cbyM/zK1Mqfp5pQPcp8E+gBqhNOoQQoqRYaSX485/hyy9h\n333hssuCXLIXXRRcE0KISiSjVa7u/oeoDRFCiELSpQscdVRwvPMOjBwJG2wQbHdy3HGw667BXDwh\nhKgEWn2cmdnF7n5xvjJxoW1LlPsvV/lSz/23SE9lb1uS2qa56t9gg2AfuyuvhAcfhIsvnsOQIbDH\nHtPYc89vWWGFuSXxeXOVz/X7olyukk+c63neXH9F5XIFvgKGt3KcDkzIJ/dYVAfK5VrW9Sv3n3Jc\nukfrZ++84/6737l37+6+++7uTzzhPndu8eovpH75eXmj53m0esrFz8kzl2tbc+hGsvicudSjaygj\nikxLv5Qrpf5C6c9VTy7lsimTiWzc97gUiLINBgwIeu1S59pdfDF880309RdSv/y8vIm7DeTn+ZUp\nFT/PaGPhckQbC4tqQBuuFpbx44NUYw8+CIccEmSi6Ns3bquE/FxUA8XaWFgIISqeAQPgttvg/feh\na1fYaCM4/PDgXAghShkFdEIIkcIKK8AVV8DHH0P//rDddrDXXvDvf8dtmRBCpCejgM7MekRtiBBC\nlBpLLw3nnQeffAI77BCkG9tuO3j+edCMDiFEKZFpD92bZvY3M9vNzHIe380FM+tnZneY2YNJ1/Y0\nsxFmdr+Z7VhMe4QQ1UfnzjBsGHz0ERx5JJxyCmyySZBDdsGCuK0TQojMA7o1gRHAYcAkM7vMzNaM\nzqxFuPun7j4k5drj7j4UOAE4oBh2lBpKFROtnmpJFVPqxN0GqfUvsUQwp+5//4MLLoCrroJ11oHR\no2HOnPz1F8rOKMvJzwtP3G2g53l+ZUrFzzMK6MItUp5394OBY4EjgLfM7GUz2zwTHWY2ysymmtn4\nlOu7mNkEM/vQzM7O0v4LgJuzLFMR6AEQrZ5qeQCUOnG3QUv1t2sXzKl780249Va4/35YbTW4/nqY\nOTN//YWyM4py8vPCE3cb6HmeX5lS8fOM59CZ2SlmVg+cAZwE9CTYWPi+DOsaDeycorcdcFN4fV3g\nYDPrH753mJlda2a9EuIpZa8Annb3tzOsXwghCooZDBoEzz0Hjz4Kr7wCq64Kl14KP/wQt3VCiGoi\n0yHXN4ClgL3cfXd3f8Td57l7PXBbJgrc/VVgesrlTYFJ7v65u88FxgB7hvJ3u/twYLaZ3QpsmOjB\nM7OTgO2B/cxsaIafQQghImPjjeGhh+Cll2DSpKDH7pxzYOrUuC0TQlQDGW0sbAXapdfM+gJPuvuA\n8HxfYOdwPhxmdiiwqbufXIC6/Nhjhy88r6vbnLq6LfJVWzI0NjbGurt41PUXSn+uenIpl02ZTGQz\nk2mid+/ajG0sN8rZzxsb23PPPV159tlO7LzzLA47bAa9es0vmP5C6JGflwbl7OfF1F9pft7Q8DoN\nDW8sPB858tq8NhbONC/q88DSSefdgWezzTMG9AXGJ53vC4xIOj8UuCGfXGZJutrMm1bOKPdftHrK\nJfefclyWfv1ff+1+zjnuyyzjfsQR7u+/X1j9+eiRn5cGleDnxdBf6X5OnrlcO2QY9y3r7gtnhLj7\ndDNbLucochGTgZWTzvuE1wrC0KFDqauro66ubuG13r17p42kGxsb005aLFX51DLFtqepqYn6+vqS\n1594na09NTU11NfXZ2V/wuZC6U8u15L9TU01QOn5Z6HkU9u02Pbk6j+p8vvuCzvt1J5//GM1tt12\nKbbcEs49t3D6c/2+1NTUNLtWCHuy0Z98j1vS39Q0jfr60vPPQsnreV7dz/OGhgYaGhqalc+WTIdc\nG4C93f2L8Lwv8Ki7b5RVZWarEAy5rh+etwcmEsyHmwK8BRzs7h9ko7eFujyTzyZEOaMcl+XHzJkw\nahRcfXWw5cl558HWWwcLLER65OeiGsg3l2umPXTnA6+a2csEq023ArJajGBm9wHbAj3M7AvgIncf\nHS5weI5ggcaoQgRzCSq5h07ykofK76GrVPmTT4bjj4d77oFjj4WuXecwePBkdtzxe5Zc0pvJl5r9\nxZav9B46yVe3fFF76ADMrCewWXj6prtPy7v2CFEPnagG1HNR/syfD888E+xn9+9/BxsXH3ccrLVW\n3JaVDvJzUQ3k20OX6bYlAB2B74GfgHXMbOtcKxVCCBHQvj385jfw1FMwbhwsuSRssw1sv32wDcrc\nuXFbKIQoBzKdQ3clcCDwHpDIXOjuvkeEtuVFsG3JsRpylXxFyzc11TBo0ICSsUfyhZGfO9cYO3Zp\n/v73Pnz2WUeOOQaGDoWVVioP+wstP3bseGpr55SMPZKXfCHlE0OuI0eOLMq2JROBjvkspy32QYVv\nWzJ5crzL+KOuv1D6c9WTS7lsymQim4lMpW/nID93f+8995NOCrY9GTzY/emn3efPz15PrvXnU0Z+\nnhny82j1lIufU6RtSz4BlgBm5xw5xkAlL4pobFx8k8Ji25Oov9T1J/Rka8/EiROztj+xLL9Q+pPv\ncWs9dJW8KCLVz4ttT67+U0j966zTmxtugMsvhzFj4Pe/h+OPn8fgwV+zxx7TWGaZeTl/X5qamrK2\nP/We5Ks/WV9L9lf6ogg9z6v7eV6oRRGZ9nY9DHwE3A7ckDjyiSSjPqjwHjptRBmtnnLZiLLSey7k\n5y2Vcz/6aPellnLfbjv34cM/948/Lk798vPCIz+PVk+5+DlF6qF7IjyEEELEzMYbB3vZ3XgjvPAC\n/OUvndh8c1huOdhjj+DYZBNol82yNyFEWZNRQOfud5lZJ2Bld58YsU0Fo5KHXOOWT+6SLkf9bcmn\n2yU8E/2Z7iyeq/7meip/yDXOTBHlIN+7Nxx9dCPnndebqVP78sYby3LMMTBtGgweHAR366wzhenT\nmyfhaWpqanatLXuykc9Ef/I9rtYh17jl9TxPr79Yz/NiD7kOJlgY8Wl4viHwRD5dg1EfaMi1rOtX\nF72Gotzl5/no+egj9+uucx80yL221n2PPdzvuCPILZtP/fLzwiM/j1ZPufg5eQ65ZtohfzGwKfBD\nGCm9DayafzgpcqWlX8qVUn+h9OeqJ5dy2ZTJRDbue1wKxN0G5eznq60Gp54KL74In38OBx4Izz8P\n/fvD5pvDfffBCivIz0uBuNugnP08qnLl6OeZ7kP3prtvZmb/dfeB4bXx7t58A6wSQZkiRDWgHfRF\ntsyZE8y7+8MfgtdXXAE77VTauWTl56IaKFYu1/fM7BCgvZmtAZwMvJ5rpcVCc+gkX+nylT6HTvLR\nyC+3HNx0E7z99qqcfPIy9OkTBHabbFKa9msOneQrWb6ouVzNrDNwPrATYMCzwB/d/Ze8LYgI9dCJ\nakA9FyJf5s2Dv/wl6LH79a/h0kthjTXitmpx5OeiGihKLld3/9ndz3f3Tdx94/B1yQZzQgghMqND\nhyCt2KRJMHBgML/uhBNgypS4LRNCZEOrAZ2Z/V/490kzeyL1KI6JQgghoqZzZzj3XJg4MXi93npw\nwQXw449xWyaEyIS2eujuDv/+GbgmzSFiIt14fSXVXyj9uerJpVw2ZTKRjfselwJxt0E1+nmPHnDN\nNfCf/8BXX8Gaa8J118Hs2dnXJT/PjLjboBr9vJBlSsXPW10U4e6JWXr1wCx3XwBgZu2BjhHbljeV\nvCiisVG5/zLRn9CTrT2lnvsvQaUvikj182Lbk6v/FFt/rt+X1nKtfvttI8OGwS67dOLmm1fk6qs7\ncc45P/OrXymXq57n8eiv1Od5sTcWfhPomnTeFXg9nw3woj7QxsJlXb82otSGq+7y86j1ZFPuX/9y\n33xz9379fvZ773WfN68w+uXn8vOo9ZTL85wibSy8pLvPSAoCZwCd8w8nhRBClANbbQWvvQannfYl\nt9wCa68Nd94Jc+fGbZkQAjJc5QrMNLONEidmVgfMisYkIYQQpYgZbL75T7zyCtx+O9x9dzDH7vbb\nF82xE0LEQ6YB3anA38zsFTN7FXgAGBadWUIIIUoVMxg0CP75T7j3Xnj8cVh9dbjhBpiln/pCxEKm\n+9CNA/oDJwDHA2v7ogUTIgbSTcyspPoLpT9XPbmUy6ZMJrJx3+NSIO42kJ+3XWaLLeDpp+Gxx2Ds\nWFh1Vbj6apgxQ36eKXG3gfw8vzKl4uetZoows+3c/UUz2yfd++7+SGSW5YkyRYhqQDvoi1Jj/Hi4\n7DJ48UU45RQYNgy6dctPp/xcVANRZ4rYOvw7OM3xm1wrFUIIUZkMGABjxsC//gUffgirrQYXXgjf\nfRe3ZUJUNq3uQwdMD/+OcvdXozam0FTyPnSSlzxU/j50ki9v+csv782FF/bmyiuD/LBHHAGnnQYd\nOmSnv9L3oZN8dcsXah+6toZc33b3Dc3sP+6+UYuCJYiGXEU1oKEoUS589RVcfz385S+w225w5plB\nb14myM9FNRD1kOsHZjYJ6G9m45OOd81sfK6VCiGEqC769AkWS3zyCay/Puy6a3CMHQv67S1E/rQa\n0Ln7wcBWwCSaz58bHLl1okXSde9WUv2F0p+rnlzKZVMmE9m473EpEHcbyM/zK5NOtls3OOusILDb\nf38YOnQum2wCDz4I8+ZlbU5FID+PVk+1PM9bDejM7J/u/jXwrLt/nnpEbp1oET0AotVTLQ+AUifu\nNpCf51emNdmOHeHoo+Hee9/hwguDPezWWgtuuQV+/jlrs8oa+Xm0eqrled7WkGsvM9sCGGxmA81s\no+QjcuuEEEJUNO3awR57wKuvBpknnn8e+vWDP/wBpk2L2zohyoe2VrleCPwe6ANcm/KeA9tFYVQy\nZtYPOB9Yyt0PCK/1B04BegAvuvttUdshhBAiWrbYAh59FCZMgGuuCdKKHXIIrLFGR3r1gt69gywV\nQojmtDWH7iF33xW4yt0HpRyRB3OhDZ+6+5CUaxPc/QTgQGCLYtghhBCiOPTvDyNHwnvvQc+eMGZM\nFwYOhOWWgx13DFbI3ntv8H61zrsTIpW25tAdCuDufzSzX6e8l1UuVzMbZWZTU1fHmtkuZjbBzD40\ns7Oz0DcY+DvwdDZ2CCGEKA969YKLL4Ybb/yeqVODLBTDh8Myy8ATT8A++wSLLDbZBIYMgZtuCoZu\nf/opbsuFKD5tzaEbnvT6xpT3js6yrtHAzskXzKwdcFN4fV3g4HA4FTM7zMyuNbNeCfHksu7+pLvv\nDhyapR0VgXL/RaunWnL/lTpxt4H8PL8yhfRzsyDA23VXOPdceOABmDgRpk4NFlTU1cH//gdnnBEM\nza6+OpxzDsycmbG5sSE/j1ZPOfl5PrS1sfB/3X1g6ut05xlVZtYXeNLdB4TnmwEXhcO6mNk5gLv7\nlUlllgEuBXYA7nD3K81sG2AfoCPwjrvfmqYubSwsKh5tuCqqgWz9fP78INi77LKgx+6mm+A3SlYp\nSpx8NxZua1GEt/A63XkurAh8mXT+FbDpYpW4fw+ckHLtZeDlAtQvhBCiwmjfHtZZB+65J1g1e+KJ\ncOedQaaKFVeM2zohoqGtgK5/OOfNgNWS5r8ZsGqklhWAoUNPX/i6rm5z6uq0fkJUFo2NTWlzXApR\nSeTj5927w+jRMHp0Leut15khQ2aw334zad++wEYKkSUNDa/T0PBGwfS1NeTat7XC2W4u3MKQ68Xu\nvkt43mzINVc05CqqAQ25imqgUH7+wQdw/PHBxsUjRsDArCYNCREtkQ65RpANwlh8ccM4YPUw0JsC\nHAQcXKjKhg4dSl1dHXV1dQuv9e7dO+3kxMbGxrQ7OUte8qUs39RUA5SOPZKXfBTyTU3T0vbQ5aL/\npZd6c+edsMsu8NvfwiWXwE8/ldbnlXx1yTc0NNDQ0NBMLmvcvSgHcB/QCMwGvgCOCq/vCkwkyBd7\nTgHr80pm8uTJFV1/ofTnqieXctmUyUQ2E5lx4+L1g6iRn0erp5r9/Jtv3I84wn2lldwfe6zg6rNC\nfh6tnnLx8zBuyTnuaWsOXcFw90NauP4M8EwUdVZyD11jY+Ni5YptT6L+Utef0JOtPRMnTsza/vr6\n+mbv5aM/+R5Xaw9dqp8X255c/afY+nP9vjQ1NWVtf+o9yVd/sr5i9NAl5JddNlgoMXYsDBkyj+uu\na+KMM75ghRXmFkR/NvJ6nlf387xoPXRAe+DefKLGOA4qvIdu3LhxFV1/ofTnqieXctmUyUQ2M5nK\n7qGTn0erR34e8Msv7hdf7N6jh/u117rPnRtpdc2Qn0erp1z8nKh76Nx9vpn1NbMad5+TfwhZPCq5\nhy5u+eRfMOWovy35pqYm6uvrs9afWqbQ+pvrqfweuuR2itueUpXP9fvS1NTU7Fpb9mQjn4n+5Htc\nzB66ZL77rpHdd29k3XU7cuWVfbnllg4cddQUDjusEyutFP/9jVpez/P0+ov1PC/qHDrgrwQLGH5P\nkD1iODA8n0gy6gP10JV1/fpFVxo9F3EjP49Wj/y8OQsWuD/xhPvmm7uvvrr7iBFBD16UyM+j1VMu\nfk6ePXRtpf5K8DFB3tR2QG3SIYQQQlQMZjB4MLz2GowaBY8+CquuCn/+M7TQ4ShESZDRogh3/wOA\nmXUNz2dEaVShqOQh19QyxbYn0cVc6vpbmoTalj01NTVZd6Gn63bPR3/qZOBqHHJNbdNi25Or/xRb\nf67fl5qammbXCmFPNvqT73FcQ64tya++em+efro3b78NV14J/foF+9gdeODXzJ79VcHs0fO8up/n\nhRpybXVj4YVCZusBdwPLhJemAYe7+3t5WxAR2lhYVAPaWFhUA6Xi5x9/DFdfDQ8+GOxhd8YZ0LfV\n7feFyJx8NxbOdMh1BMGcub7u3hc4HRiZa6VCCCFEubHaanDbbfDee9C5M2y0ERx+eHAuRNxkug9d\nF3cfmzhx95fMrEtENhWMSh5ylbzkofKHXCUveYhvyLUlefdG9t+/kV12ac9DDy3L1lsvz3rrzeCM\nM+YxePCyRbdH8uUtX+wh10eB/xAMuwIcCtS5+955WxARGnIV1UCpDEUJESWl7uezZsHo0cFwbK9e\ncPLJsO++sMQScVsmyoliDbkeDSwLPAI8DPQEjsq1UiGEEKJS6NQJTjwRPvoIzjoLRoyAVVaBP/0J\nvvkmbutEtZBpQLeDu5/s7hu5e527nwrsGKVhonXSde9WUv2F0p+rnlzKZVMmE9m473EpEHcbyM/z\nK1Ntft6+Pey1F7z4IvzjH/DFF7DWWnDkkfCf/7RcLu42kJ/nV6ZU/DzTOXTnAn/L4FpJUclz6Bob\nlfsvE/0JPdnaU+q5/xJU+hy6VD8vtj25+k+x9ef6fanmXK5Ry6+/ftBTd/nlcN11P7H77h1Zfvk5\nHHjgNwwa9AMdOrie51nqr9TneVEyRQC7AjcCU4Ebko47gbfy2dE46gNliijr+rWzeOntoB8H8vNo\n9cjPi8fcue4PP+y+zTbuffq4X3qp+zffBO/Jz6PVUy5+TsSZIhqBeuAXoCHpeALYOf9wUgghhKh8\nOnSAffaBl16Cv/892NNuzTXh6KNh4sROcZsnKoBWAzp3f8fd7wJWd/e7ko5H3H16kWwUQgghKoYN\nNgjSik2aBGusAcOHr8HWW8NDD8G8eXFbJ8qVTBdFrGJmD5nZ+2b2SeKI1DIhhBCigunZE849Fx5/\n/F1OOgluuCFIL3b55TBtWtzWiXIj00URo4GLgOuAQQRblmQaDMZGJS+KyHRSclT2KPdfc3uUy1W5\nXOPSr1yu0dhfLPmVV+7FZpvB/vvDf/8LV101k1VX7ci22/7AgQdOZa21ZkVqj57nze2p5FyuDe5e\nZ2bvuvv6ydfytiAitLGwqAZKfcNVIQpBNfr5tGlwxx1w883BnnYnnQR7763NiiuZYm0sPNvM2gGT\nzGyYme0NdM21UiGEEEK0TM+ecM458OmncMopQWDXrx9ceil8+23c1olSJNOA7hSgM3AyUAccBhwR\nlVFCCCGECFbH7rcfvPwyPPVUEOCtuWawWXEhti4TlUNGAZ27j3P3Ge7+lbsf5e77uPubURsnhBBC\niIANNgiGYT/6CNZeOxiC3XJLeOQRmD8/butE3GQU0JnZWDN7MfWI2jghhBBCLE6PHnD22fDJJ8Fw\n7NVXB9uf3HADNDXFbZ2Ii0yHXM8AzgyP3wNvE2w4LGIi3QqfSqq/UPpz1ZNLuWzKZCIb9z0uBeJu\nA/l5fmXk55mRaxt06BCsjH3jDbj3Xnj11WCe3VlnwZdfRl9/sfXLz1sno21L3D11pP41M3srAnsK\nSiVvW5KcFy4OexL1l7r+hJ5s7Sn13H8JKn3bklQ/L7Y9ufpPsfXn+n1RLtfSkC/E83yJJRo56yz4\n7W9rePDB5VhvvZ5st90czj+/Mxtv3Lo9ep43t6ficrn6oryoyyQdPQnSfk3MJ+dY1AfK5VrW9Sv3\nX/XkuGwN+Xm0euTnpUEUfvbDD+7XXOO+8sruW23l/uij7vPmFa/+KPRXup8TcS7XhQEkwRBrA/AG\ncDpwTP7hpBBCCCEKTbduMHx4kDN22LAg+8Raa8FNN8GMGXFbJ6Ig04BubXdf1d37ufsa7r4TMC5K\nw4QQQgiRHx06wAEHwJtvwl//CmPHBhsVn3MOfPVV3NaJQpJpQPd6mmtvFNIQIYQQQkSDGWyxBTz8\nMLz1FsyaBQMGwCGHwHvvdY7bPFEAWg3ozGwFM6sDOpnZQDPbKDy2JdhoWMREuomZlVR/ofTnqieX\nctmUyUQ27ntcCsTdBvLz/MrIzzOj2G2w6qpw/fXBJsV1dXD++Wuy5ZZBsBfFfnby8+Lc41ZzuZrZ\nEcCRwMYEQ6yJHGM/AXe5+yNRG5gryuUqqoFqzHEpqg/5ebTMmwePPgrXXQdTpgR5Y485JpiHJ4pH\npLlc3f0udx8EHOnu27n7oPDYsxjBnJn1M7M7zOzBlOudzWycme0WtQ1CCCFEJZPYz+7112HMGBg3\nLtjP7tRTg82LRXmQ6Ry6OjNbOnFiZt3N7E8R2bQQd//U3Yekeets4IGo6xdCCCGqiV/9Cu6/H955\nBzp2hE03hX32gVdeAQ16lTaZBnS7uvsPiRN3nw5k3DtmZqPMbKqZjU+5vouZTTCzD83s7Ax17QC8\nD3zLoiFgIYQQQhSIlVaCK6+Ezz6D7beHo4+GTTYJMlLMmhW3dSIdmQZ07c2sY+LEzDoBHVuRT2U0\nwWbECzGzdsBN4fV1gYPNrH/43mFmdq2Z9UqIJxXdFvgVcAiQrvdOCCGEEAWga1f43e9g4kS46CIY\nPRqWXRa22SY4HzsWfvklbisFZB7Q3Qv808yOMbNjgOeBv2Zaibu/CkxPubwpMMndP3f3ucAYYM9Q\n/m53Hw7MNrNbgQ0TPXjufkH43r3AyExtqDTizn+o3H/5lSmV3H+lTtxtID/Pr4z8PDPiboNM6m/X\nDgYPhhdeCBZOnHcezJ4N554LPXvCttvCxRfDSy81D/Dk56WVy/VKM3sH2CG89Ed3fzbPulcEktMH\nf0UQ5CXX+z1wQgs2tRlQDh16+sLXdXWbU1e3RU6GliJBXrjKrb9Q+nPVk0u5bMpkIpuZTFPaHJeV\ngvw8Wj3y89KgHP28Rw/Yb7/gmDnTePvtGv7znxoeeqgjn3zSgXXWmUtd3Wzq6ubQo8cU+vaNx85c\nyxXDzxsaXqehoYBb+uaSLwzYErg5yzJ9gfFJ5/sCI5LODwVuyCePWUp9beZNK2eU4zJaPeWS+085\nLsu7fvm5/Ny98vz8xx/dn3rK/cwz3TfZxL1Tp3k+aJD7rbe6z5+fu95K93PyzOWaUQ8dgJkNBA4G\nDgA+BfLdtmQysHLSeZ/wWsEYOnQodXV11NXVLbzWu3fvtBv8NTY2pu0SlXx6+cbGRurr68tWf1vy\nTU1N1NfXZ60/tUyh9TfXUwPE7w9Ryae2adz2lKp8rt+XpqamZtfasicb+Uz0J9/jlr8v09L20JVK\n+5e7fKGftzNmNLLcco0ccECQdmzSpG+YOnUNRo3qy5gxNYweHWyLUqzPW+rP84aGBhoaGprJZU1r\n0R6wJnARMAF4FTgJ+DyXyBFYBXg36bw98BFBz10N8DZBzlj10GVApf2ii0p/pf+iU89FedcvP5ef\nu1ePn8+b53711e49e7rffrv7ggW56cm1/qjKlEsP3QTgFeA37v4RgJmdlm3QaGb3EaxO7WFmXwAX\nuftoMzsJeI5gccYod/8gW92toR668vlFpx663OxXD11p218sefXQZW6/5ON9np9xRm923RWOOAIe\neQTuuAPatavu53mxeuj2Ilh9+iXBitLtgU/ziSCLdVDhPXSTJ8f7izXq+gulP1c9uZTLpkwmspnI\nVHrPhfw8Wj3y89KgGv18zhz3Sy5xX3ZZ97vuyqy3rtL9nDx76FrN5ZrAzLoQbClyMLAdwZYlj7r7\nc/mHlNGgXK6iGlCOS1ENyM8rl//+Fw4/HFZbDW6/HZZfPm6L4iPfXK6ZblsyE7gPuM/MugP7E6Tf\nKtmADjTkKvnKl6/0IVfJSx405FrJ8gMHwhNPNHLJJcY66/TkzDO/YIcdppeN/YWQL9SQa0Y9dOWI\neuhENaCeC1ENyM+rgzffDObWbbQR3HRTsNddNVGUHrpyRT10kq90efXQSb4a5NVDVx3yHTrAqFHt\nuOWWFenfvztXX93EkUc2j+pK1f5c5dVD1wbqoRPVgHouRDUgP68+Xn4ZjjoqyBn7f/8H3brFbVH0\n5NtDl2kuV1FipPs1UEn1F0p/rnpyKZdNmUxk477HpUDcbSA/z6+M/Dwz4m6DUvTzbbaBd96Bjh1h\n7ewWsukAACAASURBVLXhtNPg4YenMW9eceovRz9XQFem6AEQrZ5qeQCUOnG3gfw8vzLy88yIuw1K\n1c9ra+G22+C556B7dzj//E706gVHHw1PPAGzZkVXfzn6uebQhZT6GHupyTc2amPhdPq1sXBh5VPb\nNG57SlU+1++LNhaWfOK8lJ/n660H660Hu+32AcsuuzF33fUjl1xiHHJIZzbdtIltt53Ollv+SP/+\ny5fl87woGwuX80GFbyxcLali4tJTLqliKn3DVfl5tHrk56WB/Dw3Pd9+6z56tPuee7rX1rpvv737\njTe6f/ll/vWXY+ovDbkKIYQQouzo2ROOPBIeewymTIHf/Q7GjYMNNoBNNoHLLoOJE+O2snhU9JCr\nEEIIISqfLl1g772DY+5ceOUVePRR2HZbWGqpdTjqKDjwQOjXL25Lo6Oity059thjK3YOXWNj42Ll\nim1PU1MTtbW1Ja8/0U7Z2jN+/HjmzJmTlf0TJ06ktra2YPqT73Frc+gGDRqQ1p5y8ueW5BN+EJc9\nufpPsfXn+n2pqalhwIDs/Cf5byH0J9/jluwfO3Y8tbXZfR9L0Z9bktfzPLrvy/z5cOedH/PMM7W8\n+GJ3evWaw447fs8OO3zPRhstWxLP88QcupEjR+a1bUlFB3SV+tmESKD9uUQ1ID8XhWDePBg7Fh54\nIOi9698/6LXbf3/o1Stu67QPnRBCCCFEm3ToADvuCHfcEcy5O/98qK+HddaBQYOCLVK+/TZuK3NH\nAZ0QQgghqoqaGthtN/jrX4Pg7pRTguwUa6wBO+0E991HTpsYx4kCOiGEEEJULUsuCXvtBfffD42N\nMGQI3H47rLkm3Hor/PJL3BZmRkWvctXGwpKvdPlK31hY8pIHbSws+eLJd+4MW27ZyKqrNvLOO124\n885e/P73nTnooG8YNqw9/fs3n2yXrz3aWLjKNxaePDnejTajrr9Q+nPVk0u5bMpkIpuJTKVvuCo/\nj1aP/Lw0kJ9HqydfPx8/3v2QQ9x79HA/91z3qVOz15+JDNpYuDpJ92ugkuovlP5c9eRSLpsymcjG\nfY9LgbjbQH6eXxn5eWbE3Qby89bLrL8+3HsvvPUWTJ8erI4dNgw++yxz/cW4xwrohBBCCCHaYNVV\ngzl1778PXbtCXR0cfjh8/PGScZsGKKATQgghhMiYFVaAK66Ajz8OeutOPHEt9toL3nwzXrsU0Akh\nhBBCZMnSS8N558Hjj7/LDjsEmxRvsw2MGhUMzRYbBXRCCCGEEDmy5JILGDYMPvoITjoJnn4aVlkF\n9twTxoyBmTOLY0dFp/5SLlfl/ku0U7b2KJdracgrl6tyuYJyuUZtj57nze3J93k+Y0Z73n57Ff7x\nj+688QYMGvQzRx/dmV12gWnTlMs1K5TLVVQDynEpqgH5uShnvvkGHnoo2Lj4/fdh773h4INh222h\nfftFcsrlKoQQQghRoiy3HJx4IrzyCrz9drCQ4qyzoE+fIOXYm29CIfqfFNAJIYQQQhSBlVaCM86A\nhgZ46SVYZhk48khYbbX8dSugE0IIIYQoMmutBRddBB98AA8/nL8+BXRCCCGEEDFhBgMH5q+n5AM6\nM+tnZneY2YNJ17Yxs3+Z2a1mtnWc9sWFUsVEq0cpkUqDuNtAfp5fGfl5ZsTdBvLz/MqUip+XfEDn\n7p+6+5DUy0AT0BH4qvhWxY8eANHqqZYHQKkTdxvIz/MrIz/PjLjbQH6eX5lS8fOiBXRmNsrMpprZ\n+JTru5jZBDP70MzOzkSXu//L3XcHzgEuicJeIcqBhobX4zZBiMiRnwvRNsXsoRsN7Jx8wczaATeF\n19cFDjaz/uF7h5nZtWbWKyGeRucPQE10JgtR2jQ0vBG3CUJEjvxciLYpWkDn7q8CqdnNNgUmufvn\n7j4XGAPsGcrf7e7DgdlmdiuwYaIHz8z2NrPbgLsIAsKqo6GhoaLrL5T+XPXkUi6bMpnIxn2PS4G4\n20B+nl8Z+XlmxN0G8vP8ypSKn3eIvIbWWRH4Mun8K4IgbyHu/j1wQsq1R4FHI7euhNEDIFo91fIA\nKHXibgP5eX5l5OeZEXcbyM/zK1Mqfl7U1F9m1hd40t0HhOf7Aju7+9Dw/FBgU3c/uQB1Ke+XEEII\nIcqGfFJ/xd1DNxlYOem8T3gtb/JpFCGEEEKIcqLY25YYiy9uGAesbmZ9zawGOAh4osg2CSGEEEKU\nNcXctuQ+4HVgTTP7wsyOcvf5wEnAc8B7wBh3/6BYNgkhhBBCVAJFnUMnhBBCCCEKT9xz6IqGmXUG\nbgFmAy+7+30xmyREwTGzfsD5wFLufkDc9ggRBWa2J7A7UAv8xd2fj9kkIQpOuC/vKUAP4EV3v61V\n+WrpoQtX0E5396fMbIy7HxS3TUJEhZk9qIBOVDpmtjRwtbsfG7ctQkSFmRlwl7sf3ppcyedybYkc\nUon1YdGed/OLZqgQeVDIlHlClCp5+PkFwM3FsVKI/MjFz81sMPB34Om29JdtQEeWqcQIgrk+CdFi\nGSlEnmTr5wvFimOeEAUhaz83syuAp9397WIaKkQeZO3n7v5kmLv+0LaUl21Al20qMYLMEvuZ2c3A\nk8WzVIjcydbPzWyZ1FR5QpQ6Ofj5ScD2BM/0oUU1VogcycHPtzGz68NUp0+1pb/SFkW0mErM3X8G\njo7DKCEKTGt+3ixVnhBlSmt+fiNwYxxGCVFgWvPzl4GXM1VUtj10QgghhBAioNICushSiQlRQsjP\nRTUgPxfVQMH8vNwDOqUSE9WA/FxUA/JzUQ1E5udlG9AplZioBuTnohqQn4tqIGo/r5qNhYUQQggh\nKpWy7aETQgghhBABCuiEEEIIIcocBXRCCCGEEGWOAjohhBBCiDJHAZ0QQgghRJmjgE4IIYQQosxR\nQCeEEEIIUeYooBNCCCGEKHMU0AkhhBBClDkK6IQQQgghyhwFdEIIIYQQZY4COiGEEEKIMkcBnRBC\nCCFEmaOATgghhBCizFFAJ4QQQghR5iigE0IIIYQocxTQCSGEEEKUOQrohBBCCCHKHAV0QgghhBBl\njgI6IYQQQogyJ9aAzsz6mNmLZvaemb1rZieH17ub2XNmNtHMnjWzbkllzjWzSWb2gZntFJ/1Qggh\nhBClgbl7fJWbrQCs4O5vm1lXoAHYEzgK+M7drzKzs4Hu7n6Oma0D3AtsAvQBXgDW8Dg/hBBCCCFE\nzMTaQ+fuX7v72+HrGcAHBIHansBdodhdwF7h6z2AMe4+z90/AyYBmxbVaCGEEEKIEqNk5tCZ2SrA\nhv/f3p3HW1WW//9/XYdZQEQUEBnEEEUcEBAVzSxzygFz/qSZoqg/Tc0swcz81LdJK7MyNTVNLTWr\njwM5JGapBSocREwcsJSEowgIAmKM1++Pe5/YwDmHffbea99r7f1+Ph7rcfZee93DWftmnYs13Bfw\nLNDL3edDCPqAnrnNtgfezis2L7dOREREpGalIqDLXW79PXBx7kzdxpdQdUlVREREpBltY3fAzNoS\ngrm73P3B3Or5ZtbL3efn7rN7L7d+HtAvr3jf3Lqm6lUQKCIiIpnh7lZs2TScobsNmOXuP8lb9xBw\nRu71F4AH89afYmbtzWwgMAh4vrmK3b1ql6uuuqqq2y9X/cXWU0y51pQpZNtCthk37stRx0HSi8Z5\nsvVonKdj0ThPtp6sjPNSRT1DZ2b7A6cCL5nZC4RLq18DrgbuM7OxwBzgJAB3n2Vm9wGzgNXA+V6O\nvZBBBx10UFW3X676i62nmHKtKVPItrG/4zSIvQ80zksro3FemNj7QOO8tDJpGedRpy1JkpnVaqwn\nNeSccy7l5pt/FLsbIonSOJdaYGZ4xi+5ShEaGhqquv1y1V9sPcWUa02ZQrYtZJsRI/YruM0s0jhP\nth6N83TQOE+2nqyM81IpoMsoHQCSrScrB4ARI0YX3GYWaZwnW4/GeTponCdbT1bGeakU0ImIiIhk\nnAI6ERERkYxTQCciIiKScQroRERERDIueqYIKU6fPn2quv1y1V9sPcWUa02ZQraN/R2nQex9UIlx\nvngxPPAArFkTlrVrw9LU643XtW0Lw4bBwIH9cAdr5YQHGufpEHsf6HheWpm0jHPNQyeSYdOmNTBy\npP4gZtkdd8B3vgMHHhgCtDZtwtL4uqV1K1fC9OkwZQqsXg377rt+2Xtv6No19m9XHhrnUgtKnYdO\nZ+hERCJauBCOOgquvba0eubOhWefDcs3vgEzZsCOO24Y5O2yC9S1cKPN2rXw3nvQ0ADvvNP08uGH\n0L59WDp0aPp1U59tsQX07QsDBkD//rD99iEwTZsXXoDJk+H006snIJbakMJ/TiIitWPhQthmm9Lr\n6dsXTjghLACrVsHMmSHAe/JJ+O53Q1ujRoWlri4EaPnB28KFsPXW0KcPbLfd+mW33eCQQ8LrLl3C\n2cCVK0Mbq1YV9vr990N/5syBf/8b5s+H3r1DcNcY5OW/HjCgsgHVCy/AN78Jzz8fzm5++9tw5ZUw\nbhy0a1e5fogUS5dcRTJMl6Ky7+yzYZ99QuCQtAUL4LnnQtDSps2GQdt220GvXpU7a7Z6NcybF4K7\nxiAv//WcOeHs3oABMHz4MiZM6MrgweXvx/TpIZCbNg3Gjw/fQ6dOIcAbPx7eeisEw8cf3/p7FEVa\no9RLrgroRDJMAV32HXssfOEL8NnPxu5JuriHs3qzZ8P11y/niSe68LGPwRlnwEknQbdupdVfXx8C\nufp6mDAhBNadOm263aRJcNll4bLxNdeEex1FkqBcrjVKqWKSradWUsWkXex9UIlxXo5LrtU4zs2g\nR49w79+XvrSUt98Ogddjj4WzdqedBk88Ee77a42pU8M9i2PGwKGHwj//CRde2HQwB+FSc3192OYL\nX4Cjj4aXX25dm5tTC+M8Zj1pHuflpIAuo3QASLaeWjkApF3sfaCArrQy5Rzn7dqFYOoPf4A33giX\nqcePh4ED4etfD2fyWvL883DkkXDccXDEEaGOL34ROnbcfNt1dXDqqfDqq/DJT4blrLPCgyjlUAvj\nPGY9WRrnpVBAJyIS0YIFsO22sXuRLdtsE86Y1dfDH/8IK1bAAQfAxz8Ov/wlLF26ftvnnoPPfCbc\nA3fkkSGQu+CCwgK5jXXoAF/+Mrz+evjO9twTLr8cliwp3+8mUiwFdCIikaxZAx98AN27x+5Jdu2x\nR5jyZe5c+OpX4eGHw1Oyn/98OBN34olwzDEhkDv//BCUlWqrreD734cXXwxP6w4eDD/+cXiqVySW\n6NOWmNkvgaOA+e6+R27dVcA44L3cZl9z98dyn10OjAXWABe7++OV77WISOmWLWvLVluFJ06lNO3a\nhcDtmGPCWc977gn3xT3wQHmCuKb07Qu33Qb/+Ec4U3fddeEs4aBBsNNOYRk0KEwFI5K06AEdcDvw\nM+DOjdZf6+4bTLVpZkOAk4AhQF/gCTPbSY+zikgWLVnStixz0MmGtt0WLrqocu3tthtMnBgmc37x\nxXA2cOLEcF/f7Nkh2GwM7vIDvZ120tlZKZ/oAZ27/83MBjTxUVOP7o4B7nX3NcBbZjYbGAU8l2Qf\n00i5/5Ktp1Zy/6Vd7H2QdPtt2vQuy/1zGufpMGxYWPK5hzOGjcHd7Nnw4IPrX3foAP3778GOO4Yz\neT16hKXx9cbrkpjkWMfz0sqkZZynYh66XEA3caNLrmcAHwDTgEvd/QMz+xkwxd3vzm13K/CIu/9f\nE3XqxJ1UPc1Dl23/939w111w//2xe5Ju1TrO3UOqtdmzQ6aORYvC8v77m75+//2wbLHFhoFe//5w\n0EHwqU+FDB+SXdWay/UG4Fvu7mb2beBHwNmR+yQiUlblSvsl2WQWsnP06lXY9uvWhSd48wO+N94I\n/yG4+GLo2TMEdgcfHII83btXW1IZ0Ln7gry3twATc6/nAf3yPuubW9ekc8659L+vR4zYjxEjRpex\nlyLxNTQsY9o0zVeXVS++2IXVq41p05bF7kqqaZxvyiz8Z2CbbcLky5ddBrNnt2Pq1Pb88IcdOP30\n9vTrt4aRI1ex994rGTZsFVtsoatWaVJfP5n6+illqy8tl1x3IFxy3T33vre7v5t7fQmwt7t/zsx2\nBX4D7ANsD0wCmnwoQpdcpRZU66WoWnHJJdCvX5jbTJqncd56q1aFyZSffBL+/OcwZ99ee4UzeJ/6\nVAgCk3r6V4qT+dRfZnY3MBkYbGb/NrMzgWvMbKaZzQA+AVwC4O6zgPuAWcAjwPmK2kQkq3TJVZLS\nvn2YbPkb34Cnngr36l15ZZgr7ytfCZdnx40LgZ5Uh+gBnbt/zt37uHsHd+/v7re7++nuvoe7D3P3\nY919ft7233P3Qe4+pJbnoFOqmGTrqZVUMWkXex8k3f68ef8pS0CncZ5tldgHW2wRctd+//shn+1r\nr8GOO8IJJ8Cee67i1lth+fJk2tbxXKm/pAWxD4IK6Eork5YDQNrF3gdJt//uu2sV0GmcR9kHvXuH\nyZDfeAPGjn2LP/4xPDF7wQUwc2Z529LxXAGdiEhVW7KkrfK4SlRt2sD++y/lgQdCILfttiH37ejR\ncOed8NFHsXsohVJAJyISiTJFSJr07Qv/+7/w1lswfnxIn9b40M6rr8bunWxOKqctERGpdh99BGvW\nGF26xO6JyIbatoUxY8Ly5ptwyy1hXrshQ+Dcc8PTsnV1YTFb/7q5ZdmyNixdCp07K29xkhTQiYhE\nsGgRbLXVGszax+6KSLMGDoTvfjecuXvgAbj1VpgzJ0xyXOiyevXu1NWFiY5vvjk8nCHlp4Auo2Ln\nP1Tuv9LKpCX3X9rF3gdJtr9gAWy7bdFTTm1A4zzbYu+DQtpv3x5OOiksrdXQ8B59+vThT38KU6Uc\ncgj88Iew1Vbl72e5ymVxnKdiYuEkaGJhqQWacDW7Jk2Cq6+GJ56I3ZP00zivHkuXwoQJ8NBDcNNN\ncNRRsXuUHpmfWFhEpBZpUmGpRVtuCTfcAHfdFfLPnnZauP1ASqeATkQkAgV0Uss++cn106Tsvjv8\n4Q+xe5R9CuhERCII99DF7oVIPJ07w49/DL//PVxxBZx4Isyfv/ly0jQFdCIiEegMnUgwejTMmAGD\nBsEee8Ddd4NugW89BXQZFTtdjlJ/lVYmLali0i72Pkiy/YULoa7u/bLUpXGebbH3QRqO5x07wve+\nBw8/HPLNjhkD8+a1vp5i2y+lTFrGuQK6jNIBINl6auUAkHax90HSAZ37grLUpXGebbH3QZqO5yNH\nwrRpMHx4mMD4ttvWn63TOG+ZAjoRkQgWLIDu3dfE7oZI6rR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3cLl2+vSw3Hxz+LlmzYYB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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "TF=np.loadtxt('data/TFs/Data/RF-Lock-LBW-ETMX.txt', comments='#')\n", "f = TF[:,0]\n", "real = TF[:,1]\n", "imag = TF[:,2]\n", "mag = np.sqrt(real**2+imag**2)/Hrf\n", "phase = rad2deg(np.angle(1j*imag+real))\n", "\n", "fig = plt.figure()\n", "ax1 = fig.add_subplot(2,1,1)\n", "ax2 = fig.add_subplot(2,1,2)\n", "ax1.set_axisbelow(True)\n", "ax2.set_axisbelow(True)\n", "\n", "ax1.loglog(f, mag)\n", "ax2.semilogx(f,phase)\n", "\n", "ax1.grid(True, color=(0.6,0.6,0.8),ls='-')\n", "ax1.grid(True, which='minor', color=(0.6,0.6,0.6),ls='--')\n", "ax2.grid(True, color=(0.6,0.6,0.8),ls='-')\n", "ax2.grid(True, which='minor', color=(0.6,0.6,0.6),ls='--')\n", "\n", "ax1.set_ylabel('Actuator Efficiency [m/cnt]')\n", "ax2.set_ylabel('Phase [deg]')\n", "ax2.set_xlabel('Frequency [Hz]')\n", "\n", "\n", "ax1.set_title('K1:LSC-MICH_IN1_DQ/K1:VIS-EX_TM_ISCINF_L_OUT/Hrf')\n", "fig.set_size_inches(10,8,forward=True)" ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "We did the same measurement for ETMY" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "collapsed": false, "hide_input": false, "run_control": { "marked": false } }, "outputs": [ { "data": { "image/png": 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BqXnoNOQqhBBCCFHl1PQqV1H7tLXBJ5/A/PkrHgsWwBprwFprBUffvnFbKoQQQkRHTQd0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\nPQ+d5Otbvlx56Loacn3e3Tc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A4GZ3X+LubwKzgNEVNVoIIYQQImEkZg6dma0N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\n2ACqqlbQokV3Zs0KvWgnnRSmamnbtqZMVVXnov8mt2oFAwaE7dRTQ6/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cju3a9V0uugjG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\niKScEjoRERGRlFNCJyIiIpJy/x8xqwdX5BvuYAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "TF=np.loadtxt('data/TFs/Data/RF-Lock-LBW-ETMY.txt', comments='#')\n", "f = TF[:,0]\n", "real = TF[:,1]\n", "imag = TF[:,2]\n", "mag = np.sqrt(real**2+imag**2)/Hrf\n", "phase = rad2deg(np.angle(1j*imag+real))\n", "\n", "fig = plt.figure()\n", "ax1 = fig.add_subplot(2,1,1)\n", "ax2 = fig.add_subplot(2,1,2)\n", "ax1.set_axisbelow(True)\n", "ax2.set_axisbelow(True)\n", "\n", "ax1.loglog(f, mag)\n", "ax2.semilogx(f,phase)\n", "\n", "ax1.grid(True, color=(0.6,0.6,0.8),ls='-')\n", "ax1.grid(True, which='minor', color=(0.6,0.6,0.6),ls='--')\n", "ax2.grid(True, color=(0.6,0.6,0.8),ls='-')\n", "ax2.grid(True, which='minor', color=(0.6,0.6,0.6),ls='--')\n", "\n", "ax1.set_ylabel('Actuator Efficiency [m/cnt]')\n", "ax2.set_ylabel('Phase [deg]')\n", "ax2.set_xlabel('Frequency [Hz]')\n", "\n", "\n", "ax1.set_title('K1:LSC-MICH_IN1_DQ/K1:VIS-EY_TM_ISCINF_L_OUT/Hrf')\n", "fig.set_size_inches(10,8,forward=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the above measurements, the mysterious LFP around 400Hz is not present. The transfer function " ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.12" } }, "nbformat": 4, "nbformat_minor": 0 }