{ "cells": [ { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "# MICH Calibration" ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "This document explains the calibration procedure and results of the iKAGRA MICH signal" ] }, { "cell_type": "code", "execution_count": 51, "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", "%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_EXC channel. All the filters in the filter bank were turned off and the gain was set to 1. 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": 52, "metadata": { "hide_input": true, "run_control": { "marked": false } }, "outputs": [ { "data": { "image/png": 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PtjOrxjn99Cl5cT/SsUBOezh+fB2amnS2BLO92HVl4cIZBS4g7PZzzDHj0NQ0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\nYIz5LoAHYE1yHgbwHhE5qrDP4SIyFcBSABeIyDQtz1k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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "DC=np.loadtxt('data/Fringes/DC.dat', comments='#')\n", "RF=np.loadtxt('data/Fringes/RF.dat', comments='#')\n", "t = DC[:,0]\n", "t = t - t[0]\n", "dc = DC[:,1]\n", "rf = RF[:,1]\n", "fig = plt.figure()\n", "ax1 = fig.add_subplot(1,2,1)\n", "ax2 = fig.add_subplot(1,2,2)\n", "ax1.set_axisbelow(True)\n", "ax2.set_axisbelow(True)\n", "\n", "ax1.plot(t,dc)\n", "ax2.plot(t,rf)\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('Counts')\n", "ax1.set_xlabel('Time [sec]')\n", "ax2.set_xlabel('Time [sec]')\n", "\n", "ax1.set_title('K1:LSC-REFL_PDA1_DC_OUT')\n", "ax2.set_title('K1:LSC-REFL_PDA1_RF17_Q_ERR_EQ')\n", "fig.set_size_inches(15,5,forward=True)" ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "REFL DC power max is 7000, minimum is 1500." ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "run_control": { "marked": false } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Contrast is 64.7%\n" ] } ], "source": [ "Pmax = 7000.0\n", "Pmin = 1500.0\n", "Contrast = (Pmax - Pmin)/(Pmax + Pmin)\n", "print(\"Contrast is {0:.3}%\".format(100*Contrast))" ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "The amplitude of the DC signal Adc:" ] }, { "cell_type": "code", "execution_count": 54, "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": 55, "metadata": { "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": 56, "metadata": { "run_control": { "marked": false } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Hdc=3.25e+10[cnt/m]\n", "Hrf=5.66e+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": { "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 the output of the filter (= input to the MICH actuator) to the input to the filter (= the error signal) was measured." ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "hide_input": false, "run_control": { "marked": false } }, "outputs": [ { "data": { "image/png": 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Pmx/tk5RL+o1eTFmpa33i3HprOOkkuO8++PTTsGpou3ZhesXNN4e+feH882H8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\nOIZwdc5fAdf7QC/MmJltEeI558Db3w7z52cYlIhI5FpbC7S0ZJ9wiIj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TkWQ10vnMS1tj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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "TF=np.loadtxt('data/data/DC-Lock-MICH-OUT-to-DCPD-OUT.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-REFL_PDA1_DC_OUT/K1:LSC-MICH_OUT_DQ')\n", "fig.set_size_inches(12,8,forward=True)" ] }, { "cell_type": "markdown", "metadata": { "run_control": { "marked": false } }, "source": [ "The actuator efficiency at 100Hz is the following." ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "run_control": { "marked": false } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Transfer function magnitude at 100Hz is 0.00726\n", "Actuation efficiency at 100Hz is 2.24e-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": 59, "metadata": { "run_control": { "marked": false } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Actuation efficiency is 2.24e-09/f^2[m/cnt]\n" ] } ], "source": [ "alpha = A100*100**2 # [m*Hz^2/cnt]\n", "print(\"Actuation efficiency is {0:.3}/f^2[m/cnt]\".format(alpha))" ] }, { "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": 60, "metadata": { "hide_input": true, "run_control": { "marked": false } }, "outputs": [ { "data": { "image/png": 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5c2DZMvjhD/1Fo//zP1BSAiecANddBw8/vJ6lS7Mbj8RLIR3PuLQ1CnHGve8M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\nTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "TF=np.loadtxt('data/data/RF-Lock-MICH-OUT-to-RFPD-OUT.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_OUT_DQ')\n", "fig.set_size_inches(12,8,forward=True)" ] }, { "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": 61, "metadata": { "run_control": { "marked": false } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Transfer function magnitude at 100Hz is 0.0127\n", "Hrf from the actuation efficiency = 5.67e+10[cnt/m]\n", "Hrf from fringe amplitude = 5.66e+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": { "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": 75, "metadata": { "run_control": { "marked": false } }, "outputs": [ { "data": { "image/png": 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7PhLl8PTXWcBKEVkBTAeuV9VdbtkfgZeBtcC6cG7vDcMw/KBZs2Y888wzrFu3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\nnscff5xt27bxxBNP+C3FMAJHwnx/qWr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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": 63, "metadata": { "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": 64, "metadata": { "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": 65, "metadata": { "run_control": { "marked": false } }, "outputs": [ { "data": { "image/png": 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FQcmgqeqQouaLyOn4SumvE181yXhgjYj0xHdmkuC3erwzr6j9BxwUY4wxgQn7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\nqlpS+ZagOUnlcMFHFotIR2A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ASeA2VV3ozLfaXx5Yu3ZtyH5pRSSvYF9VEcp4VkUWz/wa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\nrkJggg==\n", "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": { "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": 67, "metadata": { "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": 67, "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": { "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.We have a non-negligible difference between the model and the measurement above $\\approx 300\\mathrm{Hz}$." ] }, { "cell_type": "code", "execution_count": 68, "metadata": { "hide_input": false, "run_control": { "marked": false }, "scrolled": true }, "outputs": [ { "data": { "image/png": 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evWDMGGPrEFzB6gOrmbd3HvP2zuPoyaOM7DySmzrfxPDw4bTwaOHs6osGSgKd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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "TF=np.loadtxt('data/data/RF-Lock-MICH-OPLG-UGFSRV-OnHold.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", "(w,h) = OPLG.freqresp(w=2*pi*f)\n", "mag2 = np.abs(h)\n", "phase2 = rad2deg(np.angle(h*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": [ "### A missing LPF ?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The discrepancy between the model and the measurement can be resolved (at least in gain) by introducing a 1st order LPF at 550Hz.So far, I have not been able to find where is this LPF. If the LPF is in the detection side (e.g. in the PD or I-Q demodulator), this will change the calibration factor at high frequencies, because we will use the error signal for the h(t) recovery in this frequency range, and the effective optical gain should include this LPF. " ] }, { "cell_type": "code", "execution_count": 80, "metadata": { "hide_input": false }, "outputs": [ { "data": { "image/png": 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p6MwvLw8WLIAffjBGzfbtCxMmGFtg8GnW5Kxh4Z6FLNy7kNPnTjO241jGRY5j\nePhwGjds7Or0RT0lBZ2oC6SgMy+zFXTpWuuYi7+/1GObE1OqP7AW2AZo6/YUkAx8AQQDOcBkrfWJ\nS7xfCro65ORJWL7c6LlbsMCYD2/CBKP3Li5Os+/4HhbuXciCPQtIKUyhf3B/xnUax9hOY4nwi3B1\n+qIekYJO1AVS0JmX2Qq6w8DngMK4l+7z809hFFjtbE3IUaSgq7vOnYPkZKO4++EHOHIExo83CryR\nI6HCs5jlmctZtHcRi/YuooVPC8Z2Gsu4TuMYGDqQhp4NXd0E4cakoBN1QVhY2AWrJwjzCA0NJTs7\n+1f7XVXQXXYClytNaVIbpKBzH5mZv9x3l5wMAwcaxd2wYRDRsZLNBzNYtHcRC/cuZNfRXQwPH87Y\nTmO5ruN1BDULcnX6ws1IQSeEcAaXFHR1gRR07qm4GJYsMS7Lrl5t9OYNGgSDBxtb65AjLN2/hEX7\nFrF031JCmocwttNYxnYaS3z7eLw8ZPliYR8p6IQQzuCqHrr5GPe0XZLWeqKtCTmKFHSOZaZRXOdp\nDVlZsGbNL9vPP/9S4CUMqKDMbxNL9i1i8b7FZB3PYlTHUYztOJYxHcfQronr7gyQUa6OjSOjXOsu\nM55brpWZ2iDnFsfGqc1zi70FnU0TCwMvA7OALOAU8K51O4kxF51wM2ZcH/D8UmR33w0ffWQUd6mp\ncP31sHUr3DrZi1sT+lP87Yu83CmdufGfMjpiNAv2LiDqzShi34nlr6v+ysa8jZyrPHfF4zmSrOXq\n2Diylmvd5Q6fgZnaIOcWx8apS+cWm64/aa3XACilZmmtY6s9NV8pleqQzISwQUgI3HGHsQH89BN8\n8w089hjs3z+Cm25qwF033cOHfz5L2uFEFu9bzO8W/I7C0kJGRozkuo7XMTpitEt774QQQohrZWsP\n3XmNlVJVi3EqpcIxJhsWwhSiouCpp4yeu7lzd9G9O8ycCcFBDXj7qcHEnphJ4h1b2fz7zYwIH8EP\nu38g6s0oLO9Y+MvKv7Ahd4MsSSaEEML07C3oHgJWK6VWK6XWAKuAB+xPSwjHCwg4w0MPwbp1sGuX\ncZ/dO++Avz9MvbE9x36cxjOdv+LQI4d5ZfQrnKs8x/2L76ftP9sy+cvJfJjxIYWl5rm0IoQQQpxn\n15A/rfUSpVQnIMq66yet9Wn70xLCufz94Xe/M7bSUli1CpYuhd/8BkpLGzBq1CBGjx7EQzf+nXON\nDrBk3xLIeNqqAAAgAElEQVSW7l/Ko8sfJahpEGM6jmFMxzH0D+6Pt5e3q5sjhBCinrOph04pVbUS\nhNb6tNZ6i3U7fanXiLrPLCO47FFTG5o2NVakePNN2LsXEhOhXz/46iuIjIRxgwPY88Xd3Nvic7L/\neJh3JryDbwNfnlrxFG1fbsvEzybyZvKb7C+6+vFAtfnzdNaxHBXXEXFsjeEOv9d1nTt8BmZqg5xb\nHBunLp1bbJ22ZAswBGNliJqs0Fr3tjEvu8m0JcIRzp6FTZtg2TJYuRI2bwaLxZjUeNgw6NjjGGvy\nl7Nk3xKW7FtCk4ZNGB0xmtEdRzM0bChNvZu6ugnCwWTaEiGEM7hqHrpsoJLLF3RHtNZ9bMzLblLQ\nCWc4eRLWrzcu0a5caYyiTUiAoUNh6FCNZ9BWVuYsZen+pSQXJGMJsFQVeNH+0Xgoe29bFa4mBZ0Q\nwhlkpYgaSEEnasPx47B2rVHcrVxpzIXXuzf07QvRfX6mov1q0ouXsWz/UopOFTEyYiSjI0YzssNI\nApoGuDp9YQMp6IQQzuC2BZ1S6n1gPHBIa93Tuq8lMA8IBbKByVrr4hreLwWdqHXFxZCSYlym3bQJ\nkpLAywvi4yGyTw5nQ5ayn2WszVtJ+2btGdlhJKMiRjEwdCC+DXxdnb64ClLQCSGcwZ0LugEYK0/M\nrVbQvQQc01r/Qyn1ONBSa/1EDe+Xgk64nNaQnf1LcZeUBDt2QJ/4CrqNTKMyfBlbSpex+dBm+gb1\nZVTEKEZFjKJnu55yedakpKATQjiDq5b+cjqt9Xrg+EW7rwfmWL+fA9xQq0nVY2Za2sZWrmiDUhAe\nDrfeCq++ahR0hYUw5bYSKrL7svCxZ8j66zpuzCzAUjGDvYdzmfzlZPxf9ue2r2/jg4wPyCvOsysH\nWZ7HuccW9nGHz8BMbZClvxwbpy6dW+wq6JRhilLqr9bHIUopZw6EaKu1PgSgtT4ItHXisUQ1Zjph\n2cosbWjaFHr0yOSttyAz07j3LrZHM7Z9NZF5U9+g7bw9TD2TTM+mw1i6fym93+5N1BtR3L/ofr7/\n6XuKyy95l0GN5KTr3GML+7jDZ2CmNkhB59g4dencYtfEwsBbGKNdhwEvAKXA10CcnXGvllxTFXWa\nUsZcd5GRMGMGlJcbK1l8/30Ys26/l65d72XmnZVEDtpM0uEfeSPlDaZ8O4UebXswssNIhncYTnz7\neBp6NnR1U4QQQriQXffQKaXStdYxSqmM83POKaW2aK17OSQ5pUKB+dXuodsFDNFaH1JK+QOrtNZd\nanivnj794arHFks/LJYER6RVLxUWFppq8kxbmKkNV5PL2bOwYYMPCxc2IjXVm/79yxk//hQ9Yk6w\nvSSF5KPrSTm6ntyf99OzZRxxrQbQp/UAOjXresH9d85qt6PiOiKOrTFseV9hYSmBgTK/oKOY6e/S\nVmZqQ23mIucW+96XlpZIWtrGqsfvvjvbrnvo0FrbvAGbAE8g3fq4DZBhT8yL4ocB26o9fgl43Pr9\n48DMy7xXC8dJSUlxdQp2M1MbrjWXI0e0fv11rWNjtQ4M1Pqxx7Tetk3rykqtj5Ud01/v/Fr/ccEf\ndeTrkbr1P1rryV9O1m+nvq33Hdunk5OTTdEGZ8axNYYt70tJKbDpWOLSzPR3aSsztaE2c3HWserr\nucVat9hcM9l7yfU14FugrVLqReA3wF/sjAmAUupTjNUoWimlcoFngZnAl0qpe4AcYLIjjiWE2bVu\nDfffb2w7d8LcuTB2rDHRcffufnTvfhPdu9/ELT2hZWg+6cdXsCJrBc+tfg7OwZjCMQwLH8bQsKEE\nNQtydXOEEEI4mF0Fndb6v0qpNGA4xqoRN2itdzkiMa31bTU8NcIR8cW1McvlBHuYqQ325NK1K8yc\naWyHDxvToGzfDlu2wH//C9u3t8fXdyrdu09lcndN45BkvBum8d1P3/HAkgdo49uGYeHDGBY+jCFh\nQ2jt27rW2+DoOHVpvUVxIXf4DMzUBlnL1bFx6tK5xdalv/wu97zWusjmjBxE5qET9ZXWkJ9vFHnb\ntkFqqrFcmdbQf0Al4fFbOdt+JXsrVrI+bx3hLcIZGjaUoeFDGRQ6iBY+LVzdBFOTeeiEEM7gqrVc\nszBGmCogBGO+OAW0AHK11uG2JuQoUtAJ8YvzExxv2PDLlpUFMXFn6dA/DcJXkue5mk2FG4lsFcnQ\nsKEMCRvCwJCBNPdp7ur0TUUKOiGEM7h0pQil1LvAt1rrRdbH12Fcdv2dzUEdRAo6IS7vxAnYuNEo\n7tasgc2boW/CGToPS0aFr2bXqVUkFybTpXUXhoQNYWjYUPqH9KeZdzNXp+5SUtAJIZzB1QXdNq11\njyvtcwUp6IS4NiUlsGoVLFsGS5fCzz/DsJGn6TBoE+UBq0g9upqUghS6tOnC4NDBDAkbwoCQAfXu\nEq0UdEIIZ3B1QbcUWAd8Yt11OzBIaz3a5qAOIgWdEPbZvx+WLzeKu1WrICwM+vYvp1XPZE62WsPO\nsjVsKthEJ79ODA4dzOCwwQwKHYRfo8veYlvnSUEnhHAGV6/l+luMuee+tW5trfuEmzHT0ja2MlMb\n6sLyPBER8Pvfw7ffwpEj8NZbENXRh6zVg1j4+DMk37+M2BXH6JbzOkdy2vDq+n8T9moYPf/dk/sX\n3c8XO77gQOkBp+XniBhm+p2or9zhMzBTG+rCuaW24ta3c4tdBZ3Wukhr/YDWurd1e8AMI1yF45np\nhGUrM7Whrp10GzSAhAR46CH47DOj9+6bb7by2CMNiWjYn6Lvn2L7E0tp+tYx2ia9R8GOMP694b90\ne6sbnV7vxLTvpzFn8xwyj2dycc95fTvpigu5w2dgpjbUtXOLM+PWt3OLXfPQKaVWcYn1VLXWw+yJ\nK4QwvxYtKoiNheuuMx5rDZmZDVi/vg9r1vRh65pH8SipJGTkDopPreXTI4t5csWTeCgPBoYOZGDI\nQAaEDKBSV7q2IUII4QbsXSni0Wrf+wA3AxV2xhRC1EFKGZdpIyJg6lRjX36+B2vW9GDNmh5sW/Mn\nTh3RxAzfT+WZdSw9sZ5/Jf2LAyUHGLh3IAOCBzAwdCCxgbH4ePm4tjFCCFHH2LtSRNpFuzYopZLt\niSmEcB/t28PttxsbwIEDirVrO7JmTUfWfnI3B/OgU/ReWozaxpbT6/l650P8dGwX0f7RDAgZQP/g\n/iQEJ9DKt5VrGyKEECZn7yXX6sPZPAALILOQCiEuKSAAbrnF2ACOHoWPPlIUFNzE2m9uYvdu6B1/\nkrD+myhkHbPzXuP2g7cT1CyI/sH9jS2kP538OqGUzYPBhBDC7dh7yTWNX1aMqACygGn2JiXMx0xr\nFdrKTG2Q9RYNrVvDbbf5cj5UcTEkJjZh7drhrH1/OJs3Q1iHCjombOPn04l8cXg5z61+jlMVp0gI\nTqjqwQtoG+CyNgj7uMNnYKY2yLnFsXHcfi3Xqjcr5aO1Lr9on7fW+rTdmdlJ5qETou47e9ZYj3bT\nJkhONr7m5kKXvvm0i93AuaANFHomsq94Fz3a9iAhOIF+7fuREJxAULMgp+Qk89AJIZzB1RMLp2ut\nY660z9GUUmOAVzEu876vtX7pEq+Rgk4IN1RcDKmpRoGXlARr10JwxM/0GJWKb1QiBzw3klSQSOOG\njauKu37t+9HLvxcNPRvafXwp6IQQzuCSgk4p5Q8EYawQcRvGJVeAZsB/tNZRtiZ0Fcf2APYAw4FC\nIAW4VWv900Wvk4JOiHrg7Fmj527pUmPbvRsGD9HEDN9H46hE9p1OJKkgiX1F+4j2jyY+KJ5+wf2I\nbx9P+2btr/l4UtAJIZzBVQXdVOAuIBZIrfZUKfCR1vobWxO6imPHA89qra+zPn4C0Bf30klBJ0T9\ndPToL0uWLV0KTZrAoEHQoUspnsGpFPluZFdpEpsKkmjo2ZD49vFVW0xADL4NfC8bXwo6IYQzuPqS\n681a669tDmDjMYHRWuv7rI+nAH201jMuep0UdELUc1rD1q3Gpdldu2DnTmM7cQI6R2lCembhHZHE\nyRZJ5Okk9pXsoHOrzvQN6kvf9n3pE9SHqNZReKhfFtWRgk4I4Qz2FnQ2jXJVSk3RWn8ChCmlHr74\nea31bFsTEuZUWFhoqpFctjBTG2ozF2cdy1FxHRGnphhKQa9exlZdcTHs2qXYuLElhYW3sTPxNg6n\ng3+zcjqOz0B7b2JR2VJeWPMCRaeKiA2MrSryvE+HAub4PXIHZvq7tJWZ2iDnFsfGsTWGK34nbJ22\npLH1axNHJXINCoCQao/bW/f9yn33PVL1vcXSD4slwbmZuTHjl9PVWdjHTG2ozVycdSxHxXVEHFti\neHlBREQhAwcab9Qa9uzxIjGxGxtejWHfvhnExJxhQv98mrffSMHBNP7vp1lsP76Zphua0q15NN1a\n9KZri2iimvegsZcrTod1n5n+Lm1lpjbIucWxcWyNcTXvS0tLJC1to22JXYJdl1xdQSnlCezGGBRx\nAEgGfqu13nXR6+SSqwOlpqYSGxvr6jTsYqY21GYuzjqWo+I6Io6tMS73vqIiWLYMFi6EJUugXTtj\n3domTYroFH+Mo97J7CtLJvVAClsObSG8RTh9gvrQJ6gPcYFx9GjXwyGjat2dmf4ubWWmNsi5xbFx\nnHFuqYlLLrlWO3gbYDoQVj2W1voee+Jejtb6nFLqfmAZv0xbsusKbxNCiGvi5we33mps584ZU6Us\nXQqJiT4sW9aJ7OxOHD16O+3bQ5/wszTruI2jR5P5dF8yL/MmB05n0r1td2IDYokLiiMuMI6o1lF4\neni6umlCCDdk70oR3wPrgB+Bc/anc3W01kuAzrV1PCFE/ebpCX37Gltq6gliY42RsOXlkJcH2dkN\nyM6OITs7hqyffk/JTqjM+pljlgxSeqSwyX8Zhzxf5ETFQXoH9CYuMI64oDhiA2OJaBkhy5gJIexm\nb0Hnq7V+3CGZCCFEHePjA506GdvFyssbs337ANLSBpCeDunpcHTfcXKi0yjtkcLydl9wyONxyikm\nNshCbEAssYHGFtYiTIo8IcQ1sbegW6CUGqu1XuSQbIRpmWUElz3M1AZZb9Gxccy43qKPD8TGGtt5\nZ860ZOfOEaSnjyAjw1jWbPPew6QGpJHVI5Wvgv7LcZ+HOOdxithAC32DY7EEWLAEWghtHuqWRZ6Z\n/i5tZaY2yLnFsXHMeG6pib3z0JVijHg9DZzFWDFCa62bOSY928mgCCGEMzh6HjqtobDQKO62bjW+\npu85wN6f02galYpvRBqlTdJQDc4QFxSDJcBCbGCsWxd5QtRHLp1Y2MykoBNCOENtTSx89iz89BNs\n2GCsV7s69QCnWqYRaEnDo30ahzzTOKfKjR68AAsxATFYAi2EtwiXIk+IOsjVK0XEXGJ3MZCjta6w\nObADSEEnhHAGV60UoTXk5MC6dUaBt24dFJYeIHJwOi27pXHGL53MU2mcPHuS3v69LyjyOvp1vGC1\nCyGE+bi6oEsCYoBt1l09gO1Ac+APWutlNge3kxR0QghnMNPSX4cOwfr11h681ZCVBZZBhwlLSMc7\nLJ3DHulkHEqj6FQR0f7R9PbvTUxADDEBMUS1jsLLw97bqIUQjuLqgu4b4Bmt9Q7r467AC8BjwDda\n62ibg9tJCjohhDOYqaC72LFjRnG3Zo1R4GVmQr9+0GdwEX7d0jnZNIOdx9NJP5BOfkk+Pdr2uKDI\n6962O95e3q5uhhD1kqsLuu1a6+6X2qeU2iwFnfsw01qFtjJTG2S9RcfGqc31Fs1c0F2sqMi4NLt6\nNSQmwo4dxooX0dHQuWcJTTtt4XTLdLJPZ5B+IJ19RfuIbBVJTEAMvf170zugN73a9aKpd1On5Wim\nv0tbmakNcm5xbJzaPLe4dKUIYIdS6t/A59bHtwA7lVLeGKNehZsw0wnLVmZqg5x0HRunLi2gXZv8\n/OD6640NjBUv9u6FLVtg8+ZmrP14IFu2DKS8HHr1gsHRp2jjvw0aZLDtcDofb/2Y7Ye3E9w8uKrI\nO/+1lW8rh+ToDp+Bmdog5xbHxqlL5xZ7C7q7gD8CD1ofbwAexSjmhtoZWwghhAN5ekJUlLHdcssv\n+w8dMoq8jIxGpC7pQ0pKH06cAIsF/hR3loCwn6BFOjmlGSzYs4DNBzfTslFLoxfvfJEX0JugpkEy\nwlYIF7GroNNanwJmWbeLnbQnthBCiNrRrh2MGmVs5x0+bKxfm5LSgJWf9SAlpQcwlbg4uLdzJU2C\nMyk/nU5uYQbrst9k65F0NPqXy7XWS7YywlaI2mFXQaeU6gT8HegK+Jzfr7XuYGdeQgghXKhtWxg7\n1tjAmDYlPx9SUmDfPg+y93QkJ6cjOTmTyc4GTy9NUOdCTkRmsDowg8Ut5nHE8wlOnjtGL/9eFxR5\nXdt0paFnQ5e2Twh3Y+8l1w+BZ4FXMC6x3g3If8WEEMLNKAXBwcZ2Ma2hqEiRkxNETk4Q2dnj2bXL\n6OHblV3EActmzvbIYFO7FRz1epkD5VlEtY4y7sU724oz7c7Qq10vGjdsXPsNE8JN2FvQNdJar1DG\nkNIc4DmlVBrwV3uCKqV+AzwHdAHitNbp1Z57ErgHqAAecOVcd/WJWW74tYeZ2iDrLTo2Tl1ab9Ed\nKQWtWhlbzEXTzZ865cfWrcNITR1GSopR5JFXxum+29jTPZ2TTTfx9f4HKDizg+BmocQG9SYmwOjJ\nc+TgC2cy0++RnFscG6cunVvsnbYkERgAfAWsBAqAmVrrznYlpVRnoBJ4G3j0fEGnlOoCfArEAe2B\nH4FOl5qfRKYtEUI4Q12atsSsTp6EjAzYvBmys40VMLJyz5JVuovSJhk0jshABWbwc9PN+Hq0ILJZ\nb/qHxzA0qjeWwBgCmwbK4Avhdlw9D10csAtoAfwNY4WIf2itk2wOemH8VcAj1Qq6JwCttX7J+ngx\n8JzWetMl3isFnRDC4aSgc66yMsjNtRZ52ZVszskkJT+DvaXpnGqRgQpMx8sLInxjiGvfm+HdetM3\nJIYOLTvI4AtRp7l0HjqtdYr125MY9885WxCwsdrjAus+IYQQbsDX95epVYxbsjtat0kcPQqbN2vW\npBeybn86C9LSmbPoUzzbPwo+xXRo1Jv40BiGde2NJSCGzq07y/Jmot6w6TddKfXD5Z7XWk+8ihjL\ngXbVdwEaeFprPd+WvC52332PVH1vsfTDYklwRFghRD1WWFhKamqhq9Oot1q0gOuHKa4fZgEslJfD\n/v0NSNlRQtJPO/lm7XY+bTEfz/YvUNHoAMHeXYhu241ufj2Iat6DDk0jaeAhI2yF66WlJZKWtvHK\nL7xKNl1yVUodAfKAz4BNGMVYFa31Gockd+VLrkuAZ+WSqxCitsglV/MrLISNG2FVYgmrdm1m78l0\nmnVOp7JdOqVembTz6EKHRhaiWsQQ3dZCTFAP/Fv70LIlNG0KHnLlVriAS+6hU0p5AiOB3wI9gYXA\nZ1rrHbYmUsNxVmEMikizPu4K/Bfoi3GpdTkyKKJWmGlpG1uZqQ2yPI9j48harnVXbfwtnDoFaWmw\ndSscPFbG3tItZJenU0g6xxqmUdZoD17FkegDMVQWxNDBx0L/iF7EW3yJjYUePcDb27VtuFpybnFs\nHLdfy1VrfQ5YAiyxrtv6W2C1Uup5rfUbtiZznlLqBuB1oDWwQCm1WWt9ndZ6p1LqC2AnxvJif5Sq\nrXaY6YRlKzO1QU66jo1Tl9ZbFBeqjc+gUSMYMMDYwBfoZ90M5RXlbDu0jfQD6STnp7Eh60M+LdnF\nD3kRkGzh5B4L4T4WBnSMriryunWDhg1rrw1XS84tjo1Tl84tNt8tai3kxmEUc2HAa8C3jkhKa/0d\n8F0Nz/0dY3UKIYQQwm4+Xj7EBcURFxTH72KNfacrTrP98HbSDqSxKS+NxKw5fFyyk2+yO0BiLCf3\nWghSsVgCo2ndIoCcHOjeHSIiwEvGYQgXsHVQxFygO7AIeF5rvd2hWQkhhBAu5O3ljSXQgiXQwn0W\nY1/1Ii85P43E7I9YULyLxqfDWbI6nrL3Yyn9KZbIFj3p0cWb6Gjo3x8slstfshXCEWz9f8QU4Gfg\nAWBGtQkeFcaghWYOyE0IIYQwjZqKvHmr51HWoozUwlSS899mz7E9lHh1YUtRLG/8M5bDW+KwBHdj\nUP8GDBgACQnGaF0hHMnWe+hkDJAQQoh6z9vLm64tuhIbG1u179TZU2w9tJWUwhRSCtezKe8V0k7k\nknOuJx9/F8eR5+IIaRDL8F6R9E/woHdviIyEBg1c2BBR58mVfnFVzHLDrz3M1AZZb9GxcerSeovi\nQu7wGVzchkYNGtG3fV/6tu9bta/kdAnpB9JJKUhh0/Af2JjzDB+dKuLrLRbOze/Dyd196NioD5bI\nIHr2UPTsCT17Qrt2xlq5tubiTHJuce6xr5VdS3+ZmUxbIoRwBpm2RDjK0bKjpBSkkFKYwsbcZDbl\nJ1NZ4UWr8j7ogj4c3dyHhkdjiY5qQWws9OtnbG3bujpz4QwuXcvVzKSgE0I4gxR0wlm01uQU55Bc\nkFy1pRWm4+fVHr/yPpzN7EteUjytK3qSEN+Afv0gPh569ZLLte5ACroaSEEnhHAGKehEbaqorGDH\n4R0kFySTlJ/EpoJNZBZlEeQZjU9RX4q3x3N0S18sHUOIi1V06wZduxpb8+auzl5cCynoaiAFnRDC\nGaSgE65WcrqE1MJUNuVvIqkgiaS8TZw9CwHn4vE+Ek/Z7n7kJcfi16QxXbtSVeSd/yqFnjlJQVcD\nKeiEEM4gBZ0wG601ucW5JOUnkZSfxMb8jWw7vI3wpp0J9exH0xPxnN7fj9wtEez+SREebsyPd34L\nD7+2gRfCOaSgq4EUdI5lpqVtbGWmNsjyPI6NI2u51l1m+ru0lZnacD6X8opyMg5ksDF/Y1WRV15R\nTp/AeMI8ElAFCRQkx7FpvS9aX1jg9e59dffkybnFse+zt6CT+eTEVSksLHR1CnYzUxtqMxdnHctR\ncR0Rx9YYZvqdqK/c4TMwUxvO5+Lj5UO/4H483O9hvpj0BXkP5ZHxuwzuir4Tb78jpLZ4nGXRbQh6\nPo4xrz6A/4h5pO/L4957oWVLY/LjGTNgzhzYvh0qKmo+lrPaYIY4dencIvPQCSGEEPVA+2btmdRt\nEpO6TQKMCZDTDqSRmJdIov6MxLA/493Rm1HtEgiq7I9HwQAWLenJiy96UVhozItnsfyyVVTIdVoz\nkYJOCCGEqIcaNWjEgJABDAgZABj34u0/vp/EvEQ25G5gfcnb5PXMo+/YvtzcdgCty/pzen88y5Y1\n4e9/h8zM3rRrB2FhEBp66c3X17VtrE9MWdAppf4BTABOA/uBu7XWJdbnngTuASqAB7TWy1yWqBBC\nCOEmlFJ09OtIR7+O3NnrTgCKThVVFXjfnXiejDMZdB7SmTF3DKDt6QBGdb6LU0f8yc6GnBxISYGv\nvoLsbMjLg5AQeP55uOUW8JCbvJzKlAUdsAx4QmtdqZSaCTwJPKmU6gpMBroA7YEflVKdZPSDEEII\n4Xh+jfwYHzme8ZHjAThdcZq0A2msz13Pgq0LmLX7H7TybcXAkIEMHD+Q34YOJKJlBEopKithzRr4\nn/+B2bPhn/+EIUNc2x53ZsqCTmv9Y7WHScDN1u8nAp9rrSuAbKXUXqAPsKmWU6x3zDKCyx5maoOs\nt+jYOHVpvUVxIXf4DMzUBmfn4u3lTUJwAgnBCUwJn4J/gD87Du9gXe46lmUu45lVz3BOnzMKvJCB\nDOoyiKRNPfjyCw/uvhu6d4eZM4058Zzdhvp2bjH9tCVKqR+Az7TWnymlXgc2aq0/tT73HrBIa/3N\nJd4nHXdCCIeTaUuEqJnWmuwT2azLXce6nHWszV3LkZ+PMCBkAP2DBnNw02A+/mc0N17vxQsvQECA\nqzM2D3unLXFZD51SajnQrvouQANPa63nW1/zNHBWa/2ZLce4775Hqr63WPphsSTYnrAQQgCFhaWk\npppnmgohzMebroyga+AIfhcIR8sPkV6URGrmJtI93qV8xgEWlcTzyR1DGdU5jhm/6UTzpqa8YOhU\naWmJpKVtdFg80/bQKaXuAqYDw7TWp637ngC01vol6+MlwLNa619dcpUeOiGEM0gPnRD2OfLzEdbl\nrmP+tjV8n7GWEx77aXWqH5ENhxDvP4ThUbF06dyAkBDw9HR1trXHLVeKUEqNAWYBg7TWx6rt7wr8\nF+gLBAHLgUsOipCCTgjhDFLQCeFYm386zpcp61iXt4qdZas5ofbjdSCBin1DCa4YQvdWFjp38qJX\nL+jXDyIi3HOpMnct6PYCDYHzxVyS1vqP1ueeBKYBZ7nMtCVS0AkhnEEKOiGcq+hUEWtz1rJs7ypW\n7F9Nfmk27emPT+FQDmwchj4QTUK8J/36GQVeXJx7zHfnlgWdI0hB51hmWqvQVmZqg6zl6tg4spZr\n3WWmv0tbmakN7nhuOVp2lDXZa1iVvYqVWSspLDlIpPcQGh8axrHUYexL6kLXLop+/WDQIBg9Gpo1\nq3vnFlnLVdQKM61VaCsztUHWcnVsnLq03qK4kDt8BmZqgzueW1r7tubmrjfzxtg32Pmnney6fwcP\njvwNHRIyKJkwlqbPB9Dy3ts4FPg+r3+SRfv2MHYsvPHGGQ4ccGwuzn6fPerfsBIhhBBC1FkBTQO4\nrcdt3NbjNgCyjmexMmslK7JWsLvBU7Qa2oQzagSLNvXlzZiJdA1rzQ03wA03QOfOLk7eiaSgE0II\nIUSdFd4ynGktpzEtZhpaa3Yc2cGPmT/ydcMP0T0e5GiDjnx+eAT/uGMErX4ewI3jfRk9Gvr3B29v\nV2fvOFLQCSGEEMItKKXo3rY73dt2Z4DXAHr17kVyQTI/Zv7Ij1F/I71wM/POxvHpeyM5dt9IBkTE\nMGqkByNGQM+edXu9WSnohBBCCOGWGng2oH9If/qH9OfZIc9SerqUtTlrWZ65nMXxd5JUcpjMY8P5\n58dyfnAAACAASURBVJOjqNg9klF9Qxg5EkaOhOBgV2d/baSgE1fFLCO47GGmNsharo6NU5fWWxQX\ncofPwExtkHPL5eM09W7KuMhxjIscx6tjIL8kn+X7l7M8djlL9z7BqnN+pG4ZxYP/Hol/+VAGx0dx\n7JgxerZRo9pvw7WQaUuEEOIayLQlQrinSl3JloNbWLZ/Gcv2LyMpL5m252LQ+8ZwOHE0AztFc90Y\nD8aMMQZXOHpyY5mHrgb/396dx0dV3Y0f/3xnksxkAxL2fZFFEK0K4lq1LrgrbZVa26p1e1q1i7Z1\nedTH1m7q09qqrVZxt1qXLi5VAX2s+lMUSRBBQQgIskTDkhCyZ5J8f3/cCUwgCZPJ3Dvb9/163dfc\nuXPvWZjk5Ms995xjAZ0xxg0W0BmTGeqa63jzszeZt3oeL6+ay5aa7QysOZHKRSeRVz6TU48ZzJln\nwsyZkJ3d+/wsoOuCBXTGGDdYQGdMZlq3fR3zVs9j3pp5vLbmdQpbxyKrT6b2w5M578tHcOF3sjnk\nkNjv3FlA1wUL6IwxbrCAzhgTag2xcNNC5q6ey/Mfz2V15Wr8648j//NT+M5hJ3P5t0cyblzP0rSA\nrgsW0Blj3GABnTFmdxW1FcxbM58nFr7CW5vmE6oawuCakznnwFO49ryjGDpw7xPe2dJfxhPJtLRN\nrJKpDum4PE8i00ml5XlMR+nwHSRTHaxtiW860aYxuGAw53/pO8y77Elqb67g7+ffyrGHF/J4+Q0M\n+8Mghv9kFj9+/H7WVW7odZm6kpQBnYjcIiIfisgHIjJXRIZEfHa9iJSJyAoRmZnIcmaSZGqwYpVM\ndbBGN77pWECXutLhO0imOljbEt90YknD7/MzgiE8cdnNbLvtPcquXMPM4bN57K232Od/D2Lwzw/g\n+/+4jrc+e4tQa6jXZWyXlAEdcLuqfklVDwJeAm4GEJEpwGxgMnAKcI9IvAcOG2NM10pLFyS6CMaY\nFDJ+2AAevvo8Kuf8lfdnV3B09f08+lAOp999NUW/GcTXn5rNI0se6XU+STmxsKrWRrzNB9rC+2cC\nT6lqC7BORMqAGcBCj4tojMlQpaXvAmcnuhjGmBQ07SA/zx50GI2Nh/Hcc7dwz2NfMG/eXJYe/XKv\n007WO3SIyK9EZD1wHvA/4cPDgcgO6E3hY8ZlpaWliS5CryVTHbwsi1t5xSvdeKQTaxrJ9DORqdLh\nO0imOljbEt903GpbgkE491x46+UhfPTXCzkv+5mY8omUsIBORF4VkaUR27Lw6xkAqnqjqo4CngB+\nkKhyGkcyNVixSqY6WKMb33QsoEtd6fAdJFMdrG2JbzpetC1jxsAvfhFTNh0k/bQlIjISeElVDxCR\n6wBV1dvCn80FblbVPbpcRSS5K2aMMcYYE6E305Yk5TN0IjJeVVeH384CPgnvvwA8ISJ/wOlqHQ+8\n31kavflHMcYYY4xJJUkZ0AG3ishEnMEQnwHfA1DV5SLyDLAcCAGX2+zBxhhjjMl0Sd/laowxxhhj\nupe0o1yNMcYYY0x0LKAzxhhjjElxGRPQichYEXkg/AyeMcbEhYicJSL3i8jfROTERJfHGJMeRGRf\nEblXRJ4Rke/t9fxMe4ZORJ5R1dmJLocxJr2ISD/gf1X10kSXxRiTPsJLnD6qqud3d17K3qETkQdF\npEJElu52/GQR+UREVonItYkqnzEmNfWibbkR+LM3pTTGpJpY2pbwYgv/Bva6NljKBnTAw8BJkQdE\nxAf8KXx8P+CbIrLvbtfZ/HTGmO70uG0RkVuBl1V1iZcFNcaklB63Lar6oqqeBnx7b4mnbECnqm8D\nVbsdngGUqepnqhoCngLOAhCRYhG5FzjQ7twZY7oSQ9vyA+B44GwRuczTwhpjUkYMbcsxInKniPwF\neGlv6SfrxMKxGg5siHi/EecfC1WtBL6fiEIZY1Jed23L3cDdiSiUMSbldde2vAm8GW1CKXuHzhhj\njDHGONItoNsEjIp4PyJ8zBhjesPaFmOMG+LWtqR6QCd0HOSwCBgvIqNFJAc4F3ghISUzxqQya1uM\nMW5wrW1J2YBORJ4EFgATRWS9iHxXVVuBHwDzgY+Bp1R1RSLLaYxJLda2GGPc4HbbknETCxtjjDHG\npJuUvUNnjDHGGGMcFtAZY4wxxqQ4C+iMMcYYY1KcBXTGGGOMMSnOAjpjjDHGmBRnAZ0xxhhjTIqz\ngM4YY4wxJsVZQGeMMcYYk+IsoDPGGGOMSXEJDehEZISIvC4iH4vIMhH5Yfh4kYjMF5GVIjJPRPpG\nXHO9iJSJyAoRmZm40htjjDHGJIeELv0lIkOAIaq6REQKgFLgLOC7wDZVvV1ErgWKVPU6EZkCPAEc\nAowAXgMmqK1fZowxxpgMltA7dKr6haouCe/XAitwArWzgEfDpz0KzArvn4mzcG2Lqq4DyoAZnhba\nGGOMMSbJJM0zdCIyBjgQeA8YrKoV4AR9wKDwacOBDRGXbQofM8YYY4zJWFmJLgBAuLv178CPVLVW\nRHbvQu1xl2onaRhjjDHGJC1VlVivTfgdOhHJwgnmHlfV58OHK0RkcPjzIcDm8PFNwMiIy0eEj3VK\nVW2L03bzzTcnvAzpVAcvy+JWXvFKNx7pxJpGLNddeunVnn13mbAl0+9lOtTB2pb4puNl29JbCQ/o\ngIeA5ap6Z8SxF4ALw/sXAM9HHD9XRHJEZCwwHnjfq4JmsqlTpya6CL2WTHXwsixu5RWvdOORTqxp\nJNPPRKZKh+8gmepgbUt800mltiWhXa4iciTwLWCZiHyA07X638BtwDMichHwGTAbQFWXi8gzwHIg\nBFyu8QhrzV6NGTMm0UXotWSqg5dlcSuveKUbj3RiTSOZfiYyVTp8B8lUB2tb4ptOKrUtCQ3oVPUd\nwN/Fxyd0cc1vgd+6VihjjOnGtGmHJ7oIxhizh2TocjXGmJQxbdoRiS6CMcbswQI6Y4wxxpgUZwGd\nMcYYY0yKs4DORGXYsGGJLkKvJVMdvCyLW3nFK914pBNrGsn0M5Gp0uE7SKY6WNsS33RSqW1J6Fqu\nbhIRGwBrjIm7kpJypk9Pnj/gJnWpKrOensWwgmEcOuJQDh1+KJMGTMIn7txrqaqCAw6A8eNh+nRn\nmzYN9tkHJObpbE28iAiayhMLG2OMMZloR9MOXl3zKpMGTGLemnmc9uRpFN9WzMzHZ3LT6zfx71X/\nZkvdlrjlV14OgQBcdx0UFcHTT8Nxx0FxMZxwAlx7LTz7LKxdC3Y/JPUkxdJfxhhjTKapbKhkYP5A\nfnzYj3ce21K3hYWbFrJw40LuWngXi8oXURQs4vCRh3PUyKM4atRR7Ddov5ju4lVWwpAhcNJJztZu\n82YoLXW2J56AH/0IgkE49VRnO/ZYyMuLQ4WNqyygM8YYYxKgqrGK4tziDscG5g/k9Imnc/rE0wFo\n0zZWbVvFgg0LeHv92/xx4R/ZXLeZw0cczpEjj+SoUUdxyPBDyMvee8RVVeXcjdvdoEFwyinOBs7d\nuY8/hpdfhttvh3PPhaOOgtNOcwK8sWN7XXXjAgvojDHGmASobKikKFjU7Tk+8bHvgH3Zd8C+XHTQ\nRQBsrtvMO+vf4Z0N73Dta9eybPMypg6aytGjjubYMcdy1Kij6Bvsu2d+lZ0HdLsTgalTne2aa2D7\ndnjtNXjpJfjlL53u2lNPhdmz4dBDY6q6cYE9Q2eiUl5enugi9Foy1cHLsriVV7zSjUc6saaRTD8T\nmSodvoNY61DZULnHHbpoDMofxFcnf5Xfzfwd713yHlt+toXbTriNPoE+/OaN3zD8juHMmDODa169\nhlfKXqGmqcbJr9IJxnqqXz84+2x4+GHnOby//hX69oXZs1s49FCnm7a5uefpdsXaltgkPKATkQdF\npEJElkYcu1lENorI4vB2csRn14tImYisEJGZiSl15snkRtcNFtDFN51UanRNR+nwHcRah6qGPbtc\nY5GXncexY47lpmNu4s6D72TrNVv53czfkZ+dz+0Lbmfo74dy2AOH8fft17GtaB71ofqY8/L5nJGx\n//M/8MwzS7jhBifQGzMGbrkFKip6XR1rW2KU8IAOeBg4qZPjd6jqweFtLoCITAZmA5OBU4B7RGyw\ntTHGmNQTTZdrLIJZQY4efTQ3H3sz/7ngP2y9Ziu3nnArocYgC/y/ZvDvBnP8Y8dz69u3UlpeSpu2\nxZSP3w9nnul0x86fD5s2wb77wvnnQ0lJnCtl9irhAZ2qvg1UdfJRZ4HaWcBTqtqiquuAMmCGi8Uz\nxhhjXBFrl2tPBbOCHDvmWMZv+Dm3jH2L8qvLueqwqyivKefb//o2g/53EN/4+zd4cPGDrK9eH1Me\nU6fCfffBmjXO/te/Dkce6XTPVlbGuUKmUwkP6LpxpYgsEZEHRKT96c7hwIaIczaFjxljjDEppaqx\niqLc+N+h60r7oIjCQCGnTzydu065ixVXrOCD//qAk/Y5idfWvsa0+6cx6U+T+PHcHzN/zXyaWpp6\nlEdxsTOQYs0a+MlPnLnuxoxxgrtf/xo++MDmuHNLUqwUISKjgRdV9YDw+4HAVlVVEfkVMERVLxGR\nu4F3VfXJ8HkPAC+r6j87SVMvvfTqne+nTTucadOO8KI6aam8vDyplreJRTLVwcuyuJVXvNKNRzqx\nphHLdeXlNQwbVtjjvEznkun3Mlax1uFnJZdw8vBZHD/0dE/KcsEFA7jmmmr22y/U5fVt2saqHR+z\nYPPrvLPlddbUrGRa/8M5cuBxHDHoOIbk7rqHEm29m5pg8eIACxYEWLAgSH29cMQRjRx5ZBMzZjRR\nUNAxDsmUtqW0dAGlpe/ufD9nzh29WikiKQO6rj4TkesAVdXbwp/NBW5W1YWdXKetrYovme9BppBM\nbnTdYAFdfNPxMqCzpb/iK5l+L2MVax2+8uhXuOnomzhu7HGelGX8eHjlFZgwIfr0ttVvY96aebxc\n9jJzV89lWOEwTp1wKqdOOJUx/jGMGjGqx2UsK3PK8fLL8M47ziCLk06CmTPhoIPgiy8ys23p7dJf\nyRLQjcEJ2vYPvx+iql+E968CDlHV80RkCvAEcChOV+urwITOFm0VEd2+Xem751Q8xhgTMwvoTLx8\n6S9f4pGzHuGgoQd5kl9xsRNM9e8f2/Wtba28v+l9Xi57mZfKXmJ99XpOnXAqs/adxcx9ZlKQU9Dj\nNOvq4I03nEEV8+fD1q1w4olOcHfiiTA8gx6qSvmATkSeBI4F+gMVwM3AV4ADgTZgHfBfqloRPv96\n4GIgBPxIVed3ka5++qnajNbGmLiygM7Ey8g/jOTt777N6H6jXc+rrQ1ycpzuT78/PmluqN7ACytf\n4PmVz/Pexvc4ZswxnDXpLM6YeAaDCwbHlOb69fDqq05w99prMHSoE9zNnOksQRYMxqfsySjlAzq3\niIiWlCjTpiW6JMaYdGIBnYmXgt8U8PlPPqcw4P4zmVVVzpJd27e7k/72xu28UvYKz698nrmr57Lf\noP2YNWkWs/adxYT+PejjjdDaCosXw7x5MHcurFwJ3/oWXHKJM5I23fQ2oEvrpb+qOpsMxRhjjEmw\n5tZmmlqbYuqmjEW0y37Fql+wH9/c/5t8c/9v0tTSxBvr3uD5lc9zzCPHMDB/IOdMOYdzppzDpAGT\nok7T74dDDnG2G2+EtWvhoYfg5JNhxAgnsPvGN6DQxigByT1tSa/Z3DfGGGOSUVVDFUXBIryaG7+q\nyt2ALlIgK8BJ40/intPuYePVG/nTKX9ic91mjnvsOA649wB++eYvWbFlRY/THTvWWUt23Tq46SZn\nbdlRo5zAbuFCmw7FAjoTlUxenscNtvRXfNNJpeV5TEfp8B3EUofKhkpX5qDrqiyxruMaS16RfOLj\ny6O/zF2n3MWGqzZwz2n3sLV+Kyc8fgJT75nKL974Bcu3LO9RullZcNpp8K9/wfLlzujdb30LDjgA\n7rprV7dyprUtFtCZqGRqo+sWC+jim04qNbqmo3T4DmIN6NxYJaK7gC7ed+h6Wm+f+Dhq1FHcecqd\nbLhqA/edfh/bG7cz8/GZfOkvX+L2d25nffX6HqU7dChcdx2sWgV33w0LFjh38i65BF5/vfcPDKZS\n22IBnTHGGOOxqsYqT5b92pmfh12u0fCJjyNHHckfTv4D669az10n38XqytUcdN9BXPbuZdxXch+V\nDdH/Eff5nFGwTz0Fn3wC48bBz362D4ceCo8+Cg0N7tUlWaR1QGeDIowxxiSjyoZKioLeLvsV7y7X\nePGJj2PGHMP9Z9xP+dXlfGvst3h93euMvXMsZ/7tTJ7+6GnqQ/VRpzd4MPz3f8Nzzy3jxhud5cdG\njYKf/hRWr3axIgmW1gGd3aEzxhiTjNzqcu0yP5dHucZLICvAMUOO4emzn2bDVRs4e8rZPLTkIYbf\nMZzvPv9d3lz3Jm3aFlVafj+ccYazIsXChc77I45wVqV45ZX0G0RhAZ0xxhjjsaqGzO5yjUafQB/O\n/9L5zPv2PFZcsYL9B+3Pla9cyYS7J3DLm7ewbvu6qNMaNw5uu82ZuPi885zn7qZOhQcfhMZG9+rg\nJQvoTFRSfa1FSK46eFkWt/KKV7rxSCfWNJLpZyJTpcN3EEsd3Opy7aosbnS5etm2DCkYwtWHX83S\n7y3lmbOfYXPdZqbfP53jHzuexz98nLrmuqjSCQbhggtgyRK48074+993TYeydWt0ZYm1Dm5L65Ui\nhg9XNm5MdEmMMenEVoow8fDtf36bk/Y5ie986Tue5Hf00U7QcswxnmTniaaWJl5c9SIPL3mYBRsW\n8LV9v8ZFB13EESOP6NH8fh9/DH/4A/zjH3DuuXDVVTBxoosF70JvV4pI+B06EXlQRCpEZGnEsSIR\nmS8iK0Vknoj0jfjsehEpE5EVIjKzu7TtDp0xxphk5NY8dF1JxS7XvQlkBTh7ytm8dN5LLL98OZMG\nTOKiFy5i6r1TuWvhXVQ1RDcycr/94IEHnNGxAwfCUUfBmWfC+++7XIE4S3hABzwMnLTbseuA11R1\nEvA6cD2AiEwBZgOTgVOAe6SbMLy1NTOGKhtjjEktiRgUkayjXONhaOFQrjnyGj654hP+fOqfeW/j\ne4y9cywXPHcBCzYsIJreyMGD4ZZbnJUoTj4ZvvY1Z/v4Y/fLHw8JD+hU9W1g9zD6LODR8P6jwKzw\n/pnAU6raoqrrgDJgRldpFxfb1CXGGGOSj9fz0KXKKNfeEhGOHXMsT379Scp+UMb+g/bnwucu5IC/\nHMDdC++O6q5dXh5cfjmUlcGRR8Jxx8H55ztrySazhAd0XRikqhUAqvoFMCh8fDiwIeK8TeFjnbKA\nzhhjTDLych66hgZnio7cXE+ySxoD8wfy0yN+ysorV3LXyXfxzoZ3GHvnWC587kIWbVq01+tzc+En\nP3ECu3HjYPp0uOIK+PxzDwofg6xEFyBKMY3c2LZtLddd9xJDh65l2rTDmTbtiHiXK2PU1NRQWFiY\n6GL0SjLVwcuyuJVXvNKNRzqxphHLdeXlNZSUpP5yVckimX4vY9XTOqgqVQ1VfLq8gQ2++P4sdVaW\nLVt8FBYOpLS0wvW8kindyHQKmcRPx9zBxUNv4MWNT3PWE19jQGAQs8dcxPFDTyPbl9NtGqefDkcd\n5ePhhwuYPDmPs86q4/zza+nbt/PwJJo6lJYuoLT03d5VMpKqJnwDRgNLI96vAAaH94cAK8L71wHX\nRpw3Fzi0izT1jDNUn3tOTRwsWrQo0UXotWSqg5dlcSuveKUbj3RiTSOW6xYt2hRTXqZzyfR7Gaue\n1qG6sVoLflPgWVmWLVOdMsWbvJIp3e7SaWlt0X+t+Jd+5ZGv6NDfDdWf/+fn+nnN51GlsWGD6mWX\nqQ4YoHrbbarNzT3LuytOSBZ7LJUsXa4S3tq9AFwY3r8AeD7i+LkikiMiY4HxQJfjUIqLbaSrMcaY\n5OL1sl/pOMK1t/w+P7P2ncXrF7zO/O/M5/Paz5n858l865/fYuHGhd1eO2IE3HcfLFgA//kPHHyw\ns59oCQ/oRORJYAEwUUTWi8h3gVuBE0VkJXB8+D2quhx4BlgOvAxcHo5qO2XP0BljjEk2Xq8SkSkD\nImI1ddBU/nL6X/j0h58ybeg0zvvnecyYM4O/LfsbLW0tXV43YYKzrNhNN8E558BllyX2JlLCAzpV\nPU9Vh6lqQFVHqerDqlqlqieo6iRVnamq2yPO/62qjlfVyao6v7u0i4rsDp0xxpjk4vUcdOk+ZUm8\nFOUWcfXhV7PqylXcdPRN3Fd6H19946v84d0/UNNU0+k1IjB7NixfDjk5zpx2f/1rYtaJTXhA5ybr\ncjXGGJNsvJ6Dzrpce8bv83PGpDN448I3uPXgW1m4aSFj7xzLda9dx6Ydmzq9pm9f+NOf4Pnn4Xe/\ngyuumEhZmbfltoDORCVT11t0i63lGt90Umm9RdNROnwHPa1DVWMVxUF3IqzOyuJWl2smtC0nTjmR\np85+ikWXLqIh1MD+9zrz2i2rWNbp+TNmQEkJnHKKcvjhzkTFTU29LkZULKAzUcnERtdNFtDFNx0L\n6FJXOnwHPa2Dm12uXQV0bnS5ZlLbMrZoLHeecierf7iaSf0ncdJfT+Lkv57M62tf32MViqws+MUv\n+rJ4MZSWwrRpsGFDZ6nHV1oHdEVFNijCGGNMcrFBEamrOLeY6798PWt/tJbZ+83m+y99nyMfOpKX\nVr20R2A3apTTBXvRRfDlL+N6F2xaB3R2h84YY0yysWlLUl8gK8BFB13E8suX86NDf8T1/3c90+6f\nxj+W/4M2betw7tVXww03wLHHwrLOe2rjwgI6Y4wxxkOVjd4OirBRru7x+/x8Y+o3WPK9Jfz82J9z\n2zu3MfWeqfx16V87THly6aXw+9/DiSfC+13Onts7XQZ0IrJjL1uNiKxyp1jx0bcv1NRAa2uiS2KM\nMcY4rMs1/fjEx5mTzmThJQu58+Q7mbN4DpP+NIk5pXNoanFGRZx7Ljz4IJx+Orzxhgtl6OazNara\np5utEKiLf5Hix++HPn2gujrRJUl95eWpv3ZlMtXBy7K4lVe80o1HOrGmkUw/E5kqHb6DntbBzUER\nnZXFrS5Xa1v2JCKcuM+J/G3m33jkrEf4x4p/MOHuCdxfej+h1hCnnQZPP+3MXffvf/e6eB10F9B9\nPYrrozknoWxy4fjIxEbXTRbQxTcdC+hSVzp8B7EEdG7dodu9LK2tsGOH02Pldl7Jlm6i25Yvj/4y\nc789l2fPeZa/L/87+/55Xx778DGOPqaVF1+Eiy92grt46TKgU9VP93ZxNOckmj1HZ4wxJplUNXrX\n5VpdDYWFTo+VSYxDRxzK/O/M56EzH2LO4jlMvXcq6/KfZt78Nq6+GubMiU8+WXs7QURqgN0XsagG\nSoCfuBnUici6cF5tQEhVZ4hIEfA0MBpYB8xW1S47VS2gM8YYkyxCrSEaQg0U5hR6kp+NcE0ex4w5\nhrcufItXP32VG1+/kabW33DjX2/hV989k5oa6XX60Yxy/SPwM2A4MAL4KfAk8BTwUK9L0L024FhV\nPUhVZ4SPXQe8pqqTgNeB67tLoLjY5qIzxhiTHKoaqyjKLUKk93/Ao2EjXJOLiDBzn5ksvGQhv/zK\nL/nLyv+h389m8IcX5/U67WgCujNV9T5VrVHVHap6P3CSqj4NuP1jIuxZxrOAR8P7jwKzukvAnqEz\nxhiTLLyeg85GuCYnEeHMSWfywX99wA3H/oyCr1/V6zSjCejqRWS2iPjC22ygMfzZ7l2x8abAqyKy\nSEQuCR8brKoVAKr6BTCouwSsyzU+MnF5HjfZ0l/xTceW/kpd6fAd9KQObg6I6Kwsbna5WtvS++t8\n4mP2frP5+IqPYsonkuy+VMUeJ4iMA+4EDscJsN4DrgI2AdNU9e1el6LrvIeq6uciMhCYD/wQeF5V\niyPO2aaq/Tu5Vi+99GqWLj2aurp+XHnlFqZNO8KtohpjMkR5eQ3Dhnnz/JNJP29XvMaznz3KnTMe\n9yS/Z5/NY82abK67zubvSjalpQsoLX135/s5c+5AVWPui99rQJcsRORmoBa4BOe5ugoRGQL8R1Un\nd3K+qiqPPAL/+Q88+ujuZxhjTM+VlJQzfXrq31UyifH4h48zd81cnvjaE57k96tfQUMD/PrXnmRn\nekFEehXQ7bXLVUQmisj/ichH4fcHiMiNsWYYLRHJE5GC8H4+MBNYBrwAXBg+7QLg+e7SKSqyQRHG\nGGOSQ2VDJcVB7x5qs1GumSOaZ+jm4IwkDQGo6lLgXDcLFTYYeFtEPsDp5n1RVecDtwEnishK4Hjg\n1u4SsWfojDHGJAsv56ADG+WaSfY6Dx2Qp6rv7zbEuqWrk+NFVdcCB3ZyvBI4Idp0LKAzxhiTLCob\nKhlXNM67/GyUa8aI5g7dVhHZh/CIVhE5G/jc1VLFkQV08ZGJy/O4yZb+im86tvRX6kqH76AndXD7\nDt3uZXGzy9XaFnfz7qloArorgPuAfUVkE/Bj4PuuliqO2p+hS5GxH0kr0xpdt1lAF990UqnRNR2l\nw3fQkzq4PQ/d7mVxs8vV2hZ38+6pvXa5hpf2OiE8MMGnqjXuFyt+gkFnDbv6esjPT3RpjDHGZDK3\n56HbIz/rcs0YXQZ0InJ1F8cBUNU7XCpT3LV3u1pAZ4wxJpGqGrwdFGGjXDNHd3fo2mfOnAQcgjNd\nCMAZwPtuFire2gO6kSMTXRJjjDGZrLKhkqJcb4adNjQ4jxvl5nqSnUmwLgM6Vf0FgIi8BRzc3tUq\nIj8HXvKkdHFSXGxz0RljjEksVaWqscqztVytuzWzRDMoYjDQHPG+OXwsZRQV2UjX3sq09RbdZmu5\nxjcdW8s1daXDdxBtHWqbawn4AwSyAp6Uxe3uVmtb3M27p6KZh+4x4H0R+Vf4/SzgEddK5AKbuqT3\nMqnR9YIFdPFNJ5UaXdNROnwH0dbBi+7WyLK4PamwtS3u5t1T0Yxy/bWIvAJ8OXzou6r6gbvFwl4L\n+AAAIABJREFUii8L6IwxxiRaIlaJsC7XzBHNHTpUdTGw2OWyuMaeoTPGGJNobs9Btzsb4ZpZunyG\nTkT2GsBFc44bRORkEflERFaJyLV7O9+eoTPGGJNoNgedcVN3d+gmi8jSbj4XoG+cy7NXIuID/gQc\nD5QDi0TkeVX9pKtrrMvVGGNMonk9B53bz9CZ5NLdKNd9ceac62o7HTjC7QJ2YgZQpqqfqWoIeAo4\nq7sLLKDrvUxbnsdttvRXfNNJpeV5TEfp8B1EWwcvulwjy+J2l6u1Le7m3VNdBnThgGlv20YvCxs2\nHNgQ8X5j+FiXLKDrvUxqdL1gAV1800mlRtd0lA7fQbR18GJQRGRZ3O5ytbbF3bx7KqpBEanqsst+\nAsCOHcWsX/9jSkqqE1yi1FVeDiUlqd3wJlMdvCyLW3nFK914pBNrGrFcV15ekzQ/R+kgmX4vYxVt\nHVau38jkvkWu1jeyLOvWFbNlSx0lJU2u55WM6SZ721JauoDS0ndjLdqeVDWlNuAwYG7E++uAazs5\nT9tt365aWKimFxYtWpToIvRaMtXBy7K4lVe80o1HOrGmEct1ixZtiikv07lk+r2MVbR1+PrTX9en\nP3ras7JMn676/vve5JWM6aZa2xKOW2KOj6JZKQIRGS0iJ4T3c0WkcG/XuGgRMD5cphzgXHatM9up\nPn2gvh5CIU/KZ4wxxuzB5qEzbtprQCcilwJ/B+4LHxoBPOdmobqjqq3AlcB84GPgKVVd0d01Is5I\nH5uLzhhjTKJ4PQ+djXLNLNE8Q3cFzsjShQCqWiYig1wt1V6o6lxgUk+uaQ/oBiW05Kkrk5bn8YIt\n/RXfdFJpeR7TUTp8Bz1Z+svtO3TtZWlthZoa6Ovi5GLWtribd09F0+XapKrN7W9EJAtQ94rkDhvp\n2juZ1Oh6wQK6+KaTSo2u6SgdvoNo6+DFPHTtZamudh438vvdzytZ0820tiWagO5NEflvIFdETgSe\nBV50t1jxZwGdMcaYRAm1hqgP1VMY8OYRdOtuzTzRBHTXAVuAZcB/AS8DN7pZKDdYQGeMMSZRtjdu\np1+wHz6Jaixir9mAiMyz12foVLUNmAPMEZFiYER4eG1KKS62QRHGGGMSo7KhkqJc726Zub1KhEk+\n0YxyfUNE+oSDuVKcwO4P7hctvoqK7A6dMcaYxPBiQESH/KzLNeNEc++3r6ruAL4GPKaqhwLHu1us\n+LMu197JpOV5vGBLf8U3nVRansd0lA7fQTR18GoOuvayeNHlam2Lu3n3VDQBXZaIDAVmA/92uTyu\nsYCudzKl0fWKBXTxTSeVGl3TUTp8B9HUwas56NrL4kWXq7Ut7ubdU9EEdLcA84DVqrpIRMYBZe4W\nK/4soDPGGJMoXkxZEsm6XDNPNIMinsWZqqT9/afA190slBtspQhjjDGJkohn6Pbf37PsTBLYa0An\nIkHgYmA/INh+XFUvcrFccWd36IwxxiRKZUMlY/qN8Sw/G+WaeaLpcn0cGAKcBLyJs5ZrjZuFEpGb\nRWSjiCwObydHfHa9iJSJyAoRmRltmhbQGWOMSRSvBkW0sy7XzBPNWq7jVfUcETlLVR8VkSeB/+d2\nwYA7VPWOyAMiMhlncMZknMDyNRGZEM28eO1drqog4k6B01kmLc/jBVv6K77ppNLyPKajdPgOoqmD\nV/PQtZfFi1Gu1ra4m3dPRXOHLhR+3S4iU4G+gBdL3HcWdp0FPKWqLaq6DmdwxoxoEsvOhtxcZ7Fi\n03OZ0uh6xQK6+KaTSo2u6SgdvoNoAzov7tC1l8WLLldrW9zNu6eiCejuF5Ei4CbgBWA5cLurpXJc\nKSJLROQBEekbPjYc2BBxzqbwsahYt6sxxphE8LLLVdW6XDNRNKNcHwjvvgmMi1fGIvIqMDjyEKDA\nDcA9wC2qqiLyK+D3wCU9zeOyy36yc3/atMMJBs/i7be3s3VrqJurjDGma+XlNZSUpP7cacZbm3ds\nZf3KJuo/c/9np7FRgCF8/PHnrudlYldauoDS0nfjlp7s7fEzEQngTFMyhogAUFVviVspus9/NPCi\nqh4gItc5Wett4c/mAjer6sJOrtvj0brjj4frr4cTTvCi5MaYdFRSUs706anfTWi8o6oEfhVgx/U7\nCGYF935BL23aBDNmOK8mdYgIqhrzU/7RdLk+j/PsWgtQF7G5RkSGRLz9GvBReP8F4FwRyRGRscB4\n4P1o07W56IwxxnitLlRHtj/bk2AOrLs1U0UT0I1Q1W+o6u2q+vv2zeVy3S4iS0VkCXAMcBWAqi4H\nnsF5ju9l4PJoRri2s2foYpcpy/N4xZb+im86qbQ8j+koHb6DvdXBq2W/2svixQjX9rySOd1Ma1ui\nCegWiIin802r6vmqeoCqHqiqs1S1IuKz36rqeFWdrKrze5KuBXSxy4RG10sW0MU3nVRqdE1H6fAd\n7K0OXi77VV5e7tmkwta2uJt3T3U5KEJEluEMUsgCvisinwJNhAcvqOoB3hQxfoqLYcuWRJfCGGNM\nJvFqDrqd+VmXa0bqbpTr6Z6VwiPFxbBqVaJLYYwxJpMkYh1XW/Yr83QX0FUA38MZeLAMeFBVWzwp\nlUuKiqzL1RhjjLeqGqsoDnoXYdk6rpmpu2foHgWm4wRzp+DMBZfS7Bk6Y4wxXktEl6sFdJmnuzt0\nU1R1fwAReZAeTA+SrCygi12mLM/jFVv6K77ppNLyPKajdPgO9lYHLwdFDBs2zLNn6KxtcTfvnuru\nDt3O5RRSvau1nQV0scuERtdLFtDFN51UanRNR+nwHeytDl4+Qzds2DDPulytbXE3757q7g7dl0Rk\nR3hfgNzw+/ZRrn1cL12c2cTCxhhjvFbZ6N08dGBdrpmqy4BOVf1eFsQL+fkQCkFjIwS9mbDbGGNM\nhvOyyxVs2pJMFc3EwmlDxPlfi92lM8YY4xWvB0XYKNfMlFEBHdhzdMYYY7xV1ejdHbrWVqipgb59\nPcnOJJGEBXQicraIfCQirSJy8G6fXS8iZSKyQkRmRhw/OLzG6yoR+WMs+dpzdLHJhOV5vGRLf8U3\nnVRansd0lA7fQTRruXoV0K1Y8Tl9+oDPg7/u1ra4m3dPJfIO3TLgq8CbkQdFZDIwG5iMM//dPSIi\n4Y/vBS5W1YnARBE5qaeZ2h262GRCo+slC+jim04qNbqmo3T4DrqrQ0tbC3XNdfQJeDOOcNWqrZ51\nt1rb4m7ePZWwgE5VV6pqGc6o2UhnAU+paouqrgPKgBkiMgQoVNVF4fMeA2b1NF8L6Iwxxnhle+N2\n+gb74hNv/tzW1GTZ83MZKhmfoRsObIh4vyl8bDiwMeL4xvCxHrGAzhhjjFe8Xse1utpvI1wzVHfz\n0PWaiLwKDI48BChwg6q+6GbeAJdd9pOd+9OmHc60aUdQX1/Axx8LJSU1bmefVsrLoaQktbtGkqkO\nXpbFrbzilW480ok1jViuKy+vSZqfo3SQTL+XsequDsuqVpLTWuBZHT/7LAuop6Rku+t5WdvSu+tK\nSxdQWvpurEXbg6sBnaqeGMNlm4CREe9HhI91dbxL99+/5/Kz770HK1bA9OmFMRQtc5WUlDN9emrP\n6J5MdfCyLG7lFa9045FOrGnEcl0y/Rylg3T49+yuDlvKPmRkxWDP6vjMM58xfnwe06fnuZ6XtS29\nu2769LOBs3e+nzPnjh7nEylZulwjn6N7AThXRHJEZCwwHnhfVb8AqkVkRniQxPnA8z3NyLpcY5MJ\ny/N4yZb+im86qbQ8j+koHb6D7urg9Rx0qkWedbla2+Ju3j2VyGlLZonIBuAw4N8i8gqAqi4HngGW\nAy8Dl6uqhi+7AngQWAWUqercnuZrAV1s0r3R9ZoFdPFNJ5UaXdNROnwH3dWhqrGK4qB3z9C1tPTx\nbFCEtS3u5t1Trna5dkdVnwOe6+Kz3wK/7eR4KbB/b/K1gM4YY4xXvB4UUVUFX/qSZ9mZJJIsXa6e\nsYmFjTHGeMXrLldbxzVzZVxAZ3fojDHGeMXLZb/A+ftm89BlpowL6Pr1gx07nPXujDHGGDdVNlRS\nFPTulllVlQV0mSrjAjq/HwoLobo60SVJLem+PI/XbOmv+KaTSsvzmI7S4Tvorg5eP0O3dWurZ12u\n1ra4m3dPZVxAB/YcXSzSvdH1mgV08U0nlRpd01E6fAfd1aGqwbsuV1WoqhIL6OKYTiq1LRkZ0Nlz\ndMYYY7zg5aCIhgbw+ZTcXE+yM0nGAjpjjDHGBapKVWOVZ8/QVVZCnz72gHimsoDOGGOMcUF9qB6/\n+MnN9uaWmRPQtXiSl0k+GRnQ2TN0xhhj3Ob1HHRVVXaHLpNlZEBnd+h6Lt2X5/GaLf0V33RSaXke\n01E6fAdd1SERc9ANGuTdAlDWtribd08lci3Xs0XkIxFpFZGDI46PFpF6EVkc3u6J+OxgEVkqIqtE\n5I+x5m0BXc+lc6ObCBbQxTedVGp0TUfp8B10VQev56CrrIRhw7wbEWFti7t591TC1nIFlgFfBe7r\n5LPVqnpwJ8fvBS5W1UUi8rKInKSq83qacXExLFvW06uMMZmqtRWamqCxEbZt81FeDi0tzvHOXlta\nIBTac4s83n7e7tftvu/3Q3a2s2VldXxt38/J6XzLzt5zv/26yM2XkX017vNyyhKwSYUzXcICOlVd\nCSAi0snHexwTkSFAoaouCh96DJgFxBTQ2R06Y1JLQ4PzB6uy0nlt3xobOwZLXb02NUFzc/ev7UHb\n7ltLCwSDEAiAyECCQSfQysrq+rWzwGn3QCw7e9f5kde272dnO0FdXd2e9dl9v7m56629/p0FmaGQ\nE9C1B3zBIOTlQW6us3W2X1DgTNDe3danj7MyT0EBdNrKZwCvJxW2dVwzWyLv0HVnjIgsBqqBm1T1\nbWA4sDHinI3hYz1mgyKMcV9bmxOI1NZCTU3H1/Zt9/e7fxYZuIHzn7Gioo5bbu6ed6/a94PBXccC\nAWfLydn1GrkfCDjnd7ZlZ+8KSkpKKpg+PfW7CdupOkFje1DY2Aj19U4A3dCw5359vfO91tQ4K+5s\n3Ojs79jhvLZvO3Y4nzc2OsFd375OgNevX8f94mLo37/zLT8/tYPBRHS5jhzpWXYmybga0InIq8Dg\nyEOAAjeo6otdXFYOjFLVqvCzdc+JyJRY8r/ssp/s3J827XCmTTvCyaA8i02biigp2RJLssaktZYW\nqK8X6up81NU5r7W10mG/ttb5bPfX9s8bGoTGRiEYVHJzlfz89tc2cnOVvDwlL8/Zz81rI5DbTCC/\njv79GxkcbCAr2Ig/UE9OXiPZuY1kBRvB30RzWxOhtmaa2l9bm2jRZprbQtS1NRNqC9GiLbSE90Ma\nPtbWQouGaG1qpbWxhZa2FlrV2dr3W7QV1TbaaKVNlTZtpY025zXifWtrG7757U2ZQzv5dxQEn/gQ\n8eHDh08EweccC7/6xU+WLxu/+PFLFlmSRZYvyzkuzvFsXw7Zvhxy/AFyfDnk+ALO+/bjvgABX5Cg\nP7fTLeDf9VmeP58cf6BHPw/td+d68/PU/jPjbEJNza7Xzz7zsXSpj+rqyE2orvbR2ir07dtGUVH7\n1kpxsbPvvDrv+/VrY8CAVoLB2MvphuVr15Prz6OkxJtVA9asKWLUqAZKSho9yc/0TmnpAkpL341b\neq4GdKp6YgzXhICq8P5iEVkDTAQ2AZH/9xgRPtal++//fafHhw1z/reZTv/Ldlt5eXnKP7ycTHVw\noyyqu+6cRN4tWbu2Er+/mOpq2L7duWuy+351tXPNjh3OHZX2LrPCviHyi+rI61dHsLCO3D71BAvr\nyS6uQ9jC8GLBF6zDF6iH7Ho0q45Wfz2tvgZCWk9DSz0NLQ3Uh+qpD9XTEGpgS3i/saWRhpYGGlsa\n8YmP3KxcgllBcrOd16AvSG5LLoGGAIHmAMGsIIGsXa8Bf4BAVoD8rCCN9Ur/vkPI8ed0umX5ssj2\nZ5PtyybLl7XzfdW2KoYOHrrzmF/8TqDl8+8MuCLf+8TH0g83c+CBQwAnaGsX+fSIqqIobdrW5dba\n1uoEmuFtZ+DZ1kKoNbTzWHNrM40tjTS1NNHU2tTpa0PLdipDDdS31FPfUN/h37t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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#A missing LPF\n", "fc = 550\n", "MLPF = ltu.lpf1(fc=fc)\n", "\n", "#Open Loop Gain\n", "OPLG2 = ltu.ltiprod(MLPF,Act, LagLead, Boost,Hrf,MICH_GAIN,UGF_SERVO_GAIN,DGS) #Open Loop Gain\n", "\n", "TF=np.loadtxt('data/data/RF-Lock-MICH-OPLG-UGFSRV-OnHold.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", "(w,h) = OPLG2.freqresp(w=2*pi*f)\n", "mag2 = np.abs(h)\n", "phase2 = rad2deg(np.angle(h*np.exp(-2j*pi*f*Td))) #Time delay is explicitly introduced as a phase delay here.\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": [ "Below is the comparison between the DC and RF transfer function measurements.Since the two curves have very similar slopes, the missing LPF is common to both. This exclude the possibility of the LPF in RFPD and I-Q demodulator." ] }, { "cell_type": "code", "execution_count": 83, "metadata": { "hide_input": true }, "outputs": [ { "data": { "image/png": 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0uZaWs9Q31rO3cS97T+xlX+M++3mj7/MTe2lpa2F22mxmp82mIK2A2WmzyUvN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\nW8vqvavZengrhemFLMpZxOLcxSzMWUh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IiIi4qKjIScCffx5WrYJzz4Uf/AAq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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "TF=np.loadtxt('data/data/DC-Lock-MICH-OUT-to-DCPD-OUT.txt', comments='#')\n", "fDC = TF[:,0]\n", "real = TF[:,1]\n", "imag = TF[:,2]\n", "magDC = np.sqrt(real**2+imag**2)\n", "phaseDC = rad2deg(np.angle(1j*imag+real))\n", "\n", "TF=np.loadtxt('data/data/RF-Lock-MICH-OUT-to-RFPD-OUT.txt', comments='#')\n", "fRF = TF[:,0]\n", "real = TF[:,1]\n", "imag = TF[:,2]\n", "magRF = np.sqrt(real**2+imag**2)\n", "phaseRF = 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(fDC, 20*np.log10(magDC))\n", "ax2.semilogx(fDC,phaseDC)\n", "ax1.semilogx(fRF, 20*np.log10(magRF))\n", "ax2.semilogx(fRF,phaseRF)\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(['REFL DC','REFL RF'])\n", "\n", "ax1.set_title('K1:LSC-REFL_PDA1_DC_OUT/K1:LSC-MICH_OUT_DQ')\n", "fig.set_size_inches(12,8,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": 70, "metadata": { "run_control": { "marked": false } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "C_err(s) = \n" ] }, { "data": { "image/png": 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hqEET6eqUcW1hxdhVSiopy2KkR4vmerNzMRJCVhw7lc/O0jHtVQFGz/JZWRQV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\nb3iceBrsw94aAAAAAElFTkSuQmCC\n", "text/latex": [ "$$\\frac{7.42393990886366 \\cdot 10^{-8} s^{23} + 0.282031690608689 s^{22} + 430413.730810063 s^{21} + 269601301309.117 s^{20} + 8.42177980018128 \\cdot 10^{16} s^{19} + 1.53534610434491 \\cdot 10^{22} s^{18} + 1.93876305180748 \\cdot 10^{27} s^{17} + 1.82188102729352 \\cdot 10^{32} s^{16} + 1.33555224173858 \\cdot 10^{37} s^{15} + 7.88094186069427 \\cdot 10^{41} s^{14} + 3.81956245279993 \\cdot 10^{46} s^{13} + 1.54446902276131 \\cdot 10^{51} s^{12} + 5.2349877264036 \\cdot 10^{55} s^{11} + 1.4863458387294 \\cdot 10^{60} s^{10} + 3.52603779751768 \\cdot 10^{64} s^{9} + 6.86548024964974 \\cdot 10^{68} s^{8} + 1.07835115995547 \\cdot 10^{73} s^{7} + 1.31761239159832 \\cdot 10^{77} s^{6} + 1.18864006681776 \\cdot 10^{81} s^{5} + 7.16968566935635 \\cdot 10^{84} s^{4} + 2.11721485728092 \\cdot 10^{88} s^{3} + 1.07484342613948 \\cdot 10^{91} s^{2} + 4.72911352932406 \\cdot 10^{93} s + 5.92502987703991 \\cdot 10^{93}}{1.0 s^{24} + 12598265.6365121 s^{23} + 47860168587311.8 s^{22} + 7.30402802408645 \\cdot 10^{19} s^{21} + 4.57507583781277 \\cdot 10^{25} s^{20} + 1.4291578374472 \\cdot 10^{31} s^{19} + 2.60544916903589 \\cdot 10^{36} s^{18} + 3.29003901334975 \\cdot 10^{41} s^{17} + 3.09169274290079 \\cdot 10^{46} s^{16} + 2.26640330059425 \\cdot 10^{51} s^{15} + 1.33737880755041 \\cdot 10^{56} s^{14} + 6.48171496352864 \\cdot 10^{60} s^{13} + 2.62093056193966 \\cdot 10^{65} s^{12} + 8.88366107348671 \\cdot 10^{69} s^{11} + 2.52229652640252 \\cdot 10^{74} s^{10} + 5.98360995385174 \\cdot 10^{78} s^{9} + 1.16505437391728 \\cdot 10^{83} s^{8} + 1.82993849828781 \\cdot 10^{87} s^{7} + 2.23583692847016 \\cdot 10^{91} s^{6} + 2.01709109542622 \\cdot 10^{95} s^{5} + 1.21424580672562 \\cdot 10^{99} s^{4} + 3.59179409500874 \\cdot 10^{102} s^{3} + 4.8182902571891 \\cdot 10^{102} s^{2} + 1.23134771745139 \\cdot 10^{104} s + 1.54046116422229 \\cdot 10^{103}}$$" ], "text/plain": [ " 23 22 2\n", " 7.42393990886366e-8⋅s + 0.282031690608689⋅s + 430413.730810063⋅s \n", "──────────────────────────────────────────────────────────────────────────────\n", " 24 23 22 \n", "1.0⋅s + 12598265.6365121⋅s + 47860168587311.8⋅s + 7.30402802408645e+19⋅s\n", "\n", "1 20 19 18\n", " + 269601301309.117⋅s + 8.42177980018128e+16⋅s + 1.53534610434491e+22⋅s \n", "──────────────────────────────────────────────────────────────────────────────\n", "21 20 19 \n", " + 4.57507583781277e+25⋅s + 1.4291578374472e+31⋅s + 2.60544916903589e+36\n", "\n", " 17 16 \n", " + 1.93876305180748e+27⋅s + 1.82188102729352e+32⋅s + 1.33555224173858e+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 + 7.88094186069427e+41⋅s + 3.81956245279993e+46⋅s + 1.54446902276131e+\n", "──────────────────────────────────────────────────────────────────────────────\n", " 15 14 13 \n", "+51⋅s + 1.33737880755041e+56⋅s + 6.48171496352864e+60⋅s + 2.620930561939\n", "\n", " 12 11 10 \n", "51⋅s + 5.2349877264036e+55⋅s + 1.4863458387294e+60⋅s + 3.52603779751768e\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 + 6.86548024964974e+68⋅s + 1.07835115995547e+73⋅s + 1.31761239159832e\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 + 1.18864006681776e+81⋅s + 7.16968566935635e+84⋅s + 2.11721485728092e\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 + 1.07484342613948e+91⋅s + 4.72911352932406e+93⋅s + 5.92502987703991e+\n", "──────────────────────────────────────────────────────────────────────────────\n", " 3 2 \n", "00874e+102⋅s + 4.8182902571891e+102⋅s + 1.23134771745139e+104⋅s + 1.54046116\n", "\n", " \n", "93 \n", "───────────\n", " \n", "422229e+103" ] }, "execution_count": 70, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Bk4GJzlIL79P1wZI3SZeIVAQeAZ7i+LlcbJKuGNO+fXtmzpzJq6++yogRI2jTpg3//e9/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\nmTlz5p+25W/6iWWWC68ZM2b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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": 71, "metadata": { "run_control": { "marked": false } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "C_fb(s) = \n" ] }, { "data": { "image/png": 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T3TyapkgJG32Md9kx+xdpUOBw4h4o0+dE0XOhpjVysdlHoTYewo5uTj5UwDj1YQcwxQ2k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\nARWXwhFTlNd78P8BFZoKTNgk2M0AAAAASUVORK5CYII=\n", "text/latex": [ "$$\\frac{5.66021524351657 \\cdot 10^{-11} s^{42} + 0.00022223515188126 s^{41} + 363.414238674799 s^{40} + 266592513.772851 s^{39} + 108147052868705.0 s^{38} + 2.84762264272472 \\cdot 10^{19} s^{37} + 5.50941670761325 \\cdot 10^{24} s^{36} + 8.40374825989005 \\cdot 10^{29} s^{35} + 1.05588874254534 \\cdot 10^{35} s^{34} + 1.12465017015503 \\cdot 10^{40} s^{33} + 1.03563455417639 \\cdot 10^{45} s^{32} + 8.36176175750905 \\cdot 10^{49} s^{31} + 5.98166728399327 \\cdot 10^{54} s^{30} + 3.821643626126 \\cdot 10^{59} s^{29} + 2.19426690519857 \\cdot 10^{64} s^{28} + 1.13777697662102 \\cdot 10^{69} s^{27} + 5.34796051360504 \\cdot 10^{73} s^{26} + 2.28508107012917 \\cdot 10^{78} s^{25} + 8.89292616610089 \\cdot 10^{82} s^{24} + 3.15587387604066 \\cdot 10^{87} s^{23} + 1.02163863112956 \\cdot 10^{92} s^{22} + 3.01593391905225 \\cdot 10^{96} s^{21} + 8.10965573384334 \\cdot 10^{100} s^{20} + 1.98241801104142 \\cdot 10^{105} s^{19} + 4.39312194182895 \\cdot 10^{109} s^{18} + 8.79175958483918 \\cdot 10^{113} s^{17} + 1.58103410745676 \\cdot 10^{118} s^{16} + 2.5386375998554 \\cdot 10^{122} s^{15} + 3.61015446722668 \\cdot 10^{126} s^{14} + 4.49973647050664 \\cdot 10^{130} s^{13} + 4.84919693386481 \\cdot 10^{134} s^{12} + 4.43654285520109 \\cdot 10^{138} s^{11} + 3.35932502777285 \\cdot 10^{142} s^{10} + 2.02796579609837 \\cdot 10^{146} s^{9} + 9.20027948221949 \\cdot 10^{149} s^{8} + 2.82601589453405 \\cdot 10^{153} s^{7} + 4.7373548907137 \\cdot 10^{156} s^{6} + 2.33762878838116 \\cdot 10^{159} s^{5} + 8.96482519981519 \\cdot 10^{161} s^{4} + 2.38700805428865 \\cdot 10^{162} s^{3} + 3.21323883628718 \\cdot 10^{163} s^{2} + 4.21972834018408 \\cdot 10^{163} s + 4.79976598559259 \\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} + 3.48086562344839 \\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} + 7.91304008790528 \\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", "5.66021524351657e-11⋅s + 0.00022223515188126⋅s + 363.414238674799⋅s + 26\n", "──────────────────────────────────────────────────────────────────────────────\n", " 41 40 39 \n", " 1.0⋅s + 19898707.9825279⋅s + 140204979770383.0⋅s + 4.2\n", "\n", " 39 38 37 \n", "6592513.772851⋅s + 108147052868705.0⋅s + 2.84762264272472e+19⋅s + 5.5094\n", "──────────────────────────────────────────────────────────────────────────────\n", " 38 37 36 \n", "9817422086958e+20⋅s + 6.30721276002286e+26⋅s + 5.05003751525654e+32⋅s + \n", "\n", " 36 35 34 \n", "1670761325e+24⋅s + 8.40374825989005e+29⋅s + 1.05588874254534e+35⋅s + 1.1\n", "──────────────────────────────────────────────────────────────────────────────\n", " 35 34 33\n", "3.25651706408734e+38⋅s + 1.63167699669109e+44⋅s + 6.29118882689929e+49⋅s \n", "\n", " 33 32 31 \n", "2465017015503e+40⋅s + 1.03563455417639e+45⋅s + 8.36176175750905e+49⋅s + \n", "──────────────────────────────────────────────────────────────────────────────\n", " 32 31 \n", " + 2.0148485075795e+55⋅s + 5.02132890886361e+60⋅s + 9.27721532289994e+65⋅s\n", "\n", " 30 29 28 \n", "5.98166728399327e+54⋅s + 3.821643626126e+59⋅s + 2.19426690519857e+64⋅s +\n", "──────────────────────────────────────────────────────────────────────────────\n", "30 29 28 \n", " + 1.38650642951997e+71⋅s + 1.70800615744304e+76⋅s + 1.79971629549211e+8\n", "\n", " 27 26 2\n", " 1.13777697662102e+69⋅s + 5.34796051360504e+73⋅s + 2.28508107012917e+78⋅s \n", "──────────────────────────────────────────────────────────────────────────────\n", " 27 26 25 \n", "1⋅s + 1.64394234357549e+86⋅s + 1.32251429513324e+91⋅s + 9.44888377329462\n", "\n", "5 24 23 \n", " + 8.89292616610089e+82⋅s + 3.15587387604066e+87⋅s + 1.02163863112956e+92\n", "──────────────────────────────────────────────────────────────────────────────\n", " 24 23 22 \n", "e+95⋅s + 6.03435562142154e+100⋅s + 3.46159654412903e+105⋅s + 1.786464559\n", "\n", " 22 21 20 \n", "⋅s + 3.01593391905225e+96⋅s + 8.10965573384334e+100⋅s + 1.98241801104142\n", "──────────────────────────────────────────────────────────────────────────────\n", " 21 20 19 \n", "5547e+110⋅s + 8.31127794472349e+114⋅s + 3.48086562344839e+119⋅s + 1.3108\n", "\n", " 19 18 17 \n", "e+105⋅s + 4.39312194182895e+109⋅s + 8.79175958483918e+113⋅s + 1.58103410\n", "──────────────────────────────────────────────────────────────────────────────\n", " 18 17 16 \n", "0803669544e+124⋅s + 4.4240041681939e+128⋅s + 1.33050515721277e+133⋅s + 3\n", "\n", " 16 15 14 \n", "745676e+118⋅s + 2.5386375998554e+122⋅s + 3.61015446722668e+126⋅s + 4.499\n", "──────────────────────────────────────────────────────────────────────────────\n", " 15 14 \n", ".54865122212777e+137⋅s + 8.29093172869544e+141⋅s + 1.68197708212625e+146⋅s\n", "\n", " 13 12 11 \n", "73647050664e+130⋅s + 4.84919693386481e+134⋅s + 4.43654285520109e+138⋅s +\n", "──────────────────────────────────────────────────────────────────────────────\n", "13 12 11 \n", " + 2.90000809661285e+150⋅s + 4.16001019850112e+154⋅s + 4.77987082985886e\n", "\n", " 10 9 \n", " 3.35932502777285e+142⋅s + 2.02796579609837e+146⋅s + 9.20027948221949e+149⋅\n", "──────────────────────────────────────────────────────────────────────────────\n", " 10 9 8 \n", "+158⋅s + 4.16424438219602e+162⋅s + 2.50306576003682e+166⋅s + 7.91304008790\n", "\n", " 8 7 6 \n", "s + 2.82601589453405e+153⋅s + 4.7373548907137e+156⋅s + 2.33762878838116e+15\n", "──────────────────────────────────────────────────────────────────────────────\n", " 7 6 5 \n", "528e+169⋅s + 3.05609950237586e+172⋅s + 1.20534163037796e+173⋅s + 2.23008821\n", "\n", " 5 4 3 \n", "9⋅s + 8.96482519981519e+161⋅s + 2.38700805428865e+162⋅s + 3.21323883628718e\n", "──────────────────────────────────────────────────────────────────────────────\n", " 4 3 2 \n", "434378e+174⋅s + 5.52032625910151e+174⋅s + 3.91817932795838e+175⋅s + 4.91734\n", "\n", " 2 \n", "+163⋅s + 4.21972834018408e+163⋅s + 4.79976598559259e+162\n", "─────────────────────────────────────────────────────────\n", " \n", "692984843e+175⋅s + 5.5709884075953e+174 " ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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aV+2UK1eOatWqkZycHBbjT6EcqB9n3+fetp/KaMC+4dZ+Ve3g4pqPgUdVdaOI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\ny8yZM7PlhatT8ab7a7CqfqK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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": 72, "metadata": { "hide_input": true, "run_control": { "marked": false } }, "outputs": [ { "data": { "image/png": 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XEWmIfCwDf5S7/yvbA0RJRbeISN2WLAnFd+Ue8Y0bN+8NHzwYunePO6mISHJF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\nadHlzHEAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "TF=np.loadtxt('data/data/RF-LBW-Lock-MICH-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 (around near 10Hz) is not so accurate. However, the measurement at 100Hz is valid because the open loop gain there is small enough." ] }, { "cell_type": "code", "execution_count": 73, "metadata": { "hide_input": true, "run_control": { "marked": false } }, "outputs": [ { "data": { "image/png": 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+CPvuC7/9LWy4YYjaXXVViOgtXVprS4UQQoj0qDZC9xngDwQHcDFghCnXgema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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "TF=np.loadtxt('data/data/RF-Lock-ETMX-to-RFPD-OUT.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": 74, "metadata": { "hide_input": true, "run_control": { "marked": false } }, "outputs": [ { "data": { "image/png": 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9FmwYhmEYRmmccAJ06ABjx7q1bD/4AWy5ZcPPLV8O48bB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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "TF=np.loadtxt('data/data/RF-Lock-ETMY-to-RFPD-OUT.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)" 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