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@alexrudy
Created April 19, 2016 02:12
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{
"cells": [
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"import h5py\n",
"import os\n",
"import numpy as np"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from telemetry.models.periodogram import frequencies\n",
"import astropy.units as u"
]
},
{
"cell_type": "code",
"execution_count": 118,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def bode_plot(transfer_data, freq, sym=True, **kwargs):\n",
" \"\"\"Helper function for making bode plots.\"\"\"\n",
" plt.plot(freq, transfer_data, **kwargs)\n",
" if sym:\n",
" plt.plot(-freq, transfer_data, **kwargs)\n",
" plt.xscale('log')\n",
" plt.yscale('log')\n",
" plt.xlim(0.5, freq.max().value)\n",
" plt.xlabel(\"Frequency (Hz)\")\n",
" plt.ylabel(r\"$\\left|\\textrm{Power}\\right|^{2}$\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Load Data\n",
"We will be working with a stacked periodogram of slopes, using the default control matrix, with a gain setting of 0.2"
]
},
{
"cell_type": "code",
"execution_count": 119,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"file = h5py.File(os.path.expanduser(\"~/Documents/Telemetry/telemetry_2016-03-22_s0156.hdf5\"))\n",
"tf = file['/transferfunction/hcoefficients/data']"
]
},
{
"cell_type": "code",
"execution_count": 120,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"transfer_functions = tf[...]\n",
"rate = 250 * u.Hz\n",
"freq = frequencies(transfer_functions.shape[0], rate)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here are all of the transfer functions we have to work with. There are 224 transfer functions (one for each WFS mode)"
]
},
{
"cell_type": "code",
"execution_count": 121,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x11ba69320>"
]
},
"execution_count": 121,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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TWRas10tc1yLLYpIkIQw3xHEkeYdITtjivcViwXa7JYr2RFHEarXEsgwMw8S2TaIo5YMP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\n5xe/+BjD0EkSUT/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qOKb6Rys5AyXrvF6vyPNUyjTEBIEvJ8QOpmlKfR4hNe26DqLl5SX7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\nDTxZAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11ba1b1d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"bode_plot(transfer_functions, freq, alpha=0.01, c='k')\n",
"plt.ylim(1e-2, 10)\n",
"plt.title(\"Transfer Functions for s0156, all modes\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"By selecting only the first 20 modes, we can look at system performance in the low-order case. The modes are roughly ordered by spatial frequency."
]
},
{
"cell_type": "code",
"execution_count": 122,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x11a730208>"
]
},
"execution_count": 122,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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uPPBsOo5LrValVNqn1aqzunrhgQnctm3u3r1LMhnnypWXp76Qj6JheMmiI1ZX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\nSSEhIiItKSRERKSl/wfCkgAIlctLrAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x114312da0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"bode_plot(transfer_functions[:,:20], freq, alpha=0.1, c='k')\n",
"plt.ylim(1e-2, 10)\n",
"plt.title(\"Transfer Functions for s0156, modes 0-20\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To make fitting a little simpler (and maybe less realistic), we will combine the first 20 modes into a single, less-noisy, transfer function."
]
},
{
"cell_type": "code",
"execution_count": 123,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x114325940>"
]
},
"execution_count": 123,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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xQ/j2ihlERug+ECIDXXf7JBKBnziLburRiiQkXbx0madfO0RkRBjfXjGD2JjI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\nFBIiIuJKISEiIq7+P5VKI8ZRjU2bAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11a12bac8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"stf = transfer_functions[:,:20].mean(axis=1)\n",
"bode_plot(stf, freq, sym=False)\n",
"plt.ylim(1e-2, 10)\n",
"plt.title(\"Mean transfer function\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## A model transfer function\n",
"We'll now build a model of our transfer function, assuming a stare time for the WFS, a hold time for the DM, and an arbitrary delay, \\\\(\\tau\\\\). Assuming a control period \\\\(T\\\\), gain \\\\(g\\\\) and integrator constant (bleed) \\\\(c\\\\), the delay contribution is given by:\n",
"\n",
"\\\\[ \\textrm{d} = \\left(\\frac{1 - \\exp\\left(-2\\pi i f T\\right)}{2\\pi i f T}\\right)^2 \\exp\\left(-2\\pi i f \\tau\\right)\\\\]\n",
"\n",
"The full transfer function is:\n",
"\n",
"\\\\[ C(z) = \\frac{g}{1 - c z^{-1}} \\\\]\n",
"\n",
"\\\\[ ETF(f) = \\left(\\frac{1}{1 + d C(z)}\\right)^{2} \\\\]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We'll implement a model transfer function using astropy modeling. It will return \\\\(\\log ETF(f)\\\\) for fitting in log space."
]
},
{
"cell_type": "code",
"execution_count": 124,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from astropy.modeling import FittableModel, Parameter\n",
"class TransferFunction(FittableModel):\n",
" \"\"\"Model of a transfer function.\"\"\"\n",
" \n",
" inputs = ('freq',)\n",
" outputs = ('y',)\n",
" \n",
" tau = Parameter(min=0.0)\n",
" gain = Parameter(min=0.0, max=1.0)\n",
" integrator = Parameter(min=1e-5, max=1.0 - 1e-3)\n",
" rate = Parameter(fixed=True)\n",
" \n",
" @staticmethod\n",
" def evaluate(freq, tau, gain, integrator, rate):\n",
" \"\"\"Evaluate a transfer function.\"\"\"\n",
" \n",
" s = 1j * 2.0 * np.pi * freq\n",
" bigT = 1.0 / rate\n",
" \n",
" sz = (s == 0)\n",
" denom = (bigT * s)\n",
" \n",
" denom[sz] = 1.0\n",
" \n",
" hdw_cont = (1.0 - np.exp(-(bigT * s))) / denom\n",
" hdw_cont[sz] = 1.0\n",
" \n",
" delay_cont = np.exp(-1.0 * tau * s)\n",
" delay_term = delay_cont * hdw_cont * hdw_cont\n",
" \n",
" zinv = np.exp(-1.0 * bigT * s)\n",
" cofz = gain / (1.0 - integrator * zinv)\n",
" \n",
" return np.log(np.abs(1.0 / (1.0 + delay_term * cofz)**2.0))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To demonstrate that this works, pick some reasonable parameters for our system, and plot the transfer function:"
]
},
{
"cell_type": "code",
"execution_count": 125,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Model: TransferFunction\n",
"Inputs: ('freq',)\n",
"Outputs: ('y',)\n",
"Model set size: 1\n",
"Parameters:\n",
" tau gain integrator rate\n",
" ----- ---- ---------- -----\n",
" 0.004 0.2 0.995 250.0\n"
]
}
],
"source": [
"model = TransferFunction(tau=0.004, rate=250, integrator=0.995, gain=0.2)\n",
"print(model)"
]
},
{
"cell_type": "code",
"execution_count": 126,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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6HVSVPHk+NV98GNuC+fy5exev7/khbd5OABwmOzc2Xs3VNWtpKso01ej1hNjd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\n++xT+PsH8NBDDwPUe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PbtWxk5cvT5Xffh4RFs375VqtAJR6tZI6I6sMdxYcBvlry8EgCs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\nkBdCCCE6KAnyQgghRAclQV4IIYTooP5/zA4RuzUiJJMAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11ba14f60>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(8,8))\n",
"plt.subplot(2,2,1)\n",
"for gain in np.arange(0, 0.5, 0.1):\n",
" model.gain = gain\n",
" bode_plot(np.exp(model(freq.value)), freq, sym=False, label=\"{:.1f}\".format(gain))\n",
"plt.legend(loc='best')\n",
"plt.title(\"Model variation with gain.\")\n",
"plt.subplot(2,2,2)\n",
"model.gain = 0.2\n",
"for tau in np.arange(0, 0.01, 0.002):\n",
" model.tau = tau\n",
" bode_plot(np.exp(model(freq.value)), freq, sym=False, label=\"{:.4f}\".format(tau))\n",
"plt.legend(loc='best')\n",
"plt.title(\"Model variation with delay.\")\n",
"model.tau = 0.004\n",
"plt.subplot(2,2,3)\n",
"for integrator in np.arange(0.99, 1.0, 0.002):\n",
" model.integrator = integrator\n",
" bode_plot(np.exp(model(freq.value)), freq, sym=False, label=\"{:.5f}\".format(integrator))\n",
"plt.legend(loc='best')\n",
"plt.title(\"Model variation with integrator c.\")\n",
"model.integrator = 0.995\n",
"plt.subplot(2,2,4)\n",
"for rate in [250, 500, 1000]:\n",
" model.rate = rate\n",
" bode_plot(np.exp(model(freq.value)), freq, sym=False, label=\"{:.0f}\".format(rate))\n",
"plt.legend(loc='best')\n",
"plt.title(\"Model variation with rate.\")\n",
"model.rate = 250"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we can try fitting our transfer function model to data. We'll use a least-squares fit in log-log space"
]
},
{
"cell_type": "code",
"execution_count": 127,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from astropy.modeling import fitting\n",
"fitter = fitting.LevMarLSQFitter()"
]
},
{
"cell_type": "code",
"execution_count": 128,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Model: TransferFunction\n",
"Inputs: ('freq',)\n",
"Outputs: ('y',)\n",
"Model set size: 1\n",
"Parameters:\n",
" tau gain integrator rate\n",
" ---------------- --------------- -------------- -----\n",
" 0.00620377307163 0.0664905381418 0.988192157637 250.0\n"
]
}
],
"source": [
"ly = np.log(stf)\n",
"x = freq\n",
"model_init = TransferFunction(tau=1.0/250, rate=250, integrator=0.995, gain=0.2)\n",
"model_conly = TransferFunction(tau=936e-6, rate=250, integrator=0.995, gain=0.2)\n",
"model = fitter(model_init, x, ly, maxiter=1000)\n",
"print(model)"
]
},
{
"cell_type": "code",
"execution_count": 130,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x11c965780>"
]
},
"execution_count": 130,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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2Vgua38qHW6v50W2zMRp0bNzfxu4jdq5YcC9bUSj0NFDcX09+fzO+z1dT//lq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\nDscAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11ba149e8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"bode_plot(stf, freq, sym=False, label=\"Data\")\n",
"bode_plot(np.exp(model(freq.value)), freq, sym=False, label=\"Best Fit Model\")\n",
"bode_plot(np.exp(model_init(freq.value)), freq, sym=False, label=\"Nominal Model\")\n",
"bode_plot(np.exp(model_conly(freq.value)), freq, sym=False, label=\"Only computational delay\")\n",
"plt.ylim(1e-2, 10)\n",
"plt.title(\"Mean transfer function with Model\")\n",
"plt.legend(loc='lower right')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This fit is pretty good, with overall low residuals except at the overshoot point. I've also plotted the nominal model and the nominal model but with only a computational delay, and you can see that they don't seem to match the data very well."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Comparison to Don's models\n",
"\n",
"The only difference between my models and Don's models appears to be whether we are examining the power squared, or just the power. My periodograms always return the power squared, and the model is squared to reflect that. Don's model is not squared, and I presume his periodograms might not be squared. The differnece is shown below."
]
},
{
"cell_type": "code",
"execution_count": 134,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x11d120160>"
]
},
"execution_count": 134,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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/32eFXftKxMxIcQsnV01g7sxSSpN9aNbWtvKX15chW/1c8a1iXvria2RrAMnq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\nhL4sa6k4qhQAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11ca54908>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"bode_plot(stf, freq, sym=False, label=\"Data\")\n",
"bode_plot(np.exp(model(freq.value)), freq, sym=False, label=\"Best Fit Model\")\n",
"bode_plot(np.exp(model_init(freq.value)), freq, sym=False, label=\"Nominal Model\")\n",
"bode_plot(np.sqrt(np.exp(model_init(freq.value))), freq, sym=False, label=\"Nominal Model, SQRT\", color=\"y\")\n",
"\n",
"plt.ylim(1e-2, 10)\n",
"plt.title(\"Mean transfer function with squared and not squared.\")\n",
"plt.legend(loc='lower right')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You can see the not-squared model, for the nominal gain (0.2) which does appear to visually match the data better in this case, but the power law slope in the gain region is clearly wrong. This leads me to believe that indeed my squared periodograms are functioning correctly."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.4.4"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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