{ "metadata": { "name": "", "signature": "sha256:68e867ca3e0114a619e9b7fda9fa11a763967798fcfd08bd21dae0c4a1d415fb" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Launch-8 PID reconstruction\n", "\n", "Data" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "import numpy as np\n", "import utils\n", "from scipy.signal import firwin, lfilter\n", "from scipy.integrate import simps\n", "from matplotlib import rcParams\n", "rcParams.update({'font.size': 14})\n", "\n", "columns = np.loadtxt('../data/Launch-8/roll/raw/output_trim.csv', delimiter=',', unpack=True, usecols=(0,1,2,3))\n", "\n", "roll_sample_rate = 1000\n", "\n", "roll_time = columns[0]\n", "roll_accel = columns[1]\n", "roll_rate = columns[2]\n", "fin_angle = columns[3]\n", "\n", "roll_time = roll_time - 4540.7\n", "roll_rate = roll_rate - roll_rate[0:10].mean()\n", "roll_rate = roll_rate / 42.9\n", "\n", "roll_accel -= roll_accel[0:10].mean()\n", "roll_accel *= -0.0068\n", "\n", "fin_angle -= fin_angle[0:10].mean()\n", "fin_angle /= (fin_angle.max()/15.0)\n", "\n", "velocity = [0]\n", "altitude = [0]\n", "roll_angle = [0]\n", "for i in range(1, len(roll_accel)):\n", " altitude.append(simps(velocity, roll_time[:i]))\n", " velocity.append(simps(roll_accel[:i], roll_time[:i]))\n", " roll_angle.append(simps(roll_rate[:i], roll_time[:i]))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Null Roll Rate\n", "\n", "If we try to set roll rate to `0` and run our PID controller, what do we get with **L-8** data?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import simulation.lv2 as model\n", "import simulation.simulate as sim\n", "import simulation.PIDcontroller as PIDcontroller\n", "\n", "pid = PIDcontroller.PIDController(p=10.0, i=0.01, d=0.1)\n", "pid.setTarget(0.0)\n", "\n", "fin = []\n", "for i, t in enumerate(roll_time):\n", " r = roll_rate[i]\n", " x = altitude[i]\n", " v = velocity[i]\n", " \n", " correction = pid.step(r)\n", " a = model.estimate_alpha(correction, x, v, t)\n", " a = model.servo(a, t)\n", " fin.append(a)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "fig = utils.Plot(r\"Fin Angle\", \"Time [$s$]\", r\"$\\alpha$ [${}^0$]\")\n", "fig.plot(roll_time, fin_angle, color=utils.blue)\n", "fig.plot(roll_time, fin)\n", "fig.ylim([-16, 16])\n", "fig.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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LmH190BJR10824iWcXE9tjF/9Ru69N/3zxK99ramfzfipyyux++V9BrbvcboW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\nubeU8lwp5atO14uaQ9pwXSBHRwEAR+1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aRmr95Gw/WZlpcT5otsiZQddNiTL3PbX5KX5u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\ne+j3n2X08pv93+PYA4yOO9DTofOMrv9D7/d474k5zZkWVHaW1G8ueb7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JX/yiJnzxi722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C6bSJZJlp02YDVzbismHpXo3Ub83Eb83EXs3Eb8ohXlOsvELpsynywjJah+DQAAkGkMw0bYSJaR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\nJknyY+Djt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"text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Null Roll Angle\n", "\n", "Now, instead, we try to make the rocket have `0` roll *angle*. This is still different than the original design." ] }, { "cell_type": "code", "collapsed": false, "input": [ "pid0 = PIDcontroller.PIDController(p=1.0, i=0.001, d=0.0)\n", "pid0.setTarget(0.0)\n", "\n", "pid1 = PIDcontroller.PIDController(p=10.0, i=0.0, d=0.0)\n", "pid1.setTarget(0.0)\n", "\n", "fin = []\n", "for i, t in enumerate(roll_time):\n", " f = roll_angle[i]\n", " r = roll_rate[i]\n", " x = altitude[i]\n", " v = velocity[i]\n", " \n", " correction0 = pid0.step(f)\n", " pid1.setTarget(correction0)\n", " correction1 = pid1.step(r)\n", " a = model.estimate_alpha(correction1, x, v, t)\n", " a = model.servo(a, t)\n", " fin.append(a)\n", "\n", "fig = utils.Plot(r\"Fin Angle, 0 Roll Angle\", \"Time [$s$]\", r\"$\\alpha$ [${}^0$]\")\n", "fig.plot(roll_time, fin)\n", "fig.plot(roll_time, fin_angle, color=utils.blue)\n", "fig.ylim([-16, 16])\n", "fig.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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GuUpvtczUUTNMPkYRNaHo0CiC6Q6V8aVLWhsOERlj7De/gWKvIiLtXMOrGE5M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"text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Roll Schedule\n", "\n", "Now we re-create to roll schedule (script) that set snap rolls for the rocket." ] }, { "cell_type": "code", "collapsed": false, "input": [ "pid0 = PIDcontroller.PIDController(p=1.0, i=0.001, d=0.01)\n", "pid0.setTarget(0.0)\n", "\n", "pid1 = PIDcontroller.PIDController(p=10.0, i=0.0, d=0.0)\n", "pid1.setTarget(0.0)\n", "\n", "fin = []\n", "for i, t in enumerate(roll_time):\n", " f = roll_angle[i]\n", " r = roll_rate[i]\n", " x = altitude[i]\n", " v = velocity[i]\n", " \n", " # schedule snap rolls\n", " if t > 4:\n", " pid0.setTarget(90.0)\n", " if t > 8:\n", " pid0.setTarget(-90.0)\n", " if t > 12:\n", " pid0.setTarget(-180.0)\n", " if t > 16:\n", " pid0.setTarget(-270.0)\n", " if t > 20:\n", " pid0.setTarget(-360.0)\n", " if t > 24:\n", " pid0.setTarget(-450.0)\n", " if t > 28:\n", " pid0.setTarget(-540.0)\n", " \n", " \n", " correction0 = pid0.step(f)\n", " pid1.setTarget(correction0)\n", " correction1 = pid1.step(r)\n", " a = model.estimate_alpha(correction1, x, v, t)\n", " a = model.servo(a, t)\n", " fin.append(a)\n", "\n", "fig = utils.Plot(r\"Fin Angle, Script Roll Angle\", \"Time [$s$]\", r\"$\\alpha$ [${}^0$]\")\n", "fig.plot(roll_time, fin)\n", "fig.plot(roll_time, fin_angle, color=utils.blue)\n", "fig.ylim([-16, 16])\n", "fig.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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Qrlt2PaKLFjVTrI4qvJ/fBbGeZ7olWKZwCn3LMnU/VYUAUNsGouUf+fF770Vy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qXuRG8SLEuw7GsRSWriW1J3KVgWhk9Gln1bfxIsAz6uP9EnWLa2bcPets2j0ojBKpTPntfTsLOx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\nkV9s5BfXc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