{ "metadata": { "kernelspec": { "codemirror_mode": { "name": "python", "version": 3 }, "display_name": "Python 3", "language": "python", "name": "python3" }, "name": "", "signature": "sha256:c9af808aafc6d0a91e68863804ae11e2de024b00530385009afac6ce313c6d1a" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# O P\u00eandulo invertido e lineariza\u00e7\u00e3o\n", "\n", "O problema do *P\u00eandulo Invertido* \u00e9 um cl\u00e1ssico da teoria de controle. Existem muitas vers\u00f5es poss\u00edveis mas vamos analisar o seguinte mod\u00ealo:\n", "![P\u1ebdndulo Invertido](http://wiki.stoa.usp.br/images/b/b6/Cart-pendulum.png)\n", "\n", "que est\u00e1 detalhado na [p\u00e1gina da Wikip\u00e9dia](http://en.wikipedia.org/wiki/Inverted_pendulum). As equa\u00e7\u00f5es do movimento s\u00e3o:\n", "$$ \\begin{gather}\\left ( M + m \\right ) \\ddot x - m l \\ddot \\theta \\cos \\theta + m l \\dot \\theta^2 \\sin \\theta = F\n", "\\\\\n", " (-g \\sin \\theta - \\ddot x \\cos \\theta + l \\ddot \\theta) = 0\\end{gather}$$\n", " Pensaremos na for\u00e7a $F$ (acelera\u00e7\u00e3o do carrinho) como o par\u00e2metro de controle. O sistema \u00e9 uma equa\u00e7\u00e3o diferencial de segunda ordem que pode ser colocado na forma explicita como:\n", " \n", " $$\n", " \\begin{equation*}\n", "\\begin{array}{l}\n", "{\n", "\\begin{bmatrix}\n", " (M + m) && - m l \\cos \\theta \\\\\n", " -\\cos \\theta && l\n", "\\end{bmatrix}\n", "}\n", "\\begin{bmatrix}\n", " \\ddot x \\\\\n", " \\ddot \\theta\n", "\\end{bmatrix}\n", "=\n", "{\n", "\\begin{bmatrix}\n", " F - m l \\dot \\theta^2 \\sin \\theta \\\\\n", " g \\sin \\theta\n", "\\end{bmatrix}}\n", "\\\\\n", "\\\\\n", "A \\ddot u = B \\text{, onde: }\n", "u = \\begin{bmatrix}\n", " x \\\\ \\theta\n", " \\end{bmatrix}\n", "\\end{array}\n", "\\end{equation*}$$\n", "Resolvendo este sistema temos\n", "\n", "$$\n", "\\begin{gather}\n", "A^{-1} = \\frac{1}{\\det(A)}adj(A) \n", "\\\\ \n", "det A = (M + m)l - ml \\cos^2 \\theta = l[(M + m) -m\\cos^2 \\theta] = l(M + (1-\\cos^2 \\theta)m) = l(M + m \\sin^2 \\theta) \\\\\n", "adj(A) = \n", "\\begin{bmatrix}\n", " l & ml \\cos \\theta \\\\\n", " \\cos \\theta & (M + m)\n", "\\end{bmatrix} \\end{gather}$$\n", "\n", "da\u00ed:\n", "$$ \\begin{gather}\n", " \\begin{bmatrix}\n", " \\ddot x \\\\\n", " \\ddot \\theta\n", "\\end{bmatrix}\n", "=\n", "\\frac{1}{l(M + m \\sin^2 \\theta)}\n", "\\begin{bmatrix}\n", " l & ml \\cos \\theta \\\\\n", "\\cos \\theta & (M + m)\n", "\\end{bmatrix}\\begin{bmatrix}\n", " F - m l \\dot{\\theta}^2 \\sin \\theta \\\\\n", " g \\sin \\theta\n", "\\end{bmatrix}\n", "\\end{gather}$$\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sistema de primeira ordem:\n", "O sistema acima pode ser colocado na forma de um sistema de primeira ordem\n", "$$\\begin{equation*}\n", "\\begin{array}{l}\n", "\\dot x = v \\\\\n", "\\dot v = \\frac{Fl - ml^2 w^2 \\sin \\theta + mlg \\cos \\theta \\sin \\theta}{l(M + m \\sin^2 \\theta) } \\\\\n", "\\dot \\theta = w \\\\\n", "\\dot w = \\frac{ F \\cos \\theta - ml w^2 \\cos \\theta \\sin \\theta + (M + m)g \\sin \\theta }{l(M + m \\sin^2 \\theta) } \n", "\\end{array}\n", "\\end{equation*}$$\n", "Tomando inicialmente $F=0$, o ponto $(x_0,0,0,0)$ \u00e9 um ponto de equil\u00edbrio do sistema." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Lineariza\u00e7\u00e3o em torno do ponto de equil\u00edbrio\n", "\n", "O lado direito do sistema acima pode ser pensando como uma fun\u00e7\u00e3o $G: \\mathbb{R}^5 \\to \\mathbb{R}^4$, ou seja\n", "$$G(x,v,\\theta,w,F) = (G_1(x,v,\\theta,w,F), G_2(x,v,\\theta,w,F), G_3(x,v,\\theta,w,F), G_4(x,v,\\theta,w,F))$$ com\n", "$$ \\begin{gather}\n", "G_1(x,v,\\theta,w,F) = v \\\\\n", "G_2(x,v,\\theta,w,F) = \\frac{Fl - ml^2 w^2 \\sin \\theta + mlg \\cos \\theta \\sin \\theta}{l(M + m \\sin^2 \\theta) } \\\\[0.5mm]\n", "G_3(x,v,\\theta,w,F) = w \\\\[0.5mm]\n", "G_4(x,v,\\theta,w,F) = \\frac{ F \\cos \\theta - ml w^2 \\cos \\theta \\sin \\theta + (M + m)g \\sin \\theta }{l(M + m \\sin^2 \\theta) }\n", " \\end{gather}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Vamos denotar $\\mathbf{x} = (x,v,\\theta,w)$. O sistema linearizado em torno do ponto de equil\u00edbrio $(x_0,0,0,0,0)$ \u00e9 o\n", "sistema:\n", "$$ \\dot{\\mathbf{y}} = \\frac{\\partial{G}}{\\partial{\\mathbf{x}}}\\mathbf{y} + \\frac{\\partial{G}}{\\partial{F}}U$$ onde\n", "Em nosso caso:\n", "$$ \\frac{\\partial{G}}{\\partial{\\mathbf{x}}} = \\begin{pmatrix}0 & 1 & 0 & 0 \\\\ 0 & 0 & \\frac{mg}{M} & 0 \\\\\n", "0 & 0 & 0 & 1 \\\\ 0 & 0 & \\frac{(M+m)g}{lM} & 0\\end{pmatrix} $$\n", "e\n", "$$ \\frac{\\partial{G}}{\\partial{F}} = \\begin{pmatrix}\n", "0 \\\\ \n", "\\frac{1}{M} \\\\ \n", "0 \\\\ \n", "\\frac{1}{lM}\n", "\\end{pmatrix}\n", "$$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "from matplotlib import pyplot as plt\n", "import numpy as np\n", "from scipy.integrate import odeint" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "def rhs(y,t):\n", " return [y[1], (F*l - m*l**2*y[3]**2*np.sin(y[2])+m*l*g*np.cos(y[2])*np.sin(y[2]))/(l*(M+m*np.sin(y[2])**2)),y[3], (F*np.cos(y[2]) -m*l*y[3]**2*np.sin(y[2])*np.cos(y[2])+(M+m)*g*np.sin(y[2]))/(l*(M+m*np.sin(y[2])**2))]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "code", "collapsed": false, "input": [ "#parametros\n", "M=5\n", "m=1\n", "l=1\n", "g=9.8\n", "F=0" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "code", "collapsed": false, "input": [ "# malha de tempo\n", "t = np.arange(0,200,0.1)\n", "# condi\u00e7\u00e3o inicial\n", "p0=[1,0.1,0,-0.1]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "sol = odeint(rhs,p0,t)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "theta = sol[:,2]\n", "omega = sol[:,3]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 9 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.plot(t,theta)\n", "plt.grid()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 11 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.plot(t,omega)\n", "plt.grid()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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kZKUzofKpfd4U8emIQ+Mfd1YamznZOJalGLCcSRxz4SWD8DYQjQEan5wd8ZlY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\n/awBKDiqiUo1eWKRlajL7c0h/3nuEtUAFF38q9Esa9yEFh1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"text": [ "" ] } ], "prompt_number": 12 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.plot(theta,omega)\n", "plt.grid()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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3+ku2/BwZS3ji1upTMtsYJ8TUpQVjLVxZuw8Tx90leXhv9KD1F7EUZLtBl2Pk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\ntWWX5cvADV1y0tR81ky99dE0dd7EmzCJoOkrd5jJld0mB/2ThDWTJ2I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