{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Control PID\n", "\n", "***Linealizar ecuaciones diferenciales no lineales para diseñar controles PID***" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "mkdir: cannot create directory ‘diagrams’: File exists\r\n" ] } ], "source": [ "# Importamos librerias que utilizaremos en el notebook\n", "\n", "%matplotlib inline\n", "\n", "import sympy\n", "import control\n", "import matplotlib.pyplot as plt\n", "import numpy\n", "import ipywidgets as widgets\n", "\n", "from graphviz import Source\n", "\n", "!mkdir diagrams;" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Linealización en control \n", "\n", "El diseño de controladores se facilita cuando tenemos sistemas que son lineales. En el proceso de diseño de controladores. Se siguen la siguientes etapas.\n", "\n", "1. Se obtiene un **modelo no lineal**.\n", "2. Se obtiene un **modelo lineal** a través de linealización. \n", "3. Se **propone un controlador** para el modelo lineal.\n", "4. Se **prueba el controlador** en el sistema real. \n", "\n", "La linealización se hace para las ecuaciones diferenciales no lineales del sistema. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Funciones no lineales\n", "\n", "Antes de linealizar ecuaciones diferenciales, empecemos analizando funciones no lineales. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x = numpy.linspace(-1, 1, 100)\n", "xpos = numpy.linspace(0.001, 1, 100)\n", "\n", "plt.figure()\n", "ax = plt.subplot(111)\n", "ax.plot(x, numpy.exp(x), label=\"$e^x$\"); # Función exponencial\n", "ax.plot(x,x*x, label=\"$x^2$\"); # Función cuadratica\n", "ax.plot(xpos, numpy.log10(xpos), label=\"$log(x)$\") # Función logaritmica\n", "ax.legend()\n", "plt.xlabel('$x$')\n", "plt.ylabel('$y$');" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Linealización de funciones\n", "\n", "Para linealizar funciones utilizamos la serie de _Taylor_. La cual se define como:\n", "\n", "$$f(x) = \\sum_{n=o}^\\infty \\, \\frac{f^{(n)}(a)}{n!}(x-a)^n$$\n", "\n", "escrita de otra forma:\n", "\n", "$$f(x) \\approx f(a) + \\frac{f'(a)}{1!}(x-a) + \\frac{f''(a)}{2!}(x-a)^2 + \\frac{f^{(3)}(a)}{3!}(x-a)^3 + \\cdots$$\n", "\n", "se toma únicamente el termino lineal.\n", "\n", "$$f(x) \\approx f(a) + \\frac{f'(a)}{1!}(x-a) $$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "24f7900e9a0b4fb282a7c932da29119a", "version_major": 2, "version_minor": 0 }, "text/plain": [ "HBox(children=(FloatSlider(value=1.0, description='a', max=2.0, min=-2.0), Output()))" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## Parametros del modelo\n", "\n", "a = widgets.FloatSlider(value=1,min=-2,max=2,step=0.1,description='a')\n", "\n", "## Definicion de la simulacion\n", "\n", "def exponencial(a):\n", " x = numpy.linspace(-2,2,100)\n", " y = numpy.exp(x)\n", " yl = numpy.exp(a) + numpy.exp(a)*(x-a)\n", " plt.plot(x,y)\n", " plt.plot(x,yl)\n", " plt.scatter(a,numpy.exp(a),c='k')\n", " plt.title('Linealización de la función exponencial')\n", " plt.xlabel('x')\n", " plt.ylabel('y')\n", "\n", "## Presentación de los resultados \n", " \n", "plot_exponencial = widgets.interactive_output(exponencial,{'a':a}) \n", "widgets.HBox([a,plot_exponencial])" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Ejemplo Tanque\n", "\n", "La ecuación del tanque es la siguiente, donde $A$ es el area del tanque, $a$ es el area del orificio del tanque, $Q(t)$ es el caudal de entrada:\n", "\n", "$$A\\,\\frac{d\\,h(t)}{dt}+a\\sqrt{2g\\,h(t)}=Q(t)$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Pasos para la linealización\n", "\n", "Los pasos para la linealización de ecuaciones diferenciales son los siguientes: \n", " \n", "- Partimos de la ecuación diferencial." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle A \\frac{d}{d t} h{\\left(t \\right)} + \\sqrt{2} a \\sqrt{g h{\\left(t \\right)}} = Q{\\left(t \\right)}$" ], "text/plain": [ "Eq(A*Derivative(h(t), t) + sqrt(2)*a*sqrt(g*h(t)), Q(t))" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "A,a,g,t,h,Q = sympy.symbols('A a g t h Q')\n", "hs = sympy.Function('h')(t)\n", "qs = sympy.Function('Q')(t)\n", "\n", "Eq_tanque = sympy.Eq(A*sympy.diff(hs,t)+a*sympy.sqrt(2*g*hs),qs); display(Eq_tanque)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- Despejamos la derivada de mayor orden y definimos esta ecuación como una función." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle F{\\left(h,Q \\right)} = \\frac{- \\sqrt{2} a \\sqrt{g h{\\left(t \\right)}} + Q{\\left(t \\right)}}{A}$" ], "text/plain": [ "Eq(F(h, Q), (-sqrt(2)*a*sqrt(g*h(t)) + Q(t))/A)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "F = sympy.Function('F')(h,Q)\n", "Fhq = sympy.solve(Eq_tanque,sympy.diff(hs,t))[0]\n", "Eq_tanque2 = sympy.Eq(F,Fhq); display(Eq_tanque2)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- Buscamos o imponemos el punto de linealización, normalmente se escoje el estado estacionario como punto de linealización. " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle h_{ss} = \\frac{Q_{ss}^{2}}{2 a^{2} g}$" ], "text/plain": [ "Eq(h_{ss}, Q_{ss}**2/(2*a**2*g))" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle Q_{ss} = \\sqrt{2} a \\sqrt{g h_{ss}}$" ], "text/plain": [ "Eq(Q_{ss}, sqrt(2)*a*sqrt(g*h_{ss}))" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "hss, qss = sympy.symbols('h_{ss} Q_{ss}')\n", "Eq_estacionario = sympy.Eq(hss,sympy.solve(Eq_tanque2.subs(F,0),hs)[0].subs(qs,qss)); display(Eq_estacionario)\n", "Eq_estacionario2 = sympy.Eq(qss,sympy.solve(Eq_tanque2.subs(F,0),qs)[0].subs(hs,hss)); display(Eq_estacionario2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Este es entonces el punto de linealización $(h_{ss},Q_{ss})$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- Aplicamos serie de _Taylor_ a la función $F$" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle F{\\left(h,Q \\right)} = \\left(- Q_{ss} + Q{\\left(t \\right)}\\right) \\frac{\\partial}{\\partial Q_{ss}} F{\\left(h_{ss},Q_{ss} \\right)} + \\left(- h_{ss} + h{\\left(t \\right)}\\right) \\frac{\\partial}{\\partial h_{ss}} F{\\left(h_{ss},Q_{ss} \\right)} + F{\\left(h_{ss},Q_{ss} \\right)}$" ], "text/plain": [ "Eq(F(h, Q), (-Q_{ss} + Q(t))*Derivative(F(h_{ss}, Q_{ss}), Q_{ss}) + (-h_{ss} + h(t))*Derivative(F(h_{ss}, Q_{ss}), h_{ss}) + F(h_{ss}, Q_{ss}))" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "taylor = sympy.Eq(F,F.subs(h,hss).subs(Q,qss)+sympy.diff(F,h).subs(h,hss).subs(Q,qss)*(hs-hss)+sympy.diff(F,Q).subs(h,hss).subs(Q,qss)*(qs-qss))\n", "display(taylor)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "para el tanque tenemos" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle F{\\left(h,Q \\right)} = - \\frac{\\sqrt{2} a \\sqrt{g h_{ss}} \\left(- h_{ss} + h{\\left(t \\right)}\\right)}{2 A h_{ss}} + \\frac{- Q_{ss} + Q{\\left(t \\right)}}{A} + \\frac{Q_{ss} - \\sqrt{2} a \\sqrt{g h_{ss}}}{A}$" ], "text/plain": [ "Eq(F(h, Q), -sqrt(2)*a*sqrt(g*h_{ss})*(-h_{ss} + h(t))/(2*A*h_{ss}) + (-Q_{ss} + Q(t))/A + (Q_{ss} - sqrt(2)*a*sqrt(g*h_{ss}))/A)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lineal = sympy.Eq(F,Fhq.subs(hs,hss).subs(qs,qss)+sympy.diff(Fhq,hs).subs(hs,hss).subs(qs,qss)*(hs-hss)+sympy.diff(Fhq,qs).subs(hs,hss).subs(qs,qss)*(qs-qss))\n", "display(lineal)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- La ecuación linearizada del tanque quedaría : " ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{d}{d t} h{\\left(t \\right)} = - \\frac{\\sqrt{2} a \\sqrt{g h_{ss}} \\left(- h_{ss} + h{\\left(t \\right)}\\right)}{2 A h_{ss}} + \\frac{- Q_{ss} + Q{\\left(t \\right)}}{A} + \\frac{Q_{ss} - \\sqrt{2} a \\sqrt{g h_{ss}}}{A}$" ], "text/plain": [ "Eq(Derivative(h(t), t), -sqrt(2)*a*sqrt(g*h_{ss})*(-h_{ss} + h(t))/(2*A*h_{ss}) + (-Q_{ss} + Q(t))/A + (Q_{ss} - sqrt(2)*a*sqrt(g*h_{ss}))/A)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lineal2 = sympy.Eq(sympy.diff(hs,t),lineal.rhs)\n", "display(lineal2)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- En la ecuación anterior vamos a remplazar las variable $h$ y $Q$ por las variables desviadas $h'$ y $Q'$.\n", "\n", "$$h' = h - h_{ss} \\qquad Q' = Q - Q_{ss}$$\n", "\n", "- Remplazando tenemos:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{d}{d t} \\operatorname{h'}{\\left(t \\right)} = - \\frac{\\sqrt{2} a \\sqrt{g h_{ss}} \\operatorname{h'}{\\left(t \\right)}}{2 A h_{ss}} + \\frac{\\operatorname{Q'}{\\left(t \\right)}}{A}$" ], "text/plain": [ "Eq(Derivative(h'(t), t), -sqrt(2)*a*sqrt(g*h_{ss})*h'(t)/(2*A*h_{ss}) + Q'(t)/A)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "hp = sympy.Function(\"h'\")(t)\n", "qp = sympy.Function(\"Q'\")(t)\n", "Eq_diff = lineal2.subs(hs,hp+hss).subs(qs,qp+qss).subs(qss,Eq_estacionario2.rhs)\n", "Eq_diff2 = sympy.Eq(sympy.simplify(Eq_diff.lhs),Eq_diff.rhs);\n", "display(Eq_diff2)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Ejercicios de Linealización\n", "\n", "Linealizar las siguientes funciones:\n", "\n", "$$m\\frac{d^2y(t)}{dt^2}+b\\frac{dy(t)}{dt}+k\\,y(t)^3 = - F(t)$$\n", "\n", "$$\\frac{d^2y(t)}{dt^2} + \\sin(\\omega t)\\frac{dy(t)}{dt} + e^{t/\\tau}y(t) = 0$$\n", "\n", "$$t\\frac{d^2y(t)}{dt^2}+\\sin(\\omega t)\\frac{dy(t)}{dt} = 0$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Root Locus\n", "\n", "El _root locus_ presenta los caminos de los polos en el plano complejo para un sistema en lazo cerrado en donde la ganancia del controlador $K$ varia de $0$ hasta $\\infty$.\n", "\n", "- **root**: o raíz, se refiere a la solución de la ecuación carácteristica de la funcion de transferencia. \n", "- **locus**: simplemente significa camino, posición o ubicación. \n", "\n", "Veremos como construir los caminos del _root locus_ a partir de la información de los polos en lazo abierto de un sistema. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Ejemplo 1\n", "\n", "Consideremos un sistema de primer orden con una constante de tiempo $\\tau=2\\text{ seg}$:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{1}{2 s + 1}$" ], "text/plain": [ "1/(2*s + 1)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ss = sympy.Symbol('s'); G1A = 1/(1+2*ss); display(G1A)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "Este sistema tiene un polo que es $s=-0.5$. Si le agregamos al sistema un controlador con ganancia $K$ en lazo abierto. " ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{K}{2 s + 1}$" ], "text/plain": [ "K/(2*s + 1)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sK = sympy.Symbol('K'); G1B = G1A*sK; display(G1B)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "La posición de polo no cambia, el polo sigue siendo $s=-0.5$, ¿qué pasa en lazo cerrado?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "En lazo cerrado, tendremos la siguiente función de transferencia. " ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{K}{K + 2 s + 1}$" ], "text/plain": [ "K/(K + 2*s + 1)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "G1C = sympy.simplify(G1B/(1+G1B)); display(G1C)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "Aquí vemos, que la posición del polo depende del valor que tome $K$. " ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle s = - \\frac{K}{2} - \\frac{1}{2}$" ], "text/plain": [ "Eq(s, -K/2 - 1/2)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "G1Cpole = sympy.Eq(ss,sympy.solve(sympy.denom(G1C),ss)[0]); display(G1Cpole)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "Comienza en $s=-0.5$ cuando $K=0$, y este polo se vuelve más negativo cuando $K$ se incrementa. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "En la siguiente figura interactiva se puede ver el comportamiento del polo:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "9d80afcf01e74226a11dd7d7ac70cabb", "version_major": 2, "version_minor": 0 }, "text/plain": [ "HBox(children=(FloatSlider(value=1.0, description='Ganacia $K$', max=20.0, orientation='vertical'), Output()))" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## Parametros del modelo\n", "\n", "param_K = widgets.FloatSlider(value=1,min=0,max=20,step=0.1,description='Ganacia $K$', orientation=\"vertical\")\n", "\n", "## Definicion de la simulacion\n", "\n", "def root_locus_ejemplo_1(K):\n", " kvals = numpy.linspace(0,20,100)\n", " real = -(kvals+1)/2\n", " imag = kvals*0\n", " plt.plot(real,imag,c='k')\n", " plt.scatter(-(K+1)/2,0,marker=\"x\")\n", " plt.title('Root locus para el ejemplo 1 con función de transferencia $1/(2\\,s+1)$')\n", " plt.xlabel('Real')\n", " plt.ylabel('Imaginario')\n", "\n", "## Presentación de los resultados \n", " \n", "plot_root_locus_ejemplo_1 = widgets.interactive_output(root_locus_ejemplo_1,{'K':param_K}) \n", "widgets.HBox([param_K,plot_root_locus_ejemplo_1])" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "root_locus_ejemplo_1(0)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Del mismo modo se puede usar la funcion *root_locus* de la libreria **control**, para obtener la gráfica. La función toma como entrada la funcion de transferencia en lazo abierto sin controlador.\n", "\n", "$$\\frac{1}{2\\,s+1}$$" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "G1D = control.tf(1,[2,1]);\n", "control.root_locus(G1D);\n", "plt.axvspan(0, 0.5, facecolor='r', alpha=0.5)\n", "plt.xlim(-1.5,0.5);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "La zona en rojo corresponde a los valores reales positivos, esta zona se conoce como lo región inestrable, si hay al menos un polo del sistema en esta zona el sistema será inestable. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Grafica del root locus manual \n", "\n", "1. El número de _locis_ (caminos) es igual al orden de la ecuación característica.\n", "2. Cada _locis_ empieza en un polo del lazo abierto ($K=0$) y termina en un cero del lazo abierto o en infinito ($K=\\infty$).\n", "3. Los _locis_ recorren el eje real, o recorren caminos simétricos con respecto al eje real cuando empiezan en polos conjugados. \n", "4. Un punto en el eje real es parte de un _locis_ si el número de polos y ceros a la derecha de ese punto es impar. \n", "5. Lejos de los polos y ceros del lazo abierto, los _locis_ se vuelven asimptoticos a una lineas que tienen angulos $\\alpha_n$ con respecto al eje real.\n", "\n", " $$\\alpha_n=\\pm \\frac{n\\pi}{P-Z} \\qquad\\text{donde,}\\quad n=1,3,5,..., P-Z$$\n", "\n", "6. Las asimptotas intersectan al eje real en un punto $S$, conocido como centroide del mapa de polos y ceros, dado por:\n", "\n", " $$S=\\frac{\\Sigma \\text{polos} - \\Sigma \\text{ceros}}{P-Z}$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Ejemplo 2\n", "\n", "Analicemos la siguiente función de transferencia. " ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{0.5 s + 1}{s \\left(0.3 s + 1\\right) \\left(0.4 s^{2} + 0.6 s + 1\\right)}$" ], "text/plain": [ "(0.5*s + 1)/(s*(0.3*s + 1)*(0.4*s**2 + 0.6*s + 1))" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "s = control.tf([1,0],1)\n", "G2s = (1+0.5*ss)/(ss*(1+0.3*ss)*(1+0.6*ss+0.4*ss**2)); display(G2s)\n", "G2 = (1+0.5*s )/(s *(1+0.3*s )*(1+0.6*s +0.4*s **2)); " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- ¿Cuántos polos tiene, y cuánto valen?" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tiene P = 4 polos y valen: \n", "\n", "(-3.3333333333333357+0j)\n", "(-0.7499999999999991+1.3919410907075038j)\n", "(-0.7499999999999991-1.3919410907075038j)\n", "0j\n" ] } ], "source": [ "polos_G2 = control.pole(G2)\n", "print(\"Tiene P = %d polos y valen: \\n\\n%s\" % (len(polos_G2),'\\n'.join(map(str, polos_G2))))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- ¿Cuántos ceros tiene, y cuánto valen?" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tiene Z = 1 ceros y vale: \n", "\n", "-2.0\n" ] } ], "source": [ "ceros_G2 = control.zero(G2)\n", "print(\"Tiene Z = %d ceros y vale: \\n\\n%s\" % (len(ceros_G2),'\\n'.join(map(str, ceros_G2))))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- ¿Cuál es la ecuación característica? " ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle s \\left(0.3 s + 1\\right) \\left(0.4 s^{2} + 0.6 s + 1\\right) = 0$" ], "text/plain": [ "Eq(s*(0.3*s + 1)*(0.4*s**2 + 0.6*s + 1), 0)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Eq_caracteristica = sympy.Eq(sympy.denom(G2s),0); display(Eq_caracteristica)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- ¿Cómo graficamos el _root locus_ de esta función de transferencia? " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Se puede partir del mapa de polos y ceros y de la reglas para graficarlo manualmente. " ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "control.pzmap(G2);\n", "plt.axvspan(0, 4, facecolor='r', alpha=0.5)\n", "plt.xlim(-5,3);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "O directamente con la función *root_locus*" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "control.root_locus(G2);\n", "plt.axvspan(0, 4, facecolor='r', alpha=0.5)\n", "plt.xlim(-10,4);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Existe un valor limite para $K$ el cual hace que los caminos pasen de la zona real negativa a la zona real positiva.** Este valor se conoce como $K_u$ la ganacia última del sistema. Para encontrarlo se puede usar criterio de _Routh_ o usando la función _margin_." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Calculo manual de la matriz de *Routh*\n", "\n", "Para la matriz de *Routh* debemos empezar por encontra la ecuación característica del sistema en lazo cerrado." ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle 0.5 K s + K + 0.12 s^{4} + 0.58 s^{3} + 0.9 s^{2} + s$" ], "text/plain": [ "0.5*K*s + K + 0.12*s**4 + 0.58*s**3 + 0.9*s**2 + s" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "carac2 = sympy.expand(sympy.denom(sympy.simplify(G2s*sK/(1+G2s*sK)))); display(carac2)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "Buscamos los coeficientes:" ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "El valor que acompaña a s^0 es K\n", "El valor que acompaña a s^1 es 0.5*K + 1\n", "El valor que acompaña a s^2 es 0.900000000000000\n", "El valor que acompaña a s^3 es 0.580000000000000\n", "El valor que acompaña a s^4 es 0.120000000000000\n" ] } ], "source": [ "coeff2 = [];\n", "for i in range(5):\n", " coeff2.append(carac2.coeff(ss,i)); print(\"El valor que acompaña a s^%d es %s\" % (i,coeff2[i]))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Completamos la matriz de *Routh*" ] }, { "cell_type": "code", "execution_count": 81, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "s⁴ \t 0.12 \t\t\t\t\t\t 0.90 \t\t K\n", "s³ \t 0.58 \t\t\t\t\t\t 0.5*K + 1 \t 0\n", "s² \t 0.693103448275862 - 0.103448275862069*K \t K\n", "s¹ \t X\n", "s⁰ \t K\n", "\n", " donde X = 1.0*(0.0517241379310345*K**2 + 0.336896551724138*K - 0.693103448275862)/(0.103448275862069*K - 0.693103448275862)\n" ] } ], "source": [ "print(\"s⁴ \\t %3.2f \\t\\t\\t\\t\\t\\t %3.2f \\t\\t %s\" %(coeff2[4],coeff2[2],coeff2[0]))\n", "print(\"s³ \\t %3.2f \\t\\t\\t\\t\\t\\t %s \\t %s\" %(coeff2[3],coeff2[1],0))\n", "\n", "s21 = sympy.simplify((coeff2[3]*coeff2[2]-coeff2[4]*coeff2[1])/coeff2[3])\n", "\n", "print(\"s² \\t %s \\t %s\" %(s21,coeff2[0]))\n", "\n", "s11 = sympy.simplify((s21*coeff2[1]-coeff2[3]*sK)/s21)\n", "\n", "print(\"s¹ \\t X\")\n", "print(\"s⁰ \\t K\")\n", "\n", "print(\"\\n donde X = %s\"%(s11))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "La primer columna de la matriz debe toda tener el mismo signo. Ya que los dos primeros elementos son positivos el resto también. " ] }, { "cell_type": "code", "execution_count": 89, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[-8.15624601369002, 1.64291268035669]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display(sympy.solve(s11,sK))\n", "\n", "s11.subs(sK,1.6); # Verificamos la desigualdad. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "De aqui tenemos que... $K_u= 1.643$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Usando la función _margin_ tenemos:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.6429126803566858" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "margin_G2,_,_,_ = control.margin(G2)\n", "display(margin_G2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "El primer valor reportado es la ganacia última $K_u \\approx 1.643$\n", "\n", "Podemos verificar que pasa al sistema en lazo cerrado con valores de $K$ alrededor de $K_u$" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "826cfa0ba2784d2fab798dbcffa861cf", "version_major": 2, "version_minor": 0 }, "text/plain": [ "VBox(children=(Output(), FloatSlider(value=1.6, description='Ganacia $K$', max=2.0, min=1.0, step=0.01)))" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## Parametros del modelo\n", "\n", "param_K = widgets.FloatSlider(value=1.6,min=1,max=2,step=0.01,description='Ganacia $K$')\n", "\n", "## Definicion de la simulacion\n", "\n", "def respuesta_ejemplo_2(K):\n", " G2_close_loop = control.feedback(G2*K,1)\n", " t, y = control.step_response(G2_close_loop)\n", " plt.plot(t,y)\n", " plt.title('Respuesta temporal para el sistema \\n%s' % (G2_close_loop))\n", " plt.xlabel('tiempo')\n", " plt.ylabel('amplitud')\n", "\n", "## Presentación de los resultados \n", " \n", "plot_respuesta_ejemplo_2 = widgets.interactive_output(respuesta_ejemplo_2,{'K':param_K}) \n", "widgets.VBox([plot_respuesta_ejemplo_2,param_K])" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Para $K=1.5$" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "respuesta_ejemplo_2(1.5)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Para $K=1.65$" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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UCTgHKAcyurDsucC8LsbxE+DZ8D7sG+I4tZ26/x3qjgSKgJeA7/dw+w8CSokSQyZwT3if0mLqXAEcCmSEtlgHnNvF5c8D5nahXhbw1fDZKO1sHuAR4Obw/uwFvAZcHvP/9ZnQPpnAD4G3Wn1un+tJe3WjXa8Gru5i3QuB04AHOpsHKAS2AucD2UA+sG/M9LXASYnctg7jS9aKU/UFDAXqgekxZX8BftrJfCfRKjm0U68SOKydabOB+aHOFuCXMdN+Ej5w2TFlRwErgRmtlvN74Avhn7lXk0N324eOk0MxYEBuTNkrwHmJbJ8wLQ34QFj/6C5s91y6nhw2AafEjP8QuKOduvOBj8aMfwJY305dAb8KXyiV4Uv0gDCtBFgBnBhTPwP4K/B/HcT6646mt6o7jy4kh1bzbOhsHmApcHrM+M+BP7RTd2R4z0bFfG67lByIks9twHZgZ/isFXdhvqvpYnKImee2zuYB/gf4SwfT15LE5ODdSvGmA41mtjymbDGw/54uWNJMol9VK9upch1wnZkNA6YAd7VMMLOrzOxsM6uLKXvRzKaa2bKYdcwGZhEliEToSft8IHQJvCHpspZCM9tCtBfyaUnpko4CJgHPtbOcPW4fAElLgFrgQeBPZra1C9vdJZJGEO0pLo4p7qx91Gp4vKSCNuqdAhxH9B4UAB8j+qLDzNaa2TQze7Klspk1mtn5ZvbldmIVMAd4o9MNS6xrgXMl5UoaR/TL+1/t1D0O2Gxm22PKDpG0TdLycKwlo515LyRqtwnAKOBSYHfvbEKPHAmUS3pB0lZJD0ma2KrOX0OX2mOSDu7L4Dw5xMsj+lUWq4Jol6/HJA0j+oX9fTOraKdaAzBVUqGZVZvZS91cRzrwO+BLZta8J/F2oLvtcxdR10oR8Dnge5LOi5l+O/A9oI6oe+XbZra+nWXtUfu0MLODgGFEv9LbS0Q9lRf+xr7HHbXPv4CvSCqStBdweSjPbaNuQ1jOPkQ3zVxqZqV7EOvVRN8Bf96DZfSGZ4iSZyXRnsZ84P7WlSSNB35L1FUbO+8BwGjgw8B5QHvHURqIksJUM2syswVm1vqz3JfGEyWsrwATgTVE/w8tzifaI5wEPAU8Kml4n0WXrF2WVH0BhwC7WpV9HXiok/na7VYi6gN/GvhjJ8uYRvTh2Ea0y3tmN2P/MnBTzPg8OuhWIkokO8NrF1F3Ucv4kt5sn5i6VwL3hOF9gBrg/URfUjOIukbOSET7tLPMpbRzjCPE2tIe1UBjzPjOduYZQauuKqIvrdc6+Gz8BtgIrAauCu9DWjv1LwcWhDa4ARjWw+3+EtGX0fhO6u2MeTWGdmgZv7IL6+mwWym87+uAbxP1u48i6h78Wat6RcCbRD8eOlrfucCCdqZlEh3jeZOo6+9nQGY7dR+O2c7a8GoZf7gL292VbqXFwJ9jxkeFz05BO/XfAj6wp5/5Ln9G+mpF/eXFu33q02LKbqWHxxzCB/5Ror7fNv/h25gnDfhI+EAO7Ubs9wM7iA6Abg7bUQH8pgvzXkT3jjl0q31i6n4TuDcMfwR4tdX0azuLt6ft086yVgIf7EK9uXTvmMPJMeM/oJ1jDm3MewnwYhfqjSZK/j/swTZfHL60J3dzvnkdfdG3M09nyaGw9Rci0YkCr8eMjwBe7cpnDPg4sLAL9UpCkvhMF+pe3dkXfRvzdCU5/IX3/pgb2botWtVfCpzV3fe7py/vVmrFzGqITgX8gaSh4VTHs4neyDiS0iTlEP0qkaScltMHwymJdxP1a15onXT1SPqkpKJQb2co7k730EVEXTgzw2s+8H2iX2W9ogftc7akEYrMJvrl+0CY/CowLZzOKklTgDOBJe0sa4/aR9KRko4Np1oOkfRNooPi/+nqMrroVuA7Ybv3IepOu7mdmMZJGhu2/0jgu0S/btuqe7ikI8LnqoYoOXar+1DS+UQHQk82s9Xdmbeb68kO/xcAWeH/Qq3rmdk2oj2YyyRlhG6TCwmfgdAd+yjwvJld2cZ6TpNUHIb3IWq/B1rXC9OPl3Rg6H6tJOpm6tXuV0mZYbvTgIyw3entVP8z8EFJM8N7+l2ig+sVih5sdEz4rOYoOuW4EHi+N+PtUF9lof70Isrg9xP9A74NfCJm2hygOmZ8LlG2j33NC9PeF8Z3Ee2Ot7zmtLPe24jORKkmOkh4zh5uxzwScyprd9rndqKDptVEu8WXt1rWx4hOua0i+pX5v7TfpbJH7RPej8VhXeVEXX3HdXHeuXR9zyEbuIl3z6r6Wsy0iSH+iWH8OKKzUnYBy4DzO1juiURfmtVE3Up/pZunRRN9ETe0+jz+vhufp7ldrLu2jf+LkjDtW8A/Y+rODMveEbbrLsJZRESJwsJnLTbmlva7JrRxDVG33A9ov6vovNDGNWGeX9O105ivpuunst7cxnZf1Nb/Rii7jKhLcQfwEDAhlO8f3usaov+fJ4FZ3Xmv9/TlT4JzzjkXx7uVnHPOxfHk4JxzLo4nB+ecc3E8OTjnnIvjycE551wcTw7OOefieHJwzjkXx5ODc865OJ4cnHPOxfHk4JxzLo4nB+ecc3E8OTjnnIvjycE551wcTw7OOefieHJwzjkXx5ODc865OJ4cnHPOxfHk4JxzLo4nB+ecc3Eykh1AbygsLLSSkpJkh+Gcc/3KggULtplZUVvTBkRyKCkpYf78+ckOwznn+hVJ69qb5t1Kzjnn4nhycM45F8eTg3POuTieHJxzzsXx5OCccy6OJwfnnHNxPDk455yL48nBOef6qZueW8M/lpQmZNmeHJxzrp/607OreXLploQs25ODc871Q03NxpaqOsYMz0nI8j05OOdcP7S1qpamZmNMwZCELN+Tg3PO9UObdtYCMNb3HJxzzrUordgN4HsOzjnn3lXasufgycE551yLTRW7yc1KZ9iQxDx5wZODc871Q6U7axlTkIOkhCw/4clB0k2Stkp6Pabs55LekrRE0n2ShofyEkm7JS0Kr98nOj7nnOuPSit2M3Z4YrqUoG/2HG4GTm1V9jhwgJkdBCwHroqZtsrMZobXpX0Qn3PO9Tsbd9Ym7HgD9EFyMLNngPJWZY+ZWWMYfQkYn+g4nHNuoKhrbGJbdeIugIPUOOZwMfDPmPG9Jb0q6WlJc9qbSdIlkuZLml9WVpb4KJ1zLkVsqagDEnemEiQ5OUj6NtAI/DUUlQITzewQ4GvA3yQNa2teM7vBzGaZ2ayioqK+Cdg551LAppZrHAbinoOki4AzgfPNzADMrM7MtofhBcAqYHqyYnTOuVSU6AvgIEnJQdKpwBXAWWa2K6a8SFJ6GJ4MTANWJyNG55xLVYm+dQZAYq6eiCHpdmAuUChpA/DfRGcnZQOPh3N0XwpnJh0H/EBSA9AMXGpm5W0u2DnnBqnSit0UDMkkNytxX+EJTw5mdl4bxTe2U/ce4J7ERuScc/1bywVwiZQKZys555zrhk0VtQm9AA48OTjnXL+zaedu33Nwzjn3rl31jVTsbvA9B+ecc+/qizOVwJODc871K31xjQN4cnDOuX4l0Q/5aeHJwTnn+pGWW2cUF2QndD2eHJxzrh8p3VlLYV422RnpCV2PJwfnnOtHNlXsTvjBaPDk4Jxz/UppReKvjgZPDs4512+YGZt2JvbxoC08OTjnXD9RXlPPrvomJozITfi6PDk451w/sX5HdKbS+BG+5+Cccy7YsCN6/M2Ekb7n4JxzLlhf7nsOzjnnWlm/YxfDczPJz8lM+Lo8OTjnXD+xYcfuPjkYDX2UHCTdJGmrpNdjykZKelzSivB3RCiXpF9LWilpiaRD+yJG55xLdRvKdzFhZOK7lKDv9hxuBk5tVXYl8KSZTQOeDOMApwHTwusS4Po+itE551JWc7MNvD0HM3sGKG9VfDZwSxi+BTgnpvxWi7wEDJc0pi/idM65VFVWXUd9U3OfHIyG5B5zKDaz0jC8GSgOw+OA9TH1NoSy95B0iaT5kuaXlZUlNlLnnEuy9eXRaazj++A0VkiRA9JmZoB1c54bzGyWmc0qKipKUGTOOZca1rdc4zCQupXasaWluyj83RrKNwITYuqND2XOOTdobejDaxwgucnhQeDCMHwh8EBM+afCWUtHAhUx3U/OOTcord+xi6L8bHIyE/schxYZfbESSbcDc4FCSRuA/wZ+Ctwl6TPAOuBjofojwOnASmAX8Om+iNE551LZ+vLdTOijvQboo+RgZue1M+nENuoa8MXERuScc/3Lhp27OHTiiD5bX0ockHbOOde+xqZmNu2s7bPjDeDJwTnnUl5pRS1NzdZnZyqBJwfnnEt5G8JzHPriVt0tPDk451yKa7nGwbuVnHPOvWND+S7SRJ88O7qFJwfnnEtxG3bsZkzBEDLT++4r25ODc86luPU7dvVplxJ4cnDOuZS3vnw34/vwTCXw5OCccymttqGJLVW1ffaQnxaeHJxzLoWtL9+FGexdOLRP1+vJwTnnUtiabTUAlIzy5OCccy5Yu92Tg3POuVbWbNvFiNxMCnIz+3S9nhyccy6Frd1WQ0kfH28ATw7OOZfS1m6vYe8+7lICTw7OOZeyahuaKK2o9T0H55xz71q3PbrhXjKSQ588Ca4tkmYAd8YUTQa+BwwHPgeUhfJvmdkjfRyec84l3bunsfbt1dGQxORgZsuAmQCS0oGNwH1Ez4z+lZldk6zYnHMuFbxzGusg7lY6EVhlZuuSHYhzzqWKtdtqGDU0i2E5fXsaK6ROcjgXuD1m/EuSlki6SVKbT9SWdImk+ZLml5WVtVXFOef6tTVJOo0VUiA5SMoCzgL+HoquB6YQdTmVAr9oaz4zu8HMZpnZrKKioj6J1Tnn+tLa7TV9fmV0i6QnB+A0YKGZbQEwsy1m1mRmzcAfgdlJjc4555JgV30jWyrrknIwGlIjOZxHTJeSpDEx0z4IvN7nETnnXJIl8zRWSOLZSgCShgInA5+PKf6ZpJmAAWtbTXPOuUFhbTiNta9v1d0iqcnBzGqAUa3KLkhSOM45lzLWJPE0VkiNbiXnnHOtrN1WQ2FeNnnZyfkN78nBOedS0Nptu9i7MDkHo8GTg3POpaS122uYlKTTWMGTg3POpZyauka2VtUl7WA0eHJwzrmUs6qsGoApRZ4cnHPOBSu2RMlh6uj8pMXgycE551LMyrJqMtPFpCRdHQ2eHJxzLuWs2FJNyaihZKYn7yvak4NzzqWYlVurmFacl9QYPDk451wKqW1o4u3yXUk93gCeHJxzLqWs2VZDs8HU0cndc+jwumxJX+toupn9snfDcc65wW3l1uhMpWmpnByAlv2aGcDhwINh/APAy4kKyjnnBqsVW6tJU/Luxtqiw+RgZt8HkPQMcKiZVYXxq4F/JDw655wbZFZurWLiyFxyMtOTGkdXjzkUA/Ux4/WhzDnnXC9aubU66QejoevPc7gVeFnSfWH8HOCWxITknHODU0NTM2u21XDivsn/7d2l5GBmP5b0T2BOKPq0mb2auLCcc27wWbd9Fw1NxtSi5B6Mhi4mB0kTgW3AfbFlZvb2ngYgaS1QBTQBjWY2S9JI4E6ghOhRoR8zsx17ui7nnEtl75yplOQL4KDr3Ur/IHqmM8AQYG9gGbB/L8VxvJltixm/EnjSzH4q6cow/s1eWpdzzqWklVurAJjSX/YczOzA2HFJhwJfSEhEkbOBuWH4FmAenhyccwPcyq3VjBs+hKFJejRorB5dIW1mC4EjeikGAx6TtEDSJaGs2MxKw/Bm2jgzStIlkuZLml9WVtZLoTjnXPKs2Fqd9CujW3T1mEPsldJpwKHApl6K4Vgz2yhpNPC4pLdiJ5qZSbLWM5nZDcANALNmzYqb7pxz/Ulzs7GqrJojJ49KdihA1/cc8mNe2UTHIM7ujQDMbGP4u5XogPdsYIukMQDh79beWJdzzqWqDTt2U9vQ3L/2HIA3zezvsQWSPgr8vZ36XSJpKJBmZlVh+BTgB0S36bgQ+Gn4+8CerMc551Ldm6WVAOw7ZliSI4l0dc/hqi6WdVcx8JykxUT3avqHmf2LKCmcLGkFcFIYd865AWtpaSVpghnFyb86Gjq/K+tpwOnAOEm/jpk0DGjc05Wb2Wrg4DbKtwMn7unynXOuv6/2p0gAAB4nSURBVFhaWklJ4VCGZCX3nkotOutW2gTMB84CFsSUVwH/L1FBOefcYLN0cyUHjR+e7DDe0dldWRcDiyX91cz2eE/BOedcvMraBtaX7+bcwycmO5R3dNatdJeZfQx4tZ3TSQ9KWGTOOTdIvFUaXRm9X4ocjIbOu5W+Ev6emehAnHNusFqaYmcqQefdSqXh77q+Ccc55wafpaWVjMjNpHhYdrJDeUdn3UpVvHvDPQCFcRFdvJw6ac455/qppaWV7Dd2GJKSHco7OttzSI0Tbp1zboBqbGrmrc1VXHDkpGSH8h5dvvVfuBPrsUR7Ds/5w36cc27Prd1eQ11jc0odb4AuXiEt6XtEt84eBRQCN0v6TiIDc865weDNcKZSqiWHru45nA8cbGa1AJJ+CiwCfpSowJxzbjBYWlpJZrpS5oZ7Lbp6b6VNQE7MeDawsffDcc65wWVpaSVTR+eTldGjx+skTFf3HCqANyQ9TnTM4WTg5Zb7LZnZ5QmKzznnBrQ3N1Vy7LTCZIcRp6vJ4b7wajGv90NxzrnBZXt1HVur6lLqyugWXX2G9C2JDsQ55wabNzZFV0anYnLo6tlKZ0p6VVK5pEpJVZIqEx2cc84NZIvX70SCA8YXJDuUOF3tVroW+BDwmpn585qdc64XLN5QwZSiPIblZCY7lDhdPTy+HnjdE4NzzvUOM2PR+p0clIJ7DdD1PYcrgEckPQ3UtRSa2S97umJJE4BbiR4VasANZnadpKuBzwFloeq3zOyRnq7HOedSUWlFLduq65g5IXUe8BOrq8nhx0A10bUOWb207kbg62a2UFI+sCCcKgvwKzO7ppfW45xzKWfx+p0AHJxCT3+L1dXkMNbMDujNFYfbgbfcErxK0lJgXG+uwznnUtWiDTvJSk9jnzGpeX/Trh5zeETSKYkKQlIJcAjwn1D0JUlLJN0kaUQ781wiab6k+WVlZW1Vcc65lLVkfQX7jsknOyM92aG0qavJ4TLgX5J29/aprJLygHuAr5pZJXA9MAWYSbRn8Yu25jOzG8xslpnNKioq6o1QnHOuTzQ1G69trODgFD3eAF2/CC5f0khgGu+9x9IekZRJlBj+amb3hnVtiZn+R+Dh3lqfc86lgtVl1VTXNabs8QboYnKQ9Fmi50mPJ7ob65HAC8CJPV2xokce3QgsjT3rSdKYlseTAh8EXu/pOpxzLhUtajkY3d/3HIgSw+HAS2Z2vKR9gP/Zw3UfA1wAvCZpUSj7FnCepJlEp7euBT6/h+txzrmUsnjDTvKzM5hcODTZobSrq8mh1sxqJSEp28zekjRjT1ZsZs8RPYu6Nb+mwTk3oC3ZUMGB4wtIS0udZ0a31tUD0hskDQfuBx6X9ACwLnFhOefcwFTb0MTS0sqU7lKCrh+Q/mAYvFrSU0AB8K+EReWccwPU0tJKGpospQ9GQ9e7ld5hZk8nIhDnnBsMFqzbAcChE1M7OaTWc+mcc26A+8+ackpG5TJ6WK9dFZAQnhycc66PNDcbr6wt5/CSkckOpVOeHJxzro+sLKtm564GZu/tycE551zwnzXlAJ4cnHPOveuVNeUUD8tm4sjcZIfSKU8OzjnXB8yMl9dExxuiuwelNk8OzjnXBzbs2M3mylqO6AddSuDJwTnn+kTL8YbDPTk455xr8cqacgqGZDJ9dGo++a01Tw7OOdcHXl5bzuElI1L6ZnuxPDk451yCba2qZc22mn5xCmsLTw7OOZdgL7ccb+gHV0a38OTgnHMJ9tyKbeTnZHDguIJkh9Jlnhyccy6BzIxnlpdxzJRCMtL7z1duykYq6VRJyyStlHRlsuNxzrmeWFVWzaaKWuZML0x2KN2SkslBUjrwW+A0YD+i50rvl9yonHOu+55Zvg2A46YVJTmS7un2w376yGxgpZmtBpB0B3A28GZvrmRrVS2PvrGFNWU1rNlWzfodu2luNjLSRXpaGpnpIiNNZKRHw5npaWSkpZGVEQ23vLLCtMyMNLLS08jKSCM7I/qblZ5GdmYa2RnpZGekkZMZ/c3OSCcnM4yHv0My08nsR7udzrnOPbOijMmFQ5nQD+6nFCtVk8M4YH3M+AbgiNgKki4BLgGYOHFij1aytbKO797/OkMy0ykpHMrUojwy0kVTs9HQZDQ2N9PYZDQ0NVPb0Ex1bSN1jc00NhuNTc3UNzbT0GzUN4bhpmjanshIE0My08nJipJFblY6Q7Kiv7lZGQzNSmdodgZDszPIzUonLzsjeuVEf/NzMsjLziQ/JxoempXRb86rdm6gqW1o4qXV2zn38J59RyVTqiaHTpnZDcANALNmzerRN/L04nxeuupEiodl99qNsJqbjfqm5ujV2ExdSBzRcBO1DdHfuoZmasN4bUPTO6/dDU3sqo+Gd9W/O1xT18j26vpQ1kh1XSO1Dc2dxpMmyM/JZNiQDAqGZMa8shiem8mI3EyG52YxIjeLkUMzGZGbxaih2QwbktEvbg7mXCpbsG4HtQ3NzJnWv443QOomh43AhJjx8aGsV2VlpLFXQe8+qi8tTeSkpZOTmd6ry21LU7NRU99IdW0jNXWNVNY2UlXbQHVdI1VhuKq2kcrdDVTsbqCytpGK3Q1srqiiYncjO3fVt7unk5EmRg7NYlReNoV5WRTmZVOUn01R+Dt6WDaj83MoHpZNfk5mwrfVuf7omeVlZKaLIyePSnYo3ZaqyeEVYJqkvYmSwrnAJ5IbUupJTxPDcjIZ1sMvZzOjuq6Rnbsa2LGrnvKaenbsqmd7dTS8vbqe7TV1lFXXs7qshm3VddQ1xu+tDM1Kp7gghzEFOew1bAhjh+cwpiD6O37EEMYNz2VIVuKTpXOp5unlZcyaNJKh2an6Vdu+lIzYzBolfQl4FEgHbjKzN5Ic1oAjifycTPJzMrt0sMzMqKprZGtlHVuraimrqmNzRS2bK2vZUlnL5opaXli1jS2VtbTeIRk1NIvxI3OZMGIIE0fmMmlULhNHDqWkMJfi/Bw/LuIGnK2Vtby1uYorTp2R7FB6JCWTA4CZPQI8kuw43Lukd/dUpo7Oa7deY1MzW6vq2LhzNxt37Gbjzt1s2LGL9eW7WbKhgn+9vvk93Vk5mWmUjBrK3oVDmVKUx+Si6O/U0Xn98heXcwDPrOifp7C28P881+sy0tMYO3wIY4cP4fCS+OmNTc1s2lnLuvIa1m7fxdptNazZVsNbm6t47M0tNMUkjrEFOUwrzmfGXvlML85nn73ymTo6r0+O6Ti3Jx5/czN7DcthvzHDkh1Kj3hycH0uIz2NiaNymTgqlznT3jutvrGZt8t3sXJrNavKqlm+pYoVW6p5cfV26sPxjvQ0MaVoKPuOGcb+Y4dxwNgC9h9bQEGuHxh3qWF3fRNPLy/jY7Mm9NsuU08OLqVkZaQxdXReXLdVY1Mz68p38VZpFUtLK1laWsnLa8p5YNGmd+pMGpXLgeMKOGh8ATMnjODAcQV+INwlxdPLy6htaObU/fdKdig95snB9QsZ6WlMKcpjSlEeZxw05p3y7dV1vLGpktc2VvD6xgpefXsnDy8pBaI9jH32yuewSSM4bNIIDp04gvEjhvj1Gy7hHn1jM8NzM/vV8xta8+Tg+rVRedkcN72I46a/e9BvW3Udi97eyaL1O3l1/Q7uWbCBW19cB8CYghwOLxnJ7L1HcuTkkUwpyvNk4XpVfWMzTyzdwqn779Wv7sLamicHN+AU5mVz0n7FnLRfMRB1SS3bUsX8tTt4eW05L63ezoOLo+6oovxsjpw8imOmjOKYqYX97v43LvW8uHo7VbWNvL8fdymBJwc3CGSkp7F/OGh94dElmBnrtu/ipdXbeWn1dl5YtZ2HQrKYNCqXOdMKOW5aEUdPLSTPT6V13fToG5vJzUrn2H54y4xY/sl3g44kSgqHUlI4lHNnT8TMWFVWzXMrtvHcym3cu3Ajt730Nhlp4vCSkZywz2iO32c0U4qGeheU61BTs/HYG1s4fp/R/f50a08ObtCTxNTR+Uwdnc9Fx+xNfWMz89eV8/TyMua9VcaPH1nKjx9ZyqRRuZy8bzEn71fMYZNG9Ov+ZJcYC9/ewbbqun59llILTw7OtZKVkcbRUwo5ekohV522Lxt27OKpZWU88eYWbn1xHX96bg0jh2Zx8r7FnHrgXhw9ZRTZGf37V6LrHf9YUkpWRhpzZ/TPq6JjeXJwrhPjR+RywZGTuODISVTXNfL0sjIefWMz/3itlDvnryc/J4NT9tuLMw8awzFTC8nK8D2Kwai+sZkHF2/i5H2LB8Sdij05ONcNedkZnHHQGM44aAx1jU08v3Ib/1iymcfe3Mw9CzdQMCST0w8cwzkzx3J4ych+e3Ws6755y7ZSXlPPhw8bl+xQeoUnB+d6KDsjnRP2KeaEfYqpazyAZ5dv4+Elm3hg0UZuf/ltxhbkcM4h4/jQoeM7vFGhGxjuWbiBwrzsfnujvdY8OTjXC7Iz0t+5tmJXfSOPv7mF+1/dyB+eWc3v5q3i4PEFfHTWBD5w8FgKhvT/Lgf3XuU19fz7ra1ceFTJgDlRwZODc70sNyuDs2eO4+yZ49haVcuDizZx94INfOf+1/nhw29y2gF7ce7siRyx90g/NXaAeHDRRhqajA8fNj7ZofQaTw7OJdDo/Bw+O2cynzl2b17fWMld89dz/6KN3L9oE5OLhnLe4RP5yGHjGTE0K9mhuj1wz8KN7DdmGPv209tzt2Vg7P84l+IkceD4An54zgG8/K2TuOajBzMiN4sfP7KUI37yJF+7axGvvr0Ds7af6e1S1/ItVby2sWJA7TVAkvYcJP0c+ABQD6wCPm1mOyWVAEuBZaHqS2Z2aTJidC5RhmSl85HDxvORw8bz1uZKbntpHfct3Mi9Czdy8PgCLjqmhNMPHOPXTvQTf5+/now0cfbMsckOpVcpGb9UJJ0C/Ds8K/p/AczsmyE5PGxmB3RnebNmzbL58+f3fqDO9ZHqukbuXbiBW15Yy6qyGgrzsvjkkZP45JGTKMzLTnZ4rh276hs58n+e5Nhphfzu/MOSHU63SVpgZrPampaUbiUze8zMGsPoS8DA2h9zrpvysjP41FElPPG19/GXz8zmoPHDufaJFRz903/zzbuXsGJLVbJDdG24Z+FGKmsb+cyxeyc7lF6XCgekLwbujBnfW9KrQCXwHTN7tq2ZJF0CXAIwceLEhAfpXF+QxJxpRcyZVsTKrdX8+fk13LNwA3fOX8+J+4zmkuMmM9vPckoJzc3Gzc+v4aDxBRw6cUSyw+l1CetWkvQE0Nbdp75tZg+EOt8GZgEfMjOTlA3kmdl2SYcB9wP7m1llR+vybiU3kJXX1HPri2u59cV1lNfUc8jE4Xxh7lRO3Ge0X4GdRPOWbeWiP7/CtR+fyTmH9M+rojvqVkrYnoOZndTRdEkXAWcCJ1rIUGZWB9SF4QWSVgHTAf/md4PWyKFZfPWk6Xz+uCncvWA9Nzy7ms/dOp/pxXlcNncKHzho7IC58Ko/uen5tYzOz+b0A8d0XrkfSsonStKpwBXAWWa2K6a8SFJ6GJ4MTANWJyNG51LNkKx0LjiqhKe+Ppfrzp1JmsT/u3MxJ/ziae54+W3qG5uTHeKgsXJrFc8sL+OCIycN2BstJmurfgPkA49LWiTp96H8OGCJpEXA3cClZlaepBidS0kZ6WmcPXMcj1w+hxsuOIzhuZlcee9rHH/NPG57aR11jU3JDnHAu/G5NWRlpPGJIwbu8c6knMra2/yYgxvMzIynl5dx3ZMrePXtnYwtyOGy46fy8VkTBuyv2mRaX76L46+Zx7mzJ/Cjcw5Mdjh7JOVOZXXO9R5JzJ0xmnsvO5pbL57NXgU5fPf+1zn+mnnc8fLbNDR5d1Nvuu7JFaSniS+fMC3ZoSSUJwfnBghJHDe9iHsuO5pbLp5NYX42V977Gif8Yh73LNhAU3P/7yVItlVl1dy7cAMXHDmJ4mE5yQ4noTw5ODfASOJ904u4/wtHc9NFsxiWk8nX/76YU371NP9YUkqzJ4keu/aJFeRkpnPp3CnJDiXhPDk4N0BJ4oR9innoS8dy/fmHIokv/m0hZ/32OZ5eXuY3+eumpaWVPLR4E58+pmRQ3NLEk4NzA1xamjjtwDE8+tXj+MVHD2bnrgYuvOllzr3hJRas25Hs8PqNnz+6jPycDC6ZM/D3GsCTg3ODRnqa+PBh4/n31+fyg7P3Z1VZDR++/gU+e8t8lm32ezd15LE3NvPvt7bypeOnUpA7OJ7k56eyOjdI7apv5Kbn1vCHp1dTXd/Ihw4Zz9dOmc644UOSHVpKqalr5ORfPs2wIZk89OVjyRxAV6P7qazOuTi5WRl86YRpPHPF8Xz22L15aMkmjr9mHj96+E121NQnO7yUcd2TK9hUUcuPP3jAgEoMnRk8W+qca9OIoVl8+4z9eOobczn74LHc9PwajvvZU/zm3yvYVd/Y+QIGsKWlldz43BrOmz2BwyaNTHY4fcqTg3MOgHHDh/Dzjx7Mv756HEdOGcU1jy3nfT+PbskxGC+kq29s5sp7llAwJJNvnrpPssPpc54cnHPvMb04nz9+ahZ3X3oUk0bm8p37X+fkXz7NQ4s3DaprJH7+6Fss3lDBj885gOG5WckOp895cnDOtWlWyUj+fulR3HjhLLIz0vny7a8OmmskHn9zC398dg0XHjWJ0wboLbk748nBOdcuSZy4bzGPfGUOv/zYu9dInPfHl1iwbmDeMHnDjl184++LOWDcML51xr7JDidpPDk45zqVniY+dGh0jcT3z9qflVtr+PD1L3Lxza/wxqaKZIfXa3bVN/LFvy6kudn47ScOJTsjPdkhJY0nB+dcl2VlpHHh0SU8c8Vcrjh1BgvW7eCMXz/HZbct4K3NHT7NN+XVNTbx+b8s4LWNFfzy4zOZNGposkNKKr8IzjnXYxW7G7jx2dXc9PxaqusaOePAMVx+4jRm7JWf7NC6panZuPz2V/nHa6X8/CMH8dFZE5IdUp/o6CI4Tw7OuT22c1c9f3p2DX9+fg019U28f/9ivnzCNA4YV5Ds0DrV1Gx8697XuHP+er5zxr58ds7kZIfUZ1LuCmlJV0vaGB4RukjS6THTrpK0UtIySe9PRnzOue4ZnpvFN94/g+e+eQKXnziNF1Zt58z/e44Lb3qZF1ZtS9mzm6rrGrnk1vncOX89l58wdVAlhs4kZc9B0tVAtZld06p8P+B2YDYwFngCmG5mHT4U1/ccnEstlbUN/OXFdfz5+TVsq67noPEFfHbOZE47YK+UuQXFpp27+cwt81m2uZLvn7U/FxxVkuyQ+lxHew4ZfR1MJ84G7jCzOmCNpJVEieLF5IblnOuOYTmZfPH4qXzm2L25d+FG/vjsai6//VWKh2XzySMmce7siRTlJ++ZCI+9sZlv3fc6tQ1N3HTR4cydMTppsaSqZCaHL0n6FDAf+LqZ7QDGAS/F1NkQyuJIugS4BGDixIkJDtU51xM5mel84oiJnHv4BOYt38rNL6zjF48v57onV3DyfsV8/PAJzJlWRHqa+iSebdV1/PeDb/CPJaXsO2YY1358Zr87eN5XEtatJOkJYK82Jn2bKAFsAwz4ITDGzC6W9BvgJTO7LSzjRuCfZnZ3R+vybiXn+o9VZdXc8fLb3LNwI+U19YzOz+aMg8bwgYPHcsiE4Ui9nyh21NRzy4tr+fPza9ld38TlJ07l8++bkjJdXMmS0mcrSSoBHjazAyRdBWBmPwnTHgWuNrMOu5U8OTjX/9Q3NvPE0i3c/+pG5i0ro76pmTEFOcydMZq5M4o4esoo8nN6/mCd5mZjycYK7n91I3e+sp7dDU2ctG8x3zx1BtOKfW8BUvCYg6QxZlYaRj8IvB6GHwT+JumXRAekpwEvJyFE51yCZWWkcfqBYzj9wDFU1jbw2BtbeOLNLTy0eBO3v/w2aYpuAnjIxBEcOK6AvQuHUlKYS3F+DmltdEPtrm9ixdYq3tpcxZINO3niza1srqwlI02cdfBYLp07hemeFLosWWcr/QWYSdSttBb4fEuykPRt4GKgEfiqmf2zs+X5noNzA0d9YzML1u3gP2u2s/DtnSx6eweVte8+VyI9TQzNSicvO4OsjDRq6puoqWtkV/27JzUOyUznuOmFnLLfXpy47+hBeVfVrkjpbqXe4MnBuYGrudnYuHM367bvYs32GjZX7KamronqukbqGpvJy44SRcGQTKaOzmPGXsOYODK3zw5y92cp163knHNdlZYmJozMZcLIXI6dVpjscAaNwX2o3jnnXJs8OTjnnIvjycE551wcTw7OOefieHJwzjkXx5ODc865OJ4cnHPOxfHk4JxzLs6AuEJaUhmwbg8WUUh0l1jXNm+fjnn7dMzbp3PJaqNJZlbU1oQBkRz2lKT57V1C7rx9OuPt0zFvn86lYht5t5Jzzrk4nhycc87F8eQQuSHZAaQ4b5+Oeft0zNuncynXRn7MwTnnXBzfc3DOORfHk4Nzzrk4gzo5SDpV0jJJKyVdmex4+oqkmyRtlfR6TNlISY9LWhH+jgjlkvTr0EZLJB0aM8+Fof4KSRcmY1sSQdIESU9JelPSG5K+Esq9jQJJOZJelrQ4tNH3Q/nekv4T2uJOSVmhPDuMrwzTS2KWdVUoXybp/cnZosSQlC7pVUkPh/H+0z5mNihfQDqwCpgMZAGLgf2SHVcfbftxwKHA6zFlPwOuDMNXAv8bhk8H/gkIOBL4TygfCawOf0eE4RHJ3rZeap8xwKFhOB9YDuznbfSeNhKQF4Yzgf+Ebb8LODeU/x64LAx/Afh9GD4XuDMM7xf+97KBvcP/ZHqyt68X2+lrwN+Ah8N4v2mfwbznMBtYaWarzaweuAM4O8kx9QkzewYob1V8NnBLGL4FOCem/FaLvAQMlzQGeD/wuJmVm9kO4HHg1MRHn3hmVmpmC8NwFbAUGIe30TvCtlaH0czwMuAE4O5Q3rqNWtrubuBESQrld5hZnZmtAVYS/W/2e5LGA2cAfwrjoh+1z2BODuOA9THjG0LZYFVsZqVheDNQHIbba6dB0X5h9/4Qol/G3kYxQpfJImArUeJbBew0s8ZQJXZ732mLML0CGMXAbqNrgSuA5jA+in7UPoM5Obh2WLQ/O+jPcZaUB9wDfNXMKmOneRuBmTWZ2UxgPNGv2X2SHFLKkHQmsNXMFiQ7lp4azMlhIzAhZnx8KBustoSuEMLfraG8vXYa0O0nKZMoMfzVzO4Nxd5GbTCzncBTwFFEXWoZYVLs9r7TFmF6AbCdgdtGxwBnSVpL1GV9AnAd/ah9BnNyeAWYFs4eyCI6CPRgkmNKpgeBlrNpLgQeiCn/VDgj50igInStPAqcImlEOGvnlFDW74W+3huBpWb2y5hJ3kaBpCJJw8PwEOBkomMzTwEfCdVat1FL230E+HfY+3oQODecrbM3MA14uW+2InHM7CozG29mJUTfLf82s/PpT+2T7KP5yXwRnWWynKiv9NvJjqcPt/t2oBRoIOrD/AxR/+aTwArgCWBkqCvgt6GNXgNmxSznYqIDZCuBTyd7u3qxfY4l6jJaAiwKr9O9jd7TRgcBr4Y2eh34XiifTPTltRL4O5AdynPC+MowfXLMsr4d2m4ZcFqyty0BbTWXd89W6jft47fPcM45F2cwdys555xrhycH55xzcTw5OOeci+PJwTnnXBxPDs455+J4cnCuA5KGS/pCGB4r6e7O5nFuIPBTWZ3rQLi30sNmdkCSQ3GuT/meg3Md+ykwRdIiSX9XeAZGuOnczyW9Ep7h8PlQPlfS05IekLRa0k8lnR+effCapCmh3s2Sfi9pvqTl4V48Lc9J+HOo+6qk45O25W5Qy+i8inOD2pXAAWY2s2UvIpR/hug2GYdLygael/RYmHYwsC/RbdFXA38ys9mKHhr0ZeCroV4J0Q3rpgBPSZoKfJHovn4HStoHeEzSdDOrTfSGOhfL9xyc65lTiO6ntIjodt6jiO57A/CKRc+EqCO67UFL0niNKCG0uMvMms1sBVES2Yfo1h23AZjZW8A6YHqCt8W5OL7n4FzPCPiymb3nRnqS5gJ1MUXNMePNvPd/rvUBPz8A6FKG7zk417EqokeFtvYocFm4tTeSpksa2s1lf1RSWjgOMZnoxmrPAue3LBOYGMqd61O+5+BcB8xsu6Tnw4HopTGT/kTURbQw3OK7jHcf+dhVbxPdgXMYcKmZ1Ur6HXC9pNeARuCi0D3lXJ/yU1mdSwJJNxOdIuvXTbiU5N1Kzjnn4vieg3POuTi+5+Cccy6OJwfnnHNxPDk455yL48nBOedcHE8Ozjnn4vx/V+6z25NfRJIAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "respuesta_ejemplo_2(1.65)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Ejercicio\n", "\n", "Para la siguiente función: " ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{1}{s \\left(s + 1\\right) \\left(s + 8\\right)}$" ], "text/plain": [ "1/(s*(s + 1)*(s + 8))" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "G3 = 1/(ss*(ss+1)*(ss+8)); display(G3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Realizar:\n", "\n", "- Encontrar el *root locus*\n", "- Identificar la ganancia última\n", "- Estudiar la respuesta temporal" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Aproximación del retardo\n", "\n", "Para considerar el retardo en los sistemas y diseñar el controlador PID, debemos aproximar el retardo:\n", " \n", "- Por serie de _Taylor_\n", "\n", "$$f(x) = \\sum_{n=0}^{\\infty}\\frac{f^{(n)}(a)}{n!}(x-a)^n \\qquad\\text{de ahí,}\\quad e^{-\\theta s}\\approx (1-\\theta s) $$\n", "\n", "- Por aproximación de _Padé_. Para el retardo tenemos\n", "\n", "$$e^{-\\theta s}\\approx \\frac{1+\\frac{\\theta s}{2}}{1-\\frac{\\theta s}{2}}$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "![USS New Mexico (BB-40) in 1921](https://cap.davinsony.com/media/slide/img/slide-561.png)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Control PID\n", "\n", "**¿Qué es PID?**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "PID es un control **p**roporcional **i**ntegral **d**erivativo. Se representa por la siguiente ecuación: \n", "\n", "$$u(t) = K_p\\,e(t) + K_i \\int_0^t e(\\tau)d\\tau + Kd_\\, \\frac{e(t)}{dt}$$\n", "\n", "Los coefficientes $K_p$, $K_i$ y $K_d$ se definen positivos. La anterior expresión puede ser escrita en el dominio de _Laplace_ de la siguiente forma: \n", "\n", "$$K(s)= K_p + \\frac{K_i}{s}+K_d\\,s$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### PID en las peliculas\n", "\n", "Intensamente (*inside-out*)\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
ProporcionalIntegralDerivativo
reactivovengativamiedoso
furiaascomiedo
" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Overwriting diagrams/PID-one-block.gv\n" ] } ], "source": [ "%%file diagrams/PID-one-block.gv\n", "// PID in one block\n", "digraph {\n", " rankdir=LR\n", " B [shape=rectangle,label=\"Kp + Ki/s + Kd s\", style=filled, fillcolor=lightgray]\n", " node[shape=\"none\"] \n", " E -> B -> U\n", "}" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Overwriting diagrams/PID-four-blocks.gv\n" ] } ], "source": [ "%%file diagrams/PID-four-blocks.gv\n", "// PID block diagram using several blocks\n", "digraph {\n", " graph [splines=ortho]\n", " rankdir=LR\n", " \n", " E[shape=none,width=0.4]\n", " U[shape=none,width=0.4]\n", " \n", " node[style=filled, fillcolor=lightgray]\n", " Sum [shape=circle, label=\"+\"]\n", " Kpp [shape=point, fillcolor=black]\n", " \n", " node[shape=rectangle,width=0.7,height=0.7,fixedsize=true]\n", " Kp [label=\"Kp\"]\n", " One [label=\"1\"]\n", " Ti [label=\"1 / Ti s\"]\n", " Td [label=\"Td s\"]\n", "\n", " // Edges\n", " E -> Kp \n", " Kp -> Kpp [dir=none] \n", " Kpp-> One\n", " Kpp-> Ti\n", " Kpp-> Td\n", " One-> Sum\n", " Ti -> Sum\n", " Td -> Sum\n", " Sum-> U\n", "}" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "sourcefile = 'diagrams/PID-one-block.gv' \n", "gv = open(sourcefile)\n", "dot = Source(gv.read(),format=\"svg\",filename = sourcefile)\n", "dot.render(sourcefile,view=False);\n", "\n", "sourcefile = 'diagrams/PID-four-blocks.gv' \n", "gv = open(sourcefile)\n", "dot = Source(gv.read(),format=\"svg\",filename = sourcefile)\n", "dot.render(sourcefile,view=False);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Diagrama de bloques de un PID\n", "\n", "Tomando la función de transferencia del **PID**\n", "\n", "![pid](diagrams/PID-one-block.gv.svg)\n", "\n", "Separando el bloque en tres de manera práctica tenemos:\n", "\n", "![pid four block](diagrams/PID-four-blocks.gv.svg)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Expresión del PID de forma práctica\n", "\n", "La forma clásica de la función de transferencia del **PID** es:\n", "\n", "$$\\frac{U(s)}{E(s)} = K_p + \\frac{K_i}{s} + K_d\\,s$$\n", "\n", "En la práctica esta función se representa de la siguiente forma: \n", "\n", "$$\\frac{U(s)}{E(s)} = K_p \\left(1 + \\frac{K_i}{K_p}\\frac{1}{s} + \\frac{K_d}{K_p} s \\right) = K_p \\left(1 + \\frac{1}{T_i\\, s} + T_d\\, s \\right)$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Variaciones del controlador PID\n", "\n", "Aquí presentamos las combinaciones para el **PID** que funcionan bien en la mayoria de los casos.\n", "\n", "| | | | Descripción |\n", "|-|-|-|:-------------------------------------------|\n", "|P| | | Control proporcional |\n", "| |I| | Control integral |\n", "|P|I| | Control proporcional integral |\n", "|P| |D| Control proporcional derivativo |\n", "|P|I|D| Control proporcional integral derivativo |" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Overwriting diagrams/closed_loop.gv\n" ] } ], "source": [ "%%file diagrams/closed_loop.gv\n", "// Closed loop diagram\n", "digraph {\n", " graph [splines=ortho]\n", " rankdir=LR\n", " \n", " NS [shape=point, fillcolor=black,pos=\"4.75,0!\"]\n", " \n", " node[shape=none,width=0.4]\n", " R[label=\"R(s)\",pos=\"0,0!\"]\n", " C[label=\"C(s)\",pos=\"5.5,0!\"]\n", " \n", " node[style=filled, fillcolor=lightgray]\n", " Sum [shape=circle, label=\"+\", pos=\"1,0!\"]\n", " \n", " node[shape=rectangle,width=0.7,height=0.7,fixedsize=true]\n", " K [label=\"K(s)\",pos=\"2.5,0!\"]\n", " G [label=\"G(s)\",pos=\"4,0!\"]\n", " H [label=\"H(s)\",pos=\"4,-1!\"]\n", "\n", " // Edges\n", " R -> Sum\n", " Sum-> K [label=\"E(s)\"]\n", " K -> G [taillabel = \" U(s)\"]\n", " G -> NS [dir=none]\n", " NS -> C\n", " NS -> H\n", " H -> Sum [taillabel=\"B(s) \", headlabel=\"- \"]\n", "}" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "sourcefile = 'diagrams/closed_loop.gv' \n", "gv = open(sourcefile)\n", "dot = Source(gv.read(),engine=\"neato\",format=\"svg\",filename = sourcefile)\n", "dot.render(sourcefile,view=False);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Control del **Error**\n", "\n", "Esta es la representación de bloques de un sistema en lazo cerrado incluyendo un controlador. \n", "\n", "![closed loop](diagrams/closed_loop.gv.svg)\n", "\n", "- La función de transferencia para la salida es:\n", "\n", "$$\\frac{C(s)}{R(s)} = \\frac{K(s)G(s)}{1+K(s)G(s)H(s)}$$\n", "\n", "- Encontremos la función de transferencia del error" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "La función de transferencia del error la calculamos sabiendo que:\n", "\n", "$$E(s) = R(s)-B(s) \\qquad\\text{y}\\qquad B(s)=H(s)C(s)$$\n", "\n", "Obtenemos lo siguiente: \n", "\n", "$$\\frac{E(s)}{R(s)} = \\frac{1}{1+K(s)G(s)H(s)}$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Controlar un proceso puede reducirse a :\n", "\n", "> \"Encontra el método que nos permita eliminar el error estacionario entre la medida y la referencia\".\n", "\n", "Suponiendo una función de transferencial polinomial:\n", "\n", "$$G(s)=\\frac{b_0+b_1\\, s+ \\cdots+ b_m\\, s^m}{a_0+a_1\\, s+ \\cdots+ b_n\\, s^n}$$\n", "\n", "aplicando el teorema del valor final al error $E(s)$, con un escalón como entrada $R(s) = A/s$ y asumiendo $K(s)=H(s)=1$, tenemos:\n", "\n", "$$\\lim_{t\\to\\infty} e(t) = \\lim_{s\\to 0} s\\, E(s) = \\frac{A}{1+g_{\\infty}} \\qquad\\text{con,}\\quad g_{\\infty} = \\lim_{s\\to 0} G(s) = \\frac{b_0}{a_0}$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Sintonia Manual de **PID**\n", "\n", "La siguinte tabla muestra el efecto que tiene incrementar un parámetro de forma independiente:\n", "\n", "|Parámetro| $t_r$ | $M_p$ | $t_s$ | $E_{ss}$ |Estabilidad |\n", "|:-------:|:--------:|:--------:|:--------:|:--------:|:----------------------|\n", "|$K_p$ |$\\searrow$|$\\nearrow$| |$\\searrow$|degrada |\n", "|$K_i$ |$\\searrow$|$\\nearrow$|$\\nearrow$|elimina |degrada |\n", "|$K_d$ | |$\\searrow$|$\\searrow$| |mejora si $K_D$ pequeño|\n", "\n", "recordemos que $t_r$ es el tiempo de subida, $M_p$ es el máximo pico, $t_s$ es el tiempo de establecimiento, $E_{ss}$ es el error estacionario. \n", "\n", "En general se sintoniza el PID empezando por **P**, luego **I** y finalmente **D**." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### Ejemplo sintonia manual\n", "\n", "![sintonia](http://cpm.davinsony.com/clases/gif/PID_compensation.gif)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Método de sintonía de *Ziegler-Nichols*\n", "\n", "Encontrando $K_u$ de forma experimental.\n", "\n", "Es un método heuristico para sintonizar el **PID**, creado en 1942. Para este método se inicia con un controlador proporcional puro **P** y se empieza a aumentar la ganancia $K_p$ hasta que el sistema se vuelva oscilatorio (oscilaciones que se mantienen en el tiempo), esta ganancia que genera este comportamiento denota la ganancia ultima $K_u$. Este movimiento de la salida tiene asociado un periodo $T_u$ de oscilación. Con estos dos valores se calculan los valores del **PID**, siguiendo la próxima tabla. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Tabla de sintonía de *Ziegler-Nichols*\n", "\n", "|Tipo de controlador | $K_p$ | $T_i$ | $T_d$ |\n", "|:----------------------|:-------:|:-------:|:------:|\n", "|P |$0.50K_u$| | |\n", "|PI |$0.45K_u$|$T_u/1.2$| |\n", "|PD |$0.80K_u$| |$T_u/8$ |\n", "|PID clásico |$0.60K_u$|$T_u/2$ |$T_u/8$ |\n", "|PID con poco sobrepico |$0.33K_u$|$T_u/2$ |$T_u/3$ |\n", "|PID sin sobrepico |$0.20K_u$|$T_u/2$ |$T_u/3$ |\n", "\n", "$K_u$ también puede ser encontrado utilizando el margen de ganancia (funcion *control.margin*). El periodo $T_u$ esta relacionado con la frecuencia a la cual ocurre el margen de ganancia. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Ejemplo 1 \n", "\n", "Analicemos la función de transferencia del error del primer ejemplo trabajado, cuya funcion de transferencia se presenta a continuación:" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{1}{2 s + 1}$" ], "text/plain": [ "1/(2*s + 1)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display(G1A)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "veamos que pasa con la función del error para este sistema en el tiempo." ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "1a1e463cf0674053917bd52e677761fe", "version_major": 2, "version_minor": 0 }, "text/plain": [ "VBox(children=(Output(), FloatSlider(value=1.0, description='Ganacia $K$', min=1.0, step=1.0)))" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## Parametros del modelo\n", "\n", "param_K = widgets.FloatSlider(value=1,min=1,max=100,step=1,description='Ganacia $K$')\n", "\n", "## Definicion de la simulacion\n", "\n", "def respuesta_error_1(K):\n", " E1 = 1/(1+K*G1D)\n", " t, y = control.step_response(E1)\n", " plt.plot(t,y)\n", " plt.title('Respuesta temporal para el sistema \\n%s' % (E1))\n", " plt.xlabel('tiempo')\n", " plt.ylabel('amplitud')\n", "\n", "## Presentación de los resultados \n", " \n", "plot_respuesta_error_1 = widgets.interactive_output(respuesta_error_1,{'K':param_K}) \n", "widgets.VBox([plot_respuesta_error_1,param_K])" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "respuesta_error_1(2)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "Para este sistema no existe un valor $K>0$ que haga el sistema inestable. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Ejemplo 2\n", "\n", "Analicemos el ejemplo número 2, cuya función de transferencia es presentada acontinuación." ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/latex": [ "$$\\frac{0.5 s + 1}{0.12 s^4 + 0.58 s^3 + 0.9 s^2 + s}$$" ], "text/plain": [ "\n", " 0.5 s + 1\n", "---------------------------------\n", "0.12 s^4 + 0.58 s^3 + 0.9 s^2 + s" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display(G2)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- ¿Cuál es la respuesta temporal para la función de transferencia del error de este sistema?" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "01e985bc8d274193986e1ef88b5ede60", "version_major": 2, "version_minor": 0 }, "text/plain": [ "VBox(children=(Output(), FloatSlider(value=1.0, description='Ganacia $K$', max=2.0, min=1.0, step=0.01)))" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## Parametros del modelo\n", "\n", "param_K = widgets.FloatSlider(value=1,min=1,max=2,step=0.01,description='Ganacia $K$')\n", "\n", "## Definicion de la simulacion\n", "\n", "def respuesta_error_2(K):\n", " E2 = 1/(1+K*G2)\n", " t, y = control.step_response(E2)\n", " plt.plot(t,y)\n", " plt.title('Respuesta temporal para el sistema \\n%s' % (E2))\n", " plt.xlabel('tiempo')\n", " plt.ylabel('amplitud')\n", "\n", "## Presentación de los resultados \n", " \n", "plot_respuesta_error_2 = widgets.interactive_output(respuesta_error_2,{'K':param_K}) \n", "widgets.VBox([plot_respuesta_error_2,param_K])" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "respuesta_error_2(1)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- ¿Qué pasa con el sistema teniendo un control diferente al control proporcional **P**?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Control por posicionamiento de polos" ] }, { "cell_type": "code", "execution_count": 92, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\frac{0.12 s^4 + 0.58 s^3 + 0.9 s^2 + s}{0.12 s^4 + 0.58 s^3 + 0.9 s^2 + 1.8 s + 1.6}$$" ], "text/plain": [ "\n", " 0.12 s^4 + 0.58 s^3 + 0.9 s^2 + s\n", "-------------------------------------------\n", "0.12 s^4 + 0.58 s^3 + 0.9 s^2 + 1.8 s + 1.6" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "K = 1.6\n", "E6 = 1/(1+K*G2); display(E6)\n", "\n", "t,y = control.step_response(E6);\n", "plt.plot(t,y);" ] }, { "cell_type": "code", "execution_count": 95, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/latex": [ "$$\\frac{0.213 s^5 + 1.029 s^4 + 1.597 s^3 + 1.775 s^2}{0.213 s^5 + 1.029 s^4 + 1.942 s^3 + 2.755 s^2 + 0.7462 s + 0.328}$$" ], "text/plain": [ "\n", " 0.213 s^5 + 1.029 s^4 + 1.597 s^3 + 1.775 s^2\n", "----------------------------------------------------------------\n", "0.213 s^5 + 1.029 s^4 + 1.942 s^3 + 2.755 s^2 + 0.7462 s + 0.328" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "Ku = 1.64\n", "Tu = 2*3.14159/1.77\n", "Ti = Tu/2\n", "Td = Tu/3\n", "K = 0.2 * Ku *(1+1/(Ti*s)+Td*s)\n", "E6 = 1/(1+K*G2); display(E6)\n", "\n", "t,y = control.step_response(E6);\n", "plt.plot(t,y);" ] }, { "cell_type": "code", "execution_count": 98, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/latex": [ "$$\\frac{0.12 s^4 + 0.58 s^3 + 0.9 s^2 + s}{0.12 s^4 + 1.58 s^3 + 4.4 s^2 + 6.5 s + 5}$$" ], "text/plain": [ "\n", " 0.12 s^4 + 0.58 s^3 + 0.9 s^2 + s\n", "-----------------------------------------\n", "0.12 s^4 + 1.58 s^3 + 4.4 s^2 + 6.5 s + 5" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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56beWse9IL1/72bO0Nddz85teFXZJIiI1kbhAB/j4dRexv6ePv9m8k9l1GW5cvSTskkREzloiAz2VMv7u7a/laN8gtz3wOLsPnuAv11xIOmVhlyYicsYS1UOvVJdN8/X3XMG7rjyfjQ/t5n13d3C8vxB2WSIiZyyxgQ6QTaf49O9dzB3rXsODu7pZe+dD/OKZQ2GXJSJyRhId6GXvfv1S7rn5SlJmrP/Kw9z+vSc4odm6iESMAr1k9bK5/ODWN/Leq5Zy98PP85bP/5h7/+8FrVcXkchQoFdoyGX45Ntew/1/+gYWtdRz2wOPs/bOh9iyfb/uASMir3gK9Am87vwWvvv+N/ClP17FQKHI++7exrV//xP+besL9BeGwi5PRGRCFtbVku3t7d7R0RHKZ5+OwlCRzU/s58s/eYbt+45yzqwcv7+qjXdcsYTl8xvDLk9EEsbMtrl7+4SvKdCr4+78vPMQ33r4ef5n50sUis6qJc1cf+l5XHfJuSxsqg+7RBFJAAV6jXUf6+e7j3TxvV/tY+eLRwG4bHEzb7lgPm++oJVL25pI6SIlEZkGCvRptLv7OD94Yj8/3PESj3UdwR2aG7KsXjqX1cvmcsXSuVy0cA65jE5XiMjZU6DPkEPH+/lZ50F++vRBtj73Ms8fOglALp3iooWzuXRRMxcunM2F587hgnNn05hP5J0XROQsnCrQlSg1dE5jnnWXtbHusjYA9vf00fH8yzzW1cOv9xzhgUe6ODEwskrm3Dl1LJs3i1e1zmLJ3AYWz21gcUsD5zXXMXdWDjO1bUSkelXN0M1sDXAnkAa+6u5/O+b1PPBN4HXAIeAd7v7cqd4zjjP0qRSLzt4jvTy5/xhPvXSMZ7qPs7v7BM8ePEFP7+hdlHKZFOfOqWPBnDyts/O0NuY5pzHP3Fk55s7K0dKQo6k+S3NDljn1WWbl0voFIJIAZzVDN7M0cBfwVqAL2Gpmm9x9R8Wwm4DD7r7czG4EPgO84+xLj5dUyoJZ+NwG3rpywajXenoH2fPySboO9/JiTy/7e/rY19NH97E+du0/xk+PHeRY3+S3I0gZNOYzzK7LMiufZlY+w6xchvpcmobSTz6Tpi6bpi6boi6bJp9JkcukyKWDP/OZFNl08JNJ28jjlJFJG5lU8Dhd+smkjFTKSFvpz9JjM0injJQZKUO/aERmSDUtl9VAp7vvBjCze4F1QGWgrwM+VXp8P/BFMzPXlkBVa6rP0tTWxMVtTZOOGSgUOXxygEPHBzjSO0DPyUF6egc52jfI0d4Cx/oGOdZf4GT/ECcGCpzoL3DweD+9g0OcHBiib3CI/sEiA0PFGfw3AzNGwp0g8EeOGVYaY6VfBsHzkeOU/pngUWksI2Nh9C+Nyt8fox4zyZhRtY7+5TPpr6JJXjibX11R/cUXzarD9aFrVvC2155X8/etJtDbgD0Vz7uA35xsjLsXzKwHOAc4WDnIzDYAGwCWLNGmEqcrl0mxYE4dC+bUndX7DBWdgUKR/sIQfYNFBoeK9BeKDBSKFIrB84GCDz8eHHKGik6h6BSGigwVR54X3YefF90pevD+PtFjd9zBCf4sFh0HiuXjHjyvHFN+HiiPG3k9OFr6s3SckeETPRy19eDo46O/p8lmI5PNU85q9hLRqY9HtfCQNdVnp+V9Z/SkqLtvBDZC0EOfyc+WEemUUZ9LU59Lh12KiNRQNYuj9wKLK54vKh2bcIyZZYAmgpOjIiIyQ6oJ9K3ACjNbZmY54EZg05gxm4A/KT3+Q+BH6p+LiMysKVsupZ74LcAWgmWLX3f37WZ2B9Dh7puArwF3m1kn8DJB6IuIyAyqqofu7puBzWOO3V7xuA/4o9qWJiIip0M3GBERiQkFuohITCjQRURiQoEuIhITod0+18y6gefP8B+fx5irUBNK34O+A9B3AMn6Ds5399aJXggt0M+GmXVMdrexJNH3oO8A9B2AvoMytVxERGJCgS4iEhNRDfSNYRfwCqHvQd8B6DsAfQdARHvoIiIyXlRn6CIiMoYCXUQkJiIX6Ga2xsx2mVmnmd0Wdj0zzcwWm9mDZrbDzLab2a1h1xQWM0ub2aNm9v2wawmLmTWb2f1m9qSZ7TSz14dd00wzsz8v/V14wszuMbOz29IrwiIV6BUbVq8FVgLrzWxluFXNuALwEXdfCVwJfCCB30HZrcDOsIsI2Z3Af7v7hcBrSdj3YWZtwIeAdne/mOAW34m9fXekAp2KDavdfQAob1idGO7+ors/Unp8jOAvcFu4Vc08M1sEXA98NexawmJmTcCbCPYjwN0H3P1IuFWFIgPUl3ZLawD2hVxPaKIW6BNtWJ24MCszs6XA5cAvw60kFP8A/AVQDLuQEC0DuoF/KbWevmpms8Iuaia5+17g88ALwItAj7v/MNyqwhO1QJcSM2sEvgv8mbsfDbuemWRmvwsccPdtYdcSsgywCviSu18OnAASdV7JzFoI/i99GXAeMMvM3hluVeGJWqBXs2F17JlZliDMv+3uD4RdTwiuAm4ws+cI2m6/bWbfCrekUHQBXe5e/j+0+wkCPkmuBZ519253HwQeAN4Qck2hiVqgV7NhdayZmRH0THe6+xfCricM7v4xd1/k7ksJ/hv4kbsnblbm7vuBPWZ2QenQNcCOEEsKwwvAlWbWUPq7cQ0JOzFcqao9RV8pJtuwOuSyZtpVwLuAx83sV6Vjf1Xa91WS54PAt0sTnN3Ae0OuZ0a5+y/N7H7gEYIVYI+S4NsA6NJ/EZGYiFrLRUREJqFAFxGJCQW6iEhMKNBFRGJCgS4iEhMKdBGRmFCgi4jExP8DCT9mMInH7+gAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "K = (2.5 + 1.5*s + 1*s**2)*2;\n", "E6 = 1/(1+K*G2); display(E6)\n", "\n", "t,y = control.step_response(E6);\n", "plt.plot(t,y);" ] }, { "cell_type": "code", "execution_count": 100, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle s^{2} + 1.5 s + 2.49999999803039$" ], "text/plain": [ "s**2 + 1.5*s + 2.49999999803039" ] }, "execution_count": 100, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sympy.expand((ss - (-0.75+1.39194109j))*(ss-((-0.75-1.39194109j))))" ] }, { "cell_type": "code", "execution_count": 101, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "image/png": 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\n", 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