{ "cells": [ { "cell_type": "markdown", "id": "d2c9eee6", "metadata": {}, "source": [ "# Tema 9\n", "\n", "\n", "\n", "**Problema 9.1**\n", "\n", "Sea el sistema de control representado en la figura:" ] }, { "cell_type": "code", "execution_count": 9, "id": "e8defb46", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": "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", "image/svg+xml": [ "\n", "\n", "\n", "\n", " \n", " \n", " \n", " \n", " 2021-05-18T11:29:19.467398\n", " image/svg+xml\n", " \n", " \n", " Matplotlib v3.3.4, https://matplotlib.org/\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", " \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", " \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", " \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", " \n", " \n", " \n", " \n", " \n", " \n", "\n" ], "text/plain": [ "PyObject " ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using PyCall, LaTeXStrings\n", "\n", "schemdraw = pyimport(\"schemdraw\")\n", "dsp = pyimport(\"schemdraw.dsp\")\n", "\n", "d = schemdraw.Drawing(unit=1, fontsize=10)\n", "\n", "d.add(dsp.Arrow().right().label(L\"R\", \"left\"))\n", "comp = d.add(dsp.Mixer(W=\"+\", S=\"-\").anchor(\"W\"))\n", "d.add(dsp.Arrow().right().at(comp.E))\n", "control = d.add(dsp.Box(h=1, w=1).label(L\"G_c\").anchor(\"W\"))\n", "d.add(dsp.Arrow().right().at(control.E))\n", "proc1 = d.add(dsp.Box(h=1, w=1).label(L\"G_1\").anchor(\"W\"))\n", "d.add(dsp.Arrow().right().at(proc1.E))\n", "proc2 = d.add(dsp.Box(h=1, w=1).label(L\"G_2\").anchor(\"W\"))\n", "d.add(dsp.Line().right().at(proc2.E))\n", "dot = d.add(dsp.Dot(radius=0))\n", "d.push()\n", "d.add(dsp.Arrow().right().label(L\"C\", \"right\"))\n", "d.pop()\n", "d.add(dsp.Line().down().length(1.5))\n", "d.add(dsp.Line().left().tox(comp.S))\n", "d.add(dsp.Arrow().up().to(comp.S))\n", "\n", "d.save(\"./img/prob901.svg\")\n", "d.draw(show=false)" ] }, { "cell_type": "markdown", "id": "cd78d380", "metadata": {}, "source": [ "donde $G_1=\\frac{1}{s+1}$ y $G_2 = \\exp(-1.02 s)$.\n", "\n", "1. Si $G_c = K_c$, determinar el _offset_ de la respuesta para una entrada en escalón unidad.\n", "2. Para eliminar el _offset_ se recomienda que el controlador sea PID. ¿Qué valores de diseño recomendaría para los parámetros del controlador PID? Se sugiere usar el método de Ziegler-Nichols.\n", "\n", "**Problema 9.2**\n", "\n", "Determinar los parámetros efectivos de un sistema a partir de la curva de reacción que se indica y calcular la frecuencia crítica y la ganancia máxima. Determinar los ajustes de los parámetros de un controlador PID según el método de Ziegler-Nichols y compararlos con los que se obtienen directamente de la curva de reacción.\n", "\n", "Tiempo (min) | Resp. (ua)\n", "-------------|-----------\n", "0 | 0\n", "1 | 0\n", "2 | 0\n", "3 | 4\n", "4 | 10\n", "5 | 19\n", "6 | 27\n", "7 | 35\n", "8 | 41\n", "9 | 45\n", "30 | 50\n", "\n", "**Problema 9.3**\n", "\n", "Determinar la ganancia de un controlador proporcional para que la razón de disminución de lazo cerrado sea 1/4. La función de transferencia que describe el proceso es:\n", "\n", "$$G_p(s)=\\frac{1}{s^2+3s+1}$$\n", "\n", "Las funciones del medidor y del elemento final de control son iguales a la unidad.\n", "\n", "**Problema 9.4**\n", "\n", "Seleccionar la ganancia y tiempo integral de un controlador PI, empleando el criterio de hacer mínima la ISE. Considerar un cambio en escalón unidad para la consigna. El proceso a controlar es de primer orden con ganancia 10 y constante de tiempo 1.0. Asumir que las funciones de transferencia del medidor y del elemento final de control son iguales a la unidad. Los parámetros seleccionades deben cumplir las siguientes restricciones:\n", "\n", "$$\\begin{cases}\n", " 100 \\ge K_c \\ge 1\\\\\n", " 10 > \\tau_I > 0.1\n", "\\end{cases}$$\n", "\n", "**Problema 9.5**\n", "\n", "Seleccionar la ganancia de un controlador proporcional utilizando el criterio de la razón de disminución 1/4. El proceso a controlar es:\n", "\n", "$$G_p(s) = \\frac{10}{(s+2)(2s+1)}$$\n", "\n", "Asumir que $G_m(s) = G_f(s) = 1$. Realizar también la sintonía utilizando el criterio del ISE mínimo con un cambio en la consigna en escalón unidad. En ambos casos se debe satisfacer la condición de que $100 \\ge K_c \\ge 0.1$. Comparar las sintonías y explicar las diferencias entre ellas.\n", "\n", "**Problema 9.6**\n", "\n", "Repetir el problema anterior utilizando la técnica de Ziegler-Nichols en lugar de minimizar el ISE. Comparar los resultados obtenidos con los del problema anterior.\n", "\n", "**Problema 9.7**\n", "\n", "Considerar un lazo de control con las siguientes funciones de transferencia:\n", "\n", "$$\\begin{align}\n", " G_f &= 5\\\\\n", " G_p &= \\frac{10}{s+4}\\\\\n", " G_m &= \\frac{1}{10s+1}\n", "\\end{align}$$\n", "\n", "1. Realizar la sintonia de un controlador PI utilizando la técnica de Cohen-Coon.\n", "\n", "2. Dibujar la curva real de reacción del proceso junto con una aproximación de primer orden con retraso.\n", "\n", "**Problema 9.8**\n", "\n", "Repetir el problema anterior con un controlador PID y las siguientes funciones de transferencia:\n", "\n", "$$\\begin{align}\n", " G_f &= 1\\\\\n", " G_p &= \\frac{\\mathrm{e}^{-s}}{s+10}\\\\\n", " G_m &= \\frac{5 \\mathrm{e}^{-0.1 s}}{0.01s+1}\n", "\\end{align}$$\n", "\n", "**Problema 9.9**\n", "\n", "Se obtiene experimentalmente la curva de reacción de un proceso y se obtienen los siguientes datos:\n", "\n", "Tiempo (min) | Variable manipulable | Salida medida\n", "-------------|-----------|-------\n", "-2 | 100 | 200\n", "-1 | 100 | 200\n", "0 | 150 | 200.1\n", "0.2 | 150 | 201.1\n", "0.4 | 150 | 204.0\n", "0.6 | 150 | 227.0\n", "0.8 | 150 | 251.0\n", "1.0 | 150 | 280.0\n", "1.2 | 150 | 302.5\n", "1.4 | 150 | 318.0\n", "1.6 | 150 | 329.5\n", "1.8 | 150 | 336.0\n", "2.0 | 150 | 339.0\n", "2.2 | 150 | 340.5\n", "2.4 | 150 | 341.0\n", "\n", "Usando esos valores:\n", "\n", "1. Aproximar la respuesta de lazo abierto a un sistema de primer orden con retraso.\n", "\n", "2. Seleccionar los parámetros de un controlador PI utilizando la técnica de Cohen-Coon.\n", "\n", "**Problema 9.10**\n", "\n", "Utilizando los datos del problema anterior contestar a las siguientes preguntas:\n", "\n", "1. Sintonizar un controlador PI utilizando la técnica de Ziegler-Nichols.\n", "\n", "2. Comparar los resultados de la sintonía obtenidos con la técnica de Cohen-Coon y a los obtenidos al minimizar la ISE para un cambio en la consigna en escalón unidad.\n", "\n", "3. Comparar la tolerancia de las diferentes sintonías a errores en la ganancia, constante de tiempo o tiempo muerto. ¿Cuál de ellas posee una tolerancia mayor?\n", "\n", "**Problema 9.11**\n", "\n", "La curva de reacción de un proceso de uns sitema de control de temperatura proporciona los siguientes valores: $K = 10$, $\\tau = 2$ min y $t_d = 0.1$ min. Responder:\n", "\n", "1. Realizar la sintonía mediante la técnica de Ziegler-Nichols.\n", "\n", "2. Comparar la sintonía anterior con la obtenida con la técnica de Cohen-Coon.\n", "\n", "3. Asumir que los valores obtenidos con el método de la curva de reacción del proceso no son muy fiables. Calcular qué procentajes de error de los valores $K$, $\\tau$ y $t_d$ puede tolerar la sintonía de Ziegler-Nichols sin volverse inestable." ] } ], "metadata": { "celltoolbar": "Tags", "kernelspec": { "display_name": "Julia 1.6.0", "language": "julia", "name": "julia-1.6" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.6.1" } }, "nbformat": 4, "nbformat_minor": 5 }