{ "cells": [ { "cell_type": "markdown", "id": "7fde017a", "metadata": {}, "source": [ "# Problema 7.3\n", "\n", "\n", "\n", "Sea el sistema de lazo de control de la figura adjunta:\n", "\n", "![prob703.svg](./img/prob703.svg)\n", "\n", "1. Dibujar el diagrama de bloques indicando la función de transferencia de cada subsitema. Suponer que el detector de nivel actua sin retraso alguno sobre el controlador\n", "\n", "2. ¿Cuál es la función de transferencia para variaciones de carga ($H/Q_1$)?\n", "\n", "3. Discutir la influencia de los parámetros de proceso y de los del controlador sobre la dinámica del sistema.\n", "\n", "---\n", "\n", "**Solución**\n", "\n", "a) En primer lugar se realizará el balance macroscópico de materia al sistema, suponiendo que la densidad es constante e independiente del tiempo:\n", "\n", "$$A \\frac{\\mathrm{d}h (t)}{\\mathrm{d}t} = q_1 (t) - q_2 (t)$$\n", "\n", "donde $A$ es el área del depósito. Acontinuación se encuentra el balance\n", "en estado estacionario:\n", "\n", "$$0 = q_{1, e} - q_{2, e}$$\n", "\n", "donde el subíndice *e* indica que se trata de los valores en estado estacionario. Es decir, los valores de las variables anteriores a cualquier cambio. Habitualmente se trata de los valores de diseño de las variables.\n", "\n", "Restando los dos balances se obtiene:\n", "\n", "$$A \\frac{\\mathrm{d}H (t)}{\\mathrm{d}t} = Q_1 (t) - Q_2 (t)$$\n", "\n", "donde se han tomado las siguientes variables de desviación: \n", "\n", "$$\\begin{aligned}\n", " H (t) &= h (t) - h_e \\\\\n", " Q_1 (t) &= q_1 (t) - q_{1, e} (t) \\\\\n", " Q_2 (t) &= q_2 (t) - q_{2, e} (t)\n", "\\end{aligned}$$\n", "\n", "A continuación se realiza la transformada de Laplace:\n", "\n", "$$\\begin{aligned}\n", " \\mathcal{L} \\left( A \\frac{\\mathrm{d}H (t)}{\\mathrm{d}t} \\right) &=\\mathcal{L} (Q_1 (t) - Q_2 (t)) \\\\\n", " As\\bar{H} (s) &= \\overline{Q_1} (s) - \\overline{Q_2} (s)\n", "\\end{aligned}$$\n", " \n", "\n", "Por tanto:\n", "\n", "$$\\bar{H} = \\overline{Q_1} \\left( \\frac{1}{As} \\right) - \\overline{Q_2} \n", " \\left( \\frac{1}{As} \\right)$$\n", " \n", "A partir del modelo matemático obtenido se puede dibujar el diagrama de bloques del proceso:" ] }, 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", "image/svg+xml": [ "\n", "\n", "\n", "\n", " \n", " \n", " \n", " \n", " 2021-05-04T12:18:18.278663\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" ], "text/plain": [ "PyObject " ] }, "execution_count": 1, "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=12)\n", "\n", "d.add(dsp.Arrow().right().label(L\"Q_1(s)\", \"left\"))\n", "proc1 = d.add(dsp.Box(h=1.25, w=1).label(L\"\\frac{1}{As}\").anchor(\"W\"))\n", "d.add(dsp.Line().right().at(proc1.E))\n", "d.add(dsp.Arrow().down())\n", "suma = d.add(dsp.Mixer(W=\"+\", E=\"-\").anchor(\"W\"))\n", "d.push()\n", "d.add(dsp.Arrow().down().at(suma.E).reverse())\n", "d.add(dsp.Line().left())\n", "proc2 = d.add(dsp.Box(h=1.25, w=1).label(L\"\\frac{1}{As}\").anchor(\"E\"))\n", "d.add(dsp.Arrow().left().label(L\"Q_2(s)\", \"left\").at(proc2.W).reverse())\n", "d.pop()\n", "d.add(dsp.Arrow().right().at(suma.N).label(L\"H(s)\", \"right\"))\n", "\n", "d.draw(show=false)" ] }, { "cell_type": "markdown", "id": "7137ece1", "metadata": {}, "source": [ "El diagrama de bloques del controlador es:" ] }, { "cell_type": "code", "execution_count": 2, "id": "0290c822", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAABHCAYAAADIkZHSAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8QVMy6AAAACXBIWXMAAA9hAAAPYQGoP6dpAAALy0lEQVR4nO3df0yUdRwH8Pcdvw648zblh+zYkFEM0CAQp7EZW822tFgrc1aE1JjVaLaa5FxJm0crQ1wG/ZHTIrBYgFttVlaGA8aYU5YEm2i6oWIYIyYhcvy4e/dHu5vnccf95M6ez2t7Nn2e7/f7fB8+z5t77uF4UJEkhBCKow72BIQQwSHhF0KhJPxCKJSEXwiFkvALoVASfiEUSsIvhEJJ+IVQKAm/EAol4RdCoST8QiiUhF8IhQoP9gT+j1paWlBZWYmJiYmg7P/69eu2fxsMhqDMQafTwWg0YvPmzUHZv1iYSn6rz/8yMzMxMDAQ7GkEXUZGBs6fPx/saQgn5JU/AKyv+Gq1GklJSYu+/2C/8g8PD8NisQTtyke4R8IfQElJSRgaGgr2NBZdcnKy3TcgEZrkhp8QCiXhF0KhJPxCKJSEXwiFkvALoVASfiEUSsIvhEJJ+IVQKAm/EAol4RdCoST8QihUQMO/d+9eZGVlwWKx2NaRxN69e9He3m7X9siRIzAYDJicnAzklO4ZfX19KCsrQ1paGjQaDWJiYpCRkYFXXnkFp0+fdnuc+WqwEKmFozNnzqC0tBQpKSmIiorCsmXLsGnTJnR2dno8ljc1AQJQFwbI9evXGRsby5aWFrv1AwMDBMCmpia79bOzs7z//vtZWVkZqCktGoPBQAA0GAxe9T9w4ADDw8O5evVq1tXV8eTJk/zpp5/44Ycf8r777mNkZCRnZ2cXHMdZDRbiay18Pf5Q8+6771KtVvPRRx9lfX0929raWF9fz+zsbKrVah49etTtsbytCen/jAQs/G+//TYNBgPNZrPd+q+++ooAePHiRYc++/fvp16v5+TkZKCm5bMDBw7w7NmztFgsTtv4cvLX1NQQACsqKhy+diQ5MzPDTz75xK2xnNXAHb7UIhTC39zczOPHj7v1TdKVyspKAmB1dbXDNpPJxLS0NOr1et68edOt8XypCenfjHgV/r/++os7duxgamoqo6KiqNfr+eCDD7Kjo4MkOT09zWXLlrGiosKuX15eHgHYLVqt1hak4eFhqlQqHjlyxMfDCpycnBwC4KpVq7h//34ODw87tPH25D9//jwjIyP51FNP+TxPZzW4c1/FxcVMSUlhZGQkExISuGHDBg4MDJD0rRahEP433niDAJiYmMidO3eyr6/P4zG6u7upVqu5bds2p2327dtHADx27NiC4/laE9K/GfE4/NPT00xPT2dBQQG/+eYbdnZ28scff2RtbS2vXbtGkuzo6CAA/vDDD3Z9z549y/z8fObl5bG7u5vd3d08d+6cXZvMzEw+/fTTPhxSYFnDb13CwsL4xBNPsLW1lSaTiaT3J/+LL75IlUrFS5cu+TxPZzUgyYsXL1Kr1fLJJ5/ksWPH2N7ezqamJpaUlNhqSHpfi1AK/51Lfn4+6+rqODo66tYYGzduZFhYGK9cueK0TUtLCwHw4MGDC47nj5qQ/suIx+E/ffo0AfCDDz7g+Pg4Z2dnHS6Brd8Nb9y44dA/ISGBO3bscDr+Cy+8wMTERE+ntWjuDv+dy9KlS/n6668zISHB45PfZDJRq9XyoYcecthmNps5OztrW9y5ZHRVg/fee48xMTELjuNtLUI1/NYlMjKSmzdvdvm24ObNmwwPD+fjjz/ucj9ffPEFAfDw4cM0mUwsLS1lcnIydTod165dy66uLltbf9SE9F9GPH6Sz8qVK5Gbm4vdu3dj9+7dAIDe3l5kZ2fb2vz5559QqVSIi4uz63vt2jWMjIxg9erVTsdPSEjAyMgI5ubmEB4e3AcNjY+PIz09HSMjI261HxsbQ11dnVf7unLlCm7duoU1a9Y4bMvJyUF/f7/t/1VVVXjnnXdcjuesBgAQFxeH27dv46WXXsL27duxbt06hIWFObTzthZTU1MA/nucV3Jystv9fDE6Oorp6Wm32s7MzKC1tRWtra2Ijo5GQ0ODw4NG+/r6MDc3hwceeMDlWN3d3QCA7OxszM3NITU1FV1dXUhOTkZjYyOKiopw9epVxMTE+KUmgP8y4nHP8fFxFBYWoqSkBHl5eYiJicHKlSvt2kxNTSEiIsJh8j09PQDgMvwajQYkYTKZoNVq7bYt9lNxSbod/PlYQ+CO0dFRAMCSJUsctjU0NMBsNuPEiRPYs2cP1q5da9t2+PBhHDx4EIODg1ixYgWOHz+OlJQUpzUAgFdffRWTk5Oor69HQ0MD4uPj8dxzz8FoNNrt31UtXLHWx2KxhPzjvKamplBdXe0Q/n/++QcAEB8f77TvxMQEmpqakJqaivz8fKhUKlRWVtq2b9u2DW+++Sb++OMP5OTk+KUmgPd1uZtH4b99+zYeeeQR7Ny5E2VlZU7bxcXFYWZmBpOTk4iNjbWt7+npsf282pmxsTFERUXNe1DV1dX31FNxPfkmlZiYCOC/K4C75ebmAgCampqgUqlsVwdVVVX47rvv0NzcjPT0dHR1ddlOVmc1AIDw8HDs2rULu3btwtDQEA4dOgSj0QiNRoN9+/bZ2rmqhSs6nQ5jY2OL+gBTT1757xQdHY2KigqH9dYrlsHBQad9P/roI0xMTKC2thYqlcph+8DAAKamppCWlgbAPzUBvK+LA0/eI5w8eZIA2NnZ6bJdQ0MDAbC3t9dufVFREfPy8lz23bBhA3Nzc+fd1tLSwoyMDBoMhqAtERERTt9LqlQqxsbGUq1W2+4BeCIrK4s6nc7hBo9VQUEBMzMzSZI3btzgkiVL5v2RKem8BvMxmUyMjo7mW2+9ZbfeVS1cuRfe8z/77LP8/vvvnb7nt1gsTEtL49KlSzk2NuawvbGxkWq1mlu2bJm3/+TkJPPz81lVVWVb54+akN7X5W4ehf/cuXNUqVTMyspiY2Mj29vb2drayvLycv7++++2dlevXiUAfvbZZ3b9S0pKqNfr+e2337K7u5uDg4N2281mM/V6/bwHHCrmu9tvvUPr693+jo4OajQaLl++nNXV1Txx4gR//vlnfv7553zmmWcYFhbG7du3k/zv5HvsscecjuWsBuXl5SwuLuaXX37JU6dOsbm5mQ8//DD1ej0vXLhga+dLLUI1/GvWrOGnn37Kv//+260x2traqNFomJaWxkOHDrGtrY1ff/01i4qKCIClpaWcmZlx6DczM8NNmzaxpKTE7ma4rzUh/ZsRj+/2Hz16lHl5eYyOjmZkZCRTUlK4detWhw8drF+/nhs3brRbd/nyZRYWFjI2NpYAWFNTY7f9119/JQD29PR4cSiL486f89fU1Mx759aXk7+/v5/PP/88k5KSGB4eTq1Wy1WrVvG1115jZ2en7WT6+OOPnb7qWM1Xg9raWq5fv54JCQmMiopiamoqX375ZV6+fNmunS+1CKXwL1++nBUVFezv7/dqnN7eXm7ZsoWJiYm2K7qUlBT+8ssv87Y3m83cunUri4qK5r2q8KUmpH8zErBP+LW2tjIsLIxDQ0Nu9ykuLmZBQUGgpuQXgf6En7tOnTrF+Ph4XrhwgWazmb/99pvD19qbGlj5UotQCL+/PuF3t+LiYkZERPDMmTPzbi8rK2NhYSGnpqbm3e5LTaz791dGAhZ+i8XCdevWsby83K32ly5dYkRExIL3E+4Fi3XyG41GJiUlUavVMj8/3+EqxNMaWPlai1AIf6CMj49zxYoVTE9P561bt+y2DQ4OEgA1Gg1jY2Nti/WTr6T3NSH9n5GAhZ8k+/r6+P7777v1wYW2tjaH90L3qlA6+T2pgZWvtQil4w9F3tSE9H9G5A91BoD1z1UZDAZF/7kupR7/vUIe5iGEQkn4hVAoCb8QCiXhF0KhJPxCKJSEXwiFkvALoVASfiEUSsIvhEJJ+IVQKAm/EAol4RdCoYL7eNz/ucV8em0oGR4eDvYUhBsk/AGg0+kA3BtPrw0k69dBhCYJfwAYjUbs2bNn0R4xHop0Oh2MRmOwpyFckN/nF0Kh5IafEAol4RdCoST8QiiUhF8IhZLwC6FQEn4hFErCL4RCSfiFUCgJvxAKJeEXQqEk/EIo1L/DC6M9biFZqAAAAABJRU5ErkJggg==", "image/svg+xml": [ "\n", "\n", "\n", "\n", " \n", " \n", " \n", " \n", " 2021-05-04T12:18:19.569641\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" ], "text/plain": [ "PyObject " ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "d = schemdraw.Drawing(unit=1, fontsize=12)\n", "\n", "d.add(dsp.Arrow().right().label(L\"\\epsilon(t)\", \"left\"))\n", "proc1 = d.add(dsp.Box(h=1, w=1.5).label(L\"G_c(s)\").anchor(\"W\"))\n", "d.add(dsp.Arrow().right().label(L\"Q_2(s)\", \"right\").at(proc1.E))\n", "\n", "d.draw(show=false)" ] }, { "cell_type": "markdown", "id": "1749dca1", "metadata": {}, "source": [ "donde la función de transferencia del controlador es:\n", "\n", "$$G_c (s) = K_c \\left( 1 + \\frac{1}{\\tau_I s} \\right)$$\n", "\n", "Suponiendo que la función de transferencia del medidor de nivel y de la válvula sean iguales a la unidad, es decir, que su dinámica sea instantánea se obtiene el siguiente diagrama de bloques del conjunto controlador-proceso:" ] }, { "cell_type": "code", "execution_count": 3, "id": "c0011a4b", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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"PyObject " ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "d = schemdraw.Drawing(unit=1.25, fontsize=11)\n", "\n", "d.add(dsp.Arrow().right().label(L\"H_{sp}(t)\", \"left\"))\n", "error = d.add(dsp.Mixer(W=\"+\", E=\"-\").anchor(\"W\"))\n", "d.add(dsp.Arrow().right().at(error.E).label(L\"\\epsilon(t)\"))\n", "menos1 = d.add(dsp.Box(w=1.25, h=1.25).anchor(\"W\").label(\"-1\"))\n", "d.add(dsp.Arrow().right().at(menos1.E))\n", "control = d.add(dsp.Box(w=1.25, h=1.25).anchor(\"W\").label(L\"G_c(s)\"))\n", "d.add(dsp.Arrow().right().at(control.E).label(L\"Q_2(s)\"))\n", "proc1 = d.add(dsp.Box(w=1.25, h=1.25).anchor(\"W\").label(L\"\\frac{1}{As}\"))\n", "d.add(dsp.Arrow().right().at(proc1.E))\n", "suma = d.add(dsp.Mixer(W=\"-\", N=\"+\").anchor(\"W\"))\n", "d.push()\n", "d.add(dsp.Arrow().up().reverse().at(suma.N))\n", "proc2 = d.add(dsp.Box(w=1.25, h=1.25).anchor(\"S\").label(L\"\\frac{1}{As}\"))\n", "d.add(dsp.Arrow().at(proc2.N).up().reverse().label(L\"Q_1(s)\", \"right\"))\n", "d.pop()\n", "d.add(dsp.Line().right().at(suma.E))\n", "dot = d.add(dsp.Dot(radius=0))\n", "d.push()\n", "d.add(dsp.Arrow().right().label(L\"H(s)\", \"right\"))\n", "d.pop()\n", "d.add(dsp.Line().down().length(1.5))\n", "d.add(dsp.Line().left().tox(error.S))\n", "d.add(dsp.Arrow().up().to(error.S))\n", "\n", "d.draw(show=false)" ] }, { "cell_type": "markdown", "id": "1f43f65e", "metadata": {}, "source": [ "Es importante destacar el bloque -1 existente entre el comparador y el controlador. En el caso de que este bloque no se incluyese el sistema sería inestable (si se utiliza una válvula de acción directa) ya que el número de cambios de signo en el interior del bucle sería par.\n", "\n", "b) La función de transferencia será:\n", "\n", "$$\\frac{\\bar{H}}{\\overline{Q_1}} = \\frac{\\frac{1}{As}}{1 + K_c \\left( 1 +\n", " \\frac{1}{\\tau_I s} \\right) \\frac{1}{As}} = \\frac{\\frac{\\tau_I}{K_c}\n", " s}{\\frac{A \\tau_I}{K_c} s^2 + \\tau_I s + 1}$$\n", " \n", "c) Al tratarse, la función de transferencia global, de un sistema de segundo orden, los parámetros que van a definir el comportamiento dinámico del lazo de control son la constante de tiempo y el coeficiente de amortiguamiento:\n", "\n", "$$\\begin{aligned}\n", " \\tau &= \\sqrt[]{\\frac{A \\tau_I}{K_c}}\\\\\n", " \\zeta &= \\frac{1}{2} \\sqrt[]{\\frac{K_c \\tau_I}{A}}\n", "\\end{aligned}$$\n", "\n", "Se pueden considerar tres casos:\n", "\n", "- Aumena la constante de tiempo integral: En este caso aumenta el\n", " coeficiente de amortiguamiento y la constante de tiempo, lo que hace\n", " que la respuesta sea más lenta y amortiguada\n", "\n", "- Aumenta la ganancia proporcional del controlador: En ese caso\n", " disminuye la constante de tiempo y aumenta el coeficiente de\n", " amortiguamiento, la respuesta debería ser más rápida y amortiguada\n", "\n", "- Aumenta el área del depósito: Aumenta la constante de tiempo, pero\n", " disminuye el coeficiente de amortiguamiento" ] } ], "metadata": { "@webio": { "lastCommId": null, "lastKernelId": null }, "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 }