Curva de reaccion y sintonia de un controlador
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Curva de reaccion y sintonia de un controlador

Course: ENGINEERIN 3003017, Spring 2011

School: Universidad Nacional de...

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INFORME DE LABORATORIO CURVA DE REACCIN Y SINTONA DE UN CONTROLADOR PID Mnica Juliana Angarita Velsquez Juan Camilo Castrilln Juan Manuel Restrepo Flrez Introduccin En el presente trabajo se pretende encontrar los parmetros de sintona de un controlador PID de presin mediante el mtodo de la curva de reaccin. El sistema de estudio en un tanque en el que se quiere controlar la presin, manipulando el flujo msico de...

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DE INFORME LABORATORIO CURVA DE REACCIN Y SINTONA DE UN CONTROLADOR PID Mnica Juliana Angarita Velsquez Juan Camilo Castrilln Juan Manuel Restrepo Flrez Introduccin En el presente trabajo se pretende encontrar los parmetros de sintona de un controlador PID de presin mediante el mtodo de la curva de reaccin. El sistema de estudio en un tanque en el que se quiere controlar la presin, manipulando el flujo msico de entrada. Se tiene como perturbacin el flujo msico de salida del equipo. Un diagrama pictrico del sistema se muestra en la figura 1. Curva de reaccin Luego de someter el sistema a una perturbacin en escaln de la variable manipulada (u) tanto por encima como por debajo del punto de ajuste, se obtienen las siguientes curvas de reaccin del equipo. 60 50 40 U D 30 Y 20 10 0 100 150 200 250 300 350 400 Figura 2. Curva de reaccin al causar un escaln por encima del punto de ajuste sobre la variable manipulada 60 50 40 U D 30 Y 20 10 0 700 720 740 760 780 800 820 840 860 880 Figura 3. Curva de reaccin al causar un escaln por debajo del punto de ajuste sobre la variable manipulada Las curvas de reaccin obtenidas muestran que la perturbacin realizada condujo al sistema a una regin de no linealidad ya que el comportamiento no es el mismo bajo las dos perturbaciones. Modelos de primer orden con retardo Con las curvas de reaccin se obtuvo un modelo de primer orden ms retardo como el que se muestra en la ecuacin 1 K u e td s Gu = +s (1) Los parmetros de la ecuacin 1 se obtienen teniendo en cuenta la representacin de la figura 4 de acuerdo a las siguientes ecuaciones. t d = t1 t 0 (2) = t 63.2 t1 (3) Ku = y u (4) Donde: t63.2 corresponde al tiempo en el cual la salida ha alcanzado el 63.2% del cambio total. t td t0 t1 t63.2 Figura 4. Esquema de una curva de reaccin para la obtencin de los parmetros del modelo de primer orden con retardo Los resultados obtenidos con las curvas de reaccin mostradas en las figuras 1 y 2 se resumen en la tabla 1. Tabla 1. Parmetros del modelo de primer orden con retardo Parmetros td (s) ku t(s) Perturbacin por encima del punto de ajuste 4 -3.3 57 Perturbacin por debajo del punto de ajuste 9 -1.029 33 Parmetros de sintona del controlador Cuando el sistema se encuentra en una regin de no linealidad como en este caso se recomienda realizar la sintona del controlador utilizando la curva de reaccin ms rpida, ya que se asume que los parmetros encontrados para sta, servirn tambin para estabilizar perturbaciones menores. De acuerdo a lo anterior, se trabaja con la curva de reaccin mostrada en la figura 1. Los parmetros de sintona tericos para el controlador PID, se encontraron empleando el criterio de Ziegler y Nichols, que establece para un sistema estable en lazo abierto: Kp = 1.2 Kutd (5) t I = 2t D d (6) t = 0.5t d (7) En la tabla 2 se resumen los parmetros tericos obtenidos por el mtodo de Ziegler y Nichols, as como los parmetros reales que se encontraron experimentalmente por tanteo. Tabla 2. Parmetros de sintona para el controlador PID de presin Parmetros Kp tI (s) tD (s) Tericos -5.18 8 2 Experimentales -1.43 20 10 En la figura 5 se muestra el comportamiento del controla dor y de la vlvula durante el proceso. Figura 5. Comportamiento del controlador y de la vlvula durante el proceso. En la figura 5 se sealan cuatro regiones con diferentes contrastes. La primera regin (500-880 seg) corresponde al controlador sintonizado con los parmetros tericos, calculados mediante el mtodo de Ziegler y Nichols (tabla 2); en esta regin el controlador se comporta de manera oscilante y es importante resaltar que los movimientos de la vlvula son bruscos y alcanzan valores extremos. Por sta razn en el proceso de sintona se decidi disminuir la ganancia del controlador. En la segunda regin (880-1470 seg) se manipularon los diferentes parmetros (K p, tI, td) hasta llegar a los valores experimentales que se reportan en la tabla 2, una vez alcanzados estos valores, el sistema se comporta de manera estable (ver regin entre 1000-1200 segundos). Cerca de los 1250 segundos (flecha hacia abajo, figura 5) el sistema es perturbado, haciendo que la presin en el tanque aumente por encima del punto de ajuste, inmediatamente se observa una accin de control de la vlvula, que se cierra para permitir que el exceso de aire sea evacuado del tanque. Una vez que el sistema alcanza el punto de ajuste, se perturba en el sentido contrario (flecha hacia arriba, figura 5) causando que la presin en el tanque disminuya; en este caso la vlvula se cierra para recuperar la presin adecuada en el tanque. Luego de causar las dos perturbaciones al sistema, se observa un comportamiento ms suave en la curva de la variable controlada cuando la presin cae dentro del tanque, mientras que con la otra perturbacin se evidencian sobreimpulsos y movimientos ms pronunciados en la vlvula. En este ltimo caso la recuperacin del sistema es ms lenta probablemente porque a pesar de que la vlvula se cierra completamente, el sistema debe esperar a que el aire sea evacuado. En la tercera regin (1470-1520 seg) se cambi el signo de la ganancia, observndose una realimentacin positiva en el sistema, ya que la vlvula acta de manera contraria a lo que la perturbacin demanda para ser controlada. En la regin final (1520-1820 seg) se cambi el punto de ajuste para probar como se comportaba el controlador diseado para regulacin en el caso del seguimiento. Como puede observarse los parmetros encontrados no son adecuados para un controlador de seguimiento, ya que la vlvula realiza movimientos muy bruscos, alcanzando valores extremos.

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Universidad Nacional de Colombia - ENGINEERIN - 3003017
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Universidad Nacional de Colombia - ENGINEERIN - 3003017
La vlvula de control acta como una resistencia variable en la lnea de proceso; medianteel cambio de su apertura se modifica la resistencia al flujo Cv y el flujo mismo f.1.1 Coeficiente de flujo, Cv de una vlvula de control y su dimensionadoEn 1944 Mas
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