Control Adaptivo En Tiempo Real Jhimy Xavier Ponce Jarrin

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Control Adaptivo En Tiempo Real Jhimy Xavier Ponce Jarrin ESCUELA POLITENICA NACIONAL FACULTAD DE INGENIERÍA ELÉCTRICA TESIS PREVIA LA OBTENCIÓN DEL TITULO DE INGENIERO EN ELECTRÓNICA Y CONTROL CONTROL ADAPTIVO EN TIEMPO REAL JHIMY XAVIER PONCE JARRIN NOVIEMBRE - 1991 AGRADECIMIENTO Mi sincero agradecimiento al Ing. Patricio Burbano por su acertada y dedicada dirección. DEDICATORIA A mis padres por su constante apoyo. CERTIFICACIÓN Cetifico que el presente trabajo ha sido realizado en su totalidad por el Sr. Jhimy Xavier Ronce Jarrín. Ing. Patricio Burbano CONTENIDO CAPITULO I INTRODUCCIÓN................... 1 1.1 INTRODUCCIÓN GENERAL AL CONTROL ADAPTIVO 2 1.2 MÉTODOS DE CONTROL ADAPTIVO............. 3 1.2.1 CONTROL ROBUSTO DE ALTA GANANCIA.- 3 1.2.2 SISTEMA ADAPTIVO AUTO-OSCILANTE.-.. .........4 1.2.3 PROGRAMACIÓN DE GANANCIAS......... 5 1.2.4 CONTROL ADAPTIVO CON REFERENCIA A MODELO (M.R.A.C)....... 5 . 1.2.5 REGULADOR SELF-TUNING (S.T.R.) 6 1.2.6P.I.D.AUTO-SINTONIZABLE .........7 1.3 CONTROL ADAPTIVO EN TIEMPO REAL.-. ......7 1.4 ALCANCE Y OBJETIVOS............... .9 CAPITULO II CONTROL ADPTIVO CON REFERENCIA A MODELO (MRAC)....... 11 2.1 INTRODUCCIÓN........ .12 2.2 ALGORITMO DE CONTROL- 1 4 2.3 IDENTIFICACIÓN.-.. 17 2.4 DISEÑO GENERAL PARA UN MRAC EXPLÍCITO DISCRETO............ 19 2.4.1 CASOS PARTICULARES Y CONEXIONES CON VARIOS ALGORITMOS EXPLÍCITOS M.R.A.C. .....23 M.R.A.C. CON INDEPENDIENTE REGULACIÓN Y SEGUIMIENTO.- 23 ALGORITMO MRAC SERIE-PARALELO...... ..23 ALGORITMO MRAC PARALELO CON COMPESADOR LINEAL.-... ....25 ALGORITMO MRAC'PARALEO CON FILTRO.- 26 2.5 PROGRAMA DE SIMULACIÓN 27 2.5.1 MODULO PRINCIPAL 28 2.6 IMPLEMENTACION EN TIEMPO REAL ..57 CAPITULO III SELF TUNING REGULATOR (STR)...... 60 3.1 CONTROLADORES CON PROPIEDAD AUTOAJUSTABLE 61 3.2 STR DE MÍNIMA VARIANZA 63 3.3 PROGRAMA DE SIMULACIÓN 64 3.4 IMPLEMENTACION EN TIEMPO REAL...... -.65 CAPITULO IV RESULTADOS , APLICACIONES Y CONCLUSIONES... 66 4.1 RESULTADOS DE U\ RUTINAS DE SIMULACIÓN 67 4.2 RESULTADOS DE LAS RUTINAS EN TIEMPO REAL.......... ....; 68 4.3 SIMULACIÓN UTILIZANDO EL PAQUETE CC .70 4.4 POTENCIALES APLICACIONES Y CONCLUSIONES... 71 PRESENTACIÓN DE REULTADOS NUMÉRICOS Y GRÁFICOS Y LISTADO DE MAGROS .....75 RESULTADOS EN TIEMPO REAL .......129 APÉNDICE A .....135 APÉNDICE B 138 APÉNDICE C 140 APÉNDICE D..... 142 BIBLIOGRAFÍA ................150 REFERENCIAS ..........151 LISTADO DE ARCHIVOS 152 CAPITULO I : INTRODUCCIÓN 1.1 INTRODUCCIÓN GENERAL AL CONTROL ADAPTIVO 1.2 MÉTODOS DE CONTROL ADAPTIVO 1.3 CONTROL ADAPTIVO EN TIEMPO REAL 2 1.1 INTRODUCCIÓN GENERAL AL CONTROL ADAPTIVO. Adaptar significa cambiar el comportamiento conforme las nuevas circunstancias. Intuitivamente un regulador adaptivo es un regulador que puede modificar su comportamiento en respuesta a cambios en la dinámica del proceso y a las perturbaciones. Se puede considerar al control adaptivo como una realimentación no lineal especial. Esto introduce la idea de dos escalas de tiempo: Una rápida para la realimentación ordinaria y otra lenta para la actualización de parámetros del regulador como se indica en la figura 1.1. Esto implica que reguladores con parámetros constantes lineales son no adaptivos ya que no hay actualización de parámetros. IDENTIFICACIÓN LAZO EXTERNO U Y REGULADOR PLANTA LAZO INTERNO DE REALIMENTACION Fig. 1.1 ESQUEMA GENERAL DE CONTROL ADAPTIVO En un control adaptivo se asume que existe realimentación desde la ejecución del sistema en lazo cerrado. Por lo que se puede concluir que una programación de ganacias no puede ser considerada como un conírolador adaptivo, ya que los parámetros son determinados por una selección sin ninguna realimentación desde la ejecución. Los sistemas adaptivos tienen grandes capacidades de uso e interesantes propiedades las cuales deben ser oportunamente incorporadas en el diseño de nuevos sistemas de control. El control adaptivo se enlaza con muchas áreas del control automático,, tales como: sistemas no lineales, ya que el control adaptivo es inherentemente no lineal; control estocástico y estimación, ya que un sistema adaptivo es visto 3 como una combinación de parámetros y control; con optimización; sistemas lineales; control por computador; el diseño de control , etc. La teoría de control clásico trata con sistemas lineales con parámetros constantes. Esto es una buena aproximación para sistemas que están regulados y con puntos de operación fijos. Con pequeñas pertubaciones y un sistema de control bien diseñado las desviaciones del punto de operación serán muy pequeñas, tal que una aproximación lineal es muy buena. Sin embargo la aproximación lineal con coeficientes constantes no siempre es satisfactoria y se tornará insuficiente cuando se produzcan cambios en las condiciones de operación. Los cambios en las condiciones de operación se dan debido a la variación de parámetros del proceso, los mismos que pueden cambiar debido a la presencia de actuadores no lineales, cambios en el proceso mismo y perturbaciones. En la práctica hay muchas fuentes de variación de parámetros, las cuales resultan de una combinación de problemas diferentes. Las razones principales para las variaciones de parámetros pueden no ser completamente entendidas ya sea porque no es posible debido a la complejidad de los procesos o económicamente porque no se puede hacer una investigación del comportamiento y modelación de las mismas. Controladores adaptivos pueden ser una buena alternativa en estos casos. En resumen los factores claves para utilizar controles adaptivos son: -Variaciones en la dinámica del proceso - Variaciones debido a las perturbaciones - Eficiencia de ingeniería. 1.2 MÉTODOS DE CONTROL ADAPTIVO.- Un regulador robusto de ganancia constante se utiliza como punto de partida para describir los métodos de control adaptivo. Este sistema incluye un modelo del comportamiento deseado. Luego se plantean distintos sistemas adapíivos tales como: controlador adaptivo autoosciiante, programación de ganancias, control con modelo de referencia y regulador autosintonizable . 1.2.1 Control robusto de alta ganancia.- 4 Es un regulador de ganancia constante diseñado para soportar variaciones de parámetros. Un diagrama de bloques se muestra en la figura 1.2. Se tiene un lazo de realimentación de alta ganancia alrededor de la planta, haciendo que la salida Y siga a la señal de referencia Ym sobre un ancho de banda Wb. Este ancho de banda variará con la dinámica del proceso. MODELO REGULADOR PROCESO Um Ym Gm Gr Gp Fig. 1.2 CONTROL ROBUSTO DE ALTA GANANCIA Si el ancho de banda del proceso es menor que Wb, la salida Y responderá a la señal de referencia Ym, especificada por el modelo, aún cuando la dinámica del proceso varié. El problema clave está en el diseño del lazo de realimentación y modelo de referencia, así la estabilidad y e! comportamiento se mantendrán aún en presencia de variaciones del proceso. 1.2.2 Sistema adaptivo auto-oscilante.- La estructura es similar al de alta ganancia. El ancho de banda del lazo de realimentación es sin embargo automáticamente ajustado para ser tan grande como sea posible. Un diagrama de bloques se indica en la figura 1.3. La ganancia de lazo alta es mantenida por introducción de un retraso en el lazo de realimentación. Esto crea una oscilación de ciclo límite. Para señales cuyas frecuencias son menores a la del ciclo límite, el sistema se autoajusta para dar un razonable margen de amplitud. Se debe notar que el sistema siempre está excitado por la oscilación de ciclo límite. La frecuencia de oscilación puede ser influenciada por el compensador adelanto - atraso indicado el la figura 1.3. La amplitud de la oscilación puede ser ajustada cambiando la amplitud del retardo. Rg 1.3.- SISTEMA ADAPTIVO AUTO-OSCILANTE 1.2.3 Programación de ganancias.- En algunos sistemas existen variables auxiliares que describen bien las características de la dinámica del proceso. Si estas variables pueden ser medidas, estas pueden ser usadas para cambiar los parámetros del regulador; esto es, se utilizan para acomodar los cambios en la ganancia del proceso. Este método es el llamado de programación de ganancias. Un esquema se presenta en la figura 1.4. PARÁMETROS DEL REGULADOR CONDICIÓN DE AJUSTE DE GANANCIA OPERACIÓN SEÑAL DE REF. SEÑAL DE REGULADOR PROCESO CONTROL RG 1.4 SISTEMA CON PROGRAMACIÓN DE GANANCIAS E! ajuste de ganancia es una compensación en lazo abierto y puede ser visto como un sistema con control de realimentación en el cual el lazo de realimentación es ajustado con compensación directa. El ajuste de ganancia es una técnica muy utilizada para reducir los efectos de la variación de parámetros, 1.2.4 Control adaptivo con referencia a modelo (M.R.A.C) Esta técnica fue propuesta para resolver un problema en el cual las especificaciones son dadas en términos de un modelo de referencia donde la salida del proceso deberá seguir a la referencia. Un esquema se muestra en la figura 1.5. i Ym MODELO r^ .MECANISMC PARÁMETROS DEL REGULADOR Uc REGULADOR PLANTA FIG. 1.5 ESQUEMA DEL M.R.A.C. En este caso el modelo está en paralelo con el sistema. El regulador consiste de los dos lazos: un interno el cual es una realimentación ordinaria conpuesta por la planta y el regulador. Los parámetros del regulador son ajustados por el lazo externo de tal forma que el error entre la salida de la planta "Y" y la referencia "Ym" sea pequeño, entonces el lazo externo también es un lazo-regulador. El problema clave es determinar un mecanismo de ajuste tal que el sistema sea estable, y lleve el error a cero. 1.2.5 Regulador self - tuning (S.T.R.) Existen dos métodos: El método directo .- en este esquema los parámetros del regulador son actualizados. El método indirecto.- los parámetros del proceso son actualizados y los parámetros del regulador se obtienen de la solución de un problema de diseño. Un diagrama de bloques de este método se ilustra en la figura 1.6. Este regulador está compuesto de dos lazos: Un lazo interno compuesto por el proceso y un regulador con realimentación ordinaria, y un lazo externo que actualiza los parámetros del proceso (modelación).
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