solucionario-1er-practica-calificada

solucionario-1er-practica-calificada

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INGENIERIA DE CONTROL DIGITAL CICLO ACADEMICO 2011-B ING. JACOB ASTOCONDOR VILLAR Página 1 SOLUCIONARIO PRIMERA PRÁCTICA CALIFICADA CONTROL DIGITAL P1.- Sea el sistema definido por las siguientes ecuaciones de estado: ( ) [ ] ( ) [ ] ( ) ( ) [ ] ( ) a) Calcular la función de transferencia pulso del sistema SOLUCION: Teniendo en cuenta la siguiente definición y las matrices de entrada y salida de la ecuación de estado anterior, se tiene: ( ) ( ) ( ) ( ) ( ) ( ) | | Operando adecuadamente: [ ] ( ) [ ] ( ) [ ( ) ( ) ( ) ( ) ] [ ] [ ] Reemplazando en la ecuación inicial y operando: ( ) ( ) ( ) FUNCION DE TRANSFERENCIA PULSO DEL SISTEMA
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INGENIERIA DE CONTROL DIGITAL CICLO ACADEMICO 2011-B ING. JACOB ASTOCONDOR VILLAR Página 2 b) Determinar la CONTROLABILIDAD y OBSERVABILIDAD del sistema SOLUCION: CONTROLABILIDAD: Para que un proceso sea completamente controlable se debe cumplir que el rango de la matriz de CONTROLABILIDAD debe ser igual al orden del proceso, lo que implica que el determinante de la matriz debe ser diferente de cero: ( ) ([ ]) Entonces: [ ] ( ) EL SISTEMA ES COMPLETAMENTE CONTROLABLE
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