FDI Robusta Para Sistemas LPV Mediante PIO
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Resumen
Resumen: Considerando los sistemas lineales invariantes en el tiempo (LTI) continuos con incertidumbres politópicas, esta contribución presenta un método para la síntesis de filtros robustos de detección y diagnóstico de fallas. Tomando
ventaja de los reconstructores de entradas desconocidas, los filtros se diseñan como observadores proporcional-integral (PIO), considerando y resolviendo un problema de control por realimentación estática de la salida (SOF), donde la ganancia de realimentación corresponde a las matrices de diseño del PIO. El método está basado en condiciones de desempeño modificadas, establecidas a partir de las normas H2/HÂ¥, las cuales se describen como desigualdades matriciales lineales, LMIs. La generación de los residuos, producto de los filtros robustos, se obtiene aplicando esas condiciones modificadas sobre los sistemas con perturbación desconocidas y sujetos a incertidumbres paramétricas. Los parámetros inciertos se suponen que pertenecen a un politopo. Las condiciones de desempeño H2/HÂ¥ extendidas se obtienen por medio del lema de proyección. El diagnóstico de las fallas se alcanza en primer lugar, estableciendo condiciones, extendidas también, de detectabilidad y separabilidad. En segundo lugar, si esas condiciones se satisfacen, diseñando un banco de filtros, es decir, por multifiltraje, basado en PIOs. Para cada falla objeto de separación, se diseña un filtro. Para
ilustrar los resultados y el desempeño del multifiltraje, se presenta además, un ejemplo numérico.
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Abstract: This paper presents a novel approach for robust fault detection and isolation (FDI), based on modifiedH2/HÂ¥ performance conditions, which are described as LMIs. The FDI filters are designed as Proportional-Integral Observers (PIO), by considering and solution of Static Feedback Output (SOF) control problem, where the feedback gain contains the matrices of the PIO. The generation of the residues, as consequence of the outputs of the robust filters, is obtained applying these conditions modified on linear systems with unknown disturbance and parametric uncertainties. The uncertainty parameters are supposed to belong to a polytope. The extended H2/HÂ¥ conditions are obtained by means of the well known projection lemma. Fault diagnosis is obtained, first of all, establishing extended conditions of detectability and separabilidad. Secondly, if these conditions are satisfied, designing a bank of filters based on PIO, which
is known as multifiltering. For each fault separation object, a filter is designed. Performance of the proposed synthesis technique is illustrated by numerical example.
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