V. López-Morales¹ & R. Valdés-Asiain² .

¹ Centro de Investigación en Tecnologías de Información y Sistemas, CITIS-ICBI-UAEH, Carr. Pachuca Tulancingo, Km. 4.5, C.U., C.P. 42084, Tel. (+52) (01-771) 71 72197, ó 72000 ext. 6734, Fax. 72000 ext. 6732, Pachuca de Soto, Hidalgo, México. virgilio@uaeh.edu.mx

² Instituto Tecnológico de Pachuca, (AP 276) Carr. México-Pachuca Km. 87.5, Col. Venta Prieta C.P.42080, Pachuca de Soto, Hidalgo, México. rvaldes@uaeh.reduaeh.mx

Received: January 25^th 2003.
Accepted March 7^th 2005.

Abstract

The main goal of this paper is twofold: To show a kind of robustness in a nonlinear multivariable (NL MIMO) system with feedback control, by employing some linearization and observation techniques well known in reference kind of model; and at the same time it is a proposal to immunize the measurements of a level capacitance-based sensor when there are changes in the measured variables properties, by employing an on-line compensation. The MIMO thermal-hydraulic nonlinear system is stabilized when some linearizing conditions are met and a design methodology for using a state feedback scheme is established. In order to assign poles to the control system, the Jacobian linearization is transformed to the controllable canonical form. This is accomplished by the Brunovsky similarity transformation, and by a static state feedback. A Luenberger observer is added to the control system in order to improve its stability. Illustrations of these techniques are shown via numerical and practical simulations carried out directly in the inexpensive physical process.

Keywords: Process modeling, Brunovsky canonical transformation, Sensor compensation, Linearized observer.

Resumen

El propósito principal de este artículo es doble: por un lado, mostrar algunos aspectos de robustez en un sistema de control por retroalimentación de un sistema multivariable (MIMO), al emplear algunas técnicas de linealización y observación, bien conocidas, en un modelo de referencia; y presentar, al mismo tiempo, una propuesta para lograr la inmunización de las mediciones de un sensor de nivel de líquido, basado en la variación de capacitancia, cuando existen cambios en las propiedades de las variables medidas, al emplear compensación en tiempo real. El sistema no lineal termo hidráulico MIMO es estabilizado, cuando algunas condiciones de linealización son cumplidas, y con esto se establece una metodología de diseño que utiliza un esquema de retroalimentación de estado. A fin de asignar los polos al sistema de control, la linealización Jacobiana es transformada a la forma canónica controlador. Lo anterior es llevado a cabo por la transformación de similaridad de Brunovsky, y una retroalimentación de estado estática. Un sencillo observador de Luenberger es agregado al sistema de control a fin de mejorar su estabilidad. La aplicación de estas técnicas es mostrada vía simulaciones numéricas y físicas realizadas directamente en esta sencilla y barata, pero útil, plataforma de pruebas de control.

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The work of Virgilio López Morales was partially supported by a project A-E-N-M02: M03 under a Grant from ANUIES ECOS NORD, and the PROMEP-RDS-01-05 project under a Grant from SEP-SESIC.

The work of René Valdes Asiain was partially supported by the Instituto Tecnológico de Pachuca and the Universidad Autónoma del Estado de Hidalgo.

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