Stabilization of third-order systems with possible complex conjugate poles and time delay

Estabilización de sistemas de tercer orden con posibles polos complejos conjugados y tiempo de retardo

M.A. Hernández-Pérez, B. del Muro-Cuéllar¹*, D. Cortés-Rodríguez and I. Araujo-Vargas

Escuela Superior de Ingeniería Mecánica y Eléctrica, Unidad Culhuacan, Instituto Politécnico Nacional, México D.F., 04430, México. *Corresponding author. E-mail: bdelmuro@ipn.mx Tel. (52)56-562058.

Abstract

The stabilization problem of third-order, time-delay unstable linear systems is analyzed. The systems under consideration have one unstable and two stable poles, which may be complex conjugate. Necessary and sufficient conditions to guarantee the stability of the closed loop system by means of a static output feedback are provided. Using such conditions, a predictor scheme that improves the transient system performance is proposed. To illustrate the application of the proposed strategy, it is applied to an unstable continuously stirred tank reactor model. Simulation results are presented.

Keywords: delay, complex conjugate poles, predictor, stabilization.

Resumen

Este trabajo considera el problema de la estabilización de sistemas lineales con tiempo de retardo de tercer orden, con un polo inestable y dos estables, los cuales pueden ser complejos conjugados. Se presentan las condiciones necesarias y suficientes para asegurar la estabilidad del sistema en lazo cerrado por medio de una retroalimentación estática de la salida. Asimismo, usando el resultado anterior se propone un esquema predictor el cual mejora el desempeño transitorio del sistema. Finalmente, el desempeño de la estrategia de control propuesta es evaluado mediante su aplicación en simulación numérica a un reactor de tanque continuamente agitado inestable.

Palabras clave: retardo, polos complejos conjugados, predictor y estabilización.

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