Nonlinear observer for switched systems: application to a batch bioreactor

Observador nolineal para sistemas conmutados: aplicación a un biorreactor en lote

F.A. Cuevas-Ortiz¹, M.I. Neria-González² and R. Aguilar-López¹*

¹ Departamento de Biotecnología y Bioingeniería, Cinvestav. Av. I.P.N. No. 2508, Col. San Pedro Zacatenco, México, D.F. 07360. *Corresponding author. E-mail: raguilar@cinvestav.mx, Tel. 57473800, ext 4307.

² División de Ingeniería Química y Bioquímica, TESE. Av. Tecnológico S/N, Col. Valle de Anáhuac, Ecatepec de Morelos, 55210, Edo. de México. México.

Received November 9, 2014
Accepted February 15, 2015

Abstract

The main objective of this work is to design a new state observer for a switched nonlinear system. The proposed observer contains a standard proportional term and a bounded feedback that improves the performance of the estimation process compared with other methodologies such as extended Luenberger-type observers. A theoretical analysis of the convergence of the proposed observer through an analysis of multiple Lyapunov functions is provided. The estimation strategy is applied to a bioreactor batch, where is performed a process of sulfate-reducing considering a hypothetical change in kinetic regime. The evolution of the reaction kinetics is described in three stages: the first stage is described by the Haldane-Boulton kinetic model; the second transitional stage called an interaction between the Haldane-Boulton and Moser-Boulton kinetic models; and the third stage is represented by the model Moser-Boulton. Sulfide concentration is considered as a measured variable of the bioreactor to implement the proposed observer. Numerical experiment results shown satisfactory performance of the considered methodology.

Key words: nonlinear observer, switched system, adaptive modeling, batch bioreactor.

Resumen

El objetivo principal del trabajo es diseñar un nuevo observador de estados para un sistema no lineal conmutado. El observador propuesto contiene un término proporcional estandar y una retroalimentación acotada que mejora el desempeño del proceso de estimación en comparación con otras metodologías, como los observadores de tipo Luenberger extendidos. Se proporciona un análisis teórico sobre la convergencia del observador propuesto a través de un análisis de funciones múltiples de Lyapunov. La estrategia de estimación es aplicada a un biorreactor en lote, donde se lleva a cabo un proceso de sulfato-reducción considerando un cambio hipotético de régimen cinético. La evolución de la cinética de reacción es descrita en tres etapas: la primera etapa es descrita por el modelo cinético de Haldane-Boulton; la segunda etapa llamada de transición se asume una interacción entre el modelo de Haldane-Boulton y el modelo cinético Moser-Boulton; y la tercera etapa es representada por el modelo de Moser-Boulton. La concentración de sulfuro se considera como una medida de la salida del biorreactor para implementar el observador propuesto. Los resultados de los experimentos numéricos muestran un desempeño satisfactorio de la metodología considerada.

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