Robust generic model feedback under model uncertainties: application of a tubular reactor for the treatment of industrial plating wastewater

 

Ricardo Aguilar-López¹, Ricardo Acevedo-Gómez¹, María Isabel Neria González² and Alma Rosa Domínguez-Bocanegra¹

 

¹ Departamento de Biotecnología y Bioingeniería, CINVESTAV-IPN Av. Instituto Politécnico Nacional No. 2508, San Pedro Zacatenco, México, D.F. 07360, MEXICO E-mail.- raguilar@cinvestav.mx Phone.- + 52 55 5747 3800, ext. 4307.

² División de Ingeniería Química y Bioquímica, Tecnológico de Estudios Superiores de Ecatepec, Av. Tecnológico s/n Esq. Av. Carlos Hank González Col. Valle de Anáhuac C.P. 55210, Ecatepec Estado de México.

 

ABSTRACT

The goal of this work is to describe the design of a feedback controller to regulate the Hexavalent chromium (Cr(VI)) concentration in industrial plating wastewater in a tubular reactor. Cr(VI) is a major pollutant present in industrial wastewaters common to the metal and mineral processing as well as to plating industries. For control purposes, a dynamic model of a plug flow reactor with dispersion is developed in the form of partial differential equations (PDE) via applying classical conservation principles; this model is experimentally corroborated using laboratory data. The proposed controller is based on uncertainty observer to infer unknown terms as diffusive transport and Cr(VI) kinetic rate; also Generic Model Controller (GMC) is coupled with this estimation methodology to provide robustness against model uncertainties. The controller leads to nonlinear PID plus double integral action, where the tuning rules are given in terms of the observer and GMC gains. A theoretical frame is given in order to show the stability properties of the closed-loop system under the proposed controller. Numerical simulation illustrates performance of the methodology proposed; a comparison with observer based I/O linearizing controller and a well tuned PID controller is done, which allows concluding that the observer based Generic Model Controller exhibits better performance.

Keywords: Cr(VI) treatment, GMC, Tubular reactor, Infinite dimensional models, Robust performance.

 

RESUMEN

El objetivo del presente trabajo es describir el diseño de un controlador retroalimentado para regular la concentración de Cromo Hexavalente (Cr(VI)) de agua residual de la industria de galvanoplastía en un reactor tubular. El Cr(VI) es uno de los más tóxicos contaminantes de esta industria. Para fines de control, se diseña un modelo dinámico del proceso, el cual es un reactor flujo pistón con dispersión descrito por ecuaciones diferenciales parciales que se basa en la aplicación de los principios básicos de balances de masa; este modelo se corrobora experimentalmente con datos de laboratorio. El controlador propuesto se basa en un estimador de incertidumbres con el fin de inferir los términos relacionados con el transporte difusivo de masa y la cinética de remoción de Cr(VI), que se asumen desconocidas; posteriormente, este estimador se acopla con un controlador de modelo genérico para generar un esquema de control robusto contra incertidumbres. El diseño del controlador propuesto es equivalente a una estructura de tipo PID más una acción doble integral no lineal, donde las reglas de sintonizado se dan en términos de las ganancias del observador de incertidumbres y del propio controlador genérico. Se proporciona el marco teórico que muestra que la metodología propuesta produce estabilidad a lazo cerrado. Simulaciones numéricas muestran el desempeño de la metodología propuesta; se realiza una comparación con un controlador linealizante basado en observador y un controlador lineal clásico PID; esto permite concluir que la estrategia de control propuesta tiene el mejor desempeño.

Palabras clave: Tratamiento de Cr(VI), control de modelo genérico, reactor tubular, modelos de dimensión infinita, desempeño robusto.

 

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