Planteamiento de una métrica de la representación linealizada de un sistema no lineal. Aplicación para reactores (bio)químicos
Approach of a measurement of linearized representation of a nonlinear system. Application to (bio)chemical reactors
J. Carrillo-Ahumada1*, D.E. Páramo-Calderón2, A. Aparicio-Saguilán2, G.C. Rodríguez-Jimenes3 y M.A. García-Alvarado3
1 Instituto de Química Aplicada. Universidad del Papaloapan. Circuito Central 200, colonia Parque Industrial, Tuxtepec, Oax. 688301, México. *E-mail: jcarrillo@unpa.edu.mx; jesuscarrillo18@yahoo.com Tel. 01 (287) 8 75 92 40 Ext. 230
2 Instituto de Biotecnología. Universidad del Papaloapan. Circuito Central 200, colonia Parque Industrial, Tuxtepec, Oax. 68301, México.
]]> 3 Departamento de Ingeniería Química y Bioquímica. Instituto Tecnológico de Veracruz. Av. Miguel Ángel de Quevedo 2779, Veracruz, Ver. 91860, México.
Recibido 12 de Diciembre de 2013.
Aceptado 16 de Marzo de 2014.
Resumen
Se plantea un métrica para determinar la representación de un sistema linealizado con respecto al sistema no lineal. Esta métrica está basada en la expansión en series de Taylor de un sistema no lineal y fue aplicada para tres reactores (bio)químicos entre ellos el biorreactor de Cholette con multiplicidad de entradas, salidas y de estados estacionarios; un biorreactor con reacción enzimática y un reactor químico, aunque puede aplicarse para cualquier sistema no lineal. Se considera que el cociente de las matrices de primeras y segundas derivadas debe ser menor a la matriz de desviación de los valores nominales. Con este análisis, es posible determinar la influencia de cada parámetro en el sistema no lineal de estudio y su aplicación se encuentra en simulación y control.
Palabras clave: sistemas no lineales, linealización, series de Taylor, reactores (bio)químicos.
Abstract
]]> A new criterion of measurement was proposed to determine the representation of a linearized system with respect to nonlinear system. This criterion is based on the Taylor series expansion of nonlinear system and was applied to three (bio)chemical reactors including the Cholette's bioreactor with multiple inputs, outputs and steady states; a reactor with enzymatic reaction and a chemical reactor. Current approach considers that matrix elements resulting from left division of matrices containing second-order and first-order partial derivatives should be smaller than deviations from the nominal values. With this analysis, is possible to determine the influence of each bifurcation parameter on the nonlinear system for simulation and control applications.Keywords: nonlinear systems, linearization, Taylor series, (bio)chemical reactors.
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Agradecimientos
Los autores agradecen al Programa de Mejoramiento del Profesorado (PROMEP) por el financiamiento parcial para esta investigación mediante el proyecto "Análisis de Estabilidad de Procesos Químicos y Alimentarios con Controladores Óptimo-Robustos" (PROMEP/103.5/12/7959; UNPA-PTC-119).
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