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Journal of Control Science and Engineering
Volume 2013, Article ID 763165, 19 pages
http://dx.doi.org/10.1155/2013/763165
Research Article

Model Reduction Using Proper Orthogonal Decomposition and Predictive Control of Distributed Reactor System

1Faculty of Minas, National University of Colombia, 050041 Medellín, Colombia
2Chemical Engineering Department, University of São Paulo, 05508-900 São Paulo, SP, Brazil

Received 28 November 2012; Revised 28 February 2013; Accepted 15 March 2013

Academic Editor: James Lam

Copyright © 2013 Alejandro Marquez et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper studies the application of proper orthogonal decomposition (POD) to reduce the order of distributed reactor models with axial and radial diffusion and the implementation of model predictive control (MPC) based on discrete-time linear time invariant (LTI) reduced-order models. In this paper, the control objective is to keep the operation of the reactor at a desired operating condition in spite of the disturbances in the feed flow. This operating condition is determined by means of an optimization algorithm that provides the optimal temperature and concentration profiles for the system. Around these optimal profiles, the nonlinear partial differential equations (PDEs), that model the reactor are linearized, and afterwards the linear PDEs are discretized in space giving as a result a high-order linear model. POD and Galerkin projection are used to derive the low-order linear model that captures the dominant dynamics of the PDEs, which are subsequently used for controller design. An MPC formulation is constructed on the basis of the low-order linear model. The proposed approach is tested through simulation, and it is shown that the results are good with regard to keep the operation of the reactor.