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Journal of Process Control, Vol.24, No.4, 448-462, 2014
Economic model predictive control of parabolic PDE systems: Addressing state estimation and computational efficiency
In a previous work [20], an economic model predictive control (EMPC) system for parabolic partial differential equation (PDE) systems was proposed. Through operating the PDE system in a time-varying fashion, the EMPC system demonstrated improved economic performance over steady-state operation. The EMPC system assumed the knowledge of the complete state spatial profile at each sampling period. From a practical point of view, measurements of the state variables are typically only available at a finite number of spatial positions. Additionally, the basis functions used to construct a reduced-order model (ROM) for the EMPC system were derived using analytical sinusoidal/cosinusoidal eigenfunctions. However, constructing a ROM on the basis of historical data-based empirical eigenfunctions by applying Karhunen-Loeve expansion may be more computationally efficient. To address these issues, several EMPC systems are formulated for both output feedback implementation and with ROMs based on analytical sinusoidal/cosinusoidal eigenfunctions and empirical eigenfunctions. The EMPC systems are evaluated using a non-isothermal tubular reactor example, described by two nonlinear parabolic PDEs, where a second-order reaction takes place. The model accuracy, computational time, input and state constraint satisfaction, and closed-loop economic performance of the closed-loop tubular reactor under the different EMPC systems are compared. (C) 2014 Elsevier Ltd. All rights reserved.
Keywords:Model predictive control;Process economics;Partial differential equations (PDEs);Process control;Transport-reaction processes