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Economic model predictive control of parabolic PDE systems using empirical eigenfunctions

This work focuses on the development of reduced-order models (ROMs) of transport-reaction processes described by nonlinear parabolic partial differential equations (PDEs) and their application in the formulation of economic model predictive control (EMPC) systems. Specifically, the reduced-order models of the PDEs are constructed on the basis of historical data-based empirical eigenfunctions by applying Karhunen-Loève expansion. Several EMPC systems each using a different ROM (i.e., different number of modes and derived from either using analytical sinusoidal/cosinusoidal eigenfunctions or empirical eigenfunctions as basis functions) are applied to a tubular reactor example where a second-order reaction occurs. The model accuracy, computational time and closed-loop economic performance of the closed-loop tubular reactor under the different EMPC systems are compared.