Shaping the Spatiotemporal Dynamics of Transport-Reaction Processes Via Adaptive Proper Orthogonal Decomposition

In recent years, the control of spatiotemporal dynamics of transport-reaction processes has been recognized as an important subject in many industrial chemical processes exemplified by flow reactors and microelectronic fabrication processes. The control problem of such systems which can be mathematically modeled by partial differential equations (PDEs) may typically be addressed via model order reduction (MOR) because the infinite dimensional representation of the PDE dynamics of the systems can be approximated by reduced order finite dimensional models [1].

We focus on shaping the spatiotemporal dynamics of such processes via regulation of error dynamics between the process and a target PDEs. The infinite dimensional representation of the error dynamics is reduced by MOR. Specifically, we apply a combination of Galerkin’s method and adaptive proper orthogonal decomposition (APOD) to construct a recursively updated reduced order model (ROM) of the spatiotemporal error dynamics [2], [3]. The ROM is then used as the basis to design the dynamic observer and nonlinear feedback controller for error dynamics regulation. The proposed control structure is successfully applied on shaping the spatiotemporal thermal dynamics in a catalytic reactor.

[1] P. D. CHRISTOFIDES, Nonlinear and robust control of PDE systems, Birkhauser, New York, 2000.  

[2] D. BABAEI POURKARGAR AND A. ARMAOU, Design of APOD-based switching dynamic observers and output feedback control for a class of nonlinear distributed parameter systems, J. Proc. Cont., to appear (2014).

[3] D. BABAEI POURKARGAR AND A. ARMAOU, Modification to adaptive model reduction for regulation of distributed parameter systems with fast transients, AIChE J., 59(12) (2013), pp. 4595–4611.