Spatiotemporal response shaping of transport-reaction processes via adaptive reduced order models

We present a framework to address the dynamic response shaping question of nonlinear transport-reaction chemical processes. The spatiotemporal behavior of such processes can be described in the form of dissipative partial differential equations (PDEs), the modal infinite-dimensional representation of which can in principle be partitioned into two subsystems; a finite-dimensional slow and its complement infinite-dimensional fast and stable subsystem. The dynamic shaping problem is addressed via regulation of error dynamics between the process and a desired spatiotemporal behavior presented by a target PDE system. We approximate the infinite-dimensional nature of the systems via model order reduction; adaptive proper orthogonal decomposition (APOD) is used to compute and recursively update the set of empirical basis functions required by Galerkin projection to build switching reduced order models of the spatiotemporal dynamics. Then, the nonlinear output feedback control design is formulated by combination of a feedback control law and a nonlinear Luenberger type dynamic observer to regulate the error dynamics. The effectiveness of the proposed control approach is demonstrated on shaping the thermal dynamics of an exothermic reaction in a catalytic chemical reactor.

[1]  Antonios Armaou,et al.  Finite-dimensional control of nonlinear parabolic PDE systems with time-dependent spatial domains using empirical eigenfunctions , 2001 .

[2]  Davood Babaei Pourkargar,et al.  Dynamic shaping of transport–reaction processes with a combined sliding mode controller and Luenberger-type dynamic observer design , 2015 .

[3]  Miroslav Krstic,et al.  On control design for PDEs with space-dependent diffusivity or time-dependent reactivity , 2005, Autom..

[4]  Hans Zwart,et al.  An Introduction to Infinite-Dimensional Linear Systems Theory , 1995, Texts in Applied Mathematics.

[5]  Davood Babaei Pourkargar,et al.  Control of spatially distributed processes with unknown transport‐reaction parameters via two layer system adaptations , 2015 .

[6]  Davood Babaei Pourkargar,et al.  APOD‐based control of linear distributed parameter systems under sensor/controller communication bandwidth limitations , 2015 .

[7]  M. Balas.  FEEDBACK CONTROL OF LINEAR DIFFUSION PROCESSES , 1979 .

[8]  Panagiotis D. Christofides,et al.  Distributed nonlinear control of diffusion-reaction processes , 2003, Proceedings of the 2003 American Control Conference, 2003..

[9]  Antonios Armaou,et al.  Output Feedback Control of Distributed Parameter Systems Using Adaptive Proper Orthogonal Decomposition , 2010 .

[10]  Michael A. Demetriou,et al.  Compensation of spatiotemporally varying disturbances in nonlinear transport processes via actuator scheduling , 2004 .

[11]  Davood Babaei Pourkargar,et al.  Modification to adaptive model reduction for regulation of distributed parameter systems with fast transients , 2013 .

[12]  Stevan Dubljevic,et al.  Optimal boundary control of a diffusion–convection-reaction PDE model with time-dependent spatial domain: Czochralski crystal growth process , 2012 .

[13]  P. Christofides,et al.  Plasma enhanced chemical vapor deposition: Modeling and control , 1999 .

[14]  Panagiotis D. Christofides,et al.  Nonlinear and Robust Control of Pde Systems , 2001 .

[15]  P. Christofides,et al.  Global stabilization of the Kuramoto–Sivashinsky equation via distributed output feedback control , 2000 .

[16]  Panagiotis D. Christofides,et al.  Distributed nonlinear control of diffusion-reaction processes , 2004 .

[17]  Davood Babaei Pourkargar,et al.  Geometric output tracking of nonlinear distributed parameter systems via adaptive model reduction , 2014 .

[18]  L. Sirovich.  Turbulence and the dynamics of coherent structures. I. Coherent structures , 1987 .

[19]  A. Armaou,et al.  Design of APOD-based switching dynamic observers and output feedback control for a class of nonlinear distributed parameter systems , 2015 .