Feedback Control of Parabolic PDE Systems

Abstract

In Chapters 2 and 3, we presented nonlinear and robust control methods for systems of first-order hyperbolic PDEs. In the remainder of this book, we focus our attention on nonlinear and robust control of parabolic PDE systems. Such systems arise naturally in the modeling of transport-reaction processes with significant diffusive and dispersive mechanisms (e.g., packed-bed reactors, rapid thermal processing systems, chemical vapor deposition reactors, etc.). In contrast to hyperbolic PDEs, the main feature of parabolic PDEs is that the eigenspectrum of the spatial differential operator can be partitioned into a finite-dimensional slow one and an infinite-dimensional stable fast complement [65, 12, 133]. This motivates addressing the controller synthesis problem for parabolic PDEs on the basis of finite-dimensional systems that accurately describe their dynamic behaviorKeywordsFast SubsystemNonlinear ControllerOutput Feedback ControllerUnstable Steady StateApproximate Inertial ManifoldThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.