Coordinating feedback and switching for control of spatially distributed processes

This work proposes a methodology for coordinating feedback controller synthesis and actuator configuration switching in control of spatially-distributed processes, described by highly dissipative partial differential equations (PDEs) with actuator constraints. Under the assumption that the eigenspectrum of the spatial differential operator can be partitioned into a finite slow set and an infinite stable fast complement, Galerkin’s method is initially used to derive a finite-dimensional system (set of ordinary differential equations (ODEs) in time) that captures the dominant dynamics of the PDE system. Using this ODE system, a stabilizing nonlinear feedback controller is designed, for a given actuator configuration, and an explicit characterization of the corresponding stability region is obtained in terms of the size of actuator constraints and the spatial locations of the actuators. Switching laws are then derived, on the basis of the stability regions, to orchestrate the transition between multiple, spatially-distributed control actuator configurations, in a way that respects actuator constraints, accommodates multiple (possibly conflicting) control objectives and guarantees closed-loop stability. Precise conditions that guarantee stability of the constrained closed-loop PDE system under switching are provided, and the proposed approach is successfully applied to the problem of constrained, fault-tolerant stabilization of unstable steady-states of a representative diffusion-reaction process and a non-isothermal tubular reactor with recycle. # 2003 Elsevier Ltd. All rights reserved.