Passive control design for distributed process systems: Theory and applications

Abstract

A recently developed theory linking passivity with the second law of thermodynamics was used to develop a robust control design methodology for process systems with states distributed in time and space. Asymptotic stabilization of the infinite dimensional state thus can be accomplished for convection–diffusion processes with nonlinear production terms. Two examples representative of these phenomena were considered: chemical reactors and thermal treatments induced by electromagnetic fields. The first case shows how mixing and reactor size are critical control design parameters. If mixing is complete, at least in some direction, exponential stabilization can be achieved by high gain control. If not, stabilization is still possible for reaction domains smaller than a critical volume. In the second case, the electromagnetic field power supplied can always be manipulated to preserve passivity for any domain size. Two important consequences are that the infinite dimensional state can be reconstructed at arbitrary precision by robust observers and that control of the energy inventory will suffice to provide asymptotic stabilization. Theoretical justification of these findings is given on a general framework and illustrated through simulation experiments