Robust control of parabolic PDE systems

This article proposes a methodology for the synthesis of nonlinear robust feedback. controllers for diffusion-convection-reaction processes with time-varying uncertain variables described by systems of quasi-linear parabolic partial differential equations (PDEs), for which the eigenspectrum of the spatial differential operator can be partitioned into a finite-dimensional (possibly unstable) slow one and an infinite-dimensional stable fast complement. Combination of Galerkin's method with approximate inertial manifolds is used to derive ordinary differential equation (ODE) systems of dimension equal to the number of slow modes that accurately describe the dominant dynamics of the PDE system. These ODE systems are used for the synthesis of robust controllers that guarantee boundedness of the state and output tracking with arbitrary degree of asymptotic attenuation of the effect of the uncertain variables on the output of the closed-loop system. The robust controllers are synthesized via Lyapunov's direct method and utilize bounding functions on the magnitude of the uncertain terms. The developed methodology is successfully applied to a catalytic packed-bed reactor with unknown heat of reaction. (C) 1998 Elsevier Science Ltd. All rights reserved.