Integral Action Based Dirichlet Boundary Control of Burgers’ Equation,” to AIAA 2004-0576

Abstract — Modeling and boundary control for Burgers Equa-tion is studied in this paper. Modeling has been done via processing of numerical observations through singular value decomposition with Galerkin projection. This results in a set of spatial basis functions together with a set of Ordinary Differential Equations (ODEs) describing the temporal evolution. Since the dynamics described by Burgers equation is nonlinear, the corre-sponding reduced order dynamics turn out to be nonlinear. The presented analysis explains how boundary condition appears as a control input in the ODEs. The controller design is based on the linearization of the dynamic model. It has been demonstrated that an integral controller, whose gain is a function of the spatial variable, is sufficient to observe reasonably high tracking performance with a high degree of robustness. I