Integral action based Dirichlet boundary control of Burgers equation

Modeling and boundary control for the Burgers equation 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 corresponding 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.