Reduced-order feedback control for liquid film flows

In this paper, we consider the Kuramoto-Sivashinsky (KS) equation, which describes the long-wave motions of a thin lm over a vertical plane. Solution procedures for the KSE often yield a large or in nite dimensional nonlinear system. We rst discuss two reduced-order methods, the Approximate Inertial Manifold and the Proper Orthogonal Decomposition, and show that these methods can be used to obtain a reduced-order system that can accurately describe the dynamics of the KSE. Moreover, from this resulting reduced-order system, the feedback controller can readily be designed and synthesized. For our control techniques, we use the linear and nonlinear quadratic regulator methods, which are the rstand second-order approximated solutions of the Hamilton-Jacobi-Bellman equation, respectively. Comparisons for the numerical solutions of the controlled problem, as well as, the robustness of the nonlinear controller are presented. submitted to: Journal of Computational and Applied Mathematics