Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9509597 | Journal of Computational and Applied Mathematics | 2005 | 19 Pages |
Abstract
In this paper, we consider the Kuramoto-Sivashinsky equation (KSE), which describes the long-wave motions of a thin film over a vertical plane. Solution procedures for the KSE often yield a large or infinite-dimensional nonlinear system. We first 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 first- and second-order approximated solutions of the Hamilton-Jacobi-Bellman equation, respectively. Numerical simulations comparing the performance of the reduced-order-based linear and nonlinear controllers are presented.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
C.H. Lee, H.T. Tran,