Integral action based Dirichlet boundary control of Burgers equation
Author
Efe, M. Ö.
Özbay, Hitay
Date
2003Source Title
Proceedings of the IEEE Conference on Control Applications, CCA 2003
Publisher
IEEE
Pages
1267 - 1272
Language
English
Type
Conference PaperItem Usage Stats
169
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Abstract
Modeling and boundary control for 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.
Keywords
Boundary conditionsControl system synthesis
Gain measurement
Galerkin methods
Integral equations
Linearization
Mathematical models
Ordinary differential equations
Performance
Robustness
Burgers equation
Dirichlet boundary control
Singular value decomposition
Control theory