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      Integral action based Dirichlet boundary control of Burgers equation

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      Author
      Efe, M. Ö.
      Özbay, Hitay
      Date
      2003
      Source Title
      Proceedings of the IEEE Conference on Control Applications, CCA 2003
      Publisher
      IEEE
      Pages
      1267 - 1272
      Language
      English
      Type
      Conference Paper
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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 conditions
      Control 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
      Permalink
      http://hdl.handle.net/11693/27505
      Published Version (Please cite this version)
      https://doi.org/10.1109/CCA.2003.1223193
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      • Department of Electrical and Electronics Engineering 3597
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