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Nonlinear Flow Control Based on a Low Dimensional Model of Fluid Flow

  • Rudibert King
  • Meline Seibold
  • Oliver Lehmann
  • Bernd. R. Noack
  • Marek Morzyński
  • Gilead Tadmor
Chapter
Part of the Lecture Notes in Control and Information Science book series (LNCIS, volume 322)

Abstract

Nonlinear control design is shown to be a critical enabler for robust model-based suppression of a flow instability. The onset of oscillatory vortex shedding is chosen as a well investigated benchmark problem of flow control. A low-dimensional Galerkin model using a Karhunen-Lo‘eve decomposition of the flow field is adopted from earlier studies of the authors as a control-oriented fluid flow representation. Several strategies of nonlinear controller design are employed, both, to the Galerkin model and to the flow via a direct numerical simulation of the Navier- Stokes equations (NSE). The aim is to find methods which respect the validity of low order models. Examples are formal methods such as input-output linearization, Lyapunov-based, backstepping controllers etc., and physically motivated controllers. Whereas the first test-bed is easily mastered by the formal methods, the application to the NSE is more critical, due to robustness issues.

Keywords: Flow control, Navier-Stokes equation, nonlinear control, Galerkin model, cylinder wake.

Keywords

Turbulent Kinetic Energy Direct Numerical Simulation Proper Orthogonal Decomposition Vortex Street Galerkin Approximation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Authors and Affiliations

  • Rudibert King
    • 1
  • Meline Seibold
    • 1
  • Oliver Lehmann
    • 1
    • 2
  • Bernd. R. Noack
    • 2
  • Marek Morzyński
    • 3
  • Gilead Tadmor
    • 4
  1. 1.Measurement and Control Group, Berlin University of TechnologyGermany
  2. 2.Hermann-Föttinger-Institut, Berlin University of TechnologyGermany
  3. 3.Institute of Combustion Engines and Transportation, Poznań University of TechnologyPoland
  4. 4.Department of Electrical and Computer Engineering, Northeastern University, BostonUSA.

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