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Robust feedback control of Rayleigh–Bénard convection

Published online by Cambridge University Press:  22 June 2001

A. C. OR ,
L. CORTELEZZI  and
J. L. SPEYER
A. C. OR
Affiliation:
Department of Mechanical & Aerospace Engineering, University of California, Los Angeles, CA 90095-1597, USA
L. CORTELEZZI
Affiliation:
Department of Mechanical Engineering, McGill University, Montreal, Canada H3A 2K6
J. L. SPEYER
Affiliation:
Department of Mechanical & Aerospace Engineering, University of California, Los Angeles, CA 90095-1597, USA
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Abstract

We investigate the application of linear-quadratic-Gaussian (LQG) feedback control, or, in modern terms, [Hscr ]2 control, to the stabilization of the no-motion state against the onset of Rayleigh–Bénard convection in an infinite layer of Boussinesq fluid. We use two sensing and actuating methods: the planar sensor model (Tang & Bau 1993, 1994), and the shadowgraph model (Howle 1997a). By extending the planar sensor model to the multi-sensor case, it is shown that a LQG controller is capable of stabilizing the no-motion state up to 14.5 times the critical Rayleigh number. We characterize the robustness of the controller with respect to parameter uncertainties, unmodelled dynamics. Results indicate that the LQG controller provides robust performances even at high Rayleigh numbers.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 437 , 25 June 2001 , pp. 175 - 202
Copyright
© 2001 Cambridge University Press

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