Positive feedback control of Rayleigh-Bénard convection
B. A. Wagner - Weierstrass-Institute for Applied Analysis and Stochastics, Mohrenstr. 39 D-10117 Berlin, Germany (email)
Abstract: We consider the problem of active feedback control of Rayleigh-Bénard convection via shadowgraphic measurement. Our theoretical studies show, that when the feedback control is positive, i.e. is tuned to advance the onset of convection, there is a critical threshold beyond which the system becomes linearly ill-posed so that short-scale disturbances are greatly amplified. Experimental observation suggests that finite size effects become important and we develop a theory to explain these contributions. As an efficient modelling tool for studying the dynamics of such a controlled pattern forming system, we use a Galerkin approximation to derive a dimension reduced model.
Keywords: Galerkin projection, control, Rayleigh-Bénard convection, illposedness.
Received: December 2002; Revised: May 2003; Available Online: August 2003.
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