Robust feedback control of Rayleigh-Benard convection

We investigate the application of linear-quadratic-Gaussian (LQG) feedback control, or, in modern terms, H-2 control, to the stabilization of the no-m otion state against the onset of Rayleigh-Benard convection in an infinite layer of Boussinesq fluid. We use two sensing and actuating methods: the pl anar 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 stat e up to 14.5 times the critical Rayleigh number. We characterize the robust ness of the controller with respect to parameter uncertainties, unmodelled dynamics. Results indicate that the LQG controller provides robust performa nces even at high Rayleigh numbers.