Amplitude control of bifurcations and application to Rayleigh-Benard convection
Bifurcation control deals with the modification of the bifurcation characteristics of a parameterized nonlinear system by a judiciously designed control input. In this paper, we focus on the problem of controlling the amplitude of bifurcated solutions. It is shown that the amplitude of the bifurcated solutions is directly related to the so-called bifurcation stability coefficient. The bifurcation amplitude control is applied to the active control of Rayleigh-Benard convection. Cubic feedback control laws are designed to suppress the convection amplitude. From the mathematical analysis of the governing partial differential equations, two (spatially) distributed cubic control laws, one in pseudo-spectral coordinates and one in physical spatial coordinates, are proposed. Simulation results demonstrate that both are able to suppress the convection amplitude. A composite bifurcation control law combining a linear control law and a cubic control law is considered to be most effective and flexible for this problem. Experimental investigations are ongoing to accompany the theoretical findings.
