Feedback stabilisation of a two-dimensional pool-boiling system by modal control

The present study concerns the feedback stabilisation of the unstable equilibria of a two-dimensional nonlinear pool-boiling system with essentially heterogeneous temperature distributions in the fluid-heater interface. Regulation of such equilibria has great potential for application in, for instance, micro-electronics cooling. Here, as a first step, stabilisation of these equilibria is considered. To this end, a control law is designed that regulates the heat supply to the heater as a function of the Fourier–Chebyshev modes of its internal temperature distribution. These modes are intimately related to the physical eigenmodes of the system and thus admit robust and efficient regulation on the basis of the natural composition of the temperature field. Key to this modal-control strategy and its application for controller design are an interchangeable PDE form and state-space form of the linearised model. Derivation of these forms is a central theme of this study. Performance of modal controllers thus designed is demonstrated and analysed by simulations of the nonlinear closed-loop system.