Stabilizing a CFD model of an unstable system through model reduction

We demonstate stabilization of a computational ‡uid dynamics model of an unstable system. The unstable heating of a two-dimensional plate is used as a case study. Active control is introduced by cooling parts of the boundaries of the plate. The high order of the original model is reduced by proper orthogonal decomposition, giving an unstable reduced order model with a state space structure convenient for controller design. A stabilizing controller based on pole placement is designed for the reduced order model and integral action is included to enhance performance. The controller is then applied to the full model, where it is shown through simulations to stabilize the system. The demonstrated procedure makes it possible to analyze stability properties and design control systems for a class of systems that would otherwise be very computationally demanding.