Feedback control of a thermal fluid using state estimation

In this paper we consider the problem of designing a feedback controller for a thermal fluid. Any practical feedback controller for a fluid flow system must incorporate some type of state estimator, Moreover, regardless of the approach, one must introduce approximations at some point in the analysis. The method presented here uses distributed parameter control theory to guide the design and approximation of practical state estimators. We use finite element techniques to approximate optimal infinite dimensional controllers based on linear quadratic Gaussian (LQG) and MinMax theory for the Boussinesq equations. These designs are then compared to full state feedback, We present several numerical experiments and we describe how these techniques can also be applied to sensor placement problems.