Control Law Design for Channel Flow - 2D Designs and 3D Performance Evaluation

The systems dealt with in flow control problems are, in control terms, very complex, nonlinear and infinite dimensional, even if the fluid flow is comparatively simple. Plane Poiseuille flow, i.e. flow between two infinite parallel plates is one of the simplest and best understood cases of fluid dynamics. Controlling this flow is, however, still a very challenging problem, even if it is assumed that deviations from the steady-state are small enough for the governing equations to be linearized. Recent work has shown that robust control of 2D channel flow is possible without a spatial periodicity assumption. This paper will first execute an H∞ based robust control law design for the 2D case and then proceed to the relatively open problem of assessing the resulting performance using a Navier Stokes CFD solver as a model of the 'real' process. The results in this second part will be on the representation (to ensure realistic results) and modelling of the disturbances used and the control of 3D disturbances.