Linear feedback stabilization of laminar vortex shedding based on a point vortex model

In this paper we use the Föppl point vortex system as a reduced-order model for stabilization of the steady symmetric solution in an unstable laminar wake. The downstream location of the Föppl vortices is chosen so as to produce the same recirculation length as in the actual flow at a given Reynolds number. When the cylinder rotation is used as flow actuation, the linearized Föppl system is shown to be stabilizable, but not controllable. With centerline velocity measurements as the system output, the linearized Föppl model is also shown to be fully observable. The Linear-Quadratic-Gaussian (LQG) control design is performed based on the linearized Föppl system which has only four degrees of freedom. Computational results show that thus designed LQG compensator stabilizes the stationary solution of the nonlinear Föppl system. When applied to an actual cylinder wake at Re=75, the LQG compensator stabilizes the downstream region of the flow. Possibilities and limitations of flow control strategies based on point vortex systems as reduced-order models are discussed.