Nonlinear feedback control of the wake past a plate with a suction point on the downstream wall

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Abstract
Active circulation control of the two-dimensional unsteady separated flow past a plate with a suction point on the downstream wall is considered. The rolling-up of the separated shear layer is modelled by a pair of point vortices whose time-dependent circulation is predicted by an unsteady Kutta condition. A nonlinear controller able to confine the wake to a single vortex pair of constant circulation is derived in closed form for any free-stream condition. Dynamical system analysis is used to explore the performance of the controlled system. Finally, the control strategy is applied to three different classes of unsteady flows and the results are discussed.