  This paper concerns feedback stabilization of point vortex equilibria above
an inclined thin plate and a three-plate configuration known as the Kasper Wing
in the presence of an oncoming uniform flow. The flow is assumed to be
potential and is modeled by the 2D incompressible Euler equations. Actuation
has the form of blowing and suction localized on the main plate and is
represented in terms of a sink-source singularity, whereas measurement of
pressure across the plate serves as system output. We focus on point-vortex
equilibria forming a one-parameter family with locus approaching the trailing
edge of the main plate and show that these equilibria are either unstable or
neutrally stable. Using methods of linear control theory we find that the
system dynamics linearised around these equilibria are both controllable and
observable for almost all actuator and sensor locations. The design of the
feedback control is based on the Linear-Quadratic-Gaussian (LQG) compensator.
Computational results demonstrate the effectiveness of this control and the key
finding is that Kasper Wing configurations are in general more controllable
than their single plate counterparts and also exhibit larger basins of
attraction under LQG feedback control. The feedback control is then applied to
systems with additional perturbations added to the flow in the form of random
fluctuations of the angle of attack and a vorticity shedding mechanism. Another
important observation is that, in the presence of these additional
perturbations, the control remains robust, provided the system does not deviate
too far from its original state. Furthermore, introducing a vorticity shedding
mechanism tends to enhance the effectiveness of the control. Physical
interpretation is provided for the results of the controllability and
observability analysis as well as the response of the feedback control to
different perturbations.
