Feedback stabilization of vortex position near a deformable foil in a uniform flow using camber control

This paper presents a feedback control design that stabilizes the position of a drifting vortex in a freestream over a deformable Joukowski foil using camber control. We derive the dynamics of a point vortex in flow around a Joukowski foil using a potential flow model and provide numerical analysis of the number, stability, and controllability of open-loop equilibrium points of the vortex-foil system. We show that the position of a point vortex can effectively be stabilized using a full-state feedback camber control law while maintaining the validity of the dynamics model. We present sample stable and unstable trajectories found using closed-loop control along with a visualization of the region of convergence.