Rotational Stabilization of Cylinder Wakes Using Linear Feedback Control

We demonstrate the feasibility of linear feedback control to stabilize vortex shedding behind twin cylinders using the cylinder rotations. Our approach is to linearize the flow about a desired steady-state flow, use interpolation-based model reduction on the resulting linear model to generate a low-dimensional model of the input-output system with input-independent error bounds, then use this reduced model to design the feedback control law. We then consider the practical issue of limited state measurements by building a nonlinear compensator that is computed from the same linear reduced-order model an constructed through an extended Kalman filter with a proper orthogonal decomposition (POD) model. Closed-loop simulations of the Navier-Stokes equations coupled with controls generated through flow measurements demonstrate the effectiveness of this control strategy.