Cylinder wake stabilization using a minimal energy compensator

In the present work a linear feedback control strategy is used to control and suppress the cylinder vortex- shedding at low Reynolds numbers. The classical minimal control energy or small gain solution of the optimal control and estimation problems is exploited in order to design a full-dimensional stabilizing com- pensator of the linearized Navier–Stokes equations. Both feedback and observer gains are efficiently com- puted based solely on the knowledge of the unstable adjoint and direct global modes, respectively. In our control setup, actuation is realized by means of angular oscillations of the cylinder surface while a single velocity sensor is employed for the state estimate. The derived compensator is shown to be able to drive the flow from the natural limit cycle to the unstable steady state which is finally restored. Then the sensitivity of the control performance to sensor placement and Reynolds number is investigated.