A PID Control of Flow Over a Circular Cylinder

In the present study, we apply proportional-integral-differential (PID) feedback controls to flow over a circular cylinder for suppression of vortex shedding in the wake. The transverse velocity at a centerline location in the wake is measured and used for the feedback control. The actuation (blowing/suction) is provided to the flow at the upper and lower slots on the cylinder surface near the separation point based on the P, PI or PD control. The sensing location is varied from 1d to 4d from the center of the cylinder. Given each sensing location, the optimal proportional gain in the sense of minimizing the sensing velocity fluctuations is obtained for the P control. The P control significantly reduces the fluctuations of the sensing velocity at certain sensing positions that is called the effective sensing region. The additions of I and D controls to the P control increase the control performance and broaden the effective sensing location. The P, PI and PD controls significantly reduce the velocity fluctuations and attenuate vortex shedding in the wake, resulting in the reductions in the mean drag and lift fluctuations.