Feedback control of a circular cylinder wake with rotational oscillation

Abstract

A new feedback control algorithm for controlling vortex shedding from a circular cylinder in a uniform flow is proposed and tested. The lift coefficient (C(L)) is employed as a feedback signal and the control forcing is given by a rotational oscillation of the cylinder. A fractional form of the transfer function for the controller is designed, into which the interaction of the phase and magnitude of the controller is fully incorporated. In the proposed feedback control algorithm, the main emphasis is placed on controlling the phase of the feedback signal. When the feedback control forcing is imposed 'out of phase' with the response (i.e. outside the range of lock-on), the response is significantly reduced. In contrast, the response is increased when the feedback forcing is imposed in an 'in phase' manner. The effect of the feedback signal phase is ascertained by calculations using the Van der Pol oscillator, and the feedback control process is analyzed in terms of energy transfer between an actuator and an oscillator. Based on the analysis, the proposed feedback control method is applied to the wake behind a circular cylinder. The mechanism by which C(L) is reduced is delineated by examining the vortex formation modes as a function of the forcing phase.