Quasi-periodic behavior of closed-loop control in convective flows

Closed-loop control of convective flows, arranged in a feedback configuration (sensors downstream of the actuators), can usually be made to establish a quasi-periodic behavior when the actuation creates a perturbation of an order one magnitude. Many studies have shown a tendency of the controller to establish this quasi-periodicity at or near the local natural frequency of the flow (at sensor location). In this presentation, we will discuss whether this is by design or by chance. We will show how convective times and amplification properties of shear layers (as an example of convective flows) can modify this quasi-periodic cycle of the feedback controller, sometimes to values very far from the natural local frequency. This can be either an advantage or a difficulty, if the objective of control depends on a precise frequency selection (as is usually the case). We will also propose an analogy between the feedback control of a free mixing layer and a mixing layer flowing over a passive cavity of given properties.