Rotationary feedback control of the cylinder wake flow using a linear dynamic model

This study presents an active feedback control of the Kármán vortex shedding flow past a circular cylinder at low Reynolds numbers. The cylinder's rotational motion functions as the control actuator, while the transverse velocities of points along the wake axis serve as the feedback signals. First, using the autoregressive with exogenous input method, a linear reduced-order model (ROM) for the unstable flow is developed to capture the input-output behavior between the cylinder's rotational displacement and the feedback signals. This model is then utilized for controller design using the proportional and linear quadratic regulator (LQR) control methods, respectively, with their effectiveness analyzed and validated through high-fidelity numerical simulations. The results show that both methods can effectively suppress the unstable vortex shedding flow, while proportional control exhibits strong sensitivity to monitoring point locations and time delays. The ROM-based model can accurately predict the stability characteristics of the control system, providing valuable guidance for selecting optimal feedback signals. Moreover, we show that by appropriately adjusting the phase angle between the control input and feedback signals via time delays, the performance of proportional control can be significantly enhanced. Lastly, based on the ROM, an output-feedback suboptimal control law is designed using the LQR method. This suboptimal feedback control transforms unstable fluid modes into stable ones, resulting in complete suppression of the unsteady vortex shedding. It is further revealed that the inherent mechanism of suboptimal flow control is to construct an optimal phase shift through the linear superposition of multiple feedback signals. Overall, model-based analysis results agree well with those obtained from direct numerical simulations, confirming the validity of the proposed ROM-based feedback control procedure.