Feedback control of transitional shear flows: sensor selection for performance recovery

The choice and placement of sensors and actuators is an essential factor determining the performance that can be realized using feedback control. This determination is especially important, but difficult, in the context of controlling transitional flows. The highly non-normal nature of the linearized Navier–Stokes equations makes the flow sensitive to small perturbations, with potentially drastic performance consequences on closed-loop flow control. Full-information controllers, such as the linear quadratic regulator (LQR), have demonstrated some success in reducing transient energy growth and suppressing transition; however, sensor-based output feedback controllers with comparable performance have been difficult to realize. In this study, we propose two methods for sensor selection that enable sensor-based output feedback controllers to recover full-information control performance: one based on a sparse controller synthesis approach, and one based on a balanced truncation procedure for model reduction. Both approaches are investigated within linear and nonlinear simulations of a sub-critical channel flow with blowing and suction actuation at the walls. We find that sensor configurations identified by both approaches allow sensor-based static output feedback LQR controllers to recover full-information LQR control performance, both in reducing transient energy growth and suppressing transition. Further, our results indicate that both the sensor selection methods and the resulting controllers exhibit robustness to Reynolds number variations. Graphic abstract