Optimal actuator selection for flow control based on empirical data

Actuator selection plays a central role in the efficacy and achievable performance of fluid flow control in practice. Here, we present a systems-theoretic approach for determining the optimal actuator location—among a set of candidate locations—for driving the flow to an arbitrary state with minimal input energy. The method only requires access to empirical data of the flow response to actuation—obtained either from numerical simulations or experiments—and is applicable in the context of stable and unstable flows alike. We use the approach to study optimal actuator selection for separation control using data gathered from high-fidelity numerical fluids simulations of a NACA 65(1)-412 airfoil. Specifically, data of lift and separation-angle responses to localized body-force actuation are used to determine the optimal actuator location on the upper-surface of the airfoil. We find that the optimal location for controlling lift differs from that for controlling separation angle. Further, when feedback separation control is being considered, our results suggest that performance can be improved by adopting separation-angle-tracking controllers over more conventional lift-tracking strategies.