Revisiting the separation principle for improved transition control

Abstract

Feedback control can be used to suppress transient energy growth and delay turbulent transition in shear flows. The separation principle of modern control theory is commonly invoked to design observer-based control laws, whereby a full-state feedback controller and a state estimator are designed independently, then combined to achieve an output feedback flow control law. In previous work, we established that transient energy growth can never be fully eliminated by observer-based control, even when an associated full-state feedback law can fully suppress such growth. In this paper, we use a linearized channel flow to show that observer-based feedback will lead to higher levels of transient energy growth than if no control is used at all. Further, we show that transient energy growth can actually be reduced via optimal static output feedback controllers, thus overcoming the performance limitations of observer-based designs. We introduce a modified AndersonMoore algorithm for efficiently computing optimal static output feedback controllers, then show that the resulting controllers reduce the worst-case transient energy growth relative to the uncontrolled system and to observer-based designs. Further, our results indicate that optimal static output feedback exhibits robustness to Reynolds number variations and modeling uncertainty. The result of this study highlight the advantages of optimal static output feedback control over observer-based designs and create opportunities for realizing improved transition control strategies in the future.