Reducing transient energy growth in a channel flow using static output feedback control

TL;DR

This paper develops static output feedback controllers using SOF-LQR to effectively reduce transient energy growth in channel flows, delaying laminar-turbulent transition and demonstrating robustness in simulations.

Contribution

It introduces a modified Anderson-Moore algorithm for designing static output feedback controllers that improve transient energy growth suppression in flow control.

Findings

SOF-LQR controllers reduce worst-case transient energy growth.

Controllers increase laminar transition thresholds under streamwise disturbances.

Robustness to Reynolds number variations is demonstrated.

Abstract

Transient energy growth of flow perturbations is an important mechanism for laminar-to-turbulent transition that can be mitigated with feedback control. Linear quadratic optimal control strategies have shown some success in reducing transient energy growth and suppressing transition, but acceptable worst-case performance can be difficult to achieve using sensor-based output feedback control. In this study, we investigate static output feedback controllers for reducing transient energy growth of flow perturbations within linear and nonlinear simulations of a sub-critical channel flow. A static output feedback linear quadratic regulator~(SOF-LQR) is designed to reduce the worst-case transient energy growth due to flow perturbations. The controller directly uses wall-based measurements to optimally regulate the flow with wall-normal blowing and suction from the upper and lower channel walls. Optimal static output feedback gains are computed using a modified Anderson-Moore algorithm that accelerates the iterative solution of the synthesis problem by leveraging Armijo-type adaptations. We show that SOF-LQR controllers can reduce the worst-case transient energy growth due to flow perturbations. Our results also indicate that SOF-LQR controllers exhibit robustness to Reynolds number variations. Further, direct numerical simulations show that the designed SOF-LQR controllers increase laminar-to-turbulent transition thresholds under streamwise disturbances and delay transition under spanwise disturbances. The results of this study highlight the advantages of SOF-LQR controllers and create opportunities for realizing improved transition control strategies in the future.