Static output feedback strategies for suppressing transient energy growth in channel flow

Transient energy growth (TEG) of disturbances can lead a laminar flow to become turbulent. Full-state feedback control can be used to suppress TEG and has been shown to delay transition in simulations. However, full-state feedback is not always possible in practical applications; instead, sensor-based output feedback is required. In this study, we consider a linearized channel flow with wall-normal blowing/suction actuation and wall shear-stress sensors. We find that widely used observer-based feedback controllers will lead to severely degraded worst-case TEG performance, even relative to the uncontrolled flow. An optimal static output feedback (SOF) approach is proposed, which is shown to reduce TEG in the case of purely spanwise disturbances. We further show that by introducing a small number of additional sensors, the optimal SOF approach can recover full-state feedback performance and reduce TEG for all disturbances.