Feedback control of transitional channel flow using Balanced Proper Orthogonal Decomposition

Reduced-order models of linearized channel flow are used to develop closed-loop controllers which are then applied to full nonlinear direct numerical simulations of the flow. The models are computed using Balanced Proper Orthogonal Decomposition (BPOD), which has been shown to yield models which capture well the input/output behavior of linear perturbations in transitional flow. We investigate the control of disturbances us- ing either localized body force or wall blowing and suction as actuation. We introduce a method of treating the inhomogeneous boundary conditions in computing the simulation snapshots for BPOD, based on regularizing the inhomogeneous particular solution which arises in the standard lifting approach for wall blowing and suction. For localized body force actuation, the closed-loop controller is able to prevent the transition to turbulence for initial perturbation amplitudes which in the uncontrolled case transition due to linear non-normal growth. Energy growth reduction for an optimal perturbation at a low Reynolds number using a model-based controller and sinusoidal wall blowing and suction in the streamwise direction as actuation is also demonstrated.