Optimal and Robust Reduced-Order Feedback Control of Turbulent Channel Flows

Optimal and robust reduced-order feedback control of near-wall turbulence in a channel flow is investigated. Controllers able to analyze distributed measurements and coordinate distributed actuators are considered. Blowing and suction at the wall of the channel are the means for suppressing near-wall disturbances. Measurements of wall-shear stresses to be fed back to the controller are provided by sensors distributed along the wall of the channel. Linear quadratic Gaussian (LQG) design, or, in modern terms, cal H2 design, in conjunction with model reduction techniques is used to derive optimal and robust feedback controllers. The cost of the wall-shear stresses being non-zero and the cost of implementing the controller itself are accounted for by introducing an optimal performance index, or cost function. Optimal controllers robust with respect to disturbances of the process and measurements as well as to system parameter uncertainties are derived. Control design is shown to decouple with respect to wave numbers. Parallel design and parallel computation of the control algorithms are discussed. Implementation of the controllers in practical engineering applications is elaborated. Controllers' performances are tested on direct numerical simulations of turbulent channel flow. Substantial modification of the structure of near-wall turbulence and significant drag reduction are obtained.