Optimal and robust control and estimation of linear paths to transition

Optimal and robust control theories are used to determine effective, estimator-based feedback control rules for laminar plane channel flows that effectively stabilize linearly unstable flow perturbations at Re = 10000 and linearly stable flow perturbations, characterized by mechanisms for very large disturbance amplification, at Re = 5000. Wall transpiration (unsteady blowing/suction) with zero net mass flux is used as the control, and the flow measurement is derived from the wall skin friction. The control objective, beyond simply stabilizing any unstable eigenvalues (which is relatively easy to accomplish), is to minimize the energy of the flow perturbations created by external disturbance forcing. This is important because, when mechanisms for large disturbance amplification are present, small-amplitude external disturbance forcing may excite flow perturbations with sufficiently large amplitude to induce nonlinear flow instability. The control algorithms used in the present work account for system disturbances and measurement noise in a rigorous fashion by application of modern linear control techniques to the discretized linear stability problem

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