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Input-output analysis, model reduction and control of the flat-plate boundary layer. (English) Zbl 1156.76374
Summary: The dynamics and control of two-dimensional disturbances in the spatially evolving boundary layer on a flat plate are investigated from an input-output viewpoint. A set-up of spatially localized inputs (external disturbances and actuators) and outputs (objective functions and sensors) is introduced for the control design of convectively unstable flow configurations. From the linearized Navier-Stokes equations with the inputs and outputs, controllable, observable and balanced modes are extracted using the snapshot method. A balanced reduced-order model (ROM) is constructed and shown to capture the input-output behaviour of the linearized Navier-Stokes equations. This model is finally used to design a \(\mathcal H_2\)-feedback controller to suppress the growth of two-dimensional perturbations inside the boundary layer.

MSC:
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76D55 Flow control and optimization for incompressible viscous fluids
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