Input–output analysis, model reduction and control of the flat-plate boundary layer

Abstract

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 a2-feedback controller to suppress the growth of two-dimensional perturbations inside the boundary layer.