H∞ control for non-periodic planar channel flows

This paper deals with finite-dimensional boundary control of the linearized 2D flow between two infinite parallel planes. Surface transpiration along a few regularly spaced sections of the bottom wall is used to control the flow. Measurements from several discrete, suitably placed shear-stress sensors provide the feedback. Unlike other studies in this area, the flow is not assumed to be periodic, and spatially growing flows are considered. An H_∞ control scheme is designed to guarantee stability for the model set and to reduce the wall-shear stress at the channel wall. This design is tested by simulations with a nonlinear Navier-Stokes PDE solver in the loop. The simulation results show that the controller is effective in reducing shear disturbances