Robust control of linearized Poiseuille flow

An approach to feedback control of linearized planar Poiseuille flow using H(infinity) control is developed. Surface transpiration is used to control the flow, and point measurements of the wall shear stress are assumed to monitor its state. A high- but finite-dimensional model is obtained via a Galerkin procedure, and this model is approximated by a low-dimensional one using Hankel-optimal model reduction. For the purposes of control design, the flow is modeled as an interconnection of this low-dimensional system and a perturbations reflecting the uncertainty in the model. The goal of control design is to achieve robust stability, that is, to stabilize any combination of the nominal plant and a feasible perturbation, and to satisfy certain performance requirements. Two different types of surface actuation are considered, harmonic transpiration and a model of a pair of suction/blowing panels. It is found that the latter is more efficient in suppressing disturbances in terms of the control effort required.