Robust Control of Linearized Poiseuille Flow

An approach to feedback control of linearized planar Poiseuille flow using H sub( 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 purpose of control design, the flow is modeled as an interconnection of this low-dimensional system and a perturbation, 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.