This paper deals with finite-dimensional boundary control of the two-dimensional (2-D) 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. Using spatial discretization in the streamwise direction, frequency responses for a relevant part of the channel are obtained. A low-order model is fitted to these data and the modeling uncertainty is estimated. An controller is designed to guarantee stability for the model set and to reduce the wall-shear stress at the channel wall. A nonlinear Navier-Stokes PDE solver was used to test the designs in the loop. The only assumption made in these simulations is that the flow is two dimensional. The results showed that, although the problem was linearized when designing the controller, the controller could significantly reduce fundamental 2-D disturbances in practice. Index Terms-control, flow control, model validation, nonperiodic flows. I. INTRODUCTION F LOW control is currently attracting considerable interest in the fluids research community. A major motivation for this is the possibility of reducing drag on a body by preventing or delaying transition from laminar to turbulent flow. The systems dealt with in these problems are, in control terms, very complex, nonlinear, and infinite dimensional, even if, in fluid mechanical terms, the structure of the flow field is simple in nature. Plane Poiseuille flow, i.e., flow between two infinite parallel plates is one of the simplest and best understood cases of fluid dynamics. Controlling this flow is, however, still an extremely challenging problem, even if it is assumed that deviations from the steady state are small enough for the governing equations to be linearized. It has become a benchmark problem for developing control algorithms for fluid flows and was considered in [4], [6], [9], [14]-[16] among others. All these references make a fundamental assumption that the flow is spatially periodic in the streamwise direction, and hence that a Fourier-Galerkin decomposition can be used to obtain independent dynamics for Manuscript
