LINEAR FEEDBACK-CONTROL OF BOUNDARY-LAYER USING ELECTROMAGNETIC MICROTILES

This paper presents a system-theory approach to control of a two-dimen sional turbulent flow of saltwater on a flat plate using Lorentz force s produced by microtiles of small magnets and electrodes. Beginning wi th the two-dimensional Navier-Stokes equations of motion, a finite, di mensional, linear state variable, approximate model is obtained using Galerkin's procedure. Based on this model, linear feedback control law s are obtained to achieve stabilization of the perturbed flow to the b ase flow. It is shown that spatially distributed longitudinal or surfa ce-normal forces stabilize the flow perturbations. However, for lower wave numbers, longitudinal forces are more effective because surface-n ormal forces require larger electrode voltages for the same response c haracteristics. Simulation results are presented to show how stabiliza tion is accomplished in the closed-loop system.