Linear Feedback Control of Boundary Layer Using Electromagnetic Microtiles

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Abstract
This paper presents a system-theory approach to control of a two-dimensional turbulent flow of saltwater on a flat plate using Lorentz forces produced by microtiles of small magnets and electrodes. Beginning with the two-dimensional Navier-Stokes equations of motion, a finite, dimensional, linear state variable, approximate model is obtained using Galerkin’s procedure. Based on this model, linear feedback control laws are obtained to achieve stabilization of the perturbed flow to the base flow. It is shown that spatially distributed longitudinal or surface-normal forces stabilize the flow perturbations. However, for lower wave numbers, longitudinal forces are more effective because surface-normal forces require larger electrode voltages for the same response characteristics. Simulation results are presented to show how stabilization is accomplished in the closed-loop system.