Linear Feedback Control of Boundary Layer Using Electromagnetic Microtiles

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Thispaper presents a system-theory approach to control of a two-dimensionalturbulent flow of saltwater on a flat plate using Lorentzforces produced by microtiles of small magnets and electrodes. Beginningwith 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 obtainedto achieve stabilization of the perturbed flow to the baseflow. It is shown that spatially distributed longitudinal or surface-normalforces stabilize the flow perturbations. However, for lower wave numbers,longitudinal forces are more effective because surface-normal forces require largerelectrode voltages for the same response characteristics. Simulation results arepresented to show how stabilization is accomplished in the closed-loopsystem.


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