Feedback Control of Linear Turbulence Using Electromagnetic Microtiles.

摘要

A small, axisymmetric body with numerous millimeter-scale microtiles embedded with thin arrays of magnets and electrodes has been designed and built at the Naval Undersea Warfare Center Division, Newport, Rl. For sea water turbulence control at high Reynolds numbers, these microtiles produce Lorentz forces of preferred orientation by crossing electric and magnetic fields. This report presents a system-theory approach to control of a two-dimensional flow on a flat plate using Lorentz forces produced by these microtiles. 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.