Design of poiseuille flow controllers using the method of inequalities

摘要

This paper investigates the use of the method of inequalities (MoI) to designoutput-feedback compensators for the problem of the control of instabilities ina laminar plane Poiseuille flow. In common with many flows, the dynamics ofstreamwise vortices in plane Poiseuille flow are very non-normal. Consequently,small perturbations grow rapidly with a large transient that may triggernonlinearities and lead to turbulence even though such perturbations would, in alinear flow model, eventually decay. Such a system can be described as aconditionally linear system. The sensitivity is measured using the maximumtransient energy growth, which is widely used in the fluid dynamics community.The paper considers two approaches. In the first approach, the MoI is used todesign low-order proportional and proportional-integral (PI) controllers. In thesecond one, the MoI is combined with McFarlane and Glover’s H ∞ loop-shapingdesign procedure in a mixed-optimization appro