Design of Poiseuille Flow Controllers Using the Method of Inequalities

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