An LPV gain scheduling approach to transition control in plane Poiseuille flow

This paper presents the synthesis of a gain scheduled controller - parameterized by the Reynolds number - for transition control in plane Poiseuille flow. In a real system, the Reynolds number is time-varying - it changes with the speed of flow. The problem considered here is to prevent the transition from laminar to turbulent flow at the very onset of turbulence, when the velocity of flow is changing with time. For this problem a gain scheduled controller, parameterized by the Reynolds number, is proposed. A linear parameter-varying (LPV) model of plane Poiseuille flow parameterized by the time-varying Reynolds number is first obtained, which is used to synthesize a gain scheduled control law. Simulation results show that this control scheme can to a significant degree reject disturbances with time-varying Reynolds number.