Transition control of plane Poiseuille flow - a spatially interconnected model

This paper proposes a new mathematical model for the transition control problem in plane Poiseuille flow. Most of the previously proposed models are based on pseudospectral approaches and are valid only for a single spatial wave number. In this work we propose a new model which is based on a finite difference approach in streamwise direction and a spectral approach in wall normal direction. The model obtained is valid for all spatial frequencies and can be used for the synthesis of controllers for flow control problems, using some recently developed ideas for spatially interconnected systems. Since these controllers are designed in physical domain they are simple to implement using MEMS arrays. The model is compared with results obtained with previously proposed models and is found to be in good agreement with them. To illustrate its usefulness, a stabilizing dynamic output feedback controller is designed for a Reynolds number of 6000.