Simultaneous Drag Reduction and Kinetic Energy Density of the Plane Poiseuille Flow

Abstract

We present in this paper a closed-loop approach to control the 2D plane Poiseuille flow in an unstable state. To do that, we propose to use a vision-based approach as proposed in our paper to estimate the state of the flow 1 . The first step is based on the evaluation of the 2D velocity field from optical flow measurements. These measurements are next used into a visual servo control scheme. However, since we are interested in the simultaneous minimization of two quantities, that is the drag and kinetic energy density of the flow, we propose to design a control law based on an advanced visual servo control approach, the so-called partitioned visual servo control 2 , first proposed in the robotics community. Simulations results validate our control scheme, including the case where noisy measurements are considered. We also compare our approaches with the most relevant ones.