Section: New Results

Visual servoing approach for fluid flow control

Fully exploitation of the controlled degrees of freedom of the 2D plane Poiseuille flow

Participants : Christophe Collewet, Xuan Quy Dao.

This works concerns the Phd of Xuan-Quy Dao and can be seen as an extension of the works carried out by Romeo Tatsambon during its post-doc position. Indeed, during this post-doc we proved that our vision-based approach overcomes the traditional approaches. Nevertheless, to compare our method with the literature, we used a traditional control law, the LQR control law. However, we can fully exploit the capabilities of visual servoing techniques by designing a more efficient control law than the LQR one. This has been done this year. We have validated our approach to the problem of minimizing the drag of the 2D plane Poiseuille flow. An important issue was also to ensure that, during the process of drag reduction, the kinetic energy density will not grow. This is of great importance since it is well known that the controlled flow may become turbulent when this kinetic energy density is growing. To cope with this problem we have proposed to design a control law based on partitioned visual servo. Indeed, following this way, we are able to simultaneously minimize the drag AND the kinetic energy density in contrast to the existing approaches. This work has been accepted to the "American control conference (ACC'12)", to the "Conférence internationale francophone d'automatique (CIFA'12)" and to the "6th AIAA Flow Control Conference". We have also explored an approach based on eigenstructure placement to ensure a strict decrease of the kinetic energy density. Another approach has also been explored, it tends to decouple all the controlled degrees of freedom of the system so that an exponential decoupled decrease of each component of the state vector is obtained. The great advantage of this approach is that all quantities depending on the state vector (like the drag) are also exponential decreasing functions.

Control behind a backward-facing step

Participant : Christophe Collewet.

Instead of setting up an experimental closed loop control problem for the plane Poiseuille flow with temporal perturbations, which is theoretically based on an unrealistic infinite channel, we explore in this axis of work a closed-loop control of a flow behind a backward step. The control is expressed through the visual servoing formalism and fast velocity measurements in the recirculation zone. This work is performed in the context of the PhD thesis of Nicolas Gautier from PMMH-ESCPI. This thesis is co-supervised with Jean-Luc Aider (CNRS/PMMH-ESPCI).