Section: New Results

Visual servoing approach for fluid flow control

Minimization of the kinetic energy density in the 2D plane Poiseuille flow

Participants : Christophe Collewet, Xuan Quy Dao.

This works concerns the PhD thesis of Xuan-Quy Dao. This year we have focused on a way to ensure a strict decreasing of the kinetic energy density. In that purpose, we have first proposed an approach to increase the controlled degrees of freedom. Indeed, the classical way to model this flow leads to only two degrees of freedom. With so few degrees of freedom it is obviously impossible to reach high desired performances as the strict minimization of the kinetic energy density. This way to proceed leads to a better minimization of the kinetic energy density. We have also proposed on approach based on a local decoupling of the controlled degree of freedom of the system so that an exponential decoupled decrease of each components of the state vector is locally obtained. This work has been presented at the CFM conference (Congrés Français de Mécanique) [32] .

Control behind a backward-facing step

Participant : Christophe Collewet.

This work is performed in the context of the PhD thesis of Nicolas Gautier from ESCPI in collaboration with J.L. Aider. The separated flow downstream a backward-facing step is studied using visual information for feedback. More precisely, flow velocity fields are computed from a real time optical flow algorithm. The control law we used is a simple PID controller. Even a better control law could be used, this study validates that visual servo control is an effective approach to control a flow.

Control of systems described by partial differential equations

Participants : Tudor-Bogdan Airimitoaie, Christophe Collewet.

This work concerns principally the post-doctoral research of Tudor-Bogdan Airimiţoaie. It aims at controlling continuously evolving systems described by partial differential equations (PDEs). This is relevant in the context of the Fluminance team because fluid flows are infinite dimensional systems and can be rigorously described only through PDEs. In spite of this, practical approaches of flow control are based on low order numerical implementation relying on space and time discretization of the continuous system. This implies to setup strategies for model reduction that must be then in return properly understood with respect to the convergence of the control law. For finite dimensional implementations, one of the research directions pursued concerns the study on the benefit of increasing the controlled degrees of freedom (see the work of Xuan-Quy Dao). Another research direction, started recently, consists in improving control by using real-time estimation of a finite number of parameters related to the original infinite dimensional system. Indeed, this opens the possibility of improving performances by using more advanced robust linear parametric varying (LPV) control techniques existing in the literature. Two conference papers on these works have been submitted at the "7th AIAA Flow Control Conference".