Marc Wijnand will defend in French his PhD thesis realized in the S3AM team at the STMS Laboratory (Ircam/CNRS/Sorbonne Université/Ministère de la Culture).
« Finite-time control of hybrid vibratory systems coupling partial differential equations to ordinary differential equations: the cases of the tom-tom drum and the overhead crane »
This PhD thesis is part of the French national research project Finite4SoS on finite-time control.
This type of nonlinear control enables us to stabilize a dynamic system at a target state in a finite time (not asymptotically).
The first contribution consists of the combination of a finite-time control law (for efficiency) with passivity (in order to guarantee robustness against, for example, a bad identification of the model parameters), for the case of a second order ODE (ordinary differential equation). This control law is used to control a loudspeaker in order to achieve an electroacoustic absorber. Next, a passive numerical method is proposed that is able to cope with the intrinsic stiffness present in EDOs controlled in finite-time. Finally, a second application concerning the control of a nonlinear string using finite-time tracking control is proposed.
The second contribution is concerned with the finite-time control of hybrid systems coupling a hyperbolic PDE (partial differential equation) to an ODE (ordinary differential equation). Two specific cases of vibratory systems are developed : a tom-tom drum (percussion instrument that has been augmented by a feedback on a loudspeaker) and a moving platform to which a heavy cable is attached (a model for the 2D movement present in a construction or overhead crane). An observerregulator is designed for the tom-tom drum using a modal approach, that is implemented on a prototype for an experimental assessment. A finite-time stabilization of the 2D crane model is achieved based on an existing theorem for the finite-time boundary control of a hyperbolic PDE.
The jury will be composed of
Yann Le Gorrec - FEMTO-ST, Besançon Referee
Cyril Touzé - ENSTA, Paris Referee
Pascal Morin - Sorbonne Université, Paris Examinator
Andrey Polyakov - Inria, Lille Examinator
Brigitte d'Andréa-Novel - Sorbonne Université, Paris Supervisor
Thomas Hélie - CNRS, Paris Co-supervisor
Lionel Rosier - Université du Littoral Co-supervisor Côte d'Opale, Calais
David Roze - CNRS, Paris Co-supervisor