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Discrétisation et commande frontière de systèmes vibro-acoustiques, une approche hamiltonienne à ports

Abstract : This thesis deals with the boundary control of an acoustic by a network of co-localised sensors/actuators which constitutes a smart skin. In order to cope with this multiphysical problem, we chose to place our study in the framework of port-Hamiltonian systems, a structured approach based on the representation of energy exchanges between different energy domains between different systems of subsystems. We proposed a port-Hamiltonian model of the wave equation interconnected through its boundary to the distributed actuation system, which corresponds to a 2D formulation of the physical problem. We developed a spatial discretization method based on the use of finite differences on several staggered grids that preserve the port-Hamiltonian structure of the wave equation. This method also permits to easily interconnect the discretized system with other subsystems, which is convenient for instance for control purposes. Its main advantage over other structure preserving methods is its simplicity of implementation which stems from the use of finite differences. In order to control the vibro-acoustic system, we proposed a control law synthesis method for systems governed by two conservation laws in 1D. The originality of this method lies in the fact that it relies on the computation of structural invariants (Casimir functions) exploited in order to modify the structure of the system in closed loop. The conditions of application of these laws on a 2D system are studied and numerical results validate the synthesized control laws.
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Submitted on : Tuesday, October 9, 2018 - 3:00:09 PM
Last modification on : Wednesday, September 16, 2020 - 10:42:49 AM

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  • HAL Id : tel-01891374, version 1

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Vincent Trenchant. Discrétisation et commande frontière de systèmes vibro-acoustiques, une approche hamiltonienne à ports. Acoustique [physics.class-ph]. Université Bourgogne Franche-Comté, 2017. Français. ⟨NNT : 2017UBFCD066⟩. ⟨tel-01891374⟩

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