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Active control of the axisymmetric vibration modes of a tom-tom drum

Abstract : This paper deals with an application of active control of percussion instruments. Our setup consists of a tom-tom drum with a circular membrane, a cylindrical cavity and a circular rigid wall on which a loudspeaker is mounted. The current applied to the loudspeaker is controlled in order to modify the frequencies of the drum membrane modes. First, a PDE model of the axisymmetric transverse vibration of the tom-tom membrane is developed. Subsequently, the equation is recast as an infinite-dimensional port-Hamiltonian system. The port-Hamiltonian framework enables us to develop a numerical scheme that preserves the power balance and guarantees a stable simulation. Finally, a control law for the loudspeaker current is designed to modify the frequency of the first axisymmetric vibration mode of the drum membrane, using finite-time and passivity-based methods.
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Submitted on : Wednesday, September 2, 2020 - 3:12:35 PM
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Marc Wijnand, Brigitte d'Andréa-Novel, Benoît Fabre, Thomas Hélie, Lionel Rosier, et al.. Active control of the axisymmetric vibration modes of a tom-tom drum. 58th IEEE Conference on Decision and Control, Dec 2019, Nice, France. pp.6887-6892, ⟨10.1109/CDC40024.2019.9029960⟩. ⟨hal-02296092⟩

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