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

Authors

Marc Wijnand, Brigitte d’Andrea-Novel, Benoit Fabre, Thomas Helie, Lionel Rosier, David Roze

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.

Citation

• Journal: 2019 IEEE 58th Conference on Decision and Control (CDC)
• Year: 2019
• Volume:
• Issue:
• Pages: 6887–6892
• Publisher: IEEE
• DOI: 10.1109/cdc40024.2019.9029960

BibTeX

@inproceedings{Wijnand_2019,
  title={{Active control of the axisymmetric vibration modes of a tom-tom drum}},
  DOI={10.1109/cdc40024.2019.9029960},
  booktitle={{2019 IEEE 58th Conference on Decision and Control (CDC)}},
  publisher={IEEE},
  author={Wijnand, Marc and d’Andrea-Novel, Brigitte and Fabre, Benoit and Helie, Thomas and Rosier, Lionel and Roze, David},
  year={2019},
  pages={6887--6892}
}

Download the bib file

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