Electroacoustic Absorbers Based on Passive Finite-Time Control of Loudspeakers: A Numerical Investigation

Authors

Tristan Lebrun, Marc Wijnand, Thomas Hélie, David Roze, Brigitte d’Andréa-Novel

Abstract

This paper proposes a numerical investigation of a controlled loudspeaker designed to absorb acoustic plane waves at a duct termination. More precisely, a nonlinear control for a current-driven loudspeaker is presented, that relies on (1) measurements of velocity and acoustic pressure at the membrane, (2) a linear electroacoustic loudspeaker model and (3) a nonlinear finite-time control method. Numerical tests are carried out by a passive-guaranteed simulation of the loudspeaker dynamics in the port-Hamiltonian systems formalism. The sound absorption efficiency is evaluated up to 300 Hz by computing the reflected pressure at the membrane. The results are compared with a similar control architecture: the finite-time control for sound absorption proves effective, especially in the low frequency range.

Keywords

Finite-time control; Port-Hamiltonian systems; Electroacoustic transducer

Citation

• ISBN: 9783030347468
• Publisher: Springer International Publishing
• DOI: 10.1007/978-3-030-34747-5_3

BibTeX

@inbook{Lebrun_2020,
  title={{Electroacoustic Absorbers Based on Passive Finite-Time Control of Loudspeakers: A Numerical Investigation}},
  ISBN={9783030347475},
  DOI={10.1007/978-3-030-34747-5_3},
  booktitle={{Nonlinear Dynamics and Control}},
  publisher={Springer International Publishing},
  author={Lebrun, Tristan and Wijnand, Marc and Hélie, Thomas and Roze, David and d’Andréa-Novel, Brigitte},
  year={2020},
  pages={23--31}
}

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References

• Bobber, R. J. An Active Transducer as a Characteristic Impedance of an Acoustic Transmission Line. The Journal of the Acoustical Society of America vol. 48 317–324 (1970) – 10.1121/1.1912131
• Rivet, E., Karkar, S. & Lissek, H. Broadband Low-Frequency Electroacoustic Absorbers Through Hybrid Sensor-/Shunt-Based Impedance Control. IEEE Transactions on Control Systems Technology vol. 25 63–72 (2017) – 10.1109/tcst.2016.2547981
• Maschke, B. M. & van der Schaft, A. J. Port-Controlled Hamiltonian Systems: Modelling Origins and Systemtheoretic Properties. IFAC Proceedings Volumes vol. 25 359–365 (1992) – 10.1016/s1474-6670(17)52308-3
• Ortega, R., van der Schaft, A., Maschke, B., Escobar, G.: Energy-shaping of port-controlled Hamiltonian systems by interconnection. In: Proceedings of the 38th IEEE Conference on Decision and Control, vol. 2, pp. 1646–1651 (1999)
• Bernuau, E., Perruquetti, W., Efimov, D. & Moulay, E. Robust finite-time output feedback stabilisation of the double integrator. International Journal of Control vol. 88 451–460 (2014) – 10.1080/00207179.2014.956340
• Wijnand, M., d’Andréa-Novel, B., Hélie, T., Roze, D.: Contrôle des vibrations d’un oscillateur passif : stabilisation en temps fini et par remodelage d’énergie. In: 14ème Congrès Français d’Acoustique, pp. 1370–1375. Le Havre, France (2018)
• Bhat, S. P. & Bernstein, D. S. Finite-Time Stability of Continuous Autonomous Systems. SIAM Journal on Control and Optimization vol. 38 751–766 (2000) – 10.1137/s0363012997321358
• Ortega, R., van der Schaft, A., Maschke, B. & Escobar, G. Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica vol. 38 585–596 (2002) – 10.1016/s0005-1098(01)00278-3
• Hélie, T., Falaize, A., Lopes, N.: Systèmes Hamiltoniens à Ports avec approche par composants pour la simulation à passivité garantie de problèmes conservatifs et dissipatifs. In: Colloque National en Calcul des Structures, vol. 12 (2015).
• Falaize, A. & Hélie, T. Passive Guaranteed Simulation of Analog Audio Circuits: A Port-Hamiltonian Approach. Applied Sciences vol. 6 273 (2016) – 10.3390/app6100273