Passive simulation of the nonlinear port-Hamiltonian modeling of a Rhodes Piano

Authors

Abstract

This paper deals with the time-domain simulation of an electro-mechanical piano: the Fender Rhodes. A simplified description of this multi-physical system is considered. It is composed of a hammer (nonlinear mechanical component), a cantilever beam (linear damped vibrating component) and a pickup (nonlinear magneto-electronic transducer). The approach is to propose a power-balanced formulation of the complete system, from which a guaranteed-passive simulation is derived to generate physically-based realistic sound synthesis. Theses issues are addressed in four steps. First, a class of Port-Hamiltonian Systems is introduced: these input-to-output systems fulfill a power balance that can be decomposed into conservative, dissipative and source parts. Second, physical models are proposed for each component and are recast in the port-Hamiltonian formulation. In particular, a finite-dimensional model of the cantilever beam is derived, based on a standard modal decomposition applied to the Euler-Bernoulli model. Third, these systems are interconnected, providing a nonlinear finite-dimensional Port-Hamiltonian System of the piano. Fourth, a passive-guaranteed numerical method is proposed. This method is built to preserve the power balance in the discrete-time domain, and more precisely, its decomposition structured into conservative, dissipative and source parts. Finally, simulations are performed for a set of physical parameters, based on empirical but realistic values. They provide a variety of audio signals which are perceptively relevant and qualitatively similar to some signals measured on a real instrument.

Keywords

Passive modeling; Numerical methods; Port-Hamiltonian systems; Multiphysics system; Time domain simulation

Citation

Journal: Journal of Sound and Vibration
Year: 2017
Volume: 390
Issue:
Pages: 289–309
Publisher: Elsevier BV
DOI: 10.1016/j.jsv.2016.11.008

BibTeX

@article{Falaize_2017,
  title={{Passive simulation of the nonlinear port-Hamiltonian modeling of a Rhodes Piano}},
  volume={390},
  ISSN={0022-460X},
  DOI={10.1016/j.jsv.2016.11.008},
  journal={Journal of Sound and Vibration},
  publisher={Elsevier BV},
  author={Falaize, Antoine and Hélie, Thomas},
  year={2017},
  pages={289--309}
}

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