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

Antoine Falaize 1, 2, 3 Thomas Hélie 4
1 Analyse et synthèse sonores [Paris]
STMS - Sciences et Technologies de la Musique et du Son
2 Equipe-Projet S3 (Systèmes et Signaux Sonores)
STMS - Sciences et Technologies de la Musique et du Son
4 S3AM - Systèmes et Signaux Sonores : Audio/Acoustique, instruMents
STMS - Sciences et Technologies de la Musique et du Son
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.
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https://hal.archives-ouvertes.fr/hal-01470949
Contributor : Thomas Hélie <>
Submitted on : Saturday, February 18, 2017 - 6:44:44 AM
Last modification on : Thursday, October 8, 2020 - 12:36:02 PM

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Antoine Falaize, Thomas Hélie. Passive simulation of the nonlinear port-Hamiltonian modeling of a Rhodes Piano. Journal of Sound and Vibration, Elsevier, 2017, 390, pp.289-309. ⟨10.1016/j.jsv.2016.11.008⟩. ⟨hal-01470949⟩

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