Passive modelling of the electrodynamic loudspeaker: from the Thiele–Small model to nonlinear port-Hamiltonian systems

Abstract

The electrodynamic loudspeaker couples mechanical, magnetic, electric and thermodynamic phenomena. The Thiele/Small (TS) model provides a low frequency approximation, combining passive linear (multiphysical or electric-equivalent) components. This is commonly used by manufacturers as a reference to specify basic parameters and characteristic transfer functions. This paper presents more refined nonlinear models of electric, magnetic and mechanical phenomena, for which fundamental properties such as passivity and causality are guaranteed. More precisely, multiphysical models of the driver are formulated in the core class of port-Hamiltonian systems (PHS), which satisfies a power balance decomposed into conservative, dissipative and source parts. First, the TS model is reformulated as a linear PHS. Then, refinements are introduced, stepby-step, benefiting from the component-based approach allowed by the PHS formalism. Guaranteed-passive simulations are proposed, based on a numerical scheme that preserves the power balance. Numerical experiments that qualitatively comply with measured behaviors available in the literature are presented throughout the paper.

A New Electromechanical Analogy Approach Based on Electrostatic Coupling for Vertical Dynamic Analysis of Planar Vehicle Models

“…In this multidomain problem, the mechanical system is replaced by its electrical equivalent and joined to the electrical one. In this way a unique electrical system is studied [14], [15]. De Silva [16] proposed the use of linear graphs for modeling multi-domain systems in a unified way, thus allowing to exploit the existing analogies across domains.…”

“…Electro-mechanical analogies have been used in vehicle suspension modeling and control [29]- [32], in vehicle drive trains [33], in structural dynamics [34], in modeling and control of flexible structures [35], in design and optimization of inductive power transfer systems [36], and in piezoelectric vibration energy harvesters [37], among others mechanical or electromechanical systems with interest in vibrations [14], [15], [38]- [42].…”

Total Harmonic Distortion of a Piezoelectric MEMS Loudspeaker in an IEC 60318-4 Coupler Estimation Using Static Measurements and a Nonlinear State Space Model

“…To model the nonlinearities of classical electrodynamic loudspeakers, state space models, port-Hamiltonian systems, Hammerstein models and power series have been extensively used [19][20][21][22][23][24][25]. State space models are the most commonly used models to simulate nonlinear effects in electrodynamic loudspeaker and have shown accurate results.…”

A new electromechanical analogy approach based on electrostatic coupling for vertical dynamic analysis of planar vehicle models

“…In this multidomain problem, the mechanical system is replaced by its electrical equivalent and joined to the electrical one. In this way and unique electrical system is studied [14,15]. De Silva [16] proposed the use of linear graphs for modeling multi-domain systems in a unified way, thus allowing to exploit the existing analogies across domains.…”

“…Eletro-mechanical analogies have been used in vehicle suspension modeling and control [27,28,29,30], in vehicle drive trains [31], in structural dynamics [32], in modeling and control of flexible structures [33], in design and optimization of inductive power transfer systems [34], and in piezoelectric vibration energy harvesters [35], among others mechanical or electromechanical systems with interest in vibrations [14,15,36,37,38].…”