Port-Hamiltonian Systems (PHS) are an extension of Hamiltonian systems, which represent open passive systems which are structured according to their conservative and dissipative parts, as well as the external sources. They are widely used in engineering as a central tool for the modelling of physical systems, their passive-guaranteed simulation, as well as for control issues [2]. In this paper, we shall recall the definition of the Port Hamiltonian systems and give some indication on how they might be used for the modelling and simulation of electro-acoustic systems, which are illustrated on some applications.

In the first part, we shall first recall the precise definition of port Hamiltonian systems [4, 5] as control systems defined on a manifold B endowed with a Dirac structure [1]. The manifold B is the product of the tangent and cotangent spaces of some base manifold augmented with two dual vector bundles representing the external variables of an open physical system. Secondly, we shall recall how Dirac structure may be derived from the topological structure of the system such as graphs of circuits [3], or from covariant formulation of systems of conservation laws.

In the second part, two applications in acoustics and electro-acoustics under current development shall be presented. The first application is the derivation of a Hamiltonian model of a non-linear electro-acoustic transducer. A structure-preserving time-discretization scheme is presented. The second application is the derivation of a simple but energetically consistent model of the coupling between an artificial lip (the musician), a jet and an acoustic tube (the instrument). Then a port-Hamiltonian formulation of finite dimensional mechanical systems including structural damping of Caughey type is presented. An extension to infinite dimensional systems is proposed with application to the Euler-Bernouilli beam.

[1] T.J. Courant. Dirac manifolds. Trans. American Math. Soc. 319, pages 631–661, 1990. 

[2] V. Duindam, A. Macchelli, S. Stramigioli, and H. eds. Bruyninckx. Modeling and Control of Complex Physical Systems - The Port-Hamiltonian Approach. Springer, Sept. 2009. ISBN 978-3-642-03195-3.
[3] A. van der Schaft and B. Maschke. Port-hamiltonian systems on graphs. SIAM Journal on Control and Optimization, 51(2):906–937, 2013.
[4] A.J. van der Schaft and B.M. Maschke. The Hamiltonian formulation of energy conserving physical systems with external ports. Archiv für Elektronik und Übertragungstechnik, 49(5/6):362–371, 1995.
[5] A.J. van der Schaft and B.M. Maschke. Hamiltonian formulation of distributed parameter systems with boundary energy flow. J. of Geometry and Physics, 42:166–174, 2002.