A port-Hamiltonian formulation of a 2D boundary controlled acoustic system

Trenchant, Vincent; Fares, Yassine; Ramírez, Héctor; Gorrec, Yann Le

doi:10.1016/j.ifacol.2015.10.245

Cited by 18 publications

(17 citation statements)

References 8 publications

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“…and, as a consequence, the conditions (11), (12) and (13). Remark 3.1: Since Φ is a vector different from 0 and J C is skew-symmetric, from (13) we obtain that necessarily…”

Section: Boundary Energy-shaping Controlmentioning

confidence: 90%

“…Future work deals with the simulation and practical implementation of the proposed control algorithm to realise an active control of sound propagation inside a rectangular cavity, able to achieve a specific attenuation level. Some preliminar work in this sense can be found in [12].…”

Section: Discussionmentioning

confidence: 99%

“…The PDE (1) can be used to model simple flexible 2D systems [10], or the dynamics of sound propagation in a rectangular cavity, [12]. For example, in the first case, p and (q x , q y ) represent the momenta and the strain, while v and (Γ x , Γ y ) the velocity and the stress.…”

Section: Rectangular Domainmentioning

confidence: 99%

“…Even if the proposed framework is quite general, possible applicative scenarios deal with flexible structures, or with sound propagation in a rectangular cavity, [12]. To give a concrete idea of the problem and of the control strategy, assume that the port-Hamiltonian system models the sound propagation in a bounded region.…”

Section: Introductionmentioning

confidence: 99%

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Boundary L<inf>2</inf>-gain stabilisation of a distributed Port-Hamiltonian system with rectangular domain

Macchelli

Gorrec

Ramírez

2015

2015 54th IEEE Conference on Decision and Control (CDC)

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The main contribution of this paper is the development of a boundary control law for a class of distributed port-Hamiltonian systems with rectangular spatial domain that is able not only to shape the closed-loop Hamiltonian, but also to achieve a specific L2-gain between a pair of input and output signals of interest. The energy-shaping control action is based on the so-called control by interconnection and Casimir generation methodology (energy-Casimir method), here extended to deal with distributed port-Hamiltonian systems with 2D domain. On the other hand, the L2-gain property is obtained via damping injection by modulating a gain associated to a dissipative relation. Such approach takes inspiration from the Passivity Observer / Passivity Controller (PO / PC) technique originally developed for telemanipulation systems. Even if the proposed framework is quite abstract and general, possible target applications deal with the stabilisation of flexible structures, or with the stabilisation and attenuation of sound propagation in rectangular cavities.

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“…and, as a consequence, the conditions (11), (12) and (13). Remark 3.1: Since Φ is a vector different from 0 and J C is skew-symmetric, from (13) we obtain that necessarily…”

Section: Boundary Energy-shaping Controlmentioning

confidence: 90%

Section: Discussionmentioning

confidence: 99%

Section: Rectangular Domainmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Boundary L<inf>2</inf>-gain stabilisation of a distributed Port-Hamiltonian system with rectangular domain

Macchelli

Gorrec

Ramírez

2015

2015 54th IEEE Conference on Decision and Control (CDC)

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“…The reduced port-Hamiltonian model (4.8) with constitutive equations (4.4) are equivalent to the model in[20] where Euler's equation (momentum conservation) and mass balance are written in vectorial form, making use of the acoustic approximation assumption:…”

mentioning

confidence: 99%

Geometric spatial reduction for port-Hamiltonian systems

Lefèvre

Maschke

2019

Systems & Control Letters

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A geometric spatial reduction method is presented in this paper. It applies to port Hamiltonian models for open systems of balance equations. It is based on system projections which make use of the symmetries in the model and preserve the "natural" power pairing. Reductions from 3D to 2D and 1D domains are illustrated via two examples. The first one is a vibro-acoustic system with cylindrical symmetry where 3D-2D reduction is applied. The second one is the poloidal magnetic flux diffusion equation for tokamak reactors where the toroidal symmetry is used to perform a 3D-1D reduction.

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Theory and Implementation of Coupled Port-Hamiltonian Continuum and Lumped Parameter Models

Argus

Bradley

Hunter

2021

J Elast

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A continuous Galerkin finite element method that allows mixed boundary conditions without the need for Lagrange multipliers or user-defined parameters is developed. A mixed coupling of Lagrange and Raviart-Thomas basis functions are used. The method is proven to have a Hamiltonian-conserving spatial discretisation and a symplectic time discretisation. The energy residual is therefore guaranteed to be bounded for general problems and exactly conserved for linear problems. The linear 2D wave equation is discretised and modelled by making use of a port-Hamiltonian framework. This model is verified against an analytic solution and shown to have standard order of convergence for the temporal and spatial discretisation. The error growth over time is shown to grow linearly for this symplectic method, which agrees with theoretical results. A modal analysis is performed which verifies that the eigenvalues of the model accurately converge to the exact eigenvalues, as the mesh is refined. The port-Hamiltonian framework allows boundary coupling with bondgraph or, more generally, lumped parameter models, therefore unifying the two fields of lumped parameter modelling and continuum modelling of Hamiltonian systems. The wave domain discretisation is shown to be equivalent to a coupling of canonical port-Hamiltonian forms. This feature allows the model to have mixed boundary conditions as well as to have mixed causality interconnections with other port-Hamiltonian models. A model of the 2D wave equation is coupled, in a monolithic manner, with a lumped parameter model of an electromechanical linear actuator. The combined model is also verified to conserve energy exactly.

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A port-Hamiltonian formulation of a 2D boundary controlled acoustic system

Cited by 18 publications

References 8 publications

Boundary L<inf>2</inf>-gain stabilisation of a distributed Port-Hamiltonian system with rectangular domain

Boundary L<inf>2</inf>-gain stabilisation of a distributed Port-Hamiltonian system with rectangular domain

Geometric spatial reduction for port-Hamiltonian systems

Theory and Implementation of Coupled Port-Hamiltonian Continuum and Lumped Parameter Models

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