Geometric spatial reduction for port-Hamiltonian systems

Ngoc Minh Trang Vu (1) , Laurent Lefevre (1) , Bernhard Maschke (2)

1 LCIS - Laboratoire de Conception et d'Intégration des Systèmes
2 LAGEPP - Laboratoire d'automatique, de génie des procédés et de génie pharmaceutique

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.

Mots clés: geometric reduction; distributed parameters systems; port Hamiltonian systems; tokamak plasma control; vibro-acoustic system

Domaines: Automatique / Robotique

Ngoc Minh Trang Vu, Laurent Lefevre, Bernhard Maschke. Geometric spatial reduction for port-Hamiltonian systems. Systems and Control Letters, 2019, 125, pp.1-8. ⟨10.1016/j.sysconle.2019.01.002⟩. ⟨hal-02074324⟩