Structure-preserving discretization and control of a two-dimensional vibro-acoustic tube

This paper deals with the structure-preserving discretization and control of a two-dimensional vibroacoustic tube using the port-Hamiltonian framework. A discretization scheme is proposed, and a set of precise basis functions are given in order to obtain a structure-preserving finite-dimensional port- Hamiltonian approximation of the two-dimensional vibro-acoustic system. Using the closed-loop structural invariants of the approximated system an energy-Casimir controller is derived. The performance of the proposed discretization scheme and the controller is shown by means of numerical simulations.