Discretized models for networks of distributed parameter port-Hamiltonian systems

Konferenz: nDS '13 - Proceedings of the 8th International Workshop on Multidimensional Systems
09.09.2013 - 11.09.2013 in Erlangen, Deutschland

Tagungsband: nDS '13

Seiten: 5Sprache: EnglischTyp: PDF

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Autoren:
Kotyczka, Paul (Institute of Automatic Control, Technische Universität München, Boltzmannstr. 15, 85748 Garching, Germany)

Inhalt:
In this paper, a systematic procedure to determine discretized models for networks of distributed parameter systems in one spatial variable is presented. The port-Hamiltonian formalism, which has proven useful for systematic physical modeling and energy based control, is exploited, and particularly a structure preserving discretization technique, which has been introduced some years ago. At the example of a network of pipelines, an easy to implement, recursive procedure to construct the system matrices of the discretized port-Hamiltonian model is derived. In a first step, the existing theory is applied to generate finite-dimensional port-Hamiltonian approximations for the subsystems, including dissipation. In a second step, the overall (simulation) model can be derived from the interconnection structure of the grid. Simulations, generated with the the open source mathematical software SAGE, are presented for a small sample network with parameters from literature.