Discretized models for networks of distributed parameter port-Hamiltonian systems

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.