APPROXIMATION OF THE TELEGRAPHER'S EQUATIONS WITH DISSIPATION

We have already proposed a representation and spatial discretization of line transmission in terms of Bond Graph (Nakrachi, 2003). In this paper, one shows that we preserve the Dirac structure of a distributed parameter system represented in the form of a port-Hamiltonian, after a space discretization. Indeed, the conservation of the Dirac structure was shown only in the conservative case, without dissipation. The study is applied to the case of a transmission line represented by the telegrapher's equations.