Port Hamiltonian Formulation of Infinite Dimensional Systems I. Modeling

In this paper, some new results concerning the modeling of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system is generalized in order to cope with the distributed parameter and multi-variable case. The resulting class of infinite dimensional systems is quite general, thus allowing the description of several physical phenomena, such as heat conduction, piezoelectricity and elasticity. Furthermore, classical PDEs can be rewritten within this framework. The key point is the generalization of the notion of finite dimensional Dirac structure in order to deal with an infinite dimensional space of power variables. In this way, also in the distributed parameter case, the variation of total energy within the spatial domain of the system can be related to the power flow through the boundary. Since this relation deeply relies on the Stokes theorem, these structures are called Stokes-Dirac structures