Port-Hamiltonian Systems

Abstract

In this chapter, we will show how the representation of a lumped-parameter physical system as a bond graph naturally leads to a dynamical system endowed with a geometric structure, called a port-Hamiltonian system. The dynamics are determined by the storage elements in the bond graph (cf. Sect. 1.6.3), as well as the resistive elements (cf. Sect. 1.6.4), while the geometric structure arises from the generalized junction structure of the bond graph. The formalization of this geometric structure as a Dirac structure is introduced as the key mathematical concept to unify the description of complex interactions in physical systems. It will also allow to extend the definition of a finite-dimensional port-Hamiltonian systems as given in this chapter to the infinite-dimensional case in Chapter 4, thus dealing with distributed-parameter physical systems. We will show how this port-Hamiltonian formulation offers powerful methods for the analysis of complex multi-physics systems, also paving the way for the results on control of port-Hamiltonian systems in Chapter 5 and in Chapter 6. Furthermore, we describe how the port-Hamiltonian structure relates to the classical Hamiltonian structure of physical systems as being prominent in e.g. classical mechanics, as well as to the Brayton-Moser description of RLC-circuits.