Automated Generation of Explicit Port-Hamiltonian Models from Multi-Bond Graphs

Port-Hamiltonian system theory is a well-known framework for the control of complex physical systems. The majority of port-Hamiltonian control design methods base on an \emph{explicit} input-state-output port-Hamiltonian model for the system under consideration. However in the literature, little effort has been made towards a systematic, automatable derivation of such explicit models.
In this paper, we present a constructive, formally rigorous method for an explicit port-Hamiltonian formulation of multi-bond graphs. Two conditions, one necessary and one sufficient, for the existence of an explicit port-Hamiltonian formulation of a multi-bond graph are given. We summarise our approach in a fully automated algorithm of which we provide an exemplary implementation along with this publication. The theoretical and practical results are illustrated through an academic example.