Input output representations of Dirac structures and junction structures in bond graphs

In this paper we present a transformation of the network interconnection structure (described in the bond graph formalism) into an equivalent one that corresponds to a particular representation of the Dirac structure, called hybrid input-output representation. The use of such a representation facilitates the graphical analysis of the solvability of the network model, of the existence of dynamic invariants and constraints, of the reduction of the obtained model, and of the preparation of the equations for numerical simulation.

[1]  A. Schaft,et al.  On Representations and Integrability of Mathematical Structures in Energy-Conserving Physical Systems , 1999 .

[2]  Arjan van der Schaft.  Interconnection and geometry , 1999 .

[3]  Irene Dorfman,et al.  Dirac Structures and Integrability of Nonlinear Evolution Equations , 1993 .

[4]  B. Moultrie,et al.  Basis order for bond-graph junction structures , 1980 .

[5]  A. Schaft,et al.  The Hamiltonian formulation of energy conserving physical systems with external ports , 1995 .

[6]  Johannes van Dijk,et al.  On the role of bond graph causality in modelling mechatronic systems , 1994 .

[7]  U. Faigle,et al.  Book reviews , 1991, ZOR Methods Model. Oper. Res..

[8]  Arjan van der Schaft,et al.  Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[9]  A. J. van der Schaft,et al.  Port-controlled Hamiltonian Systems:Modelling Origins and System-Theoretic Properties , 1992 .

[10]  Arjan van der Schaft,et al.  Note on the dynamics of LC circuits with elements in excess , 1998 .

[11]  Pieter C. Breedveld,et al.  Thermodynamic Bond Graphs and the Problem of Thermal Inertance , 1982 .

[12]  P. V. Remoortere.  Physical systems theory in terms of bond graphs : P.C. Breedveld: Vakgroep Besturingsystemen en Computertechniek, THT, Afdeling Electrotechniek, Postbus 217, 7500 AE Enschede, The Netherlands. 1984, 200 pages, ISBN 90-9000599-4 , 1984 .

[13]  Alan S. Perelson,et al.  System Dynamics: A Unified Approach , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[14]  G. Oster,et al.  Chemical reaction dynamics , 1974 .

[15]  Pieter C. Breedveld,et al.  Decomposition of multiport elements in a revised multibond graph notation , 1984 .

[16]  Bernhard Maschke,et al.  An Intrinsic Hamiltonian Formulation of Network Dynamics , 1992 .

[17]  Alan S. Perelson,et al.  Chemical reaction dynamics part II: Reaction networks , 1974 .

[18]  Johannes van Dijk,et al.  Simulation of System Models Containing Zero-order Causal Paths , 1991 .