Concept-Oriented Modeling of Dynamic Behavior

  • P.C. BreedveldEmail author


This chapter introduces the reader to the concept-oriented approach to modeling that clearly separates ideal concepts from the physical components of a system when modeling its dynamic behavior for a specific problem context. This is done from a port-based point of view for which the domain-independent bond graph notation is used, which has been misinterpreted over and over, due to the paradigm shift that concept-oriented modeling in terms of ports requires. For that reason, the grammar and semantics of the graphical language of bond graphs are first defined without making any connection to the physical modeling concepts it is used for. In order to get a first impression of how bond graphs can represent models, an existing model is transformed into bond graphs as the transformation steps also give a good impression of how this notation provides immediate feedback on modeling decisions during actual modeling. Next, physical systems modeling in terms of bond graphs is discussed as well as the importance of the role of energy and power that is built into the semantics and grammar of bond graphs. It is emphasized that, just like circuit diagrams, bond graphs are a topological representation of the conceptual structure and should not be confused with spatial structure. By means of a discussion of some examples of such confusions it is explained why bond graphs have a slow acceptance rate in some scientific communities.


Labeled di-graph Node categorization Energy and co-energy Legendre transform Thermodynamic framework of variables Generalized mechanic framework of variables Equilibrium-determining variable Equilibrium-establishing variable 


  1. 1.
    Beeren W., Roessink M. (eds) (1998) Sporen van wetenschap in kunst/Traces of Science in Art, 155pp., ISBN 90-6984-224-6.Google Scholar
  2. 2.
    Paynter H.M. (1961) Analysis and Design of Engineering Systems. MIT Press, Cambridge, MA.Google Scholar
  3. 3.
    Willems J.C. (2007) The behavioral approach to open and interconnected systems. IEEE Control Syst. Mag. Dec:46–99.Google Scholar
  4. 4.
    Bondy J.A., Murty U.S.R. (1976) Graph Theory with Applications. North-Holland, Oxford, ISBN 0-444-19451-7.Google Scholar
  5. 5.
    Breedveld P.C. (1982b) Proposition for an unambiguous vector bond graph notation. Trans. ASME, J. Dyn. Syst. Meas. Control 104(3):267–270.CrossRefGoogle Scholar
  6. 6.
    Breedveld P.C. (1986) A definition of the multibond graph language. In Complex and Distributed Systems: Analysis, Simulation and Control, Tzafestas S., Borne P. (eds) Vol. 4 of ‘IMACS Transactions on Scientific Computing’. North-Holland, Amsterdam, pp. 69–72.Google Scholar
  7. 7.
    Breedveld P.C. (1982a) Thermodynamic bond graphs and the problem of thermal inertance. J. Franklin Inst. 314(1):15–40.MathSciNetCrossRefGoogle Scholar
  8. 8.
    Karnopp D.C., Rosenberg R.C. (1968) Analysis and simulation of multiport systems. MIT Press, Cambridge, MA.Google Scholar
  9. 9.
    Hogan N.J., Fasse, E.D. (1988) Conservation principles and bond graph junction structures. Proc. ASME 1988 WAM. DSC 8:9–14.Google Scholar
  10. 10.
    Paynter H.M., Busch-Vishniac I.J. (1988) Wave-scattering approaches to conservation and causality. J. Franklin Inst. 325(3):295–313.MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Breedveld P.C. (1985) Multibond graph elements in physical systems theory. J. Franklin Inst. 319(1/2):1–36.CrossRefGoogle Scholar
  12. 12.
    Blundell A.J. (1982) Bond Graphs for Modelling Engineering Systems. Ellis Horwood, Chichester and Halsted Press, New York, NY, 151p.Google Scholar
  13. 13.
    Thoma J. (1975) Introduction to Bond Graphs and Their Applications. Pergamon Press, Oxford.Google Scholar
  14. 14.
    Breedveld P.C. (2009) Port-based modeling of dynamic systems. Chapter 1 and appendix A and B2. In Modeling and Control of Complex Physical Systems – The Port-Hamiltonian Approach, Stramigioli S., Macchelli A., Duindam V., Bruyninckx H. (eds). Springer, Berlin, pp. 1–52, 97–311, 323–328.Google Scholar
  15. 15.
    Breedveld P.C. (1984). Decomposition of multiport elements in a revised multibond graph notation. J. Franklin Inst. 318(4):253–273.zbMATHCrossRefGoogle Scholar
  16. 16.
    Breedveld P.C. (1995) Exhaustive decompositions of linear two-ports. Proceedings of SCS 1995 International Conference on Bond Graph Modeling and Simulation (ICBGM’95), SCS Simulation Series 27(1):11–16, Jan 15–18, Las Vegas, Cellier F.E., Granda J.J. (eds). ISBN 1-56555-037-4.Google Scholar
  17. 17.
    Dijk J. van, Breedveld P.C. (1991a) Simulation of system models containing zero-order causal paths – part I: Classification of zero-order causal paths. J. Franklin Inst. 328(5/6):959–979.zbMATHCrossRefGoogle Scholar
  18. 18.
    Breedveld P.C. (2007) Port-based modeling of engineering systems in terms of bond graphs. In Handbook of Dynamic System Modeling, Fishwick P.A. (ed). Chapman & Hall, London, pp. 26.1–26.29, ISBN 1-58488-565-3.Google Scholar
  19. 19.
    Dijk J. van, Breedveld P.C. (1991b) Simulation of system models containing zero-order causal paths – part II: Numerical implications of class-1 zero-order causal paths. J. Franklin Inst. 328(5/6):981–1004.zbMATHCrossRefGoogle Scholar
  20. 20.
    Feynman R, Leighton R, Sands M. (1989) The Feynman Lectures on Physics. 3 volumes 1964, 1966, Addison-Wesley, Reading, Mass, ISBN 0-201-50064-7.Google Scholar
  21. 21.
    Zill D.G. (2005) A First Course in Differential Equations. 9th edition. Brooks/Cole, Belmont, CA, ISBN-13: 978-0-495-10824, Lib. of Congress number: 2008924906.Google Scholar
  22. 22.
    Wellstead P.E. (1979) Introduction to physical systems modeling. Academic, London. ISBN: 0-12-744380-0.Google Scholar
  23. 23.
    Timoshenko S. (1976) Strength of Materials: Elementary Theory and Problems. Vol. 1 of Strength of Materials, 3rd edition, R.E. Krieger, Huntington, NY (First ed. D. Van Nostrand Company, inc., 1940).Google Scholar
  24. 24.
    Allen R.R. (1981) Dynamics of mechanisms and machine systems in accelerating reference frames. Trans. ASME J. Dyn. Syst. Meas. Control 103(4):395–403.CrossRefGoogle Scholar
  25. 25.
    Callen H.B. (1960) Thermodynamics. Wiley, New York, NY.zbMATHGoogle Scholar
  26. 26.
    Maschke B.M., van der Schaft A.J., Breedveld P.C. (1995) An intrinsic Hamiltonian formulation of the dynamics of LC-circuits. Trans. IEEE Circuits Syst. I Fundam. Theory Appl. 42(2):73–82.zbMATHCrossRefGoogle Scholar
  27. 27.
    Karnopp D.C. (1978) The energetic structure of multibody dynamic systems. J. Franklin Inst. 306(2):165–181.MathSciNetzbMATHCrossRefGoogle Scholar
  28. 28.
    Chua L.O. (1971) Memristor-the missing circuit element. IEEE Trans. Circuit Theory CT-18(5):507–519.CrossRefGoogle Scholar
  29. 29.
    Strukov D.B., Snider G.S., Stewart D.R., Williams, R.S. (2008) The missing memristor found. Nature 453. doi:10.1038/nature06932.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.University of Twente, EWI/EL/CEEnschedeThe Netherlands

Personalised recommendations