Switched bond graphs as front-end to formal verification of hybrid systems

  • Jan-Erik Strömberg
  • Simin Nadjm-Tehrani
  • Jan L. Top
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1066)


Formal verification of safety and timing properties of engineering systems is only meaningful if based on models which are systematically derived. In this paper we report on our experience using switched bond graphs for the modelling of hardware components in hybrid systems. We present the basic ideas underlying bond graphs in general and switched bond graphs in particular. Switched bond graphs are tailored for the modelling of physical systems undergoing abrupt structural changes. Such abrupt changes appear frequently in plants closed by discrete controllers. We illustrate our approach by means of an aircraft landing gear system and prove safety and timeliness properties using the proof system of extended duration calculus.


hybrid system physical modelling bond graph verification duration calculus 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. Andersson. Object-Oriented Modeling and Simulation of Hybrid Systems. PhD thesis, Lund Institute of Technology, Lund, 1994. Dissertation no. ISRN LUTFD2/TFRT-1043-SE.Google Scholar
  2. 2.
    Z. Chaochen, A.P. Ravn, and M.R. Hansen. An extended duration calculus for hybrid real-time systems. In Hybrid Systems, Lecture Notes in Computer Science, No. 736, pages 36–59, Berlin, 1993.Google Scholar
  3. 3.
    H. Elmqvist. Dymola User's Manual. Dynasim AB, Lund, 1994.Google Scholar
  4. 4.
    R.L. Grossman, A. Nerode, A.P. Ravn, and H. Rischel, editors. Proc. of Workshop on Theory of Hybrid Systems, LNCS 736, Lyngby, October 1992. Springer Verlag.Google Scholar
  5. 5.
    J.C. Hansen. Letters about a siphon machine installation at Harz: September 5, 1727–August 4, 1729. In Collection of the Royal Library, volume I.p.23:I. Stockholm, 1727. Letters 138–140, 142, 143, 147, 151, 154, 160. In German.Google Scholar
  6. 6.
    D.C. Karnopp, R.C. Rosenberg, and D. Margolis. System dynamics — A unified approach (2nd edition). John Wiley & Sons, New York, 1990.Google Scholar
  7. 7.
    S. Lindroth. Christoffer Polhem och Stora Kopparberget. Stora Kopparbergs Bergslags AB, Uppsala, 1951. In Swedish with abstract in German.Google Scholar
  8. 8.
    S.E. Mattsson and M. Andersson. Omola — An object oriented modeling language. In Jamshidi and Herget, editors, Recent advances in computer-aided control systems engineering, volume 9, pages 291–310, 1993.Google Scholar
  9. 9.
    M. Morin, S. Nadjm-Tehrani, P. Österling, and E. Sandewall. Real-time hierarchical control. IEEE software, 9(5):51–57, 1992.Google Scholar
  10. 10.
    S. Nadjm-Tehrani. Reactive Systems in Physical Environments: Compositional Modelling and Framework for Verification. PhD thesis, Linköping University, Linköping, 1994. Dissertation no. 338.Google Scholar
  11. 11.
    S. Nadjm-Tehrani and J.E. Strömberg. Proving Dynamic Properties in an Aerospace Application. In Proc. of the 16th International Symposium on Real-time Systems. IEEE Computer Society Press, December 1995.Google Scholar
  12. 12.
    S. Nadjm-Tehrani, J.E. Strömberg, and A. Jansson. Modelling and verification of the JAS landing gear and hydraulic power supply system. Technical Report to appear, Dept. of Electrical Engineering, Linköping University, Sweden, 1995.Google Scholar
  13. 13.
    H.M. Paynter. Analysis and design of engineering systems. MIT Press, Cambridge, M.A., 1961.Google Scholar
  14. 14.
    U. Söderman. Conceptual modelling of mode switching physical systems. PhD thesis, Linköping University, Linköping, 1995. Dissertation no. 375.Google Scholar
  15. 15.
    J.E. Strömberg. A mode switching modelling philosophy. PhD thesis, Linköping University, Linköping, 1994. Dissertation no. 353.Google Scholar
  16. 16.
    J.E. Strömberg, J.L. Top, and U. Söderman. Variable causality in bond graphs caused by discrete effects. In Proc. First Int. Conf. on Bond Graph Modeling (ICBGM '93), number 2 in SCS Simulation Series, volume 25, pages 115–119, San Diego, 1993.Google Scholar
  17. 17.
    J.L. Top. Conceptual modelling of physical systems. PhD thesis, University of Twente, Enschede, 1993.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Jan-Erik Strömberg
    • 1
  • Simin Nadjm-Tehrani
    • 2
  • Jan L. Top
    • 3
  1. 1.Div. of Automatic Control, Dept. of Electrical EngineeringLinköping UniversityLinköpingSweden
  2. 2.Dept. of Computer & Information ScienceLinköping UniversityLinköpingSweden
  3. 3.Agrotechnological Research Institute ATO-DLOWageningenThe Netherlands

Personalised recommendations