Encyclopedia of Systems and Control

2015 Edition
| Editors: John Baillieul, Tariq Samad

Multi-domain Modeling and Simulation

  • Martin Otter
Reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5058-9_140


One starting point for the analysis and design of a control system is the block diagram representation of a plant. Since it is nontrivial to convert a physical model of a plant into a block diagram, this can be performed manually only for small plant models. Based on research from the last 35 years, more and more mature tools are available to achieve this transformation fully automatically. As a result, multi-domain plants, for example, systems with electrical, mechanical, thermal, and fluid parts, can be modeled in a unified way and can be used directly as input–output blocks for control system design. An overview of the basic principles of this approach is given. This provides also the possibility to use nonlinear, multi-domain plant models directly in a controller. Finally, the low-level “Functional Mockup Interface” standard is sketched to exchange multi-domain models between many different modeling and simulation environments.


Block diagram Bond graph Differential-algebraic equation (DAE) system Flow variable FMI for Co-Simulation FMI for Model Exchange Functional Mockup Interface Inverse models Modelica Object-oriented modeling Potential variable Stream variable Symbolic transformation VHDL-AMS 
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  1. Blochwitz T, Otter M, Akesson J, Arnold M, Clauß C, Elmqvist H, Friedrich M, Junghanns A, Mauss J, Neumerkel D, Olsson H, Viel A (2012) The functional mockup interface 2.0: the standard for tool independent exchange of simulation models. In: Proceedings of 9th international modelica conference, Munich, 3–5 Sept 2012, pp 173–184. http://www.ep.liu.se/ecp/076/017/ecp12076017.pdf
  2. Brenan KE, Campbel SL, Petzold LR (1996) Numerical solution of initial-value problems in differential-algebraic equations. SIAM, PhiladelphiaGoogle Scholar
  3. Elmqvist H (1978) A structured model language for large continuous systems. Dissertation. Report CODEN:LUTFD2/(TFRT–1015), Department of Auto Control, Lund Institute of Technology, Lund. http://www.control.lth.se/database/publications/article.pike?action=fulltext&artkey=elm78dis
  4. FMI Group (2010) The Functional Mockup Interface for Model Exchange and for Co-Simulation, version 1.0. https://www.fmi-standard.org
  5. Franke R, Doppelhamer J (2006) Online application of Modelica models in the industrial IT extended automation system 800xA. In: Proceedings of 6th Modelica conference, Vienna, 4–5 Sept 2006, pp 293–302. https://modelica.org/events/modelica2006/Proceedings/sessions/Session3c2.pdf
  6. Franke R, Casella F, Otter M, Sielemann M, Mattsson SE, Olsson H, Elmqvist H (2009) Stream connectors – an extension of modelica for device-oriented modeling of convective transport phenomena. In: Proceedings of 7th Modelica conference, Como, pp 108–121. https://www.modelica.org/events/modelica2009/Proceedings/memorystick/pages/papers/0078/0078.pdf
  7. Frenkel J, Kunze G, Fritzson P (2012) Survey of appropriate matching algorithms for large scale systems of differential algebraic equations. In: Proceedings of the 9th international Modelica conference, Munich, 3–5 Sept 2012, pp 433–442. http://www.ep.liu.se/ecp/076/045/ecp12076045.pdf
  8. IEEE 1076.1-2007 (2007) IEEE standard VHDL analog and mixed-signal extensions. Standard of IEEE. http://standards.ieee.org/findstds/standard/1076.1-2007.html
  9. Isidori A (1995) Nonlinear control systems, 3rd edn. Springer, Berlin/New YorkGoogle Scholar
  10. Karnopp DC, Margolis DL, Rosenberg RC (2012) System dynamics: modeling, simulation, and control of mechatronic systems, 5th edn. Wiley, HobokenGoogle Scholar
  11. Looye G, Thümmel M, Kurze M, Otter M, Bals J (2005) Nonlinear inverse models for control. In: Proceedings of the 4th international Modelica conference, Hamburg, 7–8 March 2005, p 267. https://www.modelica.org/events/Conference2005/onlineproceedings/Session3/Session3c3.pdf
  12. Mattsson SE, Söderlind G (1993) Index reduction in differential-algebraic equations using dummy derivatives. SIAM J Sci Comput 14:677–692MathSciNetGoogle Scholar
  13. Mantoolh HA, Vlach M (1992) Beyond spice with saber and MAST. In: IEEE international symposium on circuits and systems, San Diego, May 10–13 1992, vol 1, pp 77–80Google Scholar
  14. Melville RC, Trajkovic L, Fang SC, Watson LT (1993) Artificial parameter homotopy methods for the DC operating point problem. IEEE Trans Comput Aided Des Integr Circuits Syst 12:861–877. http://citeseerx.ist.psu.edu/viewdoc/download?doi=
  15. Modelica Association (2012) Standard, Modelica transactions on computer – a unified object-oriented language for systems modeling. Language specification, version 3.3. https://www.modelica.org/documents/ModelicaSpec33.pdf
  16. Olsson H, Otter M, Mattsson SE, Elmqvist H (2008) Balanced models in Modelica 3.0 for increased model quality. In: Proceedings of 6th Modelica conference, Bielefeld, pp 21–33. https://modelica.org/events/modelica2008/Proceedings/sessions/session1a3.pdf
  17. Pantelides CC (1988) The consistent initialization of differential-algebraic systems. SIAM J Sci Stat Comput 9:213–233MathSciNetGoogle Scholar
  18. Sieleman M (2012) Device-oriented modeling and simulation in aircraft energy systems design. Dissertation, Dr. Hut. ISBN 3843905045Google Scholar
  19. Sielemann M, Casella F, Otter M, Clauß C, Eborn J, Mattsson SE, Olsson H (2011) Robust initialization of differential-algebraic equations using homotopy. In: 8th international Modelica conference, Dresden. https://www.modelica.org/events/modelica2011/Proceedings/pages/papers/041ID154afv.pdf
  20. Varga A (2000) A descriptor systems toolbox for Matlab. In: Proceedings of CACSD’2000 IEEE international symposium on computer-aided control system design, Anchorage, 25–27 Sept 2000, pp 150–155. http://elib.dlr.de/11629/01/vargacacsd2000p2.pdf

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© Springer-Verlag London 2015

Authors and Affiliations

  • Martin Otter
    • 1
  1. 1.Institute of System Dynamics and ControlGerman Aerospace Center (DLR)WesslingGermany