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Time-Stepping via Complementarity

  • Chapter
Dynamics and Control of Switched Electronic Systems

Part of the book series: Advances in Industrial Control ((AIC))

Abstract

In this chapter, the numerical time integration methods for switched electronic circuits are described with a focus on the event-capturing time-stepping schemes based on the complementarity theory. After briefly introducing the strengths and weaknesses of various simulation approaches (hybrid, regularised and non-smooth), the mathematical nature of solutions for dynamical complementarity systems are discussed in view of numerical time-integration. Then the formulation of the time-stepping methods via complementarity will be described. For each class of solutions, a suitable method is provided, and its properties are illustrated on simple electrical circuits. Some implementation details are then explained. Especially, the complementarity solvers that are used at each time-step are described recalling the main families of available solvers. Some insights on the software implementation are also given. Finally, numerical applications and examples on more realistic circuits are considered. We will mainly focus on the architecture of a direct current–direct current (DC–DC) buck power converter.

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Notes

  1. 1.

    A set K is called a cone if for any x∈K and any scalar a≥0, ax∈K.

  2. 2.

    The dual cone K ∗ of the cone K is the set K ∗={y | y⋅x≥0 ∀x∈K}.

  3. 3.

    This is not required with the Siconos algorithms that find a consistent initial solution from scratch.

  4. 4.

    For Ngspice, it implied a slight modification of the source code since no standard option is provided to do it.

  5. 5.

    http://www.plexim.com/.

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Acknowledgements

The author would like to warmly thank Pascal Denoyelle for his contribution in the earlier version of this work and his two main co-workers on this project Olivier Bonnefon and Bernard Brogliato. The authors acknowledge Michael Ferris (University Wisconsin–Madison) for providing us with the PATH solver. Part of this work has been supported by the ANR project VAL-AMS (ANR-06-SETI-018-01).

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  1. INRIA Rhône-Alpes, Centre de recherche Grenoble, 655 avenue de l’Europe, Inovallée de Montbonnot, 38334, St Ismier Cedex, France

    Vincent Acary

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Correspondence to Vincent Acary .

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  1. Dipartimento di Ingegneria, Grace: Group for Research, Università del Sannio in Benevento, Piazza Roma 21, Benevento, 82100, Italy

    Francesco Vasca

  2. Dipartimento di Ingegneria, GRACE - Group for Research, Università del Sannio in Benevento, Piazza Roma 21, Benevento, 82100, Italy

    Luigi Iannelli

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Acary, V. (2012). Time-Stepping via Complementarity. In: Vasca, F., Iannelli, L. (eds) Dynamics and Control of Switched Electronic Systems. Advances in Industrial Control. Springer, London. https://doi.org/10.1007/978-1-4471-2885-4_14

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  • DOI: https://doi.org/10.1007/978-1-4471-2885-4_14

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