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Dynamics and Control of Switched Electronic Systems pp 245–271Cite as

Power-Based Modelling

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

Abstract

This chapter presents a systematic method to describe a large class of switched-mode power converters within the Brayton–Moser (BM) framework, a framework that has proven to be useful for analysis and control purposes. The approach forms an alternative to the switched Lagrangian and (port-)Hamiltonian formulations. The proposed methodology allows for the inclusion of often encountered devices like diodes, nonlinear (multi-port) resistors, and equivalent series resistors, a feature that does not seem feasible in the switched Lagrangian formulation. Additionally, and besides the fact that the BM equations allow for almost any type of nonlinear resistor, the framework constitutes a practical advantage since in most control applications the usual measured quantities are voltages and currents—instead of fluxes and charges as with the Lagrangian or (port-)Hamiltonian approaches. The application of the proposed framework to stability analysis, new passivity properties and control is briefly highlighted.

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Notes

  1. 1.

    A circuit that allows for such decomposition is called topologically complete. An additional assumption is that the branch currents in Σ RL can be expressed in terms of the inductor currents and the branch voltages in Σ GC in terms of the capacitor voltages. Circuits that are not topologically complete can often be rendered topologically complete; see Sect. 8.4.

  2. 2.

    This terminology is adopted from the Lagrangian approach [19].

  3. 3.

    A practical switch is usually realised by a semi-conductor device such as a transistor, MOSFET (metal–oxide–semiconductor field-effect transistor), IGBT (insulated gate bipolar transistor), or a thyristor.

  4. 4.

    We adopt the sign convention that the power supplied to the circuit is taken with the negative sign.

  5. 5.

    A complete overview of the BM stability theorems, together with some generalisations, is presented in [14].

  6. 6.

    Systems for which P(x) is not positive semi-definite, but that do satisfy the inequality \(\frac {\mathrm {d}}{{\mathrm {d}}t}P(x) \leq - (\frac {\mathrm {d}}{{\mathrm {d}}t}x )^{\top}B(x)\sigma\), are called cyclo-passive; see e.g. [28].

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Author information

Authors and Affiliations

  1. Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD, Delft, The Netherlands

    Dimitri Jeltsema

  2. Faculty of Mathematics and Natural Sciences, University of Groningen, Nijenborgh 4, 9747 AG, Groningen, The Netherlands

    Jacquelien M. A. Scherpen

Authors
  1. Dimitri Jeltsema
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  2. Jacquelien M. A. Scherpen
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Correspondence to Dimitri Jeltsema .

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Editors and Affiliations

  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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Jeltsema, D., Scherpen, J.M.A. (2012). Power-Based Modelling. 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_8

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  • DOI: https://doi.org/10.1007/978-1-4471-2885-4_8

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-2884-7

  • Online ISBN: 978-1-4471-2885-4

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