Nonlinear Dynamics

, Volume 63, Issue 1–2, pp 19–33 | Cite as

Virtual orbits and two-parameter bifurcation analysis in a ZAD-controlled buck converter

  • Viktor Avrutin
  • Enric Fossas
  • Albert GranadosEmail author
  • Michael Schanz
Original Paper


Based on a recently obtained Lemma about periodic orbits in linear systems with a piecewise-linear non-autonomous periodic control, we describe analytically the bifurcation structures in a ZAD-controlled buck converter. This analytical description shows that the period doubling bifurcation in this system may be both subcritical or supercritical. Considering virtual orbits we show how a saddle-node bifurcation becomes feasible and how it is destroyed at a new codimension-2 bifurcation point, where the subcritical period doubling bifurcation becomes supercritical. We also show that this phenomenon does not take place when the error surface in the ZAD conditions piecewise-linear defined.


Non-smooth systems Bifurcations Virtual orbits Zero average dynamics Control Power electronics 


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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Viktor Avrutin
    • 1
  • Enric Fossas
    • 2
  • Albert Granados
    • 1
    Email author
  • Michael Schanz
    • 1
  1. 1.IPVSUniversity of StuttgartStuttgartGermany
  2. 2.IOC-ESAIIUniversitat Politècnica de CatalunyaBarcelonaSpain

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