Journal Article10.1109/81.847870
Bifurcations in one-dimensional piecewise smooth maps-theory and applications in switching circuits
TL;DR: In this paper, the authors present a systematic analysis of the bifurcation behavior of power electronic DC-DC converters through a normal form: the piecewise linear approximation in the neighborhood of the border.
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Abstract: Recent investigations on the bifurcation behavior of power electronic DC-DC converters have revealed that most of the observed bifurcations do not belong to generic classes such as saddle-node, period doubling, or Hopf bifurcations. Since these systems yield piecewise smooth maps under stroboscopic sampling, a new class of bifurcations occur in such systems when a fixed point crosses the border between the smooth regions in the state space. In this paper we present a systematic analysis of such bifurcations through a normal form: the piecewise linear approximation in the neighborhood of the border. We show that there can be many qualitatively different types of border collision bifurcations, depending on the parameters of the normal form. We present a partitioning of the parameter space of the normal form showing the regions where different types of bifurcations occur. We then use this theoretical framework to explain the bifurcation behavior of the current programmed boost converter.
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Citations
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References
•Book
Chaos: An Introduction to Dynamical Systems
Kathleen T. Alligood,Timothy Sauer,James A. Yorke,J. D. Crawford +3 more
- 07 Nov 1996
TL;DR: One-dimensional maps, two-dimensional map, fractals, and chaotic attraction attractors have been studied in this article for state reconstruction from data, including the state of Washington.
2K
Border-collision bifurcations including “period two to period three” for piecewise smooth systems
TL;DR: In this paper, the authors examine bifurcation phenomena for maps that are piecewise smooth and depend continuously on a parameter μ, and they show that stable periodic orbits occur frequently in such situations, but never or almost never occur in smooth systems.
507
Study of chaos in the buck converter
Enric Fossas,Gerard Olivar +1 more
TL;DR: In this article, the one-and two-periodic trajectories of a buck converter were analyzed and the characteristic multipliers associated with each one were computed. And a plot of the number of crossings in the ramp was drawn to investigate the evolution of the trajectories when they are close to the attractor.
Instability, subharmonics and chaos in power electronic systems
J.H.B. Deane,D.C. Hamill +1 more
- 26 Jun 1989
TL;DR: In this article, the concept of chaos is applied to a variety of nonlinear power electronic circuits and the phenomena of subharmonics, quasi-periodicity, and chaos are predicted and observed.
374
Border-collision bifurcations: An explanation for observed bifurcation phenomena.
TL;DR: A general criterion for the occurrence of border-collision bifurcations is given and illustrative numerical results, including transitions to chaotic attractors, are presented.
305