BIFURCATIONS IN <i>DC–DC</i> SWITCHING CONVERTERS: REVIEW OF METHODS AND APPLICATIONS

Aroudi, Abdelali El; Debbat, Mohamed; Giral, Roberto; Olivar, Gerard; Benadero, Luis; Toribio, E.

doi:10.1142/s0218127405012946

Cited by 129 publications

(57 citation statements)

References 49 publications

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“…The appearance of quasiperiodic dynamics has repeatedly been observed in recent numerical studies of various piecewise-smooth systems, 35,37,39,40,42,43,46 and it has been reported that such behavior can appear through a smooth Neimark-Sacker bifurcation as well as through a border collision bifurcation. Border-collision bifurcations are distinguished from the local bifurcations we know for smooth systems by the fact that the eigenvalues of the considered modes can make abrupt jumps in the complex plane.…”

Section: Discussionmentioning

confidence: 77%

“…To understand the way of working of this converter, let us first suppose that comparator 2 and switch S 2 are excluded from the circuit. In this case we have a simple dc-dc buck converter with single-zone regulation as described, for instance, by Aroudi et al 42 As switch S 1 opens and closes, the voltage applied to the LC filter varies between input voltage and zero. The LC filter smooths the signal to be applied to the load resistor R into a relatively constant voltage of a value lower than that of the input voltage.…”

Section: Experimental Confirmationmentioning

confidence: 99%

“…Recent reviews on border-collision bifurcations in piecewise-smooth mechanical and power electronic systems have been published by Banerjee and Verghese, 33 Blazejczyk-Okolewska et al, 34 Leine and Nijmeijer, 35 Tse, 36 and Zhusubaliyev and Mosekilde. 37 Evidence from the study of a large number of physical systems, 35,[37][38][39][40][41][42][43] e.g., switching circuits, impact oscillators, accumulated over the years demonstrates that quasiperiodic dynamics regularly occurs in such systems. The onset of quasiperiodic behavior has been reported in impact oscillators by Piiroinen et al 43 This article discusses the changes in system behavior that arise as parameter variations lead to the appearance of grazing intersections between quasiperiodic attractor and a two-dimensional impact surface in a threedimensional state space.…”

Section: Introductionmentioning

confidence: 99%

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Border collision route to quasiperiodicity: Numerical investigation and experimental confirmation

Zhusubaliyev

Mosekilde

Maity

et al. 2006

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Numerical studies of higher-dimensional piecewise-smooth systems have recently shown how a torus can arise from a periodic cycle through a special type of border-collision bifurcation. The present article investigates this new route to quasiperiodicity in the two-dimensional piecewiselinear normal form map. We have obtained the chart of the dynamical modes for this map and showed that border-collision bifurcations can lead to the birth of a stable closed invariant curve associated with quasiperiodic or periodic dynamics. In the parameter regions leading to the existence of an invariant closed curve, there may be transitions between an ergodic torus and a resonance torus, but the mechanism of creation for the resonance tongues is distinctly different from that observed in smooth maps. The transition from a stable focus point to a resonance torus may lead directly to a new focus of higher periodicity, e.g., a period-5 focus. This article also contains a discussion of torus destruction via a homoclinic bifurcation in the piecewise-linear normal map. Using a dc-dc converter with two-level control as an example, we report the first experimental verification of the direct transition to quasiperiodicity through a border-collision bifurcation. Application of nonlinear dynamics and chaos theory in practice, particularly in engineering, often leads to the analysis of piecewise-smooth systems. Low-dimensional models of such systems have shown that they can exhibit behavioral transitions, referred to as border-collision bifurcations, that are qualitatively different from the bifurcations we know for smooth dynamical systems. In particular, these bifurcations can produce direct transitions from periodicity to chaos or, for instance, from period-2 to period-3 dynamics. The purpose of this article is to show that torus birth bifurcations (transitions to quasiperiodicity) can also occur via border-collision bifurcations. In this case a pair of complex conjugate Floquet multipliers jump from the inside to the outside of the unit circle. We also examine the border-collision bifurcations through which the ergodic torus is transformed into a resonance torus. Torus destruction represents one of the most complicated routes to chaos, and the possible mechanisms for torus destruction in nonsmooth systems have not yet been examined in detail. A second purpose of the present article is to initiate this analysis. Finally, we illustrate our results through a practical example from power electronics and present the first experimental verification of torus birth via a border-collision bifurcation.

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Section: Discussionmentioning

confidence: 77%

Section: Experimental Confirmationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Border collision route to quasiperiodicity: Numerical investigation and experimental confirmation

Zhusubaliyev

Mosekilde

Maity

et al. 2006

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…For the case of a buck circuit topology, state variables are the capacitor voltage v C and inductor current i L . It can be demonstrated that the map that relates both samples could be expressed as [11]:…”

Section: Discrete-mapsmentioning

confidence: 99%

Demonstration of ripple-based index for predicting fast-scale instability in switching power converters

Rodríguez

Alarcón

Aroudi

2009

2009 IEEE International Symposium on Circuits and Systems

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Abstract-In this paper a simplified model based on the exact discrete-time map of a buck switching power converter with proportional control, which captures all its dynamics, allows deriving a closed-form stability condition for predicting fast-scale instability boundary. This condition analytically demonstrates the validity of the recently proposed ripple-based index to predict fast-scale period-doubling, hitherto based on an a priori hypothesis and simulation validation, thereby demonstrating the use of the ripple index as a design-oriented tool. The equivalence of the ripple index to the condition derived from the discrete-time map endorses its use as a means to characterize the complete design space against fast-scale instabilities.

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“…A large variety of complex nonlinear instability phenomena, such as period doubling leading to subharmonic oscillations, and Hopf or Neimark-Sacker bifurcations leading to slow-scale instabilities or saddle-node bifurcation leading to jump phenomenon between different steady-state solutions have been reported in switchedmode DC-DC converters. These studies, which are mostly based on accurate approaches coping with nonlinear behavior such as discrete-time mappings [3] or the Floquet theory together with Filippov's method [4]. These phenomena can have harmful effects on the system operation and may cause system failure, malfunctioning or even damages caused by the increase of the stress on the switching components which would rise the working temperature and this in turn would shorten the lifetime of the system.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of a high-step-Up DC grid-connected two-stage boost DC-DC converter

Aroudi

Giaouris

Mandal

et al. 2014

MATEC Web of Conferences

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Abstract. High conversion ratio switching converters are used whenever there is a need to step-up dc source voltage level to a much higher output dc voltage level such as in photovoltaic systems, telecommunications and in some medical applications. A simple solution for achieving this high conversion ratio is by cascading different stages of dc-dc boost converters. The individual converters in such a cascaded system are usually designed separately applying classical design criteria. However these criteria may not be applicable for the complete cascaded system . This paper first presents a glimpse on the bifurcation behavior that a cascade connection of two boost converters can exhibit. It is shown that the desired periodic orbit can undergo period doubling leading to subharmonic oscillations and chaotic regimes. Then, in order to simplify the analysis the second stage is considered as constant current sink and design-oriented analysis is carried out to obtain stability boundaries in the parameter space by taking into account slope interactions between the state variables in the two-different stages.

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BIFURCATIONS IN DC–DC SWITCHING CONVERTERS: REVIEW OF METHODS AND APPLICATIONS

Cited by 129 publications

References 49 publications

Border collision route to quasiperiodicity: Numerical investigation and experimental confirmation

Border collision route to quasiperiodicity: Numerical investigation and experimental confirmation

Demonstration of ripple-based index for predicting fast-scale instability in switching power converters

Stability analysis of a high-step-Up DC grid-connected two-stage boost DC-DC converter

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