Hopf bifurcation and chaos from torus breakdown in a PWM voltage-controlled DC-DC boost converter

Aroudi, Abdelali El; Benadero, Luis; Toribio, E.; Olivar, Gerard

doi:10.1109/81.802837

Cited by 106 publications

(58 citation statements)

References 7 publications

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“…Generally, two distinct types of bifurcations have been identified, namely, slow-scale Hopf-type bifurcation and fast-scale bifurcation. The former can be regarded as a kind of low-frequency phenomenon which is caused by the voltage feedback loop permitting low-frequency oscillation [5]- [8]. The latter, however, is related to the inner current loop instability, and often manifests as period doubling at the switching frequency, as reported in [9], [10].…”

Section: Introductionmentioning

confidence: 99%

Sustained Slow-Scale Oscillation in Higher Order Current-Mode Controlled Converter

Wong

Tse

2008

IEEE Trans. Circuits Syst. II

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Abstract-DC-DC converters under current-mode control have been known to exhibit slow-scale oscillation as a result of a Hopftype bifurcation as one or more of the parameters of the outer voltage loop are varied. In the absence of the outer voltage loop (i.e., open loop), slow-scale oscillation was generally not observed in simple low-order dc-dc converters, i.e., buck, buck-boost, and boost converters. In this paper, slow-scale bifurcation in a higher order current-mode controlled converter is studied. It has been found experimentally that, even in the absence of a closed outer voltage loop, a current-mode controlled Ć uk converter can exhibit a slow-scale Hopf-type bifurcation. The phenomenon was observed in a commercial low-ripple dc-dc converter which has been designed using the Ć uk converter and the LM2611 controller. Such slow-scale oscillation of the inner current loop can also be observed in full-circuit SPICE simulations. An averaged model has been developed and implemented in SPICE to find the Hopf bifurcation boundaries. With this averaged model, the Hopf bifurcation can be explained conveniently using the traditional loop gain analysis. Specifically, the extra degrees of freedom in higher order dc-dc converters have opened up a new possible mode of instability which has not been found in simple low-order dc-dc converters.

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Section: Introductionmentioning

confidence: 99%

Sustained Slow-Scale Oscillation in Higher Order Current-Mode Controlled Converter

Wong

Tse

2008

IEEE Trans. Circuits Syst. II

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“…It refers to a kind of bifurcation is called the Neimarck-Sacker bifurcation, or the Hopf bifurcation of the associated discrete-time dynamics and occurs on the period of the free oscillations of the RLC circuit (the natural period) being larger than the pulse width modulation (PWM) period. The behaviour of a closed loop boost converter, with a variation of the PWM period exhibits that Hopf bifurcation occurs at a certain value of the parameters [29]. [29] A fourth-order current-controlled Cuk converter operates chaotically even in free-running (autonomous) mode and the computer simulations of the circuits reveal the bifurcation from the stable equilibrium state (fixed point), through limit cycles and quasi-periodic orbits, and eventually to chaos [30].…”

Section: Types Of Bifurcations In Dc-dc Convertersmentioning

confidence: 99%

“…The behaviour of a closed loop boost converter, with a variation of the PWM period exhibits that Hopf bifurcation occurs at a certain value of the parameters [29]. [29] A fourth-order current-controlled Cuk converter operates chaotically even in free-running (autonomous) mode and the computer simulations of the circuits reveal the bifurcation from the stable equilibrium state (fixed point), through limit cycles and quasi-periodic orbits, and eventually to chaos [30].…”

Section: Types Of Bifurcations In Dc-dc Convertersmentioning

confidence: 99%

Bifurcation and Chaos in Converter Interfaces in Solar PV Systems-A Review

Subashini¹,

Ramaswamy²

2017

JESTR

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The paper attempts to present a detailed study of the nonlinear phenomena that includes bifurcations, sub-harmonics and chaos in an effort to arrive at the appropriate choice of converter interface suitable for specific PV systems and evolve criterions for their design and control. The resurgence of switching dc-dc converters as power processing units in renewable energy applications appear to open up new perceptions for harnessing energy efficiency. The focus orients to review the modelling techniques used for nonlinear analysis in the different operating modes of the converter and identify the gap in the related domain with special relevance to the converter interfaces in solar PV systems. The exercise incites to explain the forms of bifurcations, the routes to chaos and the associated control techniques for arbitrating its significance in this perspective. The benefits of analysis of nonlinear phenomena in regulatory applications claim a new space in energy processing applications and forge to explore their role as maximum power point (MPP) trackers. The emphasis endeavours to enhance the scope of use of solar energy and offer a fresh dimension to support the clean energy act and perpetuate the desire to enliven a greener world.

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“…Therefore, a range of bifurcation behaviors have been observed, such as flip bifurcation [9], Hopf bifurcation [10], border collision [11], quasi-periodicity [12], and chaos [13].…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis and Control of Nonlinear Behavior in V²Switching Buck Converter

Hu¹,

Zhang²,

Liu³

et al. 2014

Journal of Power Electronics

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Mismatch between switching frequency and circuit parameters often occurs in industrial applications, which would lead to instability phenomena. The bifurcation behavior of V 2 controlled buck converter is investigated as the pulse width modulation period is varied. Nonlinear behavior is analyzed based on the monodromy matrix of the system. We observed that the stable period-1 orbit was first transformed to the period-2 bifurcation, which subsequently changed to chaos. The mechanism of the series of period-2 bifurcations shows that the characteristic eigenvalue of the monodromy matrix passes through the unit circle along the negative real axis. Resonant parametric perturbation technique has been applied to prevent the onset of instability. Meanwhile, the extended stability region of the converter is obtained. Simulation and experimental prototypes are built, and the corresponding results verify the theoretical analysis.

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Hopf bifurcation and chaos from torus breakdown in a PWM voltage-controlled DC-DC boost converter

Cited by 106 publications

References 7 publications

Sustained Slow-Scale Oscillation in Higher Order Current-Mode Controlled Converter

Sustained Slow-Scale Oscillation in Higher Order Current-Mode Controlled Converter

Bifurcation and Chaos in Converter Interfaces in Solar PV Systems-A Review

Stability Analysis and Control of Nonlinear Behavior in V²Switching Buck Converter

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Hopf bifurcation and chaos from torus breakdown in a PWM voltage-controlled DC-DC boost converter

Cited by 106 publications

References 7 publications

Sustained Slow-Scale Oscillation in Higher Order Current-Mode Controlled Converter

Sustained Slow-Scale Oscillation in Higher Order Current-Mode Controlled Converter

Bifurcation and Chaos in Converter Interfaces in Solar PV Systems-A Review

Stability Analysis and Control of Nonlinear Behavior in V2Switching Buck Converter

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Product

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Stability Analysis and Control of Nonlinear Behavior in V²Switching Buck Converter