Switchings, bifurcations, and chaos in DC/DC converters

Bernardo, Mario di; Garefalo, F.; Glielmo, Luigi; Vasca, Francesco

doi:10.1109/81.661675

Cited by 230 publications

(138 citation statements)

References 12 publications

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“…The studied converter presents a chaotic behavior depending on the input voltage E (when E ≥ 32.34 V). 2,15,16 Figure 4 shows that the ripple is increased again (≈ 1 V) and therefore, another solution has to be found.…”

Section: Generating Chaosmentioning

confidence: 99%

“…The voltage v of the capacitor C and the inductance current i are chosen as state variables. 2,16 The model of the converter can be written as…”

Section: The Buck Convertermentioning

confidence: 99%

“…1,2 They are usually used in situations where there is the need of stabilizing a given input DC voltage to a higher (Boost), a lower (Buck) or a generic (Buck-Boost) output voltage. 3 This is generally achieved by chopping and filtering the input voltage through an appropriate switching action, mostly implemented via a pulse width modulation.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Improvement of Power Supply Electromagnetic Compatibility by Extension of Chaos Anticontrol

Morel

Bourcerie

Chapeau‐Blondeau

2005

J CIRCUIT SYST COMP

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Switch-mode power supplies usually emit electromagnetic interferences at the switching frequency and its harmonics. Inducing chaos in these systems has recently been suggested as a means of reducing these spectral emissions, yet at the expense of aggravating the overall magnitude of the ripple in the output voltage. We propose here a new nonlinear feedback control method, which induces chaos, and which is able at the same time to achieve low spectral emission and to maintain a small ripple in the output. The feasibility and usefulness of this new and simple method is shown here with a numerical example, which includes a comparison with the previous control method.

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Section: Generating Chaosmentioning

confidence: 99%

“…The voltage v of the capacitor C and the inductance current i are chosen as state variables. 2,16 The model of the converter can be written as…”

Section: The Buck Convertermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Improvement of Power Supply Electromagnetic Compatibility by Extension of Chaos Anticontrol

Morel

Bourcerie

Chapeau‐Blondeau

2005

J CIRCUIT SYST COMP

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“…Recent studies of their dynamics has shown grazing singularities that form organising centers of stability, such as limit cycle bifurcations described by di Bernardo et al (2008) and routes to chaos described by Galvanetto (1997); di Bernardo et al (1998); Zhusubalyev and Mosekilde (2003).…”

Section: Introductionmentioning

confidence: 99%

Two-folds in nonsmooth dynamical systems

Jeffrey

2009

IFAC Proceedings Volumes

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In a three dimensional dynamical system with a discontinuity along a codimension one switching manifold, orbits of the system may be tangent to both sides of the switching manifold generically at isolated points. It is perhaps surprising, then, that examples of such 'two-fold' singularities are difficult to find amongst physical models. They occur where the relative curvature between the flow field and the switching manifold is nonsymmetric about the discontinuity. Here we motivate their study with a local form model of nonlinear control that exhibits the two-fold singularity, where the flow is constant either side of a curved switching manifold. We describe the local dynamics around general two-fold singularities, then consider their effect on global dynamics via one parameter bifurcations of limit cycles.

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“…f i = f j , ∂fi ∂x = ∂fj ∂x , but ∂ n fi ∂x n = ∂ n fj ∂x n . Examples include, to mention just a few, vibro-impacting machines in mechanical engineering and systems with friction [1], switching circuits in power electronics [2], [3] physiological models [4], internal combustion engines [5], walking machines [6]; more generally, k.camlibel@uvt.nl all those systems which are intrinsically non-smooth on macroscopic time-scales.…”

Section: Introductionmentioning

confidence: 99%

Structural Stability of Boundary Equilibria in a class of hybrid systems: Analysis and Use for Control System Design

Bernardo

Camlibel

Proceedings of the 44th IEEE Conference on Decision and Control

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Abstract-This paper is concerned with the structural stability of boundary equilibria in a class of hybrid systems, that of piecewise linear continuous systems. Specifically, we study the structural stability under parameter variations of equilibria lying on discontinuity boundaries in phase space dividing regions where the system under investigation is smooth. We show that it is possible to give a set of conditions to account for the possible dynamical scenarios that can be observed. We present a novel scenario where under perturbations, the equilibrium of interest does not persist and a family of stable limit cycles is generated with amplitudes increasing linearly under parameter perturbations. We propose a novel switching control strategy based on the use of the results presented in the paper.

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Switchings, bifurcations, and chaos in DC/DC converters

Cited by 230 publications

References 12 publications

Improvement of Power Supply Electromagnetic Compatibility by Extension of Chaos Anticontrol

Improvement of Power Supply Electromagnetic Compatibility by Extension of Chaos Anticontrol

Two-folds in nonsmooth dynamical systems

Structural Stability of Boundary Equilibria in a class of hybrid systems: Analysis and Use for Control System Design

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