A new technique to generate independent periodic attractors in the state space of nonlinear dynamic systems

Morel, Cristina; Vlad, R.C.; Chauveau, Éric

doi:10.1007/s11071-009-9519-7

Cited by 9 publications

(5 citation statements)

References 30 publications

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“…The first one is the generation of several independent periodic attractors. Recently, [21] demonstrated that the equidistant repartition of these attractors is in a precise zone (a controllable state space area) of a precise curve, which depends of the sine anticontrol feedback v c (t) frequency. Then, the state space domains where the attractors are generated from different initial conditions were determined.…”

Section: Anticontrol Of Chaosmentioning

confidence: 99%

“…Then, the state space domains where the attractors are generated from different initial conditions were determined. Also, a mathematical formula giving the maximal attractors number in function of the controller piecewise-constant values has been deduced [21]. In this paper, we are interested by the second property: the size of the attractors.…”

Section: Anticontrol Of Chaosmentioning

confidence: 99%

“…After the study of the photovoltaic systems [22][23],the purpose of this article is to introduce a nonlinear feedback controller that maintains a small ripple in the output voltage and also achieves a low spectral emission. Its design is based upon a property exhibited in [19]- [21]: a chaotified nonlinear system presents many small independent chaotic attractors. The initial nonlinear system is chaotified using a simple sine function of the system state, as in [7], but with large amplitude.…”

Section: Introductionmentioning

confidence: 99%

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Reducing the Spectral Emissions of PFC Converters by Anticontrol of Chaos

Merhy¹,

Morel²,

Chauveau³

et al. 2013

International Journal of Power Electronics and Drive Systems (IJPEDS)

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Switch-mode power supplies usually emit electromagnetic interferences at the switching frequency and its multiple harmonics. We propose a feedback control method improving switchmode power supplies electromagnetic compatibility (spectral peaks compliance). Inducing chaos in these systems has recently been suggested as a means of reducing these spectral emissions. Indeed, the application of the classical method of chaos anticontrol to these systems leads the output voltage to have an excessive ripple or an undesirable spectrum, whereas these problems are solved with ours. We propose here a converter, able at the same time to achieve low spectral emission and to maintain a small ripple. The design of this controller is based on the property that chaotified nonlinear systems present many independent chaotic attractors of small dimensions. To confirm the efficiency of this method, a comparison with the anticontrol method is included, together with a numerical example clearly showing the effect of this control.

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Section: Anticontrol Of Chaosmentioning

confidence: 99%

Section: Anticontrol Of Chaosmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Reducing the Spectral Emissions of PFC Converters by Anticontrol of Chaos

Merhy¹,

Morel²,

Chauveau³

et al. 2013

International Journal of Power Electronics and Drive Systems (IJPEDS)

Self Cite

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“…Due to the strong non-linear modeling of switching converters [9], these converters can exhibit complex dynamical behaviors such as bifurcation and chaos with variation of a bifurcation parameter [10]. This bifurcation parameter can be the load [11], the reference voltage [12], the reference current [13,14], the inductance [15] of the converter, or a control parameter [16,17]. There is a bifurcation route towards chaos when increasing or decreasing these parameters, forcing the MOSFET to operate under harsh conditions.…”

Section: Introductionmentioning

confidence: 99%

Impact of Chaos on MOSFET Thermal Stress and Lifetime

Morel,

Morel

2024

Electronics

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The reliability of power electronic switching components is of great concern for many researchers. For their usage in many mission profiles, it is crucial for them to perform for the duration of their intended lifetime; however, they can fail because of thermal stress. Thus, it is essential to analyze their thermal performance. Non-linear switching action, bifurcation and chaotic events may occur in DC-DC power converters. Consequently, they show different behaviors when their parameters change. However, this is an opportunity to study these bifurcation phenomena and the existence of chaos, e.g., in boost converters, on their performance as the effects of load variations (mission profiles) on the system’s behavior. These variations generate many non-linear phenomena such as periodic behavior, repeated period-doubling bifurcations and chaos in the MOSFET drain-source current. Thus, we propose, for the first time, an analysis of the influence of chaos on the junction temperature. First of all, this paper provides a step-by-step procedure to establish an electrothermal model of a C2M0080120D MOSFET with integrated power loss. Then, the junction temperature is estimated by computing the power losses and a thermal impedance model of the switch. Additionally, this model is used to investigate the bifurcation and chaotic behavior of the MOSFET junction temperature. The paper contributes by providing a mathematical model to calculate several coefficients based on experimental data and thermal oscillations. Estimation of the number of cycles to failure is given by the Coffin–Manson equation, while temperature cycles are counted using the rainflow counting algorithm. Further, the accumulated damage results are calculated using the Miner’s model. Finally, a comparison is made between the damage accumulated during different mission profiles: significant degradation of the MOSFET’s lifetime is pointed out for chaotic currents compared to periodic ones.

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“…After the study of the harmonics of chaotic systems [16,18], we generated attractors using a switching piecewisebinary controller in a precise but uncontrollable area of the state space [15] [17]. In this paper, we propose a switching piecewise-constant controller in continuous-time systems to generate several independent 1 chaotic attractors in a controllable state space area.…”

Section: Introductionmentioning

confidence: 99%

Generating chaotic attractors on a surface

Morel

Vlad

Morel

et al. 2011

Mathematics and Computers in Simulation

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The present paper introduces a new method to generate several independent periodic attractors, based on a switching piecewiseconstant controller. We demonstrate here that the state space equidistant repartition of these attractors is on an arbitrarily precise zone of a paraboloid or plane. We determine the state space domains where the attractors are generated from different initial conditions. A mathematical formula giving their maximal number in function of the controller piecewise-constant values is then deduced.

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A new technique to generate independent periodic attractors in the state space of nonlinear dynamic systems

Cited by 9 publications

References 30 publications

Reducing the Spectral Emissions of PFC Converters by Anticontrol of Chaos

Reducing the Spectral Emissions of PFC Converters by Anticontrol of Chaos

Impact of Chaos on MOSFET Thermal Stress and Lifetime

Generating chaotic attractors on a surface

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