Smale Horseshoes and Symbolic Dynamics in the Buck-Boost DC-DC Converter

DC-DC converter, which is used to change and control voltage magnitude, is a really important part of the power electronic conditioning systems. Study of nonlinear dynamics and chaos in power electronics are becoming increasingly significant in the power quality and stability of distributed power ge...

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Published inIEEE transactions on industrial electronics (1982) Vol. 65; no. 1; pp. 800 - 809
Main Authors Wang, Yanfen, Yang, Ru, Zhang, Bo, Hu, Wei
Format Journal Article
LanguageEnglish
Published New York IEEE 01.01.2018
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Buck–boost converter
Chaos
Circuit stability
DC-DC power converters
Dependence
Dynamical systems
Electric power distribution
Electric power generation
Fixed points (mathematics)
Invariants
Manifolds
Nonlinear dynamics
Nonlinear systems
Numerical stability
Poincare maps
Power converters
smale horseshoe
Stability criteria
symbolic dynamics
Voltage converters (DC to DC)
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Abstract DC-DC converter, which is used to change and control voltage magnitude, is a really important part of the power electronic conditioning systems. Study of nonlinear dynamics and chaos in power electronics are becoming increasingly significant in the power quality and stability of distributed power generation systems. In this paper, the mechanisms that give rise to chaotic dynamical in the buck- boost power converter is studied. The Poincare map of a buck-boost converter system possesses the invariant manifolds having a delightfully complicated structure. Based on the Smale-Birkhoff homoclinic theorem, the structure of invariant manifolds of a fixed point indicates the presence of Smale horseshoe. The horseshoe map of the system is topologically conjugate with the shift map of the symbolic dynamics. The system can be identified with the Smale horseshoe by means of its symbolic descriptions. Furthermore, since the Smale horseshoe map implies sensitive dependence on the initial condition, homoclinic intersection of stable and unstable manifolds may be applied to illustrate the existence of chaos.
AbstractList DC-DC converter, which is used to change and control voltage magnitude, is a really important part of the power electronic conditioning systems. Study of nonlinear dynamics and chaos in power electronics are becoming increasingly significant in the power quality and stability of distributed power generation systems. In this paper, the mechanisms that give rise to chaotic dynamical in the buck- boost power converter is studied. The Poincare map of a buck-boost converter system possesses the invariant manifolds having a delightfully complicated structure. Based on the Smale-Birkhoff homoclinic theorem, the structure of invariant manifolds of a fixed point indicates the presence of Smale horseshoe. The horseshoe map of the system is topologically conjugate with the shift map of the symbolic dynamics. The system can be identified with the Smale horseshoe by means of its symbolic descriptions. Furthermore, since the Smale horseshoe map implies sensitive dependence on the initial condition, homoclinic intersection of stable and unstable manifolds may be applied to illustrate the existence of chaos.
Author Bo Zhang
Ru Yang
Yanfen Wang
Wei Hu
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SubjectTerms Buck–boost converter
Chaos
Circuit stability
DC-DC power converters
Dependence
Dynamical systems
Electric power distribution
Electric power generation
Fixed points (mathematics)
Invariants
Manifolds
Nonlinear dynamics
Nonlinear systems
Numerical stability
Poincare maps
Power converters
smale horseshoe
Stability criteria
symbolic dynamics
Voltage converters (DC to DC)
Title Smale Horseshoes and Symbolic Dynamics in the Buck-Boost DC-DC Converter
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