中国物理B ›› 2006, Vol. 15 ›› Issue (11): 2535-2540.doi: 10.1088/1009-1963/15/11/013

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Existence of horseshoe maps in voltage-mode controlled buck converters

谢智刚1, 戴栋2, 马西奎2   

  1. (1)Department of Electronic and Information Engineering,Hong Kong Polytechnic University, Hong Kong, China; (2)State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi'an Jiaotong University, Xi'an, 710049, China
  • 收稿日期:2005-07-23 修回日期:2006-01-05 出版日期:2006-11-20 发布日期:2006-11-20
  • 基金资助:
    Project supported by National Natural Science Foundation of China (Grant No 50577047), Specialized Research Fund for the\linebreak \makebox[1.6mm]{}Doctoral Program of Higher Education of China (Grant No 20050698004).

Existence of horseshoe maps in voltage-mode controlled buck converters

Dai Dong(戴栋)a)†, Tse Chi-Kong(谢智刚)b), and Ma Xi-Kui(马西奎)a)   

  1. a State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi'an Jiaotong University, Xi'an 710049, China; b Department of Electronic and Information Engineering,Hong Kong Polytechnic University, Hong Kong, China
  • Received:2005-07-23 Revised:2006-01-05 Online:2006-11-20 Published:2006-11-20
  • Supported by:
    Project supported by National Natural Science Foundation of China (Grant No 50577047), Specialized Research Fund for the\linebreak \makebox[1.6mm]{}Doctoral Program of Higher Education of China (Grant No 20050698004).

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摘要： In this paper, chaos in a voltage-mode controlled buck converter is studied. The existence of chaos is proven theoretically in this system. The proof consists of showing that the dynamics of the system is semiconjugate to that of a one-sided shift map, which implies positive entropy of the system and hence chaotic behaviour. The essential tool is the horseshoe hypotheses proposed by Kennedy and Yorke, which will be reviewed prior to the discussion of the main finding.

关键词: power electronics, proof of chaos, horseshoe map

Abstract: In this paper, chaos in a voltage-mode controlled buck converter is studied. The existence of chaos is proven theoretically in this system. The proof consists of showing that the dynamics of the system is semiconjugate to that of a one-sided shift map, which implies positive entropy of the system and hence chaotic behaviour. The essential tool is the horseshoe hypotheses proposed by Kennedy and Yorke, which will be reviewed prior to the discussion of the main finding.

Key words: power electronics, proof of chaos, horseshoe map

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a