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为确定不同反馈系数k下DC-DC变换器系统的行为, 结合系统处于周期状态时的稳定性和系统处于混沌时不会重复经过每一点的特点, 提出了一种采用极限思想和信息熵来估计DC-DC变换器非线性行为的方法. 该方法能准确分析系统处于周期状态和混沌状态的熵值, 量化了DC-DC变换器倍周期分叉和混沌行为. 以一阶电压反馈DCM Boost变换器和DCM Buck变换器为例进行仿真. 研究结果表明, 所提出的信息熵可以准确反映分叉点、周期数及产生混沌的位置, 完善了该类变换器非线性动力学分析的理论和方法.
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关键词:
- 混沌 /
- 信息熵 /
- DC-DC /
- Lyapunov指数
In order to identify the DC-DC converter system behavior with different feedback coefficient k, we propose a method, which adopts the ideas of limit and the information about entropy to estimate the DC-DC converter nonlinear behavior by considering the characteristics that the stability of the system in a state of cycle and when the system is in chaos will not be repeated. This method analyses the entropy of the system in periodic and chaotic states and can quantify the period-doubling and chaos behaviors in DC-DC converters. In this paper, we simulate the first-order voltage feedback DCM Boost converter and DCM Buck converter. Results indicate that, according to the proposed information entropy, the bifurcation point, cycle number, and the location of the chaos can be accurately reflected. The above method improves the theory and method of the converter nonlinear dynamics analysis.-
Keywords:
- chaos /
- information entropy /
- DC-DC /
- Lyapunov exponent
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[2] Liu F 2010 Chin. Phys. B 19 080511
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[8] Tse C K, Lai Y M, Iu H H C 2000 IEEE Trans. Circ. Syst. I 47 448
[9] Yuan G H, Banerjee S, Ott E, Yorke J A 1998 IEEE Trans. Circ. Syst. I 45 707
[10] Wang X M, Zhang B, Qiu D Y, Chen L G 2008 Acta Phys. Sin. 57 6112 (in Chinese) [王学梅, 张波, 丘东元, 陈良刚 2008 物理学报 57 6112]
[11] Xu H M, Jin Y G, Guo S X 2013 Acta Phys. Sin. 62 248401 (in Chinese) [徐红梅, 金永镐, 郭树旭 2013 物理学报 62 248401]
[12] Tian Z Q, Zhou Y 2002 J. Inner Mongolia Normal Univ. 31 347 (in Chinese) [田振清, 周越2002内蒙古师范大学学报31 347]
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[14] Yu W B 2008 Experiment and Analysis of Chaos (Beijing: Science Press) p27 (in Chinese) [于万波2008 (北京: 科学出版社)第27页]
[15] Hao B L 1993 Starring with Parabolas An Introduction to Chaotic Dynamics (Shanghai: Shanghai Scientific and Technological Education Publishing House) p19 (in Chinese) [郝柏林1993 从抛物线谈起-混沌动力学引论 (上海: 上海科技教育出版社)第19页]
[16] Tse C K 1994 Int. J. Circ. Theory Appl. 22 263
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[1] Kapitaniak T (translated by Zhu S J, Yu X, Lou J J) 2008 Chaos for Engineers Theory, Applications, and Control (Beijing: National Defense Industry Press) p106 (in Chinese) [卡毕坦尼亚克著(朱石坚, 俞翔, 楼京俊译)面向工程的混沌学: 理论应用及控制2008 (北京: 科学出版社)第106页]
[2] Liu F 2010 Chin. Phys. B 19 080511
[3] Wang F Q, Ma X K 2013 Chin. Phys. B 22 050306
[4] Wu S R, He S Z, Xu J P, Zhou G H, Wang J P 2013 Acta Phys. Sin. 62 218403 (in Chinese) [吴松荣, 何圣仲, 许建平, 周国华, 王金平 2013 物理学报 62 218403]
[5] Yang N N, Liu C X, Wu C J 2012 Chin. Phys. B 21 080503
[6] Zhou G H, Xu J P, Bao B C, Jin Y Y 2010 Chin. Phys. B 19 060508
[7] Chan W C Y, Tse C K 1997 IEEE Power Electronics Specialists Conference 2 1317
[8] Tse C K, Lai Y M, Iu H H C 2000 IEEE Trans. Circ. Syst. I 47 448
[9] Yuan G H, Banerjee S, Ott E, Yorke J A 1998 IEEE Trans. Circ. Syst. I 45 707
[10] Wang X M, Zhang B, Qiu D Y, Chen L G 2008 Acta Phys. Sin. 57 6112 (in Chinese) [王学梅, 张波, 丘东元, 陈良刚 2008 物理学报 57 6112]
[11] Xu H M, Jin Y G, Guo S X 2013 Acta Phys. Sin. 62 248401 (in Chinese) [徐红梅, 金永镐, 郭树旭 2013 物理学报 62 248401]
[12] Tian Z Q, Zhou Y 2002 J. Inner Mongolia Normal Univ. 31 347 (in Chinese) [田振清, 周越2002内蒙古师范大学学报31 347]
[13] Tse C K 1994 IEEE Trans. Circ. Syst. I 41 16
[14] Yu W B 2008 Experiment and Analysis of Chaos (Beijing: Science Press) p27 (in Chinese) [于万波2008 (北京: 科学出版社)第27页]
[15] Hao B L 1993 Starring with Parabolas An Introduction to Chaotic Dynamics (Shanghai: Shanghai Scientific and Technological Education Publishing House) p19 (in Chinese) [郝柏林1993 从抛物线谈起-混沌动力学引论 (上海: 上海科技教育出版社)第19页]
[16] Tse C K 1994 Int. J. Circ. Theory Appl. 22 263
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