V2控制Buck变换器分岔与混沌行为的机理及镇定

张方樱; 杨汝; 龙晓莉; 谢陈跃; 陈虹

doi:10.7498/aps.62.218404

摘要

V2控制的Buck变换器在反馈放大系数变化的情况下表现出丰富的非线性行为. 本文建立了V2控制Buck变换器的离散迭代模型, 利用单值矩阵方法研究了系统不稳定行为. 随着反馈放大系数的增大, 变换器从稳定的周期一状态发生一系列的倍周期分岔现象进入周期二、周期四, 不断倍化直至混沌态. 同时其单值矩阵的最大特征值也沿着实负轴穿越单位圆, 从而从稳定性的角度揭示了系统发生一系列倍周期分岔的机理. 基于单值矩阵理论, 利用正弦电压补偿方法镇定了系统的分岔和混沌行为, 得到了镇定后系统的稳定边界. 仿真和实验结果证明了本文分析方法和结论的正确性.

关键词:

V2控制 /
Buck变换器 /
分岔 /
镇定控制

Abstract

Along with the variation of the feedback amplify coefficient, V2 controlled Buck converter exhibits abundant nonlinear dynamical behaviors. By establishing the discrete-time model of the system, this paper has studied the instability phenomena based on the monodromy matrix method. With increasing feedback factor, the analysis indicated that the converter entered from a stable period-one statue into a period-doubling statue. Finally, it showed chaos. Mechanism of the bifurcation generated by the system was fully analyzed based on the monodromy matrix, which showed that as the increase of the feedback coefficient, an eigenvalue of the monodromy matrix went out of the unit circle; this was the reason why the system generated period-doubling bifurcation. Also presented was the sinusoidal voltage compensation method to extend the stability margin based on the monodromy matrix theory, by which the instability behavior was effectively handled. Simulation and experimental results confirmed the analytical method.

Keywords:

作者及机构信息

1.
广州大学实验中心, 广州 510006;

2.
广州大学物理与电子工程学院, 广州 510006

基金项目: 国家自然科学基金(批准号: 51277035)和广州市对外科技合作专项(批准号: 2013J4500029)资助的课题.

Authors and contacts

1.
Labcenter, Guangzhou University, Guangzhou 510006, China;

2.
School of Physics and Electronic Engineering, Guangzhou University, Guangzhou 510006, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51277035), and the International Science and Technology Cooperation Program of Guangdong Province, China (Grant No. 2013J4500029).

参考文献

[1]	Li J, Lee F C 2010 IEEE Trans. Circuits Syst. I, Reg. Papers 57 2552
[2]	Goder D, Pelletier W 1996 Proceedings of High Frequency Power Conversion 1996 19
[3]	Wang F Y, Xu J P, Xu J F 2005 Proc. the CSEE 25 67 (in Chinese) [王凤岩, 许建平, 许峻峰 2005 中国电机工程学报 25 67]
[4]	Song Q 2001 Proceedings of APEC’ 2001 507
[5]	Wang F Y, Wu S R, Xu J P 2002 International Conference on Communications, Circuits and Systems and West Sino Expositions New York, USA June 29-July 1, 2002 p1711
[6]	Wang F Y, Xu J F, Xu J P 2004 International Conference on Communications, Circuits and Systems Chengdu, China, June 27–29, 2004 p1358
[7]	Yang R, Zhang B, Chu L L 2008 Acta Phys. Sin. 57 2770 (in Chinese) [杨汝, 张波, 褚利丽 2008 57 2770]
[8]	Wang F Q, Ma X K, Yan Y 2011 Acta Phys. Sin. 60 060510 (in Chinese) [王发强, 马西奎, 闫晔 2011 60 060510]
[9]	Xie L L, Gong R X, Zhuo H Z 2012 Acta Phys. Sin. 61 058401 (in Chinese) [谢玲玲, 龚仁喜, 卓浩泽 2012 61 058401]
[10]	Liu F 2008 Chin. Phys. B 17 2394
[11]	Lu W G, Zhou L W, Luo Q M, Du X 2007 Acta Phys. Sin. 56 6275 (in Chinese) [卢伟国, 周雒维, 罗全明, 杜雄 2007 56 6275]
[12]	Zhou G H, Xu J P, Jin Y Y, Jin S 2010 International Conference on Communications, Circuits and Systems Chengdu, China, July 28–30, 2010 p551
[13]	He S Z, Zhou G H, Xu J P 2013 Acta Phys. Sin. 62 (in Chinese) [何圣仲, 周国华, 许建平, 包伯成, 杨平 2013 62 110503]
[14]	Zhou Y F, Tse C K, Qiu S, Lau F 2005 Chin. Phys. 14 61
[15]	Kavitha A. Uma G 2010 Int. J. Contr, Autom, Systems 8 1320
[16]	Giaouris D, Banerjee S, Zahawi B, Pickert V 2008 IEEE Trans. Circuits Syst. I, Reg. Papers 55 1084
[17]	Leine R I, VAN Campen D H, VAN DE VRANDE B L Nonlinear Dynam. 23 105
[18]	Filippov A F 1964 American Mathematical Society Translations, Series 2 42 199
[19]	Xie F, Yang R, Zhang B 2010 Acta Phys. Sin. 59 8393 (in Chinese) [谢帆, 杨汝, 张波 2010 59 8393]

施引文献

[1]	Li J, Lee F C 2010 IEEE Trans. Circuits Syst. I, Reg. Papers 57 2552
[2]	Goder D, Pelletier W 1996 Proceedings of High Frequency Power Conversion 1996 19
[3]	Wang F Y, Xu J P, Xu J F 2005 Proc. the CSEE 25 67 (in Chinese) [王凤岩, 许建平, 许峻峰 2005 中国电机工程学报 25 67]
[4]	Song Q 2001 Proceedings of APEC’ 2001 507
[5]	Wang F Y, Wu S R, Xu J P 2002 International Conference on Communications, Circuits and Systems and West Sino Expositions New York, USA June 29-July 1, 2002 p1711
[6]	Wang F Y, Xu J F, Xu J P 2004 International Conference on Communications, Circuits and Systems Chengdu, China, June 27–29, 2004 p1358
[7]	Yang R, Zhang B, Chu L L 2008 Acta Phys. Sin. 57 2770 (in Chinese) [杨汝, 张波, 褚利丽 2008 57 2770]
[8]	Wang F Q, Ma X K, Yan Y 2011 Acta Phys. Sin. 60 060510 (in Chinese) [王发强, 马西奎, 闫晔 2011 60 060510]
[9]	Xie L L, Gong R X, Zhuo H Z 2012 Acta Phys. Sin. 61 058401 (in Chinese) [谢玲玲, 龚仁喜, 卓浩泽 2012 61 058401]
[10]	Liu F 2008 Chin. Phys. B 17 2394
[11]	Lu W G, Zhou L W, Luo Q M, Du X 2007 Acta Phys. Sin. 56 6275 (in Chinese) [卢伟国, 周雒维, 罗全明, 杜雄 2007 56 6275]
[12]	Zhou G H, Xu J P, Jin Y Y, Jin S 2010 International Conference on Communications, Circuits and Systems Chengdu, China, July 28–30, 2010 p551
[13]	He S Z, Zhou G H, Xu J P 2013 Acta Phys. Sin. 62 (in Chinese) [何圣仲, 周国华, 许建平, 包伯成, 杨平 2013 62 110503]
[14]	Zhou Y F, Tse C K, Qiu S, Lau F 2005 Chin. Phys. 14 61
[15]	Kavitha A. Uma G 2010 Int. J. Contr, Autom, Systems 8 1320
[16]	Giaouris D, Banerjee S, Zahawi B, Pickert V 2008 IEEE Trans. Circuits Syst. I, Reg. Papers 55 1084
[17]	Leine R I, VAN Campen D H, VAN DE VRANDE B L Nonlinear Dynam. 23 105
[18]	Filippov A F 1964 American Mathematical Society Translations, Series 2 42 199
[19]	Xie F, Yang R, Zhang B 2010 Acta Phys. Sin. 59 8393 (in Chinese) [谢帆, 杨汝, 张波 2010 59 8393]

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