电流反馈型Buck变换器二维分段光滑系统边界碰撞和分岔研究

谢帆; 杨汝; 张波

doi:10.7498/aps.59.8393

摘要

最近几年,边界碰撞分岔已经引起了越来越多的关注.以不连续导通模式下的电流反馈型Buck变换器为例,推导出两个边界三段形式的分段光滑系统的离散映射模型.数值仿真得到以参考电流为分岔参数的分岔图,然后具体分析定点的稳定存在域、分叉图中各段的映射构成和边界碰撞点处工作模式的转换.最后软件仿真和实验验证了二维分段光滑系统边界碰撞和分岔行为的正确性.

关键词:

Border collision bifurcations have received much attention in recent years. A class of piecewise smooth maps with two border and three zones is derived to describe the dynamics of a current-programmed Buck converter operating in a discontinuous mode. The numerical simulation is carried out and the bifurcation diagrams with the reference current as a parameter are obtained. Then, a concrete analysis of the stable existence condition of the fixed point is made, and the structure of bifurcation diagrams and a change in operation mode of the converter at the border collision point are studied. Finally, simulation and experimental results show that the theoretical analysis is correct.

Keywords:

作者及机构信息

(1)广州大学物理与电子工程学院,广州 510006; (2)华南理工大学电力学院,广州 510640

基金项目: 国家自然科学基金重点项目(批准号:50937001)和国家自然科学基金(批准号:50877028,50777009)资助的课题.

Authors and contacts

(1)College of Electric Power, South China University of Technology, Guangzhou 510640, China; (2)School of Physics and Electronic Engineering, Guangzhou University, Guangzhou 510006, China

参考文献

[1]	Hamill D C, Jefferies D J 1988 IEEE Trans. Circ. Syst. 35 1059
[2]	Deane J, Hamill D C 1990 IEEE Trans. Power Electron. 5 260
[3]	Luo X S, Wang B H, Chen G R, Quan H J, Fang J Q, Zou Y L, Jiang P Q 2003 Acta Phys. Sin. 52 12 (in Chinese)[罗晓曙、汪秉宏、陈关荣、全宏俊、方锦清、邹艳丽、蒋品群 2003 物理学报 52 12]
[4]	Zhang B, Qu Y 2003 Proc. Chin. Soc. Electr. Eng. 23 99 (in Chinese) [张波、曲颖 2003 中国电机工程学报 23 99]
[5]	Wang X M, Zhang B, Qiu D Y 2008 Acta Phys. Sin. 57 2728 (in Chinese)[王学梅、张波、丘东元 2008 物理学报 57 2728]
[6]	Yang R, Zhang B, Chu L L 2008 Acta Phys. Sin. 57 2770 ( in Chinese) [杨汝、张波、褚利丽 2008 物理学报 57 2770]
[7]	Nusse H E, Ott E, Yorke J A 1994 Phys. Rev. E 49 1073
[8]	Yang T, Jin Y H, Cheng S D 2009 Acta Phys. Sin. 58 5224 (in Chinese)[杨谈、金跃辉、程时端 2009 物理学报 58 5224]
[9]	Banerjee S, Grebogi C 1999 Phys. Rev. E 59 4052
[10]	Roy I, Roy A R 2008 Int. J. Bifur. Chaos 18 577
[11]	Banerjee S, Grebogi C, Ranjian P 2000 IEEE Trans. Circ. Syst. Ⅰ 47 633
[12]	Banerjee S, Karthik M S, Yuan G, Yorke J A 2000 IEEE Trans. Circ. Syst. Ⅰ 47 389
[13]	Wang X M, Zhang B 2009 Proc. Chin. Soc. Electr. Eng. 29 22 (in Chinese) [王学梅、张波 2009 中国电机工程学报 29 22]
[14]	Robert B, Robert C 2002 Int. J. Contr. 75 1356
[15]	Maity S, Tripathy D, Bhattacharya K T, Banerjee S 2007 IEEE Trans. Circ. Syst. Ⅰ 54 1120
[16]	Zhusubaliyev Z T, Soukhoterin E A, Mosekilde E 2003 IEEE Trans. Circ. Syst. Ⅰ 50 1047
[17]	Bao B C, Xu J P, Liu Z 2009 Acta Phys. Sin. 58 2949 (in Chinese) [包伯成、许建平、刘中 2009 物理学报 58 2949]
[18]	Dai D, Ma X K, Li X F 2003 Acta Phys. Sin. 52 2729 ( in Chinese) [戴栋、马西奎、李小峰 2003 物理学报 52 2729]
[19]	Li M, Ma X K, Dai D, Zhang H 2005 Acta Phys. Sin. 54 1084 ( in Chinese) [李明、马西奎、戴栋、张浩 2005 物理学报 54 1084]
[20]	Liu B Z, Peng J H 2004 Nonlinear Dynamics (Beijing:Higher Education Press) p268 (in Chinese) [刘秉正、彭建华 2004 非线性动力学 (北京:高等教育出版社) 第268页]

施引文献

[1]	Hamill D C, Jefferies D J 1988 IEEE Trans. Circ. Syst. 35 1059
[2]	Deane J, Hamill D C 1990 IEEE Trans. Power Electron. 5 260
[3]	Luo X S, Wang B H, Chen G R, Quan H J, Fang J Q, Zou Y L, Jiang P Q 2003 Acta Phys. Sin. 52 12 (in Chinese)[罗晓曙、汪秉宏、陈关荣、全宏俊、方锦清、邹艳丽、蒋品群 2003 物理学报 52 12]
[4]	Zhang B, Qu Y 2003 Proc. Chin. Soc. Electr. Eng. 23 99 (in Chinese) [张波、曲颖 2003 中国电机工程学报 23 99]
[5]	Wang X M, Zhang B, Qiu D Y 2008 Acta Phys. Sin. 57 2728 (in Chinese)[王学梅、张波、丘东元 2008 物理学报 57 2728]
[6]	Yang R, Zhang B, Chu L L 2008 Acta Phys. Sin. 57 2770 ( in Chinese) [杨汝、张波、褚利丽 2008 物理学报 57 2770]
[7]	Nusse H E, Ott E, Yorke J A 1994 Phys. Rev. E 49 1073
[8]	Yang T, Jin Y H, Cheng S D 2009 Acta Phys. Sin. 58 5224 (in Chinese)[杨谈、金跃辉、程时端 2009 物理学报 58 5224]
[9]	Banerjee S, Grebogi C 1999 Phys. Rev. E 59 4052
[10]	Roy I, Roy A R 2008 Int. J. Bifur. Chaos 18 577
[11]	Banerjee S, Grebogi C, Ranjian P 2000 IEEE Trans. Circ. Syst. Ⅰ 47 633
[12]	Banerjee S, Karthik M S, Yuan G, Yorke J A 2000 IEEE Trans. Circ. Syst. Ⅰ 47 389
[13]	Wang X M, Zhang B 2009 Proc. Chin. Soc. Electr. Eng. 29 22 (in Chinese) [王学梅、张波 2009 中国电机工程学报 29 22]
[14]	Robert B, Robert C 2002 Int. J. Contr. 75 1356
[15]	Maity S, Tripathy D, Bhattacharya K T, Banerjee S 2007 IEEE Trans. Circ. Syst. Ⅰ 54 1120
[16]	Zhusubaliyev Z T, Soukhoterin E A, Mosekilde E 2003 IEEE Trans. Circ. Syst. Ⅰ 50 1047
[17]	Bao B C, Xu J P, Liu Z 2009 Acta Phys. Sin. 58 2949 (in Chinese) [包伯成、许建平、刘中 2009 物理学报 58 2949]
[18]	Dai D, Ma X K, Li X F 2003 Acta Phys. Sin. 52 2729 ( in Chinese) [戴栋、马西奎、李小峰 2003 物理学报 52 2729]
[19]	Li M, Ma X K, Dai D, Zhang H 2005 Acta Phys. Sin. 54 1084 ( in Chinese) [李明、马西奎、戴栋、张浩 2005 物理学报 54 1084]
[20]	Liu B Z, Peng J H 2004 Nonlinear Dynamics (Beijing:Higher Education Press) p268 (in Chinese) [刘秉正、彭建华 2004 非线性动力学 (北京:高等教育出版社) 第268页]

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