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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.
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Keywords:
- Buck converter /
- border collision point /
- bifurcations /
- stabile existence condition
[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 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 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 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 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 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 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 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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[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 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 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 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 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 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 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 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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