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A novel concept of switching block is presented via detecting the switching behavior of each switching period in piecewise smooth system of DC-DC switching converter, and logical arithmetic method of computer is used to obtain decimal system from binary system, so complex degree of the system during one switching period is quantized as switching block and the symbolic time sequence of the piece smooth system is established. Weight Lempel-Ziv (L-Z) complexity is derived based on the L-Z complexity and the symbolic time sequence, and the qualitative analysis of nonlinear and complex degree in piecewise smooth system from symbolic time sequence with single variable is carried out. The motion rule and the dynamics structure of the whole system are revealed. Finally, The present current mode controlled buck converter is studied as an example to establish symbolic time sequence and to illustrate the applications of weight L-Z complexity.
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Keywords:
- DC-DC switching converter /
- switching block /
- symbolic time sequence /
- weight Lempel-Ziv complexity
[1] Banerjee S, George C V 2001 Nonlinear Phenomena in Power Electronics (IEEE press) p4
[2] [3] Iu H H C, Tse C K 2000 IEEE Trans. Circuits Syst. I: Fundam. Theory Appl. 47 913
[4] 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]
[5] [6] Kaspar F, Schuster H G 1987 Phys. Rev. A 36 842
[7] [8] Liu B Z, Peng J H 2004 Nonlinear Dynamics (Beijing: Higher Education Press) p430 (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430页]
[9] [10] [11] Zhu Y H, Dong Y J 2001 Acta Math. Sci. A 21 527 ( in Chinese) [朱勇华, 董亚鹃 2001 数学 A 21 527]
[12] [13] Hou W, Feng G L, Dong W J 2005 Acta Phys. Sin. 54 3940 (in Chinese) [侯威, 封国林, 董文杰 2005 54 3940]
[14] Liu X F, Yu W L 2008 Acta Phys. Sin. 57 2587 (in Chinese) [刘小峰, 俞文莉 2008 57 2587]
[15] [16] Lempel A, Ziv J 1976 IEEE Trans. Inform. Theory 22 75
[17] [18] [19] Yang R, Zhang B, Zhao S B, Lao Y J 2010 Acta Phys. Sin. 59 3756 (in Chinese) [杨汝, 张波, 赵寿柏, 劳裕锦 2010 59 3756]
[20] Tse C K 1994 IEEE Trans. Circuits Syst. I: Fundam. Theory Appl. 41 16
[21] [22] L J H, Chen G R, Yu X H, Leung H 2004 IEEE Trans. Circuits Syst. I: Reg. Papers 51 2476
[23] [24] [25] L J H, Yu S M, Leung H, Chen G R 2006 IEEE Trans. Circuits Syst. I: Reg. Papers 53 149
[26] [27] L J H, Chen G R 2006 Int. J. Bifurcat. Chaos 16 775
[28] [29] L J H, Han F L, Yu X H, Chen G R 2004 Automatica 40 1677
[30] Xie F, Yang R, Zhang B 2011 IEEE Trans. Circuits Syst. I: Reg. Papers 58 2269
[31] [32] Xie F, Yang R, Zhang B 2010 Acta Phys. Sin. 59 8393 (in Chinese) [谢帆, 杨汝, 张波 2010 59 8393]
[33] [34] [35] Tse C K, Dai D 2005 Int. J. Bifurcat. Chaos 15 2263
[36] Dai D, Tse C K, Ma X 2005 IEEE Trans. Circuits Syst. I: Reg. Papers 52 1632
[37] [38] [39] Dai D, Tse C K 2004 International Workshop on Nonlinear Circuit Signal Process Waikiki, USA, March 5--7, 2004 p519
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[1] Banerjee S, George C V 2001 Nonlinear Phenomena in Power Electronics (IEEE press) p4
[2] [3] Iu H H C, Tse C K 2000 IEEE Trans. Circuits Syst. I: Fundam. Theory Appl. 47 913
[4] 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]
[5] [6] Kaspar F, Schuster H G 1987 Phys. Rev. A 36 842
[7] [8] Liu B Z, Peng J H 2004 Nonlinear Dynamics (Beijing: Higher Education Press) p430 (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430页]
[9] [10] [11] Zhu Y H, Dong Y J 2001 Acta Math. Sci. A 21 527 ( in Chinese) [朱勇华, 董亚鹃 2001 数学 A 21 527]
[12] [13] Hou W, Feng G L, Dong W J 2005 Acta Phys. Sin. 54 3940 (in Chinese) [侯威, 封国林, 董文杰 2005 54 3940]
[14] Liu X F, Yu W L 2008 Acta Phys. Sin. 57 2587 (in Chinese) [刘小峰, 俞文莉 2008 57 2587]
[15] [16] Lempel A, Ziv J 1976 IEEE Trans. Inform. Theory 22 75
[17] [18] [19] Yang R, Zhang B, Zhao S B, Lao Y J 2010 Acta Phys. Sin. 59 3756 (in Chinese) [杨汝, 张波, 赵寿柏, 劳裕锦 2010 59 3756]
[20] Tse C K 1994 IEEE Trans. Circuits Syst. I: Fundam. Theory Appl. 41 16
[21] [22] L J H, Chen G R, Yu X H, Leung H 2004 IEEE Trans. Circuits Syst. I: Reg. Papers 51 2476
[23] [24] [25] L J H, Yu S M, Leung H, Chen G R 2006 IEEE Trans. Circuits Syst. I: Reg. Papers 53 149
[26] [27] L J H, Chen G R 2006 Int. J. Bifurcat. Chaos 16 775
[28] [29] L J H, Han F L, Yu X H, Chen G R 2004 Automatica 40 1677
[30] Xie F, Yang R, Zhang B 2011 IEEE Trans. Circuits Syst. I: Reg. Papers 58 2269
[31] [32] Xie F, Yang R, Zhang B 2010 Acta Phys. Sin. 59 8393 (in Chinese) [谢帆, 杨汝, 张波 2010 59 8393]
[33] [34] [35] Tse C K, Dai D 2005 Int. J. Bifurcat. Chaos 15 2263
[36] Dai D, Tse C K, Ma X 2005 IEEE Trans. Circuits Syst. I: Reg. Papers 52 1632
[37] [38] [39] Dai D, Tse C K 2004 International Workshop on Nonlinear Circuit Signal Process Waikiki, USA, March 5--7, 2004 p519
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