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A dynamical model is proposed and the corresponding characteristic aligns are derived for voltage-mode bi-frequency controlled switching converter operating in discontinuous conduction mode. According to the dynamical model, the border-collision bifurcation and multi-period behaviors, such as period-2, period-3, period-4, and so on, are studied using bifurcation diagrams as the circuit parameters are varied. It is found that the converter behaves along the bifurcation route of period-1, multi-period, and period-1, and the change of period state is induced by border-collision bifurcation. Based on the characteristic equation, the converter stability is investigated by the Lyapunov exponent. It is shown that Lyapunov exponent is always smaller than zero with the variation of circuit parameters and the converter operates in stable period state all the time. Also, it is validated that period-3 behavior of voltage-mode bi-frequency controlled switching converter does not predicate its inevitable chaos. Time-domain waveforms, phase portraits, and frequency spectra of voltage-mode bi-frequency controlled switching converter are analyzed by circuit simulation, which validates the feasibility of dynamical model and the correctness of theoretical analysis. Simulation results are verified by experiments in this paper.
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Keywords:
- switching converter /
- bi-frequency control /
- border-collision bifurcation /
- multi-period behavior
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[2] Wang F Q, Zhang H, Ma X K 2012 Chin. Phys. B 21 020505
[3] Banerjee S, Parui S, Gupta A 2004 IEEE Trans. Circuits Syst. II 51 649
[4] Sha J, Bao B C, Xu J P, Gao Y 2012 Acta Phys. Sin. 61 120501 (in Chinese) [沙金, 包伯成, 许建平, 高玉 2012 物理学报 61 120501]
[5] Aroudi A El, Bernadero L, Toribio E, Olivar G 1999 IEEE Trans. Circuits Syst. I 46 1374
[6] 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 物理学报 60 060510]
[7] Iu H H C, Tse C K, Pjevalica V, Lai Y M 2001 Int. J. Circ. Theor. Appl. 29 281
[8] Zhou G H, Bao B C, Xu J P 2013 Int J Bifurcation and Chaos 23 1350062
[9] Zhou Y F, Chen J N, IU H H C, Tse C K 2008 Int J Bifurcation and Chaos 18 121
[10] Maity S, Tripathy D, Bhattacharya T K, Banerjee S 2007 IEEE Trans. on Circuits and Systems I 54 1120
[11] Zhou G H, Xu J P, Bao B C 2010 Acta Phys. Sin. 59 2272 (in Chinese) [周国华, 许建平, 包伯成 2010 物理学报 59 2272]
[12] Zhou G H, Xu J P, Bao B C, Jin Y Y 2010 Chin. Phys. B 19 060508
[13] Zhou G H, Xu J P, Bao B C 2012 Int J Bifurcation and Chaos 22 1250008
[14] Zhou G H, Bao B C, Xu J P, Jin Y Y 2010 Chin. Phys. B 19 050509
[15] Yang P, Bao B C, Sha J, Xu J P 2013 Acta Phys. Sin. 62 010504 (in Chinese) [杨平, 包伯成, 沙金, 许建平 2013 物理学报 62 010504]
[16] Yang N N, Liu C X, Wu C J 2012 Chin. Phys. B 21 080503
[17] He S Z, Zhou G H, Xu J P, Bao B C, Yang P 2013 Acta Phys. Sin. 62 110503 (in Chinese) [何圣仲, 周国华, 许建平, 包伯成, 杨平 2013 物理学报 62 110503]
[18] Wang F Q, Zhang H, Ma X K 2008 Acta Phys. Sin. 57 2842 (in Chinese) [王发强, 张浩, 马西奎 2008 物理学报 57 2842]
[19] Wang F Q, Zhang H, Ma X K 2008 Acta Phys. Sin. 57 1522 (in Chinese) [王发强, 张浩, 马西奎 2008 物理学报 57 1522]
[20] Wang J P, Xu J P, Zhou G H, Mi C B, Qin M 2011 Acta Phys. Sin. 60 048402 (in Chinese) [王金平, 许建平, 周国华, 米长宝, 秦明 2011 物理学报 60 048402]
[21] Wang J P, Xu J P, Xu Y J 2011 Acta Phys. Sin. 60 058401 (in Chinese) [王金平, 许建平, 徐扬军 2011 物理学报 60 058401]
[22] Zhang X, Bao B C, Wang J P, Ma Z H, Xu J P 2012 Acta Phys. Sin. 61 160503 (in Chinese) [张希, 包伯成, 王金平, 马正华, 许建平 2012 物理学报 61 160503]
[23] Wang J P, Xu J P, Qin M, Mu Q B 2003 Proceeding of the CSEE 30 1 (in Chinese) [王金平, 许建平, 秦明, 牟清波 2010 中国电机工程学报 30 1]
[24] Xu J P, Wang J P 2011 IEEE Trans Industrial Electronics 58 3658
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[1] Chan W C Y, Tse C K 1997 IEEE Trans. Circuits Syst. I 44 1129
[2] Wang F Q, Zhang H, Ma X K 2012 Chin. Phys. B 21 020505
[3] Banerjee S, Parui S, Gupta A 2004 IEEE Trans. Circuits Syst. II 51 649
[4] Sha J, Bao B C, Xu J P, Gao Y 2012 Acta Phys. Sin. 61 120501 (in Chinese) [沙金, 包伯成, 许建平, 高玉 2012 物理学报 61 120501]
[5] Aroudi A El, Bernadero L, Toribio E, Olivar G 1999 IEEE Trans. Circuits Syst. I 46 1374
[6] 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 物理学报 60 060510]
[7] Iu H H C, Tse C K, Pjevalica V, Lai Y M 2001 Int. J. Circ. Theor. Appl. 29 281
[8] Zhou G H, Bao B C, Xu J P 2013 Int J Bifurcation and Chaos 23 1350062
[9] Zhou Y F, Chen J N, IU H H C, Tse C K 2008 Int J Bifurcation and Chaos 18 121
[10] Maity S, Tripathy D, Bhattacharya T K, Banerjee S 2007 IEEE Trans. on Circuits and Systems I 54 1120
[11] Zhou G H, Xu J P, Bao B C 2010 Acta Phys. Sin. 59 2272 (in Chinese) [周国华, 许建平, 包伯成 2010 物理学报 59 2272]
[12] Zhou G H, Xu J P, Bao B C, Jin Y Y 2010 Chin. Phys. B 19 060508
[13] Zhou G H, Xu J P, Bao B C 2012 Int J Bifurcation and Chaos 22 1250008
[14] Zhou G H, Bao B C, Xu J P, Jin Y Y 2010 Chin. Phys. B 19 050509
[15] Yang P, Bao B C, Sha J, Xu J P 2013 Acta Phys. Sin. 62 010504 (in Chinese) [杨平, 包伯成, 沙金, 许建平 2013 物理学报 62 010504]
[16] Yang N N, Liu C X, Wu C J 2012 Chin. Phys. B 21 080503
[17] He S Z, Zhou G H, Xu J P, Bao B C, Yang P 2013 Acta Phys. Sin. 62 110503 (in Chinese) [何圣仲, 周国华, 许建平, 包伯成, 杨平 2013 物理学报 62 110503]
[18] Wang F Q, Zhang H, Ma X K 2008 Acta Phys. Sin. 57 2842 (in Chinese) [王发强, 张浩, 马西奎 2008 物理学报 57 2842]
[19] Wang F Q, Zhang H, Ma X K 2008 Acta Phys. Sin. 57 1522 (in Chinese) [王发强, 张浩, 马西奎 2008 物理学报 57 1522]
[20] Wang J P, Xu J P, Zhou G H, Mi C B, Qin M 2011 Acta Phys. Sin. 60 048402 (in Chinese) [王金平, 许建平, 周国华, 米长宝, 秦明 2011 物理学报 60 048402]
[21] Wang J P, Xu J P, Xu Y J 2011 Acta Phys. Sin. 60 058401 (in Chinese) [王金平, 许建平, 徐扬军 2011 物理学报 60 058401]
[22] Zhang X, Bao B C, Wang J P, Ma Z H, Xu J P 2012 Acta Phys. Sin. 61 160503 (in Chinese) [张希, 包伯成, 王金平, 马正华, 许建平 2012 物理学报 61 160503]
[23] Wang J P, Xu J P, Qin M, Mu Q B 2003 Proceeding of the CSEE 30 1 (in Chinese) [王金平, 许建平, 秦明, 牟清波 2010 中国电机工程学报 30 1]
[24] Xu J P, Wang J P 2011 IEEE Trans Industrial Electronics 58 3658
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