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With current-controlled buck-boost converter used as an example, through a detailed description of the switch state of the switching converter under wide circuit parameter variation, such as input voltage and load resistance variation, two inductor current borders in the current controlled switching converter are derived and an accurate discrete-time model is established. The validation of the discrete-time model is verified by a piecewise-linear model. Based on the discrete-time model, the complex dynamical behaviors existing in switching converter, such as period-double bifurcation, border-collision bifurcation, robust chaos and intermittent chaos, etc., are revealed. By formulating the Jacobian, the maximum Lyapunov exponent and the movement trajectories of eigvalues with the variations of circuit parameters are obtained. By utilizing the parameter-space maps, the operation-state regions corresponding to circuit parameter regions are estimated. Finally, an experimental setup is implemented, the corresponding observation results are consistent with those of theory analyses. In this paper the dynamics theory in switching converters is investigated systematically; the analysis methods and research results are helpful for designing and controlling switching converters.
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Keywords:
- current control /
- discrete-time model /
- border-collision bifurcation /
- switching converter
[1] Deane J H B, Hamill D C 1990 IEEE Trans. Power Electron. 5 260
[2] Liu F 2010 Chin. Phys. B 19 080511
[3] Wang J P, Xu J P, Xu Y J 2011 Acta Phys. Sin. 60 058401 (in Chinese) [王金平, 许建平, 徐杨军 2011 物理学报 60 058401]
[4] Zhou G H, Xu J P, Bao B C, Jin Y Y 2010 Chin. Phys. B 19 060508
[5] 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]
[6] Basak B, Parui S 2010 IEEE Trans. Power Electron. 25 1556
[7] Tse C K, Bernardo M D 2002 Proc. IEEE 90 768
[8] Giral R, El Aroudi A, Martinez-Salamero L, Leyva R, Maixe J 2001 Electron. Lett. 37 274
[9] El Aroudi A, Rodriguez E, Leyva R, Alarcon E 2010 IEEE Trans. Circuits Syst. II, Exp. Briefs 57 218
[10] Bao B C, Xu J P, Liu Z 2008 J. Univ. of Electronic Science and Technology of China 37 397 (in Chinese) [包伯成, 许建平, 刘中2008 电子科技大学学报 37 397]
[11] 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]
[12] Banerjee S, Parui S, Gupta A 2004 IEEE Trans. Circuits and Systems-II 51 649
[13] Parui S, Banerjee S 2003 IEEE Trans. Circuits and Systems -I 50 1464
[14] Saito T, Kabe T, Ishikawa Y, Matsuoka Y, Torikai H 2007 Int. J. Bifur. Chaos 17 3373
[15] Bao B C, Zhou G H, Xu J P, Liu Z 2011 IEEE Trans. Power Electron. 26 1968
[16] Bao B C, Xu J P, Liu Z 2009 Chin. Phys. B 18 4742
[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] Xie F, Yang R, Zhang B 2010 Acta Phys. Sin. 59 8393 (in Chinese) [谢帆, 杨汝, 张波 2010 物理学报 59 8393]
[19] Elaydi S N 2008 Discrete Chaos With Applications in Science and Engineering (Chapman & Hall/CRC)
[20] Chen Y F, Tse C K, Qiu S S, Lindenmüller L, Schwarz W 2008 IEEE Trans. Circuits Syst. -I 55 3335
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[1] Deane J H B, Hamill D C 1990 IEEE Trans. Power Electron. 5 260
[2] Liu F 2010 Chin. Phys. B 19 080511
[3] Wang J P, Xu J P, Xu Y J 2011 Acta Phys. Sin. 60 058401 (in Chinese) [王金平, 许建平, 徐杨军 2011 物理学报 60 058401]
[4] Zhou G H, Xu J P, Bao B C, Jin Y Y 2010 Chin. Phys. B 19 060508
[5] 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]
[6] Basak B, Parui S 2010 IEEE Trans. Power Electron. 25 1556
[7] Tse C K, Bernardo M D 2002 Proc. IEEE 90 768
[8] Giral R, El Aroudi A, Martinez-Salamero L, Leyva R, Maixe J 2001 Electron. Lett. 37 274
[9] El Aroudi A, Rodriguez E, Leyva R, Alarcon E 2010 IEEE Trans. Circuits Syst. II, Exp. Briefs 57 218
[10] Bao B C, Xu J P, Liu Z 2008 J. Univ. of Electronic Science and Technology of China 37 397 (in Chinese) [包伯成, 许建平, 刘中2008 电子科技大学学报 37 397]
[11] 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]
[12] Banerjee S, Parui S, Gupta A 2004 IEEE Trans. Circuits and Systems-II 51 649
[13] Parui S, Banerjee S 2003 IEEE Trans. Circuits and Systems -I 50 1464
[14] Saito T, Kabe T, Ishikawa Y, Matsuoka Y, Torikai H 2007 Int. J. Bifur. Chaos 17 3373
[15] Bao B C, Zhou G H, Xu J P, Liu Z 2011 IEEE Trans. Power Electron. 26 1968
[16] Bao B C, Xu J P, Liu Z 2009 Chin. Phys. B 18 4742
[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] Xie F, Yang R, Zhang B 2010 Acta Phys. Sin. 59 8393 (in Chinese) [谢帆, 杨汝, 张波 2010 物理学报 59 8393]
[19] Elaydi S N 2008 Discrete Chaos With Applications in Science and Engineering (Chapman & Hall/CRC)
[20] Chen Y F, Tse C K, Qiu S S, Lindenmüller L, Schwarz W 2008 IEEE Trans. Circuits Syst. -I 55 3335
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