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According to the charge variation of output capacitor in a switching cycle, the output voltage variation in a switching cycle can be obtained, from which an approximate discrete-time model of pulse train (PT) controlled buck converter operating in discontinuous conduction mode (DCM) is established. Based on the model, the border-collision bifurcations of the PT controlled DCM buck converter with the variations of the load resistance and the input voltage are studied. By constructing the corresponding iterative map curves, the stabilities of the fixed points, formed by the orbits of period-1, period-2, period-3 and so on, are analyzed, and the mechanisms of border-collision bifurcations of the converter under different operation states are revealed. The analysis results indicate that with the variation of parameters, the PT controlled DCM buck converter always operates in different periodic states, in which the change of the operation mode with periodic state is caused by the border-collision bifurcation and the lyapunov exponent is always less than zero. By using PSIM circuit simulation software, the time domain waveforms and phase portraits under different load resistances are obtained. Experimental results are provided to verify the correctnesses of theoretical analyses and circuit simulations and the feasibility of dynamical modelling.
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Keywords:
- pulse train control /
- border-collision bifurcation /
- buck converter /
- discontinuous conduction mode (DCM)
[1] Wang X M, Zhang B, Qiu D Y 2008 Acta Phys. Sin. 57 2736 (in Chinese) [王学梅, 张波, 丘东元 2008 物理学报 57 2736]
[2] Liu F 2010 Chin. Phys. B 19 080511
[3] Zhou G H, Bao B C, Xu J P, Jin Y Y 2010 Chin. Phys. B 19 050509
[4] Zhou G H, Xu J P, Bao B C, Jin Y Y 2010 Chin. Phys. B 19 060508
[5] Xie F, Yang R, Zhang B 2011 IEEE Trans. Circuits Syst. I 58 2269
[6] Bao B C, Xu J P, Liu Z 2009 Chin. Phys. B 18 4742
[7] Bao B C, Zhou G H, Xu J P, Liu Z 2011 IEEE Trans. Power Electronics 26 1968
[8] Yuan G, Banerjee S, Ott E, Yorke J A 1998 IEEE Trans. Circuits Syst. I 45707
[9] Ma Y, Tes C K, Kousaka T, Kawakami H 2005 IEEE Trans. on Circuit and Systems- II 52 581
[10] Wang F Q, Zhang H, Ma X K 2008 Acta Phys. Sin. 57 2842 (in Chinese)[10] Wang F Q, Zhang H, Ma X K 2008 Acta Phys. Sin. 57 2842 (in Chinese)[王发强, 张浩, 马西奎, 闫晔 2008 物理学报 57 2842]
[11] Khaligh A, Emadi A 2008 IEEE Trans. on Aerospace and Electronic Systems 44 766
[12] Xu J P, Wang J P 2011 IEEE Trans. Industrial Electron. 58 3658
[13] Kapat S, Banerjee S, Patra A 2010 IEEE Trans. Circuits Syst. I 57 1793
[14] Qin M, Xu J P 2009 Acta Phys. Sin. 58 7603 (in Chinese) [秦明, 许建平 2009 物理学报 58 7603]
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[1] Wang X M, Zhang B, Qiu D Y 2008 Acta Phys. Sin. 57 2736 (in Chinese) [王学梅, 张波, 丘东元 2008 物理学报 57 2736]
[2] Liu F 2010 Chin. Phys. B 19 080511
[3] Zhou G H, Bao B C, Xu J P, Jin Y Y 2010 Chin. Phys. B 19 050509
[4] Zhou G H, Xu J P, Bao B C, Jin Y Y 2010 Chin. Phys. B 19 060508
[5] Xie F, Yang R, Zhang B 2011 IEEE Trans. Circuits Syst. I 58 2269
[6] Bao B C, Xu J P, Liu Z 2009 Chin. Phys. B 18 4742
[7] Bao B C, Zhou G H, Xu J P, Liu Z 2011 IEEE Trans. Power Electronics 26 1968
[8] Yuan G, Banerjee S, Ott E, Yorke J A 1998 IEEE Trans. Circuits Syst. I 45707
[9] Ma Y, Tes C K, Kousaka T, Kawakami H 2005 IEEE Trans. on Circuit and Systems- II 52 581
[10] Wang F Q, Zhang H, Ma X K 2008 Acta Phys. Sin. 57 2842 (in Chinese)[10] Wang F Q, Zhang H, Ma X K 2008 Acta Phys. Sin. 57 2842 (in Chinese)[王发强, 张浩, 马西奎, 闫晔 2008 物理学报 57 2842]
[11] Khaligh A, Emadi A 2008 IEEE Trans. on Aerospace and Electronic Systems 44 766
[12] Xu J P, Wang J P 2011 IEEE Trans. Industrial Electron. 58 3658
[13] Kapat S, Banerjee S, Patra A 2010 IEEE Trans. Circuits Syst. I 57 1793
[14] Qin M, Xu J P 2009 Acta Phys. Sin. 58 7603 (in Chinese) [秦明, 许建平 2009 物理学报 58 7603]
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