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在多频率控制开关变换器的工作原理及状态方程的基础上，建立了多频率控制断续导电模式开关变换器的离散迭代映射模型，并推导了相应的特征值方程和Lyapunov指数. 根据离散迭代映射模型，对多频率控制开关变换器进行了分岔分析. 结果表明：在电路参数变化时，变换器存在边界碰撞分岔行为和多周期行为；当误差界限电压较大时，变换器表现出自相似现象，而当误差界限电压较小时，变换器则表现出混频现象. 采用Lyapunov指数研究了变换器的稳定性，验证了分岔分析的正确性. 经过电路仿真，进一步分析了负载变化时变换器的时域波形和相轨图，并验证了离散迭代映射模型的有效性和理论分析的正确性. 最后通过实验结果验证了文中的仿真结果.Based on the operation principle and state equations of multi-frequency (MF) controlled switching converter, the discrete iterative map model is established, the corresponding characteristics equation and Lyapunov exponent of MF controlled switching converter operating in discontinuous conduction mode are derived. According to the discrete iterative map model, its bifurcation behaviors are investigated. It is found that the border-collision bifurcation and the multi-period behaviors occur in converter, when the circuit parameters are varied. When the voltage error boundary is too large, the converter behaves as self-similarity phenomenon, and when the voltage error boundary is too small, the converter behaves as frequency-mixing phenomenon. The converter stability is investigated by Lyapunov exponent, which validates the correctness of bifurcation analysis. Time-domain waveforms and phase portraits of converter with the load varied, are analyzed by circuit simulation, which validates the validity of discrete iterative map model and the correctness of theoretical analysis. Finally, simulation results in this paper are verified by experimental results.
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Keywords:
- multi-frequency control /
- switching converter /
- self-similarity /
- frequency-mixing
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[1] Maity S, Tripathy D, Bhattacharya T K, Banerjee S 2007 IEEE Trans. Circ. Syst.-I 54 1120
[2] 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 62 010504]
[3] Bao B C, Yang P, Ma Z H, Zhang X 2012 Acta Phys. Sin. 61 220502 (in Chinese) [包伯成, 杨平, 马正华, 张希 2012 61 220502]
[4] Wang F Q, Zhang H, Ma X K 2012 Chin. Phys. B 21 020505
[5] Zhou G H, Bao B C, Xu J P, Jin Y Y 2010 Chin. Phys. B 19 050509
[6] Zhou Y F, Chen J N, Iu H H C, Tse C K 2008 Int. J. Bifurc. Chaos 18 121
[7] Zhou Y F, Chen J N, Ke D M 2005 Acta Electron. Sin. 33 915 (in Chinese) [周宇飞, 陈军宁, 柯导明 2005 电子学报 33 915]
[8] 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 59 2272]
[9] Zhou G H, Xu J P, Bao B C 2012 Int. J. Bifurc. Chaos 22 1250008
[10] Zhou G H, Xu J P, Bao B C, Jin Y Y 2010 Chin. Phys. B 19 060508
[11] 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 60 058401]
[12] 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 61 160503]
[13] 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 57 2842]
[14] 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 57 1522]
[15] Xu J P, Wang J P 2011 IEEE Trans. Industr. Electron. 58 3658
[16] Khaligh A, Emadi A 2008 IEEE Trans. Aerosp. Electron. Syst. 44 766
[17] Wang J P, Xu J P, Qin M, Mu Q B 2010 Proc. 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]
[18] 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 60 048402]
[19] 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 61 120501]
[20] Wu S R, He S Z, Xu J P, Zhou G H, Wang J P 2013 Acta Phys. Sin. 62 218403 (in Chinese) [吴松荣, 何圣仲, 许建平, 周国华, 王金平 2013 62 218403]
[21] Xu J P, Wang J P, Zhou G H, Qin M, Wu S R, Mu Q B 2010 Chinese Patent ZL 2009 2 0079219.X [2010-01-13] (in Chinese) [许建平, 王金平, 周国华, 秦明, 吴松荣, 牟清波 2010 中国专利 ZL2009 2 0079219.X[2010-01-13]]
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