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基于双缘调制的数字电压型控制Buck变换器离散迭代映射建模与动力学分析

刘啸天 周国华 李振华 陈兴

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基于双缘调制的数字电压型控制Buck变换器离散迭代映射建模与动力学分析

刘啸天, 周国华, 李振华, 陈兴

Discrete iterative-map modeling and dynamical analysis of digital voltage-mode controlled buck converter with dual-edge modulation

Liu Xiao-Tian, Zhou Guo-Hua, Li Zhen-Hua, Chen Xing
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  • 建立了双缘调制数字电压型控制Buck变换器的离散迭代映射模型. 在该模型的基础上, 详细研究了双缘调制数字电压型控制Buck变换器的非线性动力学行为. 以输入电压、负载电阻等电路参数作为分岔参数, 绘制了输出电压和电感电流的分岔图, 并通过分岔图的分析发现了两种相似却又不同的Hopf分岔现象. 采用庞加莱截面、时域仿真波形和相轨图, 对比分析了两种不同的Hopf分岔和低频振荡现象, 并引入离散迭代映射模型的雅克比矩阵的特征值分析方法, 从理论上证明了两种Hopf分岔的存在性和差异性. 首次观察到基于双缘调制的数字电压型控制Buck变换器出现了奇数倍周期分岔现象, 并通过时域仿真波形和相轨图验证了该现象的真实性. 为更加接近实际电路, 考虑电容和电感的等效串联电阻, 使用Psim进行仿真, 其结果与理论仿真结果基本一致, 验证了理论仿真的正确性.
    The operation principle of digital voltage-mode controlled buck converter with dual-edge modulation is analyzed in this paper. Based on the state equation of buck converter and six possible evolutions in one switching cycle, the discrete iterative-map model of digital voltage-mode controlled buck converter with dual-edge modulation is established. Ignoring the quantization error of analog-digital converter and on the basis of its discrete iterative-map model, the nonlinear dynamical behavior of digital voltage-mode controlled buck converter with dual-edge modulation is investigated in detail. Taking the input voltage and the load resistance as bifurcation parameters, the output voltage bifurcation diagram and the inductor current bifurcation diagram are plotted. Through analyzing the bifurcation diagrams, it is indicated that there are two kinds of similar but different Hopf bifurcation phenomena. By use of Poincar section, time-domain simulation waveforms and phase portraits, two different Hopf bifurcations and low-frequency oscillation phenomena are compared and studied. Observing the inductor current and capacitor voltage waveforms respectively, it is obviously found that their oscillation frequencies and amplitudes are different, the shapes of two Poincar$ sections and phase portraits are also different. In order to verify the correctness of the simulation and theoretical analysis, the eigenvalues of Jacobian matrix of the discrete iterative map model are introduced and solved in two kinds of stable evolutions. Through analyzing variation of eigenvalues of Jacobi matrix with input voltage, the existence and difference of two kinds of Hopf bifurcation phenomena are proved theoretically. Moreover, it is observed in this paper that the odd period-doubling bifurcation phenomenon exists in digital voltage-mode controlled buck converter with dual-edge modulation for the first time, where the operation state of the buck converter turns from period-one into period-three. Its authenticity is verified by using the time-domain simulation waveforms and phase portraits. In order to approach to the actual circuit, the equivalent series resistances of capacitor and inductor are considered. The actual circuit is simulated by using the software Psim. A comparison shows that there are little differences between the theoretical simulation and the actual circuit simulation. So the theoretical simulation can be used to analyze the performances of the actual circuit. The research results in this paper have guiding significance and practical value for designing the digital voltage-mode controlled buck converter with dual-edge modulation.
      通信作者: 周国华, ghzhou-swjtu@163.com
    • 基金项目: 国家自然科学基金(批准号: 61371033)、全国优秀博士学位论文作者专项资金(批准号: 201442)、霍英东教育基金会高等院校青年教师基金(批准号: 142027)和四川省青年科技基金(批准号: 2014JQ0015, 2013JQ0033)资助的课题.
      Corresponding author: Zhou Guo-Hua, ghzhou-swjtu@163.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61371033), the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 201442), the Fok Ying-Tung Education Foundation for Young Teachers in the Higher Education Institutions of China (Grant No. 142027), and the Sichuan Provincial Youth Science and Technology Fund, China (Grant Nos. 2014JQ0015, 2013JQ0033).
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    Aroudi A E, Leyva R 2001 IEEE Trans. Circuit Syst. I 48 967

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    Zhou G H, Bao B C, Xu J P 2013 Int. J. Bifurcat. Chaos 23 1350062

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    Zhou Y F, Tse C K, Qiu S S, Chen J N 2005 Chin. Phys. 14 0061

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    Yang N N, Liu C X, Wu C J 2012 Chin. Phys. B 21 080503

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    Wang F Q, Zhang H, Ma X K 2012 Chin. Phys. B 21 020505

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    He S Z, Xu J P, Zhou G H, Bao B C, Yan T S 2015 Chin. J. Electron. 24 295

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    Xie F, Zhang B, Yang R 2013 IEEE Tran. Ind. Electron. 60 3145

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    Zhou G H 2011 Ph. D. Dissertation (Chengdu: Southwest Jiaotong University) (in Chinese) [周国华 2011 博士学位论文 (成都: 西南交通大学)]

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  • [1]

    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]

    [2]

    Maity S, Tripathy D, Bhattacharya T K, Banerjee S 2007 IEEE Trans. Circuit Syst. I 54 1120

    [3]

    Zhou G H, Bao B C, Xu J P, Jin Y Y 2010 Chin. Phys. B 19 050509

    [4]

    Deivasundari P, Uma G, Poovizhi R 2013 IET Power Electr. 6 763

    [5]

    Xie F, Yang R, Zhang B 2011 IEEE Trans. Circuit Syst. I 58 2269

    [6]

    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]

    [7]

    Dai D, Li S N, Zhang B, Ma X K 2008 Proc. CSEE 28 1 (in Chinese) [戴栋, 李胜男, 张波, 马西奎 2008 中国电机工程学报 28 1]

    [8]

    Aroudi A E, Benadero L, Toribio E, Olivar G 1999 IEEE Trans. Circuit Syst. I 46 1374

    [9]

    Aroudi A E, Benadero L, Toribio E, Machiche S 2000 Int. J. Bifurcat. Chaos 10 359

    [10]

    Zhang X T, Ma X K, Zhang H 2008 Acta Phys. Sin. 57 6174 (in Chinese) [张笑天, 马西奎, 张浩 2008 物理学报 57 6174]

    [11]

    Huang M, Wong S C, Tse C K, Ruan X B 2013 IEEE Trans. Circuit Syst. I 60 1062

    [12]

    Aroudi A E, Leyva R 2001 IEEE Trans. Circuit Syst. I 48 967

    [13]

    Zhou G H, Bao B C, Xu J P 2013 Int. J. Bifurcat. Chaos 23 1350062

    [14]

    Zhou Y F, Tse C K, Qiu S S, Chen J N 2005 Chin. Phys. 14 0061

    [15]

    Yang N N, Liu C X, Wu C J 2012 Chin. Phys. B 21 080503

    [16]

    Wang F Q, Zhang H, Ma X K 2012 Chin. Phys. B 21 020505

    [17]

    He S Z, Xu J P, Zhou G H, Bao B C, Yan T S 2015 Chin. J. Electron. 24 295

    [18]

    Xie F, Zhang B, Yang R 2013 IEEE Tran. Ind. Electron. 60 3145

    [19]

    Zhao Y B, Feng J C, Chen Y F 2013 Int. J. Bifurcat. Chaos 23 1350113

    [20]

    Zhou G H 2011 Ph. D. Dissertation (Chengdu: Southwest Jiaotong University) (in Chinese) [周国华 2011 博士学位论文 (成都: 西南交通大学)]

    [21]

    Tse C K 2004 CRC Press Data pp96-132

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出版历程
  • 收稿日期:  2015-04-28
  • 修回日期:  2015-07-09
  • 刊出日期:  2015-11-05

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