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以电流控制Buck-Boost变换器为例, 通过对输入电压和负载电阻等电路参数宽范围变化时开关变换器的开关状态的完整描述, 导出了电流控制开关变换器的两个电感电流边界, 建立了它的精确离散时间模型, 并利用分段线性模型验证了离散时间模型的正确性. 基于离散时间模型, 揭示了开关变换器存在周期分岔、边界碰撞分岔、鲁棒混沌和阵发混沌等复杂动力学行为;通过推演Jacobi矩阵, 给出了电路参数变化时最大Lyapunov指数和特征值的运动轨迹;并采用参数空间映射图, 由电路参数域对开关变换器的工作状态域进行了估计. 最后进行了电路实验制作, 实验观察结果与理论分析结果一致. 本文系统研究了开关变换器的动力学理论, 其分析方法和研究结果对开关变换器的设计及控制都具有重要的指导意义.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 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 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 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 58 2949]
[18] Xie F, Yang R, Zhang B 2010 Acta Phys. Sin. 59 8393 (in Chinese) [谢帆, 杨汝, 张波 2010 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 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 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 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 58 2949]
[18] Xie F, Yang R, Zhang B 2010 Acta Phys. Sin. 59 8393 (in Chinese) [谢帆, 杨汝, 张波 2010 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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