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峰值电流和谷值电流控制开关DC-DC变换器在较宽的电路参数范围内具有对称动力学现象.文中建立了峰值电流和谷值电流控制buck，boost，及buck-boost变换器的统一离散迭代映射模型，并导出了统一的分段光滑迭代映射方程及特征值方程，通过数值仿真得到了占空比变化时的正、逆分岔图和Lyapunov指数谱.研究结果表明，峰值/谷值电流型控制开关变换器的分岔图和Lyapunov指数具有关于点或轴对称的现象.时域仿真结果验证了数值仿真结果，并进一步表明，随着占空比的变化，峰值/谷值电流型控制开关变换器具有对称动力学现象、对称动力学现象和非对称动力学现象共存、非对称动力学现象.Peak current and valley current controlled switching DC-DC converters show symmetrical dynamic phenomenon within a wide circuit parameter range. The unified discrete iterative map model of peak current and valley current controlled buck, boost, and buck-boost converters is established, and the unified piecewise smooth iterative map and their corresponding characteristic equations are also derived. The forward and inverse bifurcation diagrams and Lyapunov exponent spectrums with duty ratio as parameter are obtained by numerical simulation. The research results indicate that the bifurcation diagrams and Lyapunov exponent of peak and valley current-mode controlled switching converters show symmetrical dynamic phenomenon corresponding to a symmetrical point or a symmetrical axis. The numerical simulation results are verified by the time-domain simulation, which further indicates that with the duty ratio varying, the peak and valley current-mode controlled switching converter reveals a symmetrical dynamic phenomenon, or a symmetrical dynamic phenomenon accompanying an asymmetrical dynamic phenomenon, or an asymmetrical dynamic phenomenon.
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Keywords:
- switching converters /
- iterative map /
- current-mode control /
- symmetrical dynamic phenomenon
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[1] ［1］Zhou Y F, Chen J N, Iu H H C, Tse C K 2008 Int. J. Bifur. Chaos 18 121
[2] ［2］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］
[3] ［3］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 物理学报 57 1522］
[4] ［4］Ma X K, Zhang H, Zhang X T 2008 Acta Phys. Sin. 57 6174 (in Chinese) ［马西奎、张浩、张笑天 2008 物理学报 57 6174］
[5] ［5］Lu W G, Zhou L W, Luo Q M, Du X 2007 Acta Phys. Sin. 56 6275 (in Chinese)［卢伟国、周雒维、罗全明、杜雄 2007 物理学报 56 6275］
[6] ［6］Zhao Y B, Luo X S, Fang J Q, Wang B H 2005 Acta Phys. Sin. 54 5022 (in Chinese) ［赵益波、罗晓曙、方锦清、汪秉宏 2005 物理学报 54 5022］
[7] ［7］Donato C, Giuseppe G 2006 Nonlinear Dynam. 44 251
[8] ［8］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］
[9] ［9］Sajid I, Masood A, Suhail A Q 2007 Int. J. Electric. Comput. Syst. Engng. 1 166
[10] ］Wong S C, Tse C K, Tam K C 2004 Int. J. Bifur. Chaos 14 1971
[11] ］Iu H H C, Tse C K 2003 IEEE Trans. Circ. Syst. -Ⅰ 50 679
[12] ］Bernardo M D, Vasca F 2003 IEEE Trans. Circ. Syst. -Ⅰ 47 133
[13] ］Cheng K W E, Liu M, Wu J, Cheung N C 2001 IEEE Ind. Electron. Conf.838
[14] ］Banerjee S, Parui S, Gupta A 2004 IEEE Trans Circ. Syst. -Ⅱ 51 649
[15] ］Bao B C, Xu J P, Liu Z 2008 J. Univ. Electron. Sci. Technol. Chin. 37 397 (in Chinese) ［包伯成、许建平、刘中 2008 电子科技大学学报 37 397］
[16] ］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］
[17] ］Zhou Y F, Chen J N, Tse C K, Ke D M, Shi L X, Sun W F 2004 Acta Phys. Sin. 53 3676 (in Chinese) ［周宇飞、陈军宁、谢智刚、柯导明、时龙兴、孙伟锋 2004 物理学报 53 3676］
[18] ］Zhao Y B, Zhang D Y, Zhang C J 2007 Chin. Phys. 16 933
[19] ］Lu W G, Zhou L W, Luo Q M 2007 Chin. Phys. Lett. 24 1837
[20] ］Cheng W B, Guo Y N, Huo A Q, Kang S M, Tang N, Wang Y L 2009 Acta Phys. Sin. 58 4439 (in Chinese) ［程为彬、郭颖娜、霍爱清、康思民、汤楠、汪跃龙 2009 物理学报 58 4439］
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