Study on discrete time mapping modeling and stability analysis for piecewise autonomous oscillation systems

被引：4
作者：
Dai, Xin [1 ]
Huang, Xi-Yue [1 ]
Sun, Yue [1 ]
机构：
[1] Automation College, Chongqing University
来源：
Zidonghua Xuebao/Acta Automatica Sinica | 2007年 / 33卷 / 01期
关键词：
Autonomous piecewise; Discrete mapping modeling; Frequency bifurcation;
D O I：
10.1360/aas-007-0072
中图分类号：
学科分类号：
摘要：
System modeling and local stability analysis of equilibrium points are indispensable for analysis of bifurcation and chaos behaviors observed in piecewise autonomous oscillation system. This paper presents a novel dynamic discrete mapping modeling method and local stability criterion of equilibrium points. This modeling method sets up discrete mapping model and boundary equations in analytic form respectively. With the aid of Newton-Raphson algorithm, the boundary equations can be solved dynamically. Combining the mapping model with boundary dynamic solutions, this mapping model can fulfill the requirements of fast-scale bifurcation analysis. To verify this modeling method, an autonomous oscillation circuit used in power electronics soft switched converter is constructed. A frequency bifurcation phenomenon is captured in both simulation results and experiment system. The analysis results of this bifurcation phenomena show consistency between model simulation and experiment system.
引用
收藏
页码：72 / 77
页数：5
相关论文
共 20 条
  • [1] Jin J.-D., Guan L.-Z., Fourier series solution of forced vibration of a multi-degree-of-freedom system with piecewise-linear elastic elements, Journal of Vibration Engineering, 16, 3, pp. 373-378, (2003)
  • [2] Chen Y.-S., Nonlinear Vibrations, pp. 109-116, (2002)
  • [3] Qi Q., Li P., Zhang B., Methods for analyzing and modeling bifurcations and chaos in DC-DC converter, Proceedings of the Chinese Society for Electrical Engineering, 22, 11, pp. 81-86, (2002)
  • [4] Hamill D.C., Deane J.H.B., Jefferies D.J., Modeling of chaotic DC-DC converters by iterated nonlinear mappings, IEEE Transactions on Power Electronics, 7, 1, pp. 25-36, (1992)
  • [5] Tse C.K., Bernardo M.D., Complex behaviour in switching power converters, Proceedings of IEEE, 90, 5, pp. 768-781, (2002)
  • [6] Chan W.C., Tse C.K., Study of bifurcations in current-programmed DC/DC boost converters: From quasiperiodicity to period-doubling, IEEE Transactions on Circuits and Systems, 44, 12, pp. 1129-1142, (1997)
  • [7] Ei A.A., Benadero L., Toribio E., Olivar G., Hopf bifurcation and chaos from torus breakdown in a PWM voltage-controlled DC-DC boost converter, IEEE Transactions on Circuits and Systems, 46, 11, pp. 1374-1382, (1999)
  • [8] Middlebrook R.D., Cuk S., General unified approach to modeling switching-converter power stages, International Journal of Electronics, 42, 6, pp. 521-550, (1977)
  • [9] Sanders S.R., Noworolski J.M., Liu X.Z., Verghese G.C., Generalized averaging method for power conversion circuits, IEEE Transactions on Power Electronics, 6, 2, pp. 251-259, (1991)
  • [10] Jalali S., Dobson I., Lasseter R.H., Venkataramanan G., Switching time bifurcations in a thyristor controlled reacctor, IEEE Transactions on Circuits and Systems, 43, 3, pp. 209-218, (1996)
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