分段光滑电路中的多尺度分岔与混沌行为及其控制方法研究
|
摘要
非线性电路中的复杂动力学行为是现代电路理论及其应用中的一个重要研究课题,它包含着丰富的研究内容和广阔的应用前景。本文以分段光滑电路为对象,着重在以下几个方面开展了研究工作:
1.能产生多混沌吸引子分段光滑自治电路的研究。提出了两类能够产生多涡卷混沌吸引子和一类能产生多折叠环面多涡卷混沌吸引子的分段光滑自治电路。建立了这三类分段光滑自治电路的数学模型,分析了电路参数对电路中出现的混沌动力学行为的影响,并指出了电路通向混沌的道路,同时,给出了混沌吸引子的个数与开关闭合个数的关系。
2.单周控制DC-DC电路中多尺度分岔的研究。采用电路仿真、理论分析和电路实验分别研究了单周控制Buck电路中的快尺度分岔和单周控制Boost电路中的慢尺度分岔。研究结果表明:单周控制Buck电路中的快尺度分岔主要是由于电路工作频率小于时钟频率而引起的;单周控制Boost电路中的慢尺度分岔实质上是电路在远低于开关频率区域内发生了Hopf分岔。
3.平均电流控制Boost PFC电路中多尺度分岔的研究。通过建立平均电流控制Boost PFC电路的简化模型,采用小信号模型方法分析了电路中的中尺度分岔,采用谐波平衡法和Floquet理论分析了电路中的慢尺度分岔以及采用非线性模型分析了电路中的次慢尺度分岔。给出了电路发生分岔行为的物理机理,并通过电路仿真和电路实验证实了各种简化模型的有效性和理论分析的正确性。
4.含输入滤波器的平均电流控制Boost PFC电路中多尺度分岔的研究。通过建立含输入滤波器的平均电流控制Boost PFC电路的数学模型,采用谐波平衡法和Floquet理论分析了电路中的慢尺度分岔以及采用非线性模型分析了电路中的次慢尺度分岔。研究结果表明:滤波器参数(Rf,Cf,Lf)取值合适的情况下,输入滤波器的加入可能会使平均电流控制Boost PFC电路的稳定区域扩大,从而纠正了以往人们认为输入滤波器的加入只会导致平均电流控制Boost PFC电路失去原来稳定性的结论。
5.多级PFC电路中多尺度分岔的研究。基于一定的假设条件,建立了级联PFC电路的简化模型,采用小信号模型方法分析了级联PFC电路中的中尺度分岔以及采用增量谐波平衡法和Floquet理论分析了级联PFC电路中的慢尺度分岔。电路仿真和电路实验证实了理论分析的正确性。此外,基于合适的假设,还建立了并联PFC电路的简化模型,采用谐波平衡法和Floquet理论分析了并联PFC电路中的慢尺度分岔,并指出了电路参数对并联PFC电路稳定性的影响与对单级PFC电路稳定性的影响存在着明显的差别。
6.分段光滑电路中混沌与多尺度分岔控制方法的研究。首先提出采用线性反馈控制方法实现了蔡氏电路的同步控制。其次,提出了基于无源控制理论,设计无源控制器,实现了变型蔡氏电路的同步控制。而后,提出了采用电流反馈控制方法实现了单周控制Boost电路中慢尺度分岔的控制,确定了使电路运行于稳定状态时控制参数的取值范围,并通过电路仿真和电路实验验证了该控制方法的有效性和理论分析的正确性。最后,提出采用负载电流反馈控制方法实现了平均电流控制Boost PFC电路中慢尺度分岔的控制,采用谐波平衡法和Floquet理论确定了使电路运行于稳定状态时控制参数的取值范围,并通过电路仿真和电路实验验证了该控制方法的有效性和理论分析的正确性。
The complex behavior in nonlinear circuit has become an important research subject in the modern circuit, which include extremely abundant contents and wide application prospects. In this dissertation, as an important part of nonlinear circuit research, the complex behavior in the piece-wise smooth circuit is investigated and the details are presented as follows:
1. The multiple chaotic attractor in autonomous piece-wise smooth circuit is studied. Two kinds of multi-scroll chaotic attractor and another kind of multi-folded torus chaotic attractor in the autonomous piece-wise smooth circuits are constructed and analyzed. The mathmatical models are established, the effects of parameters on the chaos of the circuit and the route to chaos of the circuit are analyzed. Moreover, the relationship between the number of chaotic attractor and the number of closed switches are given.
2. The multi-scale bifurcation in the one-cycle controlled DC-DC circuit is studied. The fast-scale bifurcation in the one-cycle controlled Buck circuit and the slow-scale bifurcation in one-cycle controlled Boost circuit are invesigated respectively with the circuit simulation, theoretical analysis and circuit experiment. The results shows: the main reason for the occurrence of fast-scale bifurcation in the one-cycle controlled Buck circuit is that the operation frequency of the circuit is lower than the clock frequency. But, for the slow-scale bifurcation in the one-cycle controlled Boost circuit, in fact, it is that the Hopf bifurcation happens in the area where the frequency is much lower than the switching frequency.
3. The multi-scale bifurcation in average current controlled Boost PFC circuit is studied. By establishing the simplified models, the medium-scale bifurcation is investigated based on the small-sigal model, and the slow-scale bifurcation is investigated based on the harmonic balance method and Floquet theory, and also, the subslow-scale bifurcation is investigated based on the nonlinear model. The under mechanism of the above three kinds of bifurcaton are given. Finally, the effectiveness of the simplified models and the validity of the theoretical analyses are confirmed by the circuit simulations and circuit experiments.
4. The multi-scale bifurcation in the averge current controlled Boost PFC with an input filter is studied. The mathematical models of the circuit are constructed, the slow-scale bifurcaiton in the circuit is analyzed by means of the harmonic balance method and Floquet theory and the subslow-scale bifurcation is analyzed by means of the nonlinear model. The results show that the stable area may be enlarged when the extra input filter is added into the average current controlled Boost PFC circuit. These results change the conclusions that the extra input filter will only degrade the stability of the average current controlled Boost PFC circuit.
5. The multi-scale bifurcation in the multi-stage PFC circuit is studied. Based on certain suitable assumptions, the simplified model of the cascade PFC circuit are established. And then, the medium-scale bifurcation is analyzed by using the small-signal model, and the slow-scale bifurcation is analyzed by using the method of incremental harmonic balance and Floquet theory. The effectiveness of the simplified model and the validity of the theoretical analysis are both confirmed by the circuit simulation and circuit experiment. Furthermore, the slow-scale bifurcation in parallel PFC circuit is analyzed by using the method of harmonic balance and Floquet theory. It is found that there are very important differences between the single-stage PFC circuit and the parallel PFC circuit.
6. Control of multi-scale bifurction and chaos in the piece-wise smooth circuit is studied. Firstly, the linear feedback control is proposed to realize the synchronization of the Chua’s circuit. Secondly, based on the passive control theory, the passive controller is designed to realize the synchronization of the modified Chua’s circuit. Thirdly, the current feedback control is applied to realize the control of the slow-scale bifurcation in the one-cycle controlled Boost circuit. The span of the control parameters for maintaining the circuit in stable operation are fixed. Moreover, the effectiveness of the control method and the validity of the theoretical analysis are confirmed by the circuit simulation and circuit experiment. Finally, the load current feedback control is applied to control the slow-scale bifurcation in average current controlled Boost PFC circuit. Based on the simplified model, the span of control parameters for maintaining the circuit in stable operation is analzed by using the method of harmonic and Floquet theory, and then the effectiveness of the control method and the validity of the theoretical analysis are confirmed by the circuit simulation and circuit experiment.
1.能产生多混沌吸引子分段光滑自治电路的研究。提出了两类能够产生多涡卷混沌吸引子和一类能产生多折叠环面多涡卷混沌吸引子的分段光滑自治电路。建立了这三类分段光滑自治电路的数学模型,分析了电路参数对电路中出现的混沌动力学行为的影响,并指出了电路通向混沌的道路,同时,给出了混沌吸引子的个数与开关闭合个数的关系。
2.单周控制DC-DC电路中多尺度分岔的研究。采用电路仿真、理论分析和电路实验分别研究了单周控制Buck电路中的快尺度分岔和单周控制Boost电路中的慢尺度分岔。研究结果表明:单周控制Buck电路中的快尺度分岔主要是由于电路工作频率小于时钟频率而引起的;单周控制Boost电路中的慢尺度分岔实质上是电路在远低于开关频率区域内发生了Hopf分岔。
3.平均电流控制Boost PFC电路中多尺度分岔的研究。通过建立平均电流控制Boost PFC电路的简化模型,采用小信号模型方法分析了电路中的中尺度分岔,采用谐波平衡法和Floquet理论分析了电路中的慢尺度分岔以及采用非线性模型分析了电路中的次慢尺度分岔。给出了电路发生分岔行为的物理机理,并通过电路仿真和电路实验证实了各种简化模型的有效性和理论分析的正确性。
4.含输入滤波器的平均电流控制Boost PFC电路中多尺度分岔的研究。通过建立含输入滤波器的平均电流控制Boost PFC电路的数学模型,采用谐波平衡法和Floquet理论分析了电路中的慢尺度分岔以及采用非线性模型分析了电路中的次慢尺度分岔。研究结果表明:滤波器参数(Rf,Cf,Lf)取值合适的情况下,输入滤波器的加入可能会使平均电流控制Boost PFC电路的稳定区域扩大,从而纠正了以往人们认为输入滤波器的加入只会导致平均电流控制Boost PFC电路失去原来稳定性的结论。
5.多级PFC电路中多尺度分岔的研究。基于一定的假设条件,建立了级联PFC电路的简化模型,采用小信号模型方法分析了级联PFC电路中的中尺度分岔以及采用增量谐波平衡法和Floquet理论分析了级联PFC电路中的慢尺度分岔。电路仿真和电路实验证实了理论分析的正确性。此外,基于合适的假设,还建立了并联PFC电路的简化模型,采用谐波平衡法和Floquet理论分析了并联PFC电路中的慢尺度分岔,并指出了电路参数对并联PFC电路稳定性的影响与对单级PFC电路稳定性的影响存在着明显的差别。
6.分段光滑电路中混沌与多尺度分岔控制方法的研究。首先提出采用线性反馈控制方法实现了蔡氏电路的同步控制。其次,提出了基于无源控制理论,设计无源控制器,实现了变型蔡氏电路的同步控制。而后,提出了采用电流反馈控制方法实现了单周控制Boost电路中慢尺度分岔的控制,确定了使电路运行于稳定状态时控制参数的取值范围,并通过电路仿真和电路实验验证了该控制方法的有效性和理论分析的正确性。最后,提出采用负载电流反馈控制方法实现了平均电流控制Boost PFC电路中慢尺度分岔的控制,采用谐波平衡法和Floquet理论确定了使电路运行于稳定状态时控制参数的取值范围,并通过电路仿真和电路实验验证了该控制方法的有效性和理论分析的正确性。
The complex behavior in nonlinear circuit has become an important research subject in the modern circuit, which include extremely abundant contents and wide application prospects. In this dissertation, as an important part of nonlinear circuit research, the complex behavior in the piece-wise smooth circuit is investigated and the details are presented as follows:
1. The multiple chaotic attractor in autonomous piece-wise smooth circuit is studied. Two kinds of multi-scroll chaotic attractor and another kind of multi-folded torus chaotic attractor in the autonomous piece-wise smooth circuits are constructed and analyzed. The mathmatical models are established, the effects of parameters on the chaos of the circuit and the route to chaos of the circuit are analyzed. Moreover, the relationship between the number of chaotic attractor and the number of closed switches are given.
2. The multi-scale bifurcation in the one-cycle controlled DC-DC circuit is studied. The fast-scale bifurcation in the one-cycle controlled Buck circuit and the slow-scale bifurcation in one-cycle controlled Boost circuit are invesigated respectively with the circuit simulation, theoretical analysis and circuit experiment. The results shows: the main reason for the occurrence of fast-scale bifurcation in the one-cycle controlled Buck circuit is that the operation frequency of the circuit is lower than the clock frequency. But, for the slow-scale bifurcation in the one-cycle controlled Boost circuit, in fact, it is that the Hopf bifurcation happens in the area where the frequency is much lower than the switching frequency.
3. The multi-scale bifurcation in average current controlled Boost PFC circuit is studied. By establishing the simplified models, the medium-scale bifurcation is investigated based on the small-sigal model, and the slow-scale bifurcation is investigated based on the harmonic balance method and Floquet theory, and also, the subslow-scale bifurcation is investigated based on the nonlinear model. The under mechanism of the above three kinds of bifurcaton are given. Finally, the effectiveness of the simplified models and the validity of the theoretical analyses are confirmed by the circuit simulations and circuit experiments.
4. The multi-scale bifurcation in the averge current controlled Boost PFC with an input filter is studied. The mathematical models of the circuit are constructed, the slow-scale bifurcaiton in the circuit is analyzed by means of the harmonic balance method and Floquet theory and the subslow-scale bifurcation is analyzed by means of the nonlinear model. The results show that the stable area may be enlarged when the extra input filter is added into the average current controlled Boost PFC circuit. These results change the conclusions that the extra input filter will only degrade the stability of the average current controlled Boost PFC circuit.
5. The multi-scale bifurcation in the multi-stage PFC circuit is studied. Based on certain suitable assumptions, the simplified model of the cascade PFC circuit are established. And then, the medium-scale bifurcation is analyzed by using the small-signal model, and the slow-scale bifurcation is analyzed by using the method of incremental harmonic balance and Floquet theory. The effectiveness of the simplified model and the validity of the theoretical analysis are both confirmed by the circuit simulation and circuit experiment. Furthermore, the slow-scale bifurcation in parallel PFC circuit is analyzed by using the method of harmonic balance and Floquet theory. It is found that there are very important differences between the single-stage PFC circuit and the parallel PFC circuit.
6. Control of multi-scale bifurction and chaos in the piece-wise smooth circuit is studied. Firstly, the linear feedback control is proposed to realize the synchronization of the Chua’s circuit. Secondly, based on the passive control theory, the passive controller is designed to realize the synchronization of the modified Chua’s circuit. Thirdly, the current feedback control is applied to realize the control of the slow-scale bifurcation in the one-cycle controlled Boost circuit. The span of the control parameters for maintaining the circuit in stable operation are fixed. Moreover, the effectiveness of the control method and the validity of the theoretical analysis are confirmed by the circuit simulation and circuit experiment. Finally, the load current feedback control is applied to control the slow-scale bifurcation in average current controlled Boost PFC circuit. Based on the simplified model, the span of control parameters for maintaining the circuit in stable operation is analzed by using the method of harmonic and Floquet theory, and then the effectiveness of the control method and the validity of the theoretical analysis are confirmed by the circuit simulation and circuit experiment.
引文
[1] Chua LO. Nonlinear circuit theory[M]. Berkeley: University of California, 1978.
[2] Matsumoto T. A chaotic attractor from Chua’s Circuit[J]. IEEE Transactions on Circuits and Systems, 1984, 31(12): 1055-1058.
[3] Matsumoto T, Chua LO, Komuro M. The double scroll[J]. IEEE Transactions on Circuits and Systems, 1985, 32(8): 798-818.
[4] Chua LO, Komuro M, Matsumto T. The double scroll family[J]. IEEE Transactions on Circuits and Systems, 1986, 33(11): 1073-1118.
[5] Matsumoto T, Chua LO, Kobayashi K. Hyperchaos: Laboratory experiment and numerical confirmation[J]. IEEE Transactions on Circuits and Systems, 1986, 33(11): 1143-1147.
[6]高金峰.非线性电路与混沌[M].北京:科学出版社, 2005.
[7]杨晓松,李清都.混沌系统与混沌电路[M].北京:科学出版社, 2007.
[8] Erichson RW, Maksimovic D. Fundametals of power electronics [M]. Norwell, Massachusetts, USA: Kluwer Academic, 2001.
[9]周志敏,周纪海,纪爱华.开关电源功率因数校正电路设计与应用[M].北京:人民邮电出版社, 2004.
[10]毛兴武,祝大卫.功率因数校正原理与控制IC及其应用设计[M].北京:中国电力出版社, 2007.
[11]戴栋.分段光滑系统中的边界碰撞分岔现象与混沌控制、同步方法的研究[D].西安:西安交通大学, 2003.
[12]姚齐国.几种非线性电路的数值分析与优化设计[D].武汉:华中科技大学, 2007.
[13] Di Bernardo M, Feigin MI, Hogan S, et al. Local analysis of C-bifurcation in n-dimensional piecewise-smooth dynamical systems[J]. Chaos Solitons and Fractals, 1999, 10(11): 1881-1908.
[14] Di Bernardo M, Budd CJ, Champneys AR. Normal form maps for grazing bifurcations in n-dimensional piecewise-smooth dynamical systems[J]. Physica D, 2001, 160(3-4): 222-254.
[15]王发强,刘崇新.新的变形蔡氏电路及实验[J].通信学报, 2006, 27(6): 102-105.
[16] Tang KS, Man KF, Zhong GQ, et al. Modified Chua’s circuit with x|x|[J]. Control Theory & Applications, 2003, 20(2): 223-227.
[17]邢岩,蔡宣三.高频功率开关变换技术[M].北京:机械工业出版社, 2005: 17-18, 82-95.
[18]杨旭,裴云庆,王兆安.开关电源技术[M].北京:机械工业出版社, 2004: 260.
[19] Bonani F, Gilli M. Analysis of stability and bifurcations of limit cycles in Chua’s circuit through the harmonic-banlance approach[J]. IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Apllications, 1999, 46(8): 881-890.
[20] Kahan S, Sicardi-schifino AC. Homoclinic bifurcations in Chua’s circuit[J]. Physica A, 1999, 262: 144-152.
[21] Yang XS, Li QD. On entropy of Chua’s circuits[J]. International Journal of Bifurcation and Chaos, 2005, 15(5): 1823-1828.
[22] Chua LO. A zoo of strange attractors from the canonical Chua’s circuits[C]. Proceedings of the 35th Midwest Symposium on Circuits and Systems, 1992: 916-926.
[23] Yin YZ. Experimental demonstration of chaotic synchronization in the modified Chua’s oscillations[J]. International Journal of Bifurcation and Chaos, 1997, 7(6): 1401-1410.
[24] Yu SM, Qiu SS, Lin QH. New results study on generating multiple-scroll chaotic attractors[J]. Science in China(Series F), 2003, 46(2): 104-115.
[25]禹思敏,林清华,丘水生.四维系统中多涡卷混沌与超混沌吸引子的仿真研究[J].物理学报, 2003, 52(1): 25-33.
[26]禹思敏,丘水生. N涡卷超混沌吸引子产生与同步的研究[J].电子学报, 32(5): 814-818.
[27] Matsumoto T, Chua LO, Tokunaga R. Chaos via torus breakdown[J]. IEEE Transactions on Circuit and Systems, 1987, 34(3): 240-253.
[28]禹思敏,林清华,丘水生.一类多折叠环面混沌吸引子[J].物理学报, 2004, 53(7): 2084-2088.
[29] Yalcin ME, Suykens JAK, Vandewalle J. Families of scroll grid attractors[J]. International Journal of Bifurcation and Chaos, 2002, 12(1): 23-41.
[30] Yang XS, Li QD, Chen GR. A twin-star hyperchaotic attractor and its circuit implementation[J]. International Journal of Circuit Theory and Applications, 2003, 31: 637-640.
[31] Yu SM, Tang WKS, LüJH, et al. Generation of n m-wing Lorenz-like attractors from a modified Shimizu-Morioka model[J]. IEEE Transactions on Circuits and Systems-II: Express Briefs, 2008, 55(11): 1168-1172.
[32] LüJH, Chen GR. Generating multiscroll chaotic attractors: theories, methods and applications[J]. International Journal of Bifurcation and Chaos, 2006, 16(4): 775-858.
[33] Bilotta E, Pantano P, Stranges F. A gallery of Chua attractors: part I[J]. International Journal of Bifurcation and Chaos, 2007, 17(1): 1-60.
[34] Bilotta E, Pantano P, Stranges F. A gallery of Chua attractors: part II[J] . International Journal of Bifurcation and Chaos, 2007, 17(2): 293-380.
[35] Bilotta E, Stranges F, Pantano P. A gallery of Chua attractors: part III[J] . International Journal of Bifurcation and Chaos, 2007, 17(3): 657-734.
[36] Bilotta E, Blasi GD, Stranges F, et al. A gallery of Chua attractors: part IV[J] . International Journal of Bifurcation and Chaos, 2007, 17(4): 1017-1077.
[37] Bilotta E, Blasi GD, Stranges F, et al. A gallery of Chua attractors: part V[J] . International Journal of Bifurcation and Chaos, 2007, 17(5): 1383-1511.
[38] Bilotta E, Blasi GD, Stranges F, et al. A gallery of Chua attractors. part VI[J] . International Journal of Bifurcation and Chaos, 2007, 17(6): 1801-1910.
[39]关新平,范正平,陈彩莲等.混沌控制及其在保密通信中的应用[M].北京:国防工业出版社, 2006.
[40] Hu J, Chen SH, Chen L. Adaptive control for anti-synchronization of Chua’s chaotic system[J]. Physics Letters A, 2005, 339: 455-460.
[41] Sun JT, Zhang YP. Impulsive control and synchronization of Chua’s oscillators[J]. Mathematics and computers in simulation, 2004, 66: 499-508.
[42] Tang F, Wang L. Synchronization of modified Chua’s circuit with x|x| function[J]. Communication in Theroretical Physics, 2005, 44(2): 303-306.
[43] Hamill DC, Jefferies DJ. Subharmonics and chaos in a controlled switched-mode power converter[J]. IEEE Transactions on Circuits and Systems-I, 1988, 35(8): 1059-1061.
[44] Deane JHB, Hamill DC. Instability, subharmonics, and chaos in power electronic systems[J]. IEEE Transactions on Power Electronics, 1990, 5(3): 260-268.
[45] Dean JHB, Hamill DC. Analysis, simulation and experimental study of chaos in the buck converter[C]. IEEE Power Electronics Specialists Conference, 1990: 491-498.
[46] Hamill DC, Deane JHB, Jefferies DJ. Modeling of chaotic dc/dc converter by iterated nonlinear mappings[J]. IEEE Transactions on Power Electronics, 1992, 7(1): 25-36.
[47] Deane JHB. Chaos in a current-mode controlled boost DC-DC converter[J]. IEEE Transactions on Circuits and Systems– I, 1992, 39(8): 680-683.
[48] Tse CK. Chaos from a buck switching regulator operating in discontinuous mode[J]. Internaitional Journal of Circuit Theory & Applications, 1994, 22(4): 263-278.
[49] Tse CK. Flip bifurcation and chaos in three-state boost switching regulators[J]. IEEE Transactions on Circuits and Systems– I, 1994, 41(1): 16-23.
[50] Tse CK, Chan WCY. Instability and chaos in a current-mode controlled Cuk converter[C]. IEEE Power Electronics Specialists Conference,1995: 608-613.
[51] Chan WCY, Tse CK. Study of bifurcations in current-programmed DC/DC boost converters: from quasi-periodicity to period-doubling[J]. IEEE Transactions on Circuits and Systems–I, 1997, 44(12): 1129-1142.
[52] Chan WCY, Tse CK. Bifurcation in current-programmed dc/dc buck switching regulators- conjecturing a universal bifurcation path[J]. International Journal of Circuit Theory & Applications, 1998, 26(2): 127-146.
[53] Deane JHB, Ashwin P, Hamill DC,et al. Calculation of the periodic spectral components in a chaotic DC-DC converter[J]. IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Apllications, 1999, 46(11): 1313-1319.
[54] Yuan GH, Banerjee S, Ott E, et al. Border-collision bifurcations in the buck converter[J]. IEEE Transacations Circuits Systems-I, 1998, 45(7): 707-716.
[55] Banerjee S, Grebogi C. Border collision bifurcations in two-dimensional piecewise smooth maps[J]. Physical Review E, 1999, 59(4): 4052-4061.
[56] Zhusubaliyev ZT, Soukhoterin EA, Mosekilde E. Quasi-periodicity and border-collision bifurcations in a DC-DC converter with pulsewidth modulation[J]. IEEE Transactions on Circuits and Systems– I, 2003, 50(8): 1047-1057.
[57] Ma Y, Tse CK, Kousaka T, et al. Connecting border collision with saddle-node bifurcation in switched dynamical systems[J]. IEEE Transactions on Circuits and Systems-II, 2005, 52(9): 581-585.
[58]戴栋,马西奎,李小峰.一类具有两个边界的分段光滑系统中边界碰撞分岔现象及混沌[J].物理学报, 2003, 52(11): 2729-2736.
[59]李明,马西奎,戴栋等.基于符号序列描述的一类分段光滑系统中分岔现象与混沌分析[J].物理学报, 2005, 54(3): 1084-1091.
[60] Aroudi AE, Benadero L, Toribio E, et al. Hopf bifurcation and chaos from torus breakdown in a PWM voltage-controlled DC-DC boost converter[J]. IEEE Transactions on Circuits and Systems–I, 1999, 46(11): 1374-1382.
[61] Tse CK, Lai YM, Iu HHC. Hopf bifurcation and chaos in a free-running current-controlled Cuk switching regulator[J]. IEEE Transations on Circuits and Systems-I, 2000, 47(4): 448-457.
[62]刘健,王媛彬. PWM开关DC-DC变换器的低频波动[J].中国电机工程学报, 2004, 24(4): 174-178.
[63] Mazumder SK, Nayfeh AH, Boroyevich D. Theoretical and experimental investigation of the fast- and slow-scale instabilities of a DC-DC converter[J]. IEEE Transactions on Power Electronics, 2001, 16(2): 201-216.
[64] Iu HHC, Tse CK. Study of low-frequency bifurcation phenomena of a parallel-connected boost converter system via simple averaged models[J]. IEEE Transactions on Circuits and Systems-I, 2003, 50(5): 679-686.
[65] Kavitha A, Urna G. Experimental verification of Hopf bifurcation in DC-DC Luo converter[J]. IEEE Transactions on Power Electronics, 2008, 23(6): 2878-2883.
[66] Lim YH. Hamill AC. Problems of computing lyapunov exponents in power electronics[C]. Proceedings of the 1999 IEEE International Symposium on Circuits and Systems, 1999: 297-301.
[67]李小峰,马西奎,李明. DC/DC变换器的最大Lyapunov指数计算及其非线性特性的实验研究[J].电工技术学报, 2005, 20(4): 21-27.
[68] Bernardo MD, Vasca F. Discrete-time maps for the analysis of bifurcations and chaos in DC/DC converters[J] IEEE Transactions on Circuits and Systems– I, 2000, 47(2): 130-143.
[69] Tse CK, Bernardo M D. Complex behavior in switching power converters[J]. Proceeding of the IEEE, 2002, 90(5): 768-781.
[70] Aroudi AE, Debbat M, Giral R, et al. Bifurcations in DC-DC switching converters: review of methods and applications[J]. International Journal of Bifurcation and Chaos, 2005, 15(5): 1549-1578.
[71]张波.电力电子变换器非线性混沌现象及其应用研究[J].电工技术学报, 2005, 20(12): 1-6.
[72]张波.电力电子学亟待解决的若干基础问题探讨[J].电工技术学报, 2006, 21(3): 24-35.
[73]马西奎,李明,戴栋等.电力电子电路与系统中的复杂行为研究综述[J].电工技术学报, 2006, 21(12): 1-11.
[74] Bnarjee S, Verghese GC. Nonlinear phenomena in power electronics[M]. New York: IEEE Press, 2000.
[75] Tse CK. Complex behavior of switching power converters[M]. New York: CRC Press, 2003.
[76] Batlle C, Fossas E, Olivar G. Stabilization of periodic orbits of the buck converter by time-delayed feedback[J]. International Journal of Circuit Theory & Applications, 1999, 27(6): 617-631.
[77] Zhou YF, Tse CK, Qiu SS, et al. Applying resonant parametric perturbation to control chaos in the buck dc/dc converter with phase shift and frequency mismatch considerations[J]. International Journal of Bifurcation and Chaos, 2003, 13(11): 3459-3471.
[78]邹艳丽,罗晓曙,方锦清等.脉冲电压微分反馈法控制buck功率变换器中的混沌[J].物理学报, 2003, 52(12): 2978-2984.
[79]张浩. PFC变换器中的非线性现象分析与混沌控制方法研究[D].西安:西安交通大学, 2005.
[80] Orabi M, Ninomiya T, Jin CF. Nonlinear dynamics and stability analyses of Boost power-factor- correction circuit[C]. International Conference on Power System Technology, 2002, 1: 600-605.
[81] Orabi M, Ninomiya T. Nonlinear dynamics of power-factor-correction converter[J]. IEEE Transactions on Industrial Electronics, 2003, 50(6): 1116-1125.
[82] Orabi M, Ninomiya T. Numerical and experimental study of instability and bifurcation in AC/DC PFC circuit[J]. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2004, E87-A(9): 2256-2266.
[83] Orabi M, Haron R, EI-Aroudi A. Comparison between nonlinear-carrier control and averge- current- mode control for PFC converters[C]. IEEE Power Electronics Specialists Conference, 2007: 1349-1355
[84] Orabi M, EI-Aroudi A. Different frequency instabilities of averaged current controlled Boost PFC AC-DC regulators[C]. INTELEC’06.28th Annual International Telecommunications Energy Conference, 2006: 1-8.
[85] Wong SC, Tse CK, Orabi M, et al. The method of doubling averaging: an approach for modeling power-factor-correction switching converters[J]. IEEE Transactions on Circuits and Systems-I, 2006, 53(2): 454-462.
[86]邹建龙,马西奎.一类由饱和引起的非线性现象[J].物理学报, 2008, 57(2): 720-725.
[87]任海鹏.平均电流控制型PFC Boost变换器中的低频分岔现象研究[J].电子学报, 2006, 34(5): 784-789.
[88]任海鹏,刘丁.基于Matlab的PFC Boost变换器仿真研究和实验验证[J].电工技术学报, 2006, 21(5): 29-35.
[89] Iu HHC, Zhou Y, Tse CK. Fast-scale instability in a PFC boost converter under avergecurrent-mode control[J]. International Journal of Circuit Theory and Applications, 2003, 31: 611-624.
[90]邹建龙,马西奎.功率因数校正Boost变换器中快时标分岔的实验研究[J].中国电机工程学报, 2008, 28(12): 38-43.
[91] Dranga O, Tse CK, Iu HHC, et al. Bifurcation behavior of a power-factor-correction Boost converter[J]. International Journal of Bifurcation and Chaos, 2003, 13(10): 3107-3114.
[92] Zhang H, Ma XK, Xue BL, et al. Study of intermittent bifurcations and chaos in boost PFC converters by nonlinear discrete models[J]. Chaos Solitons & Fractals, 2005, 23(2): 431-444.
[93]马西奎,刘伟增,张浩.快时标意义下Boost PFC变换器中的分岔与混沌现象分析[J].中国电机工程学报, 2005, 25(5): 61-67.
[94]刘伟增,张浩,马西奎.基于频闪映射的Boost PFC变换器中的间歇性分岔和混沌现象分析[J].中国电机工程学报, 2005, 25(1): 43-48.
[95] Zou JL, Ma XK, Tse CK, et al. Fast-scale bifurcation in power-factor-correction buck-boost converters and effects of incompatible periodicities[J]. International Journal of Circuit Theory and Applications, 2006, 34: 251-264.
[96] EI-Aroudi A, Orabi M, Martinez-Salamero L, et al. Investigating stability and bifurcations of a Boost PFC circuit under peak current mode control[C]. IEEE International Symposium on Circuits and Systems, 2005: 2835-2838.
[97] Wu XQ, Tse CK, Dranga O, et al. Fast-scale instability of single-stage power factor-correction power supplies[J]. IEEE Transactions on Circuits and Systems-I: Regular Papers, 2006, 53(1): 204-213.
[98] Dai D, Li SN, Ma XK, et al. Slow-scale instability of single-stage power-factor-correction power supplies[J]. IEEE Transactions on Circuits and Systems-I: Regular Papers, 2007, 54(8): 1724-1735.
[99] Dai D, Tse CK, Zhang B, et al. Hopf bifurcation as an intermediate-scale instability in single-stage power-factor-correction power supplies: analysis, simulations and experimental verification[J]. International Journal of Bifurcation and Chaos, 2008, 18(7): 2095-2109.
[100] Orabi M, Ninomiya T. Identification of bifurcation parameters in switching power converter composed of cascade two-stage PFC circuit[C]. The 2004 47th Midwest Symposium on Circuits and Systems, 2004: 1-417-20.
[101] Orabi M, Ninomiya T. Study of alternative regimes to analyze two-stage PFC converter[C]. APEC 04’. 9th Annual IEEE Applied Power Electronics Conference and Exposition, 2004: 1488-1494.
[102] Orabi M, Ninomiya T. Stability investigation of the cascade two-stage PFC converter[J]. IEICE Transactions on Communication, E87-B(12): 3506-3514.
[103] Dranga O, Chu G, Tse CK, et al. Stability analysis of two-stage power supplies[C]. 37th IEEE Power Electronics Specialists Conference, 2006, 594-598.
[104] Chu G, Tse CK, Wong SC. Line-frequency instability of PFC power supplies[J]. IEEE Transactions on Power Electronics, 2009, 24(2): 469-482.
[105] Giaouris D, Banerjee S, Zahawi B, et al. Control of fast scale bifurcations in power-factor-correction converters[J]. IEEE Transactions on Circuits and Systems-II: Express Briefs, 2007, 54(9): 805-809.
[106]刘秉正,彭建华.非线性动力学[M].北京:高等教育出版社, 2004: 74.
[107]黄润生,黄浩.混沌及其应用(第二版)[M].武汉:武汉大学出版社, 2005: 88.
[108]张锦炎.常微分方程几何理论与分支问题[M].北京:北京大学出版社, 2000: 343.
[109]王洪礼,张琪昌.非线性动力学理论及其应用[M].天津:天津科学技术出版社, 2002: 241-242.
[110]吴浩.可倾瓦滑动轴承—转子系统非线性动力学特性分析[D].哈尔滨工业大学, 2007: 37-39.
[111] Smedley KM, Cuk S. One-cycle control of switching converters[J]. IEEE Transactions on Power Electronics, 1995, 10(6): 625-633.
[112] Smedley KM, Cuk S. Dynamics of one-cycle controlled Cuk converters[J]. IEEE Transactions on Power Electronics, 1995, 10(6): 634-639.
[113]胡宗波,张波,胡少甫等. Boost功率因数校正变换器单周期控制适用性的理论分析和实验验证[J].中国电机工程学报, 2005, 25(21): 19-23.
[114]周雒维,龚伟,苏向丰.一种改进的单周控制的开关功率放大器[J].电工技术学报, 2004, 19(5): 106-110.
[115] Qiao CM, Jin TT, Smedley KM. One-cycle control of three-Phase active power filter with vector operation[J]. IEEE Transactions on Industrial Electronics, 2004, 51(2): 455-463.
[116]朱锋,刘磊,龚春英.基于IT1150S与UC3854的Boost PFC变换器比较[J].电源技术应用, 2007, 10(3): 36-42.
[117] Tang W, Lee Fred C, Ridley RB, et al. Charge control: modeling, analysis, and design [J]. IEEE Transactions on Power Electronics, 1993, 8(4): 396-403.
[118]张卫平.开关变换器的建模与控制.北京:中国电力出版社, 2006: 6.
[119] Todd PC. UC3854 controlled power factor correction circuit design. Unitrode Product and Applications Handbook, 1995–1996, 10.303–10.322.
[120] Huliehel FA, Lee FC, Cho BH. Small-signal modeling of the single-phase Boost high power factor converter with constant frequency control[C]. IEEE power Electronics Specialists Conference, 1992: 475-482.
[121] Choi B, Hong SS, Park H. Modeling and small-signal analysis of controlled on-time Boost power-factor-correction circuit[J]. IEEE Transactions on Industrial Electronics, 2001, 48(1): 136–142.
[122] Sun J. Input impedance analysis of single-phase PFC converters[J]. IEEE Transactions on Power Electronics, 2005, 20(2): 308-314.
[123]曲小慧.基于航空交流电网的单相PFC技术的研究[D].南京:南京航空航天大学, 2006, 13.
[124]张志朝,张尧,张建设等. Hopf分岔的劳斯判据及其在电力系统中的应用[J].继电器, 2005, 33(1): 34-37.
[125] Itovich GR, Moiola JL. On period doubling bifurcations of cycles and the harmonic balance method[J]. Chaos, Solitons and Fractals, 2006, 27(3): 647-665.
[126] Belendez A, Pascual C, Mendez DI, et al. Solution of the relativistic (an) harmonic oscillator using the harmonic balance method[J]. Journal of Sound and Vibration, 2008, 311: 1447-1456.
[127] Shen JH, Lin KC, Chen SH, et al. Bifurcation and route-to-chaos analyses for Mathieu-Duffing oscillator by the incremental harmonic balance method[J]. Nonlinear Dynamics, 2008, 52: 403-414.
[128] Roy S, Got P, Ammari M. Stability considerations for a single phase generator-rectifier interface[C]. INTELEC. 20th International Telecommunications Energy Conference,1998: 151-155.
[129] Spiazzi G, Pornilio JA. Interaction between EMI filter and power factor preregulators with average current control: analysis and design considerations[J]. IEEE Transactions on Industrial Electronics, 1999, 46(3): 577-584.
[130] Raghothama A, Narayanan S. Bifurcation and chaos in geared rotor bearing system by incremental harmonic balance method[J]. Journal of Sound and Vibration, 1999, 226(3): 469-492.
[131] Raghothama A, Narayanan S. Bifurcation and chaos of an articulated loading platform with piecewise non-linear stiffness using the incremental harmonic balance method[J]. Ocean Engineering, 2000, 27: 1087-1107.
[132] Xu L, Lu MW, Cao Q. Nonlinear vibrations of dynamical systems with a general form of piecewise-linear viscous damping by incremental harmonic balance method[J]. Physics Letters A, 2002, 301: 65-73.
[133]贤燕华,罗晓曙,翁甲强.并联Buck电路变换器的非线性动力学性质与均流关系的研究[J].自然科学进展, 2004, 14(11): 1291-1296.
[134]王发强,刘崇新. Liu混沌系统的线性反馈同步控制及电路实验的研究[J].物理学报, 2006, 55(10): 5055-5060.
[135] Yu W. Passive equivalence of chaos in Lorenz system[J]. IEEE Transactions on Circuit and Systems-I: Fundamental Theory and Applications, 1999, 46(7): 876-878.
[136] Qi DL, Zhao GZ, Song YZ. Passive control of Chen chaotic system[C]. Proceeding of the 5th World Congress on Intelligent Control and Automation, 2004: 1284-1286.
[137]齐冬莲,厉小润,赵光宙.一类混合混沌系统的无源控制[J].浙江大学学报(工学版), 2004, 38(1): 86-89.
[2] Matsumoto T. A chaotic attractor from Chua’s Circuit[J]. IEEE Transactions on Circuits and Systems, 1984, 31(12): 1055-1058.
[3] Matsumoto T, Chua LO, Komuro M. The double scroll[J]. IEEE Transactions on Circuits and Systems, 1985, 32(8): 798-818.
[4] Chua LO, Komuro M, Matsumto T. The double scroll family[J]. IEEE Transactions on Circuits and Systems, 1986, 33(11): 1073-1118.
[5] Matsumoto T, Chua LO, Kobayashi K. Hyperchaos: Laboratory experiment and numerical confirmation[J]. IEEE Transactions on Circuits and Systems, 1986, 33(11): 1143-1147.
[6]高金峰.非线性电路与混沌[M].北京:科学出版社, 2005.
[7]杨晓松,李清都.混沌系统与混沌电路[M].北京:科学出版社, 2007.
[8] Erichson RW, Maksimovic D. Fundametals of power electronics [M]. Norwell, Massachusetts, USA: Kluwer Academic, 2001.
[9]周志敏,周纪海,纪爱华.开关电源功率因数校正电路设计与应用[M].北京:人民邮电出版社, 2004.
[10]毛兴武,祝大卫.功率因数校正原理与控制IC及其应用设计[M].北京:中国电力出版社, 2007.
[11]戴栋.分段光滑系统中的边界碰撞分岔现象与混沌控制、同步方法的研究[D].西安:西安交通大学, 2003.
[12]姚齐国.几种非线性电路的数值分析与优化设计[D].武汉:华中科技大学, 2007.
[13] Di Bernardo M, Feigin MI, Hogan S, et al. Local analysis of C-bifurcation in n-dimensional piecewise-smooth dynamical systems[J]. Chaos Solitons and Fractals, 1999, 10(11): 1881-1908.
[14] Di Bernardo M, Budd CJ, Champneys AR. Normal form maps for grazing bifurcations in n-dimensional piecewise-smooth dynamical systems[J]. Physica D, 2001, 160(3-4): 222-254.
[15]王发强,刘崇新.新的变形蔡氏电路及实验[J].通信学报, 2006, 27(6): 102-105.
[16] Tang KS, Man KF, Zhong GQ, et al. Modified Chua’s circuit with x|x|[J]. Control Theory & Applications, 2003, 20(2): 223-227.
[17]邢岩,蔡宣三.高频功率开关变换技术[M].北京:机械工业出版社, 2005: 17-18, 82-95.
[18]杨旭,裴云庆,王兆安.开关电源技术[M].北京:机械工业出版社, 2004: 260.
[19] Bonani F, Gilli M. Analysis of stability and bifurcations of limit cycles in Chua’s circuit through the harmonic-banlance approach[J]. IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Apllications, 1999, 46(8): 881-890.
[20] Kahan S, Sicardi-schifino AC. Homoclinic bifurcations in Chua’s circuit[J]. Physica A, 1999, 262: 144-152.
[21] Yang XS, Li QD. On entropy of Chua’s circuits[J]. International Journal of Bifurcation and Chaos, 2005, 15(5): 1823-1828.
[22] Chua LO. A zoo of strange attractors from the canonical Chua’s circuits[C]. Proceedings of the 35th Midwest Symposium on Circuits and Systems, 1992: 916-926.
[23] Yin YZ. Experimental demonstration of chaotic synchronization in the modified Chua’s oscillations[J]. International Journal of Bifurcation and Chaos, 1997, 7(6): 1401-1410.
[24] Yu SM, Qiu SS, Lin QH. New results study on generating multiple-scroll chaotic attractors[J]. Science in China(Series F), 2003, 46(2): 104-115.
[25]禹思敏,林清华,丘水生.四维系统中多涡卷混沌与超混沌吸引子的仿真研究[J].物理学报, 2003, 52(1): 25-33.
[26]禹思敏,丘水生. N涡卷超混沌吸引子产生与同步的研究[J].电子学报, 32(5): 814-818.
[27] Matsumoto T, Chua LO, Tokunaga R. Chaos via torus breakdown[J]. IEEE Transactions on Circuit and Systems, 1987, 34(3): 240-253.
[28]禹思敏,林清华,丘水生.一类多折叠环面混沌吸引子[J].物理学报, 2004, 53(7): 2084-2088.
[29] Yalcin ME, Suykens JAK, Vandewalle J. Families of scroll grid attractors[J]. International Journal of Bifurcation and Chaos, 2002, 12(1): 23-41.
[30] Yang XS, Li QD, Chen GR. A twin-star hyperchaotic attractor and its circuit implementation[J]. International Journal of Circuit Theory and Applications, 2003, 31: 637-640.
[31] Yu SM, Tang WKS, LüJH, et al. Generation of n m-wing Lorenz-like attractors from a modified Shimizu-Morioka model[J]. IEEE Transactions on Circuits and Systems-II: Express Briefs, 2008, 55(11): 1168-1172.
[32] LüJH, Chen GR. Generating multiscroll chaotic attractors: theories, methods and applications[J]. International Journal of Bifurcation and Chaos, 2006, 16(4): 775-858.
[33] Bilotta E, Pantano P, Stranges F. A gallery of Chua attractors: part I[J]. International Journal of Bifurcation and Chaos, 2007, 17(1): 1-60.
[34] Bilotta E, Pantano P, Stranges F. A gallery of Chua attractors: part II[J] . International Journal of Bifurcation and Chaos, 2007, 17(2): 293-380.
[35] Bilotta E, Stranges F, Pantano P. A gallery of Chua attractors: part III[J] . International Journal of Bifurcation and Chaos, 2007, 17(3): 657-734.
[36] Bilotta E, Blasi GD, Stranges F, et al. A gallery of Chua attractors: part IV[J] . International Journal of Bifurcation and Chaos, 2007, 17(4): 1017-1077.
[37] Bilotta E, Blasi GD, Stranges F, et al. A gallery of Chua attractors: part V[J] . International Journal of Bifurcation and Chaos, 2007, 17(5): 1383-1511.
[38] Bilotta E, Blasi GD, Stranges F, et al. A gallery of Chua attractors. part VI[J] . International Journal of Bifurcation and Chaos, 2007, 17(6): 1801-1910.
[39]关新平,范正平,陈彩莲等.混沌控制及其在保密通信中的应用[M].北京:国防工业出版社, 2006.
[40] Hu J, Chen SH, Chen L. Adaptive control for anti-synchronization of Chua’s chaotic system[J]. Physics Letters A, 2005, 339: 455-460.
[41] Sun JT, Zhang YP. Impulsive control and synchronization of Chua’s oscillators[J]. Mathematics and computers in simulation, 2004, 66: 499-508.
[42] Tang F, Wang L. Synchronization of modified Chua’s circuit with x|x| function[J]. Communication in Theroretical Physics, 2005, 44(2): 303-306.
[43] Hamill DC, Jefferies DJ. Subharmonics and chaos in a controlled switched-mode power converter[J]. IEEE Transactions on Circuits and Systems-I, 1988, 35(8): 1059-1061.
[44] Deane JHB, Hamill DC. Instability, subharmonics, and chaos in power electronic systems[J]. IEEE Transactions on Power Electronics, 1990, 5(3): 260-268.
[45] Dean JHB, Hamill DC. Analysis, simulation and experimental study of chaos in the buck converter[C]. IEEE Power Electronics Specialists Conference, 1990: 491-498.
[46] Hamill DC, Deane JHB, Jefferies DJ. Modeling of chaotic dc/dc converter by iterated nonlinear mappings[J]. IEEE Transactions on Power Electronics, 1992, 7(1): 25-36.
[47] Deane JHB. Chaos in a current-mode controlled boost DC-DC converter[J]. IEEE Transactions on Circuits and Systems– I, 1992, 39(8): 680-683.
[48] Tse CK. Chaos from a buck switching regulator operating in discontinuous mode[J]. Internaitional Journal of Circuit Theory & Applications, 1994, 22(4): 263-278.
[49] Tse CK. Flip bifurcation and chaos in three-state boost switching regulators[J]. IEEE Transactions on Circuits and Systems– I, 1994, 41(1): 16-23.
[50] Tse CK, Chan WCY. Instability and chaos in a current-mode controlled Cuk converter[C]. IEEE Power Electronics Specialists Conference,1995: 608-613.
[51] Chan WCY, Tse CK. Study of bifurcations in current-programmed DC/DC boost converters: from quasi-periodicity to period-doubling[J]. IEEE Transactions on Circuits and Systems–I, 1997, 44(12): 1129-1142.
[52] Chan WCY, Tse CK. Bifurcation in current-programmed dc/dc buck switching regulators- conjecturing a universal bifurcation path[J]. International Journal of Circuit Theory & Applications, 1998, 26(2): 127-146.
[53] Deane JHB, Ashwin P, Hamill DC,et al. Calculation of the periodic spectral components in a chaotic DC-DC converter[J]. IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Apllications, 1999, 46(11): 1313-1319.
[54] Yuan GH, Banerjee S, Ott E, et al. Border-collision bifurcations in the buck converter[J]. IEEE Transacations Circuits Systems-I, 1998, 45(7): 707-716.
[55] Banerjee S, Grebogi C. Border collision bifurcations in two-dimensional piecewise smooth maps[J]. Physical Review E, 1999, 59(4): 4052-4061.
[56] Zhusubaliyev ZT, Soukhoterin EA, Mosekilde E. Quasi-periodicity and border-collision bifurcations in a DC-DC converter with pulsewidth modulation[J]. IEEE Transactions on Circuits and Systems– I, 2003, 50(8): 1047-1057.
[57] Ma Y, Tse CK, Kousaka T, et al. Connecting border collision with saddle-node bifurcation in switched dynamical systems[J]. IEEE Transactions on Circuits and Systems-II, 2005, 52(9): 581-585.
[58]戴栋,马西奎,李小峰.一类具有两个边界的分段光滑系统中边界碰撞分岔现象及混沌[J].物理学报, 2003, 52(11): 2729-2736.
[59]李明,马西奎,戴栋等.基于符号序列描述的一类分段光滑系统中分岔现象与混沌分析[J].物理学报, 2005, 54(3): 1084-1091.
[60] Aroudi AE, Benadero L, Toribio E, et al. Hopf bifurcation and chaos from torus breakdown in a PWM voltage-controlled DC-DC boost converter[J]. IEEE Transactions on Circuits and Systems–I, 1999, 46(11): 1374-1382.
[61] Tse CK, Lai YM, Iu HHC. Hopf bifurcation and chaos in a free-running current-controlled Cuk switching regulator[J]. IEEE Transations on Circuits and Systems-I, 2000, 47(4): 448-457.
[62]刘健,王媛彬. PWM开关DC-DC变换器的低频波动[J].中国电机工程学报, 2004, 24(4): 174-178.
[63] Mazumder SK, Nayfeh AH, Boroyevich D. Theoretical and experimental investigation of the fast- and slow-scale instabilities of a DC-DC converter[J]. IEEE Transactions on Power Electronics, 2001, 16(2): 201-216.
[64] Iu HHC, Tse CK. Study of low-frequency bifurcation phenomena of a parallel-connected boost converter system via simple averaged models[J]. IEEE Transactions on Circuits and Systems-I, 2003, 50(5): 679-686.
[65] Kavitha A, Urna G. Experimental verification of Hopf bifurcation in DC-DC Luo converter[J]. IEEE Transactions on Power Electronics, 2008, 23(6): 2878-2883.
[66] Lim YH. Hamill AC. Problems of computing lyapunov exponents in power electronics[C]. Proceedings of the 1999 IEEE International Symposium on Circuits and Systems, 1999: 297-301.
[67]李小峰,马西奎,李明. DC/DC变换器的最大Lyapunov指数计算及其非线性特性的实验研究[J].电工技术学报, 2005, 20(4): 21-27.
[68] Bernardo MD, Vasca F. Discrete-time maps for the analysis of bifurcations and chaos in DC/DC converters[J] IEEE Transactions on Circuits and Systems– I, 2000, 47(2): 130-143.
[69] Tse CK, Bernardo M D. Complex behavior in switching power converters[J]. Proceeding of the IEEE, 2002, 90(5): 768-781.
[70] Aroudi AE, Debbat M, Giral R, et al. Bifurcations in DC-DC switching converters: review of methods and applications[J]. International Journal of Bifurcation and Chaos, 2005, 15(5): 1549-1578.
[71]张波.电力电子变换器非线性混沌现象及其应用研究[J].电工技术学报, 2005, 20(12): 1-6.
[72]张波.电力电子学亟待解决的若干基础问题探讨[J].电工技术学报, 2006, 21(3): 24-35.
[73]马西奎,李明,戴栋等.电力电子电路与系统中的复杂行为研究综述[J].电工技术学报, 2006, 21(12): 1-11.
[74] Bnarjee S, Verghese GC. Nonlinear phenomena in power electronics[M]. New York: IEEE Press, 2000.
[75] Tse CK. Complex behavior of switching power converters[M]. New York: CRC Press, 2003.
[76] Batlle C, Fossas E, Olivar G. Stabilization of periodic orbits of the buck converter by time-delayed feedback[J]. International Journal of Circuit Theory & Applications, 1999, 27(6): 617-631.
[77] Zhou YF, Tse CK, Qiu SS, et al. Applying resonant parametric perturbation to control chaos in the buck dc/dc converter with phase shift and frequency mismatch considerations[J]. International Journal of Bifurcation and Chaos, 2003, 13(11): 3459-3471.
[78]邹艳丽,罗晓曙,方锦清等.脉冲电压微分反馈法控制buck功率变换器中的混沌[J].物理学报, 2003, 52(12): 2978-2984.
[79]张浩. PFC变换器中的非线性现象分析与混沌控制方法研究[D].西安:西安交通大学, 2005.
[80] Orabi M, Ninomiya T, Jin CF. Nonlinear dynamics and stability analyses of Boost power-factor- correction circuit[C]. International Conference on Power System Technology, 2002, 1: 600-605.
[81] Orabi M, Ninomiya T. Nonlinear dynamics of power-factor-correction converter[J]. IEEE Transactions on Industrial Electronics, 2003, 50(6): 1116-1125.
[82] Orabi M, Ninomiya T. Numerical and experimental study of instability and bifurcation in AC/DC PFC circuit[J]. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2004, E87-A(9): 2256-2266.
[83] Orabi M, Haron R, EI-Aroudi A. Comparison between nonlinear-carrier control and averge- current- mode control for PFC converters[C]. IEEE Power Electronics Specialists Conference, 2007: 1349-1355
[84] Orabi M, EI-Aroudi A. Different frequency instabilities of averaged current controlled Boost PFC AC-DC regulators[C]. INTELEC’06.28th Annual International Telecommunications Energy Conference, 2006: 1-8.
[85] Wong SC, Tse CK, Orabi M, et al. The method of doubling averaging: an approach for modeling power-factor-correction switching converters[J]. IEEE Transactions on Circuits and Systems-I, 2006, 53(2): 454-462.
[86]邹建龙,马西奎.一类由饱和引起的非线性现象[J].物理学报, 2008, 57(2): 720-725.
[87]任海鹏.平均电流控制型PFC Boost变换器中的低频分岔现象研究[J].电子学报, 2006, 34(5): 784-789.
[88]任海鹏,刘丁.基于Matlab的PFC Boost变换器仿真研究和实验验证[J].电工技术学报, 2006, 21(5): 29-35.
[89] Iu HHC, Zhou Y, Tse CK. Fast-scale instability in a PFC boost converter under avergecurrent-mode control[J]. International Journal of Circuit Theory and Applications, 2003, 31: 611-624.
[90]邹建龙,马西奎.功率因数校正Boost变换器中快时标分岔的实验研究[J].中国电机工程学报, 2008, 28(12): 38-43.
[91] Dranga O, Tse CK, Iu HHC, et al. Bifurcation behavior of a power-factor-correction Boost converter[J]. International Journal of Bifurcation and Chaos, 2003, 13(10): 3107-3114.
[92] Zhang H, Ma XK, Xue BL, et al. Study of intermittent bifurcations and chaos in boost PFC converters by nonlinear discrete models[J]. Chaos Solitons & Fractals, 2005, 23(2): 431-444.
[93]马西奎,刘伟增,张浩.快时标意义下Boost PFC变换器中的分岔与混沌现象分析[J].中国电机工程学报, 2005, 25(5): 61-67.
[94]刘伟增,张浩,马西奎.基于频闪映射的Boost PFC变换器中的间歇性分岔和混沌现象分析[J].中国电机工程学报, 2005, 25(1): 43-48.
[95] Zou JL, Ma XK, Tse CK, et al. Fast-scale bifurcation in power-factor-correction buck-boost converters and effects of incompatible periodicities[J]. International Journal of Circuit Theory and Applications, 2006, 34: 251-264.
[96] EI-Aroudi A, Orabi M, Martinez-Salamero L, et al. Investigating stability and bifurcations of a Boost PFC circuit under peak current mode control[C]. IEEE International Symposium on Circuits and Systems, 2005: 2835-2838.
[97] Wu XQ, Tse CK, Dranga O, et al. Fast-scale instability of single-stage power factor-correction power supplies[J]. IEEE Transactions on Circuits and Systems-I: Regular Papers, 2006, 53(1): 204-213.
[98] Dai D, Li SN, Ma XK, et al. Slow-scale instability of single-stage power-factor-correction power supplies[J]. IEEE Transactions on Circuits and Systems-I: Regular Papers, 2007, 54(8): 1724-1735.
[99] Dai D, Tse CK, Zhang B, et al. Hopf bifurcation as an intermediate-scale instability in single-stage power-factor-correction power supplies: analysis, simulations and experimental verification[J]. International Journal of Bifurcation and Chaos, 2008, 18(7): 2095-2109.
[100] Orabi M, Ninomiya T. Identification of bifurcation parameters in switching power converter composed of cascade two-stage PFC circuit[C]. The 2004 47th Midwest Symposium on Circuits and Systems, 2004: 1-417-20.
[101] Orabi M, Ninomiya T. Study of alternative regimes to analyze two-stage PFC converter[C]. APEC 04’. 9th Annual IEEE Applied Power Electronics Conference and Exposition, 2004: 1488-1494.
[102] Orabi M, Ninomiya T. Stability investigation of the cascade two-stage PFC converter[J]. IEICE Transactions on Communication, E87-B(12): 3506-3514.
[103] Dranga O, Chu G, Tse CK, et al. Stability analysis of two-stage power supplies[C]. 37th IEEE Power Electronics Specialists Conference, 2006, 594-598.
[104] Chu G, Tse CK, Wong SC. Line-frequency instability of PFC power supplies[J]. IEEE Transactions on Power Electronics, 2009, 24(2): 469-482.
[105] Giaouris D, Banerjee S, Zahawi B, et al. Control of fast scale bifurcations in power-factor-correction converters[J]. IEEE Transactions on Circuits and Systems-II: Express Briefs, 2007, 54(9): 805-809.
[106]刘秉正,彭建华.非线性动力学[M].北京:高等教育出版社, 2004: 74.
[107]黄润生,黄浩.混沌及其应用(第二版)[M].武汉:武汉大学出版社, 2005: 88.
[108]张锦炎.常微分方程几何理论与分支问题[M].北京:北京大学出版社, 2000: 343.
[109]王洪礼,张琪昌.非线性动力学理论及其应用[M].天津:天津科学技术出版社, 2002: 241-242.
[110]吴浩.可倾瓦滑动轴承—转子系统非线性动力学特性分析[D].哈尔滨工业大学, 2007: 37-39.
[111] Smedley KM, Cuk S. One-cycle control of switching converters[J]. IEEE Transactions on Power Electronics, 1995, 10(6): 625-633.
[112] Smedley KM, Cuk S. Dynamics of one-cycle controlled Cuk converters[J]. IEEE Transactions on Power Electronics, 1995, 10(6): 634-639.
[113]胡宗波,张波,胡少甫等. Boost功率因数校正变换器单周期控制适用性的理论分析和实验验证[J].中国电机工程学报, 2005, 25(21): 19-23.
[114]周雒维,龚伟,苏向丰.一种改进的单周控制的开关功率放大器[J].电工技术学报, 2004, 19(5): 106-110.
[115] Qiao CM, Jin TT, Smedley KM. One-cycle control of three-Phase active power filter with vector operation[J]. IEEE Transactions on Industrial Electronics, 2004, 51(2): 455-463.
[116]朱锋,刘磊,龚春英.基于IT1150S与UC3854的Boost PFC变换器比较[J].电源技术应用, 2007, 10(3): 36-42.
[117] Tang W, Lee Fred C, Ridley RB, et al. Charge control: modeling, analysis, and design [J]. IEEE Transactions on Power Electronics, 1993, 8(4): 396-403.
[118]张卫平.开关变换器的建模与控制.北京:中国电力出版社, 2006: 6.
[119] Todd PC. UC3854 controlled power factor correction circuit design. Unitrode Product and Applications Handbook, 1995–1996, 10.303–10.322.
[120] Huliehel FA, Lee FC, Cho BH. Small-signal modeling of the single-phase Boost high power factor converter with constant frequency control[C]. IEEE power Electronics Specialists Conference, 1992: 475-482.
[121] Choi B, Hong SS, Park H. Modeling and small-signal analysis of controlled on-time Boost power-factor-correction circuit[J]. IEEE Transactions on Industrial Electronics, 2001, 48(1): 136–142.
[122] Sun J. Input impedance analysis of single-phase PFC converters[J]. IEEE Transactions on Power Electronics, 2005, 20(2): 308-314.
[123]曲小慧.基于航空交流电网的单相PFC技术的研究[D].南京:南京航空航天大学, 2006, 13.
[124]张志朝,张尧,张建设等. Hopf分岔的劳斯判据及其在电力系统中的应用[J].继电器, 2005, 33(1): 34-37.
[125] Itovich GR, Moiola JL. On period doubling bifurcations of cycles and the harmonic balance method[J]. Chaos, Solitons and Fractals, 2006, 27(3): 647-665.
[126] Belendez A, Pascual C, Mendez DI, et al. Solution of the relativistic (an) harmonic oscillator using the harmonic balance method[J]. Journal of Sound and Vibration, 2008, 311: 1447-1456.
[127] Shen JH, Lin KC, Chen SH, et al. Bifurcation and route-to-chaos analyses for Mathieu-Duffing oscillator by the incremental harmonic balance method[J]. Nonlinear Dynamics, 2008, 52: 403-414.
[128] Roy S, Got P, Ammari M. Stability considerations for a single phase generator-rectifier interface[C]. INTELEC. 20th International Telecommunications Energy Conference,1998: 151-155.
[129] Spiazzi G, Pornilio JA. Interaction between EMI filter and power factor preregulators with average current control: analysis and design considerations[J]. IEEE Transactions on Industrial Electronics, 1999, 46(3): 577-584.
[130] Raghothama A, Narayanan S. Bifurcation and chaos in geared rotor bearing system by incremental harmonic balance method[J]. Journal of Sound and Vibration, 1999, 226(3): 469-492.
[131] Raghothama A, Narayanan S. Bifurcation and chaos of an articulated loading platform with piecewise non-linear stiffness using the incremental harmonic balance method[J]. Ocean Engineering, 2000, 27: 1087-1107.
[132] Xu L, Lu MW, Cao Q. Nonlinear vibrations of dynamical systems with a general form of piecewise-linear viscous damping by incremental harmonic balance method[J]. Physics Letters A, 2002, 301: 65-73.
[133]贤燕华,罗晓曙,翁甲强.并联Buck电路变换器的非线性动力学性质与均流关系的研究[J].自然科学进展, 2004, 14(11): 1291-1296.
[134]王发强,刘崇新. Liu混沌系统的线性反馈同步控制及电路实验的研究[J].物理学报, 2006, 55(10): 5055-5060.
[135] Yu W. Passive equivalence of chaos in Lorenz system[J]. IEEE Transactions on Circuit and Systems-I: Fundamental Theory and Applications, 1999, 46(7): 876-878.
[136] Qi DL, Zhao GZ, Song YZ. Passive control of Chen chaotic system[C]. Proceeding of the 5th World Congress on Intelligent Control and Automation, 2004: 1284-1286.
[137]齐冬莲,厉小润,赵光宙.一类混合混沌系统的无源控制[J].浙江大学学报(工学版), 2004, 38(1): 86-89.