电力电子电路中快标分叉及混沌控制研究
|
摘要
电力电子电路属于强非线性电路系统,由于器件的非线性和开关的切换作用,在其电路工作过程中可能会出现一些非线性现象,导致电路的许多工作性能变坏。通过对电力电子电路中的分叉及混沌控制研究,可以揭示该电路的非线性本质,提高电路的各项性能指标,为电路的稳定运行提供有力保障,为实际电路的稳定设计提供理论依据。具体工作内容包括：
(1)介绍了混沌动力学的一些相关基本知识,这些基本知识为电力电子电路中的快标分叉及混沌控制研究提供了理论指导。并对本论文的结构进行了安排；
(2)介绍了分叉及混沌控制的一些方法,分析比较了各自的特点。尽管目前已取得了一定的成果,但混沌控制仍是热点研究领域；
(3)对开关功率变换器中的快标分叉控制进行了深入的研究。深入分析了电力电子电路在工程实践应用过程中,随着电路中某些系统参数的变化,电路将出现分叉直至进入混沌状态,使系统的性能变差。在实际工程中,希望其稳定地工作在开关频率上,避免任何分叉和混沌行为的出现。斜坡补偿是一种简单而有效的方法,它对控制对象有很好的适用性,同样适用于电力电子电路的分叉和混沌控制。本文从非线性系统的分叉控制理论出发,对峰值电流模式控制的几个典型的电路中的斜坡补偿进行了详细地分析,并得出了优化的补偿结果。精确的仿真结果充分验证了理论分析的有效和正确。该方法同样适用于其他的电力电子电路稳定性分析与设计；
(4)深入研究了单个和并联SPWM逆变器中的分叉控制。分析其在工程实践应用时,当系统参数发生变化,逆变器将出现分叉直至进入混沌状态,使系统的性能变差。本文从非线性系统的分叉控制理论出发,对峰值电流模式控制的单相和并联SPWM逆变器中的斜坡补偿进行了详细地分析,并得出了优化的补偿结果。精确的仿真结果充分验证了理论分析的有效和正确。该方法同样适用于其他的电力电子电路稳定性分析与设计；
(5)对电力电子电路中的比较复杂的电路,如单相SPWM逆变器、PFC Boost变换器中的混沌现象,应用了延迟反馈法进行了有效的控制,实现了混沌状态到稳定态的周期状态转化。控制的结果使系统回到了原系统的混沌中的不稳定周期轨道(UPO)。并通过大量仿真总结了不同的反馈增益k1、不同的延迟时间τ对系统性能是如何影响的?以及各电路参数对反馈增益k1的影响,为电路的稳定设计提供可靠的理论指导；
Power electronic circuit belongs to the strongly nonlinear circuit system. Due to the non-linearity of the device and the switching function of the switch, a variety of nonlinear phenomena will occur in the operational process, which worsens many performances of the circuit.Through the research of the bifurcation and chaos control in the power electronic circuit, it can reveal the nonlinear nature of the circuit, improve varied performance indicators of the circuit, provide an effective guarantee for the stable operation of the circuit, and supply the theoretical basis for the design of the stability of practical circuits. The detailed contents are as follows:
(1) The paper introduces some basic knowledge related to the chaotic dynamics, which provides a theoretical guidance for the research of fast-scale bifurcation and chaos control in the power electronic circuit. Also, it points out the structure for the whole paper.
(2) In this paper, we introduce some metods of the bifurcation and chaos control, and analyze their respective characteristics. Although many achievements have been made now, the chaos control is still a hot research field.
(3) The fast-scale bifurcation control in the switching power converter has been researched deeply.The power electronic circuit has been widely applied in engineering practices. With the changes of some system parameters in the circuit, the bifurcation of the circuit will occur and then changes into the chaotic state, which degrades the performance of the system. In the actual project, we hope the circuit work steadily on the switching frequency to avoid any bifurcation and chaotic behavior. Slope compensation is a simple and effective way. It has good applicability and is suitable for bifurcations and chaos control in power electronic circuits. This paper starts from the theory of bifurcation control of nonlinear systems, and makes a detailed analysis of the slope compensation in several typical circuits under the peak current-mode control, and then comes to the optimal compensation results. The accurate simulation results verify the effectiveness and correctness of the theoretical analysis. This method is also applicable to the stability analysis and the design of other power electronic circuits.
(4) The single and parallel single-phase SPWM inverters, wideley used in engineering practices, have been researched extensively. When system parameters change, the inverters will appear to be bifurcate and then go into the chaotic state, which degrades the performance of the system. Based on the theory of bifurcation control of nonlinear systems, the paper makes a detailed analysis of the slope compensation in the single and parallel single-phase SPWM inverters under the peak current-mode control, and then reaches the optimal compensation results. The accurate simulation results prove the effectiveness and correctness of the theoretical analysis. This method is also applicable to the stability analysis and the design of the power electronic circuits.
(5) The delayed feedback approach is adopted to deal with the chaotic phenomena occurring in the more complex circuits in power electronic circuits, like single-phase SPWM inverter and PFC Boost Converter. The chaotic phenomena get effective control and achieve the transformation of the periodic state from the chaotic state to the steady state. The results of the control make the system back to the unstable periodic orbits (UPO) in the chaos of the original system. Through a large number of simulations, we summarize how the different feedback gainK1and different delay time r influence the system performance and how the circuit parameters affect the feedback gainK1, so as to provide a reliable theoretical guidance for the design of the circuit stability.
(1)介绍了混沌动力学的一些相关基本知识,这些基本知识为电力电子电路中的快标分叉及混沌控制研究提供了理论指导。并对本论文的结构进行了安排；
(2)介绍了分叉及混沌控制的一些方法,分析比较了各自的特点。尽管目前已取得了一定的成果,但混沌控制仍是热点研究领域；
(3)对开关功率变换器中的快标分叉控制进行了深入的研究。深入分析了电力电子电路在工程实践应用过程中,随着电路中某些系统参数的变化,电路将出现分叉直至进入混沌状态,使系统的性能变差。在实际工程中,希望其稳定地工作在开关频率上,避免任何分叉和混沌行为的出现。斜坡补偿是一种简单而有效的方法,它对控制对象有很好的适用性,同样适用于电力电子电路的分叉和混沌控制。本文从非线性系统的分叉控制理论出发,对峰值电流模式控制的几个典型的电路中的斜坡补偿进行了详细地分析,并得出了优化的补偿结果。精确的仿真结果充分验证了理论分析的有效和正确。该方法同样适用于其他的电力电子电路稳定性分析与设计；
(4)深入研究了单个和并联SPWM逆变器中的分叉控制。分析其在工程实践应用时,当系统参数发生变化,逆变器将出现分叉直至进入混沌状态,使系统的性能变差。本文从非线性系统的分叉控制理论出发,对峰值电流模式控制的单相和并联SPWM逆变器中的斜坡补偿进行了详细地分析,并得出了优化的补偿结果。精确的仿真结果充分验证了理论分析的有效和正确。该方法同样适用于其他的电力电子电路稳定性分析与设计；
(5)对电力电子电路中的比较复杂的电路,如单相SPWM逆变器、PFC Boost变换器中的混沌现象,应用了延迟反馈法进行了有效的控制,实现了混沌状态到稳定态的周期状态转化。控制的结果使系统回到了原系统的混沌中的不稳定周期轨道(UPO)。并通过大量仿真总结了不同的反馈增益k1、不同的延迟时间τ对系统性能是如何影响的?以及各电路参数对反馈增益k1的影响,为电路的稳定设计提供可靠的理论指导；
Power electronic circuit belongs to the strongly nonlinear circuit system. Due to the non-linearity of the device and the switching function of the switch, a variety of nonlinear phenomena will occur in the operational process, which worsens many performances of the circuit.Through the research of the bifurcation and chaos control in the power electronic circuit, it can reveal the nonlinear nature of the circuit, improve varied performance indicators of the circuit, provide an effective guarantee for the stable operation of the circuit, and supply the theoretical basis for the design of the stability of practical circuits. The detailed contents are as follows:
(1) The paper introduces some basic knowledge related to the chaotic dynamics, which provides a theoretical guidance for the research of fast-scale bifurcation and chaos control in the power electronic circuit. Also, it points out the structure for the whole paper.
(2) In this paper, we introduce some metods of the bifurcation and chaos control, and analyze their respective characteristics. Although many achievements have been made now, the chaos control is still a hot research field.
(3) The fast-scale bifurcation control in the switching power converter has been researched deeply.The power electronic circuit has been widely applied in engineering practices. With the changes of some system parameters in the circuit, the bifurcation of the circuit will occur and then changes into the chaotic state, which degrades the performance of the system. In the actual project, we hope the circuit work steadily on the switching frequency to avoid any bifurcation and chaotic behavior. Slope compensation is a simple and effective way. It has good applicability and is suitable for bifurcations and chaos control in power electronic circuits. This paper starts from the theory of bifurcation control of nonlinear systems, and makes a detailed analysis of the slope compensation in several typical circuits under the peak current-mode control, and then comes to the optimal compensation results. The accurate simulation results verify the effectiveness and correctness of the theoretical analysis. This method is also applicable to the stability analysis and the design of other power electronic circuits.
(4) The single and parallel single-phase SPWM inverters, wideley used in engineering practices, have been researched extensively. When system parameters change, the inverters will appear to be bifurcate and then go into the chaotic state, which degrades the performance of the system. Based on the theory of bifurcation control of nonlinear systems, the paper makes a detailed analysis of the slope compensation in the single and parallel single-phase SPWM inverters under the peak current-mode control, and then reaches the optimal compensation results. The accurate simulation results prove the effectiveness and correctness of the theoretical analysis. This method is also applicable to the stability analysis and the design of the power electronic circuits.
(5) The delayed feedback approach is adopted to deal with the chaotic phenomena occurring in the more complex circuits in power electronic circuits, like single-phase SPWM inverter and PFC Boost Converter. The chaotic phenomena get effective control and achieve the transformation of the periodic state from the chaotic state to the steady state. The results of the control make the system back to the unstable periodic orbits (UPO) in the chaos of the original system. Through a large number of simulations, we summarize how the different feedback gainK1and different delay time r influence the system performance and how the circuit parameters affect the feedback gainK1, so as to provide a reliable theoretical guidance for the design of the circuit stability.
引文
[1]Hao B L. Chaos. Singapore: World Scientific,1984.
[2]Hao B L. Chaos Ⅱ. Singapore:World Scientific,1990.
[3]郝柏林.分岔、混沌、奇怪吸引子、湍流及其他——关于确定论系统的内在随机性.物理学进展,1983,3(3)：329-416.
[4]吕金虎.一个统一混沌系统及其研究.北京：中国科学院研究生院(数学与系统科学研究院)博士学位论文,2002.
[5]吕金虎,陆均安,陈士华.混沌时间序列分析及其应用.武汉：武汉大学出版社,2002.
[6]陈关荣,吕金虎Lorenz系统族的动力学分析、控制与同步.北京：科学出版社,2003.
[7]Sivakumar B. Chaos theory in hydrology: important issues and interpretations. Journal of Hydrology,2000,227 (1-4):1-20.
[8]Haykin S, Principe J. Making sence of a complex world [chaotic events modeling]. IEEE Signal Processing Magazine,1998,15 (3):66-81.
[9]Nishimura K, Yano M. On the existence of chaotic solutions in dynamic linear programming. Mathematics and Computers in Simulation,1999,48 (4-6): 487-496.
[10]赵永龙,丁晶,邓育仁.混沌分析在水文预测中的应用和展望.水科学进展,1998,9(2)：181-186.
[11]黄润生.混沌及其应用.武汉：武汉大学出版社,2000.
[12]G. Chen, X. Dong,From chaos to order:perspective and methodologies in controlling chaotic nonlinear dynamical system. Int. J. Bifur. Chaos,1993 3: 1363-1409.
[13]徐京华.人脑功能的混沌动力学.科学,1990,42：266-270.
[14]郝柏林.自然界中的有序和混沌.百科知识,1984,1：69-72.
[15]Lorenz E N. Deterministic nonperiodic flow. Journal of Atmos. Sci.,1963,20: 130-141.
[16]Henon M. A two-dimensional mapping with a strange attractor. Commun. Math. Phys.,1976,50:69-77.
[17]Li T Y, Yorke J A. Period three implies chaos. America Mathematics Monthly, 1975,82:985-992.
[18]Feigenbaum M J. Quantitative uniwersality for a class of nonlinear transformations. Journal of Stat. Phys.,1978,19: 25-52.
[19]Grassberger P, Procaccia I. Measuring the strangeness of strange attractors. Physica D,1983,9:189-208.
[20]May R M. Simple mathematical models with very complicated dynamics. Nature, 1976,261:459-467.
[21]李浙生.攸忽之间——混沌与认识.北京：冶金工业出版社,2002.
[22]El A. Aroudi, R. Leyva. Quasi-periodic route to chaos in a PWM voltage-controlled DC-DC boost coverter[J].IEEE Trans, Circuits and Systems-I, 2001,48(8):967-978.
[23]C K. Tse, M. di Bernardo,.Complex behavior in switching power converter[J]. Proceedings of IEEE,2002,90(5):768-781.
[24]J. H. B. Deane, D. C. Hamill, Instability, subharmonics, and chaos in power electronic systems, IEEE Trans. Power Electron.,1990,5(3):260-268.
[25]张波,李萍,齐群DC-DC变换器分岔和混沌现象的建模和分析方法[J].中国电机工程学报2002,22(10)：81-85.
[26]周宇飞,陈军宁.开关变换器中吸引子共存现象的仿真与实验研究[J].中国电机工程学报,2005,21(21)：96-101.
[27]P. T. Krein and R. M. Bass. Types of instabilities encountered in simple power electronics circuits:Unboundedness, chattering and chaos [C], in Proc. IEEE Applied Power Electronics Conf.,1990, ppl91-194.
[28]C.K. Tse and W.C. Y.Chan.Chaos from a current programmed Cuk converter[J]. Int. J. Circuit Theory Appl.,1995,23(3):217-225.
[29]I Zafrany and S.A. Ben-Yaakov chaos model of subharmonic oscillations in current mode PWM boost converters[C].IEEE Power Electron.Specialists Conf.Rec,Atlanta,GA,June 1995, pp5.4.5/1-5.4.5/5.
[30]J H B. Deane and D C. Hamill.Chaotic behaviour in current-mode controlled dc/dcconverters[J].IEE.Electron.Lett,1991,27(13):1172-1173.
[31]J H B Deane.Chaos in a current-mode controlled boost dc/dc converter[J]. IEEE Trans. Circ.Syst.-1,1992,39(8):680-683.
[32]C.Y. Willam Chan and Chi K.Tse.Study of bifurcations in current-programmed dc/dc boost converters:From quasi-periodicity to period-doubling[J]. IEEE Trans.Circ.Syst.-1,1997,44(12):1129-1142.
[33]C K. Tse.Flip bifurcation and chaos in a three-state boost switching regulater[J]. IEEE Trans. Circ.Syst.-1,1994,41(1):16-23.
[34]C K. Tse.Chaos from a buck switching regulator operation in discontinuous mode[J]. Int. J. Circ.TheoryAppl,1994,22(4):263-278.
[35]W C Y. Chan and C K. Tse On the form of control function that can lead to chaos in discontinuous-mode dc/dc converters[C].IEEE Power Electron.Spec.Conf. Rec, 1997,1317-1322.
[36]Soumitro Banerjee.Coexisting Attractors,Chaotic Saddles and Fractal Basins in a Power Electron Circuit[J]. IEEE Trans. Circ.Syst.-1,1997,44(9):847-849.
[37]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叉现象与混沌分析[J].物理学报,2005,54(3)：1084-1091.
[38]H. Zhan, X K. Ma, B L. Xue, et al. Study of intermittent bifurcation and chaos in boost PFC converters by nonlinear discrete model[J].Chaos, Solitons and Fractals,2005,25(1):43-48.
[39]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叉和混沌现象分析[J].中国电机工程学报,2005,25(1)：43-48.
[40]H. E. Nusse, J A. York. Border-collision bifurcation including period two to period three for piecewise smooth system[J].Phsica D,1992,57(1-2):39-57.
[41]张琪昌.分岔与混沌理论及应用.天津：天津大学出版社,2005.
[42]Sivakumar B. chaos theory in hydrology:important issues and interpretations. Journal of Hydrology,2000,227(1-4):1-20.
[43]Sivakumar B. chaos theory in geophysics:past, present and future. Chaos Solitons & Fractals,2004,19:441-462.
[44]Schertzer D. Tchiguirinskaia I, Lovejoy S, Hubert P,et al., Reply to which chaos in the rainfall-runoff process ? Hydrological Sciences Journal-Journal Des Sciences Hydrologiques,2002,47 (1):139-158.
[45]Rudnicki R . Chaos for some infinite-dimensional dynamical systerms Mathematical Methods in the Applied Sciences,2004,27:723-738.
[46]Man K S. Long memory time series and short term forecasts. International Journal of Forecasting,2003,19 (3):477-491.
[47]王洪瑞,宋宇,刘昌明,陈家军.混沌理论及在水科学中的应用与存在的问题.2004,15(3)：400-407.
[48]汪剑鸣,许镇琳.PWM型DC/DC变换器基于混沌动力学的建模、控制及应用[D],天津大学博士毕业论文,2002,5-14.
[49]W.C.Y.Chan, C.K.Tse. Bifurcations in current-programmed DC/DC Buck switching regulators——conjecturing a universal bifurcation path[J]. Int.J.Circuit Theory and Applications,1998,26(2):127-145.
[50]周宇飞,陈军宁.电流模式控制Boost变换器中的切分叉及阵发混沌现象[J].中国电机工程学报,2005,25((1)：23-26.
[51]李胜男,张浩,马西奎,李明.Buck-Boost DC/DC变换器中的边界碰撞分叉现象的实验研究[J].西安交通大学学报.2006,40(4)：27-30.
[52]S Banerjee,G Verghese. Nonlinear phenomena in power electronics:attractors, bifurcations,chaos,and nonlinear control [M].New York:IEEE PRESS,2001.
[53]CK Tse. Complex Behavior of swithing Power Converters [M].Boca Raton,FL:CRC Press,2003.
[54]CC Fang. Sampled-data analysis and control of DC-DCswitching converters[D].Ph.D.thesis,University of Maryland, College Park,1997.
[55]G Olivar. Chaos in the Buck converter[D].Ph.D.thesis,Universitat Polit ecnica de Catalunya,1997.
[56]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.
[57]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.
[58]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.
[59]ZT Zhusubaliyev, E Mosekilde. Bifurcations and chaos in Piecewise smooth dynamical systems [M].Pulisher: World Scientific Publishing Company,2003.
[60]AF Filippov.Differential equations with discontinuous righthand sides [M].Amsterdam, Netherlands:Kluwer,1998.
[61]RI Leine, H Nijmeijer. Dynamics and bifurcation in non-smooth mechanical systems[M],New York: springer,2004.
[62]RI Leine, DHV Campen,et al. Bifurcations in nonlinear discontinuous systems [J].Nonliear Dynamics,2000,23:105-164.
[63]T Kousaka,T Ueta, Y Ma, H Kawakami. Control of chaos in a Piecewise smooth nonlinear system[J]. Chaos, Solitons and Fractals,2006,27:1019-1025.
[64]M Bernaedo, CJ Budd, AR Champneys, P Kowalczyk. Piecewise smooth dynamical systems theory and applications[M],Publisher:Springer-Verlag, London,2008.
[65]T Kousaka, T Ueta, H Kawakami. Bifurcation in switched nonlinear dynamical systems[J].
[66]C Batle, E Fossas, G Olivar. From Floquet exponents to control of chaos in piecewise linear systems[C]. IEEE International Symposium on Circuits and Systems, Geneva, Switzerland, May 28-31,2000.
[67]SK Mazumder, AH Nayfeh ,D Boroyevich.Theoretical and experimental investigation of the fast-and slow-scale instabilities of a DC-DC converter [J].IEEE Transacations on Power Electronics,2001,16(2):201-216.
[68]M Orabi, T Ninomiya. Nonlinear dynamics of a power-factor-converter [J]. IEEE Transactions on Industrial Electronics,2003,50(6):1117-1125.
[69]M Orabi, T Ninomiya. A simple criterion to judge PFC converter statability [C]. The International Symposium on Circuits and Systems 2003,3:260-263.
[70]O Dranga, CK Tse, HHC Iu, I Nagy. Bifurcation behavior of a power-factor-correction boost converter [J]. International Journal of Bifurcation and Choas,2003,13(10):3107-3144.
[71]Iu HHC, Zhou Y, Tse CK. Fast-scale instability in a pfc boost converter under average current-mode control [J]. International Journal of Circuit Theory and Applications,2003,31(6):611-624.
[72]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.
[73]Ren HP, Liu D. Bifurcation behaviours of peak current controlled pfc boost converter[J]. Chinese Physics,2005,14(7):1352-1358.
[74]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.
[75]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(012)：38-43.
[76]Dai D, Li S, Ma X, et al. Slow-scale instability of single-stage power-factor-correction power supplies[J]. IEEE Transactions on Circuits and Systems-I 2007,54(8):1724-1735.
[77]Robert B, Robert C. Border collision bifurcations in a one-dimensional piecewise smooth map for a PWM current-programmed H-bridge inverter[J]. International Journal of Control,2002(75):1356-1367.
[78]JHB Deane, DC Hamill. Improvement of power supply EMC by chaos [J]. Electronics Letters,1996,32:1045-1046.
[79]C Morel, M Bourcerie, F Chapeau-Blondeau. Extension of chaos anticontrol applied to the improvement of switch-mode power supply electronics,2004 1:447-452.
[80]高金峰,吴振军,赵坤.混沌调制技术降低Buck型变换器电磁干扰水平研究[J].电工技术学报,2003,18(6)：23-27.
[81]李志忠,丘水生,张黎.混沌频率调制增强开关变换器EMC的研究[J].电子学报,2005,33(011)：1983-1987.
[82]李志忠,丘水生,陈艳峰.混沌映射抑制DC-DC变换器EMI水平的实验研究[J].中国电机工程学报,2006,26(5)：76-81.
[83]PJ Aston, JHB Deane, DC Hamill. Targeting in systems with discontinuites, with applications to power electronics[J]. IEEE Transactions on Circuits and Systems-I:Fundamental Theory and Applications,1997,44(10):1034-1039.
[84]Shinbrot T,Ott. E, Grebogi C, and Yorke J A. Using chaos to direct trajectories to targets. Phys. Kev. Lett.,1990,65:3215-3218.
[85]Epureanu B I and Dowell E H. System identification for the Ott-Grebogi-York controller design. Phys. Rev. E,1997,56:5327-5331.
[86]In V, Ditto W L, and Spano M L. Adaptive control and tracking of chaos in a magnetoelastic ribbon. Phys. Rev. E,1995,51:R2689-R2692.
[87]K. Pyragas. Control of chaos by self-controlling feedback. Phys. Lett. A,1992, 170,421-428.
[88]裴长江,黄俊等.自适应延迟反馈控制混沌[J].控制理论与应用,1999,16 (2),298-300.
[89]任海鹏,刘丁,李浩.永磁同步电动机中混沌运动的延迟反馈控制[J].中国电机工程学报,2003,23(6)：175-178.
[90]T. Ushio. Limitation of delayed feekback control in nonlinear discrete time system.IEEE Trans. On Circuits and systems-1,1996,43(9),815-816.
[91]Pyragas K and Tamasevicius A. Expemental Control of chaos by delayed self-controlling feedback. Phys. Lett. A,1993,180(1,2),99-102.
[92]G. Chen and X. Dong. On feedback control of chaotic dynamic system. Int.J. Bifurcation and chaos,1992,2,407-411.
[93]G. Chen and X. Dong. On feedback control of chaotic continuous-time systems. IEEE Trans. On circuits and system-J,1993,40(9):591-600.
[94]G. Chen and X. Dong. Ordering chaos in Chua's circuit and systems,Chicago,1993,4,2604-2607.
[95]AROUDI A EL, LEYVA R. Quasi-periodic route to chaos in a PWM voltage-controlled DC-DC boost converter[J]. IEEE Trans. Circuits and Systems-1,2001,48(8):967-978.
[96]Tse C K,BERNARDO M DI.Complex behavior in switching power converter [J]. Proceedings of IEEE,2002,90(5):768-781.
[97]J. H. B. Deane, D. C. Hamill, "Instability, subharmonics, and chaos in power electronic systems," IEEE Trans. Power Electron.,1990,5(3):260-268.
[98]朱士海,吴卫民,钱照明.一种新型高性能功率因数校正整流电路[J].电工电能新技术,2003,22(2)：68-71.
[99]Iu H H C, Zhou Y, Tse C K. Fast-scale instability in a PFC boost converter under average current mode control. Int J Circuit Theory Appl,2003,31(6):611-624.
[100]Wu X, Tse C K, Dranga O, et al. Fast-scale instability of single-stage power-factor-correction power supplies. IEEE Trans Circ Syst I,2006,53(1): 204-213.
[101]Zou J L, Ma X, Tse C K, et al. Fast-scale bifurcation in power-factor-correction buck-boost converters and effects of incompatible periodicities. Int J Circuit Theory Appl,2006,34(3):251-264.
[102]陈明亮马伟明.多级并联电流反馈型DC-DC升压变换器中的分岔与混沌[J].中国电机工程学报,2005,25(6)：67-70.
[103]Tao Fengfen, Lee Fred C. Interleaved singe-stage PFC electronic ballast [A]. IEEE APEC [A]. USA,2000. Vol.1:617-623.
[104]Jindong Zhang, Jianwen Shao, Xu Peng. Evaluation of input current in the critical mode boost PFC converter for distributed power systems. IEEE APEC [C]. USA,2001.Vol.1:130-136.
[105]Pinheiro Jose R, Grundling Hilton A, Vidor Dalton L R. Control strategy of an interleaved boost power factor correction converter [A]. IEEE PESC [C]. USA, 1999. Vol.1:137-142.
[106]Zhou Y, Jiang X, Chen J. Analysis of complex intermittency in Boost converter from a bifurcation control viewpoint .Sci China Ser F-Inf Sci,2008,51(12):2135-2149.
[107]Tse C K and Lai Y M. Control of bifurcation in current-programmed DC-DC converter, an alternative viewpoint of ramp compensation. Circuit, System and Signal Processing,USA.2001,20(6):695-707.
[108]Chung-Chich Fang. Exact orbital stability analysis of static and dynamic ramp compensations in DC-DC converters. IEEE ISIE Pusan KOREA.2001,6(3):2124-2129.
[109]王发强、马西奎、闫晔.不同开关频率下电压控制升压变换器中的Hopf分岔分析[J].物理学报,2011,60(6)：605101-605106.
[110]周宇飞,陈军宁.开关变换器中吸引子共存现象的仿真与实验研究[J].中国电机工程学报,2005,25(21)：30-33.
[111]Iu H H C, Robert B. Control of chaos in a PWM current-mode H-bridge inverter using time-delayed feedback [J]. IEEE Trans. Circuits System-I, 2003, 50(8):1125-1129.
[112]王学梅,张波,丘东元.H桥正弦逆变器的快变和慢变稳定性及混沌行为研究[J].物理学报,2009,58(4)：2248-2254.
[113]雷博、肖国春、吴旋律、齐元瑞.单相全桥DC-AC电压逆变电路数字控制中的振荡现象分析[J].物理学报,2011,60(9)：90501-90510.
[114]徐德鸿,马皓等.电力电子技术[M].北京：科学出版社,2006.
[115]Zhao Y B, Zhang C J, Zhang D Y 2007 Chin.Phys. 16 933.
[116]Poddar G, Chakrabarty K, Banerjee S 1995 Electronics Letters 31 841.
[117]Zhou Y, Tse CK, Qiu SS, et al. An improved resonant parametric perturbation for chaos control with applications to control of dc/dc converters[J]. Chinese Physics,2005,14:61-66.
[118]周宇飞等.参数共振微扰法在Boost变换器混沌控制中的实现及其优[J].物理学报,2004,53(11)：3676-3683.
[119]Tse C K and Lai Y M. Controlling bifurcation in power electronics: a conventional practice re-visited. Latin American Applied Research, 2001,31(3):177-184.
[120]Fossas E, Olivar G. Study of chaos in the Buck converter[J]. IEEE Trans. Circuits System-I,1996,43(1):13-25.
[121]张波曲颖.电压反馈型Boost变换器DCM的精确离散映射及其分岔和混沌现象[J].电工技术学报,2002,17(3)：43-47.
[122]Aroudi A E, Debbat M, et al. Bifurcations in DC/DC switching converters: review of methods and applications[J]. Int. J. Bifurcation and Chaos,2005, 15(5):1549-1578.
[123]Tse C K, Lai Y M, Iu H H C. Hopf bifurcation and chaos in a free-running current-controlled Cuk switching regulator[J]. IEEE Trans. Circuit System-I, 2000,47(4):448-457.
[124]卢伟国,周雒维,罗全明,等.BOOST变换器延迟反馈混沌控制及其优化[J].物理学报,2007,56(11)：6275-6281.
[125]周宇飞,黄家成,王诗兵,江伟,陈军宁PFC Boost变换器中的斜坡补偿设计原理.中国科学：F刊信息科学2009,39(11)：1217-1223.
[2]Hao B L. Chaos Ⅱ. Singapore:World Scientific,1990.
[3]郝柏林.分岔、混沌、奇怪吸引子、湍流及其他——关于确定论系统的内在随机性.物理学进展,1983,3(3)：329-416.
[4]吕金虎.一个统一混沌系统及其研究.北京：中国科学院研究生院(数学与系统科学研究院)博士学位论文,2002.
[5]吕金虎,陆均安,陈士华.混沌时间序列分析及其应用.武汉：武汉大学出版社,2002.
[6]陈关荣,吕金虎Lorenz系统族的动力学分析、控制与同步.北京：科学出版社,2003.
[7]Sivakumar B. Chaos theory in hydrology: important issues and interpretations. Journal of Hydrology,2000,227 (1-4):1-20.
[8]Haykin S, Principe J. Making sence of a complex world [chaotic events modeling]. IEEE Signal Processing Magazine,1998,15 (3):66-81.
[9]Nishimura K, Yano M. On the existence of chaotic solutions in dynamic linear programming. Mathematics and Computers in Simulation,1999,48 (4-6): 487-496.
[10]赵永龙,丁晶,邓育仁.混沌分析在水文预测中的应用和展望.水科学进展,1998,9(2)：181-186.
[11]黄润生.混沌及其应用.武汉：武汉大学出版社,2000.
[12]G. Chen, X. Dong,From chaos to order:perspective and methodologies in controlling chaotic nonlinear dynamical system. Int. J. Bifur. Chaos,1993 3: 1363-1409.
[13]徐京华.人脑功能的混沌动力学.科学,1990,42：266-270.
[14]郝柏林.自然界中的有序和混沌.百科知识,1984,1：69-72.
[15]Lorenz E N. Deterministic nonperiodic flow. Journal of Atmos. Sci.,1963,20: 130-141.
[16]Henon M. A two-dimensional mapping with a strange attractor. Commun. Math. Phys.,1976,50:69-77.
[17]Li T Y, Yorke J A. Period three implies chaos. America Mathematics Monthly, 1975,82:985-992.
[18]Feigenbaum M J. Quantitative uniwersality for a class of nonlinear transformations. Journal of Stat. Phys.,1978,19: 25-52.
[19]Grassberger P, Procaccia I. Measuring the strangeness of strange attractors. Physica D,1983,9:189-208.
[20]May R M. Simple mathematical models with very complicated dynamics. Nature, 1976,261:459-467.
[21]李浙生.攸忽之间——混沌与认识.北京：冶金工业出版社,2002.
[22]El A. Aroudi, R. Leyva. Quasi-periodic route to chaos in a PWM voltage-controlled DC-DC boost coverter[J].IEEE Trans, Circuits and Systems-I, 2001,48(8):967-978.
[23]C K. Tse, M. di Bernardo,.Complex behavior in switching power converter[J]. Proceedings of IEEE,2002,90(5):768-781.
[24]J. H. B. Deane, D. C. Hamill, Instability, subharmonics, and chaos in power electronic systems, IEEE Trans. Power Electron.,1990,5(3):260-268.
[25]张波,李萍,齐群DC-DC变换器分岔和混沌现象的建模和分析方法[J].中国电机工程学报2002,22(10)：81-85.
[26]周宇飞,陈军宁.开关变换器中吸引子共存现象的仿真与实验研究[J].中国电机工程学报,2005,21(21)：96-101.
[27]P. T. Krein and R. M. Bass. Types of instabilities encountered in simple power electronics circuits:Unboundedness, chattering and chaos [C], in Proc. IEEE Applied Power Electronics Conf.,1990, ppl91-194.
[28]C.K. Tse and W.C. Y.Chan.Chaos from a current programmed Cuk converter[J]. Int. J. Circuit Theory Appl.,1995,23(3):217-225.
[29]I Zafrany and S.A. Ben-Yaakov chaos model of subharmonic oscillations in current mode PWM boost converters[C].IEEE Power Electron.Specialists Conf.Rec,Atlanta,GA,June 1995, pp5.4.5/1-5.4.5/5.
[30]J H B. Deane and D C. Hamill.Chaotic behaviour in current-mode controlled dc/dcconverters[J].IEE.Electron.Lett,1991,27(13):1172-1173.
[31]J H B Deane.Chaos in a current-mode controlled boost dc/dc converter[J]. IEEE Trans. Circ.Syst.-1,1992,39(8):680-683.
[32]C.Y. Willam Chan and Chi K.Tse.Study of bifurcations in current-programmed dc/dc boost converters:From quasi-periodicity to period-doubling[J]. IEEE Trans.Circ.Syst.-1,1997,44(12):1129-1142.
[33]C K. Tse.Flip bifurcation and chaos in a three-state boost switching regulater[J]. IEEE Trans. Circ.Syst.-1,1994,41(1):16-23.
[34]C K. Tse.Chaos from a buck switching regulator operation in discontinuous mode[J]. Int. J. Circ.TheoryAppl,1994,22(4):263-278.
[35]W C Y. Chan and C K. Tse On the form of control function that can lead to chaos in discontinuous-mode dc/dc converters[C].IEEE Power Electron.Spec.Conf. Rec, 1997,1317-1322.
[36]Soumitro Banerjee.Coexisting Attractors,Chaotic Saddles and Fractal Basins in a Power Electron Circuit[J]. IEEE Trans. Circ.Syst.-1,1997,44(9):847-849.
[37]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叉现象与混沌分析[J].物理学报,2005,54(3)：1084-1091.
[38]H. Zhan, X K. Ma, B L. Xue, et al. Study of intermittent bifurcation and chaos in boost PFC converters by nonlinear discrete model[J].Chaos, Solitons and Fractals,2005,25(1):43-48.
[39]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叉和混沌现象分析[J].中国电机工程学报,2005,25(1)：43-48.
[40]H. E. Nusse, J A. York. Border-collision bifurcation including period two to period three for piecewise smooth system[J].Phsica D,1992,57(1-2):39-57.
[41]张琪昌.分岔与混沌理论及应用.天津：天津大学出版社,2005.
[42]Sivakumar B. chaos theory in hydrology:important issues and interpretations. Journal of Hydrology,2000,227(1-4):1-20.
[43]Sivakumar B. chaos theory in geophysics:past, present and future. Chaos Solitons & Fractals,2004,19:441-462.
[44]Schertzer D. Tchiguirinskaia I, Lovejoy S, Hubert P,et al., Reply to which chaos in the rainfall-runoff process ? Hydrological Sciences Journal-Journal Des Sciences Hydrologiques,2002,47 (1):139-158.
[45]Rudnicki R . Chaos for some infinite-dimensional dynamical systerms Mathematical Methods in the Applied Sciences,2004,27:723-738.
[46]Man K S. Long memory time series and short term forecasts. International Journal of Forecasting,2003,19 (3):477-491.
[47]王洪瑞,宋宇,刘昌明,陈家军.混沌理论及在水科学中的应用与存在的问题.2004,15(3)：400-407.
[48]汪剑鸣,许镇琳.PWM型DC/DC变换器基于混沌动力学的建模、控制及应用[D],天津大学博士毕业论文,2002,5-14.
[49]W.C.Y.Chan, C.K.Tse. Bifurcations in current-programmed DC/DC Buck switching regulators——conjecturing a universal bifurcation path[J]. Int.J.Circuit Theory and Applications,1998,26(2):127-145.
[50]周宇飞,陈军宁.电流模式控制Boost变换器中的切分叉及阵发混沌现象[J].中国电机工程学报,2005,25((1)：23-26.
[51]李胜男,张浩,马西奎,李明.Buck-Boost DC/DC变换器中的边界碰撞分叉现象的实验研究[J].西安交通大学学报.2006,40(4)：27-30.
[52]S Banerjee,G Verghese. Nonlinear phenomena in power electronics:attractors, bifurcations,chaos,and nonlinear control [M].New York:IEEE PRESS,2001.
[53]CK Tse. Complex Behavior of swithing Power Converters [M].Boca Raton,FL:CRC Press,2003.
[54]CC Fang. Sampled-data analysis and control of DC-DCswitching converters[D].Ph.D.thesis,University of Maryland, College Park,1997.
[55]G Olivar. Chaos in the Buck converter[D].Ph.D.thesis,Universitat Polit ecnica de Catalunya,1997.
[56]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.
[57]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.
[58]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.
[59]ZT Zhusubaliyev, E Mosekilde. Bifurcations and chaos in Piecewise smooth dynamical systems [M].Pulisher: World Scientific Publishing Company,2003.
[60]AF Filippov.Differential equations with discontinuous righthand sides [M].Amsterdam, Netherlands:Kluwer,1998.
[61]RI Leine, H Nijmeijer. Dynamics and bifurcation in non-smooth mechanical systems[M],New York: springer,2004.
[62]RI Leine, DHV Campen,et al. Bifurcations in nonlinear discontinuous systems [J].Nonliear Dynamics,2000,23:105-164.
[63]T Kousaka,T Ueta, Y Ma, H Kawakami. Control of chaos in a Piecewise smooth nonlinear system[J]. Chaos, Solitons and Fractals,2006,27:1019-1025.
[64]M Bernaedo, CJ Budd, AR Champneys, P Kowalczyk. Piecewise smooth dynamical systems theory and applications[M],Publisher:Springer-Verlag, London,2008.
[65]T Kousaka, T Ueta, H Kawakami. Bifurcation in switched nonlinear dynamical systems[J].
[66]C Batle, E Fossas, G Olivar. From Floquet exponents to control of chaos in piecewise linear systems[C]. IEEE International Symposium on Circuits and Systems, Geneva, Switzerland, May 28-31,2000.
[67]SK Mazumder, AH Nayfeh ,D Boroyevich.Theoretical and experimental investigation of the fast-and slow-scale instabilities of a DC-DC converter [J].IEEE Transacations on Power Electronics,2001,16(2):201-216.
[68]M Orabi, T Ninomiya. Nonlinear dynamics of a power-factor-converter [J]. IEEE Transactions on Industrial Electronics,2003,50(6):1117-1125.
[69]M Orabi, T Ninomiya. A simple criterion to judge PFC converter statability [C]. The International Symposium on Circuits and Systems 2003,3:260-263.
[70]O Dranga, CK Tse, HHC Iu, I Nagy. Bifurcation behavior of a power-factor-correction boost converter [J]. International Journal of Bifurcation and Choas,2003,13(10):3107-3144.
[71]Iu HHC, Zhou Y, Tse CK. Fast-scale instability in a pfc boost converter under average current-mode control [J]. International Journal of Circuit Theory and Applications,2003,31(6):611-624.
[72]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.
[73]Ren HP, Liu D. Bifurcation behaviours of peak current controlled pfc boost converter[J]. Chinese Physics,2005,14(7):1352-1358.
[74]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.
[75]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(012)：38-43.
[76]Dai D, Li S, Ma X, et al. Slow-scale instability of single-stage power-factor-correction power supplies[J]. IEEE Transactions on Circuits and Systems-I 2007,54(8):1724-1735.
[77]Robert B, Robert C. Border collision bifurcations in a one-dimensional piecewise smooth map for a PWM current-programmed H-bridge inverter[J]. International Journal of Control,2002(75):1356-1367.
[78]JHB Deane, DC Hamill. Improvement of power supply EMC by chaos [J]. Electronics Letters,1996,32:1045-1046.
[79]C Morel, M Bourcerie, F Chapeau-Blondeau. Extension of chaos anticontrol applied to the improvement of switch-mode power supply electronics,2004 1:447-452.
[80]高金峰,吴振军,赵坤.混沌调制技术降低Buck型变换器电磁干扰水平研究[J].电工技术学报,2003,18(6)：23-27.
[81]李志忠,丘水生,张黎.混沌频率调制增强开关变换器EMC的研究[J].电子学报,2005,33(011)：1983-1987.
[82]李志忠,丘水生,陈艳峰.混沌映射抑制DC-DC变换器EMI水平的实验研究[J].中国电机工程学报,2006,26(5)：76-81.
[83]PJ Aston, JHB Deane, DC Hamill. Targeting in systems with discontinuites, with applications to power electronics[J]. IEEE Transactions on Circuits and Systems-I:Fundamental Theory and Applications,1997,44(10):1034-1039.
[84]Shinbrot T,Ott. E, Grebogi C, and Yorke J A. Using chaos to direct trajectories to targets. Phys. Kev. Lett.,1990,65:3215-3218.
[85]Epureanu B I and Dowell E H. System identification for the Ott-Grebogi-York controller design. Phys. Rev. E,1997,56:5327-5331.
[86]In V, Ditto W L, and Spano M L. Adaptive control and tracking of chaos in a magnetoelastic ribbon. Phys. Rev. E,1995,51:R2689-R2692.
[87]K. Pyragas. Control of chaos by self-controlling feedback. Phys. Lett. A,1992, 170,421-428.
[88]裴长江,黄俊等.自适应延迟反馈控制混沌[J].控制理论与应用,1999,16 (2),298-300.
[89]任海鹏,刘丁,李浩.永磁同步电动机中混沌运动的延迟反馈控制[J].中国电机工程学报,2003,23(6)：175-178.
[90]T. Ushio. Limitation of delayed feekback control in nonlinear discrete time system.IEEE Trans. On Circuits and systems-1,1996,43(9),815-816.
[91]Pyragas K and Tamasevicius A. Expemental Control of chaos by delayed self-controlling feedback. Phys. Lett. A,1993,180(1,2),99-102.
[92]G. Chen and X. Dong. On feedback control of chaotic dynamic system. Int.J. Bifurcation and chaos,1992,2,407-411.
[93]G. Chen and X. Dong. On feedback control of chaotic continuous-time systems. IEEE Trans. On circuits and system-J,1993,40(9):591-600.
[94]G. Chen and X. Dong. Ordering chaos in Chua's circuit and systems,Chicago,1993,4,2604-2607.
[95]AROUDI A EL, LEYVA R. Quasi-periodic route to chaos in a PWM voltage-controlled DC-DC boost converter[J]. IEEE Trans. Circuits and Systems-1,2001,48(8):967-978.
[96]Tse C K,BERNARDO M DI.Complex behavior in switching power converter [J]. Proceedings of IEEE,2002,90(5):768-781.
[97]J. H. B. Deane, D. C. Hamill, "Instability, subharmonics, and chaos in power electronic systems," IEEE Trans. Power Electron.,1990,5(3):260-268.
[98]朱士海,吴卫民,钱照明.一种新型高性能功率因数校正整流电路[J].电工电能新技术,2003,22(2)：68-71.
[99]Iu H H C, Zhou Y, Tse C K. Fast-scale instability in a PFC boost converter under average current mode control. Int J Circuit Theory Appl,2003,31(6):611-624.
[100]Wu X, Tse C K, Dranga O, et al. Fast-scale instability of single-stage power-factor-correction power supplies. IEEE Trans Circ Syst I,2006,53(1): 204-213.
[101]Zou J L, Ma X, Tse C K, et al. Fast-scale bifurcation in power-factor-correction buck-boost converters and effects of incompatible periodicities. Int J Circuit Theory Appl,2006,34(3):251-264.
[102]陈明亮马伟明.多级并联电流反馈型DC-DC升压变换器中的分岔与混沌[J].中国电机工程学报,2005,25(6)：67-70.
[103]Tao Fengfen, Lee Fred C. Interleaved singe-stage PFC electronic ballast [A]. IEEE APEC [A]. USA,2000. Vol.1:617-623.
[104]Jindong Zhang, Jianwen Shao, Xu Peng. Evaluation of input current in the critical mode boost PFC converter for distributed power systems. IEEE APEC [C]. USA,2001.Vol.1:130-136.
[105]Pinheiro Jose R, Grundling Hilton A, Vidor Dalton L R. Control strategy of an interleaved boost power factor correction converter [A]. IEEE PESC [C]. USA, 1999. Vol.1:137-142.
[106]Zhou Y, Jiang X, Chen J. Analysis of complex intermittency in Boost converter from a bifurcation control viewpoint .Sci China Ser F-Inf Sci,2008,51(12):2135-2149.
[107]Tse C K and Lai Y M. Control of bifurcation in current-programmed DC-DC converter, an alternative viewpoint of ramp compensation. Circuit, System and Signal Processing,USA.2001,20(6):695-707.
[108]Chung-Chich Fang. Exact orbital stability analysis of static and dynamic ramp compensations in DC-DC converters. IEEE ISIE Pusan KOREA.2001,6(3):2124-2129.
[109]王发强、马西奎、闫晔.不同开关频率下电压控制升压变换器中的Hopf分岔分析[J].物理学报,2011,60(6)：605101-605106.
[110]周宇飞,陈军宁.开关变换器中吸引子共存现象的仿真与实验研究[J].中国电机工程学报,2005,25(21)：30-33.
[111]Iu H H C, Robert B. Control of chaos in a PWM current-mode H-bridge inverter using time-delayed feedback [J]. IEEE Trans. Circuits System-I, 2003, 50(8):1125-1129.
[112]王学梅,张波,丘东元.H桥正弦逆变器的快变和慢变稳定性及混沌行为研究[J].物理学报,2009,58(4)：2248-2254.
[113]雷博、肖国春、吴旋律、齐元瑞.单相全桥DC-AC电压逆变电路数字控制中的振荡现象分析[J].物理学报,2011,60(9)：90501-90510.
[114]徐德鸿,马皓等.电力电子技术[M].北京：科学出版社,2006.
[115]Zhao Y B, Zhang C J, Zhang D Y 2007 Chin.Phys. 16 933.
[116]Poddar G, Chakrabarty K, Banerjee S 1995 Electronics Letters 31 841.
[117]Zhou Y, Tse CK, Qiu SS, et al. An improved resonant parametric perturbation for chaos control with applications to control of dc/dc converters[J]. Chinese Physics,2005,14:61-66.
[118]周宇飞等.参数共振微扰法在Boost变换器混沌控制中的实现及其优[J].物理学报,2004,53(11)：3676-3683.
[119]Tse C K and Lai Y M. Controlling bifurcation in power electronics: a conventional practice re-visited. Latin American Applied Research, 2001,31(3):177-184.
[120]Fossas E, Olivar G. Study of chaos in the Buck converter[J]. IEEE Trans. Circuits System-I,1996,43(1):13-25.
[121]张波曲颖.电压反馈型Boost变换器DCM的精确离散映射及其分岔和混沌现象[J].电工技术学报,2002,17(3)：43-47.
[122]Aroudi A E, Debbat M, et al. Bifurcations in DC/DC switching converters: review of methods and applications[J]. Int. J. Bifurcation and Chaos,2005, 15(5):1549-1578.
[123]Tse C K, Lai Y M, Iu H H C. Hopf bifurcation and chaos in a free-running current-controlled Cuk switching regulator[J]. IEEE Trans. Circuit System-I, 2000,47(4):448-457.
[124]卢伟国,周雒维,罗全明,等.BOOST变换器延迟反馈混沌控制及其优化[J].物理学报,2007,56(11)：6275-6281.
[125]周宇飞,黄家成,王诗兵,江伟,陈军宁PFC Boost变换器中的斜坡补偿设计原理.中国科学：F刊信息科学2009,39(11)：1217-1223.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |