PWM型DC/DC变换器混沌机理及控制研究
|
摘要
混沌是发生在非线性系统内部的一种内在随机运动,它是非线性系统的一种性能表征,近二十年来引起人们的广泛关注。开关式 DC/DC 变换器是一个强非线性系统,在一定的参数条件下,DC/DC 变换器会产生混沌现象。因此,仅仅从线性论和确定论角度去分析 DC/DC 变换器中的不稳定及次谐波现象已不能满足对 DC/DC 变换器控制性能日益提高的要求。在某些特定的条件下,从混沌理论的角度去解释 DC/DC 变换器中的不稳定现象显得更加合理和易于接受。在混沌理论的基础上,研究相应的控制手段,对提高 DC/DC 变换器的控制性能具有重要的意义。本文研究了 PWM 型 DC/DC 变换器中混沌产生的机理并在混沌控制方面作了进一步的探索。
采用分段线性数值仿真法分别对 Buck 及 Boost 变换器的动力学行为进行仿真,对 DC/DC 变换器在某些特定的参数下出现的混沌现象及从稳态通向混沌的倍周期分岔行为进行分析,并分别在时域和频域对 DC/DC 变换器处于各周期态及混沌态时输出电压特性进行比较、分析。针对如何识别变换器中混沌现象问题,首先提出用付里叶描述符法提取 DC/DC 变换器输出信号特征值,在此基础上,提出采用 BP 神经网络进行信号识别,并对 BP 神经网络算法加以改进,最终测试结果表明 BP 神经网络对变换器输出信号识别率达到 100%。在理论研究的基础上,通过实验展示了 DC/DC 变换器的工作状态随电路参数变化从稳态通向混沌态的演化过程,验证了理论分析的正确性。
研究 PWM 型 DC/DC 变换器处于混沌态时特点,分别采用 OGY 法、外力反馈控制法及延时反馈控制法对 DC/DC 变换器进行混沌控制研究。分析、比较每种控制方法的特点、控制效果及局限性。实验中,以外力反馈控制法为指导思想,设计控制电路并对 DC/DC 变换器进行混沌控制,实验结果证实了 DC/DC 变换器混沌控制的可行性。
将混沌反控制技术应用到 DC/DC 变换器控制中,分别采用外部噪声混沌反控制法、延时反馈控制法及利用混沌信号对处于高周期态或混沌态的变换器进行混沌反控制,使变换器进入新的混沌态。从几何学的角度分析 DC/DC 变换器在混沌反控制前、后混沌吸引子在相空间中的变化特点,对混沌吸引子的结构参数以量值化加以定义,通过分析混沌吸引子在相空间中结构的变化折射出 DC/DC 变换器输出电压中交流分量变化特性,从而对 DC/DC 变换器在混沌反控制前、后输出质量作定量评价。
Chaos is a kind of internal random movement, which appears in non-linearsystems. In recent 20 years, it has been paid great attention as a property token ofnon-linear system. A switched-mode DC/DC converter is a high non-linear controlsystem, which can produce chaotic phenomenon under certain parameters. Soanalyzing the phenomenon of unstable action and subharmonic of DC/DC converterfrom the angle of linear theory and definiteness theory can not meet the increasingrequirement of control performance of DC/DC converter. Under some specialconditions, explaining unstable phenomenon of DC/DC converter from chaotic theorycan be more reasonable and easily accepted. Based on chaotic theory, researching anddesigning corresponding control method can give great help to increase controlperformance of DC/DC converter. This dissertation makes more studies on chaosmechanism and chaotic control of PWM DC/DC converters.
Theoretically analyzes and emulates chaos and period-doubling bifurcation ofBuck and Boost converters with piecewise linear numerical emulation. Performancesof the output ripples of DC/DC converter from stable state to chaotic state areanalyzed in time domain and frequency domain respectively. Aim at identifying chaosof DC/DC converter, the method of using Fourier Descriptor to extract output signalscharacteristics is put forward, based on which an improved BP neural network is thenused to identify the output signals of DC/DC converter. Finally, the testing resultindicates the identification rate of the output signals of DC/DC converter using thisBP neural network can reach to 100%. Based on theoretical research, an experimentis done to exhibit chaos and evolution from stable state to chaotic state of DC/DCconverter, which validate the correctness of theoretical analysis.
Study the features of DC/DC converter in chaotic state, OGY method, outsideforce feedback control method and delay feedback control method are usedrespectively to control chaos in DC/DC converter. Then features, effects andlimitations of every control method are analyzed and compared one another.According to the principle of outside force feedback control method, a chaotic controlcircuit is designed to control chaos in DC/DC converter. The result of experimentvalidates the feasibility of chaotic control in DC/DC converter.
Apply the technology of chaotic anti-control to DC/DC converter. Externalnoise driving method, delay feedback control method and chaotic signal drivingmethod are used respectively to give a chaotic anti-control over DC/DC converter inunstable or chaotic state in order to make it come into a new chaotic state. Analyzethe feature of chaotic attractor in phase space of DC/DC converter before and after
anti-control from the angle of geometry. Define two structure parameters of chaoticattractor in order to reflect the trait of output ripples of DC/DC converter according tothe change of these two structure parameters, so the quality of the output performanceof DC/DC converter can be estimated quantificationally.
采用分段线性数值仿真法分别对 Buck 及 Boost 变换器的动力学行为进行仿真,对 DC/DC 变换器在某些特定的参数下出现的混沌现象及从稳态通向混沌的倍周期分岔行为进行分析,并分别在时域和频域对 DC/DC 变换器处于各周期态及混沌态时输出电压特性进行比较、分析。针对如何识别变换器中混沌现象问题,首先提出用付里叶描述符法提取 DC/DC 变换器输出信号特征值,在此基础上,提出采用 BP 神经网络进行信号识别,并对 BP 神经网络算法加以改进,最终测试结果表明 BP 神经网络对变换器输出信号识别率达到 100%。在理论研究的基础上,通过实验展示了 DC/DC 变换器的工作状态随电路参数变化从稳态通向混沌态的演化过程,验证了理论分析的正确性。
研究 PWM 型 DC/DC 变换器处于混沌态时特点,分别采用 OGY 法、外力反馈控制法及延时反馈控制法对 DC/DC 变换器进行混沌控制研究。分析、比较每种控制方法的特点、控制效果及局限性。实验中,以外力反馈控制法为指导思想,设计控制电路并对 DC/DC 变换器进行混沌控制,实验结果证实了 DC/DC 变换器混沌控制的可行性。
将混沌反控制技术应用到 DC/DC 变换器控制中,分别采用外部噪声混沌反控制法、延时反馈控制法及利用混沌信号对处于高周期态或混沌态的变换器进行混沌反控制,使变换器进入新的混沌态。从几何学的角度分析 DC/DC 变换器在混沌反控制前、后混沌吸引子在相空间中的变化特点,对混沌吸引子的结构参数以量值化加以定义,通过分析混沌吸引子在相空间中结构的变化折射出 DC/DC 变换器输出电压中交流分量变化特性,从而对 DC/DC 变换器在混沌反控制前、后输出质量作定量评价。
Chaos is a kind of internal random movement, which appears in non-linearsystems. In recent 20 years, it has been paid great attention as a property token ofnon-linear system. A switched-mode DC/DC converter is a high non-linear controlsystem, which can produce chaotic phenomenon under certain parameters. Soanalyzing the phenomenon of unstable action and subharmonic of DC/DC converterfrom the angle of linear theory and definiteness theory can not meet the increasingrequirement of control performance of DC/DC converter. Under some specialconditions, explaining unstable phenomenon of DC/DC converter from chaotic theorycan be more reasonable and easily accepted. Based on chaotic theory, researching anddesigning corresponding control method can give great help to increase controlperformance of DC/DC converter. This dissertation makes more studies on chaosmechanism and chaotic control of PWM DC/DC converters.
Theoretically analyzes and emulates chaos and period-doubling bifurcation ofBuck and Boost converters with piecewise linear numerical emulation. Performancesof the output ripples of DC/DC converter from stable state to chaotic state areanalyzed in time domain and frequency domain respectively. Aim at identifying chaosof DC/DC converter, the method of using Fourier Descriptor to extract output signalscharacteristics is put forward, based on which an improved BP neural network is thenused to identify the output signals of DC/DC converter. Finally, the testing resultindicates the identification rate of the output signals of DC/DC converter using thisBP neural network can reach to 100%. Based on theoretical research, an experimentis done to exhibit chaos and evolution from stable state to chaotic state of DC/DCconverter, which validate the correctness of theoretical analysis.
Study the features of DC/DC converter in chaotic state, OGY method, outsideforce feedback control method and delay feedback control method are usedrespectively to control chaos in DC/DC converter. Then features, effects andlimitations of every control method are analyzed and compared one another.According to the principle of outside force feedback control method, a chaotic controlcircuit is designed to control chaos in DC/DC converter. The result of experimentvalidates the feasibility of chaotic control in DC/DC converter.
Apply the technology of chaotic anti-control to DC/DC converter. Externalnoise driving method, delay feedback control method and chaotic signal drivingmethod are used respectively to give a chaotic anti-control over DC/DC converter inunstable or chaotic state in order to make it come into a new chaotic state. Analyzethe feature of chaotic attractor in phase space of DC/DC converter before and after
anti-control from the angle of geometry. Define two structure parameters of chaoticattractor in order to reflect the trait of output ripples of DC/DC converter according tothe change of these two structure parameters, so the quality of the output performanceof DC/DC converter can be estimated quantificationally.
引文
[1] 李浙生编著,倏忽之间-混沌与认识,北京,冶金工业出版社,2002:31～37
[2] 黄润生编著,混沌及其应用,湖北,武汉大学出版社,2000:4～8
[3] 锦清编著,驾驭混沌与发展高新技术,北京,原子能出版社,2002:30～32
[4] 王东生,曹磊,混沌、分形及其应用,合肥:中国科技大学出版社,1995
[5] Jonathan R.Wood, Chaos :a real phenomenon in power electronics, IEEE Transactions on Circuits and Systems-Ⅰ:Vol. 36, No. 3, 1989:115～124
[6] Takuji Kousaka, Bifurcation of Switched Nonlinear Dynamical Sysytems, IEEE Transactions on Circuits and Systems-Ⅱ: Analog and Digital Signal Processing, Vol. 46, No. 7, 1999: 878～884
[7] Jonathan H.B, David C..Hamill, Instablity, Subharmonics, and Chaos in Power Electronic Systems, IEEE Transactions on Power Electronics, Vol. 5, No. 3, 1999: 260～268
[8] J. Baillieul, Roger W, Chaotic Motion in Nonlinear Feedback Systems, IEEE Transactions on Circuits and Systems-Ⅱ:Vol. 27, No. 11, Nov. 1980: 990～997
[9] 尹奕光,于盛林,电力电子电路非线性现象研究的发展综述,电子工程师,Vol. 27, No. 2, 2001:58～61
[10] 尹奕光,刘文波,功率电子电路中的混沌现象,南京理工大学学报,Vol. 24, No. 2, 2000:164～167
[11] 丁道宏,电力电子技术,北京,航空工业出版社,1992
[12] 张占松,蔡宣三,开关电源的原理与设计,北京,电子工业出版社,1998
[13] 蔡宣三,龚绍文,高频功率电子学,北京,科学出版社,1993
[14] 何希才,新型开关电源设计与应用,北京,科学出版社,2001
[15] 林波涛,丘水生,DC/DC 开关功率变换器分析方法的述评,电路与系统学报,Vol. 3, No. 3, 1998: 65～72
[16] Jonathan H.B. Deane, David C. Hamill, Analysis, Simulation and Experimental Study of Chaos in the Buck Converter, IEEE Power Electronics Specialist Conference, 1990:491～498
[17] Enric Fossas, Gerand Olivar, Study of Chaos in the Buck Converter, IEEE Transactions on Circuits and Systems-Ⅰ:Fundamental Theory and Applications, Vol. 43, No. 1, 1996: 13～25
[18] David C. Hamill, Modeling of Chaotic DC/DC Converters by Iterated Nonlinear Mappings, IEEE Transactions on Power Electronics, Vol. 7, No. 1, 1992: 25～36
[19] Mario di Bernardo, Franco Garofalo, Switchings, Bifurcations, and Chaos in DC/DC Converters, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 45, No. 2, 1998: 133～141
[20] Mario di Bernardo, Discrete-Time Maps for the Analysis of Bifurcations and Chaos in DC/DC Converters, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 47, No. 2, 2000: 130～143
[21] Guohui Yuan, Soumitro Banerjee, Border-Collision Bifurcations in the Buck Converter, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 45, No. 7, 1998: 707～716
[22] Jonathan H. B. Deane, Chaos in a Current-Mode Controlled Boost DC/DC Converter, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 39, No. 8, 1992: 680～683
[23] H. H. C. Iu, C. K. Tse, Bifurcation Behaviour in Parallel-Connected Boost Converter, International Journal of Current Theory and Applications, Vol. 29, 2001: 281～298
[24] H. H. C. Iu, C. K. Tse, Bifurcation Behavior in Parallel-Connected Buck Converter, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 48, No. 2, 2001:233～240
[25] William C. Y. Chan, Chi K. Tse, Study of Bifurcations in Current-Programmed DC/DC Boost Converter: From Quasi-Periodicity to Period-Doubling, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 44, No. 12, 1997: 1129～1142
[26] Abdelai EI Aroudi, Luis Benadero, Hopf Bifurcation and Chaos from Torus Breakdown in a PWM Voltage-Controlled DC/DC Boost Converter, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 46, No. 11, 1999: 1374～1381
[27] Sudip K. Mazumder, Ali H. Nayfeh, Theoretical and Experimental Investigation of the Fast- and Slow-Scale Instabilities of a DC/DC Converter, IEEE Transactions on Power Electronics, Vol. 16, No. 2, 2001: 201～216
[28] C. K. Tse, Flip Bifurcation and Chaos in Three-State Boost Switching Regulators, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 41, No. 1, 1994: 16～23
[29] Andreas Magauer, Soumitro Banerjee, Bifurcations and Chaos in the Tolerance Band PWM Technique, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 47, No. 2, 2000: 254～258
[30] Sasan Jalali, Ian Dobson, Switching Time Bifurcations in a Thyristor Controlled Reactor, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 43, No. 3, 1996: 209～218 '
[31] C. K. TSE, W. C. Y. Chan, Chaos From a Current-Programmed C UK Converter, International Journal of Current Theory and Applications, Vol. 23, 1995: 217～225 '
[32] H. H. C. Iu, C. K. Tse, A Study of Synchronization in Chaotic Autonomous C UK DC/DC Converter, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 47, No. 6, 2000: 913～918 '
[33] C. k. Tse, Hopf Bifurcation and Chaos in a Free-Running Current-Controlled C UK Switching Regulator, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 47, No.4, 2000: 448～456 '
[34] C. K. Tse, S. C. Fung, Experimental Confirmation of Chaos in a Current-Programmed C UK Converter, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 43, No. 7, 1996: 605～608
[35] 尹奕光,PWM 型变换器混沌机理的研究,博士学位论文,南京航空航天大学,2000
[36] 葛真,徐云,非线性电路及混沌,重庆:重庆大学出版社,1989
[37] 李忠,毛宗源,混沌控制综述,电路与系统学报,Vol. 3, No. 1, 1998: 59～65
[38] Guckemhei mer J,Hool mes P, Nonlinear Oscillation,Dynamical Systems and Bifurcations of Vector Fields, Springer-Verlag, New York, 1983
[39] Hele J, Kocak H, Dynamics and Bifurcations, Springer-Velag, New Yord, 1991
[40] Wiggins S, Introduction to Applies Nonlinear Dynamical Systems and Chaos, Springer-Velag, New York, 1981
[41] 王光瑞,于熙龄,陈式刚,混沌的控制、同步与利用,北京,国防工业出版社,2001
[42] A. Babloyantz, Analysis and Stabilization of Nonlinear Chaotic Systems, Computers Matn. Applic. Vol. 34, No. 2-4, 1997: 355～368
[43] Krishnendu Chakrabarty, Soumitro Banerjee, Control of Chaos in Piecewise Linear Systems With Switching Nonlinearity, Physics Letters A 200, 1995: 115～120
[44] Kathryn Glass, Michael Renton, Creating Periodic Orbits in Chaotic Systems, Physics Letters A 203, 1995: 107～114
[45] Moez Feki, An Adaptive Feedback Control of Linearizable Chaotic Systems, Chaos, Solution and Fractals 15, 2003: 883～890 '
[46] Jia Yi, Xue-ye Wei, Chaos in PWM Controller of a C UK Converter, Proceeding of the First International Conference on Machine Learning and Cybemetics, Beijing, 4-5, 2002: 210～213
[47] Chung-Chieh Fang, Eyadh. Abed, Robust Feedback Stabilization of Limit Cycles in PWM DC/DC Converters, Nonlinear Dynamics No. 27, 2002: 295～309
[48] C.K. Tse, Y. M. Lai, Control of Bifurcation in Current-Programmed DC/DC Converters An Alternative Viewpoint of Ramp Compensation, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 47, No.12, 2000: 2413～2418
[49] S. Rajasekar, Control of Chaos by Nonfeedback Methods in a Simple Electronic Circuit System and FitzHugh-Nagumo Equation, Chaos, Solution and Fractals Vol. 8, No. 9, 1997: 1545～1558
[50] Mario di Bernardo, Controlling Switching Systems: A Bifurcatuion Approach, IEEE International Symposium on Circuits and Systems, 2000: 377～380
[51] Guanrong Chen, Onfeedback Control of Chaotic Continuous-Time Systems, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 40, No.9, 1993: 591～601
[52] E. Ott, C. Grebogi, J.A. Yorke, controlling chaos, phys, Rev., Lett., Vol. 64, No., 11, 1990, 1196～1199
[53] 薛福珍,韩怀中,结合混沌预测的改进的 OGY 控制方法,控制与决策,Vol. 17, No. 5, 2002: 536～540
[54] 杨凌,刘曾荣,OGY 方法的改进及证明,应用数学和力学,Vol. 19, No. 1, 1998: 1～7
[55] Roberto Santos Bueno, Application of the OGY Method to the Control of Chaotic DC/DC Converters: Theory and Experiments, IEEE International Symposium on Circuits and Systems, 2000: 369～372
[56]. G. Poddar, K. Chakrabarty, and S. Banerjee, Control of Chaos in DC/DC Converters, IEEE Transactions On Circuits and Systems-Ⅰ:Fundamental Theory and Applications, Vol. 45, No.6, 1998: 672～676
[57] Hubler A. W., Adapitive control of chaotic systems, Helvetica Physica Acta, Vol. 62, 1989,341～346
[58] Jackson E. A., On the control of comkplex dynamic systems, Physica D, Vol. 50, 1991a, 341～366
[59] Jackson E. A., The entrainment and migration controls of multiple-attractor systems, Phys. Lett. A, Vol. 151, 1990,478～484
[60]. 陈维、李敏远,BUCK 变换器的一种新型模糊控制方法,《电气开关》,2000,NO.2, 10～ 13.
[61]. Chen F, Cai X S. “Design of Feedback Control Laws for Switching Regulators Based on the Bilinear Large Signal Model”, IEEE Trans, on Power Electronics, 1990, Vol. 5, No. 2, 236～240.
[62] Carles Batlle, Enric F ossas, From Floquet Exponents to Control of Chaos in Piecewise Linear Systems, IEEE International Symposium on Circuits and Systems, 2000: 100～103
[63] C. K. Tse, Quasi-Linear Moldeling and Control of DC/DC Converters, IEEE Transactions on Power Electronics, Vol. 7, No. 2, 1992: 315～323
[64] Pyragas K. , Control of Chaos by Self-controlling Feedback, Phys. Lett. A, Vol.170, No. 6, 1992, 421～428
[65]. 董大群, 曾南, 从噪声中提取瞬态信号-自适应权向量法[J]. 西北工业大学学报,. Vol.12, No. 3, 1994, 347～353.
[66]. 吴淼,张燕. 超声检测缺陷分类的小波分析与神经网络方法[J],中国矿业大学学报, Vol. 29, No. 3, 2000, 239-243.
[67] C. K. Tse, Qualitative Analysis and Control of a DC-to-DC Boost Converter Operating in Discontinuous Mode, IEEE Transactions on Power Electronics, Vol. 5, No. 3, 1990: 323～ 330
[68] K. K. Tse, Heny Shu-Hung, Analysis and Spectral Characteristics of a Spread-Spectrum Technique for Conducted EMI Suppression, IEEE Transactions on Power Electronics, Vol. 15, No. 2, 2000: 399～410
[69] Wing-Hung Ki, Analysis of Subarmonics Oscillation of Fixed-Frequency Current-Programmed Switch Mode Power Converters, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 45, No. 1, 1998: 104～108
[70] K.W. Eric Cheng, Minjian Liu, Study of Bifurcation and Chaos in the Current-Mode Controlled Buck-Boost DC/DC Converter, The 27th Annual Conference of the IEEE Industrial Society, 2001: 838～842
[71] S. Y. Hui, Yash Shrivastava, A Comparsion of Nondeterministic and Deterministic Switching Method for DC/DC Power Converters, IEEE Transactions on Power Electronics, Vol. 13, No. 6, 1998: 1046～1054
[72] Yash Shrivastava, S. Y. Hui, Harmonic Analysis of Nonderministic Switching Methods for DC/DC Power Converters, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 47, No. 6, 2000: 868～883
[73] William C. Y. Chan, C. K. Tse, What Form of Control Function Can Drive a Discontinuous-Mode Boost Converter to Chaos via Period-Doubling?, International Journal of Circuit Theory and Applications, Appl, 26, 1998: 281～286
[74] Hebertt Sira-Ramirez,Nonlinear P-I Controller Design for Switchmode DC-to-DC Power Converters, IEEE Transactions on Circuits and Systems, Vol. 38, No. 4, 1991: 410～417
[75] David C. Hamill, David J. Jeffries, Subharmonics and Chaos in a Controlled Switched-Mode Power Converter, IEEE Transactions on Circuits and Systems, Vol.
35, No. 8, 1988: 1059～1061
[76] Ruslan L. Davidchack, Ying-Cheng Lai, Towards complete detection of Unstable periodic orbits in Chaotic Systems, Physics Letter A 287, 2001: 99～104
[77] Kathryn Glass, Michael Renton, Creating Periodic Orbits in Chaotic Systems, Physics Letter A 203, 1995: 107～114
[78] Roberto Santos Bueno, Jose Luis Rodriguez Marrero, Control of DC/DC Converter in the Chaotic Regime, Proceedings of the 1998 IEEE International Conference on Control Applications, Trieste, Italy 1-4 1998: 832～837
[79] William C. Y. Chan, C. K. Tse, Bifurcation in Current-Programmed DC/DC Buck Switching Regulators-Conjecturing a Universal Bifurcation Path, International Journal of Circuit Theory and Applications, Vol.26, 1998: 127～145
[80] Brad Lehaman, Richard M. Bass, Extensions of Averaging Theory for Ppwer Electronic Systems, IEEE Transactions on Power Electronics, Vol. 11, No. 4, 1996: 542～553
[81] Yung-Chia Hsiao, Pi-Cheng Tung, Controlling Chaos for Nonautonomous Systems by Detecting Unstable Periodic Orbits, Chaos, Solutions and Fractals 13, 2002: 1043～1051
[82] 罗晓曙,翁甲强,正弦周期信号微扰实现的混沌控制,Vol. 19, No. 3, 1998: 9～12
[83] K. K. Tse, Henry Shu-hung Chung, A Comparative Investigation on the Use of Random Modulation Schemes for DC/DC Converters, IEEE Transactions on Industrial Electronics, Vol. 47, No. 2, 2000: 253～263
[84] Aleksandar M. Stankovic, David J. Perreault, Analysis and Synthesis of Randomized Modulation Sachemes for Power Converters, IEEE Transactions on Power Electronics, Vol. 10, No. 5, 1995: 680～693
[85]. 黄浴、强伯涵,一种提取特征值的新型 systolic 阵列算法,西安电子科技大学学报, Vol.21, No.1, 1994: 33～40
[86]. 吴淼,张海燕,超声检测缺陷分类的小波分析与神经网络方法,中国矿业大学学报, Vol.29, No.32000, 239～243.
[87]. Udpa SS, Lord W. A Fourier descriptor classification scheme for differential probe signals, in Materials Evaluation, Vol. 42, No. 8, 1984: 1136～1141
[88] R.Lynn Kirlin, Sam Kwork, Power Spectra of a PWM Inverter with Randomized Pulse Position, IEEE Transactions on Power Electronics, Vol. 9, No. 5, 1994, 463～472
[89] Yie-Tone Chen, A New Quasi-Parallel Resonant DC Link for Soft-Switching PWM Inverters, IEEE Transactions on Power Electronics, Vol. 13, No. 3, 1998, 427～435
[90] 吴从中, DC/DC 电源系统的优化设计, 电子技术应用,Vol. 12, 2001: 34～35
[91] Michael M. Bech, John K. Pedersen, A Methodology for True Comparison of Analytical Measured Frequency Domain Spectra in Random PWM Converters, IEEE Transactions on Power Electronics, Vol. 14, No. 3, 1999, 578～586.
[92] Yen-Shin Lai, Ye-Then Chang, Design and Implementation of Vector-Controlled Induction Motor Drives Using Random Switchoing Technique with Constant Sampling Frequency, IEEE Transactions on Power Electronics, Vol. 16, No. 3, 2001, 400～409.
[93] Thomas G. Habetler, Acoustic Noise Reduction in Sinusoidal PWM Drives Using a Randomly Modulated Carrier, IEEE Transactions on Power Electronics, Vol. 6, No. 3, 1991, 356～363.
[94] K. K. Tse, S. Y. R. Hui, H. C. So, Spectral Characteristics of Randomly Switched PWM DC/DC Converters Operating in Discontinuous Conduction Mode, IEEE Transactions on Industrial Electronics, Vol. 47, No. 4, 2000, 759～768.
[95] C. M. Liaw, Y. M. Lin, C. H. Wu, etal., Analysis, Design, and Implentation of a Random Frequency PWM Inverter, IEEE Transactions on Power Electronics, Vol. 15, No. 5, 2000, 843854.
[96] Chi-Chuan Hwang, Rong-Fong Fung, Jin-Yuan Hsieh, A nonlinear Feedback Control of the Lorenz Equation, International Journal of Engineering Science, Vol. 37, 1999: 1893～1900
[97].黄春琳、邱玲“数字调制信号的神经网络识别方法”,国防科技大学学报, NO.2, 1999, 58～61.
[98].韩冰、王滨生“基于神经网络的 VEP 波形自动识别方法”,临床脑电学杂志, Vol.8, No.2,1999, 76～81
[99].张定会、戴署光“神经网络数据融合和目标识别”,仪器仪表学报,Vol.22,No.4,2001, 285～286.
[100].周继成,《人工神经网络-第六代计算机的实现》,北京,科学普及出版社,1993.
[101].罗发龙、李衍达,《神经网络信号处理》,北京,电子工业出版社,1993.
[102].钟洁,“用人工神经网络识别涡流检测信号的工程应用研究”(硕士学位论文),1997
[2] 黄润生编著,混沌及其应用,湖北,武汉大学出版社,2000:4～8
[3] 锦清编著,驾驭混沌与发展高新技术,北京,原子能出版社,2002:30～32
[4] 王东生,曹磊,混沌、分形及其应用,合肥:中国科技大学出版社,1995
[5] Jonathan R.Wood, Chaos :a real phenomenon in power electronics, IEEE Transactions on Circuits and Systems-Ⅰ:Vol. 36, No. 3, 1989:115～124
[6] Takuji Kousaka, Bifurcation of Switched Nonlinear Dynamical Sysytems, IEEE Transactions on Circuits and Systems-Ⅱ: Analog and Digital Signal Processing, Vol. 46, No. 7, 1999: 878～884
[7] Jonathan H.B, David C..Hamill, Instablity, Subharmonics, and Chaos in Power Electronic Systems, IEEE Transactions on Power Electronics, Vol. 5, No. 3, 1999: 260～268
[8] J. Baillieul, Roger W, Chaotic Motion in Nonlinear Feedback Systems, IEEE Transactions on Circuits and Systems-Ⅱ:Vol. 27, No. 11, Nov. 1980: 990～997
[9] 尹奕光,于盛林,电力电子电路非线性现象研究的发展综述,电子工程师,Vol. 27, No. 2, 2001:58～61
[10] 尹奕光,刘文波,功率电子电路中的混沌现象,南京理工大学学报,Vol. 24, No. 2, 2000:164～167
[11] 丁道宏,电力电子技术,北京,航空工业出版社,1992
[12] 张占松,蔡宣三,开关电源的原理与设计,北京,电子工业出版社,1998
[13] 蔡宣三,龚绍文,高频功率电子学,北京,科学出版社,1993
[14] 何希才,新型开关电源设计与应用,北京,科学出版社,2001
[15] 林波涛,丘水生,DC/DC 开关功率变换器分析方法的述评,电路与系统学报,Vol. 3, No. 3, 1998: 65～72
[16] Jonathan H.B. Deane, David C. Hamill, Analysis, Simulation and Experimental Study of Chaos in the Buck Converter, IEEE Power Electronics Specialist Conference, 1990:491～498
[17] Enric Fossas, Gerand Olivar, Study of Chaos in the Buck Converter, IEEE Transactions on Circuits and Systems-Ⅰ:Fundamental Theory and Applications, Vol. 43, No. 1, 1996: 13～25
[18] David C. Hamill, Modeling of Chaotic DC/DC Converters by Iterated Nonlinear Mappings, IEEE Transactions on Power Electronics, Vol. 7, No. 1, 1992: 25～36
[19] Mario di Bernardo, Franco Garofalo, Switchings, Bifurcations, and Chaos in DC/DC Converters, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 45, No. 2, 1998: 133～141
[20] Mario di Bernardo, Discrete-Time Maps for the Analysis of Bifurcations and Chaos in DC/DC Converters, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 47, No. 2, 2000: 130～143
[21] Guohui Yuan, Soumitro Banerjee, Border-Collision Bifurcations in the Buck Converter, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 45, No. 7, 1998: 707～716
[22] Jonathan H. B. Deane, Chaos in a Current-Mode Controlled Boost DC/DC Converter, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 39, No. 8, 1992: 680～683
[23] H. H. C. Iu, C. K. Tse, Bifurcation Behaviour in Parallel-Connected Boost Converter, International Journal of Current Theory and Applications, Vol. 29, 2001: 281～298
[24] H. H. C. Iu, C. K. Tse, Bifurcation Behavior in Parallel-Connected Buck Converter, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 48, No. 2, 2001:233～240
[25] William C. Y. Chan, Chi K. Tse, Study of Bifurcations in Current-Programmed DC/DC Boost Converter: From Quasi-Periodicity to Period-Doubling, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 44, No. 12, 1997: 1129～1142
[26] Abdelai EI Aroudi, Luis Benadero, Hopf Bifurcation and Chaos from Torus Breakdown in a PWM Voltage-Controlled DC/DC Boost Converter, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 46, No. 11, 1999: 1374～1381
[27] Sudip K. Mazumder, Ali H. Nayfeh, Theoretical and Experimental Investigation of the Fast- and Slow-Scale Instabilities of a DC/DC Converter, IEEE Transactions on Power Electronics, Vol. 16, No. 2, 2001: 201～216
[28] C. K. Tse, Flip Bifurcation and Chaos in Three-State Boost Switching Regulators, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 41, No. 1, 1994: 16～23
[29] Andreas Magauer, Soumitro Banerjee, Bifurcations and Chaos in the Tolerance Band PWM Technique, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 47, No. 2, 2000: 254～258
[30] Sasan Jalali, Ian Dobson, Switching Time Bifurcations in a Thyristor Controlled Reactor, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 43, No. 3, 1996: 209～218 '
[31] C. K. TSE, W. C. Y. Chan, Chaos From a Current-Programmed C UK Converter, International Journal of Current Theory and Applications, Vol. 23, 1995: 217～225 '
[32] H. H. C. Iu, C. K. Tse, A Study of Synchronization in Chaotic Autonomous C UK DC/DC Converter, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 47, No. 6, 2000: 913～918 '
[33] C. k. Tse, Hopf Bifurcation and Chaos in a Free-Running Current-Controlled C UK Switching Regulator, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 47, No.4, 2000: 448～456 '
[34] C. K. Tse, S. C. Fung, Experimental Confirmation of Chaos in a Current-Programmed C UK Converter, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 43, No. 7, 1996: 605～608
[35] 尹奕光,PWM 型变换器混沌机理的研究,博士学位论文,南京航空航天大学,2000
[36] 葛真,徐云,非线性电路及混沌,重庆:重庆大学出版社,1989
[37] 李忠,毛宗源,混沌控制综述,电路与系统学报,Vol. 3, No. 1, 1998: 59～65
[38] Guckemhei mer J,Hool mes P, Nonlinear Oscillation,Dynamical Systems and Bifurcations of Vector Fields, Springer-Verlag, New York, 1983
[39] Hele J, Kocak H, Dynamics and Bifurcations, Springer-Velag, New Yord, 1991
[40] Wiggins S, Introduction to Applies Nonlinear Dynamical Systems and Chaos, Springer-Velag, New York, 1981
[41] 王光瑞,于熙龄,陈式刚,混沌的控制、同步与利用,北京,国防工业出版社,2001
[42] A. Babloyantz, Analysis and Stabilization of Nonlinear Chaotic Systems, Computers Matn. Applic. Vol. 34, No. 2-4, 1997: 355～368
[43] Krishnendu Chakrabarty, Soumitro Banerjee, Control of Chaos in Piecewise Linear Systems With Switching Nonlinearity, Physics Letters A 200, 1995: 115～120
[44] Kathryn Glass, Michael Renton, Creating Periodic Orbits in Chaotic Systems, Physics Letters A 203, 1995: 107～114
[45] Moez Feki, An Adaptive Feedback Control of Linearizable Chaotic Systems, Chaos, Solution and Fractals 15, 2003: 883～890 '
[46] Jia Yi, Xue-ye Wei, Chaos in PWM Controller of a C UK Converter, Proceeding of the First International Conference on Machine Learning and Cybemetics, Beijing, 4-5, 2002: 210～213
[47] Chung-Chieh Fang, Eyadh. Abed, Robust Feedback Stabilization of Limit Cycles in PWM DC/DC Converters, Nonlinear Dynamics No. 27, 2002: 295～309
[48] C.K. Tse, Y. M. Lai, Control of Bifurcation in Current-Programmed DC/DC Converters An Alternative Viewpoint of Ramp Compensation, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 47, No.12, 2000: 2413～2418
[49] S. Rajasekar, Control of Chaos by Nonfeedback Methods in a Simple Electronic Circuit System and FitzHugh-Nagumo Equation, Chaos, Solution and Fractals Vol. 8, No. 9, 1997: 1545～1558
[50] Mario di Bernardo, Controlling Switching Systems: A Bifurcatuion Approach, IEEE International Symposium on Circuits and Systems, 2000: 377～380
[51] Guanrong Chen, Onfeedback Control of Chaotic Continuous-Time Systems, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 40, No.9, 1993: 591～601
[52] E. Ott, C. Grebogi, J.A. Yorke, controlling chaos, phys, Rev., Lett., Vol. 64, No., 11, 1990, 1196～1199
[53] 薛福珍,韩怀中,结合混沌预测的改进的 OGY 控制方法,控制与决策,Vol. 17, No. 5, 2002: 536～540
[54] 杨凌,刘曾荣,OGY 方法的改进及证明,应用数学和力学,Vol. 19, No. 1, 1998: 1～7
[55] Roberto Santos Bueno, Application of the OGY Method to the Control of Chaotic DC/DC Converters: Theory and Experiments, IEEE International Symposium on Circuits and Systems, 2000: 369～372
[56]. G. Poddar, K. Chakrabarty, and S. Banerjee, Control of Chaos in DC/DC Converters, IEEE Transactions On Circuits and Systems-Ⅰ:Fundamental Theory and Applications, Vol. 45, No.6, 1998: 672～676
[57] Hubler A. W., Adapitive control of chaotic systems, Helvetica Physica Acta, Vol. 62, 1989,341～346
[58] Jackson E. A., On the control of comkplex dynamic systems, Physica D, Vol. 50, 1991a, 341～366
[59] Jackson E. A., The entrainment and migration controls of multiple-attractor systems, Phys. Lett. A, Vol. 151, 1990,478～484
[60]. 陈维、李敏远,BUCK 变换器的一种新型模糊控制方法,《电气开关》,2000,NO.2, 10～ 13.
[61]. Chen F, Cai X S. “Design of Feedback Control Laws for Switching Regulators Based on the Bilinear Large Signal Model”, IEEE Trans, on Power Electronics, 1990, Vol. 5, No. 2, 236～240.
[62] Carles Batlle, Enric F ossas, From Floquet Exponents to Control of Chaos in Piecewise Linear Systems, IEEE International Symposium on Circuits and Systems, 2000: 100～103
[63] C. K. Tse, Quasi-Linear Moldeling and Control of DC/DC Converters, IEEE Transactions on Power Electronics, Vol. 7, No. 2, 1992: 315～323
[64] Pyragas K. , Control of Chaos by Self-controlling Feedback, Phys. Lett. A, Vol.170, No. 6, 1992, 421～428
[65]. 董大群, 曾南, 从噪声中提取瞬态信号-自适应权向量法[J]. 西北工业大学学报,. Vol.12, No. 3, 1994, 347～353.
[66]. 吴淼,张燕. 超声检测缺陷分类的小波分析与神经网络方法[J],中国矿业大学学报, Vol. 29, No. 3, 2000, 239-243.
[67] C. K. Tse, Qualitative Analysis and Control of a DC-to-DC Boost Converter Operating in Discontinuous Mode, IEEE Transactions on Power Electronics, Vol. 5, No. 3, 1990: 323～ 330
[68] K. K. Tse, Heny Shu-Hung, Analysis and Spectral Characteristics of a Spread-Spectrum Technique for Conducted EMI Suppression, IEEE Transactions on Power Electronics, Vol. 15, No. 2, 2000: 399～410
[69] Wing-Hung Ki, Analysis of Subarmonics Oscillation of Fixed-Frequency Current-Programmed Switch Mode Power Converters, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 45, No. 1, 1998: 104～108
[70] K.W. Eric Cheng, Minjian Liu, Study of Bifurcation and Chaos in the Current-Mode Controlled Buck-Boost DC/DC Converter, The 27th Annual Conference of the IEEE Industrial Society, 2001: 838～842
[71] S. Y. Hui, Yash Shrivastava, A Comparsion of Nondeterministic and Deterministic Switching Method for DC/DC Power Converters, IEEE Transactions on Power Electronics, Vol. 13, No. 6, 1998: 1046～1054
[72] Yash Shrivastava, S. Y. Hui, Harmonic Analysis of Nonderministic Switching Methods for DC/DC Power Converters, IEEE Transactions on Circuits and Systems-Ⅰ: Fundamental Theory and Applications, Vol. 47, No. 6, 2000: 868～883
[73] William C. Y. Chan, C. K. Tse, What Form of Control Function Can Drive a Discontinuous-Mode Boost Converter to Chaos via Period-Doubling?, International Journal of Circuit Theory and Applications, Appl, 26, 1998: 281～286
[74] Hebertt Sira-Ramirez,Nonlinear P-I Controller Design for Switchmode DC-to-DC Power Converters, IEEE Transactions on Circuits and Systems, Vol. 38, No. 4, 1991: 410～417
[75] David C. Hamill, David J. Jeffries, Subharmonics and Chaos in a Controlled Switched-Mode Power Converter, IEEE Transactions on Circuits and Systems, Vol.
35, No. 8, 1988: 1059～1061
[76] Ruslan L. Davidchack, Ying-Cheng Lai, Towards complete detection of Unstable periodic orbits in Chaotic Systems, Physics Letter A 287, 2001: 99～104
[77] Kathryn Glass, Michael Renton, Creating Periodic Orbits in Chaotic Systems, Physics Letter A 203, 1995: 107～114
[78] Roberto Santos Bueno, Jose Luis Rodriguez Marrero, Control of DC/DC Converter in the Chaotic Regime, Proceedings of the 1998 IEEE International Conference on Control Applications, Trieste, Italy 1-4 1998: 832～837
[79] William C. Y. Chan, C. K. Tse, Bifurcation in Current-Programmed DC/DC Buck Switching Regulators-Conjecturing a Universal Bifurcation Path, International Journal of Circuit Theory and Applications, Vol.26, 1998: 127～145
[80] Brad Lehaman, Richard M. Bass, Extensions of Averaging Theory for Ppwer Electronic Systems, IEEE Transactions on Power Electronics, Vol. 11, No. 4, 1996: 542～553
[81] Yung-Chia Hsiao, Pi-Cheng Tung, Controlling Chaos for Nonautonomous Systems by Detecting Unstable Periodic Orbits, Chaos, Solutions and Fractals 13, 2002: 1043～1051
[82] 罗晓曙,翁甲强,正弦周期信号微扰实现的混沌控制,Vol. 19, No. 3, 1998: 9～12
[83] K. K. Tse, Henry Shu-hung Chung, A Comparative Investigation on the Use of Random Modulation Schemes for DC/DC Converters, IEEE Transactions on Industrial Electronics, Vol. 47, No. 2, 2000: 253～263
[84] Aleksandar M. Stankovic, David J. Perreault, Analysis and Synthesis of Randomized Modulation Sachemes for Power Converters, IEEE Transactions on Power Electronics, Vol. 10, No. 5, 1995: 680～693
[85]. 黄浴、强伯涵,一种提取特征值的新型 systolic 阵列算法,西安电子科技大学学报, Vol.21, No.1, 1994: 33～40
[86]. 吴淼,张海燕,超声检测缺陷分类的小波分析与神经网络方法,中国矿业大学学报, Vol.29, No.32000, 239～243.
[87]. Udpa SS, Lord W. A Fourier descriptor classification scheme for differential probe signals, in Materials Evaluation, Vol. 42, No. 8, 1984: 1136～1141
[88] R.Lynn Kirlin, Sam Kwork, Power Spectra of a PWM Inverter with Randomized Pulse Position, IEEE Transactions on Power Electronics, Vol. 9, No. 5, 1994, 463～472
[89] Yie-Tone Chen, A New Quasi-Parallel Resonant DC Link for Soft-Switching PWM Inverters, IEEE Transactions on Power Electronics, Vol. 13, No. 3, 1998, 427～435
[90] 吴从中, DC/DC 电源系统的优化设计, 电子技术应用,Vol. 12, 2001: 34～35
[91] Michael M. Bech, John K. Pedersen, A Methodology for True Comparison of Analytical Measured Frequency Domain Spectra in Random PWM Converters, IEEE Transactions on Power Electronics, Vol. 14, No. 3, 1999, 578～586.
[92] Yen-Shin Lai, Ye-Then Chang, Design and Implementation of Vector-Controlled Induction Motor Drives Using Random Switchoing Technique with Constant Sampling Frequency, IEEE Transactions on Power Electronics, Vol. 16, No. 3, 2001, 400～409.
[93] Thomas G. Habetler, Acoustic Noise Reduction in Sinusoidal PWM Drives Using a Randomly Modulated Carrier, IEEE Transactions on Power Electronics, Vol. 6, No. 3, 1991, 356～363.
[94] K. K. Tse, S. Y. R. Hui, H. C. So, Spectral Characteristics of Randomly Switched PWM DC/DC Converters Operating in Discontinuous Conduction Mode, IEEE Transactions on Industrial Electronics, Vol. 47, No. 4, 2000, 759～768.
[95] C. M. Liaw, Y. M. Lin, C. H. Wu, etal., Analysis, Design, and Implentation of a Random Frequency PWM Inverter, IEEE Transactions on Power Electronics, Vol. 15, No. 5, 2000, 843854.
[96] Chi-Chuan Hwang, Rong-Fong Fung, Jin-Yuan Hsieh, A nonlinear Feedback Control of the Lorenz Equation, International Journal of Engineering Science, Vol. 37, 1999: 1893～1900
[97].黄春琳、邱玲“数字调制信号的神经网络识别方法”,国防科技大学学报, NO.2, 1999, 58～61.
[98].韩冰、王滨生“基于神经网络的 VEP 波形自动识别方法”,临床脑电学杂志, Vol.8, No.2,1999, 76～81
[99].张定会、戴署光“神经网络数据融合和目标识别”,仪器仪表学报,Vol.22,No.4,2001, 285～286.
[100].周继成,《人工神经网络-第六代计算机的实现》,北京,科学普及出版社,1993.
[101].罗发龙、李衍达,《神经网络信号处理》,北京,电子工业出版社,1993.
[102].钟洁,“用人工神经网络识别涡流检测信号的工程应用研究”(硕士学位论文),1997