一类快慢耦合电路的复杂动力学特性及控制
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摘要
引入周期激励建立了一类光滑的三维非自治快慢耦合簇发振荡电路。通过调节外激励交变电流源的频率使系统呈现出明显的两尺度效应即快变量和慢变量,结合数值仿真与两时间尺度法分析该电路模型系统在不同激励频率和幅值下系统的簇发机理和分岔模式,并通过分数阶混沌电路对系统的动力学行为演变进行控制。结果表明:若系统固有频率与外激励频率存在量级上的差异,则系统存在明显的快慢耦合簇发现象,且外激励频率越小,幅值微变或不变时系统快慢效应和簇发现象越明显;同时利用分数阶混沌电路对动力学系统演化过程进行了有效的轨道控制。
A kind of smooth three-dimensional non-autonomous fast and slow coupled tufting oscillation circuit is established by introducing periodic excitation. By adjusting the frequency of the external excitation alternating current source,the system exhibits obvious two-scale effects,namely fast and slow variables. Combining with numerical simulation and two time scale method is used to analyze the cluster mechanism and bifurcation mode of the circuit model system under different excitation frequencies and amplitudes. The fractional chaotic circuit is used to control the evolution of the dynamic behavior of the system. The results show that if there is a difference in magnitude between the natural frequency of the system and the frequency of the external excitation,the system has obvious tufting phenomena of fast and slow coupling. The smaller the external excitation frequency is,the faster and slower the system effect when the amplitude is small or constant,and the more obvious the phenomenon is. At the same time,the fractional-order chaotic circuit is used to control the evolution of dynamic system effectively.
A kind of smooth three-dimensional non-autonomous fast and slow coupled tufting oscillation circuit is established by introducing periodic excitation. By adjusting the frequency of the external excitation alternating current source,the system exhibits obvious two-scale effects,namely fast and slow variables. Combining with numerical simulation and two time scale method is used to analyze the cluster mechanism and bifurcation mode of the circuit model system under different excitation frequencies and amplitudes. The fractional chaotic circuit is used to control the evolution of the dynamic behavior of the system. The results show that if there is a difference in magnitude between the natural frequency of the system and the frequency of the external excitation,the system has obvious tufting phenomena of fast and slow coupling. The smaller the external excitation frequency is,the faster and slower the system effect when the amplitude is small or constant,and the more obvious the phenomenon is. At the same time,the fractional-order chaotic circuit is used to control the evolution of dynamic system effectively.
引文
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[2]谢帆,杨汝,张波.电流反馈型Buck变换器二维分段光滑系统边界碰撞和分岔研究[J].物理学报,2010,59(12):8393-8406Xie F,Yang R,Zhang B. Study on border collision and bifurcation of two-dimensional piecewise smooth systems in current mode controlled Buck converter[J]. Acta Physica Sinica,2010,59(12):8393-8406(in Chinese)
[3]余跃,张春,毕勤胜.非线性切换系统的振荡行为及其Lyapunov指数计算[J].江苏大学学报:自然科学版,2014,35(5):611-615Yue Y, Zhang C, Bi Q S. Oscillated behavior and Lyapunov exponent calculation of nonlinear switching systems[J]. Journal of Jiangsu University:Natural Science Edition,2014,35(5):611-615(in Chinese)
[4]张舒,徐鉴.时滞耦合系统非线性动力学的研究进展[J].力学学报,2017,49(3):565-587Zhang S, Xu J. Review on nonlinear dynamics in systems with coulpling delays[J]. Chinese Journal of Theoretical and Applied Mechanics,2017,49(3):565-587(in Chinese)
[5]梅宇健.非线性电路求解及电热耦合分析[D].西安:西安电子科技大学,2015Mei Y J. Solution of the nonlinear circuit and electrothermal analysis[D]. Xi'an:Xi'an University of Electronic Science and Technology,2015(in Chinese)
[6] Panyam M,Daqaq M E. Characterizing the effective bandwidth of tri-stable energy harvesters[J]. Journal of Sound and Vibration,2017,386:336-358
[7] Mohiuddin S M,Mahmud M A,Haruni A M O,et al.Design and implementation of partial feedback linearizing controller for grid-connected fuel cell systems[J].International Journal of Electrical Power and Energy Systems,2017,93:414-425
[8] Bragatto F,Cresta M,Gatta F M,et al. Underground MV power cable joints:A nonlinear thermal circuit model and its experimental validation[J]. Electric Power Systems Research,2017,149:190-197
[9] Jafarnejad R,Jannesari A,Sobhi J. A linear ultra wide band low noise amplifier using pre-distortion technique[J]. AEUEInternational Journal of Electronics and Communications,2017,79:172-183
[10] Zeldenrust F,Wadman W J. Modulation of spike and burst rate in a minimal neuronal circuit with feed-forward inhibition[J]. Neural Networks,2013,40:1-17
[11]陈鹏,葛红娟,倪一洋,等.电脉冲除冰系统非线性等效电路分析[J].北京航空航天大学学报,2015,41(8):1539-1545Chen P,Ge H J,Ni Y Y,et al. Nonlinear equivalent circuit analysis of electro-impulse de-icing system[J].Journal of Beijing University of Aeronautics and Astronautics,2015,41(8):1539-1545(in Chinese)
[12]公忠盛,徐光宪,南敬昌,等.基于改进混合蜂群算法的非线性电路谐波平衡分析[J].计算机应用研究,2018,35(7):1970-1973,1995Gong Z S,Xu G X,Nan J C,et al. Harmonic balance analysis of non-linear circuits based on improved mixed bee colony algorithm[J]. Application Research of Computers, 2018,35(7):1970-1973,1995(in Chinese)
[13]杜秀云.Duffing型电路信号的特性与仿真分析[J].光电技术应用,2017,32(4):64-67Du X Y. Characteristic and simulation analysis of duffing circuit signal[J]. Electro-Optic Technology Applications,2017,32(4):64-67(in Chinese)
[14]黄承代.几类分数阶系统的动力学分析与控制[D].南京:东南大学,2016Huang C D. Dynamical analysis and control for several classes of fractional systems[D]. Nanjing:Dongnan University,2016(in Chinese)
[15]卫一恒.不确定分数阶系统的自适应控制研究[D].合肥:中国科学技术大学,2015Wei Y H. Adaptive control for uncertain fractional order systems[D]. Hefei:University of Science and Technology of China,2015(in Chinese)
[16]马英东.不确定分数阶系统鲁棒控制的若干问题研究[D].上海:上海交通大学,2014Ma Y D. Studies on the robust control of uncertain fractional order systems[D]. Shanghai:Shanghai Jiao Tong University,2014(in Chinese)