含PID控制器的迟滞非线性控制系统的主共振及奇异性
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摘要
针对含PID控制器的迟滞非线性闭环控制系统,用Backlash神经网络模型逼近系统迟滞非线性部分,建立动力学模型。研究了系统在简谐激励下的主共振,利用平均法得到了系统的分岔方程,并用奇异性理论进行了分析,得到了转迁集和分岔图。另外还研究了系统参数对开折参数和分岔参数的影响,从而为系统参数的选择提供理论指导。
A hysteretic closed-loop nonlinear control system with a PID controller was studied. A model based on Backlash neutral network was adopted to approach the hysteretic nonlinear part of the system,the dynamic model of the system was established. The principal resonance of the system under a simple harmonic excitation was studied. The bifurcation equation of the system was obtained with the averaging method,and then the system's singularity was analyzed completely,the transition sets and bifurcation plots were gained. The effects of the system's parameters on its unfolding and bifurcation parameters were discussed. The results provided a theoretical guidance for selecting the system's parameters.
A hysteretic closed-loop nonlinear control system with a PID controller was studied. A model based on Backlash neutral network was adopted to approach the hysteretic nonlinear part of the system,the dynamic model of the system was established. The principal resonance of the system under a simple harmonic excitation was studied. The bifurcation equation of the system was obtained with the averaging method,and then the system's singularity was analyzed completely,the transition sets and bifurcation plots were gained. The effects of the system's parameters on its unfolding and bifurcation parameters were discussed. The results provided a theoretical guidance for selecting the system's parameters.
引文
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[11]金栋平,陈予恕.滞后非线性系统的分岔和奇异性[J].天津大学学报,1997,30(3):299-304.JIN Dong-ping,CHEN Yu-shu.The bifurcations and singularities in systems with hysteretic nonlinearity[J].Journal of Tianjin University,1997,30(3):299-304.
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[2]李鸿光,孟光,闻邦椿.带间隙的双线性滞回系统的非线性振动[J].机械工程学报,2004,40(7):10-13.LI Hong-guang,MENG Guang,WEN Bang-chun.Nonlinear oscillation of bilinear hysteresis system with clearance[J].Chinese Journal of Mechanical Engineering,2004,40(7):10-13.
[3]侯晓东,刘彬,时培明.一类滞后相对转动动力学方程的分岔特性及其解析近似解[J].物理学报,2009,58(9):5942-5948.HOU Xiao-dong,LIU Bin,SHI Pei-ming.The bifurcation of a kind of relative rotational dynamic equation with hysteresis and its approximate solution[J].Acta Physica Sinica,2009,58(9):5942-5948.
[4]Appelbe B,Rachinskii D,Zhezherun A.Hopf bifurcation in a van der Pol type oscillator with magnetic hysteresis[J].Physica B:Condensed Matter,2008,403(2-3):301-304.
[5]Krasnosel’skii A,Rachinskii D.Bifurcation of forced periodic oscillations for equations with Preisach hysteresis[J].Journal of Physics:Conference Series,2005,22:93-102.
[6]LI Hong-guang,MENG Guang.Nonlinear dynamics of a SDOF oscillator with Bouc-Wen hysteresis[J].Chaos Solitons&Fractals,2007,34(2):337-343.
[7]李鸿光,何旭,孟光.Bouc-Wen滞回系统动力学特性的仿真研究[J].系统仿真学报,2009,16(9):2009-2011.LI Hong-guang,HE Xu,MENG guang.Numerical simulation for dynamic characteristics of Bouc-Wen hysteretic system[J].Journal of System Simulation,2009,16(9):2009-2011.
[8]曹树谦,付耀东,贺微波.基于三次迟滞模型的超声电机圆环定子主共振响应[J].振动与冲击,2009,28(1):38-41.CAO Shu-qian,FU Yao-dong,HE Wei-bo.Primary resonance of a ring-type stator of ultrasonic motors based on cubic polynomial hysteresis model[J].Journal of Vibration and Shock,2009,28(1):38-41.
[9]杨绍普,陈予恕.一类单自由度滞后-自激振动系统的分叉[J].振动工程学报,1991,4(2):95-101.YANG Shao-pu,CHEN Yu-shu.Bifurcation of single degree of freedom and self-excited vibration system[J].Journal of Vibration Engineering,1991,4(2):95-101.
[10]李韶华,杨绍普.一种非线性汽车悬架的亚谐共振及奇异性[J].振动工程学报,2007,20(2):168-173.LI Shao-hua,YANG Shao-pu.Sub-harmonic resonance and singularity of a nonlinear vehicle suspension system[J].Journal of Vibration Engineering,2007,20(2):168-173.
[11]金栋平,陈予恕.滞后非线性系统的分岔和奇异性[J].天津大学学报,1997,30(3):299-304.JIN Dong-ping,CHEN Yu-shu.The bifurcations and singularities in systems with hysteretic nonlinearity[J].Journal of Tianjin University,1997,30(3):299-304.
[12]苏密勇,谭永红,杨晓明.一类具有迟滞-蠕变非线性对象的内模控制[J].吉林大学学报(工学版),2004,34(z1):64-67.SHU Mi-yong,TAN Yong-hong,YANG Xiao-ming.Modeling and internal model control for systems with hysteresis and creep[J].Journal of Jilin University(Engineering and Technology Edition),2004,34(z1)64-67.
[13]Low T S,Guo W.Modeling of a three-layer piezoelectric bimorph beam with hysteresis[J].Journal of Microelectromechanical Systems,1995,4(4):230-237.