超磁致伸缩致动器非线性动力学的分数阶时滞反馈控制  

Fractional-order time-delayed feedback control of nonlinear dynamics in a giant magnetostrictive actuator

作　　者：闫洪波[1] 付鑫 汪建新[1] 于均成 马庆振 杨伯军 YAN Hong-bo;FU Xin;WANG Jian-xin;YU Jun-cheng;MA Qing-zhen;YANG Bo-jun(College of Mechanical Engineering,Inner Mongolia University of Science&Technology,Baotou 014010,China;National Engineering Research Center for Technological Innovation Method and Tool,Hebei University of Technology,Tianjin 300131,China)

机构地区：[1]内蒙古科技大学机械工程学院,内蒙古包头014010 [2]河北工业大学国家技术创新方法与实施工具工程技术研究中心,天津300131

出　　处：《振动工程学报》2024年第4期632-644,共13页Journal of Vibration Engineering

基　　金：内蒙古自然科学基金资助项目(2020LH05023)。

摘　　要：设计了一种分数阶时滞反馈控制器,用于控制单自由度的超磁致伸缩致动器(GMA)的非线性动态响应。考虑到预压碟形弹簧机构引入的几何非线性因素影响,建立了GMA系统的非线性数学模型。利用平均法求解系统在含分数阶时滞反馈控制策略下主共振的幅频响应方程,根据Routh-Hurwitz准则得到系统的稳定性条件。通过数值模拟研究GMA系统中关键结构参数对幅频响应特性的影响,以及主共振峰值和系统稳定性随每个时滞反馈参数变化的特性规律;通过分岔图和Lyapunov指数图得到外激励幅值对系统混沌运动的影响;最后调节时滞反馈增益和分数阶次抑制系统的混沌运动。结果表明,时滞反馈增益和分数阶次能够有效抑制系统的主共振峰值和不稳定区域,可以将系统响应从混沌运动调整为稳定的周期运动,提高系统的稳定性。In this paper,a fractional-order time-delayed feedback controller is designed to control the nonlinear dynamic response of a single-degree-of-freedom giant magnetostrictive actuator(GMA).Considering the effect of geometric nonlinear factors introduced by the preloaded disc spring mechanism,a nonlinear mathematical model of the GMA system is established.The amplitudefrequency response equation of the main resonance of the system under the feedback control strategy with fractional-order time-delayed is obtained by the averaging method,and the stability condition of the system is obtained according to the Routh-Hurwitz criterion.The influence of key structural parameters in the GMA system on the amplitude-frequency response characteristics,as well as the characteristic law of the main resonance peak and system stability with each time-delayed feedback parameter are studied through numerical simulation.The bifurcation diagram and Lyapunov exponent diagram are obtained and the influence of the external excitation amplitude on the chaotic motion of the system is studied;finally,the time-delayed feedback gain and fractional order are used to suppress the chaotic motion of the system.The results show that the time-delayed feedback gain and fractional order can effectively suppress the main resonance peak and unstable region of the system,and the system response can be adjusted from chaotic motion to stable periodic movement to improve the stability of the system.

关 键 词：几何非线性 超磁致伸缩致动器 混沌 时滞反馈 稳定性 

分 类 号：O322[理学—一般力学与力学基础] TB381[理学—力学]