AFM-TM微悬臂梁系统混沌运动及控制算法分析  

Chaotic Motion and Control Algorithm Analysis of AFM-TM Microcantilever System

作　　者：宋佩颉 褚衍东[1] 张航 俞睿 SONG Peijie;CHU Yandong;ZHANG Hang;YU Rui(School of Mechanical and Electrical Engineering,Lanzhou Jiaotong University,Lanzhou,Gansu 730070,China;Length Measurement Institute,Gansu Institute of Metrology,Lanzhou,Gansu 730050,China)

机构地区：[1]兰州交通大学机电工程学院,甘肃兰州730070 [2]甘肃省计量研究院长度计量研究所,甘肃兰州730050

出　　处：《计量学报》2024年第3期356-363,共8页Acta Metrologica Sinica

基　　金：西藏自治区科技计划(XZ202301YD0004C);甘肃省青年科技基金(21JR7RA316);中国计量科学研究院科研项目(AKYZD2307);甘肃省计量研究院科研项目(GJY2023003)。

摘　　要：针对轻敲式原子力显微镜微(AFM-TM)悬臂梁系统的混沌运动会严重影响到AFM-TM的测量精度的问题,对该系统动力学特性及控制算法进行了分析。首先,通过数值仿真,综合利用Lyapunov指数、分岔图、Poincaré截面和相位图分析了外部激励幅值变化时AFM-TM微悬臂梁系统运动特性的演化;然后,提出将延时反馈控制和模糊自适应延时反馈,用于控制系统的混沌运动;最后,对两种控制算法进行了比较。研究结果表明,当无量纲外部激励幅值在[0.65,0.85]等取值区间内取值时,系统表现出明显的混沌运动特性;延时反馈控制和模糊自适应延时反馈控制均能有效的将系统的混沌运动拉回到周期轨道,但模糊自适应延时反馈更适用于AFM-TM被测样品变化的复杂情况。结果对AFM-TM微悬臂梁外部激励参数选择、非线性系统复杂动力学特性分析和混沌运动控制提供有意义的理论参考。To address the issue of measurement accuracy in atomic force microscope in tapping mode(AFM-TM) caused by the chaotic motion of the AFM-TM cantilever beam system,this study focused on analyzing the dynamic characteristics and control algorithm of the system.Through numerical simulation,the Lyapunov index,bifurcation diagram,Poincaré cross section,and phase diagram were used to analyze the evolution of the motion characteristics of AFM-TM microcantilever beam system when the external excitation amplitude changes.The delayed feedback control and fuzzy adaptive delayed feedback were proposed to control the chaotic motion of the system.Finally,the two control algorithms were compared.The results showed that the system exhibited obvious chaotic motion characteristics when the dimensionless external excitation amplitude was within the range of values such as [0.65,0.85].Both the time-delay feedback control and the fuzzy adaptive time-delay feedback control could effectively pull the chaotic motion of the system back to the periodic orbit,but the fuzzy adaptive time-delay feedback was more suitable for the complex situation of the change of the AFM-TM sample.The research results provide a significant theoretical reference for selecting external excitation parameters of AFM-TM microcantilever beams,analyzing complex dynamic characteristics of nonlinear systems and controlling chaotic motion.

关 键 词：几何量计量 轻敲式原子力显微镜 微悬臂梁 混沌运动 延时反馈控制 模糊控制 

分 类 号：TB92[一般工业技术—计量学]