摘要轻敲式原子力显微镜微(atomic force microscope in tapping mode , 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，发现并控制系统的混沌运动是近年来AFM-TM研究的重点。本文首先通过数值仿真，综合利用Lyapuov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，然后提出了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。研究结果表面，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。研究结果对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了有意义的理论参考。
Abstract：The chaotic motion of the atomic force microscope in tapping mode (AFM-TM) cantilever beam system seriously affects the measurement accuracy of AFM-TM, and the detection and control of the chaotic motion is the focus of AFM-TM research. In this paper, through numerical simulation, the Lyapuov 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 when the dimensionless external excitation amplitude was within the range of values such as [0.65,0.85], the system exhibited obvious chaotic motion characteristics. 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 the selection of external excitation parameters of AFM-TM microcantilever beams, the analysis of complex dynamic characteristics of nonlinear systems and the control of chaotic motion.
2024, Vol. 45 
