Atomic force microscope (AFM) is one of the most powerful tools for surface scanning, force measurement, and nano‐manipulation. To improve its performance, vibration and control of AFM micro‐cantilever (MC) should be studied. Hysteresis, as an undesired phenomenon affecting vibration amplitude and phase, is also another important issue to be examined. In this paper, vibration analysis and control of a ZnO non‐uniform multi‐layered piezoelectric MC has been investigated in non‐contact mode. A modified couple stress theory has been used to obtain the strain energy for modeling the MC. In order to control the amplitude, a sliding mode controller (SMC) has been utilized on AFM, due to its application in uncertain and nonlinear systems. For applying the control signal, two methods of piezo and base actuation are studied. The results are compared with proportional integral derivative (PID) control method and it is demonstrated that SMC method reduces the control input close to the surface and increases the accuracy near the surface. In addition to MC control, hysteresis amplitude and phase differences are investigated by applying the Prandtl–Ishlinskii model. Also, surface topography is studied with hysteresis. The simulations show backward phase difference and an increase in amplitude, accordingly.

中文翻译：

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基于改进耦合应力理论的多层非均匀原子力显微镜压电微悬臂梁控制和振动分析

原子力显微镜（AFM）是用于表面扫描，力测量和纳米处理的最强大的工具之一。为了改善其性能，应研究AFM微悬臂梁（MC）的振动和控制。磁滞是影响振动幅度和相位的不良现象，也是要研究的另一个重要问题。本文以非接触模式研究了ZnO非均匀多层压电MC的振动分析和控制。改进的耦合应力理论已被用来获得用于建模MC的应变能。为了控制振幅，由于其在不确定和非线性系统中的应用，已经在AFM上使用了滑模控制器（SMC）。为了施加控制信号，研究了压电和基础致动的两种方法。将结果与比例积分微分（PID）控制方法进行比较，结果表明SMC方法减少了靠近表面的控制输入并提高了靠近表面的精度。除了MC控制外，还通过应用Prandtl–Ishlinskii模型研究了磁滞幅度和相位差。而且，表面形貌具有滞后性。仿真显示了反向相位差并相应地增加了幅度。