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Multimodal analysis of force spectroscopy based on a transfer function study of micro-cantilevers

机译:基于微悬臂梁传递函数研究的力谱多峰分析

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摘要

Quantitative force spectroscopy experiments require a comprehensive knowledge of the frequency response characteristics of the micro-cantilever. To establish a generic theoretical model an analytical mathematical description of the cantilever dynamics in force spectroscopy was developed using a transfer function approach. This study allows for quantitative evaluation of force spectroscopy experiments and analysis of stability and controllability of an atomic force microscope (AFM). The model accounts for the dynamic characteristics of the extended cantilever beam and for elastic sample properties. The system dynamics were investigated using an exact system-theoretic approach. The step and frequency responses are given for force spectroscopy experiments in different experimental configurations. The transfer function approach used in this study allows us to investigate very significant dynamic aspects that simple first mode approximations cannot capture. Only extended beam models account for both poles and zeros of the transfer function and can thus reproduce important features that are related to the zero dynamics. These features include pole-zero cancellations or non-minimum phase response. The possibility of non-minimum phase response in AFM is highly important for the design of inverse filters. The presence of zeros in the right half of the Laplace plane immediately implies that the inverse system is unstable.
机译:定量力谱实验需要对微悬臂梁的频率响应特性有全面的了解。为了建立通用的理论模型,使用传递函数方法开发了力谱中悬臂动力学的解析数学描述。这项研究可以定量评估力光谱实验,并分析原子力显微镜(AFM)的稳定性和可控性。该模型考虑了扩展悬臂梁的动态特性以及弹性样品的特性。使用精确的系统理论方法研究了系统动力学。给出了在不同实验配置下进行力谱实验的阶跃和频率响应。本研究中使用的传递函数方法使我们能够研究非常重要的动态方面,而简单的第一模式近似无法捕获这些动态方面。只有扩展的光束模型同时考虑了传递函数的极点和零点,因此可以重现与零动力学有关的重要特征。这些功能包括零极点消除或非最小相位响应。 AFM中非最小相位响应的可能性对于逆滤波器的设计非常重要。拉普拉斯平面的右半部分中零的存在​​立即暗示该逆系统是不稳定的。

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