System Modeling of an AFM System in Z-axis

Motivated by increasing the scanning performance of the atomic force microscope (AFM), many efforts have been made to analyze the system behavior of an AFM system, mainly in Z-axis, and then to develop more advanced controllers. However, most of the previously derived models involve complex physical or mathematical analysis, and many parameters need to be identified for actual application. In this paper, an empirical model is obtained for the Z-axis dynamics of an AFM system by utilizing experimental data. Specifically, the model consists of a dynamical component and multiple static gains. As introduced in the paper, the N4SID algorithm is first employed to derive the dynamical part based on input-output data. Then the static gains of the piezo-actuator are calibrated experimentally. It can be seen from the experimental data that the main source of time delay in Z-axis is the finite retraction/protraction velocity of the piezo-actuator.