Nonlinear Controller Design for High Speed Dynamic Atomic Force Microscope System

Abstract

In this study, the performances of conventionally used PI controller and a nonlinear H∞ controller, are compared in the state-of-the-art High-Speed Dynamic Atomic Force Microscope (HS-AFM). The state-of-the-art HS-AFM system is modeled via MATLAB/ SIMULINK for four different cantilevers, i.e., small high-frequency and regular lowfrequency cantilevers used in air and liquid environments. For the modeled system, PI and H∞ controllers are designed and implemented by using both analytical methods and toolboxes available in MATLAB. Simulations are performed in ideal condition, and under exogenous effects such as noise, disturbance and parametric uncertainty. In ideal condition, achieved maximum frame rate, and the percentage of topography acquisition error with two controllers are calculated for each cantilever. Also, performances of controllers in the system are tested under exogenous effects. It is observed that with the H∞ controller, the topography of the selected sample can be obtained with up to 2 times less acquisition error. It is also observed that PI controller is better in disturbance rejection, but H∞ controller is more robust under the effect of noise. For each cantilever, similar results to the ideal condition is obtained in case of uncertainty. Most distinctive results are obtained with high-frequency cantilevers, as H∞ controller enables a 2 times higher frame rate (14.3 fps) compared to the PI controller (7.1 fps) with the same level of acquisition error in the state-of-the-art HS-AFM operated in liquid environment.