Output feedback robust adaptive controller design for dynamic atomic force microscopy

This paper analyzes the dynamics of amplitude modulation atomic force microscope (AM-AFM) which is the mostly employed mode in current AFMs. A reduced model is proposed to approximate the function of tip-sample separation to oscillation amplitude. Considering the fact that the model parameters vary with different combinations of piezo-scanner and cantilever as well as the measured sample, a robust adaptive controller is designed to reduce the system regulation error. Specifically, by using the K-filter, an observer is designed firstly for this output feedback problem. Based on this observer, we design a robust adaptive controller consisting of two parts: an adaptive component is used to deal with the unknown parameters, while the model uncertainty and system disturbance are accounted for by a robust control part. With the aid of Lyapunov technique, the stability of this control method is guaranteed and GUUB result is obtained. Additionally, the attractive region is analyzed particularly in the case of measurement saturation which usually occurs in dynamic AFM mode. To verify its effectiveness, some simulation results are included to show the performance of the proposed control strategy.