Designing nonlinear observer for topography estimation in trolling mode atomic force microscopy

In this study, a nonlinear observer for high-speed estimation of the sample surface topography in a small duration of the probe transient motion utilizing a 2DOF model of TR-AFM is proposed. Since the time duration to reach the steady-state periodic motion of the oscillating probe in conventional imaging methods is relatively high, the proposed nonlinear observer in this research is able to address this limitation and estimate the surface topography throughout transient oscillation of the microcantilever. With this aim, topography estimation process utilizing a Thau observer without any linearization of the system dynamics is designed and coupled with the system dynamics to achieve sample topography. The stability of the proposed observer coupled with controller is verified by the Lyapunov stability theorem for the first time, and hence, linearization of the model is not required. Simulation results demonstrate the feasibility of the presented approach to estimate different sample heights with high accuracy and a relatively high scanning speed. Additionally, the effects of measurement noise and horizontal nanoneedle tip displacement on the performance of proposed technique are investigated.