High performance raster scanning of atomic force microscopy using Model-free Repetitive Control

Abstract

The image quality of an atomic force microscope highly depends on the tracking performance of the lateral X–Y axis scanner. To reduce the requirement for accurate system models, this article describes a method based on Model-free Repetitive Control (MFRC) for high performance control of fast triangular trajectories in the X-axis while simultaneously achieving coupling compensation from the X-axis to Y-axis. The design and stability analysis of the MFRC scheme are presented in detail. The tracking results are experimentally evaluated with a range of different load conditions, showing the efficacy of the method with large variations in plant dynamics. To address the coupling from the X-axis to the Y-axis while tracking the non-periodic staircase trajectories, a pre-learning step is used to generate the compensation signals, which are combined with the baseline Proportional–Integral (PI) control in a feedforward manner in real-time implementations. This approach is also applied to address the problem of longer convergence if needed. Experimental tracking control and coupling compensation are demonstrated on a commercially available piezo-actuated scanner. The proposed method reduces the root-mean-square coupled tracking errors in Y-axis from 191.4 nm in open-loop control or 194.6 nm with PI control, to 2.8 nm with PI+MFRC control at 100 Hz tracking frequency, which demonstrates the significant improvement achieved by the proposed method.