High Performance Raster Scanning of Atomic Force Microscopy Using Model-free Repetitive Control

The image quality of an atomic force microscope depends on the tracking performance of the lateral X and Y axis positioner. 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, and a slow staircase trajectory in the Y-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 experimen­ tally 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 is combined 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 is demonstrated on a commercially available piezoelectric-actuated scanner. The proposed method reduces the root-mean-square tracking from 191.4 nm in open­ loop or 194.6 nm with PI control, to 2.8 nm with PI+MFRC control at 100 Hz scan rate, which demonstrates the significant improvement achieved by the proposed method.