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.
This work was partially supported by the National Natural Science Foundation of China under Grant Nos. 52105581, U2013211, and 51975375, the China Postdoctoral Science Foundation (No. 2021M692065), and the Open Foundation of the State Key Laboratory of Fluid Power and Mechatronic Systems, China under Grant No. GZKF-202003, and the CDSC Scholarship, University of Newcastle, Australia, awarded to Linlin Li.
- atomic force microscopy
- raster scanning
- tracking control
- repetitive control