Data-driven based cross-coupling compensation method for the piezoelectric tube scanner of atomic force microscopes

In this work, a data-driven based cross-coupling compensation (DD-CCC) method is proposed to suppress the cross-coupling effect of the scanner in atomic force microscopy (AFM). Firstly, the phase difference method is employed to accurately estimate the frequencies, amplitudes and phases of the harmonic components of the periodic compensation signal obtained from the fractional model-free repetitive control with the nonsynchronized sampling. Afterwards, the compensation signal is constructed analytically via summing the harmonic components, which requires very little memory units. In AFM scanning, the constructed compensation signal is applied in a feedforward manner, which is combined with a baseline tracking controller to follow the desired staircase trajectories. A series of scanning and imaging tests are conducted on an AFM with a fixed sampling frequency and different scanning rates. The results demonstrate that high performance AFM scanning and imaging can be achieved under the scanning rate of 120 Hz with the DD-CCC method.