Hysteresis modeling with frequency-separation-based Gaussian process and its application to sinusoidal scanning for fast imaging of atomic force microscope

Rate-dependent hysteresis of the piezoelectric tube scanner (PTS) used in the atomic force microscope (AFM) deteriorates the tracking performance of the PTS and thus causes image distortion of the AFM, especially in high-speed operations. Additionally, the traditional raster pattern scanning technique also limits fast imaging of the AFM. In this work, the frequency-separation-based Gaussian Process (FSGP) is proposed to model the hysteresis of the PTS for sinusoidal scanning. In order to properly describe the rate-dependency of the hysteresis, the training dataset of the model is obtained by exciting the PTS using a sinusoidal chirp signal. So, it contains a large number of datapoints which brings a heavy computational burden. Different from the conventional Gaussian Process (GP) which utilizes the whole training dataset at test-stage, the FSGP separates the training dataset according to the target frequency of the testing reference. Only the optimal subset of the training dataset is selected for making predictions. By this way, the computational efficiency as well as the model accuracy are improved significantly. Without the inversion calculation, an inverse hysteresis compensator (IHC) is directly constructed by using the FSGP. Based on the IHC, open-loop and closed-loop controllers are designed and tested. Experiments are carried out on a commercial AFM. The tracking and imaging results demonstrate the effectiveness and superiority of the FSGP-based modeling and compensation method.