Nonlinear Modeling of a Piezoelectric Actuator-Driven High-Speed Atomic Force Microscope Scanner Using a Variant DenseNet-Type Neural Network

Piezoelectric actuators (PEAs) are extensively used for scanning and positioning in scanning probe microscopy (SPM) due to their high precision, simple construction, and fast response. However, there are significant challenges for instrument designers due to their nonlinear properties. Nonlinear properties make precise and accurate control difficult in cases where position feedback sensors cannot be employed. However, the performance of PEA-driven scanners can be significantly improved without position feedback sensors if an accurate mathematical model with low computational costs is applied to reduce hysteresis and other nonlinear effects. Various methods have been proposed for modeling PEAs, but most of them have limitations in terms of their accuracy and computational efficiencies. In this research, we propose a variant DenseNet-type neural network (NN) model for modeling PEAs in an AFM scanner where position feedback sensors are not available. To improve the performance of this model, the mapping of the forward and backward directions is carried out separately. The experimental results successfully demonstrate the efficacy of the proposed model by reducing the relative root-mean-square (RMS) error to less than 0.1%.