Improving Atomic Force Microscopy Imaging by a Direct Inverse Asymmetric PI Hysteresis Model

Dong Wang,Lianqing Liu,Zaili Dong,Wen Li,Lei Zhou,Ho-Yin Chan,Feifei Wang,Peng Yu

doi:10.3390/s150203409

Abstract

A modified Prandtl–Ishlinskii (PI) model, referred to as a direct inverse asymmetric PI (DIAPI) model in this paper, was implemented to reduce the displacement error between a predicted model and the actual trajectory of a piezoelectric actuator which is commonly found in AFM systems. Due to the nonlinearity of the piezoelectric actuator, the standard symmetric PI model cannot precisely describe the asymmetric motion of the actuator. In order to improve the accuracy of AFM scans, two series of slope parameters were introduced in the PI model to describe both the voltage-increase-loop (trace) and voltage-decrease-loop (retrace). A feedforward controller based on the DIAPI model was implemented to compensate hysteresis. Performance of the DIAPI model and the feedforward controller were validated by scanning micro-lenses and standard silicon grating using a custom-built AFM.

Highlights

The atomic force microscope (AFM) is a powerful tool for nanoscale imaging and manipulation [1,2]
Several methods have been proposed to compensate the hysteresis effect. They can be generally classified into two categories: (1) feedback control; and (2) model-based feedforward control
To characterize and compensate asymmetric hysteresis without increasing model complexity, we describe in this paper our work on developing an inverse asymmetric PI (API) hysteresis model with different slope parameters in trace and retrace branches

Summary

Introduction

The atomic force microscope (AFM) is a powerful tool for nanoscale imaging and manipulation [1,2]. In an AFM, piezoelectric materials are often used as nanopositioning actuators to drive a scanning probe because of their high resolution capabilities and fast response time [3]. The inherent nonlinearities in piezoelectric actuators, especially the hysteresis [4], will lead to displacement errors in horizontal direction in AFM scanning images [5]. Several methods have been proposed to compensate the hysteresis effect. They can be generally classified into two categories: (1) feedback control; and (2) model-based feedforward control. As for model-based feedforward control, it improves performance without incurring the stability problems associated with feedback design. The challenges associated with model-based feedforward control are model accuracy and computational complexity [8]

Methods

Results

Conclusion