Improving atomic force microscopy imaging by a direct inverse asymmetric PI hysteresis model

Area of Science:

• Materials Science
• Mechanical Engineering
• Control Systems

Background:

• Piezoelectric actuators in Atomic Force Microscopy (AFM) exhibit nonlinear behavior.
• Standard symmetric Prandtl-Ishlinskii (PI) models struggle to accurately represent the asymmetric motion of these actuators.
• This asymmetry leads to displacement errors, impacting AFM scan precision.

Purpose of the Study:

• To develop and implement a modified PI model, termed the Direct Inverse Asymmetric PI (DIAPI) model.
• To reduce displacement errors in piezoelectric actuators used in AFM systems.
• To enhance the accuracy of AFM scans by compensating for actuator nonlinearity.

Main Methods:

• A modified PI model (DIAPI) was developed, incorporating two series of slope parameters.
• These parameters describe the distinct voltage-increase (trace) and voltage-decrease (retrace) loops of the actuator's motion.
• A feedforward controller based on the DIAPI model was implemented to compensate for hysteresis.

Main Results:

• The DIAPI model effectively addresses the asymmetric motion of piezoelectric actuators.
• The feedforward controller successfully compensated for hysteresis, reducing displacement errors.
• Experimental validation using micro-lenses and silicon gratings demonstrated improved AFM scan accuracy.

Conclusions:

• The DIAPI model offers a significant improvement over standard PI models for piezoelectric actuator control in AFM.
• Accurate modeling of asymmetric hysteresis is crucial for high-precision AFM imaging.
• The developed DIAPI-based feedforward controller enhances the reliability and accuracy of AFM systems.