Rate-Dependent Hysteresis Modeling and Hybrid Inverse Compensation Control for Piezoelectric Actuators

Area of Science:

• Mechanical Engineering
• Control Systems Engineering
• Materials Science

Background:

• Piezoelectric ceramic actuators are crucial for precision micro-motion systems.
• Their accuracy is compromised by hysteresis and residual disturbances.
• Existing linearization methods are insufficient for high-precision applications.

Purpose of the Study:

• To develop an integrated modeling and control framework for piezoelectric actuators.
• To enhance accuracy by addressing rate-dependent hysteresis and disturbances.
• To achieve a balance between model precision, computational efficiency, and robust control.

Main Methods:

• A polynomial model with explicit rising/falling branches and frequency-dependent coefficients was developed.
• Direct inverse feedforward compensation and disturbance-observer-based adaptive sliding-mode feedback were combined.
• A multilayer piezoelectric stack coupled to an electrical-mechanical-sensing plant was modeled.
• Branch-state logic resolved multivalued inverse mapping; a seventh-order model was selected.

Main Results:

• The proposed branch model reduced static fitting error from 4.50-6.21% to 1.28-2.58%.
• Direct inverse compensation decreased linearity error from 8.56-13.88% to 0.53-1.024%.
• The hybrid controller achieved a 1% settling time of 8.6 ms and minimal tracking error (0.0051 µm).

Conclusions:

• The developed framework offers a significant improvement in piezoelectric actuator precision.
• It provides an embedded-oriented solution balancing model accuracy and computational simplicity.
• The results demonstrate robust closed-loop precision for micro-motion applications.