A Comparison of Hysteresis Models with the Hammerstein Structure for Piezoelectric Actuators

Piezoelectric actuators (PEAs) can provide precision motion with fast response dynamics, large mechanical force, and high resolution. However, the strong hysteresis nonlinearity limits its application. In the last decades, lots of efforts on hysteresis cancellation have been made. Recent review articles have already described the progress of different hysteresis modeling and control approaches, but these articles focused mainly on the qualitative analysis of different models. This paper presents a comparison with both qualitative and quantitative analysis of these hysteresis models with the Hammerstein structure, including the differential-based models: a) Bouc-Wen (BW) and b) Asymmetrical BW (ABW) and the operator-based models: a) Prandtl-Ishlinskii (PI), b) PI with delay operators (DPI) and c) PI with polynomial (PPI). This paper presents an intuitive comparison of the characteristics of typical hysteresis models and detailed guidance to build a hysteresis model for the designers.