Modeling rate-dependent hysteresis in piezoelectric actuators using T-S fuzzy system based on expanded input space method

•A novel hysteretic operator is proposed to describe the change tendency and extract the dynamic property of rate-dependent hysteresis.•The proposed hysteretic operator is added into the inputs to construct the expanded input space. Thus, it may transform the multi-valued mapping of hysteresis to one-to-one mapping, which enables the T-S fuzzy system to model the hysteresis.•The proposed T-S model can update the parameter online to adapt the variation of operating condition for the rate-dependent hysteresis. Furthermore, this model can be treated as weighted stack of multiple linear systems, which is convenient for controller design. Piezoelectric actuators (PEAs) are favorable choices in the nanopositioning applications due to their high stiffness, fast response and ultrahigh precision. However, the undesired hysteresis nonlinearity in PEAs can dramatically degrade the positioning/tracking performance. In this paper, a Takagi-Sugeno (T-S) fuzzy system-based approach of identification for rate-dependent hysteresis is proposed. First, a novel hysteretic operator is proposed to describe the change tendency and extract the dynamic property of rate-dependent hysteresis. Then, the proposed hysteretic operator is added into the inputs to construct the expanded input space. Thus, it may transform the multi-valued mapping of hysteresis into one-to-one mapping, which enables the T-S fuzzy system to model the hysteresis. Finally, the experimental results are presented to illustrate the potential of the proposed modeling technique.