Development of the rate-dependent Prandtl–Ishlinskii model for smart actuators

A generalized Prandtl–Ishlinskii model is proposed for characterizing the rate-dependent hysteresis behavior of smart actuators. A rate-dependent play operator is formulated and integrated to the Prandtl–Ishlinskii model together with a dynamic density function to predict hysteresis properties as a function of the rate of change of the input. Relaxation functions are further proposed to relax the congruency in the output of the Prandtl–Ishlinskii model. The fundamental properties of the proposed rate-dependent operator are systematically provided, which conform with important effects of the time rate of input on the hysteresis output established from the reported experimental data. Additional laboratory experiments were performed to characterize the rate-dependent hysteresis behavior of a PZT actuator under excitation in the 1–500 Hz frequency range. The measured data were used to demonstrate the validity of the proposed generalized model. The comparisons suggest that the proposed rate-dependent operator and density functions allow for prediction of the rate-dependent hysteresis under dynamically varying inputs. From the simulation results attained under varied dynamic inputs, it is shown that the proposed model can predict both major and minor hysteresis loops, and that the hysteresis increases significantly with increasing frequency.