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

Abstract

A generalized Prandtl–Ishlinskii model is proposed for characterizing the rate-dependenthysteresis behavior of smart actuators. A rate-dependent play operator is formulated andintegrated to the Prandtl–Ishlinskii model together with a dynamic density function topredict 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 thePrandtl–Ishlinskii model. The fundamental properties of the proposed rate-dependentoperator are systematically provided, which conform with important effects of the time rateof input on the hysteresis output established from the reported experimental data.Additional laboratory experiments were performed to characterize the rate-dependenthysteresis 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 generalizedmodel. The comparisons suggest that the proposed rate-dependent operator and densityfunctions allow for prediction of the rate-dependent hysteresis under dynamically varyinginputs. From the simulation results attained under varied dynamic inputs, it isshown that the proposed model can predict both major and minor hysteresisloops, and that the hysteresis increases significantly with increasing frequency.