Modelling rate-dependent symmetric and asymmetric hysteresis loops of smart actuators

Abstract

Smart material actuators invariably exhibit hysteresis that may be either symmetric or asymmetric depending upon the actuation principle. Moreover, the shape of hysteresis loop depends on the rate of change of the input. In this study, a generalised rate-dependent Prandtl-Ishlinskii model is proposed to characterise both the symmetric and asymmetric input-output hysteresis effects of smart material-based actuators. The model is realised upon formulation and integration of a generalised rate-dependent play operator. The validity of the generalised model is demonstrated by comparing its displacement responses with the measured symmetric and asymmetric responses obtained for piezoceramic and magnetostrictive actuators under different input frequencies in the 1?200 Hz and 10?100 Hz ranges, respectively. The results suggest that the proposed rate-dependent Prandtl-Ishlinskii model can effectively characterise the symmetric as well asymmetric hysteresis properties of the smart material actuators over a wide range of input frequencies.