A generalized rate dependent play operator for characterizing asymmetric and symmetric hysteresis nonlinearities

In this paper, a generalized rate dependent Prandtl-Ishlinskii model is proposed to characterize both the symmetric and asymmetric input-output hysteresis, as a function of the time rate of input. The model is realized upon formulation and integration of a generalized rate dependent play operator capable of generating minor as well as major hysteresis loops with varying slopes of ascending and descending input-output curves. A dynamic threshold function is proposed to enhance the prediction of rate-dependent hysteresis nonlinearities. The validity of the generalized model is demonstrated by comparing its displacement responses with the measured symmetric and asymmetric responses obtained for piezoceramic and magnetostrictive actuators under input frequencies of 50- 200 Hz and 10-50 Hz, respectively. The results show the capability of the proposed model to characterize asymmetric and symmetric rate dependent hysteresis nonlinearities in smart actuators.