A Generalized Prandtl-Ishlinskii Model for Characterizing Rate Dependent Hysteresis

A generalized Prandtl-Ishlinskii model is proposed for characterizing the rate dependent hysteresis. A rate dependent play and stop operators are formulated and integrated to the Prandtl-Ishlinskii model together with a rate dependent density function to predict hysteresis properties as a function of rate of change of the input. The fundamental properties of the proposed rate dependent play and stop operators are evaluated and discussed. Experimental data obtained for a piezoceramic actuator under excitations in a wide frequency range (1-500 Hz) are analyzed to demonstrate rate dependence of the hysteretic responses. The validity of the proposed model is illustrated by comparing simulation results with the measured data over a wide frequency range. The comparisons suggest that the proposed rate dependent operator and density functions allow for accurate prediction of the rate dependent hysteresis under dynamically varying inputs.