A generalized asymmetric play hysteresis operator for modeling hysteresis nonlinearities of smart actuators

Smart actuators such as shape memory alloy actuators, magnetostrictive actuators, and piezoceramic actuators show different symmetric and asymmetric hysteresis loops. Shape memory alloy actuators and magnetostrictive actuators, as an example, exhibit saturated output at maximum and/or minimum input. In this paper, a generalized Prandtl-Ishlinskii model is formulated to characterize hysteresis nonlinearities of different smart actuators. In this model, a generalized asymmetric play hysteresis operator is proposed and integrated with a density function to characterize different asymmetric hysteresis loops of smart actuators. This modified play hysteresis operator shows the capability to generate minor and major hysteresis loops with varying slopes of ascending and descending input-output curve. Moreover, this operator exhibits saturated major and minor input-output relationships. The capability ability of the proposed model to characterize hysteresis loops of different smart actuators is demonstrated by comparing its output with measured saturated symmetric and asymmetric hysteresis loops of SMA actuators and magnetostrictive actuators.