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Smart actuators, such as magnetorestrictive actuators, shape memory alloy (SMA) actuators, and piezoceramic actuators, generally exhibit symmetric and asymmetric hysteresis loops. In this paper, a generalized Prandtl-Ishlinskii model with an asymmetric play operator is utilized for describing asymmetric hysteresis nonlinearities in smart actuators. Furthermore, a corresponding inverse of the asymmetric Prandtl-Ishlinskii model is presented as a compensator for the purpose of removing the hysteresis effects in the control systems. Such a compensation is experimentally illustrated by a piezoceramic actuator.