Inverse compensation error of the Prandtl-Ishlinskii model

Compensation of hysteresis nonlinearity of smart actuators through applications of an inverse hysteresis model generally yields errors when coupled with a plant. In this study, the resulting compensation error is analytically derived considering the Prandtl-Ishlinskii model and its inverse, which has not yet been reported. The proposed analytical error formulation could be conveniently applied in controller design for effective hysteresis compensation and thereby enhanced tracking performance of the smart material actuators. The initial loading curve and its inverse are presented for formulation of the estimated Prandtl-Ishlinskii model for describing hysteresis nonlinearity of a smart actuator and its inverse. The compensation error is subsequently derived analytically from composition of the Prandtl-Ishlinskii model with its inverse based on the inverse of initial loading curve. The properties of the compensation error are further illustrated, which also exhibits hysteresis nonlinearity that can be further characterized by a Prandtl-Ishlinskii model. The integration of the proposed analytical error model with the composition resulted in only negligible hysteresis compensation error. The simulation results suggest that a significantly improved tracking performance can be achieved in the closed-loop control system using the proposed analytical error model.