Adaptive inverse control of non-linear systems with unknown complex hysteretic non-linearities

This study addresses the problem of inverse hysteretic compensation for a class of uncertain dynamic non-linear systems preceded by unknown hysteretic non-linearities, where the hysteresis is described by Prandtl-Ishlinskii (P-I) model. First, the continuous P-I hysteresis model is decomposed into a discrete P-I operator and a small-bounded error. Then, the inverse discrete P-I operator is constructed to eliminate the hysteresis effects, and the bounded error is estimated by the controller. To avoid the possible chattering caused by the sign function, a smooth robust adaptive controller with the hyperbolic tangent function is designed based on the backstepping technique. The proposed controller ensures the closed-loop system is uniformly ultimately bounded. Finally, the simulation results demonstrate the effectiveness of the proposed scheme..