Characteristics of the direct inverse modeling approach for hysteresis compensation of piezoelectric actuators

Prandtl-Ishlinskii (PI) model is widely utilized in hysteresis modeling and compensation of piezoelectric actuators. For rate-independent hysteresis, the PI model is attractive as its inversion can be analytically obtained and is also of the PI type. However, it has been found that the hysteresis of piezoelectric actuators exhibits strong rate-dependence. Currently, the valid and applicable inversion law for the rate-dependent PI model is not yet available. It has become a common practice of simply replacing all the rate-independent terms in the conventional inversion law with the rate-dependent terms. However, this approximation will suffer from the inherent theoretical modeling error and can only achieve acceptable results at very slow trajectories when the rate-dependence is not noticeable. This paper introduces a new direct inverse modeling approach to obtain the rate-dependent inverse hysteresis model directly from the measured data. As no inversion calculation is involved, this approach is time-efficient and the modeling error can be significantly reduced. Trajectory tracking experiments have been implemented to validate the superiority of the direct inverse modeling approach over the conventional “modeling-inversion” approach.