A Novel Direct Inverse Modeling Approach for Hysteresis Compensation of Piezoelectric Actuator in Feedforward Applications

The Prandtl-Ishlinskii (PI) model is widely utilized in hysteresis modeling and compensation of piezoelectric actuators. For systems with rate-independent hysteresis, the inverse PI model is analytically feasible and it can be adopted as a feedforward compensator for the hysteretic nonlinearity of piezoelectric actuators. However, for the rate-dependent PI model, the applicable valid inversion methodology is not yet available. Although simply replacing all the rate-independent terms in the conventional inversion law with the rate-dependent terms can achieve acceptable results at very slow trajectories. However, a large theoretical modeling error is inevitable at fast trajectories, which is investigated through simulations. This paper proposes a new direct approach to derive the inverse PI model directly from experimental data. As no inversion calculation is involved, the proposed direct approach is efficient and the theoretical modeling error can be avoided. In order to validate the accuracy of the direct approach, a number of experiments have been implemented on a piezo-driven compliant mechanism by utilizing the inverse PI model as a feedforward controller. The tracking performance of the mechanism is significantly improved by the direct approach.