Hysteresis compensation of piezoelectric actuator using direct inverse modeling approach and adaptive projection algorithm

The inherent hysteresis significantly degrades the accuracy of a piezoelectric actuator (PEA). Prandtl-Ishlinskii (PI) model has become popular in the hysteresis modeling and compensation of PEA as the rate-independent PI model is analytically invertible. The inverse PI model, if cascaded in the feedforward loop, acts as the hysteresis compensator. However, for rate-dependent PI models, the inversion calculation remains challenging. Currently, no widely applicable inversion law is available, though few trials were reported. This paper combines the idea of direct inverse hysteresis modeling and the adaptive projection algorithm such that the weights of the backlash operators in the inverse PI model can be directly identified online with no inversion calculation. Since no inversion calculation is involved, the proposed approach is applicable for both rate-dependent and rate-independent PI models. In this paper, two adaptive hysteresis compensators are proposed: one is based on the direct inverse modeling approach and the other based on the model-inversion approach. Simulation results on the trajectory tracking show that the direct inverse approach can achieve better performance.