Experimental model inverse-based hysteresis compensation on a piezoelectric actuator

This paper presents a comparison of several open-loop methods for hysteresis compensation on a lab-made micro-/nanopositioning device. The classical Preisach model with the inverse multiplicative structure, and the Classical/Modified Prandtl-Ishlinskii models with model inversion, are considered. The classical Preisach method though suited for asymmetric hysteresis, does not have an analytic inverse model. However, it can be used directly in the inverse multiplicative structure, thus avoiding the computationally intensive numerical inversion of the Preisach model. The classical Prandtl-Ishlinskii (PI) model is accurate and has an analytic solution, which makes it interesting for real-time applications. However, the model captures only the symmetrical hysteresis curves. Modified Prandtl-Ishlinskii (MPI) model has all of the advantages of the classical PI model and extends it for asymmetric hysteresis. The considered methods are compared experimentally, and illustrative results are given for tracking triangular references of different frequencies.