Modeling Major and Minor Hysteresis Loops in Galfenol-Driven Micro-Positioning Actuators Using a Memory-Based Hysteresis Framework

Abstract

This article presents a memory-based hysteresis modeling framework which uses a mathematical mapping technique for accurate prediction of major and minor hysteresis loops in Galfenol-driven actuators. The model is based on three properties of hysteretic materials which have been recently established for piezoelectric actuators. These properties are: targeting of turning points, curve alignment and the wiping-out effect. To describe the anhysteretic behavior of the actuator, we initially separate the nonlinearity of the hysteretic response from the hysteresis looping effect and approximate it with a piecewise exponential function. This function is then utilized in a nonlinear mapping procedure, where it is mapped between consequent turning points recorded in the model’s memory unit. This mapping requires two constant shaping parameters for the ascending and two for the descending trajectories. To assess the performance of the proposed model and for experimental verification, a Galfenol-driven micro-positioning cantilever actuator is utilized. The results indicate that the model is able to precisely predict the response of the actuator for its full-range motion including both major and minor hysteresis loops. The maximum error percentage and the average error between the experiment and the model for a 120 μm stroke are 1.5% and 435 nm, respectively. With using only 14 coefficients, the proposed framework not only offers a precise model, but also a computationally efficient algorithm to quantify the hysteresis response of Galfenol-driven actuators.