A precision-drive hysteresis model with an equal-density weight function for GMA feedforward compensation

Giant magnetostrictive actuators (GMAs) are a widely used type of micro-nano actuator, and they are greatly significant in the field of precision engineering. The accuracy of a GMA often depends on its hysteresis model. However, existing models have some limitations, including the difficulty of identifying their parameters and the tradeoff between the quantity of modeling data required and the level of precision achieved. To solve these problems, in this paper, we propose a Preisach inverse model based on equal-density segmentation of the weight function (E-Preisach). The weight function used to calculate the displacement is first discretized. Then, to obtain a finer weight distribution, the discretized geometric units are uniformly divided by area. This can further minimize the output displacement span, and it produces a higher-precision hysteresis model. The process of parameter identification is made easier by this approach, which also resolves the difficulty of obtaining high precision using a small amount of modeling data. The Preisach and the E-Preisach inverse models were investigated and compared using experiments. At frequencies of 1 and 5 Hz, it was found that the E-Preisach inverse model decreases the maximum error of the feedforward compensation open-loop control to within 1 µm and decreases the root-mean-square error in displacement to within 0.5 µm without the need to increase the number of measured hysteresis loops. As a result, the E-Preisach inverse model streamlines the structure of the model and requires fewer parameters for modeling. This provides a high-precision modeling method using a small amount of modeling data; it will have applications in precision engineering fields such as active vibration damping and ultra-precision machining.