New Hammerstein Modeling of Hysteresis Characteristics of Giant Magnetostrictive Materials

Giant magnetostrictive material（GMM）, as a new type of functional material, was widely used in energy harvesting, micro displacement driving, precision positioning control and other fields due to its advantages of large magneto mechanical coupling coefficient, fast response speed, and good frequency response characteristics. However, the complex hysteresis nonlinearity of the material affected the positioning accuracy of its actuator. In order to identify the hysteresis nonlinearity in GMM materials, this paper proposed a new Hammerstein model modeling method. The advantage of this method was that the model could better approximate hysteresis nonlinearity, provide higher accuracy, and reduce the workload of parameter identification in the series link. Firstly, an extreme learning machine model was constructed based on hyperbolic functions to represent the static nonlinear part of the new Hammerstein model in the extended space of hysteresis operators. Secondly, the extracted weights and bias parameters of the fully connected layers of the extreme learning machine model was used to construct the state space equation of the dynamic linear part in the new model, which reduced the workload of identifying model parameters in the traditional model with serial links.Finally, a new Hammerstein model was established to describe the hysteresis characteristics of giant magnetostrictive materials. The modeling relative error percentage of the new Hammerstein model is 0. 86% to 3. 69%, and the average absolute error percentage is 2. 63%, which is about 0. 8 μm lower than the root mean square error of the traditional Hammerstein model, and the average absolute percentage error increases 4%.The simulation results demonstrate the effectiveness of the new Hammerstein model in modeling the complex hysteresis characteristics of giant magnetostrictive materials.