Rate-Dependent Modeling and <inline-formula> <tex-math notation="LaTeX">$\text{H}_{\mathrm {\infty }}$ </tex-math></inline-formula> Robust Control of GMA Based on Hammerstein Model With Preisach Operator

Abstract

In this brief, a new Hammerstein model is proposed for a rate-dependent hysteresis in giant magnetostrictive actuators (GMAs). A Preisach operator and an autoregressive model with exogenous input are used to represent, respectively, the static nonlinear function and the linear dynamic subsystem of this model. It is shown that the proposed model can satisfactorily describe the hysteresis of a GMA within a frequency range of 0–100 Hz. Based on this model, a 2 DOF control scheme with an $\text{H}_{\infty }$ robust controller combined with an inverse compensator is proposed for real-time trajectory tracking. The proposed control scheme can maintain system stability and tracking performance in the presence of system uncertainties and external disturbances. The simulation and experimental results show that the proposed model and the corresponding control scheme can significantly improve the performance of the rate-dependent hysteresis system.