Model reference control with adaptive inverse compensation for systems preceded by stress-dependent hysteresis of GMA

Giant Magnetostrictive Actuator (GMA) has been used in precise position, active vibration control with characteristics of large output force and displacement. Hysteresis nonlinearity is main drawback of GMA, which causes undesirable inaccuracies, oscillations, even instability to systems and restricts its potential application. Specially, Stress-Dependent hysteresis is encountered in GMA, which means that the hysteresis nonlinearity of GMA depends on the stress applied on GMA. Several models have been proposed to characterize the stress-dependent hysteresis for GMA. It is challenging to control a system preceded by unknown stress-dependent hysteresis nonlinearity, which motivate interest in developing adaptive control scheme for stress-dependent hysteresis system. This paper presents a control scheme that combines inverse compensation with model reference control to control linear systems preceded by unknown stress-dependent hysteresis. Stress-Dependent Prandtl-Ishlinskii (SDPI) hysteresis model is adopted in this paper to describe the stress-dependent hysteresis of GMA as its analytical inversion. By deriving the relationship between the tracking error of the system and parameters error of SDPI, then an adaptive update law of parameters of model can be developed to ensure the tracking error asymptotically converges to zero.