A generalized Stress-Dependent Prandtl-Ishlinskii model and its adaptive inverse compensation with model reference for GMA

Giant Magnetostrictive Actuator (GMA) show strong stress-dependent hysteresis nonlinearity. A generalized Stress-Dependent Prandtl-Ishlinskii (GSDPI) model is formulated to characterize the stress-dependent effects of giant magnetostrictive actuator. In this model, a generalized play operator is proposed and integrated with stress-dependent weights to construct stress-dependent hysteresis model for GMA. Good agreements are shown between model simulation results and measured hysteresis loops. The analytical inversion of proposed model is given and employed in a control scheme, which combines inverse compensation with model reference control to control linear systems preceded by unknown stress-dependent hysteresis. By deriving the relationship between the tracking error of the system and parameters error of GSDPI, then an adaptive update law of parameters of model can be developed to ensure the tracking error asymptotically converges to zero. Simulation results validate the effectiveness of the proposed approach.