Fixed/Predefined-Time Parameter Estimation for Magnetostrictive Actuated Positioning System

This article introduces new fixed-time and predefined-time parameter estimation approaches for micro/nano positioning systems driven by magnetostrictive actuators, i.e., magnetostrictive actuated positioning systems (MAPS), which have inherent hysteresis nonlinearity. First, a generalized Prandtl–Ishlinskii (GPI) model is used to describe the hysteretic dynamics, which can be incorporated into the system model. By implementing a K-filter operation, an integrated parametric model that depends on the input/output information is constructed, such that the assumption of fully known system states and the use of unmeasured intermediate hysteresis variable for parameter estimation can be avoided. Furthermore, a new parameter estimation algorithm using a modified error variable dedicated to mitigating the influence of regression is presented, which guarantees that the estimation error can converge to zero within a fixed-time independent of the initial conditions. Finally, a further tailored adaptive law is presented, which ensures the convergence within a user-set predetermined-time to further improve the estimation performance and facilitate the parameter adjustment. The feasibility of the proposed approaches is demonstrated through simulations and experiments.