Spline adaptive filter with fractional-order adaptive strategy for nonlinear model identification of magnetostrictive actuator

The spline adaptive filter (SAF) is recently proposed to identify wiener-type nonlinear systems, which consists of an infinite impulse response filter followed by an adaptable look-up table and interpolated by a local low-order polynomial spline curve. To improve the performance of magnetostrictive actuator (MA), SAF is introduced to identify the hysteresis model of MA in this paper. In addition, a direct approach that is convenient to implement to derive the inverse model directly from experimental data is proposed to decrease the difficulty of obtaining the accurate inverse model. In order to improve the identification accuracy, a variable order fractional-order least mean square (VO-FLMS) algorithm is formulated for SAF by exploiting the fractional calculus concepts in parameters adaptation mechanism. VO-FLMS dynamically adapts the order of the fractional derivative based on the error power to achieve faster convergence rate with smaller steady-state error than least mean square algorithm and modified fractional-order least mean square algorithm. Simulation results confirm the effectiveness of SAF with VO-FLMS for nonlinear system identification. In particular, VO-FLMS can adapt nonlinearity better than other compared algorithms. Moreover, the hysteresis model and direct inverse model of MA can be precisely identified online by the proposed method in the experiments.