High-Precision Position Tracking Control of Giant Magnetostrictive Actuators Using Fractional-Order Sliding Mode Control with Inverse Prandtl-Ishlinskii Compensator

Giant magnetostrictive actuators (GMAs) are increasingly being applied in ultra-precision motion platforms due to its high energy density, fast response and high displacement resolution. However, due to the inherent hysteresis nonlinearity of giant magnetostrictive materials, high-precision position tracking control of GMAs becomes very challenging. In this paper, a fractional-order sliding mode control (FSMC) strategy based on inverse Prandtl-Ishlinskii (PI) model (FSMC-PI) is proposed for GMAs. The inverse PI model is established to compensate for the hysteresis nonlinearity. Besides, based on the traditional sliding mode control (SMC), the proposed FSMC-PI introduces the fractional calculus term into the sliding surface, which ensures that the state converges to the fractional-order sliding manifold with fast response and small overshoot, and the position tracking performance of GMAs is enhanced. Moreover, as a feedback control method, FSMC can further effectively suppress the uncertainties and external disturbances that the inverse PI model cannot deal with. The stability of FSMC is analyzed and proved according to the Lyapunov Theorem. In addition, a double integrator is connected in series after the FSMC system, which can further improve the dynamic characteristics of the GMA system so as to guarantee the overall position tracking control performance. Finally, experiments are conducted on a GMA system with very low load, and the results demonstrate that the proposed approach can improve the position tracking performance and disturbance suppression capability more effectively, compared with four different control schemes.