USDE-Based Fast Sliding Mode Control for Magnetostrictive Actuated Positioning Systems With Hysteresis

The inherent hysteresis nonlinearity in the magnetostrictive actuators (MAs) restricts their application in high-precision positioning systems. While direct inverse compensation has been widely used to mitigate hysteresis effects, it suffers from complexities in computing the inverse model, and addressing the residual modeling and compensation errors. In this respect, this paper introduces a composite control strategy to enhance the control performance of magnetostrictive actuated positioning system (MAPS) by presenting a new inverse-based compensator for the hysteresis. The key innovation lies in the derivation of an analytical expression for the inverse compensation error based on a generalized Prandtl-Ishlinskii (GPI) model, and the design of an unknown system dynamics estimator (USDE) to estimate this residual error. The USDE has a simple structure and easy parameter tuning, and can be trivially integrated into the closed-loop control system. Furthermore, a fast reaching law (FRL) is developed to design a composite sliding mode control (SMC), which uses both the inverse-based compensator and the USDE. This control with the FRL can achieve both the enhanced control response and the reduced chattering, compared with the standard SMC techniques. Finally, the effectiveness of the proposed approaches is confirmed by comparative simulations and experiments.