Observer-Based Finite-Time Adaptive Motion Control for Nonlinear Asymmetric Hysteresis Systems in Pure-Feedback Form

This study focused on finite-time adaptive motion control for nonlinear pure-feedback systems subject to unknown asymmetric hysteresis and immeasurable states. Accordingly, a finite-time output-feedback dynamic surface control algorithm based on the inverse hysteresis compensator was developed. A fuzzy state observer was utilized to estimate the immeasurable states. A rate-dependent asymmetric Prandtl–Ishlinskii model-based direct inverse compensator was developed to overcome the actuator hysteresis behavior. The finite-time command filter was designed to avoid the “differential explosion” problem due to the repetitive derivatives of the virtual control law. The finite-time compensated signals were designed to eliminate the filtering errors caused by the command filters. The proposed control strategy ensured that all signals in the closed-loop system were finite-time bounded. The effectiveness of the investigated method was demonstrated on the piezoelectric micro-positioning stage, which is a mechanical system with unknown actuator rate-dependent asymmetric hysteresis.