Robust Adaptive Fixed-Time Fast Integral Terminal Sliding Mode Control for PMLSM Position Tracking

Abstract

A robust adaptive fixed-time integral terminal sliding mode control (AFITSMC) method is proposed in this study to solve the problems of the slow convergence, low position-tracking accuracy, and inability to achieve stability within a fixed time of a permanent magnet linear synchronous motor (PMLSM) servo system. First, a dynamical mathematical model of PMLSM is established to describe the thrust and unknown uncertainty in the motion process. Second, a novel sliding mode surface is designed to address the problem of the slow convergence of traditional controllers. In addition, an adaptive law is used to dynamically estimate the lumped uncertain parameters to achieve high position-tracking accuracy, considering the existence of uncertain factors, such as friction, load change, and parameter change in the system, which always decrease position-tracking accuracy. The proposed adaptive control is completely chattering-free, Lipschitz continuous and no gain overestimation exists, which is critical to practical applications under measurement noises. Third, a fixed-time fast integral terminal sliding mode control strategy is proposed in this study, namely, the AFITSMC strategy, to address the problem of traditional controllers' inability to achieve fixed-time convergence. The controller can drive the sliding mode surface near the predefined equilibrium within a fixed time and make it converge within a finite time. Last, experiments are conducted, and the results show that the proposed controller can achieve not only system state convergence within a fixed time but also fast convergence and high position-tracking accuracy. © 2026 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.