An adaptive fractional-order logarithmic sliding mode control for linear motor system with backlash-like hysteresis and actuator saturation

This paper develops a novel Adaptive Fractional Order Logarithmic Sliding Mode Control (AFOLSMC) scheme for permanent magnet linear motor (PMLM) systems subjected to nonlinear backlash-like hysteresis, actuator saturation, and severe dynamic uncertainties encompassing periodic/nonperiodic disturbances as well as unmodeled dynamics. Compared with conventional sliding mode control (SMC) methodologies, the proposed AFOLSMC features six prominent design innovations: a dedicated fractional-order logarithmic function structure to achieve high-precision tracking and fast finite-time convergence; an innovative fuzzy neural network approximation module for handling unknown friction dynamics; tailored adaptive control laws to attenuate heterogeneous disturbances separately; a specialized compensation mechanism for backlash-like hysteresis nonlinearity; an auxiliary anti-saturation system to tackle input saturation constraints; and a robust feedback control term to compensate for residual approximation errors. Extensive simulation results validate that the proposed AFOLSMC exhibits strong robustness against input saturation and dynamic uncertainties, delivers superior transient and steady-state control performance with rapid response and high accuracy, and guarantees markedly alleviated chattering behavior in the closed-loop system.