Adaptive LMS Method for Multi-Source Disturbance Rejection in Frictional Rotational Systems

This paper proposes an adaptive LMS framework integrated with phase compensation to address multi-source disturbances in rotational systems dominated by LuGre friction dynamics. The LuGre model's nonlinear characteristics-including presliding hysteresis, Stribeck effects, and stick-slip transitions-induce velocity-dependent disturbances that interact with external periodic disturbances. A adaptive LMS architecture is developed to simultaneously estimate friction-induced oscillations and external harmonic disturbances through parallel adaptive filters. Key innovations include a model-free phase lead compensation mechanism counteracting the combined phase lag from LuGre friction and system dynamics, and a multi-frequency suppression structure resolving disturbance harmonics generated during low-velocity crawling. Simulation tests demonstrate significant reduction in tracking error compared to conventional PID control, with spectral analysis showing effective attenuation of both external disturbances and friction-induced vibrations.