Adaptive Finite-Time Backstepping Sliding Mode Control for PMSM System With Backlash

The rapid tracking stabilization problem of the servo system with gear backlash and unmatched unknown disturbance is investigated. In this article, a novel finite-time sliding mode surface with a faster convergence rate is proposed to improve the anti-interference of the gear transmission servo system. This surface not only can adaptively and dynamically regulate the integral capability together with disturbances and tracking error variations, but also does not create singularity issues. An adaptive fixed-time reaching law (AFTRL) is proposed, which performs a faster convergence rate and chattering-free performances. The adaptive mechanism ensures the continuous property of the control output and dynamically regulates the fixed-time convergence rate regardless of initial states. The dSPACE platform is employed to validate the excellent tracking performance of the gear transmission servo system.