Adaptive Fixed-time Backstepping SMC for Gear Transmission System with Backlash

In this paper, an adaptive fixed-time backstepping sliding mode control (AFTBSMC) method is proposed for gear transmission system with gear backlash and mismatched disturbances. First, an adaptive fixed-time sliding mode surface and an adaptive fixed-time reaching law are proposed so that the system state converges to a domain near the origin in a fixed time. Second, a backstepping control scheme is designed to solve the higher-order state equations of the gear transmission system. Meanwhile, the adaptive estimation is used to deal with the problem of mismatched disturbances, and through the advantage of fixed-time stability, AFBSMC makes it possible to make the closed-loop system can be guaranteed to be rapid and robust without being affected by the initial state of the system. Finally, the effectiveness of AFBSMC is verified on the dSPACE gearbox physical platform.