Fixed-time composite anti-disturbance control for flexible-link manipulators based on disturbance observer

In this paper, a novel fixed-time composite anti-disturbance control framework is proposed for n-degrees of freedom (n-DOF) flexible-link manipulator systems with modelling uncertainties and external disturbances. The aim is to ensure that the considered system achieves suppression of elastic vibrations while tracking time-varying trajectories. First, based on the singular perturbation theory, the nonlinear coupled system is decomposed into a slow subsystem and a fast subsystem. Second, a disturbance observer based on the super-twisting algorithm is designed to estimate multiple disturbances within a fixed time, and then the fixed-time tracking control scheme for the slow subsystem is developed by means of the designed observer. For fast dynamics, a barrier Lyapunov function is introduced to implement the fixed-time vibration suppression control scheme. The fixed-time stability of the tracking error system is demonstrated via the Lyapunov function method. Finally, simulation results of two-link flexible manipulator systems verify that the proposed control algorithm can improve the tracking speed and precision.