Fixed-time Disturbance Observer-Based Terminal Sliding Mode Control for Manipulators with a Novel Reaching Law (June 2024)

In this paper, a fast terminal sliding mode control strategy based on a novel reaching law and fixed-time disturbance observer is proposed to improve the tracking performance of robot manipulators in the presence of disturbance. Firstly, aiming at the problems of chattering and slow convergence rate of traditional reaching laws, a novel variable exponential power reaching law is designed to adaptively change the convergence rate according to the system’s initial state, and its characteristic of finite time convergence is analyzed as well. Secondly, a fixed-time disturbance observer is constructed to approximate the lumped disturbance and realize online compensation for the controller. Thirdly, to solve the problems of singularity and slow convergence rate associated with the traditional terminal sliding mode surface, a fast non-singular terminal sliding mode surface is proposed, which guarantees the tracking error converges to zero in a finite time. Finally, a fast non-singular terminal sliding mode tracking controller for the manipulator is designed, and the system stability is proved by the Lyapunov theorem. Moreover, a large number of simulation experiments are carried out to verify the validity and superiority of the proposed controller.