Adaptive Fractional-order Non-singular Fast Terminal Sliding Mode Control Based on Fixed Time Observer

Abstract

Aiming at the problem of low tracking accuracy of the manipulator in the presence of model parameter errors and external disturbance, this paper proposes an adaptive fractional-order non-singular fast terminal sliding mode (AFONFTSM) controller based on a fixed-time disturbance observer (FTDO). The controller is split into three portions. First, a fractional-order non-singular fast terminal sliding mode (FONFTSM) surface is designed to improve the tracking accuracy and convergence speed of the error state. Second, to enhance the performance of the system state in the approaching mode, an adaptive variable exponential power reaching law (AVEPRL) is designed, which changes the coefficient of the exponential term through the size of the system state. Meanwhile, adaptive control is used to modulate one item of the reaching law, which improves the anti-interference of the system. In the end, the real-time estimation of the external disturbance is carried out by the FTDO, which solves the problem that the magnitude of the external disturbance is difficult to be determined in the actual engineering. And the stability is verified by the Lyapunov theory. The simulation results display that the controller raised in this paper has better tracking precision, faster convergence speed, and stronger robustness.