Adaptive Fractional‐Order Nonsingular Fast Terminal Sliding Mode Control for Manipulators

Abstract

When the manipulator system is subject to unknown disturbance, in order to improve the tracking accuracy of the manipulator, this paper designs a fractional-order nonsingular fast terminal sliding mode (FONFTSM) controller. The controller is divided into three parts. First of all, in order to improve the performance of the sliding stage, this paper designs a FONFTSM surface. By introducing a fractional-order operator, the convergence speed and accuracy of the system state are effectively improved. Secondly, in view of the problems of large chattering and slow convergence speed in the reaching stage, this paper designs a variable exponential power-reaching law (VEPRL), which has the ability to change the exponential coefficients according to the system state adaptively. At the same time, an adaptive law is designed to adjust the coefficients of the reaching law adaptively, which enhances the robustness of the control system. Finally, a disturbance observer is used to estimate the unknown external disturbance in real time so as to perform feedforward compensation for the control system, which effectively improves the accuracy of the manipulator control system. The stability of the manipulator control system is proved by the Lyapunov function. Simultaneously, the controller designed in this paper is compared with different controllers, which proves that the controller designed in this paper has strong robustness, high control accuracy, and fast convergence speed.

Adaptive super‐twisting algorithm‐based fractional‐order sliding mode control of redundantly actuated cable driving parallel robot with uncertainty and disturbance estimation

“…Definition 1 [38,39]. The Riemann-Liouville (R-L) fractional derivative of the function f (t ) from t 0 to t is given as where j is a positive integer, 𝛼 is the fractional order, and satisfying j − 1 ≤ 𝛼 < j , Γ( j − 𝛼) = ∫ ∞ 0 t j −𝛼−1 e −t dt is the gamma function.…”

“…Definition 2 ( [38,39]). The R-L fractional integration of function f (t ) from t 0 to t is given as…”

“…Property 1. ( [38,39]). The R-L fractional derivative symbol D 𝛼 t 0 ,t f (t ) commutes with d k ∕dt k and can be described as…”