Fixed‐time tracking control of manipulators based on a fast variable power reaching law

Abstract

SummaryAs for the problem of trajectory tracking of a two‐joint series manipulator, a novel fixed‐time control scheme is proposed based on non‐singular fast terminal sliding mode (NFTSM) control and a fast variable power reaching law. The innovation of the proposed method is: (1) by employing the NFTSM surface, we solve the singularity problem existed in traditional terminal sliding mode surface. (2) The convergence rate is increased by 50% by the combination of fixed‐time control and NFTSM surface control. (3) A new fast variable power reaching law is presented, which combines the advantages of the double power reaching law and the fast power reaching law, and it effectively improves the reaching rate and reduces the amplitude by 40–60 N m. Theoretical analysis proves that the better tracking performance is obtained, and its convergence time upper limit is not affected by the initial states of the system. Finally, the effectiveness and feasibility of our controller are verified through a numerical simulation.