A new continuous fractional-order nonsingular terminal sliding mode control for cable-driven manipulators

Abstract

To ensure satisfactory control performance for the cable-driven manipulators under complex lumped uncertainties, a new continuous fractional-order nonsingular terminal sliding mode (CFONTSM) control scheme based on time delay estimation (TDE) is proposed and studied in this paper. The proposed control scheme contains three elements, a TDE element adopted to suitably cancel out the unknown lumped dynamics with purposely time-delayed signals of the closed-loop control system, a newly proposed FONTSM manifold adopted to realize finite-time convergence in the sliding mode phase and a fast-TSM-type reaching law adopted to ensure finite-time convergence in the reaching phase. The proposed control scheme is model-free and no longer needs system dynamics benefiting from TDE, which is very suitable and easy to use in practical applications. Meanwhile, high precision, fast convergence and good robustness against lumped uncertainties are ensured thanks to the newly proposed FONTSM manifold and adopted fast-TSM-type reaching law. Integrated stability analysis of the closed-loop control system is presented based on Lyapunov stability theory. Finally, the effectiveness of our proposed control scheme is demonstrated by comparative 2-DoFs (degrees-of-freedom) simulation and experiments.