Adaptive fractional-order nonsingular terminal sliding mode control for cable-driven serial manipulator

Abstract

This paper proposes a new adaptive fractional-order nonsingular terminal sliding mode control scheme integrated with time delay estimation (AFONTSMC–TDE) for cable-driven manipulators. The proposed AFONTSMC–TDE scheme consists of three key elements: time-delay estimation (TDE), a fractional-order nonsingular terminal sliding mode (FONTSM) manifold, and an adaptive variable-gain reaching law. The TDE utilizes intentionally delayed signals to estimate unknown system dynamics, thereby providing a model-free control framework. The FONTSM manifold ensures fast finite-time convergence while inherently avoiding singularity, and the adaptive reaching law dynamically adjusts control gains to achieve rapid response and effective chattering suppression simultaneously. The tracking error is proved to be uniformly ultimately bounded (UUB) via Lyapunov stability analysis. Finally, the superiorities of the proposed AFONTSMC–TDE scheme are validated through experiments on a cable-driven manipulator, demonstrating significant improvements in tracking accuracy over existing fractional-order sliding mode control methods.