Robust Continuous Terminal Sliding Mode Control for Flexible Joint Manipulators With Singular Perturbation

ABSTRACT In many control designs of the flexible joint manipulators (FJMs), the high order derivatives of the system states are required due to under‐actuation, nonlinearities, and uncertainties. However, in practice, there are many noises, including the poor resolutions of sensors, which makes the control very challenging. This paper proposes a robust continuous terminal sliding mode control (CTSMC) to improve the tracking performance of the FJMs by using a singular perturbation (SP) and a finite‐time extended state observer (FTESO). First, the SP is used to simplify the fourth‐order FJM into two second‐order slow and fast subsystems, in which the proposed control requires only second‐order derivatives rather than fourth. Second, the FTESO is devised for the slow subsystem to estimate the velocity state and the lumped disturbances of the slow subsystem, and a finite‐time state differentiator (FTSD) is designed to estimate the motor velocity and acceleration. Third, based on the state estimations, two CTSMC schemes are designed for both subsystems not only to ensure the finite‐time convergence of tracking error and fast variable but also to reduce control chattering problem and guarantee a full robustness against noise, system uncertainties, closed‐loop and external disturbances. Finally, the stability proof and the finite‐time convergence of the whole closed‐loop system under the proposed control are rigorously guaranteed using the Lyapunov theory, which are the key contributions of this work. The effectiveness of the proposed scheme is demonstrated through comparative simulations and experiments in the actual FJM system.