Robust-Adaptive Finite-Time Sliding Mode Control for Flexible Joint Manipulators Facing Unknown Unbounded Disturbances

This paper addresses the stabilization of flexible joint manipulators (FJMs) under the influence of unknown and unbounded faults, model uncertainties, and external disturbances. To achieve this, the upper bound of model uncertainties and external disturbances is treated as a nonlinear function of the system states with unknown parameters. A novel robust-adaptive finite-time sliding mode controller (RAFSMC) is designed, where the unknown coefficients of the functional upper bound of disturbances are estimated using stable adaptive laws. The RAFSMC enhances the convergence speed of the flexible joints to their desired values, offering a more practical solution for the finite-time control of FJMs, even in scenarios where disturbances may have unbounded amplitudes. Initially, the equations governing the FJM model are segmented into two subsystems, after which the innovative robust-adaptive sliding mode controller is formulated, featuring a third-order finite-time sliding mode surface, a continuous control approach, and stable adaptive laws. The finite-time convergence of the FJM system states to the sliding surface is established, and a new approximation for the sign function is introduced to further reduce chattering. Stability proofs are provided using finite-time Lyapunov theory, and the simulation results, along with comparative analyses presented at the conclusion of the paper, demonstrate the effectiveness of the proposed methodology.