Hierarchical non-singular terminal sliding mode controller for a single link flexible joint robot manipulator

This paper studies the control motion of a single link flexible joint robot by using a hierarchical non-singular terminal sliding mode controller (HNTSMC). In comparison to the conventional sliding mode controller (CSMC), the proposed algorithm (NTSMC) not only can conserve characteristics of the convention CSMC, such as easy implementation, guaranteed stability and good robustness against system uncertainties and external disturbances, but also can ensure a faster convergence rate of the systems states to zero in a finite time and singularity free. The flexible joint robot (FJR) is a two degree of freedom (2DOF) nonlinear and underactuated system. The system here is modeled as a fourth order system by using Lagrangian method. Based on the modeling dynamics, the system is decomposed hierarchically into two-second order subsystems, namely, a rigid body and a flexible subsystem. In the first level, the sliding manifold for each subsystem is designed based on the NTS surfaces. Then, in the second level, the total sliding surface is constructed as the linear combination of NTS surfaces of two subsystems. Thereafter, a HNTSM control is obtained based on Lyapunov theorem to drive both subsystems to their equilibrium points in the finite time. Simulation results demonstrate the effectiveness of proposed scheme (HNTSMC) over (HCSMC).