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The flexible joint robot (FJR) typically experiences parametric variations, nonlinearities, underactuation, noise propagation, and external disturbances which seriously degrade the FJR tracking. This article proposes an adaptive integral sliding mode controller (AISMC) based on a singular perturbation method and two state observers for the FJR to achieve high performance. First, the underactuated FJR is modeled into two simple second-order fast and slow subsystems by using Olfati transformation and singular perturbation method, which handles underactuation while reducing noise amplification. Then, the AISMC is proposed to effectively accomplish the desired tracking performance, in which the integral sliding surface is designed to reduce chattering based on two-state observers with no requirements of the velocity and acceleration measurements in the FJR system. Furthermore, an adaptive laws for switching gains are proposed for both slow and fast subsystems in the FJR to remove the requirements of knowing the up-bound of the disturbances and uncertainties. The closed loop stability of not only slow and fast subsystems but also the overall FJR is proved using the Lyapunov theorem. Finally, the simulation and experimental results demonstrate the superiority of proposed control in terms of less tracking error, significant noise suppression, and strong robustness in comparison with existing controllers.
Khan et al. (Mon,) studied this question.