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This article presents a new cascaded extended state observer (CESO)-based sliding-mode control (SMC) for an underactuated flexible joint robot (FJR). The control of the FJR has many challenges, including coupling, underactuation, nonlinearity, uncertainties and external disturbances, and the noise amplification especially in the high-order systems. The proposed control integrates the CESO and SMC, in which the CESO estimates the states and disturbances, and the SMC provides the system robustness to the uncertainty and disturbance estimation errors. First, a dynamic model of the FJR is derived and converted from an underactuated form to a canonical form via the Olfati transformation and a flatness approach, which reduces the complexity of the controller design. Furthermore, by taking the advantage of available measurable states, the CESO is adopted to attenuate the noises and make SMC feasible for high-order systems. Moreover, the CESO estimates the disturbances, which relaxes the upper bound of the disturbance in the SMC and reduces the chattering due to smaller switching gains. A stability analysis of the closed-loop system is presented based on the Lyapunov method. The effectiveness of the proposed control is verified in simulations and experimentally on a real-time FJR system.
Rsetam et al. (Thu,) studied this question.