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In this paper, a robust adaptive fuzzy proportional-derivative inverse dynamics decoupling control scheme with fuzzy-based linear extended state observer (FLESO) is presented and applied to the trajectory tracking control of a two degree-of-freedom (2-DOF) spherical motion mechanism (SMM). The dynamics of the SMM has the characteristics of multivariable nonlinearity, uncertainties and strong coupling. Uncertainties like the modeling errors and external disturbances affect the tracking performance, and coupling increases the difficulty of controller design and reduces the tracking precision. Therefore, a novel hybrid control scheme that is composed of a fuzzy proportional-derivative (FPD) feedback control with varying gains, inverse dynamic model-based feed-forward decoupling term, FLESO with varying bandwidth, and robust term is developed. The novel control strategy combines the advantages of simplicity and easy design of the FPD control, the effectiveness of the FLESO to handle the modeling errors and external disturbances, and the robustness of the robust term to estimation errors of the FLESO. First, introduce the structure of the SMM and establish the dynamic model. Second, the feed-forward decoupling principle is derived based on the inverse dynamic model. Then the FPD control with two-inputs and two-outputs is designed, whose rule base is derived by the phase plane method. The linear extended state observer is designed, whose bandwidth is tuned via the fuzzy logic system. Furthermore, the asymptotic stability of the proposed controller is proved by the Lyapunov theorem. Finally, the high tracking performance of the proposed controller is validated via both simulation and experiment results.

A Robust Fuzzy PD Inverse Dynamics Decoupling Control of Spherical Motion Mechanism With Fuzzy Linear Extended State Observer