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Fuzzy sliding mode controller design for spacecraft attitude tracking in terms of quaternion

In this paper a fuzzy sliding mode control (FSMC) for spacecraft attitude tracking in terms of quaternion is designed. For this purpose, at first, the spacecraft dynamic and kinematic equations based on quaternion are described. Then, the design procedure of related variable structure controller is presented. To prove the system stability in sliding mode and also to guarantee the convergence of quaternion vectors to desired state, a lemma is presented which is proved by using Lyapunov direct method. In continuation, in order to improve the controller performance, tuning of the sliding mode gain is accomplished by using fuzzy logic approach. Finally, the proposed controller design is simulated on an assumed case study with uncertain parameters and external disturbances. The simulation results are provided to show the effectiveness of the method and its robustness to parameter uncertainties and disturbances.