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This paper considers the problem of a three-axis flexible satellite attitude stabilisation subject to the vibration of flexible appendages and external environmental disturbances, which affect the rigid body motion. To solve this problem, a disturbance observer is proposed to estimate and thereby reject the flexible appendage vibration. Based on the H∞ and Linear Matrix Inequality (LMI) approach, a controller for spacecraft with flexible appendages is proposed to ensure robustness as well as attitude stability with high precision. Stability analysis of the overall closed-loop system is provided via the Lyapunov method. The simulation results of three-axis flexible spacecraft demonstrate the robustness and effectiveness of the proposed method.

In this paper, a robust control scheme is proposed for flexible satellite attitude stabilization in the presence of multiple disturbances including the disturbances caused by flexible appendages with the sloshing dynamics of the liquid propellant and external disturbances from space environment. A composite control scheme is designed by combining a composite disturbance observer (CDO) with feed-forward controller. First, a CDO is constructed to estimate the lumped disturbances, where the lumped disturbances in the system are equivalent into two parts: a slow varying disturbance and periodic disturbance.  Then a PD controller is adopted to stabilize the system and restrain the residue disturbance. Finally, the simulation results for flexible satellite verify that the proposed method can make the satellite asymptotically stable and demonstrate the effectiveness of the proposed scheme.