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中文摘要：
以3D刚体摆为研究对象，将地球静止轨道（GEO）航天器简化成3D刚体摆，此模型由一刚体绕一个固定且无摩擦的支点旋转且有3个转动自由度，刚体受恒重力（或万有引力）作用。利用滑模结构方法设计了分层滑模控制器，并用Lyapunov稳定性理论、Filippov等效定理与Barbalat引理以及推论，详细证明了该控制律的全局渐近稳定性。仿真实验结果表明，该方法能够有效地实现3D刚体摆悬垂和倒立平衡位置处的姿态渐进稳定性控制。
英文摘要：
The attitude control problem of 3D rigid pendulum is studied in this paper,reducing the model of GEO stationary spacecraft as the 3D rigid pendulum. It consists of a rigid body supported by a fixed and frietionless pivot with three rotational degrees, a constant gravitational force being acted. For nonlinear control design problem of underaetuated 3D rigid pendulum, Lyapunov method, Filippov equivalence theory and Barbalat theory are used to prove global asymptotic stability of the control law. Simulation results show that this method can effectively achieve asymptotic stability control of 3D rigid body pendulum suspended and inverted posture in the equilibrium position.
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