摘要
3D刚体摆是研究地球静止轨道航天器的一个力学简化模型,它绕一个固定、无摩擦的支点旋转,具有3个转动自由度.文章给出基于修正型罗德里格斯(Rodrigues)参数描述的3D刚体摆的姿态动力学方程,针对3D刚体摆姿态和角速度稳定的非线性控制设计问题,基于无源性控制理论利用能量法设计了3D刚体摆的系统控制器,并证明了系统满足无源性.构造了系统的李雅普诺夫(Lyapunov)函数,利用能量法设计出3D刚体摆的姿态控制律,并由拉萨尔(La Salle)不变集原理证明了该控制律的渐近稳定性.仿真实验给出了3D刚体摆在倒立平衡位置的姿态和角速度的渐近稳定性,仿真实验结果表明基于能量方法的3D刚体摆姿态控制是有效的.
The 3D rigid pendulum is a simplified mechanical model of the GEO(Geostationary) stationary spacecraft,and it is a rigid body with three rotational degrees of freedom, connected with a fixed pivot without consideration of the friction. The attitude dynamics equations of the 3D rigid pendulum based on the modified Rodrigues parameters are derived in this paper. For the 3D rigid pendulum's attitude and angular velocity stability as a nonlinear control design problem, by using the energy method, the system controller is designed based on the passive control theory. It is shown that the system can meet the passive condition. By constructing the system's Lyapunov function, the attitude control law of the 3D rigid pendulum is obtained by using the energy method, and the La Salle invariant principle is used to prove the asymptotic stability of the control law.The simulation results show that the attitude and angular velocity are asymptotically stable in the case of the inverted equilibrium and the simulation results verify the reliability of the method.
出处
《力学与实践》
北大核心
2015年第3期361-366,共6页
Mechanics in Engineering
基金
国家自然科学基金资助项目(11472058)
