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3D刚体摆为一个刚体在重力、扰动和控制力或力矩的作用下绕一个固定、无摩擦的支点旋转,具有三个转动自由度的刚体摆模型.针对3D刚体摆姿态稳定的非线性控制设计问题,给出基于欧拉四元数描述的3D刚体摆的姿态运动方程,证明了系统满足无源性条件,构造了系统的Lyapunov函数,利用能量法设计出3D刚体摆的姿态控制律,并由LaSalle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刚体摆在悬垂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.
3D rigid body pendulum is a rigid body pendulum model with three rotational degrees of freedom, which is rotated by a fixed, frictionless fulcrum under the action of gravity, disturbance and control force or moment. The nonlinear control design Problem is solved. The equations of motion of the rigid body are given based on the Eulerian quaternions. The system is proved to be passive, the Lyapunov function of the system is constructed, and the attitude control law of 3D rigid body pendulum is designed by energy method. The asymptotic stability of the control law is proved by the LaSalle invariant set theory.The simulation results show the asymptotic stability of the attitude and angular velocity of 3D rigid body in suspension equilibrium position.The simulation results show that the 3D rigid body swing based on energy method Gesture control is effective.