基于Legendre伪谱法的3D刚体摆姿态轨迹跟踪控制

Trajectory Tracking Control of 3D Rigid Body Pendulum Attitude Based on Legendre Pseudospectral Method

研究3D刚体摆在有初始扰动情况下的姿态运动最优控制问题。结合3D刚体摆转动的姿态与角速度特点,针对外部扰动设计闭环反馈姿态跟踪控制器。首先,利用Legendre伪谱法规划出3D刚体摆开环的姿态运动轨迹。然后,将系统的运动方程线性化,并以3D刚体摆的实际运动姿态轨迹与参考运动姿态轨迹之间的差值作为控制量,将姿态跟踪问题转换为线性时变系统的姿态调节问题。最后,对基于Legendre伪谱法的3D刚体摆姿态最优控制的闭环控制方法进行仿真分析,验证在具有初始扰动情况下算法的有效性。

The optimal control of the attitude motion of 3D rigid pendulum with initial disturbance is investigated. Combined with the characteristics of the attitude and angular velocity of the 3D rigid pendulum, the closed-loop feedback attitude tracking controller is designed for the external disturbance. Firstly, 3D rigid pendulum attitude trajectory is designed for open loop by use of Legendre pseudospectra method. Then the system＇s motion equation is linearized, and the difference between the attitude reference trajectory and actual trajectory motion in 3D rigid pendulum is considered as control variable. Attitude tracking problem is converted to linear time-varying systems attitude regulation problem. Finally, the closed-loop control based on the Legendre pseudospectral method is simulated and analyzed for the optimal control of 3D rigid pendulum, and simulations show that the effectiveness in the case of initial disturbance.