刚体卫星相平面控制闭环系统稳定性分析

摘要： 针对航天器姿态控制系统相平面控制的稳定性分析这一难题，本文提出一种简化相平面控制律，并选取刚体卫星作为被控对象，研究闭环控制系统的稳定性.利用相平面分析方法对闭环系统轨线进行定量估计，证明闭环控制系统存在特定的稳态区域，并给出该稳态区域的计算公式.采用相平面分析方法定量估计闭环系统轨线的思想，证明当控制律参数满足适当条件时，从任意初值状态出发的闭环控制系统轨线都可以在有限时间内到达稳态区域，并且一直保持在稳态区域中，从而证明闭环控制系统的全局一致最终有界性.推导出闭环控制系统的轨线从初值状态到达稳态区域所用时间的估算公式.仿真验证了结果的有效性.

Stability Analysis of the Closed Loop System of a Phase Plane Controlled Rigid Satellite

Abstract：Considering the problem of stability analysis of the satellite attitude system controlled by a phase plane controller, a simplified phase plane control method is proposed, and then the stability of the rigid satellite attitude system under the proposed controller is investigated in detail. By estimating the closed loop system’s trajectories with the phase plane analysis method, the existence of a stable region of the closed loop system is proved, which satisfies certain properties. The formula to determine the stable region is derived in terms of control parameters. Under certain conditions, it is proved that the trajectories can reach the stable region in finite time from any initial value. Therefore, the sufficient condition is obtained to guarantee the globally uniformly ultimate boundedness of the closed loop system. In addition, the formula to estimate the reach time is provided. Simulations are provided to illustrate the effectiveness of proposed formulas and methods.