采用修正的Rodrigues参数(MRP),建立了飞行器姿态控制系统的数学模型;利用刚体姿态动力学方程和运动学方程建立了带有转动惯量体坐标系各轴间耦合量的非线性控制系统模型;在镇定控制器设计中,用消去法建立了控制器与Lyapunov函数之间的关系,减少了在迭代算法求解过程中的迭代次数,提出了基于平方和(SOS)方法的一种新的设计方法。仿真结果表明,用这种方法设计镇定控制器简化了设计过程,并且控制器具有较快的响应速度和较好的收敛性。

In this paper, the corrected modified Rodrigues parameter(MRP) was used for building the mathematic model of spacecraft attitude control system; The rigid dynamics equation and kinetics differential equation were used to build up a nonlinear control system model with coupling moment of inertia between the axes of reference frame; In the course of designing stabilizing controller, the relation between controller and Lyapunov function was set up by the expunction method so as to reduce the number of iterative times in calculation process of iterative method. A new design method based on SOS was presented. The simulation results demonstrate the effectiveness and feasibility of the designed controller.