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由于卫星各轴角速度之间是相互耦合的,故当姿态作大角度机动时需要考虑其非线性的动力学特性。此外,表示姿态的运动学微分方程也是非线性的。针对这类非线性系统的控制设计,文章提出了一种采用平方和(SOS)的综合方法。虽然SOS法是一种数值计算的方法,但文中表明设计结果却具有清晰的物理意义。所得的控制律可以视为是非线性版本的PD控制。由于修正Rodrigues参数(MRP)本身特性的关系,控制输入会出现峰值,因而文章提出了一种饱和设计。根据此类姿态系统的无源性本质,可以证明饱和下系统的响应是收敛的。同时,提出了一种利用对角优势的设计思路来减少SOS法的数值误差。SOS法可以求解不容易解析求解的非线性问题,具有广阔的应用前景。
Due to the mutual coupling of the angular velocities of the satellites, it is necessary to consider their nonlinear dynamics when the attitude is maneuvering at high angles. In addition, the kinematic differential equations that represent the pose are also nonlinear. Aiming at the control design of this kind of nonlinear system, this paper presents an integrated method using SOS. Although the SOS method is a numerical method, the text shows that the design results have clear physical meaning. The resulting control law can be considered as a non-linear version of PD control. Due to the nature of the modified Rodrigues parameter (MRP) itself, the peak of the control input appears, so the article presents a saturated design. According to the passive nature of such attitude systems, we can prove that the system response under saturation is convergent. At the same time, a design idea using diagonal advantage is proposed to reduce the numerical error of SOS method. SOS method can solve non-linear problem which is not easy to solve and has broad application prospect.