挠性航天器姿态机动时间最优控制研究

针对挠性航天器单轴姿态快速机动的控制问题,将系统的模型处理成非约束模型,采用极小值原理求解了问题的时间最优控制律,并结合边值条件推导了时间最优控制的切换时间应满足的充要条件.利用切换时间所满足的非线性方程组分析和证明了时间最优控制的对称性及满足的条件:在不考虑阻尼系数时,问题的时间最优控制是机动时间上的对称函数.利用这个规律,对刚体+1阶挠性模态的时间最优姿态机动问题进行了解析求解.针对挠性模态阶次较高时难以求解非线性方程组的问题,将模型离散化,把问题处理成一系列受约束的最小二乘优化问题来求解,数学仿真表明了该方法的有效性.

Time-Optimal Control for Flexible Spacecraft Attitude Maneuver

The problem of single-axis fast attitude maneuver for a flexible spacecraft is considered in this article.By converting the system into unconstrained model and applying the Minimum Principle,the solution for time-optimal control is obtained,while the necessary and sufficient condition for the control-switching time are also established under boundary value conditions.By analyzing the nonlinear equations of the switching time,it is found that if the damping coefficient can be negligible,the control input for time-optimal attitude maneuver will be a symmetrical function of the maneuver time,and the complexity of solving the nonlinear equations could be reduced greatly.Based on this kind of symmetry,an analytic solution for the rigid body with only one flexible mode is obtained.To overcome the difficulty in solving the nonlinear equations with large number of flexible modes,the system is then transformed into a discrete-time model and further simplified to a set of constrained least-squares problems.Finally,numerical simulation is conducted to demonstrate the effectiveness of the method.