基于Gauss伪谱法的固体运载火箭上升段轨迹快速优化研究

摘要

研究Gauss伪谱法在多级固体运载火箭上升段轨迹快速优化设计中的应用.针对多级固体运载火箭上升段轨迹优化的特点,研究了求解多阶段最优控制问题的Gauss伪谱法,引入连接点概念处理间断点,设计了边界控制变量计算方法.为进一步提高轨迹优化速度,设计了含初值生成器的Gauss伪谱法串行轨迹优化策略,实现了固体运载火箭上升段轨迹快速优化.仿真结果表明,采用提出的优化方法优化一条上升段轨迹所用时间为2～3分钟,终端约束和路径约束均得到很好满足,算法求解精度高,对初值依赖性小,设计的边界控制变量计算方法可行.%The rapid optimum design of ascent trajectory for a multi-stage solid launch vehicle is researched based on Gauss pseudospectral method ( GPM). The GPM for solving multi-phase optimal control problem is researched, the concept of linkage node is introduced to cope with the discontinuity of trajectory, and the computational method of boundary control variables is designed. In order to further improve the optimization efficiency, the optimization strategy constructing initial value generator for GPM is proposed, and the rapid optimum design of ascent trajectory for the solid launch vehicle is realized. Simulation results show that computational time required for optimizating one trajectory is 2～ 3 minutes in the proposed method, boundary constrains and path constrains are well satisfied , the optimization accuracy is high , the method is not sensitive to the initial value, and the computational method for boundary controls is feasible.