基于hp自适应伪谱法的组合动力可重复使用运载器轨迹优化

Trajectory optimization of reusable vehicle with combined power based on hp adaptive pseudospectral algorithm

针对传统化学火箭难以重复使用、发射成本高的问题,提出了一种水平起飞/降落的新一代可重复使用运载器飞行方案,并对其动力模式设计和上升段轨迹优化方法等关键技术进行深入研究。设计了一种涡轮\冲压发动机结合火箭\冲压发动机的组合动力模式,建立了发动机推力与高度、马赫数等变量间的耦合模型,根据动力形式将上升段轨迹分为两段并采用全局搜索法确定动力切换的最佳时机。根据分段结果,分别以燃料最省和终端速度最大为指标,利用hp自适应伪谱法对两段进行轨迹优化设计。该算法基于双层策略求解最优控制问题,兼备伪谱法和有限元法的优点,与打靶法、伪谱法和间接法相比,初值更易选取,收敛速度更快。

In view that traditional chemical rocket is hard to be reused and suffers from high launch cost, a novel flight scheme based on horizontally taking off and landing is proposed, by which a vehicle can be completely reusable.The power mode and the optimization algorithm of the ascend trajectory are designed.A combined power mode of turbo-based combined cycle and rocket-based combined cycle is presented, and the engine model is built based on the relationship between thrust and height/velocity.Then the ascend trajectory is divided into two phases depending on the power mode.A universal searching method is employed to confirm the best opportunity in changing the engine mode, and an hp-adaptive pseudospectral method（HPM） is developed, which takes into account the influences of various constrains and value functions on the results of the universal searching method in different phases.The HPM adopts dual-layer strategy to solve the optimal control problem, and has both the merits of the finite element method and the pseudo-spectral method.The HPM can choose the initial value more easily, and has even faster convergence speed, compared with the shooting method, the pseudo-spectral method and the indirect method.