无尾舵布局超空泡航行体弹道优化设计

给出了无尾舵布局超空泡航行体在纵垂面内的受力分析及运动方程,建立了变深度机动最优轨迹问题的数学模型。针对空泡扩张与收缩带来的延时效应,提出改进的延时型高斯伪谱法,利用所有高斯节点的运动状态插值获得整个运动过程的状态量,由此得到各个时刻的实时超空泡航行微分方程。通过计算各节点处运动方程约束,对其变深度机动轨迹进行数值求解,得到相应的优化弹道结果及控制策略。对给定布局方案的超空泡航行体下潜机动最优弹道问题进行求解,计算结果表明,采用空化器偏转控制策略,无尾舵布局超空泡航行体可满足运动稳定性与机动性要求,所提出的延时型高斯伪谱法能够处理超空泡航行弹道优化中的延时效应,具有较好的快速收敛性。

Trajectory optimization of planing supported supercavitating flight

Forces and dynamic equations of supercavitating vehicles were analyzed in detail in the paper; the mathematic model of the optimal diving trajectory was established in the vertical plane. Considering the time-delay effect during the expansion and contraction of supercavity, the Time Delay Gauss Pseudospectral Method(TDGPM) was introduced. Based on the information of discretized nodes, the TDGPM interpolated the real time cavity shape for each node and calculated the dynamic equations, which were used as constraints during the optimization process. Numerical solution of optimal diving trajectories and corresponding maneuvers were obtained. Results show that supercavitating vehicles without fins can achieve stable and maneuverable flight by applying proper cavitator control. Results also indicate the feasibility of TDGPM and its fast convergence.