热率约束下高超声速飞行器Gauss时间网格参数化轨迹规划

Gauss time grid parameterization reentry trajectory planning of hypersonic vehicle under heating rate constraint

中文关键词  高超声速飞行器  轨迹优化  热率约束  非均匀离散  控制向量参数化  飞行路径

英文关键词  hypersonic vehicle (HV)  trajectory optimization  heating rate constraint  nonuniform discretization  control variable parameterization  flight path

中文摘要

      针对热率约束下高超声速飞行器(HV)再入轨迹规划, 提出一种结合光滑化不等式约束处理和非均匀Gauss离散时间网格的改进控制变量参数化(CVP)优化算法. 首先, 结合HV动力学方程和约束条件建立了HV再入轨迹优化问题; 然后, 采用光滑化函数对不等式路径约束进行处理并引入附加状态变量转化进微分方程中; 进一步, 在CVP算法框架下, 给出了基于Gauss分布的时间网格控制参数化策略, 以此改善HV攻角控制精度进而提升HV再入航程; 最后, 在通用航空器模型上进行仿真测试, 验证提出方法的性能并分析不同热率约束限值对最大航程规划的影响. 结果显示, 相较于均匀时间网格参数化CVP–S–P方法, 改进方法再入航程增加320.1 km(提升4.1%), 表明了改进算法的有效性; 同时, 基于本文方法仿真结果, 热率限值降低对HV最大航程减少有限, 当热率限值降低15%时, 最大航程损失仅3.16%, 展示了本文方法对HV热防护设计的理论价值.

英文摘要

      An improved control variable parameterization (CVP) optimization method combining with the inequality path constraints smoothing handling and the nonuniform Gauss discrete time grid is proposed for the hypersonic vehicle (HV) reentry trajectory planning with heating rate constraint. Firstly, the HV reentry trajectory planning optimization problem is established by analyzing the HV dynamic equations and constraint limitations. Next, a smoothing function is employed to handle inequality path constraints and an extra state parameter is introduced to transform them into state equations. Accordingly, a non-uniform Gauss discrete time grid strategy is proposed under the CVP approach frame to improve the angle of attack control precision and the HV reentry downrange. Finally, the simulation tests are carried out on a common aero vehicle to verify the performance of the proposed method and then to analyze the impact of different heating rate constraints on maximal reentry downrange. Test results reveal that the maximal reentry downrange of the proposed method increases by 320.1 km (4.1% improvement) compared with the uniform time grid discretization CVP–S–P method, showing the effectiveness of the improvement. Meanwhile, numerical tests show that the influence of maximal heating rate reduction to downrange is limited, and the results reveal that when heating rate constraint decreases by 15%, maximal downrange only reduces 3.16%, indicating the theoretical value of the proposed method in HV thermal protection system design.