Optimal take-off trajectories in the presence of windshear
Optimal take-off trajectories in the presence of windshear
复制标题
存在风切变时的最佳起飞轨迹
DOI：
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发表时间：
1986
期刊：
影响因子：
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通讯作者：
W. Melvin
中科院分区：
文献类型：
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作者：
A. Miele;T. Wang;W. Melvin
本文研究在风切变存在时的最佳飞行轨迹。特别是关于起飞，在假定功率设定值保持在最大值和飞机通过迎角控制的情况下，用公式表示了八个基本的最优化问题[问题（P1）-（P8）]，问题（P1）-（P3）是Bolza型的最小二乘问题。问题（P4）-（P8）是切比雪夫型的极大极小问题，通过适当的变换可以将其转化为Bolza问题。采用最优控制问题的双序贯梯度恢复算法（DSGRA）求解这些问题，得到了大量性能指标、边界条件、风切变模式和风切变强度组合的数值结果。然而，为了简洁起见，本文的介绍仅限于问题（P6），minimax <$Δh <$和问题（P7），minimax <$Δγ <$。通过对迎角和迎角对时间的导数进行不等式约束，得到如下结论：（1）最优轨迹明显上级常迎角轨迹，（2）最优轨迹在风切变结束时达到最小速度，（3）最优轨迹在风切变结束时达到最小速度，（4）最优轨迹在风切变结束时达到最小速度，（5）最优轨迹在风切变结束时达到最小速度。（iii）可找出最佳的飞行轨迹，使飞机在风切变下由准定常状态转为准定常状态;（iv）当边界条件放宽时，可以获得更高的最终高度，尽管代价是相当大的速度损失;（v）在所研究的最佳轨迹中，解决问题（P7）的那些轨迹是优选的，因为高度分布表现出单调行为;此外，对于边界条件BC 2和BC 3，最大迎角低于最大允许值;（vi）采用优化的飞行策略，中等风切变和相对严重的风切变是可以生存的;但是，即使采用优化的飞行策略，极端严重的风切变也是不能生存的;和（vii）序列梯度恢复算法（SGRA），采用其对偶形式（DSGRA），已被证明是求解风切变中最佳飞行轨迹问题的一种强有力的算法。
This paper is concerned with optimal flight trajectories in the presence of windshear. With particular reference to take-off, eight fundamental optimization problems [Problems (P1)–(P8)] are formulated under the assumptions that the power setting is held at the maximum value and that the airplane is controlled through the angle of attack.Problems (P1)–(P3) are least-square problems of the Bolza type. Problems (P4)–(P8) are minimax problems of the Chebyshev type, which can be converted into Bolza problems through suitable transformations. These problems are solved employing the dual sequential gradient-restoration algorithm (DSGRA) for optimal control problems.Numerical results are obtained for a large number of combinations of performance indexes, boundary conditions, windshear models, and windshear intensities. However, for the sake of brevity, the presentation of this paper is restricted to Problem (P6), minimax ∣Δh∣, and Problem (P7), minimax ∣Δγ∣. Inequality constraints are imposed on the angle of attack and the time derivative of the angle of attack.The following conclusions are reached: (i) optimal trajectories are considerably superior to constant-angle-of-attack trajectories; (ii) optimal trajectories achieve minimum velocity at about the time when the windshear ends; (iii) optimal trajectories can be found which transfer an aircraft from a quasi-steady condition to a quasi-steady condition through a windshear; (iv) as the boundary conditions are relaxed, a higher final altitude can be achieved, albeit at the expense of a considerable velocity loss; (v) among the optimal trajectories investigated, those solving Problem (P7) are to be preferred, because the altitude distribution exhibits a monotonic behavior; in addition, for boundary conditions BC2 and BC3, the peak angle of attack is below the maximum permissible value; (vi) moderate windshears and relatively severe windshears are survivable employing an optimized flight strategy; however, extremely severe windshears are not survivable, even employing an optimized flight strategy; and (vii) the sequential gradient-restoration algorithm (SGRA), employed in its dual form (DSGRA), has proven to be a powerful algorithm for solving the problem of the optimal flight trajectories in a windshear.