Minimum-Cost Cruise at Constant Altitude of Commercial Aircraft Including Wind Effects
Minimum-Cost Cruise at Constant Altitude of Commercial Aircraft Including Wind Effects
复制标题
商用飞机恒定高度的最低成本巡航（包括风效应）
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
D. Rivas
中科院分区：
文献类型：
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作者：
Antonio Franco;D. Rivas
从定义导致节能飞行的最佳飞行程序的角度来看，IRCRAFT轨迹优化是空中交通管理中非常重要的主题。在实践中，航空公司考虑成本指数（CI），并将直接运营成本（DOC）定义为由CI加权的燃料消耗和飞行时间的综合成本。他们的目标是尽量减少DOC。然而，在存在意外风的情况下，飞行时间可能与预定时间相差很大，这导致可以添加到DOC以获得总成本（TC）的到达错误成本。不同的作者研究了最小DOC轨迹[1-6]。在文献[3，5，7]中，最小燃油和固定最终时间的相关问题被分析为最小DOC和自由最终时间的问题（问题是找到相应的自由最终时间DOC最优轨迹在指定时间到达的时间成本）;在文献[8]中，分析了在由最终巡航和下降段形成的场景中错误建模的风的影响。在[9，10]中分析了最小成本飞行的问题，不仅考虑DOC，而且考虑到达错误成本，考虑了机组人员加班成本，乘客不满成本和由于错过连接而造成的损失等因素。在本文中，分析了在强风存在时，在恒定高度上的最小费用巡航问题，包括到达误差费用，考虑了一般的非定常问题，飞机质量可变，巡航高度没有任何限制。主要目标是分析导致最小成本的最佳轨迹，定义为最佳速度定律（速度作为飞机质量的函数）。分析是用奇异最优控制理论（见[11]）进行的，它具有提供反馈控制律（控制变量是状态变量的函数）的巨大优点，可以直接用来引导飞机沿着最优路径飞行。在本文中，初始速度和最终速度是给定的，因此最优控制是bang-singular-bang型的，最优路径由一个奇异弧和两个连接奇异弧与给定的初始点和最终点的最小/最大推力弧形成（见[6，12]）。在以前有关恒定高度最佳巡航的工作中[13，14]，只研究了奇异弧;因此，除了考虑到达误差代价和包括风效应（平均水平风）之外，现在讨论最佳问题的更一般的公式。在对最小TC问题的分析中，到达误差成本取决于实际飞行时间和计划飞行时间之间的差异，并且它被定义为正值，因此迟到和早到都受到惩罚（目标是实现高到达时间精度）。它将被证明，对于某些值的参数的问题，最小成本时，获得的最终时间与预定的到达时间相一致，也就是说，当到达误差成本为零。这种临界情况实际上是一个具有固定最终时间的问题。结果是一个模型的波音767- 300 ER。
A IRCRAFT trajectory optimization is a subject of great importance in air traffic management from the point of view of defining optimal flight procedures that lead to energy-efficient flights. In practice, the airlines consider a cost index (CI) and define the direct operating cost (DOC) as the combined cost of fuel consumed and flight time weighted by the CI. Their goal is to minimize the DOC. However, in the presence of unexpected winds, the flight timemay differ considerably from the scheduled time, which leads to an arrival-error cost that can be added to the DOC to obtain the total cost (TC). Minimum-DOC trajectories have been studied by different authors [1–6]. The related problem of minimum fuel with fixed final time has been analyzed as a minimum-DOC problem with free final time in [3,5,7] (the problem is to find the time cost for which the corresponding free final time DOC-optimal trajectory arrives at the assigned time); this same problem is addressed in [8], analyzing the effects of mismodeled winds in a scenario formed by the final cruise and descent segments. The problem of minimum-cost flight, considering not only the DOC but also the arrival-error cost, is analyzed in [9,10], taking into account factors such as crew overtime cost, passenger dissatisfaction cost, and losses due to missed connections. In this Note, the problem of minimum-cost cruise at constant altitude in the presence of strong winds, including the arrival-error cost, is analyzed, considering the general unsteady problem, with variable aircraft mass, and without any restriction on cruise altitude. The main objective is to analyze the optimal trajectories that lead to minimum cost, defined as optimal speed laws (speed as a function of aircraft mass). The analysis is made using the theory of singular optimal control (see [11]), which has the great advantage of providing feedback control laws (control variables as functions of the state variables) that can be directly used to guide the aircraft along the optimal path. These optimal control laws are analyzed as well. In this work, the initial and final speeds are given, so that the optimal control is of the bang-singular-bang type, and the optimal paths are formed by a singular arc and two minimum/maximumthrust arcs joining the singular arc with the given initial and final points (see [6,12]). In previous work related to optimum cruise at constant altitude [13,14], only the singular arc was studied; hence, a more general formulation of the optimal problem is addressed now, apart from considering the arrival-error cost and including wind effects (average horizontal winds). In this analysis of the minimum-TC problem, the arrival-error cost depends on the difference between the actual and the scheduledflight times, and it is defined to be positive, so that both late and early arrivals are penalized (the objective is to achieve high arrival-time accuracy). It will be shown that, for some values of the parameters of the problem, minimum cost is obtained when the final time coincides with the scheduled time of arrival; that is, when the arrival-error cost is zero. This critical case is in fact a problem with fixed final time. Results are presented for a model of a Boeing 767-300ER.