Aircraft trajectory planning is affected by various uncertainties. Among them, those in weather prediction have a large impact on the aircraft dynamics. Trajectory planning that assumes a deterministic weather scenario can cause significant performance degradation and constraint violation if the actual weather conditions are significantly different from the assumed ones. The present study proposes a fundamental framework to plan four-dimensional optimal descent trajectories that are robust against uncertainties in weather-prediction data. To model the nature of the uncertainties, we utilize the Global Ensemble Forecast System, which provides a set of weather scenarios, also referred to as members. A robust trajectory planning problem is constructed based on the robust optimal control theory, which simultaneously considers a set of trajectories for each of the weather scenarios while minimizing the expected value of the overall operational costs. We validate the proposed planning algorithm with a numerical simulation, assuming an arrival route to Leipzig/Halle Airport in Germany. Comparison between the robust and the inappropriately-controlled trajectories shows the proposed robust planning strategy can prevent deteriorated costs and infeasible trajectories that violate operational constraints. The simulation results also confirm that the planning can deal with a wide range of cost-index and required-time-of-arrival settings, which help the operators to determine the best values for these parameters. The framework we propose is in a generic form, and therefore it can be applied to a wide range of scenario settings.
The increasing influence of current research in air traffic management on daily flight operations leads to a stronger consideration of individually optimized aircraft trajectories. However, in the dichotomy between ecological, economic, and safety-based optimization goals, four-dimensionally optimized trajectories are subject to severe constraints in terms of position and speed. To fully assess the performance envelope of these trajectories, precise modelling of the influence of secondary control surfaces on flight performance is necessary. In particular, the use of speed brakes can significantly influence the descent and speed profile and allows the implementation of different cost indices. In this study, we present a modelling approach of the influence of extended speed brakes on flight performance and apply this method in a simulation environment for trajectory modelling of twelve different aircraft types. In doing so, we can determine an almost linear influence of the additional fuel requirement from the effective area of the speed brakes. The results can be implemented in any flight performance model and enable more precise modelling of future aircraft trajectories. Specifically, optimization targets regarding the required time of arrival, or the cost index and the consideration of the dynamic impact of atmospheric conditions in the trajectory optimization, only becomes possible through the calculation of the influence of the speed brake on lift and drag.
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