Suboptimal longitudinal reference trajectory computation for time based continuous descent operations

This paper addresses a specific aspect of air traffic control services, namely the achievement of an orderly and expeditious flow of air traffic under time constrained continuous descent approach. More specifically, a futuristic 4D trajectory application where the air traffic controller will ask an aircraft to overfly a meter fix at a specific time is addressed. The main benefit expected from this application is to improve flight efficiency by more precise maneuvering resulting from on-board capabilities as well as noise abatement and fuel saving. More precise maneuvers are also expected to increase sector capacity. Indeed moving from radar vectoring to monitoring precomputed trajectories would contribute to decrease controller's workload and therefore to increase sector capacity. This paper presents a new methodology to compute a reference trajectory for time based continuous descent operations and focuses on aircraft longitudinal motion including known wind. As far as time constrained operations are assumed, final time as well as final altitude and along track distance to be flown are imposed. We propose a new methodology to compute a reference calibrated airspeed (CAS) and a reference vertical speed to achieve imposed final position and altitude at a prescribed time which solve the Two-point Boundary Value Problem (TPBVP) where initial and final constraints are coupled with the set of ordinary differential equations associated with the aircraft motion. The aircraft is considered as a point mass model. The optimal control problem consists in minimizing fuel consumption while ensuring that the maximum longitudinal and normal accelerations remain lower than the acceptable level for civil flights. The computed trajectory is a time parametrized trajectory which will be used as a reference trajectory by some envisioned tracking controller installed on board the aircraft. Nevertheless the design of the tracking controller is out of the scope of this paper. Numerical simulations using Bada 3.11 9 are provided to illustrate the suboptimal trajectory generation method and achieved results.