Optimal Control Based Vertical Trajectory Determination for Continuous Descent Arrival Procedures

Abstract

Continuous descent arrival (CDA) procedures provide time and fuel savings, and reduce the noise impact of aircraft operations near airports. To date, these procedures have been designed to limit the performance envelopes to achieve trajectory commonality. In this paper, the performance bounds of CDA procedure via multiphase optimal vertical trajectory generation problems with respect to two performance indices—flight time and fuel consumption—have been investigated. The optimal CDA vertical profile is first divided into two segments: the cruise segment before the top of descent (TOD) and the descent segment from the TOD. Then, the second segment is further subdivided based on flap setting and speed constraints. Finally, the resulting multiphase optimal control problem is solved using a pseudospectral method. Two different types of aircraft, B737-500 (light) and B767-400 (heavy), are used in a numerical study, and the optimal CDA trajectories of the two types are compared with a typical vertical navigation (VNAV) CDA trajectory used in CDA applications at several airports. Then, the utility of suboptimal VNAV CDA trajectories that can be created with known flight management system (FMS) VNAV descent modes is explored, and thereby enabling onboard calculation in the FMS via the sensitivity analysis that is performed with various wind conditions.