Optimal Control Framework for Cruise Economy Mode of Flight Management Systems

摘要

The main contribution of this paper is to propose optimal and suboptimal control solutions to the cruise economy mode problem in a flight management system for flights below the drag divergence Mach number. The problem is formulated as an optimization of a functional that trades off the fuel and time-related costs of a flight using a (crew-supplied) cost index CI. A novel approach is proposed based on solving the problem analytically using a combination of Pontryagin's maximum principle and the Hamilton-Jacobi-Belhnan equation. A suboptimal analytical solution for the true airspeed is obtained in state feedback form, which reduces to the well-known optimal solution for maximum range when the cost index vanishes. An analytical solution for the speed target as a function of the cost index gives physical insight, allows one to analytically compute sensitivities, and eliminates the need to have a performance database to store the optimal speed schedules in the system. An extension shows that the approach is valid when the aircraft is turning with a small bank angle. Overall, this work provides not only a very efficient means of implementing the optimal speed schedules in an onboard flight management system for flights below the divergence Mach number, but also extends the theory of aircraft performance to the more general case based on a nonzero cost index. The new results are compared with flight simulation data for an A320 Airbus aircraft.