State Feedback Optimal Solution For The Econ Mode Velocity For A Cruising Turbojet

The main contribution of this paper is to propose a two-part approach to determine the optimal state-feedback solution for the cruise economy mode problem of a flight management system for a jet powered aircraft. This is currently an open problem for which analytical solutions are only available for suboptimal speeds. The paper assumes that the aircraft is cruising below its drag divergence Mach number at constant altitude. The problem is formulated as the minimization of a direct operating cost parameterized by a coefficient index which is the ratio of the cost of a unit of time to the cost of a unit of weight of fuel burned. The approach is summarized in an algorithm that can be programmed on a flight management system. By using the methods outlined in this paper and summarized in Algorithm 1, the optimal speed, final weight, final cruising time, and total cost of cruise can be approximated with negligible error. A numerical example of an Airbus A320 will illustrate the proposed algorithm.