Publication Date:
2016-07-19
Description:
This paper proposes an optimal control framework for the climb and descent economy modes of a flight management system (FMS) yielding a solution that can be implemented in real-time flights below the drag divergence Mach number. The problem is formulated as the optimization of a functional that trades off the fuel- and time-related costs of a flight as a function of a (crew-supplied) parameter called the cost index. The work builds on previous research of the authors for the cruise phase and extends it to the climb and descent phases of flight. More specifically, for both climb and descent, it is found that suboptimal solutions can be obtained as the positive real roots of a fifth-degree polynomial lying inside the flight envelope, which can be found using fast-converging algorithms such as Newton's method. The main contributions of this work are threefold. First, the proposed method gives physical insight because there is an analytical expression for each coefficient of the polynomial. Second, this approach eliminates the need to have a performance database in the system, thus making its implementation faster in real-time. Third, the solution exhibits the same behavior of airborne FMS units as a function of the cost index, which is justified in this paper based on Bellman's principle of optimality. This justification is an important theoretical contribution of the paper. A validation of the approximate solution is obtained using the shooting method to compute the optimal trajectories and compare them against the proposed suboptimal solution. Simulation results show that, for an Airbus A320 model and for a Gulfstream-IV aircraft model, the relative error of the suboptimal trajectories when compared to the optimal trajectories is small for climb and descent trajectories, respectively.
Print ISSN:
0018-9251
Electronic ISSN:
1557-9603
Topics:
Electrical Engineering, Measurement and Control Technology
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Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
