Optimization and acceleration guidance of flight trajectories in a windshear

Abstract

This paper is concerned with guidance strategies for near-optimum performance in a windshear. The takeoff problem is considered with reference to flight in a vertical plane. In addition to the horizontal shear, the presence of a downdraft is assumed. First, trajectories for optimum performance in a windshear are determined for different windshear models and intensities. Use is made of the methods of optimal control theory in conjunction with the dual sequential gradient-restoration algorithm (DSGRA) for optimal control problems. In this approach, global information on the wind flowfield is needed. Then, guidance strategies for near-optimum performance in a windshear are developed, starting from the optimal trajectories. Specifically, an acceleration guidance scheme based on the relative acceleration is presented in both analytical and feedback control forms. In this approach, local information on the wind flowfield is needed. Numerical experiments show that the acceleration guidance scheme produces trajectories that are quite close to the optimum trajectories. In addition, the near-optimum trajectories are superior to the trajectories arising from alternative guidance schemes. An important characteristic of the acceleration guidance scheme is its simplicity. Indeed, this guidance scheme is implementable if local information on the windshear, the downdraft, and the state of the aircraft is available. ARL-acceleration of gravity, ft s~2 --altitude, ft s gain coefficient = lift force, Ib s mass, Ib ft -1 s 2 = reference surface, ft 2 = thrust force, Ib = relative velocity, ft s" 1 = absolute velocity, ft s" 1 = mg = weight, Ib = wind velocity, ft s~l = /*-cpmponent of wind velocity, ft s" 1 -^-component of wind velocity, ft s" 1 = horizontal distance, ft -relative angle of attack, rad = absolute angle of attack, rad = engine power setting = relative path inclination, rad = absolute path inclination, rad = thrust inclination, rad = pitch attitude angle, rad = air density, Ib ft" 4 s 2

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