Real-time control of aircraft take-off in windshear. Part I: Aircraft model and control schemes

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In this paper, the problem of aircraft control during take-off in the presence of windshears is considered. The paper consists of two parts. In the first part, a pointmass model of a generic modern regional jet aircraft flying in a vertical plane is described. It is assumed that the autopilot manages the angle of attack and the power setting. The influence of wind is unpredictable. Autopilot's control is designed in the following way. The time interval of the process is divided into short time subintervals, and the aircraft dynamics is linearized at the beginning of each subinterval around a straightforward equilibrium trajectory providing a good climb and preventing, whenever possible, the aerodynamic velocity from decreasing. The linearized dynamics is considered on the current time subinterval as a differential game where the first player, autopilot, strives to keep the state of the linearized dynamics close to zero, so that the state vector of the nonlinear dynamics follows, as far as possible, the straightforward equilibrium linearization trajectory. The second player, wind, plays in the linearized dynamics against the autopilot. A feedback control found from the linearized dynamics is used in the nonlinear one on the current time subinterval. Then, the procedure is being repeated for the next time subinterval. It should be noted that a very quick method for approximate solving auxiliary linearized differential games on the time subintervals is used. Thus, the procedure can be implemented as a real-time control scheme. Several variants of control design are proposed, and two microburst models providing wind disturbances are outlined. Numerous simulations of the corresponding aircraft trajectories are given in the second part of the paper.