Optimal lateral-escape maneuvers for microburst encounters during final approach

Abstract

This paper is concerned with the optimization of lateral-escape trajectories in a microburst wind field for an aircraft on final approach. The objective is to minimize the peak value of altitude drop. An extensive numerical effort has been undertaken to investigate the characteristics of open-loop extremal solutions for various locations of the microburst. When a sufficiently large aerodynamic roll-angle limit is specified and the center of the microburst is not too far offset from the centerline extension of the approach runway, typically three trajectories can be found that satisfy the first-order necessary conditions of optimality for a given set of boundary conditions, namely, a trajectory that passes the microburst center to the left, a trajectory passing the center to the right, and a trajectory passing right through the center. The results bear out that a lateral-escape maneuver, in which an aircraft is turned away from the microburst center, may significantly improve an aircraft's surv ivability, in comparison to an escape maneuver that is restricted to a vertical plane. One of the most striking observations in this study is that, in contrast to nonturning escape maneuvers, lateral-escape maneuvers often exhibit a climb, rather than a descent, in the initial phase. The insight obtained from the present study may help the development of near-optimal lateral-escape guidance strategies for onboard application.

Minimax Optimal Control Analysis of Lateral Escape Maneuvers for Microburst Encounters

“…Obviously, the homotopy chain was started with K 1 D K 2 D 0, which corresponds to the previously established results involving the integral performance measure only. 5 Note that because for any nite value of K 1 there will always be an integral part in the composite performance measure (24), the speci cation of a "pure" Chebyshev performance measure is precluded.…”

“…As in Ref. 5, instantaneous angle of attack and roll angle response have been assumed here. This contrasts with the work of Miele et al, 2¡4 where not only is a bound imposed on the maximum value of the angle of attack but also the rate of change of this variable is limited.…”

“…In Ref. 5 it was noted that instead of the Bolza performance index approximation, it is also possible to apply another transformation technique to solve the original minimax problem. More speci cally, the minimax problem can be reformulated as a standard optimal control problem with state variable inequality constraints.…”

“…Optimal trajectory studies have contributed signi cantly to insight about how to best y an aircraft in a windshear encounter. 1 The pioneering work in this area is due to Miele et al 2¡4 In addition to optimal control studies to improve the takeoff performance during microburst encounters, 2 they also have considered several approach-to-landing cases. 3;4 Upon encountering a microburst in a glideslope approach, the pilot has essentially two options: to abort the landing or to proceed.…”

“…Following Miele's lead, the abort-landing results were later extended to ight in three dimensions, i.e., to optimal trajectories that feature lateral maneuvering. 5 The performance index considered in both Refs. 4 and 5 is of the so-called minimax (or Chebyshev) type.…”