Optimal take-off trajectories in the presence of windshear View Full Text


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Article Info

DATE

1986-04

AUTHORS

A. Miele, T. Wang, W. W. Melvin

ABSTRACT

This paper is concerned with optimal flight trajectories in the presence of windshear. With particular reference to take-off, eight fundamental optimization problems [Problems (P1)–(P8)] are formulated under the assumptions that the power setting is held at the maximum value and that the airplane is controlled through the angle of attack.Problems (P1)–(P3) are least-square problems of the Bolza type. Problems (P4)–(P8) are minimax problems of the Chebyshev type, which can be converted into Bolza problems through suitable transformations. These problems are solved employing the dual sequential gradient-restoration algorithm (DSGRA) for optimal control problems.Numerical results are obtained for a large number of combinations of performance indexes, boundary conditions, windshear models, and windshear intensities. However, for the sake of brevity, the presentation of this paper is restricted to Problem (P6), minimax ∣Δh∣, and Problem (P7), minimax ∣Δγ∣. Inequality constraints are imposed on the angle of attack and the time derivative of the angle of attack.The following conclusions are reached: (i) optimal trajectories are considerably superior to constant-angle-of-attack trajectories; (ii) optimal trajectories achieve minimum velocity at about the time when the windshear ends; (iii) optimal trajectories can be found which transfer an aircraft from a quasi-steady condition to a quasi-steady condition through a windshear; (iv) as the boundary conditions are relaxed, a higher final altitude can be achieved, albeit at the expense of a considerable velocity loss; (v) among the optimal trajectories investigated, those solving Problem (P7) are to be preferred, because the altitude distribution exhibits a monotonic behavior; in addition, for boundary conditions BC2 and BC3, the peak angle of attack is below the maximum permissible value; (vi) moderate windshears and relatively severe windshears are survivable employing an optimized flight strategy; however, extremely severe windshears are not survivable, even employing an optimized flight strategy; and (vii) the sequential gradient-restoration algorithm (SGRA), employed in its dual form (DSGRA), has proven to be a powerful algorithm for solving the problem of the optimal flight trajectories in a windshear. More... »

PAGES

1-45

References to SciGraph publications

  • 1982-09. Numerical solution of minimax problems of optimal control, part 1 in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1970-04. Sequential gradient-restoration algorithm for optimal control problems in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1982-09. Numerical solution of minimax problems of optimal control, part 2 in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1975-12. Recent advances in gradient algorithms for optimal control problems in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1986-07. Guidance strategies for near-optimum take-off performance in a windshear in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1980-09. A property of an autonomous minimax optimal control problem in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1974-02. Sequential gradient-restoration algorithm for optimal control problems with nondifferential constraints in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1978-11. Sequential gradient-restoration algorithm for optimal control problems with general boundary conditions in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1985. Minimax Optimal Control and Its Application to the Reentry of a Space Glider in RECENT ADVANCES IN THE AEROSPACE SCIENCES
  • 1979-07. A minimax optimal control problem in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1981. The Calculus of Variations and Optimal Control, An Introduction in NONE
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    http://scigraph.springernature.com/pub.10.1007/bf00939246

    DOI

    http://dx.doi.org/10.1007/bf00939246

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