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Guidance strategies for near-optimum take-off performance in a windshear

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Abstract

This paper is concerned with guidance strategies for near-optimum performance in a windshear. This is a wind characterized by sharp change in intensity and direction over a relatively small region of space. The take-off problem is considered with reference to flight in a vertical plane.

First, trajectories for optimum performance in a windshear are determined for different windshear models and different windshear 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 flow field is needed.

Then, guidance strategies for near-optimum performance in a wind-shear are developed, starting from the optimal trajectories. Specifically, three guidance schemes are presented: (A) gamma guidance, based on the relative path inclination; (B) theta guidance, based on the pitch attitude angle; and (C) acceleration guidance, based on the relative acceleration. In this approach, local information on the wind flow field is needed.

Next, several alternative schemes are investigated for the sake of completeness, more specifically: (D) constant alpha guidance; (E) constant velocity guidance; (F) constant theta guidance; (G) constant relative path inclination guidance; (H) constant absolute path inclination guidance; and (I) linear altitude distribution guidance.

Numerical experiments show that guidance schemes (A)–(C) produce trajectories which are quite close to the optimum trajectories. In addition, the near-optimum trajectories associated with guidance schemes (A)–(C) are considerably superior to the trajectories arising from the alternative guidance schemes (D)–(I).

An important characteristic of guidance schemes (A)–(C) is their simplicity. Indeed, these guidance schemes are implementable using available instrumentation and/or modification of available instrumentation.

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References

  1. Miele, A., Wang, T., andMelvin, W. W.,Optimal Take-Off Trajectories in the Presence of Windshear, Journal of Optimization Theory and Applications, Vol. 49, No. 1, pp. 1–45, 1986.

    Google Scholar 

  2. Miele, A., Wang, T., andMelvin, W. W.,Guidance Strategies for Near-Optimum Performance in a Windshear, Part 1, Take-Off, Basic Strategies, Rice University, Aero-Astronautics Report No. 201, 1986.

  3. Miele, A., Wang, T., andMelvin, W. W.,Guidance Strategies for Near-Optimum Performance in a Windshear, Part 2, Take-Off, Comparison Strategies, Rice University, Aero-Astronautics Report No. 202, 1986.

  4. Anonymous, N. N.,Low Altitude Windshear and Its Hazard to Aviation, National Academy Press, Washington, DC, 1983.

  5. Miele, A.,Flight Mechanics, Vol. 1, Theory of Flight Paths, Addison-Wesley Publishing Company, Reading, Massachusetts, 1962.

    Google Scholar 

  6. Frost, W., andCrosby, B.,Investigations of Simulated Aircraft Flight through Thunderstorm Outflows, NASA, Contractor Report No. 3052, 1978.

  7. McCarthy, J., Blick, E. F., andBensch, R. R.,Jet Transport Performance in Thunderstorm Windshear Conditions, NASA, Contractor Report No. 3207, 1979.

  8. Psiaki, M. L., andStengel, R. F.,Analysis of Aircraft Control Strategies for Microburst Encounter, Paper No. AIAA-84-0238, AIAA 22nd Aerospace Sciences Meeting, Reno, Nevada, 1984.

  9. Frost, W., andBowles, R. L.,Windshear Terms in the Equations of Aircraft Motion, Journal of Aircraft, Vol. 21, No. 11, pp. 866–872, 1984.

    Google Scholar 

  10. Zhu, S. X., andEtkin, B.,Fluid-Dynamic Model of a Downburst, University of Toronto, Institute for Aerospace Studies, Report No. UTIAS-271, 1983.

  11. Alexander, M. B., andCamp, D. W.,Wind Speed and Direction Shears with Associated Vertical Motion during Strong Surface Winds, NASA, Technical Memorandum No. 82566, 1984.

  12. Frost, W., Chang, H. P., Elmore, K. L., andMcCarthy, J.,Simulated Flight through JAWS Windshear: In-Depth Analysis Results, Paper No. AIAA-84-0276, AIAA 22nd Aerospace Sciences Meeting, Reno, Nevada, 1984.

  13. Campbell, C. W.,A Spatial Model of Windshear and Turbulence for Flight Simulation, NASA, Technical Paper No. 2313, 1984.

  14. Anonymous, N. N.,Flight Path Control in Windshear, Boeing Airliner, pp. 1–12, January–March 1985.

  15. Leitmann, G.,The Calculus of Variations and Optimal Control, Plenum Publishing Corporation, New York, New York, 1981.

    Google Scholar 

  16. Miele, A., Pritchard, R. E., andDamoulakis, J. N.,Sequential Gradient-Restoration Algorithm for Optimal Control Problems, Journal of Optimization Theory and Applications, Vol. 5, No. 4, pp. 235–282, 1970.

    Google Scholar 

  17. Miele, A., Damoulakis, J. N., Cloutier, J. R., andTietze, J. L.,Sequential Gradient-Restoration Algorithm for Optimal Control Problems with Nondifferential Constraints, Journal of Optimization Theory and Applications, Vol. 13, No. 2, pp. 218–255, 1974.

    Google Scholar 

  18. Miele, A.,Recent Advances in Gradient Algorithms for Optimal Control Problems, Journal of Optimization Theory and Applications, Vol. 17, Nos. 5/6, pp. 361–430, 1975.

    Google Scholar 

  19. Gonzalez, S., andMiele, A.,Sequential Gradient-Restoration Algorithm for Optimal Control Problems with General Boundary Conditions, Journal of Optimization Theory and Applications, Vol. 26, No. 3, pp. 395–425, 1978.

    Google Scholar 

  20. Miele, A.,Gradient Algorithms for the Optimization of Dynamic Systems, Control and Dynamic Systems, Advances in Theory and Application, Edited by C. T. Leondes, Academic Press, New York, New York, Vol. 16, pp. 1–52, 1980.

    Google Scholar 

  21. Miele, A., andWang, T.,Primal-Dual Properties of Sequential Gradient-Restoration Algorithms for Optimal Control Problems, Part 1: Basic Problem, Rice University, Aero-Astronautics Report No. 183, 1985.

  22. Miele, A., andWang, T.,Primal-Dual Properties of Sequential Gradient-Restoration Algorithms for Optimal Control Problems, Part 2: General Problem, Rice University, Aero-Astronautics Report No. 184, 1985.

  23. Johnson, C. D.,Optimal Control with Chebyshev Minimax Performance Index, Journal of Basic Engineering, Vol. 89, No. 2, pp. 251–262, 1967.

    Google Scholar 

  24. Michael, G. J.,Computation of Chebyshev Optimal Control, AIAA Journal, Vol. 9, No. 5, pp. 973–975, 1971.

    Google Scholar 

  25. Warga, J.,Minimax Problems and Unilateral Curves in the Calculus of Variations, SIAM Journal on Control, Vol. 3, No. 1, pp. 91–105, 1965.

    Google Scholar 

  26. Powers, W. F.,A Chebyshev Minimax Technique Oriented to Aerospace Trajectory Optimization Problems, AIAA Journal, Vol. 10, No. 10, pp. 1291–1296, 1972.

    Google Scholar 

  27. Holmaker, K.,A Minimax Optimal Control Problem, Journal of Optimization Theory and Applications, Vol. 28, No. 3, pp. 391–410, 1979.

    Google Scholar 

  28. Holmaker, K.,A Property of an Autonomous Minimax Optimal Control Problem, Journal of Optimization Theory and Applications, Vol. 32, No. 1, pp. 81–87, 1980.

    Google Scholar 

  29. Miele, A., Mohanty, B. P., Venkataraman, P., andKuo, Y. M.,Numerical Solution of Minimax Problems of Optimal Control, Part 1, Journal of Optimization Theory and Applications, Vol. 38, No. 1, pp. 97–109, 1982.

    Google Scholar 

  30. Miele, A., Mohanty, B. P., Venkataraman, P., andKuo, Y. M.,Numerical Solution of Minimax Problems of Optimal Control, Part 2, Journal of Optimization Theory and Applications, Vol. 38, No. 1, pp. 111–135, 1982.

    Google Scholar 

  31. Miele, A., andVenkataraman, P.,Optimal Trajectories for Aeroassisted Orbital Transfer, Acta Astronautica, Vol. 11, Nos. 7/8, pp. 423–433, 1984.

    Google Scholar 

  32. Miele, A., andVenkataraman, P.,Minimax Optimal Control and Its Application to the Reentry of a Space Glider, Recent Advances in the Aerospace Sciences, Edited by L. Casci, Plenum Publishing Corporation, New York, New York, pp. 21–40, 1985.

    Google Scholar 

  33. Miele, A., andBasapur, V. K.,Approximate Solutions to Minimax Optimal Control Problems for Aeroassisted Orbital Transfer, Acta Astronautica, Vol. 12, No. 10, pp. 809–818, 1985.

    Google Scholar 

  34. Miele, A., Basapur, V. K., andMease, K. D.,Nearly-Grazing Optimal Trajectories for Aeroassisted Orbital Transfer, Journal of the Astronautical Sciences, Vol. 34, No. 1, pp. 3–18, 1986.

    Google Scholar 

  35. Miele, A., andWang, T.,An Elementary Proof of a Functional Analysis Result Having Interest for Minimax Optimal Control of Aeroassisted Orbital Transfer Vehicles, Rice University, Aero-Astronautics Report No. 182, 1985.

  36. Cottrell, R. G.,Optimal Intercept Guidance for Short-Range Tactical Missiles, AIAA Journal, Vol. 9, No. 7, pp. 1414–1415, 1971.

    Google Scholar 

  37. Asher, R. B., andMatuzewski, J. P.,Optimal Guidance for Maneuvering Targets, Journal of Spacecraft and Rockets, Vol. 11, No. 3, pp. 204–206, 1974.

    Google Scholar 

  38. Stengel, R. F.,Optimal Guidance for the Space Shuttle Transition, Journal of Spacecraft and Rockets, Vol. 11, No. 3, pp. 173–179, 1974.

    Google Scholar 

  39. Nazaroff, G. J.,An Optimal Terminal Guidance Law, IEEE Transactions on Automatic Control, Vol. AC-21, No. 3, pp. 407–408, 1976.

    Google Scholar 

  40. Guelman, N., andShinar, J.,Optimal Guidance Law in the Plane, Journal of Guidance, Control, and Dynamics, Vol. 7, No. 4, pp. 471–476, 1984.

    Google Scholar 

  41. Miele, A., Wang, T., andMelvin, W. W.,Optimization and Acceleration Guidance of Flight Trajectories in a Windshear, Paper No. AIAA-86-2036-CP, AIAA Guidance, Navigation, and Control Conference, Williamsburg, Virginia, 1986.

  42. Miele, A., Wang, T., andMelvin, W. W.,Optimization and Gamma/Theta Guidance of Flight Trajectories in a Windshear, Paper No. ICAS-86-564, 15th Congress of the International Council of the Aeronautical Sciences, London, England, 1986.

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Author information

Authors and Affiliations

  1. Aero-Astronautics Group, Rice University, Houston, Texas

    A. Miele (Professor of Astronautics and Mathematical Sciences) & T. Wang (Senior Research Associate)

  2. Delta Airlines, Atlanta, Georgia

    W. W. Melvin (Captain)

  3. Airworthiness and Performance Committee, Air Line Pilots Association (ALPA), Washington, DC

    W. W. Melvin (Captain)

Authors
  1. A. Miele
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  2. T. Wang
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  3. W. W. Melvin
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Additional information

Portions of this were presented at the AIAA 24th Aerospace Sciences Meeting, Reno, Nevada, January 6–9, 1986. The authors are indebted to Boeing Commercial Aircraft Company, Seattle, Washington and to Pratt and Whittney Aircraft, East Hartford, Connecticut for supplying some of the technical data pertaining to this study.

The authors are indebted to Dr. R. L. Bowles, NASA-Langley Research Center, Hampton, Virginia for helpful discussions. They are also indebted to Mr. Z. G. Zhao, Aero-Astronautics Group, Rice University, Houston, Texas for analytical and computational assistance.

This research was supported by NASA-Langley Research Center, Grant No. NAG-1-516. This paper, a continuation of Ref.1, is based in part on Refs. 2–3.

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Miele, A., Wang, T. & Melvin, W.W. Guidance strategies for near-optimum take-off performance in a windshear. J Optim Theory Appl 50, 1–47 (1986). https://doi.org/10.1007/BF00938475

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