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Controllability Investigations of a Two-Stage-To-Orbit Vehicle

  • Bernd Kugelmann
  • Hans Josef Pesch
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 111)

Abstract

For the real-time computation of closed-loop controls, guidance methods have been recently developed by the authors which are based on the theory of neighboring extremals and/or the multiple shooting algorithm. Because of their close relationship, these methods have a comparable domain of controllability, i.e., the set of all deviations from the nominal optimal trajectory which can be compensated in real time. Therefore, the multiple shooting method can be used to get an estimation for the size of these domains. In this way, the domain of controllability has been investigated for the payload maximum ascent of a two-stage rocket-propelled space vehicle from Earth into a circular target orbit. Here, the staging and the mass ratio of the two stages are optimized simultaneously.

Keywords

Optimal Control Problem Newton Method Multiple Shooting Feedback Scheme Adjoint Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Bulirsch, R. (1971), Die Mehrzielmethode zur numerischen Lösung von nichtlinearen Randwertproblemen und Aufgaben der optimalen Steuerung. Deutsche Forschungs- und Versuchsanstalt für Luft- und Raumfahrt, Report of the Carl-Cranz Gesellschaft, Ober-pfaffenhofen, Germany.Google Scholar
  2. Bulirsch, R. and H.-W. Branca (1974), Computation of Real-Time-Control in Aerospace Applications by Multiple Shooting Procedures. In: R. A. Willoughby (Ed.), Stiff Differential Systems, Proc. of a Conference held at Wildbad, Germany, 1973, Plenum Press, New York, New York, pp. 49–50.CrossRefGoogle Scholar
  3. Bulirsch, R., K. Chudej and K. D. Reinsch (1990), Optimal Ascent and Staging of a Two-stage Space Vehicle System. Jahrestagung der Deutschen Gesellschaft für Luft- und Raumfahrt, Friedrichshafen, 1990, DGLR-Jahrbuch 1990, Vol. 1, 243–249.Google Scholar
  4. Bulirsch, R. and K. Chudej (1991), Ascent Optimization of an Airbreathing Space Vehicle. AIAA Guidance, Navigation and Control Conference, New Orleans, Louisiana, 1991, AIAA Paper No. 91–2656.Google Scholar
  5. Bulirsch, R., F. Montrone and H. J. Pesch (1991a), Abort Landing in the Presence of a Windshear as a Minimax Optimal Control Problem, Part 1: Necessary Conditions. J. of Optimization Theory and Applications, Vol. 70, 1–23.Google Scholar
  6. Bulirsch, R., F. Montrone and H. J. Pesch (1991b), Abort Landing in the Presence of a Windshear as a Minimax Optimal Control Problem, Part 2: Multiple Shooting and Homotopy. J. of Optimization Theory and Applications, Vol. 70, 221–252.Google Scholar
  7. Kugelmann, B. and H. J. Pesch (1990a), New General Guidance Method in Constrained Optimal Control, Part 1: Numerical Method. J. of Optimization Theory and Applications, Vol. 67, 421–435.Google Scholar
  8. Kugelmann, B. and H. J. Pesch (1990b), New General Guidance Method in Constrained Optimal Control, Part 2: Application to Space Shuttle Guidance. J. of Optimization Theory and Applications, Vol. 67, 437–446.Google Scholar
  9. Oberle, H. J. (1982), Numerische Berechnung optimaler Steuerungen von Heizung und Kühlung für ein realistisches Sonnenhausmodell. Habilitationsschrift, Munich University of Technology, Munich, Germany.Google Scholar
  10. Pesch, H. J. (1989a), Real-time Computation of Feedback Controls for Constrained Optimal Control Problems, Part 1: Neighbouring extremals. Optimal Control Applications & Methods, Vol. 10, 129–145.CrossRefGoogle Scholar
  11. Pesch, H. J. (1989b), Real-time Computation of Feedback Controls for Constrained Optimal Control Problems, Part 2: A Correction Method Based on Multiple Shooting. Optimal Control Applications & Methods, Vol. 10, 147–171.CrossRefGoogle Scholar
  12. Pesch, H. J. (1990), Optimal and Nearly Optimal Guidance by Multiple Shooting. In: Centre National d’Etudes Spatiales (Ed.), Proc. of the Inter. Symp. Mécanique Spatiale -Space Dynamics, Toulouse, France, 1989, Cepadues Editions, Toulouse, France, 761–771.Google Scholar
  13. Sänger, E. (1962), Raumfahrt — gestern, heute und morgen. Astronautica Acta VIII 6, 323–343.Google Scholar
  14. Shau, G.-C. (1973), Der Einfluß flugmechanischer Parameter auf die Aufstiegsbahn von horizontal startenden Raumtransportern bei gleichzeitiger Bahn- und Stufungsopti-mierung. Dissertation, Department of Mechanical and Electrical Engineering, University of Technology, Braunschweig, Germany.Google Scholar
  15. Stoer, J. and R. Bulirsch (1980), Introduction to Numerical Analysis. Springer, New York, New York.Google Scholar
  16. Vinh, N. X., A. Busemann and R. D. Culp (1980), Hypersonic and Planetary Entry Flight Mechanics. University of Michigan Press, Ann Arbor, Michigan.Google Scholar

Copyright information

© Birkhäuser Verlag 1993

Authors and Affiliations

  • Bernd Kugelmann
    • 1
  • Hans Josef Pesch
    • 1
  1. 1.Mathematisches InstitutTechnische Universität MünchenMünchen 2Germany

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