Dynamics and Control

, Volume 1, Issue 2, pp 177–198 | Cite as

Development of guidance laws for a variable-speed missile

  • R. Gazit
  • S. Gutman
Article

Abstract

The most used guidance law for short-range homing missiles is proportional navigation (PN). In PN, the acceleration command is proportional to the line-of-sight (LOS) angular velocity. Indeed, if a missile and a target move on a collision course with constant speeds, the LOS rate is zero. The speed of a highly maneuverable modem missile varies considerably during flight. The performance of PN is far from being satisfactory in that case.

In this article we analyze the collision course for a variable-speed missile and define a guidance law that steers the heading of the missile to the collision course. We develop guidance laws based on optimal control and differential game formulations, and note that both optimal laws coincide with the Guidance to Collision law at impact. The performance improvement of the missile using the new guidance law as compared to PN is demonstrated.

Keywords

Angular Velocity Performance Improvement Constant Speed Differential Game Target Move 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    C.L. Yuan, “Homing and navigational courses of automatic target-seeking devices,”J. Appl Phys., vol. 19, pp. 1122–1128, 1948.Google Scholar
  2. 2.
    A.E. Bryson and Yu-Chi Ho,Applied Optimal Control, Hemisphere Publishing Corp.: New York, 1975.Google Scholar
  3. 3.
    E. Kreindler, “Optimality of proportional navigation,”AIAA J., vol. 11, no. 6, pp. 878–880, 1973.Google Scholar
  4. 4.
    F. H. Kishi and T. S. Bettwy, “Optimal and suboptimal designs of proportional navigation systems,” inRecent Advances in Optimization Techniques (A. Lavi and T.P. Vogl, eds.), John Wiley: New York, 1965.Google Scholar
  5. 5.
    Y.C. Ho, A.E. Bryson, and S. Baron, “Differential games and optimal pursuit-evasion strategies,”IEEE Trans. Automatic Control, vol. AC-10, no. 4, pp. 385–389, 1965.Google Scholar
  6. 6.
    S. Gutman and G. Leitmann, “Optimal strategies in the neighborhood of a collision course,”AIAA J., vol. 14, no. 9, pp. 1210–1212, 1976.Google Scholar
  7. 7.
    P. Garnell,Guided Weapon Control Systems, 2nd ed., Pergamon Press: New York, 1980.Google Scholar
  8. 8.
    T. Riggs, “Linear optimal guidance for short range air to air missile,”Proc. Nat. Aerospace Electron. Conf., vol. 11, pp. 757–764, 1979.Google Scholar
  9. 9.
    G. K. F. Lee, “Estimation of the time-to-go parameter for air to air missiles,”J. Guidance Control Dynamics, vol. 8, no. 2, pp. 262–266, 1985.Google Scholar
  10. 10.
    P.L. Vergez, “Linear optimal guidance for an AIM-9L missile,”J. Guidance Control Dynamics, vol. 4, no. 6, pp. 662–663, 1981.Google Scholar
  11. 11.
    D.G. Hull and R.E. Mack, “Prediction of time-to-go for a homing missile using bang-bang control,” AIAA paper No. 88-4065-CP, 1988.Google Scholar
  12. 12.
    Y. Yavin and R. De Villiers, “Proportional navigation and the game of two cars: the case of pursuer with variable speed,”Computers Math. Applic., vol. 18, no. 1–3, pp. 69–76, 1989.Google Scholar
  13. 13.
    A. Green, J. Shinar, and M. Guelman, “Guidance law synthesis based on a planar pursuit-evasion game solution,” inDifferential Games and Applications (T.S. Basar and P Bernhard, eds.,). Lecture Notes in Control and Information Sciences, no. 119, Springer Verlag, 1990.Google Scholar
  14. 14.
    B. Sridhar and N.K. Gupta, “Missile guidance laws based on singular perturbation methodology,”J. Guidance Control Dynamics, vol. 3, no. 2, pp. 158–165, 1980.Google Scholar
  15. 15.
    V.H.L. Cheng and N. K. Gupta, “Advanced midcourse guidance for air to air missiles,”J. Guidance Control Dynamics, vol. 9, pp. 135–142, 1986.Google Scholar
  16. 16.
    F. Goldstein and A. Calise, “Non linear state feedback control for near optimal intercept in three dimensions,” AIAA Paper no. 79-1673, 1979.Google Scholar
  17. 17.
    V. Garber, “Optimum intercept laws for accelerating targets,”AIAA. vol. 6, no. 7, pp. 2196–2198, 1968.Google Scholar
  18. 18.
    S. Gutman, “On optimal guidance for homing missiles,”J. Guidance Control Dynamics, vol. 2, no. 4, pp. 296–300, 1979.Google Scholar
  19. 19.
    J. Jerger,Systems Preliminary Design, D. Van Nostrand: New York, 1960.Google Scholar

Copyright information

© Kluwer Academic Publishers 1991

Authors and Affiliations

  • R. Gazit
    • 1
  • S. Gutman
    • 2
  1. 1.Faculty of Aerospace EngineeringTechnician-Israel Institute of TechnologyHaifaIsrael
  2. 2.Faculty of Mechanical EngineeringTechnician-Israel Institute of TechnologyHaifaIsrael

Personalised recommendations