Absolute Stability Margins in Missile Guidance Loop

  • Kim, Jong-Ju (Agency for Defense Development) ;
  • Lyou, Joon (Department of Electronics Engineering, Chungnam National University)
  • Published : 2008.06.30

Abstract

This paper deals with the stability analysis of a missile guidance loop employing an integrated proportional navigation guidance law. The missile guidance loop is formulated as a closed-loop control system consisting of a linear time-invariant feed-forward block and a time-varying feedback gain. Based on the circle criterion, we have defined the concept of absolute stability margins and obtained the gain and phase margins for the system assuming 1 st order missile/autopilot dynamics. The correlation between the absolute stability margins and the margins derived from the frozen system analysis is also discussed.

Keywords

References

  1. M. Guelman, "The stability of proportional navigation systems," AIAA Paper 90-3380, July 1990
  2. T. Tanaka and E. Hirofumi, "An extended guidance loop and the stability of the homing missiles," Proc. of the 27th JSASS Aircraft Symposium, 1990
  3. T. Tanaka and E. Hirofumi, "Hyperstable range in homing missiles," AIAA Paper 90-3381, July 1990
  4. D. Y. Rew, M. J. Tahk, and H. Cho, "Short time stability of proportional navigation guidance loop," IEEE Trans. on Aerospace and Electronic Systems, vol. 32, no. 4, pp. 1107-1115, 1996 https://doi.org/10.1109/7.532269
  5. P. Gurfil, M. Jodorkovsky, and M. Guelman, "Finite time stability approach to proportional navigation systems analysis," Journal of Guidance, Control, and Dynamics, vol. 21, no. 6, pp. 853-861, Nov.-Dec. 1998 https://doi.org/10.2514/2.4348
  6. P. F. Curran, "Proof of the circle criterion for state space systems via quadratic Lyapunov functions-Part 1," International Journal of Control, vol. 57, no. 4, pp. 921-955, 1993 https://doi.org/10.1080/00207179308934421
  7. P. F. Curran, "Proof of the circle criterion for state space systems via quadratic Lyapunov functions-Part 2," International Journal of Control, vol. 57, no. 4, pp. 957-969, 1993 https://doi.org/10.1080/00207179308934422
  8. S. T. Impram and N. Munro, "A note on absolute stability of uncertain systems," Automatica, vol. 37, no. 4, pp. 605-610, April 2001 https://doi.org/10.1016/S0005-1098(00)00194-1
  9. H. Weiss and G. Hexner, "Stability of modern guidance laws with model mismatch," Proc. of the American Control Conference, Boston, Massachusetts, pp. 3634-3639, June 30 - July 2, 2004
  10. T. Hagiwara and M. Araki, "Absolute stability of sampled-data systems with a sector nonlinearity," Systems & Control Letters, vol. 27, pp. 293-304, 1996 https://doi.org/10.1016/0167-6911(96)00003-5
  11. P. Garnel, Guided Weapon Control Systems, 2nd Ed., Pergamon Press, p. 218, 1980
  12. H. R. Mohler, Nonlinear Systems: Vol. 1, Dynamics and Control, Prentice-Hall, Inc. Englewood Cliffs, NJ, 1991
  13. M. A. Aizerman and F. R. Gantmacher, Absolute Stability of Regulator Systems, Holden-Day, Inc., San Francisco, 1964