Journal of the Korean Society for Aeronautical & Space Sciences (한국항공우주학회지)

The Korean Society for Aeronautical and Space Sciences (한국항공우주학회)
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Design of Aim Angle Following Guidance Law Using Lyapunov Theory

르야프노프 이론을 이용한 목표각 추종 유도법칙 설계

  • 김기석 (서울대학교 항공우주공학과 대학원) ;
  • 김유단 (서울대학교 기계항공공학부)
  • Published : 2002.10.01
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Abstract

Guidance laws can be conceptually classified into three categories although their mathematical representations are various and different. In this paper, a generalized conceptual guidance law including the concepts of the above categories is proposed. The aim angle is introduced using the geometry of the collision triangle. The aim angle represents the arbitrary angle between the pursuit angle and the expected collision angle. The objective of the proposed guidance law is to make the aim angle zero asymptotically. It can be shown that the aim angle error response for the considered system is same as that of the first order system. When the autopilot of the missile system has slow dynamics, autopilot time lag may deteriorate the performance of the guidance law performance. In this case, another new guidance law compensating the autopilot time lag effect is proposed. To verify the proposed guidance laws, several numerical simulations are performed.

현재까지 개발된 다양한 형태의 유도법칙은, 유도개념에 따라 추적방식, 미사일과 표적에 의해 정의되는 방위각을 일정하게 유지시키는 유도법칙, 그리고 표적의 기동 예측에 기반한 유도법칙 등으로 분류할 수 있다. 본 논문에서는 이러한 개념적인 유도목적을 일반화한 유도법칙을 제안하였다. 제안한 유도법칙은 충돌삼각형 상에서 정의된 목표각을 사용하는데, 목표각은 매개변수의 설정에 따라 다양한 형태가 될 수 있다. 르야프노프 이론을 사용하여, 제안한 유도법칙은 목표각 오차의 반응이 1차 시스템과 동일함을 증명하였다. 그리고 자동조종장치의 동역학이 느릴 경우는, 목표각 오차 반응을 2차 시스템으로 모사할 수 있는 유도법칙도 제안하였다. 제안한 유도법칙의 유용성을 보이기 위하여 측정잡음을 포함한 시뮬레이션을 수행하고 결과를 제시하였다.

Keywords

References

  1. Ghose, D., "Lecture Notes on Guidance Laws and Their Applications," Automatic Control Research Center, Seoul National University, 1996, pp. 39-64.
  2. Park, J, and Kabamba, P. T., "Miss Distance Analysis in a New Guidance Law," Proceedings of the American Control Conference, San Diego, California, 1999.
  3. Lin, J., and Mon, Y., "Fuzzy Logic-based CLOS Guidance Law Design," IEEE Transactions on Aerospace and Electronic Systems, Vol. 37, No. 2, 2001, pp. 719-727. https://doi.org/10.1109/7.937484
  4. Ghawghawe, S. N., and Ghose, D., "Pure Proportional Navigation Against Time-Varying Target Maneuvers," IEEE Transactions on Aerospace and Electronic Systems, Vol, 32, No. 4, 1996, pp. 1-12. https://doi.org/10.1109/TAES.1996.543875
  5. 문종기, 김유단, "가변구조 제어기법을 이용한 미사일의 유도법칙 설계," 한국항공우주학회지, Vol. 28, No. 3, pp. 108-113.
  6. Ha, I., Hur, J., Ko, M., and Song, T., "Performance Analysis of PNG Laws for Randomly Maneuvering Targets," IEEE Transactions on Aerospace and Electronic Systems, Vol, 26, No. 5, 1990, pp. 713-719. https://doi.org/10.1109/7.102706
  7. Yang, C, and Yang, C, "A Unified Approach to Proportional Navigation," IEEE Transactions on Aerospace and Electronic Systems, Vol. 33, No. 2, 1997, pp. 557-567. https://doi.org/10.1109/7.575895
  8. Cho, H., Ryoo, C, and Tahk, M., "Implementation of Optimal Guidance Laws Using Predicted Missile Velocity Profiles," Journal of Guidance, Control, and Dynamics, Vol 22, No. 4, 1999, pp. 579-588. https://doi.org/10.2514/2.4420
  9. Zhou, D., Mu, C, Ling, Q., and Xu, W., "Optimal Sliding-Mode Guidance of a Homing-Missile," Proceedings of the 38th Conference on Decision and Control, Phoenix, Arizona, USA, 1999.
  10. Ben-Asher, J. Z., and Yaesh, I., "Optimal Guidance with Reduced Sensitivity to Time-to-Go Estimation Errors," Journal of Guidance, Control, and Dynamics, Vol. 20, No. 1, 1997, pp. 158-163. https://doi.org/10.2514/2.4010
  11. 김요섭, 탁민제, "BTT 미사일의 최적유도법칙에 관한 연구," 한국항공우주학회지, Vol. 22, No. 2, pp. 67-80.
  12. Rusnak, I., and Meir, L., "Optimal Guidance for Acceleration Constarined Missile and Maneuvering Target," IEEE Transactions on Aerospace and Electronic Systems, Vol, 26, No. 4, 1990, pp. 713-719. https://doi.org/10.1109/7.102706
  13. Babu, K. R., Sarma, I. G., and Swamy, K. N., "Two Robust Homing Missile Guidance Laws Based on Sliding Mode Control Theory," IEEE National Aerospace and Electronics Conference, 1994, pp. 540-547.