Analysis and Improvement of Time Sampling effects on Singular Perturbation based Control Systems - Its Aplication to Design of Singular Pertubation based STT Missible Digital Autopilot

특이섭동 기법 기반 제어 시스템에 대한 샘플링 영향 분석 및 개선 - 특이섭동 기법 기반 STT 미사일 디지털 자동조정장치 설계에의 적용

  • Jeong, Seon-Tae (Dept.of Information Communication Electronics Engineering, Soongsil University)
  • 정선태 (숭실대학교 정보통신전자공학부)
  • Published : 2000.05.01

Abstract

The guarantee of the fast dynamics stability is essential for successful application of singular Perturbation technique to control systems design. Even though the fast dynamics of the control systems is rendered stable by an analog controller, the fast dynamics stability of the control systems resulted from an digital implementation of the analog controller can be impaired severely. In this paper, we first investigate the time sampling effects on singular perturbation based control systems by centering on a design example of recently developed singular perturbation based STT missile autopilot with high performance. The investigation shows that the stability margin the fast dynamics of the STT misile autopilot system decreases rapidly as the sampling interval of discretizing the analog autopilot increases. Under this analysis, we propose a composite digital controller with compensation for the decreasing stability margin of the fast dynamics due to time sampling to achieve better performance with respect to sampling time. The improved performance of the proposed composite digital controller is verified by simulation. This result shows that one needs to investigate time sampling effects in the digital implementation of singular perturbation based controllder, and then can have benefit from the investigation.

특이섭동 기법을 이용한 제어 시스템의 설계가 가능하기 위해서는 무엇보다도, 빠른 동력학의 안정성이 중요하다. 그런데, 제어기의 디지털 구현으로 인하여, 이 빠른 동력학의 안정도가 영향을 받을 수 있다. 본 논문은 최근의 개발된 우수한 성능의 특이섭동 기반의 STT 자동조정장치(autopilot) 설계의 경우를 들어 이러한 특이섭동 기법에 기반하여 설계된 제어 시스템에 대한 샘플링 영향을 조사하고 개선된 제어기 설계의 예를 제시하여, 특이섭동 기반 제어 시스템 에 대한 샘플링 영향 분석의 필요성 및 유효성을 밝혔다.

Keywords

References

  1. K. Astrom and B. Wittenmark(1984), Computer Controlled Systems, Theory and Design, Prentice-Hall
  2. S.-T. Chung and J. W. Grizzle, 'Sampled-Data Observer Error Linearization', Automatica, Vol. 26, pp. 997-1007, 1990 https://doi.org/10.1016/0005-1098(90)90084-U
  3. J. H. Chow and P. Kokotovic (1976), 'A Decomposition of Near-Optimum Regulators for Systems with Slow and Fast Modes,' IEEE Trans. Automat. Contr., vol. AC-21, pp. 710-705 https://doi.org/10.1109/TAC.1976.1101342
  4. K. Khorasani and P. Kokotovic (1986), 'A Corrective Feedback Design for Nonlinear Systems with Fast Actuators,' IEEE Trans. Automat. Contr., vol. AC-31, pp. 67-69 https://doi.org/10.1109/TAC.1986.1104099
  5. P. Kokotovic, A. Bensoussan and G. Blankenship (1987), Singular Perturbations and Asymptotic Analysis in Control Systems, Lecture Notes in Control and Information Sciences, Springer-Verlag https://doi.org/10.1007/BFb0007175
  6. P. Kokotovic, H. K. Khalil and J. OReilly(1986), Singular Perturbation Methods in Control : Analysis and Degisn, Academy Press
  7. B. Litkouhi and H. K. Khalil(1985), 'Multirate and Composite Control of Two-Time-Scale Discrete-Time Systems,' IEEE Trans. Automat. Contr., vol. AC-30, pp. 645-651 https://doi.org/10.1109/TAC.1985.1104024
  8. H.-G. Lee, A. Arapostathis and S.I. Marcus, 'On the digital control of nonlinear systems', Proc. of the 27th IEEE Conf. Decision and Contr., Austin, TX., pp. 480-481, 1988 https://doi.org/10.1109/CDC.1988.194357
  9. Ju Il Lee, Jae-Hyuk Oh, In-Joong Ha, Eul-Gon Kim and Hang-Ju Cho, 'A New Approach to Autopilot Design for Highly Nonlinear Missiles,' AIAA Guidance, Navigation, and Control Conference, July, 1996
  10. Ju Il Lee, In-Joong Ha, 'Autopilot Design for Highly Maneuvering STT Missiles via Sigular Perturbation-like Technique,' To Appear in IEEE Trans. on Control Systems Technology https://doi.org/10.1109/87.784417
  11. M. Vidyasagar, Nonlinear Systems Analysis, Englewood Cliffs, N.J., Prentice-Hall, 1978
  12. 오재혁, 하인중, 조항주, 송택렬, '부분선형화와 상태변수 변환에 의한 STT방식 미사일의 자동 조정장치 설계,' 한국항공공학회지 제 22권 제 1호, pp. 73-87, 1994
  13. 정선태, '개선된 선형 샘플치 출력 조절기', 대한전자공학회지 제 35권 S편 제10호, 1998, 10월, pp. 1355-1363
  14. 정선태, '비선형 시스템 출력조절과 샘플링 영향', 대한전자공학회지 제 35권 S편 제11호, 1998, 11월, pp. 1558-1568
  15. 하인중, 정선태, 송용규, '비행체제의 비선형제어에 관한 연구', 유도제어 연구실 연구보고서, 자동제어특화연구센터, 1997