DOI QR코드

DOI QR Code

Dynamic Positioning Control System Design for Surface Vessel: Observer Design Based on H Control Approach

수상선박의 위치 및 자세제어시스템 설계에 관한 연구 : 강인제어기법에 의한 관측기 설계

  • Kim, Young-Bok (Dept. of Mechanical System Engineering, Pukyong Nat'l Univ.)
  • 김영복 (부경대학교 기계시스템공학과)
  • Received : 2012.03.12
  • Accepted : 2012.07.11
  • Published : 2012.10.01

Abstract

In this study, we consider a dynamic positioning system (DPS) design problem that can be extended to many application fields. Toward this end, tracking and positioning control problems are discussed. In particular, we design a tracking control system that incorporates an observer based on the 2-DOF servo system design approach in order to obtain the desired state information. In the case of observer design, a weighted $H_{\infty}$ error bound approach for a state estimator is considered. Based on an algebraic Riccati equation (inequality) approach, a necessary and sufficient condition for the existence of a full-order estimator that satisfies the weighted $H_{\infty}$ error bound is introduced. The condition for the existence of the estimator is denoted by a linear matrix inequality (LMI) that yields an optimized solution and the observer gain.

본 논문에서는 선박운동제어를 위한 제어시스템 설계문제에 대해 고찰한다. 특히 강인한 추종성능을 가진 2자유도 서보계 설계법을 이용하여 선박의 위치 및 자세제어를 위한 제어기를 설계하고, 실험 등의 실제적인 제어시스템 구축시 센서로부터 모든 정보를 획득할 수 없으므로 이에 필요한 상태를 추정하기 위한 관측기 설계 문제에 대해 고려하고 있다. 그래서 본 논문에서는 실제 상태정보와 추정된 상태정보와의 오차를 최소화하도록 $H_{\infty}$ 오차 바운드를 설정하는 기법으로 관측기의 이득을 구한다. 특히 $H_{\infty}$ 오차 바운드를 만족하는 관측기가 존재하기 위한 조건을 LMI형식으로 변환하여 표현함으로써 관측기 이득 계산을 효율적으로 수행하여 최적의 이득을 구할 수 있음을 보이고 시뮬레이션을 통해 그 유용성을 확인한다.

Keywords

References

  1. Nomoto, K. T., Taguchi, K. H. and Hirano, S, 1957, "On the Steering Qualities of Ships," Technical Report, International Shipbuilding Progress, pp. 3554-370.
  2. Holzhuter, T., 1997, "LQG Approach for the High Precision Track Control of Ships," Proc. of IEE Control Theory Applications, Vol. 144, No.2, pp. 121-127. https://doi.org/10.1049/ip-cta:19971032
  3. Fossen, T. I. and Berge, S. P., 1997, "Nonlinear Vectorial Backstepping Design for Global Exponential Tracking of Marine Vessels in the Presence of Actuator Dynamics," Proc. of 36th Conference on Decision and Control, pp. 4237-4242.
  4. Zhang, R. C., Sun, Z., Sun, F. and Xu, H., 1998, "Path Control of a Surface Ship in Restricted Waters Using Sliding Mode," Proc. of 37th IEEE Conference on Decision and Control, pp. 4237-4244.
  5. Im, K. H., Chwa, D. and Choi, J. Y., 2006, "Multi Input Multi Output Nonlinear Autopilot Design for Ship to Ship Missiles," International Journal of Control, Automation, and System, Vol. 4, No. 2, pp. 255-270.
  6. Jammazi, C., 2008, "Backstepping and Partial Asymptotic Stabilization: Application to Partial Attitude Control," International Journal of Control, Automation, and System, Vol. 6, No. 6, pp. 859-872.
  7. Fujisaki, Y. and Ikeda, M., 1991, "Synthesis of Two-Degree-of-Freedom Servosystem," Trans. on SICE of Japan, Vol. 27, No. 8, pp.907-914. https://doi.org/10.9746/sicetr1965.27.907
  8. Kim, Y. B., Ikeda, M. and Fujisaki, Y., 1996, "Robust Stability and High-gain Integral Compensation of Two-Degree-of-Freedom Servosystem," Trans. on SICE of Japan, Vol. 32, No. 2, pp. 180-187. https://doi.org/10.9746/sicetr1965.32.180
  9. Kim, Y. B., 2000, "Robust Stability of a Two-Degree-of-Freedom Servosystem with Structured and Unstructured Uncertainties," KSME International Journal, Vol. 14, No. 11, pp. 1198-1205.
  10. Fossen, T. I., 2002, Marine Control System : Guidance, Navigation, Rigs and Underwater Vehicle, Trondheim, Norway, Norwegian University of Science and Technology.
  11. Sordalen, O. J., 1997, "Optimal Thrust Allocation for Marine Vessels," Control Engineering Practice, Vol. 5, No. 9, pp. 1223-1231. https://doi.org/10.1016/S0967-0661(97)84361-4
  12. Bodson, M., 2002, "Evaluation of Optimization Methods for Control Allocation," Journal of Guidance, Control, and Dynamics, Vol. 25, No. 4, pp. 703-711. https://doi.org/10.2514/2.4937