$H_\infty$ Depth Controller Design for Underwater Vehicles

수중운동체의 $H_\infty$ 심도제어기 설계

  • 이만형 (부산대학교 기계공학부, 정밀정형 및 금형가공연구소) ;
  • 정금영 (부산대학교 지능기계공학과) ;
  • 김인수 (부산대학교 지능기계공학과) ;
  • 주효남 (삼성전자 생산기술센터 자동화연구소) ;
  • 양승윤 (국방과학연구소)
  • Published : 2000.05.01

Abstract

In this paper, the depth controller of an underwater vehicle based on an $H_\infty$ servo control is designed for the depth keeping of the underwater vehicle under wave disturbances. The depth controller is designed in the form of the $H_\infty$ servo controller, which has robust tracking property, and an $H_\infty$ servo problem is considered for the $H_\infty$ servo controller design. In order to solve the $H_\infty$ servo problem for the underwater vehicle, this problem is modified as an $H_\infty$ control problem for the generalized plant that includes a reference input mode, and a suboptimal solution that satisfies a given performance criteria is calculated with the LMI (Linear Matrix Inequality) approach. The $H_\infty$ servo controller is designed to have robust stability about the perturbation of the parameters of the underwater vehicle and the robust tracking property of the underwater vehicle depth under wave force and moment disturbances. The performance, robustness about the uncertainties, and depth tracking property, of the designed depth controller is evaluated by computer simulation, and finally these simulation results show the usefulness and applicability of the proposed $H_\infty$ depth control system.

Keywords

References

  1. G. F. Gueler, 'Modeling, design and analysis of an autopilot for submarine vehicles,' Inst. Shipbuilding Progress, vol. 36, pp. 51-85, 1989
  2. M. J. Ruth, Application of synthesis to control design for a submersible vehicle, Lecture notes from MUSYN, CA, Arcadia, September, 1989
  3. S. J. Williams and W. B. Marshfield, '$H_{\infty}$ multivariable design of a submarine depth control system,' Inst. of Meas. and Contr., Symp. Appl. Multivariable Syst. Techniques, pp. 104-205, 1990
  4. W. B. Marshfield, 'Submarine periscope-depth depth keeping using an H-infinity controller together with sea-noise-reduction notch filters,' Trans. Inst. Mech. Contr., vol. 13, no. 5, pp. 233-240, 1991
  5. P. Gahinet, 'Explicit controller formulas for LMI based $H_{\infty}$ synthesis,' Automatica, vol. 32, no. 7, pp. 1007-1014, 1996 https://doi.org/10.1016/0005-1098(96)00033-7
  6. P. Gahinet and P. Apkarian, 'A linear matrix inequality approach to $H_{\infty}$ control,' International Journal qf Robust and Nonlinear Control, vol. 4, pp. 421-448, 1994
  7. J. Hozumi, S. Hara, and H. Fujioka, 'Robust servo problem with $H_{\infty}$ norm constraint,' International Journal of Control, vol. 66, no. 6, pp. 803-823, 1997
  8. Doyle, J.C., Glover, K., Khargovekar, P.P. and Francis, B.A., 1999, 'State-space Solutions to Standard $H_2$ and $H_{\infty}$ Control Problems,' IEEE Trans. on Automatic Control, Vol. 34, No. 8, pp. 831-847 https://doi.org/10.1109/9.29425
  9. M. A. Abkowitz, Lectures on ship hydrodynamics steering and maneuverability, Hydrodynamics Department Hydro-og Aerodynamisk Laboratorium Lyngby, Denmark, 1964
  10. 양승윤, 이만형, '무인 수중운동체의 경로추적기와 심도제어기 설계 연구,' 제어.자동화.시스템공학논문지, 제4권 제1호, pp. 45-55, 1998
  11. 이경중, 이균정, '해상상태와 그 영향에 대한 모델링(I),' 국방과학연구소 NWSD-513-92800, 1993
  12. E. Liceaga-Castro and G. M. van der Molen, 'Submarine $H_{\infty}$ depth control under wave disturbances,' IEEE Transactions on Control System Technology, vol. 3, no. 3, pp. 338-346, 1995 https://doi.org/10.1109/87.406981