Tracking Control of Variable Structure System with a New Variable Boundary Layer

새로운 가변 경계층을 갖는 가변 구조 제어 시스템의 추적 제어

  • 이희진 (국립한경대학교 제어계측공학과) ;
  • 김은태 (국립한경대학교 제어계측공학과) ;
  • 김동연 (국립한경대학교 전자공학과)
  • Published : 2000.05.01

Abstract

This paper suggests the variable structure controller with a new variable boundary layer for the accurate tracking control of the variable structure systems. Up to now, variable structure controller (VSC) applying the variable boundary layer did not remove chattering from an arbitrary initial state of the system trajectory because VSC has the limited initial state according to the fixed sliding surface. But, by using the linear time-varying sliding surfaces, the scheme has the robustness against chattering from all states. The suggested method can be applied to the second-order nonlinear systems with parameter uncertainty and extraneous disturbances, and has better tracking performance than the conventional method. To demonstrate the advantages of the proposed algorithm, it is applied to a two-link manipulator.

본 논문이 제안하는 제어기는 새로운 가변 경계층을 이용하여 가변 구조 시스템의 정확한 추적 제어가 이루어지게 한다. 지금까지 가변 경계층을 적용한 가변 구조 제어기는 고정된 슬라이딩면의 사용으로 초기 위치가 제한되었으며 이로 인해 임의의 초기 위치에서부터 시스템 상태 궤적의 채터링을 감소시킬 수 없다. 그러나 제안된 제어기는 선형 시변 슬라이딩면을 이용함으로서 모든 상태로부터 외부 외란과 불확실한 매개변수에 대한 강인한 특성을 지니게 되며 새로운 가변 경계층의 적용으로 채터링과 추적 성능에서 기존 방법에 비해 우수한 특성을 보이고 있다. 따라서 본 논문은 2 관절 매니퓰레이터에 제안된 알고리즘을 적용하여 제시한 방법의 타당성을 입증하였다.

Keywords

References

  1. W. Gao and J. C. Hung, 'Variable structure control of nonlinear systems: a new approach,' IEEE Trans. Ind. Electron, vol. 40, no. 1, pp. 45 - 55, Feb. 1993 https://doi.org/10.1109/41.184820
  2. J. Y. Hung, W. Gao, and J. C. Gao, 'Variable structure control: a survey,' IEEE Trans. Ind. Electron., vol. 40, no. 1, pp. 2 - 22, Feb. 1993 https://doi.org/10.1109/41.184817
  3. J. J. Slotine and W. Li, Applied Nonlinear Control, Englewood Cliffs, NJ: Prentice Hall, 1991
  4. R. A. Decarlo, S. H. Zak, and G. P. Matthews, 'Variable structure control of nonlinear multivariable systems: a tutorial,' Proceeding of the IEEE, vol. 76, no. 3, pp. 212 - 232, March 1988 https://doi.org/10.1109/5.4400
  5. J. D. Wang, T. L. Lee, and Y. t. Juang, 'New methods to design an integral variable structure controller,' IEEE Trans. Automat. Contr., vol. 41, no. 1, pp. 140 - 143, Jan. 1996 https://doi.org/10.1109/9.481620
  6. W. C. Su, S. Y. Drakunov, and U. Ozguner, 'Constructing discontinuity surfaces for variable structure systems: a Lyaupunov approach,' Automatica, vol. 32, no. 6, pp. 925 - 928, 1996 https://doi.org/10.1016/0005-1098(96)00017-9
  7. J. J. Slotine, 'The robust control of robot manipulators,' The Inter. Journ. of Robotics Research, vol. 4, no. 2, pp. 49 - 64, 1985 https://doi.org/10.1177/027836498500400205
  8. S. Choi, C. Cheon, and D. Park, 'Moving switching surfaces for robust control of second order variable structure systems,' The Inter. Journ. of Control, vol. 58, no. 1, pp. 229 - 245, 1993 https://doi.org/10.1080/00207179308922999
  9. V. I. Utkin, Sliding Modes and Their Application in Variable Structure Systems, Moscow: MIR Publishers, 1978
  10. Y. R. Hwang and M. Tomizuka, 'Fuzzy smoothing algorithms for variable structure systems,' IEEE Trans. Fuzzy Systems, vol. 2, no. 4, pp. 277-285, Nov. 1994 https://doi.org/10.1109/91.324807
  11. J. J. Slotine and S. S. Sastry, 'Tracking control of nonlinear systems using sliding surfaces, with application to robot manipulators,' The Inter. Journ. of Control, vol. 38, no. 2, pp. 465 - 492, 1983 https://doi.org/10.1080/00207178308933088
  12. Y. Stepanenko and C. Su, 'Variable structure control of robot manipulators with nonlinear sliding manifolds,' International Journal of Control, vol. 58, no. 2, pp. 285-300, 1993 https://doi.org/10.1080/00207179308923003
  13. U. Itks, Control Systems cf Variable Structure, New York: John Willy & Sons, 1976
  14. M. Vidyasaga, Nonlinear Systems Analysis, Englewood Cliffs, NJ: Prentice Hall, 1978
  15. F. L. Lexis, C. T. Abdallah, and D. M. Dawson, Control of Robot Manipulator, New York: Macmillan, 1993
  16. R. A. Decarlo, 'Variable structure system with sliding modes,' IEEE Trans. Automat. Contr., vol. AC-22, no. 2, pp. 212 - 222, 1977 https://doi.org/10.1109/TAC.1977.1101446
  17. H. Lee, E. Kim, H. Kang and M. Park, 'Design of a sliding mode controller with fuzzy sliding surfaces,' IEE Proceedings - Control Theory and Applications, vol. 145, no. 5, pp. 411 - 418, Sep. 1998 https://doi.org/10.1049/ip-cta:19982242
  18. N. Bekiroglu, H. I. Bozman, and Y. Istefanopulos, 'Model reference adaptive approach to sliding mode control,' Proceeding of the American Control Conference, Seattle, Washington, pp.1028 - 1032, 1995
  19. H. Lee, E. Kim, and M. Park, 'Variable structure control of manipulator using linear time-varying sliding surfaces', Proceedings of IROS'98, pp. 806 - 811, 1998 https://doi.org/10.1109/IROS.1998.727296
  20. 野波健藏, 田宏奇, スライディソグモ-ド制御, コロナ社, 1994