Journal of the Institute of Electronics Engineers of Korea SC (전자공학회논문지SC)

The Institute of Electronics and Information Engineers (대한전자공학회)
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A study on the Stability of Discrete-time Affine Type III Fuzzy Control System

이산 시간 어핀 Type III 퍼지 제어 시스템의 안정도에 대한 연구

  • Kim, Eun-Tai (Hankyong National University, Dept. of Control and Instrumentation Engr.) ;
  • Lee, Hee-Jin (Hankyong National University, Dept. of Control and Instrumentation Engr.)
  • 김은태 (국립 한경대학교, 제어계측공학과) ;
  • 이희진 (국립 한경대학교, 제어계측공학과)
  • Published : 2001.08.31
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Abstract

In this paper, we propose the stability analysis and design methodology for the discrete-time affine Type III fuzzy system via the convex optimization technique. First, the stability condition is derived under which the discrete-time affine Type III fuzzy system is quadratically stable in the large. Next, the derived condition is reformulated into the convex optimization problem called Linear Matrix Inequalities (LMI) and numerically addressed. Finally, the effectiveness and the feasibility of the proposed analysis and design methodology is highlighted via an example and its computer simulation result.

본 논문에서는 이산 시간 어핀 Type III 퍼지 시스템의 안정도를 판정하고 이에 의하여 제어기를 설계하는 방식을 제안하도록 한다. 제안되는 안정도 해석 및 설계 방식은 컨벡스 최적화 기업에 근거한 방식으로， 우선 이산 시간 어핀 Type III 퍼지 시스템이 2차적으로 안정하게 되는 조건을 유도하도록 한다. 그 이후 이를 선형 행렬 부등식의 형태로 변형하여 수치적 접근방식을 제안하고 제안한 안정조건을 이용하여 어핀 Type III 퍼지 시스템으로 표현된 플랜트에 대하여 안정도가 보장되는 퍼지 제어기를 설계하도록 한다. 끝으로 컴퓨터 모의 실험을 통하여 제안한 방법의 타당성을 확인한다.

Keywords

References

  1. L. A. Zadeh, 'Fuzzy algorithm,' lnformation and Control, vol. 12, pp.91-102, 1968
  2. E. H. Mamdani, 'Applications of fuzzy algorithms for control of simple dynamic plant,' Proc. IEE, vol.121, No.2, pp 1585-1588, 1971
  3. L. P. Holmblad and J. J. Osterguard, 'Control of a cement kiln by fuzzy logic,' in M. M. Gupta and E. Sanchez, eds., Fuzzy Information and decision Processes, Noth Holland:Amsterdam, pp. 398-409, 1982
  4. T. Terano, K. Asai, and M. Sugeno, eds., Applied Fuzzy System', Academic Press:MA, 1994
  5. M. Sugeno, 'On stability of fuzzy systems expressed by fuzzy rules with singleton consequents,' IEEE Trans. Fuzzy Systems, vol. 7, No.2, pp 201 204, Apr., 1999 https://doi.org/10.1109/91.755401
  6. T. Takagi and M. Sugeno, 'Fuzzy identification of systems and its applications to modeling and control,' IEEE Trans. Systems Man Cybernet, vol. 15, No.1, pp116-132, 1985
  7. K. Tanaka and M. Sugeno, 'Stability analysis and design of fuzzy control systems,' Fuzzy Sets and System, vol. 45, 136-156, 1992 https://doi.org/10.1016/0165-0114(92)90113-I
  8. K. Tanaka, A Theory of Advanced Fuzzy Control, Japan:Kyuoritsu Pub, 1994. (In Japanese)
  9. K. Tanaka and M. Sano, 'A robust stabilization problem of fuzzy control systems and its application to backing up control of a truck-trailer,' IEEE Trans. Fuzzy Systems, vol. 2, No. 2, pp 119-134, May 1994 https://doi.org/10.1109/91.277961
  10. H. O. Wang, K. Tanaka, M. F. Griffin, 'An approach to fuzzy control of nonlinear systems: stability and design issues,' IEEE Trans. Fuzzy Systems, vol. 4, No. 1, pp 14 23, Feb 1996 https://doi.org/10.1109/91.481841
  11. K. Tanaka. T. Ikeda and H. O. Wang, 'An LMI approach to fuzzy controller designs based on the relaxed stability conditions,' in Proc. of IEEE Int. Conf. Fuzzy Systems (FUZZ/IEEE), pp.171-176, 1997 https://doi.org/10.1109/FUZZY.1997.616364
  12. K. Tanaka, T. Ikeda and H. O. Wang, 'Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stahilizahility, $H^{\infty}$ control theory, and linear matrix inequalities,' IEEE Trans. Fuzzy Systems, vol. 4, No.1, pp. 1-13, Feb. 1996 https://doi.org/10.1109/91.481840
  13. M A. L. Thathachar and P. Viswanath, 'On the stability of fuzzy systems,' IEEE Trans. Fuzzy Systems, vol. 5, No.1, pp 145-151, Feb 1997 https://doi.org/10.1109/91.554461
  14. H. Lam, F. Leung and P. Tam, 'Stable and robust fuzzy control for nonlinear systems based on a grid-point approach,' in Proc. of IEEE Int'l Conf. Fuzzy Systems (FUZZ/IEEE), pp. 88-92, 1997 https://doi.org/10.1109/IECON.1997.671076
  15. S. Kim, E. Kim and M. Park, 'A new fuzzy adaptive controller using the parallel structure of fuzzy controllers and its application,' Fuzzy sets and Systems, vol. 81, pp 205-226, 1996 https://doi.org/10.1016/0165-0114(95)00206-5
  16. D. Liberzon and A. S. Morse, 'Basic problem in stability and desing of switched systems,' IEEE Control Systems Magazine, vol. 19, no. 5, pp. 59-70, 1999 https://doi.org/10.1109/37.793443
  17. C. Fantuzzi and R. Rovatti, 'On the approximation capabilities of the homogeneous Takagi Sugeno model,' in Proc. of the 5th IEEE Int. Corf. on Fuzzy Systems, pp. 1067-1072, New Orleans, USA, 1996
  18. M. Sugeno and G. T. Kang, 'Fuzzy modeling and control of multilayer incinerator', Fuzzy Sets and Systems, Vol. 18, pp 329-346, 1986 https://doi.org/10.1016/0165-0114(86)90010-2
  19. E. Kim, M. Park, S. Ji and M. Park, 'A new approach to fuzzy modeling,' IEEE Trans. Fuzzy Systems, vol. 5, No. 3, pp. 328-337, Aug, 1997 https://doi.org/10.1109/91.618271
  20. S. Boyd, L. Ghaoui, E. Feron and V. Balaluishnan, Linear Matrix Inequalities in System and Control Theory, SIAM: Philadelphia, 1994