전기학회논문지 (The Transactions of The Korean Institute of Electrical Engineers)

  • 제59권9호
  • /
  • Pages.1680-1685
  • /
  • 2010
  • /
  • 1975-8359(pISSN)
  • /
  • 2287-4364(eISSN)
대한전기학회 (The Korean Institute of Electrical Engineers)
권호 표지
DOI QR코드

DOI QR Code

Utkin 정리의 다입력 불확실 선형 시스템에 대한 증명

A Poof of Utkin's Theorem for a MI Uncertain Linear Case

  • 이정훈 (경상대학교 공대 제어계측공학과)
  • 투고 : 2010.05.12
  • 심사 : 2010.07.13
  • 발행 : 2010.09.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this note, a proof of Utkin's theorem is presented for a MI(Multi Input) uncertain linear case. The invariance theorem with respect to the two transformation methods so called the two diagonalization methods are proved clearly and comparatively for MI uncertain linear systems. With respect to the sliding surface transformation and the control input transformation, the equation of the sliding mode i.e., the sliding surface is invariant. Both control inputs have the same gains. By means of the two transformation methods the same results can be obtained. Through an illustrative example and simulation study, the usefulness of the main results is verified.

키워드

참고문헌

  1. V.I. Utkin,, Sliding Modes and Their Application in Variable Structure Systems. Moscow, 1978.
  2. Decarlo, R.A., Zak, S.H., and Mattews, G.P., "Variable Structure Control of Nonlinear Multivariable Systems: A Tutorial," Proc. IEEE, 1988, 76, pp.212-232. https://doi.org/10.1109/5.4400
  3. Young, K.D., Utkin, V.I., Ozguner, U, "A Control Engineer's Guide to Sliding Mode Control," 1996 IEEE Workshop on Variable Structure Systems, pp.1-14
  4. Drazenovic, B.:The invariance conditions in variable structure systems, Automatica, 1969, (5), pp.287-295. https://doi.org/10.1016/0005-1098(69)90071-5
  5. J. H. Lee and M. J. Youn, "An Integral-Augmented Optimal Variable Structure control for Uncertain dynamical SISO System, KIEE(The Korean Institute of Electrical Engineers), vol.43, no.8, pp.1333-1351, 1994.
  6. V. I. Utkin and K. D. Yang, "Methods for Constructing Discontinuity Planes in Multidimentional Variable Structure Systems," Automat. Remote Control, vol. 39 no. 10 pp.1466-1470, 1978.
  7. D. M. E. El-Ghezawi, A. S. I. and S. A. Bilings, "Analysis and Design of Variable Structure Systems Using a Geometric Approach," Int. J. Control, vol,38, no.3 pp.657-671,1 1983. https://doi.org/10.1080/00207178308933100
  8. A. Y. Sivaramakrishnan, M. Y. Harikaran, and M. C. Srisailam, " Design of Variable Structure Load Frequency cntroller Using Pole Assignment Technique," Int. J. Control, vol,40 no.3, pp. 487-498, 1984. https://doi.org/10.1080/00207178408933289
  9. C. M. Dorling and A. S. I. Zinober, "Two approaches to Hyperplane Design in Muntivariable Variable Structure Control systems," Int. J. Control, vol,44 no.1, pp. 65-82 1986. https://doi.org/10.1080/00207178608933583
  10. S. V. Baida and D. B. Izosimov, "Vector Method of Design of Sliding Motion and Simplex Algorithms." Automat. Remote Control, vol. 46 pp.830-837, 1985. Variable Structure Control systems," Int. J. Control, vol,44 no.1, pp. 65-82 1986. https://doi.org/10.1080/00207178608933583
  11. B. Fernandez and J. K. Hedrick, "Control of Multivariable Nonlinear System by the Sliding Mode Method," I. J. Control, vol.46, no.3 pp.1019-1040, 1987. https://doi.org/10.1080/00207178708547410
  12. S. R. Hebertt, "Differential Geometric Methods in Variable Structure Control," Int. J. Control, vol,48 no.4, pp.1359-1390, 1988. https://doi.org/10.1080/00207178808906256
  13. T. L. Chern and Y. C. Wu, "An Optimal Variable Structure Control with Integral Compensation for Electrohydraulic postion Servo Control Systems," IEEE T. Industrial Electronics, vol.39, no.5 pp460-463, 1992. https://doi.org/10.1109/41.161478
  14. K. Yeung, C. Cjiang, and C. Man Kwan, "A Unifying Design of Sliding Mode and Classical Controller' IEEE T. Automatic Control, vol.38, no.9 pp1422-1427, 1993. https://doi.org/10.1109/9.237660
  15. S. H. Zak and S. Hui, "Output Feedback Variable Structure Controllers and State Estimators for Uncertain/Nonlinear Dynamic Systems," IEE Proc. vol. 140, no.1 pp.41-50, 1993 https://doi.org/10.1049/ip-d.1993.0006
  16. R. DeCarlo and S. Drakunov, "Sliding Mode Control Design via Lyapunov Approach," Proc. 33rd IEEE Conference on CDC, pp.1925-1930, 1994.
  17. W. C. Su S. V. Drakunov, and U. Ozguner, "Constructing Discontinuity Surfaces for Variable Structure Systems: A Lyapunov Approach," Automatica, vol.32 no.6 pp.925-928,1996 https://doi.org/10.1016/0005-1098(96)00017-9
  18. J. Ackermann and V. I. Utkin, " Sliding Mode Control Design based on Ackermann's Formula," IEEE T. Automatic Control, vol.43, no.9 pp.234-237, 1998. https://doi.org/10.1109/9.661072
  19. T. Acarman and U. Ozguner, "Relation of Dynamic Sliding surface Design and High Order Sliding Mode Controllers," Proc. 40th IEEE Conference on CDC, pp.934-939, 2001.
  20. W. J. Cao and J. X. Xu, "Nonlinear Integral-Type Sliding Surface for Both Matched and Unmatched Uncertain Systems," IEEE T. Automatic Control, vol.49, no83 pp1355-1360,2004. https://doi.org/10.1109/TAC.2004.832658
  21. H. H. Choi, " LMI-Based Sliding Surface Design for Integral Sliding Mode Control of Mismatched Uncertain Systems, IEEE T. Automatic Control, vol.52, no.2 pp736-742, 2007. https://doi.org/10.1109/TAC.2007.894543
  22. J. H. Lee, 'A Poof of Utkin's Theorem for a SI Uncertain Linear Case," KIEE (to be appear)
  23. J. H. Lee, 'A Poof of Utkin's Theorem for a SI Uncertain Integral System," KIEE (to be appear)
  24. M. Zohdy, M. S. Fadali, and J. Liu, "Variable Structure Control Using Decomposition," IEEE T. Automatic Control, vol.37, no.10 pp1514-1517, 1992. https://doi.org/10.1109/9.256371