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

  • 제66권11호
  • /
  • Pages.1612-1619
  • /
  • 2017
  • /
  • 1975-8359(pISSN)
  • /
  • 2287-4364(eISSN)
대한전기학회 (The Korean Institute of Electrical Engineers)
권호 표지
DOI QR코드

DOI QR Code

단일입력 불확실 비선형 시스템에 대한 Utkin 정리의 증명

A Poof of Utkin's Theorem for SI Uncertain Nonlinear Systems

  • Lee, Jung-Hoon (Dept. of Control & Instrumentation Eng. Gyeongsang Nat. University)
  • 투고 : 2017.06.16
  • 심사 : 2017.09.27
  • 발행 : 2017.11.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this note, a complete proof of Utkin's theorem is presented for SI(single input) uncertain nonlinear systems. The invariance theorem with respect to the two nonlinear transformation methods so called the two diagonalization methods is proved clearly, comparatively, and completely for SI uncertain nonlinear systems. With respect to the sliding surface and control input transformations, the equation of the sliding mode i.e., the sliding surface is invariant, which is proved completely. Through an illustrative example and simulation study, the usefulness of the main results is verified. By means of the two nonlinear transformation methods, the same results can be obtained.

키워드

참고문헌

  1. A. Salihbegovic, "Multivariable Sliding Mode Approach with Enhanced Robustness Properties Based on the Robust Internal-Loop Compensator for a class of Nonlinear Mechanical Systems" 2016 European Control Conferenece(ECC), June 29 -July 1, Aaiborg Denmark, pp. 382-387, 2016.
  2. O. Bicer, M. U. Salamci, and F. Kodalak, "State Dependent Riccati Equation Based Sliding Mode Control for Nonlinear Systems with Mismatched Uncertainties" 2016 17th International Carpathian Control Conference (ICCC), pp. 54-59, 2016.
  3. 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
  4. V.I. Utkin, Sliding Modes and Their Application in Variable Structure Systems. Moscow, 1978.
  5. 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.
  6. 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
  7. Drazenovic, B.: The invariance conditions in variable structure systems, Automatica, 1969, (5), pp. 287-295.
  8. 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.
  9. 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
  10. 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.
  11. 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
  12. A. Y. Sivaramakrishnan, M. Y. Harikaran, and M. C. Srisailam, "Design of Variable Structure Load Frequency controller Using Pole Assignment Technique," Int. J. Control, vol, 40, no. 3, pp. 487-498, 1984. https://doi.org/10.1080/00207178408933289
  13. C. M. Dorling and A. S. I. Zinober, "Two approaches to Hyperplane Design in Multivariable Variable Structure Control systems," Int. J. Control, vol. 44, no. 1, pp. 65-82, 1986. https://doi.org/10.1080/00207178608933583
  14. 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.
  15. 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
  16. 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, pp. 460-463, 1992. https://doi.org/10.1109/41.161478
  17. 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, pp. 1422-1427, 1993. https://doi.org/10.1109/9.237660
  18. R. DeCarlo and S. Drakunov, "Sliding Mode Control Design via Lyapunov Approach," Proc. 33rd IEEE Conference on CDC, pp. 1925-1930, 1994.
  19. 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
  20. 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.
  21. 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, no. 83, pp. 1355-1360, 2004. https://doi.org/10.1109/TAC.2004.832658
  22. 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, pp. 736-742, 2007. https://doi.org/10.1109/TAC.2007.894543
  23. J. H. Lee, "A Proof of Utkin's Theorem for a MI Uncertain Linear Case", KIEE(The Korean Institute of Electrical Engineers), vol. 59, no. 9, pp. 1680-11685, 2010.