Journal of IKEEE (전기전자학회논문지)

Institute of Korean Electrical and Electronics Engineers (한국전기전자학회)
권호 표지
DOI QR코드

DOI QR Code

Proofs of Utkin's Theorem for MIMO Uncertain Integral Linear Systems

  • Lee, Jung-Hoon (ERI, Dept. of Control & Instrum. Eng., Gyeongsang National University)
  • Published : 2014.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

The uncertain integral linear system is the integral-augmented uncertain system to improve the resultant performance. In this note, for a MI(Multi Input) uncertain integral linear case, Utkin's theorem is proved clearly and comparatively. With respect to the two transformations(diagonalizations), the equation of the sliding mode is invariant. By using the results of this note, in the SMC for MIMO uncertain integral linear systems, the existence condition of the sliding mode on the predetermined sliding surface is easily proved. The effectiveness of the main results is verified through an illustrative example and simulation study.

Keywords

References

  1. T. L. Chern and Y. C. Wu, "Design of Integral Variable Structure Controller and Application to Electrohydraulic Velocity Servosystems, lEE Proceedings-D, vol. 138, no.5, pp.439-444, 1991.
  2. T. L. Chern and Y. C. Wu, "An Optimal Variable Structure Control with Integral Compensation for Electrohydraulic Position Servo Control Systems, IEEE Trans. Industrial Electronics, vol. 39, no. 5, pp.460-463, 1992. https://doi.org/10.1109/41.161478
  3. 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.
  4. 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
  5. J. H. Lee, Design of Integral-Augmented Optimal Variable Structure Controllers. Ph. D. Dissertation, KAIST, 1995.
  6. H. C. Tseng and P. V. Kokotovic, "Tracking and Disturbance Rejection in Nonlinear Systems: the Integral Manifold Approach," Proceedings of the 27Th. Conference on Decision and Control(CDC'88), vo1.1, pp.459,463, 1988.
  7. L. W. Chang, "A MIMO Sliding Control with a First-Order Plus Integral Sliding Condition," Autometica, vol. 27, no. 5, pp.853-858, 1991. https://doi.org/10.1016/0005-1098(91)90040-9
  8. E. Y. Y. Ho and P. C. Sen, "Control Dynamics of Speed Drive Systems Using Sliding Mode Controllers with Integral Compensation" IEEE Trans. Industry Applications, vol. 27, no. 5 Set/Oct. pp.883-892, 1991. https://doi.org/10.1109/28.90343
  9. J. J. Kim, Design of Variable Structure Controllers with Time-Varying Switching Surfaces. Ph. D. Dissertation, KAIST, 1993.
  10. V. I. Utkin and J. Shi, "Integral Sliding Mode in System Operating Under Uncertainty Conditions," Proc. 35rd IEEE Conference on CDC, pp.4591-4596, 1996.
  11. J. D. Wang, T. L. Lee and Y. T. Juang, "New Methods to Design an Integral Variable Structure Controller," IEEE T. Automatic Control, vol.41, no.9 pp140-143, 1996. https://doi.org/10.1109/9.481620
  12. J. H. Lee, "A New Robust Integral Variable Structure Controller for Uncertain More Affine Nonlinear Systems with Mismatched Uncertainties," KIEE, vol.59, no.6, pp.1173-1178, 2010.
  13. V. I. Utkin, Sliding Modes and Their Application in Variable Structure Systems. Moscow, 1978.
  14. R. A. Decarlo, S. H. Zak, and G. P. Mattews, "Variable Structure Control of Nonlinear Multivariable Systems: A Tutorial," Proc. IEEE, vol. 76, pp.212-232, 1988. https://doi.org/10.1109/5.4400
  15. K. D. Young, V. I. Utkin, and U. Ozguner, "A Control Engineer's Guide to Sliding Mode Control," IEEE Workshop on Variable Structure Systems, pp.1-14, 1996.
  16. B. Drazenovic, "The Invariance Conditions in Variable Structure systems," Automatica, vol. 5, pp.287-295, 1969. https://doi.org/10.1016/0005-1098(69)90071-5
  17. V. 1. Utkin and K. D. Yang, "Methods for Constructing Discontinuity Planes in Multidemensional Variable Structure Systems," Automat. Remote Control, vol. 39, no. 10, pp.1466-1470, 1978.
  18. C. M. Dorling and A. S. 1. 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
  19. D. M. E. El-Ghezawi, A. S. 1. Zinober, 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, 1983. https://doi.org/10.1080/00207178308933100
  20. 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
  21. 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
  22. 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
  23. R. DeCarlo and S. Drakunov, "Sliding Mode Control Design via Lyapunov Approach," Proc. 33rd IEEE Conference on CDC, pp.1925-1930, 1994.
  24. 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
  25. 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.
  26. 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
  27. 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
  28. 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.
  29. 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
  30. G, Bartolini and A. Ferrara, "Multi-Input Sliding Mode Control f a Class of Uncertain Nonlinear Systems," IEEE T. Automatic Control, vol.41, no11 pp.1662-1666, 1996. https://doi.org/10.1109/9.544004