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

The Korean Institute of Electrical Engineers (대한전기학회)
권호 표지
DOI QR코드

DOI QR Code

A New Robust Variable Structure Controller for Uncertain Affine Nonlinear Systems with Mismatched Uncertainties

부정합조건 불확실성을 갖는 비선형 시스템을 위한 새로운 강인한 가변구조제어기

  • 이정훈 (ERI, 경상대학교 공대 전기전자공학부 제어계측공학과)
  • Received : 2009.11.03
  • Accepted : 2010.02.16
  • Published : 2010.05.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, a systematic design of a new robust nonlinear variable structure controller based on state dependent nonlinear form is presented for the control of uncertain affine nonlinear systems with mismatched uncertainties and matched disturbance. After an affine uncertain nonlinear system is represented in the form of state dependent nonlinear system, a systematic design of a new robust nonlinear variable structure controller is presented. To be linear in the closed loop resultant dynamics, the linear sliding surface is applied. A corresponding control input is proposed to satisfy the closed loop exponential stability and the existence condition of the sliding mode on the linear sliding surface, which will be investigated in Theorem 1. Through a design example and simulation study, the usefulness of the proposed controller is verified.

Keywords

References

  1. M. Vidyasagar, "New Directions of Research in Nonlinear System Theory," Proc. of the IEEE vol.74 no.8 pp.1060-1091, 1986. https://doi.org/10.1109/PROC.1986.13595
  2. P Kokotovic and M. Arcak, "Constructive Nonlinear Control: a Historical Perspective," Automatica, vol.37, pp.637-662, 2001. https://doi.org/10.1016/S0005-1098(01)00002-4
  3. B. D. O. Anderson and J. B. More, Optimal Control, Prentice-Hall, 1990.
  4. I. Horowitz, "Survey of Quantitative Feedback Theory(QFT), Int. J. Control, vol.53, no.2 pp.255-291, 1991. https://doi.org/10.1080/00207179108953619
  5. W. J. Rugh and J. Shamma, "Research on Gain Scheduling," Automatica, vol.36, pp.1401-1425, 2000. https://doi.org/10.1016/S0005-1098(00)00058-3
  6. X. Cai, R. Lin and S. Su, "Robust stabilization for a class of Nonlinear Systems, IEEE CDC pp.4840-4844, 2008.
  7. S. Gutman, "Uncertain dynamical Systems:A Lyapunov Min-Max Approach," IEEE Trans. Autom. Contr, AC-24, no. 1, pp.437-443, 1979.
  8. L. R. Hunt, R. Su, and G. Meyer, "Global Transformations of Nonlinear Systems," IEEE Trans. Autom. Contr, AC-28, no. 1, pp.24-31, 1987.
  9. A Isidori, Nonliear Control System, 2e Springer-Verlag, 1989.
  10. J. J. E. Slottine and W Li, Applied Nonlinear Control, Prentice-Hall, 1991.
  11. H. K. Khalil, Nonlinear Systems, 2e Prentice-Hall, 1996.
  12. L. Lijun and X Chengkand, "Robust Backstepping Design of a Nonlinear Output Feedbcak System," IEEE CDC 2008, pp.5095-5099.
  13. K. S. Narendra, "Parameter Adaptive Control-the End...or the Beginning-" Proc. 33rd IEEE CDC, 1994.
  14. Q. Zheng and F. Wu, "Lyapunov Redesign of Adpative Controllers for Polynomial Nonlinear systems," Proc. IEEE ACC 2009, pp.5144-5149.
  15. V.I. Utkin,, Sliding Modes and Their Application in Variable Structure Systems. Moscow, 1978.
  16. 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
  17. 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
  18. Drazenovic, B.:The invariance conditions in variable structure systems, Automatica, 1969, (5), pp.287-295.
  19. B. C. Toledo and R. C. Linares, "On Robust Regulation via sliding Mode for Nonlinear Systems," System & Control Letters, vol.24, pp.361-371, 1995. https://doi.org/10.1016/0167-6911(94)00039-X
  20. G. Bartolini and A Ferrara, "On Multi-Input Sliding Mode Control of Uncertain Nonlinear Systems," Proc. IEEE 34th CDC, p.2121-2124, 1995.
  21. X. Y. Lu and S. K. Spurgeon, "Robust Sliding Mode Control of Uncertain Nonlinear System," System & control Letters, vol.32, pp.75-90, 1997. https://doi.org/10.1016/S0167-6911(97)00061-3
  22. G. Bartolini A. Pisano, E. Usai, " Digital Second-Order sliding Mode Control for Uncertain Nonlinear Systems," Automatica, vol.37 pp.1371-1377, 2001. https://doi.org/10.1016/S0005-1098(01)00085-1
  23. J. Adamy and A. Flemming, "Soft Variable Structure Control:a survey," Automatica, vol.40, pp.1821-1844, 2004. https://doi.org/10.1016/j.automatica.2004.05.017
  24. Y. Wang, C. Jiang, D. Zhou, F. Gao, "Variable Structure Control for a Class of Nonlinear Systems with Mismatched Uncertainties," Applied Mathematics and Computation, pp.1-14, 2007.
  25. G. Y. Tang, R. Dong, and H. W. Gao, "Optimal sliding Mode Control for Nonlinear System with Time Delay," Nonlinear Analysis: Hybrid Systems, vol.2, pp891-899, 2008. https://doi.org/10.1016/j.nahs.2008.02.003
  26. Y. D. Pan, K. D. Kumar, G. J. Liu, and K. Furuta, "Design of Variable Strucutre Control system with Nonlinear Time Varying sliding Sector," IEEE Trans. Autom. Contr, AC-54, no. 8, pp.1981-1986, 2009.
  27. X. Hu and C. Martin, " Linear Reachability Versus Global Stabilization," IEEE Trans. Autom. Contr, AC-44, no. 6, pp.1303-1305, 1999.
  28. Y. M. Sun, " Linear Controllability Versus Global Controllability," IEEE Trans. Autom. Contr, AC-54, no. 7, pp.1693-1697, 2009.
  29. W. H. Chen, D. J. Ballance, and P. J. Gawthrop, "Optimal Control of Nonlinear System:A Predictive Control Approach," Automatic, vol. 39, pp633-641, 2003 https://doi.org/10.1016/S0005-1098(02)00272-8
  30. 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.
  31. J. H. Lee, "Highly robust position control of BLDDSM using an improved integral variable structure system," Automatica, vol.42,, pp.929-935, 2006 https://doi.org/10.1016/j.automatica.2006.01.021