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

The Institute of Electronics and Information Engineers (대한전자공학회)
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A New Robust Continuos VSCS by Saturation Function for Uncertain Nonlinear Plants

불확실 비선형 플랜트를 위한 포화 함수에 의한 새로운 강인한 연속 가변구조제어시스템

  • Lee, Jung-Hoon (Dept of Control & Instrum. Eng., Gyeongsang National University)
  • 이정훈 (국립 경상대학교 제어계측공학과)
  • Received : 2011.01.21
  • Accepted : 2011.05.12
  • Published : 2011.05.25
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Abstract

In this note, a systematic design of a new robust nonlinear continuous variable structure control system(VSCS) based on the modified 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 VSCS is presented. The uncertainty of the nonlinear system function is separated into the tow parts, i.e., state dependent term and state independent term for extension of target plants. To be linear in the closed loop resultant dynamics and in order to easily satisfy the existence condition of the sliding mode, the transformed 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 transformed sliding surface, which will be investigated in Theorem 1. For practical application, the discontinuity of the control input as the inherent property of the VSS is improved dramatically. Through a design example and simulation studies, the usefulness of the proposed controller is verified.

본 연구에서는 수정된 상태변수 의존 비선형 형을 바탕으로 부정합조건 불확실성과 정합조건 외란을 갖는 비선형 시스템의 제어를 위한 새로운 둔감한 비선형 연속 가변구조제어기의 체계적인 설계를 제안한다. 부정합조건 불확실과 정합조건 외란 비선형 시스템을 상태변수 의존 비선형 시스템 형으로 표현한 후 체계적인 둔감한 새로운 제어기 설계를 한다. 대상 시스템의 확장을 위하여 비선형 시스템 함수의 불확정성을 상태변수 의존 항과 비의존 항 두 부분으로 나눈다. 본 비선형 제어는 제어 결과 동특성을 선형으로하기 위하여 그리고 슬라이딩 모드 존재조건을 쉽게 만족시키기 위하여 변환된 선형 슬라이딩 면을 선정한다. 선정된 슬라이딩 면 위에 슬라이딩 존재조건과 폐루프 지수 안정성을 만족하는 제어입력을 제안한다. 정리를 통하여 증명한다. 본 제어의 실용성을 위하여 가변구조제어의 내재된 특성인 제어입력의 불연속성을 극적으로 개선한다. 설계 예와 시뮬레이션 연구를 통하여 제안된 제어기의 유용성을 입증한다.

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," vol.37, pp.637-662, 2001.
  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, "A New Robust Variable Structure Controller for Uncertain Affine Nonlinear Systems with Mismatched Uncertainties," KIEE, vol.59, no.5, pp.945-949, 2010.
  31. Chern, T.L. and Wu., Y.C., "Design of Integral Variable Structure Controller and Application to Electrohydraulic Velocity Servosystems," IEE Proceedings-D, 1991, 138, No.5, pp.439-444.
  32. J. H. Lee, "A Poof of Utkin's Theorem for a MI Uncertain System," KIEE, vol.59, no.9, pp.1680-1685, 2010.