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 Dynamic Output Feedback Variable Structure Controller for Uncertain Systems with Unmatched System Matrix Uncertainty

부정합 시스템 행렬 불확실성을 갖는 시스템을 위한 동적 출력 궤환 가변 구조 제어기

  • 이정훈 (경상대학교 공대 제어계측공학과)
  • Received : 2010.04.21
  • Accepted : 2010.09.16
  • Published : 2010.11.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, a variable structure dynamic output feedback controller with an transformed sliding surface is designed for the improved robust control of a uncertain system under unmatched system uncertainty, matched input matrix uncertainty, and disturbance satisfying some conditions. This paper is extended from the results of the static output feedback VSS in [9]. To effectively remove the reaching phase problems, an initial condition of the dynamic output is determined. The previous some limitations on the dynamic output feedback variable structure controller is overcome in this systematic design. A stabilizing control is designed to generate the sliding mode on the predetermined sliding surface S=0 and as a results the closed loop exponential stability is obtained and proved together with the existence condition of the sliding mode on S=0 for all unmatched system matrix uncertainties. To show the usefulness of the algorithm, a design example and computer simulations are presented.

Keywords

References

  1. V. L. Syrmos, C. T. Abdallaah, P. Dorato, and K. Grigoriadis, "Static Output Feedback-A Survey," Automatica, vol.33 no.2 pp.125-137, 1997. https://doi.org/10.1016/S0005-1098(96)00141-0
  2. S. V. Emelyanov, S. K. Korovin, A. L. Nersisian, and Y. E. Nisenzon, "Output Feedback Stabilization of Uncertain Plants: A Variable Structure systems Approach," I. J. Control, vol.55, on.1 pp.61-81, 1992 https://doi.org/10.1080/00207179208934226
  3. S. Oh and H. K. Khalil, "Output Feedback Stabilization Using Variable Structure Control," I. J. Control, vol.62, on.4 pp.831-848, 1995. https://doi.org/10.1080/00207179508921571
  4. E. J. Davision and S. H. Wang, "On Pole Assignment in Linear Multivariable System Using Output Feedback," IEEE T. on Automatic Control, vol.20, pp.516-518, 1975 https://doi.org/10.1109/TAC.1975.1101023
  5. B. A. White, "Some Problems in Output Feedback in Variable Structure Control Systems," in Proc. 7th IFAC/IFORS : also in Identification and system Parameter Estimation, 1985 York, UK Pergamon Press, pp.1921-1925, Oxford 1985.
  6. S. H. Zak and S. Hui, "On Variable Structure Output Feedback Controllers for Uncertain Dynamic Systems," IEEE T. on Automatic Control, vol.38, no.10 pp.1509-1512, 1993. https://doi.org/10.1109/9.241564
  7. C. M. Kwan, "Further Results on Variable Output Feedback controllers," IEEE T. on Automatic Control, vol.46 no.9, pp.1505-1508, 2001. https://doi.org/10.1109/9.948487
  8. H. H. Choi, "Variable Structure Output Feedback Control Design for a class of Uncertain Dynamic Systems," Automatica, vol.38, pp.335-341, 2002. https://doi.org/10.1016/S0005-1098(01)00211-4
  9. J. H. Lee, "A Static Output Feedback Integral Variabke Strucutre Controller for Uncertian System with Unmatched System Matrix Uncertainty," KIEE(The Korean Institute of Electrical Engineers), vol.59, no.2, pp.411-416, 2010.
  10. V.I. Utkin,, Sliding Modes and Their Application in Variable Structure Systems. Moscow, 1978.
  11. 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
  12. A. Steinberg and E. P. Ryan, "Dynamic Output Feedback Control of a Class of Uncertain System," IEEE T. on Automatic Control, vol.31, no.12, pp.1163-1165, 1986 https://doi.org/10.1109/TAC.1986.1104201
  13. S. S. Stanlovic, D. M. Stipanovic, D. D. Siljak, "Decentralized Dynamic Output Feedback for Robust Stabilization of a Class of Nonlinear Interconnected System," Automatica, vol43, pp.861-867,, 2007. https://doi.org/10.1016/j.automatica.2006.11.010
  14. M. B. Diong and J. V. Medanic, "Dynamic Output Feedback Variable Structure Control for System Stabilization," Proceedings. of ACC'91, pp.609-614, 1991.
  15. M. B. Diong and J. V. Medanic, "Dynamic Output Feedback Variable Structure Control for System Stabilization," Int. J. Control, vol.56, no.3 pp.607-630, 1992. https://doi.org/10.1080/00207179208934331
  16. S. K. Bag, S. K. Spurgeon, and C Edwards, "Output Feedback Sliding Mode Design forl Linear Uncertain Sytems," IEE Proc.- Control Theory-Appl., vol.144, no.3 pp.209-216, 1997. https://doi.org/10.1049/ip-cta:19971122
  17. K. K. Shyu, Y. W. Tsai, and C. K. Lai, "A Dynamic Output Feedback Controller for Mismatched Uncertain Variable Structure Systems," Automatica, vol. 37, pp.775-779, 2001 https://doi.org/10.1016/S0005-1098(01)00014-0
  18. P. G. Park, D. J. Choi, S. G. Kong, "Output Feedback Variable Structure Control for Linear system with Uncertainties and Disturbances," Automatica, vol.43, pp.72-79, 2007. https://doi.org/10.1016/j.automatica.2006.07.015
  19. J. L. Chang, "Dynamic Output Integral Sliding Mode Control with Disturbance Attenuation," IEEE T. on Automatic Control, vol.54 no.11, pp.2653-2658, 2009 https://doi.org/10.1109/TAC.2009.2031569
  20. J. L. Chang, "Dynamic Output Feedback Sliding Mode Control for Uncertain Mechanical Systems without Velocity Measurements, " ISA Transactions, vol.49 pp229-234, 2010. https://doi.org/10.1016/j.isatra.2009.11.002
  21. 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.
  22. J. H. Lee, 'A Poof of Utkin's Theorem for a MI Uncertain System," KIEE, vol.59, no.9, 2010.
  23. J. H. Lee, 'A Poof of Utkin's Theorem for a SI Uncertain Integral System," KIEE (to be appear)
  24. 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.
  25. J. H. Lee, 'A MIMO VSS with an Integral-Augmented Sliding Surface for Uncertain Multivariable Systems," KIEE, vol.59, no.5, pp.950-958, 2010.
  26. 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.
  27. J. H. Lee, 'A New Robust Variable Structure Controller with Nonlinear Integral-Type Sliding Surface for Uncertain More Affine Nonlinear systems with Mismatched Uncertainties and Disturbances," KIEE, vol.59, no.7, pp.1295-1301, 2010.
  28. J. H. Lee, 'A New Robust Discrete Static Output Feedback Variable Structure Controller with Disturbance Observer for Uncertain Discrete Systems," KIEE, vol.59, no.3, pp.630-635, 2010.
  29. J. H. Lee, 'A New Robust Variable Structure Controller with Nonlinear Integral-Type Sliding Surface for Uncertain Systems with Mismatched Uncertainties and disturbances," KIEE, vol.59, no.3, pp.623-629, 2010.
  30. J. H. Lee, 'A New Discrete Integral Variable Structure Controller with Disturbance Observer for Uncertain discrete Systems," KIEE, vol.59, no.6, pp.1167-1172, 2010.
  31. J. H. Lee, 'A New Robust Discrete Integral Static Output Feedback Variable Structure Controller with Disturbance Observer and Integral Dynamic-Type Sliding Surface for Uncertain Discrete Systems," KIEE, vol.59, no.7, pp.1289-1294, 2010.