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The Korean Institute of Electrical Engineers (대한전기학회)
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A Robust Sliding Mode Controller for Unmatched Uncertain Severe Sate Time-Delay Systems

큰 상태변수 시간 지연 부정합조건 불확실성 시스템을 위한 강인한 슬라이딩 모드 제어기

  • 이정훈 (공학연구원, 경상대학교 공대 제어계측공학과)
  • Received : 2010.04.15
  • Accepted : 2010.09.13
  • Published : 2010.10.01
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Abstract

This note is concerned with a robust sliding mode control(SMC) for a class of unmatched uncertain system with severe commensurate state time delay. The suggested method is extended to the control of severe state time delay systems with unmatched uncertainties except the matched input matrix uncertainty. A transformed sliding surface is proposed and a stabilizing control input is suggested. The closed loop stability together with the existence condition of the sliding mode on the proposed sliding surface is investigated through one Lemma and two Theorems by using the Lyapunov direct method with the concept of the control Lyapunov function instead of complex Lyapunov-Kravoskii functionals. Through an illustrative example and simulation study, the usefulness of the main results is verified.

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References

  1. J. P. Richard, "Time-Delay Systems: An Overview of Some Recent Advances and Open Problems," Automatica, vol.39, pp1667-1694, 2003. https://doi.org/10.1016/S0005-1098(03)00167-5
  2. V. L. Kharitonov, "Robust stability Analysis of Time Delay Systems: A Survey," Annual Review in Control, vol.23, pp185-196, 1999. https://doi.org/10.1016/S1367-5788(99)90087-1
  3. S. Majhi and D. Atherton, "A New Smith Predictor and Controller for Unstable and integrating Processes with time delay," In 37th IEEE CDC98, Tamp, FL, December, pp1341-1345, 1998.
  4. W. H. Kwon and A. E. Pearson, "A Note on Feedback Stabilization of a Differential-Difference System," IEEE T. Automatic Control, vol.22, no.6 pp.468-470, 1977. https://doi.org/10.1109/TAC.1977.1101522
  5. W. H. Kwon and A. E. Pearson, "Feedback Stabilization of Linear Systems with Delayed Control," IEEE T. Automatic Control, vol.25, no.2 pp.266-269, 1980. https://doi.org/10.1109/TAC.1980.1102288
  6. Y. A. Fiagbeldzi and A. E. Pearson, "Feedback Stabilization of Linear Autonomous Time Lag Systems," IEEE T. Automatic Control, vol.31, no.9 pp.847-855, 1986. https://doi.org/10.1109/TAC.1986.1104417
  7. M. S. Mahmoud and N. F. Al-Muhairi, "Quadratic Stabilization of Continuous Time Systems with State Delay and Norm-Bounded Time-Varying Uncertainties," IEEE T. Automatic Control, vol.39, no.10 pp.2135-1741, 1994 https://doi.org/10.1109/9.328812
  8. H. H. Choi and M. J. Chung, "An LMI Approach to $H_\infty$ Controller Design for Linear Time-Delay Systems," Automatica, vol.33 no.4 pp. 737-739, 1997. https://doi.org/10.1016/S0005-1098(96)00242-7
  9. H. H. Choi and M. J. Chung, "Robust Observer-Based $H_\infty$ Controller Design for Linear Uncertain Time-Delay Systems," Automatica, vol.33 no.9 pp. 1749-1752, 1997. https://doi.org/10.1016/S0005-1098(97)82235-2
  10. M. Jankovic, "Control Lyapunov-Razumikhin unctions and Robust Stabilization of Time-Delay Systems," IEEE T. Automatic Control, vol.46, no.7 pp.1048-1060, 2001.
  11. S. K. Nguang, "Robust Stabilization of a Class of Time-Delay Nonlinear Systems," IEEE T. Automatic Control, vol.45, no.4 pp.756-762, 2000. https://doi.org/10.1109/9.847117
  12. F. Mazenc and S. I. Niculescu, "Lyapunov Stability Analysis for Nonlinear Delay Systems," System & Control Letters, vol.42 pp.245-251, 2001. https://doi.org/10.1016/S0167-6911(00)00093-1
  13. V. L. Kharitonov and A. P. Zhabko, "Lyapunov-Krasovskii Approach to the Robust Stability Analysis of Time-Delay Systems," Automatica, vol.39, pp.15-20, 2003. https://doi.org/10.1016/S0005-1098(02)00195-4
  14. V. L. Kharitonov, "Lyapunov-Krasovskii Functionals for Scalar Time Delay Equations," System & Control Letters, vol.51, pp.133-149, 2004. https://doi.org/10.1016/S0167-6911(03)00221-4
  15. X. J. Jing, D. L. Tan, and Y. C. Wang, "An LMI Approach to Stability of Systems with Severe Time Delay," IEEE T. Automatic Control, vol.49, no.7 pp.1192-1195, 2004. https://doi.org/10.1109/TAC.2004.831109
  16. X. Jiao and T. Shen, "Adaptive Feedback Control of Nonlinear Time Delay Systems:The Lasalle-Razumikhin-Based Approach," IEEE T. Automatic Control, vol.49, no.7 pp.1192-1195, 2004. https://doi.org/10.1109/TAC.2004.831109
  17. C. Hua, X. Guan, and P. Shi, "Robust Backstepping Control for a class of Time Delayed Systems," IEEE T. Automatic Control, vol.50, no.6 pp.894-899, 2005. https://doi.org/10.1109/TAC.2005.849255
  18. C. Hua, X. Guan, and G. Feng, "Robust Stabilization for a Class of Time-Delay Systems with Triangular Structure," IET Control Theory Appl. vol.1 no.4 pp875-879, 2007. https://doi.org/10.1049/iet-cta:20060404
  19. L. Wu and W. X. Zheng, "Passivity-Based Sliding Mode Control of Uncertain Singular Time-Delay System," Automatica, vol.45 pp.2120-2127, 2009. https://doi.org/10.1016/j.automatica.2009.05.014
  20. K. Shyu and J. Yan, "Robust Stability of Uncertain Time-Delay Systems and its Stabilization by Variable Structure Control," Int. J. Control, vol.57, pp.237-246, 1993. https://doi.org/10.1080/00207179308934385
  21. R El-Khazail, "Variabel Structure Robust Control of Uncertain Time-Delay Systems," Automatica, vol.34 no.3 pp. 327-332, 1998. https://doi.org/10.1016/S0005-1098(97)00200-8
  22. K. J. Hu, V. R. Basker, and O. D. Crisalle, "Sliding Mode Control of Uncertain Input-Delay Systems, Proceedings of ACC, Pennsylvania, June, pp.564-568, 1998.
  23. Y. H. Roh and J. H. Oh, "Sliding Mode Control with Delay Compensation for Uncertain Input-Delay Systems," Proceedings of ACC, California, June, pp.309-313, 1999.
  24. E. M. Jafarov, "Design of Sliding Mode Control for Multi-Input Systems with Multiple State Delays," Proceedings of ACC, Chicago, June, pp.1139-1143, 2000.
  25. X. Li and R. A. DeCarlo, "Memoryless Sliding Mode Control of Uncertain Time-Delay Systems," Proceedings of ACC, Arlington, June, pp.25-27, 2001.
  26. Y. Xia, J. Han, and Y. Jia, "A Sliding Mode Control for Linear Systems with Input and State Delays," Proceedings of ACC, Las Vegas December, pp.3332-3337, 2002.
  27. Y. Xia and Y. Jia, "Robust Sliding Mode Control for Uncertain Time-Delay Systems: An LMI Approach," IEEE T. Automatic Control, vol.48, no.6 pp.1086-1092, 2003. https://doi.org/10.1109/TAC.2003.812815
  28. Y. J. Pan, "A New Sliding Mode Control Approach for a Class of Nonlinear Uncertain Systems with State Time Delays," Proceedings of ACC, New York July, pp.5869-5874, 2007.
  29. G. Tang, R. Dong, and H. Gao, "Optimal Sliding Mode Control for Nonlinear Systems with Time Delay," Nonlinear Analysis: Hybrid Systems, vol.2 pp.891-899, 2008. https://doi.org/10.1016/j.nahs.2008.02.003
  30. L. Huang and X. Mao, "SMC Design for Robust $H_\infty$ Control of Uncertain Stochastic Delay Systems," Automatica, vol.46 pp.405-412, 2010. https://doi.org/10.1016/j.automatica.2009.11.013
  31. Z. Artstein, "Linear Systems with Delayed Controls: A Reduction," IEEE T. Automatic Control, vol.27, no.4 pp.869-879, 1982. https://doi.org/10.1109/TAC.1982.1103023
  32. J. L. Ramos and A. E. Pearson, "Output Feedback Stabilizing Controller for Time-Delay Systems," Automatica, vol.36 pp.613-617, 2000. https://doi.org/10.1016/S0005-1098(99)00150-8
  33. V.I. Utkin,, Sliding Modes and Their Application in Variable Structure Systems. Moscow, 1978.
  34. 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
  35. J. J. E. Slottine and W Li, Applied Nonlinear Control(2e), Prentice-Hall, 1991.
  36. J. H. Lee, 'A Poof of Utkin's Theorem for a MI Uncertain System," KIEE, vol.59, no.9, 2010.
  37. J. H. Lee, 'A Poof of Utkin's Theorem for a SI Uncertain Integral System," KIEE (to be appear)
  38. 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.
  39. 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.
  40. 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.
  41. 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.