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Observer-based adaptive sliding mode control for nonlinear uncertain state-delayed systems

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  • Control Theory
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Abstract

This paper presents a methodological approach to design observer-based adaptive sliding mode control for a class of nonlinear uncertain state-delayed systems with immeasurable states. A novel switching surface is proposed and a state observer is employed to reconstruct the sliding mode control action. The proposed method does not need a priori knowledge of upper bounds on the norm of the uncertainties, but estimates them by using the adaptation technique so that the reaching condition can be satisfied. Based on Lyapunov stability theorem and linear matrix inequality (LMI) technique, the stability of the overall closed-loop nonlinear uncertain state-delayed system is guaranteed for the proposed control scheme under certain conditions. Furthermore, the state observer and control law can be constructed from the positive-definite solutions of two LMIs, and the design technique is simple and efficient. The validity of the proposed control methodology is demonstrated by simulation results.

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References

  1. B. Drazenovic’, “The invariant condition in variable structure systems,” Automatica, vol. 5, pp. 287–295, 1969.

    Article  MathSciNet  Google Scholar 

  2. V. I. Utkin, “Variable structure systems with sliding modes,” IEEE Trans. on Automatic Control, vol. 22, no. 2, pp. 212–222, 1977.

    Article  MATH  MathSciNet  Google Scholar 

  3. M. S. Mahmoud, “Dynamic control of systems with variable state-delay,” Int. J. Robust and Nonlinear Control, vol. 6, pp. 123–146, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  4. Y. H. Roh and J. H. Oh, “Sliding mode control for robust stabilization of uncertain input-delay systems,” Trans. on Control Automation, and Systems Engineering, vol. 2, no. 2, pp. 98–103, 2000.

    Google Scholar 

  5. C. H. Chou and C. C. Cheng, “Design of adaptive variable structure controller for perturbed time-varying state delay systems,” Journal of the Franklin Institute, vol. 338, pp. 35–46, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  6. D. Yue, S. Won, and O. Kwon, “Note on robust stabilization of uncertain input-delay systems by sliding mode control with delay compensation,” Trans. on Control Automation, and Systems Engineering, vol. 4, no. 3, pp. 195–198, 2002.

    Google Scholar 

  7. X. Li and R. A. DeCarlo, “Robust sliding mode control of uncertain time delay systems,” International Journal of Control, vol. 76, no. 13, pp. 1296–1305, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  8. Y. Xia and Y. Jia, “Robust sliding-mode control for uncertain time-delay systems: an LMI approach,” IEEE Trans. on Automatic Control, vol. 48, no. 6, pp. 1086–1092, 2003.

    Article  MathSciNet  Google Scholar 

  9. J. Xiang, H. Y. Su, J. Chu, and K. Q. Zhang, “LMI approach to robust delay dependent/independent sliding mode control of uncertain time-delay systems,” Proc. of the IEEE International Conference on Systems, Man and Cybernetics, vol. 3, pp. 2266–2271, 2003.

    Google Scholar 

  10. S. C. Qu and Y. J. Wang, “Sliding mode control for a class of uncertain input-delay systems,” Proc. of the 5th World Congress on Intelligent Control and Automation, Hangzhou, P. R. China, pp. 1184–1186, 2004.

  11. E. Leksono, A. Wijayanto, and K. Ohnishi, “Motion controller algorithm based on sliding mode controller/observer scheme,” Proc. of the 26th Annual Conference of IEEE on Industrial Electronics Society, vol. 3, pp. 1532–1537, 2000.

    Google Scholar 

  12. M. C. Pai and A. Sinha, “Sliding mode control of vibration in a flexible structure via estimated states and H ∞/µ techniques,” Proc. of American Control Conference, Chicago, pp. 1118–1123, 2000.

  13. M. K. Park, M. C. Lee, and S. J. Go, “The design of sliding mode controller wiht perturbation estimator using observer-based fuzzy adaptive network,” Trans. on Control Automation, and Systems Engineering, vol. 3, no. 2, pp. 117–123, 2001.

    Google Scholar 

  14. S. I. Han, “Sliding mode control with friction observer for a precise mechanical system in the presence of nonlinear dynamic friction,” Trans. on Control Automation, and Systems Engineering, vol. 4, no. 4, pp. 296–304, 2002.

    Google Scholar 

  15. J. L. Chang, “Output feedback sliding mode controller design via H ∞ theory,” Asian Journal of Control, vol. 5, pp. 24–31, 2003.

    Google Scholar 

  16. J. L. Chang, “Design of a robust controller using only output feedback to solve the servomechanism problem,” IEE Proc.-Control Theory Appl., vol. 150, no. 1, pp. 28–36, 2003.

    Article  Google Scholar 

  17. Q. P. Ha, H. Trinh, H. T. Nguyen, and H. D. Tuan, “Dynamic output feedback sliding-mode control using pole placement and linear functional observers,” IEEE Trans. on Industrial Electronics, vol. 50, no. 5, pp. 1030–1037, 2003.

    Article  Google Scholar 

  18. H. H. Choi and K. S. Ro, “LMI-based sliding-mode observer design method,” IEE Proc. — Control Theory Appl., vol. 152, no. 1, pp. 113–115, 2005.

    Article  Google Scholar 

  19. Z. Y. Shen, J. Zhao, and X. S. Gu, “On the design approach of robust sliding mode observers by using LMI,” Proc. of the IEEE International Conference on Automation and Logistics, pp. 1404–1408, 2007.

  20. Y. Niu, J. Lam, X. Wang, and D. W. C. Ho, “Observer-based sliding mode control for nonlinear state-delayed systems,” International Journal of Systems Science, vol. 35, no. 2, pp. 139–150, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  21. P. Gahinet, A. Nemirovski, A. Laub, and M. Chilali, LMI Control Toolbox User’s Guide, Massachusetts: The Mathworks, 1995.

    Google Scholar 

  22. J. G. VanAntwerp and R. D. Braatz, “A tutorial on linear and bilinear matrix inequalities,” Journal of Process Control, vol. 10, pp. 363–385, 2000.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Automation Engineering, Nan Kai University of Technology, Nantou, 54210, Taiwan R.O.C.

    Ming-Chang Pai

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  1. Ming-Chang Pai
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Correspondence to Ming-Chang Pai.

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Recommended by Editorial Board member Ju Hyun Park under the direction of Editor Young IL Lee.

Ming-Chang Pai received the M.S. and Ph.D. degrees in mechanical engineering in 1994 and 1998 from Pennsylvania State University, State College, P.A.. He is currently an Associate Professor in the Department of Automation Engineering at Nan Kai University of Technology. His research interests are in mechatronics, robots, robust control and nonlinear control.

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Pai, MC. Observer-based adaptive sliding mode control for nonlinear uncertain state-delayed systems. Int. J. Control Autom. Syst. 7, 536–544 (2009). https://doi.org/10.1007/s12555-009-0405-3

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  • DOI: https://doi.org/10.1007/s12555-009-0405-3

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