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Saturating composite disturbance-observer-based control and H ∞ control for discrete time-delay systems with nonlinearity

International Journal of Control, Automation and Systems volume 7, pages 691–701 (2009)Cite this article

Abstract

This note is concerned with a saturating composite disturbance-observer-based control (DOBC) and H ∞ control for a class of discrete time-delay systems with nonlinearity and disturbances. The disturbances are supposed to include two parts. One in the input channel is generated by an exogenous system with uncertainty, which can represent the harmonic signals with modeling perturbations. The other is supposed to have the bounded H 2 norm, which can represent parametric uncertainties and external disturbance existing in the controlled object. The design approaches of reduced-order disturbance observer are presented for the estimation of the disturbance. By composite control law with saturation, the disturbances can be rejected and attenuated, simultaneously, the desired dynamic performances can be guaranteed for discrete time-delay systems with known and unknown nonlinear dynamics, respectively. Simulation for a flight control system is provided to show the effectiveness of the proposed scheme compared with the previous schemes.

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References

  1. K. J. Åström, Introduction to Stochastic Control Theory, Academic Press, New York, 1970.

    MATH  Google Scholar 

  2. A. J. Van der Schaft, “L2-gain analysis of nonlinear systems and nonlinear state feedback H Infinte control,” IEEE Trans. Automat. Control, vol. 37, pp. 770–784, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  3. A. Isidori, Nonlinear Control Systems, Springer, Berlin, 1995.

    MATH  Google Scholar 

  4. K. Zhou and J. C. Doyle, Essentials of Robust Control, Prentice Hall, 1997.

  5. K. Ohishi, M. Nakao, K. Ohnishi, and K. Miyachi, “Microprocessor-controlled DC motor for load-insensitive position servo system,” IEEE Trans. on Industrial Electronics, vol. 34, pp. 44–49, 1987.

    Article  Google Scholar 

  6. T. Umeno and Y. Hori, “Robust speed control of DC servomotors using modem two-degree-of-freedom controller design,” IEEE Trans. on Industrial Electronics, vol. 38, pp. 363–368, 1991.

    Article  Google Scholar 

  7. H. X. Li and P. P. J. Van Den Bosch, “A robust disturbance-based control and its application,” Int. J. Control, vol. 58, pp. 537–554, 1993.

    Article  MATH  Google Scholar 

  8. C. S. Liu and H. Peng, “Disturbance observer based tracking control,” ASME Journal of Dynamic Systems, Control and Measurement, vol. 122, pp. 332–335, 2000.

    Article  Google Scholar 

  9. B. K. Choi, W. K. Choi, and H. Lim, “Nonlinear predictive PID controller,” IEEE/ASME Trans. on Mechatronics, vol. 4, pp. 157–168, 1999.

    Article  Google Scholar 

  10. C. J. Kemf and S. Kobayashi, “Disturbance observer and feedforward design for a high speed direct-drive positioning table,” IEEE Trans. on Control System Technology, vol. 7, pp. 513–526, 1999.

    Article  Google Scholar 

  11. K. H. Kim, I. C. Baik, G.-W. Moon, and M. J. Youn, “A current control for a permanent magnet synchronous motor with a simple disturbance estimation scheme,” IEEE Trans. on Control System Technology, vol. 7, pp. 513–526, 1999.

    Article  Google Scholar 

  12. Y. H. Huang and W. Massner, “A novel disturbance observer design for magnetic hard drive servo system with rotary actuator,” IEEE Trans. on Magnetics, vol. 34, pp. 1892–1894, 1998.

    Article  Google Scholar 

  13. L. Guo and W. H. Chen, “Disturbance attenuation and rejection for systems with nonlinearity via DOBC approach,” Int. J. Robust Nonlinear Control, vol. 15, pp. 109–125, 2005.

    Article  MATH  MathSciNet  Google Scholar 

  14. W. H. Chen, “Disturbance observer based control for nonlinear systems,” IEEE/ASME Transactions on Mechatronics, vol. 9, pp. 706–710, 2004.

    Article  Google Scholar 

  15. X. M. Zhu, C. C. Hua, and S. Wang, “State feedback controller design of networked control systems with time delay in the plant,” Int. J. of Innovative Computing, Information and Control, vol. 4, no. 2, pp. 283–290, 2008.

    Google Scholar 

  16. M. S. Mahmoud, Y. Shi, and H. N. Nounou, “Resilient observerbased control of uncertain time-delay systems,” Int. J. of Innovative Computing, Information and Control, vol. 3, no. 2, pp. 407–418, 2007.

    Google Scholar 

  17. X. M. Sun, J. Zhao, and W. Wang, “Two design schemes for robust adaptive control of a class of linear uncertain neutral delay systems,” Int. J. of Innovative Computing, Information and Control, vol. 3, no. 2, pp. 385–396, 2007.

    Google Scholar 

  18. H. J. Gao and T. W. Chen. “New results on stability of discrete-time systems with time-varying state delay,” IEEE Trans. on Automatic Control, vol. 52, no. 2, pp. 328–334, 2007.

    Article  MathSciNet  Google Scholar 

  19. H. J. Gao and C. Wang, “A delay-dependent approach to robust H Infinte filtering for uncertain discrete-time state-delayed systems,” IEEE Trans. Signal Processing, vol. 52, pp. 1631–1640, 2004.

    Article  MathSciNet  Google Scholar 

  20. L. Guo and W. H. Chen, “Output feedback H Infinte control for a class of uncertain nonlinear discrete-time delay systems,” Trans. of the Insititute of Measurement and Control, vol. 25, no. 2, pp. 107–121, 2003.

    Article  Google Scholar 

  21. H. R. Karimi, “Observer-based mixed H2/H∞ control design for linear systems with time-varying delays: An LMI approach,” Int. J. of Control, Automation, and Systems, vol. 6, no. 1, pp. 1–14, 2008.

    Google Scholar 

  22. J. H. Chou, I. R. Honng, and B. S. Chen, “Dynamical feedback compensator for uncertain time-delay systems containing saturating actuator,” Int. J. Contr., vol. 49, pp. 961–968, 1989.

    MATH  Google Scholar 

  23. S. Oucheriah, “Global stabilization of a class of linear continuous time-delay systems with saturating controls,” IEEE Trans. Circ. Syst., vol. 43, pp. 1012–1015, 1996.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Information, Ludong University, Yantai, China

    Xinjiang Wei & Huifeng Zhang

  2. Institute of Instrument Science and Optoelectronics Engineering, Beihang University, Beijing, China

    Lei Guo

Authors
  1. Xinjiang Wei
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  2. Huifeng Zhang
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  3. Lei Guo
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Corresponding author

Correspondence to Xinjiang Wei.

Additional information

Recommended by Editorial Board member Bin Jiang under the direction of Editor Young Il Lee. This work was supported by National Science Foundation of China 60774013, 60774016; Science and Technology Plan of University in Shandong Province J09LG27; Science Foundation of Ludong University 22300301.

Xinjiang Wei was born in Dongying, China, in 1977. He received the B.S. degree from Yantai Normal University, China in 1999, the M.S. degree from Bohai University in 2002, and the Ph.D. degree in Department of Information from Northeastern University in 2005. From 2006 to Present, he was with Ludong University as an associate professor. From 2006 to 2009, he was a postdoctoral fellow at Southeast University. His research interests include robust control, nonlinear control, and fuzzy control.

Huifeng Zhang was born in Donge, China, in 1975. He received the B.S. degree from Yantai Normal University, China in 1999, the M.S. degree from Northwest A&F University in 2005. From 2006 to Present, she was with Ludong University as a lecturer. Her research interests include robust control, nonlinear control.

Lei Guo was born in Qufu, China, in 1966. He received the B.S. and M.S. degrees from Qufu Normal University (QFNU), China in 1988 and 1991, respectively, and the Ph.D. degree in Control Engineering from Southeast University (SEU) in 1997. From 1991 to 1994, he was with Qingdao University (QDU) as a lecturer. From 1997 to 1999, he was a postdoctoral fellow at Southeast University. From 1999 to 2000, he was a research fellow in IRCCyN, Nantes, France. From 2000 to 2003, he was a research fellow at Glasgow University, Loughborough University, and UMIST, UK. In 2004, he joined the Institute of Automation in Southeastern University as a Professor. His research interests include robust control, stochastic systems, fault detection, filter design and nonlinear control with their applications to aerospace systems.

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Wei, X., Zhang, H. & Guo, L. Saturating composite disturbance-observer-based control and H ∞ control for discrete time-delay systems with nonlinearity. Int. J. Control Autom. Syst. 7, 691–701 (2009). https://doi.org/10.1007/s12555-009-0501-4

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  • DOI: https://doi.org/10.1007/s12555-009-0501-4

Keywords

  • Discrete system
  • disturbance-observer-based control
  • H infinite control
  • saturating control
  • time-delay system