The Transactions of The Korean Institute of Electrical Engineers (전기학회논문지)

The Korean Institute of Electrical Engineers (대한전기학회)
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[ $H_{\infty}$ ] Tracking Control of Time-delayed Linear Systems with Saturating Actuators

포화 구동기를 갖는 시간지연 선형시스템의 $H_{\infty}$ 추종 제어기

  • 이연규 (충북대학교 대학원 제어계측공학과) ;
  • 김진훈 (충북대학교 전기전자공학부)
  • Published : 2008.04.01
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Abstract

In this paper, we considered the $H_{\infty}$ tracking control for time-delayed linear systems with saturating actuators. The considered time delay is a time varying one having bounded magnitude and rate, and the considered tracking reference is a general one only known its bounds of magnitude and rate. First, we have converted the $H_{\infty}$ tracking control problem into an equivalent $H_{\infty}$ disturbance attenuation problem using two steps of transformations. Next, based on a new Lyapunov-Krasovskii functional, we have derived the result in the form of LMI with two non-convex parameters. Finally, by numerical examples, we have shown the usefulness and effectiveness of our result.

Keywords

References

  1. P. O. Gutman and P. Hagander, "A new design of constrained controllers for linear systems," IEEE Trans. Autom. Contrl, vol. 30, pp. 22-33, 1985 https://doi.org/10.1109/TAC.1985.1103785
  2. J. -H. Kim and Z. Bien, "Robust stability of uncertain linear systems with saturating actuators," IEEE Trans. Autom. Control, vol. 39, pp. 202-207, 1994
  3. D. S. Bernstein and A. N. Michel(Eds), "Special issue:saturating actuator," Int, J. Robust and Nonlinear Control, vol. 5, pp. 375-540, 1995 https://doi.org/10.1002/rnc.4590050502
  4. Z. Lin and A. Saberi, "A semi-global low-and-high gain design technique for linear systems with input saturation-stabilization and disturbance rejection," Int, J. Robust and Nonlinear Control, vol. 5, pp. 381-398, 1995 https://doi.org/10.1002/rnc.4590050503
  5. Y. xia and Y. Jia, "Robust control of state delayed systems with polytopic type uncertainties via parameter-dependent Lyapunov functionals," Syst. Control Lett., vol. 50, pp. 183-193, 2003 https://doi.org/10.1016/S0167-6911(03)00153-1
  6. E. Fridman, A. Pila and U. Shaked, "Regional stabilization and control of time-delay systems with saturating actuators," Int, J. Robust and Nonlinear Control, vol. 13, pp. 885-907, 2003 https://doi.org/10.1002/rnc.852
  7. Niculescu, S. -I., neto, A. T., Dion, J. -M., and Dugard, L., 1995 "Delay-Dependent Stability of Linear Systems with Delayed State: An LMI Approach," Proc. 34th IEEE Conf. on Decision and Control, pp. 1495-1497
  8. M. Wu, Y. He, J. H. She and G. P. Liu "Delay-dependent criteria for robust stability of time-varying delay systems," Automatica, vol. 40, pp. 1435-1439, Mar, 2004 https://doi.org/10.1016/j.automatica.2004.03.004
  9. E. Fridman and U. Shaked, "An improved stabilization method for linear time-delay systems," IEEE Trans. Autom. Control, vol. 47, no. 11,pp. 1931-1937, Nov. 2002 https://doi.org/10.1109/TAC.2002.804462
  10. X. Li and C. E. de Souza, "Delay-dependent robust stability and stabilization of uncertain linear delay systems: A linear matrix inequality approach," IEEE Trans. Autom. Control, vol. 42, no. 8,pp. 1144-1148, Aug. 1997 https://doi.org/10.1109/9.618244
  11. S. Oucheriah, "Robust tracking and model following of uncertain dynamic systems by memoless linear controllers," IEEE Trans. Autom. Control, vol. 44, no. 7, pp. 1473-1577, July. 1999 https://doi.org/10.1109/9.774126
  12. H. Wu, "Adaptive robust tracking and model following of uncertain dynamical systems with multiple time delays," IEEE Trans. Autom. Control, vol. 49, no. 4, pp. 611-616, Apr. 2004 https://doi.org/10.1109/TAC.2004.825634
  13. P. Park, "A delay-dependent stability criterion for system with uncertain time-invariant delays," IEEE. Trans. Autom. Control, vol. 44,no. 4,pp. 876-877, Apr, 1999 https://doi.org/10.1109/9.754838
  14. S.-I. Niculescu, "Memoryless control with an -stability constrint for time-delay systems: An LMI approach," IEEE. Trans. Autom. Control, vol. 43,no. 5, pp. 739-743, May, 1998 https://doi.org/10.1109/9.668850
  15. S. Tarbouriech and J. M. Gomes da Silva Jr, "Synthesis of controllers for continuous-time delay systems with saturating controls via LMI's," IEEE. Trans. Autom. Control, vol. 45, pp. 105-111, 2000 https://doi.org/10.1109/9.827364
  16. J. H. Kim, "Delay and its time-derivative dependent robust stability of time-delayed linear systems with uncertainty," IEEE. Trans. Autom. Control, vol. 46, no. 5, pp. 789-792, May, 2001 https://doi.org/10.1109/9.920802
  17. L. Zaccarian and A. R. Teel, "A common framework for anti-windup, bumpless transfer and reliable design," Automatica, vol. 38, pp. 1735-1744, 2002 https://doi.org/10.1016/S0005-1098(02)00072-9
  18. H. Gao and C. Wang, "Delay-dependent robust and filtering for a class of uncertain nonlinear time-delay systems," IEEE. Trans. Autom. Control, vol. 48,no. 9, pp. 1661-1666, Sep, 2003 https://doi.org/10.1109/TAC.2003.817012
  19. 이연규, 김진훈, "제한된 구동기 용량을 갖는 시간지연 선형시스템의 제어," 전기학회 논문지, 56권, 9호, pp.1648-1654, 2007. 9
  20. S. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory. Philadelphia, PA: SIAM, 1994
  21. T. Hu and Z. Lin, Control Systems with Actuator Saturation, Birkhauser, 2001
  22. W. J. Rogh, Linear System Theory. Upper Saddle River, New Jersey:Prentice Hall, 1996