시간 지연 시스템을 위한 적분 슬라이딩 모드 제어기의 LMI 기반 설계

LMI-based Design of Integral Sliding Mode Controllers for Time-Delay Systems

  • 최한호 (동국대학교 전기공학과)
  • 발행 : 2009.12.01

초록

This paper presents an LMI-based method to design a integral sliding mode controller for a class of uncertain time-delay systems. Using LMIs we derive an existence condition of a sliding surface guaranteeing the asymptotic stability of the sliding mode dynamics. And we give a switching feedback control law. Our method is a generalization of the previous integral sliding mode control design methods. Since our method is based on LMIs, it gives design flexibility for combining various useful design criteria that can be captured in the LMI-based formulation. We also give LMI existence conditions of sliding surfaces guaranteeing a-stability or LQ performance constraint. Finally, we give a numerical design example to show the effectiveness of the proposed method.

키워드

참고문헌

  1. E.M. Jafarov, 'Robust sliding mode controllers design techniques for stabilization of multi variable time-delay systems with parameter perturbations and external disturbances,', Int. J. Systems Science, vol. 36, pp. 433-444, 2005 https://doi.org/10.1080/00207720500156363
  2. H.H. Choi, 'Sliding-mode output feedback control design,' IEEE Trans. Ind. vol. 55, pp. 4047-4054, 2008 https://doi.org/10.1109/TIE.2008.2004386
  3. R. El-Khazali, 'Variable structure robust control of uncertain time-delay systems,' Automatica, vol. 34, pp. 327-332, 1998 https://doi.org/10.1016/S0005-1098(97)00200-8
  4. S. Oucheriah, 'Exponential stabilization of linear delayed systems using sliding-mode controllers,' IEEE Trans. Circuits Syst. I, vol. 55, pp. 826-830, 2003 https://doi.org/10.1109/TCSI.2003.812622
  5. J. Ackermann and V.I. Utkin, 'Sliding mode control design based on Ackermann's formula', IEEE Trans. Automat Contr., vol. 43, no. 2, pp. 234-237, 1998 https://doi.org/10.1109/9.661072
  6. S. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in system and Control Theory, Philadelphia, SIAM, 1994
  7. U. Shaked 'An LPD approach to robust $H_2$ and $H_{\infty}$ static output-feedback design,' IEEE Trans. Automat. Contr., vol. 48, no.5, pp.866-872, 2003 https://doi.org/10.1109/TAC.2003.811270