Journal of Institute of Control, Robotics and Systems (제어로봇시스템학회논문지)

Institute of Control, Robotics and Systems (제어로봇시스템학회)
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An LMI-based PID Control Design Method for Uncertain MIMO Systems

불확실성을 갖는 MIMO 시스템을 위한 선형행렬부등식 기반 PID 제어기 설계 방법

  • Published : 2005.09.01
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Abstract

This paper deals with the design problem of multivariable PID controllers guaranteeing the closed-loop system stability and a prescribed $H_\infty$ norm bound constraint. We reduce the problem to the static output feedback stabilization problem. We derive a necessary and sufficient condition f3r the existence of PID controllers and we give an explicit formula of PID controllers. We also give an existence condition of PID controllers guaranteeing a prescribed decay rate. Finally, we give an LMI-based design algorithm, together with a numerical design example.

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References

  1. E. Graassi, K .S. Tsakalis, S. Dash, S. V. Gaikwad, W. MacArthur, and G. Stein, 'Integrated system identification and PiD controller tuning by frequency loop-shaping,' IEEE Trans. Control System Technology, vol. 9, pp. 285-294, 2001 https://doi.org/10.1109/87.911380
  2. H. Panagopoulos, K. J. Astrom and T. Hagglund, 'Design of PID controllers based on constrained optimisation,' IEE Proc. Control Theory Appl., vol. 149, pp. 32-40, 2002 https://doi.org/10.1049/ip-cta:20020102
  3. A. J. Isaksson and S. F. Graebe, 'Derivative filter is an integral part of PID design,' IEE Proc. Control Theory Appl., vol. 149, pp. 41-45, 2002 https://doi.org/10.1049/ip-cta:2002011
  4. P. Cominos and N. Munro, 'PID controllers: recent tuning methods and design to specification,' IEE Proc. Control Theory Appl., vol. 149, pp. 46-53, 2002 https://doi.org/10.1049/ip-cta:20020103
  5. F. Zheng, Q.-G. Wang, and T.R. Lee, 'On the design of multi val abel PID controllers via LMI approach,' Automatica, vol. 38, pp. 517-526, 2002 https://doi.org/10.1016/S0005-1098(01)00237-0
  6. P. Gahinet, A. Nemirovski and A. J. Laub, LMI Control Toolbox User's Guide, Natic, MA:The MathWorks Inc., 1995
  7. S. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in system and Control Theory, Philadelphia, SIAM, 1994
  8. L. El Ghaoui, F. Oustry and M. Rami, 'A cone complementarity linearization algorithm for static output feedback and related problems', IEEE Trans. on Automatic Control, Vol. 42, No.8, 1171-1176, 1997 https://doi.org/10.1109/9.618250
  9. U. Shaked, 'An LPD approach to robust $H_2$ and $H_{\infty}$ static output-feedback design,' IEEE Trans. Automat. Contr., vol. 48, pp. 866-872, 2003 https://doi.org/10.1109/TAC.2003.811270