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LMI-Based Intelligent Digital Redesign for Multirate Sampled-Data Fuzzy Systems

  • Published : 2006.02.01

Abstract

This paper presents a new linear-matrix-inequality-based intelligent digital redesign (LMI-based IDR) technique to match the states of the analog and the digital T-S fuzzy control systems at the intersampling instants as well as the sampling ones. The main features of the proposed technique are: 1) the affine control scheme is employed to increase the degree of freedom; 2) the fuzzy-model-based periodic control is employed, and the control input is changed n times during one sampling period; 3) The proposed IDR technique is based on the approximately discretized version of the T-S fuzzy system, but its discretization error vanishes as n approaches the infinity. 4) some sufficient conditions involved in the state matching and the stability of the closed-loop discrete-time system can be formulated in the LMIs format.

Keywords

References

  1. Y. H. Joo, L. S. Shieh, and G. Chen, 'Hybrid state space fuzzy model-based controller with dual-rate sampling for digital control of chaotic systems,' IEEE Trans. Fuzzy Syst., voL 7, no. 4, pp. 394-408, 1999 https://doi.org/10.1109/91.784199
  2. W. Chang, J. B. Park, Y. H. Joo, and G. Chen, 'Design of sampled-data fuzzy-model-based control systems by using intelligent digital redesign,' IEEE Trans. Circ. Syst. I, vol. 49, no. 4, pp. 509-517, 2002 https://doi.org/10.1109/TCSI.2002.995668
  3. W. Chang, J B. Park, and Y. H. Joo, 'GA-basedintelligent digital redesign of fuzzy-model-based controllers,' IEEE Trans. Fuzzy Syst., vol. 11, no. 1, pp. 35-44, 2003 https://doi.org/10.1109/TFUZZ.2002.806315
  4. W. Chang, J B. Park, H. J. Lee, and Y. H. Joo, 'LMI approach to digital redesign of linear time-invarint systems,' lEE Proc., Control Theory Appl., vol. 149, no. 4, pp. 297-302, 2002 https://doi.org/10.1049/ip-cta:20020430
  5. H. J. Lee, J. B. Park, and Y. H. Joo, 'An efficient observer-based sampled-data control: Digital redesign approach,' IEEE Trans. Circuits Syst. I, vol. 50, no. 12, pp. 1595-1601, 2003 https://doi.org/10.1109/TCSI.2003.819832
  6. H. J. Lee, H. Kim, Y. H. Joo, W. Chang, and J. B. Park, 'A new intelligent digital redesign for T - S fuzzy systems: global approach,' IEEE Trans.Fuzzy Syst., vol. 12, no. 2, pp. 274-284, 2004 https://doi.org/10.1109/TFUZZ.2003.819826
  7. T. Chen and B. Francis, 'Optimal Sampled-Data Control Systems,' Springer, 1995
  8. B. A. Francis and T. T. Georgiou, 'Stability theory for linear time-invariant plants with periodic digital controllers,' IEEE Trans. Automat.Contr., vol. 33, no. 9, pp. 820-832, 1988 https://doi.org/10.1109/9.1310
  9. L. S. Shieh, W. M. Wang, J. Bain, and J. W. Sunkel, 'Design of lifted dual-rate digital controllers for X-38 vehicle,' Jounal of Guidance,Contr. Dynamics, vol. 23, pp. 629-339, Jul., 2000 https://doi.org/10.2514/2.4608
  10. H. O. Wang, K. Tananka, and M. F. Griffin, 'An approach to fuzzy control of nonlinear systems: Stability and design issues,' IEEE Trans. Fuzzy Syst., vol. 4, no. 1, pp. 14-23, 1996 https://doi.org/10.1109/91.481841
  11. K. Tananka, T. Kosaki, and H. O. Wang, 'Backing control problem of a mobile robot with multiple trailers: fuzzy modeling and LMI-based design,' IEEE Trans. Syst. Man, Cybem. C., vol. 28, no. 3, pp. 329-337, 1998 https://doi.org/10.1109/5326.704559
  12. H. Fujimoto, Y. Hori, and A. Kawamura, 'Perfect tracking control based on multirate feedforward control with generalized sampling periods,' IEEE Trans. Ind. Electron., vol. 48, no. 3, pp. 636-644, 2001 https://doi.org/10.1109/41.925591
  13. T. Chen and L. Qiu, 'H$\infty$ design of general multirate sampled-data control systems,' Automatica, vol. 30, pp. 1139-1152, 1994 https://doi.org/10.1016/0005-1098(94)90210-0
  14. L. Qiu and T. Chen, 'H2 -optimal design of multirate sampled-data systems,' IEEE Trans. Automat. Contr., vol. 39, pp. 2506-2511, 1994 https://doi.org/10.1109/9.362836
  15. P. Colaneri and G. De Nicolao, 'Multirate LQG control of continuous- time stochastic systems,' Automatica, vol. 31, pp. 591-596, 1995 https://doi.org/10.1016/0005-1098(95)98488-R
  16. P. G.Voulgaris and B. Barnieh, 'Optimal H$\infty$ and H$\in$: control of hybrid multirate systems,' Syst.Contr. Lett., vol. 20, pp. 249-261, 1993 https://doi.org/10.1016/0167-6911(93)90001-M
  17. P. G. Voulgaris, M. A. Dahleh, and L. S. Valavani, 'H$\infty$ and H$\in$: optimal controllers for periodic and multirate systems,' Automatica, vol. 30, pp. 251-263, 1994 https://doi.org/10.1016/0005-1098(94)90028-0
  18. H. Bo and A. N. Michel, 'Some qualitative properties of multirate digital control systems,' IEEE Trans. Automat. Contr., vol. 44, pp. 765- 770, 1999 https://doi.org/10.1109/9.754814
  19. G. J. Pappas and S. Simic , 'Consistent abstractions of affine control systems,' IEEE Trans. Automat. Contr., vol. 47, pp. 745 - 756, 2002 https://doi.org/10.1109/TAC.2002.1000269