International Journal of Control, Automation, and Systems

Institute of Control, Robotics and Systems (제어로봇시스템학회)
권호 표지

Robust Switching-Type Fuzzy-Model-Based Output Tracker

  • Lee, Ho-Jae (Department of Electrical Engineering, Yonsei University) ;
  • Park, Jin-Bae (Department of Electrical and Electronic Engineering, Yonsei University) ;
  • Joo, Young-Hoon (School of Electronic and Information Engineering, Kunsan National University)
  • Published : 2005.09.01
Download PDF
⟨ Previous Next ⟩

Abstract

This paper discusses an output-tracking control design method for Takagi-Sugeno fuzzy systems with parametric uncertainties. We first represent the concerned system as a set of uncertain linear systems. The tracking problem is then converted into a stabilization problem thereby leading to a more feasible control design procedure. A sufficient condition for robust practical output tracking is derived in terms of a set of linear matrix inequalities. A numerical example for a flexible-joint robot-arm model has been demonstrated, to convincingly show effectiveness of the proposed system modeling and control design.

Keywords

References

  1. H. J. Lee, J. B. Park, and G. Chen, 'Robust fuzzy control of nonlinear systems with parametric uncertainties,' IEEE Trans. on Fuzzy Systems, vol. 9, no. 2, pp. 369-379, 2001 https://doi.org/10.1109/91.919258
  2. 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. on Fuzzy Systems, vol. 7, no. 4, pp. 394-408, 1999 https://doi.org/10.1109/91.784199
  3. W. Chang, J. B. Park, Y. H. Joo, and G. Chen, 'Design of robust fuzzy-model-based controller with sliding mode control for SISO nonlinear systems,' Fuzzy Sets and Systems, vol. 125, no. 1, pp. 1-22, 2002 https://doi.org/10.1016/S0165-0114(01)00038-0
  4. 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. on Circuits and Systems I, vol. 49, no. 4, pp. 509-517, 2002
  5. W. Chang, J. B. Park, and Y. H. Joo, 'GA-based intelligent digital redesign of fuzzy-model-based controllers,' IEEE Trans. on Fuzzy Systems, vol. 11, no. 1, pp. 35-44, 2003 https://doi.org/10.1109/TFUZZ.2002.806315
  6. W. Chang, J. B. Park, Y. H. Joo, and G. Chen, 'Static output feedback fuzzy controller for Chen's chaotic attractor with uncertainties,' Inform. Sci., vol. 151, pp. 227-244, 2003 https://doi.org/10.1016/S0020-0255(02)00297-9
  7. H. J. Lee, J. B. Park, and Y. H. Joo, 'Comments on 'Output tracking and regulation of nonlinear system based on Takagi-Sugeno fuzzy model',' IEEE Trans. on Systems, Man and Cybernetics B, vol. 33, no. 3, pp. 521-523, 2003 https://doi.org/10.1109/TSMCB.2003.811124
  8. K. Kiriakidis, 'Robust stabilization of the Takagi-Sugeno fuzzy model via bilinear matrix inequalities,' IEEE Trans. on Fuzzy Systems, vol. 9, no. 2, pp. 269-277, 2001 https://doi.org/10.1109/91.919248
  9. H. J. Lee, H. Kim, Y. H. Joo, W. Chang, and J. B. Park, 'A new intelligent digital redesign: Global approach,' IEEE Trans. on Fuzzy Systems, vol. 12, no. 2, pp. 274-284, 2004 https://doi.org/10.1109/TFUZZ.2003.819826
  10. K. Tanaka, T. Ikeda, and H. O.Wang, 'Fuzzy regulators and fuzzy observers: Relaxed stability conditions and LMI-based designs,' IEEE Trans. on Fuzzy Systems, vol. 6, no. 2, pp. 250-265, 1998 https://doi.org/10.1109/91.669023
  11. C. H. Hu, J. H. Zhu, X. L. Huang, J. C. Hu, and Z. Q. Sun, 'Output tracking of an unmanned tandem helicopter based on dynamic augment method,' International Journal of Control, Automation, and Systems, vol. 2, no. 2, pp. 156-164, 2004
  12. E. T. Jeung, D. C. Oh, and H. B. Park, 'Delay dependent control for time-delayed T–S fuzzy systems using descriptor representation,' International Journal of Control, Automation, and Systems, vol. 2, no. 2, pp. 182-188, 2004
  13. Y. Wang, Z. Q. Sun, and F. C. Sun, 'Robust fuzzy control of a class of nonlinear descriptor systems with time-varying delay,' International Journal of Control, Automation, and Systems, vol. 2, no. 1, pp. 76-82, 2004
  14. Y. W. Cho and C. W. Park, 'On-line parameter estimation scheme for uncertain Takagi-Sugeno fuzzy models,' International Journal of Control, Automation, and Systems, vol. 2, no. 1, pp. 68-75, 2004
  15. M. Feng and C. J. Harris, 'Piecewise Lyapunov stability conditions of fuzzy systems,' IEEE Trans. on Systems, Man and Cybernetics B, vol. 31, no. 2, pp. 259-262, 2001 https://doi.org/10.1109/3477.915350
  16. H. J. Lee, J. B. Park, and Y. H. Joo, 'Robust control for uncertain T–S fuzzy systems with time-varying input delay,' Trans. ASME, Journal of Dynamic Systems, Measurement, and Control, vol. 127, no. 2, pp. 302-306, 2005
  17. J. Ma and G. Feng, 'An approach to H1 control of fuzzy dynamic systems,' Fuzzy Sets and Systems, vol. 137, no. 3, pp. 367-386, 2003 https://doi.org/10.1016/S0165-0114(02)00281-6
  18. X. J. Ma and Z. Q. Sun, 'Output tracking and regulation of nonlinear system based on Takagi- Sugeno fuzzy model,' IEEE Trans. on Systems, Man and Cybernetics B, vol. 30, no. 1, pp. 47-59, Feb., 2000 https://doi.org/10.1109/3477.826946
  19. O. Begovich, E. N. Sanchez, and M. Maldonado, 'Takagi-Sugeno fuzzy scheme for real-time trajectory tracking of an underactuated robot,' IEEE Trans. on Control Systems Technology, vol. 10, no. 1, pp. 14-20, January 2002 https://doi.org/10.1109/87.974334
  20. T. H. Hopp and W. E. Schimitendorf 'Design of a linear controller for robust tracking and model following,' Trans. ASME, Journal of Dynamic Systems, Measurement, and Control, vol. 112, pp. 552-558, 1990 https://doi.org/10.1115/1.2896179
  21. S. H. Za˙k, 'Stabilizing fuzzy system models using linear controllers,' IEEE Trans. on Fuzzy Systems, vol. 7, no. 2, pp. 236-240, 1999 https://doi.org/10.1109/91.755404
  22. V. S. Chellaboina, A. Leonessa, and W. M. Haddad, 'Generalized Lyapunov and invarinat set theorems for nonlinear dynamical systems,' Systems & Control Letters, vol. 38, pp. 289-295, 1999 https://doi.org/10.1016/S0167-6911(99)00076-6
  23. I. R. Petersen, 'A stabilization algorithm for a class of uncertain linear systems,' Systems & Control Letters, vol. 8, pp. 351-357, 1987 https://doi.org/10.1016/0167-6911(87)90102-2
  24. H. A. Malki, D. Misir, D. Feigespan, and G. Chen, 'Fuzzy PID control of a flexible-joint robot arm with uncertainties from time-varing loads,' IEEE Trans. on Control Systems Technology, vol. 5, no. 3, pp. 371-378, 1997 https://doi.org/10.1109/87.572133
  25. B. A. Francis, 'The linear multivariable regulator problem,' SIAM Journal on Control and Optimization, vol. 15, pp. 486-505, 1977 https://doi.org/10.1137/0315033