Deriving analytical input-output relationship for fuzzy controllers using arbitrary input fuzzy sets and Zadeh fuzzy AND operator

IEEE Transactions on Fuzzy Systems

Volumn 14, Issue 5, 2006, Pages 654-662

  Ying, Hao ^a  

^a WAYNE STATE UNIVERSITY   (United States)

Author keywords

Design; Fuzzy control; Input output relation; PID control; Structure analysis; Structure derivation

Indexed keywords

CONTROL SYSTEM ANALYSIS; CONTROL SYSTEM SYNTHESIS; CONTROL THEORY; FUZZY SETS; GENETIC ALGORITHMS; NEURAL NETWORKS; THREE TERM CONTROL SYSTEMS;

INPUT-OUTPUT RELATION; STRUCTURE ANALYSIS; STRUCTURE DERIVATION;

FUZZY CONTROL;

EID: 33750210679     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2006.877355     Document Type: Article

References (29)

1. K. J. Astrom and T. Haagglund, "The future of PID control," Control Eng. Prac., vol. 9, pp. 1163-1175, 2001.
2. C.-L. Chen, S.-N. Wang, C.-T. Hsieh, and F.-Y. Chang, "Theoretical analysis of crisp-type fuzzy logic controllers using various t-norm sum-gravity inference methods," IEEE Trans. Fuzzy Syst., vol. 6, no. 1, pp. 122-136, Feb. 1998.
3. C.-L Chen, S.-N. Wang, C.-T. Hsieh, and F.-Y. Chang, "Theoretical analysis of a fuzzy logic controller with unequally spaced triangular membership functions," Fuzzy Sets Syst., vol. 101, pp. 87-108, 1999.
4. G.-R Chen and H. Ying, "BIBO stability of nonlinear fuzzy PI control systems," J. Intell. Fuzzy Syst., vol. 5, pp. 245-256, 1997.
5. D. Driankov, H. Hellendoorn, and M. Reinfrank An Introduction to Fuzzy Control. New York: Springer-Verlag, 1993.
6. A. E. Hajjaji and A. Raclud, "Explicit formulas for fuzzy controller," Fuzzy Sets Syst., vol. 62, pp. 135-141, 1994.
7. A. Homaifar and E. McCormick, "Simultaneous design of membership functions and rule sets for fuzzy controllers using genetic algorithms," IEEE Trans. Fuzzy Syst., vol. 3, no. 1, pp. 129-139, Feb. 1995.
8. S. Jagannathan and F. L. Lewis, "Discrete-time neural net controller for a class of nonlinear dynamical systems," IEEE Trans. Autom. Control, vol. 41, no. 11, pp. 1693-1699, Nov. 1996.
9. J.-S. Jang, C.-T Sun, and E. Mizutani, Neuro-Fuzzy and Soft Computing. Upper Saddle River, NJ: Prentice-Hall, 1997.
10. H. X. Li and H. B. Gatland, "A new methodology for designing a fuzzy logic controller," IEEE Trans. Syst., Man, Cybern., vol. 25, no. 3, pp. 505-512, Mar. 1995.
11. W. Li, "Design of a hybrid fuzzy logic proportional plus conventional integral-derivative controller," IEEE Trans. Fuzzy Syst., vol. 6, no. 4, pp. 449-463, Nov. 1998.
12. C.-T. Lin and C. S. Lee, Neural Fuzzy Systems. Upper Saddle River, NJ: Prentice-Hall, 1996.
13. H. A. Malki, H. D. Li, and G. R. Chen, "New design and stability analysis of fuzzy proportional-derivative control system," IEEE Trans. Fuzzy Syst., vol. 6, no. 4, pp. 245-254, Nov. 1994.
14. G. K. Mann, B.-G. Hu, and R. G. Gosine, "Analysis of direct action fuzzy PID controller structures," IEEE Trans. Syst., Man, Cybern., B, Cybern., vol. 29, pp. 371-388, 1999.
15. K. M. Passino and S. Yurkovich, Fuzzy Control. Reading, MA: Addison-Wesley, 1998.
16. C. C. Wong, C. H. Chou, and D. L. Mon, "Studies on the output offuzzy controller with multiple inputs," Fuzzy Sets Syst., vol. 57, pp. 149-158, 1993.
17. J.-X. Xu, C. Liu, and C. C. Hang, "Tuning of fuzzy PI controllers based on gain/phase margin specifications and ITAE index," ISA Trans., vol. 35, pp. 79-91, 1996.
18. J. Yen and R. Langari, Fuzzy Logic: Intelligence, Control, and Information. Upper Saddle River, NJ: Prentice-Hall, 1999.
19. H. Ying, W. Siler, and J. J. Buckley, "Fuzzy control theory: A Nonlinear case," Automatica, vol. 26, pp. 513-520, 1990.
20. H. Ying, M. McEachern, D. Eddleman, and L. C. Sheppard, "Fuzzy control of mean arterial pressure in postsurgical patients with sodium nitroprusside infusion," IEEE Trans. Biomed. Eng., vol. 39, no. 10, pp. 1060-1070, Oct. 1992.
21. H. Ying, "The simplest fuzzy controllers using different inference methods are different nonlinear proportional-integral controllers with variable gains," Automatica, vol. 29, pp. 1579-1589, 1993.
22. H. Ying, "General analytical structure of typical fuzzy controllers and their limiting structure theorems," Automatica, vol. 29, pp. 1139-1143, 1993.
23. H. Ying, "Analytical structures of fuzzy controllers with linear control rules," Inf. Sci., vol. 81, pp. 213-227, 1994.
24. H. Ying, "Practical design of nonlinear fuzzy controllers with stability analysis for regulating processes with unknown mathematical models," Automatica, vol. 30, pp. 1185-1195, 1994.
25. H. Ying, "Constructing nonlinear variable gain controllers via the Takagi-Sugeno fuzzy control," IEEE Trans. Fuzzy Syst., vol. 6, no. 2, pp. 226-234, May 1998.
26. H. Ying, "Analytical structure of the typical fuzzy controllers employing trapezoidal input fuzzy sets and nonlinear control rules," Inf. Sci., vol. 116, pp. 177-203, 1999.
27. H. Ying, Fuzzy Control and Modeling: Analytical Foundations and Applications. Piscataway, NJ: IEEE Press, 2000.
28. H. Ying, "A general technique for deriving analytical structure of fuzzy controllers that use arbitrary trapezoidal/triangular input fuzzy sets and Zadeh fuzzy logic and operator," Automatica, vol. 39, pp. 1171-1184, 2003.
29. Y.-S. Zhou and L.-Y. Lai, "Optimal design for fuzzy controllers by genetic algorithms," IEEE Trans. Ind. Appl., vol. 36, no. 1, pp. 93-97, Jan. 2000.