×

zbMATH — the first resource for mathematics

Structure analysis and system design for a class of Mamdani fuzzy controllers. (English) Zbl 1154.93381
Summary: Analytical analysis of the structure of fuzzy controllers is important as it provides insightful information and makes it possible to eliminate or reduce the trial-and-error effort in system design. Most results available in the literature only deal with the fuzzy controllers using up to three input variables (i.e. PI, PD, or PID type with the input space being three dimensional at most). In this paper, we study a class of Mamdani fuzzy controllers whose input space can be arbitrary dimension. We derived mathematically the input-output relation for these fuzzy controllers. We also investigated the bounded-input bounded-output global stability as well as local stability of the fuzzy control systems. Based on the explicit input-output relation and the local stability property, a procedure for designing the fuzzy controllers regulating (nonlinear) plants is proposed. Its effectiveness is demonstrated by a numerical example with computer simulations.

MSC:
93C42 Fuzzy control/observation systems
93D25 Input-output approaches in control theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Chen C., Fuzzy Sets and Systems 101 pp 87– (1999) · Zbl 0989.93532 · doi:10.1016/S0165-0114(97)00046-8
[2] Ding Y., Information Sciences 151 pp 245– (2003) · Zbl 1032.93043 · doi:10.1016/S0020-0255(02)00302-X
[3] Du X., Chinese Journal of Electronics 13 pp 654– (2004)
[4] Fan X., Chinese Journal of Electronics 10 pp 326– (2001)
[5] Hu B., IEEE Transactions on Fuzzy Systems 7 pp 521– (1999) · doi:10.1109/91.797977
[6] Hu B., IEEE Transactions on Fuzzy Systems 9 pp 699– (2001) · doi:10.1109/91.963756
[7] Khalil H.K., Nonlinear System (1996)
[8] Lee C.C., IEEE Transactions on Systems, Man and Cybernetics 20 pp 404– (1990) · Zbl 0707.93036 · doi:10.1109/21.52551
[9] Lewis F.L., Automatica 32 pp 167– (1996) · Zbl 0845.93048 · doi:10.1016/0005-1098(96)85547-6
[10] Misumoto M., Information Science 45 pp 129– (1988) · doi:10.1016/0020-0255(88)90037-0
[11] Raju G.V.S., International Journal of Control 54 pp 1201– (1991) · Zbl 0741.93001 · doi:10.1080/00207179108934205
[12] Slotine J.E., Applied Nonlinear Control (1991) · Zbl 0753.93036
[13] Sun H., Fuzzy Sets and systems 131 pp 265– (2002) · Zbl 1010.93510 · doi:10.1016/S0165-0114(02)00110-0
[14] Wong C., Fuzzy Sets and Systems 57 pp 149– (1993) · Zbl 0792.93082 · doi:10.1016/0165-0114(93)90154-A
[15] Ying H., Automatica 29 pp 1139– (1993) · Zbl 0782.93062 · doi:10.1016/0005-1098(93)90115-A
[16] Ying H., Automatica 30 pp 1185– (1994) · Zbl 0800.93711 · doi:10.1016/0005-1098(94)90213-5
[17] Ying H., Fuzzy Control and Modeling: Analytical Foundations and Application (2000)
[18] Ying H., Automatica 26 pp 513– (1990) · Zbl 0713.93036 · doi:10.1016/0005-1098(90)90022-A
[19] Zeng K., Science in China (E) 43 pp 263– (2000) · Zbl 0964.93061 · doi:10.1007/BF02916830
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.