zbMATH — the first resource for mathematics

Nonlinear fuzzy controller. (English) Zbl 0744.93065
Summary: We consider a fuzzy controller with two inputs, triangular fuzzy numbers, Zadeh logic to evaluate linear control rules, and a center of gravity defuzzifier. We derive a closed form expression for the defuzzified output and show it is a nonlinear controller. We then analyze the nonlinearities of the fuzzy controller with respect to the PI controller.

93C42 Fuzzy control/observation systems
Full Text: DOI
[1] Braae, M.; Rutherford, D.A., Fuzzy relations in a control setting, Kybernetes, 7, 185-188, (1978) · Zbl 0387.93004
[2] Braae, M.; Rutherford, D.A., Selection of parameters for a fuzzy logic controller, Fuzzy sets syst., 2, 185-199, (1979) · Zbl 0418.94034
[3] Buckley, J.J., Fuzzy controller: further limit theorems for linear control rules, Fuzzy sets syst., 36, 225-233, (1990) · Zbl 0719.93059
[4] Buckley, J.J., Further results for the linear fuzzy controller, Kybernetes, 18, 48-55, (1989) · Zbl 0699.93036
[5] J. J. Buckley, Fuzzy vs non-fuzzy controllers, Control Cybernet., forthcoming.
[6] J. J. Buckley and H. Ying, Expert fuzzy controller, Fuzzy Sets Syst., forthcoming.
[7] Buckley, J.J.; Ying, H., Linear fuzzy controller: it is a linear non-fuzzy controller, Inform. sci., 51, 183-192, (1990) · Zbl 0718.93037
[8] Buckley, J.J.; Ying, H., Fuzzy controller theory: limit theorems for linear fuzzy control rules, Automatica, 25, 469-472, (1989) · Zbl 0685.93003
[9] Gupta, M.M.; Kiszka, J.B.; Trojan, G.M., Multivariable structure of fuzzy control systems, IEEE trans. syst. man cybernet., 16, 638-657, (1986) · Zbl 0619.93044
[10] Kiszka, J.B.; Gupta, M.M.; Nikiforuk, P.N., The influence of some fuzzy implication operators on the steady state and dynamical properties of a fuzzy logic controller, Control cybernet., 13, 251-260, (1984) · Zbl 0551.93003
[11] Kiszka, J.B.; Gupta, M.M.; Nikiforuk, P.N., Some properties of expert control systems, (), 283-306 · Zbl 0551.93003
[12] Kiszka, J.B.; Kochanska, M.E.; Sliwinska, D.S., The influence of some parameters on the accuracy of a fuzzy model, (), 187-230
[13] Mizumoto, M., Fuzzy controls under various defuzzifier methods, (), 252-253
[14] Mizumoto, M., Fuzzy controls under various fuzzy reasoning methods, Inform. sci., 45, 129-152, (1988)
[15] Siler, W.; Ying, H., Fuzzy control theory: the linear case, Fuzzy sets syst., 33, 275-290, (1989) · Zbl 0683.93002
[16] Ying, H.; Siler, W.; Buckley, J.J., Fuzzy control theory: A nonlinear case, Automatica, 26, 513-520, (1990) · Zbl 0713.93036
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.