# Analysis, Design, Implementation and Critical Appreciation of Fuzzy Logic Controller

## Abstract

Immediate after World War II people were very keen to develop sophisticated tool for communication and control. Despite the landmark achievement of the classical control theory through the launching of the first sputnik in 1957 and the subsequent developments of the classical control theory to modern control theory which has been tested through a number of important high- technology projects (viz the U.S. Apollo project), there are still serious problems in the control of complex system. In manufacturing technology such as in chemical processes or the steel industry, in power generations industry etc. the conventional control algorithms are unable to manage the huge uncertainties involved in the entire process and thus require human interventions for readjustments of the designed scheme.

Zadeh first realized that people can base decisions on imprecise, nonnumerical information. In 1965, he was implicity advancing a thesis which indicates that under uncertain complex situations people are better at control than Machine. In this connection Zadeh’s significant achievements are the seminal paper on the linguistic approach and system analysis based on the theory of fuzzy sets xc17,18,19,20,21,22.

Being motivated by the above said contributions of zadeh, in mid 70’s Mamdani and his colleagues first demonstrated the successful applications of the fuzzy logic controller (FLC). About the same time the first significant industrial application of the FLC came up in Denmark at F.L. Smidth corp’s cement kiln.

During the past several years, fuzzy control has emerged as one of the most potential areas for research in the application of fuzzy set theory. The con- cepts of FLC is now an important adjunct to conventional control theory. The tremendous applications of FLC indicated its effective utilization in the context of complex ill-defined systems that can be controlled by a skilled human oper- ator without the quantitative knowledge (in terms of deterministic algebra and differential equations) of their dynamics.

The essential component of FLC is a set of linguistic control rules which are generated by an experienced operator and which can be related by the dual concepts of fuzzy implications and the compositional rule of inference.

## Keywords

Membership Function Fuzzy Control Fuzzy Controller Fuzzy Logic Controller Fuzzy Subset## Preview

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## References

- 1.Z. Cao and A. Kandel “Applicability of some fuzzy implication operators” in
*Fuzzy Sets and Systems*31 (1989), pp. 151–186.CrossRefMathSciNetGoogle Scholar - 2.J. a. Goguen “The logic of inexact concepts”
*Sunthese*(1969) 19, pp. 325–327.MATHCrossRefGoogle Scholar - 3.W.J.M. Kickert and H.R. Van Nauta Lemke “Application of a fuzzy controller in a warm water plant” in
*Automatica*, (1976), 12,2, pp. 301–308.CrossRefGoogle Scholar - 4.W.J.M. Kickert and E.H. Mamdani “Analysis of a fuzzy logic controller” in
*Fuzzy Sets and Systems*, (1978), 1,1, pp. 29–44.MATHCrossRefGoogle Scholar - 5.E.H. Mamdani “Application of fuzzy algorithm for control of simple dynamic plant” in
*Proc. IEEE*, (1974), 12,12, pp. 1585–1588.Google Scholar - 6.E.H. Mamdani “Advances in the linguistic synthesis of fuzzy controllers” in
*Int. J. Man-Machine Studies*, (1976), 8, pp. 669–678.MATHGoogle Scholar - 7.E.H. Mamdani “Application of fuzzy logic to approximate reasoning using linguistic systems” in
*IEEE Trans. Comput.*, (1977), 26, pp. 1182–1191.MATHGoogle Scholar - 8.E.H. Mamdani, and S. Assilian. “An experiment in linguistic synthesis with a fuzzy logic controller”, in
*Fuzzy reasoning and its applications*, (1981), (Eds. E.H. Mamdani and B.R. Gaines). Academic Press, New York, USA, pp. 311–323.Google Scholar - 9.E.H. Mamdani, and N. Baaklini. “Prscriptive methods for deriving control policy in a fuzzy logic controller” in
*Electron. Lett.*, (1975), 11, pp. 625–626.CrossRefGoogle Scholar - 10.E.H. Mamdani, J.J. Ostergaard and E. Lemblesis. “Use of fuzzy logic for implementing rule — based control of industrial processes” in TIMS’ Studies in
*the management Sciences*, (1984), 20, pp. 429–445.Google Scholar - 11.M. Mizumato. “Fuzzy controls under various defuzzier methods” in
*International workshop on fuzzy system applications*, (1988), pp. D7Google Scholar - 12.S. Raha, and K.S. Ray “Analogy between Approximate reasoning and method of interpolation”, in
*Fuzzy Sets and Systems*, (1992). vol. 51 pp. 259–266.CrossRefMathSciNetGoogle Scholar - 13.K.S. Ray “Application of fuzzy logic controller to a block-decoupled nonlinear steam generating unit (210 [MW])” in
*Control Theory and Advanced Technology*, (1987), Vol. 3, No. 4, pp. 343–374.MathSciNetGoogle Scholar - 14.K. S. Ray and D. Dutta Majumder “Application of circle criteria for stability analysis of linear SISO and MIMO systems associated with fuzzy logic controller” in
*IEEE Trans. Systems, MAn and Cybernetics*, (1984a), SMC, 14,2, pp. 345–349.MathSciNetGoogle Scholar - 15.K. S. Ray and D. Dutta Majumder “Simulation of a nonlinear steam generation unit” in
*Proc. Int. Conf. on Syst. Man and Cybernet.*, sponsored by SMC Society of IEEE, Delhi — Bombay, India, (1984b), pp. 705–708.Google Scholar - 16.K. S. Ray and D. Dutta Majumder “ Fuzzy logic control of a nonlinear multivariable stem generating unit (200 [MW]) using decuoupling theory” in
*IEEE Trans. Systems, Man and Cybernetics*, (1985), SMC 15,4, pp. 539–558.Google Scholar - 17.K. S. Ray, A. M. Ghosh and D. Dutta Majumder
*L*_{2}— “stability and the related design concept fot SISO linear system associated with fuzzy logic controller” in*IEEE Trans. System, Man and Cybernetics*, (1984), SMC 14,6, 932–939.MathSciNetGoogle Scholar - 18.L.A. Zadeh, “Toward a theory of fuzzy systems” in
*Aspects of Nework and System Theory*. Ed. New York: Holt, Rinchart and Winston, (1971), pp. 469–490.Google Scholar - 19.L.A. Zadeh, “A rationale for fuzzy control”.
*Trans ASME. J. Dynam. Syst, Measur, Control*. (1972) Vol 94, pp, 3–4.Google Scholar - 20.L.A. Zadeh, “Outline of a new approach to the analysis complex systems and decision processes“.
*IEEE Trans Syst, Man Cybern.*, (1973) Vol SMC-3 pp. 28–44MathSciNetGoogle Scholar - 21.L.A. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning 1, 11, 111,“
*In formal Sci.*, (1975), vol. 8,, pp.199–251, pp. 301–357, vol. 9 pp. 43–80.MathSciNetGoogle Scholar - 22.L.A. Zadeh “Theory of approximate reasoning” in
*Machine Intelligence 9*eds. J.E. HAYES, DONALD MICHIE, L.I. MIKULICH. Eillis Horwood Limited (1970), pp. 149–194.Google Scholar - 23.M. Mizumoto, “Extended fuzzy reasoning“ in
*Approximate reasoning in Expert systems*, Gupta, Kandel, Bandler and Kizzka eds. North Holland, Amsterdam, (1985), pp. 71–85.Google Scholar - 24.S. Fukami, M. Mizumoto, and K. Tanaka, “Some considerations of fuzzy conditional inference.”
*Fuzzy Sets Syst.*, (1980) vol. 4, pp. 243–273.MATHCrossRefMathSciNetGoogle Scholar - 25.B. Kosko, “Neural networks and fuzzy systems: A dynamical systems approach to machine intelligence,”
*Prentice Hall, Englewood Cliffs, NJ*(1991).Google Scholar - 26.Y. Murayama and T. Terano, “Optimizing control of fiesel engine,” in
*Industrial Applications of Fuzzy Control*, M. Sugeno, Ed. Amsterdam: North-Holland, (1985), pp. 63–72.Google Scholar - 27.A. Kaufmann and M. M. Gupta,
*Introduction to Fuzzy Arithmetic*New York: Van Nostrand. 1985.MATHGoogle Scholar - 28.D. Dubois and H. Prade, “Unfair coins and necessity measures: Toward a possibilistic interpretation of histograms“,
*Fuzzy sets and system*(1985) vol-10, No 1, pp. 15–20.CrossRefGoogle Scholar - 29.L. Iarkin, “A fuzzy logic controller for aircraft flight control“,
*In industrial application of fuzzy control*,*M. Sugen*,*Ed. Amsterdam: North Holland*(1985) pp. 87–104.Google Scholar - 30.M. Sugeno, “And introductory survey of fuzzy control“,
*Information sciences*(1985) vol. 36, pp. 59–83.MATHCrossRefMathSciNetGoogle Scholar - 31.B. Kuipers, “Qualitative simulation“,
*Artificial intelligence*(1986) vol. 29, pp. 289–338.MATHCrossRefMathSciNetGoogle Scholar - 32.E. Lembessis, “Dynamical learning behavior of a rule-based self-organising controller,” Ph. D. thesis, Queen Mary College, Univ. of London, 1984.Google Scholar
- 33.E. M. Scharf and N.J. Mandic, “The application of a fuzzy controller to the control of a multi-degree-freedom robot arm,” in
*Industrial Applications of Fuzzy Control*, M. Sugeno, Ed. Amsterdam: North-Holland, (1985), pp 41–62.Google Scholar - 34.K. Sgiyama, “Analysis and synthesis of the rule based self-organising controler.” Ph. D thesis, Queen Mary College, Univ. of London, 1986.Google Scholar
- 35.S. Shao, “Fuzzy self-organizing controller and its application for dynamic processes.”
*Fuzzy Sets Syst.*, (1988), vol. 26, pp. 151–164.CrossRefGoogle Scholar - 36.R. Tanscheit and E.M. Scharf, “Experiments with the use of a rule-based self-organising controller for robotics applications,”
*Fuzzy Sets Syst.*, (1988) vol. 26, pp. 195–214.CrossRefGoogle Scholar - 37.M. Sugeno and K. Muralami, “Fuzzy parking control of model car,”
*23rd IEEE Conf. on Decision and Control*, Las Vegas, 1984.Google Scholar - 38.M. Sugeno and K. Muralami, “An experimental study of fuzzy parking control using a model car,” in
*Industrial Applications of Fuzzy Control*, M. Sugeno, ED. Amsterdam: North-Holland. (1985), pp. 125–138.Google Scholar - 39.S. Yasunobu and S. Miyamoto, “Automatic train operation by predictive fuzzy control,” in
*Industrial Application of Fuzzy Control*, M. Sugeno, Ed. Amsterdam: North-Holland, (1985), pp. 1–18.Google Scholar - 40.S. Yasunobu and T. Hasegawa, “Automatic train operation by predictive fuzzy control.”
*Control Theory Adv. Technol.*, (1986). vol. 2, no. 3, pp. 419–432.Google Scholar - 41.S. Yasunobu and T. Hasegawa, “Evaluation of an automatic container crane operation system based on predictive fuzzy control.”
*Control Theory Adv. Technol.*(1986) vol. 2, no.3 pp. 419–432.Google Scholar - 42.S. Yasunobu, S. Sekino. and T. Hasegawa. “Automatic train operation and automatic crane operation systems based on predictive fuzzy control,” in
*Proc. 2nd IFSA Congress*.*Tokyo Japan*. July (1987) pp. 835–838.Google Scholar - 43.N. Baaklini and E. H. Mamdani, “Prescriptive methods for deriving control policy in a fuzzy-logic controller.”
*Electron. Lett.*(1975) vol. 11 pp. 625–626.CrossRefGoogle Scholar - 44.M. Braae and D. A. Rutherford, “Selection of parameters for a fuzzy logic controller.”
*Fuzzy Sets System*(1979) vol. 2, no. 3, pp. 185–199.MATHCrossRefGoogle Scholar - 45.M. Braae and D. A. Rutherford, “Theoretical and linguistic aspects of the fuzzy logic controller.”
*Automatica*(1979) vol. 15, no. 5, pp 553–577.MATHCrossRefGoogle Scholar - 46.M. Sugeno and G. T. Kang. “Structure identification of fuzzy model,”
*Fuzzy Sets Syst.*, (1988) vol. 28, no. 1, pp. 15–33.MATHCrossRefMathSciNetGoogle Scholar - 47.T. Takagi and M. Sugeno, “Derivation of fuzzy control rules from human operator’s control actions.” in
*Proc. of the IFAC Symp. on Fuzzy Information, Knowledge Representation and Decision Analysis*, Marseilles, France, July (1983) pp.55–60.Google Scholar - 48.T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control.”
*IEEE Trans. Syst. Man Cybern.*, (1985), vol. SMC-15, no. 1, pp.116–132.Google Scholar - 49.T. C. Chang, K. Hasegawa and C.W. Ibbs, “ The effects of membership function on fuzzy reasoning.”
*Fuzzy Set. System*(1991) vol. 44, pp. 169–186.MATHCrossRefMathSciNetGoogle Scholar - 50.A. Kaufmann,
*Introduction to Theory of Fuzzy Subsets*. New York, Academic, (1975)MATHGoogle Scholar - 51.M. Mizumoto, “Note on the arithmetic rule by Zadeh for fuzzy conditional inference,”
*Cybern. Syst.*, (1981) vol. 12, pp. 247–306.MATHCrossRefMathSciNetGoogle Scholar - 52.S. Gottwald and W. Pedrycz, “ Problems of the design of fuzzy controllers.” in
*Approximate Reasoning in Expert Systems*, M.M. Gupta A. Kandel, W. Bandler, and J. B. Kiszka, Ed. Amsterdam: North-Holland, (1985), pp. 393–405.Google Scholar - 53.B.R. Gaines and L.J. Kohout, “The fuzzy decade: “A bibliography of fuzzy systems and closely related topics,”
*Int. J. Man. Mach. Studies*, (1977) vol. 9, pp. 1–68.MATHGoogle Scholar - 54.M.M. Gupta, G.M. Trojan, and J.B. Kiszka, “Controllabilitity of fuzzy control systems,”
*IEEE Trans. Syst. Man Cybern.*, (1986) vol. SMC-16, no. 4, pp. 576–582.CrossRefGoogle Scholar - 55.B. Bharathi Devi and V.V.S. Sarms, “Estimation of fuzzy memberships from histograms,”
*Inform. Sci.*, (1985) vol. 35, pp. 43–59.MATHCrossRefGoogle Scholar - 56.D. Dubois and H. Prade, “Fuzzy logic and the generalized modus ponens revisited,”
*Cybern. Syst.*, (1984) vol. 15, pp. 3–4.MathSciNetGoogle Scholar - 57.E. Czogala and W. Pedrycz, “Some problems concerning the construction of algorithms of decision making in fuzzy systems,”
*Int. J. Man. Mach. Studies*, (1981) vol. 15, pp.201–221.MATHMathSciNetGoogle Scholar - 58.E.H. Mamdani and S. Assilian, “An experiment in linguistic synthesis with a fuzzy logic controller,”
*Int. J. Man Mach. Studies*(1975) vol.7 no. 1, pp. 1–13.MATHGoogle Scholar - 59.J.C.T Vander Veen, “Fuzzy sets, theoretical reflections, applications to ship steering.”
*M. Sc thesis*,*Deprt. Elect. Eng., Delft Univ., Technol. Natherland*.Google Scholar - 60.C.C. Lee, “Fuzzy logic in control systems: Fuzzy logic controller — Part I & II”,
*IEEE Trans. Syst. Man and Cybern.*(1990) vol.-20, no.2, pp.404–435.MATHCrossRefGoogle Scholar - 61.K. Hirota and W. Pedrycz, “Analysis and synthesis of fuzzy systems by the use of fuzzy sets, “Fuzzy Sets Syst., (1983) vol. 10, no. 1, pp. 1–14.MATHCrossRefMathSciNetGoogle Scholar
- 62.W. Pedrycz, “Fuzzy control and Fuzzy system,”
*John Willey and Sons INC. New York*(1989).Google Scholar - 63.R.M. Tong, “A retrospective view of fuzzy control systems,”
*Fuzzy Sets. Syst*,. (1984) vol. 14, pp. 199–210.MATHCrossRefGoogle Scholar - 64.R.M. Tong, M.B. Beck and A. Latten, “Fuzzy control of the activated sludge wastewater treatment process,”
*Automatica*(1980) vol. 16, no. 6, pp. 695–701.MATHCrossRefGoogle Scholar - 65.O. Itoh, K. Gotoh, T. Nakauama, and S. Takamizawa, “Application of fuzzy control to activated sludge process,” in
*Proc. 2nd IFSA Congress*,*Tokyo, Japan*July (1987) pp. 282–285.Google Scholar - 66.C.P. Pappis and E.H. Mamdani,“A fuzzy logic controller for a traffic junction,” IEEE Trans. Syst. Man Cybern. (1977) vol. SMC 7, no. 10 pp. 707–717.Google Scholar
- 67.P.M. Larsen, “Industrial applications of fuzzy logic control,”
*Int. J. Man Mach. Studies.*, (1980) vol.12, no. 1, pp. 3–10CrossRefGoogle Scholar - 68.I.G. Umbers and P.J. King, “An analysis of human decision making in cement kiln control and the implications for automation.”
*Int. J. Man Mach. Studies*. (1980) vol.12, no. 1, pp.11–23.Google Scholar - 69.D. Willaeys, “Optimal control of fuzzy systems,” in
*Proc. Int. Congress on Applied Systems Research and Cybern*.*Acapulco*,*Dec.*(1980)Google Scholar - 70.M. Uragami, M. Mizumoto, and K. Tananka, “Fuzzy robot control”.
*Cybern.*(1976) vol.6, pp. 39–64.CrossRefMATHGoogle Scholar - 71.S. Murakami and M. Maeda, “Application of fuzzy controller to automobile speed control system,” in
*Industrial Applications of Fuzzy Control*, M. Sugeno, Ed. Amsterdam: North-Holland. (1985) pp. 105–124.Google Scholar - 72.Y. Sakai, “A fuzzy controller in turning process automation,” in
*Industrial Applications of Fuzzy Control*, M. Sugeno, Ed. Amsterdam: North-Holland, (1985) pp. 139–152.Google Scholar - 73.S. Murakami, “Application of fuzzy controller to automobile speed control system,”in
*Proc. of the IFAC Symp. on Fuzzy Information, Knowledge Representation and Decision Analysis*. Marseille, France, (1983) pp. 43–48.Google Scholar - 74.O. Yagishita, O. Itoh, and M. Sugeno, “Application of fuzzy reasoning to the water purification process,”
*Industrial Applications of Fuzzy Control*, M. Sugeno, Ed. Amsterdam: North-Holland, (1985) pp. 19–40.Google Scholar - 75.F. Fujitec, “FLEX-8800 series elevator group control system,” Fujitec Co., Ltd., Osaka, Japan, (1988)Google Scholar
- 76.Y. Kasai and Y. Morimoto, “Electronically controlled continuously variable transmission,” in
*Proc. Int. Congress on Transportation Electronics*, Dearborn, MI, (1988).Google Scholar - 77.J.A. Bernard, “Use of rule-based system for process control,”
*IEEE Contr. Syst. Mag.*, (1988) vol. 8, no. 5, pp. 3–13.CrossRefGoogle Scholar - 78.M. Togai and H. Watanabe, “Expert system on a chip: An engine for real-time approximate reasoning,”
*IEEE Expert Syst. Mag.*, (1986) vol.1, pp. 55–62.Google Scholar - 79.T. Yamakawa, “A simple fuzzy computer hardware system employing min and max operations — A challenge to 6th generation computer,” in
*Proc. 2nd IFSA Cnogress*, Tokyo, Japan, July (1987).Google Scholar - 80.S. Yasunobu, S. Miyamoto, and H. Ihara, “Fuzzy control for automatic train operation system,” in
*Proc. 4th IFAC/IFIP/IFORS Int. Congress on Control in Transportation Systems*, Baden, April (1983).Google Scholar - 81.M. Mizumoto and H-J Zimmermann, “Comparison of fuzzy reasoning methods, ”
*Fuzzy Sets and Systems*(1982) vol. 8, pp. 253–283.MATHCrossRefMathSciNetGoogle Scholar - 82.G.J. Klir and T.A. Folger,
*Fuzzy Sets, Uncertainty, and Information*. Englewood Cliffs, NJ: Prentice Hall, (1988). 268MATHGoogle Scholar - 83.C.V. Negoita, “On the stability of fuzzy systems,” in Proc. IEEE Int. Conf. on Cybernetics and Society, (1978) pp. 936–937.Google Scholar
- 84.J.B. Kiszka, M.M. Gupta, and P.N. Nikiforuk, “Energetistic stability of fuzzy dynamic systems,”
*IEEE Trans. Syst. Man Cybern.*, (1985) vol. SMC-15, no. 5, pp. 783–792.Google Scholar - 85.K. Tanaka and M. Sugeno, “Stability analysis and design of fuzzy control system,”
*Fuzzy Sets and Systems*(1992) vol. 45, pp. 135–156.MATHCrossRefMathSciNetGoogle Scholar - 86.T. Yamaguchi, T. Takagi and T. Mita, “Self-organizing control using fuzzy neural networks,”
*Int. J. Control*, (1992) vol. 56, no. 2, pp. 415–439.MATHCrossRefGoogle Scholar