Abstract
The stability analysis for the fuzzy logic controller (FLC) has widely been reported. Furthermore some researches have been introduced to simplify the design process of FLC’s. One of them is to decrease the number of parameters representing the antecedent part of the fuzzy control rule. So we briefly explain a simple-structured fuzzy logic controller (SFLC) which uses only a single variable at the antecedent part of a fuzzy control rule. We analyze that it is absolutely stable based on the sector bounded condition. We expand a nonlinear controlled plant into a Taylor series about a nominal operating point. The fuzzy control system is transformed into a Lure system with nonlinearities. We also show the feasibility of the proposed stability analysis through a numerical example of a mass-damper-spring system.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Choi, B.-J., Kwak, S.-W., and Kim, B. K.: 1999, Design of a single-input fuzzy logic controller and its properties, Fuzzy Sets Systems 106, 299–308.
Choi, B.-J., Kwak, S.-W., and Kim, B. K.: 1997, A study on a new design method of the PD-type fuzzy logic controller, J. Electrical Engrg. Inform. Sci. 2, 49–56.
Driankov, D., Hellendoorn, H., and Rainfrank, M.: 1993, An Introduction to Fuzzy Control, Springer-Verlag, Berlin/Heidelberg.
Fuh, C.-C. and Tung, P.-C.: 1997, Robust stability analysis of fuzzy control systems, Fuzzy Sets Systems 88, 289–298.
Galichet, S. and Foulloy, L.: 1995, Fuzzy controllers: Synthesis and equivalences, IEEE Trans. Fuzzy Systems 3, 140–148.
Harris, C. J., Moore, C. G., and Brown, M.: 1993, Intelligent Control: Aspects of Fuzzy Logic and Neural Nets, World Scientific, Singapore.
Khalil, H. K.: 1996, Nonlinear Systems, Macmillan, New York.
Kickert, W. J. M. and Mamdani, E. H.: 1978, Analysis of a fuzzy logic controller, Fuzzy Sets Systems 1, 29–44.
Li, H.-X. and Gatland, H. B.: 1996, Conventional fuzzy control and its enhancement, IEEE Trans. Systems Man Cybernet. (B) 26, 791–797.
Malki, H. L., Li, H., and Chen, G.: 1994, New design and stability analysis of fuzzy PD control systems, IEEE Trans. Fuzzy Systems 2, 245–254.
Palm, R.: 1994, Robust control by fuzzy sliding mode, Automatica 30, 1429–1437.
Park, C. W.: 2003, LMI-based robust stability analysis for fuzzy feedback linearization regulators with its applications, Inform. Sci. 152, 287–301.
Ray, K. S. and Majumder, D. D.: 1984, Application of circle criteria for stability analysis of linear SISO and MIMO systems associated with fuzzy logic controller, IEEE Trans. Systems Man Cybernet. 14, 345–349.
Tanaka, K. and Sugeno, M.: 1992, Stability analysis and design of fuzzy control systems, Fuzzy Sets Systems 45, 135–156.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Choi, BJ., Kwak, SW. & Wang, H. Stability Analysis of a Simple-Structured Fuzzy Logic Controller. J Intell Robot Syst 42, 169–178 (2005). https://doi.org/10.1007/s10846-004-0045-z
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s10846-004-0045-z