×

Structure and BIBO stability of a three-dimensional fuzzy two-term control system. (English) Zbl 1196.93043

Summary: A novel three-Dimensional Fuzzy Logic Controller (3D FLC) was developed recently for spatially distributed systems. In this study, the inherent spatial structure feature of a 3D FLC with two spatial inputs (also called as 3D two-term FLC) is first exposed via an analytical model. Then, the global Bounded-Input/Bounded-Output (BIBO) stability of the 3D fuzzy two-term control system is discussed. A sufficient condition is derived and provided as a useful criterion for the controller design of the 3D two-term FLC. Finally, a catalytic packed-bed reactor is presented as an example of spatially distributed process to demonstrate the effectiveness of the controller.

MSC:

93C42 Fuzzy control/observation systems
93D25 Input-output approaches in control theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] G.R. Chen, Stability of nonlinear systems, in: K. Chang (Ed.), Encyclopedia of RF and Microwave Engineering, Wiley, 2004, pp. 4881-4896.; G.R. Chen, Stability of nonlinear systems, in: K. Chang (Ed.), Encyclopedia of RF and Microwave Engineering, Wiley, 2004, pp. 4881-4896.
[2] Chen, G. R.; Ying, H., BIBO stability of nonlinear fuzzy PI control systems, J. Intell. Fuzzy Syst., 5, 245-256 (1997)
[3] Christofides, P. D., Robust control of parabolic PDE systems, Chem. Eng. Sci., 53, 16, 2949-2965 (1998)
[4] Christofides, P. D., Nonlinear and Robust Control of Partial Differential Equation Systems: Methods and Applications to Transport-Reaction Processes (2001), Birkhäuser: Birkhäuser Boston
[5] Desoer, C. A.; Vidyasagar, M., Feedback Systems: Input-Output Properties (1975), Academic Press: Academic Press New York · Zbl 0327.93009
[6] Fromion, V.; Monaco, S.; Normand-Cyrot, D., The weighted incremental norm approach: from linear to nonlinear \(H_∞\) control, Automatica, 37, 1585-1592 (2001) · Zbl 0995.93021
[7] Khalil, H. K., Nonlinear Systems (1996), Prentice-Hall: Prentice-Hall New Jersey · Zbl 0626.34052
[8] Lee, C. C., Fuzzy logic in control systems: fuzzy logic controller—part I, IEEE Trans. Syst. Man Cybern., 20, 2, 404-418 (1990) · Zbl 0707.93036
[9] Li, H. X.; Gatland, H. B., Conventional fuzzy control and its enhancement, IEEE Trans. Syst. Man Cybern. Part B, 26, 5, 791-797 (1996)
[10] Li, H. X.; Gatland, H. B.; Green, A. W., Fuzzy variable structure control, IEEE Trans. Syst. Man Cybern. Part B, 27, 2, 306-312 (1997)
[11] Li, H. X.; Zhang, X. X.; Li, S. Y., A three-dimensional fuzzy control methodology for a class of distributed parameter system, IEEE Trans. Fuzzy Syst., 15, 3, 470-481 (2007)
[12] Mamdani, E. H.; Assilian, S., An experiment in linguistic synthesis with a fuzzy logic controller, Int. J. Man Mach. Stud., 7, 1, 1-13 (1974) · Zbl 0301.68076
[13] Mendel, J. M., Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions (2001), Prentice Hall, Upper Saddle River: Prentice Hall, Upper Saddle River New York · Zbl 0978.03019
[14] Michels, K.; Klawonn, F.; Kruse, R.; Nürnberger, A., Fuzzy Control—Fundamentals, Stability and Design of Fuzzy Controllers (2006), Springer-Verlag: Springer-Verlag Berlin, Heidelberg · Zbl 1099.93025
[15] Mohan, B. M.; Patel, A. V., Analytical structure and analysis of the simplest fuzzy PD controllers, IEEE Trans. Syst. Man Cybern. Part B, 32, 2, 239-248 (2002)
[16] Ray, W. H., Advanced Process Control (1981), McGraw-Hill: McGraw-Hill New York
[17] Schiesser, W. E., The Numerical Methods of Lines Integration of Partial Differential Equations (1991), Academic Press: Academic Press San Diego · Zbl 0763.65076
[18] Ying, H., Fuzzy Control and Modeling: Analytical Foundations and Applications (2000), IEEE Press: IEEE Press New York
[19] Zadeh, L. A., Outline of a new approach to the analysis of complex systems and decision processes, IEEE Trans. Syst. Man Cybern., 3, 1, 28-44 (1973) · Zbl 0273.93002
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.