Structure and BIBO stability of a three-dimensional fuzzy two-term control system

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.

[1]  B. M. Mohan,et al.  Corrections to "analytical structures and analysis of the simplest fuzzy PD controllers" , 2002, IEEE Trans. Syst. Man Cybern. Part B.

[2]  Vincent Fromion,et al.  The weighted incremental norm approach: from linear to nonlinear Hinfinity control , 2001, Autom..

[3]  Shaoyuan Li,et al.  A Three-Dimensional Fuzzy Control Methodology for a Class of Distributed Parameter Systems , 2007, IEEE Transactions on Fuzzy Systems.

[4]  B. M. Mohan,et al.  Analytical structures and analysis of the simplest fuzzy PI controllers , 2002, Autom..

[5]  Derek P. Atherton,et al.  Stability of nonlinear systems , 1981 .

[6]  C. Desoer,et al.  Feedback Systems: Input-Output Properties , 1975 .

[7]  E. H. Mamdani,et al.  An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller , 1999, Int. J. Man Mach. Stud..

[8]  Fuzzy Logic in Control Systems : Fuzzy Logic , 2022 .

[9]  Panagiotis D. Christofides,et al.  Nonlinear and Robust Control of Pde Systems , 2001 .

[10]  Han-Xiong Li,et al.  Conventional fuzzy control and its enhancement , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[11]  Guanrong Chen.  Stability of Nonlinear Systems , 1999 .

[12]  Hao Ying,et al.  Fuzzy Control and Modeling: Analytical Foundations and Applications , 2000 .

[13]  Panagiotis D. Christofides.  Robust Control of Parabolic PDE Systems , 1998 .

[14]  Han-Xiong Li,et al.  Fuzzy variable structure control , 1997, IEEE Trans. Syst. Man Cybern. Part B.

[15]  Frank Klawonn,et al.  Fuzzy Control - Fundamentals, Stability and Design of Fuzzy Controllers , 2006, Studies in Fuzziness and Soft Computing.

[16]  J. Mendel.  Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions , 2001 .

[17]  W. Schiesser.  The Numerical Method of Lines: Integration of Partial Differential Equations , 1991 .

[18]  Lotfi A. Zadeh,et al.  Outline of a New Approach to the Analysis of Complex Systems and Decision Processes , 1973, IEEE Trans. Syst. Man Cybern..

[19]  Costas J. Spanos,et al.  Advanced process control , 1989 .

[20]  John E. Rijnsdorp,et al.  Advanced process control: W. Harmon Ray , 1982, Autom..

[21]  Guanrong Chen,et al.  BIBO Stability of Nonlinear Fuzzy PI Control Systems , 1997, J. Intell. Fuzzy Syst..