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Analysis of FLC with changing fuzzy variables in frequency domain

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Abstract

This paper discusses a simple method for analyzing FLC in frequency domain based on describing function. Since nonlinear characteristics of FLC make it difficult FLC analysis, it usually requires a big deal of trial-and-error procedures based on computer simulation. The proposed method is simple and easy to understand, because it is based on the Nyquist stability criterion used to analyze absolute and relative stability, phase and gain margin of a linear system. To linearize in frequency domain, a describing function for FLC is derived by using a piecewise linearization of the FLC response plot. This describing function is represented as a function of magnitude of input sinusoid and nonlinear parameters x 1 and x 2 which change consequence fuzzy variables and nonlinearity of FLC. The describing function is redefined without the magnitude of sinusoid input because maximum values of the describing function can explain the stability of the system. This redefined describing function is used to get minimum stability characteristic, an absolute stability, phase margin and gain margin, of FLC. Using this function, we can explicitly figure out various characteristic of FLC according to x 1 and x 2 in frequency domain. In this work, we suggest a minimum phase margin (MPM) and a minimum gain margin (MGM) for FLC which can be used to determine whether the system is stable or not and how stable it is. For simplicity, we use one-input FLC with three rules. For various nonlinear response of FLC, changing fuzzy variables of a consequence membership function is used. Simulation results show that these parameters are effective in analyzing FLC.

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Authors and Affiliations

  1. Department of Control and Instrumentation Eng., Chosun University, Gwangju, Korea

    Kyoung-woong Lee & Hansoo Choi

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  1. Kyoung-woong Lee
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  2. Hansoo Choi
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Corresponding author

Correspondence to Hansoo Choi.

Additional information

Recommended by Editorial Board member Eun Tai Kim under the direction of Editor Young-Hoon Joo. This study was supported by research funds from Chosun University, 2007.

Kyoung-woong Lee received his B.S. and M.S. degrees in Control and Instrumentation from Chosun University, Korea in 1998 and 2003 respectively. He is currently working toward a Ph.D. degree at the same university. His research interests are intelligent control, distributed control and network system.

Hansoo Choi received his B.S. and M.S. degrees in Electrical Engineering from Chosun University, Korea in 1980 and 1982 respectively. He received his Ph.D. degree in Electrical Engineering from Chonbuk University, Korea, in 1994. Since 1984 he has been a professor in the Department of Control, Instrumentation and Robot Eng., Chosun University, Korea. His research interests are fuzzy system, neural system, intelligent system, and intelligent control.

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Lee, Kw., Choi, H. Analysis of FLC with changing fuzzy variables in frequency domain. Int. J. Control Autom. Syst. 8, 695–701 (2010). https://doi.org/10.1007/s12555-010-0324-3

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