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Research Papers

Stability Analysis of Nonlinear Dynamic Systems by Nonlinear Takagi–Sugeno–Kang Fuzzy Systems

[+] Author and Article Information
Zahra Namadchian

Islamic Azad University,
Gonabad Branch, Iran
e-mail: Zahra.namadchian@gmail.com

Assef Zare

Islamic Azad University,
Gonabad Branch, Iran
e-mail: Assefzare@gmail.com

Ali Namadchian

Islamic Azad University,
Mashhad Branch, Iran
e-mail: Ali_namadchian@yahoo.com

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received May 19, 2013; final manuscript received October 14, 2013; published online December 16, 2013. Assoc. Editor: Hashem Ashrafiuon.

J. Dyn. Sys., Meas., Control 136(2), 021019 (Dec 16, 2013) (6 pages) Paper No: DS-13-1205; doi: 10.1115/1.4025803 History: Received May 19, 2013; Revised October 14, 2013

This paper proposes a systematic procedure to address the limit cycle prediction of a Nonlinear Takagi–Sugeno–Kang (NTSK) fuzzy control system with adjustable parameters. NTSK fuzzy can be linearized by describing function method. The stability of the equivalent linearized system is then analyzed using the stability equations and the parameter plane method. After that the gain–phase margin (PM) tester has been added, then gain margin (GM) and phase margin for limit cycle are analyzed. Using NTSK fuzzy control system can help to have fewer rules. In order to analyze the stability with the same technique of stability analysis, the results of NTSK fuzzy control system will be compared with Dynamic fuzzy control system [1]. Computer simulations show differences between both systems.

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References

Figures

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Fig. 3

A general linearized system including gain–phase margin tester

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Fig. 4

Premise membership functions of NTSK fuzzy controller (x(t) = x1(t))

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Fig. 5

Premise membership functions of NTSK fuzzy controller (x(t) = x2(t))

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Fig. 2

Premise membership functions of NTSK fuzzy controller

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Fig. 1

NTSK fuzzy control system

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Fig. 11

Limit cycle loci in parameter plane (NTSK fuzzy control system)

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Fig. 12

Limit cycle loci in parameter plane (Dynamic fuzzy control system)

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Fig. 13

Input signal x(t)

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Fig. 14

Sets of GM and PM

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Fig. 6

Limit cycle loci in parameter plane (NTSK fuzzy control system)

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Fig. 7

Limit cycle loci in parameter plane (dynamic fuzzy control system)

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