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http://dx.doi.org/10.5302/J.ICROS.2009.15.5.525

Consideration to the Stability of FLC using The Circle Criterion  

Lee, Kyoung-Woong (조선대학교 대학원 제어계측공학과)
Choi, Han-Soo (조선대학교 제어계측로봇공학과)
Publication Information
Journal of Institute of Control, Robotics and Systems / v.15, no.5, 2009 , pp. 525-529 More about this Journal
Abstract
Most of FLC received input data from error e and change-of-error e' with no relation with system complexity. Basic scheme follows typical PD and PI or PID Controller and that has been developed through fixed ME In this paper, We studied the relationship between MF and system response and system response through changing Fuzzy variable of consequence MF and propose the simple FLC using this relationship. The response of FLC is changed according to the width of Fuzzy variable of consequence MF. As changing the Fuzzy variable of consequence MF shows various nonlinear characteristic, we studied the relation between response and MF using analytical method. We designed the effective FLC using three-variable MF and nine rules and took simulation for verification. In this study, we propose the method to design system with FLC in stability point which is an impotent characteristic of designing system. The circle criterion which is adapted to analysis the nonlinear system is put to use for proposed method. Since SISO FLC has a time-invariant and odd characteristic we can use the critical point not disk which is generally used to determine the stability in the circle criterion, to determine the stability. Using this, we can get the maximum critical point plot of SISO FLC with changing the consequence fuzzy variables. The predetermined critical point plot of FLC can be used to decide the region of the system to be stable. This method is effectively used to design the SISO FLC.
Keywords
fuzzy logic control; describing function; stability;
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1 B. Hu, G.K.I. Mann, and R. G Gosine, 'A systematic study of fuzzy PID controllers-function-based evaluation approach,' IEEE Trans. on FuzzySyst., vol. 9, no. 5. pp. 699-712, 2001   DOI   ScienceOn
2 $\check{S}$. Tomislav, S. Te$\check{s}$njak, S. Kulja$\check{c}$a Og-jen, 'Stability analysis of fuzzy control system using describing function method,'Proceedings of 9th Mediterranean Conference on Control and Automation, Dubrovnik, Croatia, 2001
3 C.-T. Chao and C.-C. Teng 'A PD-like self-tuning fuzzy controller without steady-state error,' Fuzzy Sets and Systems, vol. 87, no. 2, pp. 141-154, 1997   DOI   ScienceOn
4 R.-E. Precup and S. Preitl 'Popov-type stability analysis method for fuzzy control systems,' Proceedings of Fifth EUFIT'97 European Congress, Aachen, Germany vol. 2, pp. 1306-1310, 1997
5 M. Sugeno, 'On stability of fuzzy systems expres- sed by fuzzy rules with singleton consequents,' IEEE Transactions on Fuzzy Systems, vol. 7, pp. 201-224, 1999   DOI   ScienceOn
6 K. M. Passino and S. Yurkovich, Fuzzy Control, Addison Wesley Longman, Inc., Menlo Park, CA, 1998
7 H. Kiendl, 'Harmonic balance for fuzzy control systems,' Proceedings of First EUFJT'93 European Congress, Aachen, Germany, vol. 1,pp. 137-141, 1993
8 H. Ying, 'Analytical structure of a two-input two-output fuzzy controller and its relation to PI and multilevel relay controllers,' Fuzzy Sets and Systems, vol. 63, pp. 21-33, 1994   DOI   ScienceOn
9 F. Gordillo, J. Aracil, and T. Alamo 'Detennining limit cycles in fuzzy control systems,' Proceedings of FUZZ-IEEE '97 Conference, Barcelona, Spain, pp. 193-198, 1997
10 G. Calcev, 'Some remarks on the stability of Mam- dani fuzzy control systems,' IEEE Transactions on Fuzzy Systems, vol. 6, pp.436-442, 1998   DOI   ScienceOn
11 C. W. de Silva, Intelligent Control: Fuzzy Logic Applications. Boca Ration. FL: CRC, 1995
12 W. Silver and H. Ying, 'Fuzzy control theory: The Ii near case,' Fuzzy Sets Syst., vol. 33, pp. 275-290, 1989   DOI   ScienceOn
13 H. Ying, W. Silver, and J.J. Buckley, 'Fuzzy cont- rol theory: A nonlinear case,' Automatica, vol. 26, pp. 513-520, 1990   DOI   ScienceOn
14 B. Hu, G.K. I. Mann, and R. G. Gosine, 'New methodology for analytical and optimal design of fuzzy PID controllers,' IEEE Trans. on Fuzzy Syst., vol. 7, no. 5. pp. 521-539,1999   DOI   ScienceOn
15 H.-P. Opitz, 'Fuzzy control and stability criteria,' P- roceedings of First EUFIT'93 European Congress, Aachen, Germany, vol. 1,pp.130-136,1993
16 D. Driankov, H. Hellendoom, and M. Reinfrank, An Introduction to Fuzzy Control, 2nd Ed., Springer-Verlag, New York, 1996
17 J. Aracil, A. Ollero, and A. Garcia-Cerezo 'Stabi-lity indices for the global analysis of expert control systems,' IEEE Transactions on Systems, Man, and Cybernetics, vol. 19, pp. 998-1007,1989   DOI   ScienceOn
18 R.-E. Precup, S. Doboli, and S. Preitl 'Stability analysis and development of a class of fuzzy control systems,' Engineering Applications of Artificial Intelligence, vol. 13, pp. 237-247, 2000   DOI   ScienceOn