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Reduction of Fuzzy Rules and Membership Functions and Its Application to Fuzzy PI and PD Type Controllers  

Chopra Seema (Department of Electronics and Computer Engineering, Indian Institute of Technology)
Mitra Ranajit (Department of Electronics and Computer Engineering, Indian Institute of Technology)
Kumar Vijay (Department of Electronics and Computer Engineering, Indian Institute of Technology)
Publication Information
International Journal of Control, Automation, and Systems / v.4, no.4, 2006 , pp. 438-447 More about this Journal
Abstract
Fuzzy controller's design depends mainly on the rule base and membership functions over the controller's input and output ranges. This paper presents two different approaches to deal with these design issues. A simple and efficient approach; namely, Fuzzy Subtractive Clustering is used to identify the rule base needed to realize Fuzzy PI and PD type controllers. This technique provides a mechanism to obtain the reduced rule set covering the whole input/output space as well as membership functions for each input variable. But it is found that some membership functions projected from different clusters have high degree of similarity. The number of membership functions of each input variable is then reduced using a similarity measure. In this paper, the fuzzy subtractive clustering approach is shown to reduce 49 rules to 8 rules and number of membership functions to 4 and 6 for input variables (error and change in error) maintaining almost the same level of performance. Simulation on a wide range of linear and nonlinear processes is carried out and results are compared with fuzzy PI and PD type controllers without clustering in terms of several performance measures such as peak overshoot, settling time, rise time, integral absolute error (IAE) and integral-of-time multiplied absolute error (ITAE) and in each case the proposed schemes shows an identical performance.
Keywords
Extraction of rules; fuzzy control; fuzzy subtractive clustering; membership functions;
Citations & Related Records

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1 F. Klawonn and R. Kruse, 'Constructing a fuzzy controller from data,' Fuzzy Sets and Systems, vol. 85, pp. 177-193, 1997   DOI   ScienceOn
2 T. D. Gedeon, H. Kuo, and P. M. Wong, 'Rule extraction using fuzzy clustering for a sedimentary rock data set,' International Journal of Fuzzy System, vol. 4, no. 1, pp. 600- 605, March 2002
3 S. L. Chiu, 'Fuzzy model identification based on cluster estimation,' Journal of Intelligent and Fuzzy System, vol. 2, pp. 267-278, 1994
4 S. L. Chiu, 'Extracting fuzzy rules from data for function approximation and pattern classification,' to appear as Chapter 9 in Fuzzy Set Methods in Information Engineering: A Guided Tour of Applications, D. Dubois, H. Prade, and R. Yager, ed., John Wiley, 1997
5 S. L. Chiu, 'An efficient method for extracting fuzzy classification rules from high dimensional data,' J. Advanced Computational Intelligence, vol. 1, no. 1, pp. 31-36, 1997   DOI
6 K. Pal, R. K. Mudi, and N. R. Pal, 'A new scheme for fuzzy rule-based system identification and its application to self-tuning fuzzy controllers,' IEEE Trans. on Systems, Man, and Cybernetics-Part B: Cybernetics, vol. 32, no. 4, pp. 470-482, Aug. 2002   DOI   ScienceOn
7 D. Driankov, H. Hellendorn, and M. Reinfrank, An Introduction to Fuzzy Control, Springer-Verlag, New York, 1993
8 T. B. Cheng, D. B. Goldgof, and L. O. Hall, Fast clustering with application to fuzzy rule generation. Available: http://www.morden.csee.usf.edu/~hall/mrfcm.pdf
9 M. Setnes, 'Supervised fuzzy clustering for rule extraction,' Proc. of the IEEE International Conference on Fuzzy System, pp. 1270-1274, 1999
10 R. Nikhil, K. Pal, J. C. Bezdek, and T. A. Runkler, 'Some issues in system identification using clustering,' Proc. of International Conference on Neural Networks, vol. 4, pp. 2524-2529, 1997
11 M. Hanss, 'Identification of enhanced fuzzy models with special membership functions and rule base,' Engineering Application of Artificial Intelligence, vol. 12, pp. 309-319, 1999   DOI   ScienceOn
12 J. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithm, Plenum Press, New York, 1981
13 P. Grabusts, 'Clustering methods in neuro-fuzzy modeling.' Available: http://www.dssg.cs.rtu.lv/download/publications/2002/Garbusts-RA-2002.pdf
14 P. Pivonka, 'Comparative analysis of fuzzy PI/PD/PID controller based on classical PID controller approach.' Available: http://www.feec.vutbr.cz/~pivonka
15 M. Gopal, Control Systems Principles and Design, Tata McGraw-Hill, India, 1993
16 J. Carvajal, G. Chen, and H. Ogmen, 'Fuzzy PID controller: Design, performance evaluation, and stability analysis,' Information Sciences, vol. 123, pp. 249- 270, 2000   DOI   ScienceOn
17 R. R. Yager and D. P. Filev, 'Generation of fuzzy rules by mountain clustering,' Journal of Intelligent and Fuzzy System, vol. 2, pp. 209-219, 1994
18 C.-F. Juang and C.-T. Lin, 'An on-line selfconstructing neural fuzzy inference network and its applications,' IEEE Trans. on Fuzzy System, vol. 6, no. 2, pp. 13-31, 1999
19 T. Takagi and M. Sugeno, 'Fuzzy identification of systems and its application to modeling and control,' IEEE Trans. on Systems, Man, and Cybernetics, vol. SMC-15, no. 1, pp. 116-132, 1985   DOI
20 T. Kohonen, 'The self-organizing map,' Proc. of IEEE, vol. 78, no. 9, pp. 1464-1480, September 1990   DOI   ScienceOn
21 T. A. Runkler and R. H. Palm, 'Identification of nonlinear systems using regular fuzzy celliptotype clustering,' Proc. of the Fifth IEEE International Conference on Fuzzy Systems, vol. 2, pp. 1026-1030, 1996
22 S. Chopra, R. Mitra, and V. Kumar, 'Identification of rules using subtractive clustering with application to fuzzy controllers,' Proc. of the Third International Conference on Machine Learning and Cybernetics, pp. 4125-4131, 2004
23 S. Chopra, R. Mitra, and V. Kumar, 'Identification of self-tuning fuzzy PI type controllers with reduced rule set,' Proc. of the IEEE International Conference on Networking, Sensing and Control, pp. 537-542, March 2005
24 M. S. Yang, 'A survey of fuzzy clustering,' Math. Comput. Modeling, vol. 18, pp. 177-200, 1993
25 S. K. Sin and Rui J. P. DeFigueiredo, 'Fuzzy system design through fuzzy clustering and optimal pre defuzzification,' Proc. of IEEE International Conference on Fuzzy Systems, San Francisco, pp. 190-195, 1993
26 R. K. Mudi and N. R. Pal, 'A robust self-tuning scheme for PI and PD type fuzzy controllers,' IEEE Trans. on Fuzzy System., vol. 7, no. 1, pp. 2-16, 1999   DOI   ScienceOn
27 K. Ogata, Modern Control Engineering, Prentice- Hall, Englewood Cliffs, NJ, 1970
28 A. Kusiak and W. S. Chow, 'An efficient cluster identification algorithm,' IEEE Trans. on Systems, Man, and Cybernetics-Part B: Cybernetics, vol. SMC-17, no. 4, pp. 696-699, Jul.-Aug. 1987