International Journal of Control, Automation, and Systems

Institute of Control, Robotics and Systems (제어로봇시스템학회)
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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)
  • Published : 2006.08.01
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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

References

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