Stability Analysis and Proposal of a Simple Form of a Fuzzy PID Controller

Abstract

This paper suggests the simple form of a fuzzy PID controller and describes the design principle, tracking performance, stability analysis and changes of parameters of a suggested fuzzy PID controller. A fuzzy PID controller is derived from the design procedure of fuzzy control. It is well known that a fuzzy PID controller has a simple structure of the conventional PID controller but posses its self-tuning control capability and the gains of a fuzzy PID controller become nonlinear functions of the inputs. Nonlinear calculation during fuzzification, defuzzification and the fuzzy inference require more time in computation. To increase the applicability of a fuzzy PID controller to digital computer, a simple form of a fuzzy PID controller is introduced by the backward difference mapping and the analysis of the fuzzy input space. To guarantee the BIBO stability of a suggested fuzzy PID controller, ‘small gain theorem’ which proves the BIBO stability of a fuzzy PI and a fuzzy PD controller is used. After a detailed stability analysis using ‘small gain theorem’, from which a simple and practical method to decide the parameters of a fuzzy PID controller is derived. Through the computer simulations for the linear and nonlinear plants, the performance of a suggested fuzzy PID controller will be assured and the variation of the gains of a fuzzy PID controller will be investigated.

Keywords

• Fuzzy controller;
• Fuzzy PID controller Stability analysis;
• Small gain theorem

File

Download PDF

References

1. A. Heidar, M. H. Li and G. Chern, 'New Design and Stability Analysis of Fuzzy Proportional-Derivative Control Systems,' IEEE Transactions on Fuzzy Systems, Vol. 2, pp. 245-254. 1994 https://doi.org/10.1109/91.324804
2. G. Chen and H. Ying. 'Stability Analysis of Nonlinear Fuzzy PI Control Systems,' Proceeding of 3rd International Conference on Fuzzy Logic Application, pp. 128-133. 1993
3. J. H. Kim. 'A Suggestion of Nonlinear Fuzzy PID Controller to Improve Transient Responses of Nonlinear or Uncertain Systems.' Korea Journal of Fuzzy Logic and Intelligent Systems. Vol. 5. No.4, pp. 87-100, 1995
4. L. Wang, A Course in Fuzzy Systems and Control, Prentice-Hall, 1977
5. K. M. Passino and S. Yurkovich, Fuzzy Control, Addison Wesely, 1999
6. K. J. Astrom and B. Wittenmark, Computer-Controlled Systems Theory and Design, Prentice-Hall. 1990
7. S. Kitamura and T. kurozumi, 'Extended Circle Criterion and Stability Analysis of Fuzzy Control Systems,' Proceeding of International Fuzzy Engineering Symposium. pp. 634-643, 1991
8. E. Furutani, M. Saeki and M. Araki. 'Shifted Popov Criterion and Stability Analysis of Fuzzy Control Systems,' Proceeding of IEEE Control and Decision Conference, pp. 2709-2795, 1992
9. S. Singth, 'Stability Analysis of Discrete Fuzzy Control Systems,' Proceeding of 1st IEEE International Conference, pp. 527-534, 1992
10. K. Tanaka and M. Sugeno. 'Stability Analysis and Design of Fuzzy Control Systems,' Fuzzy Sets and Systems, Vol. 45. pp. 135-156, 1992
11. K. H. Cho, C. W. Kim and J. T. Lim, 'On Stability Analsis of Nonlinear Plants with Fuzzy Logic Controllers,' Proceeding IFSA '93. pp. 1094-1097, 1993
12. C. A. Desoer and M. Vidyasagar. Feedback Systems: Input-Output Properties, New York Academic, 1975
13. R. J. P. de Figueiredo and G. Chen, Nonlinear Feedback Control Systems: An Operator Approach, New York Academic, 1993