Analytical structure and stability analysis of a fuzzy PID controller

Analytical structure for a fuzzy PID controller is introduced by employing two fuzzy sets for each of the three input variables and four fuzzy sets for the output variable. This structure is derived via left and right trapezoidal membership functions for inputs, trapezoidal membership functions for output, algebraic product triangular norm, bounded sum triangular co-norm, Mamdani minimum inference method, and center of sums (COS) defuzzification method. Conditions for bounded-input bounded-output (BIBO) stability are derived using the Small Gain Theorem. Finally, two numerical examples along with their simulation results are included to demonstrate the effectiveness of the simplest fuzzy PID controller.

[1]  C. A. Desoer,et al.  Nonlinear Systems Analysis , 1978 .

[2]  Hao Ying,et al.  Fuzzy Control and Modeling: Analytical Foundations and Applications , 2000 .

[3]  Michael Margaliot,et al.  New Approaches to Fuzzy Modeling and Control - Design and Analysis , 2000, Series in Machine Perception and Artificial Intelligence.

[4]  Chang Chieh Hang,et al.  Parallel structure and tuning of a fuzzy PID controller , 2000, Autom..

[5]  Engin Yesil,et al.  Self-tuning of PID-type fuzzy logic controller coefficients via relative rate observer , 2003 .

[6]  Guanrong Chen,et al.  New design and stability analysis of fuzzy proportional-derivative control systems , 1994, IEEE Trans. Fuzzy Syst..

[7]  Kazuo Tanaka,et al.  Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach , 2008 .

[8]  Hung-Yuan Chung,et al.  A PID type fuzzy controller with self-tuning scaling factors , 2000, Fuzzy Sets Syst..

[9]  Guanrong Chen,et al.  Fuzzy PID controller: Design, performance evaluation, and stability analysis , 2000, Inf. Sci..

[10]  Han-Xiong Li,et al.  Conventional fuzzy control and its enhancement , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[11]  Masaharu Mizumoto,et al.  PID type fuzzy controller and parameters adaptive method , 1996, Fuzzy Sets Syst..

[12]  Jin-Jye Lin,et al.  A fuzzy PID controller being like parameter varying PID , 1999, FUZZ-IEEE'99. 1999 IEEE International Fuzzy Systems. Conference Proceedings (Cat. No.99CH36315).

[13]  J. Aracil,et al.  Stability Issues in Fuzzy Control , 2000 .

[14]  Marjan Golob Decomposed fuzzy proportional-integral-derivative controllers , 2001, Appl. Soft Comput..

[15]  George K. I. Mann,et al.  A systematic study of fuzzy PID controllers-function-based evaluation approach , 2001, IEEE Trans. Fuzzy Syst..

[16]  Wei Li,et al.  Design of a hybrid fuzzy logic proportional plus conventional integral-derivative controller , 1998, IEEE Trans. Fuzzy Syst..

[17]  William Siler,et al.  Fuzzy control theory: A nonlinear case , 1990, Autom..

[18]  B. M. Mohan,et al.  Analytical structures and analysis of the simplest fuzzy PI controllers , 2002, Autom..

[19]  Jun Hwan Kim,et al.  A fuzzy PID controller for nonlinear and uncertain systems , 2000, Soft Comput..

[20]  B. M. Mohan,et al.  Analytical structures and analysis of the simplest fuzzy PD controllers , 2002, IEEE Trans. Syst. Man Cybern. Part B.

[21]  M. Mizumoto Realization of PID controls by fuzzy control methods , 1995 .