Conventional controller design based on Takagi–Sugeno fuzzy models

Abstract

a r t i c l e i n f o a b s t r a c tArticle history: Available online 15 November 2014 Keywords: Expert system Knowledge base PID controller Ziegler-Nichols step response method Chien Hrones and Reswick design method Fuzzy system Feedback controlAlthough it is long since the first PID controller design method was developed, new methods are still being created and no general applicable method has been found. The paper extends the set of designing methods of PID controllers. Design methods can be divided into classic (analytical tuning methods, optimization methods etc.) and not so common fuzzy knowledge based methods. In this case, a conjunction of both methods is presented. The classic design methods (Ziegler-Nichols step response method and Chien, Hrones and Reswick design method) are used for achieving the knowledge of fuzzy knowledge based design methods. The fuzzy knowledge based design methods are based on Takagi-Sugeno model. It is defined as a class of systems for which -using the new proposed method -the settling time is shorter or the settling time is nearly the same but without overshoot, which could be also very useful. The proof of efficiency of the proposed methods and a numerical experiment is presented including a comparison with the conventional methods (simulated in the software environment Matlab-Simulink).

Modelling of the simplest fuzzy PID controller of Takagi-Sugeno type using algebraic product t-norm and Maximum t-co-norm

“…(5,8,18), (5,8,19) µ Ne µ N ∆ 2 e µ Pe µ P ∆ 2 e 17. (6,7,14), (6,8,13), (6,8,20) µ Ne µ N ∆ 2 e µ Ne µ P ∆ 2 e 18. (7,14,6), (8,13,6), (8,20,6) …”

“…(8,18,5), (8,19,5) µ N ∆e µ N ∆ 2 e µ P ∆e µ P ∆ 2 e 21. (9,11,13), (9,11,20), (10,11,19) µ Pe µ P ∆ 2 e µ Ne µ P ∆ 2 e 22. (9,12,14), (9,12,15) µ Pe µ P ∆ 2 e µ Ne µ N ∆ 2 e 23.…”

“…(10,11,18), (10,12,16), (10,12,17) µ Pe µ P ∆ 2 e µ Pe µ N ∆ 2 e 24. (11,13,9), (11,19,10), (11,20,9) µ P ∆e µ P ∆ 2 e µ P ∆e µ N ∆ 2 e 25. (11,18,10), (12,16,10), (12,17,10) µ P ∆e µ P ∆ 2 e µ N ∆e µ P ∆ 2 e 26.…”

“…(12,5,9), (12,14,9) µ P ∆e µ P ∆ 2 e µ N ∆e µ N ∆ 2 e 27. (13,9,11),(19,10,11),(20, 9,11) µ Pe µ P ∆e µ Pe µ N ∆e 28. (13,16,8),(14,6,7),(20, 6,8) µ Ne µ N ∆e µ Pe µ N ∆e 29.…”

“…Some analytical structures for Mamdani type PID controllers [3][4][5][6]8,9] are available, but analytical structures for TS type PID controllers [7,11] are rather limited. Some design methods of Mamdani type [10] and TS type [13] PID controllers have been reported. A review on PID controllers may be found in [12].…”