Fuzzy control theory: a nonlinear case
Automatica (Journal of IFAC)
General analytical structure of typical fuzzy controllers and their limiting structure theorems
Automatica (Journal of IFAC) - Special section on fault detection, supervision and safety for technical processes
Studies on the output of fuzzy controller with multiple inputs
Fuzzy Sets and Systems
Explicit formulas for fuzzy controller
Fuzzy Sets and Systems
Industrial Applications of Fuzzy Logic and Intelligent Systems
Industrial Applications of Fuzzy Logic and Intelligent Systems
Information Sciences: an International Journal
Analysis of direct action fuzzy PID controller structures
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
IEEE Transactions on Fuzzy Systems
Constructing nonlinear variable gain controllers via the Takagi-Sugeno fuzzy control
IEEE Transactions on Fuzzy Systems
Design of a hybrid fuzzy logic proportional plus conventional integral-derivative controller
IEEE Transactions on Fuzzy Systems
New design and stability analysis of fuzzy proportional-derivative control systems
IEEE Transactions on Fuzzy Systems
The explicit linear quadratic regulator for constrained systems
Automatica (Journal of IFAC)
Three-dimensional min--max-gravity based fuzzy PID inference analysis and tuning
Fuzzy Sets and Systems
IEEE Transactions on Fuzzy Systems
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Deriving the analytical structure of fuzzy controllers is very important as it creates a solid foundation for better understanding, insightful analysis, and more effective design of fuzzy control systems. We previously developed a technique for deriving the analytical structure of the fuzzy controllers that use Zadeh fuzzy AND operator and the symmetric, identical trapezoidal or triangular input fuzzy sets. Many fuzzy controllers use arbitrary trapezoidal/triangular input fuzzy sets that are asymmetric. At present, there exists no technique capable of deriving the analytical structure of these fuzzy controllers. Extending our original technique, we now present a novel method that can accomplish rigorously the structure derivation for any fuzzy controller, Mamdani type or TS type, that employs the arbitrary trapezoidal input fuzzy sets and Zadeh fuzzy AND operator. The new technique contains our original technique as a special case. Given the importance of PID control, we focus on Mamdani fuzzy PI and PD controllers in this paper and show in detail how to use the new technique for different configurations of the fuzzy PI/PD controllers. The controllers use two arbitrary trapezoidal fuzzy sets for each input variable, four arbitrary singleton output fuzzy sets, four fuzzy rules, Zadeh fuzzy AND operator, and the centroid defuzzifier. This configuration is more general and complicated than the Mamdani fuzzy PI/PD controllers in the current literature. It actually contains them as special cases. We call this configuration the generalized fuzzy PI/PD controller.