B.M. Mohan

Modeling and analysis of the simplest fuzzy PID controller of Takagi–Sugeno type with modified rule base

This paper deals with the simplest fuzzy PID controllers of the Takagi–Sugeno (TS) type. The term simplest is coined since minimal (two) number of fuzzy sets is used for fuzzification in these controllers. The mathematical models of these controllers are found using a modified rule base. The rule base consists of two rules which reduce the number of tuning parameters. Two classes of the simplest fuzzy PID controller are defined using algebraic product triangular norm and bounded sum/maximum triangular co-norm. It is shown that the fuzzy PID controller with modified TS rule base is equivalent to a nonlinear variable gain/ structure controller. The BIBO stability of the closed-loop control system is studied using the small gain theorem. The computational aspects of the controllers are investigated. The applicability of the simplest fuzzy PID controllers is demonstrated with the help of examples.

Stability Analysis of General Takagi-Sugeno Fuzzy Two-Term Controllers

ABSTRACT This paper deals with general fuzzy two-term controllers of Takagi-Sugeno (TS) type. Analytical structures and properties of general fuzzy PI/PD controllers are investigated with a modified rule base. The rule base contains three rules which effectively reduce the number of tuning parameters of the controllers. The fuzzy two-term controller uses at least three triangular or trapezoidal fuzzy sets on each input variable, algebraic product/minimum t-norm, bounded sum/maximum t-co-norm, and Centre of Gravity (CoG) defuzzification strategy. Four new models of TS type fuzzy controllers are proposed. The general fuzzy PI/PD controller with modified TS rule base is analogous to a variable gain (nonlinear) PI/PD controller. The gain either varies or remains constant in different regions of the input plane. The gain variations of the controller and the stability analysis of closed-loop control system with any one of the proposed models in the loop have been investigated. The applicability of the proposed controllers is shown with the help of examples.

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

In this paper analytical structure of the simplest fuzzy PID controller with modified Takagi-Sugeno (TS) rule base is found. Minimal number (two) of fuzzy sets is employed on each input variable. The modified rule base uses only two rules so that the number of adjustable parameters is reduced. The triangular norm and co-norm are chosen as Algebraic Product (AP) and Maximum (Max), respectively. It is shown that the fuzzy PID controller with modified TS rule scheme is equivalent to a nonlinear variable gain PID controller.