Modeling the synthesis of Takagi — Sugeno — Kang fuzzy controllers in some control systems

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Abstract:

Modern challenges in a post-industrial society require further development of management systems for complex technical and technological phenomena and processes. Effective control of an object is possible if a controller, or a fuzzy controller, correctly generates the required control action. Recently, fuzzy controllers have been very popular. Fuzzy logical statements in this case help considering various nonlinear relationships. The synthesis of the fuzzy controller parameters allows for more efficient operation of the control system. A possible option for obtaining the best set of parameters for a fuzzy controller is the use of genetic algorithms for its synthesis. The use of genetic algorithms for the fuzzy controllers synthesis can lead to the fact that the elements of its parameters array will change in such a way that an incorrect value of one or more elements will occur. This situation leads to impossibility of composing membership functions for the terms of the variables of the fuzzy controller. Incorrect value formation is excluded by constructing a limited functional dependency.

This paper proposes a mathematical model of the parameters of the term-set of variables of a fuzzy controller of the Takagi — Sugeno — Kang type of the zero and first orders. The authors disclose the content of the conditions and conclusions of the rule base for the fuzzy controller of the above type.

As a result of the simulation, some operations of the genetic algorithm are implemented using a random number generator. Graphical models of the membership functions of the input variables of the fuzzy controller of the type under consideration clearly illustrate the occurrence of all parameters in their range of possible values. A description of the control system operation with two control parameters and one control action at the specified values of the control parameters is presented.

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