Background. Fuzzy logic provides many opportunities for application and allows you to display knowledge bases and expert systems of a new type that are able to remember and process inaccurate information. In addition, systems with fuzzy logic are applied in automatic systems for various purposes. However, the apparatus of the theory of fuzzy sets is nontrivial to implement and requires a clear understanding of the process and the correctness of setting the rules. Objective. The aim of the paper is to analyze mathematical methods in the design and adjustment of regulators based on fuzzy logic. Methods. The algorithm for the synthesis of the fuzzy logic controller consists of four phases: phasification, a description of fuzzy rules (through which the choice of control influence is carried out), aggregation and dephasing. The basis of the study was a gas turbine engine, which is a complex thermodynamic system. Three terms were used to describe the input and output logical variables. The input variable is the magnitude of the error between the current and the required rotational speed of the power turbine, and the output is the value of the required derivative of the turbocharger rotor speed. The result of the synthesis is a fuzzy P-regulator, defined as static with a nonlinear gain. Results. The obtained simulation results show that the fuzzy P-controller provides an adequate margin of stability, high static accuracy and aperiodic transient process, which gives significant advantages when the gas turbine engine is operating, since the oscillatory process can lead to disruption of the rotor and its failure. Conclusions. The introduction of a fuzzy logical P-type apparatus drastically changes the transition process to aperiodic type with a smooth start. A fuzzy rule base has been compiled providing a faster system performance by 43%, increasing the static accuracy by ten times and completely eliminates overshoot. The use of fuzzy regulators leads to an increase in the quality of regulation in the conditions of the impossibility of using traditional regulators.
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