Demkiv L. Analysis and synthesis of fuzzy controllers of dynamical systems

In this paper, we study the approaches to the synthesis of dynamic systems using the theory of fuzzy sets. Particular attention is paid to the case when one of the subsystems of a family of dynamical systems is unstable due to the action of the synthesized regulator. It is shown that such an approach enables the general system of new properties to be improved and increases the transcoding swquid, without causing inadmissible overlaps of intermediate and initial coordinates. It is shown that the overall system remains stable. An approach to the synthesis of the regulator is provided, which provides controlled oscillatory mode in the vicinity of the working point, which can be stopped if necessary. The amplitude and frequency of oscillations, in this case, depend on the parameters of the fuzzy controller. To solve problems where there is a need to limit the values ​​of the intermediate coordinates of the state vector of the system, a cascade fuzzy controller was used. Such a regulator allows not only to limit the value of the mentioned parameters, but also to provide the desired performance of the system. In this case, there is a significant gain in the number of rules in the base rules of the fuzzy controller. For a system with variable parameters it is shown that a synthesized fuzzy controller ensures its robustness. The proposed approaches are used for the synthesis of the fuzzy regulator of an arc furnace and an unclear correction of the electromotive velocity sensor.