Analysis and synthesis of intelligent automatic control systems with type-1 fuzzy regulator

Objectives. The active development of intelligent automatic control systems, which is associated with increasing requirements to the quality and accuracy of control systems of modern technical systems, requires the development of new approaches to their analysis and synthesis. A promising class of intelligent control devices is based on regulators that use fuzzy-logic inference technology. The purpose of this work is to develop a method for the complex synthesis of type-1 fuzzy regulator parameters on the basis of the Yakubovich circle criterion.
Methods. The proposed methodology is based on a consideration of fuzzy regulators in terms of the corresponding nonlinear transformation that support the use of methods derived from the theory of nonlinear automatic control systems. Analogs of the degrees of stability and oscillation are used as quality indicators. The synthesis of the parameters of the nonlinear transformation can be reduced to determining sufficient regions of absolute stability of the system with the shifted and extended Nyquist plot obtained using the Yakubovich circle stability criterion.
Results. In accordance with the theory of fuzzy sets and algorithms of fuzzy logical inference described by Takagi–Sugeno, the possibility of one-to-one correspondence of the nonlinear transformation and the parameters of an appropriately arranged knowledge base of the fuzzy controller is shown. A procedure proposed for synthesizing the parameters of the type-1 fuzzy regulator is aimed at ensuring complex requirements for the quality of the control system according to the degree of stability, the degree of oscillation, and steady-state mode accuracy. The effectiveness of the proposed technique, which guarantees the absolute stability not only of the equilibrium position but also of the processes, is confirmed by the results of model experiments.
Conclusions. The paper proposes a convenient engineering technique for determining the parameters of an intelligent controller constructed using fuzzy logic inference technology based on methods informed by automatic control theory. The convenience of using such indirect quality indicators as the degree of stability, the degree of oscillation, and accuracy in steady-state mode, is demonstrated. These indicators are explicable for developers of applied control systems.

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