Synthesis of a Fuzzy Controller According to the Degree of Stability of the Control System

Abstract

The article is devoted to solving the problem of analysis and synthesis of a control system with a fuzzy controller (fuzzy control system) in terms of the degree of stability. As interest in fuzzy control systems grows, various approaches to the study of such systems are being developed more and more actively. One of the most actively developing areas is based on the modification of methods for assessing the stability regions of nonlinear ACS, however, when solving most practical problems, this knowledge is not enough, since the developer needs to provide the required qualitative characteristics of the transient process (and, in particular, the control time). Therefore, the synthesis of fuzzy ACS in terms of the degree of stability seems to be quite constructive, since it allows quite accurately assessing the performance of a fuzzy ACS. The proposed solution is based on the criterion of absolute stability for a system with an approximated nonlinear characteristic of a fuzzy controller, which can be obtained directly on the basis of the Sugeno method. The article develops Yakubovich’s circular criterion of absolute stability, modified for a fuzzy control system, using a shifted AFC of the linear part. With this approach, it is possible to obtain a completely constructive solution to the problem of synthesizing the parameters of a fuzzy controller in the frequency domain. On the example of fuzzy control systems with static and astatic linear parts, the features of the application of the developed approach are shown and methods for synthesizing the parameters of a fuzzy controller are proposed. The analysis of the influence of individual components of the nonlinear transformation on the quality of the transient process is carried out, and on the basis of this a number of practical recommendations are given for correcting the fuzzy controller settings that provide the required performance.