Estimation of the Accuracy of a Control System with a Fuzzy PID Controller Based on the Approximation of the Static Characteristic of the Controller

Abstract

The problem of estimating the accuracy of an automatic control system with a fuzzy PID controller is solved. To describe a fuzzy controller, its static characteristic is used, which is approximated by two piecewise-linear and one piecewise-constant sections. This approach makes it possible to study the system as a linear one at each section of the approximated characteristic, and accordingly develop the calculation methods known in control engineering, taking into account the features of the system under consideration. In the article, to calculate the error in the steady state, the theorem on the final value of the original is used. For two different types of second-order control objects — static and astatic — on the basis of this theorem, analytical expressions are obtained that relate the accuracy of the control system with the values of the target and disturbance with a different structure of the controller (P-, PI-, PD-). When conducting experimental studies, the fuzzy PID controller was compared with a linear one tuned by the method of the maximum stability. Research results show that a fuzzy controller ensures the accuracy of the control system is not worse than a linear one, while increasing the dynamics of the system. The analytical expressions presented in the article make it possible to assess the accuracy of a control system with a fuzzy controller and can be used as a technique for adjusting the controller based on the accuracy requirements.