Method for the fuzzy control system synthesis for the analytical approximation characteristics of the typical nonlinear elements characteristics

Kuban state technological University, Krasnodar, Russia

^* Corresponding author: vf.lubentsov@yandex.ru

Abstract

The solution of the problem concerning the control system synthesis with a fuzzy controller on the basis of typical nonlinear analytical approximation characteristics with continuous differentiable functions like sigmoid type has been considered. A method of synthesis which is based on the fact that the rulebase and membership function are formed by the way of comparing the control or corrective impacts of the fuzzy controller (prototype) or a controller with approximating control (CAC) has been suggested for problem solving. For the CAC construction the closest coincidence of graphically installed controllers’ impacts are taken. This makes it possible to exclude subjective errors connecting with a possible non-representative ruleset for the rulebase forming. The result of the work is to obtain a new class of controllers based on the approximating continuous functions, which are simpler for constructing multi-mode control systems. The practical significance lies in the fact, that the tuning of the fuzzy controller based on the analytical continuous approximation of the typical nonlinear elements’ characteristics comes down to two basic parameters: the coefficient that determines the curvature (slope) of the characteristic in the transit mode and the parameter that determines the control impact value in the static mode. The advantage of this smooth characteristic in relation to the piecewise linear approximation is that there is no need to determine the moments (points) of switching nonlinear characteristics during the system operation.