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.
Highlights
The improvement in the quality of control was due to the difficulty of obtaining adequate mathematical models for many industrial processes
The problem of synthesis of fuzzy controllers with approximating nonlinear functions in the control algorithm (CAC-controllers) for the construction of automatic control systems for industrial objects is considered as an integral part of the general process of building and researching the system, including:
The analysis of the obtained dependences showed that they can be approximated by a sigmoid function or a combination of sigmoid functions. This makes it possible to implement the following method for the synthesis of a fuzzy controller: to reduce the solution of the formulated problem of synthesis of a fuzzy controller with approximating control (CAC)-controller to the use of the base of rules and membership functions of a known fuzzy controller and an algorithm for a simple correction of the parameters of the CAC-controller, which is solved using known fuzzy transformations based on limited information about the control object and the constraints imposed on the control
Summary
The improvement in the quality of control was due to the difficulty of obtaining adequate mathematical models for many industrial processes In such cases, traditional methods of synthesis of automatic control systems (ACS) based on simplified, inaccurate models do not always lead to the desired results. In this case, only one rule will be active, as a result of which three clear values appear at the output: -1, 0, 1. It uses the equivalence of graphical control dependencies U(ε) on the mismatch signal ε obtained by approximating nonlinear discontinuous functions (relay, relay with dead zone and saturation, or their combinations), and for various parameters of the membership functions
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