A synthesis method for fuzzy controllers based on clustering

The goal of this work is to develop a method for synthesizing fuzzy controllers from experimental data based on clustering, since this is the simplest way to determine the number of membership functions and create a rule base. To achieve this goal, it is proposed to use experimental data on the input and output signals of the control system for a technical object with a classical controller. The developed method for data clustering is based on the experimental data and makes it possible to determine the term-sets of input and output linguistic variables of a fuzzy controller that implements the Mamdani fuzzy inference algorithm and to compose a rule base. Clustering is performed by evaluating the boundaries of the experimental data variation intervals, uniform division into clusters depending on the required power of term-sets of linguistic variables and determining if the data belongs to certain clusters. Since the experimental data are connected, that is, for each moment of time, data on both the input and output signals of the classical controller are stored and their belonging to clusters is determined, the development of the fuzzy controller rule base does not cause difficulties. To simplify the research, the authors have developed software in the MatLab environment. It makes it possible both to obtain experimental data, to synthesize a fuzzy controller and check its performance. The control system model is developed in the Simulink environment, the method of clustering and determining the parameters of linguistic variables is implemented as a program in an m-file; the fuzzy controller is implemented in the Fuzzy Logic Toolbox extension package. The high degree of integration of MatLab expansion packages made it possible to simplify the procedure of synthesizing fuzzy controllers as much as possible and to reduce it to determining the number of input and output variables and analyzing the simulation results. The paper presents the process of filling connected containers as an example, its mathematical model is a second-order transfer function with delay. To select an optimal structure of a fuzzy controller, the authors have carried out a study based on experimental data. The results obtained in this work were compared with the classical PD-controller, the model of which was implemented in the Simulink environment. The research results will be useful for developers of fuzzy control models.