Event under the auspices of the Ministry of Economy of Slovak Republic

Optimal PI fuzzy controller for nonlinear systems

Daniela Perdukova
Department of Electrical Engineering and Mechatronics

Pavol Fedor
Department of Electrical Engineering and Mechatronics

     Last modified: 2017-06-12

The paper describes the procedure of designing a PI fuzzy controller for a nonlinear system that guarantees optimal control dynamics in terms of the selected criterion. For the sake of simplicity we have chosen the optimality criterion in the form of the integral of the quadratic deviation of system output from desired value. Fuzzy controller design is based on the idea that if there exists for a controlled system a satisfactory input signal time sequence that will achieve the control target in an optimal way, it is then possible to simply design a fuzzy controller for this system on basis of this sequence (the optimal input vector). Finding the optimal input vector involves repeated application of various input vectors to the controlled system and optimality criterion evaluation for each one of them. The database for PI fuzzy controller design is obtained by applying the optimal input vector to the controlled system input for concrete reference value. Using the measured data database, the particular fuzzy controller is designed by standardly known procedures of clustering the data into significant clusters and their description by rules, e.g. by the Anfisedit tool of the Matlab programme.
The fuzzy controller design method enables the use of standard soft computing tools in the design process. Significant simulations and experimental measurements on a real nonlinear dual axis mechanical system that have been carried out have confirmed the rightness of the proposed method and the good dynamic properties of the developed PI fuzzy controller.
The main aim of the presented paper was to develop a fuzzy control design approach with as little system information as possible and to avoid the heuristic search for a rule-based fuzzy controller.
With this method no principal limitations for the investigated system´s nonlinearities are defined, and therefore there is good reason to assume that the presented method will find wide use in various sectors of industry.


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