FRACTIONAL PROPORTIONAL-INTEGRAL-DIFFERENTIATING REGULATORS IN ELECTROTECHNIC SYSTEMS

Abstract

Fractional PIaDb-regulators in astatic closed-loop control systems allow to significantly improve the dynamic performance due to the increase in stability stocks with simultaneous expansion of the bandwidth of the circuit. In addition, when an object can be described by fractional-differential equations, or in its mathematical model power functions of fractional order are present, such regulators more accurately compensate for such features of the object. The aim of the work is research of the dynamic and static characteristics of closed loop systems with a fractional order of astaticism from 0.5 to 2. Based on the analysis of frequency characteristics and transient processes of such systems, methods for the synthesis of regulators for the order of astaticism are proposed, both less than 1 and more 1. Rules for selecting the structure of regulators and necessary transfer functions of regulators for typical control objects. Their parameters are chosen in accordance with the proposed calculation dependencies. This ensures that the overshoot is limited at a given level and the speed is higher than for systems with an integer order of astaticism. Approximate analytical expressions are found that allow us to calculate the parameters of regulators without preliminary calculation of transient processes. A method for calculating the output signals of regulators with fractional integral and differentiating components, which is applicable in microprocessor control systems, is described. Taking into account the processing power of modern single-chip processors, this makes it possible to apply fractional-integral calculus methods both for controlling slow processes (in microclimate appliances, in charge / discharge systems of supercapacitors and accumulators with a quantization period of 1 s), and in relatively fast systems , for example, controlling the current in the circuit with the inductor taking into account the magnetization curve with a quantization period of the order of 1-10 ms.

Author Biography

Виктор Владимирович Бушер, Odessa National Polytechnic University

Dr. of Science, Professor of the Department of electromechanical system with computer control, Odessa National Polytechnic University

Published
2018-06-26
How to Cite
Бушер, В. (2018). FRACTIONAL PROPORTIONAL-INTEGRAL-DIFFERENTIATING REGULATORS IN ELECTROTECHNIC SYSTEMS. Electrotechnic and Computer Systems, (27(103), 258-263. https://doi.org/10.15276/eltecs.27.103.2018.30
Section
Dynamic Systems' Modelling

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