FRACTIONAL PROPORTIONA LINTEGRAL DIFFERENTIATING REGULATORS IN ELECTROTECHNIC SYSTEMS

Fractional PID-regulators in astatic closed-loop control systems allow to significantly im-prove 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 modelpower functionsof fractional order are present, such regulators more accurately compensate for such features of the object. The aim of the work is research ofthe dynamic and static charac-teristics of closed loop systems with a fractional order of astaticism from 0.5 to2.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 regula-tors 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 analyt-ical expressions are found that allow us to calculate the parameters of regulators without preliminary calcu-lation of transient processes. A method for calculating the output signals of regulators with fractional inte-gral 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 ac-count the magnetization curve with a quantization period of the order of 1-10 ms.