Isolation of domains of stability of linear dynamic systems with fractional regulators

Abstract

Introduction. The research of linear dynamic systems of regulation of the process of biological purification of contaminated water with fractional regulators was conducted in order to determine the boundaries of D-domains of their global stability and to determine the space of the parameters of the adjustment of the fractional controller for fixed orders of the diereintegrators in its composition.Materials and methods. Studies were conducted on the stability of the automatic control of the water treatment process. Using the Dsplit method, we obtain analytical formulas that determine the limits of the region of stable stabilization of the "object" + "fractionalregulator" system.Result and discussion. Automatic control systems of fractional order are more precisely described by dynamic equations, in which the order of derivatives can be any number, valid and not only integer. Proportional-integral-differential (PID-) regulators that are widely used in practice of automation also fall under a fractional generalization, if in their structure, instead of ordinary integer derivatives and integrals, fractional analogues are used. The