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- Title
Isolation of domains of stability of linear dynamic systems with fractional regulators.
- Authors
Lobok, Oleksii; Goncharenko, Borys; Vykhrova, Larysa; Sych, Maryna
- 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 controllers of the fractional order denote how PI λDμ, where λ and μ are the orders of integration and differentiation of the error signal, with orders λ and μ may have valid non-integer (fractional) values. On the basis of the D-split method, analytical formulas are described that describe the boundaries of global stability of linear dynamic systems of fractional order. Domains of stability are built in the space of parameters of the configuration of fractional domains PI λDμ -regulators for fixed orders of dipintegrators. An appropriate algorithmic software is developed that implements the proposed method for selecting the domain of stability. Some results of computational experiments are given, an estimation of fractional PI λDμ - regulator efficiency is given. Conclusions. On the basis of the D-split method, analytical expressions were obtained, which describe the boundaries of the global region of stability of linear dynamic systems of fractional order of type "input-output" with fractional PI λDμ -regulators.
- Subjects
WATER purification; LINEAR dynamical systems; AUTOMATIC control systems; PID controllers; FRACTIONAL calculus
- Publication
Ukrainian Journal of Food Science, 2017, Vol 5, Issue 2, p283
- ISSN
2310-1008
- Publication type
Article
- DOI
10.24263/2310-1008-2017-5-2-12