Open AccessСИНТЕЗ СИСТЕМ УПРАВЛІННЯ ЕЛЕКТРОПРИВОДАМИ З КОВЗНИМИ РЕЖИМАМИ
Author(s) -
А. Б. Жукевич,
О. А. Жукевич
Publication year - 2021
Publication title -
otkrytye informacionnye i kompʹûternye integrirovannye tehnologii
Language(s) - English
Resource type - Journals
eISSN - 2663-2411
pISSN - 2071-1077
DOI - 10.32620/oikit.2021.92.09
Subject(s) - nonlinear system , control theory (sociology) , linear quadratic regulator , parametric statistics , computer science , linear system , superposition principle , property (philosophy) , mathematics , optimal control , mathematical optimization , control (management) , mathematical analysis , philosophy , statistics , physics , epistemology , quantum mechanics , artificial intelligence
Synthesis of electric drive control systems by methods of the theory of analytical design of optimal controllers (ACOR) allows to obtain structures with sliding modes, which are characterized by high dynamic performance and the property of roughness relative to parametric and coordinate perturbations. At the same time, due to the presence of a relay regulator operating in sliding mode, such systems are nonlinear, described by differential equations with a discontinuous right-hand side. At the same time, one of the problems of ACOR is the problem of choosing the weights of optimizing functionals, which has not received an acceptable solution for designers: the choice of these coefficients is not predetermined by physically clear recommendations. If in the linear case the selection of weights of quadratic criteria can be organized by computer simulation of transients in a closed linear system, then in the nonlinear case such an approach is mathematically incorrect. This is due to the well-known fact that for nonlinear systems the principle of superposition is false, and their behavior in contrast to linear depends significantly on the initial conditions. In this regard, choosing as a result of modeling a nonlinear system on a computer those or other seemingly appropriate weights of the relevant criteria, you can get almost inoperable nonlinear system, because under other initial conditions, its behavior can change qualitatively. Surprisingly, this well-known fact in the literature is obscured, although its influence on the behavior of synthesized systems is fundamental.There are methods for constructing optimal systems based on the synthesis of regulators based on setting the desired quality indicators of transients, taking into account the known behavior of the system with a certain characteristic equation. The article substantiates the method of finding the feedback coefficients of the relay controller from the condition of providing the dynamic characteristics of the system, given the desired characteristic equation.