Journal of Dynamics and VibroacousticsJournal of Dynamics and Vibroacoustics2409-4579Samara National Research University297210.18287/2409-4579-2016-3-1-39-46UnknownSTUDY OF THIRD-ORDER SYSTEM STABILITY IN THE SPACE OF CHARACTERISTIC EQUATION COEFFICIENTSProkofevA. B.proka@mail.ruSafonovS. V.safonov@vorstu.ruSamara State Aerospace University (national research university) 443086, Russia, Samara,
Moskovskoye shosse, 34Voronezh State Technical University 394026, Russia, Voronezh, Moskovskiy prospect, 14160320163139461402201602052017Copyright © 2017,2017<p><em>The problem of building the stability space for third-order control system is solved. The 3D stability space has coefficients of characteristic equation as coordinates. Analytical conditions of system stability are defined. Different variants of crossing of stability border surface by coefficients of characteristic equation are considered. The analysis of changes in location of roots of system characteristic equation and in types of step responses under these variants is fulfilled.</em></p>Control systemstabilitycharacteristic equationstep responseСистема автоматического управленияустойчивостьхарактеристическое уравнениепереходный процесс[[1] Gimadiev, A.G., Kruchkov, A.N., Prokofev, A.B., Shakhmatov, E.V. and Shorin, V.P. (2002), Avtomatika i regulirovanie aviacionnikh dvigatelei i energeticheskikh ustanovok. Chast 1. Teoriya avtomaticheskogo regulirovaniya [Automatic and control of aviation engines and power plants. Part 1. Theory of automatic control], SSAU, Samara, 139 p. (in Russian).][[2] Dyadic, V.F., Baydaly, S.A. and Krinicin, N.S. (2011), Teoriya avtomaticheskogo regulirovaniya [Theory of automatic control], TPU, Tomsk, 196 p. (in Russian).][[3] Vasilev, K.K. (2001), Teoriya avtomaticheskogo regulirovaniya (sledyaschie sistemi) [Theory of automatic control (servo systems)], Ulanovsk, 98 p. (in Russian).][[4] Kozlov, D.V. (2011), Optimalnoe po bistrodeystviyu posicionirovanie dvigatelya postoyannogo toka (Sistema tretego poryadka) [Optimum speed positioning of direct current electric engine (third-order system)] // Izvestiya TulGU. Technicheskiye nauki [Gerald of TulSU. Technical sciences], TulSU publ., Tula, Issue 5, Part 1, pp. 134 – 142. (in Russian).][[5] Dobrobaba, U.P., Murlin, A.U., Chumak, I.A., Voevodov, A.A. and Stepkin, A.A. (1998), Obosnovanie etalonnikh peredatochnikh funkciy system tretego poryadka [Reasoning of reference transfer functions of third-order systems] // Izvestiya vishikh uchebnikh zavedenij. Pischevaya technologiya [High schools’ Gerald. Food technology], Kuban State Technology University publ., Krasnodar, no. 2-3, pp. 75-76. (in Russian).][[6] Yingchun Zhong and Yan Luo (2011), Comparative study of single-loop control of third-order object, Procedia Engineering, Vol. 15, pp. 783 – 787.]