STUDY OF THIRD-ORDER SYSTEM STABILITY IN THE SPACE OF CHARACTERISTIC EQUATION COEFFICIENTS

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Abstract

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.

About the authors

A. B. Prokofev

Samara State Aerospace University (national research university) 443086, Russia, Samara,
Moskovskoye shosse, 34

Author for correspondence.
Email: proka@mail.ru

Доктор технических наук, профессор кафедры автоматических систем энергетических установок

Russian Federation

S. V. Safonov

Voronezh State Technical University 394026, Russia, Voronezh, Moskovskiy prospect, 14

Email: safonov@vorstu.ru

References

  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 , SSAU, Samara, 139 p. (in Russian).
  2. Dyadic, V.F., Baydaly, S.A. and Krinicin, N.S. (2011), Teoriya avtomaticheskogo regulirovaniya , TPU, Tomsk, 196 p. (in Russian).
  3. Vasilev, K.K. (2001), Teoriya avtomaticheskogo regulirovaniya (sledyaschie sistemi) , Ulanovsk, 98 p. (in Russian).
  4. Kozlov, D.V. (2011), Optimalnoe po bistrodeystviyu posicionirovanie dvigatelya postoyannogo toka (Sistema tretego poryadka) // Izvestiya TulGU. Technicheskiye nauki , 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 // Izvestiya vishikh uchebnikh zavedenij. Pischevaya technologiya , 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.

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Copyright (c) 2017 Андрей Брониславович Прокофьев

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Journal of Dynamics and Vibroacoustics

ISSN 2409-4579 (Online)

Publisher and Founder: Samara National Research University, 34, Moskovskoye shosse, Samara, 443086, Russian Federation.

Extract from the register of registered media

Editor-in-chief:  Academician of the RAS
E. V. Shakhmatov 

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Address for correspondence: 34, Moskovskoye shosse, Samara, 443086, Russian Federation, Samara National Research University (room 324, building 14)

Phone: 8 (846) 267 47 66

e-mail: dynvibro@ssau.ru

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