Certificate of Registration Media number Эл #ФС77-53688 of 17 April 2013. ISSN 2308-6033. DOI 10.18698/2308-6033
  • Русский
  • Английский

Stability of a relay dynamic system with non-linear speed sensor and delay under constant disturbance

Published: 11.03.2020

Authors: Simonyants R.P., Khudaybergenov B.R.

Published in issue: #3(99)/2020

DOI: 10.18698/2308-6033-2020-3-1966

Category: Aviation and Rocket-Space Engineering | Chapter: Aircraft Dynamics, Ballistics, Motion Control

The paper considers the joint effect of the control delay and speed sensor output signal limiting on the stability of the relay dynamic system under the constant disturbance. It is shown that in this case a new property is detected in the system – the appearance of the unstable limit cycle. Phase trajectories are drawn to a stable limit cycle only from the area of initial conditions where their boundaries are determined by the trajectory of an unstable limit cycle. Using the method of Poincare mappings, the parameters of fixed points defining the unstable limit cycle as the boundary of the stability region are found. A simplified method for approximate determination of simple limit cycles and stability in the “large” is proposed based on the property of dynamic symmetry of the system. The method allows the study of the problem under consideration to be limited to applying shift and symmetry mappings to the switching lines.

[1] Bobtsov A.A., Kolubin S.A., Pyrkin A.A. Avtomatika i telemekhanika — Automation and Remote Control, 2015, no. 1, pp. 21–30.
[2] Mozzhorov A.V., Faldin N.V. Izvestiya RAN. Teoriya i sistemy upravleniya — Journal of Computer and Systems Sciences International, 2008, no. 4, pp. 5–14.
[3] Fridman L. Semiglobal stabilization of linear uncertain system via delayed relay control. In: Variable Structure Systems: from Principles to Implementation. London, The Institution of Engineering and Technology Publ., 2004, pp. 377–400.
[4] Peregudova O.A. Avtomatika i telemekhanika — Automation and Remote Control, 2009, no. 5, pp. 95–105.
[5] Pavlikov S.V. Mekhanika tvordogo tela — Solid mechanics, 2005, no. 35, pp. 212–216.
[6] Pavlikov S.V. Doklady RAN — Reports of RAS, 2007, vol. 412, no. 2, pp. 176–178.
[7] Shilnikov L.P., Shilnikov A.L., Turaev D.V., Chua L. Metody kachestvennoy teorii v nelineynoy dinamike. Chast 2 [Methods of qualitative theory in nonlinear dynamics. Part 2]. Moscow, Izhevsk, NITS «Regulyarnaya i khaoticheskaya dinamika», Institut komputernykh issledovaniy Publ., 2009, 548 p.
[8] Gaushus E.V. Issledovanie dinamicheskikh sistem metodom tochechnykh preobrazovaniy [Research of dynamic systems by the point transformation method]. Moscow, Nauka Publ., 1976, 368 p.
[9] Simonyants R.P. Vestnik MGTU im. N.E. Baumana. Ser. Priborostroenie — Herald of the Bauman Moscow State Technical University. Series: Instrument Engineering, 2016, no. 3, pp. 88–101. DOI: 10.18698/0236-3933-2016-3-88-101
[10] Neymark Yu.I. Metod tochechnykh otobrazheniy v teorii nelineynykh kolebaniy [Point mapping method in the theory of nonlinear vibrations]. Moscow, Nauka Publ., 1972, 472 p.
[11] Lerman L.M., Turayev D.V. Nelineynaya dinamika — Russian Journal of Nonlinear Dynamics, 2012. vol. 8, no. 2, pp. 323–343.
[12] Nikulichev Ye.V. Vestnik Tambovskogo Universiteta — Tambov University Review, 2003, vol. 8, no. 3, pp. 423.