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

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.


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