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Dynamics and control of the active control system with the state-dependent actuation time delay

Authors
  • Pei, Lijun1
  • Jia, Huifang1, 2
  • 1 School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, P.R. China , Zhengzhou (China)
  • 2 Basic Teaching Department, Zhengzhou University of Industry Technology, Zhengzhou, Henan 451100, P.R. China , Zhengzhou (China)
Type
Published Article
Journal
The European Physical Journal Special Topics
Publisher
Springer Berlin Heidelberg
Publication Date
Sep 28, 2020
Volume
229
Issue
12-13
Pages
2275–2293
Identifiers
DOI: 10.1140/epjst/e2020-900148-9
Source
Springer Nature
License
Yellow

Abstract

In this paper, a model of active control system with state-dependent actuation time delay is investigated. Galerkin projection scheme is used to obtain its low dimensional approximation system. State-dependency and effect on dynamics and performance of actuation delay in this active control system are considered. The following results are obtained. Firstly, a state-dependent actuation delay is proposed, which has never been reported in the previous works. It displays that actuation delay is state-dependent. Secondly, employing Galerkin projection scheme, low dimensional approximation system of this delayed active control system is obtained. At last, its stability and Hopf bifurcation are investigated by Routh-Hurwitz Criterion and Hopf bifurcation theory. Using software WinPP, numerical simulation is executed and supports the theoretical results in this paper.

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