Eur. Phys. J. Special Topics 229, 2275–2293 (2020)
https://doi.org/10.1140/epjst/e2020-900148-9

Regular Article

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

¹ School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, P.R. China
² Basic Teaching Department, Zhengzhou University of Industry Technology, Zhengzhou, Henan 451100, P.R. China

^a e-mail: peilijun@zzu.edu.cn

Received: 21 July 2019
Accepted: 8 June 2020
Published online: 28 September 2020

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.