Control of Hopf Bifurcation in Internet Congestion Control Model via Time-delayed Feedback Control

2013 ◽  
Vol 12 (18) ◽  
pp. 4493-4497
Author(s):  
Xu Xian-Fan ◽  
Guo Fan ◽  
Ding Da-Wei ◽  
Liu Yi ◽  
Han Liu-Jun
Keyword(s):  
Hopf Bifurcation ◽  
Feedback Control ◽  
Congestion Control ◽  
Control Model ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Internet Congestion Control ◽  
Internet Congestion ◽  
Time Delayed Feedback

Hopf bifurcation in an Internet congestion control model

2004 ◽  
Vol 19 (4) ◽  
pp. 853-862 ◽  
Author(s):  
Chunguang Li ◽  
Guanrong Chen ◽  
Xiaofeng Liao ◽  
Juebang Yu
Keyword(s):  
Hopf Bifurcation ◽  
Congestion Control ◽  
Control Model ◽  
Internet Congestion Control ◽  
Internet Congestion

CONTROLLING HOPF BIFURCATION IN FLUID FLOW MODEL OF INTERNET CONGESTION CONTROL SYSTEM

2009 ◽  
Vol 19 (04) ◽  
pp. 1415-1424 ◽  
Author(s):  
DAWEI DING ◽  
JIE ZHU ◽  
XIAOSHU LUO ◽  
YULIANG LIU
Keyword(s):  
Fluid Flow ◽  
Control System ◽  
Hopf Bifurcation ◽  
Congestion Control ◽  
Flow Model ◽  
Delayed Feedback ◽  
Control Approach ◽  
Internet Congestion Control ◽  
Delayed Feedback Controller ◽  
Internet Congestion

In this paper, a time-delayed feedback controller is applied to a fluid flow model of Internet congestion control system in order to control Hopf bifurcation. It has been shown that the system without control loses stability and a Hopf bifurcation occurs when the bifurcation parameter, which is the communication delay of the model, passes through a critical value. Therefore, a control approach based on delayed feedback is proposed to postpone the onset of undesired Hopf bifurcation. Theoretical analysis and numerical simulations confirm that the controller is efficient in bifurcation control of the Internet congestion control system.

Criticality of Hopf Bifurcation in Precision Motion Stage With PID and Time-Delayed Feedback Controls

2020 ◽  
Author(s):  
Sunit K. Gupta ◽  
Jiamin Wang ◽  
Oumar R. Barry
Keyword(s):  
Hopf Bifurcation ◽  
Feedback Control ◽  
Delayed Feedback ◽  
State Feedback Control ◽  
Lumped Parameter Model ◽  
Delayed Feedback Control ◽  
Use Of Time ◽  
Motion Stage ◽  
Precision Motion ◽  
Time Delayed Feedback

Abstract The use of precision motion stages is very popular among advanced manufacturing and machining industries. However, the performance of these motion stages is usually undermined by friction-induced vibration. In this paper, we propose the use of time-delayed feedback control to minimize the undesirable effects of friction-induced vibrations. The use of time-delayed feedback control is well established in the literature; however, the use of time-delayed feedback control in PID controlled motion-stages has not been explored yet. Here, we consider a lumped parameter model of the PID controlled precision motion stage with a linear time-delayed state feedback control. The dynamical friction in the systemis modeled using the LuGre model. Stability and nonlinear analysis of the system are carried out using analytical methods. The stability analysis reveals the existence of multiple stability lobes and codimension-2 Hopf points for a given choice of system parameters. Also, the nature of Hopf bifurcation is determined by using the method of multiple scales. We observe the existence of both subcritical and supercritical Hopf bifurcations in the system, depending on the choice of control parameters. This observation implies that the nonlinearity in the system could both be stabilizing or destabilizing in nature.

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