First-passage failure of quasi linear systems subject to multi-time-delayed feedback control and wide-band random excitation

2009 ◽  
Vol 24 (2) ◽  
pp. 144-150 ◽  
Author(s):  
X.P. Li ◽  
Z.H. Liu ◽  
W.Q. Zhu
Keyword(s):  
Feedback Control ◽  
Linear Systems ◽  
Wide Band ◽  
Random Excitation ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
First Passage ◽  
First Passage Failure ◽  
Time Delayed Feedback

Reliability of Duffing-van der Pol Oscillator with Delayed Feedback Control under Wide-Band Noise Excitation

2013 ◽  
Vol 302 ◽  
pp. 717-722 ◽  
Author(s):  
Ting Zhang ◽  
Chang Shui Feng ◽  
Qiao Yi Wang
Keyword(s):  
Feedback Control ◽  
First Passage Time ◽  
Wide Band ◽  
Reliability Function ◽  
Passage Time ◽  
Delayed Feedback ◽  
Van Der Pol Oscillator ◽  
Delayed Feedback Control ◽  
Control Force ◽  
First Passage

The first passage type reliability of Duffing-van der Pol oscillator with time-delayed feedback control under wide-band noise excitations is studied. First, the time-delayed feedback control force is expressed approximately in terms of the system state variables without time delay. Then, the averaged Itô stochastic differential equations for the system are derived by using the stochastic averaging method, from which a backward Kolmogorov equation governing the conditional reliability function and a Pontryagin equation governing the conditional mean of the first passage time are established. Finally, the conditional reliability function and the conditional mean of first passage time are obtained by solving these equations together with suitable initial condition and boundary conditions. The effect of time delay in feedback control force on the reliability is analyzed. The theoretical results are well verified through digital simulation.

Stationary Response of Duffing-van der Pol Oscillator with Delayed Feedback Control under Wide-Band Noise Excitation

2013 ◽  
Vol 300-301 ◽  
pp. 1518-1524
Author(s):  
Peng Lin ◽  
Chang Shui Feng ◽  
Qiao Yi Wang
Keyword(s):  
Feedback Control ◽  
Wide Band ◽  
Delayed Feedback ◽  
Van Der Pol Oscillator ◽  
Delayed Feedback Control ◽  
Control Force ◽  
Van Der Pol ◽  
Stationary Response ◽  
Wide Band Noise ◽  
Time Delayed Feedback

The stationary response of Duffing-van der Pol oscillator with time-delayed feedback control under wide-band noise excitations is studied. First, the time-delayed feedback control force is expressed approximately in terms of the system state variables without time delay. Then, the averaged Itô stochastic differential equations for the system are derived by using the stochastic averaging method. Finally, the stationary response of the system is obtained by solving the Fokker-Plank-Kolmogorov equation associated with the averaged Itô equation. The effect of time delay in feedback control force on the response is analyzed. The theoretical results are well verified through digital simulation.

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