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Journal of Zhejiang University SCIENCE A 2009 Vol.10 No.1 P.54-61

http://doi.org/10.1631/jzus.A0720115


Response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control


Author(s):  Chang-shui FENG, Wei-qiu ZHU

Affiliation(s):  Institute of Mechatronic Engineering, Hangzhou Dianzi University, Hangzhou 310018, China; more

Corresponding email(s):   wqzhu@yahoo.com

Key Words:  Nonlinear system, Delayed feedback bang-bang control, Combined harmonic and white noise excitation, Stochastic averaging, Stationary response, Stochastic jump


Chang-shui FENG, Wei-qiu ZHU. Response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control[J]. Journal of Zhejiang University Science A, 2009, 10(1): 54-61.

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%A Wei-qiu ZHU
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%DOI 10.1631/jzus.A0720115

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T1 - Response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control
A1 - Chang-shui FENG
A1 - Wei-qiu ZHU
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EP - 61
%@ 1673-565X
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.A0720115


Abstract: 
We studied the response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control using the stochastic averaging method. First, the time-delayed feedback bang-bang 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 using the stochastic averaging method. Finally, the response of the system is obtained by solving the Fokker-Plank-Kolmogorov (FPK) equation associated with the averaged Itô equations. A Duffing oscillator with time-delayed feedback bang-bang control under combined harmonic and white noise excitations is taken as an example to illustrate the proposed method. The analytical results are confirmed by digital simulation. We found that the time delay in feedback bang-bang control will deteriorate the control effectiveness and cause bifurcation of stochastic jump of Duffing oscillator.

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Reference

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[8] Li, X.Y., Ji, J.C., Hansen, C.H., Tan, C.X., 2006. The response of a Duffing-van der Pol oscillator under delayed feedback control. Journal of Sound and Vibration, 291(3-5):644-655.

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