Full Text:   <1707>

CLC number: O324

On-line Access: 

Received: 2007-12-10

Revision Accepted: 2008-05-30

Crosschecked: 2008-10-29

Cited: 0

Clicked: 3765

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
1. Reference List
Open peer comments

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

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.

@article{title="Response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control",
author="Chang-shui FENG, Wei-qiu ZHU",
journal="Journal of Zhejiang University Science A",
volume="10",
number="1",
pages="54~61",
year="2009",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A0720115"
}

%0 Journal Article
%T Response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control
%A Chang-shui FENG
%A Wei-qiu ZHU
%J Journal of Zhejiang University SCIENCE A
%V 10
%N 1
%P 54~61
%@ 1673-565X
%D 2009
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A0720115

TY - JOUR
T1 - Response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control
A1 - Chang-shui FENG
A1 - Wei-qiu ZHU
J0 - Journal of Zhejiang University Science A
VL - 10
IS - 1
SP - 54
EP - 61
%@ 1673-565X
Y1 - 2009
PB - Zhejiang University Press & Springer
ER -
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.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1] Agrawal, A.K., Yang, J.N., 1997. Effect of fixed time delay on stability and performance of actively controlled civil engineering structures. Earthquake Engineering & Structural Dynamics, 26(11):1169-1185.

[2] Den Hartog, J.P., 1956. Mechanical Vibrations (4th Ed.). McGraw Hill, New York.

[3] Di Paola, M., Pirrotta, A., 2001. Time delay induced effects on control of linear systems under random excitation. Probabilistic Engineering Mechanics, 16(1):43-51.

[4] Grigoriu, M., 1997. Control of time delay linear systems with Gaussian white noise. Probabilistic Engineering Mechanics, 12(2):89-96.

[5] Hu, H.Y., Wang, Z.H., 2002. Dynamics of Controlled Mechanical Systems with Delayed Feedback. Springer, Berlin.

[6] Huang, Z.L., Zhu, W.Q., Suzuki, Y., 2000. Stochastic averaging of strongly nonlinear oscillators under combined harmonic and white noise excitations. Journal of Sound and Vibration, 238(2):233-256.

[7] Kuo, B.C., 1987. Automatic Control Systems. Prentice-Hall, Englewood Cliffs, NJ.

[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.

[9] Malek-Zavarei, M., Jamshidi, M., 1987. Time-delay Systems: Analysis, Optimization and Applications. North-Holland, New York.

[10] Pu, J.P., 1998. Time-delay compensation in active control of structure. Journal of Engineering Mechanics, 124(9):1018-1028.

[11] Stepan, G., 1989. Retarded Dynamical Systems: Stability and Characteristic Functions. Longman Scientific and Technical, Essex.

[12] Zhu, W.Q., Liu, Z.H., 2007a. Response of quasi-integrable Hamiltonian systems with delayed feedback bang-bang control. Nonlinear Dynamics, 49(1-2):31-47.

[13] Zhu, W.Q., Liu, Z.H., 2007b. Stochastic averaging of quasi-integrable Hamiltonian systems with delayed feedback control. Journal of Sound and Vibration, 299(1-2):178-195.

[14] Zhu, W.Q., Wu, Y.J., 2005. Optimal bounded control of harmonically and stochastically excited strongly nonlinear oscillators. Probabilistic Engineering Mechanics, 20(1):1-9.

Open peer comments: Debate/Discuss/Question/Opinion

<1>

Please provide your name, email address and a comment





Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - Journal of Zhejiang University-SCIENCE