Please wait a minute...
ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2009, Vol. 10 Issue (1): 54-61    DOI: 10.1631/jzus.A0720115
Mechanical & Civil Engineering     
Response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control
Chang-shui FENG, Wei-qiu ZHU
Institute of Mechatronic Engineering, Hangzhou Dianzi University, Hangzhou 310018, China; State Key Laboratory of Fluid Power Transmission and Control, Department of Mechanics, Zhejiang University, Hangzhou 310027, China
Download:     PDF (0 KB)     
Export: BibTeX | EndNote (RIS)      

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.

Key words： Nonlinear system      Delayed feedback bang-bang control      Combined harmonic and white noise excitation      Stochastic averaging      Stationary response      Stochastic jump     
Received: 10 December 2007     
CLC:  O324  
Service
E-mail this article
Add to my bookshelf
Add to citation manager
E-mail Alert
RSS
Articles by authors
Chang-shui FENG
Wei-qiu ZHU
Cite this article:

Chang-shui FENG, Wei-qiu ZHU. Response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2009, 10(1): 54-61.

URL:

http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.A0720115     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2009/V10/I1/54

[1] Shan-shan Pan, Wei-qiu Zhu, Rong-chun Hu, Rong-hua Huan. Stationary response of stochastically excited nonlinear systems with continuous-time Markov jump[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2017, 18(2): 83-91.
[2] Lin-cong CHEN, Rong-hua HUAN, Wei-qiu ZHU. Feedback maximization of reliability of MDOF quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2009, 10(9): 1245-1251.
[3] Yong WANG, Zu-guang YING, Wei-qiu ZHU. A minimax optimal control strategy for uncertain quasi-Hamiltonian systems[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2008, 9(7): 950-954.
[4] Xue-ping LI, Wei-qiu ZHU, Zu-guang YING. Optimization of time-delayed feedback control of seismically excited building structures[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2008, 9(3): 330-337.
[5] Rong-hua HUAN, Wei-qiu ZHU, Yong-jun WU. Nonlinear stochastic optimal bounded control of hysteretic systems with actuator saturation[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2008, 9(3): 351-357.
[6] DENG Mao-lin, ZHU Wei-qiu. On the stochastic dynamics of molecular conformation[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2007, 8(9): 1401-1407.
[7] SAHOO Bikash, SHARMA H.G.. Existence and uniqueness theorem for flow and heat transfer of a non-Newtonian fluid over a stretching sheet[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2007, 8(5): 766-771.
[8] Liu Mei-qin. Interval standard neural network models for nonlinear systems[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2006, 7(4 ): 8-.
[9] Ke Hai-sen, Ye Xu-dong. Robust adaptive controller design for a class of nonlinear systems with unknown high frequency gains[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2006, 7(3 ): 6-.
[10] Wen Xiang-jun, Zhang Yu-nong, Yan Wei-wu, Xu Xiao-ming. Nonlinear decoupling controller design based on least squares support vector regression[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2006, 7(2): 275-284.
[11] SUN Tao, CAO Guang-yi, ZHU Xin-jian. Nonlinear modeling of PEMFC based on neural networks identification[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2005, 6( 5): 3-.
[12] ZHANG Ke-qin, ZHUANG Kai-yu, SU Hong-ye, CHU Jian, GAO Hong. Sliding mode identifier for parameter uncertain nonlinear dynamic systems with nonlinear input[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2002, 3(4): 426-430.
[13] SHAO Jian, Li Da-kan. SOLUTION OF NONLINEAR TWO-POINT BOUNDARY VALUE PROBLEMS BY GENERAL ORTHOGONAL POLYNOMIALS[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2000, 1(3): 331-336.