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First-passage failure of harmonically and stochastically excited Duffing oscillator with delayed feedback control

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Abstract

The first-passage failure of Duffing oscillator with the delayed feedback control under the combined harmonic and white-noise excitations is investigated. 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. A backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of the first-passage time are established. Finally, the conditional reliability function, the conditional probability density and moments of the first-passage time are obtained by solving the backward Kolmogorov equation and generalized Pontryagin equations with suitable initial and boundary conditions. The effects of time delay in feedback control force on the conditional reliability function, conditional probability density and moments of the first-passage time are analyzed. The validity of the proposed method is confirmed by digital simulation.

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Authors and Affiliations

  1. Institute of Mechatronic Engineering, Hangzhou Dianzi University, Hangzhou, 310018, China

    ChangShui Feng

  2. Department of Mechanics, State Key Laboratory of Fluid Transmission and Control, Zhejiang University, Hangzhou, 310027, China

    WeiQiu Zhu

Authors
  1. ChangShui Feng
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  2. WeiQiu Zhu
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Correspondence to WeiQiu Zhu.

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Feng, C., Zhu, W. First-passage failure of harmonically and stochastically excited Duffing oscillator with delayed feedback control. Sci. China Technol. Sci. 54, 1072–1077 (2011). https://doi.org/10.1007/s11431-011-4356-6

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  • DOI: https://doi.org/10.1007/s11431-011-4356-6

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