Response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control |
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| Authors: | Chang-shui Feng Wei-qiu Zhu |
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| Institution: | (1) Institute of Mechatronic Engineering, Hangzhou Dianzi University, Hangzhou, 310018, China;(2) State Key Laboratory of Fluid Power Transmission and Control, Department of Mechanics, Zhejiang University, Hangzhou, 310027, China |
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| 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 Ito 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 Ito equations. A Duffing oscillator with time-delayed feedback bang-bang control under combined harmonic and white noise excitations is taken as an example to illus-trate 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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| Keywords: | Nonlinear system Delayed feedback bang-bang control Combined harmonic and white noise excitation Stochastic averaging Stationary response Stochastic jump |
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