Optimal control of parametric excitated nonlinearvibration system with delayed linear and nonlinear feedback controllers

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Journal of Vibration and Shock ›› 2015, Vol. 34 ›› Issue (20) : 6-9.

LIU Can-chang，YUE Shu-chang，XU Ying-zi，SHEN Yu-feng，REN Chuan-bo，LIU Lu，JING Dong

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Abstract

The determination of optimal control parameters of resonant response is studied for Duffing-Van der Pol oscillator with the delayed linear and nonlinear feedback controllers. For the weak nonlinearity, weak feedback control, small damping, and soft excitation, the average equations of the amplitude and phase of the stable vibration is obtained. The regions of the feedback gains for stable vibration of the nonlinear vibration system are obtained by using the stable conditions of eigenvalue equation. The nonlinear vibration energy attenuation ratio is defined by taking the proportion of square of the vibration peak of primary resonance for the suspension system with and without control. Taking the energy attenuation ratio as objective function, the stable conditions and the optimal delay as constraint conditions, the optimal feedback control gains can be worked out by using optimal method. It is found that an optimal feedback gain can lead to an optimal control performance.

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Nonlinear vibration / control / time delay / parametric excitation

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LIU Can-chang，YUE Shu-chang，XU Ying-zi，SHEN Yu-feng，REN Chuan-bo，LIU Lu，JING Dong. Optimal control of parametric excitated nonlinearvibration system with delayed linear and nonlinear feedback controllers[J]. Journal of Vibration and Shock, 2015, 34(20): 6-9

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