摘要研究含时滞的线性、非线性复合时滞反馈控制Duffing-Van der Pol振子主参数共振响应最优化控制参数确定。基于弱非线性、弱反馈控制、弱参数激励及小阻尼假设，据平均法获得稳态响应振幅、相位平均方程。通过非线性振动能量比值定义衰减率。以衰减率为振动控制参数优化目标，以非线性振动系统振动、最值、最优时滞为约束条件，利用最优化方法计算获得最佳线性、非线性反馈控制参数。
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.
刘灿昌，岳书常，许英姿，沈玉凤，任传波，刘 露，荆 栋. 参数激励非线性振动时滞反馈最优化控制[J]. 振动与冲击, 2015, 34(20): 6-9.
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. JOURNAL OF VIBRATION AND SHOCK, 2015, 34(20): 6-9.
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