The space flexible arm has the characteristics of large flexibility and size, and external excitation will cause harmful vibration. In this paper, the dynamic response of flexible arms is analyzed, and the vibration control is studied when nonlinear factors are considered. First, the vibration equation is established according to the Hamilton’s principle, and the generalized force is derived by using rod model and beam model, respectively. Then the Runge–Kutta method is used to solve the vibration equation, and the dynamic response is obtained. Finally, the PD and fuzzy control simulations of three arms are established, and the dead zone and saturation nonlinearities are applied in the programs. The numerical results show that the external force causes significant response, and the vibration control method is effective. Besides, in order to achieve vibration control effect, it is necessary to reduce the dead zone nonlinear range.

中文翻译：

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两种非线性因素的柔性臂的响应分析与振动控制

空间柔性臂具有柔性大、尺寸大的特点，外力激励会产生有害振动。本文分析了柔性臂的动态响应，研究了考虑非线性因素时的振动控制。首先，根据哈密顿原理建立振动方程，分别利用杆模型和梁模型推导出广义力。然后用龙格-库塔法求解振动方程，得到动态响应。最后，建立了三臂的PD和模糊控制仿真，并在程序中应用了死区和饱和非线性。数值结果表明，外力引起的响应显着，振动控制方法是有效的。除了，