中文摘要：

研究具有轴向运动速度、变长度悬臂梁的横向振动控制，提出了两种主动控制方案。采用Hamilton原理得到了端部带主动振子或跨内含有主动控制力的轴向运动悬臂梁的振动方程和边界条件。运用修正的伽辽金法得到了求解系统响应的近似方程。运用LQR法设计了主动振子和主动力的控制器，其中采用加权系数法选择Q，R矩阵。用数值计算仿真了两种控制方案的效果。结果表明采用主动振子或主动力都能够有效地控制轴向运动悬臂梁的横向振动。在相同的初始条件下，主动力控制的效果比主动振子要好，但主动振子的物理可实现性要优于主动力。

英文摘要：

The control of tbe transverse vibration of an axially moving cantilever beam is studied and two control methods are presented in the paper. The transverse vibration equation and boundary conditions are formulated by the Hamilton principle.The instant linearized equations are set up based on Galerkin method for the approximation solution. The controllers for active vibrator and active force are designed based on LQR method. The optimal Q and R matrices are selected by the weighting coefficient method. The two control methods are simulated by a numerical example. The results show that the two control methods can all suppress the transverse vibration effectively. The control result of the latter method is better than that of the active vibrator method, but the active vibrator is more realizable than the former in practice.