非惯性系下柔性悬臂梁的振动主动控制

采用变结构控制方法对非惯性系下柔性悬臂梁的振动主动控制进行研究．重点通过算例揭示一次近似模型与传统的零次近似模型的巨大差异，以及变结构方法在控制非惯性系下柔性悬臂梁的稳态振动的有效性．结果表明，当大范围旋转运动角速度较大时，传统零次近似模型不能对动力系统进行正确的数学描述；变结构控制方法能够使得非惯性系下梁的稳态振动得到完全镇定，且该方法对转动角速度变化具有较好的鲁棒性；采用零次近似模型进行控制设计的控制效果将在某一临界角速度条件下出现失效，该临界角速度值大于静止悬臂梁的基频．

Active vibration control of a cantilever beam in non-inertial system

For a flexible cantilever beam with rotating motion, the traditional model assumes the small deformation in structural dynamics where axial and transverse displacements at any point in the beam are uncoupled. This traditional hybrid coordinate model is referred as the zeroth-order approximation (ZOA) model in this paper, which may result in divergence to the dynamic problem of a flexible cantilever beam with a high rotational speed. If the ZOA model is adopted as control model in control design, numerical result obtained is suspicious in fact. In this paper, a first-order approximation (FOA) model is used for vibration control of flexible cantilever beam in non-inertial system, where variable structure control (VSC) is adopted as control strategy. The FOA model for the system considers the second-order coupling quantity of the axial displacement caused by the transverse displacement of the beam. Emphasis is placed on numerical simulations to demonstrate the effectiveness of the VSC, and some features in using the ZOA and FOA models. Simulation results indicate that the VSC is effective in suppressing the vibration of the rotating beam in non-inertial system. The beam can be fully controlled by the VSC. In addition, the VSC method is highly robust to the variance of the rotating angular velocity of the beam. The ZOA model is only applicable to the case with a small rotational speed when without control for the beam and the critical angular velocity is about the fundamental frequency of the beam with no rotation. For the case with control for the beam, instability may occur at one certain critical angular velocity when the controller designed based on the zeroth-order approximation model is used for the real structure described by the first-order approximation dynamic model, and the critical angular velocity is much larger than the fundamental frequency of the cantilever beam with no rotation. The FOA model is available not only for small angular velocity but also for large one, and is applicable to the cases with or without control for the beam.