Elastic vibration can arise in annular and thin-walled rotor structures, impacting on operating performance and the risk of failure. Feedback control to reduce flexural vibration can be realized using lightweight actuators and sensors embedded in the rotor structure. To design optimal controllers, rotating-frame models of both the structural dynamics and sources of excitation are required. This paper describes a solution to this problem for the case of an annular rotor equipped with piezo patch actuators and sensors. To account for space-fixed external excitation sources, a forcing function is considered involving specified spatial and frequency domain distributions. A model-based ${\mathcal{H}}_2$ synthesis is used to compute optimal control solutions. These are tested experimentally on a thin-walled cylindrical steel rotor for cases with narrowband and broadband excitation sources, applied from the fixed frame. The results show that frequency-splitting within the rotating-frame dynamics plays a key role in predicting and controlling resonance. The effectiveness of the optimal control methodology in reducing circumferential vibration of the annular rotor is also confirmed.

环形和薄壁转子结构中会出现弹性振动，从而影响运行性能和故障风险。使用嵌入转子结构的轻型致动器和传感器可以实现反馈控制以减少弯曲振动。为了设计最佳控制器，需要结构动力学和激励源的旋转框架模型。本文针对配备压电贴片执行器和传感器的环形转子的情况描述了该问题的解决方案。为了说明空间固定的外部激励源，考虑了一个强制函数，涉及指定的空间和频域分布。基于模型的${\mathcal{H}}_2$综合用于计算最优控制解决方案。这些是在薄壁圆柱形钢转子上进行实验测试的，适用于从固定框架施加的窄带和宽带激励源。结果表明，旋转框架动力学中的分频在预测和控制共振方面起着关键作用。优化控制方法在减少环形转子圆周振动方面的有效性也得到了证实。