For a rotating thin-walled cylinder subject to flexural vibration, active control can be applied using surface-mounted actuators and sensors. To achieve acceptable vibration control performance, the dependency of the dynamic behaviour on rotational speed must be accounted for in the control system design, including the selection and positioning of actuators and sensors. A key issue is that the natural modes of vibration of the cylinder wall involve circumferential travelling waves and, for certain rotational speeds, the frequency of a backward wave for a low order mode can become equal to that of a forward wave for a high order mode. It is shown that these frequency-crossings have important implications for the actuator/sensor placement problem due to the potential for loss of controllability. Accordingly, an actuator/sensor placement approach is introduced based on a mini-max optimization, where the system controllability is maximized for the worst-case rotational speed within a specified interval. Placement solutions are obtained through the application of a nested particle swarm optimization algorithm, used to find saddle-point solutions. The approach is shown to be effective for cases involving 2, 3 and 4 actuator/sensor pairs and with multi-mode model (including up to 16 modes). The results are confirmed by experiments on a thin-walled rotor system with piezo patch actuators and sensors, where ${\mathcal{H}}_2$ control algorithms are applied to suppress vibrational resonances within a control bandwidth of 200-1200 Hz. The potential for loss of controllability at certain rotational speeds is confirmed, as well as the effectiveness of the optimal placement solutions in maintaining control performance over a targeted range of speeds.

对于受到弯曲振动的旋转薄壁圆筒，可以使用表面安装的执行器和传感器进行主动控制。为了获得可接受的振动控制性能，必须在控制系统设计中考虑动态行为对转速的依赖性，包括选择和定位执行器和传感器。一个关键问题是，汽缸壁的固有振动模式涉及周向行波，并且对于某些转速，低阶模式的反向波的频率可以等于高阶模式的正向波的频率。 。结果表明，由于可能失去可控制性，这些频率交叉对致动器/传感器放置问题具有重要意义。因此，基于最小最大优化引入了执行器/传感器放置方法，其中在指定间隔内针对最坏情况下的转速使系统可控制性最大化。放置解决方案是通过应用嵌套粒子群优化算法获得的，该算法用于查找鞍点解决方案。对于涉及2、3和4个执行器/传感器对以及多模式模型（包括多达16个模式）的情况，该方法被证明是有效的。实验结果在带有压电膜片执行器和传感器的薄壁转子系统上进行了实验证实，其中 放置解决方案是通过应用嵌套粒子群优化算法获得的，该算法用于查找鞍点解决方案。对于涉及2、3和4个执行器/传感器对以及多模式模型（包括多达16个模式）的情况，该方法被证明是有效的。实验结果在带有压电膜片执行器和传感器的薄壁转子系统上进行了实验证实，其中 放置解决方案是通过应用嵌套粒子群优化算法获得的，该算法用于查找鞍点解决方案。对于涉及2、3和4个执行器/传感器对以及多模式模型（包括多达16个模式）的情况，该方法被证明是有效的。实验结果在带有压电膜片执行器和传感器的薄壁转子系统上进行了实验证实，其中${\mathcal{H}}_{\mathrm{2个}}$应用控制算法以将振动共振抑制在200-1200 Hz的控制带宽内。确认了在某些转速下可能失去可控制性的可能性，以及最佳放置解决方案在目标速度范围内保持控制性能的有效性。