Mini-max optimization of actuator/sensor placement for flexural vibration control of a rotating thin-walled cylinder over a range of speeds

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 H₂ 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.