Controllability and actuator placement optimization for active damping of a thin rotating ring with piezo-patch transducers

A study on optimal actuator placement for controlling flexural vibration of a thin rotating ring is reported. Piezoelectric patch actuators and sensors may be applied with feedback control to provide active damping of structural vibration involving circumferential travelling waves. To determine the optimum patch positions, a model-based cost function is defined involving a time-weighted controllability Gramian, with balanced model realization for combined treatment of sensors and actuators in collocated pairs. Analytical and numerical results indicate that, without rotation, at least two actuator/sensor pairs are required to achieve controllability of any given set of natural vibration modes. Also, the optimal angular separation varies with rotational speed due to the combined influence of initial damping and Coriolis forces on the vibratory dynamics. To obtain a practical solution, a finite range of speeds is considered within a mini-max optimization criterion for the placement problem. Experiments have been conducted on a thin steel ring where a synthetic proof-mass-damper control law was used to suppress vibration involving the six lowest frequency vibration modes (with natural frequencies of 161, 442 and 846 Hz without rotation). The results show that, although a single actuator-sensor pair can achieve improved damping at high rotational speeds, the optimized configuration of two pairs provides effective damping over the full range of operating speeds.