Adaptive suppression of linear structural vibration using control moment gyroscopes

The application of the simple adaptive control (SAC) to the cantilevered gyroelastic body is presented. The dynamic equations of a cantilevered gyroelastic body are linearized and the modal analysis is performed to obtain the system state-space representation. The strictly passive (SP) of the system is proven. It shows that the lightly damped flexible structure with collocated control moment gyroscopes (CMGs) and angular rate sensors are always strictly passive. Thus, the SAC method is applicable to the cantilevered gyroelastic body. The controller only requires measuring the angular rates of the locations where the actuators are mounted. Numerical examples of a beam and a plate actuated by CMGs verify the efficacy of the proposed method.