Singularity analysis of control moment gyros on gyroelastic body

Control moment gyro (CMG) is a widely used device for generating control torques for spacecraft attitude control without expending propellant. Because of its effectiveness and cleanness, it has been considered to be mounted on a space structure to achieve vibration suppression. The resultant system is the so-called gyroelastic body, on which the CMGs could exert both torques and modal forces. Therefore, the CMGs can be used to simultaneously achieve attitude maneuver and vibration reduction of a flexible spacecraft. In this paper, we consider the singularity problem in such an application of CMGs. The dynamics of an unconstrained gyroelastic body is established, from which the output equation of the CMGs is extracted. Then, torque singular state and modal force singular state are defined and visualized to demonstrate the singularity problem. Numerical examples of several typical configuration on a gyroelastic body are given. Finally, a steering law allowing output error is designed.