Steering law for control moment gyroscopes based on H∞ theory

The complete dynamic equations for rotational maneuvers of spacecraft with a cluster of CMGs are derived. The mathematical control model of spacecraft is based on quaternion, which could avoid the singularity phenomenon of the Euler method when we describe the spacecraft eigenaxis rotational maneuvers. Then from a control perspective, a novel approach for the generation of gimbal commands for a cluster of Single-Gimbal CMG is presented and analysed. This steering law has a dynamics structure, and considers the relationship between torque error and gimbal rate limits. Comparing to the Moore-Penrose inverse, the proposed steering law effectively generates torque error when the CMG system become near singular. In the vicinity of the singular point, the torque error will produce value for the gimbal rates through the singular point, as a result, this will steers the gimbal angle away from the singularity though at an expense of some vibrating. The new steering law based on H_∞ for CMG developed by this method not only complete the attitude control for spacecraft, but also could avoid the singular state. The numerical simulation results proved availability of the proposed steering law.