Rate Damping of a Spacecraft Using Two Single-Gimbal Control Moment Gyros

In this study, the problem of rate damping a spacecraft by using two single-gimbal control moment gyros in an arbitrary configuration is considered. A feedback control law for a two- single-gimbal control moment gyro system is designed based on Lyapunov analysis and is applicable to the fault-tolerant control of a redundant-single-gimbal control moment gyro system, such as a pyramid-type system. A steady-state analysis is conducted and presented in detail. Rate damping is achieved for almost all initial conditions if the total angular momentum of the spacecraft is less than the sum of the angular momenta of the single-gimbal control moment gyros, in which case the angular velocity of the spacecraft is decreased to zero. In contrast, rate damping is not achieved if the total angular momentum of the spacecraft is greater than the sum of the angular momenta of the single-gimbal control moment gyros, in which case the spacecraft converges to a spinning motion for almost all initial conditions. The results of the analysis are demonstrated through numerical simulations.