Feedback-Based Steering Law for Control Moment Gyros

A new approach for solving the singularity avoidance problem is presented, based on the observation that the gimbal rates can be derived by minimizing (in a feedback loop) the difference between the demanded torque and the control moment gyro output torque. The derivations are approached from a control prospective, but the final solution results in a structure very similar to the classical singularity robust steering law. Some differences, however, need to be acknowledged. Because the gimbal rates are related to the demanded torque through the control sensitivity function, the solutions are generated in a feedback loop, and thus the algorithm does not require computations of matrix inversion and matrix determinant. The steering law has a dynamic structure, and a relationship is established between the torque error and the gimbal-rate capacity of the actuator. The new steering law also breaks the symmetry in the computation in the gimbal rates, and thus the gimbal trajectories avoid the internal singularities, rather than passing through them. Consequently, the full control moment gyro momentum space is used. Examples with some typical maneuvers are presented to justify this numerically. For the derivation of the steering law, 7-1,, theory is used, and an efficient adaptation algorithm is developed to account for the dependence of the Jacobian on the gimbal angles. Derivation and implementation steps are presented with numerical examples.