Optimal feedback control for nonlinear control moment gyro systems

A study was made, leading to development and analysis of a technique allowing the control moment gyro (CMG) momentum vectors to avoid adverse orientations and thus to provide optimal control for the Apollo Telescope Mount. The technique was formulated in terms of a feedback scheme using a check factor, K, formed as the product of the dot products of the three CMG momentum unit vectors. The parameter K approaches unity for all adverse orientations and was used to initiate a single correction maneuver to rotate the CMG momenta away from a pending adverse orientation and to reduce K to an acceptable value. A digital computer program for ATM simulations was modified to incorporate this correction maneuver and performance was evaluated in simulated cases. Antiparallelism was used as the primary example for the evaluation of the feedback optimization technique.