Feedback control law for variable speed control moment gyros
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Variable speed control moment gyroscopes are currently being considered to control spacecraft attitudes. They combine positive features of both the classical reaction wheels and the single-gimbal control moment gyroscopes by having the rotating disk no longer being restricted to a constant speed, but allowing it to be spun up or down. We present the equations of motion of a generic rigid body with several such variable speed CMGs attached. The formulation is such that it can easily accommodate the classical cases of having either control moment gyros or reaction wheels to control the spacecraft attitude. A globally asymptotically stabilizing nonlinear feedback control law is presented. For a redundant control system, a weighted minimum norm inverse is used to determine the control vector. This approach allows the variable speed control moment gyroscopes to behave either more like classical reaction wheels or more like control moment gyroscopes, depending on the local optimal steering logic. Where classical control moment gyroscope control laws have to deal with singular gimbal angle configurations, the variable speed control moment gyroscopes are shown not to encounter any singularities for many representative examples considered. Both a gimbal angle velocity and an acceleration based steering law is presented. Since gimbaling is more efficient energy consumption wise, the steering law presented only utilizes the reaction wheel modes in the vicinity of the classical control moment gyroscope singularities. Further, the use of the VSCMG null motion is discussed to reconfigure the gimbal angles to preferred sets. Having a variable reaction wheel speed allows for a more general redistribution of the internal momentum vector.