Feedback Control Law for Variable Speed Control Moment Gyros
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Feedback Control Law for Variable Speed Control Moment Gyros Hanspeter Schaub, 1 Srinivas R. Vadali,2 and John L. Junkins 3 Abstract Variable speed control moment gyroscopes (CMG) are single-gimbal gyroscopes where the fly wheel speed is allowed to be variable. The equations of motion of a generic rigid body with several such variable speed CMGs attached are presented. 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 are presented. Further, the use of the variable speed CMG 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.
Introduction Instead of using thrusters to perform precise spacecraft attitude maneuvers, control moment gyros (CMGs) or reaction wheels (RWs) are usually used. A single-gimbal CMG contains a wheel spinning at a constant rate. In order to exert a torque onto the spacecraft this wheel is gimbaled or rotated about a body-fixed axis [1-3]. The rotation axis and rotation angle are referred to as the gimbal axis and gimbal angle respectively. A separate feedback control loop is used to 'Graduate Research Assistant, Aerospace Engineering Department, Texas A&M University, College Station TX 77843. 2professor, Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843. 3George J. Eppright Distinguished Chair Professor of Aerospace Engineering, Aerospace Engineering Department, Texas A&M University, College Station TX 77843. Fellow AAS. 307
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spin up the rotor to the required spin rate and maintain it. The advantage of a CMG is that a relatively small gimbal torque input is required to produce a large effective torque output on the spacecraft. This makes a cluster of CMGs a very popular choice for reorienting large space structures such as the space station or Skylab. The drawback of the single-gimbal CMGs is that their control laws can be fairly complex and that such CMG systems encounter certain singular gimbal angle configurations. At these singular configurations the CMG cluster is unable to produce the required torque exactly, or any torque at all if the required torque is orthogonal to the pl
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