Optimal steering laws for control moment gyros

Abstract

Singularity avoidance steering laws for control momentum gyros(CMGs) and variable speed control moment gyros(VSCMGs) are addressed in this thesis. The proposed methodology is based on constrained optimization theory. The key idea of the strategy is to minimize a cost function which consists of singularity indices and energy terms. The proposed method enables CMG/VSCMG clusters not to come across the singularity. It turns out that the proposed optimal singularity avoidance steering law is equivalent to a general solution including the conventional null motion approach as well as the pseudo-inverse based steering logic. Also, an optimal steering law is developed to overcome the possibility of wheel speed saturation during the operation of VSCMG clusters. As a new approach different from the previous studies for the issue of singularity avoidance, virtual actuator concept is presented in this dissertation. This concept provides ultimately the global existence of the pseudo-inverse instead of the torque error. Nevertheless, the new concept has several advantages compared with the classical singularity robustness method. This thesis is also focused on designing an implementable control law to perform spacecraft various missions using momentum exchange devices such as reaction wheels(RWs) and control moment gyros(CMGs). A compact equation of motion of a spacecraft installed with various momentum exchange devices is derived. A hybrid control law is proposed for precision attitude control of agile spacecraft. The control law proposed in this thesis allocates control torque to the CMGs and the RWs adequately to satisfy the precision attitude control and large angle maneuver simultaneously. The saturation problem of reaction wheels and the singularity problem of control moment gyros are considered. The problems are successfully resolved by using the proposed hybrid closed loop control law. Constant torque input in general induces unescapable singularity conditi...