The parameters optimisation design for variable speed control momentum gyroscopes

Control momentum gyroscopes (CMGs) have many advantages over other actuators for the attitude control of a spacecraft. Compared with the single-gimbal control moment gyroscopes (SGCMGs), the mass and power of the flywheel of variable-speed control moment gyroscopes (VSCMGs) are greatly increased. In this paper, a new solving strategy of singularity problem is proposed, which concludes the exchangeable momentum and steering law, and the parameters of VSCMGs are designed based on the constraint of singular problem. The configuration characteristics of VSCMGs with the constraint of upper and lower bounds of the flywheel regulation speed are revealed. The steering characteristics of weighted pseudo-inverse with null motion (WPINM) are analysed, then the flywheel torque requirement of WPINM is evaluated based on the geometry theory. At last, the parameter design problem of VSCMGs is cast as multi-objectives and bi-level programming problem. The bi-level programming is transformed into a single-level programming problem by using of the Karush–Kuhn–Tucker condition. Finally, the intelligent algorithm of particle swarm optimisation is presented to solve the nonlinear multi-objective problem.