Steering laws analysis of SGCMGs based on singular value decomposition theory

The steering laws of single gimbal control moment gyros （SGCMGs） are analyzed and compared in this paper for a spacecraft attitude control system based on singular value decomposition （SVD） theory. The mechanism of steering laws escaping singularity, especially how the steering laws affect singularity of gimbal configuration and the output torque error, is studied using SVD theory. Performance of various steering laws are analyzed and compared quantitatively by simulation. The obtained results can be used as a reference for designers.

Cooperative game theory-based steering law design of a CMG system

Spacecraft require a large-angle manoeuvre when performing agile manoeuvring tasks, therefore a control moment gyroscope(CMG) is employed to provide a strong moment.However, the control of the CMG system easily falls into singularity, which renders the actuator unable to output the required moment. To solve the singularity problem of CMGs, the control law design of a CMG system based on a cooperative game is proposed. First, the cooperative game model is constructed according to the quadratic programming problem, and the cooperative strategy is constructed. When the strategy falls into singularity, the weighting coefficient is introduced to carry out the strategy game to achieve the optimal strategy. In theory, it is proven that the cooperative game manipulation law of the CMG system converges, the sum of the CMG frame angular velocities is minimized, the energy consumption is small, and there is no output torque error. Then, the CMG group system is simulated.When the CMG system is near the singular point, it can quickly escape the singularity. When the CMG system falls into the singularity, it can also escape the singularity. Considering the optimization of angular momentum and energy consumption, the feasibility of the CMG system steering law based on a cooperative game is proven.

Error analysis and a new steering law design for spacecraft control system using SGCMGs

Based on the singular value decomposition theory,this paper analyzed the mechanism of escaping/avoiding singularity using generalized and weighted singularity-robust steering laws for a spacecraft that uses single gimbal control moment gyros （SGCMGs） as the actuator for the attitude control system.The expression of output-torque error is given at the point of singularity,proving the incompatible relationship between the gimbal rate and the output-torque error.The method of establishing a balance between the gimbal rate and the output-torque error is discussed,and a new steering law is designed.Simulation results show that the proposed steering law can effectively drive SGCMGs to escape away from singularities.

Improved optimal steering law for SGCMG and adaptive attitude control of flexible spacecraft

The issue of attitude maneuver of a flexible spacecraft is investigated with single gimbaled control moment gyroscopes （SGCMGs） as an actuator. To solve the inertia uncertainty of the system, an adaptive attitude control algorithm is designed by applying a radial basis function （RBF） neural network. An improved steering law for SGCMGs is proposed to achieve the optimal out- put torque. It enables the SGCMGs not only to avoid singularity, but also to output more precise torque. In addition, global, uniform, ultimate bounded stability of the attitude control system is proved via the Lyapunov technique. Simulation results demonstrate the effectiveness of the new steering law and the algorithm of attitude maneuver of the flexible spacecraft.

An improved constrained steering law for SGCMGs with DPC

An improved constrained （IC） steering law for single gimbal control moment gyros （SGCMGs） with deformed pyramid configuration （DPC） is proposed, First of all, the original system with five pyramid configuration （FPC） whose two adjacent gyros are in failure state is reconfigured as a degraded system with DPC. Then, the singular angular momentum hypersurfaces of the original and the degraded systems are plotted via the singular angular momentum equa- tion of SGCMGs. Based on singular surfaces, the differences between FPC and DPC in singularity and momentum envelope are obtained directly, which provide an important reference for steering law design of DPC. Finally, an IC steering law is designed and applied to DPC. The simulation results demonstrate that the IC steering law has advantages in simplicity of calculation, avoidance of singularity and exactness of output torque, which endow the degraded system with fine controllability in a restricted workspace.

Optimizing Designed Variable Speed Control Moment Gyroscopes with Variable Skew Angle

Large torque can be output by the single gimbal control momentum gyroscope (SGCMG) based on the principle of the gyroscopic precession. However, the singularity is a major obstacle to successfully implement the task of the attitude control. The singularity can be avoided by the additional variable flywheel speed of variable speed control moment gyroscopes (VSCMG). Unfortunately, some kind of singularity cannot be effectively avoided. Consequently, the output toque can be only supported by the reaction torque of the flywheel when the singularity is encountered, and the consume power that is determined by the flywheel speed and reaction torque can be greatly increased when the flywheel spin rate over one thousand revolutions per minute. In this paper, the pyramid configuration with variable skew angle of the VSCMG is considered. A new steering law for the VSCMG with variable skew angle is proposed. The singularity that cannot be avoided by the varying flywheel speed can be effectively avoided with assisting of varying the skew angle. Consequently, the requirement of flywheel torque can be reduced. At last, the optimizing VSCMG with variable skew angle can be cast as a multi-objective function with multi-constraints. The particle swarm optimization method is used to solve the optimizing problem. In summary, the VSCMG with variable skew angle can be redesigned with considering of the singularity avoidance and minimizing system power.

Singularity radius gradient-based rapid singularity-escape steering law for SGCMGs

In order to visualize singularity of SGCMGs in gimbal angle space,a novel continuous bounded singularity parameter--Singularity Radius,whose sign can distinctly determine singularity type,is proposed.Then a rapid singularity-escape steering law is proposed basing on gradient of Singularity Radius and residual base vector to drive the SGCMG system to neighboring singular boundary,and quickly escape elliptic singularities.Finally,simulation results on Pyramid-type and skew-type configuration demonstrate the effectiveness and rapidness of the proposed steering law.