Research On Steering Methods Of Control Moment Gyros For Spacecraft Attitude Maneuver

In view of the requirement for large angle or rapid attitude maneuver mission of agile spacecraft,this thesis studies the singularity of SGCMG system and the SGCMGs steering method during spacecraft attitude maneuver.The main content are as follows:In order to directly describe property of singular states of SGCMG system,a novel singular parameter,i.e.singularity radius,is proposed base on Gaussian curvature,the corresponding theoretical expression is derived,and then a singular type determination method is concluded based on singularity radius.Through comparing with Gaussian curvature in two kinds of special singular states and analyzing the curve of singularity radius in pyramid-type configuration,singularity radius is proved to be a continuously bounded singular description parameter which is better than Gaussian curvature.Afterwards,considering that the SGCMG system is got stuck in singularity,an analytical rapid singularity escape steering law is proposed.In internal elliptic singularity of SGCMG configuration,the null motion item of the proposed steering law which is generated by gradient of singularity radius would quickly guide the SGCMG system to the singular boundary,and the item generated by residual vector would directly drive SGCMGs to leave singularity from the singular boundary,thus the proposed steering law can reduce the effect of singularity on the performance of attitude control.Besides,comparing with other rapid singularity escape steering law,the proposed steering law requires no extra storage and numerical calculation.Considering the singularity avoidance problem of redundant SGCMG configuration,the mapping relation between singular direction and singular state is analyzed by inverse mapping method,all singular states of arbitrary SGCMG system and all non-singular states of redundant SGCMG configuration are both demonstrated to be path connectedness which implies the feasibility of singularity avoidance.For situation that spacecraft conducts attitude maneuver around the Euler axis,the distribution of directional vectors of elliptic and hyperbolic singular angular momentum which belong to the same piece of singular surface in pyramid-type configuration is analyzed.By introducing inequality constraint of singularity radius and independent variables,directional vector of singular angular momentum is one-to-one correlated with singular direction,and the solving problem of singular state under directional constraint about singular angular momentum is converted to a series of nonlinear optimization problem which has unique solution.Then,derivations of target function and constraint function are derived,sequential quadratic programming method is applied to search singular states under directional constraint,and a singularity avoidance steering law is proposed.During attitude maneuver with the proposed steering law,hyperbolic and elliptic singularity could be avoided by gradient of singular measurement parameter and error gimbal angles respectively.As for the singularity avoidance problem of failure configuration,the property of all failure configurations of regular pentagonal SGCMG system with one or two SGCMG failed are analyzed,a steering law conversion strategy which can convert any failure configuration to the chosen failure configuration with same number of SGCMGs is proposed.Then,expression of initial gimbal angles of failure 4-SGCMG configuration is derived according to angular moment constraint equation,the distribution of all initial gimbal angles is made clear,and solving method of initial gimbal angles of failure 5-SGCMG configuration is similarly obtained.Afterwards,the optimal initial gimbal angles are acquired on the basis of extremum condition of singular measurement parameter,and the corresponding terminal singular surfaces are obtained through numerical simulations.On account of derivation of spacecraft maneuver direction,conical constraint equation about directional vector of commanded torque is introduced,the feasible direction under constraint is obtained by numerical analysis,and a robust singularity avoidance steering law is proposed.According to the directional vector of initial commanded torque,a proper optimal initial gimbal angle,which is feasible under constraint,is chosen as starting point by the proposed method,and singularity avoidance could still be achieved even when there exists inertia uncertainty during attitude maneuver.