Optimization Design Of Steering Law And Parameters For Variable-speed Control Moment Gyroscopes With Pyramid Configuration

The singularity problem of single-gimbal control moment gyroscopes(SGCMG)cluster can be avoided by variable-speed control moment gyroscopes(VSCMG)cluster without additional hardware.The requirement of attitude control(AC)task and the integrated power/attitude control(IPAC)task could be satisfied by VSCMG cluster with variable speed flywheel,respectively.The research and application for VSCMG has important practical significance for the development attitude control technology of angular momentum for a spacecraft.The research process of VSCMG cluster are still in the stage of laboratory verification.Until now,the technology is not well developed.The flywheel power of VSCMG cluster can be very large,which is the major problem for VSCMG cluster in the application of space field.In this article,the steering law with minimum requirement of flywheel torque is proposed,so the flywheel power can be reduced.On this basis,the optimization design method for the parameters of VSCMG cluster,which can satisfy the requirements of AC task and IPAC task is given,respectively.Firstly,the angular momentum envelope characteristics of VSCMG cluster are analyzed for VSCMG cluster with upper and lower bound of flywheel regulation speed.The singularity for AC task and IPAC task of VSCMG cluster is analyzed,and the singularity can be encountered or not is also analyzed.Based on the result of the above analysis,the constraint relation between the singularity of VSCMG cluster and the design parameters of VSCMG cluster is given.The exchange characteristics and constraint characteristics of VSCMG cluster with AC task and IPAC task is given.So the relation between the size of momentum envelop and the design parameters of VSCMG cluster can be provided.Secondly,based on the analysis results of SGCMG singular characteristics,the steering law is analyzed under the typical working condition.The steering characteristics of steering law with weighted pseudo inverse,the steering law of weighted pseudo inverse with null motion and the steering law with ability of flywheel speed equalization is revealed.The requirements of flywheel torque with different steering laws are given.So the above analysis results can lay the foundation for steering law design with minimum requirement of flywheel torque.Thirdly,the steering law with minimum requirement of the flywheel torque is proposed by designing the weighted matrix based on appropriating design the expected flywheel speed equalization with AC task.So the SGCMG cluster singularity can be avoided and each flywheel speed can be approached to the average speed.The constraint conditions of flywheel torque and gyroscopic moment are given in the absence of encounter singularity based on analysis of the new designing steering law.The parameters designing problem of VSCMG cluster with AC task is solved by the multi-objective optimization method with the maximum size of the exchangeable angular momentum space and the minimum whole system power.Fourthly,the steering law with the minimum requirement of the flywheel power is proposed at the cost of reducing the size of the exchangeable angular momentum space of VSCMG cluster with IPAC task.So the integrated power/attitude control system(IPACS)singularity can be avoided and each flywheel speed can be approached to the average speed.The purpose of uniformly distributing the power of each flywheel can be achieved.The constraint conditions of flywheel torque and gyroscopic moment are given in the absence of encounter IPACS singularity based on analysis of the new designing steering law.The parameters designing problem of VSCMG cluster with IPAC task is solved by the multi-objective optimization method with the maximum size of the exchangeable angular momentum space and the minimum gimbal system power.Finally,the following conclusions can be obtained according to the comparative analysis of the system performance for the designed VSCMG cluster with energy storage and without energy storage.The certain energy storage can be realized of VSCMG cluster with AC task at cost of reducing the size of the exchangeable angular momentum space.At the same time,the output torque of VSCMG cluster in the absence of encounter singularity remains constant.But only one unit can be allowed failure,and the system performance can be reduced.The size of the exchangeable angular momentum space can be increased of VSCMG cluster with IPAC task in the absence of energy storage.At the same time,the output torque of VSCMG cluster in the absence of encounter singularity remains constant.Only two units can be allowed failure at most.