具有单框架控制力矩陀螺航天器的建模及可控性分析

针对具有单框架控制力矩陀螺的航天器姿态控制问题，将航天器与控制力矩陀螺看作整体系统，应用Lagrangian方程与Hamiltonian方程建立系统在重力场中的数学模型。在考虑航天器短时间内大角度机动前提下，将系统在Lagrangian形式下的状态方程简化成仿射非线性形式，以控制力矩陀螺框架角速度为输入变量，回避控制力矩陀螺在奇异情况下对系统的影响。随后应用系统Hamiltonian形式的保体积性与非线性系统可控性定理证明该系统可控，且系统可控性不受单框架控制力矩陀螺群个数、构型、奇异问题的影响。系统在重力场中的数学模型与可控性结论为以后进一步研究航天器姿态控制方法，航天器系统稳定性问题提供了理论依据。

Modeling of spacecraft attitude systems with single gimbal control moment gyros and controllability analysis

For a spacecraft using single gimbal control moment gyros(SGCMGs) as actuators,taking the spacecraft and SGCMGs as a whole system,the model of the attitude control system is constructed in the gravitational field by using Lagrangian and Hamilton equations.In the case of large-angle maneuvers of the spacecraft in short time,the state equation of the system in Lagrangian form is simplified as an affine nonlinear equation,with the angular velocity of SGCMG gimbals as an input variables,which avoids the singularity problem arising in conventional treatment.Finally,the controllability of the system is analyzed by using the preservation of the system volume in Hamiltonian form.The controllability property holds in spite of the number of the SGCMGs,their configuration and the presence of singularity.The model and the controllability of the attitude control system provide a theoretical basis of the further investigation on the control and stability analysis of the spacecraft system.