论文部分内容阅读
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。
Aiming at spacecraft attitude control problem with single-frame control moment gyroscope, the spacecraft and control moment gyroscope are considered as a whole system. The mathematical model of the system in gravity field is established by using Lagrangian equation and Hamiltonian equation. Considering the large-angle maneuver of the spacecraft in a short period of time, the state equation of the system in Lagrangian form is simplified to an affine nonlinear form, the angular velocity of the moment gyroscope frame is controlled as the input variable, and the control moment gyro is avoided under the singularity of the system Impact. Subsequently, the Hamiltonian form of the guaranteed volume and nonlinear system controllability theorems prove that the system is controllable, and the system controllability is not affected by the number of single-frame control moment gyroscope groups, configuration and singularity problems. The mathematical model and controllability conclusion of the system in the gravitational field provide the theoretical basis for further research on spacecraft attitude control and spacecraft system stability.