单框架控制力矩陀螺奇异问题研究

Research on Singularity Questions of Single-gimbal Control Moment Gyros

研究单框架控制力矩陀螺群的奇异问题。给出了一种新的奇异度量,并推导出利用该度量的简洁的零运动公式。对于不同的构型,该度量反映了陀螺群Jacobian矩阵求逆运算的误差灵敏度,且具有相同的取值范围,因此在分析各种构型的优劣时具有可比性。上述结论通过数值仿真给出了验证。对常用的行列式形式奇异度量,给出其零运动的清晰公式。基于奇异值分解,给出陀螺群的各类操纵律,证明了奇异方向与分解矩阵的关系,明确框架锁死出现的条件和鲁棒操纵律调控的依据。给出五棱锥构型奇异角动量体的切片图,为角动量体内奇异的出现提供了认识的方法;对失效情况下的五棱锥构型,通过奇异角动量曲面图和具体的切片图,直观地得到其内部形式和特性的显著变化。

Singularity questions of single-gimbal control moment gyros （SCMGs） are developed. A new singularity measure is presented. A null motion is deduced using the measure. To different configurations of SCMGs, the measure with the same range of value represents the error sensitivity in numerical inverse operation on a Jacobian matrix and has comparability. These conclusions are tested by simulation. The compact formula of the null motion using the common determinant measure is also given. Based on the singular value decomposition, all kinds of steering laws can be obtained. The relation between the singular direction and the decomposed matrix is proved. The condition of gimbal locked states is given, as well as the regulation of the robust steering law. Singularity angular momentum slices of the regular dodecahedron configuration are given. This can provide a new way to explicitly recognize the singular states in angular momentum envelop. For failure, singularity angular momentum surfaces distinguished impassable and passable states are plotted as well as their slices. Envelops and distributions of singularities are very changed by the failing.