Singularity problem of control moment gyro cluster with vibration isolators

As powerful torque amplification actuators, control moment gyros (CMGs) are often used in the attitude control of many state-of-the-art high resolution satellites. However, the distur-bance generated by the CMGs can not only reduce the attitude stability of a satellite but also dete-riorate the performance of optic payloads. Currently, CMG vibration isolators are widely used to target this problem. The isolators can affect the singularity of the CMG system as they are placed between the CMGs and the satellite bus and provide additional freedoms to the CMG system due to their flexibility. The formulation of the output torque of a CMG is studied first considering the dynamic imbalance of its spin rotor and then the deformation angle as a result of the isolator’s flex-ibility is calculated. With the additional freedoms, the influence of isolator on the singularity problem is studied and a new steering logic to escape from the singular states is proposed.     

A new steering approach for VSCMGs with high precision

A new variable speed control moment gyro (VSCMG) steering law is proposed in order to achieve higher torque precision. The dynamics of VSCMGs is established, and two work modes are then designed according to command torque:control momentum gyro (CMG)/reaction wheel (RW) hybrid mode for the large torque case and RW single mode for the small. When working in the CMG/RW hybrid mode, the steering law deals with the gimbal dead-zone nonlinearity through compensation by RW sub-mode. This is in contrast to the conventional CMG singularity avoidance and wheel speed equalization, as well as the proof of definitely hyperbolic singular property of the CMG sub-mode. When working in the RW single mode, the motion of gimbals will be locked. Both the transition from CMG/RW hybrid mode to RW single mode and the reverse are studied. During the transition, wheel speed equalization and singularity avoidance of both the CMG and RW sub-modes are considered. A steering law for the RWs with locked gimbals is presented. It is shown by simulations that the VSCMGs with this new steering law could reach a better torque precision than the normal CMGs in the case of both large and small torques.     

使用VSCMGs的IPACS的奇异性分析与操纵律设计

 研究使用变速控制力矩陀螺群(VSCMGs)的能量/姿态一体化控制系统(IPACS)的奇异性分析与操纵律设计问题。提出了VSCMGs的CMG奇异与IPACS奇异两种概念。对于给定的CMG奇异方向,采用优化理论得到了在该方向上VSCMGs的转子达到角动量饱和时的转速表达式,并给出了IPACS奇异的充要条件及其证明。分析了考虑星体角速度影响时的实际IPACS的奇异性质。在此基础上为实现合理的动量管理,采用加权矩阵的方法设计了IPACS的操纵律。最后通过算例验证了所得到的IPACS奇异判据的正确性,并通过数值仿真,验证了所设计的操纵律的正确性及其良好的动量管理性能。     

单框架控制力矩陀螺奇异问题研究

 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。     

采用框架角受限控制力矩陀螺的航天器姿态机动控制

以框架角受限的金字塔构型控制力矩陀螺(CMG)为执行机构,研究了航天器欧拉姿态机动控制问题.考虑控制力矩及航天器角速度约束等因素,对已有的姿态机动控制律进行了改进,使其能实现绕欧拉轴的大角度姿态机动.同时考虑力矩陀螺框架角受限情况,通过适当加入空转指令对框架角进行重构,设计了复合控制形式的控制力矩陀螺操纵律,并通过过渡...     

基于矩阵奇异值理论的颤振分析新方法

根据颤振分析的基本概念,提出了一类基于矩阵奇异值理论的颤振分析新方法。该方法的特点是,以计算颤振矩阵最小奇异值或条件数的倒数来直接搜索颤振临界点。证明了这两个指标在颤振临界点处的等价性。根据指标在颤振临界点附近取极小值的特点,编制了相应的算法,在确定颤振临界点时无需计算颤振特征根,避免了“窜支”问题,从而减少了人工干预,提高了计算自动化程度。数值算例结果表明,采用该方法计算得到的颤振临界速度和颤振频率与p-k法计算结果的精度相当,且两个指标对应的计算结果一致,验证了其等价性。     

Singularity radius gradient-based rapid singularity-escape steering law for SGCMGs

In order to visualize singularity of SGCMGs in gimbal angle space, a novel continuous bounded singularity parameter--Singularity Radius, whose sign can distinctly determine singularity type, is proposed. Then a rapid singularity-escape steering law is proposed basing on gradient of Singularity Radius and residual base vector to drive the SGCMG system to neighboring singular boundary, and quickly escape elliptic singularities. Finally, simulation results on Pyramid-type and skew-type configuration demonstrate the effectiveness and rapidness of the proposed steering law.     

利用变速控制力矩陀螺的航天器集成能量与姿态控制

 利用变速控制力矩陀螺(VSCMG)的航天器姿态与能量一体化控制问题。针对以VSCMG为姿态控制执行机构的刚体航天器设计了全局渐近稳定的姿态跟踪控制律。将VSCMG的框架角速度和转子角加速度作为控制输入向量设计操纵律。利用加权的最小范数解得到VSCMG的姿态控制输入向量,并用与之正交的控制输入向量来以给定的功率存储/释放能量。提出了同时表征力矩陀螺模式构型奇异和转子轮速平衡的混合指标函数。对控制自由度有冗余的系统,在混合指标函数的基础上利用梯度法构建了VSCMG的空转运动,以回避力矩陀螺模式的构型奇异,并同时减小转子转速差过大引起的转速饱和以及VSCMG零奇异的可能性。利用反馈转子动能的方法规划日照期间的储能功率,以维持系统长时间工作的能量平衡。基于某太阳同步轨道卫星的数值仿真结果验证了系统的有效性。     

高转矩密度磁力齿轮的拓扑结构设计与性能比较

永磁行星齿轮和同轴永磁齿轮是两类具有不同拓扑结构和运行原理的磁力齿轮,采用定量设计比较法设计了具有相同有效体积和永磁体用量的上述两类磁齿轮,并通过有限元分析法对二者的转矩传递性能进行比较研究。研究结果表明,永磁行星齿轮较同轴永磁齿轮有更高的转矩密度和更低的转矩脉动。此外,由于永磁行星齿轮具有更加灵活的运行模式,并且能实现功率分流,使其在混合动力汽车领域有很好的应用前景。加工了一台永磁行星齿轮样机,并搭建试验平台进行了相关的试验,结果表明了该拓扑结构的有效性。     

单框架控制力矩陀螺群的奇异几何分析

使用几何方法对单框架控制力矩陀螺群（包括转子恒速的CSCMG和转子变速的VSCMG）的奇异性进行了分析。通过绘制CSCMG的奇异角动量超曲面,并标识隐奇异和显奇异在该曲面上对应的点,直观地表述了CSCMG的可操纵空间,得出星体三轴角动量可交换的具体范围。比较奇异角动量超曲面图,可以看出金字塔构型在角动量饱和包络面内部存在显奇异,而五棱锥构型的显奇异十分接近饱和包络面。文中分析了金字塔和五棱锥两种构型的CSCMG可能的退化隐奇异点,并给出了退化隐奇异点在奇异角动量超曲面上的具体位置及其高斯曲率特性。对集成的能量和姿态一体化控制系统（IPACS）可能出现的无法操纵的情况进行了补充分析,给出了使用VSCMG的IPACS不会出现操纵奇异的构型设计的充分条件。给出在某一瞬时能量下,VSCMG转子角速率范围有限制时的角动量包络图,从中得到CSCMG与VSCMG角动量体的变化和联系。