基于单框控制力矩陀螺的敏捷小卫星姿态机动控制研究
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摘要
敏捷小卫星具有比常规小卫星至少高一个数量级的快速机动能力,该敏捷机动能力是很多军事或商业任务如空间监视、高精度对地观测的要求,为了实现该类小卫星的大角度快速机动,单框架控制力矩陀螺(SGCMG)系统因具有力矩放大能力和低功耗等优点而成为其姿态控制系统(ACS)执行机构的理想选择。但是SGCMG的框架转动将使得卫星惯性矩阵随之变化,给ACS建模增加了难度,同时SGCMG系统固有的奇异问题在像金字塔这样的安装构型中表现尤为严重,为使执行机构良好地跟踪控制输入既需要设计有效的SGCMG系统操纵律以克服其奇异问题,也需要设计高效的卫星机动控制律以克服快速机动带来的控制输入过大等问题,本论文对这些问题均做了深入的研究:
(1)论述了卫星姿态描述与姿态运动学方程,通过详细推导,建立了更精确而实用的ACS动力学模型以及SGCMG力矩放大倍数公式,研究了SGCMG大小选型问题;本文与现有很多文献处理方法不同,对于卫星整星惯性矩阵中SGCMG系统相对于其自身质心的惯性矩阵部分没有全部使用或全部忽略,而是分离了其中的非零常值分量与零均值周期分量,分别提出处理方法。
(2)针对SGCMG系统奇异问题,建立了系统各个奇异量之间的关系,并基于代数与微分几何的思想和方法,研究了系统角动量奇异面以及框架角空间奇异面,推导角动量奇异面的几何特征量表达式,同时在前人研究的基础上,完整推导了系统奇异时框架角速率空间之子空间的基,利用系统雅可比矩阵零空间基研究了基于零运动的系统奇异状态可脱离性,归纳了可脱离的两个必要条件。通过以三平行构型SGCMG系统为例验证了诸多理论结果。
(3)对现有SGCMG操纵律作了简要分类归纳,研究了典型的框架角速率操纵律并分析了其中存在的缺点与问题,为克服操纵律中存在的框架“锁死”,基于奇异值分解(SVD)理论提出了一种新的改进奇异方向回避(SDA)操纵律,并研究了其参数整定方法,仿真结果显示了该操纵律的有效性。
(4)以再定向大角度机动为例,研究了传统的四元数反馈机动控制律,发现其普遍存在控制力矩指令峰值过大、系统后半段收敛缓慢等缺点,为克服这些缺点,基于反步法(Backstepping Design),应用变增益控制等思想,设计了一种新的非线性反步机动控制律,并针对其参数较多的问题提出了参数整定方法,ACS闭环仿真显示应用该控制律能大幅抑制控制力矩指令峰值,同时保证控制律的光滑性、稳定性。
The agile small satellite has rapid maneuver capability with at least an order of magnitude greater than conventional microsatellite, and this rapid maneuver capability is required for many military or commercial missions, for example, space surveillance, high-precision earth observation. In order to achieve a large angle rapid maneuvers of such small satellites, the Single Gimbal Control Moment Gyro (SGCMG) systems are the ideal candidate for the actuators of its’Attitude Control Systems (ACS) for the reasons of possessing the capability of torque amplification and lower power consumption. However, the difficulty of the mathematical modeling of ACS is increased for which the inertia matrix of the satellite is varied with the rotation of the gimbal of SGCMG, meanwhile, the inherent singular problem of SGCMG is particularly serious in the installation configuration such as pyramid. In order to make the actuator tracking the control input well, not only an effective SGCMG system steering law is needed to design to overcome its singularity problem, but also a high efficient attitude maneuver control law is required to design to overcome the problems such as excessive control input bought by the rapid maneuvers. All these problems are lucubrated in this thesis.
(1) Attitude representation & kinematic equations of the satellite are summarized, and a more accurate but practical dynamic model of ACS as well as the SGCMG torque magnification formula are established, and the selection problem of the size of SGCMG is also studied. In this paper, the methods different from the existing literature are used in dealing with the of inertia matrix of SGCMG system with respect to its own center of mass which is part of the inertia matrix of the entire satellite. This part is not all of use or all of neglect, while the non-zero components and the cycle components with zero-mean are separated and treated respectively.
(2) Aimed at singular problems of SGCMG system, the relationships between each singular parameter of system are established. the angular moment singular surfaces as well as the singular surfaces in gimbal configuration space are investigated, and the geometric characteristic expressions of the angular moment singular surfaces are also derived based on the ideas and methods of the algebra and differential geometry. Meanwhile, based on previous research, the bases of the subspaces in the gimbal angle tangent space at the singular states are fully derived,and Escapability at the singular state of system is also studied through the used of null space bases of the system’s Jacobian matrix; Two necessary conditions of the Escapability are summarized. Many theoretical results are verified through an example of three SGCMGs with parallel gimbal axes.
(3) The existing SGCMG system steering laws are briefly summarize and classified. The typical gimal angular rate steering laws are analyzed as well as the problems and their shortcomings. To overcome the gimbal“lock”phenomenon existed in those steering laws, an improved singular direction avoidance (SDA) steering law is proposed based on the singular value decomposition (SVD ) Theory, and its parameters tuning method is also investigated. Effectiveness of the new steering law is showed by some simulation results.
(4) Trough the example of large angle re-orientation maneuver, the traditional quaternion feedback control law for maneuvers are studied, found some shortcomings that the peak of control torque command is too large,and convergence of the second half phase of the system is also slow and so on. To overcome those shortcomings, a new nonlinear backstepping control law is proposed based on the backstepping design method as well as the application of ideas such as variable gain control, and its parameters tuning method is also proposed aimed at the problem of too many parameters. The ACS closed-loop simulation results shows that the control law can be applied significantly inhibited the peak of control torque command, while ensuring the smooth of control law and stability of the system.
(1)论述了卫星姿态描述与姿态运动学方程,通过详细推导,建立了更精确而实用的ACS动力学模型以及SGCMG力矩放大倍数公式,研究了SGCMG大小选型问题;本文与现有很多文献处理方法不同,对于卫星整星惯性矩阵中SGCMG系统相对于其自身质心的惯性矩阵部分没有全部使用或全部忽略,而是分离了其中的非零常值分量与零均值周期分量,分别提出处理方法。
(2)针对SGCMG系统奇异问题,建立了系统各个奇异量之间的关系,并基于代数与微分几何的思想和方法,研究了系统角动量奇异面以及框架角空间奇异面,推导角动量奇异面的几何特征量表达式,同时在前人研究的基础上,完整推导了系统奇异时框架角速率空间之子空间的基,利用系统雅可比矩阵零空间基研究了基于零运动的系统奇异状态可脱离性,归纳了可脱离的两个必要条件。通过以三平行构型SGCMG系统为例验证了诸多理论结果。
(3)对现有SGCMG操纵律作了简要分类归纳,研究了典型的框架角速率操纵律并分析了其中存在的缺点与问题,为克服操纵律中存在的框架“锁死”,基于奇异值分解(SVD)理论提出了一种新的改进奇异方向回避(SDA)操纵律,并研究了其参数整定方法,仿真结果显示了该操纵律的有效性。
(4)以再定向大角度机动为例,研究了传统的四元数反馈机动控制律,发现其普遍存在控制力矩指令峰值过大、系统后半段收敛缓慢等缺点,为克服这些缺点,基于反步法(Backstepping Design),应用变增益控制等思想,设计了一种新的非线性反步机动控制律,并针对其参数较多的问题提出了参数整定方法,ACS闭环仿真显示应用该控制律能大幅抑制控制力矩指令峰值,同时保证控制律的光滑性、稳定性。
The agile small satellite has rapid maneuver capability with at least an order of magnitude greater than conventional microsatellite, and this rapid maneuver capability is required for many military or commercial missions, for example, space surveillance, high-precision earth observation. In order to achieve a large angle rapid maneuvers of such small satellites, the Single Gimbal Control Moment Gyro (SGCMG) systems are the ideal candidate for the actuators of its’Attitude Control Systems (ACS) for the reasons of possessing the capability of torque amplification and lower power consumption. However, the difficulty of the mathematical modeling of ACS is increased for which the inertia matrix of the satellite is varied with the rotation of the gimbal of SGCMG, meanwhile, the inherent singular problem of SGCMG is particularly serious in the installation configuration such as pyramid. In order to make the actuator tracking the control input well, not only an effective SGCMG system steering law is needed to design to overcome its singularity problem, but also a high efficient attitude maneuver control law is required to design to overcome the problems such as excessive control input bought by the rapid maneuvers. All these problems are lucubrated in this thesis.
(1) Attitude representation & kinematic equations of the satellite are summarized, and a more accurate but practical dynamic model of ACS as well as the SGCMG torque magnification formula are established, and the selection problem of the size of SGCMG is also studied. In this paper, the methods different from the existing literature are used in dealing with the of inertia matrix of SGCMG system with respect to its own center of mass which is part of the inertia matrix of the entire satellite. This part is not all of use or all of neglect, while the non-zero components and the cycle components with zero-mean are separated and treated respectively.
(2) Aimed at singular problems of SGCMG system, the relationships between each singular parameter of system are established. the angular moment singular surfaces as well as the singular surfaces in gimbal configuration space are investigated, and the geometric characteristic expressions of the angular moment singular surfaces are also derived based on the ideas and methods of the algebra and differential geometry. Meanwhile, based on previous research, the bases of the subspaces in the gimbal angle tangent space at the singular states are fully derived,and Escapability at the singular state of system is also studied through the used of null space bases of the system’s Jacobian matrix; Two necessary conditions of the Escapability are summarized. Many theoretical results are verified through an example of three SGCMGs with parallel gimbal axes.
(3) The existing SGCMG system steering laws are briefly summarize and classified. The typical gimal angular rate steering laws are analyzed as well as the problems and their shortcomings. To overcome the gimbal“lock”phenomenon existed in those steering laws, an improved singular direction avoidance (SDA) steering law is proposed based on the singular value decomposition (SVD ) Theory, and its parameters tuning method is also investigated. Effectiveness of the new steering law is showed by some simulation results.
(4) Trough the example of large angle re-orientation maneuver, the traditional quaternion feedback control law for maneuvers are studied, found some shortcomings that the peak of control torque command is too large,and convergence of the second half phase of the system is also slow and so on. To overcome those shortcomings, a new nonlinear backstepping control law is proposed based on the backstepping design method as well as the application of ideas such as variable gain control, and its parameters tuning method is also proposed aimed at the problem of too many parameters. The ACS closed-loop simulation results shows that the control law can be applied significantly inhibited the peak of control torque command, while ensuring the smooth of control law and stability of the system.
引文
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