WO2021052087A1 - 一种适合非冗余sgcmg群的操纵方法 - Google Patents

一种适合非冗余sgcmg群的操纵方法 Download PDF

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WO2021052087A1
WO2021052087A1 PCT/CN2020/109919 CN2020109919W WO2021052087A1 WO 2021052087 A1 WO2021052087 A1 WO 2021052087A1 CN 2020109919 W CN2020109919 W CN 2020109919W WO 2021052087 A1 WO2021052087 A1 WO 2021052087A1
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sgcmg
frame
frame angle
nominal
jacob
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PCT/CN2020/109919
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French (fr)
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袁利
雷拥军
刘洁
张科备
田科丰
姚宁
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北京控制工程研究所
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
    • B64G1/00—Cosmonautic vehicles
    • B64G1/22—Parts of, or equipment specially adapted for fitting in or to, cosmonautic vehicles
    • B64G1/24—Guiding or controlling apparatus, e.g. for attitude control
    • B64G1/36—Guiding or controlling apparatus, e.g. for attitude control using sensors, e.g. sun-sensors, horizon sensors
    • B64G1/369—Guiding or controlling apparatus, e.g. for attitude control using sensors, e.g. sun-sensors, horizon sensors using gyroscopes as attitude sensors
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
    • B64G1/00—Cosmonautic vehicles
    • B64G1/22—Parts of, or equipment specially adapted for fitting in or to, cosmonautic vehicles
    • B64G1/24—Guiding or controlling apparatus, e.g. for attitude control
    • B64G1/28—Guiding or controlling apparatus, e.g. for attitude control using inertia or gyro effect
    • B64G1/286—Guiding or controlling apparatus, e.g. for attitude control using inertia or gyro effect using control momentum gyroscopes (CMGs)
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
    • B64G1/00—Cosmonautic vehicles
    • B64G1/22—Parts of, or equipment specially adapted for fitting in or to, cosmonautic vehicles
    • B64G1/24—Guiding or controlling apparatus, e.g. for attitude control
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
    • B64G1/00—Cosmonautic vehicles
    • B64G1/22—Parts of, or equipment specially adapted for fitting in or to, cosmonautic vehicles
    • B64G1/24—Guiding or controlling apparatus, e.g. for attitude control
    • B64G1/244—Spacecraft control systems
    • B64G1/245—Attitude control algorithms for spacecraft attitude control
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

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  • the present invention is a control method suitable for non-redundant SGCMG group, relates to the field of spacecraft attitude control, and is suitable for high-stability attitude control using a control moment gyro CMG group.
  • the satellite In order to achieve the requirements of multi-axis rapid attitude maneuvering for the entire satellite, the satellite generally adopts the control moment gyro CMG group and its corresponding control algorithm.
  • the technical means widely adopted by satellites are: the use of control moment gyroscope groups for satellite attitude control.
  • the specific steps are: first calculate the Jacobian matrix, singularity and singularity avoidance vector according to the frame angle measured by CMG in real time, then calculate the singularity avoidance parameter according to the singularity, and finally calculate the angular velocity command of each CMG frame according to the Jacobian matrix and the expected torque , Perform attitude control.
  • the system In view of the dual requirements of spacecraft's three-axis attitude control and singularity avoidance, the system generally adopts no less than 4 SGCMG configurations.
  • the corresponding frame angle vector is a connected area in the frame angle space, with frame angle reconstruction to achieve singularity
  • the conditions for avoiding and fleeing, so the existing control method research mainly focuses on the redundant configuration system. Long-term rapid maneuvering in orbit may cause frequent radial eccentric loads of the CMG high-speed rotor shaft system, which can easily lead to problems such as poor lubrication of mechanical bearings and failure of the whole machine. This type of problem has repeatedly occurred on the International Space Station.
  • the system becomes a non-redundant configuration.
  • the specific CMG angular momentum of non-redundant systems corresponds to the frame angle vector as a limited isolated point in the frame space, so that singularity evasion and escape cannot be achieved through frame reconstruction.
  • the CMG angular momentum returns to the initial state after the end of the attitude maneuver, the frame angle cannot be guaranteed to return to the initial state and enter another unexpected state. If the state is close to the singular point or it is a singular state, it will lead to subsequent attitude stability control The attitude of part of the spacecraft is out of control, so the existing control laws based on redundant CMG systems are no longer applicable to non-redundant systems.
  • the technical solution of the present invention is to overcome the shortcomings of the prior art and propose a manipulation method suitable for non-redundant SGCMG groups.
  • This method can not only be used for the manipulation of redundant SGCMGs, but also solves the problem of only 3 SGCMGs that are non-redundant.
  • the system cannot realize the singular avoidance and escape in control through the commonly used frame reconstruction strategies. After the attitude maneuver, the frame configuration approaches or is trapped in a singular state, and the system loses its attitude maneuverability.
  • a control method suitable for non-redundant SGCMG groups The satellite is equipped with n SGCMGs, and each SGCMG has the same angular momentum. The steps are as follows:
  • Step 1) Determine the nominal frame angle vector of the n SGCMG configurations according to the configuration and synthetic angular momentum of the n SGCMGs; Step 1) The nominal frame angle vector of the n SGCMG configurations satisfies the synthesis of the n SGCMGs The angular momentum H is zero and the singularity JD of n SGCMG configurations is the largest.
  • the step 2) the method for determining the Jacobian matrix Jacob of the frame angular motion equation is as follows:
  • ⁇ i is the frame angle of the i-th SGCMG, i ⁇ [1, n], the n SGCMGs are numbered from 1 to n according to any rule;
  • a and B are related to the installation direction of the n SGCMG frame shafts 3 ⁇ n-dimensional coefficient matrix, the i-th column of the A matrix corresponds to the i-th SGCMG frame angle of 90°, the i-th SGCMG high-speed rotor angular momentum direction three-axis components, the i-th column of the B matrix corresponds to the i-th When the frame angle of each SGCMG is 0°, the three-axis components of the angular momentum direction of the i-th high-speed rotor.
  • the present invention has the following beneficial effects:
  • the method proposed in the present invention makes full use of the existing actuator configuration, and obtains a new control law of the CMG system based on the multi-objective optimization technology, which solves the problem that the system cannot achieve the singularity avoidance and escape in the control through the commonly used frame reconstruction strategy , Which makes the satellite lose its attitude maneuverability;
  • the method of the present invention is based on the construction of a multi-objective optimization cost function considering the deviation of the frame angle from the nominal distance, the frame angle command amplitude and the torque output deviation, and the multi-objective CMG control law is obtained through the optimization method, which harmonizes the CMG frame singularity avoidance
  • the contradiction between the torque and the attitude control torque ensures that high-performance attitude control can be achieved when maneuvering along any attitude.
  • Figure 1 is a flow chart of the method of the present invention
  • Figure 2 shows the three-axis attitude angle and angular velocity curve of the satellite
  • Figure 3 is the SGCMG low-speed frame angular velocity command curve.
  • the single-frame control moment gyro group is the SGCMG group.
  • the configuration of the SGCMG group system has become a major trend in the international high-performance attitude maneuvering spacecraft. Long-term on-orbit rapid maneuvers may have the risk of the frame configuration approaching or stuck in a strange state after the maneuvering, leading to system instability.
  • the present invention is a control method suitable for non-redundant SGCMG group, which creatively constructs considering the deviation of frame angle from the nominal distance, frame angle command amplitude and torque output deviation Based on the multi-objective optimization cost function of the multi-objective optimization technology, a new type of manipulation law of the new CMG system is obtained.
  • This method realizes the singularity avoidance in the attitude maneuver and the return of the nominal position of the frame after the maneuver, reconciles the contradiction between the singularity avoidance of the CMG frame and the attitude control torque, ensures the high-performance realization of maneuvering along any attitude, and greatly improves the CMG system Attitude stability and attitude maneuverability.
  • the effectiveness of the algorithm has been verified by mathematical simulation.
  • Step1 Determine the nominal frame angle vectors of various combinations of SGCMG groups according to factors such as the synthetic angular momentum of the SGCMG group is zero, the configuration of the SGCMG group is relatively singular, and the torque output capacity of the SGCMG in all directions is equivalent;
  • Step4 Construct a comprehensive multi-objective optimization cost function considering the deviation of the frame angle from the nominal distance, the frame angle command amplitude and the torque output deviation, and calculate the SGCMG frame angular velocity command by minimizing the cost function Perform attitude control.
  • the specific steps are to first adjust the singular point avoidance parameters ⁇ 1 and ⁇ 2 in real time when the cyclic attitude maneuver situation and singularity situation, and then calculate the angular velocity commands of each CMG frame according to the Jacobian matrix and the control torque command ⁇ r Perform attitude control.
  • the present invention is suitable for a non-redundant SGCMG group manipulation method, including the following steps:
  • the nominal frame angle vectors of the n SGCMG configurations satisfy that the synthetic angular momentum H of the n SGCMG configurations is zero and the singularity JD of the n SGCMG configurations is maximized.
  • JD det(Jacob ⁇ Jacob T ) takes the maximum value
  • Jacob A cos ⁇ 0 -B sin ⁇ 0
  • H the synthetic angular momentum of the n SGCMGs
  • a and B are the coefficient matrices related to the installation direction of the SGCMG frame axis
  • the i-th of the A matrix The column corresponds to the three-axis component of the angular momentum direction of the i-th SGCMG high-speed rotor when the frame angle of the i-th SGCMG is 90°
  • the i-th column of the B matrix corresponds to the i-th SGCMG frame angle of 0°.
  • E is the n-dimensional unit vector
  • E [1 1 ... 1] T
  • JD is the singularity of the configuration
  • det is the determinant.
  • sin ⁇ 0 and cos ⁇ 0 are respectively the sine and cosine diagonal matrix corresponding to the i-th SGCMG nominal frame angle, as follows:
  • n SGCMGs According to the current frame angle ⁇ i , i ⁇ [1, n] of each SGCMG in real time, n SGCMGs, corresponding to ⁇ 1 ⁇ 2 ... ⁇ n , determine the Jacobian matrix Jacob of the frame angle motion equation; at the same time According to the current real-time frame angle vector of each SGCMG and the nominal frame angle vector of the n SGCMG configurations determined in step 1), determine the deviation ⁇ of the frame angle from the nominal;
  • sin ⁇ is the diagonal sine matrix corresponding to the frame angle
  • cos ⁇ is the diagonal cosine matrix corresponding to the frame angle
  • the element on the diagonal of the sin ⁇ matrix is the sine value of the i-th SGCMG frame angle ⁇ i
  • the diagonal of the cos ⁇ matrix is the cosine value of the i-th SGCMG frame angle ⁇ i.
  • ⁇ i is the frame angle of the i-th SGCMG, i ⁇ [1, n].
  • a and B are 3 ⁇ n-dimensional coefficient matrices related to the installation direction of n SGCMG frame shafts.
  • the i-th column of A matrix corresponds to the angular momentum direction of the i-th SGCMG when the frame angle of the i-th SGCMG is 90°.
  • the i-th column of the B matrix corresponds to the angular momentum direction of the i-th high-speed rotor when the i-th SGCMG frame angle is 0°;
  • the method for determining the deviation ⁇ of the frame angle deviation from the nominal is specifically as follows:
  • ⁇ 0 [ ⁇ 01 ... ⁇ 0i ... ⁇ 0n ] T
  • ⁇ [ ⁇ 1 ... ⁇ i ... ⁇ n ] T
  • ⁇ 0i is the nominal frame angle of the i-th SGCMG.
  • ⁇ 0 is the nominal frame angle vector of n SGCMG configurations.
  • the SGCMG control law that integrates the above objectives is obtained through the optimization method, and the torque command ⁇ obtained according to the attitude control r and the deviation of the Jacobian matrix Jacob and the frame angle determined in step 2) from the nominal, the SGCMG frame angular velocity is determined by the following multi-objective optimization control law
  • the SGCMG frame angular velocity is used as a frame angular velocity command, and the SGCMG low-speed frame shaft is controlled to rotate according to the frame angular velocity command to control the attitude of the satellite.
  • the step 3) Determine the angular velocity of the SGCMG frame
  • the method specifically:
  • ⁇ r ⁇ 1 (( ⁇ 1 + ⁇ 2 )I+Jacob T ⁇ Jacob)-1 ⁇ + ⁇ -T s (( ⁇ 1 + ⁇ 2 )I+Jacob T ⁇ Jacob) -1 ⁇ Jacob T ⁇ ⁇ r /h,
  • ⁇ r is the frame angle command
  • T s is the sampling period of SGCMG
  • h is the angular momentum of SGCMG
  • I is the n-dimensional unit matrix
  • ⁇ 1 and ⁇ 2 are the designed singularity avoidance parameters, ⁇ 1 ⁇ 0, And ⁇ 2 ⁇ 0, and it can be adjusted in real time according to the current period attitude maneuvering situation and singularity situation.
  • Embodiment 1 For the satellites of the CMG group installed with 3 high-precision star sensors, 6 high-precision gyroscopes, and 6 pentagonal pyramids, mark the CMG numbers as CMG1, CMG2, CMG3, CMG4, CMG5, CMG6.
  • a multi-objective optimization control law of the SGCMG system is specifically implemented as follows:
  • the nominal frame angle ⁇ CMG0 [88.03; -92.32; -92.41; 60.740591; -116.144; -145.265] is selected to make the three-axis configuration

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Abstract

一种适合非冗余SGCMG群的操纵方法，包括步骤：1）根据n个SGCMG的构型及合成角动量，确定n个SGCMG构型的标称框架角向量，n≥3；2）根据每个SGCMG的框架角，确定框架角运动方程的Jacob及框架角偏离标称的偏差；3）根据步骤2）确定的所述Jacob及框架角偏离标称的偏差，确定SGCMG框架角速度指令。本发明方法通过考虑框架角偏离标称的距离、框架角指令幅值及力矩输出偏差，具有姿态机动中奇异规避及机动后框架标称位置返回的能力，调和了CMG框架奇异规避与姿态控制力矩之间的矛盾，能够确保沿任意姿态机动高性能实现。

Description

一种适合非冗余SGCMG群的操纵方法
本申请要求于2019年9月16日提交中国专利局、申请号为201910872892.7、发明名称为“一种SGCMG的框架角速度确定方法”的中国专利申请的优先权，其全部内容通过引用结合在本申请中。
技术领域
本发明一种适合非冗余SGCMG群的操纵方法，涉及航天器姿态控制领域，适用于采用控制力矩陀螺CMG群的高稳定度姿态控制。
背景技术
为实现整星多轴快速姿态机动要求，卫星一般采用控制力矩陀螺CMG群及其相应控制算法。卫星广泛采用的技术手段为：采用控制力矩陀螺群进行卫星姿态控制。具体步骤为首先根据CMG实时测量的框架角，计算雅克比矩阵、奇异度及奇异回避向量，其次再根据奇异度计算奇异点规避参数，最后根据雅克比矩阵、期望力矩，计算各个CMG框架角速度指令，进行姿态控制。鉴于航天器三轴姿态控制与奇异规避双重需求，系统一般采用不少于4台SGCMG配置方式，对特定CMG角动量其对应框架角向量在框架角空间为连通区域，具备框架角重构实现奇异规避与逃离的条件，故现有操纵方法研究主要针对冗余配置系统。长期在轨姿态快速机动可能引起的CMG高速转子轴系径向频发偏载极易导致机械轴承润滑不良等问题而使整机失效，在国际空间站上多次出现该类问题。
一旦SGCMG系统由于故障仅剩3台可工作时则系统成为非冗余配置。与冗余系统不同，非冗余系统的特定CMG角动量对应框架角向量在框架空间上为有限的孤立点，以致无法通过框架重构方式实现奇异规避及逃离。当姿态机动结束后CMG角动量回到初始状态时，框架角无法保证回到初始状态而进入另一非预期状态，若该状态临近奇异点或本身即为奇异状态则继而导致后续姿 态稳定控制中航天器部分通道姿态失控，故已有基于冗余CMG系统的操纵律对非冗余系统均已无法适用。
发明内容
本发明的技术解决问题是：克服现有技术的不足，提出了一种适合非冗余SGCMG群的操纵方法，该方法不仅可用于冗余SGCMG的操纵，还解决了仅3台SGCMG非冗余系统无法通过常用的框架重构策略实现控制中的奇异规避及逃离，姿态机动后框架构型临近或陷于奇异状态系统失稳风险，使得卫星失去姿态机动能力的问题。
本发明的技术方案为：
一种适合非冗余SGCMG群的操纵方法，卫星安装有n个SGCMG，每个SGCMG的角动量相同，包括步骤如下：
1)根据n个SGCMG的构型及合成角动量，确定n个SGCMG构型的标称框架角向量；步骤1)所述n个SGCMG构型的标称框架角向量满足使n个SGCMG的合成角动量H为零且n个SGCMG构型奇异度JD最大。
2)根据当前实时每个SGCMG的框架角，确定框架角运动方程的雅克比矩阵Jacob；同时根据当前实时每个SGCMG的框架角向量和步骤1)确定的n个SGCMG构型的标称框架角向量，确定框架角偏离标称的偏差Δδ；
3)根据步骤2)确定的所述雅克比矩阵Jacob及框架角偏离标称的偏差Δδ，确定SGCMG框架角速度
Figure PCTCN2020109919-appb-000001
将所述SGCMG框架角速度作为框架角速度指令。
所述步骤2)框架角运动方程的雅克比矩阵Jacob的确定方法，具体如下：
Jacob＝A cosδ-B sinδ，
Figure PCTCN2020109919-appb-000002
其中，δ i为第i个SGCMG的框架角，i∈[1，n]，所述n个SGCMG以任意 规律由1～n编号处理；A、B为与n个SGCMG框架轴安装指向相关的3×n维系数矩阵，A矩阵的第i列对应第i个SGCMG的框架角为90°时，第i个SGCMG高速转子的角动量方向的三轴分量，B矩阵的第i列对应第i个SGCMG框架角为0°时，第i个高速转子的角动量方向的三轴分量。
本发明与现有技术相比的有益效果在于：
1)本发明提出的方法充分利用已有执行机构配置，基于多目标优化技术得到了一种CMG系统的新型操纵律，解决了系统无法通过常用的框架重构策略实现控制中的奇异规避及逃离，使得卫星失去姿态机动能力的问题；
2)本发明方法基于构建考虑框架角偏离标称的距离、框架角指令幅值及力矩输出偏差的多目标优化代价函数，通过最优化方法得到多目标的CMG操纵律，调和了CMG框架奇异规避与姿态控制力矩之间的矛盾，确保沿任意姿态机动均能实现高性能姿态控制。
附图说明
图1为本发明方法流程图；
图2为卫星三轴姿态角和角速度曲线；
图3为SGCMG低速框架角速度指令曲线。
具体实施方式
单框架控制力矩陀螺群即SGCMG群，SGCMG群系统配置已成为国际上高性能姿态机动航天器的一大趋势。长期在轨姿态快速机动可能存在姿态机动后框架构型临近或陷于奇异状态，导致系统失稳的风险。鉴于航天器三轴姿态机动控制与奇异规避双重需求，本发明一种适合非冗余SGCMG群的操纵方法，创造性地构造了考虑框架角偏离标称的距离、框架角指令幅值及力矩输出偏差的多目标优化代价函数，基于多目标优化技术得到了一种新型CMG系统的新型操纵律。该方法实现了姿态机动中奇异规避及机动后框架标称位置的返回，调和了CMG框架奇异规避与姿态控制力矩之间的矛盾，确保沿任意姿态机动的高性能实现，大大提高了CMG系统的姿态稳定和姿态机动能力。该算法的 有效性通过了数学仿真验证。
本发明方法步骤如下：
Step1：根据SGCMG群的合成角动量为零、SGCMG群构型奇异度较大、SGCMG在各个方向力矩输出能力相当等因素确定各种不同组合的SGCMG群的标称框架角向量；
Step2：采集当前实时每个SGCMG的框架角向量为δ，计算框架角运动方程的雅克比矩阵Jacob及框架角偏离标称的偏差Δδ＝δ 0-δ；
Step4：构造考虑框架角偏离标称的距离、框架角指令幅值及力矩输出偏差的综合多目标优化代价函数，通过极小化代价函数计算SGCMG框架角速度指令
Figure PCTCN2020109919-appb-000003
进行姿态控制。具体步骤为首先当周期姿态机动情况、奇异度情况实时调整奇异点规避参数α 1、α 2，再根据雅克比矩阵、控制力矩指令τ r，计算各个CMG框架角速度指令
Figure PCTCN2020109919-appb-000004
进行姿态控制。
切换新的SGCMG组合后，需要根据新的SGCMG组合的角动量包络调整姿态机动的角速度和角加速度以及相关控制器参数。
如图1所示，本发明一种适合非冗余SGCMG群的操纵方法，包括步骤如下：
1)将n个SGCMG以任意规律由1～n编号处理，根据n个SGCMG的构型及合成角动量，确定n个SGCMG构型的标称框架角向量δ 0＝[δ 01 ...δ 0i... δ 0n] T，其中，δ 0i为第i个SGCMG的标称框架角，i∈[1,n]；n为正整数，且n≥3；
所述n个SGCMG构型的标称框架角向量满足使n个SGCMG的合成角动量H为零且n个SGCMG构型奇异度JD最大。
即H＝h(A sinδ 0+B cosδ 0)E＝[0 0 0] T，且JD＝det(Jacob·Jacob T)取最大值，其中，Jacob＝A cosδ 0-B sinδ 0，h为SGCMG的角动量，卫星安装有n个SGCMG，每个SGCMG的角动量相同，H为n个SGCMG的合成角动量，A、B为与SGCMG框架轴安装指向相关的系数矩阵，A矩阵的第i列对应第i个SGCMG 的框架角为90°时，第i个SGCMG高速转子的角动量方向的三轴分量，B矩阵的第i列对应第i个SGCMG框架角为0°时，第i个高速转子的角动量方向的三轴分量；E为n维单位矢量，E＝[1 1 ... 1] T，JD为构型的奇异度，det为求行列式。sinδ 0、cosδ 0分别为第i个SGCMG标称框架角对应的正、余弦对角阵，具体如下：
Figure PCTCN2020109919-appb-000005
2)根据当前实时每个SGCMG的框架角δ i，i∈[1，n]，n个SGCMG，分别对应δ 1 δ 2 ... δ n，确定框架角运动方程的雅克比矩阵Jacob；同时根据当前实时每个SGCMG的框架角向量和步骤1)确定的n个SGCMG构型的标称框架角向量，确定框架角偏离标称的偏差Δδ；
所述框架角运动方程的雅克比矩阵Jacob的确定方法，具体如下：
Jacob＝A cosδ-B sinδ，
Figure PCTCN2020109919-appb-000006
其中，sinδ为框架角对应的正弦对角阵，cosδ为框架角对应的余弦对角阵，sinδ矩阵对角线上的元素为第i个SGCMG框架角δ i的正弦值，cosδ矩阵对角线上的元素为第i个SGCMG框架角δ i的余弦值。δ i为第i个SGCMG的框架角，i∈[1，n]。A、B为与n个SGCMG框架轴安装指向相关的3×n维系数矩阵，A矩阵的第i列对应第i个SGCMG的框架角为90°时，第i个SGCMG高速转子的角动量方向，B矩阵的第i列对应第i个SGCMG框架角为0°时，第i个高速转子的角动量方向；
所述框架角偏离标称的偏差Δδ的确定方法，具体为：
Δδ＝δ 0-δ，
δ 0＝[δ 01 ...δ 0i... δ 0n] T，δ＝[δ 1 ...δ i... δ n] T，
其中，δ 0i为第i个SGCMG的标称框架角。δ 0为n个SGCMG构型的标称框架角向量。
3)基于构建考虑框架角偏离标称的距离、框架角指令幅值及力矩输出偏差的多目标优化代价函数，通过最优化方法得到综合上述目标的SGCMG操纵律，根据姿态控制得到的力矩指令τ r和步骤2)确定的所述雅克比矩阵Jacob及框架角偏离标称的偏差，由下式多目标优化操纵律确定SGCMG框架角速度
Figure PCTCN2020109919-appb-000007
将所述SGCMG框架角速度作为框架角速度指令，控制SGCMG低速框架轴按照所述框架角速度指令转动，控制卫星姿态。
所述步骤3)确定SGCMG框架角速度
Figure PCTCN2020109919-appb-000008
的方法，具体为：
Figure PCTCN2020109919-appb-000009
δ r＝α 1((α 1+α 2)I+Jacob T·Jacob)-1·Δδ+δ-T s((α 1+α 2)I+Jacob T·Jacob) -1·Jacob T·τ r/h，
其中，δ r为框架角指令，T s为SGCMG的采样周期，h为SGCMG的角动量，I为n维的单位阵，α 1、α 2为设计的奇异点规避参数，α 1≥0，且α 2≥0，并可根据当周期姿态机动情况、奇异度情况实时调整。
实施例1：对于安装3个高精度星敏感器、6个高精度陀螺、6个五棱锥安装的CMG群的卫星，记各CMG标号为CMG1、CMG2、CMG3、CMG4、CMG5、CMG6。一种SGCMG系统的多目标优化操纵律，按照如图1的方法流程图，具体实施如下：
1)卫星初始运行时所有CMG均正常工作，该组合情况下选取标称框架角δ CMG0＝[88.03；-92.32；-92.41；60.740591；-116.144；-145.265]，使得该构型情况下三轴合成角动量H为零，奇异度JD＝7.299，CMG在各个方向力矩输出能力相当。
2)卫星运行至2000秒时，CMG1、CMG2、CMG5发生故障，仅为其余 3台非冗余CMG工作，该组合情况下选取标称框架角δ CMG0＝[0；0；242.2276997；297.7723；0；270]，使得该构型情况下三轴合成角动量H为零，奇异度JD＝0.72最大，CMG在各个方向力矩输出能力相当。
3)卫星运行至5000秒时，注入滚动轴机动30度。此时根据CMG3、CMG4、CMG6实时测量的框架角和多目标优化技术，选取奇异点规避参数α 1、α 2，同时根据卫星三轴姿态角和角速度控制误差进行控制力矩指令计算，进而计算各个CMG框架角速度指令，进行姿态机动和姿态控制，如图3为计算的各个CMG框架角速度指令曲线，如图2为卫星三轴姿态角和角速度曲线，姿态机动和姿态控制正常。
本发明说明书中未作详细描述的内容属本领域技术人员的公知技术。

Claims (5)

  1. 一种适合非冗余SGCMG群的操纵方法，卫星安装有n个SGCMG，每个SGCMG的角动量相同，n为正整数，且n≥3，其特征在于，包括步骤如下：
    1)根据n个SGCMG的构型及合成角动量，确定n个SGCMG构型的标称框架角向量；
    2)根据当前实时每个SGCMG的框架角，确定框架角运动方程的雅克比矩阵Jacob；同时根据当前实时每个SGCMG的框架角向量和步骤1)确定的n个SGCMG构型的标称框架角向量，确定框架角偏离标称的偏差Δδ；
    3)根据步骤2)确定的所述雅克比矩阵Jacob及框架角偏离标称的偏差Δδ，确定SGCMG框架角速度
    Figure PCTCN2020109919-appb-100001
    将所述SGCMG框架角速度作为框架角速度指令。
  2. 根据权利要求1所述的一种适合非冗余SGCMG群的操纵方法，其特征在于，步骤1)所述n个SGCMG构型的标称框架角向量满足使n个SGCMG的合成角动量H为零且n个SGCMG构型奇异度JD最大。
  3. 根据权利要求1或2之一所述的一种适合非冗余SGCMG群的操纵方法，其特征在于，所述步骤2)框架角运动方程的雅克比矩阵Jacob的确定方法，具体如下：
    Jacob＝A cosδ-B sinδ，
    Figure PCTCN2020109919-appb-100002
    其中，δ i为第i个SGCMG的框架角，i∈[1，n]，所述n个SGCMG以任意规律由1～n编号处理；A、B为与n个SGCMG框架轴安装指向相关的3×n维系数矩阵，A矩阵的第i列对应第i个SGCMG的框架角为90°时，第i个SGCMG高速转子的角动量方向的三轴分量，B矩阵的第i列对应第i个 SGCMG框架角为0°时，第i个高速转子的角动量方向的三轴分量。
  4. 根据权利要求3所述的一种适合非冗余SGCMG群的操纵方法，其特征在于，所述步骤2)框架角偏离标称的偏差Δδ的确定方法，具体为：
    Δδ＝δ 0-δ，
    δ 0＝[δ 01 ...δ 0i... δ 0n] T，δ＝[δ 1 ...δ i... δ n] T，
    其中，δ 0为n个SGCMG构型的标称框架角向量，δ 0i为第i个SGCMG的标称框架角。
  5. 根据权利要求4所述的一种适合非冗余SGCMG群的操纵方法，其特征在于，所述步骤3)确定SGCMG框架角速度
    Figure PCTCN2020109919-appb-100003
    的方法，具体为：
    Figure PCTCN2020109919-appb-100004
    δ r＝α 1((α 1+α 2)I+Jacob T·Jacob) -1·Δδ+δ-T s((α 1+α 2)I+Jacob T·Jacob) -1·Jacob T·τ r/h，
    其中，T s为SGCMG的采样周期，h为SGCMG的角动量，I为n维的单位阵，α 1≥0，且α 2≥0，α 1、α 2为设计的奇异点规避参数；δ r为SGCMG框架角指令，τ r为控制力矩指令。
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