CN102566578B

CN102566578B - Singular value decomposition-based coordination control method of single gimbal control moment gyros (SGCMGs)

Info

Publication number: CN102566578B
Application number: CN 201210009458
Authority: CN
Inventors: 金磊; 桂海潮; 徐世杰
Original assignee: Beihang University
Current assignee: Beihang University
Priority date: 2012-01-12
Filing date: 2012-01-12
Publication date: 2013-06-19
Anticipated expiration: 2032-01-12
Also published as: CN102566578A

Abstract

The invention relates to a singular value decomposition-based coordination control method of single gimbal control moment gyros (SGCMGs). The singular value decomposition-based coordination control method comprises the following steps of: distributing instruction moment required for controlling an entire spacecraft to two sets of SGCMGs according to a certain proportion; decomposing the instruction moment distributed to the set A of SGCMGs again by using a singular value decomposition method; distributing an instruction moment component in the singular direction of the set A of SGCMGs to the set B of SGCMGs; still distributing an instruction moment component perpendicular to the singular direction of the set A of SGCMGs to the set A of SGCMGs; after distribution, solving instruction gimbal angular velocities of the two sets of SGCMGs respectively; operating according to the respective instruction gimbal angular velocity; and acting the sum of output moment on the spacecraft to finish accurate attitude control. According to the singular value decomposition-based coordination control method, the gyros can still accurately and effectively output control moment to control the attitude of the spacecraft while a part of gyros fails and the gyros are singular and the probability of premature saturation of a single set of SGCMGs is also avoided to the greatest extent without configuring an extra execution mechanism.

Description

Single frame control moment gyroscope group coordinated control method based on singular value decomposition

技术领域 technical field

本发明涉及一种航天器的姿态控制方法，具体涉及一种单框架控制力矩陀螺群的控制方法。The invention relates to an attitude control method of a spacecraft, in particular to a control method of a single-frame control moment gyroscope group.

背景技术 Background technique

随着航天事业的发展，现代航天器对姿态控制系统的精度、寿命以及可靠性的要求越来越高。航天器在轨姿态控制主要是通过执行机构输出控制力矩来实现。With the development of the aerospace industry, modern spacecraft have higher and higher requirements for the accuracy, life and reliability of the attitude control system. The on-orbit attitude control of the spacecraft is mainly realized through the output control torque of the actuator.

目前航天器采用的姿态控制执行机构主要有喷气推力器、角动量交换装置、磁力矩器等。其中角动量交换装置具有能够提供连续姿态控制力矩、不消耗燃料、不污染光学设备和飞行环境、不易激发航天器挠性附件的振动等优点，因而作为航天器姿态控制系统的主执行机构而广泛应用于高精度、长寿命的航天器。At present, the attitude control actuators used by spacecraft mainly include jet thrusters, angular momentum exchange devices, and magnetic torque devices. Among them, the angular momentum exchange device has the advantages of being able to provide continuous attitude control torque, not consuming fuel, not polluting optical equipment and the flight environment, and not easily exciting the vibration of the spacecraft's flexible accessories, so it is widely used as the main actuator of the spacecraft attitude control system. Applied to high-precision, long-life spacecraft.

角动量交换装置的工作原理建立在角动量守恒的基础上，当其角动量的大小或者方向按一定规律变化时，将产生连续的反作用力矩作用在航天器本体上，从而达到控制航天器姿态的目的。在各类角动量交换装置中，单框架控制力矩陀螺群(Single Gimbal Control Moment Gyros，SGCMGs)不仅能输出大幅值控制力矩，还具有结构简单、可靠性高、系统响应快、控制更精确等优点，已成为工程实际中大型长寿命航天器的首选姿态控制执行机构，如美国的大型太空望远镜(LST)以及前苏联发射的和平号空间站(MIR)都采用了SGCMGs作为姿态控制主执行机构。中国关于CMGs的研究起步较晚，北京控制工程研究所于1999年开始研制机械轴承SGCMGs，并首次成功应用于2011年9月发射的天宫一号目标飞行器。The working principle of the angular momentum exchange device is based on the conservation of angular momentum. When the magnitude or direction of its angular momentum changes according to a certain law, it will generate continuous reaction torque to act on the spacecraft body, so as to achieve the purpose of controlling the attitude of the spacecraft. . Among all kinds of angular momentum exchange devices, Single Gimbal Control Moment Gyros (SGCMGs) can not only output large-scale control torque, but also have the advantages of simple structure, high reliability, fast system response, and more precise control. , has become the preferred attitude control actuator for large and long-lived spacecraft in engineering practice. For example, the Large Space Telescope (LST) in the United States and the Mir space station (MIR) launched by the former Soviet Union have adopted SGCMGs as the main attitude control actuator. China's research on CMGs started relatively late. The Beijing Institute of Control Engineering began to develop mechanical bearing SGCMGs in 1999, and was successfully applied to the Tiangong-1 target aircraft launched in September 2011 for the first time.

在运用SGCMGs对航天器进行姿态控制时，需要首先设计SGCMGs的操纵律，由指令控制力矩确定陀螺框架角速度，使陀螺输出力矩与航天器姿态控制系统要求的指令力矩一致。然而，SGCMGs固有的构型奇异问题却给操纵律设计带来了很大困难。SGCMGs的构型奇异是指当处于某些框架角组合时，各陀螺的输出力矩矢量共面，而使得在垂直于该平面的方向即奇异方向上无法提供要求的力矩，特别是当SGCMGs中有部分陀螺失效时，对应于奇异的框架角组合的数量会急剧增多，使得奇异问题更加严重。虽然许多学者对此进行了大量研究，但所设计的操纵律仍存在一些问题，如零运动操纵律无法避免显奇异点，且在SGCMGs构型接近奇异时，框架角速度解过大甚至无解；鲁棒伪逆和广义鲁棒伪逆操纵律都会引入力矩误差，使姿态控制精度下降。When using SGCMGs to control the attitude of the spacecraft, it is necessary to design the control law of the SGCMGs first, and determine the angular velocity of the gyro frame by the command control torque, so that the gyro output torque is consistent with the command torque required by the spacecraft attitude control system. However, the inherent singularity of SGCMGs brings great difficulties to the design of steering laws. The singular configuration of SGCMGs means that when they are in certain frame angle combinations, the output torque vectors of each gyroscope are coplanar, so that the required torque cannot be provided in the direction perpendicular to the plane, that is, the singular direction, especially when there are When some gyroscopes fail, the number of frame angle combinations corresponding to singularity will increase sharply, making the singularity problem more serious. Although many scholars have done a lot of research on this, there are still some problems in the designed steering law, such as the zero-motion steering law cannot avoid the apparent singularity, and when the configuration of SGCMGs is close to singularity, the frame angular velocity solution is too large or even has no solution; Both robust pseudo-inverse and generalized robust pseudo-inverse maneuvering laws will introduce torque errors, which will reduce the accuracy of attitude control.

另一方面，目前世界上已有的大型组合体航天器大都采用多舱段的结构，其姿态控制执行机构至少包含有两套五棱锥构型SGCMGs，分别安装于核心舱和对接的应用舱之一。传统的控制方案中，核心舱SGCMGs通常用于单独核心舱以及对接后整个组合体的姿态控制，而应用舱SGCMGs仅用于对接前应用舱的姿态控制。这种方案最大的问题在于，当仅利用核心舱SGCMGs进行组合体控制时，若部分陀螺发生故障，则现有操纵律无法保证SGCMGs能同时实现奇异的完全避免和力矩的精确输出。On the other hand, most of the existing large-scale combined spacecraft in the world currently adopt a multi-chamber structure, and its attitude control actuators include at least two sets of SGCMGs in a pentagonal pyramid configuration, which are respectively installed between the core module and the docking application module. one. In the traditional control scheme, the core module SGCMGs are usually used for the attitude control of the core module and the whole assembly after docking, while the application module SGCMGs are only used for the attitude control of the application module before docking. The biggest problem with this scheme is that when only the SGCMGs in the core cabin are used to control the assembly, if part of the gyro fails, the existing control law cannot guarantee that the SGCMGs can achieve both complete singularity avoidance and precise torque output.

本发明正是针对这一难点问题，提出一种应用于SGCMGs的基于奇异值分解的协调控制方法，旨在为国内现今的和将来的大型航天器姿态控制任务提供技术支持。The present invention just aims at this difficult problem, and proposes a coordinated control method based on singular value decomposition applied to SGCMGs, aiming at providing technical support for domestic current and future large-scale spacecraft attitude control tasks.

发明内容 Contents of the invention

本发明的目的是针对具有两套五棱锥构型SGCMGs控制的航天器，提出一种SGCMGs协调控制方法，保证在部分陀螺失效时和陀螺奇异时，仍能使陀螺精确有效地输出控制力矩以控制航天器的姿态。The purpose of the present invention is to propose a SGCMGs coordinated control method for a spacecraft controlled by two sets of pentagonal pyramid configuration SGCMGs, to ensure that the gyroscope can still output control torque accurately and effectively to control the attitude of the spacecraft.

本发明提供了一种基于奇异值分解的单框架控制力矩陀螺群协调控制方法，在航天器具有两套五棱锥构型SGCMGs，并且其中A套的部分陀螺(包括1、2或3个)失效，B套正常工作的情况下，可以适用本发明的方法。The present invention provides a single-frame control moment gyroscope group coordinated control method based on singular value decomposition. The spacecraft has two sets of pentagonal pyramid configuration SGCMGs, and wherein part of the gyroscopes (including 1, 2 or 3) of the A set fail , under the condition that the B set works normally, the method of the present invention can be applied.

本发明的方法包括以下步骤：Method of the present invention comprises the following steps:

步骤一、将控制整个航天器所需的指令力矩按一定比例分配给两套SGCMGs；Step 1. Distribute the command torque required to control the entire spacecraft to the two sets of SGCMGs in a certain proportion;

步骤二、利用奇异值分解的方法对分配给A套SGCMGs的指令力矩进行再次分解，将其中沿A套SGCMGs奇异方向的指令力矩分量分配给B套SGCMGs，而垂直于A套SGCMGs奇异方向的指令力矩分量仍分配给A套SGCMGs；Step 2: Use the method of singular value decomposition to decompose the command torque assigned to the SGCMGs of the set A again, assign the command torque component along the singular direction of the SGCMGs of the set A to the SGCMGs of the set B, and the command torque component perpendicular to the singular direction of the SGCMGs of the set A The moment component is still assigned to the A set of SGCMGs;

步骤三、分配完成后，A套SGCMGs利用伪逆操纵律求解出其指令框架角速度，B套SGCMGs利用伪逆加零运动操纵律求解出其指令框架角速度；Step 3: After the allocation is completed, the A set of SGCMGs uses the pseudo-inverse manipulation law to obtain the command frame angular velocity, and the B set of SGCMGs uses the pseudo-inverse plus zero motion manipulation law to solve the command frame angular velocity;

步骤四、两套SGCMGs分别按各自的指令框架角速度运转，输出力矩之和作用于航天器，完成精确的姿态控制。Step 4. The two sets of SGCMGs operate according to their respective command frame angular velocities, and the sum of the output torque acts on the spacecraft to complete precise attitude control.

有益效果Beneficial effect

在无需配置额外执行机构的情况下，本发明方法充分利用两套SGCMGs的控制能力，通过两套SGCMGs的协调控制，很好的解决了单独利用一套SGCMGs进行航天器姿态控制时无法解决的问题，保证在部分陀螺失效时和陀螺奇异时，仍能使陀螺精确有效地输出控制力矩以控制航天器的姿态，还在最大程度上避免了单套SGCMGs过早饱和的可能性。The method of the present invention makes full use of the control capabilities of the two sets of SGCMGs without the need to configure additional actuators, and through the coordinated control of the two sets of SGCMGs, it solves the problem that cannot be solved when a single set of SGCMGs is used for spacecraft attitude control , to ensure that when part of the gyro fails or when the gyro is singular, the gyro can still output the control torque accurately and effectively to control the attitude of the spacecraft, and also avoids the possibility of premature saturation of a single set of SGCMGs to the greatest extent.

附图说明 Description of drawings

图1为单框架控制力矩陀螺(SGCMG)的结构示意图。Figure 1 is a schematic diagram of the structure of a single frame control moment gyroscope (SGCMG).

图2为两套SGCMGs的构型示意图。Figure 2 is a schematic diagram of the configuration of two sets of SGCMGs.

图3为基于奇异值分解的两套SGCMGs协调控制方法原理图。Fig. 3 is a schematic diagram of two sets of SGCMGs coordinated control method based on singular value decomposition.

图4为基于两套SGCMGs的组合体航天器姿态控制系统。Figure 4 shows the combined spacecraft attitude control system based on two sets of SGCMGs.

图5为A套SGCMGs的奇异度量结果图。Fig. 5 is the graph of singularity measurement results of set A of SGCMGs.

图6为A套SGCMGs的实际框架角速度结果图。Fig. 6 is the actual frame angular velocity results of set A of SGCMGs.

图7为两套SGCMGs的实际输出力矩与指令控制力矩的误差结果图。Fig. 7 is the error result diagram of the actual output torque and command control torque of two sets of SGCMGs.

具体实施方式 Detailed ways

下面结合附图，详细说明本发明的优选实施方式。Preferred embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings.

为更清楚的介绍本实施例，首先简单说明SGCMG输出力矩的原理，再结合两套五棱锥构型的SGCMGs说明本方法的实施。需要强调的是，该方法只需要两套五棱锥构型的SGCMGs，而并不依赖于具体的安装方式。In order to introduce this embodiment more clearly, the principle of the SGCMG output torque is briefly described first, and then the implementation of the method is described in conjunction with two sets of SGCMGs of pentagonal pyramid configuration. It should be emphasized that this method only requires two sets of SGCMGs in pentagonal pyramid configuration, and does not depend on the specific installation method.

参见图1，SGCMG由一个恒速转动的转子和支撑转子的框架组成，

为转子自旋轴方向，

为框架轴转速方向，

与输出控制力矩方向相反。转子自旋轴与框架轴正交安装，分别由转子电机和框架电机驱动。转子电机驱动转子绕自旋轴恒速旋转，产生一个恒定角动量。框架电机根据控制指令使框架绕固连于航天器本体的框架轴以角速度

转过框架角δ。由于框架轴的转动，导致转子自旋轴方向改变，使转子的角动量发生改变，从而输出一个陀螺力矩。对于单个SGCMG，根据以上介绍的工作原理，可以得到其所输出的控制力矩为Referring to Figure 1, SGCMG consists of a rotor rotating at a constant speed and a frame supporting the rotor,

is the direction of the rotor spin axis,

is the rotational speed direction of the frame shaft,

It is opposite to the direction of the output control torque. The rotor spin axis is installed orthogonally to the frame axis, and is driven by the rotor motor and the frame motor respectively. The rotor motor drives the rotor to rotate at a constant speed around the spin axis, generating a constant angular momentum. The frame motor drives the frame at an angular velocity around the frame axis fixed to the spacecraft body according to the control command.

Turn frame angle δ. Due to the rotation of the frame shaft, the direction of the spin axis of the rotor changes, which changes the angular momentum of the rotor, thereby outputting a gyro torque. For a single SGCMG, according to the working principle introduced above, the output control torque can be obtained as

$\overset{&RightArrow; &Right Arrow;}{T T} = = - - ((\overset{\cdot \cdot}{δ δ} \overset{&RightArrow; &Right Arrow;}{g g})) \times \times (({h h}_{00} \overset{&RightArrow; &Right Arrow;}{s the s})) = = - - {h h}_{00} \overset{\cdot &Center Dot;}{δ δ} \overset{&RightArrow; &Right Arrow;}{t t} - - - - - - ((11))$

其中，

表示单个SGCMG输出的力矩矢量，h₀为陀螺转子的标称角动量。in,

Indicates the torque vector output by a single SGCMG, and _h0 is the nominal angular momentum of the gyro rotor.

单只SGCMG产生的陀螺力矩只在与其框架轴垂直的平面上，而为了对航天器进行三轴控制，一般需要不少于3只SGCMG组成陀螺群，通过不同框架角组合方式调整输出力矩的方向和大小。对于由多个陀螺构成的SGCMGs系统来讲，为使控制逻辑简单，陀螺群中的单个陀螺在质量，转子转速和转动惯量等参数方面取相同值，因此单只陀螺提供的角动量幅值h₀都相同。设陀螺群由n只陀螺组成，第i只陀螺的框架轴方向单位矢量为

转子角动量方向单位矢量为

陀螺输出力矩反方向单位矢量为

则陀螺群的总角动量可以表示为The gyro torque generated by a single SGCMG is only on the plane perpendicular to its frame axis, and in order to control the spacecraft in three axes, generally no less than 3 SGCMGs are required to form a gyro group, and the direction of the output torque is adjusted by combining different frame angles and size. For the SGCMGs system composed of multiple gyroscopes, in order to make the control logic simple, the individual gyroscopes in the gyroscope group take the same values in terms of mass, rotor speed and moment of inertia, so the angular momentum amplitude h provided by a single gyroscope is ₀ are the same. Assuming that the gyro group is composed of n gyroscopes, the unit vector of the frame axis direction of the i-th gyroscope is

The unit vector of rotor angular momentum direction is

The unit vector of the gyro output torque in the opposite direction is

Then the total angular momentum of the gyro group can be expressed as

${\overset{&RightArrow; &Right Arrow;}{h h}}_{c c} = = {h h}_{00} {Σ Σ}_{i i = = 11}^{n no} {\overset{&RightArrow; &Right Arrow;}{s the s}}_{i i} - - - - - - ((22))$

其中，

为系统的总角动量矢量，将其写成在航天器本体坐标系f_b(o_bx_by_bz_b)下的分量列阵形式为in,

is the total angular momentum vector of the system, and it is written as a component array in the spacecraft body coordinate system f _b (o _b x _b y _b z _b ) as

h_c＝A_sh₀ (3)h _c ＝A _s h ₀ (3)

其中，A_s＝[s₁ s₂ … s_n]，s_i为对应的第i个SGCMG的角动量方向单位矢量

在f_b中的分量列阵。Among them, A _s =[s ₁ s ₂ … s _n ], s _i is the angular momentum direction unit vector of the corresponding i-th SGCMG

Array of components in f _b .

同理，根据式(1)，可以得到陀螺群输出的总力矩矢量为Similarly, according to formula (1), the total torque vector output by the gyro group can be obtained as

${\overset{&RightArrow; &Right Arrow;}{T T}}_{c c} = = {- - h h}_{00} {Σ Σ}_{i i = = 11}^{n no} {\overset{\cdot &Center Dot;}{δ δ}}_{i i} \overset{&RightArrow; &Right Arrow;}{{t t}_{i i}} - - - - - - ((44))$

其中，

为n只陀螺产生的合成力矩矢量，

为第i只陀螺的框架角速度。将其写成在f_b(o_bx_by_bz_b)下的分量列阵形式为in,

is the resultant torque vector generated by n gyroscopes,

is the frame angular velocity of the i-th gyroscope. Write it as a component array form under f _b (o _b x _b y _b z _b ) as

${T T}_{c c} = = {- - h h}_{00} {A A}_{t t} \overset{\cdot \cdot}{δ δ} - - - - - - ((55))$

其中，A_t＝[t₁ t₂ … t_n]，t_i为对应的第i个SGCMG的输出力矩反方向单位矢量

在f_b中的分量列阵，

\overset{\cdot}{δ} = {[\begin{matrix} {\overset{\cdot}{δ}}_{1} & {\overset{\cdot}{δ}}_{2} & \cdot \cdot \cdot & {\overset{\cdot}{δ}}_{n} \end{matrix}]}^{T}

为框架角速度列向量。Among them, A _t =[t ₁ t ₂ … t _n ], t _i is the unit vector in the opposite direction of the output torque of the corresponding i-th SGCMG

array of components in f _b ,

\overset{\cdot}{δ} = {[\begin{matrix} {\overset{\cdot}{δ}}_{1} & {\overset{&Center Dot;}{δ}}_{2} & &Center Dot; &Center Dot; &Center Dot; & {\overset{&Center Dot;}{δ}}_{no} \end{matrix}]}^{T}

is the frame angular velocity column vector.

在式(3)和式(5)中，A_s和A_t为变量，随陀螺框架角δ变化，可写为In formulas (3) and (5), A _s and A _t are variables that vary with the gyro frame angle δ, which can be written as

A_s＝A_s0d[cosδ]+A_t0d[sinδ] (6)A _s ＝A _s0 d[cosδ]+A _t0 d[sinδ] (6)

A_t＝A_t0d[cosδ]-A_s0d[sinδ] (7)A _t ＝A _t0 d[cosδ]-A _s0 d[sinδ] (7)

式中，A_s0和A_t0分别为A_s和A_t的初始值，cosδ＝[cosδ₁ cosδ₂ ... cosδ_n]^T，sinδ＝[sinδ₁ sinδ₂ ... sinδ_n]^T。对任意n维向量x＝[x₁ x₂ … x_n]^T，算子d[x]定义为如下对角阵In the formula, A _s0 and A _t0 are the initial values of A _s and A _t respectively, cosδ=[cosδ ₁ cosδ ₂ ... cosδ _n ] ^T , sinδ=[sinδ ₁ sinδ ₂ ... sinδ _n ] ^T . For any n-dimensional vector x=[x ₁ x ₂ … x _n ] ^T , the operator d[x] is defined as the following diagonal matrix

d[x]＝diag(x₁ x₂ … x_n) (8)d[x]=diag(x ₁ x ₂ … x _n ) (8)

以上分别得到了n个陀螺组成的SGCMGs的角动量方程(3)和力矩方程(5)。The angular momentum equation (3) and moment equation (5) of the SGCMGs composed of n gyroscopes are respectively obtained above.

参见图2，五棱锥构型由6只SGCMG组成，它们被分别安装在正十二面体相邻的6个侧面上，任意相邻两面的夹角为116.51°，各陀螺的框架轴对称分布，分别垂直于其所在侧面。考虑有A和B两套五棱锥构型的SGCMGs安装在航天器中，假设A套SGCMGs中有部分陀螺失效，剩余正常工作的陀螺的个数为n(3≤n≤6)，而B套SGCMGs则完全正常工作，航天器本体坐标系仍然记为f_b(o_bx_by_bz_b)。下面即是本发明的具体实施步骤。Referring to Figure 2, the pentagonal pyramid configuration is composed of 6 SGCMGs, which are respectively installed on the 6 adjacent sides of the dodecahedron. The angle between any two adjacent sides is 116.51°, and the frames of the gyroscopes are symmetrically distributed. respectively perpendicular to its side. Consider two sets of SGCMGs with a pentagonal pyramid configuration, A and B, installed in the spacecraft, assuming that some gyros in the A set of SGCMGs fail, and the number of remaining normal working gyros is n (3≤n≤6), while the B set SGCMGs are fully functional, and the spacecraft body coordinate system is still recorded as f _b (o _b x _by y _b z _b ). The following is the specific implementation steps of the present invention.

第一步：将控制整个航天器所需的指令力矩按一定比例分配给两套SGCMGs。优选的方案是，依据两套SGCMGs的最小包络角动量大小进行力矩分配。假设从所设计的姿态控制器得到的总指令控制力矩为T_c，从避免两只陀螺饱和的角度出发，可以首先依据两套SGCMGs的最小包络角动量大小对总指令控制力矩进行分配，其中，分配给A套失效SGCMGs的指令控制力矩为T_ca，表示为Step 1: Distribute the command torque required to control the entire spacecraft to the two sets of SGCMGs in a certain proportion. The preferred solution is to distribute the moment according to the minimum envelope angular momentum of the two sets of SGCMGs. Assuming that the total command control torque obtained from the designed attitude controller is T _c , from the perspective of avoiding the saturation of the two gyroscopes, the total command control torque can be distributed according to the minimum envelope angular momentum of the two sets of SGCMGs, where , the commanded control torque assigned to the failed SGCMGs of A set is T _ca , expressed as

${T T}_{ca ca} = = \frac{{h h}_{an an}}{{h h}_{an an} + + 4.4719 4.4719} {T T}_{c c} - - - - - - ((99))$

分配给B套SGCMGs的指令控制力矩为T_cb，表示为The command control torque assigned to set B of SGCMGs is T _cb , expressed as

${T T}_{cb cb} = = \frac{4.4719 4.4719}{{h h}_{an an} + + 4.4719 4.4719} {T T}_{c c} - - - - - - ((1010))$

其中，h_an等于A套正常工作的n(3≤n≤6)个SGCMGs的包络的最小角动量，可以利用数值方法从公式(3)中计算出来(参考：章仁为，《卫星轨道姿态动力学与控制》，北京航空航天大学出版社，281-285)。Among them, h _an is equal to the minimum angular momentum of the envelope of n (3≤n≤6) SGCMGs working normally in A set, which can be calculated from formula (3) by numerical method (reference: Zhang Renwei, "Satellite Orbit Attitude Dynamics and Control", Beihang University Press, 281-285).

第二步，基于奇异值分解理论的力矩再分配。利用奇异值分解的理论对T_ca进行再次分配，分别得到垂直于A套SGCMGs奇异方向的力矩分量T_ca1和沿A套SGCMGs奇异方向的力矩分量T_ca2。为详细说明本实施例的实施过程，下面将详细说明如何得到T_ca1和T_ca2的表达式。The second step is the moment redistribution based on the singular value decomposition theory. The theory of singular value decomposition is used to redistribute T _ca , and the moment component T _ca1 perpendicular to the singular direction of A set of SGCMGs and the moment component T _ca2 along the singular direction of A set of SGCMGs are respectively obtained. In order to describe the implementation process of this embodiment in detail, how to obtain the expressions of T _ca1 and T _ca2 will be described in detail below.

参见图3，

为A套SGCMGs的奇异方向的单位矢量，令(i＝1，2，...，n)(3≤n≤6)表示奇异时刻A套SGCMGs中剩余的n个正常陀螺的输出力矩反方向单位矢量。为了对

再次分配，确定奇异方向是关键。对失效SGCMGs的输出力矩系数矩阵C_a进行奇异值分解，得到See Figure 3,

is the unit vector of the singular direction of A set of SGCMGs, let (i=1,2,...,n)(3≤n≤6) represents the unit vector in the opposite direction of output torque of the remaining n normal gyroscopes in set A of SGCMGs at the singular moment. for the sake of

Assignment again, determining the singular direction is the key. Singular value decomposition is performed on the output moment coefficient matrix C _a of the failed SGCMGs to obtain

C_a＝h₀A_at＝USV^T (11)C _a =h ₀ A _at =USV ^T (11)

式中，A_at＝A_at0d[cosδ_a]-A_as0d[sinδ_a]，U∈R^3×3，V∈R^n×n，为酉矩阵。S∈R^3×n可写为如下形式In the formula, A _at ＝A _at0 d[cosδ _a ]-A _as0 d[sinδ _a ], U∈R ^3×3 , V∈R ^n×n are unitary matrices. S∈R ^3×n can be written as the following form

S＝[S₁ 0_3×(n-3)] (12)S＝[S ₁ 0 _3×(n-3) ] (12)

式中In the formula

S₁＝diag(σ₁ σ₂ σ₃) (13)S ₁ =diag(σ ₁ σ ₂ σ ₃ ) (13)

其中σ₁、σ₂和σ₃为C_a的奇异值，且满足σ₁≥σ₂≥σ₃。V也可写为Among them, σ ₁ , σ ₂ and σ ₃ are singular values of C _a , and satisfy σ ₁ ≥σ ₂ ≥σ ₃ . V can also be written as

V＝[V₁ V₂] (14)V＝[V ₁ V ₂ ] (14)

式中V₁∈R^n×3，V₂∈R^n×(n-3)。U和V₁可由其列向量表示为U＝[U₁ U₂ U₃]，V₁＝[V₁₁ V₁₂ V₁₃]，则针对失效SGCMGs的输出力矩方程可写为In the formula, V ₁ ∈ R ^n×3 , V ₂ ∈ R ^n×(n-3) . U and V ₁ can be expressed by their column vectors as U=[U ₁ U ₂ U ₃ ], V ₁ =[V ₁₁ V ₁₂ V ₁₃ ], then the output torque equation for the failed SGCMGs can be written as

${C C}_{a a} {\overset{\cdot \cdot}{δ δ}}_{a a} = = {US US}_{11} {V V}_{11}^{T T} {\overset{\cdot \cdot}{δ δ}}_{a a} = = {Σ Σ}_{i i = = 11}^{33} {σ σ}_{i i} {U u}_{i i} {V V}_{11 i i}^{T T} {\overset{\cdot \cdot}{δ δ}}_{a a} = = - - {T T}_{ca ca 11} - - - - - - ((1515))$

式中T_ca1即为分配给失效SGCMGs的垂直于奇异方向的指令力矩。当SGCMGs完全陷入奇异时，σ₃＝0，可知此时U₃方向输出力矩为零，也说明U₃即为SGCMGs的奇异方向。而当SGCMGs接近奇异时，σ₃也接近于零，这时U₃也就接近奇异方向，可称为准奇异方向。一旦确定了奇异方向U₃，就可以将SGCMGs接近奇异时指令力矩在U₃上的部分分量以及SGCMGs完全奇异时指令力矩在U₃上的全部分量分配给B套SGCMGs，由B套SGCMGs输出，以避免失效的A套SGCMGs接近奇异时σ₃→0导致框架角速度解过大或无解的现象发生。where T _ca1 is the command torque perpendicular to the singular direction assigned to the failed SGCMGs. When the SGCMGs completely fall into the singularity, σ ₃ =0, it can be seen that the output torque in the U ₃ direction is zero at this time, which also shows that U ₃ is the singular direction of the SGCMGs. And when SGCMGs are close to singularity, σ ₃ is also close to zero, and U ₃ is also close to the singular direction, which can be called quasi-singular direction. Once the singular direction U ₃ is determined, the partial component of the command torque on U 3 when the SGCMGs are close to the singularity and all the components of the command torque on U ₃ when the SGCMGs are completely singular can be assigned to the B set of SGCMGs, and _output by the B set of SGCMGs, To avoid the phenomenon that the frame angular velocity solution is too large or has no solution when the failed A set of SGCMGs is close to singularity, σ ₃ →0.

令分配到B套SGCMGs的U₃方向上的指令力矩为Let the command torque assigned to the U ₃ direction of the B set of SGCMGs be

${T T}_{ca ca 22} = = \frac{α α}{{σ σ}_{33} + + α α} {U u}_{33} {U u}_{33}^{T T} {T T}_{ca ca} - - - - - - ((1616))$

式中In the formula

$α α = = \{\begin{matrix} 00 & {D D.}_{a a} &GreaterEqual; &Greater Equal; ϵ ϵ \\ k k {(({D D.}_{a a} - - ϵ ϵ))}^{22},, & ϵ ϵ > > {D D.}_{a a} &GreaterEqual; &Greater Equal; 00 \end{matrix} - - - - - - ((1717))$

其中D_a为失效SGCMGs的奇异度量，表示为where D _a is the singularity measure of the failed SGCMGs, expressed as

D_a＝det(A_atA_at ^T) (18)D _a =det(A _at A _at ^T ) (18)

ε为正的门限值，k为正的标量参数，两者可以根据实际情况选定。则失效SGCMGs的指令力矩为ε is a positive threshold value, and k is a positive scalar parameter, both of which can be selected according to the actual situation. Then the command torque of the failed SGCMGs is

T_ca1＝T_ca-T_ca2＝US_aU^TT_ca (19)T _ca1 =T _ca -T _ca2 =US _a U ^T T _ca (19)

其中in

${S S}_{a a} = = diag diag (\begin{matrix} 11 & 11 & \frac{{σ σ}_{33}}{{σ σ}_{33} + + α α} \end{matrix}) - - - - - - ((2020))$

由式(16)和(19)可知，当D_a≥ε，可认为A套SGCMGs远离奇异，α＝0，σ₃＞0，则S_a＝E₃，T_ca1＝T_ca，T_ca2＝0，三轴指令力矩T_ca完全分配给A套SGCMGs。而当D_a＜ε，A套SGCMGs逐渐接近奇异时，α增大，σ₃减小，则分配给B套SGCMGs的在奇异方向U₃上的指令力矩也不断增大，同时分配给A套SGCMGs的在奇异方向U₃上的指令力矩则不断减小。最终，当SGCMGs奇异时，σ₃＝0，

U₃上的指令力矩完全分配给B套SGCMGs，保证在奇异时执行机构仍能准确输出三轴指令力矩。From formulas (16) and (19), it can be seen that when D _a ≥ ε, it can be considered that the set of SGCMGs of A is far from singularity, α = 0, σ ₃ > 0, then S _a = E ₃ , T _ca1 = T _ca , T _ca2 = 0, the three-axis command torque T _ca is completely distributed to the A set of SGCMGs. And when D _a < ε, when the SGCMGs of set A are gradually approaching the singularity, α increases and σ ₃ decreases, the command torque in the singular direction U ₃ allocated to the SGCMGs of set B also increases continuously, and at the same time, the command torque allocated to set A The command moment of SGCMGs in the singular direction U ₃ decreases continuously. Finally, when SGCMGs are singular, σ ₃ =0,

The command torque on U ₃ is completely distributed to the B set of SGCMGs to ensure that the actuator can still output the three-axis command torque accurately when there is a singularity.

至此，完全得到了T_ca1和T_ca2的表达式如式(19)和(16)所示。So far, the expressions of T _ca1 and T _ca2 are completely obtained as shown in formulas (19) and (16).

第三步，确定最终分配到两套SGCMGs的力矩。经过两次力矩分配后，最后T_c中分配给A套SGCMGs的指令控制力矩分量T′_ca表示为In the third step, determine the moments that are finally assigned to the two sets of SGCMGs. After two torque distributions, the command control torque component T′ _ca distributed to the SGCMGs of A set in the final T _c is expressed as

${T T}_{ca ca}^{' '} = = {T T}_{ca ca 11} = = {US US}_{a a} {U u}^{T T} {T T}_{ca ca} = = \frac{{h h}_{an an}}{{h h}_{an an} + + 4.4719 4.4719} {US US}_{a a} {U u}^{T T} {T T}_{c c} - - - - - - ((21 twenty one))$

分配给B套SGCMGs的指令控制力矩分量T′_cb表示为The command control torque component T′ _cb assigned to set B of SGCMGs is expressed as

${T T}_{cb cb}^{' '} = = {T T}_{cb cb} + + {T T}_{ca ca 22} = = \frac{4.4719 4.4719}{{h h}_{an an} + + 4.4719 4.4719} {T T}_{c c} + + \frac{α α}{{σ σ}_{33} + + α α} \cdot \cdot \frac{{h h}_{an an}}{{h h}_{an an} + + 4.4179 4.4179} {U u}_{33} {U u}_{33}^{T T} {T T}_{c c} - - - - - - ((22 twenty two))$

第四步，两套SGCMGs的操纵律设计。对于A套SGCMGs，当其陷入奇异时，只需输出垂直于奇异方向的力矩，因此可以根据式(15)和(21)直接求框架角速度的伪逆解，得到The fourth step is to design the manipulation laws of the two sets of SGCMGs. For a set of SGCMGs, when it falls into a singularity, it only needs to output the moment perpendicular to the singularity direction, so the pseudo-inverse solution of the frame angular velocity can be obtained directly according to formulas (15) and (21), and we get

${\overset{\cdot \cdot}{δ δ}}_{ca ca} = = - - \frac{{h h}_{an an}}{{h h}_{an an} + + 4.4719 4.4719} {V V}_{11} {S S}_{11}^{- - 11} {S S}_{a a} {U u}^{T T} {T T}_{c c} - - - - - - ((23 twenty three))$

对于B套SGCMGs，由于其各个陀螺都正常工作，可以将其可控角动量体设置为以包络最小角动量为半径的球体，这样在此角动量体内仅有隐奇异点，就可以有效的使用零运动操纵律。即便当A套SGCMGs陷入奇异，利用零运动操纵律也能完全操纵B套SGCMGs躲避奇异点，并输出沿A套SGCMGs奇异方向的力矩。B套SGCMGs的零运动操纵律设计为For the B set of SGCMGs, since all the gyroscopes are working normally, the controllable angular momentum body can be set as a sphere whose radius is the minimum angular momentum of the envelope, so that there is only a hidden singularity in this angular momentum body, and the effective Use the zero-motion manipulation law. Even when the SGCMGs of the A set fall into the singularity, the SGCMGs of the B set can be completely manipulated to avoid the singularity point by using the zero-motion manipulation law, and the torque along the singular direction of the SGCMGs of the A set can be output. The zero-motion manipulation law of set B of SGCMGs is designed as

${\overset{\cdot \cdot}{δ δ}}_{cb cb} = = - - {A A}_{bt bt}^{T T} {(({A A}_{bt bt} {A A}_{bt bt}^{T T}))}^{- - 11} \frac{{T T}_{cb cb}^{' '}}{{h h}_{00}} + + β β (({I I}_{66 \times \times 66} - - {A A}_{bt bt}^{T T} {(({A A}_{bt bt} {A A}_{bt bt}^{T T}))}^{- - 11} {A A}_{bt bt})) \frac{{&PartialD; &PartialD; D D.}_{b b} (({δ δ}_{b b}))}{{&PartialD; &PartialD; δ δ}_{b b}} - - - - - - ((24 twenty four))$

式中，A_bt＝A_bt0d[cosδ_b]-A_bs0d[sinδ_b]，标量参数β选取如下，In the formula, A _bt ＝A _bt0 d[cosδ _b ]-A _bs0 d[sinδ _b ], the scalar parameter β is selected as follows,

$\{\begin{matrix} β β = = 00,, & {D D.}_{b b} > > 11 \\ β β = = 55,, & {D D.}_{b b} \leq \leq 0.5 0.5 \\ β β = = 2020 {(({D D.}_{b b} - - 11))}^{22},, & 0.5 0.5 < < {D D.}_{b b} \leq \leq 11 \end{matrix} - - - - - - ((2525))$

其中，D_b＝det(A_btA_bt ^T)为B套SGCMGs的奇异度量。此部分的具体理论可以参考相关文献(参考：章仁为，《卫星轨道姿态动力学与控制》，北京航空航天大学出版社，291-293)。Wherein, D _b =det(A _bt A _bt ^T ) is the singularity measure of the B set of SGCMGs. The specific theory of this part can refer to relevant literature (reference: Zhang Renwei, "Dynamics and Control of Satellite Orbital Attitude", Beijing University of Aeronautics and Astronautics Press, 291-293).

至此，已经完全得到了A套与B套SGCMGs各自的框架指令角速度

与

只需要以这两个指令角速度分别驱动A套与B套SGCMGs的框架轴转动就能够保证在部分陀螺失效时和陀螺奇异时，控制力矩得以精确有效地输出，进而控制航天器的姿态。So far, the frame command angular velocities of the sets A and B set SGCMGs have been completely obtained

and

It is only necessary to drive the frame shafts of the A set and the B set of SGCMGs to rotate at these two command angular velocities, which can ensure that the control torque can be output accurately and effectively when some gyros fail or when the gyro is singular, and then control the attitude of the spacecraft.

参见图4，本发明的方案在整个航天器控制回路中所处的位置为图中虚线框部分。图中，(1)为实际姿态角和角速度信息；(2)为估计姿态角和角速度信息；(3)为期望姿态角和角速度信息；(4)为指令控制力矩；(5)为分配给失效陀螺群的指令控制力矩；(6)为分配给正常工作陀螺群的指令控制力矩；(7)为(6)中垂直于失效陀螺群奇异方向的力矩分量；(8)为(5)沿失效陀螺群奇异方向的力矩分量；(9)为失效陀螺群的指令框架角速度；(10)为正常工作陀螺群的指令框架角速度；(11)为失效陀螺群的实际框架角速度；(12)为正常工作陀螺群的实际框架角速度；(13)为失效陀螺群的实际输出力矩；(14)为正常工作陀螺群的实际输出力矩；(15)为两套陀螺群总输出力矩；(16)为外干扰力矩。基于两套SGCMGs的航天器姿态控制系统由姿态敏感器、姿态控制器、执行机构(两套SGCMGs)和航天器本体一起构成闭环控制回路。姿态敏感器测量和确定航天器相对于空间某些已知基准目标的方位，再通过姿态确定算法对测得的信息进一步处理后确定航天器姿态。然后根据航天器期望的姿态信息以及姿态确定环节得到的姿态信息，选择合适的控制算法设计姿态控制器，从而得到控制航天器所需的指令控制力矩。接下来就是利用所提出的两套SGCMGs协调控制方案，操纵两套SGCMGs各个陀螺的框架按一定规律运动从而保证两套SGCMGs能按控制指令产生所需的控制力矩。最后，两套SGCMGs输出的总力矩作用于航天器本体，依据所建立的航天器姿态动力学方程即可得到航天器的姿态响应。由于两套SGCMGs能准确输出控制力矩，因此航天器将按照期望的姿态角和角速度运动规律进行转动。Referring to Fig. 4, the position of the scheme of the present invention in the whole spacecraft control loop is the dotted box part in the figure. In the figure, (1) is the actual attitude angle and angular velocity information; (2) is the estimated attitude angle and angular velocity information; (3) is the expected attitude angle and angular velocity information; (4) is the command control torque; The command control torque of the failed gyroscope group; (6) is the command control torque assigned to the normal working gyroscope group; (7) is the moment component perpendicular to the singular direction of the failed gyroscope group in (6); (8) is the The moment component in the singular direction of the failed gyroscope group; (9) is the command frame angular velocity of the failed gyroscope group; (10) is the command frame angular velocity of the normal working gyroscope group; (11) is the actual frame angular velocity of the failed gyroscope group; (12) is The actual frame angular velocity of the normal working gyroscope group; (13) is the actual output torque of the failed gyroscope group; (14) is the actual output torque of the normal working gyroscope group; (15) is the total output torque of the two sets of gyroscope groups; (16) is External disturbance torque. The spacecraft attitude control system based on two sets of SGCMGs consists of an attitude sensor, an attitude controller, an actuator (two sets of SGCMGs) and a spacecraft body to form a closed-loop control loop. The attitude sensor measures and determines the orientation of the spacecraft relative to some known reference targets in space, and then further processes the measured information through the attitude determination algorithm to determine the attitude of the spacecraft. Then, according to the expected attitude information of the spacecraft and the attitude information obtained in the attitude determination process, an appropriate control algorithm is selected to design an attitude controller, so as to obtain the command control torque required to control the spacecraft. The next step is to use the proposed two sets of SGCMGs coordinated control scheme to manipulate the frame of each gyroscope of the two sets of SGCMGs to move according to a certain law so as to ensure that the two sets of SGCMGs can generate the required control torque according to the control command. Finally, the total torque output by the two sets of SGCMGs acts on the spacecraft body, and the attitude response of the spacecraft can be obtained according to the established spacecraft attitude dynamic equation. Because the two sets of SGCMGs can accurately output the control torque, the spacecraft will rotate according to the desired attitude angle and angular velocity motion law.

下面结合某一个组合体航天器姿态控制仿真结果对本方案作具体的说明。The following is a specific description of this scheme in combination with the simulation results of the attitude control of a certain assembly spacecraft.

参见图2，假定空间站组合体中的核心舱与应用舱之一都各安装有一套五棱锥构型SGCMGs。图中，o_bx_by_bz_b为核心舱本体坐标系，原点o_b取在核心舱模块的质心，x_b、y_b和z_b固连于核心舱上，

和

分别为安装于核心舱的A套SGCMGs的1-6陀螺的框架轴方向单位矢量，

和

分别为A套SGCMGs的1-6陀螺的转子轴方向单位矢量。

和

分别为安装于应用舱的B套SGCMGs的1-6陀螺的框架轴方向单位矢量，

和

分别为B套SGCMGs的1-6陀螺的转子轴方向单位矢量。两套SGCMGs相对于核心舱本体坐标系的安装方位如图2，A套SGCMGs中第一个陀螺的框架轴沿着

在

与

组成平面的投影与

方向一致，B套SGCMGs中第一个陀螺的框架轴

沿着

在

与

组成平面的投影与

方向一致。选择这种安装方位的原因在于当两套SGCMGs都正常工作或者有部分陀螺失效时，这种安装方位都能保证陀螺群具有较好的包络和奇异性能指标。两套SGCMGs的各陀螺初始时刻转子角动量方向单位矢量和输出力矩反方向单位矢量在核心舱本体系下的分量列阵为Referring to Fig. 2, it is assumed that one of the core module and the application module in the space station assembly is equipped with a set of SGCMGs in a pentagonal pyramid configuration. In the figure, o _b x _b y _b z _b is the body coordinate system of the core cabin, the origin o _b is taken at the center of mass of the core cabin module, x _b , y _b and z _b are fixedly connected to the core cabin,

and

are the frame axis direction unit vectors of the 1-6 gyroscopes of set A SGCMGs installed in the core cabin,

and

are the unit vectors in the direction of the rotor axis of the 1-6 gyroscopes of the A set of SGCMGs, respectively.

and

are the frame axis unit vectors of the 1-6 gyroscopes of the B set of SGCMGs installed in the application cabin,

and

are the unit vectors in the direction of the rotor axis of the 1-6 gyroscopes of the B set of SGCMGs, respectively. The installation orientation of the two sets of SGCMGs relative to the core cabin body coordinate system is shown in Figure 2, the frame axis of the first gyro in the A set of SGCMGs along

exist

and

The projections that make up the plane and

Consistent orientation, frame axis of first top in set B SGCMGs

along

exist

and

The projections that make up the plane and

The same direction. The reason for choosing this installation orientation is that when both sets of SGCMGs are working normally or some gyros fail, this installation orientation can ensure that the gyro group has better envelope and singularity performance indicators. The component arrays of the unit vector of the rotor angular momentum direction and the unit vector of the output torque in the opposite direction of each gyro in the core cabin system at the initial moment of the two sets of SGCMGs are:

s_a10＝[1 0 0]^T，s_a20＝[-sin18° 0 -cos18°]^T，s_a30＝[-1 0 0]^T，s_a40＝[-sin18° 0 cos18°]^T，s _a10 =[1 0 0] ^T , s _a20 =[-sin18° 0 -cos18°] ^T , s _a30 =[-1 0 0] ^T , s _a40 =[-sin18° 0 cos18°] ^T ,

s_a50＝[cos36° 0 sin36°]^T，s_a60＝[cos36° 0 -sin36°]^T，t_a10＝[0 0 -1]^T，s _a50 =[cos36° 0 sin36°] ^T , s _a60 =[cos36° 0 -sin36°] ^T , t _a10 =[0 0 -1] ^T ,

t_a20＝[-sin26.57°cos18° -cos26.57° sin26.57°sin18°]^T，t _a20 =[-sin26.57°cos18°-cos26.57° sin26.57°sin18°] ^T ,

t_a30＝[0 -cos26.57° sin26.57°]^T，t _a30 =[0 -cos26.57° sin26.57°] ^T ,

t_a40＝[sin26.57°cos18° -cos26.57° sin26.57°sin18°]^T，t _a40 =[sin26.57°cos18°-cos26.57° sin26.57°sin18°] ^T ,

t_a50＝[sin26.57°sin36° -cos26.57° -sin26.57°cos36°]^T，t _a50 =[sin26.57°sin36°-cos26.57°-sin26.57°cos36°] ^T ,

t_a60＝[-sin26.57°sin36° -cos26.57° -sin26.57°cos36°]^T。t _a60 =[-sin26.57°sin36°-cos26.57°-sin26.57°cos36°] ^T .

s_b10＝[0 0 1]^T，s_b20＝[0-cos18° -sin18°]^T，s_b30＝[0 0 -1]^T，s_b40＝[0cos18° -sin18°]^T，s _b10 =[0 0 1] ^T , s _b20 =[0-cos18° -sin18°] ^T , s _b30 =[0 0 -1] ^T , s _b40 =[0cos18° -sin18°] ^T ,

s_b50＝[0sin36°cos36°]^T，s_b60＝[0 -sin36° cos36°]^T，t_b10＝[0 -1 0]^T，s _b50 =[0 sin36°cos36°] ^T , s _b60 =[0 -sin36° cos36°] ^T , t _b10 =[0 -1 0] ^T ,

t_b20＝[-cos26.57°sin26.57°sin18°-sin26.57°cos18°]^T，t _b20 =[-cos26.57°sin26.57°sin18°-sin26.57°cos18°] ^T ,

t_b30＝[-cos26.57°sin26.57°0]^T，t _b30 =[-cos26.57°sin26.57°0] ^T ,

t_b40＝[-cos26.57°sin26.57°sin18°sin26.57°cos18°]^T，t _b40 =[-cos26.57°sin26.57°sin18°sin26.57°cos18°] ^T ,

t_b50＝[-cos26.57°-sin26.57°cos36°sin26.57°sin36°]^T，t _b50 =[-cos26.57°-sin26.57°cos36°sin26.57°sin36°] ^T ,

t_b60＝[-cos26.57°-sin26.57°cos36°-sin26.57°sin36°]^T。t _b60 =[-cos26.57°-sin26.57°cos36°-sin26.57°sin36°] ^T .

假设每个陀螺的标称角动量为180Nms，并且假设A套SGCMGs的第5和第6个陀螺失效，A套SGCMGs的初始框架角δ_a0＝[π/2 0 0 0]^T，B套SGCMGs的初始框架角δ_b0＝[π/2 0 0 0 0 0]^T。为了进行数值仿真，还需要对A套和B套SGCMGs最终的输出力矩进行合成。具体做法是：假设各个陀螺的框架伺服系统能实现精确控制，则可以认为各个陀螺的实际框架角速度与指令框架角速度相等，即

在实施步骤中的第四步中到了A套SGCMGs和B套SGCMGs各陀螺的指令框架角速度后，于是再根据陀螺输出力矩方程(5)，可以得到A套和B套SGCMGs的实际输出力矩分别为Assuming that the nominal angular momentum of each gyro is 180Nms, and assuming that the 5th and 6th gyroes of the A set of SGCMGs fail, the initial frame angle δ _a0 of the A set of SGCMGs = [π/2 0 0 0] ^T , and the B set of SGCMGs The initial frame angle δ _b0 = [π/2 0 0 0 0 0] ^T . In order to carry out the numerical simulation, it is also necessary to synthesize the final output torques of the A set and the B set SGCMGs. The specific method is: assuming that the frame servo system of each gyroscope can realize precise control, it can be considered that the actual frame angular velocity of each gyroscope is equal to the command frame angular velocity, that is,

In the fourth step of the implementation steps, after the command frame angular velocity of each gyro of the A set of SGCMGs and the B set of SGCMGs is obtained, then according to the gyro output torque equation (5), the actual output torques of the A set and the B set of SGCMGs can be obtained respectively

${T T}_{ra ra} = = {- - h h}_{00} {A A}_{at at} {\overset{\cdot &Center Dot;}{δ δ}}_{ra ra} - - - - - - ((2626))$

${T T}_{rb rb} = = {- - h h}_{00} {A A}_{bt bt} {\overset{\cdot &Center Dot;}{δ δ}}_{rb rb} - - - - - - ((2727))$

最终通过力矩合成，可以得到两套SGCMGs总的输出力矩为Finally, through torque synthesis, the total output torque of the two sets of SGCMGs can be obtained as

T_r＝T_ra+T_rb (28)T _r =T _ra +T _rb (28)

采用PID控制律进行组合体航天器的大角度机动控制。如图5和图6可见，在仿真运行到2800s左右时，A套SGCMGs非常接近奇异，但此时其框架角速度并没有发生突变，且在整个过程中A套SGCMGs都维持可控。同时，如图7所示，整个过程中两套SGCMGs总输出力矩与指令控制力矩误差都维持在10-14Nm内，力矩输出精度很高。The large-angle maneuvering control of the combined spacecraft is carried out by using the PID control law. As can be seen from Figures 5 and 6, when the simulation runs to about 2800s, the SGCMGs of set A are very close to singularity, but at this time the angular velocity of the frame does not change suddenly, and the SGCMGs of set A remain controllable during the whole process. At the same time, as shown in Figure 7, the error between the total output torque of the two sets of SGCMGs and the command control torque was maintained within 10-14Nm during the whole process, and the torque output accuracy was very high.

综上所述，本发明给出了一种基于奇异值分解的单框架控制力矩陀螺群协调控制方法。当空间站组合体上安装的一套五棱锥构型SGCMGs至多有3个陀螺发生故障时，可以联合已安装的另一套SGCMGs进行协调控制。利用奇异值分解的方法使故障SGCMGs仅需要输出垂直于奇异方向的指令力矩，而将沿奇异方向的指令力矩分配给正常SGCMGs。采用这种协调控制方案，既能保证故障SGCMGs在遭遇奇异时的完全可控性，又能保证两套SGCMGs的总输出力矩与指令力矩完全相符，从而提高了姿态控制的精度。本发明可以在空间站等大型航天器任务中得到应用。In summary, the present invention provides a single-frame control moment gyroscope group coordination control method based on singular value decomposition. When at most 3 gyroscopes of a set of pentagonal pyramid SGCMGs installed on the space station assembly fail, they can be coordinated with another set of SGCMGs already installed. Using the method of singular value decomposition, the faulty SGCMGs only need to output the command torque perpendicular to the singular direction, and distribute the command torque along the singular direction to the normal SGCMGs. Adopting this coordinated control scheme can not only ensure the complete controllability of the faulty SGCMGs when encountering a singularity, but also ensure that the total output torque of the two sets of SGCMGs is completely consistent with the command torque, thereby improving the accuracy of attitude control. The invention can be applied in large spacecraft missions such as space stations.

以上所述仅是本发明的优选实施方式，应当指出，对于本技术领域的普通技术人员来说，在不脱离本发明原理的前提下，还可以做出若干改进，或者对其中部分技术特征进行等同替换，这些改进和替换也应视为本发明的保护范围。The above description is only the preferred embodiment of the present invention, and it should be pointed out that for those of ordinary skill in the art, without departing from the principle of the present invention, some improvements can also be made, or some technical features can be improved. Equivalent replacement, these improvements and replacements should also be regarded as the protection scope of the present invention.

Claims

1. A single-frame control moment gyroscope group coordinated control method based on singular value decomposition, the method is applicable to spacecraft with two sets of pentagonal pyramid configuration single-frame control moment gyroscope groups, and wherein A cover has 1, 2 or When 3 gyroscopes fail and set B works normally, the following steps are included:

Step 1. Moment distribution is carried out according to the minimum envelope angular momentum of the two sets of single-frame control moment gyroscope groups: assuming that the command torque required to control the entire spacecraft is T _c , the command assigned to the A set of failed single-frame control moment gyroscope groups The torque is T _ca , expressed as

{T T}_{ca ca} = = \frac{{h h}_{an an}}{{h h}_{an an} + + 4.4719 4.4719} {T T}_{c c}

The command torque assigned to the B-set single-frame control torque gyro group is T _cb , expressed as

{T T}_{cb cb} = = \frac{4.4719 4.4719}{{h h}_{an an} + + 4.4719 4.4719} {T T}_{c c}

Among them, h _an is the minimum angular momentum of the envelope of n single-frame control moment gyroscopes in A set of normal work, and the value range of n is 3≤n≤6;

Step 2: Use the singular value decomposition method to decompose the command torque assigned to the A set of single-frame control moment gyroscopes again, and assign the command moment components along the singular direction of the A set of single-frame control moment gyroscopes to the B set of single frames Control moment gyro group, and the command moment component perpendicular to the singular direction of A set of single frame control moment gyro group is still assigned to A set of single frame control moment gyro group;

Step 3: After the allocation is completed, the single-frame control moment gyroscope group of A set uses the pseudo-inverse manipulation law to solve its command frame angular velocity, and the B-set single-frame control moment gyro group uses the pseudo-inverse plus zero motion control law to solve its command frame angular velocity;

Step 4. The two sets of single-frame control moment gyroscopes operate according to their respective command frame angular velocities, and the sum of the output torque acts on the spacecraft to complete precise attitude control.