CN111966963A - Method for rapidly analyzing singular angular momentum of control moment gyroscope combination - Google Patents
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Abstract
A method for rapidly analyzing the combination singular angular momentum of a control moment gyroscope belongs to the technical field of spacecraft attitude control. The invention comprises the following steps: calculating a corresponding combined angle dynamic quantity value and a corresponding configuration matrix value according to the control moment gyro frame angle combined value; calculating singular values and quasi-singular characteristic values according to the configuration matrix values; calculating the quasi-singular moment direction according to the configuration matrix value and the quasi-singular characteristic value; and calculating a torque realizability index according to the specified command torque value. And the potential singular direction of the command moment is quickly calculated according to the frame angle combination value, and an intuitive evaluation index is provided for evaluating the realization capability of the frame angle combination on the specified command moment. The method has small calculated amount, does not need complex solving processes such as matrix inversion or LU decomposition and the like, and is extremely suitable for actual requirements such as on-orbit real-time calculation, ground rapid analysis and the like. The method well solves the problem of rapid analysis of the singular angular momentum of the control moment gyro combination.
Description
Technical Field
The invention relates to a method for rapidly analyzing singular angular momentum of a control moment gyroscope combination, and belongs to the technical field of spacecraft attitude control.
Background
The control moment gyro combination is used for controlling the satellite attitude and can provide agile maneuvering capability, and in the use of the control moment gyro, the singular problem based on dynamic configuration is the bottleneck of restricting the control method from fully excavating the control capability of the control moment gyro. The configuration singularity of the control moment gyro depends on the combined value of the frame angles and is related to the direction of the command moment, and the analysis is complex and unintuitive. The existing singular angular momentum analysis method is difficult to directly reveal the inherent relation between the singular problem and the frame angle combination and the instruction moment, and is time-consuming to operate.
Disclosure of Invention
The technical problem solved by the invention is as follows: the method overcomes the defects of the prior art, provides a method for rapidly analyzing the singular angular momentum of the control moment gyro combination, rapidly calculates the singular direction of the potential instruction moment according to the combination value of the frame angle, and provides an intuitive evaluation index for evaluating the realization capability of the frame angle combination on the appointed instruction moment. The method has small calculated amount, does not need complex solving processes such as matrix inversion or LU decomposition and the like, and is extremely suitable for actual requirements such as on-orbit real-time calculation, ground rapid analysis and the like. The method well solves the problem of rapid analysis of the singular angular momentum of the control moment gyro combination.
The technical solution of the invention is as follows: a method for rapidly analyzing the combination singular angular momentum of a control moment gyroscope comprises the following steps:
calculating a corresponding combined angle dynamic quantity value and a corresponding configuration matrix value according to the control moment gyro frame angle combined value;
calculating singular values and quasi-singular characteristic values according to the configuration matrix values;
calculating the quasi-singular moment direction according to the configuration matrix value and the quasi-singular characteristic value;
and calculating a torque realizability index according to the specified command torque value.
Further, the combined angular momentum value is H () ═ H (a sin + B cos) E; wherein,
＝[1,...,n]Tis the frame angle measurement value of each CMG, n is the number of CMGs, and E is [1]TIs a full 1 vector of n x 1 dimensions, h is a nominal rotor angle momentum value of a single CMG,
and
and i is 1, …, and n is the direction vector of the angular momentum of the CMG rotor when the CMG frame angle is at 90 degrees and 0 degrees respectively.
Further, the configuration matrix value is G ═ CCT(ii) a Wherein, the moment matrix C is C () ═ A cos-B sin.
Further, the singular value is D ═ g11g22g33+2g12g23g13-g11g23 2-g22g13 2-g33g12 2(ii) a Wherein, g11、g12、g13、g12、g22、g23、g13、g23And g33Are all elements of a configuration matrix and satisfy the configuration matrix
Further, the method for calculating the quasi-singular eigenvalue comprises the following steps:
calculating parameters b, c and d according to elements of the configuration matrix;
calculating parameters A, B, C and delta according to the parameters B, C and d;
calculating a plurality of characteristic values to be selected according to the parameter delta;
and selecting the smallest one from the eigenvalues to be selected as the quasi-singular eigenvalue lambda.
Further, the parameters b, c and d are b ═ g respectively11+g22+g33)，c＝g11g22+g22g33+g33g11-g12 2-g23 2-g13 2，d＝g11g23 2+g22g13 2+g33g12 2-g11g22g33-2g12g23g13。
Further, the parameters A, B, C and delta are respectively
Further, the method for calculating the plurality of feature values to be selected according to the parameter Δ includes:
when the value of a is 0, the value of a,
when Δ ≠ 0, it is,
where arccos () is an inverse cosine function.
Further, the method for calculating the quasi-singular moment direction comprises the following steps:
calculating quasi-singular matrix A according to configuration matrix G and quasi-singular eigenvalue lambdaλ：AλG- λ I, where I is a 3-order identity matrix;
registering singular matrix AλThe elements in the formula are as follows:
registering singular matrix AλThe row i1 in which the element with the maximum absolute value is located is listed as j 1;
aligned singular matrix AλThe individual elements in row no i1 and column no j1 are calculated as follows:
Note bijThe row i2 in which the element with the maximum absolute value is located is listed as j 2;
the notation i 3-6-i 1-i2, j 3-6-j 1-j 2;
calculating quasi-singular vector xi according to the following formula0＝[ξ1 ξ2 ξ3]T：
Aligned singular vector xi0And (3) performing unitized processing to obtain a quasi-singular moment direction xi:
ξ＝ξ0/|ξ0|。
further, the torque realizability κμComprises the following steps:
where μ is the specified command torque value, which is a 3 x 1-dimensional vector, max (x, y) is a maximum function, the result is the larger of x and y, and h is the nominal rotor angular momentum value of a single CMG.
Compared with the prior art, the invention has the advantages that:
the invention provides a method for rapidly analyzing the singular angular momentum of a control moment gyro combination, which is a novel analysis method for solving the problem of the singular of a satellite control moment gyro combination and well meets the requirements of directly revealing the singular problem, the internal relation of the frame angle combination and the instruction moment and rapidly analyzing the problem. Compared with the prior art, the method is simple and intuitive in analysis and small in calculated amount, and can realize quick analysis of the combination singular angular momentum of the control moment gyroscope.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
In order to better understand the technical solutions, the technical solutions of the present application are described in detail below with reference to the drawings and specific embodiments, and it should be understood that the specific features in the embodiments and examples of the present application are detailed descriptions of the technical solutions of the present application, and are not limitations of the technical solutions of the present application, and the technical features in the embodiments and examples of the present application may be combined with each other without conflict.
The method for rapidly analyzing the singular angular momentum of the control moment gyroscope combination provided by the embodiment of the application is further described in detail with reference to the attached drawings in the specification, as shown in fig. 1, and the method comprises the following specific implementation processes:
(1) and calculating the corresponding combined angular momentum value and configuration matrix value according to the control moment gyro frame angle combined value.
In the scheme provided by the embodiment of the application, the method specifically comprises the following steps:
in one possible implementation, the combined angular momentum value H (), is calculated as follows:
H()＝h(A sin+B cos)E，
wherein
＝[1,...,n]TIs the frame angle measurement value of each CMG, n is the number of CMGs, and E is [1]TIs a full 1 vector of n x 1 dimensions, and h is a nominal rotor angle momentum value of a single CMG;
wherein
And
(i ═ 1, …, n) are the direction vectors of the angular momentum of the CMG rotors at 90 degrees and 0 degrees respectively for each CMG frame angle;
in one possible implementation, the moment matrix C (), is calculated as follows:
C()＝A cos-B sin，
in one possible implementation, the configuration matrix G is calculated as follows:
G＝CCT；
(2) and calculating the singular value and the quasi-singular eigenvalue by using the formula provided by the invention according to the configuration matrix value.
In the scheme provided by the embodiment of the application, the method specifically comprises the following steps:
in one possible implementation, the elements in the configuration matrix G are as follows:
the property of the configuration matrix G being a symmetric matrix is used.
In one possible implementation, the singular value D is calculated as follows:
D＝g11g22g33+2g12g23g13-g11g23 2-g22g13 2-g33g12 2
in one possible implementation, the parameters b, c, d are calculated as follows:
b＝-(g11+g22+g33)
c＝g11g22+g22g33+g33g11-g12 2-g23 2-g13 2
d＝g11g23 2+g22g13 2+g33g12 2-g11g22g33-2g12g23g13
in one possible implementation, the parameters a, B, C, Δ are calculated as follows:
A＝b2-3ac
B＝bc-9ad
C＝c2-3bd
Δ＝B2-4AC
in one possible implementation, the values according to the parameter Δ are calculated according to the following equations:
when delta is 0, the candidate characteristic value lambda is calculated according to the following formula1,λ2,λ3：
When delta is not equal to 0, the characteristic value lambda to be selected is calculated according to the following formula1,λ2,λ3：
Where arccos () is an inverse cosine function.
In a possible implementation manner, the characteristic value λ to be selected is selected1,λ2,λ3The smallest one as quasi-singular eigenvalueλ。
(3) And calculating the quasi-singular moment direction by using the formula provided by the invention according to the configuration matrix value and the quasi-singular characteristic value.
In the scheme provided by the embodiment of the application, the method specifically comprises the following steps:
in one possible implementation, the quasi-singular matrix A is calculated from the configuration matrix G and the quasi-singular eigenvalues λ according to the following formulaλ：
Aλ＝G-λI，
Wherein I is a 3-order identity matrix;
in one possible implementation, the singular matrix A is registeredλThe elements in the formula are as follows:
registering singular matrix AλThe row i1 in which the element with the maximum absolute value is located is listed as j 1;
in one possible implementation, the singular matrix A is alignedλThe individual elements in row no i1 and column no j1 are calculated as follows:
Note bijThe row i2 in which the element with the maximum absolute value is located is listed as j 2;
the notation i 3-6-i 1-i2, j 3-6-j 1-j2
In one possible implementation, the quasi-singular vector ξ is calculated as follows0＝[ξ1 ξ2 ξ3]T：
ξj3＝1
In one possible implementation, the singular vector ξ is aligned0And (3) performing unitized processing to obtain a quasi-singular moment direction xi:
ξ＝ξ0/|ξ0|
(4) and calculating the torque realizability index by using the formula provided by the invention according to the specified command torque value.
In the scheme provided by the embodiment of the application, the method specifically comprises the following steps:
in one possible implementation, the moment realizability κ is calculated as followsμ：
Where μ is the specified command torque value, which is a 3 x 1 dimensional vector, and max (x, y) is the maximum function, the result being the larger of x, y.
Examples
The process of the present invention will be described in detail with reference to examples.
Example 1: the satellite uses a control moment gyro to combine the parameters as shown in the table below.
TABLE 1
The initial satellite is in a stable operation state of the ground zero attitude, and the attitude maneuver of rolling for 45 degrees is started according to the remote control instruction. The frame angle changes during the attitude maneuver are shown in the following table.
TABLE 2
According to the method for rapidly analyzing the singular angular momentum of the control moment gyroscope combination, the combined angular momentum is calculated for each group of frame angle combinations in the attitude maneuver process in the table above, and the result is shown in the table below.
TABLE 3
According to the quick analysis method for the singular angular momentum of the control moment gyro combination, the singular value, the quasi-singular characteristic value, the quasi-singular moment direction and the moment realizability are calculated for each group of frame angle combinations in the attitude maneuver process in the table 1, and the results are shown in the following table. The specified torque used for the torque realizability is [ 100 ═ mu%]T。
TABLE 4
As can be seen from the data in the table above, compared with the traditional single singular value, the quasi-singular characteristic values, the quasi-singular moment directions, the moment realizability and other analysis results provided by the invention are more intuitive, and the singular characteristics in the control moment gyro combination and the realizability of the external moment requirements can be effectively prompted. The calculation process of the calculation formula is not complex, and the requirements of quick calculation and quick analysis are met.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present application without departing from the spirit and scope of the application. Thus, if such modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is intended to include such modifications and variations as well.
Those skilled in the art will appreciate that those matters not described in detail in the present specification are well known in the art.
Claims (10)
1. A method for rapidly analyzing the combination singular angular momentum of a control moment gyroscope is characterized by comprising the following steps:
calculating a corresponding combined angle dynamic quantity value and a corresponding configuration matrix value according to the control moment gyro frame angle combined value;
calculating singular values and quasi-singular characteristic values according to the configuration matrix values;
calculating the quasi-singular moment direction according to the configuration matrix value and the quasi-singular characteristic value;
and calculating a torque realizability index according to the specified command torque value.
2. The method for rapidly analyzing the combined singular angular momentum of the control moment gyroscope according to claim 1, wherein the method comprises the following steps: the combined angular momentum value is H () ═ H (Asin + Bcos) E; wherein,
＝[1,...,n]Tis the frame angle measurement value of each CMG, n is the number of CMGs, and E is [1]TIs a full 1 vector of n x 1 dimensions, h is a nominal rotor angle momentum value of a single CMG,
and
and i is 1, …, and n is the direction vector of the angular momentum of the CMG rotor when the CMG frame angle is at 90 degrees and 0 degrees respectively.
3. The method for rapidly analyzing the combined singular angular momentum of the control moment gyroscope according to claim 2, wherein the method comprises the following steps: the configuration matrix value is G ═ CCT(ii) a Wherein, the moment matrix C is C () ═ Acos-Bsin.
4. The method for rapidly analyzing the combined singular angular momentum of the control moment gyroscope according to claim 1, wherein the method comprises the following steps: the singular value is D ═ g11g22g33+2g12g23g13-g11g23 2-g22g13 2-g33g12 2(ii) a Wherein, g11、g12、g13、g12、g22、g23、g13、g23And g33Are all elements of a configuration matrix and satisfy the configuration matrix
5. The method for rapidly analyzing the combined singular angular momentum of the control moment gyroscope according to claim 4, wherein the method for calculating the quasi-singular eigenvalue comprises the following steps:
calculating parameters b, c and d according to elements of the configuration matrix;
calculating parameters A, B, C and delta according to the parameters B, C and d;
calculating a plurality of characteristic values to be selected according to the parameter delta;
and selecting the smallest one from the eigenvalues to be selected as the quasi-singular eigenvalue lambda.
6. The method for rapidly analyzing the combined singular angular momentum of the control moment gyroscope according to claim 5, wherein the method comprises the following steps: the parameters b, c and d are respectively b ═ g11+g22+g33)，c＝g11g22+g22g33+g33g11-g12 2-g23 2-g13 2，d＝g11g23 2+g22g13 2+g33g12 2-g11g22g33-2g12g23g13。
7. The method for rapidly analyzing the combined singular angular momentum of the control moment gyroscope according to claim 6, wherein the method comprises the following steps: the parameters A, B, C and delta are respectively
8. The method for rapidly analyzing the combined singular angular momentum of the control moment gyroscope according to claim 7, wherein the method comprises the following steps: the method for calculating the plurality of candidate characteristic values according to the parameter delta comprises the following steps:
when the value of a is 0, the value of a,
when Δ ≠ 0, it is,
where arccos () is an inverse cosine function.
9. The method for rapidly analyzing the combined singular angular momentum of the control moment gyroscope according to claim 1, wherein the method for calculating the quasi-singular moment direction comprises the following steps:
calculating quasi-singular matrix A according to configuration matrix G and quasi-singular eigenvalue lambdaλ：AλG- λ I, where I is a 3-order identity matrix;
registering singular matrix AλThe elements in the formula are as follows:
registering singular matrix AλThe row i1 in which the element with the maximum absolute value is located is listed as j 1;
aligned singular matrix AλThe individual elements in row no i1 and column no j1 are calculated as follows:
Note bijThe row i2 in which the element with the maximum absolute value is located is listed as j 2;
the notation i 3-6-i 1-i2, j 3-6-j 1-j 2;
calculating quasi-singular vector xi according to the following formula0＝[ξ1 ξ2 ξ3]T：
Aligned singular vector xi0And (3) performing unitized processing to obtain a quasi-singular moment direction xi:
ξ＝ξ0/|ξ0|。
10. according to claim 9The method for rapidly analyzing the singular angular momentum of the control moment gyroscope combination is characterized in that the moment realizability degree kappaμComprises the following steps:
where μ is the specified command torque value, which is a 3 x 1-dimensional vector, max (x, y) is a maximum function, the result is the larger of x and y, and h is the nominal rotor angular momentum value of a single CMG.
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US9567112B1 (en) * | 2013-06-27 | 2017-02-14 | The United States Of America, As Represented By The Secretary Of The Navy | Method and apparatus for singularity avoidance for control moment gyroscope (CMG) systems without using null motion |
| CN106896821A (en) * | 2017-03-10 | 2017-06-27 | 北京航空航天大学 | A kind of angular momentum management method of variable speed control moment gyro |
| CN110990943A (en) * | 2019-11-13 | 2020-04-10 | 上海航天控制技术研究所 | Singular point judgment method based on singular geometric meaning of control moment gyro group |
| US10671697B1 (en) * | 2017-02-24 | 2020-06-02 | Cyber Atomics, Inc. | Iterative and efficient technique for singular value decomposition |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US9567112B1 (en) * | 2013-06-27 | 2017-02-14 | The United States Of America, As Represented By The Secretary Of The Navy | Method and apparatus for singularity avoidance for control moment gyroscope (CMG) systems without using null motion |
| US10671697B1 (en) * | 2017-02-24 | 2020-06-02 | Cyber Atomics, Inc. | Iterative and efficient technique for singular value decomposition |
| CN106896821A (en) * | 2017-03-10 | 2017-06-27 | 北京航空航天大学 | A kind of angular momentum management method of variable speed control moment gyro |
| CN110990943A (en) * | 2019-11-13 | 2020-04-10 | 上海航天控制技术研究所 | Singular point judgment method based on singular geometric meaning of control moment gyro group |
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