A control moment gyro group directional singular escape maneuver law calculation method suitable for agile platform

Abstract

A method for calculating the directional singular escape control law for a control moment gyroscope group applicable to agile platforms is disclosed. The method uses a group of n control moment gyroscopes installed in a specific configuration as the controlled object. The steps are as follows: 1. Calculate the torque matrix based on the current actual frame angle position of the gyroscope group; 2. Calculate the error vector from the actual frame angle to the target frame angle, taking the initial frame angle of the gyroscope group's actual configuration as the target frame angle driven by the control law; 3. Calculate the desired directional frame rotation speed for movement towards the target frame angle based on the onboard software's operating cycle and the maximum rotation speed of the control moment gyroscope frame; 4. Construct a quadratic index based on the joint optimality of output torque error and directional frame motion error, and design the distribution coefficient matrix for the two error terms; 5. Solve for the optimal frame rotation speed using partial derivative calculations to obtain the calculation formula for the directional singular escape control law. This invention can simultaneously handle singular attitude escape and frame directional motion, exhibiting strong adaptability.

Description

Technical Field

[0001] This invention relates to the field of control moment gyroscope group manipulation technology, and more specifically to a method for calculating the directional singular escape manipulation law of control moment gyroscope groups applicable to agile platforms. Background Technology

[0002] Single-frame control torque gyroscope groups are a widely used high-torque actuator. With appropriate redundancy configuration, they can respond to torque commands in any axis, enabling frequent attitude maneuvers of agile platforms. The control law is a crucial algorithm for converting control torque commands into control torque gyroscope group frame rotation speed commands. It ensures high-precision torque output in non-singular conditions and requires reliable escape from singularities in singular conditions.

[0003] The singular configuration of the control moment gyroscope group is a problem that must be addressed in its application. In the singular state, the control law calculation based on the pseudo-inverse solution cannot be performed. At this time, a singular robust control law is required to drive the control moment gyroscope group out of the singular state. There are many methods for designing singular robust control laws, but in essence, they all artificially introduce control torque errors to make the current frame position no longer a singular point, thereby enabling the normal calculation of the control law.

[0004] Currently, the design ideas for singular robust manipulation laws mainly focus on optimizing and improving the mathematics of pseudo-inverse solutions, such as adding small coefficient identity matrices, matrix singular value decomposition, and constructing off-diagonal matrices. The purpose of these methods is to eliminate the problem of pseudo-inverse solution acquisition caused by the non-full rank of the control torque gyroscope group torque matrix. The relevant algorithms can achieve singular escape effects, but they lack consideration for engineering application background.

[0005] Control moment gyroscope groups are commonly used in satellite platforms requiring agile attitude maneuvers. To achieve continuous and frequent agile maneuvers, engineering practice typically requires the control moment gyroscope group frame position to be close to a pre-calculated initial frame angle to obtain continuous high torque output capability and ensure agile maneuver performance. Considering the practical application context of agile maneuvering satellite platforms, it is necessary to balance singular escape capability and the requirement to approach the target frame angle. Designing a singular escape control law that can effectively improve the reliability of continuous agile attitude maneuvers of on-orbit satellites is an urgent problem to be solved. Summary of the Invention

[0006] The purpose of this invention is to provide a method for calculating the control moment gyroscope group directional singularity escape maneuvering law applicable to agile platforms. This method can take into account both singularity escape and frame directional motion, effectively avoiding problems such as "frame lock-in". It also drives the control moment gyroscope group to escape the singularity while moving towards the target frame angle. The closer to the singularity, the greater the directional motion force, and the stronger the adaptability to subsequent agile maneuvering tasks after escaping the singularity.

[0007] To achieve the above objectives, this invention provides a method for calculating the directional singular escape control law for a control moment gyroscope group applicable to agile platforms. The method uses a group of n control moment gyroscopes installed in a certain configuration as the controlled object. The method comprises the following steps: S1. Calculating the moment matrix based on the current actual frame angle position of the control moment gyroscope group; S2. Using the initial frame angle in the actual configuration of the control moment gyroscope group as the target frame angle driven by the control law, calculating the error vector from the actual frame angle to the target frame angle; S3. Calculating the desired directional frame rotation speed for movement towards the target frame angle based on the onboard software's operating cycle and the maximum rotation speed of the control moment gyroscope frame; S4. Constructing a quadratic index based on the joint optimality of the output moment error and the directional frame motion error, and designing the allocation coefficient matrix for the two error terms; S5. Solving for the optimal frame rotation speed using partial derivative calculations to obtain the specific calculation formula for the directional singular escape control law.

[0008] Furthermore, in S1, the control torque gyroscope group installation matrix and the current actual frame angular position vector δ = [δ1 δ2 … δ n Calculate the moment matrix to obtain:

[0009]

[0010] Where C is the torque matrix, and A and B are the control torque gyroscope group installation matrices.

[0011] Furthermore, for redundant control moment gyroscope groups, all n units are usually connected to closed-loop control. When cold backup is required or some individual units fail, there may be n-1 or n-2 units connected to the closed loop. Therefore, for different access states under a specific configuration, the ground needs to calculate the initial frame angle in advance for different access states as input for subsequent calculations.

[0012] Furthermore, in S2, the satellite autonomously looks up the corresponding initial frame angle from a table based on the current control moment gyroscope group access state, and sets it as the target frame angle position vector δ for directional driving. des Therefore, the error vector δ between the current actual frame angle and the target frame angle is... err for:

[0013] δ err =δ des -δ,

[0014] Where δ is the current actual frame angular position vector.

[0015] Furthermore, within the n-dimensional frame angular space, the expected angular velocity of the frame angular orientation motion. for:

[0016]

[0017] Where Δt is the onboard software running cycle, and m is a natural number; it represents reaching the target frame angle after m control cycles.

[0018] Furthermore, in S3, the maximum frame rotation speed limit allowed by the control torque gyroscope unit needs to meet the following requirements:

[0019]

[0020] in, To control the maximum rotational speed of the torque gyroscope frame, For vectors The i-th element;

[0021] Solving the inequality, we get:

[0022]

[0023] Here, is the i-th element of the vector, and the symbol "|·|" represents the absolute value operation.

[0024] Furthermore, in S4, while improving the accuracy of the output torque, the directional singular escape manipulation law aims to achieve frame angle directional drive. Therefore, a joint quadratic optimization index is introduced, as follows:

[0025]

[0026] in, The control torque gyroscope group frame rotation speed vector; h is the nominal angular momentum of the inner rotor; T c For controlling torque commands; This indicates the rotational speed error of the directional drive frame; This represents the output torque error; P and Q are the coefficient matrices of the two aforementioned errors, respectively. By changing the values ​​of matrices P and Q, the weights of the two errors can be adjusted.

[0027] Furthermore, in S5, if the joint quadratic optimization index is denoted as L, then:

[0028]

[0029] Design matrices P and Q as diagonal matrices. When L reaches its minimum value, we have:

[0030]

[0031] Solving the equation yields:

[0032]

[0033] Furthermore, let P = λE n Q = E3, E nLet E and E3 be the n-dimensional and 3-dimensional identity matrices, respectively. Then:

[0034]

[0035] Here, the coefficient λ represents the weighting relationship between the two errors. When the distance from the target frame angle is large, it is desirable for λ to take a large value, and when the distance from the target frame angle is small, it is desirable for λ to take a small value. Therefore, the coefficient λ is designed as follows:

[0036]

[0037] The symbol “||·||” represents the calculation of the vector magnitude.

[0038] Furthermore, calculations yield the final control torque gyroscope group orientation singular escape manipulation law as follows:

[0039]

[0040] In summary, compared with the prior art, the control moment gyroscope group directional singularity escape manipulation law calculation method applicable to agile platforms of the present invention can take into account both singular attitude escape and frame directional motion, effectively avoiding problems such as "frame locking"; and while driving the control moment gyroscope group to escape the singularity, it moves towards the target frame angle, and the closer to the singularity, the greater the directional motion force, and the stronger the adaptability to subsequent agile maneuvering tasks after escaping the singularity. Attached Figure Description

[0041] Figure 1 This is a flowchart illustrating the process of controlling the directional singularity escape group manipulation of the torque gyroscope according to the present invention;

[0042] Figure 2 This is a schematic diagram of the desired rotational speed vector of the orientation frame in this invention;

[0043] Figure 3 This is a diagram showing the angular momentum trajectory of the controlled torque gyroscope group during its escape from a singularity. Detailed Implementation

[0044] The present invention will be further described below with reference to the accompanying drawings and by providing a detailed description of a preferred embodiment.

[0045] like Figure 1 As shown, the present invention discloses a method for calculating the directional singular escape manipulation law of a control moment gyroscope group applicable to an agile platform. This method uses a group of n control moment gyroscopes installed in a certain configuration as the controlled object, and specifically includes the following steps:

[0046] S1. Calculate the torque matrix based on the current actual frame angle position of the control torque gyroscope group;

[0047] S2. Using the initial frame angle of the actual configuration state of the control moment gyroscope group as the target frame angle driven by the manipulation law, calculate the error vector from the actual frame angle to the target frame angle.

[0048] S3. Calculate the desired orientation frame rotation speed for the target frame angle motion based on the onboard software's operating cycle and the maximum rotation speed of the control moment gyroscope frame.

[0049] S4. Construct a quadratic index based on the joint optimality of output torque error and orientation frame motion error, and design the allocation coefficient matrix of the two error terms;

[0050] S5. The frame rotation speed at the optimal quadratic index is solved by partial derivative calculation, and the specific calculation formula of the directional singular escape control law is obtained.

[0051] Furthermore, in S1, the control torque gyroscope group installation matrix and the current actual frame angular position vector δ = [δ1 δ2 … δ n Calculate the moment matrix to obtain:

[0052]

[0053] Where C is the torque matrix, A and B are the control torque gyroscope group installation matrices, and the symbol "*" indicates matrix multiplication.

[0054] Furthermore, for redundant control moment gyroscope groups, all n units are usually connected to closed-loop control. When cold backup is required or some individual units fail, there may be n-1 or n-2 units connected to the closed loop. Therefore, for different access states under a specific configuration, the ground needs to calculate the initial frame angle in advance for different access states as input for subsequent calculations.

[0055] Furthermore, in S2, the satellite autonomously looks up the corresponding initial frame angle from a table based on the current control moment gyroscope group access state, and sets it as the target frame angle position vector δ for directional driving. des Therefore, the error vector δ between the current actual frame angle and the target frame angle is... err for:

[0056] δ err =δ des -δ,

[0057] Where δ is the current actual frame angular position vector.

[0058] Furthermore, within the n-dimensional frame angular space, the rotational speed of the ideal frame under directional drive is calculated, such as... Figure 2 As shown in the figure, the horizontal axis span(δ1,…,δ) k ) represents the expression composed of δ1, ..., δ kZhang Cheng's subspace, with the vertical axis span(δ) k+1 ,…,δ n ) represents the result of δ k+1 , ..., δ n Zhang Cheng's subspace, where k < n. Within this space, the desired angular velocity of the frame's angular orientation motion. for:

[0059]

[0060] Where Δt is the onboard software running cycle; m is a natural number, representing the time taken to reach the target frame angle through m control cycles.

[0061] The smaller m is, the higher the required rotational speed of the control torque gyroscope frame. Within the maximum rotational speed range of the control torque gyroscope frame, m should generally be as small as possible.

[0062] Furthermore, in S3, the maximum frame rotation speed limit allowed by the control torque gyroscope unit needs to meet the following requirements:

[0063]

[0064] in, To control the maximum rotational speed of the torque gyroscope frame, For vectors The i-th element.

[0065] Solving the above inequality, we get:

[0066]

[0067] Where, δ erri For vector δ err The i-th element, the symbol “|·|” represents the absolute value operation.

[0068] In a preferred embodiment of the present invention, based on the actual control torque gyroscope product's maximum outer frame rotation speed and the practical requirement of escaping singularities, m is taken as the minimum value satisfying the above formula. Correspondingly, the desired frame rotation speed is... This was subsequently determined.

[0069] Furthermore, in S4, the directional singular escape manipulation law aims to improve the accuracy of the output torque while also achieving frame angle directional drive. Therefore, a joint quadratic optimization index is introduced, as follows:

[0070]

[0071] in, The control torque gyroscope group frame rotation speed vector; h is the nominal angular momentum of the inner rotor; T c For controlling torque commands; This indicates the rotational speed error of the directional drive frame; This represents the output torque error; P and Q are the coefficient matrices of the two aforementioned errors, respectively. By changing the values ​​of matrices P and Q, the weights of the two errors can be adjusted.

[0072] Specifically, if the focus is on output torque accuracy, the coefficient matrix corresponding to the output torque error is set to be larger; if the focus is on singularity escape capability, the coefficient matrix corresponding to the orientation frame motion error is set to be larger. In a preferred embodiment of the present invention, Q can be set to the identity matrix I, and P can be λ times the identity matrix I. When λ < 1, it indicates that output torque accuracy is valued more; when λ > 1, it indicates that singularity escape capability is valued more.

[0073] Furthermore, in S5, if the joint quadratic optimization index is denoted as L, then:

[0074]

[0075] Design matrices P and Q as diagonal matrices. When L reaches its minimum value, we have:

[0076]

[0077] Solving the equation yields:

[0078]

[0079] Let P = λE n Q = E3, E n E and E3 are the n-dimensional and 3-dimensional identity matrices, respectively. The above equation simplifies to:

[0080]

[0081] Here, the coefficient λ represents the weighting relationship between the two errors. When the distance from the target frame angle is large, it is desirable for λ to have a large value, and when the distance from the target frame angle is small, it is desirable for λ to have a small value. Therefore, the coefficient λ can be designed as follows:

[0082]

[0083] The symbol “||·||” represents the calculation of the vector magnitude.

[0084] Therefore, the control torque gyroscope group orientation singularity escape manipulation law implemented in this invention is as follows:

[0085]

[0086] Furthermore, such as Figure 3As shown in the figure, this figure is a diagram of the angular momentum trajectory of the control moment gyroscope group during the escape from the singularity process of the present invention. In the preferred embodiment of the present invention, taking a five-sided pyramidal control moment gyroscope group as an example, using the directional singularity escape control law proposed in the present invention, during the acceleration process, the angular momentum of the control moment gyroscope group encounters the apparent singularity surface 1 inside the momentum body. After escaping the singularity, it switches to the pseudo-inverse control law with zero motion, and then encounters the apparent singularity surface 1 again. After escaping twice in a row using the directional singularity escape control law, it successfully bypasses the apparent singularity surface and maintains the high torque acceleration capability, successfully completing the current attitude maneuvering task, and finally forming the angular momentum trajectory 2.

[0087] In summary, the present invention provides a method for calculating the control moment gyroscope group directional singularity escape maneuvering law applicable to agile platforms. This method can take into account both singularity escape and frame directional motion, effectively avoiding problems such as "frame locking". Furthermore, while driving the control moment gyroscope group to escape the singularity, it moves towards the target frame angle. The closer to the singularity, the greater the directional motion force, resulting in stronger adaptability to subsequent agile maneuvering tasks after escaping the singularity.

[0088] Although the present invention has been described in detail through the preferred embodiments above, it should be understood that the above description should not be considered as a limitation of the present invention. Various modifications and substitutions to the present invention will be apparent to those skilled in the art after reading the above description. Therefore, the scope of protection of the present invention should be defined by the appended claims.

Claims

1. A control torque gyro cluster directional singularity escape maneuver law calculation method suitable for agile platforms, to n A control torque gyro cluster installed in a certain configuration as a control object, characterized by, Includes the following steps: S1. Calculate the torque matrix based on the current actual frame angle position of the control torque gyroscope group; S2. Using the initial frame angle of the actual configuration state of the control moment gyroscope group as the target frame angle driven by the manipulation law, calculate the error vector from the actual frame angle to the target frame angle. S3. Calculate the desired orientation frame rotation speed for the target frame angle motion based on the onboard software's operating cycle and the maximum rotation speed of the control moment gyroscope frame. S4. Construct a quadratic index based on the joint optimality of output torque error and orientation frame motion error, and design the allocation coefficient matrix of the two error terms; S5. The frame rotation speed at the optimal quadratic index is solved by partial derivative calculation, and the specific calculation formula of the directional singular escape control law is obtained.

2. The method for calculating the control torque gyroscope group orientation singular escape manipulation law applicable to agile platforms as described in claim 1, characterized in that, In S1, the control torque gyroscope group installation matrix and the current actual frame angular position vector are used. Calculate the moment matrix to obtain: ， in, C The moment matrix, A , B Install a matrix to control the torque gyroscope group.

3. The method for calculating the control torque gyroscope group orientation singular escape manipulation law applicable to agile platforms as described in claim 2, characterized in that, For redundant control torque gyroscope groups, usually all n Each unit is connected to closed-loop control. In situations requiring cold backup or partial unit failure, there may be issues. n -1 unit or n -2 units are connected to the closed loop. Therefore, for different access states under a specific configuration, the ground needs to calculate the initial frame angle in advance for different access conditions as input for subsequent calculations.

4. The method for calculating the control torque gyroscope group orientation singular escape manipulation law applicable to agile platforms as described in claim 2, characterized in that, In S2, the satellite autonomously looks up the corresponding initial frame angle from a table based on the current control moment gyroscope group access status, and sets it as the target frame angle position vector for directional driving. Therefore, the error vector from the current actual frame angle to the target frame angle is... for: ， in, This is the current actual frame angular position vector.

5. The method for calculating the control torque gyroscope group orientation singular escape manipulation law applicable to agile platforms as described in claim 4, characterized in that, exist n The desired angular velocity of the frame angular orientation motion within the angular space of the frame. for: ， in, For the onboard software's runtime cycle; m For natural numbers, it means through m The control cycle reaches the target frame angle.

6. The method for calculating the control torque gyroscope group orientation singular escape manipulation law applicable to agile platforms as described in claim 5, characterized in that, In S3, the maximum frame rotation speed limit allowed by the control torque gyroscope unit must meet the following requirements: ， in, To control the maximum rotational speed of the torque gyroscope frame, For vectors The i One element; Solving the inequality, we get: ， in, For vectors The i-th element, the symbol "|·|" represents the absolute value operation.

7. The method for calculating the control torque gyroscope group orientation singular escape manipulation law applicable to agile platforms as described in claim 5, characterized in that, In S4, the directional singular escape control law aims to improve the accuracy of the output torque while also providing directional drive for the frame angle. Therefore, a joint quadratic optimization index is introduced, as follows: ， in, To control the rotational speed vector of the torque gyroscope group frame; h The nominal angular momentum of the internal rotor; For controlling torque commands; This indicates the rotational speed error of the directional drive frame; Indicates the output torque error; P , Q These are the coefficient matrices of the two errors mentioned above. By changing the matrices... P and Q The value can adjust the weights of the two errors.

8. The method for calculating the control torque gyroscope group orientation singular escape manipulation law applicable to agile platforms as described in claim 7, characterized in that, In S5, the joint quadratic optimization index is expressed as: L ,but: ， Design Matrix P , Q For a diagonal matrix, when L When the minimum value is obtained, we have: ， Solving the equation yields: 。 9. The method for calculating the control torque gyroscope group orientation singular escape manipulation law applicable to agile platforms as described in claim 8, characterized in that, make , , and They are respectively n Given a 3D identity matrix, then: ， Among them, coefficient Characterizing the weighted relationship between the two errors, when the target frame angle is far away, we hope... Taking the larger value, when it is close to the corner of the target frame, is desirable. Take the smaller value, therefore the coefficient Designed as follows: ， Among them, the symbol " " indicates the calculation of vector magnitude.

10. The method for calculating the control torque gyroscope group orientation singular escape manipulation law applicable to agile platforms as described in claim 9, characterized in that, The final control torque gyroscope group orientation singular escape manipulation law can be obtained by calculation as follows: 。

Images