Arbitrary axial attitude maneuvering hierarchical saturation angular velocity limiting method

Abstract

The application provides a motorized hierarchical saturation angular velocity limiting method for any axial posture, comprising the following steps: S1, obtaining an arbitrary Euler axis direction posture motorized angular velocity limiting value ω max and a maximum angular momentum H max that can be provided by an actuator max ; S2, based on the maximum control torque T max that can be provided by the actuator and ω max , hierarchical saturation control laws are respectively designed for three body axis directions of a satellite body system, and three body axis directions are obtained as control parameters for motorized tasks; S3, calculating a posture deviation quaternion q err from a current posture to a target posture, calculating a current space motorized Euler axis direction vector V err according to q euler , performing normalization processing on V euler , and obtaining a space motorized Euler axis direction unit vector u euler ; S4, calculating a current motorized Euler axis direction posture deviation limiting parameter q euler according to the control parameters and u max_euler ; and S5, based on a hierarchical saturation algorithm, calculating a control torque instruction T c for a current motorized Euler axis direction posture motor.

Description

Technical Field

[0001] This invention relates to the field of satellite attitude control technology, and in particular to a method for limiting the stepwise saturation angular velocity of arbitrary axial attitude maneuvers. Background Technology

[0002] Euler's rotation theorem states that by rotating a rigid body about an axis fixed in both its home system and inertial frame, the body's attitude can be changed from any given orientation to any other orientation. This axis of rotation is called the Euler axis, and its direction remains unchanged in both the home system and inertial frame. Compared to traditional maneuvering modes that involve rotating sequentially around the body axis according to a certain rotation sequence, satellite attitude maneuvers involving rotation around the Euler axis enable three-axis attitude control to move towards the target in space along the "shortest path," significantly reducing maneuvering time.

[0003] The hierarchical saturated PID control law applies appropriate saturation limiting to components such as deviation attitude angle and output torque based on the traditional PID control algorithm, thereby satisfying the objective constraints of the limited range of actuator output torque and angular momentum. In single-axis maneuver control, it can achieve near-time-optimal dynamic performance without prior planning of the maneuver process, making it highly suitable for frequent maneuvering tasks with multiple modes and arbitrary axes.

[0004] For traditional satellites with a single maneuvering mode, the required maneuvering function can be achieved by designing control parameters and limit values ​​for a specific maneuvering axis (i.e., the Euler axis mentioned above) during the application of a hierarchical saturation control algorithm. However, next-generation multi-mode complex maneuvering satellites typically need to possess maneuvering capabilities along any axis in space (i.e., any Euler axis direction). Since the maneuvering axis changes continuously depending on the mode or mission, it is impossible to design parameters in advance. Using inherent parameters will lead to a mismatch between the angular velocity limit and the design value, potentially causing angular momentum saturation of the actuators and severely impacting the maneuvering process.

[0005] To meet the new maneuvering modes and control requirements, it is necessary to design a stepwise saturation angular velocity limiting control method that can adapt to arbitrary axial attitude maneuvers in space and is feasible in engineering. Summary of the Invention

[0006] The purpose of this invention is to provide a method for limiting the saturated angular velocity of arbitrary axial attitude maneuvers. Based on the conventional design of saturated control parameters for the satellite's body axis, this method projects any Euler axis direction in space onto the three body axes of the satellite. Through spatial geometric transformation, the attitude deviation limiting value in any Euler axis direction is calculated, thus achieving angular velocity limiting in any Euler axis direction. This invention can fully utilize the angular momentum space of the actuator and effectively avoids the problem of inconsistent dynamic characteristics of maneuvers in different axial directions when the control bandwidth and damping ratio are designed inconsistently for each body axis direction.

[0007] To achieve the above objectives, the present invention provides a method for limiting the stepped saturation angular velocity of arbitrary axial attitude maneuvers, comprising the following steps:

[0008] S1, Based on the satellite's maximum moment of inertia I max and the maximum angular momentum H that the actuator can provide max Obtain the limit value ω of the attitude maneuver angular velocity in the Euler axis direction for arbitrary maneuvers. max ;

[0009] S2, based on the maximum control torque T that the actuator can provide. max and the angular velocity limit value ω max A hierarchical saturation control law is designed for each of the three body axis directions of the satellite system, and control parameters for on-orbit maneuvering missions are obtained for the three body axis directions.

[0010] S3. Calculate the quaternion q representing the attitude deviation of the satellite from its current attitude to the target attitude. err According to the attitude deviation quaternion q err Calculate the Euler axis direction vector V of the current space maneuver. euler ; for the space maneuver Euler axis direction vector V euler After normalization, the unit vector u of the Euler axis direction for space maneuvering is obtained. euler ;

[0011] S4. Based on the control parameters in the three body axis directions and the unit vector u in the Euler axis direction of the space maneuver... euler Calculate the current maneuvering Euler axis attitude deviation limit value q. max_euler ;

[0012] S5. Based on the hierarchical saturation algorithm, calculate the control torque command T for the current maneuvering attitude maneuver in the Euler axis direction. c ; via the control torque command T c To ensure that the angular velocity of the current maneuver along the Euler axis does not exceed the specified limit value ω. max .

[0013] Optionally, in step S1:

[0014] The angular velocity limit value

[0015] k is a coefficient less than or equal to 1, and the symbol "·" indicates multiplication.

[0016] Optionally, the hierarchical saturation control law in step S2 is:

[0017]

[0018] Where: i = X, Y, Z, representing the direction of the satellite's body axis; Tci K is the control torque command in the i-axis direction. pi K Ii K di The control parameter q is located in the i-axis direction. ei ω ei q maxi These represent the control attitude error, control angular velocity error, and attitude deviation limit value along the i-axis, respectively. maxi The calculation method is as follows:

[0019]

[0020] The SAT function is a saturation function. For any vector 'a' and a limiting value 'b', the SAT function is defined as follows:

[0021] .

[0022] Optionally, step S3 includes:

[0023] S31. Calculate the quaternion q representing the attitude deviation of the satellite from its current attitude to the target attitude. err ,

[0024]

[0025] q0, q mb These are quaternions representing the current pose and the target pose, respectively.

[0026] S32, Based on the attitude deviation quaternion q err Calculate the Euler axis direction vector V of the current space maneuver. euler ;

[0027] ;

[0028] Where sign(·) is the sign function, q err (0) represents the attitude deviation quaternion q. err The mark part, q err (1) q err (2) q err (3) is the attitude deviation quaternion q err of Yabe.

[0029] S33, Regarding the space maneuver Euler axis direction vector V euler After normalization, the unit vector u of the Euler axis direction for space maneuvering is obtained. euler ;

[0030]

[0031] Where ||·|| represents the calculation of vector magnitude.

[0032] Optionally, step S4 includes:

[0033] S41, in the satellite body coordinate system Ox b y b z b Within the space, traversing all the Euler axes of motion, the Euler axis attitude deviation limit value q is determined. max_euler An ellipsoid is formed in space, in the coordinate system Ox b y b z b The equation of the inner ellipsoid is:

[0034] ;

[0035] in: (x,y,z) are the coordinates of any point on the ellipsoid;

[0036]

[0037] Where α∈[0,π] and β∈[-π,π] represent the coordinate system Ox, respectively. b y b z b Azimuth and elevation angles within the interior;

[0038] The attitude deviation limit value q max_euler Represented in matrix form, we get

[0039]

[0040] The symbol “*” represents matrix multiplication.

[0041] Optionally, the control torque command T mentioned in step S5 c The expression is:

[0042] ;

[0043] Wherein: T c q e ω e Both are 3×1 dimensional spatial vectors; q e ω e K represents the three-axis attitude error and three-axis angular velocity error for attitude maneuvering along arbitrary Euler axes in space, respectively; p K I K d For the control parameter matrix,

[0044]

[0045] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0046] The proposed method for progressively saturated angular velocity limiting for arbitrary axial attitude maneuvers extends the method applicable to single-axis directions to arbitrary Euler-axis directions in space. This avoids the problem of incorrect angular velocity limiting when using single-axis control parameters for maneuvers in arbitrary Euler-axis directions. Based on the independent design of control parameters for each body axis of the satellite, the method utilizes the projection relationship between the actual Euler-axis direction and the satellite's body axis direction to achieve attitude maneuver control with the same angular velocity limiting in any spatial axis (i.e., any Euler-axis direction). This effectively avoids the problem of actuator angular momentum saturation that may be caused by incorrect angular velocity limiting, thus improving the reliability of attitude maneuver missions. This invention is particularly suitable for satellites frequently performing large-angle attitude maneuvers in arbitrary axes, ensuring equal limiting control of attitude angular velocities across different maneuver axes (i.e., Euler axes), guaranteeing that the angular momentum of the control moment gyroscope group does not exceed the usable range, and improving the reliability of the control system. Attached Figure Description

[0047] To more clearly illustrate the technical solution of the present invention, the accompanying drawings used in the description will be briefly introduced below. Obviously, the drawings in the following description are one embodiment of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort:

[0048] Figure 1 This is a flowchart of the stepwise saturation angular velocity limiting method for arbitrary axial attitude maneuvering according to the present invention;

[0049] Figure 2 This is a schematic diagram illustrating the attitude maneuvering achieved by the present invention around the spatial Euler axis;

[0050] Figure 3 The arbitrary maneuvering Euler axis attitude deviation limit value of the present invention in the body coordinate system Ox b y b z b Schematic diagram of the formed spatial ellipsoid;

[0051] Figure 4 u is the unit vector along the Euler axis of the present invention. euler In the satellite body coordinate system Ox b y b z b A schematic diagram of the internal projection. Detailed Implementation

[0052] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0053] It should be understood that, when used in this specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0054] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the scope of the application. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0055] It should also be further understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0056] As used in this specification and the appended claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrases "if determined" or "if [described condition or event] is detected" may be interpreted, depending on the context, as "once determined," "in response to determination," "once [described condition or event] is detected," or "in response to detection of [described condition or event]."

[0057] Furthermore, in the description of this application, the terms "first," "second," "third," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0058] This invention provides a method for limiting the stepped saturation angular velocity of arbitrary axial attitude maneuvers, such as... Figure 1 As shown, the steps include:

[0059] S1, Based on the satellite's maximum moment of inertia I max and the maximum angular momentum H that the actuator can provide max Obtain the limit value ω of the attitude maneuver angular velocity in the Euler axis direction for arbitrary maneuvers. max ;

[0060] The angular velocity limit value

[0061] k is a coefficient less than or equal to 1, used to set the angular momentum range margin; the symbol "·" indicates multiplication. Through mathematical simulation or ground experiments, the parameter K is... pi K Ii K di The parameters are then corrected to obtain control parameters that can be used for on-orbit maneuvering missions.

[0062] For compact, agile maneuvering satellites, once the control system completes the individual component matching, overall satellite structure design, and layout design, the satellite's rotational inertia parameters can be calculated relatively accurately, including the satellite's maximum rotational inertia I. max This can also be obtained. Simultaneously, the angular momentum envelope of the actuator is also determined, and the maximum angular momentum H that can be provided for attitude maneuvers is determined accordingly. max The maximum control torque T that can be output max Accordingly, it is determined that it will be used as the input to the limiting method of the present invention.

[0063] S2, based on the maximum control torque T that the actuator can provide. max and the angular velocity limit value ω max A hierarchical saturation control law is designed for each of the three body axis directions of the satellite system, and control parameters for on-orbit maneuvering missions are obtained for the three body axis directions.

[0064] The hierarchical saturation control law mentioned in step S2 is:

[0065]

[0066] Where: i = X, Y, Z, representing the direction of the satellite's body axis; T ci K is the control torque command in the i-axis direction. pi K Ii K di The control parameter q is located in the i-axis direction. ei ω ei q maxi These represent the control attitude error, control angular velocity error, and attitude deviation limit value along the i-axis, respectively; q maxi The calculation method is as follows:

[0067]

[0068] The SAT function is a saturation function. For any vector 'a' and a limiting value 'b', the SAT function is defined as follows:

[0069]

[0070] S3. Calculate the quaternion q representing the attitude deviation of the satellite from its current attitude to the target attitude.err According to the attitude deviation quaternion q err Calculate the Euler axis direction vector V of the current space maneuver. euler ; for the space maneuver Euler axis direction vector V euler After normalization, the unit vector u of the Euler axis direction for space maneuvering is obtained. euler ;

[0071] like Figure 2 As shown, according to Euler's theorem, the satellite's own system maneuvers from the current coordinate system Ox0y0z0 to the target coordinate system Ox mb y mb z mb This can be accomplished by one rotation around the Euler axis.

[0072] Step S3 includes:

[0073] S31. Calculate the quaternion q representing the attitude deviation of the satellite from its current attitude to the target attitude. err ,

[0074]

[0075] q0, q mb These are quaternions representing the current pose and the target pose, respectively.

[0076] S32, Based on the attitude deviation quaternion q err Calculate the Euler axis direction vector V of the current space maneuver. euler ;

[0077]

[0078] Where sign(·) is the sign function, q err (0) represents the attitude deviation quaternion q. err The mark part, q err (1) q err (2) q err (3) is the attitude deviation quaternion q err of Yabe.

[0079] S33, Regarding the space maneuver Euler axis direction vector V euler After normalization, the unit vector u of the Euler axis direction for space maneuvering is obtained. euler ;

[0080]

[0081] Where ||·|| represents the calculation of vector magnitude.

[0082] S4. Based on the control parameters in the three body axis directions and the unit vector u in the Euler axis direction of the space maneuver...euler Calculate the current maneuvering Euler axis attitude deviation limit value q. max_euler ;

[0083] like Figure 3 As shown, step S4 includes:

[0084] S41, in the satellite body coordinate system Ox b y b z b Within the space, traversing all the Euler axes of motion, the Euler axis attitude deviation limit value q is determined. max_euler An ellipsoid is formed in space, in the coordinate system Ox b y b z b The equation of the inner ellipsoid is:

[0085]

[0086] in: (x,y,z) are the coordinates of any point on the ellipsoid;

[0087] like Figure 4 As shown, based on the polar coordinate representation of points on the ellipsoid, the attitude deviation limit value along any maneuvering Euler axis can be expressed as:

[0088]

[0089] Where α∈[0,π] and β∈[-π,π] represent the coordinate system Ox, respectively. b y b z b Azimuth and elevation angles within the interior;

[0090] The attitude deviation limit value q max_euler Represented in matrix form, we get

[0091]

[0092] The symbol “*” represents matrix multiplication.

[0093] S5. Based on the hierarchical saturation algorithm, calculate the control torque command T for the current maneuvering attitude maneuver in the Euler axis direction. c ; via the control torque command T c To ensure that the angular velocity of the current maneuver along the Euler axis does not exceed the specified limit value ω. max .

[0094] The control torque command T mentioned in step S5 c The expression is:

[0095]

[0096] Wherein: T c q e ω e Both are 3×1 dimensional spatial vectors; q e ω e K represents the three-axis attitude error and three-axis angular velocity error for attitude maneuvering along arbitrary Euler axes in space, respectively; p K I K d For the control parameter matrix,

[0097]

[0098] The arbitrary-axis attitude maneuvering stepwise saturation angular velocity limiting method of this invention extends the stepwise saturation angular velocity limiting method applicable to single-axis directions to arbitrary Euler axis directions in space, avoiding the problem of incorrect angular velocity limiting when using single-axis control parameters for maneuvers in arbitrary Euler axis directions in space. Based on the independent design of control parameters for each body axis of the satellite, by utilizing the projection relationship of the actual Euler axis direction onto the satellite's body axis direction, attitude maneuvering control with the same angular velocity limiting along any maneuvering axis in space (i.e., any maneuvering Euler axis direction) can be achieved using control parameters on the body axis. This effectively avoids the problem of actuator angular momentum saturation that may be caused by incorrect angular velocity limiting, improving the reliability of attitude maneuvering missions. This invention is particularly suitable for satellites frequently performing arbitrary-axis, large-angle attitude maneuvers, ensuring equal limiting control of attitude angular velocities along different maneuvering axes, guaranteeing that the angular momentum of the control moment gyroscope group does not exceed the usable range, and improving the reliability of the control system.

[0099] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0100] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for limiting the stepped saturation angular velocity of arbitrary axial attitude maneuvers, characterized in that, Includes the following steps: S1, Based on the satellite's maximum moment of inertia I max and the maximum angular momentum H that the actuator can provide max Obtain the limit value ω of the attitude maneuver angular velocity in the Euler axis direction for arbitrary maneuvers. max ; S2, based on the maximum control torque T that the actuator can provide. max and the angular velocity limit value ω max A hierarchical saturation control law is designed for each of the three body axis directions of the satellite system, and control parameters for on-orbit maneuvering missions are obtained for the three body axis directions. S3. Calculate the quaternion q representing the attitude deviation of the satellite from its current attitude to the target attitude. err According to the attitude deviation quaternion q err Calculate the Euler axis direction vector V of the current space maneuver. euler ; The Euler axis direction vector V of the space maneuver euler After normalization, the unit vector u of the Euler axis direction for space maneuvering is obtained. euler ; S4. Based on the control parameters in the three body axis directions and the unit vector u in the Euler axis direction of the space maneuver... euler Calculate the current maneuvering Euler axis attitude deviation limit value q. max_euler ; S5. Based on the hierarchical saturation algorithm, calculate the control torque command T for the current maneuvering attitude maneuver in the Euler axis direction. c ; via the control torque command T c To ensure that the angular velocity of the current maneuver along the Euler axis does not exceed the specified limit value ω. max .

2. The arbitrary axial attitude maneuvering stepwise saturation angular velocity limiting method as described in claim 1, characterized in that, In step S1: The angular velocity limit value k is a coefficient less than or equal to 1, and the symbol "·" indicates multiplication.

3. The arbitrary axial attitude maneuvering stepwise saturation angular velocity limiting method as described in claim 2, characterized in that, The hierarchical saturation control law mentioned in step S2 is: Where: i = X, Y, Z, representing the direction of the satellite's body axis; T ci K is the control torque command in the i-axis direction. pi K Ii K di The control parameter q is located in the i-axis direction. ei ω ei q maxi These represent the control attitude error, control angular velocity error, and attitude deviation limit value along the i-axis, respectively. maxi The calculation method is as follows: The SAT function is a saturation function. For any vector 'a' and a limiting value 'b', the SAT function is defined as follows: 。 4. The arbitrary axial attitude maneuvering stepwise saturation angular velocity limiting method as described in claim 3, characterized in that, Step S3 includes: S31. Calculate the quaternion q representing the attitude deviation of the satellite from its current attitude to the target attitude. err , q0, q mb These are quaternions representing the current pose and the target pose, respectively. S32, Based on the attitude deviation quaternion q err Calculate the Euler axis direction vector V of the current space maneuver. euler ; ； Where sign(·) is the sign function, q err (0) represents the attitude deviation quaternion q. err The mark part, q err (1) q err (2) q err (3) is the attitude deviation quaternion q err of Yabe; S33, Regarding the space maneuver Euler axis direction vector V euler After normalization, the unit vector u of the Euler axis direction for space maneuvering is obtained. euler ; Where ||·|| represents the calculation of vector magnitude.

5. The arbitrary axial attitude maneuvering stepwise saturation angular velocity limiting method as described in claim 4, characterized in that, Step S4 includes: S41, in the satellite body coordinate system Ox b y b z b Within the space, traversing all the Euler axes of motion, the Euler axis attitude deviation limit value q is determined. max_euler An ellipsoid is formed in space, in the coordinate system Ox b y b z b The equation of the inner ellipsoid is: ； in: (x,y,z) are the coordinates of any point on the ellipsoid; Where α∈[0,π] and β∈[-π,π] represent the coordinate system Ox, respectively. b y b z b Azimuth and elevation angles within the interior; The attitude deviation limit value q max_euler Represented in matrix form, we get The symbol "*" represents matrix multiplication.

6. The arbitrary axial attitude maneuvering stepwise saturation angular velocity limiting method as described in claim 5, characterized in that, The control torque command T mentioned in step S5 c The expression is: ； Wherein: T c q e ω e Both are 3×1 dimensional spatial vectors; q e ω e K represents the three-axis attitude error and three-axis angular velocity error for attitude maneuvering along arbitrary Euler axes in space, respectively; p K I K d For the control parameter matrix,

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