Low-orbit flexible satellite attitude stabilization control method of SADA device

Abstract

The present application relates to the field of aerospace technology, in particular to a kind of low-orbit flexible satellite attitude stabilization control method with SADA device, comprising: using attitude quaternion to satellite attitude kinematics dynamics modeling;Desired quaternion is used to error attitude kinematics dynamics modeling;S3. the method for adopting classic feedback control combined with nonlinear compensation control, error attitude kinematics dynamics equation design obtains attitude controller;Real-time acquisition satellite rotational inertia parameters, and based on the relationship between the attitude controller control parameter and satellite rotational inertia parameters design attitude controller control parameter;Real-time satellite rotational inertia is obtained, and the parameter of attitude controller in step S4 is updated using real-time calculated satellite rotational inertia parameter.The present application uses the way of mathematical analysis calculation, according to the rotation of SADA, the current satellite rotational inertia is calculated in real time, and is used to update the parameter of attitude controller, and the global stability of attitude control is guaranteed.

Description

Technical Field

[0001] This invention relates to the field of aerospace technology, and more specifically to a method for ground attitude stabilization control of a low-orbit flexible satellite with an SADA device. Background Technology

[0002] In recent years, with the rapid development of aerospace technology, multiple small satellite constellations have been built worldwide. While these satellites cover various Earth observation fields such as remote sensing, communication, and meteorology, they share certain commonalities in their operating modes: all operate in a stable Earth-orbiting attitude. Currently, to achieve long-term Earth observation missions, some small low-Earth orbit (LEO) satellites are equipped with Solar Aid Controllers (SADA) devices. Under long-term Earth-orbiting attitude conditions, the solar panel angle can be controlled to ensure the solar panel normal points towards the sun, achieving a balance between mission execution and energy balance. For example, publication number CN117742148A, entitled "A Method for Optimizing Planning and Control Parameters for Stereo Imaging of Low-Earth Orbit Optical Remote Sensing Satellites," illustrates this. However, the presence of SADA devices reduces the stiffness of the solar panels, introducing flexibility issues into the attitude control system. Simultaneously, the rotation of the solar panels causes time-varying moments of inertia, further increasing the difficulty of attitude stabilization control.

[0003] Therefore, for low-orbit flexible satellites equipped with SADA devices, those skilled in the art urgently need to provide a novel method to overcome the technical problems existing in the prior art. Summary of the Invention

[0004] Therefore, the technical problem to be solved by the present invention is to overcome the defects existing in the prior art, thereby providing a method for stabilizing the attitude of a low-orbit flexible satellite with an SADA device.

[0005] A method for ground attitude stabilization control of a low-Earth orbit flexible satellite with SADA device, comprising:

[0006] S1. Modeling satellite attitude kinematics and dynamics using attitude quaternions;

[0007] S2. Model the kinematics and dynamics of the error posture using expected quaternions;

[0008] S3. An attitude controller is designed using a combination of classical feedback control and nonlinear compensation control, along with the error attitude kinematics and dynamics equations.

[0009] S4. Real-time acquisition of satellite rotational inertia parameters, and design of attitude controller control parameters based on the relationship between attitude controller control parameters and satellite rotational inertia parameters;

[0010] S5. Obtain the real-time satellite moment of inertia and update the parameters of the attitude controller in step S4 using the real-time calculated satellite moment of inertia parameters.

[0011] Preferably, the expression for the attitude controller obtained in step S3 is:

[0012] ;

[0013] in, Represents the proportional control gain matrix; This represents the proportional control parameters for the three coordinate axes; This indicates the control torque of the reaction flywheel; Representing error quaternions The vector part; express The antisymmetric matrix; Represents the differential control gain matrix; This represents the differential control parameters for the three coordinate axes; Indicates the error angular velocity; express The antisymmetric matrix; This represents the total moment of inertia matrix of the satellite; Indicates the satellite's attitude angular velocity; This represents the control angular momentum of the reaction flywheel; Representing the error quaternion The rotation transformation matrix; Indicates the satellite in the inertial coordinate system The expected angular velocity.

[0014] Preferably, the satellite's rotational inertia parameters are acquired in real time, and the attitude controller control parameters are designed based on the relationship between the attitude controller control parameters and the satellite's rotational inertia parameters. Specific steps include:

[0015] For the relationship between the imaginary part of the error quaternion of any coordinate axis of the satellite and the deviation angle under small angle conditions, differential calculation is performed, and the following approximate expression is obtained using the satellite x-axis as an example:

[0016] (1); The subscript x indicates the component of the variable on the satellite's x-axis;

[0017] Based on the relationship disclosed in formula (1), under approximate conditions, any coordinate axis of the satellite has the following transfer function relationship:

[0018] ;

[0019] Assumption , ;

[0020] To ensure that the attitude controller passively eliminates the disturbance torque of the solar panels, given parameters... ,but and Designed as follows:

[0021] ;

[0022] Therefore, the final parameter design for the attitude controller used for feedback control is as follows:

[0023] ;

[0024] Similarly, the design yields , , , Parameters;

[0025] In the formula, Representing the error quaternion x-axis component; Indicates the roll error angle of the satellite; Represents the total moment of inertia matrix of the satellite. The principal component on the x-axis; The transfer function is represented by s; the complex frequency variable is represented by s. The disturbance torque of the solar panel along the x-axis is represented. Indicates the cutoff frequency of the designed controller; The fundamental frequency of the flexible solar panel; and These are hypothetical variables.

[0026] Preferably, the real-time satellite moment of inertia is obtained, and the parameters of the attitude controller in step S4 are updated using the real-time calculated satellite moment of inertia parameters, specifically including:

[0027] Based on the rotational coupling coefficient of the solar panel relative to the satellite connection point, the rotational coupling coefficient of the solar panel relative to the satellite coordinate system is obtained.

[0028] The rotational inertia parameters of the entire satellite are obtained based on the rotational inertia of the central rigid body and the rotational coupling coefficient of the solar panels relative to the satellite coordinate system.

[0029] The expression for the moment of inertia parameter of the entire star is as follows: ;

[0030] Input the real-time acquired rotational inertia parameters of the entire star into step S4;

[0031] In the formula, This represents the total moment of inertia matrix of the satellite; This represents the moment of inertia of the central rigid body. This represents the rotational coupling coefficient of the solar panel relative to the satellite coordinate system.

[0032] Preferably, the error attitude kinematics dynamics model is obtained by using expected quaternions to model the kinematics dynamics of the satellite, and the resulting error attitude kinematics dynamics equations are:

[0033] ;

[0034] In the formula, Represents the error quaternion; Representing the error quaternion The scalar part; Representing the error quaternion The vector part; express The antisymmetric matrix; Represents a 3×3 identity matrix; Indicates the error angular velocity; This represents the total moment of inertia matrix of the satellite; Indicates the satellite's attitude angular velocity; express The antisymmetric matrix; This represents the control angular momentum of the reaction flywheel; Representing the error quaternion The rotation transformation matrix; Indicates the satellite in the inertial coordinate system The expected angular velocity; This represents the rotational coupling coefficient of the solar panel relative to the satellite coordinate system; This indicates the mode of a solar panel with SADA (Satellite Adaptor and Radiation Protection). This indicates the control torque of the reaction flywheel.

[0035] Preferably, the expression for the disturbance torque of the solar panel is: ;

[0036] In the formula, This represents the disturbance torque of the solar panel; This represents the rotational coupling coefficient of the solar panel relative to the satellite coordinate system; This indicates the mode of a solar panel with SADA.

[0037] The technical solution of this invention has the following advantages:

[0038] This invention patent discloses a method for attitude stabilization control of a low-Earth orbit flexible satellite with a SADA device, which effectively suppresses the disturbance torque of the flexible components. Simultaneously, it employs mathematical analytical calculation to calculate the current satellite rotational inertia in real time based on the rotation of the SADA device, and uses this calculation to update the attitude controller parameters, ensuring global stability of attitude control. The method proposed in this patent guarantees that the attitude control indicators of the low-Earth orbit flexible satellite with the SADA device meet the requirements of Earth observation missions. It also allows for effective solar charging while conducting observation missions, indirectly and significantly increasing the satellite's operational time. The designed method has a simple structure, high economic value, and is suitable for the design of attitude control systems for small-scale, batch-produced low-Earth orbit flexible satellites in practical engineering applications. Attached Figure Description

[0039] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0040] Figure 1-3 A graph of Euler angles for the orbital system;

[0041] Figure 4-7 A graph of attitude quaternions;

[0042] Figure 8-10 The graph shows the attitude angular velocity.

[0043] Figure 11-14 A graph of error quaternions;

[0044] Figure 15-17 This is a graph of the error angular velocity. Detailed Implementation

[0045] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. 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.

[0046] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0047] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0048] Furthermore, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0049] Example 1

[0050] The purpose of this embodiment is to provide a method for stabilizing the attitude of a low-Earth orbit flexible satellite with an SADA device, ensuring stable attitude control of the low-Earth orbit flexible satellite with an SADA device, and realizing an all-weather, high-efficiency, and highly stable Earth observation mission.

[0051] Therefore, this embodiment discloses a method for ground attitude stabilization control of a low-Earth orbit flexible satellite with SADA device, including:

[0052] S1. Modeling satellite attitude kinematics and dynamics using attitude quaternions;

[0053] S2. Model the kinematics and dynamics of the error posture using expected quaternions;

[0054] S3. An attitude controller is designed using a combination of classical feedback control and nonlinear compensation control, along with the error attitude kinematics and dynamics equations.

[0055] S4. Real-time acquisition of satellite rotational inertia parameters, and design of attitude controller control parameters based on the relationship between attitude controller control parameters and satellite rotational inertia parameters;

[0056] S5. Obtain the real-time satellite moment of inertia and update the parameters of the attitude controller in step S4 using the real-time calculated satellite moment of inertia parameters.

[0057] Step S1:

[0058] The satellite's attitude reference is the geocentric inertial coordinate system. Since satellites operate in a ground-oriented attitude for extended periods, their attitude variation range in the inertial coordinate system is 0° to 360°. Because Euler angles represent an attitude range of 0° to 180°, and quaternions can non-singularly characterize the satellite's omnidirectional attitude, attitude quaternions are used in this paper. To represent the satellite's body coordinate system Relative to the inertial coordinate system The posture, among which, The coordinate system origin is represented by X, Y, and Z, which represent the three axes of the coordinate system. The subscripts B and I are only used to distinguish between the satellite body coordinate system and the geocentric inertial coordinate system. The scalar part representing the attitude quaternion. The vector part representing the attitude quaternion, express The transpose of , and satisfies the constraints. The kinematic and dynamic equations of satellite attitude in attitude quaternion form are as follows:

[0059] ;

[0060] In the formula, This represents the total moment of inertia matrix of the satellite; express The antisymmetric matrix; Represents a 3×3 identity matrix; Indicates the satellite's attitude angular velocity; This represents the total moment of inertia matrix of the satellite; This represents the control angular momentum of the reaction flywheel; for The differential; for The differential;

[0061] The disturbance moment of a solar panel is related to the structural modes of the panel, and the expression for the disturbance moment is: ;

[0062] In the formula, This represents the disturbance torque of the solar panel; This represents the rotational coupling coefficient of the solar panel relative to the satellite coordinate system; This indicates the mode of a solar panel with SADA (Satellite Adaptor and Radiation Protection). express The second derivative of .

[0063] The modal dynamics equations of the solar panel are:

[0064] ;

[0065] in, , These are the modal frequencies of the solar array, with a total of n orders; It represents the square of the nth frequency;

[0066] Step S2:

[0067] Define the satellite in the geocentric inertial coordinate system Expected posture quaternion The attitude control error is then expressed through the error quaternion. The calculation formula is as follows:

[0068] ;

[0069] In the formula, Represents the expected quaternion The reverse; This represents quaternion multiplication; it should be noted that any two quaternions... and The multiplication operation relationship is: ;

[0070] Define the satellite in the geocentric inertial coordinate system Expected angular velocity Then the angular velocity control error can be controlled by the error angular velocity. The calculation formula is as follows:

[0071] ;

[0072] in, Representing the error quaternion The rotation transformation matrix;

[0073] ;

[0074] By using expected quaternions to model the kinematics and dynamics of the satellite's attitude error, the resulting kinematics and dynamics equations for the satellite's attitude error are:

[0075] ;

[0076] In the formula, Representing the error quaternion The vector part; express The antisymmetric matrix; express An antisymmetric matrix.

[0077] Step S3:

[0078] To ensure the stability and tracking performance of the attitude system, an attitude controller is designed using a combination of classical feedback control and nonlinear compensation control. The resulting expression for the attitude controller is:

[0079] ;

[0080] in, Represents the proportional control gain matrix; This represents the proportional control parameters for the three coordinate axes; Represents the differential control gain matrix; This represents the differential control parameters for the three coordinate axes.

[0081] Step S4:

[0082] The satellite's rotational inertia parameters are acquired in real time, and the attitude controller control parameters are designed based on the relationship between the attitude controller control parameters and the satellite's rotational inertia parameters. Specific steps include:

[0083] For the relationship between the imaginary part of the error quaternion of any coordinate axis of a satellite and the deviation angle under small angle conditions, taking the satellite x-axis as an example. By performing differential calculations, we can approximate the following relational expression:

[0084] (1); In formula (1), the subscript x represents the component of the variable on the satellite x-axis;

[0085] Based on the relationship disclosed in formula (1), under approximate conditions, any coordinate axis of the satellite has the following transfer function relationship:

[0086] ;

[0087] Assumption , Further simplified to:

[0088] ;

[0089] To ensure that the attitude controller passively eliminates the disturbance torque of the solar panels, given parameters... ,but and Designed as follows:

[0090] ;

[0091] Therefore, the final parameter design for the attitude controller used for feedback control is as follows:

[0092] ;

[0093] Similarly, the design yields , , , Parameters;

[0094] In the formula, Representing the error quaternion x-axis component; Indicates the roll error angle of the satellite; Represents the total moment of inertia matrix of the satellite. The principal component on the x-axis; The transfer function is represented by s; the complex frequency variable is represented by s. The disturbance torque of the solar panel along the x-axis is represented. Indicates the cutoff frequency of the designed controller; The fundamental frequency of the flexible solar panel; and These are hypothetical variables.

[0095] Step S5:

[0096] The resolution in step S4 reveals that the feedback control parameters are related to the satellite's moment of inertia. Since the SADA drives the solar panels to rotate, the satellite's moment of inertia changes in real time. Therefore, to ensure the stability of the attitude controller, the satellite's moment of inertia needs to be calculated in real time. A flexible satellite with SADA consists of two parts: solar panels and a central rigid body. The moment of inertia of the central rigid body is defined as... And the rotational coupling coefficient of the solar panel relative to the satellite connection point is The rotational coupling coefficient of the solar panel relative to the satellite coordinate system. Approximately:

[0097] ;

[0098] in: This represents the rotation transformation matrix from the solar panel coordinate system to the satellite coordinate system, which is directly calculated from the SADA rotation angle.

[0099] Furthermore, the expression for the rotational inertia parameter of the entire star is obtained as follows:

[0100] ;

[0101] Finally, the controller parameters in step 4 are updated based on the real-time calculated moment of inertia parameters to ensure the stability of the satellite's attitude control when observing the Earth, thus achieving a stable and reliable Earth observation mission.

[0102] Input the real-time acquired rotational inertia parameters of the entire star into step S4;

[0103] In the formula, This represents the moment of inertia of the central rigid body.

[0104] verify:

[0105] This embodiment illustrates the attitude determination accuracy of the method through a stable attitude control process relative to the three ground coordinate axes. The analysis process lasts 200 seconds, with 0-50 seconds representing a 0° attitude relative to the three ground coordinate axes, followed by a 10° lateral swing attitude relative to the three ground coordinate axes after 50 seconds. The Euler angles of the orbital system corresponding to the three coordinate axes at the same time are determined. , and like Figure 1-3 As shown. The four vector parts of the attitude quaternion at the same moment. , , , The corresponding control curve is as follows Figure 4-7 As shown, the attitude angular velocities corresponding to the three coordinate axes at the same time are... , , Control curves as follows Figure 8-10 As shown in the figure, attitude control is stable and smooth. Although the disturbance torque of the flexible sail has some impact on attitude during the initial stage of maneuvering, it dissipates quickly. The four vector parts of the attitude quaternion at the same moment are also shown. , , , Corresponding control error as follows Figures 11-14 As shown; the error angular velocities corresponding to the three coordinate axes at the same time. , , Control error such as Figures 15-17 As shown, the control error converged quickly. Table 1 shows the relevant parameters for this embodiment.

[0106] Table 1 Relevant Parameters

[0107]

[0108] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A method for stabilizing the attitude of a low-Earth orbit flexible satellite with an SADA device, characterized in that, include: S1. Modeling satellite attitude kinematics and dynamics using attitude quaternions; S2. Using expected quaternions to model the kinematics and dynamics of the error attitude, the resulting equations of motion for the satellite's error attitude are: ； In the formula, Represents the error quaternion; Representing the error quaternion The scalar part; Representing the error quaternion The vector part; express The antisymmetric matrix; Represents a 3×3 identity matrix; This represents the total moment of inertia matrix of the satellite; Indicates the satellite's attitude angular velocity; Indicates the error angular velocity; express The antisymmetric matrix; This represents the control angular momentum of the reaction flywheel; Representing the error quaternion The rotation transformation matrix; Indicates the satellite in the inertial coordinate system The expected angular velocity; This represents the rotational coupling coefficient of the solar panel relative to the satellite coordinate system; This indicates the mode of a solar panel with SADA (Satellite Adaptor and Radiation Protection). This indicates the control torque of the reaction flywheel; S3. An attitude controller is designed using a combination of classical feedback control and nonlinear compensation control, based on the error attitude kinematics and dynamics equations. The expression for the attitude controller obtained in step S3 is: ； in, Represents the proportional control gain matrix; This represents the proportional control parameters for the three coordinate axes; Represents the differential control gain matrix; The differential control parameters represent the three coordinate axes; S4. Acquire satellite rotational inertia parameters in real time, and design attitude controller control parameters based on the relationship between attitude controller control parameters and satellite rotational inertia parameters; specific steps include: For the relationship between the imaginary part of the error quaternion of any coordinate axis of the satellite and the deviation angle under small angle conditions, differential calculation is performed, and the following approximate expression is obtained using the satellite x-axis as an example: （1）； Based on the relationship disclosed in formula (1), under approximate conditions, any coordinate axis of the satellite has the following transfer function relationship: ； Assumption , ; To ensure that the attitude controller passively eliminates the disturbance torque of the solar panels, given parameters... ,but and Designed as follows: ； Therefore, the final parameter design for the attitude controller used for feedback control is as follows: ； Similarly, the design yields , , , Parameters; In the formula, Representing the error quaternion x-axis component; Indicates the roll error angle of the satellite; Represents the total moment of inertia matrix of the satellite. The principal component on the x-axis; The transfer function is represented by s; the complex frequency variable is represented by s. The disturbance torque of the solar panel along the x-axis is represented. Indicates the cutoff frequency of the designed controller; The fundamental frequency of the flexible solar panel; and Assumption variables; This represents the error angular velocity corresponding to the satellite's x-axis; S5. Obtain the real-time satellite moment of inertia and update the attitude controller parameters in step S4 using the real-time calculated satellite moment of inertia parameters, specifically including: Based on the rotational coupling coefficient of the solar panel relative to the satellite connection point, the rotational coupling coefficient of the solar panel relative to the satellite coordinate system is obtained. The rotational inertia parameters of the entire satellite are obtained based on the rotational inertia of the central rigid body and the rotational coupling coefficient of the solar panels relative to the satellite coordinate system. The expression for the moment of inertia parameter of the entire star is as follows: ; Input the real-time acquired rotational inertia parameters of the entire star into step S4; In the formula, This represents the moment of inertia of the central rigid body.

2. The method for attitude stabilization control of a low-orbit flexible satellite with SADA device according to claim 1, characterized in that, The expression for the disturbance torque of the solar panel is: In the formula, This represents the disturbance torque of the solar panel.

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