A micro-satellite orbit control method for only single-sided single-axis SADA

Abstract

This invention belongs to the field of satellite orbit control technology. It discloses a method for orbit control of a microsatellite with only a single-sided, single-axis SADA (Satellite Adaptor Control), comprising the following steps: S1. Obtaining the satellite's center of mass position corresponding to different rotation angles of the single-sided, single-axis SADA; S2. Calculating the thrust vector deviation arm based on the satellite's center of mass position, determining the safe attitude range during orbit control, and calculating the position with the longest orbit control time; S3. Calculating the satellite position and time corresponding to the SADA rotation angle based on the relationship between the SADA rotation angle and the satellite's vector to the sun.

Description

Technical Field

[0001] This invention relates to the field of satellite orbit control technology, and in particular to a method for orbit control of microsatellites with only single-sided single-axis SADA. Background Technology

[0002] With the development of aerospace technology, microsatellites have been widely used due to their advantages such as light weight, small size, low cost, and short development cycle. However, due to payload limitations, some microsatellites need to maintain a long-term Earth-oriented working attitude, requiring the installation of a Solar Actuation and Driving (SADA) mechanism to control the solar panels for solar-oriented charging to ensure the satellite's overall energy security. Due to the demand for low cost and lightweight design, some microsatellites are designed using only a single-sided, single-axis SADA to reduce overall cost and weight. For microsatellites, due to the need for low cost and lightweight design, the propulsion system typically only has one orbit control thruster, without an attitude control thruster. Attitude stability during orbit control missions is ensured by a three-axis reaction flywheel. Due to factors such as satellite structural design, installation deviations, and thruster performance, the thrust vector of the thruster cannot strictly pass through the satellite's center of mass during orbit control missions. This deviation of the thrust vector relative to the center of mass creates a deviation torque. Sustained deviation torque will increase the overall angular momentum of the satellite, which requires the three-axis reaction flywheel to absorb it. As the orbit control time increases, the deviation angular momentum will lead to the saturation of the flywheel assembly's angular momentum, which in turn will affect the attitude safety of the entire satellite.

[0003] Based on this, those skilled in the art urgently need to propose an orbit control method for single-sided, single-axis SADA microsatellites that are only equipped with orbit control thrusters and have limited control capabilities of three-axis reaction flywheels. Summary of the Invention

[0004] In view of this, the present invention provides a global automatic coverage method for a large-scale remote sensing satellite constellation. Based on the characteristics of the change in the satellite's center of mass position when rotating on a single side and a single axis (SADA), and the available output torque of the flywheel, the present invention analyzes the range of SADA rotation angles when the satellite's attitude is stable during the orbit control mission and calculates the SADA rotation angle when the orbit control time is the longest. Based on the relationship between the SADA rotation angle and the satellite's vector to the sun, the present invention calculates the satellite position and time corresponding to the SADA rotation angle and plans the orbit control mission according to the available arc segment.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: A method for orbit control of microsatellites with only single-sided, single-axis SADA (Supervisory Aided Assist) includes the following steps: S1. Obtain the position of the satellite's centroid when the single-axis SADA rotates at different angles on one side; S2. Based on the satellite's center of mass position, calculate the thrust vector deviation arm, determine the safe range of attitude during orbit control, and calculate the position with the longest orbit control time; S3. Based on the relationship between the SADA rotation angle and the satellite's vector to the sun, calculate the satellite position and time corresponding to the SADA rotation angle.

[0006] Preferably, the position of the satellite's centroid is obtained when the single-sided single-axis SADA rotates at different angles, specifically as follows: Based on the satellite model centroid position data corresponding to different angles of rotation of the single-sided single-axis SADA, the least squares method is used to perform circular curve fitting to generate a centroid position change curve. Based on the sampling point information and the centroid position change curve, the position of the satellite centroid corresponding to any rotation angle of SADA is obtained.

[0007] Preferably, the thrust vector deviation lever arm is calculated based on the satellite's center of mass position, specifically including: In a satellite system, the axis of the orbital control thruster nozzle is usually parallel to one coordinate axis. The positional deviation between the orbital control thruster nozzle and the center of mass on the other two coordinate axes perpendicular to the nozzle axis forms the thrust vector deviation lever arm. The two coordinates of the mid-orbit control thruster nozzle in the direction of the thrust vector deviation lever arm are respectively The deviation lever arms formed by the thrust on the two coordinate axes are respectively and ,but ； Where (x,y) represents the coordinates of the satellite's centroid; p is undefined and is only used for distinction.

[0008] Preferably, the range for determining attitude safety during track control specifically includes: If the maximum control torque provided by a single-axis flywheel during track control is M, and the thrust is F, then the first judgment condition is met during track control: ; Based on the first judgment condition and the centroid position change curve, the range of SADA rotation angle when the thrust vector deviation arm meets the actual requirements is obtained.

[0009] Preferred locations for calculating the longest track control time include: The threshold for angular momentum absorption by a single flywheel during orbit control is H. Based on the thrust vector deviation arm, the theoretical longest orbit control time t is: .

[0010] Preferably, based on the relationship between the SADA rotation angle and the satellite's vector to the sun, the satellite position and time corresponding to the SADA rotation angle are calculated, including: By integrating the satellite's orbital dynamics model, the satellite's position and velocity at the termination of the orbital recursion can be obtained; Based on the satellite's position and velocity at the termination time of the orbital recursion, calculate the satellite's position and velocity in the underground inertial frame; Since the +Yo axis of the satellite orbital coordinate system is the normal vector of the XoOZo plane of the satellite orbital coordinate system, let the position vector of the sun in the geocentric inertial frame be... The projection of the satellite's vector to the Sun onto the XoOZo plane of the orbital coordinate system is... for: ; In the formula, Represents the normalized vector along the +Yo axis. Indicates the position of the satellite in a geocentric inertial frame; Regarding the SADA rotation angle, when the projection of the solar vector on the orbital plane coincides with the +Zo axis of the orbital coordinate system, the corresponding SADA rotation angle is ±180°. When the solar vector coincides with the -Zo axis of the orbital coordinate system, the corresponding SADA rotation angle is 0°. Rotating counterclockwise around the +Yo axis of the orbital coordinate system is considered as an increase in angle. Since the SADA rotation angle corresponds to both the thrust vector deviation arm of the satellite and the satellite's on-orbit position, the satellite position corresponding to the SADA rotation angle meeting the requirements can be obtained by analyzing the available SADA rotation angle range and optimal value for orbit control. Based on the correspondence between the satellite position and time, the available time range for orbit control and the time corresponding to the optimal value can be obtained.

[0011] Preferably, the orbital dynamics model expression of the satellite is: ; in, ; In the formula, the satellite's position vector in the Earth-fixed system is: The magnitude of the position vector is The Earth's gravitational constant is The Earth's equatorial radius is The satellite's orbital dynamics model only considers the two-body problem and J2 perturbation; Indicates satellite position The second derivative, Indicates a two-body perturbation term. This represents the J2 perturbation term.

[0012] Preferably, the expressions for the satellite's position and velocity at the termination of the orbit recursion are as follows: ; The initial time when the satellite begins orbit recursion is The location is The speed is The orbital recursion termination time is The satellite's position at the time the orbit recursion terminates. and speed .

[0013] Preferably, the angles between the projection vector and the satellite position and velocity vectors are respectively: ; The rotation angle of SADA is expressed as: ; in, Represents the projection vector The angle between the vector and the satellite's position vector Represents the projection vector The angle between the vector and the satellite's velocity vector This represents the velocity of a satellite in a geocentric inertial frame of reference.

[0014] Preferred options also include: The satellite positions that meet the SADA rotation angle range for orbit control are converted into latitude and longitude of the nadir point. Based on the latitude and longitude of the ground station and its measurement and control range, the arc segment and time range for the ground station to track the orbit control process in real time are calculated.

[0015] As can be seen from the above technical solution, compared with the prior art, this invention discloses a method for orbit control of microsatellites equipped with only a single-sided, single-axis SADA. For microsatellites equipped with only a single-sided, single-axis SADA, the attitude safety of the entire satellite during orbit control missions is affected by the rotation angle of the SADA. Therefore, based on the correspondence between the SADA rotation angle, the center of mass position, and the satellite's on-orbit position, the technical solution of this invention can rationally select the orbit control timing, and while ensuring the attitude safety of the entire satellite during orbit control missions, maximize the control capability of a single orbit control mission, and plan the orbit control missions and command uploads in advance according to the real-time telemetry requirements of the ground station. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0017] Figure 1The attached figure is a graph showing the variation of the X-axis and Z-axis coordinates of the satellite's center of mass in the celestial coordinate system according to an embodiment of the present invention; Figure 2 is a diagram showing the SADA rotation angle of 142.9° in an embodiment of the present invention and the corresponding satellite sub-satellite point position. Figure 3 shows the SADA rotation angle of this embodiment of the invention at -36.1° and the corresponding satellite sub-satellite point position. Figure 4 is a diagram showing the SADA rotation angle of -130° in an embodiment of the present invention and the corresponding satellite sub-satellite point position. Figure 5 shows the SADA rotation angle of the embodiment of the present invention at 130° and the corresponding satellite sub-satellite point position. Figure 6 shows the SADA rotation angle of the embodiment of the present invention at -126.6° and the corresponding satellite sub-satellite point position. Detailed Implementation

[0018] The technical solutions in the embodiments of the present invention will be clearly and completely described below. 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.

[0019] This embodiment was implemented on a satellite of a certain model manufactured by Changguang Satellite Technology Co., Ltd. The nominal orbit of this satellite is a sun-synchronous orbit with an altitude of 500 km, a descending node local time of 10:35 am, and an orbital period of 5676.98 s. This satellite is equipped with one orbit control thruster with a thrust of 0.05 N, mounted on the XOZ plane in the satellite coordinate system. The thrust vector is in the same direction as the +Y axis of the satellite coordinate system. The coordinates of the thrust nozzle in the satellite coordinate system are (19 mm, 13.5 mm, 23 mm). The rotation axis of the satellite's SADA mechanism is parallel to the Y axis of the satellite coordinate system. Three flywheels are respectively mounted on the X, Y, and Z axes of the satellite coordinate system. During orbit control, the maximum output torque available for a single flywheel is 1.5 mN·m, and the maximum absorbable angular momentum available for a single flywheel is 12.5 mN·m·s.

[0020] For this type of satellite, the position of the satellite's center of mass when the single-axis SADA rotates at different angles in the celestial coordinate system is shown in Table 1.

[0021] Table 1. Position of the satellite's center of mass when rotating the single-axis SADA at different angles in the stellar coordinate system.

[0022] This embodiment discloses a method for orbit control of microsatellites with only single-sided single-axis SADA, including the following steps: S1. Obtain the position of the satellite's centroid when the single-axis SADA rotates at different angles on one side; S2. Based on the satellite's center of mass position, calculate the thrust vector deviation arm, determine the safe range of attitude during orbit control, and calculate the position with the longest orbit control time; S3. Based on the relationship between the SADA rotation angle and the satellite's vector to the sun, calculate the satellite position and time corresponding to the SADA rotation angle.

[0023] Specifically: In this embodiment, when the single-axis SADA rotates on one side, the solar array connected to the SADA rotates together. For charging efficiency, the mass and size of the single-sided solar array are relatively large. The rotation of the solar array causes a significant change in the satellite's center of mass position, which is the main factor affecting this change.

[0024] Since the maximum range of rotation angle of the single-sided single-axis SADA relative to the overall satellite attitude is -180° to 180°, and the coordinates of the satellite's center of mass along the axis of rotation of the single-sided solar array do not change, the change in the satellite's center of mass position occurs on two coordinate axes perpendicular to the axis of rotation of the single-sided solar array. The change curve is approximately circular, corresponding one-to-one with the rotation angle of the SADA. Based on the satellite model's center of mass position data corresponding to different rotation angles of the single-sided single-axis SADA, a circular curve is fitted using the least squares method. The fitted circle coordinates (A, B) and radius R are obtained. Let the two coordinates of the satellite's center of mass position change be (x, y). The standard equation of the circular curve is: ; Based on the sampling point information and the centroid position change curve, the satellite centroid position corresponding to any rotation angle of SADA is obtained. In this embodiment, the center coordinates are (-11.14, 0.62) mm, and the radius is 19.43 mm. Therefore, the X-axis and Z-axis coordinates of the satellite centroid satisfy...

[0025] The curves showing the changes in the X-axis and Z-axis coordinates of the satellite's center of mass are as follows: Figure 1 As shown.

[0026] For microsatellites, the axis of the orbital control thruster nozzle in the satellite's internal system is usually parallel to one coordinate axis. However, since the actual thrust vector cannot pass precisely through the satellite's center of mass, the nozzle and the center of mass are located on another axis perpendicular to the nozzle axis. 2 Positional deviations on the coordinate axes will formThe thrust vector deviation arm, or deviation arm for short, is the deviation torque generated under thrust that affects the attitude stability of the entire satellite. Since microsatellites rely solely on a three-axis reaction flywheel for attitude control, if the deviation torque generated by the thrust is greater than or equal to the control torque provided by the flywheel during orbit control, the satellite's attitude will become unstable, affecting its overall attitude safety. The two coordinates of the thruster nozzle in the direction generating the thrust vector deviation arm are... The deviation lever arms formed by the thrust on the two coordinate axes are respectively and ,but ； Where (x,y) represents the coordinates of the satellite's centroid; p is undefined and is only used for distinction.

[0027] In this embodiment, since the thrust vector is in the same direction as the +Y axis in the celestial coordinate system, the thrust deviation arm is mainly generated in the X and Z axis directions. Let the component of the deviation arm in the X axis direction be l. x The component in the Z-axis direction is l z If the X-axis and Z-axis coordinates of the satellite's center of mass are (x, z), then l x lz satisfies: , . The specific range for determining attitude safety during track control includes: If the maximum control torque provided by a single-axis flywheel during track control is M, and the thrust is F, then the first judgment condition is met during track control: ; Based on the first judgment condition and the change curve of the center of mass position, the range of SADA rotation angle is obtained when the thrust vector deviation lever arm meets the actual requirements.

[0028] Specifically: In this embodiment, to ensure attitude stability, orbit control should be performed within the range of the SADA rotation angle. Considering attitude safety during orbit control, the thrust deviation lever arm should satisfy: ; ; ; Based on the deviation lever arm limit and the fitting curve of the center of mass position, the range of X-axis and Z-axis coordinates of the satellite's center of mass when the attitude is stable is (0.3018, -15.0838) ~ (-22.8639, 16.1143), corresponding to SADA rotation angles of -36.1° to -180° and 142.9° to 180°. The positions with the longest orbit control time are calculated, specifically including: The threshold for a single flywheel to absorb angular momentum during orbit control is H. Based on the thrust vector deviation lever arm, the theoretical longest orbit control time t is: ; In this embodiment, while ensuring attitude safety, the theoretically longest orbit control time meets the following requirements. ; Since the flywheel can only absorb a limited amount of angular momentum during orbit control, the larger the deviation arm, the larger the deviation torque, and the shorter the time it takes to absorb angular momentum to reach the threshold, resulting in a shorter orbit control time. Therefore, the orbit control time is longest when the resultant arm is the smallest. Thus, the orbit control capability of this satellite is optimized. The objective function J and constraints of the optimization problem are described as follows:

[0029] In the formula, (A,B) are the coordinates of the center of the fitted circular curve, and R is the radius of the fitted circular curve. In this embodiment ; The interior point method is used to solve this optimization problem. When the X and Z coordinates of the satellite's center of mass are (4.4580, 12.2011), the resultant arm is the smallest and the orbit control time is the longest. The solution shows that the SADA rotation angle at this time is -126.6°. Based on the threshold for flywheel angular momentum absorption during orbit control, the theoretically longest orbit control time reaches: .

[0030] Based on the relationship between the SADA rotation angle and the satellite's vector to the sun, calculate the satellite position and time corresponding to the SADA rotation angle. In the satellite's orbital coordinate system, the origin O coincides with the satellite's center of mass. The +Zo axis points towards the Earth's center, meaning the satellite's center of mass is in the opposite direction to the Earth's radius vector. The +Xo axis is perpendicular to the +Zo axis in the orbital plane, pointing in the direction of the satellite's velocity. The +Yo axis is perpendicular to the orbital plane and forms a right-handed coordinate system with the other two axes; the orbital plane is the XoOZo plane. For satellites with single-degree-of-freedom solar panels, the commonly used attitude orientation mode is Earth-to-space attitude stability, meaning that when the satellite is not performing a mission, the three axes of the celestial coordinate system and the orbital coordinate system coincide. In this mode, the optimal state for solar panel charging efficiency is when the normal to the solar panel and the projection of the satellite-to-sun vector onto the orbital plane are in the same direction. The rotation angle of the projection of the satellite-to-sun vector onto the orbital plane is the same as the SADA rotation angle, thus establishing a correspondence between the satellite's on-orbit position and the SADA rotation angle.

[0031] Considering that the satellite obtains its orbital information as a three-axis position and velocity in the Earth-fixed frame from the navigation receiver, let the satellite's position vector in the Earth-fixed frame be... The magnitude of the position vector is The Earth's gravitational constant is μ e The Earth's equatorial radius is re The satellite's orbital dynamics model only considers the two-body problem and J2 perturbation. The satellite's orbital dynamics model is as follows: ; in,

[0032] The initial time when the satellite begins orbit recursion is The location is The speed is The orbital recursion termination time is By integrating the satellite's orbital dynamics model, the satellite's position at the termination of the orbital recursion can be obtained. and speed for: ; The obtained satellite position and velocity in the Earth-fixed frame are transformed using coordinate system transformation to calculate the satellite's position in the geocentric inertial frame. and speed .

[0033] Considering that the +Zo axis of the satellite orbital coordinate system is opposite to the direction of the satellite's position, and the +Xo axis is in the same direction as the satellite's velocity, the normalized vector representation of the +Yo axis of the satellite orbital coordinate system in the geocentric inertial frame is as follows:

[0034] Since the +Yo axis of the satellite orbital coordinate system is the normal vector of the XoOZo plane of the satellite orbital coordinate system, let the position vector of the sun in the geocentric inertial frame be... The projection of the satellite's vector to the Sun onto the XoOZo plane of the orbital coordinate system is... for: In the formula, Represents the normalized vector along the +Yo axis. Indicates the position of the satellite in a geocentric inertial frame; Then, for the angles between the projection vector and the satellite position and velocity vectors, we have: ; Regarding the rotation angle of SADA, when the projection of the solar vector onto the orbital plane coincides with the +Zo axis of the orbital coordinate system, the corresponding SADA rotation angle is ±180°; when the solar vector coincides with the -Zo axis of the orbital coordinate system, the corresponding SADA rotation angle is 0°. Counterclockwise rotation around the +Yo axis of the orbital coordinate system is considered an increase in angle. Therefore, the SADA rotation angle can be expressed as...

[0035] Since the SADA rotation angle corresponds to both the thrust deviation arm of the satellite and the satellite's on-orbit position, the satellite position corresponding to the SADA rotation angle meeting the requirements can be obtained by analyzing the available SADA rotation angle range and optimal value for orbit control. Based on the correspondence between the satellite position and time, the available time range for orbit control and the time corresponding to the optimal value can be obtained.

[0036] Considering that when initially applying this strategy for orbit control, it is necessary to monitor the attitude safety of the entire satellite and confirm the effectiveness of the method through real-time telemetry from the ground station, this embodiment also includes step four: converting the satellite position that meets the SADA rotation angle range available for orbit control into the latitude and longitude of the nadir point, and calculating the arc segment and time range of the real-time tracking orbit control process of the ground station based on the latitude and longitude of the ground station and its measurement and control range.

[0037] It should be noted that traditional microsatellites with SADA (Satellite Adaptive Assist) typically employ symmetrical solar arrays in their design. This design helps maintain attitude stability in space, and under normal conditions, the single-axis SADAs on both sides of the satellite rotate simultaneously at the same speed, keeping the satellite's center of mass relatively stable. However, some microsatellites, in order to reduce overall cost and mass, use only a single-sided, single-axis SADA. To ensure overall charging efficiency, the size and mass of the single-sided solar array are relatively large. The rotation of this single-sided solar array causes a significant change in the satellite's center of mass, resulting in a corresponding change in the thrust vector's deviation from the center of mass. If this change in the satellite's center of mass leads to an excessive deviation in the thrust vector, the excessively large deviation in angular momentum can cause rapid saturation of the flywheel assembly's angular momentum, reducing the satellite's orbital control time. In more severe cases, the change in the satellite's center of mass can cause the thrust deviation torque to exceed the output torque of the three-axis reaction flywheel, making it impossible for the satellite to maintain stable attitude during orbital control missions and affecting the overall attitude safety of the satellite.

[0038] Therefore, this embodiment discloses a method for orbit control of microsatellites equipped with only a single-sided, single-axis SADA. For microsatellites with only a single-sided, single-axis SADA, the overall attitude safety of the satellite during orbit control is affected by the SADA rotation angle. Therefore, based on the correspondence between the SADA rotation angle, the center of mass position, and the satellite's on-orbit position, the technical solution of this invention can rationally select the orbit control timing. Furthermore, while ensuring the overall attitude safety of the satellite during orbit control, it maximizes the control capability of a single orbit control mission, and allows for advance planning of orbit control missions and command uploads based on the real-time telemetry requirements of the ground station.

[0039] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0040] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for orbit control of microsatellites with only single-sided, single-axis SADA, characterized in that, Includes the following steps: S1. Obtain the satellite centroid position corresponding to different angles of rotation of a single-axis SADA; specifically: Based on the satellite model centroid position data corresponding to different angles of rotation of the single-sided single-axis SADA, the least squares method is used to perform circular curve fitting to generate a centroid position change curve. Based on the sampling point information and the centroid position change curve, the position of the satellite centroid corresponding to any rotation angle of SADA is obtained; S2. Based on the satellite's center of mass position, calculate the thrust vector deviation arm, determine the safe range of attitude during orbit control, and calculate the position with the longest orbit control time; The specific range for determining attitude safety during track control includes: If the maximum control torque provided by a single-axis flywheel during track control is M, and the thrust is F, then the first judgment condition is met during track control: ； Based on the first judgment condition and the centroid position change curve, the range of SADA rotation angle when the thrust vector deviation lever arm meets the actual requirements is obtained. S3. Based on the relationship between the SADA rotation angle and the satellite's vector to the sun, calculate the satellite position and time corresponding to the SADA rotation angle.

2. The orbit control method for microsatellites with only single-sided single-axis SADA as described in claim 1, characterized in that, Based on the satellite's center of mass position, the thrust vector deviation lever is calculated, specifically including: In a satellite system, the axis of the orbital control thruster nozzle is usually parallel to one coordinate axis. The positional deviation between the orbital control thruster nozzle and the center of mass on the other two coordinate axes perpendicular to the nozzle axis forms the thrust vector deviation lever arm. In the satellite system, the two coordinates of the orbital control thruster nozzle in the direction of the thrust vector deviation lever arm are respectively The deviation lever arms formed by the thrust on the two coordinate axes are respectively and ,but ； Where (x,y) represents the coordinates of the satellite's centroid; p is undefined and is only used for distinction.

3. The orbit control method for microsatellites with only single-sided single-axis SADA as described in claim 2, characterized in that, The location with the longest track control time is calculated, specifically including: The threshold for angular momentum absorption by a single flywheel during orbit control is H. Based on the thrust vector deviation arm, the theoretical longest orbit control time t is: 。 4. The orbit control method for microsatellites with only single-sided single-axis SADA as described in claim 3, characterized in that, Based on the relationship between the SADA rotation angle and the satellite's vector to the sun, calculate the satellite position and time corresponding to the SADA rotation angle, including: By integrating the satellite's orbital dynamics model, the satellite's position and velocity at the termination of the orbital recursion can be obtained; Based on the satellite's position and velocity at the termination time of the orbital recursion, calculate the satellite's position and velocity in the underground inertial frame; Since the +Yo axis of the satellite orbital coordinate system is the normal vector of the XoOZo plane of the satellite orbital coordinate system, let the position vector of the sun in the geocentric inertial frame be... The projection of the satellite's vector to the Sun onto the XoOZo plane of the orbital coordinate system is... for: ； In the formula, Represents the normalized vector along the +Yo axis. Indicates the position of the satellite in a geocentric inertial frame; Regarding the SADA rotation angle, when the projection of the solar vector on the orbital plane coincides with the +Zo axis of the orbital coordinate system, the corresponding SADA rotation angle is ±180°. When the solar vector coincides with the -Zo axis of the orbital coordinate system, the corresponding SADA rotation angle is 0°. Rotating counterclockwise around the +Yo axis of the orbital coordinate system is considered as an increase in angle. Since the SADA rotation angle corresponds to both the thrust vector deviation arm of the satellite and the satellite's on-orbit position, the satellite position corresponding to the SADA rotation angle meeting the requirements can be obtained by analyzing the available SADA rotation angle range and optimal value for orbit control. Based on the correspondence between the satellite position and time, the available time range for orbit control and the time corresponding to the optimal value can be obtained.

5. A method for orbit control of a microsatellite with only single-sided single-axis SADA as described in claim 4, characterized in that, The orbital dynamics model expression of the satellite is as follows: ； in, ; In the formula, the satellite's position vector in the Earth-fixed system is: The magnitude of the position vector is The Earth's gravitational constant is The Earth's equatorial radius is The satellite's orbital dynamics model only considers the two-body problem and J2 perturbation; Indicates satellite position The second derivative, Indicates a two-body perturbation term. This represents the J2 perturbation term.

6. The orbit control method for a microsatellite with only single-sided single-axis SADA as described in claim 4, characterized in that, The expressions for the satellite's position and velocity at the termination of the orbital recursion are: ； The initial time when the satellite begins orbit recursion is The location is The speed is The orbital recursion termination time is The satellite's position at the time the orbit recursion terminates. and speed .

7. A method for orbit control of a microsatellite with only single-sided single-axis SADA as described in claim 4, characterized in that, Regarding the angles between the projection vector and the satellite position and velocity vectors, we have: ； The rotation angle of SADA is expressed as: ； in, Represents the projection vector The angle between the vector and the satellite's position vector Represents the projection vector The angle between the vector and the satellite's velocity vector This represents the velocity of a satellite in a geocentric inertial frame of reference.

8. The orbit control method for a microsatellite with only single-sided single-axis SADA as described in claim 1, characterized in that, Also includes: The satellite positions that meet the SADA rotation angle range for orbit control are converted into latitude and longitude of the nadir point. Based on the latitude and longitude of the ground station and its measurement and control range, the arc segment and time range for the ground station to track the orbit control process in real time are calculated.

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