Method for near real-time orbit maintenance and compensation of electric propulsion low earth orbit satellites

Abstract

The application discloses a kind of electric propulsion low-orbit satellite near real-time orbit maintenance and compensation method, solve the problem of low orbit in-orbit accuracy, belong to the field of orbit control;Including: the difference between the standard orbit position vector of task preset and real-time orbit position vector is used as current position deviation to obtain position compensation amount;Satellite-borne computer obtains perturbation force compensation amount by built-in high-precision orbit perturbation model;Center gravity compensation amount is obtained based on the earth's gravitational constant, standard orbit position vector and real-time orbit position vector;The sum of position compensation amount, perturbation force compensation amount and center gravity compensation amount is obtained to obtain total compensation amount to obtain thrust command;When the thrust module value in thrust command is greater than the actual maximum thrust size, generate maximum thrust execution instruction to update thrust command;After thrust command execution is completed, the next control cycle is started, until current position deviation is less than threshold value;The application improves the in-orbit accuracy of orbit, ensures that position accuracy meets the best efficiency of sensor.

Description

Technical Field

[0001] This invention belongs to the field of orbit control technology and relates to a near-real-time orbit maintenance and compensation method for electrically propelled low-Earth orbit satellites. Background Technology

[0002] During their operation in orbit, low-Earth orbit satellites are significantly affected by various perturbations, including the Earth's non-spherical gravity, atmospheric drag, and solar radiation pressure. To maintain their pre-programmed mission orbit, satellites must periodically perform orbit maintenance maneuvers to ensure the detection performance of their payloads in high-precision imaging, data acquisition, and other missions.

[0003] Electric propulsion systems are systems that use electrical energy to ionize and accelerate propellant (such as xenon) through the core actuator, the electric thruster, to generate thrust. In recent years, electric propulsion systems have been widely used in large-scale constellation satellites such as Starlink and OneWeb due to their advantages of high specific impulse and high control precision. Therefore, it is necessary to study an effective orbit maintenance scheme that uses electric propulsion systems to compensate for perturbation deviations and extend the on-orbit life of low-Earth orbit satellites.

[0004] For low-Earth orbit satellites operating at altitudes of 200-2000 km, continuous low-thrust orbit maintenance methods, represented by electric propulsion system control, can be divided into two categories: Method 1 is to apply a constant thrust, and determine the direction and duration of the thrust based on the orbital deviation; Method 2 is to apply thrust with varying magnitude and direction, and determine the magnitude and direction of the thrust by compensating for atmospheric drag or using control methods such as model prediction; the measurement and evaluation of atmospheric drag is the key to this method.

[0005] For Method 1, in order to calculate constant thrust and propulsion time, Mo Fan, Ding Jianzhao, Ren Fang, et al. An Autonomous Orbit Control Method for Low-Earth Orbit Remote Sensing Satellites [J]. Spacecraft Engineering, 2020, 29(3): 12-17, proposed an autonomous control method for low-Earth orbit remote sensing satellites. The method uses orbital element deviation as the control variable and combines the remaining fuel and orbit recursion algorithm to calculate the application time of constant small thrust to achieve autonomous orbit maintenance. Ning Kai, Wu Baolin. Event-Driven Trajectory Maintenance Control of Spacecraft Sub-Satellite Points [J]. Acta Aeronautica Sinica, 2024, 45(10): 291-303, focused on high-precision control of ultra-low-Earth orbit spacecraft and proposed an event-driven fuzzy adaptive method to ensure the life of electric thrusters and reduce the burden of inter-satellite communication with constant thrust, while balancing atmospheric drag disturbances. This type of method has low computational complexity and is suitable for on-board autonomous control; however, its propulsion time is discrete and cannot achieve optimal energy consumption or optimal control time. Publication number: CN108536009A, invention title: A method for orbit maintenance and disturbance suppression of hybrid low-thrust spacecraft. It designs a sliding mode variable structure controller for hybrid low-thrust spacecraft, which can maintain the characteristics of being insensitive to parameters and disturbances even when the thrust is limited. However, it is not applicable to low-orbit small satellites.

[0006] Regarding Method 2, publication number: CN114771873A, invention title: A method for autonomous and precise maintenance of ultra-low orbit satellite orbit; in the absence of accelerometers for atmospheric drag acceleration measurement, the magnitude of atmospheric drag is determined by the change in the deviation of the semi-major axis, and the orbit control thrust is corrected and compensated in real time based on the determined atmospheric drag, thus realizing a method for maintaining and controlling ultra-low orbit satellite orbit with meter-level accuracy. However, this method cannot compensate for the offset of thrust inclination caused by long-term perturbations. In LucMaisonobe1, Pascal Parraud2. Very Low Thrust Station-Keeping for Low EarthOrbiting Satellites[J]. Advances in Space Research,2023,Vol.71(3): 1558-1593, for the maintenance of the sub-satellite point in a sun-synchronous orbit, a ground trajectory grid is defined and an alternating two-leg control strategy is proposed. The semi-major axis change rate is adjusted by alternating control of "maximum thrust-zero thrust" to constrain the trajectory within the dead zone. In Mahfouz, A.; Gaias, G.; Venkateswara Rao, DMKK; Voos, H. Autonomous Optimal Absolute OrbitKeeping through Formation Flying Techniques[J]. Aerospace 2023, 10, 959, a model predictive control scheme is proposed based on formation flight technology. The virtual spacecraft orbit is used as a reference to take into account both multi-satellite scenarios and absolute orbit control requirements, so as to achieve absolute orbit maintenance in multi-satellite scenarios. The orbit control law can achieve high-precision orbit control and target optimization, but its derivation and control rely on high-performance computing, and the control accuracy requires high thrusters and has low fault tolerance. Summary of the Invention

[0007] Existing orbit maintenance methods fail to fully utilize the advantages of electric thrusters—high specific impulse and precise thrust control—and, based on the core logic of "correction after orbit deviation," inherently suffer from control lag. This makes them unable to offset the dynamic effects of perturbations on the orbit in real time and ill-suited to the real-time management requirements of multi-satellite coordination in large-scale constellations. This invention proposes a near-real-time orbit maintenance and compensation method for electric-propelled low-Earth orbit (LEO) satellites. This method combines high-precision orbit determination, accurate perturbation prediction, and the characteristics of electric propulsion, proposing an efficient, near-real-time orbit maintenance method for "bias-free" orbital operation of electric-propelled spacecraft. It strengthens the core logic of orbit maintenance by applying continuous small thrusts to the LEO satellite to achieve "near-real-time orbit correction," enabling it to autonomously and stably operate on a preset trajectory without significant external interference. This improves on-orbit orbit accuracy, ensuring that positional accuracy meets the requirements for optimal sensor performance in complex space missions.

[0008] The objective of this invention is specifically achieved through the following technical solutions:

[0009] This invention discloses a near-real-time orbit maintenance and compensation method for electrically propelled low-Earth orbit satellites, the method comprising:

[0010] Step 1: The onboard computer converts the real-time data of the low-Earth orbit satellites acquired by the onboard GNSS receiver into the real-time orbital position vector and real-time velocity vector of the low-Earth orbit satellites in the geocentric inertial coordinate system (ECI).

[0011] Step 2: The difference between the preset standard orbit position vector and the real-time orbit position vector is taken as the current position deviation; the proportional term of the current position deviation is combined with the integral and differential terms of the current position deviation, and the control weight is adjusted according to different orbit tasks to obtain the position compensation amount.

[0012] Step 3: The onboard computer uses a built-in high-precision orbital perturbation model, taking the real-time orbital position vector and real-time velocity vector as inputs, and sums the output forces of atmospheric drag, solar radiation pressure, three-body gravity, tidal forces, and relativistic effects to obtain the perturbation force compensation amount.

[0013] Step 4: Based on the Earth's gravitational constant, obtain the central gravitational compensation amount from the standard orbital position vector and the real-time orbital position vector;

[0014] Step 5: Sum the position compensation, perturbation compensation, and central gravity compensation to obtain the total amount to be compensated; transform the total amount to be compensated into the satellite body coordinate system RTN to obtain the thrust command of the electric thruster; when the magnitude of the thrust generated by the electric thruster in the thrust command is greater than the actual maximum thrust of the electric thruster, the maximum thrust command is generated from the maximum thrust constraint and updated into the thrust command.

[0015] Step six: The onboard computer sends thrust commands to the electric propulsion system, which then controls the electric thrusters to execute the thrust commands for orbit correction. After the thrust commands are executed, the low-Earth orbit satellite enters a pre-set time-free coasting phase, returns to step one, and begins the next control cycle until the current position deviation is less than the threshold, at which point the control cycle ends.

[0016] In step two, the current position deviation is calculated as follows:

[0017] ;

[0018] In the formula, The deviation is the current position at time t, where t is the current time. The standard orbital position vector preset for the mission, Let be the standard orbital position vector at time t. ; This represents the coordinates of the standard orbital position vector in the geocentric inertial coordinate system (ECI). This is the real-time orbital position vector. Let be the real-time orbital position vector at time t. ; This represents the coordinates of the real-time orbital position vector in the geocentric inertial coordinate system (ECI).

[0019] In step two, the method for calculating the position compensation amount is as follows:

[0020] ;

[0021] In the formula, For position compensation amount, This is the percentage of the current position deviation. This is the integral term of the current position deviation. This is the differential term of the current position deviation. The proportional coefficient controls the weight. The integral coefficient controls the weight. The differential coefficients control the weights.

[0022] In step two, the integral term of the current position deviation is calculated as follows:

[0023] ;

[0024] The differential term of the current position deviation is calculated as follows:

[0025] ;

[0026] In the formula, The step size for each measurement and control is shorter than the orbit maintenance cycle. Let i be the current position deviation at time i. Indicates the integration interval. t represents the current time. The deviation of the current position at time t-1. This represents the current position deviation at time t-2.

[0027] In step three, the calculation method for the perturbation force compensation is as follows:

[0028] ;

[0029] In the formula, For the amount of perturbation force compensation, For atmospheric drag, Solar radiation pressure, For three-body gravity, Tidal forces This is the force generated by relativistic effects.

[0030] In step four, the calculation method for the central gravitational compensation is as follows:

[0031] ;

[0032] In the formula, For the central gravitational compensation amount, is the Earth's gravitational constant.

[0033] In step five, the total amount to be compensated The calculation method is as follows:

[0034] .

[0035] In step five, the thrust generated by the electric thruster in the thrust command is:

[0036] ;

[0037] In the formula, The thrust generated by the electric thruster in the thrust command includes its magnitude and direction; that is, the total amount to be compensated at time t under RTN. Here are the coordinates of the total quantities to be compensated in the RTN coordinate system; the unit vectors of the RTN coordinate system in the geocentric inertial frame are respectively... , , ,in, This represents the direction vector from the Earth's center to the satellite's center of mass; It represents the direction of the orbital angular momentum and is perpendicular to the orbital plane; The direction is in the orbital plane and The axis is perpendicular to the direction of satellite motion, satisfying the right-hand rule.

[0038] In step five, , , The calculation method is as follows:

[0039] ;

[0040] ;

[0041] ;

[0042] In the formula, For modulus, express The modulus; express The modulus; For real-time velocity vectors, Let be the real-time velocity vector at time t. ; This represents the coordinates of the real-time velocity vector in the geocentric inertial coordinate system (ECI).

[0043] In step five, the maximum thrust constraint is:

[0044] ;

[0045] In the formula, The maximum thrust of the electric thruster to be updated in the maximum thrust command, including its magnitude and direction. for The modulus, This represents the actual maximum thrust of the electric thruster.

[0046] The beneficial effects of this invention are:

[0047] 1. A unified "perception-compensation" framework based on the ECI coordinate system:

[0048] This invention transforms the real-time data of low-orbit satellites acquired by the spaceborne GNSS receiver, as well as the calculation of perturbation forces and perturbation force compensation, into the geocentric inertial coordinate system (ECI). The thrust command is then calculated in the ECI, eliminating the errors introduced by coordinate system transformation and Earth rotation. This ensures the consistency of the dynamic model and provides a precise mathematical basis for the entire control loop, serving as the theoretical foundation for achieving high-precision control.

[0049] 2. A strategy combining position deviation correction and perturbation force compensation:

[0050] In this invention, the onboard computer uses a built-in high-precision orbital perturbation model to calculate in real time the forces generated by atmospheric drag, solar radiation pressure, three-body gravity, tidal forces, and relativistic effects, obtaining the perturbation force compensation amount. This compensates in advance for the deviation caused by the current perturbation force on the future orbital position. This is a key step in achieving "near real-time" and "high efficiency." Traditional methods often only focus on the current satellite orbital offset, calculating thrust compensation amount simply based on the positional deviation, resulting in a lag in orbital maintenance. Compared to traditional orbital maintenance, this invention additionally considers the current perturbation force. Instead of laboriously "pulling back" the satellite after it has deviated from its orbit, it actively "counters" the impending deviation, enabling the satellite to fly close to its nominal orbit. This significantly reduces the fuel consumption required for long-term maintenance.

[0051] 3. Achieve continuous fine-tuning of electric thrusters with "high frequency and small dosage":

[0052] This invention designs a step size that is much shorter than the traditional orbit maintenance period (on the order of several hours). This fully leverages the characteristics of electric thrusters: low thrust, long lifespan, and fine adjustment. Through continuous fine-tuning with "high frequency and small doses," the perturbation force is smoothly offset, avoiding the control errors and efficiency losses associated with traditional high-thrust maneuvers.

[0053] 4. Achieve near real-time high-precision maintenance effect:

[0054] This invention fully utilizes the high measurement accuracy and frequency of the combined spaceborne GNSS system and the high control accuracy of the electric thruster to establish a high-frequency (minutes to hours) sensing-control cycle, suppressing orbital deviations to the centimeter level. The satellite orbit is no longer a periodic, large-amplitude "sawtooth" fluctuation, but rather a "tiny amplitude" fluctuation around the nominal orbit, achieving quasi-continuous precision orbit maintenance.

[0055] 5. Ensure extremely high orbital stability of the satellite:

[0056] By employing a feedforward-feedback composite control strategy of "current deviation correction + future attenuation prediction," this invention can actively counteract perturbation forces rather than passively respond to them. This makes the satellite platform exceptionally stable, which is particularly beneficial for the stable implementation of satellite imaging and communication missions.

[0057] 6. Enabling Satellites to Manage Their Autonomous Orbits: This paper utilizes onboard GNSS for measurement and onboard calculated thrust to execute commands, which are then executed via electric thrusters, achieving highly automated orbit maintenance without human intervention. Compared to the traditional controllable orbit maintenance process of ground-based calculation and command uploading, this method enables a single satellite or an entire constellation to maintain precise orbits and configurations without ground intervention. Attached Figure Description

[0058] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0059] Figure 1 This is a schematic diagram of relative position deviation under uncontrolled conditions provided in an embodiment of the present invention.

[0060] Figure 2 This is a schematic diagram of relative velocity deviation under uncontrolled conditions provided in an embodiment of the present invention.

[0061] Figure 3 This is a schematic diagram of the relative position deviation after control provided in an embodiment of the present invention.

[0062] Figure 4 This is a schematic diagram of the relative speed deviation after control provided in an embodiment of the present invention. Detailed Implementation

[0063] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. 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 should fall within the scope of protection of the present invention.

[0064] This invention provides a near-real-time orbit maintenance and compensation method for electrically propelled low-Earth orbit satellites, the method comprising:

[0065] Step 1: The onboard computer converts the real-time data of the low-Earth orbit satellites acquired by the onboard GNSS receiver into the real-time orbital position vector and real-time velocity vector of the low-Earth orbit satellites in the geocentric inertial coordinate system (ECI).

[0066] The onboard GNSS receiver operates continuously, acquiring real-time three-dimensional position and velocity information of the satellite at a high update rate. The onboard computer uses this raw observation data, through filtering algorithms and coordinate transformations, to obtain the satellite's real-time position vector in the geocentric inertial coordinate system (ECI, typically the J2000 inertial frame). and velocity vector .

[0067] Step 2: The difference between the preset standard orbit position vector and the real-time orbit position vector is taken as the current position deviation; the proportional term of the current position deviation is combined with the integral and differential terms of the current position deviation, and the control weight is adjusted according to different orbit tasks to obtain the position compensation amount.

[0068] The pre-defined standard orbital position vectors for a mission are converted from the pre-defined orbital elements into a set of time-corresponding position vectors in the ECI coordinate system. .

[0069] Step 3: The onboard computer uses a built-in high-precision orbital perturbation model, taking the real-time orbital position vector and real-time velocity vector as inputs, and sums the output forces of atmospheric drag, solar radiation pressure, three-body gravity, tidal forces, and relativistic effects to obtain the perturbation force compensation amount.

[0070] Step 4: Based on the Earth's gravitational constant, obtain the central gravitational compensation amount from the standard orbital position vector and the real-time orbital position vector;

[0071] Step 5: Sum the position compensation, perturbation compensation, and central gravity compensation to obtain the total amount to be compensated; transform the total amount to be compensated into the satellite body coordinate system RTN to obtain the thrust command of the electric thruster; when the magnitude of the thrust generated by the electric thruster in the thrust command is greater than the actual maximum thrust of the electric thruster, the maximum thrust command is generated from the maximum thrust constraint and updated into the thrust command;

[0072] Step six: The onboard computer sends thrust commands to the electric propulsion system, which then controls the electric thrusters to execute the thrust commands for orbit correction. After the thrust commands are executed, the low-Earth orbit satellite enters a pre-set time-free coasting phase, returns to step one, and begins the next control cycle until the current position deviation is less than the threshold, at which point the control cycle ends.

[0073] The low-Earth orbit satellite enters a pre-set, unpowered coasting phase to allow the onboard GNSS receiver to collect data again and evaluate the actual effect of the thrust execution. The threshold can be set according to the specific mission and scenario.

[0074] This method constructs a closed-loop control system with feedback adjustment capability, which can continuously correct model errors and execution errors, and achieve long-term accurate control.

[0075] In step two, the current position deviation is calculated as follows:

[0076] ;

[0077] In the formula, The deviation is the current position at time t, where t is the current time. The standard orbital position vector preset for the mission, Let be the standard orbital position vector at time t. ; This represents the coordinates of the standard orbital position vector in the geocentric inertial coordinate system (ECI). This is the real-time orbital position vector. Let be the real-time orbital position vector at time t. ; This represents the coordinates of the real-time orbital position vector in the geocentric inertial coordinate system (ECI).

[0078] In step two, the method for calculating the position compensation amount is as follows:

[0079] ;

[0080] In the formula, For position compensation amount, This is the percentage of the current position deviation. This is the integral term of the current position deviation. This is the differential term of the current position deviation. The proportional coefficient controls the weight. The integral coefficient controls the weight. The differential coefficients control the weights. , , The value needs to be adjusted according to different orbital missions.

[0081] In step two, the integral term of the current position deviation is calculated as follows:

[0082] ;

[0083] The differential term of the current position deviation is calculated as follows:

[0084] ;

[0085] In the formula, The step size for each measurement and control is shorter than the orbit maintenance cycle. Let i be the current position deviation at time i. Indicates the integration interval. t represents the current time. The deviation of the current position at time t-1. This represents the current position deviation at time t-2.

[0086] In step three, the calculation method for the perturbation force compensation is as follows:

[0087] ;

[0088] In the formula, For the amount of perturbation force compensation, For atmospheric drag, Solar radiation pressure, For three-body gravity, Tidal forces This is the force generated by relativistic effects.

[0089] For atmospheric drag, Solar radiation pressure, For three-body gravity, Tidal forces The high-precision orbital perturbation models built into the onboard computer used to calculate the forces generated by relativistic effects are shown in Table 1. The calculation methods for each model force are detailed in "Spacecraft Orbital Mechanics Theory and Methods (Second Edition)" and can be consulted.

[0090] Table 1

[0091]

[0092] In step four, the calculation method for the central gravitational compensation is as follows:

[0093] ;

[0094] In the formula, For the central gravitational compensation amount, is the Earth's gravitational constant.

[0095] In step five, the total amount to be compensated The calculation method is as follows:

[0096] .

[0097] In step five, the thrust generated by the electric thruster in the thrust command is:

[0098] ;

[0099] In the formula, The thrust generated by the electric thruster in the thrust command includes its magnitude and direction; that is, the total amount to be compensated at time t under RTN. Here are the coordinates of the total quantities to be compensated in the RTN coordinate system; the unit vectors of the RTN coordinate system in the geocentric inertial frame are respectively... , , ,in, This represents the direction vector from the Earth's center to the satellite's center of mass; It represents the direction of the orbital angular momentum and is perpendicular to the orbital plane; The direction is in the orbital plane and The axis is perpendicular to the direction of satellite motion, satisfying the right-hand rule.

[0100] In step five, , , The calculation method is as follows:

[0101] ;

[0102] ;

[0103] ;

[0104] In the formula, For modulus, express The modulus; express The modulus; For real-time velocity vectors, Let be the real-time velocity vector at time t. ; This represents the coordinates of the real-time velocity vector in the geocentric inertial coordinate system (ECI).

[0105] In step five, the maximum thrust constraint is:

[0106] ;

[0107] In the formula, The maximum thrust of the electric thruster to be updated in the maximum thrust command, including its magnitude and direction. for The modulus, This represents the actual maximum thrust of the electric thruster.

[0108] Verification experiment:

[0109] To verify the effectiveness of the technical solution of the present invention, a verification experiment is provided for illustration:

[0110] The STARLINK2406 satellite is selected as the simulation example, and its position must be near its nominal value, with an error not exceeding ±1 km. The Starlink satellite constellation typically operates in low Earth orbit at an altitude of 350 km–550 km. All satellites in the constellation are equipped with a single, continuously low-thrust electric thruster. Orbital parameters are shown in Table 2.

[0111] Table 2

[0112]

[0113] Satellite parameters: drag coefficient Cd 2.2, surface mass ratio 0.005m 2 / kg, solar reflectance coefficient of the specular surface is 0.5.

[0114] Perturbation model: Earth's gravitational field model: EGM08 70*70; Atmospheric model: NRLMSISE-00; The 81-day average of solar 10.7cm radiation is 200, and the short-term average is 250; the geomagnetic index is 6.

[0115] In practice, noise interference is common. Under simulation conditions, an additional 20% atmospheric density error and an 8% thrust error result in measurement errors of 1 cm and 1 cm / s for relative velocity and relative displacement (GNSS orbit determination accuracy is typically 1 cm).

[0116] The weighting parameters in the control process are shown in Table 3:

[0117] Table 3

[0118]

[0119] Control duration setting: 1 cycle.

[0120] S1 orbital status awareness:

[0121] The onboard GNSS receiver operates continuously, acquiring real-time data on the satellite's three-dimensional position and velocity at a high update rate. The onboard computer utilizes this raw real-time data, employing filtering algorithms and coordinate transformations, to output the satellite's real-time orbital position vector in a geocentric inertial coordinate system (ECI, typically the J2000 inertial frame). and real-time velocity vector .

[0122] S2 track deviation calculation:

[0123] S21 Obtains the Standard Track Position Vector .

[0124] S22 position deviation calculation: .

[0125] S23 position compensation calculation: where At this point, the position compensation amount is:

[0126] ,in , , .

[0127] S24 perturbation compensation calculation: Utilizing the high-precision orbital perturbation model built into the onboard computer, and As input, calculate the perturbation force compensation:

[0128] .

[0129] Calculation of gravitational compensation at the center of S25: .

[0130] Optimization calculation of continuous thrust applied by S3:

[0131] The combined results of S31 and S2: Total amount to be compensated = Position compensation + Perturbation compensation + Central gravitational deviation. That is: .

[0132] S32 will have a total amount to be compensated. Transform to the satellite's RTN coordinate system. Define the unit vectors of the RTN coordinate system in the Earth's inertial frame as R, T, and N, then: , , At this point, the thrust generated by the thruster should be: .

[0133] S33 considers the maximum thrust constraint of the electric thruster. When Greater than the actual maximum thrust of the electric thruster ,at this time The maximum thrust command is updated into the thrust command.

[0134] S34 outputs the thrust command for the current moment: thrust magnitude and direction.

[0135] S4 thrust execution and closed-loop verification:

[0136] The onboard computer sends the thrust commands generated by S3 to the electric propulsion system, and the electric thrusters execute the thrust precisely according to the thrust commands.

[0137] After the thrust command is executed, the satellite enters a brief "unpowered coasting" phase to collect data again and evaluate the actual effect of the thrust execution.

[0138] The process then immediately returns to S1 and begins the next control loop. This continues until the current position deviation... If the value is less than 10m, the control loop ends.

[0139] Through this cycle, the orbital altitude of the low-Earth orbit satellite will exhibit slight fluctuations around the nominal value, rather than the "sawtooth" descents and rises observed in traditional methods, thus achieving true "orbit maintenance." Examples show the relative position and velocity deviations between the actual and desired orbits of low-Earth orbit satellites with and without compensation. Figures 1 to 4 As shown. Comparison Figure 1 , Figure 2 and Figure 3 , Figure 4 The position and velocity deviations show that within one simulation cycle, Figure 1 and Figure 2 When no control is applied, the x-axis deviation reaches 2 × 10⁻⁶. 4 m, y-axis deviation reaches 2×10 4 m, z-axis deviation reaches 6×10 4 m, Figure 3and Figure 4 After applying control, the x-axis deviation is limited to within 1m, the y-axis deviation to within 1m, and the z-axis deviation to within 2m. This demonstrates the effectiveness of this method in high-precision track maintenance. The current control algorithm is simple in principle and steps, and has certain feasibility in engineering implementation.

[0140] 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 variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included 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 near-real-time orbit maintenance and compensation of electrically propelled low-Earth orbit satellites, characterized in that, The method includes: Step 1: The onboard computer converts the real-time data of the low-Earth orbit satellites acquired by the onboard GNSS receiver into the real-time orbital position vector and real-time velocity vector of the low-Earth orbit satellites in the geocentric inertial coordinate system (ECI). Step 2: The difference between the preset standard orbit position vector and the real-time orbit position vector is taken as the current position deviation; the proportional term of the current position deviation is combined with the integral and differential terms of the current position deviation, and the control weight is adjusted according to different orbit tasks to obtain the position compensation amount. Step 3: The onboard computer uses a built-in high-precision orbital perturbation model, taking the real-time orbital position vector and real-time velocity vector as inputs, and sums the output forces of atmospheric drag, solar radiation pressure, three-body gravity, tidal forces, and relativistic effects to obtain the perturbation force compensation amount. Step 4: Based on the Earth's gravitational constant, obtain the central gravitational compensation amount from the standard orbital position vector and the real-time orbital position vector; Step 5: Sum the position compensation, perturbation compensation, and central gravity compensation to obtain the total amount to be compensated; transform the total amount to be compensated into the satellite body coordinate system RTN to obtain the thrust command of the electric thruster; when the magnitude of the thrust generated by the electric thruster in the thrust command is greater than the actual maximum thrust of the electric thruster, the maximum thrust command is generated from the maximum thrust constraint and updated into the thrust command. Step six: The onboard computer sends thrust commands to the electric propulsion system, which then controls the electric thrusters to execute the thrust commands for orbit correction. After the thrust commands are executed, the low-Earth orbit satellite enters a pre-set time-free coasting phase, returns to step one, and begins the next control cycle until the current position deviation is less than the threshold, at which point the control cycle ends.

2. The near-real-time orbit maintenance and compensation method for electrically propelled low-Earth orbit satellites as described in claim 1, characterized in that, In step two, the current position deviation is calculated as follows: ； In the formula, The deviation is the current position at time t, where t is the current time. Let be the standard orbital position vector at time t. ; This represents the coordinates of the standard orbital position vector in the geocentric inertial coordinate system (ECI). Let be the real-time orbital position vector at time t. ; This represents the coordinates of the real-time orbital position vector in the geocentric inertial coordinate system (ECI).

3. The near-real-time orbit maintenance and compensation method for electrically propelled low-Earth orbit satellites as described in claim 2, characterized in that, In step two, the method for calculating the position compensation amount is as follows: ； In the formula, For position compensation amount, This is the percentage of the current position deviation. This is the integral term of the current position deviation. This is the differential term of the current position deviation. The proportional coefficient controls the weight. The integral coefficient controls the weight. The differential coefficients control the weights.

4. The near-real-time orbit maintenance and compensation method for electrically propelled low-Earth orbit satellites as described in claim 3, characterized in that, In step two, the integral term of the current position deviation is calculated as follows: ； The differential term of the current position deviation is calculated as follows: ； In the formula, The step size for each measurement and control is shorter than the orbit maintenance cycle. for Current position deviation at any given moment Indicates the integration interval. t represents the current time. The deviation of the current position at time t-1. This represents the current position deviation at time t-2.

5. A near-real-time orbit maintenance and compensation method for electrically propelled low-Earth orbit satellites as described in claim 4, characterized in that, In step three, the calculation method for the perturbation force compensation is as follows: ； In the formula, For the amount of perturbation force compensation, For atmospheric drag, Solar radiation pressure, For three-body gravity, Tidal forces This is the force generated by relativistic effects.

6. The near-real-time orbit maintenance and compensation method for electrically propelled low-Earth orbit satellites as described in claim 5, characterized in that, In step four, the calculation method for the central gravitational compensation is as follows: ； In the formula, For the central gravitational compensation amount, is the Earth's gravitational constant.

7. A near-real-time orbit maintenance and compensation method for electrically propelled low-Earth orbit satellites as described in claim 6, characterized in that, In step five, the total amount to be compensated The calculation method is as follows: 。 8. A near-real-time orbit maintenance and compensation method for electrically propelled low-Earth orbit satellites as described in claim 7, characterized in that, In step five, the thrust generated by the electric thruster in the thrust command is: ； In the formula, The thrust generated by the electric thruster in the thrust command includes its magnitude and direction; that is, the total amount to be compensated at time t under RTN. Here are the coordinates of the total quantities to be compensated in the RTN coordinate system; the unit vectors of the RTN coordinate system in the geocentric inertial frame are respectively... , , ,in, This represents the direction vector from the Earth's center to the satellite's center of mass; It represents the direction of the orbital angular momentum and is perpendicular to the orbital plane; The direction is in the orbital plane and The axis is perpendicular to the direction of satellite motion, satisfying the right-hand rule.

9. A near-real-time orbit maintenance and compensation method for electrically propelled low-Earth orbit satellites as described in claim 8, characterized in that, In step five, , , The calculation method is as follows: ； ； ； In the formula, For modulus, express The modulus; express The modulus; Let be the real-time velocity vector at time t. ; This represents the coordinates of the real-time velocity vector in the geocentric inertial coordinate system (ECI).

10. A near-real-time orbit maintenance and compensation method for electrically propelled low-Earth orbit satellites as described in claim 9, characterized in that, In step five, the maximum thrust constraint is: ； In the formula, The maximum thrust of the electric thruster to be updated in the maximum thrust command, including its magnitude and direction. for The modulus, This represents the actual maximum thrust of the electric thruster.

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