A north-south electric tilt angle maintaining control method and device

Abstract

The application discloses a north-south electric propulsion inclination angle keeping control method and device. The application separates the long-term term and the half-year period term of the GEO satellite orbit inclination angle, respectively constructs motion equations, and constructs keeping constraint conditions by making full use of the relationship between the half-year period term perturbation law and the north-south keeping range, so that the keeping strategy calculated based on the keeping constraint conditions not only takes into account the advantage of high control stability of the electric propulsion method, but also improves the accuracy of the control time and the ignition time by respectively calculating the control strategy of the long-term term and the half-year period, can effectively reduce the electric propulsion ignition time length, realizes the premise that the orbit inclination angle meets the keeping requirements, reduces the influence of the electric propulsion method on the satellite longitude, reduces fuel consumption, and the ignition point longitude fluctuation in the control strategy cycle is small.

Description

Technical Field

[0001] This invention relates to satellite orbit control, and more particularly to a method and apparatus for maintaining north-south electric thrust tilt angle. Background Technology

[0002] Currently, when geostationary orbit (GEO) satellites are used for north-south control, the ground control center needs to calculate a control strategy to maintain the GEO satellite's orbital inclination within the required range based on the satellite's real-time orbital conditions and the thruster type and parameters of the satellite's control actuators. This strategy is then uploaded to the onboard actuators. There are two existing inclination maintenance methods: electric thrust and chemical thrust. If the satellite uses chemical thrusters for control, the control strategy is calculated based on the long-term perturbation law of the orbital inclination, employing a negative inclination control calculation method to control the orbital inclination from a positive value to a negative value. As satellite electric thrust control technology matures, GEO satellites can also be equipped with Hall thrusters for north-south control. When the satellite uses electric thrusters for north-south control, the control plan involves firing the thrusters near the ascending and descending nodes each day within a selected control period (typically 7 days) to maintain the satellite's orbital inclination within the required range. The control strategy is calculated based on the combined perturbation velocity and direction of the satellite's orbital inclination at that time.

[0003] Existing tilt-maintaining methods use orbital tilt as the control element for north-south tilt maintenance. When using chemical thrust for north-south tilt maintenance, fuel consumption is high, and there is significant longitude disturbance to the satellite. After control is completed, east-west correction control is required immediately to prevent east-west longitude deviation caused by north-south control. This results in high execution risk and significant longitude disturbance to the satellite. If the electric thruster method calculates the control quantity and timing based on the comprehensive tilt perturbation velocity and direction of the GEO satellite, the ignition duration and right ascension of each cycle fluctuate greatly due to the weak regularity of the tilt perturbation. This is not conducive to the execution of control strategies and the arrangement of control plans. Furthermore, the comprehensive tilt perturbation of the GEO satellite orbit is composed of long-term and long-period terms. If the control strategy is calculated based on the comprehensive perturbation velocity, the obtained thruster ignition duration will be too large, possibly exceeding the thruster ignition duration threshold. An excessively large ignition duration will also have a significant impact on east-west longitude, reducing the holding period of east-west control. Summary of the Invention

[0004] This invention provides a method and apparatus for maintaining tilt angle of electric propulsion in the north-south direction, so as to reduce the ignition time of each cycle of the electric propulsion method, improve the stability of ignition right ascension fluctuation and improve the tilt angle maintenance effect.

[0005] To address the aforementioned technical problems, embodiments of the present invention provide a north-south electric thruster tilt angle maintenance control method, comprising:

[0006] Based on the perturbation law of GEO orbit inclination, the long-term perturbation equation of the GEO orbit inclination and the semi-annual perturbation equation of the GEO orbit inclination are constructed;

[0007] Based on the long-term perturbation equation and the semi-annual period perturbation equation, tilt angle preservation constraints are constructed;

[0008] The target tilt vector is obtained based on the tilt angle holding constraint and the half-year cycle perturbation equation. The initial tilt vector is obtained, and the first control time and the first ignition duration are obtained based on the target tilt vector and the initial tilt vector. Tilt initialization control is performed based on the first control time and the first ignition duration.

[0009] The direction and magnitude of the long-term tilt perturbation are calculated based on the long-term perturbation equation. The second control time is calculated based on the direction of the long-term tilt perturbation and the second ignition duration is calculated based on the magnitude of the long-term tilt perturbation. Tilt holding control is then performed based on the second control time and the second ignition duration.

[0010] This invention separates the long-term and semi-annual periodic terms of the GEO satellite's orbital inclination and constructs motion equations for each separately. This allows for the full utilization of the perturbation law of the semi-annual periodic term and the relationship between the north-south maintenance range to construct maintenance constraints. The maintenance strategy calculated based on these constraints not only retains the high stability of electric propulsion control but also improves the accuracy of control timing and ignition timing by calculating the control strategy separately for the long-term and semi-annual periods. This effectively reduces the electric propulsion ignition time, thereby minimizing the impact of electric propulsion on the satellite's longitude while ensuring the orbital inclination meets maintenance requirements, reducing fuel consumption, and minimizing fluctuations in the ignition point's right ascension within the control strategy period.

[0011] Furthermore, the construction of tilt angle preservation constraints based on the long-term perturbation equation and the semi-annual period perturbation equation includes:

[0012] An angle perturbation circle is constructed based on the semi-annual period perturbation equation, and an angle preservation circle is constructed based on the long-term term perturbation equation;

[0013] Obtain the geometric relationship between the tilt perturbation circle and the tilt holding circle, and obtain the tilt holding constraint condition based on the geometric relationship. The tilt holding constraint condition includes that when the centers of the tilt perturbation circle and the tilt holding circle are at the origin, the tilt vector of the GEO orbit tilt is on the tilt perturbation circle.

[0014] Furthermore, obtaining the first control moment and the first ignition duration based on the target tilt vector and the initial tilt vector includes:

[0015] Calculate the solar right ascension, and calculate the rate of change of the tilt vector based on the solar right ascension and the semi-annual perturbation equation;

[0016] The target tilt vector is calculated based on the tilt angle maintenance constraint and the tilt vector change rate.

[0017] Furthermore, obtaining the first control moment and the first ignition duration based on the target tilt angle vector includes:

[0018] A first inclination increment is obtained based on the target inclination vector and the initial inclination vector, wherein the first inclination increment includes the magnitude of the first inclination increment and the direction of the first inclination increment.

[0019] The right ascension of the tilt initialization control is calculated based on the first tilt increment direction, and the first control time is calculated based on the right ascension of the tilt initialization control;

[0020] The speed increment of the tilt angle initialization control is based on the first tilt angle increment, and the first ignition duration is calculated based on the speed increment of the tilt angle initialization control.

[0021] Furthermore, the calculation of the direction and magnitude of the long-term dip perturbation based on the long-term perturbation equation includes:

[0022] The second dip angle increment is calculated based on the long-term perturbation equation, and the magnitude and direction of the second dip angle increment are obtained.

[0023] The right ascension for tilt hold control is calculated based on the second tilt increment direction, and the second control time is calculated based on the right ascension for tilt hold control;

[0024] The speed increment of tilt hold control is calculated based on the second tilt angle increment, and the second ignition duration is calculated based on the speed increment of tilt hold control.

[0025] In a second aspect, the present invention provides a north-south electric thruster tilt angle holding control device, comprising: an equation construction module, a constraint construction module, a target tilt angle calculation module, a tilt angle initialization module, and a tilt angle holding module;

[0026] The equation construction module is used to construct the long-term perturbation equation of the GEO orbit inclination and the semi-annual periodic perturbation equation of the GEO orbit inclination based on the perturbation law of the GEO orbit inclination.

[0027] The constraint construction module is used to construct tilt angle maintenance constraints based on the long-term perturbation equation and the semi-annual period perturbation equation.

[0028] The target tilt angle calculation module is used to obtain the target tilt angle vector based on the tilt angle holding constraint and the semi-annual period perturbation equation;

[0029] The tilt initialization module is used to obtain an initial tilt vector, obtain a first control moment and a first ignition duration based on the target tilt vector and the initial tilt vector, and perform tilt initialization control based on the first control moment and the first ignition duration.

[0030] The tilt holding module is used to calculate the tilt long-term perturbation direction and magnitude based on the long-term perturbation equation, calculate the second control time based on the tilt long-term perturbation direction and the second ignition duration based on the tilt long-term perturbation magnitude, and perform tilt holding control based on the second control time and the second ignition duration.

[0031] Furthermore, the constraint construction module is used for:

[0032] An angle perturbation circle is constructed based on the semi-annual period perturbation equation, and an angle preservation circle is constructed based on the long-term term perturbation equation;

[0033] Obtain the geometric relationship between the tilt perturbation circle and the tilt holding circle, and obtain the tilt holding constraint condition based on the geometric relationship. The tilt holding constraint condition includes that when the centers of the tilt perturbation circle and the tilt holding circle are at the origin, the tilt vector of the GEO orbit tilt is on the tilt perturbation circle.

[0034] Furthermore, the target tilt angle calculation module is used for:

[0035] Calculate the solar right ascension, and calculate the rate of change of the tilt vector based on the solar right ascension and the semi-annual perturbation equation;

[0036] The target tilt vector is calculated based on the tilt angle maintenance constraint and the tilt vector change rate.

[0037] Furthermore, the tilt initialization module is used for:

[0038] A first inclination increment is obtained based on the target inclination vector and the initial inclination vector, wherein the first inclination increment includes the magnitude of the first inclination increment and the direction of the first inclination increment.

[0039] The right ascension of the tilt initialization control is calculated based on the first tilt increment direction, and the first control time is calculated based on the right ascension of the tilt initialization control;

[0040] The speed increment of the tilt angle initialization control is based on the first tilt angle increment, and the first ignition duration is calculated based on the speed increment of the tilt angle initialization control.

[0041] Furthermore, the tilt-holding module is used for:

[0042] The second dip angle increment is calculated based on the long-term perturbation equation, and the magnitude and direction of the second dip angle increment are obtained.

[0043] The right ascension for tilt hold control is calculated based on the second tilt increment direction, and the second control time is calculated based on the right ascension for tilt hold control;

[0044] The speed increment of tilt hold control is calculated based on the second tilt angle increment, and the second ignition duration is calculated based on the speed increment of tilt hold control. Attached Figure Description

[0045] Figure 1 A flowchart illustrating a north-south electric thruster tilt angle maintenance control method provided in an embodiment of the present invention;

[0046] Figure 2 A geometric relationship diagram of an inclination perturbation circle and an inclination holding circle provided in an embodiment of the present invention;

[0047] Figure 3 A schematic diagram illustrating the calculation of a first tilt angle increment provided in an embodiment of the present invention;

[0048] Figure 4 This is another schematic flowchart of a north-south electric thruster tilt angle maintenance control method provided in an embodiment of the present invention. Detailed Implementation

[0049] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0050] The terms "first" and "second," etc., in the specification, claims, and drawings of this application are used to distinguish different objects, not to describe a specific order. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to such processes, methods, products, or apparatus.

[0051] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0052] Example 1

[0053] See Figure 1 , Figure 1 This is a flowchart illustrating a north-south electric thruster tilt angle maintenance control method according to an embodiment of the present invention. The embodiment of the present invention provides a north-south electric thruster tilt angle maintenance control method, including steps 101 to 105, as detailed below:

[0054] Step 101: Construct the long-term perturbation equation of the GEO orbit inclination and the semi-annual periodic perturbation equation of the GEO orbit inclination based on the perturbation law of the GEO orbit inclination;

[0055] In this embodiment, the GEO orbital inclination perturbation law includes the influence of perturbations such as the Earth's non-spherical gravity, the gravitational pull of the Sun and Moon, and solar radiation pressure on the GEO satellite's orbital inclination. Specifically, the perturbation of the Earth's eurygoid harmonics causes the satellite's orbital plane to precess in the opposite direction at a rate of 4.9° per year, meaning the orbital inclination remains constant in magnitude but precesses in direction at a period of 73.46 years. The maximum value of the GEO orbital inclination perturbation caused by solar radiation pressure is approximately 3.5° × 10⁻⁶. -5 This value is much smaller than the north-south control range of 0.05°. Therefore, the effects of Earth's non-spherical perturbation and solar radiation pressure perturbation on the orbital inclination of GEO satellites are neglected in the calculation of the north-south control strategy; the main calculation focuses on the influence of lunar and solar gravitational perturbations on the geostationary orbit inclination.

[0056] In this embodiment, a long-term perturbation equation for the GEO orbital inclination is constructed based on the perturbation law of the GEO orbital inclination and the long-term change of the inclination caused by the gravitational forces of the Sun and Moon. A semi-annual perturbation equation is constructed based on the perturbation law of the GEO orbital inclination and the orbital inclination perturbation caused by the gravitational forces of the Sun.

[0057] In this embodiment, the inclination angle of the GEO orbit is... The components of the GEO orbital inclination angle in the x-direction are obtained by decomposition. and the component in the y direction ,in , , Ω represents the magnitude of the inclination angle, and Ω represents the right ascension of the ascending node, i.e., the direction of the inclination vector.

[0058] In this embodiment, a long-term perturbation equation for the GEO orbit inclination is constructed based on the perturbation law of the GEO orbit inclination. Specifically, this long-term perturbation equation for the GEO orbit inclination is as follows:

[0059] (1)

[0060] in, The ecliptic longitude of the ascending intersection of the celestial equator is calculated as follows: T stands for Relative Julian Day, that is, relative to January 1, 1950.

[0061] In this embodiment, only the long-term change of the tilt angle caused by the gravitational pull of the Sun and Moon is related to the ecliptic longitude of the ascending node of the ecliptic. The precession period of the ecliptic longitude of the ascending node of the ecliptic is 18.6 years, which can be considered a constant in the short term.

[0062] In this embodiment, the perturbation direction and velocity of the inclination perturbation can be calculated based on the long-term perturbation equation of the GEO orbit inclination angle. Specifically:

[0063] (2)

[0064] in, The direction of the tilt perturbation. The velocity of the tilt perturbation is expressed in ° / d.

[0065] In this embodiment, based on the long-term inclination perturbation equation, it can be seen that the perturbation direction and perturbation velocity of the inclination vector change slightly every year. When the lunar orbital longitude is closer to the vernal equinox, the inclination perturbation velocity is greater, reaching a maximum of 0.95° per year. When the lunar orbital longitude is 180° away from the vernal equinox, the inclination perturbation velocity is the minimum, close to 0.75° per year. The inclination perturbation direction is approximately 89°~91°.

[0066] In this embodiment, the semi-annual periodic motion equation is calculated based on the orbital inclination perturbation motion of the GEO satellite caused by solar gravity, and its corresponding amplitude is calculated.

[0067] In this embodiment, the orbital inclination perturbation motion of the GEO satellite caused by solar gravity is a semi-annual periodic motion equation, specifically:

[0068] (3)

[0069] Where n is the average angular velocity of the GEO satellite. The average angular velocity of the sun's motion. Right ascension of the sun, This is the angle between the equatorial plane and the ecliptic plane. (From...) ,therefore:

[0070] (4)

[0071] Among them, the semi-annual cycle motion equation contains The periodic term has an average change of 0 in the tilt vector over a year, but there is a perturbation with a period of six months, or 182.63 days, and its amplitude is:

[0072] (5)

[0073] In this embodiment, the orbital inclination perturbation of the GEO satellite caused by lunar gravity is a semi-lunar periodic motion, and the equation of motion is:

[0074] (6)

[0075] in, n is the average angular velocity of the GEO satellite. The semi-lunar periodic motion equation contains a periodic term with a semi-lunar period. The average change in the tilt vector within a month is 0, but there is a perturbation with a period of half a month, or 13.7 days, and its amplitude is:

[0076] (7)

[0077] In this embodiment, when the north-south range of the GEO satellite is 0.05°, the amplitude of the semi-lunar periodic perturbation caused by the moon's gravity is not on the same order of magnitude as the range and can be ignored. Therefore, only the semi-annual periodic motion equation caused by the sun's gravity is calculated, i.e., the semi-annual periodic perturbation equation.

[0078] In this embodiment, the long-term term and the semi-annual period term of the GEO satellite orbital inclination are separated and motion equations are constructed separately. The control strategy is calculated separately using the equations constructed by the long-term term and the semi-annual period term, which improves the accuracy of the control timing and ignition timing and can effectively reduce the electric propulsion ignition time.

[0079] Step 102: Construct tilt angle preservation constraints based on the long-term perturbation equation and the semi-annual period perturbation equation;

[0080] In this embodiment, constructing the tilt angle preservation constraint based on the long-term perturbation equation and the semi-annual period perturbation equation includes:

[0081] An angle perturbation circle is constructed based on the semi-annual period perturbation equation, and an angle preservation circle is constructed based on the long-term term perturbation equation;

[0082] Obtain the geometric relationship between the tilt perturbation circle and the tilt holding circle, and obtain the tilt holding constraint condition based on the geometric relationship. The tilt holding constraint condition includes that when the centers of the tilt perturbation circle and the tilt holding circle are at the origin, the tilt vector of the GEO orbit tilt is on the tilt perturbation circle.

[0083] As a specific example of an embodiment of the present invention, please refer to Figure 2 , Figure 2 This is a geometric diagram showing the relationship between a tilt angle perturbation circle and a tilt angle holding circle, provided for an embodiment of the present invention.

[0084] In this embodiment, an inclination-maintaining circle is constructed based on the long-term perturbation equation. When the north-south maintenance range of the GEO satellite is 0.05° and there is no offset of the center of the inclination vector perturbation circle, the inclination-maintaining range can be expressed as:

[0085] (8)

[0086] In this embodiment, an angle-maintaining circle can be constructed based on the angle-maintaining range.

[0087] In this embodiment, an inclination perturbation circle is constructed based on the semi-annual perturbation equation. Based on the semi-annual motion equation, the semi-annual perturbation equation for the GEO satellite orbital inclination caused by the sun is an ellipse with a major semi-axis of 0.0235 and a minor semi-axis of 0.0215. If its center is located at the origin, the equation of the inclination perturbation circle is:

[0088] (9)

[0089] In this embodiment, an inclination perturbation circle is constructed based on the semi-annual period perturbation equation, and an inclination maintenance circle is constructed based on the long-term perturbation equation.

[0090] In this embodiment, based on the geometric relationship between the tilt perturbation circle and the tilt holding circle, the tilt holding constraint condition is determined. When the centers of both the tilt perturbation circle and the tilt holding circle are at the origin, the tilt vector is always within the holding range, satisfying the holding requirement. Therefore, when calculating the north-south holding strategy, the initial tilt angle is controlled to the semi-annual period perturbation circle with the origin as its center. Then, the long-term tilt perturbation is overcome by orbit control. At this time, the tilt angle only has semi-annual period perturbation and semi-monthly period perturbation, which can satisfy the holding requirement under free perturbation motion.

[0091] In this embodiment, the north-south electric propulsion holding strategy is divided into two stages based on the tilt holding constraint. The first stage is tilt initialization control, which mainly considers the semi-annual perturbation of the tilt angle. The second stage is tilt maintenance control, which mainly considers the long-term perturbation of the tilt angle. Since the perturbation speed and direction of the long-term and semi-annual perturbation terms are relatively stable in the short term, the calculated control duration and control time are also relatively stable with small fluctuations.

[0092] Step 103: Obtain the target tilt angle vector based on the tilt angle maintenance constraint and the semi-annual period perturbation equation;

[0093] In this embodiment, tilt initialization control is the process of controlling the tilt vector from its initial position to the perturbation circle with the center as the origin. This process is divided into target tilt vector calculation and control strategy calculation. Specifically, the target tilt vector calculation involves combining the half-year perturbation equation to calculate the corresponding position on the perturbation circle as the target tilt angle.

[0094] In this embodiment, obtaining the target tilt vector based on the tilt angle maintenance constraint and the semi-annual period perturbation equation includes:

[0095] Calculate the solar right ascension, and calculate the rate of change of the tilt vector based on the solar right ascension and the semi-annual perturbation equation;

[0096] The target tilt vector is calculated based on the tilt angle maintenance constraint, the tilt vector change rate, and the semi-annual perturbation equation.

[0097] In this embodiment, the rate of change of the tilt angle vector can be obtained based on the six-month cycle motion equation. The rate of change of the tilt angle vector is:

[0098] (10)

[0099] in, The right ascension of the sun can be determined through planetary ephemeris prediction. The angle between the equatorial plane and the ecliptic plane is 23.4437°.

[0100] In this embodiment, the solar right ascension is calculated based on planetary ephemeris prediction, thereby calculating the rate of change of the tilt vector. Based on the rate of change of the tilt vector and the equation of the tilt perturbation circle, the rate of change of the tilt vector can be obtained as follows:

[0101] (11)

[0102] Based on the aforementioned rate of change of the dip angle vector and the semi-annual perturbation equation, the target dip angle vector is calculated, specifically:

[0103] (12)

[0104] in, , That is, the target tilt angle for tilt angle initialization.

[0105] Step 104: Obtain the initial tilt vector, and obtain the first control moment and the first ignition duration based on the target tilt vector and the initial tilt vector, and perform tilt initialization control based on the first control moment and the first ignition duration;

[0106] In this embodiment, obtaining the first control moment and the first ignition duration based on the target tilt angle vector includes:

[0107] A first inclination increment is obtained based on the target inclination vector and the initial inclination vector, wherein the first inclination increment includes the magnitude of the first inclination increment and the direction of the first inclination increment.

[0108] The right ascension of the tilt initialization control is calculated based on the first tilt increment direction, and the first control time is calculated based on the right ascension of the tilt initialization control;

[0109] The speed increment of the tilt angle initialization control is based on the first tilt angle increment, and the first ignition duration is calculated based on the speed increment of the tilt angle initialization control.

[0110] In this embodiment, the first tilt angle increment is calculated based on the initial tilt angle vector and the target tilt angle vector.

[0111] Please refer to Figure 3 , Figure 3 This is a schematic diagram illustrating the calculation of a first tilt angle increment, provided as an embodiment of the present invention.

[0112] In this embodiment, The target tilt angle vector, Let be the initial tilt angle vector, and Δi be the first tilt angle increment.

[0113] In this embodiment, the first tilt angle increment is specifically:

[0114] (13)

[0115] In this embodiment, the magnitude and direction of the first tilt angle increment are obtained based on the first tilt angle increment, specifically as follows:

[0116] (14)

[0117] in, This represents the magnitude of the first tilt angle increment. The direction of the first tilt angle increment.

[0118] In this embodiment, the tilt angle controlled each time is calculated based on the magnitude of the first tilt angle increment. Specifically:

[0119] (15)

[0120] in, D represents the tilt angle controlled each time, and D represents the total number of control days, with two controls per day.

[0121] In this embodiment, the relationship between the first inclination increment and the normal velocity increment of the GEO satellite orbit is as follows:

[0122] (16)

[0123] in, This represents the normal velocity increment.

[0124] In this embodiment, the duration of the first ignition of the thruster is calculated based on the velocity increment. Specifically:

[0125] (17)

[0126] Where d is the duration of the first ignition of the thruster, F is the thrust magnitude of the thruster, and M is the mass of the satellite.

[0127] In this embodiment, the direction of the first inclination increment is the right ascension of the satellite in the true equatorial coordinate system at the first control moment. Therefore, the right ascension at the first control moment is calculated based on the direction of the first inclination increment as follows:

[0128] (18)

[0129] In this embodiment, the first control time can be obtained through satellite right ascension prediction. , Therefore, the ignition times are twice a day as follows:

[0130] (19)

[0131] Based on the thruster's ignition timing and first ignition duration parameters, the satellite can perform tilt initialization control.

[0132] Step 105: Calculate the direction and magnitude of the tilt angle long-term perturbation based on the long-term perturbation equation, calculate the second control time based on the direction of the tilt angle long-term perturbation and the second ignition duration based on the magnitude of the tilt angle long-term perturbation, and perform tilt angle holding control based on the second control time and the second ignition duration.

[0133] In this embodiment, calculating the direction and magnitude of the long-term dip perturbation based on the long-term perturbation equation includes:

[0134] The second dip angle increment is calculated based on the long-term perturbation equation, and the magnitude and direction of the second dip angle increment are obtained.

[0135] The right ascension for tilt hold control is calculated based on the second tilt increment direction, and the second control time is calculated based on the right ascension for tilt hold control;

[0136] The speed increment of tilt hold control is calculated based on the second tilt angle increment, and the second ignition duration is calculated based on the speed increment of tilt hold control.

[0137] In this embodiment, after the tilt initialization control is completed, the satellite orbit tilt vector is located on the semi-annual period perturbation circle centered at the origin. At this point, it is only necessary to calculate the control strategy based on the long-term tilt perturbation law to overcome the long-term gravitational perturbation of the sun and moon.

[0138] In this embodiment, to overcome the long-term tilt perturbation, it is only necessary to have the tilt increment generated by the thruster be opposite in direction and equal in magnitude to the long-term tilt perturbation.

[0139] In this embodiment, in order to control the generated tilt increment to be opposite to the direction of the long-term perturbation, the right ascension of the second control time near the ascending and descending nodes each day during the tilt maintenance phase is [formula missing].

[0140] (20)

[0141] In this embodiment, the second control time can be obtained through satellite right ascension prediction. , .

[0142] In this embodiment, the daily perturbation amount of the long-term term perturbation of the tilt angle is calculated based on the long-term perturbation equation. Therefore, the tilt angle control amount at the ascending and descending nodes is...

[0143] △ = (twenty one)

[0144] In this embodiment, the normal velocity increment is calculated based on the tilt control value, and the second ignition duration at the ascending and descending nodes can be determined as d based on the normal velocity increment. Therefore, the ignition times for twice a day are:

[0145] (twenty two)

[0146] Based on the ignition timing and duration of the thrusters, the satellite can perform tilt-holding control.

[0147] This invention separates the long-term and semi-annual periodic terms of the GEO satellite's orbital inclination and constructs motion equations for each separately. This allows for the full utilization of the perturbation law of the semi-annual periodic term and the relationship between the north-south maintenance range to construct maintenance constraints. The maintenance strategy calculated based on these constraints not only retains the high stability of electric propulsion control but also improves the accuracy of control timing and ignition timing by calculating the control strategy separately for the long-term and semi-annual periods. This effectively reduces the electric propulsion ignition time, thereby minimizing the impact of electric propulsion on the satellite's longitude while ensuring the orbital inclination meets maintenance requirements, reducing fuel consumption, and minimizing fluctuations in the ignition point's right ascension within the control strategy period.

[0148] Please refer to Figure 4 , Figure 4 This is another schematic flowchart of a north-south electric thruster tilt angle maintenance control method provided in an embodiment of the present invention.

[0149] In this embodiment, the solar right ascension is calculated based on planetary ephemeris prediction; the rate of change of the semi-annual tilt perturbation is calculated based on the solar right ascension; the target tilt vector is calculated by combining the rate of change of the tilt vector and the equation of the semi-annual perturbation ellipse; the tilt increment between the target tilt vector and the initial tilt vector is calculated; the right ascension for tilt control is calculated based on the direction of the tilt increment; the velocity increment for tilt control is calculated based on the magnitude of the tilt increment; the control time parameter is calculated based on the right ascension of the control time; the thruster ignition duration is calculated based on the velocity increment; the direction and magnitude of the long-term tilt perturbation are calculated; the right ascension for tilt control time is calculated based on the direction of the long-term tilt perturbation; the velocity increment required for tilt control is calculated based on the magnitude of the long-term tilt perturbation; the control time parameter is calculated based on the right ascension of the control time; and the thruster ignition duration is calculated based on the velocity increment.

[0150] This invention also provides a north-south electric thruster tilt angle holding control device, comprising: an equation construction module, a constraint construction module, a tilt angle initialization module, and a tilt angle holding module;

[0151] The equation construction module is used to construct the long-term perturbation equation of the GEO orbit inclination and the semi-annual periodic perturbation equation of the GEO orbit inclination based on the perturbation law of the GEO orbit inclination.

[0152] The constraint construction module is used to construct tilt angle maintenance constraints based on the long-term perturbation equation and the semi-annual period perturbation equation.

[0153] The tilt initialization module is used to obtain a target tilt vector based on the tilt holding constraint and the semi-annual cycle perturbation equation, and to obtain a first control moment and a first ignition duration based on the target tilt vector, and to perform tilt initialization control based on the first control moment and the first ignition duration;

[0154] The tilt holding module is used to calculate the tilt long-term perturbation direction and magnitude based on the long-term perturbation equation, calculate the second control time based on the tilt long-term perturbation direction and the second ignition duration based on the tilt long-term perturbation magnitude, and perform tilt holding control based on the second control time and the second ignition duration.

[0155] In this embodiment, the constraint construction module is used for:

[0156] An angle perturbation circle is constructed based on the semi-annual period perturbation equation, and an angle preservation circle is constructed based on the long-term term perturbation equation;

[0157] Obtain the geometric relationship between the tilt perturbation circle and the tilt holding circle, and obtain the tilt holding constraint condition based on the geometric relationship. The tilt holding constraint condition includes that when the centers of the tilt perturbation circle and the tilt holding circle are at the origin, the tilt vector of the GEO orbit tilt is on the tilt perturbation circle.

[0158] In this embodiment, the tilt initialization module is used for:

[0159] Calculate the right ascension of the sun, and calculate the rate of change of the tilt vector based on the right ascension of the sun;

[0160] The target tilt vector is calculated based on the tilt angle maintenance constraint, the tilt vector change rate, and the semi-annual perturbation equation.

[0161] In this embodiment, the tilt initialization module is further configured to:

[0162] Based on the first inclination increment between the target inclination vector and the initial inclination vector, the magnitude and direction of the first inclination increment are obtained;

[0163] The right ascension of the tilt initialization control is calculated based on the direction of the first tilt increment, and the first control moment is calculated based on the right ascension of the tilt initialization control;

[0164] The speed increment of the tilt initialization control is calculated based on the first tilt increment, and the first ignition duration is calculated based on the speed increment of the tilt initialization control.

[0165] In this embodiment, the tilt angle maintaining module is used for:

[0166] The second dip angle increment is calculated based on the long-term perturbation equation, and the magnitude and direction of the second dip angle increment are obtained.

[0167] The right ascension for tilt hold control is calculated based on the second tilt increment direction, and the second control time is calculated based on the right ascension for tilt hold control;

[0168] The speed increment of tilt hold control is calculated based on the second tilt angle increment, and the second ignition duration is calculated based on the speed increment of tilt hold control.

[0169] In this embodiment of the invention, a terminal device is also provided, including a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor. When the processor executes the computer program, it implements the above-described method for calculating the north-south electric propulsion maintenance strategy.

[0170] In this embodiment of the invention, a computer-readable storage medium is also provided, which includes a stored computer program, wherein the computer program controls the device where the computer-readable storage medium is located to execute the above-described north-south electric propulsion holding strategy calculation method when it is running.

[0171] For example, a computer program can be divided into one or more modules, one or more of which are stored in memory and executed by a processor to perform the present invention. The one or more modules can be a series of computer program instruction segments capable of performing a specific function, which describe the execution process of the computer program in a terminal device.

[0172] The terminal device may be a desktop computer, laptop, handheld computer, or cloud server, etc. The terminal device may include, but is not limited to, a processor, memory, and display. Those skilled in the art will understand that the above components are merely examples of terminal devices and do not constitute a limitation on the terminal device. It may include more or fewer components, or combinations of certain components, or different components. For example, the terminal device may also include input / output devices, network access devices, buses, etc.

[0173] The processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor. The processor is the control center of the terminal device, connecting all parts of the terminal device through various interfaces and lines.

[0174] Memory can be used to store computer programs and / or modules. The processor implements various functions of the terminal device by running or executing the computer programs and / or modules stored in the memory, and by accessing data stored in the memory. Memory can mainly include a program storage area and a data storage area. The program storage area can store the operating system, application programs required for at least one function (such as sound playback, text conversion, etc.), etc.; the data storage area can store data created based on the use of the mobile phone (such as audio data, text message data, etc.). In addition, memory can include high-speed random access memory, and can also include non-volatile memory, such as hard disks, RAM, plug-in hard disks, smart media cards (SMC), secure digital cards (SD cards), flash cards, at least one disk storage device, flash memory device, or other volatile solid-state storage devices.

[0175] In this invention, modules for processing multi-device access platforms, if implemented as software functional units and sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. Computer-readable media can include: any entity or device capable of carrying computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. Those skilled in the art can understand and implement this invention without any inventive effort.

[0176] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the scope of protection of the present invention. In particular, it should be noted that any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention for those skilled in the art.

Claims

1. A method for maintaining the tilt angle of a north-south electric thruster, characterized in that, include: Based on the perturbation law of GEO orbit inclination, the long-term perturbation equation of the GEO orbit inclination and the semi-annual perturbation equation of the GEO orbit inclination are constructed; Based on the long-term perturbation equation and the semi-annual period perturbation equation, tilt angle preservation constraints are constructed; The target tilt angle vector is obtained based on the tilt angle preservation constraint and the semi-annual perturbation equation; Obtain the initial tilt vector, obtain the first control moment and the first ignition duration based on the target tilt vector and the initial tilt vector, and perform tilt initialization control based on the first control moment and the first ignition duration; The direction and magnitude of the long-term tilt perturbation are calculated based on the long-term perturbation equation. The second control time is calculated based on the direction of the long-term tilt perturbation and the second ignition duration is calculated based on the magnitude of the long-term tilt perturbation. Tilt holding control is then performed based on the second control time and the second ignition duration.

2. The north-south electric thruster tilt angle maintenance control method as described in claim 1, characterized in that, The construction of tilt angle preservation constraints based on the long-term perturbation equation and the semi-annual period perturbation equation includes: An angle perturbation circle is constructed based on the semi-annual period perturbation equation, and an angle preservation circle is constructed based on the long-term term perturbation equation; Obtain the geometric relationship between the tilt perturbation circle and the tilt holding circle, and obtain the tilt holding constraint condition based on the geometric relationship. The tilt holding constraint condition includes that when the centers of the tilt perturbation circle and the tilt holding circle are at the origin, the tilt vector of the GEO orbit tilt is on the tilt perturbation circle.

3. The north-south electric thruster tilt angle maintenance control method as described in claim 2, characterized in that, The process of obtaining the target tilt angle vector based on the tilt angle maintenance constraint and the semi-annual period perturbation equation includes: Calculate the solar right ascension, and calculate the rate of change of the tilt vector based on the solar right ascension and the semi-annual perturbation equation; The target tilt vector is calculated based on the tilt angle maintenance constraint and the tilt vector change rate.

4. The north-south electric thruster tilt angle maintenance control method as described in claim 3, characterized in that, The step of obtaining the first control moment and the first ignition duration based on the target tilt vector and the initial tilt vector includes: A first inclination increment is obtained based on the target inclination vector and the initial inclination vector, wherein the first inclination increment includes the magnitude of the first inclination increment and the direction of the first inclination increment. The right ascension of the tilt initialization control is calculated based on the first tilt increment direction, and the first control time is calculated based on the right ascension of the tilt initialization control; The speed increment of the tilt initialization control is calculated based on the first tilt increment, and the first ignition duration is calculated based on the speed increment of the tilt initialization control.

5. The north-south electric thruster tilt angle maintenance control method as described in claim 4, characterized in that, The calculation of the direction and magnitude of the long-term dip perturbation based on the long-term perturbation equation includes: The second dip angle increment is calculated based on the long-term perturbation equation, and the magnitude and direction of the second dip angle increment are obtained. The right ascension for tilt hold control is calculated based on the second tilt increment direction, and the second control time is calculated based on the right ascension for tilt hold control; The speed increment of tilt hold control is calculated based on the second tilt angle increment, and the second ignition duration is calculated based on the speed increment of tilt hold control.

6. A north-south electric thruster tilt angle holding control device, characterized in that, include: Equation construction module, constraint construction module, target tilt angle calculation module, tilt angle initialization module, and tilt angle holding module; The equation construction module is used to construct the long-term perturbation equation of the GEO orbit inclination and the semi-annual periodic perturbation equation of the GEO orbit inclination based on the perturbation law of the GEO orbit inclination. The constraint construction module is used to construct tilt angle maintenance constraints based on the long-term perturbation equation and the semi-annual period perturbation equation. The target tilt angle calculation module is used to obtain the target tilt angle vector based on the tilt angle holding constraint and the semi-annual period perturbation equation; The tilt initialization module is used to obtain an initial tilt vector, obtain a first control moment and a first ignition duration based on the target tilt vector and the initial tilt vector, and perform tilt initialization control based on the first control moment and the first ignition duration. The tilt holding module is used to calculate the tilt long-term perturbation direction and magnitude based on the long-term perturbation equation, calculate the second control time based on the tilt long-term perturbation direction and the second ignition duration based on the tilt long-term perturbation magnitude, and perform tilt holding control based on the second control time and the second ignition duration.

7. The north-south electric thruster tilt angle holding control device as described in claim 6, characterized in that, The constraint construction module is used for: An angle perturbation circle is constructed based on the semi-annual period perturbation equation, and an angle preservation circle is constructed based on the long-term term perturbation equation; Obtain the geometric relationship between the tilt perturbation circle and the tilt holding circle, and obtain the tilt holding constraint condition based on the geometric relationship. The tilt holding constraint condition includes that when the centers of the tilt perturbation circle and the tilt holding circle are at the origin, the tilt vector of the GEO orbit tilt is on the tilt perturbation circle.

8. The north-south electric thruster tilt angle holding control device as described in claim 7, characterized in that, The target tilt angle calculation module is used for: Calculate the solar right ascension, and calculate the rate of change of the tilt vector based on the solar right ascension and the semi-annual perturbation equation; The target tilt vector is calculated based on the tilt angle maintenance constraint and the tilt vector change rate.

9. The north-south electric thruster tilt angle holding control device as described in claim 8, characterized in that, The tilt angle initialization module is used for: A first inclination increment is obtained based on the target inclination vector and the initial inclination vector, wherein the first inclination increment includes the magnitude of the first inclination increment and the direction of the first inclination increment. The right ascension of the tilt initialization control is calculated based on the first tilt increment direction, and the first control time is calculated based on the right ascension of the tilt initialization control; The speed increment of the tilt initialization control is calculated based on the first tilt increment, and the first ignition duration is calculated based on the speed increment of the tilt initialization control.

10. The north-south electric thruster tilt angle holding control device as described in claim 9, characterized in that, The tilt-holding module is used for: The second dip angle increment is calculated based on the long-term perturbation equation, and the magnitude and direction of the second dip angle increment are obtained. The right ascension for tilt hold control is calculated based on the second tilt increment direction, and the second control time is calculated based on the right ascension for tilt hold control; The speed increment of tilt hold control is calculated based on the second tilt angle increment, and the second ignition duration is calculated based on the speed increment of tilt hold control.

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