South-north electric push inclination angle keeping control method and device

Abstract

The invention discloses a north-south electric push inclination angle keeping control method and device. According to the method, the long-term item and the half-year period item of the GEO satellite orbit inclination angle are separated, and motion equations are constructed respectively, so that the relation between the perturbation law of the half-year period item and the north-south keeping range is fully utilized to construct the keeping constraint condition, and the keeping strategy is calculated based on the keeping constraint condition; the advantage of high control stability of the electric pushing method is considered, the accuracy of the control moment and the ignition moment is improved by calculating the control strategy through the long-term item and the half-year period respectively, the electric pushing ignition duration can be effectively shortened, and the influence of the electric pushing method on the satellite longitude is reduced on the premise that the orbit inclination angle meets the maintaining requirement. Fuel consumption is reduced, and the right ascension fluctuation of an ignition point in a control strategy period is small.

Description

Technical Field

[0001] The invention relates to satellite orbit control, and in particular to a north-south electric propulsion inclination maintaining control method and device. Background Art

[0002] At present, when a geostationary orbit satellite (GEO) performs north-south control, the ground control center needs to calculate the control strategy to keep the orbit inclination of the GEO satellite within the required range based on the real-time orbit of the satellite, combined with the thruster type and parameters of the satellite control actuator, and upload it to the onboard actuator. There are two 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, and the negative inclination control calculation method is used to control the orbital inclination from a positive value to a negative value; as the satellite electric thrust control technology gradually 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 is to ignite the thrusters near the ascending node and the descending node every day in a control cycle (generally 7 days) on the selected control days (generally 5 days) to control the satellite orbital inclination within the required maintenance range. The control strategy is calculated according to the comprehensive perturbation speed and direction of the satellite orbital inclination at that time.

[0003] In the existing inclination holding method, the control factor for north-south holding is the orbital inclination. When the chemical propulsion method is used for north-south holding control, the fuel consumption is large and the disturbance to the satellite longitude is large. After the control is completed, it is necessary to immediately perform corrective control in the east-west direction to prevent the east-west longitude from being out of the loop caused by the north-south control. The execution risk is high and the disturbance to the satellite longitude is large. If the electric propulsion method calculates the control amount and control time according to the speed and direction of the comprehensive perturbation of the GEO satellite inclination, the ignition duration and ignition right ascension of each cycle calculated will fluctuate greatly due to the lack of regularity of the comprehensive perturbation of the inclination, which is not conducive to the execution of the control strategy and the arrangement of the control plan. In addition, the comprehensive perturbation of the GEO satellite orbital inclination is composed of long-term terms and long-period terms. If the control strategy is calculated according to the comprehensive perturbation speed, the thruster ignition duration obtained will be too long and may exceed the thruster ignition duration threshold. The long ignition duration will also have a greater impact on the east-west longitude and reduce the holding period of the east-west control. Summary of the invention

[0004] The present invention provides a north-south electric propulsion tilt angle maintenance control method and device, so as to reduce the ignition time of each cycle of the electric propulsion method, improve the ignition right ascension fluctuation stability and improve the tilt angle maintenance effect.

[0005] In order to solve the above technical problems, an embodiment of the present invention provides a north-south electric propulsion tilt angle maintenance control method, comprising:

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

[0007] Constructing a tilt angle maintenance constraint condition based on the long-term perturbation equation and the semi-annual period perturbation equation;

[0008] Based on the tilt angle holding constraint condition and the semi-annual period perturbation equation, a target tilt angle vector is obtained, an initial tilt angle vector is obtained, and based on the target tilt angle vector and the initial tilt angle vector, a first control moment and a first ignition duration are obtained, and tilt angle initialization control is performed based on the first control moment and the first ignition duration;

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

[0010] The present invention separates the long-term term and the half-year cycle term of the GEO satellite orbit inclination, and constructs the motion equations respectively, so as to make full use of the relationship between the perturbation law of the half-year cycle term and the north-south holding range to construct the holding constraint condition, and the holding strategy calculated based on the holding constraint condition 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 calculating the control strategy separately through the long-term term and the half-year cycle, which can effectively reduce the electric propulsion ignition time, and achieve the premise that the orbit inclination meets the holding requirements, reduce the influence of the electric propulsion method on the satellite longitude, reduce fuel consumption, and small fluctuation of the right ascension of the ignition point within the control strategy period.

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

[0012] Constructing an inclination perturbation circle based on the semi-annual period perturbation equation, and constructing an inclination preservation circle based on the long-term perturbation equation;

[0013] A geometric relationship between the inclination perturbation circle and the inclination maintaining circle is obtained, and an inclination maintaining constraint condition is obtained based on the geometric relationship, wherein the inclination maintaining constraint condition includes that when the centers of the inclination perturbation circle and the inclination maintaining circle are at the origin, the inclination vector of the GEO orbit inclination is on the inclination perturbation circle.

[0014] Further, the obtaining of the first control moment and the first ignition duration based on the target inclination vector and the initial inclination vector includes:

[0015] Calculating the solar right ascension, and calculating the rate of change of the inclination vector based on the solar right ascension and the semi-annual period perturbation equation;

[0016] A target tilt vector is calculated based on the tilt maintaining constraint condition and the tilt vector change rate.

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

[0018] Acquire a first tilt angle increment based on the target tilt angle vector and the initial tilt angle vector, wherein the first tilt angle increment includes a first tilt angle increment magnitude and a first tilt angle increment direction;

[0019] Calculating the right ascension of the tilt angle initialization control based on the first tilt angle increment direction, and calculating the first control time based on the right ascension of the tilt angle initialization control;

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

[0021] Further, the calculating the long-term perturbation direction and the long-term perturbation magnitude of the inclination angle based on the long-term perturbation equation includes:

[0022] Calculate a second inclination increment based on the long-term perturbation equation, and obtain a second inclination increment size and a second inclination increment direction;

[0023] Calculating the right ascension of the tilt-hold control based on the second tilt-angle increment direction, and calculating the second control time based on the right ascension of the tilt-hold control;

[0024] A speed increment of the tilt angle holding control is calculated based on the second tilt angle increment size, and a second ignition duration is calculated based on the speed increment of the tilt angle holding control.

[0025] In a second aspect, the present invention provides a north-south electric propulsion tilt angle maintenance 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 maintenance module;

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

[0027] The constraint building module is used to build a tilt angle maintenance constraint condition based on the long-term perturbation equation and the semi-annual period perturbation equation;

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

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

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

[0031] Furthermore, the constraint building module is used to:

[0032] Constructing an inclination perturbation circle based on the semi-annual period perturbation equation, and constructing an inclination preservation circle based on the long-term perturbation equation;

[0033] A geometric relationship between the inclination perturbation circle and the inclination maintaining circle is obtained, and an inclination maintaining constraint condition is obtained based on the geometric relationship, wherein the inclination maintaining constraint condition includes that when the centers of the inclination perturbation circle and the inclination maintaining circle are at the origin, the inclination vector of the GEO orbit inclination is on the inclination perturbation circle.

[0034] Furthermore, the target inclination angle calculation module is used to:

[0035] Calculating the solar right ascension, and calculating the rate of change of the inclination vector based on the solar right ascension and the semi-annual period perturbation equation;

[0036] A target tilt vector is calculated based on the tilt maintaining constraint condition and the tilt vector change rate.

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

[0038] Acquire a first tilt angle increment based on the target tilt angle vector and the initial tilt angle vector, wherein the first tilt angle increment includes a first tilt angle increment magnitude and a first tilt angle increment direction;

[0039] Calculating the right ascension of the tilt angle initialization control based on the first tilt angle increment direction, and calculating the first control time based on the right ascension of the tilt angle initialization control;

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

[0041] Furthermore, the inclination angle maintaining module is used to:

[0042] Calculate a second inclination increment based on the long-term perturbation equation, and obtain a second inclination increment size and a second inclination increment direction;

[0043] Calculating the right ascension of the tilt-hold control based on the second tilt-angle increment direction, and calculating the second control time based on the right ascension of the tilt-hold control;

[0044] A speed increment of the tilt angle holding control is calculated based on the second tilt angle increment size, and a second ignition duration is calculated based on the speed increment of the tilt angle holding control. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 A schematic flow chart of a north-south electric propulsion tilt angle maintenance control method provided by an embodiment of the present invention;

[0047] Figure 2 A geometric relationship diagram of an inclination perturbation circle and an inclination maintaining circle provided in an embodiment of the present invention;

[0048] Figure 3 A schematic diagram of calculating a first tilt angle increment provided by an embodiment of the present invention;

[0049] Figure 4 Another flow chart of a north-south electric propulsion tilt angle maintenance control method provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0050] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0051] The terms "first" and "second" and the like in the specification, claims and drawings of this application are used to distinguish different objects, rather than to describe a specific order. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device comprising 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 these processes, methods, products or devices.

[0052] Reference to "embodiments" herein means that a particular feature, structure, or characteristic described in conjunction with the embodiments may be included in at least one embodiment of the present application. The appearance of the phrase in various locations in the specification does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment that is mutually exclusive with other embodiments. It is explicitly and implicitly understood by those skilled in the art that the embodiments described herein may be combined with other embodiments.

[0053] Example 1

[0054] See also Figure 1 , Figure 1 A flowchart of a north-south electric propulsion tilt angle maintenance control method provided by an embodiment of the present invention. The embodiment of the present invention provides a north-south electric propulsion tilt angle maintenance control method, including steps 101 to 105, which are as follows:

[0055] Step 101: constructing a long-term perturbation equation of the GEO orbit inclination and a semi-annual period perturbation equation of the GEO orbit inclination based on the perturbation law of the GEO orbit inclination;

[0056] In this embodiment, the GEO orbit inclination perturbation law includes the influence of the GEO satellite orbit inclination on the non-spherical gravity of the earth, the gravity of the sun and the moon, the solar pressure and other perturbations. Among them, the perturbation of the harmonic term of the earth's flat belt causes the satellite orbit plane to precess in the opposite direction, and the precession speed is 4.9° per year, that is, the orbit inclination remains unchanged, and the direction precesses at a period of 73.46 years; the maximum value of the GEO orbit inclination perturbation caused by the solar pressure is about 3.5°×10 -5 , which is much smaller than the north-south holding range of 0.05°. Therefore, the influence of the Earth's non-spherical perturbation and the solar light pressure perturbation on the GEO satellite orbit inclination is ignored in the calculation of the north-south control strategy, and the main calculation is the influence of the solar and lunar gravitational perturbation on the geostationary orbit inclination.

[0057] 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 in the inclination caused by the gravity of the sun and the moon, and a semi-annual period perturbation equation is constructed based on the perturbation law of the GEO orbital inclination and the orbital inclination perturbation caused by the gravity of the sun.

[0058] In this embodiment, the GEO orbit inclination angle i is decomposed to obtain the component i of the GEO orbit inclination angle in the x direction. x and the y-component i y , where i x =i cosΩ,i y =i sinΩ, i is the magnitude of the inclination angle, Ω is the right ascension of the ascending node, that is, the direction of the inclination vector.

[0059] In this embodiment, the long-term perturbation equation of the GEO orbital inclination is constructed based on the perturbation law of the GEO orbital inclination. The long-term perturbation equation of the GEO orbital inclination is specifically:

[0060]

[0061] Among them, Ω sm is the ecliptic longitude of the ascending node of the ecliptic, and its calculation method is Ω sm=12.111-0.052954T, where T is the relative Julian day, i.e., relative to January 1, 1950.

[0062] In this embodiment, only the long-term change in the inclination caused by the gravitational force of the sun and the 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.

[0063] In this embodiment, the perturbation direction and perturbation speed of the inclination perturbation can be calculated based on the long-term perturbation equation of the GEO orbit inclination. Specifically:

[0064]

[0065] Among them, Ω d is the direction of the inclination perturbation, is the velocity of the inclination perturbation, in degrees / d.

[0066] In this embodiment, based on the perturbation equation of the long-term inclination, it can be obtained that the perturbation direction and perturbation speed of the inclination vector change slightly every year. When the lunar mean ecliptic longitude is closer to the vernal equinox, the inclination perturbation speed is greater, and the maximum value reaches 0.95° per year. When the lunar mean ecliptic longitude is 180° away from the vernal equinox, the inclination perturbation speed is the smallest, and the minimum is close to 0.75° per year. The inclination perturbation direction is approximately 89°~91°.

[0067] In this embodiment, the semi-annual periodic motion equation is calculated based on the GEO satellite orbit inclination perturbation motion caused by the sun's gravity, and its corresponding amplitude is calculated.

[0068] In this embodiment, the GEO satellite orbit inclination perturbation motion caused by the sun's gravity is a semi-annual period motion equation, specifically:

[0069]

[0070] Where n is the average angular velocity of the GEO satellite, n s is the average angular velocity of the sun, λ s is the solar right ascension, i s is the angle between the equatorial plane and the ecliptic plane. s =n s t, therefore:

[0071]

[0072] Among them, the equation of motion for the half-year period contains λ s The average change of the inclination vector in one year is 0, but there is a perturbation with a period of half a year, that is, 182.63 days, and its amplitude is:

[0073]

[0074] In this embodiment, the GEO satellite orbit inclination perturbation caused by the moon's gravity is a semi-lunar periodic motion, and the motion equation is:

[0075]

[0076] in, n m is the average angular velocity of the moon, λ m is the lunar right ascension, and n is the average angular velocity of the GEO satellite. The semi-monthly periodic motion equation is m , the average change of the inclination vector in one month is 0, but there is a perturbation with a period of half a month, that is, 13.7 days, and its amplitude is:

[0077]

[0078] In this embodiment, when the north-south holding range of the GEO satellite is 0.05°, the amplitude of the semi-monthly periodic perturbation motion caused by the lunar gravity is not in the same order of magnitude as the holding range and can be ignored. Therefore, only the semi-annual periodic motion equation caused by the solar gravity, that is, the semi-annual periodic perturbation equation, is calculated.

[0079] In this embodiment, the long-term term and the semi-annual periodic term of the GEO satellite orbital inclination are separated, and the motion equations are constructed separately. The control strategies are calculated respectively by the equations constructed by the long-term term and the semi-annual periodic term, thereby improving the accuracy of the control timing and the ignition timing, and can effectively reduce the electric propulsion ignition time.

[0080] Step 102: constructing a tilt angle keeping constraint condition based on the long-term perturbation equation and the semi-annual period perturbation equation;

[0081] In this embodiment, the step of constructing the tilt angle maintenance constraint condition based on the long-term perturbation equation and the semi-annual period perturbation equation includes:

[0082] Constructing an inclination perturbation circle based on the semi-annual period perturbation equation, and constructing an inclination preservation circle based on the long-term perturbation equation;

[0083] A geometric relationship between the inclination perturbation circle and the inclination maintaining circle is obtained, and an inclination maintaining constraint condition is obtained based on the geometric relationship, wherein the inclination maintaining constraint condition includes that when the centers of the inclination perturbation circle and the inclination maintaining circle are at the origin, the inclination vector of the GEO orbit inclination is on the inclination perturbation circle.

[0084] As a specific example of an embodiment of the present invention, please refer to Figure 2 , Figure 2A geometric relationship diagram of an inclination perturbation circle and an inclination maintaining circle provided in an embodiment of the present invention.

[0085] In this embodiment, the tilt angle holding circle is constructed based on the long-term perturbation equation. When the north-south holding range of the GEO satellite is 0.05° and does not involve the tilt vector perturbation circle center offset, the tilt angle holding range can be expressed as:

[0086]

[0087] In this embodiment, a tilt angle maintaining circle can be constructed based on the tilt angle maintaining range.

[0088] In this embodiment, the inclination perturbation circle is constructed based on the semi-annual period perturbation equation. Based on the semi-annual period motion equation, the semi-annual period term perturbation equation of the GEO satellite orbit 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 the center of the circle is at the origin, the inclination perturbation circle equation is:

[0089]

[0090] In this embodiment, the inclination perturbation circle is constructed based on the semi-annual period perturbation equation, and the inclination maintaining circle is constructed based on the long-term term perturbation equation.

[0091] In this embodiment, based on the geometric relationship between the inclination perturbation circle and the inclination maintaining circle, the inclination maintaining constraint condition is determined. When the centers of the inclination perturbation circle and the inclination maintaining circle are both at the origin, the inclination vector is always within the maintaining range, and the maintaining requirement is met. Therefore, when calculating the north-south maintaining strategy, the initial inclination is controlled to the half-year cycle perturbation circle with the origin as the center, and then the long-term inclination perturbation is overcome by orbit control. At this time, the inclination only has half-year cycle perturbations and half-month cycle perturbations, which can meet the maintaining requirement under free perturbation motion.

[0092] In this embodiment, the north-south electric propulsion holding strategy is divided into two stages based on the tilt angle holding constraint condition. The first stage is the tilt angle initialization control, which mainly considers the half-year cycle perturbation of the tilt angle, and the second stage is the tilt angle maintenance control, which mainly considers the long-term term perturbation of the tilt angle. Since the perturbation speed and perturbation direction of the long-term term and the half-year cycle term are relatively stable in the short term, the control duration and control time calculated according to them are relatively stable with small fluctuations.

[0093] Step 103: acquiring a target inclination vector based on the inclination-keeping constraint condition and the semi-annual period perturbation equation;

[0094] In this embodiment, the tilt angle initialization control is the process of controlling the tilt angle vector from the initial position to the half-year period perturbation circle with the center as the origin. This process is divided into target tilt angle vector calculation and control strategy calculation. Among them, the target tilt angle vector calculation is to combine the half-year period perturbation equation and calculate the corresponding position on the perturbation circle as the target tilt angle.

[0095] In this embodiment, the step of acquiring the target inclination vector based on the inclination maintaining constraint condition and the semi-annual period perturbation equation includes:

[0096] Calculating the solar right ascension, and calculating the rate of change of the inclination vector based on the solar right ascension and the semi-annual period perturbation equation;

[0097] The target tilt vector is calculated based on the tilt-keeping constraint, the tilt vector change rate, and the semi-annual period perturbation equation.

[0098] In this embodiment, the change rate of the inclination vector can be obtained based on the half-year period motion equation, and the change rate of the inclination vector is:

[0099]

[0100] Among them, λ s is the solar right ascension, which can be obtained through the planetary ephemeris prediction, i s It is the angle between the equatorial plane and the ecliptic plane, which is 23.4437°.

[0101] In this embodiment, the solar right ascension is calculated based on the planetary ephemeris forecast, thereby calculating the inclination vector change rate. Based on the inclination vector change rate and the inclination perturbation circle equation, the inclination vector change rate can be obtained as follows:

[0102]

[0103] Based on the inclination vector change rate and the semi-annual period perturbation equation, the target inclination vector is calculated, specifically:

[0104]

[0105] Among them, i tx 、i ty That is, the target inclination angle for inclination initialization.

[0106] Step 104: acquiring an initial tilt angle vector, and acquiring a first control moment and a first ignition duration based on the target tilt angle vector and the initial tilt angle vector, and performing tilt initialization control based on the first control moment and the first ignition duration;

[0107] In this embodiment, the acquiring the first control moment and the first ignition duration based on the target tilt angle vector includes:

[0108] Acquire a first tilt angle increment based on the target tilt angle vector and the initial tilt angle vector, wherein the first tilt angle increment includes a first tilt angle increment magnitude and a first tilt angle increment direction;

[0109] Calculating the right ascension of the tilt angle initialization control based on the first tilt angle increment direction, and calculating the first control time based on the right ascension of the tilt angle initialization control;

[0110] A speed increment of the tilt angle initialization control is measured based on the first tilt angle increment, and a first ignition duration is calculated based on the speed increment of the tilt angle initialization control.

[0111] In this embodiment, the first tilt angle increment is calculated based on the initial tilt angle vector and the target tilt angle vector.

[0112] Please refer to Figure 3 , Figure 3 A schematic diagram of calculating a first tilt angle increment provided in an embodiment of the present invention.

[0113] In this embodiment, i t is the target inclination vector, i i is the initial inclination vector, and △i is the first inclination increment.

[0114] In this embodiment, the first inclination angle increment is specifically:

[0115]

[0116] In this embodiment, the magnitude and direction of the first tilt angle increment are obtained according to the first tilt angle increment, specifically:

[0117]

[0118] Among them, △i normal is the first inclination increment, △i direction is the direction of the first tilt increment.

[0119] In this embodiment, the inclination angle size of each control is calculated based on the first inclination angle increment size, specifically:

[0120] △i s = △i normal / (2D) (15)

[0121] Among them, △i s is the inclination angle of each control, D is the total number of control days, and the control is 2 times a day.

[0122] In this embodiment, there is a relationship between the first inclination increment of the GEO satellite orbit and the normal velocity increment as follows:

[0123]

[0124] Among them, △V N is the normal velocity increment.

[0125] In this embodiment, the first ignition duration of each thruster control is calculated based on the speed increment, specifically:

[0126]

[0127] Among them, d is the first ignition duration of the thruster, F is the thrust of the thruster, and M is the mass of the satellite.

[0128] In this embodiment, the direction of the first tilt angle increment is the right ascension of the satellite in the true equatorial coordinate system at the first control time, so the right ascension at the first control time is calculated based on the direction of the first tilt angle increment as follows:

[0129]

[0130] In this embodiment, the first control time T can be obtained by the satellite right ascension prediction. m1 , T m2 , so the ignition time twice a day is:

[0131]

[0132] According to the thruster ignition timing and the first ignition duration parameters, the satellite can perform inclination initialization control.

[0133] Step 105: Calculate the long-term perturbation direction and the long-term perturbation magnitude of the tilt angle based on the long-term perturbation equation, calculate the second control moment based on the long-term perturbation direction of the tilt angle and calculate the second ignition duration based on the long-term perturbation magnitude of the tilt angle, and perform tilt holding control based on the second control moment and the second ignition duration.

[0134] In this embodiment, the calculating of the long-term perturbation direction and the long-term perturbation magnitude of the inclination angle based on the long-term perturbation equation includes:

[0135] Calculate a second inclination increment based on the long-term perturbation equation, and obtain a second inclination increment size and a second inclination increment direction;

[0136] Calculating the right ascension of the tilt-hold control based on the second tilt-angle increment direction, and calculating the second control time based on the right ascension of the tilt-hold control;

[0137] A speed increment of the tilt angle holding control is calculated based on the second tilt angle increment size, and a second ignition duration is calculated based on the speed increment of the tilt angle holding control.

[0138] In this embodiment, after completing the inclination initialization control, the satellite orbit inclination vector is already located on a half-year perturbation circle with its center at the origin. At this time, it is only necessary to calculate the control strategy based on the long-term perturbation law of the inclination to overcome the long-term perturbation of the sun and the moon's gravity.

[0139] In this embodiment, if the long-term perturbation of the inclination angle is to be overcome, the inclination angle increment generated by the thruster only needs to be opposite in direction to the long-term perturbation of the inclination angle and equal in magnitude.

[0140] In this embodiment, in order to control the generated inclination increment to be opposite to the direction of the long-term perturbation, the right ascension at the second control time near the ascending node and the descending node every day during the inclination maintenance phase is

[0141]

[0142] In this embodiment, the second control time T can be obtained by the satellite right ascension prediction. m1 , T m2 .

[0143] In this embodiment, the daily perturbation of the long-term term perturbation of the inclination angle is calculated based on the long-term term perturbation equation, so the inclination control amount at the ascending node and the descending node is

[0144]

[0145] In this embodiment, the normal velocity increment is calculated based on the inclination angle control amount, and based on the normal velocity increment, it can be obtained that the second ignition duration at the ascending node and the descending node is d, so the ignition time twice a day is:

[0146]

[0147] Based on the thruster ignition timing and the second ignition duration, the satellite can perform inclination hold control.

[0148] The present invention separates the long-term term and the half-year cycle term of the GEO satellite orbit inclination, and constructs the motion equations respectively, so as to make full use of the relationship between the perturbation law of the half-year cycle term and the north-south holding range to construct the holding constraint condition, and the holding strategy calculated based on the holding constraint condition 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 calculating the control strategy separately through the long-term term and the half-year cycle, which can effectively reduce the electric propulsion ignition time, and achieve the premise that the orbit inclination meets the holding requirements, reduce the influence of the electric propulsion method on the satellite longitude, reduce fuel consumption, and small fluctuation of the right ascension of the ignition point within the control strategy period.

[0149] Please refer to Figure 4 , Figure 4 Another flow chart of a north-south electric propulsion tilt angle maintenance control method provided in an embodiment of the present invention.

[0150] In this embodiment, the solar right ascension is calculated based on the planetary ephemeris forecast; the rate of change of the semi-annual period perturbation of the inclination angle is calculated based on the solar right ascension; the target inclination angle vector is calculated by combining the rate of change of the inclination angle vector and the semi-annual period perturbation ellipse equation; the inclination angle increment between the target inclination angle vector and the initial inclination angle vector is calculated; the right ascension of the inclination angle control is calculated based on the direction of the inclination angle increment; the speed increment of the inclination angle control is calculated based on the size of the inclination angle increment; the control time parameter is calculated based on the right ascension at the control time; the thruster ignition duration is calculated based on the speed increment; the direction and size of the long-term inclination angle perturbation are calculated; the right ascension at the inclination angle control time is calculated based on the direction of the long-term inclination angle perturbation; the speed increment required for the inclination angle control is calculated based on the size of the long-term inclination angle perturbation; the control time parameter is calculated based on the right ascension at the control time; and the thruster ignition duration is calculated based on the speed increment.

[0151] The embodiment of the present invention also provides a north-south electric propulsion tilt angle keeping control device, comprising: an equation building module, a constraint building module, a tilt angle initialization module and a tilt angle keeping module;

[0152] The equation construction module is used to construct the long-term perturbation equation of the GEO orbit inclination and the semi-annual period perturbation equation of the GEO orbit inclination based on the perturbation law of the GEO orbit inclination;

[0153] The constraint building module is used to build a tilt angle maintenance constraint condition based on the long-term perturbation equation and the semi-annual period perturbation equation;

[0154] The tilt angle initialization module is used to obtain a target tilt angle vector based on the tilt angle maintenance constraint condition and the semi-annual period perturbation equation, and obtain a first control moment and a first ignition duration based on the target tilt angle vector, and perform tilt angle initialization control based on the first control moment and the first ignition duration;

[0155] The tilt angle holding module is used to calculate the tilt angle long-term perturbation direction and the tilt angle long-term perturbation magnitude based on the long-term perturbation equation, calculate the second control moment based on the tilt angle long-term perturbation direction and calculate the second ignition duration based on the tilt angle long-term perturbation magnitude, and perform tilt angle holding control based on the second control moment and the second ignition duration.

[0156] In this embodiment, the constraint building module is used to:

[0157] Constructing an inclination perturbation circle based on the semi-annual period perturbation equation, and constructing an inclination preservation circle based on the long-term perturbation equation;

[0158] A geometric relationship between the inclination perturbation circle and the inclination maintaining circle is obtained, and an inclination maintaining constraint condition is obtained based on the geometric relationship, wherein the inclination maintaining constraint condition includes that when the centers of the inclination perturbation circle and the inclination maintaining circle are at the origin, the inclination vector of the GEO orbit inclination is on the inclination perturbation circle.

[0159] In this embodiment, the tilt angle initialization module is used to:

[0160] Calculating the solar right ascension, and calculating the rate of change of the inclination vector based on the solar right ascension;

[0161] The target tilt vector is calculated based on the tilt-keeping constraint, the tilt vector change rate, and the semi-annual period perturbation equation.

[0162] In this embodiment, the tilt angle initialization module is further used for:

[0163] Based on a first tilt angle increment between the target tilt angle vector and the initial tilt angle vector, obtaining a first tilt angle increment magnitude and a first tilt angle increment direction;

[0164] Calculating the right ascension of the tilt initialization control based on the direction of the first tilt angle increment, and calculating the first control time based on the right ascension of the tilt initialization control;

[0165] A speed increment of the tilt angle initialization control is calculated based on the first tilt angle increment size, and a first ignition duration is calculated based on the speed increment of the tilt angle initialization control.

[0166] In this embodiment, the inclination angle maintaining module is used to:

[0167] Calculate a second inclination increment based on the long-term perturbation equation, and obtain a second inclination increment size and a second inclination increment direction;

[0168] Calculating the right ascension of the tilt-hold control based on the second tilt-angle increment direction, and calculating the second control time based on the right ascension of the tilt-hold control;

[0169] A speed increment of the tilt angle holding control is calculated based on the second tilt angle increment size, and a second ignition duration is calculated based on the speed increment of the tilt angle holding control.

[0170] In an embodiment of the present 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, the above-mentioned north-south electric propulsion holding strategy calculation method is implemented.

[0171] In an embodiment of the present invention, a computer-readable storage medium is also provided, and the computer-readable storage medium includes a stored computer program, wherein when the computer program is running, the device where the computer-readable storage medium is located is controlled to execute the above-mentioned north-south electric propulsion maintenance strategy calculation method.

[0172] Exemplarily, the computer program may be divided into one or more modules, one or more modules are stored in a memory and executed by a processor to implement the present invention. One or more modules may be a series of computer program instruction segments capable of implementing specific functions, and the instruction segments are used to describe the execution process of the computer program in a terminal device.

[0173] The terminal device may be a computing device such as a desktop computer, a notebook, a PDA, and a cloud server. The terminal device may include, but is not limited to, a processor, a memory, and a display. Those skilled in the art will appreciate that the above components are merely examples of the terminal device and do not constitute a limitation on the terminal device. The terminal device may include more or fewer components than the components, or may combine certain components, or different components. For example, the terminal device may also include input and output devices, network access devices, buses, etc.

[0174] The processor may be a central processing unit (CPU), other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor, etc. The processor is the control center of the terminal device, and uses various interfaces and lines to connect various parts of the entire terminal device.

[0175] The memory can be used to store computer programs and / or modules. The processor realizes various functions of the terminal device by running or executing the computer programs and / or modules stored in the memory, and calling the data stored in the memory. The memory can mainly include a program storage area and a data storage area, wherein the program storage area can store an operating system, an application required for at least one function (such as a sound playback function, a text conversion function, etc.), etc.; the data storage area can store data created according to the use of the mobile phone (such as audio data, text message data, etc.), etc. In addition, the memory can include a high-speed random access memory, and can also include a non-volatile memory, such as a hard disk, a memory, a plug-in hard disk, a smart memory card (Smart Med i aCard, SMC), a secure digital (Secure Digital, SD) card, a flash card (Flash Card), at least one disk storage device, a flash memory device, or other volatile solid-state storage devices.

[0176] Among them, if the module based on the processing of the multi-device access platform is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on such an understanding, the present invention implements all or part of the processes in the above-mentioned embodiment method, and can also be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium, and the computer program can implement the steps of the above-mentioned various method embodiments when executed by the processor. Among them, the computer program includes computer program code, and the computer program code can be in source code form, object code form, executable file or some intermediate form. The computer-readable medium may include: any entity or device capable of carrying computer program code, recording medium, U disk, mobile hard disk, disk, optical disk, computer memory, read-only memory (ROM, Read-Only Memory), random access memory (RAM, RandomAccess Memory), electric carrier signal, telecommunication signal and software distribution medium, etc. Ordinary technicians in this field can understand and implement it without paying creative labor.

[0177] The specific embodiments described above further illustrate the purpose, technical solutions and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. It is particularly pointed out that for those skilled in the art, any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the scope of protection of the present invention.

Claims

1. A north-south electric propulsion tilt angle maintenance control method, characterized in that: include: Based on the GEO orbit inclination perturbation law, a long-term perturbation equation of the GEO orbit inclination and a semi-annual period perturbation equation of the GEO orbit inclination are constructed; Constructing a tilt angle maintenance constraint condition based on the long-term perturbation equation and the semi-annual period perturbation equation; Acquire a target inclination vector based on the inclination-maintaining constraint condition and the semi-annual period perturbation equation; Acquire an initial tilt angle vector, acquire a first control moment and a first ignition duration based on the target tilt angle vector and the initial tilt angle vector, and perform tilt initialization control based on the first control moment and the first ignition duration; The long-term perturbation direction and the long-term perturbation magnitude of the tilt angle are calculated based on the long-term perturbation equation, the second control moment is calculated based on the long-term perturbation direction of the tilt angle and the second ignition duration is calculated based on the long-term perturbation magnitude of the tilt angle, and the tilt angle holding control is performed based on the second control moment and the second ignition duration.

2. A north-south electric propulsion tilt angle control method as claimed in claim 1, characterized in that: The step of constructing the tilt angle maintenance constraint condition based on the long-term perturbation equation and the half-year period perturbation equation includes: Constructing an inclination perturbation circle based on the semi-annual period perturbation equation, and constructing an inclination preservation circle based on the long-term perturbation equation; A geometric relationship between the inclination perturbation circle and the inclination maintaining circle is obtained, and an inclination maintaining constraint condition is obtained based on the geometric relationship, wherein the inclination maintaining constraint condition includes that when the centers of the inclination perturbation circle and the inclination maintaining circle are at the origin, the inclination vector of the GEO orbit inclination is on the inclination perturbation circle.

3. A north-south electric propulsion tilt angle maintenance control method as claimed in claim 2, characterized in that: The obtaining of the target inclination vector based on the inclination maintaining constraint condition and the semi-annual period perturbation equation comprises: Calculating the solar right ascension, and calculating the rate of change of the inclination vector based on the solar right ascension and the semi-annual period perturbation equation; A target tilt vector is calculated based on the tilt maintaining constraint condition and the tilt vector change rate.

4. A north-south electric propulsion tilt angle maintenance control method as claimed in claim 3, characterized in that: The acquiring a first control moment and a first ignition duration based on the target inclination vector and the initial inclination vector comprises: Acquire a first tilt angle increment based on the target tilt angle vector and the initial tilt angle vector, wherein the first tilt angle increment includes a first tilt angle increment magnitude and a first tilt angle increment direction; Calculating the right ascension of the tilt angle initialization control based on the first tilt angle increment direction, and calculating the first control time based on the right ascension of the tilt angle initialization control; A speed increment of the tilt angle initialization control is measured based on the first tilt angle increment, and a first ignition duration is calculated based on the speed increment of the tilt angle initialization control.

5. A north-south electric propulsion tilt angle maintenance control method as claimed in claim 4, characterized in that: The calculating the long-term perturbation direction and the long-term perturbation magnitude of the inclination angle based on the long-term perturbation equation comprises: Calculate a second inclination increment based on the long-term perturbation equation, and obtain a second inclination increment size and a second inclination increment direction; Calculating the right ascension of the tilt-hold control based on the second tilt-angle increment direction, and calculating the second control time based on the right ascension of the tilt-hold control; A speed increment of the tilt angle holding control is calculated based on the second tilt angle increment size, and a second ignition duration is calculated based on the speed increment of the tilt angle holding control.

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

7. A north-south electric propulsion tilt angle control device as claimed in claim 6, characterized in that: The constraint building module is used to: Constructing an inclination perturbation circle based on the semi-annual period perturbation equation, and constructing an inclination preservation circle based on the long-term perturbation equation; A geometric relationship between the inclination perturbation circle and the inclination maintaining circle is obtained, and an inclination maintaining constraint condition is obtained based on the geometric relationship, wherein the inclination maintaining constraint condition includes that when the centers of the inclination perturbation circle and the inclination maintaining circle are at the origin, the inclination vector of the GEO orbit inclination is on the inclination perturbation circle.

8. A north-south electric propulsion tilt angle control device as claimed in claim 7, characterized in that: The target inclination angle calculation module is used for: Calculating the solar right ascension, and calculating the rate of change of the inclination vector based on the solar right ascension and the semi-annual period perturbation equation; A target tilt vector is calculated based on the tilt maintaining constraint condition and the tilt vector change rate.

9. A north-south electric propulsion tilt angle control device as claimed in claim 8, characterized in that: The inclination angle initialization module is used to: Acquire a first tilt angle increment based on the target tilt angle vector and the initial tilt angle vector, wherein the first tilt angle increment includes a first tilt angle increment magnitude and a first tilt angle increment direction; Calculating the right ascension of the tilt angle initialization control based on the first tilt angle increment direction, and calculating the first control time based on the right ascension of the tilt angle initialization control; A speed increment of the angle initialization control is measured based on the first inclination angle increment, and a first ignition duration is calculated based on the speed increment of the inclination angle initialization control.

10. A north-south electric propulsion tilt angle control device as claimed in claim 9, characterized in that: The inclination angle maintaining module is used for: Calculate a second inclination increment based on the long-term perturbation equation, and obtain a second inclination increment size and a second inclination increment direction; Calculating the right ascension of the tilt-hold control based on the second tilt-angle increment direction, and calculating the second control time based on the right ascension of the tilt-hold control; A speed increment of the tilt angle holding control is calculated based on the second tilt angle increment size, and a second ignition duration is calculated based on the speed increment of the tilt angle holding control.

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