CN113968361B - Analytic calculation method suitable for geosynchronous satellite fixed-point control planning - Google Patents
Analytic calculation method suitable for geosynchronous satellite fixed-point control planning Download PDFInfo
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Abstract
The invention relates to an analytic calculation method suitable for geosynchronous satellite fixed-point control planning, which is implemented by the following steps: step 1, establishing a fixed point capture orbit control model, and determining a control target variable and a design variable; step 2, establishing a fixed point capturing control terminal constraint model according to the fixed point capturing track control model; step 3, determining a three-pulse constraint model according to the fixed point capturing track control model and the fixed point capturing control terminal constraint model, and calculating to obtain the size of three pulses and the control time of the three pulses; and 4, determining the three-pulse control parameters meeting the terminal conditions under the full-shooting condition by using a perturbation iteration method. According to the method, the three-pulse constraint model is established through the fixed point capturing track control model and the fixed point capturing control terminal constraint model, all possible working conditions of fixed point capturing control can be covered through three conditions, the iteration process is simple, the target value can be converged for 2-3 times, the process is simple, and the calculated amount is small.
Description
Technical Field
The invention belongs to the technical field of satellite navigation information processing, and relates to an analytic calculation method suitable for geosynchronous satellite fixed-point control planning.
Background
The geosynchronous orbit satellite needs fixed-point capture control before entering a working orbit, requires that the orbit height, the orbit eccentricity ratio and the direction and the fixed-point position meet the requirements, and essentially belongs to the problem of three-pulse orbit transfer in a plane. The fixed-point capturing control is carried out for several times at the end, and the control times and the control time can be adjusted to know and master the distribution condition of the subsequent control, so that the task staff can reasonably arrange the subsequent work. The basic idea of fixed point capture control is as follows: in the existing longitude deviation, a satellite longitude drift rate is set at a proper orbital position, orbit control is carried out for a plurality of times during the process that the satellite drifts to a fixed point position, and when the satellite drifts to the fixed point position, the longitude drift rate, the eccentricity and the average longitude difference all meet the requirements of an acquisition completion index. The existing fixed point capturing control algorithm is complex and relates to various working conditions.
Disclosure of Invention
The invention aims to provide an analytic calculation method suitable for geosynchronous satellite fixed point control planning, and aims to solve the technical problems of complex process and overlarge calculated amount of the analytic calculation method of the existing geosynchronous satellite fixed point control planning.
The technical scheme adopted by the invention is as follows: an analytic calculation method suitable for geosynchronous satellite fixed-point control planning is implemented according to the following steps:
step 3, determining a three-pulse constraint model according to the fixed point capturing track control model and the fixed point capturing control terminal constraint model, and calculating to obtain the size of three pulses and the control time of the three pulses;
and 4, determining the three-pulse control parameters meeting the terminal conditions under the full-shooting condition by using a perturbation iteration method.
The present invention is also characterized in that,
the specific calculation formula of the fixed point capturing orbit control model in the step 1 is as follows:
where Δ v is the tangential control pulse, a s ＝42165.7km，V s 3074.6M/s are the semi-major axis and speed of the satellite reference orbit, l Ω + ω + M is the equatorial eminence of the satellite, Δ a, Δ λ, Δ e x 、Δe y The track variation under the action of pulse control, namely semimajor axis, mean longitude and eccentricity vector variation, and subscripts 0 and f represent the states before and after orbital transfer.
In the step 1, the target variables are a semi-major axis a of the track, a longitude degree lambda of the track and an eccentricity vector e under the action of pulse control x And e y The design variable being the third tangential pulse Deltav 1 、Δv 2 、Δv 3 And the first pulse controls the position of the right ascension channel 1 Definition of x ═ Δ v 1 Δv 2 Δv 3 l 1 ] T 。
The calculation formula of the fixed point capturing control terminal constraint model in the step 2 is as follows:
three times of tangential pulses, second and third times of pulses control position of Pingtianjing 2 And l 3 Respectively as follows:
where m is 1 or 2, n is 1 or 2, representing half a day or 1 day apart, and k is 0, 1, 2 … representing an additional whole number of days apart.
Step 3, the calculation formula of the three-pulse constraint model is as follows:
wherein, Δ t 2 Time interval of the first pulse and the third pulse, Δ t 3 The time interval between the second pulse and the third pulse.
The first pulse controls the level of the right ascension l 1 From equations (4), (7) and (8):
wherein the content of the first and second substances,
further calculating the time interval between the first pulse acting time and the initial time:
wherein l 0 At the beginning of the right ascension, T s Is a sidereal day.
Triple tangential pulse Deltav 1 、Δv 2 、Δv 3 The method is obtained by combining and solving the formulas (4) to (11).
The specific process of the step 4 is as follows:
the algorithm in the step 1-3 is based on approximate analytic solution of a two-body model, corrects a two-body calculation result, obtains a three-pulse control parameter meeting a terminal condition under a perturbation condition by utilizing perturbation iteration, and obtains an initial value a of a state variable based on a full-motion model 0 ，λ 0 ，e 0 ，Ω 0 ，ω 0 Extrapolating delta t to obtain a set of ingested state variables a' 0 ，λ′ 0 ，e′ 0 ，Ω′ 0 ，ω′ 0 With a target value a of the state variable f ，λ f ，e f ，Ω f ，ω f And comparing to obtain state deviation:
and step 3 is executed again, specific conditions are selected according to needs, corresponding control time and control quantity are calculated, iteration is carried out for 2-3 times to obtain a solution meeting the index requirement, and the first iteration is carried out by taking the value of delta t-delta t 2 。
The invention has the beneficial effects that: the analytic calculation method suitable for the geostationary satellite fixed-point control planning establishes the three-pulse constraint model through the fixed-point capture orbit control model and the fixed-point capture control terminal constraint model, can cover all possible working conditions of fixed-point capture control through three conditions, has a concise analytic solution for capturing and controlling three pulses, is simple in iterative process, can converge to a target value for 2-3 times, and is simple in process and small in calculation amount.
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FIG. 1 is a control flow diagram of an analytic computing method suitable for geosynchronous satellite positioning control planning in accordance with the present invention;
fig. 2 is a timing chart of fixed point acquisition control of an analytic computing method suitable for geosynchronous satellite fixed point control planning according to the present invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention is an analytic calculation method suitable for geosynchronous satellite fixed-point control planning, which is realized by firstly establishing a fixed-point capture control terminal constraint model according to a fixed-point capture orbit control model, determining a control opportunity constraint model and a pulse size constraint model of three pulses, then solving the size of the three pulses and the control opportunity thereof according to three conditions of time intervals of the control pulses, and finally determining three-pulse control parameters meeting terminal conditions under a full-shooting condition by utilizing perturbation iteration, as shown in figures 1 to 2, and specifically implemented according to the following steps:
this is an in-plane impulse thrust control equation where Δ v is the tangential control impulse, a s ＝42165.7km，V s 3074.6M/s are the semi-major axis and speed of the satellite reference orbit, l Ω + ω + M is the equatorial eminence of the satellite, Δ a, Δ λ, Δ e x 、Δe y Respectively, the track variation under the action of pulse control, i.e. the vector variation of semimajor axis, mean longitude and eccentricity, Delta a, Delta lambda and Delta e x 、Δe y The calculation formula of (a) is as follows:
where subscripts 0 and f represent the state before and after track change, respectively. The direction of the track eccentricity vector points to the near point, and the magnitude is the eccentricity. When the satellite is subjected to arch point control, only the magnitude of the eccentricity is changed; when controlling at non-center of curvature, not only the magnitude of the eccentricity is changed, but also the direction of the eccentricity is changed. The fixed point capture essentially belongs to the problem of three-pulse orbit transfer in a plane, and a control target comprises a, lambda and e according to the fixed point capture control requirement x And e y Four variables. Considering three times of orbital transfer control, respectively selecting three times of tangential pulses delta v 1 、Δv 2 、Δv 3 And the first pulse controls the position of the right ascension channel 1 As a design variable, x ═ Δ v is defined 1 Δv 2 Δv 3 l 1 ] T 。
controlling the position l according to the task requirements by the second and third pulses 2 And l 3 Respectively as follows:
where m is 1 or 2, n is 1 or 2, representing half a day or 1 day apart, and k is 0, 1, 2 … representing an additional whole number of days apart.
Step 3, determining a three-pulse constraint model according to the fixed point capturing orbit control model in the step 1 and the fixed point capturing control terminal constraint model in the step 2, and calculating to obtain the size and the control time of the three-pulse, wherein the calculation formula of the three-pulse constraint model is as follows:
wherein, Δ t 2 Time interval of the first pulse and the third pulse, Δ t 3 The time interval between the second pulse and the third pulse.
Step 3.1, solving the size of the three pulses and the control time thereof in three situations;
firstly, the second and third pulse control positions l obtained in the step 2 are controlled 2 And l 3 Substituting the formula (4) into the three-pulse constraint model calculation formula (7) and(8) the position of the first pulse in the right ascension can be found:
wherein the content of the first and second substances,
it can further be calculated that the time interval between the first pulse application time and the initial time is:
wherein l 0 At the beginning of the right ascension, T s Is a sidereal day.
The analytical solution for fixed-point capture is obtained in three cases:
1) when m is 1 and n is 1, this case corresponds to the first two pulse interval days of 0.5 sidereal days and the second two pulse interval days of 0.5 sidereal days, i.e., Δ t 2 ＝T s ，Δt 3 ＝0.5T s . From equations (5) and (6):
changing m to 1, n to 1, Δ t 2 ＝T s ，Δt 3 ＝0.5T s Substituting equations (4), (7) and (8) can obtain:
wherein the content of the first and second substances,
and redefines the function s K The parity whose value depends on K differs as follows:
solving a linear equation system composed of equations (12) to (14):
2) when m is 2 and n is 1, this case corresponds to the first two pulse intervals of 1 sidereal day and the second two pulse intervals of 0.5 sidereal day, i.e., Δ t 2 ＝1.5T s ，Δt 3 ＝0.5T s . The derivation from the first case yields:
solving the above equation set:
3) when m is 1 and n is 2, this corresponds to the first two pulse interval times of 0.5 sidereal days and the second two pulse interval times of 1 sidereal day, i.e. Δ t 2 ＝1.5T s ，Δt 3 ＝T s . The derivation from the first case yields:
solving the equation set to obtain:
when m is 2 and n is 2, the first two pulse intervals are 1 sidereal day and the second two pulse intervals are 1 sidereal day. The following can be obtained:
in this case the first and third equations are linearly related, only if
It is true only when it is used, and it cannot be used as a general solution.
Step 4, determining a three-pulse control parameter meeting a terminal condition under a full-shooting condition by utilizing perturbation iteration;
considering that the algorithm in the steps 1 to 3 is based on an approximate analytic solution of a two-body model, and in practical application, orbit perturbation needs to be considered, and in this case, each orbit control parameter is coupled, so that a two-body calculation result needs to be corrected, and a three-pulse control parameter meeting a terminal condition under a perturbation condition can be obtained by utilizing perturbation iteration. The specific correction process is as follows: initial value a of state variable is determined based on total shooting model (earth gravitational field 10 × 10, sun-moon gravitational perturbation, sunlight pressure perturbation) 0 ，λ 0 ，e 0 ，Ω 0 ，ω 0 Extrapolating delta t to obtain a set of ingested state variables a' 0 ，λ′ 0 ，e′ 0 ，Ω′ 0 ，ω′ 0 With a target value a of the state variable f ，λ f ，e f ，Ω f ，ω f And comparing to obtain state deviation:
then step 3 is executed, the specific situation is selected according to the requirement, and the corresponding calculation is carried outControl timing and control amount of (2). Generally speaking, iteration is performed for 2-3 times to obtain a solution meeting the index requirement, wherein Δ t is taken as Δ t in the first iteration 2 . In addition, in an actual situation, considering propeller deviation and subsequent holding time requirements, fixed-point capture may need 4-5 times of orbital transfer control, but the theory is still suitable, and only the former N-3 times of control quantity designation is adopted, and the latter three times of control quantity is solved by the method.
Claims (2)
1. An analytic calculation method suitable for geosynchronous satellite fixed-point control planning is characterized by comprising the following steps of:
step 1, establishing a fixed point capture orbit control model, and determining a control target variable and a design variable;
step 2, establishing a fixed point capturing control terminal constraint model according to the fixed point capturing track control model;
step 3, determining a three-pulse constraint model according to the fixed point capture track control model and the fixed point capture control terminal constraint model, and calculating to obtain the time interval delta t between the first pulse action time and the initial time 1 The time interval delta t between the first pulse and the third pulse 2 The time interval delta t between the second pulse and the third pulse 3 First tangential pulse Deltav 1 Second tangential pulse Deltav 2 Third tangential pulse Δ v 3 ；
Step 4, calculating the time interval delta t between the first pulse acting time and the initial time 1 The time interval delta t between the first pulse and the third pulse 2 The time interval delta t between the second pulse and the third pulse 3 First tangential pulse Deltav 1 Second tangential pulse Deltav 2 Third tangential pulse Δ v 3 Determining a three-pulse control parameter meeting a terminal condition under a full-shooting condition by using a perturbation iteration method;
the specific calculation formula of the fixed point capturing orbit control model in the step 1 is as follows:
where Δ v is the tangential control pulse, a s ＝42165.7km，V s 3074.6M/s are the semi-major axis and speed of the satellite reference orbit, l Ω + ω + M is the equatorial eminence of the satellite, Δ a, Δ λ, Δ e x 、Δe y Respectively representing the track variation under the action of pulse control, namely the variation of a semimajor axis, a mean longitude, an eccentricity vector x axis and an eccentricity vector y axis, wherein subscripts 0 and f respectively represent the states before and after orbital transfer;
the target variables in the step 1 are a semi-major axis a of the track, a longitude flatness lambda and an eccentricity vector e under the action of pulse control x And e y The design variable being the third tangential pulse Deltav 1 、Δv 2 、Δv 3 And the first pulse controls the position of the right ascension channel 1 In the definition of x ═ Δ v 1 Δv 2 Δv 3 l 1 ] T ；
The calculation formula of the fixed point capturing control terminal constraint model in the step 2 is as follows:
the third tangential pulse controls the level right ascension l of the position 2 And l 3 Respectively as follows:
where m is 1 or 2, n is 1 or 2, representing half a day or 1 day apart, k is 0, 1, 2 … representing an additional whole number of days apart;
the calculation formula of the three-pulse constraint model in the step 3 is as follows:
wherein, Δ t 2 Time interval of the first pulse and the third pulse, Δ t 3 The time interval between the second pulse and the third pulse;
the first pulse controls the level right ascension l of the position 1 From equations (4), (7) and (8):
wherein the content of the first and second substances,
further calculating the time interval between the first pulse acting time and the initial time:
wherein l 0 At the beginning of the right ascension, T s Is a sidereal day;
the three tangential pulses Deltav 1 、Δv 2 、Δv 3 The solution is obtained by combining equations (4) to (11).
2. The analytic computing method suitable for geosynchronous satellite positioning control planning as claimed in claim 1, wherein the specific process of step 4 is as follows:
the algorithm in the step 1-3 is based on approximate analytic solution of a two-body model, corrects a two-body calculation result, obtains a three-pulse control parameter meeting a terminal condition under a perturbation condition by utilizing perturbation iteration, and obtains an initial value a of a state variable based on a full-motion model 0 ，λ 0 ，e 0 ，Ω 0 ，ω 0 Extrapolating delta t to obtain a set of ingested state variables a' 0 ，λ′ 0 ，e′ 0 ，Ω′ 0 ，ω′ 0 With a target value a of the state variable f ，λ f ，e f ，Ω f ，ω f And comparing to obtain state deviation:
and step 3 is executed again, specific conditions are selected according to needs, corresponding control time and control quantity are calculated, iteration is carried out for 2-3 times to obtain a solution meeting the index requirement, and the first iteration is carried out by taking the value of delta t-delta t 2 。
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| US5124925A (en) * | 1990-01-16 | 1992-06-23 | Space Systems/Loral, Inc. | Method for controlling east/west motion of a geostationary satellite |
| CN109552670A (en) * | 2018-12-03 | 2019-04-02 | 西安四方星途测控技术有限公司 | Application of low-thrust control in geostationary satellite orbit dip angle maintenance |
| CN110032768A (en) * | 2019-03-15 | 2019-07-19 | 中国西安卫星测控中心 | A kind of four pulse-orbits intersection optimization method using precise kinetic model |
| CN111338367A (en) * | 2020-02-27 | 2020-06-26 | 中国西安卫星测控中心 | Method for determining middle track under double-pulse control of same track for freezing eccentricity ratio |
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