CN113934233B - Satellite formation control thruster calibration method - Google Patents
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Abstract
The invention discloses a thruster calibration method for satellite formation control, which comprises the following steps of firstly, calculating theoretical configuration parameters before and after control according to the number of double-star orbit flat roots; theoretical configuration parameters comprise a short half axis p of a projected ellipse in an x-y plane; amplitude s of the z-direction motion; a phase angle θ relative to the eccentricity vector; the phase angle ψ of the relative tilt vector; track direction distance l; and selecting a corresponding calibration method according to the variation of the formation configuration parameter numerical control front control and the control strategy, and calculating the calibration coefficient of the thruster according to the calibration method of the thruster. The thruster calibration method aims to provide accurate calibration coefficients for formation control, provide references for subsequent formation control and further realize high-precision formation control.
Description
Technical Field
The invention belongs to the technical field of aerospace measurement and control, and particularly relates to a thruster calibration method for satellite formation control.
Background
With the continuous development of satellite application technology, satellite formation is a commonly used satellite application mode. Compared with the control of the traditional satellites, the control of the formation satellites has higher requirements on the control precision of the inter-satellite distances, and often involves small-scale control in an orbit plane and out of plane, and the traditional thruster calibration method based on the single-satellite orbit determination result often causes inaccurate thruster calibration results because of insufficient single-satellite orbit measurement precision. The high-precision relative orbit measurement information among the formation satellites is considered, so that the method can be used for calibrating the thruster under the condition of small control quantity, and the calibration precision can be effectively improved.
Disclosure of Invention
The invention aims to provide a thruster calibration method for satellite formation control, which solves the problem of inaccurate thruster calibration during semi-long axis small-scale control.
The technical scheme adopted by the invention is that the satellite formation control thruster calibration method is implemented according to the following steps:
step 1, calculating theoretical configuration parameters before and after control according to the number of the double-star orbit flat roots; theoretical configuration parameters comprise a short half axis p of a projected ellipse in an x-y plane; amplitude s of the z-direction motion; a phase angle θ relative to the eccentricity vector; the phase angle ψ of the relative tilt vector; track direction distance l;
and 2, selecting a corresponding calibration method according to the variation of the formation configuration parameter numerical control front control and the control strategy, and calculating the calibration coefficient of the thruster according to the calibration method of the thruster.
The present invention is also characterized in that,
in the step 1, theoretical configuration parameters before and after control can be calculated according to six orbit numbers of double stars, wherein the six orbit numbers refer to an orbit semi-long axis a, an eccentricity e, an inclination i, an ascending intersection point right angle omega, a near-place amplitude angle omega and a near-point angle M; the configuration parameters were calculated by the following formula:
Δu＝ω 2 +M 2 -(ω 1 +M 1 )；
Δe x and Δe y Δi, two components of the relative eccentricity vector x And Δi y Two components that are relative tilt vectors; e, e 1 Is the eccentricity of the main star e 2 Is the eccentricity of the satellite; omega 1 Is the amplitude angle, omega of the near-site of the main star 2 Is the near-place amplitude angle of the auxiliary star; omega shape 1 Is the right ascent point of the principal star, the right ascent point is the right ascent point, and the right ascent point is the right ascent point 2 Is the right ascent point of the auxiliary star; i.e 1 Is the inclination angle of the main star, i 2 Is the inclination angle of the auxiliary star, M 1 Is the normal point angle of the main star, M 2 Is an auxiliary starIs a straight-up point angle of (c).
In the step 2, if the configuration parameter l needs to be adjusted, the adjustment is mainly realized by changing the semi-long axis; considering that tangential control generally changes the eccentricity and semi-long axis, when the semi-long axis and the eccentricity change amounts satisfy:
(Δa/a 2 ) 2 >(Δe) 2
wherein deltaa is the control quantity of the semi-long axis of the auxiliary star, deltae is the modulus value of the change quantity of the eccentricity vector of the auxiliary star, namely the main control quantity is the semi-long axis in the case, and a relative semi-long axis calibration method is adopted;
taking into account the error of instantaneous level conversion of the number of tracks, the level half long axis difference of the double stars before control is obtained by extrapolating the track for a period of time delta t 0 According to the track direction distance drift delta l 0 Inversion is carried out, namely the theoretical value of the difference of the horizontal half long axes of the two stars before control is calculated by using the following formula;
wherein Deltal 0 For controlling front delta t of track 0 The track direction distance drift amount caused by the double-star semi-major axis difference in time can be obtained through track extrapolation, n is the average angular velocity of the track of the formation main star, and can be obtained through the orbit determination data of the main star, and the theoretical value of the double-star flat semi-major axis after control is also obtained through the method;
the actual value of the controlled double-star semi-long axis difference is obtained by inversion according to the change quantity of the remote-measured track distance l, namely
Wherein Deltal' f Is the delta t after rail control f The distance drift quantity of the track direction caused by the difference of the two stars and the semi-long axis in time is further calculated to obtain the calibration coefficient eta controlled by the relative semi-long axis f ；
Wherein eta 0 The calibration coefficient after the last control is used; Δa 0 And Deltaa f And theoretical values before and after the difference control of the two-star semi-long axis respectively; Δa' 0 And Δa' f The actual values of the two stars and the half long axis are respectively the actual values of the front control and the rear control.
In step 2, if configuration parameters p and θ need to be adjusted, the eccentricity is mainly changed, and the change amounts of the semi-major axis and the eccentricity meet the following conditions:
(Δa/a 2 ) 2 <(Δe) 2
the main control quantity is an eccentricity vector, and a relative eccentricity vector calibration method is adopted in the situation;
the pre-control theoretical value and the post-control theoretical value of the relative eccentricity vector mode delta e can be calculated by the orbit root number of double stars, and the post-control actual value can be calculated by the following formula
Wherein p' f Projection of elliptical short half-axis in plane for post-control formation configuration, relative eccentricity vector controlled calibration coefficient κ f ；
Wherein, kappa 0 The calibration coefficient after the last control is used; delta e 0 And delta e f Theoretical values before and after the control of the relative eccentricity vector module value are respectively; delta e' 0 And δe' f The actual values before and after the control of the relative eccentricity vector module value are respectively; θ 0 And theta f Theoretical values before and after the initial phase control of the relative eccentricity vector are respectively; θ'. 0 And θ' f The actual values before and after the initial phase control of the relative eccentricity vector are respectively.
In the step 2, if the formation control is out-of-plane control, the control quantity only changes the inclination angle and the right ascent and descent point, and only the amplitude s of the out-of-plane motion of the track and the phase angle psi of the relative inclination angle vector in 5 configuration parameters are changed, and in this case, a relative inclination angle vector calibration method is adopted;
calibration coefficient k of out-of-plane control f ；
Wherein k is 0 The calibration coefficient after the last control is used; s is(s) 0 Sum s f Theoretical values before and after the control of the out-of-plane amplitude of the relative motion are respectively; s' 0 And s' f The actual values before and after the control of the amplitude outside the relative motion plane are respectively; psi phi type 0 Sum phi f Theoretical values before and after the initial phase control of the relative dip angle vector are respectively; psi' 0 And psi' f The actual values before and after the initial phase control of the relative inclination angle vector are respectively.
The thruster calibration method provided by the invention has the beneficial effects that the thruster calibration method is used for providing accurate calibration coefficients for formation control, providing references for subsequent formation control and further realizing high-precision formation control.
Drawings
FIG. 1 is a schematic representation of the variation of in-plane control versus semi-major axis control front to back in the method of the present invention;
FIG. 2 is a schematic diagram of the theoretical and actual changes in relative eccentricity vectors during in-plane control in the method of the present invention;
fig. 3 is a schematic representation of the theoretical and actual changes in out-of-plane control relative to the tilt angle vector in the method of the present invention.
Detailed Description
The present invention will be described in detail with reference to the following detailed description and the accompanying drawings.
The invention discloses a satellite formation control thruster calibration method, which is implemented according to the following steps:
step 1, calculating theoretical configuration parameters before and after control according to the number of the double-star orbit flat roots;
theoretical configuration parameters include 5, the physical meaning of which is as follows:
the shorter half axle of the projection ellipse in the p, x-y plane (orbit plane);
s, amplitude of z-direction (out of orbit plane) motion;
θ, the phase angle of the relative eccentricity vector reflects the initial phase of motion in the orbital plane;
psi, the phase angle of the relative dip angle vector reflects the initial phase of the out-of-plane motion of the orbit;
and l, the track direction distance reflects the distance between the center of the formation configuration and the main star.
The theoretical configuration parameters after front control and back control can be calculated according to six orbit numbers of double stars, wherein the six orbit numbers refer to an orbit semi-long axis a, an eccentricity e, an inclination i, an ascending intersection point right through omega, a near-place amplitude angle omega and a flat-near point angle M; the 5 configuration parameters can be calculated by the following formula:
Δu＝ω 2 +M 2 -(ω 1 +M 1 )；
Δe x and Δe y Δi, two components of the relative eccentricity vector x And Δi y Two components that are relative tilt vectors;
e 1 is the eccentricity of the main star e 2 Is the eccentricity of the satellite; omega 1 Is the amplitude angle, omega of the near-site of the main star 2 Is the near-place amplitude angle of the auxiliary star; omega shape 1 Is the right ascent point of the principal star, the right ascent point is the right ascent point, and the right ascent point is the right ascent point 2 Is the right ascent point of the auxiliary star; i.e 1 Is the inclination angle of the main star, i 2 Is the inclination angle of the auxiliary star, M 1 Is the normal point angle of the main star, M 2 Is the normal point angle of the auxiliary star; the subscript 1 indicates the orbit count of the main star, the subscript 2 indicates the orbit count of the auxiliary star, and the orbit count without the subscript indicates the orbit count of the main star, wherein the orbit count is used for calculating the configuration parameters.
Step 2, selecting a calibration method according to the variable quantity of the formation configuration parameters before and after numerical control and a control strategy;
(1) Considering that specific configuration parameters are often selected and controlled according to the needs during formation control, if the configuration parameters l need to be adjusted, the control is mainly realized by changing a semi-long axis; as shown in fig. 1, considering that tangential control generally changes the eccentricity and the semi-long axis, when the amount of change in the semi-long axis and the eccentricity satisfies:
(Δa/a 2 ) 2 >(Δe) 2
wherein deltaa is the control quantity of the semi-long axis of the auxiliary star, deltae is the modulus value of the change quantity of the eccentricity vector of the auxiliary star, namely the main control quantity is the semi-long axis in the case, and a relative semi-long axis calibration method is adopted;
ideally, the semi-major axes of the two stars are required to be equal when forming the formation, but before the formation is formed, there is a semi-major axis difference between the two stars, which can cause the phase difference of the two stars over time, thereby causing drift in the track direction distance. Taking into account the error of instantaneous level conversion of the number of tracks, the level half long axis difference of the double stars before control is obtained by extrapolating the track for a period of time delta t 0 According to the track direction distance drift delta l 0 Inversion is carried out, namely the theoretical value of the difference of the horizontal half long axes of the two stars before control is calculated by using the following formula;
wherein Deltal 0 For controlling front delta t of track 0 The track direction distance drift amount caused by the double-star semi-long axis difference in time can be obtained through track extrapolation, n is the average angular speed of the track of the formation main star, and can be obtained through the track data of the main star. The theoretical value of the double star flat semi-major axis control is also obtained by the method.
The actual value of the controlled double-star semi-long axis difference is obtained by inversion according to the change quantity of the remote-measured track distance l, namely
Wherein Deltal' f Is the delta t after rail control f And the distance drift amount of the track direction caused by the difference of the semi-long axes of the double satellites in time. Further calculating the calibration coefficient eta relative to the semi-major axis control f ；
Wherein eta 0 The calibration coefficient after the last control is used; Δa 0 And Deltaa f And theoretical values before and after the difference control of the two-star semi-long axis respectively; Δa' 0 And Δa' f The actual values of the two stars and the half long axis are respectively the actual values of the front control and the rear control. In fact, the actual value before control and the theoretical value before control in the engineering application are equal, i.e. Δa 0 ＝Δa′ 0 。
(2) If the configuration parameters p and θ need to be adjusted, this is mainly achieved by changing the eccentricity, as shown in fig. 2, where the amount of change in the semi-major axis and the eccentricity satisfies:
(Δa/a 2 ) 2 <(Δe) 2
i.e. the main control quantity is the eccentricity vector, in which case a relative eccentricity vector calibration method is used.
The pre-control theoretical value and the post-control theoretical value of the relative eccentricity vector mode delta e can be calculated by the orbit root number of double stars, and the post-control actual value can be calculated by the following formula
Wherein a is the major axis of the principal star, p' f The shorter half axle of the ellipse projected in the plane for the formation configuration after control can be obtained by telemetry.
Calibration coefficient kappa for relative eccentricity vector control f ；
Wherein, kappa 0 The calibration coefficient after the last control is used; delta e 0 And delta e f Theoretical values before and after the control of the relative eccentricity vector module value are respectively; delta e' 0 And δe' f The actual values before and after the control of the relative eccentricity vector module value are respectively; θ 0 And theta f Theoretical values before and after the initial phase control of the relative eccentricity vector are respectively; θ'. 0 And θ' f The actual values before and after the initial phase control of the relative eccentricity vector are respectively.
The theoretical value before and after the central control of the parameters is obtained by a resolving method in the step (1), the actual value after the central control is obtained by telemetry and data downloading resolving, and the actual value before the central control is equal to the theoretical value before the central control in engineering. The physical meaning of the calibration method is clear, namely the ratio of the actual control quantity to the theoretical control quantity of the relative eccentricity vector. For double pulse control, especially for the case that the two control pulses are opposite in direction and equivalent in magnitude, the advantage of the combined calibration method is obvious when the time interval is short, such as half a track period and no track data exists in the period.
(3) If the formation control is out-of-plane control, the control quantity only changes the inclination angle and the right ascent and descent point, and only the amplitude s of the out-of-plane motion of the track and the phase angle psi of the relative inclination angle vector in 5 configuration parameters are changed, and in this case, a relative inclination angle vector calibration method is adopted, as shown in fig. 3;
calibration coefficient k of out-of-plane control f ；
Wherein k is 0 The calibration coefficient after the last control is used; s is(s) 0 Sum s f Theoretical values before and after the control of the out-of-plane amplitude of the relative motion are respectively; s' 0 And s' f The actual values before and after the control of the amplitude outside the relative motion plane are respectively; psi phi type 0 Sum phi f Theoretical values before and after the initial phase control of the relative dip angle vector are respectively; psi' 0 And psi' f The actual values before and after the initial phase control of the relative inclination angle vector are respectively.
Similarly, the theoretical values before and after control are obtained by the calculation in the step (1), the actual value after control is obtained by telemetry and downloaded, and the actual value before control and the theoretical value before control in engineering application are equal, namely psi 0 ＝ψ′ 0 ，s 0 ＝s′ 0 . The physical meaning of the calibration method is clear, namely the ratio of the actual control quantity to the theoretical control quantity of the relative inclination angle vector. For the condition of smaller control quantity outside the track surface, the inclination angle, the ascent and intersection point, or the angle controlled by the combination of the inclination angle and the ascent and descent angle is very small, and the accuracy of single-star orbit determination is limited.
The thruster calibration method aims at providing accurate calibration coefficients for formation control and providing references for subsequent formation control, thereby realizing high-precision formation control, and has the following advantages:
(1) Aiming at the situation that the control quantity of the semi-major axis is smaller, such as a control quantity of a few meters, the orbit determination error can influence the calibration precision, the variation quantity of the formation configuration parameter l obtained based on high-precision inter-satellite measurement is the quantity which is increased or decreased linearly along with the accumulation of time, and the inter-satellite semi-major axis difference can be inverted more accurately by data within 0.5 day, so that the calibration of the semi-major axis small control quantity is realized;
(2) For the double pulse control, especially for the situation that the directions of two control pulses are opposite and the magnitudes are equivalent, and meanwhile, when the time interval is shorter, such as half track period, and no orbit data exists in the period, the traditional method adopting speed increment change or half long axis difference cannot be calibrated, for example, the first control speed increment is-0.092 m/s, the second control speed increment is 0.097 m/s, the synthesized speed increment is 0.005 m/s, the control quantity of the half long axis realized by synthesis is m-level, the control errors of the two control errors possibly offset each other and also can be overlapped with each other, so that the control effect cannot be evaluated, and the calibration method adopting the relative eccentricity vector based on the inter-satellite configuration parameter can reflect the control effect through the change of the configuration parameters p and theta, and although the two control quantities are equivalent in size, the parameters p and theta have obvious change, such as the change of p is 335 m, and the change of theta is 32 degrees, so that the control effect can be evaluated more accurately;
(3) For the situation that the out-of-plane control quantity is smaller, for example, the inclination angle of an auxiliary star is unchanged, the change quantity of the right ascent and intersection point is 0.003 degrees, the orbit determination precision of a single star is limited, the traditional thruster calibration method cannot accurately evaluate the control effect, the control effect can be reflected through the change of configuration parameters s and psi by adopting the relative inclination angle vector calibration method based on the inter-star configuration parameters, and the change of the inclination angle and the right ascent and intersection point is smaller, but the change of the parameters s and psi is obvious, for example, the change quantity of s is 125 meters, and the change quantity of psi is 4.5 degrees, so that the control effect can be evaluated accurately.
Claims (1)
1. The satellite formation control thruster calibration method is characterized by comprising the following steps:
step 1, calculating theoretical configuration parameters before and after control according to the number of the double-star orbit flat roots; theoretical configuration parameters comprise a short half axis p of a projected ellipse in an x-y plane; amplitude s of the z-direction motion; a phase angle θ relative to the eccentricity vector; the phase angle ψ of the relative tilt vector; track direction distance l;
the theoretical configuration parameters after front control and back control can be calculated according to six orbit numbers of double stars, wherein the six orbit numbers refer to an orbit semi-long axis a, an eccentricity e, an inclination i, an ascending intersection point right through omega, a near-place amplitude angle omega and a flat-near point angle M; the configuration parameters were calculated by the following formula:
Δu＝ω 2 +M 2 -(ω 1 +M 1 )；
Δe x and Δe y Δi, two components of the relative eccentricity vector x And Δi y Two components that are relative tilt vectors; e, e 1 Is the eccentricity of the main star e 2 Is the eccentricity of the satellite; omega 1 Is the amplitude angle, omega of the near-site of the main star 2 Is the near-place amplitude angle of the auxiliary star; omega shape 1 Is the right ascent point of the principal star, the right ascent point is the right ascent point, and the right ascent point is the right ascent point 2 Is the right ascent point of the auxiliary star; i.e 1 Is the inclination angle of the main star, i 2 Is the inclination angle of the auxiliary star, M 1 Is the normal point angle of the main star, M 2 Is the straight-up point angle of the main star;
step 2, selecting a corresponding calibration method according to the variation of the formation configuration parameters after numerical control front control and a control strategy, and calculating the calibration coefficient of the thruster according to the calibration method of the thruster;
if the configuration parameter I needs to be adjusted, the configuration parameter I is mainly realized by changing a semi-long axis; considering that tangential control generally changes the eccentricity and semi-long axis, when the semi-long axis and the eccentricity change amounts satisfy:
(Δa/a 2 ) 2 >(Δe) 2
wherein deltaa is the control quantity of the semi-long axis of the auxiliary star, deltae is the modulus value of the change quantity of the eccentricity vector of the auxiliary star, namely the main control quantity is the semi-long axis in the case, and a relative semi-long axis calibration method is adopted;
taking into account the error of instantaneous level conversion of the number of tracks, the level half long axis difference of the double stars before control is obtained by extrapolating the track for a period of time delta t 0 According to the track direction distance drift delta l 0 Inversion is carried out, namely the theoretical value of the difference of the horizontal half long axes of the two stars before control is calculated by using the following formula;
wherein Deltal 0 For controlling front delta t of track 0 The track direction distance drift amount caused by the double-star semi-major axis difference in time can be obtained through track extrapolation, n is the average angular velocity of the track of the formation main star, and can be obtained through the orbit determination data of the main star, and the theoretical value of the double-star flat semi-major axis after control is also obtained through the method;
the actual value of the controlled double-star semi-long axis difference is obtained by inversion according to the change quantity of the remote-measured track distance l, namely
Wherein Deltal' f Is the delta t after rail control f The distance drift quantity of the track direction caused by the difference of the two stars and the semi-long axis in time is further calculated to obtain the calibration coefficient eta controlled by the relative semi-long axis f ；
Wherein eta 0 The calibration coefficient after the last control is used; Δa 0 And Deltaa f And theoretical values before and after the difference control of the two-star semi-long axis respectively; Δa' 0 And Δa' f The actual values of the two stars and the half long axis are respectively the actual values of the front control and the rear control;
if the configuration parameters p and theta need to be adjusted, the eccentricity is mainly changed, and the change of the semi-long axis and the eccentricity meets the following conditions:
(Δa/a 2 ) 2 <(Δe) 2
the main control quantity is an eccentricity vector, and a relative eccentricity vector calibration method is adopted in the situation;
the pre-control theoretical value and the post-control theoretical value of the relative eccentricity vector mode delta e can be calculated by the orbit root number of double stars, and the post-control actual value can be calculated by the following formula
Wherein p' f Projection of elliptical short half-axis in plane for post-control formation configuration, relative eccentricity vector controlled calibration coefficient κ f ；
Wherein, kappa 0 The calibration coefficient after the last control is used; delta e 0 And delta e f Theoretical values before and after the control of the relative eccentricity vector module value are respectively; delta e' 0 And δe' f The actual values before and after the control of the relative eccentricity vector module value are respectively; θ 0 And theta f Theoretical values before and after the initial phase control of the relative eccentricity vector are respectively; θ'. 0 And θ' f The actual values before and after the initial phase control of the relative eccentricity vector are respectively;
if the formation control is out-of-plane control, the control quantity only changes the inclination angle and the right ascent and descent point, and only the amplitude s of the out-of-plane motion of the track and the phase angle psi of the relative inclination angle vector in 5 configuration parameters are changed, and a relative inclination angle vector calibration method is adopted under the condition;
calibration coefficient k of out-of-plane control f ；
Wherein k is 0 The calibration coefficient after the last control is used; s is(s) 0 Sum s f Theoretical values before and after the control of the out-of-plane amplitude of the relative motion are respectively; s' 0 And s' f The actual values before and after the control of the amplitude outside the relative motion plane are respectively; psi phi type 0 Sum phi f Theoretical values before and after the initial phase control of the relative dip angle vector are respectively; psi' 0 And psi' f The actual values before and after the initial phase control of the relative inclination angle vector are respectively.
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