CN107891997A - Taper layout electric propulsion satellite failure mode position keeps optimal thrust distribution method - Google Patents
Taper layout electric propulsion satellite failure mode position keeps optimal thrust distribution method Download PDFInfo
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Abstract
The invention provides taper layout electric propulsion satellite failure mode position to keep optimal thrust distribution method, and this method carries out the electric thruster position under taper layout fault mode using analytic method and keeps control distribution.First, a pair of thrusters not broken down that control is kept for position are chosen according to the thruster to break down；Afterwards, two kinds of different methods of salary distribution of the thruster pair are obtained, and are chosen；Finally, evaded by changing electric thruster start moment progress shadow region.The present invention by the way of parsing completely, solve fault mode electric propulsion position and keep thruster assignment problem, it is optimal fuel consumption, the thruster start number in the orbital period is reduced simultaneously, to realize that the fault mode electric propulsion position of satellite keeps providing a kind of effective thruster distribution method.
Description
Technical Field
The invention relates to a method for distributing electric propulsion position keeping control thrusters, which is mainly used on an earth stationary orbit satellite with an electric thruster in a conical layout, is used for position keeping control thrust distribution under the condition of failure of a certain thruster, and belongs to the technical field of satellite attitude and orbit control.
Background
The electric propulsion satellite is used for maintaining and controlling the position of a geosynchronous orbit, the installation configuration of the electric thruster adopts a conical layout mode, and four thrusters are symmetrically and obliquely arranged on four sides of a back floor in pairs. This thruster configuration is less redundant. When the four thrusters can work normally, the four thrusters jet air successively in one track period to generate control force required by keeping the south, north, east and west positions of the static track. When one electric thruster fails, the electric propulsion satellite enters a failure mode, and the position maintenance and the angular momentum unloading are carried out only by two diagonal electric thrusters which do not fail. The position maintenance fuel consumption and the starting times of a single thruster in the failure mode are obviously more than those in the normal mode. Therefore, the ignition distribution mode of the electric thruster in the failure mode needs to be designed.
The existing fault mode ignition distribution mode realizes position holding control by two times of ignition of two normal diagonal on-line thrusters in each orbit period. When the satellite reaches the vicinity of 90 ° of the right ascension, the north thruster NW or NE ignites; when the satellite reaches the vicinity of 270 degrees of right ascension, the southward thruster SE or SW ignites; in addition, the two thrusters are sequentially ignited at a certain intermediate position in addition to the above. The combination of permutations of four firings is relied upon while maintaining the satellite's sub-satellite geographic longitude and latitude within the "dead space" required by the mission. Although simple and intuitive, the method has the following defects when being applied to the satellite: (1) the optimal problem of fuel consumption is not considered in the formula distribution mode, and redundant fuel consumption exists; (2) the same thruster needs to be opened twice per rail in the distribution mode, which is twice of the normal mode, and the service life of the thruster can be influenced. Therefore, a more optimized method for distributing the electric propulsion fault mode position maintaining thrust considering both fuel consumption and the number of times of starting the thruster is needed to be designed, so that the service life of the stationary orbit electric propulsion satellite in the fault mode is prolonged, and the reliability is increased.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method overcomes the defects of the prior art, provides the optimal thrust distribution method for maintaining the position of the electric propulsion satellite in the failure mode in the conical layout, adopts a complete analysis method to calculate the three-time starting time and the speed increment, enables the fuel consumption to be optimal, and meets the task requirement of maintaining the position of the electric propulsion satellite in the failure mode of the stationary orbit satellite.
The invention comprises the following technical scheme: the method for distributing optimal thrust for maintaining the failure mode position of the cone-shaped layout electric propulsion satellite comprises four electric thrusters which are symmetrically and obliquely arranged in pairs at the four corners of the satellite back floor, namely northwest, northeast, southwest and southeast, which are respectively marked as NW, NE, SW and SE, and comprises the following steps within one orbit period:
(1) According to the thruster that breaks down, choose for use the combination of position holding thruster pair, the position holding thruster has two kinds to the combination: NW and SE combinations, NE and SW combinations;
(2) Obtaining the position holding inclination angle control vector (di) x 、di y ) Calculating a position holding direction angle coefficient kappa;
(3) And according to the unit vectors of the installation directions of the four thrusters, the radial, transverse and normal absolute values e under the satellite body coordinate system r 、e t 、e n And the rotational angular velocity omega of the earth E Nominal speed V of stationary track s Calculating the failure mode position holding control coefficients of the four thrusters;
(4) Respectively calculating three-time starting time satellite horizontal ascension and speed increment thereof when the selected thruster combines two thrust distribution modes of twice northbound, once southward starting and twice southward and once northbound starting according to the position keeping direction angle coefficient kappa and the failure mode position keeping control coefficient of the thruster;
(5) Selecting a distribution mode with positive speed increment of three startup and less fuel consumption as an optimal distribution mode;
(6) And judging whether the satellite at the third boot time is in a shadow region or not according to the satellite level right ascension at the third boot time, if the satellite at any one boot time is in the shadow region, adjusting the position and keeping the direction angle coefficient kappa, and re-executing the steps (3) to (6) to calculate the optimal distribution mode until the three boot time satellites are in the illumination region.
The calculation formula of the failure mode position holding control coefficients of the four thrusters is as follows:
A NW ＝3·e t ·ω E /V s ，B1 NW ＝2·e t /Vs，B2 NW ＝e r /Vs，E NW ＝e n /Vs；
A NE ＝-3·e t ·ω E /V S ，B1 NE ＝-2·e t /Vs，B2 NE ＝e r /Vs，E NE ＝e n /Vs；
A SW ＝3·e t ·ω E /V s ，B1 SW ＝2·e t /Vs，B2 SW ＝e r /Vs，E SW ＝-e n /Vs；
A SE ＝-3·e t ·ω E /V s ，B1 SE ＝-2·e t /Vs，B2 SE ＝e r /Vs，E SE ＝-e n /Vs；
in the formula, A NW 、B1 NW 、B2 NW 、E NW Maintaining a control coefficient for a failure mode position of the NW thruster; a. The NE 、B1 NE 、B2 NE 、E NE Of NE thrustersA failure mode position maintenance control coefficient; a. The SW 、B1 SW 、B2 SW 、E SW Maintaining a control coefficient for a failure mode position of the SW thruster; a. The SE 、B1 SE 、B2 SE 、E SE The control coefficient is maintained for the fault mode position of the SE thruster.
The unit vectors of the installation directions of the four thrusters have the same absolute values in the radial direction, the transverse direction and the normal direction under the satellite body coordinate system, and all the absolute values are e r 、e t 、e n And (4) calculating the three-time starting time and the speed increment thereof by adopting any one distribution mode of the thruster to the combination in the following method:
(4.1) calculating the satellite horizontal ascension alpha of the thruster at the starting time of one of the thrusters which are started twice in the combination according to the position keeping direction angle coefficient kappa and the distribution mode:
when the distribution mode is as follows: when the computer is started twice in the north direction and once in the south direction, the alpha = kappa + pi/2;
when the distribution mode is as follows: when the computer is started twice in the south direction and once in the north direction,
(4.2) adopting the selected thruster to keep and control the fault mode position of the thruster which is started twice in the combination as the coefficients A, B1, B2 and E of the fault mode position keeping control, and keeping and controlling the coefficients A, B1, B2 and E and the preset position keeping inclination angle control vector (di) according to the fault mode position x 、di y ) Position preserving eccentricity vector (de) x 、de y ) Position keeping longitude drift rate dD, calculating speed increment [ delta V ] of three times of starting in failure mode 1 ΔV 2 ΔV 3 ]And the satellite horizontal right ascension beta and gamma at the other two times of starting, so that after three times of starting, the position keeps the inclination angle control vector, the position keeps the eccentricity vector, and the position keeps the horizontal longitude drift rate equal to a preset value.
The step (4.2) is specifically as follows:
(4.2.1) calculating the speed of the thruster at the starting time corresponding to the thruster at the starting timeIncrement of Δ V 3 The method specifically comprises the following steps:
(a) Obtaining delta V by solving the following equation set 3 ：
ΔV 3 ＝XX/(2·B2·E)；
(b) When Δ V 3 For Δ V < 0 3 The following modifications were made:
XX＝-XX；
ΔV 3 ＝-ΔV 3 ；
(4.2.2) and defining the speed increment delta V corresponding to the satellite horizontal right ascension alpha at one time of starting up the thrusters in the combinations of the thrusters for two times 1 The speed increment delta V of the starting time corresponding to the thruster started once 3 Substituting the satellite horizontal ascension alpha at one time of starting the thruster twice into the following equation set, and resolving the equation set to obtain the speed increment delta V corresponding to the two times of starting the thruster twice 1 、ΔV 2 ：
X1＝(di y ·B1-B2·di x +de y ·E)；
X2＝(di x ·B1+B2·di y +de x ·E)；
X3＝(di y ·de x -di x ·de y )·A 2 ；
X4＝E·dD 2 ·B2；
X6＝A 2 ·(B2·di x -B1·di y ) 2 ；
X8＝(di y ·de y +di x ·de x )·A 2 ；
X10＝A 2 ·(B1·di x +B2·di y ) 2 ；
X11＝(-X1·A 2 ·cosα+X2·A 2 ·sinα-2·E·dD·B2·A)·XX+2·A·B2·E·cosα·dD·X1-2·A·B2·E·dD·sinα·X2+X7·A 2 +2·B1·E·X8+2·E 2 ·dD 2 ·B2 2 ；
ΔV 1 ＝(X3-X4+XX·A·dD)/(-A 2 ·XX+X1·cosα·A 2 -X2·sinα·A 2 +2·E·dD·B2·A)；
(4.2.3) calculating the satellite horizontal right ascension beta of the thruster at the starting time of the thruster for two times of starting and the satellite horizontal right ascension gamma of the thruster at the starting time of the thruster for one time of starting:
cosβ＝-((-X1·A 2 -2·cosα·E·dD·B2·A)·XX+(X5+X6)·cosα-A 2 ·sinα·X1·X2+2·A·B2·E·dD·X1)/X11；
sinβ＝((-X2·A 2 +2·sinα·E·dD·B2·A)·XX+A 2 ·cosα·X1·X2+(X9-X10)·sinα+2·A·B2·E·dD·X2)/X11；
cosγ＝(di y ·B1+di x ·B2+de y ·E)/XX；
sinγ＝(-di x ·B1+di y ·B2-de x ·E)/XX；
β＝arctan(sinβ,cosβ)；
γ＝arctan(sinγ,cosγ)。
a shadow region avoiding method is carried out by adjusting the position keeping direction angle coefficient kappa: k = k + (-1) n Δ κ, where Δ κ is the adjustment step size, n is alternately set to 0 or 1 until the three satellites are in the illumination area at the boot time.
The principle of selecting the combination of the position keeping thrusters is as follows: when the thruster with the fault is NE and/or SW, the combination of NW and SE is selected; when the thrust device with the fault is NW and/or SE, the NE and SW combination is selected.
The fuel consumption minimum is determined by the sum of the speed increments of three starts. Compared with the prior art, the invention has the beneficial effects that:
(1) The method firstly adopts an analytic method to obtain an optimization result that the total starting time of each orbit period thruster is shortest and the satellite speed increment generated by four thrusters is minimum, so that the position maintenance fuel consumption is saved, and the service life of the electric propulsion satellite in a failure mode is prolonged;
(2) The method firstly reduces the starting-up of the thruster per track in the original failure mode under the electric propulsion protection to three times, reduces the starting-up times of a single thruster, and prolongs the service life of the thruster;
(3) Compared with the traditional iterative processing method, the analytic method has the advantages that the calculated amount is small, and the on-satellite calculation resource requirement is reduced;
(4) The invention further provides a shadow region evasion strategy, and the phenomenon that the electric thruster is started and the shadow region conflicts can be effectively prevented.
Drawings
FIG. 1 is a flow chart of a method for distributing position holding thrust in an electric propulsion fault mode according to the present invention;
FIG. 2 is a schematic view of a conical electric thruster layout;
FIG. 3 is a schematic view of a failure mode thrust distribution;
FIG. 4 simulation example-geographical latitude and longitude graph;
FIG. 5 simulation example-fuel consumption versus map (versus conventional distribution);
fig. 6 simulates an example-fuel consumption map (versus a numerical optimization allocation).
Detailed Description
The following describes embodiments of the present invention in further detail with reference to the accompanying drawings.
The static orbit satellite which uses the electric thruster to maintain the position usually adopts the cone thruster layout mode, the cone layout electric propulsion satellite comprises four electric thrusters, and the four electric thrusters are symmetrically and obliquely arranged in pairs at four corners of the northwest, the northeast, the southwest and the southeast of the back floor of the satellite, and are respectively marked as NW, NE, SW and SE. Fig. 2 is a schematic view of the mounting direction of the thruster under the satellite system. When any one of the four electric thrusters fails, the satellite enters a position holding failure mode, and position holding control and angular momentum unloading are completed by using a pair of thrusters on diagonal lines without failure. If NE or SW break down, utilize NW and SE to carry on the position holding control; when the NW or SE fails, the position holding control is performed by the NE and the SW.
The invention provides a method for distributing optimal thrust for maintaining the position of a conical-layout electric propulsion satellite in a fault mode. In the failure mode, two thrusters on each rail are started up three times, and the inclination angle, the eccentricity ratio and the longitude are controlled by the combination of the three-time starting-up position holding control quantity. Fig. 3 is a schematic diagram of failure mode thrust distribution, with two potential combinations when using NW and SE for control: in one track period, the NW is started for 2 times, and the SE is started for 1 time; SE is turned on 2 times and NW is turned on 1 time in one track period, and when controlling with NE and SW there are two potential combinations: in a track cycle, NE is started for 2 times, and SW is started for 1 time; within one orbital period SW is turned on 2 times and NE is turned on 1 time.
Fig. 2 is a block flow diagram of the electric propulsion position maintaining control method during a control cycle. As shown in fig. 2, the method for distributing optimal thrust for maintaining a fault mode position, which is adopted by the present invention, includes selecting a pair of normal thrusters for maintaining a position, acquiring two different distribution modes of the pair of normal thrusters, selecting the pair of normal thrusters, and finally avoiding a shadow area. Specifically, the following steps are executed in one track cycle:
(1) According to the thruster with the fault, the combination of the position keeping thruster pairs is selected, and the combination of the position keeping thruster pairs has two types: NW and SE combinations, NE and SW combinations;
under the two diagonal combinations, the satellite can simultaneously have the capability of performing track control to east, west, south and north. The principle of selecting the combination of the position keeping thrusters is as follows: when the thruster with the fault is NE and/or SW, the combination of NW and SE is selected; when the thrust device with the fault is NW and/or SE, the NE and SW combination is selected.
(2) Respectively calculating three-time starting time and speed increment of the selected thruster pair combination in two thrust distribution modes of twice-north starting, once-south starting and twice-south starting and once-north starting;
for NW and SE combinations, there are two possible ways of thruster allocation:
the first method comprises the following steps: the north thruster NW ignites the south thruster SE once every rail twice;
and the second method comprises the following steps: the distribution mode is as follows: the south thruster SE fires twice the north thruster NW.
For NE and SW combinations, there are two possible thruster assignments:
the first method comprises the following steps: the north thruster NE ignites the south thruster SW once per rail twice;
and the second method comprises the following steps: the south thruster SW fires twice the north thruster NE fires once.
The method for calculating the three-time starting time and the speed increment thereof by adopting any distribution mode of the thruster pair combination comprises the following steps:
(2.1) calculating failure mode position holding control coefficients of the four thrusters according to radial, transverse and normal absolute values of unit vectors of the installation directions of the four thrusters in a satellite body coordinate system:
because the absolute values of the field angles of the four thrusters from the XOZ surface and the YOZ surface of the satellite body coordinate system are consistent, the radial, transverse and normal absolute values of unit vectors of the installation directions of the four thrusters in the satellite body coordinate system are the same and are all e r 、e t 、e n The calculation formula of the failure mode position holding control coefficients of the four thrusters is as follows:
A NW ＝3·e t ·ω E /V s ，B1 NW ＝2·e t /Vs，B2 NW ＝e r /Vs，E NW ＝e n /Vs；
A NE ＝-3·e t ·ω E /V s ，B1 NE ＝-2·e t /Vs，B2 NE ＝e r /Vs，E NE ＝e n /Vs；
A SW ＝3·e t ·ω E /V S ，B1 SW ＝2·e t /Vs，B2 SW ＝e r /Vs，E SW ＝-e n /Vs；
A SE ＝-3·e t ·ω E /V s ，B1 SE ＝-2·e t /Vs，B2 SE ＝e r /Vs，E SE ＝-e n /Vs；
in the formula, A NW 、B1 NW 、B2 NW 、E NW Maintaining a control coefficient for a failure mode position of the NW thruster; a. The NE 、B1 NE 、B2 NE 、E NE Maintaining a control coefficient for a failure mode position of the NE thruster; a. The SW 、B1 SW 、B2 SW 、E SW Maintaining a control coefficient for a failure mode position of the SW thruster; a. The SE 、B1 SE 、B2 SE 、E SE The control coefficient is maintained for the fault mode position of the SE thruster.
(2.2) obtaining the position holding inclination control vector (di) x 、di y ) The position-holding-direction angle coefficient κ is calculated as:
κ＝arctan(-di y ,-di x )-π/2；
(2.3) calculating the satellite horizontal ascension alpha of the thruster at the starting time of one of the thrusters which are started twice in the combination according to the position keeping direction angle coefficient kappa and the distribution mode:
when the distribution mode is as follows: when the computer is started twice in the north direction and once in the south direction, the alpha = kappa + pi/2;
when the distribution mode is as follows: when the computer is started twice in the south direction and once in the north direction,
(2.4) adopting the selected coefficients of the failure mode position holding control of the thruster started twice in the thruster pair combination as the coefficients A, B1, B2 and E of the failure mode position holding control, and controlling the coefficients A, B1, B2 and E and the position holding inclination angle control vector (di) according to the failure mode position holding control x 、di y ) Position-preserving eccentricity vector (de) x 、de y ) Position keeping longitude drift rate dD, calculating speed increment [ delta V ] of three times of starting in failure mode 1 ΔV 2 ΔV 3 ]And satellite Pingtianchi [ alpha beta gamma ] at the time of three times of starting]So that the position after three times of power-on maintains the tilt control vector (di) x 、di y ) Position preserving eccentricity vector (de) x 、de y ) The position hold mean longitude drift rate dD is equal to a preset value.
Taking the combination of the NW and the SE thrusters as an example, the NW is started for 2 times, the SE is started for 1 time, and the satellite Pingthong meridian alpha of the thrusters which are started twice in the combination at one starting time is solved in the step (2) SW1 Then there are also five unknown variables to solve for: speed increment of three boot-ups [ Delta V ] 1 ΔV 2 ΔV 3 ]And the other two times of starting, the satellite's right ascension beta and gamma, the purpose of position holding control is to hold the inclination angle control vector (di) after starting up for three times per orbit x 、di y ) Position preserving eccentricity vector (de) x 、de y ) The position keeping mean longitude drift rate dD is equal to a preset value, and therefore, an equation can be establishedThe groups were as follows:
dD NW1 +dD NW2 +dD SE3 ＝dD
wherein dD NW1 、dD NW2 、dD SE3 The flatness drift rate increment generated by the first startup of NW, the second startup of NW and the first startup of SE is respectively,the tilt angles di generated by the first startup of NW, the second startup of NW and the first startup of SE x The number of increments,the tilt angles di generated by the first power-on of NW, the second power-on of NW and the first power-on of SE y The number of increments,eccentricity de generated by first starting of NW, second starting of NW and first starting of SE x The number of increments, eccentricity de generated by first starting of NW, second starting of NW and first starting of SE y And (4) increasing. The speed increment [ delta V ] of three times of starting can be obtained by solving the equation set NW1 ΔV NW2 ΔV SE3 ]And another two times of start-up time satellite's Pingthongjing beta NW2 、γ SE3 。
According to the above thought, the distribution mode of the position maintaining thrusters when any one or a pair of diagonals of the thrusters fails under the arrangement of the tapered thrusters can be obtained, and the specific analysis result can be obtained through the following steps:
(2.4.1) calculating the speed increment delta V of the thruster at the starting time corresponding to the starting time once 3 The method specifically comprises the following steps:
(a) Obtaining delta V by solving the following equation set 3 ：
ΔV 3 ＝XX/(2·B2·E)；
(b) When is Δ V 3 For Δ V < 0 3 The following modifications were made:
XX＝-XX；
ΔV 3 ＝-ΔV 3 ；
(2.4.2) defining the speed increment delta V corresponding to the satellite horizontal right ascension alpha at one time of starting up the thrusters in the combinations of the thrusters and starting up the thrusters twice 1 The speed increment delta V of the starting time corresponding to the thruster started once 3 Substituting the satellite horizontal ascension alpha at one time of starting the thruster twice into the following equation set, and resolving the equation set to obtain the speed increment delta V corresponding to the two times of starting the thruster twice 1 、ΔV 2 ：
X1＝(di y ·B1-B2·di x +de y ·E)；
X2＝(di x ·B1+B2·di y +de x ·E)；
X3＝(di y ·de x -di x ·de y )·A 2 ；
X4＝E·dD 2 ·B2；
X6＝A 2 ·(B2·di x -B1·di y ) 2 ；
X8＝(di y ·de y +di x ·de x )·A 2 ；
X10＝A 2 ·(B1·di x +B2·di y ) 2 ；
X11＝(-X1·A 2 ·cosα+X2·A 2 ·sinα-2·E·dD·B2·A)·XX+2·A·B2·E·cosα·dD·X1-2·A·B2·E·dD·sinα·X2+X7·A 2 +2·B1·E·X8+2·E 2 ·dD 2 ·B2 2 ；
ΔV 1 ＝(X3-X4+XX·A·dD)/(-A 2 ·XX+X1·cosα·A 2 -X2·sinα·A 2 +2·E·dD·B2·A)；
(2.4.3), calculating the satellite horizontal right ascension beta of the thruster at the starting time of the thruster for two times of starting and the satellite horizontal right ascension gamma of the thruster at the starting time of the thruster for one time of starting:
cosβ＝-((-X1·A 2 -2·cosα·E·dD·B2·A)·XX+(X5+X6)·cosα-A 2 ·sinα·X1·X2+2·A·B2·E·dD·X1)/X11；
sinβ＝((-X2·A 2 +2·sinα·E·dD·B2·A)·XX+A 2 ·cosα·X1·X2+(X9-X10)·sinα+2·A·B2·E·dD·X2)/X11；
cosγ＝(di y ·B1+di x ·B2+de y ·E)/XX；
sinγ＝(-di x ·B1+di y ·B2-de x ·E)/XX；
β＝arctan(sinβ,cosβ)；
γ＝arctan(sinγ,cosγ)。
for the first allocation of NW and SE combinations (see fig. 3 (a)): a = A NW ，B1＝B1 NW ，B2＝B2 NW ，E＝E NW Substituting alpha = kappa + pi/2 into the above steps to obtain [ delta V [ ] NW1 ΔV NW2 ΔV SE3 ]And corresponding [ alpha ] NW1 β NW2 γ SE3 ]。
For a second allocation of NW and SE combinations (see fig. 3 (b)): a = A SE ，B1＝B1 SE ，B2＝B2 SE ，E＝E SE By substituting α = κ +3 · π/2 into the above steps, [ Δ V ] can be obtained SE1 ΔV SE2 ΔV NW3 ]And corresponding [ alpha ] SE1 β SE2 γ NW3 ]。
For the first allocation of NE and SW combinations (see fig. 3 (c)): a = A NE ，B1＝B1 NE ，B2＝B2 NE ，E＝E NE Substituting alpha = kappa + pi/2 into the above steps to obtain [ delta V [ ] NE1 ΔV NE2 ΔV SW3 ]And corresponding [ alpha ] NE1 β NE2 γ SW3 ]。
For a second allocation of NE and SW combinations (see fig. 3 (d)): a = A SW ，B1＝B1 SW ，B2＝B2 SW ，E＝E SW α = κ +3 · π/2 into the above step,then [ Delta V ] can be obtained SW1 ΔV SW2 ΔV NE3 ]And corresponding alpha SW1 β SW2 γ NE3 。
(3) And selecting a distribution mode with positive speed increment of three startup and less fuel consumption as an optimal distribution mode.
The three-start speed increments characterize fuel consumption, and therefore the fuel consumption minimum is determined by the sum of the three-start speed increments.
Taking the combination of NW and SE as an example, if the speed increment of the first allocation is: [ Delta V ] NW1 ΔV NW2 ΔV SE3 ]The speed increment of the second distribution mode is: [ Delta V SE1 ΔV SE2 ΔV NW3 ]，ΔV NW1 、ΔV NW2 、ΔV SE3 、ΔV SE1 、ΔV SE2 And Δ V NW3 Are all integers, then if Δ V NW1 +ΔV NW2 +ΔV NW3 <ΔV SE1 +ΔV SE2 +ΔV NW3 Then, the first allocation is selected.
(4) And judging whether the satellite at the third starting time is in a shadow area or not according to the satellite level red channel [ alpha beta gamma ] at the third starting time, if the satellite at any one starting time is in the shadow area, adjusting the position and keeping the direction angle coefficient, and recalculating the third starting time and the speed increment of the selected thruster for combining the two distribution modes until the satellite at the three starting times is in the illumination area.
The method for adjusting the position holding direction angle coefficient kappa comprises the following steps: k = k + (-1) n Δ κ, where Δ κ is the adjustment step size and n alternatively takes the value 0 or 1.
Considering the maximum range of the shadow region which can be met by the geostationary orbit satellite, the adjustment step size delta kappa ranges from 0 to 17.4 degrees, and the delta kappa sequentially increases in the range.
For example, for a certain distribution of a certain thruster pair combination:
the first calculation results in the satellite being in the shadow region at a certain turn-on time, let Δ κ =0.1 °: adjustment position holding direction angle coefficient κ:
κ＝κ-Δκ；
then according to the adjusted position keeping direction angle coefficient kappa, recalculating the third starting time of the thruster to the combined distribution mode and the speed increment thereof; if there is still a shadow area of the satellite at a certain boot time in the calculated three boot times, let Δ κ =0.3 ° adjust the position holding direction angle coefficient κ:
κ＝κ+Δκ；
and recalculating the three-time starting time and the speed increment thereof of the thruster in the combined distribution mode, and if a satellite is in a shadow region at a certain starting time in the calculated three-time starting time, keeping the adjustment position of delta kappa =0.5 degrees and keeping the direction angle coefficient kappa:
κ＝κ-Δκ；
and recalculating the three startup time and the speed increment of the thruster in the combined distribution mode, and repeating iterative operation in such a way until the satellites are all in the illumination area at the three startup time.
When the electric thruster is ignited, the three thrusters are all in an illumination area. Because the electric thruster relies on the solar sailboard to provide energy, when the satellite encounters a ground shadow, the sailboard cannot provide energy, so that the electric thruster cannot be normally ignited to start up, shadow avoidance is carried out by using the method, the satellite can be effectively prevented from encountering the shadow during propulsion control, and the position maintaining control effect is not influenced.
Example 1
The thrust of a single electric thruster is 100mN, the directions of the three-axis thrusts are 0.19,0.5 and 0.84, and the mass of the satellite is 4458kg. The date is 2017, 1 month and 1 day. The thruster SW fails.
The fault judgment in the step (1) specifically comprises the following steps:
with known thruster SW malfunctioning, a pair of NW and SE thrusters is selected for control.
And (3) calculating two possible allocation modes of the target thruster pair combination in the step (2).
(1) Calculating a position-holding coefficient of
A 0 ＝0.0676
B1 0 ＝1.25e-4
B2 0 ＝2.73e-4
E 0 ＝1.66e-4
The coefficients for the failure mode position holding control of NW and SE are:
A NW ＝A 0 ，B1 NW ＝B1 0 ，B2 NW ＝B2 0 ，E NW ＝E 0 ；
A SE ＝-A 0 ，B1 SE ＝-B1 0 ，B2 SE ＝B2 0 ，E SE ＝-E 0 ；
knowing the Sitting Tilt control amount di x 、di y The orientation angle coefficient of the position protection is as follows:
κ＝0.71°；
(2) and acquiring the speed increment of the three times of starting in the failure mode and the satellite right ascension at the starting time.
(3) The thruster allocation of any pair of thruster pairs can be obtained through the step (2):
for the NW and SE combination, there are two possible ways of thruster allocation: north thruster NW fires once for south thruster SE twice per rail and south thruster SE fires once for north thruster NW twice.
In the first case (fig. 3 (a)), a = a NW ，B1＝B1 NW ，B2＝B2 NW ，E＝E NW Substituting α = κ + π/2 into step (2) to obtain [ Δ V [ + ] NW1 ＝0.18 ΔV NW2 ＝-0.10 ΔV SE3 ＝0.18]And corresponding [ alpha ] NW1 ＝90.71° β NW2 ＝9.54° γ SE3 ＝-121.6°]。
In the second case (fig. 3 (b)), let a = a SE ，B1＝B1 SE ，B2＝B2 SE ，E＝E SE Substituting alpha = kappa + 3. Pi./2 into the step (2), the [ Delta V ] can be obtained SE1 ＝0.19 ΔV SE2 ＝0.1 ΔV NW3 ＝0.19]And corresponding [ alpha ] SE1 ＝270.71° β SE2 ＝161.3° γ NW3 ＝120.5°]。
Selecting a distribution mode which has physical significance and consumes less fuel in the step (3):
north 2 south 1 type combination delta V N1 ＞0，ΔV N2 Less than 0, south 2 north 1 combination delta V S1 > 0 and Δ V S2 Is greater than 0. Therefore, the method of starting the NW once and starting the SE twice is selected.
Avoiding shadow areas in the step (4):
the simulation time was 1 month and 1 day, and the absence of the ground shadow was recognized from the solar altitude at that time. No circumvention is necessary.
Example 2
And setting the longitude of the satellite fixed point to be 80 degrees E, the fault thruster to be SW, and the simulation time length to be 1 year. The simulation result is shown in fig. 4, and the thruster allocation method provided by the invention can keep the satellite within a dead zone range of the fixed point longitude and latitude +/-0.05 degrees.
Example 3
The east-west position and the south-north position of each day are set to keep the control quantity constant, the traditional analysis is used for four times of orbit change, the optimization algorithm is used for carrying out a large amount of iterative calculation on the optimal four times of orbit change of any right ascension and any air injection time length, and the optimal four times of orbit change is compared with the thruster allocation mode generated by the three times of orbit change strategy, and the simulation time length is 2 years. Fig. 5 is a ratio of daily fuel consumption of the conventional 4-time rail transfer allocation method and the 3-time rail transfer method of the present invention, and it can be seen that the 3-time rail transfer method of the present invention is significantly smaller than the four-time rail transfer method. FIG. 6 is a numerically optimized ratio of daily fuel consumption for the four-way distribution, and it can be seen that the wall ratio is close to 1, so the method is an optimal solution.
Through simulation verification, the method can realize the distribution of the position maintaining control electric thruster in a fault mode, meets optimality, and can be used for the position maintaining control of the geosynchronous orbit.
In conclusion, by using the optimal thrust distribution method for maintaining the position of the conical layout electric propulsion fault mode, thrust distribution can be performed on the position maintaining control under the conical layout fault mode, so that the fuel consumption of the thruster is optimal, and the phenomenon of insufficient energy on the satellite caused by starting up of the electric thruster in a shadow area is avoided.
Those skilled in the art will appreciate that the invention may be practiced without these specific details.
Claims (7)
1. The method for distributing optimal thrust for maintaining the failure mode position of the cone-shaped layout electric propulsion satellite comprises four electric thrusters which are symmetrically and obliquely arranged in pairs at four corners of the satellite back floor, namely northwest, northeast, southwest and southeast, which are respectively marked as NW, NE, SW and SE, and is characterized in that the method comprises the following steps within one orbit period:
(1) According to the thruster with the fault, the combination of the position keeping thruster pairs is selected, and the combination of the position keeping thruster pairs has two types: NW and SE combination, NE and SW combination;
(2) Obtaining the position holding inclination angle control vector (di) x 、di y ) Calculating a position holding direction angle coefficient kappa;
(3) And according to the unit vectors of the installation directions of the four thrusters, the absolute values e of the radial direction, the transverse direction and the normal direction under the satellite body coordinate system r 、e t 、e n And the rotational angular velocity omega of the earth E Nominal speed V of stationary track s Calculating the failure mode position holding control coefficients of the four thrusters;
(4) Respectively calculating the satellite horizontal-red longitude and the speed increment of the selected thruster at the three-time starting time by combining two thrust distribution modes of twice north, once south and once north according to the position keeping direction angle coefficient kappa and the failure mode position keeping control coefficient of the thruster;
(5) Selecting a distribution mode with positive speed increment of three startup and less fuel consumption as an optimal distribution mode;
(6) And judging whether the satellite at the third boot time is in a shadow region or not according to the satellite level right ascension at the third boot time, if the satellite at any one boot time is in the shadow region, adjusting the position and keeping the direction angle coefficient kappa, and re-executing the steps (3) to (6) to calculate the optimal distribution mode until the three boot time satellites are in the illumination region.
2. The method for distributing optimal thrust for maintaining the failure mode positions of the electric propulsion satellite in the conical layout according to claim 1, wherein the calculation formula of the failure mode position maintaining control coefficients of the four thrusters is as follows:
A NW ＝3·e t ·ω E /V s ，B1 NW ＝2·e t /Vs，B2 NW ＝e r /Vs，E NW ＝e n /Vs；
A NE ＝-3·e t ·ω E /V s ，B1 NE ＝-2·e t /Vs，B2 NE ＝e r /Vs，E NE ＝e n /Vs；
A SW ＝3·e t ·ω E /V S ，B1 SW ＝2·e t /Vs，B2 SW ＝e r /Vs，E SW ＝-e n /Vs；
A SE ＝-3·e t ·ω E /V s ，B1 SE ＝-2·e t /Vs，B2 SE ＝e r /Vs，E SE ＝-e n /Vs；
in the formula, A NW 、B1 NW 、B2 NW 、E NW Maintaining a control coefficient for a failure mode position of the NW thruster; a. The NE 、B1 NE 、B2 NE 、E NE Maintaining a control coefficient for a failure mode position of the NE thruster; a. The SW 、B1 SW 、B2 SW 、E SW Maintaining a control coefficient for a failure mode position of the SW thruster; a. The SE 、B1 SE 、B2 SE 、E SE Is the reason of SE thrusterThe barrier mode position maintains the control coefficient.
3. The method for distributing optimal thrust for maintaining failure mode positions of electric propulsion satellites in conical layout according to claim 1, wherein unit vectors of installation directions of the four thrusters have the same absolute values of radial direction, transverse direction and normal direction in a satellite body coordinate system, and all the unit vectors are e r 、e t 、e n And (4) calculating the three-time starting time and the speed increment thereof by adopting any one distribution mode of the thruster to the combination in the following method:
(4.1) calculating the satellite horizontal ascension alpha of the thruster at the starting time of one of the thrusters which are started twice in the combination according to the position keeping direction angle coefficient kappa and the distribution mode:
when the distribution mode is as follows: when the machine is started twice in the north direction and once in the south direction, the alpha = kappa + pi/2;
when the distribution mode is as follows: when the computer is started twice in the south direction and once in the north direction,
(4.2) adopting the failure mode position holding control coefficients of the selected thruster to the thruster started twice in the combination as the coefficients A, B1, B2 and E of failure mode position holding control, and keeping the control coefficients A, B1, B2 and E of failure mode position and the preset position holding inclination angle control vector (di) according to the coefficients A, B1, B2 and E of failure mode position holding control x 、di y ) Position preserving eccentricity vector (de) x 、de y ) Position keeping longitude drift rate dD, calculating speed increment [ delta V ] of three times of starting in failure mode 1 ΔV 2 ΔV 3 ]And the satellite horizontal right ascension beta and gamma at the other two times of starting, so that after three times of starting, the position keeps the inclination angle control vector, the position keeps the eccentricity vector, and the position keeps the horizontal longitude drift rate equal to a preset value.
4. The cone-shaped layout electric propulsion satellite fault mode location preserving optimal thrust distribution method according to claim 3, characterized in that the step (4.2) is embodied as:
(4.2.1) calculating the speed increment delta V of the thruster corresponding to the starting time at the starting time 3 The method specifically comprises the following steps:
(a) Obtaining delta V by solving the following equation set 3 ：
ΔV 3 ＝XX/(2·B2·E)；
(b) When is Δ V 3 For Δ V < 0 3 The following modifications were made:
XX＝-XX；
ΔV 3 ＝-ΔV 3 ；
(4.2.2) and defining the speed increment delta V corresponding to the satellite horizontal right ascension alpha at one time of starting up the thrusters in the combinations of the thrusters for two times 1 And increasing the speed delta V of the thruster at the starting time corresponding to the thruster at the starting time once 3 Substituting the satellite horizontal ascension alpha at one time of starting the thruster twice into the following equation set, and resolving the equation set to obtain the speed increment delta V corresponding to the two times of starting the thruster twice 1 、ΔV 2 ：
X1＝(di y ·B1-B2·di x +de y ·E)；
X2＝(di x ·B1+B2·di y +de x ·E)；
X3＝(di y ·de x -di x ·de y )·A 2 ；
X4＝E·dD 2 ·B2；
X6＝A 2 ·(B2·di x -B1·di y ) 2 ；
X8＝(di y ·de y +di x ·de x )·A 2 ；
X10＝A 2 ·(B1·di x +B2·di y ) 2 ；
X11＝(-X1·A 2 ·cosα+X2·A 2 ·sinα-2·E·dD·B2·A)·XX+2·A·B2·E·cosα·dD·X1-2·A·B2·E·dD·sinα·X2+X7·A 2 +2·B1·E·X8+2·E 2 ·dD 2 ·B2 2 ；
ΔV 1 ＝(X3-X4+XX·A·dD)/(-A 2 ·XX+X1·cosα·A 2 -X2·sinα·A 2 +2·E·dD·B2·A)；
(4.2.3) calculating the satellite horizontal right ascension beta of the thruster at the starting time of the thruster for two times of starting and the satellite horizontal right ascension gamma of the thruster at the starting time of the thruster for one time of starting:
cosβ＝-((-X1·A 2 -2·cosα·E·dD·B2·A)·XX+(X5+X6)·cosα-A 2 ·sinα·X1·X2+2·A·B2·E·dD·X1)/X11；
sinβ＝((-X2·A 2 +2·sinα·E·dD·B2·A)·XX+A 2 ·cosα·X1·X2+(X9-X10)·sinα+2·A·B2·E·dD·X2)/X11；
cosγ＝(di y ·B1+di x ·B2+de y ·E)/XX；
sinγ＝(-di x ·B1+di y ·B2-de x ·E)/XX；
β＝arctan(sinβ,cosβ)；
γ＝arctan(sinγ,cosγ)。
5. the electric propulsion position maintaining control thruster allocation method according to claim 1, wherein the shadow region avoiding method is performed by adjusting a position maintaining direction angle coefficient κ: k = k + (-1) n Δ κ, where Δ κ is the adjustment step size, n is alternately set to 0 or 1 until the three satellites are in the illumination area at the boot time.
6. The distribution method of electric propulsion position maintaining control thrusters according to claim 1, wherein the principle of selecting the combination of the position maintaining thrusters is as follows: when the thruster with the fault is NE and/or SW, the combination of NW and SE is selected; when the thrust device with the fault is NW and/or SE, the NE and SW combination is selected.
7. The electric propulsion position maintaining control thruster distributing method according to claim 1, wherein: the minimum fuel consumption is determined by the minimum sum of the speed increments of three starting.
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