CN113703487B - Small satellite formation configuration control method based on single electric push - Google Patents
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Abstract
The invention discloses a control method for a small satellite formation configuration based on single electric push, which comprises the following steps: calculating formation configuration parameter deviation; calculating the suboptimal three pulse size of the fuel and the corresponding pulse applying time, and the optimal single pulse size of the out-of-plane fuel and the corresponding pulse applying time; calculating the total duration of the application of the continuous low thrust at each pulse; setting continuous low-thrust application duration of each continuous low-thrust application arc section, and reserving gesture maneuvering time; maneuvering the satellite attitude to a target attitude that can produce a thrust in a predetermined direction during an attitude maneuver period; applying continuous low-thrust control at each set continuous low-thrust application arc segment, and maneuvering the satellite to a conventional attitude; and updating the current formation configuration parameters until the deviation of the formation configuration parameters is judged to be within a preset range. By using the invention, the control of the small satellite formation configuration with only a single electric propulsion, which is less in fuel consumption, is realized. The method can be widely applied to the field of satellite formation configuration control.
Description
Technical Field
The invention relates to the field of satellite formation configuration control, in particular to a small satellite formation configuration control method based on single electric push.
Background
Compared with the traditional single large satellite, the small satellite formation control has the advantages of meeting task requirements, along with small size, low cost, high reliability and strong flexibility. In order to prolong the on-orbit life of the formation satellite, the total fuel consumption required by formation configuration control is usually used as an optimization target, and a pulse-based formation configuration reconstruction control optimization solution is obtained, but when a propulsion system of the formation system is electric propulsion or micro-cooling air propulsion, the suboptimal pulse solution is not applicable any more, and a formation continuous low-thrust configuration control method meeting both control precision requirements and suboptimal fuel consumption needs to be provided for the conditions of continuous low thrust and single electric propulsion.
Disclosure of Invention
In order to solve the technical problems, the invention aims to provide a small satellite formation configuration control method based on single electric propulsion, which realizes formation continuous low-thrust configuration control with suboptimal fuel consumption.
The technical scheme adopted by the invention is as follows: a control method for a small satellite formation configuration based on single electric push comprises the following steps:
s1, calculating formation configuration parameter deviation according to a current formation configuration parameter and a target formation configuration parameter;
s2, judging that the deviation of formation configuration parameters exceeds a preset threshold, and calculating the in-plane suboptimal three-pulse size, the corresponding suboptimal pulse application latitude amplitude angle, the out-of-plane optimal pulse size and the corresponding optimal pulse application latitude amplitude angle by taking less fuel consumption as a target according to the current formation configuration parameters;
s3, calculating the total duration of continuous small thrust application at each pulse according to the speed increment which can be provided in the unit time of the maximum thrust of the single electric propeller;
s4, considering the influence of the continuous small thrust application duration of each track on the formation configuration control time and the fuel consumption, setting the continuous small thrust application duration of each track and the attitude maneuver time which can generate the thrust in the required direction before and after each pulse application moment;
s5, maneuvering the satellite attitude to a target attitude capable of enabling a single electric propulsion to be adjusted to generate a preset control thrust direction in the attitude maneuvering time period;
s6, applying continuous low-thrust control at the set continuous low-thrust application position of each track, and maneuvering the satellite to a conventional posture after the application of the continuous low-thrust control is finished;
and S7, updating the current formation configuration parameters and returning to the step S1 until the deviation of the formation configuration parameters is judged to be within a preset range.
Further, the formation configuration parameter deviation comprises a difference between a formation auxiliary star and a main star semi-long axis, a relative eccentricity vector, a relative inclination vector and a formation around a flying center along a track direction offset distance.
Further, the calculation formula of the in-plane suboptimal three-pulse size is as follows:
in the above-mentioned method, the step of,
representing the first pulse size in plane, +.>
Representing in-plane second pulse size, < >>
Representing the third pulse size in plane, Δa m Indicating the expected suboptimal pulse control of the second half long axis change in ignition, Δλ sm Representing the amount of change in the constant offset along the track, Δe m The magnitude change of the E vector is represented, n represents the angular velocity of the primary star orbit, and T represents the period of the formation primary star orbit.
Further, the calculation formula of the latitude argument of the corresponding suboptimal pulse application is as follows:
in the above-mentioned method, the step of,
representing the corresponding latitude depression angle of the application of the first pulse in the plane, < >>
Indicating correspondence when applying in-plane second pulsesIs a latitude depression angle,/>
Representing the corresponding latitude depression angle of the application of the third pulse in the plane,/>
Component representing the desired change in the y-direction of the relative eccentricity vector,/->
Representing the component of the desired change in the x-direction of the relative eccentricity vector.
Further, the calculation formula of the out-of-plane optimal pulse size is as follows:
δv n1 ＝na|Δi target -Δi current |＝na|Δi man |
in the above, δv n1 Represents the out-of-plane optimal pulse size, n represents the primary satellite orbit angular velocity, a represents the primary satellite orbit semi-major axis, Δi man Representing the relative tilt angle vector of the desired change.
Further, the calculation formula of the corresponding latitude amplitude of the optimal pulse application is as follows:
in the above, u n1 Representing the corresponding optimal pulse application latitude argument,
component representing the desired change in the y-direction of the relative tilt vector, is provided>
Representing the component of the desired change in the x-direction of the relative tilt vector.
Further, the calculation formula of the total duration of the continuous small thrust application at each pulse is as follows:
in the above-mentioned method, the step of,
indicates the duration of the force application required to achieve the first pulse size,/->
Indicates the duration of the force required to achieve the second pulse size,/->
Indicating the duration of the force applied, deltaT, required to achieve the third pulse size n1 Represents the duration of the applied force, deltaV, required to achieve an out-of-plane optimum pulse size max Representing the speed increase that can be provided per unit time of maximum thrust of a single electric propulsion.
Further, the formula for setting the continuous low thrust application duration per track before and after each pulse application time is as follows:
k∈1,2,3
in the above-mentioned method, the step of,
indicates the start time of each low thrust control in the plane, < > and the like>
Indicating the end time of each low thrust control in the plane, < > and the like>
Indicates the in-plane force application time length, (T) n1 ) start The out-of-plane single low thrust control start time is represented by (T) n1 ) end And the out-of-plane single small thrust control end time is indicated.
The method and the system have the beneficial effects that: according to the invention, the pulse control suboptimal solution is decomposed into continuous low-thrust formation configuration control near the suboptimal application point, and for the limitation of single electric pushing of a satellite, the direction control of the thrust is realized by regulating the gesture through a satellite flywheel at the suboptimal pulse, so that the aims of simultaneously meeting formation configuration control precision and saving fuel consumption are fulfilled.
Drawings
FIG. 1 is a flow chart of the steps of a control method for a formation configuration of a small satellite based on a single electric push.
Detailed Description
The invention will now be described in further detail with reference to the drawings and to specific examples. The step numbers in the following embodiments are set for convenience of illustration only, and the order between the steps is not limited in any way, and the execution order of the steps in the embodiments may be adaptively adjusted according to the understanding of those skilled in the art.
Referring to fig. 1, the invention provides a control method for a small satellite formation configuration based on single electric push.
In a first embodiment, in-plane formation configuration control:
s101, according to the current in-plane formation configuration parameter delta alpha current ＝(Δa current ,Δe current ,Δi current ,Δλ current ) T And a target in-plane formation configuration parameter Δα target ＝(Δa target ,Δe target ,Δi target ,Δλ target ) T Calculating the in-plane formation configuration parameter deviation delta alpha error ＝(Δa error ,Δe error ,Δi error ,Δλ error ) T Wherein Δa=a deputy -a chief To form the difference between the minor and major semi-major axes of the minor and major stars, Δe= (Δe) x ,Δe y ) T ＝(e d cosω d -e c cosω c ,e d sinω d -e c sinω c ) T As relative eccentricity vector, Δi= (Δi) x ,Δi y ) T ＝(i d -i c ,(Ω d -Ω c )sini c ) T As relative tilt vector, Δλ=Δu+ΔΩ cosi c Offset distances along the track around the center of flight for formation.
S102, judging the deviation delta alpha of formation configuration parameters in a plane error Exceeding a preset threshold Δα predefined According to the current in-plane formation parameter Deltaalpha current And calculating the suboptimal three-pulse size and the corresponding suboptimal pulse application latitude amplitude angle in the plane.
Specifically, based on the characteristic that in-plane and out-of-plane movements of the formation can be decoupled, the in-plane configuration parameter delta alpha is calculated for the formation in-plane ＝(Δa,Δe,Δλ) T Control target, calculating the magnitude of sub-optimal along-track three-pulse control quantity by taking fuel consumption as target
And a corresponding latitude amplitude u t1 ，u t2 ，u t3 The method comprises the steps of carrying out a first treatment on the surface of the Aiming at the control target of the formation out-of-plane configuration parameter delta i, calculating the optimal out-of-plane single pulse control quantity of fuel>
And a corresponding latitude amplitude u n1 。
The calculation formula is as follows:
wherein Δa m ＝Δa target -Δa current ，Δe m ＝|Δe m |＝|Δe target -Δe current And n is the angular velocity of the orbit of the main star, and T is the orbit period of the main star.
The corresponding latitude amplitude of application is:
the corresponding time is +.>
S103, calculating the total duration of continuous small thrust application at each pulse according to the speed increment which can be provided in the unit time of the maximum thrust of the single electric propeller;
in particular, based on the use of continuously small thrust to achieve equivalent pulse controlThe thinking of the control effect is based on the maximum thrust F of a single electric propeller max Speed increment DeltaV capable of being provided in unit time (1 s) max Calculating the total duration DeltaT of the application of successive low thrust forces at each sub-optimal pulse 1 ，ΔT 2 ，ΔT 3 Wherein
m is the current satellite mass. />
To achieve a speed pulse with continuously low thrust +.>
The required continuous low thrust on-time. And so on to obtain the total duration of continuous small thrust application at the other two suboptimal pulses +.>
And->
S104, considering the influence of the continuous small thrust application duration of each track on the formation configuration control time and the fuel consumption, setting the continuous small thrust application duration of each track and the attitude maneuver time which can generate the thrust in the required direction before and after each pulse application moment;
specifically, considering that only one point of time is required for pulse application and continuous small thrust is required to be continuously applied for a certain period of time, in order to achieve approximately equivalent pulse control effect with continuous small thrust, it is preferable that each small thrust control start time in the plane is
Ending time of +.>
Wherein k is 1,2,3.
S105, single electric pushing of the satellite is adjusted to a control direction in a gesture maneuvering time period;
in particular, considering that the satellite has only a single electric propulsion and that the electric propulsion is fixed on the satellite, in order to provide a continuous small thrust along the track, it is necessary to apply at each time a continuous small thrust is applied
Previously, the satellite needs to be reserved from the normal attitude q normal Motorized to a target attitude enabling a single electric propulsion to generate thrust along the track +.>
Time of (2)>
S106, applying continuous low-thrust control at the set continuous low-thrust application position of each track, and maneuvering the satellite to a conventional posture after the application of the continuous low-thrust control is finished;
specifically, considering that the number of satellite attitude maneuvers is reduced as much as possible, 3m consecutive small thrust application arcs along the track may be set as a period in which the satellite attitude remains in a target attitude that can produce consecutive small thrust along the track. Outside the period, the satellite performs attitude maneuver and returns to the normal attitude q normal 。
And S107, updating the current in-plane formation configuration parameters and returning to the step S101 until the in-plane formation configuration parameter deviation is judged to be within a preset range.
Specifically, after a continuous low thrust control period, the configuration parameters in the current formation plane are updated
And updating the deviation of the configuration parameters in the current formation plane +.>
If->
Then the formation control based on the single electric push is ended, otherwise, the step S101 is returned to, and the iterative control is performed until +.>
I.e. the deviation of the configuration parameters in the formation plane is within a preset allowable range.
In a second embodiment, the out-of-plane formation configuration control:
s201, according to the current out-of-plane formation configuration parameter delta i current And a target out-of-plane formation configuration parameter Δi target Calculating out-of-plane formation configuration parameter deviation delta i error ；
S202, judging that the deviation of the out-of-plane formation configuration parameters exceeds a preset threshold, namely delta i error ＞Δi predefined Calculating a fuel optimal out-of-plane optimal pulse size based on the current out-of-plane formation parameters, targeting a minimum fuel consumption
And the corresponding optimal pulse application latitude argument u n1 。
The control quantity of single pulse outside the track plane is as follows:
δv n1 ＝na|Δi target -Δi current |＝na|Δi man |
the corresponding latitude amplitude of application is:
the corresponding time is +.>
In the above formula, δi is the configuration out-of-plane reconstruction control I vector change amount.
S203, calculating the total duration of continuous small thrust application at each pulse according to the speed increment which can be provided in the unit time of the maximum thrust of the single electric propeller;
specifically, based on the thought of realizing the equivalent pulse control effect by adopting continuous small thrust, the method is as followsAccording to the maximum thrust F of a single electric propeller max Speed increment DeltaV capable of being provided in unit time (1 s) max Calculating the total duration DeltaT of the application of successive low thrust forces at each optimal out-of-plane pulse n1 Wherein
m is the current satellite mass. />
To achieve a speed pulse with continuously low thrust +.>
The required continuous low thrust on-time.
S204, considering the influence of the continuous small thrust application duration of each track on the formation configuration control time and the fuel consumption, setting the continuous small thrust application duration of each track and the attitude maneuver time which can generate the thrust in the required direction before and after each pulse application moment;
specifically, considering that only one point in time is required for pulse application and continuous small thrust is required to be continuously applied for a period of time, in order to achieve approximately equivalent pulse control effect with continuous small thrust, the out-of-plane single small thrust control start time may be
Ending time of +.>
S205, single electric pushing of the satellite is adjusted to a control direction in the attitude maneuver time period;
in particular, considering that the satellite has only a single electric push and that the electric push is fixed on the satellite, in order to provide a continuous small thrust out of plane, it is necessary to apply at each time a continuous small thrust is applied
Previously, the satellite needs to be reserved from the normal attitude q normal Motorized toTarget posture enabling single electric propulsion to generate out-of-plane thrust +.>
Time of (2)>
S206, applying continuous low-thrust control at the set continuous low-thrust application position of each track, and maneuvering the satellite to a conventional posture after the application of the continuous low-thrust control is finished;
specifically, considering that the number of satellite attitude maneuvers is reduced as much as possible, p out-of-plane continuous low-thrust application arcs may be set as a period, and the satellite attitude in the period is kept at a target attitude that can generate out-of-plane continuous low thrust. Outside the period, the satellite performs attitude maneuver and returns to the normal attitude q normal 。
S207, updating the current out-of-plane formation configuration parameters and returning to the step S201 until the deviation of the out-of-plane formation configuration parameters is judged to be within a preset range.
Specifically, after a continuous low thrust control period, the current formation out-of-plane configuration parameter Δi is updated current And update the current formation out-of-plane configuration parameter deviation deltai error If Δi error ≤(Δi error ) predefined If the formation control based on the single electric push is finished, otherwise, returning to step S201, and performing iterative control until delta i is reached error ≤(Δi error ) predefined I.e. the deviation of the formation out-of-plane configuration parameters is within a preset allowable range.
While the preferred embodiment of the present invention has been described in detail, the invention is not limited to the embodiment, and various equivalent modifications and substitutions can be made by those skilled in the art without departing from the spirit of the invention, and these modifications and substitutions are intended to be included in the scope of the present invention as defined in the appended claims.
Claims (8)
1. The control method for the formation configuration of the small satellite based on single electric push is characterized by comprising the following steps of:
s1, calculating formation configuration parameter deviation according to a current formation configuration parameter and a target formation configuration parameter;
s2, judging that the deviation of formation configuration parameters exceeds a preset threshold, and calculating the in-plane formation configuration control suboptimal three-pulse size, the corresponding suboptimal pulse application latitude amplitude angle, the out-of-plane formation configuration control optimal pulse size and the corresponding optimal pulse application latitude amplitude angle according to the current formation configuration parameters by taking less fuel consumption as a target;
s3, calculating the total duration of continuous small thrust application at each pulse according to the speed increment which can be provided in the unit time of the maximum thrust of the single electric propeller;
s4, considering the influence of the continuous small thrust application duration of each track on the formation configuration control time and the fuel consumption, setting the continuous small thrust application duration of each track and the attitude maneuver time which can generate the thrust in the required direction before and after each pulse application moment;
s5, maneuvering the satellite attitude to a target attitude capable of enabling a single electric propulsion to generate a preset thrust direction in an attitude maneuvering time period;
s6, applying continuous low-thrust control at the set continuous low-thrust application position of each track, and maneuvering the satellite to a conventional posture after the application of the continuous low-thrust control is finished;
and S7, updating the current formation configuration parameters and returning to the step S1 until the deviation of the formation configuration parameters is judged to be within a preset range.
2. The method for controlling the formation configuration of the small satellites based on single electric propulsion according to claim 1, wherein the deviation of the formation configuration parameters comprises the difference between the auxiliary satellites and the semi-long axes of the main satellites, the relative eccentricity vector, the relative inclination vector and the formation offset distance along the track around the center of flight.
3. The method for controlling the formation configuration of the small satellite based on single electric push according to claim 1, wherein the calculation formula of the in-plane formation configuration for controlling the suboptimal three pulse size is as follows:
in the above-mentioned method, the step of,
representing the first pulse size in plane, +.>
Representing in-plane second pulse size, < >>
Representing the third pulse size in plane, Δa m Indicating the expected suboptimal pulse control of the second half long axis change in ignition, Δλ sm Representing the amount of change in the constant offset along the track, Δe m The magnitude change of the E vector is represented, n represents the angular velocity of the primary star orbit, and T represents the period of the formation primary star orbit.
4. A control method for a formation configuration of a small satellite based on single electric propulsion according to claim 3, wherein the calculation formula of the latitude angle of application of the corresponding suboptimal pulse is as follows:
in the above-mentioned method, the step of,
representing the corresponding latitude depression angle of the application of the first pulse in the plane, < >>
Representing the corresponding latitude depression angle of the application of the second pulse in the plane,/>
Representing the corresponding latitude depression angle of the application when the third pulse in the plane is applied,
component representing the desired change in the y-direction of the relative eccentricity vector,/->
Representing the component of the desired change in the x-direction of the relative eccentricity vector.
5. The method for controlling the formation configuration of the small satellite based on single electric push as claimed in claim 4, wherein the calculation formula of the optimal pulse size for controlling the formation configuration outside the plane is as follows:
δv n1 ＝na|Δi target -Δi current |＝na|Δi man |
in the above, δv n1 Represents the out-of-plane optimal pulse size, n represents the primary satellite orbit angular velocity, a represents the primary satellite orbit semi-major axis, Δi man Representing the relative tilt vector, Δi, of the desired change target Representing the out-of-plane formation configuration parameters of the object, Δi current Representing current out-of-plane formation configuration parameters.
6. The control method of the small satellite formation configuration based on single electric push according to claim 5, wherein the calculation formula of the corresponding optimal pulse application latitude amplitude angle is as follows:
in the above, u n1 Representing the corresponding optimal pulse application latitude argument,
component representing the desired change in the y-direction of the relative tilt vector, is provided>
Representing the component of the desired change in the x-direction of the relative tilt vector.
7. The control method of the formation configuration of the small satellites based on single electric propulsion according to claim 6, wherein the calculation formula of the total duration of the continuous small thrust application at each pulse is as follows:
in the above-mentioned method, the step of,
indicates the duration of the force application required to achieve the first pulse size,/->
Indicates the duration of the force required to achieve the second pulse size,/->
Indicating the duration of the force applied, deltaT, required to achieve the third pulse size n1 Represents the duration of the applied force, deltaV, required to achieve an out-of-plane optimum pulse size max Representing the speed increase that can be provided per unit time of maximum thrust of a single electric propulsion.
8. The control method for a single electric propulsion-based minisatellite formation configuration according to claim 7, wherein the formula for setting the duration of each track of continuous small propulsion application before and after each pulse application time is as follows:
in the above-mentioned method, the step of,
indicates the start time of each low thrust control in the plane, < > and the like>
Indicating the end time of each low thrust control in the plane, < > and the like>
Indicates the in-plane force application time length, (T) n1 ) start The out-of-plane single low thrust control start time is represented by (T) n1 ) end And the out-of-plane single small thrust control end time is indicated. />
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