CN110127088B - Double hysteresis method for unloading satellite synthetic angular momentum by using magnetic torquer - Google Patents

Double hysteresis method for unloading satellite synthetic angular momentum by using magnetic torquer Download PDF

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CN110127088B
CN110127088B CN201910368565.8A CN201910368565A CN110127088B CN 110127088 B CN110127088 B CN 110127088B CN 201910368565 A CN201910368565 A CN 201910368565A CN 110127088 B CN110127088 B CN 110127088B
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unloading
angular momentum
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陆栋宁
王淑一
雷拥军
顾斌
刘洁
田科丰
傅秀涛
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Beijing Institute of Control Engineering
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
    • B64G1/00—Cosmonautic vehicles
    • B64G1/22—Parts of, or equipment specially adapted for fitting in or to, cosmonautic vehicles
    • B64G1/24—Guiding or controlling apparatus, e.g. for attitude control
    • B64G1/36—Guiding or controlling apparatus, e.g. for attitude control using sensors, e.g. sun-sensors, horizon sensors
    • B64G1/366—Guiding or controlling apparatus, e.g. for attitude control using sensors, e.g. sun-sensors, horizon sensors using magnetometers

Abstract

The invention relates to a double hysteresis method for unloading satellite synthetic angular momentum by using a magnetic torquer, belonging to the technical field of satellite attitude control. The method aims at the problem of frequent switching of magnetic control voltage near an orbit arc segment where magnetic unloading just meets the unloading condition in the direction of the geomagnetic field, introduces a double hysteresis unloading strategy aiming at an angular momentum error and an included angle between a geomagnetic field vector and the angular momentum error vector, and finally outputs the unloading voltage after filtering and smoothing, thereby effectively reducing the influence of magnetic control torque on the attitude stability of the satellite and realizing the high-stability attitude control of the satellite. Compared with the traditional magnetic unloading method, the method can reduce the fluctuation of the satellite attitude angle and the angular speed caused by magnetic control moment, and effectively overcome the bad influence of magnetic unloading on the satellite attitude stability.

Description

Double hysteresis method for unloading satellite synthetic angular momentum by using magnetic torquer
Technical Field
The invention relates to a double hysteresis method for unloading satellite synthetic angular momentum by using a magnetic torquer, belonging to the technical field of satellite attitude control.
Background
In the process of in-orbit flight of the satellite, the satellite is influenced by various environmental interferences, so that the attitude angle and the attitude angular velocity of the satellite deviate. In order to keep the three-axis attitude of the satellite stable, contemporary satellites generally adopt a momentum wheel equal-angle momentum exchange device, which converts the interference of the external environment to the attitude of the satellite into angular momentum to be stored in the momentum wheel, and when the angular momentum reaches a certain degree, a magnetic torquer is started to generate magnetic unloading moment to unload the angular momentum to the momentum wheel, which is called the 'magnetic unloading' of the angular momentum. The conventional magnetic unloading generally carries out magnetic control voltage calculation according to the angular momentum accumulation condition of the satellite, but when the unloading condition is just met, the situation that the magnetic control voltage is frequently switched occurs, and at the moment, the magnetic control moment can cause the fluctuation of the attitude angle and the angular velocity of the satellite, so that the high stability control of the satellite is badly influenced.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method further reduces the influence of magnetic control torque on the attitude stability of the satellite, and realizes the high-stability attitude control of the satellite.
The technical solution of the invention is as follows:
a double hysteresis method for unloading satellite synthetic angular momentum by using a magnetic torquer uses three magnetic torquers which are positively arranged along a body coordinate system to unload the satellite synthetic angular momentum in three directions under the body coordinate system, and comprises the following steps:
(1) calculating the magnetic field B of the space environment of the satellite according to the position of the satellite in the orbitb；
Bb＝[Bbx Bby Bbz]TIn which B isbx，Bby，BbzThe three-axis component of the magnetic field intensity in a satellite body coordinate system is shown;
(2) calculating the resultant angular momentum Δ H of the satelliteb；
Initial t0Resultant angular momentum Δ H of time satelliteb0＝0；
t1Resultant angular momentum of time satellites
Figure GDA0002649102880000021
t2Resultant angular momentum of time satellites
Figure GDA0002649102880000022
…
tiResultant angular momentum of time satellites
Figure GDA0002649102880000023
ti+1Resultant angular momentum of time satellites
Figure GDA0002649102880000024
Wherein Js is the moment of inertia of the satellite, ωOIThe angular velocity of the satellite orbit coordinate system relative to the inertial coordinate system;
ωt1is t1Angular velocity of the satellite at time of day, C, relative to the inertial frameBO1Is t1A transformation matrix of the time satellite from the orbital coordinate system to the body coordinate system,
Figure GDA0002649102880000025
is t1The resultant angular momentum of the moment satellite momentum wheel combination;
ωt2is t2Angular velocity of the satellite at time of day, C, relative to the inertial frameBO2Is t2A transformation matrix of the time satellite from the orbital coordinate system to the body coordinate system,
Figure GDA0002649102880000026
is t2The resultant angular momentum of the moment satellite momentum wheel combination;
ωtiis tiAngular velocity of the satellite at time of day, C, relative to the inertial frameBOiIs tiA transformation matrix of the time satellite from the orbital coordinate system to the body coordinate system,
Figure GDA0002649102880000027
is tiThe resultant angular momentum of the moment satellite momentum wheel combination;
ωti+1is ti+1Angular velocity of the satellite at time of day, C, relative to the inertial frameBOi+1Is ti+1A transformation matrix of the time satellite from the orbital coordinate system to the body coordinate system,
Figure GDA0002649102880000028
is ti+1The resultant angular momentum of the moment satellite momentum wheel combination;
(3) calculating the magnetic field B of the space environment where the satellite is located, which is obtained in the step (1) at the current momentbThe direction of (3) and the synthetic angular momentum Δ H of the satellite at the current time obtained in step (2)bThe cosine value cos absolute value | cos | of the angle;
(4) calculating the resultant angular momentum of the satellite at the current timeΔHbNorm of | | | Δ Hb||；
(5) According to the absolute value | cos | of the cosine value cos obtained in the step (3) and the norm | Δ H obtained in the step (4)bJudging whether the synthesized angular momentum of the satellite at the current moment needs to be unloaded or not, and not unloading the synthesized angular momentum of the satellite at the initial moment;
first, when the current time | cos-<a time and current time | | Δ HbUnloading the synthetic angular momentum of the satellite when the | is greater than b;
second, when the current time | cos | > c or the current time | | | Δ Hb||<d, the resultant angular momentum of the satellite is not unloaded;
a. b, c and d are all set thresholds, and a < c, b > d;
third, when the current time | cos-<a time and d is less than or equal to | Delta H at the current momentbWhen | | is less than or equal to b, unloading or not unloading is carried out according to the unloading condition at the previous moment of the current moment;
fourth case, when the current time | | | Δ HbWhen | is greater than b and the present moment a is less than or equal to | cos | is less than or equal to c, unloading or not unloading is carried out according to the unloading condition at the previous moment of the present moment;
in the fifth case, when the current time a is less than or equal to | cos | < c and the current time d is less than or equal to | Δ HbWhen | | is less than or equal to b, unloading or not unloading is carried out according to the unloading condition at the previous moment of the current moment;
(6) according to the judgment result of the step (5), if unloading is needed, entering a step (6), and if unloading is not needed, outputting unloading voltage to the magnetic torquer to be zero; when the judgment result is unloading, the unloading voltage V in the x direction under the satellite body coordinate systemm1 *Comprises the following steps:
Figure GDA0002649102880000031
unloading voltage V in y direction under satellite body coordinate systemm2 *Comprises the following steps:
Figure GDA0002649102880000032
unloading voltage V in z direction under satellite body coordinate systemm3 *Comprises the following steps:
Figure GDA0002649102880000033
wherein the content of the first and second substances,
Figure GDA0002649102880000034
Figure GDA0002649102880000035
Figure GDA0002649102880000041
Figure GDA0002649102880000042
kPMUthe magnetic unloading coefficient is a set value;
Mmlfthe maximum magnetic moment of the magnetic torquer;
Vmmlfthe amplitude limit value of the voltage is a set value;
ΔHbx、ΔHby、ΔHbzas a resultant angular momentum of the satellite Δ HbThree components in a satellite body coordinate system;
Bbx、Bby、Bbzmagnetic field B of space environment of satellitebThree components in a satellite body coordinate system;
(7) filtering the unloading voltage obtained in the step (6), and outputting the voltage to a magnetic torquer to enable the magnetic torquer to unload the synthetic angular momentum of the satellite in three directions under the body coordinate system; the filter formula is as follows:
Figure GDA0002649102880000043
Figure GDA0002649102880000044
Figure GDA0002649102880000045
wherein k isvmIs a filter coefficient, is a set value,
Figure GDA0002649102880000046
is the filtered voltage output at the previous time.
Compared with the prior art, the invention has the beneficial effects that:
(1) the invention completely solves the problem of spacecraft attitude angular velocity fluctuation caused by frequent switching of magnetic control voltage by utilizing the double hysteresis design of the synthetic angular momentum and the included angle between the synthetic angular momentum and the magnetic field intensity;
(2) the method filters the magnetic control voltage, and the influence of magnetic unloading on the attitude stability of the spacecraft can be effectively reduced by using the algorithm;
(3) the algorithm provided by the invention has small required calculation amount, does not need to increase extra calculation resources, and is suitable for realizing a satellite-borne computer.
(4) The invention relates to a double hysteresis method for unloading by using a magnetic torquer, belonging to the technical field of satellite attitude maneuver control. The method aims at the problem of frequent switching of magnetic control voltage near an orbit arc segment where magnetic unloading just meets the unloading condition in the direction of the geomagnetic field, introduces a double hysteresis unloading strategy aiming at an angular momentum error and an included angle between a geomagnetic field vector and the angular momentum error vector, and finally outputs the unloading voltage after filtering and smoothing, thereby effectively reducing the influence of magnetic control torque on the attitude stability of the satellite and realizing the high-stability attitude control of the satellite. Compared with the traditional magnetic unloading method, the method can reduce the fluctuation of the satellite attitude angle and the angular speed caused by magnetic control moment, and effectively overcome the bad influence of magnetic unloading on the satellite attitude stability.
Drawings
FIG. 1 is a schematic diagram of an angle unloading condition determining hysteresis loop;
FIG. 2 is a schematic diagram of determining hysteresis for angular momentum unloading conditions;
FIG. 3 is a schematic diagram of magnetic field strength in a body coordinate system;
FIG. 4 is a schematic diagram of a satellite synthetic angular momentum in a body coordinate system;
fig. 5 is a schematic diagram of the output voltage of the magnetic torquer.
Detailed Description
The invention is described in detail below with reference to the figures and specific examples.
Examples
The present invention is described in detail below:
the orbit is assumed to run on a sun synchronous orbit with the orbit height of about 500km and the inclination angle of 97 degrees. The satellite is provided with three satellites with maximum magnetic moments Mmlf of 200Am2The magnetic torquer of (1), as shown in fig. 5;
(1) calculating the magnetic field B of the space environment of the satellite according to the geographical position of the satelliteb；
Assuming that the current geographic position of the satellite is 94 DEG east longitude, 0.03 DEG north latitude and 492km height, the three-axis component of the environment magnetic field strength under the body coordinate system is
time t 1:
Bb＝[-3.0084979825743828e-005,5.9109881461567932e-006,-8.4364482182156017e-006]nT。
time t 2:
Bb＝[-6.8490665271550280e-007,1.0552072686590731e-005,-4.2079269982111809e-005]nT。
(2) calculating the resultant angular momentum Δ H of a satellite systemb；
Figure GDA0002649102880000061
Assuming a satellite rotational inertia of
Js＝[14621.6,0.61,-267.410.61,12589.8,-365.91-267.41,-365.91,9798.9]km2，
time t 1:
inertial attitude angular velocity
ωt＝[-2.2149997569679649e-007,-0.0011087167831417878,1.6974443286667434e-007]Trad/s，
Angular velocity of the track
ωOI＝[0.00000000000000000,-0.0011090212798321923,-1.4176809860738920e-010]rad/s
Transformation matrix C from orbital coordinate system to body coordinate systemBOIs composed of
CBO＝[0.99999999040172949,4.0952297969409912e-008,0.00013855157646493720；-4.0944417217803064e-008,0.99999999999999756,-5.6882073697646742e-008；-0.00013855157646716225,5.6876400156833425e-008,0.99999999040172871]
Angular momentum of the angular momentum exchange device on the satellite is
Figure GDA0002649102880000062
The satellite synthesized angular momentum is
ΔHb＝[-0.00328328008216102880.0081412978437776368-0.011836565394696311]Nms
time t 2:
inertial attitude angular velocity
ωt＝[-3.1584609477267775e-005,-0.0011078694158919362,-6.3864276869319853e-005]Trad/s，
Angular velocity of the track
ωOI＝[0.00000000000000000,-0.0011090212798321923,-1.4176809860738920e-010]rad/s
Transformation matrix C from orbital coordinate system to body coordinate systemBOIs composed of
CBO＝[0.99959534255428351,0.028445577847135126,-1.5643765823580846e-005；-0.028445577909407362,0.99959534266780548,-3.7726131908166760e-006；1.5530121296791766e-005,4.2160825343001695e-006,0.99999999987052002]
Angular momentum of the angular momentum exchange device on the satellite is
Figure GDA0002649102880000071
The satellite synthesized angular momentum is
ΔHb＝[1.0632997724936242-0.26045473119030199-0.50341287228167142]Nms
(3) Calculating the magnetic field B of the space environment where the satellite is located, which is obtained in the step (1) at the current momentbThe direction of (3) and the synthetic angular momentum Δ H of the satellite at the current time obtained in step (2)bThe absolute value | cos! of the cosine value cos of the angle of inclusion
time t 1: 0.5266 |, cos | >
time t 2: 1.7531e-005 | cos | -
(4) Calculating the resultant angular momentum Δ H of the satellite at the current momentbNorm of | | | Δ Hb||；
time t 1: | Δ Hb|＝0.0147Nms
time t 2: | Δ Hb|＝1.2049Nms
(5) According to the absolute value | cos | of the cosine value cos obtained in the step (3) and the norm | Δ H obtained in the step (4)bJudging whether the synthesized angular momentum of the satellite at the current moment needs to be unloaded or not, and not unloading the synthesized angular momentum of the satellite at the initial moment;
let a be 0.707, b be 1.2, and c be 0.7660; d is 1.2;
time t 1: due to | | Δ Hb||＝0.0147<d, so no unloading is performed;
time t 2: since | cos | ═ 1.7531e-005<a, and | | | Δ Hb||＝1.2049>1.2, therefore, unloading is required;
(6) according to the judgment result of the step (5), when the judgment result is unloading, the unloading is carried out
time t 1: vm1 *＝Vm2 *＝Vm3 *＝0
time t 2:
unloading voltage V in x direction under satellite body coordinate systemm1 *Comprises the following steps:
Vm1 *＝-0.15989443994619182V
unloading voltage V in y direction under satellite body coordinate systemm2 *Comprises the following steps:
Vm2 *＝0.27521345483441662V
unloading voltage V in z direction under satellite body coordinate systemm3 *Comprises the following steps:
Vm3 *＝0.073318359058691107V
wherein kPMU is 0.0005, Mmlf is 200,
Mx＝0.43219029156920075；
My＝1.1975601839719610；
Mz＝0.29327343623476432；
kmm＝max(|Mx/Mmlf|,|My/Mmlf|,|Mz/Mmlf|,1)
＝max(|0.43219029156920075/200|,|1.1975601839719610/200|,|0.29327343623476432/200|,1)
＝1
Vmmlf＝5.0V；
(7) filtering the unloading voltage obtained in the step (6), and outputting the voltage to a magnetic torquer to enable the magnetic torquer to unload the synthetic angular momentum of the satellite in three directions under the body coordinate system; the filter formula is as follows:
Figure GDA0002649102880000091
Figure GDA0002649102880000092
Figure GDA0002649102880000093
wherein
Figure GDA0002649102880000094
kvm＝0.9
The unloading voltage in this period is:
Vm1＝-0.015989443994619178V
Vm2＝0.027521345483441654V
Vm3＝0.0073318359058691090V
those skilled in the art will appreciate that those matters not described in detail in the present specification are well known in the art.

Claims (2)

1. A double hysteresis method for unloading satellite synthetic angular momentum by using a magnetic torquer is characterized in that: the method for unloading the synthetic angular momentum of the satellite in three directions under the body coordinate system by using three magnetic torquers which are positively arranged along the body coordinate system comprises the following steps:
(1) calculating the magnetic field B of the space environment of the satellite according to the position of the satellite in the orbitb；
(2) Calculating the resultant angular momentum Δ H of the satelliteb；
Initial t0Resultant angular momentum Δ H of time satelliteb0＝0；
t1Resultant angular momentum of time satellites
Figure FDA0002649102870000011
t2Resultant angular momentum of time satellites
Figure FDA0002649102870000012
…
tiResultant angular momentum of time satellites
Figure FDA0002649102870000013
ti+1Resultant angular momentum of time satellites
Figure FDA0002649102870000014
(3) Calculating the magnetic field B of the space environment where the satellite is located, which is obtained in the step (1) at the current momentbThe direction of (3) and the synthetic angular momentum Δ H of the satellite at the current time obtained in step (2)bThe cosine value cos absolute value | cos | of the angle;
(4) calculating the resultant angular momentum Δ H of the satellite at the current momentbNorm of | | | Δ Hb||；
(5) According to the absolute value | cos | of the cosine value cos obtained in the step (3) and the norm | Δ H obtained in the step (4)bIf the unloading is needed, the step (6) is carried out, and if the unloading is not needed, the unloading voltage output to the magnetic torquer is zero;
(6) according to the judgment result in the step (5), when the judgment result is unloading, the unloading voltage V in the x direction under the satellite body coordinate systemm1 *Comprises the following steps:
Figure FDA0002649102870000015
unloading voltage V in y direction under satellite body coordinate systemm2 *Comprises the following steps:
Figure FDA0002649102870000016
unloading voltage V in z direction under satellite body coordinate systemm3 *Comprises the following steps:
Figure FDA0002649102870000021
wherein the content of the first and second substances,
Figure FDA0002649102870000022
Figure FDA0002649102870000023
Figure FDA0002649102870000024
Figure FDA0002649102870000025
kPMUthe magnetic unloading coefficient is a set value;
Mmlfthe maximum magnetic moment of the magnetic torquer;
Vmmlfthe amplitude limit value of the voltage is a set value;
ΔHbx、ΔHby、ΔHbzas a resultant angular momentum of the satellite Δ HbThree components in a satellite body coordinate system;
Bbx、Bby、Bbzmagnetic field B of space environment of satellitebThree components in a satellite body coordinate system;
(7) filtering the unloading voltage obtained in the step (6), and outputting the voltage to a magnetic torquer to enable the magnetic torquer to unload the synthetic angular momentum of the satellite in three directions under the body coordinate system; the filter formula is as follows:
Figure FDA0002649102870000026
Figure FDA0002649102870000027
Figure FDA0002649102870000028
wherein k isvmIn order to be a filter coefficient, the filter coefficient,
Figure FDA0002649102870000029
the filtered voltage output at the previous moment;
in the step (5), the synthetic angular momentum of the satellite is not unloaded at the initial moment;
first, when the current time | cos-<a time and current time | | Δ HbUnloading the synthetic angular momentum of the satellite when the | is greater than b;
second, when the current time | cos | > c or the current time | | | Δ Hb||<d, the resultant angular momentum of the satellite is not unloaded;
a. b, c and d are all set thresholds, and a < c, b > d;
third, when the current time | cos-<a time and d is less than or equal to | Delta H at the current momentbWhen | | is less than or equal to b, unloading or not unloading is carried out according to the unloading condition at the previous moment of the current moment;
fourth case, when the current time | | | Δ HbWhen | is greater than b and the present moment a is less than or equal to | cos | is less than or equal to c, unloading or not unloading is carried out according to the unloading condition at the previous moment of the present moment;
in the fifth case, when the current time a is less than or equal to | cos | < c and the current time d is less than or equal to | Δ HbWhen | | is less than or equal to b, unloading or not unloading is carried out according to the unloading condition at the previous moment of the current moment;
in step (1), Bb＝[Bbx Bby Bbz]TIn which B isbx，Bby，BbzThe three-axis component of the magnetic field intensity in a satellite body coordinate system is shown;
in the step (2), Js is the rotational inertia of the satellite, omegaOIThe angular velocity of the satellite orbit coordinate system relative to the inertial coordinate system;
ωt1is t1Angular velocity of the satellite at time of day, C, relative to the inertial frameBO1Is t1A transformation matrix of the time satellite from the orbital coordinate system to the body coordinate system,
Figure FDA0002649102870000031
is t1The resultant angular momentum of the moment satellite momentum wheel combination;
ωt2is t2Angular velocity of the satellite at time of day, C, relative to the inertial frameBO2Is t2A transformation matrix of the time satellite from the orbital coordinate system to the body coordinate system,
Figure FDA0002649102870000032
is t2The resultant angular momentum of the moment satellite momentum wheel combination;
ωtiis tiAngular velocity of the satellite at time of day, C, relative to the inertial frameBOiIs tiA transformation matrix of the time satellite from the orbital coordinate system to the body coordinate system,
Figure FDA0002649102870000033
is tiThe resultant angular momentum of the moment satellite momentum wheel combination;
ωti+1is ti+1Angular velocity of the satellite at time of day, C, relative to the inertial frameBOi+1Is ti+1A transformation matrix of the time satellite from the orbital coordinate system to the body coordinate system,
Figure FDA0002649102870000034
is ti+1The composite angular momentum of the moment satellite momentum wheel combination.
2. The double hysteresis method for unloading satellite synthetic angular momentum using a magnetic torquer as claimed in claim 1, wherein: in step (7), kvmIs a set value.
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