Summary of the invention
The present invention is the problem that will solve existing method operative installations unloading and discharging gear costliness, proposes a kind of method of utilizing satellite pitch axis attitude maneuver unloading pitch axis moment of momentum.
A kind of method of utilizing satellite pitch axis attitude maneuver unloading pitch axis moment of momentum, detailed process is as follows:
The pitch axis angular momentum h that satellite need unload is determined in step 1, measurement
Un_y, concrete steps are:
Measure the moment of momentum of each momentum exchange actuating unit at the component of body coordinate system, with i momentum exchange actuating unit moment of momentum at the representation in components of body coordinate system be
Can obtain the total angular momentum of all momentum exchange actuating units thus at the component h of pitch axis
Un_y, expression formula is:
In the formula, described body coordinate system is body coordinate system ox
b, y
bz
bOverlap with inertia principal axes system, initial point is at the barycenter of satellite, and each coordinate axle and satellite body are connected, body coordinate system ox
by
bz
bMiddle ox
bBe the axis of rolling, oy
bBe pitch axis, oz
bBe yaw axis, symbol b represents the amount relevant with body coordinate system;
Be 3 * 1 array, represent i momentum exchange actuating unit moment of momentum at the component of body coordinate system,
Represent the summation of all actuating unit moment of momentums at the component of body coordinate system,
Represent that the summation of all actuating unit moment of momentums is at the component of body coordinate system pitch axis, h
Un_yBe the pitch axis moment of momentum size of needs unloading,
Be the pitch axis of the body coordinate system component in body coordinate system, n is the quantity of actuating unit, and i is the integer greater than 0;
Step 2, determine the gravity gradient torque that satellite is suffered according to the satellite rotor inertia: the body coordinate system of normal conditions satellite overlaps with principal axis of inertia system of axes, so the expression formula of gravity gradient torque can be expressed as:
In the formula, μ is the terrestrial gravitation constant, and R represents the distance of satellite barycenter and earth centroid,
Suffered three gravity gradient torques of expression satellite are at the component of body series, I
x, I
y, I
zRepresent the satellite axis of rolling, pitch axis, the corresponding principal moments of yaw axis respectively,
θ represents to change roll angle and the pitch angle that order is described by 3-2-1; Wherein, described 3-2-1 changes in the order 3 representatives around oz
bRotate, 2 representatives are around oy
bAxle rotates, and 1 representative is around ox
bRotate.
Step 3, the motor-driven θ of estimation satellite pitch axis
mNeeded time t
End, and the angular momentum h that gravity gradient torque accumulates at pitch axis in the mobile process
Manu
The motor-driven θ of satellite pitch axis
mThe used time can be expressed as:
t
end=ω
ymax/a
ymax+θ
m/ω
ymax (3)
In the formula, t
EndBe the motor-driven θ of satellite pitch axis
mThe used time, ω
YmaxBe the maximum angular rate in the satellite pitch axis mobile process, a
YmaxMaximum angular acceleration in the satellite pitch axis mobile process;
Employing is got the method for mobile process gravity gradient torque aviation value and is estimated h
Manu, satellite is in the three axis stabilization state before the unloading, and three suffered gravity gradient torques are 0, motor-driven θ
mAfter the angle, only pitch axis is subjected to the gravity gradient torque effect, and expression formula is:
In the formula,
The expression gravity gradient torque is at the component of body series pitch axis;
Mean gravity gradient moment according to motor-driven front and back can be estimated the moment of momentum that accumulates in the mobile process, and expression formula is:
Step 4, according to h
Un_yWith h
ManuFind the solution satellite and need motor-driven angle θ
m
Step 5, according to h
Un_y, h
ManuWith the determined θ of step 4
m, calculate the time t that needs to keep this angle
Hold:
Need after the unloading motor-drivenly to be the three axis stabilization state because satellite is finished, so satellite is keeping θ
mThe moment of momentum that accumulates during motion should satisfy relation
Therefore can solve satellite and keep θ
mTime t
HoldFor:
Step 6, determine to guarantee that satellite has enough moment of momentums space to carry out motor-driven satellite rotor inertia distribution form:
Its relational expression that specifically needs to satisfy is:
I
z□I
x (8)
In the formula, symbol represents I
xBe far longer than I
z
Effect of the present invention:
(1) do not need to use other pitch axis discharging gears, only pass through the motor-driven of pitch axis, can unload the moment that pitch axis accumulates, saved cost and the space of satellite;
(2) discharging method simple possible, and have certain precision, be fit to the actual satellite application with fast reserve ability;
(3) provided the inertia distribution form that uses the satellite that this method unloads the pitch axis moment of momentum, actual satellite can be in conjunction with the unloading strategy design satellite task of pitch axis and the distribution of inertia, the realization task and unload between balance.
The specific embodiment
The specific embodiment one: present embodiment is described in conjunction with Fig. 1~Fig. 5: a kind of method of utilizing satellite pitch axis attitude maneuver unloading pitch axis moment of momentum, detailed process is as follows:
The pitch axis angular momentum h that satellite need unload is determined in step 1, measurement
Un_y, concrete steps are:
Measure the moment of momentum of each momentum exchange actuating unit at the component of body coordinate system, with i momentum exchange actuating unit moment of momentum at the representation in components of body coordinate system be
Can obtain the total angular momentum of all momentum exchange actuating units thus at the component h of pitch axis
Un_y, expression formula is:
In the formula, described body coordinate system is body coordinate system ox
by
bz
bOverlap with inertia principal axes system, initial point is at the barycenter of satellite, and each coordinate axle and satellite body are connected, body coordinate system ox
by
bz
bMiddle ox
bBe the axis of rolling, oy
bBe pitch axis, oz
bBe yaw axis, symbol b represents the amount relevant with body coordinate system;
Be 3 * 1 array, represent i momentum exchange actuating unit moment of momentum at the component of body coordinate system,
Represent the summation of all actuating unit moment of momentums at the component of body coordinate system,
Represent that the summation of all actuating unit moment of momentums is at the component of body coordinate system pitch axis, h
Un_yBe the pitch axis moment of momentum size of needs unloading,
Be the pitch axis of the body coordinate system component in body coordinate system, n is the quantity of actuating unit, and i is the integer greater than 0;
Step 2, determine the gravity gradient torque that satellite is suffered according to the satellite rotor inertia: the body coordinate system of normal conditions satellite overlaps with principal axis of inertia system of axes, so the expression formula of gravity gradient torque can be expressed as:
In the formula, μ is the terrestrial gravitation constant, and R represents the distance of satellite barycenter and earth centroid,
Suffered three gravity gradient torques of expression satellite are at the component of body series, I
x, I
y, I
zRepresent the satellite axis of rolling, pitch axis, the corresponding principal moments of yaw axis respectively,
θ represents to change roll angle and the pitch angle that order is described by 3-2-1; Wherein, described 3-2-1 changes in the order 3 representatives around oz
bRotate, 2 representatives are around oy
bAxle rotates, and 1 representative is around ox
bRotate.
Step 3, the motor-driven θ of estimation satellite pitch axis
mNeeded time t
End, and the angular momentum h that gravity gradient torque accumulates at pitch axis in the mobile process
Manu
The motor-driven θ of satellite pitch axis
mThe used time can be expressed as:
t
end=ω
ymax/a
ymax+θ
m/ω
xmax(11)
In the formula, t
EndBe the motor-driven θ of satellite pitch axis
mThe used time, ω
YmaxBe the maximum angular rate in the satellite pitch axis mobile process, a
YmaxMaximum angular acceleration in the satellite pitch axis mobile process;
Employing is got the method for mobile process gravity gradient torque aviation value and is estimated h
Manu, satellite is in the three axis stabilization state before the unloading, and three suffered gravity gradient torques are 0, motor-driven θ
mAfter the angle, only pitch axis is subjected to the gravity gradient torque effect, and expression formula is:
In the formula,
The expression gravity gradient torque is at the component of body series pitch axis;
Mean gravity gradient moment according to motor-driven front and back can be estimated the moment of momentum that accumulates in the mobile process, and expression formula is:
Step 4, according to h
Un_yWith h
ManuFind the solution satellite and need motor-driven angle θ
m
Step 5, according to h
Un_y, h
ManuWith the determined θ of step 4
m, calculate the time t that needs to keep this angle
Hold:
Need after the unloading motor-drivenly to be the three axis stabilization state because satellite is finished, so satellite is keeping θ
mThe moment of momentum that accumulates during motion should satisfy relation
Therefore can solve satellite and keep θ
mTime t
HoldFor:
Step 6, determine to guarantee that satellite has enough moment of momentums space to carry out motor-driven satellite rotor inertia distribution form:
Its relational expression that specifically needs to satisfy is:
I
z□I
z (16)
In the formula, symbol represents I
xBe far longer than I
z
In the present embodiment, the satellite rotor inertia:
The maximum output torque of pitch axis actuating unit is 0.4Nm, and the lock angle momentum is 50Nms;
Initial parameter: the satellite initial attitude is Φ
0=[0 0 0] °, the initial angular momentum of actuating unit is h
C0=[0 45 0] Nms, satellite moves at circular orbit, and orbit angular velocity is 0.00107rad/s;
h
Un_y=-45Nm, because | h
Un_y|>| 2h
Manu(45 °) |, so satellite needs motor-driven pitching angle theta
m=45 °, according to the ability of actuating unit, getting maximum motor-driven cireular frequency is ω
Ymax=0.005rad/s estimates that the motor-driven used time of satellite is t
End=207s, the moment of momentum that accumulates in the estimation satellite mobile process is h
Manu=1.068Nms, can calculate satellite needs θ
mTime be t
Hold=8517s;
Unloading strategy begins unloading for 200s, and satellite is motor-driven to arrive θ=45 °, at 200s+207s+t
HoldThe start of evolution of=8924s satellite is ° motor-driven to θ=0 ° by θ=45, finishes unloading.This example is used Matlab/Simulink software, adopts the ODE4 algorithm, simulation step length 0.1s.
The present embodiment effect:
(1) do not need to use other pitch axis discharging gears, only pass through the motor-driven of pitch axis, can unload the moment that pitch axis accumulates, saved cost and the space of satellite;
(2) discharging method simple possible, and have certain precision, be fit to the actual satellite application with fast reserve ability;
(3) provided the inertia distribution form that uses the satellite that this method unloads the pitch axis moment of momentum, actual satellite can be in conjunction with the unloading strategy design satellite task of pitch axis and the distribution of inertia, the realization task and unload between balance.
The specific embodiment two: what present embodiment and the specific embodiment one were different is: find the solution the motor-driven required time t of satellite in the step 3
EndDetailed process be:
Step 3 one: the motor-driven form of satellite is: beginning is with the maximum torque accelerated movement, when the satellite rotating speed reaches ω
YmaxAfter stop satellite being applied moment, allow satellite with ω
YmaxCireular frequency carries out normal speed and rolls, and at last the maximum torque of satellite time direction is slowed down, and guarantee that the satellite attitude angle reaches designated value, and attitude angular velocity is 0;
Step 3 two: according to the motor-driven form of satellite, maximum motor-driven angular velocity omega
YmaxAnd the angular acceleration a of satellite maximum
Ymax, the used time of satellite accelerating sections and accelerating sections that can estimate is
t
1=t
end-t
2=ω
ymax/a
ymax (17)
In the formula, t
1Be used time of satellite accelerating sections, t
2The time that reduces speed now for satellite;
Step 3 three: the area that Satellite Angle speed and coordinate axle surround equals motor-driven attitude angle θ
mThereby, can obtain expression formula
t
2=θ
m/ω
ymax (18)
At last, can get expression formula by formula (17) and formula (18)
t
end=ω
ymax/a
ymax+θ
m/ω
ymax (19)
Other step and parameter are identical with the specific embodiment one.
The specific embodiment three: what present embodiment was different with the specific embodiment one or two is: the detailed process of step 4 is:
Step 4 one: make the amplitude of gravity gradient torque get maxim, i.e. θ
m=45 °, calculate satellite by 0 ° of motor-driven angular momentum h that accumulates in 45 ° the process
Manu(45 °), satellite is identical by the moment of momentum that accumulates in 45 ° of motor-driven processes of 0 ° with satellite by the moment of momentum that accumulates in 0 ° of motor-driven process of 45 °, therefore, as motor-driven angle θ
mUnder=45 ° the prerequisite, the moment of momentum summation that accumulates in the satellite mobile process is 2h
Manu(45 °);
Step 4 two: relatively | 2h
Manu(45 °) | with | h
Un_y| size:
If | h
Un_y| 〉=| 2h
Manu(45 °) | then get θ
m=45 °;
If | h
Un_y|<| 2h
Manu(45 °) |, θ then
mShould satisfy equation:
In the formula, h
Manu(θ
m) and t
End(θ
m) expression h
ManuWith t
EndBe θ
mFunction, the nonlinear equation of finding the solution formula (20) namely can solve required motor-driven angle θ
m, satellite does not keep θ in this case
mProcess, only be motor-driven to θ by 0 ° fast
m, motor-driven to 0 ° more at once, finish unloading.Other step and parameter are identical with the specific embodiment one or two.
The specific embodiment four: what present embodiment was different with one of specific embodiment one to three is: the concrete solution procedure of the distribution mode of the described satellite rotor inertia of step 6 is:
Can utilize satellite pitch axis attitude maneuver unloading pitch axis moment of momentum, need the inertia distribution of satellite to satisfy condition:
(1) satellite can provide enough big gravity gradient torque, therefore need satisfy condition | I
z-I
x| 0;
(2) to have enough moment of momentum spaces to carry out motor-driven for satellite, and namely pitch axis motor-driven do not need actuating unit to the saturated direction motion of moment of momentum:
Make a concrete analysis of as follows: if satellite pitch axis actuating unit has moment of momentum at pitch axis
And near saturation value, need the angular momentum h of unloading this moment
Un_y<0, this moment, satellite can only provide moment
(moment of momentum that guarantees the mobile process actuating unit does not increase), this moment, satellite can only be motor-driven to θ
m>0, in order to guarantee t
Hold>0, need to guarantee I according to formula (7)
z<I
xIf in like manner
Can shift onto out equally and need satisfy I
z<I
x
Comprehensively (1) and (2) can obtain being applicable to the distribution of the satellite rotor inertia of the motor-driven unloading pitch axis of pitch axis moment of momentum the I that should satisfy condition
zI
xOther step and parameter are identical with one of specific embodiment one to three.