1. Background
AT Satellite
[1] is being developed. This satellite aims at investigating the plasma physics in the aurora zone in order to better understand the spacecraft charging. Also it provides data for the comparison of in-orbit Field-Aligned-Currents with those of ground-based observations. The system-level characteristics of QSAT are shown in Table 1. In order to aIn cecraft attitude must be known and controlled. One function of the Attitude Determination and Control
a
Size
480 x 480 x 300 mm
Mass
< 50 kg
Power
30 W
Attitude Control
3-axis Stabilization
Lifetime
1 year
Orbit
Sun Synchronous
Launch
H-IIA Piggy Back
Launch Date
2009 or Later Table 1 Characteristics of QSAT
Attitude Determination Attitude Sun Sensor Unit(2 units)Pointing Error 1
2
de
oys
e
th
he
Subsequently, the normal-mode attitude
iated. The normal-mode
attit e
nd Kalman-filter estimation
st-Square method uses the
ter measurements and the
Eac three Position
Sens ices (P the sur te of the
satellitefs body. Th t ca hown
in
2. Concept of Attitude System The ADCS must support the following operations:‡@ De-tumbling phase, ‡A Boom extension phase, ‡B Normal-mode phase. In the first phase, the ADCS controls the satellite attituby means of the B-dot control algorithm which emplthe change of the magnetic field as observed within thtumbling satellite. After the rotation rate of the satellitehas been reduced, the boom is extended in the Eardirection to improve the attitude stability by means of tEarthfs gravity-gradient torque.
determination and control is init
ude determination is based on a combination of th
Weighted-Least-Square a
methods. The Weighted-Leae
Sun sensor and magnetom
Kalman-filter combines the resulting angular observations with the gyro rate measurements. The nomal-mode attitude control is performed by the three-axis magnetorquer on the basis of a Proportional-Derivative (PD) control law. 3. Sensors
The sensor and the magnetorquer units that are part of ADCS have been completely integrated and tested at Kyushu University. The specifications of the sensors used in each unit are summarized in Table 2.
h Sun-sensor unit (Fig.4) has
ing Dev
SDfs) on
face pla
e Sunfs ligh
n be sensed as s
Fig. 3.
ctuator The magnetorquer (Fig.7) is manufactured and tested at Kyushu University. The materials and specifications are described in Table 3. The magnetorquer will control the satellite to the desired attitude. Although there are several disturbance torques, the satellitefs residual magnetic field could be the most critical. As a measur
e to reduce the residual magnetic field, twisting the conductive wires will be performed. Fortunately, the on-ground tests confirm that the residual magnetism is sufficiently small. Description
Maximum
Moment Material of Core PB (Ni-Fe) Permalloy Material of
Conductive Core Number of Coils 1200
5
. Attitude Determination The Weighted-Least-Square method is used to
pth
measurements provideint of time. Subsequent
the sensors at a singlhese observations are used
pa
s the inputs for the Kalman-filter as shown in Figure 8.
Sensor Factor Value Sensitivity 320~1100 (nm) Sun Sensor Positioning Error +/- 8.33 ~ 10-2 (mm) Field RangeRate Range+/- 100 (deg/sec)Resolution 0.16 (deg/sec) Gyro Sensor Bias 3.0 %FS*
g. 4 Sun Sensor Unit Table 2 Specifications of Sensors
agneto
FiTable 3 Specifications of Magnetorquer * FS: Fu
3
4.
the
tant.
Th dy
es,
1 Weighted-Least-Square Method In order to construct the measurement equation,transformation between the reference frames is impore transformation from the orbit frame to the boframe can be defined by the 3 Tait-Bryan angl
,,?ƒÆƒÕi
The measurement vector contains the Sun vector S and the magnetic field vector B and is defined as;
(;)T=ySB1
[]00[]BOƒµ??=??ƒµ??yy
where the superscripts B and O designate the ents in the body frame and the orbit frame,
[]ƒµ
matrix in the Tait-Bryan angles ,,?ƒÆƒÕ:
[]ƒµ= coscoscossinsinsinsincosƒÆƒÕƒÆƒÕƒÆ
cossinsinsinsincoscossincoscossincossinsinsinsincossincoscossin?ƒÆƒÕ????? (3) Tait-Bryan angles (,,?ƒÆƒÕ) shown in Figure 9 can be assumed relatively small, so that Eq. (3) becomes: []
1ƒÕƒÆƒÕ????ƒµ=??
W
e
[]BOM=?=yyyx
(,,)T?ƒÆƒÕ=xmtriy:
000[]OOzyOxOOyxSSSSSM
000
yx??????????=???? The measurement equation to be used in the Weighted-Least-Square model, inrement noise w, an be written as: []LSLSM=+yx (7) Finally, the solution of the Weig
?(,,)TLSLSLSLS?ƒÆƒÕ=x
111?([][][])[][]TTLSLMRMMR???=xynoise vector w:
[]{}TRE=wwi
The Kalman-filter estimates the attitude angles and rates based on the Weighted-Least-Square observations of the angles ?LSxp
dynamics model etween successive measurements. The components of state and measurement vector are defined as: LS
123(,,;,,)TLSTherefor man filter
e,the measurement equation of the Kalis:
[]H=+y (12)
w
(,,;,xy?ƒÆƒÕƒÖƒÖ=x
,)T
z,andxyzggg are the gyro rate measurements, and v
is the process noise. Using the kinematic equations[2] and the Euler equation, we obtain the discrete state model: 1[]kkk+
k=ƒ³+xxuƒÕ
ƒÆƒÆ
?R?S?R'?R'?R''??=R''x3 2 1
?S'?S'?Wxyz :
Body Frame RSW :
Orbit Frame
Weighted-Least-Square
Sun Vector Gyro Rates Attitude Angles Observations t = tkFig.
4
the integrated process noise vector q described as:
0
0 0 1
[ ]
1 0
k
a t t
a t
? ƒ¢ ƒ¢ ?
?
ƒ³ =??
0 ƒ¢ ?
2
/ 2
/ 2
/ 2
/ 2
x k
k
x k x z k
y k y z k
z k
t
t
t a t
t a t
t
ƒÑ
ƒÑ ƒÑ
ƒÑ
? ƒ¢ ?
? ?
with the transition matrix []kƒ³[3], the torque vector uk, and
k
100
10000010kkkkkxkatttat???ƒ¢ƒ¢???ƒ¢?ƒ¢?? (14)
001yk??????
22/2yzkkkttuƒÑƒÑƒÑƒÑƒ¢????
22ƒ¢=??ƒ¢+ƒ¢u?? (15)
1[()]()kktkktdƒÑƒÑƒÑ?=ƒ³çqv
?k?x?k+x ation[4ky: ?])kk?
??x (17)
1[][][][][][][]TTkkkkkkkKPHHPHR????=??where []kRis thehe measurement
define[]kP?xpressed in the transition matrix Eq. (14): 1111[][][][]]TkkkkkPP?+????=ƒ³ƒ³+ (19) where, []kQis te covariance matrix of te system noise
defined as []kQE=se defined in Eq.(16).
{}T
The update of the c []([]][]kkkPIRK+=
1The esttes of the attitude angles and rates plus their covariances are obtained by the above algorithm. Attitude ContIn the de controls its attitude b the magnetorquers generating the magnetic moment, w the time variation of the geomagneti, i.e. the B-dot control low[5]. Finally, the
satellite rotates only slowly about its ax magnetic moment generated by the magnetorquekef the magnetorquer is given by:
sgniidBmMdt??=????? (i = x, y, z) (21)
B
rough Earth poin[6]
00()yzxxIIInI??