1. Introduction
Recently, JAXA has initiated the study of a new
type of earth observation satellite which can select
observation areas using an attitude large angle
maneuver actively. Because this kind of satellite
requires a high-torque attitude control system, a control
moment gyro (CMG) is considered as an actuator
candidate. The maximum torque produced by a CMG
can be dozens of times the torque produced by a
reaction wheel. Because the torque vector of CMG
changes according to the gimbal angle, careful
consideration must be given to singularity
configurations. In the singularity configurations, the
compound torque vector from CMGs is restricted to
two dimensions. For that reason, a satellite loses
tri-axial attitude control capability. Many researchers of
CMG singularity avoidance problems have studied this
problem and created various CMG steering logics. We
must verify CMG control logic methods not only
through numerical simulations, but also through
experimentation using CMG hardware to develop
satellite-mount CMGs.
Since 2005, we have studied CMG singularity
avoidance logic in numerical simulations using
Matlab/Simulink (The MathWorks Inc.). Then we
developed CMG Software Evaluation Equipment from
2006. This equipment is now under construction; we
present details of its features in this paper. Furthermore,
we are developing a CMG Test Bed for use as ground
test equipment to perform Dynamic Closed Loop Tests
with CMG EM and Attitude and Orbit Control System
(AOCS) Hardware. Details are described in Chapter 5.
2. Overview of CMG S/W Evaluation
Equipment
An overview of the CMG Software Evaluation
Equipment is presented in Figure 1. We developed an
air bearing that comprises a ball and a saucer to
demonstrate tri-axial free motion like that of a satellite
in orbit. This ball floats in the saucer with air and
rotates freely on three axes. An aluminum square pipe
is attached over the air bearing as a balance. Four
CMGs are mounted on one side of the balance (Fig. 1,
right). The MPU, gyros and battery are mounted in the
other side of the balance (Fig. 1, left). We call them
collectively the floating subsystem.
Figure 1 CMG S/W Evaluation Equipment
We designed the specification of CMG S/W Evaluation
Equipment as shown in Table 1. We assembled this
equipment using commercial off-the-shelf components.
Table 1 CMG Evaluation Equipment Specifications
Radius of Air Bearing 200 mm
CMG Rotor 3000 rpm
CMG Rotor Inertial 1.4 ~ 10-3 [kgEm2]
Gimbal Axis Max Rate 5 [deg/s]
Floating
Subsystem Mass
ca. 70 [kg]
Control Cycle 1 [Hz]
Air Bearing No limit around vertical axis
Before evaluating the CMG S/W, we must
evaluate basic characteristics of the air bearing using
the following evaluation points.
1) The difference between the center of gravity (CG)
of the floating subsystem and the center of rotation
(CR) of the air bearing
2) The value of the air bearing friction torque
The next chapter describes their evaluation and
important results.
3. Air bearing performance validation
3.1. The CG floating subsystem adjustment
The difference between the CR of the air bearing
and the CG of the floating subsystem affects the
tri-axial free motion of the floating subsystem. Torque
produced by gravity around the CR of the air bearing
affects the motion of the floating subsystem, which is
called pendulum motion if the difference is sufficiently
large.
We propose a CG adjustment method that includes
two steps. In the first step, we move CG on the vertical
axis through CR by putting some weight on the floating
subsystem. This process is depicted in Figure 2. We can
estimate the CG position using that level. We put the
level on the balance, as shown in Figure 3.
Center of Rotation
Center of Gravity
Floating Subsystem
Ball
Saucer
Air Air
Vertical Axis through the Center of Rotation
Adju tment
Figure 2 CG Adjustment (STEP 1)
Air Bearing
CMGs
MPU, Gyros
Battery
Balance
Figure 3 Level and weights at Step 2
In the second step, we move the CG close to CR by
adjusting the two weightsf positions as depicted in
Figure 4. We can move CG along the vertical axis
through CR under conditions of
l r L = L . (1)
r L l L
Figure 4 CG Adjustment (STEP 2)
The distance between CR and CG can be
estimated using the period of the pendulum motion of
the floating subsystem. We define the vertical axis and
its origin as shown in Figure 5. Furthermore, we
describe the CR as A y , the CG of weights as m y , the
CG of the floating subsystem as M m y + , and the CG of
the floating subsystem without weights as M y .
Figure 5 Definitions of CR and CG
The pendulum motion can be described as shown
below.
( ) ( ) A M m A I = ? M + m g y ? y +
&& (2)
In Eq. 2, A I is the inertial moment of the floating
subsystem around CR, is the rotating angle of the
floating subsystem, M is the mass of the floating
subsystem without weights, m denotes the mass of
weights, and g indicates the gravitational acceleration.
Using Eq. 2, we can solve the angular frequency of
this pendulum motion
( )
( )2
2
( )
( )
M m A M m
A M m
I M m y y
M m g y y
+ +
+
+ + ?
+ ?
= . (3)
In Eq. 3, M m I + signifies the inertial moment of the
floating subsystem around the CG of the subsystem.
In Eq. (3) M m I + and M m y + , (CG of the floating
subsystem) are unknown values. We set the positions of
weights arbitrarily as m1 y and m2 y then measure the
pendulum angular frequency corresponding to each
case as 1
and 2 to estimate these values.
level
weights
( )
( ( ) ) ( )
( ) ( ) ( ) ??
?
??
?
? + ? + + ? +
? + ? + + ? +
~
??
?
??
?
?
?
?
= ??
?
??
?
m m ac m ac
m m ac m ac
M
M
I my M m y mgy M m gy
I my M m y mgy M m gy
Mg Mg
y Mg
I
2
2
2
2 2
2
1
2
1
2 2
1
2
1
2
2
2
1
2
2
0 1
Using m1 y , m2 y , 1
, 2 and known physical
parameters, we can solve M 0 y (inertial moment of the
floating subsystem without weights around origin) and
M y from Eq. 4.
(4)
We can obtain the CG of the floating subsystem
without weights M y . The position of the weights must
be selected under the constraint of
? = 0 A M +m y y . (5)
Therefore, we can place the weights as shown below
( )
y
y A M
m m
M m y M y
y
+ ? ?
= (6)
We next present the experimental results. The first case
we set m1 y on 0.55 [m]. The motion of the floating
subsystem is shown in Figure 6
-2
-1
0
1
2
3
4
5
00:00
00:08
00:16
00:24
00:32
00:41
00:49
00:57
01:05
01:13
01:21
01:29
01:37
01:45
01:53
02:01
02:10
02:18
02:26
02:34
Time[min.:sec.]
Rate [deg/s]
Angle [deg]
Figure 6 Pendulum motion of the floating subsystem
( 0.55 1 = m y [m])
Using Figure 6, we can calculate the angular
frequency 1
as 0.48 [rad/s]. Then, as in the second
time, we set the position of weights m2 y on 0.31 [m].
The motion of the floating subsystem is depicted in
Figure 7. It is readily apparent that the angular
frequency 2 is about 0.1 [rad/s].
-20
-15
-10
-5
0
5
10
00:00
00:12
00:24
00:36
00:48
01:00
01:12
01:24
01:36
01:48
02:00
02:12
02:24
02:36
02:48
03:00
03:12
03:24
03:36
Time [min:sec]
Rate [deg/s]
Angle [deg]
Figure 7 Pendulum motion of the floating
subsystem ( 0.31 1 = m y [m])
Consequently, we set the weights at 0.3 [m].
3.2. Air bearing friction torque
The air flow rate is an important parameter; it
affects the friction torque between the ball and saucer.
Because the rate is too small, the ball contacts with the
saucer and the torque increases. On the other hand, if
the air flow rate is too high, the air flow between the
ball and the saucer will affect the free motion of the
floating subsystem because the disturbance and the air
flow excites a pneumatic hammer. In this chapter, we
describe a method of setting the air flow and its results.
Figure 8 depicts the air flow system of the CMG
S/W Evaluation Equipment. The air compressor
maintains the air tank pressure automatically as 0.8?1
[MPa]. We set regulator 1 as 0.7 [MPa] and regulator 2
as 0.65 [MPa]. Then we attempted to evaluate the
torque loss by adjusting regulator 3.
Figure 8 Air Flow System
The ball rotates on the saucer on three axes, but we
evaluate the loss torque around the vertical axis as
depicted in Figure 9.
Figure 9 Torque Loss Evaluation
Figure 10 and Figure 11 show the free rotate motion of
the floating subsystem in the case for which the value of
Regulator 3 is 0.027 [MPa]. We applied a shock to the
floating subsystem to create rotation around its vertical
axis.
-6
-5
-4
-3
-2
-1
0
1
00:00
00:26
00:52
01:19
01:45
02:11
02:37
03:03
03:30
03:56
04:22
04:48
05:14
05:41
06:07
06:33
06:59
07:25
07:52
Time [min:sec]
Rate [deg/s]
Figure 10 Rate of the floating subsystem (Regulator
3 = 0.027 [MPa]
-200
-150
-100
-50
0
50
100
150
200
00:00
00:27
00:54
01:22
01:49
02:16
02:43
03:10
03:38
04:05
04:32
04:59
05:26
05:54
06:21
06:48
07:15
07:42
Time [min:sec]
Angle [deg]
Figure 11 Angle of the floating subsystem
(Regulator 3 = 0.027 [MPa])
Figure 12 and Figure 13 show the other case in which
the value of Regulator 3 is 0.027 [MPa].
-14
-12
-10
-8
-6
-4
-2
0
2
00:00
00:57
01:54
02:51
03:48
04:45
05:42
06:39
07:36
08:33
09:30
10:27
11:24
12:21
13:18
14:15
15:12
16:09
Time [min:sec]
Rate [deg/s]
Figure 12 Rate of the floating subsystem (Regulator
3 is 0.042 MPa)
-200
-150
-100
-50
0
50
100
150
200
00:00
00:58
01:56
02:54
03:52
04:50
05:48
06:46
07:44
08:42
09:40
10:38
11:36
12:34
13:32
14:30
15:28
16:26
Time [min:sec]
Angle [deg]
Figure 13 Angle of the floating subsystem
(Regulator 3 is 0.042 MPa)
From Figure 12, we can infer that the loss torque is a
quadratic curve depending on the rate. Consequently,
we can estimate the loss torque as shown below.
Table 2 Loss Torque at the air bearing
Rate [deg/s] Torque Loss [Nm]
5 0.007
4 0.005
3 0.005
2 0.002?0.003
4. Maneuver Experiment using CMG
In Chapter 3, we described the setup of CMG S/W
Evaluation Equipment. Next, we present the
experimental results. We select the maneuver situation
that the floating subsystem rotates 60 [deg] along the
vertical axis. The CMG logic that we have proposed
includes Feed Forward and Feed Back. As depicted in
Figure 14, we roughly rotate the floating subsystem
Vertical Axis
Shock Shock
Shock
using Feed Forward logic. Then we control the floating
subsystem using Feed Back logic. For the Feed
Forward, we use a Bang-Bang Control theory and
steering pair with a CMG gimbal with the same angle.
-10
0
10
20
30
40
50
60
70
0
7
14
21
28
35
42
49
56
63
70
77
84
Time [sec]
Angle [deg]
Figure 14 Experiment result (Angle)
-1
-0.5
0
0.5
1
1.5
0
6
12
18
24
30
36
42
48
54
60
66
72
78
84
Time [sec]
Rate [deg/s]
Figure 15 Experiment result (Rate)
Figure 14 and Figure 15 show that the floating
subsystem was controlled as designed. We can
conclude that the equipment is useful to evaluate CMG
control logic.
5. The CMG Test Bed
The CMG S/W Evaluation Equipment is used to
evaluate only the CMG Control logic. We have just
begun to develop the CMG Test Bed to evaluate not
only S/W but also the H/W. The concept is presented in
Figure 16. An especially ambitious undertaking is to
mount an experimental electronics device in the ball to
eliminate moving limit (roll, pitch, yaw). The ball must
be large. As shown in Figure 17, we produced an
aluminum hemisphere with radius of 2000 [mm].
Figure 16 The CMG Test Bed Concept
Figure 17 Aluminum hemisphere (2000)
Feed Forward
Feed Back