A magnetically suspended, tetrahedron-shaped antenna pointing system is proposed for use in a multibeam broadcasting satellite system in the future. The structure of this system is presented, along with its design concept and the functional test results which were obtained in a laser tracking system in the laboratory. According to these results, it has been confirmed that the system has many advantages over conventional systems and excellent performance

Ohashi, Toshiro

Ozawa, Tamane

Shingu, Shitta

Sugiura, Hitoshi

Takahara, Kenichi

Takahashi, Hiroshi

English

NASA Technical Reports Server

N88-21478
DEVELOPMENT OF A MAGNETICALLY SUSPENDED, TETRAHEDRON-SHAPED
ANTENNA POINTING SYSTEM
Kenichi Takahara*, Tamane Ozawa*, Hiroshi Takahashi*,
Shitta Shingu*, Toshiro Ohashi**, Hitoshi Sugiura**
ABSTRACT
A magnetically suspended, tetrahedron-shaped antenna pointing system is
proposed for use in a multibeam broadcasting satellite system in the future.
This paper presents the structure of this system, its design concept and the
functional test results which were obtained in a laser tracking system in the
laboratory. According to these results, it has been confirmed that the system
has many advantages over conventional systems and excellent performance.
INTRODUCTION
Satellite broadcasting, which aims at regional services such as high
definition television and digital television, is planned in the near future in
Japan using 22 GHz-band beams. In one of the plans for this broadcasting
system, Japan will be served with 6 precision beams for regional broadcasting
as shown in Fig. 1 (ref. I) .
Whereas the distance between a geostationary satellite and the earth is
about 36000 km, the attitude control error (0.1 degree in conventional
control methods for a satellite stabilized in three axes) corresponds to
about 60 km distance on the earth. In order to realize an effective regional
broadcasting system, this corresponding distance should be less than 6 km on
the earth. Accordingly, the required pointing error for the antenna system is
less than 0.01 degree. An offset Cassegrain antenna consisting of a main
reflector, a sub reflector, and horns will be mounted in the satellite antenna
system shown in Fig. 2. Since the main reflector is fixed to the satellite
body, directly driving this large reflector is almost impossible. Rather, the
small sized sub reflector must be driven by an Antenna Pointing Mechanism
(APM). By driving the sub reflector to compensate for the satellite
perturbation movement, the transmitted and received electric waves will be
correctly directed to Japan in conformity with the RF beacon from the earth
station.
In conventional APMs, lubricated ball bearings or flexible pivots are used
(refs. 2 and 3). On the other hand, an APM using magnetic suspension has
Toshiba Corporation, Kawasaki, Japan
* Research and Development Center, Mechanical Engineering Laboratory
** Komukai Works, Space Programs Division
PRECEDING PACE BLANK NOT FILMED
133
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such advantages as no wear, no friction and no lubrication requirement (ref.
4). For this application, the magnetically suspended, tetrahedron-shaped APM
(T-MAPS: Toshiba type Magnetically Suspended Antenna Pointing System) is
proposed. The important feature of the T-MAPS is the use of a tetrahedral
armature. Because of the simplicity of the tetrahedron, the T-MAPS is able to
drive the armature contactlessly in 6 degrees of freedom and is therefore
clearly superior to other mechanical APMs. The T-MAPS has demonstrated a
0.002 degree pointing accuracy during laboratory tracking tests utilizing a
laser beam.
REQUIREMENT
According to the plan for the satellite broadcasting system, aperture
diameters for the main and sub reflectors are about 3 meters and 0.7 meters
respectively.
In the total antenna system, the pointing error based on RF sensor signals
should be less than 0.01 degree. However the required pointing accuracy for
the T-MAPS, which drives the sub reflector with 0.7 kg.m 2 moment of inertia
and 2.0 kg mass, is 0.002 degree. The pointing ranges required are +1.5
degrees which includes satellite movements and misalignment between the
antennas and the satellite body. Specified power consumption is less than 0.2
W in orbit.
Mechanical life is expected to be virtually infinite. Life limiting items
are limited to electronic devices.
DESIGN CONCEPT
REDUCTION IN NUMBER OF ELECTROMAGNETS
For the previously manufactured 6 degree-of-freedom APM, it was necessary
to use more than 12 electromagnets, because the electromagnets exerted only a
pull force. The mechanism was very complicated, requiring a large number of
displacement sensors and electromagnets. Furthermore, it became too heavy to
be practical in a flight model. In the redesigned APM, the authors carefully
considered a reduction in the number of electromagnets and arrived at the
tetrahedron configuration. The tetrahedron is a most simple geometric shape
and is nonorthogonal. Using these factors, the 12 active electromagnets were
reduced to 9 without any functional loss. Consequently, reduced weight and
increased reliability were obtained.
_lUh_aht¢/
Though an electromagnet generates only a pull force in one direction, a
displacement sensor is available in both plus and minus directions. There-
fore, essentially only 6 sensors are required. Accordingly, even in the case
of damage to any of the three sensors, the T-MAPS maintains normal operation
by changing the sensor signal processing algorithm.
134
Similarly, the minimum number of electromagnets required to maintain
freedom positioning is 7. Therefore, the T-MAPS with 9 electromagnets has
redundant actuation capability.
MECHANISM DESCRIPTION
The T-MAPS is illustrated in Fig. 3. Fig. 4 shows a photograph, illus-
trating the sub reflector fixed to the mechanism. The T-MAPS consists of a
tetrahedral armature fixed to a support shaft, 9 electromagnets, 9 eddy
current displacement sensors, several support members and a base. The sub
reflector will be fixed to the top of the support shaft. Nine electro-
magnet and sensor units are placed so that 3 units are attached to the top
face of the armature, and 6 units attach to 3 side faces. Each electromagnet
consists of a horseshoe-shaped ferromagnetic material with coils wound around
the yoke. The armature is enclosed inside 4 support members, to which each
electromagnet and sensor unit is fixed. The clearance gap between individual
magnet units and the armature corresponds to the pointing range for the
T-MAPS. Consequently, the T-MAPS is simpler than any other mechanical APM.
On the other hand, the T-MAPS requires two special considerations with
regard to its control method, due to adopting the tetrahedron and the electro-
magnet units, as described later.
The specifications for the T-MAPS are shown in Table i.
Since the T-MAPS is a bread board model, a launch lock device, thermal
protection (if needed) and other special equipment suited to space environment
have not been built. However, these technologies are already established, so
the T-MAPS can easily be converted into a flight model with conventional
technologies. Similarly, it is expected that the mechanism and its drive
electronics will be substantially lightened for the flight units.
MAGNETIC SUSPENSION CONTROL SYSTEM
CONTROLLER DESCRIPTION
The magnetic suspension control system is shown in Fig. 5. In this servo
control system, each electromagnet is independently controlled by an indi-
vidual analog PD controller in a local coordinate system with each electro-
magnet. The displacements between the armature and the sensors are detected
by each sensor. These signals are then fed back to compensators. In this
control block diagram, there are two special transformers which need careful
treatment. One is a command transformation matrix, R, in which commands in a
Cartesian coordinate system are transformed into local commands in local
(actuator) coordinates. The other is a position transformation matrix, P, in
which displacement signals of each sensor are transformed into displacement
signals in the local (actuator) coordinates.
135
COMMAND TRANSFORMATION
Six independent commands, which determine the armature position, are
described in vector form by C (Cl, ..., c9) and the displacement vectors
perpendicular to the plane, which a magnetic force operates on, are described
by A(a I, ..., a9) . The relationship between the commands and the displace-
ments is as follows:
A = F 1 (C) (i)
where F1 is a high order vector function which is geometrically obtained from
the armature dimensions, electromagnet arrangement and magnetic force vector
directions. In practice, the command transformation circuits should be as
simple as possible. So applying the linear approximation around the center of
the pointing ranges, the eq. (i) becomes:
AA=R- C (2)
where R is a command transformation matrix, which is obtained from the
mathematical model under the above geometrical conditions.
pOSITION TRANSFORMATION
Similarly to the previous procedure, displacement vectors perpendicular to
the sensor positions are described by S (s I, ..., s9). The relational
equation between C and S is shown as:
S = F 2 (C) (3)
where F 2 is another vector function. Applying the linear approximation to the
eq. (3), the following relationship is obtained.
AS = D- AC (4)
Eliminating AC using eqs. (2) and (4), the instant transformation matrix,
P, with which sensor position displacements can be transformed into operating
force point displacements, will be obtained. However, the transformation
matrix, D, does not have an inverse, because 6A and AS differ from AC in
matrix order.
Therefore, using the method of least squares, the position transformation
matrix P is finally obtained as follows:
A = P- S (5)
p = R. (DT.D)-I.DT (6)
where Dt denotes the transposed matrix for D and (DT-D) -I represents the
inverse matrix for (DT-D) .
The two transformation matrices, R and P, have only constant elements.
Accordingly, the transformation calculation involves simple multiplication of
matrices, and its analog circuits can be easily constructed.
136
PD COMPENSATOR
The transfer function for the PD compensator in the magnetic suspension
system is shown in Fig. 6. This figure indicates the typical phase lead-lag
compensation. The tetrahedral armature can be stably levitated by use of this
PD compensator in all actuator coordinates. In order to suppress excitation
over 1 kHz, the gain would be gradually reduced. It was realized, in
experiments, that the frequency range for phase lead should be adjusted to the
natural frequency of the magnetic suspension system in consideration of
mechanical conditions.
FUNCTIONAL TEST
Functional tests were performed in atmosphere at room temperature, on the
following three items:
(a) Magnetic levitational characteristics.
(b) Frequency response.
(c) Resolution.
(a) Using the controller shown in Fig. 5 and adjusting the compensators to
magnetically levitate the armature fixed to the sub reflector, it was
demonstrated that the system could be stably levitated without a gravity-
compensating support. The armature was magnetically levitated in a nominal
position by applying a 3 A bias current to each of the 3 electromagnets
mounted to the top face of the armature. The magnetic suspension rigidity was
200 N/mm in each of the three lateral directions.
(b) Frequency response for the suspended system was obtained by converting
swept sine signals into commands. Test results are shown in Fig. 7. In the
z-axis case, the armature precisely tracked the command with no phase lag in
the frequency range up to 2 Hz. Similar results were obtained for other axes.
(c) The resolution of the T-MAPS was evaluated by converting micro-rectangular
signals into commands. The test results are shown in Fig. 8. In these
figures, the upper plot is the input command, and the lower plot shows the
signal from the displacement sensor. Jagged signals observed in these figures
are natural noises. These figures show that the translational resolution of
the armature is less than 0.5 um. Similarly to the measurement in Fig. 8, the
rotational motion resolution is less than 5 x 10 -4 degree, as shown in Fig. 9.
LASER TRACKING SYSTEM
TEST EQUIPMENT DESCRIPTION
A system using a laser beam instead of an RF beam (see Fig. i0) was
constructed to confirm the T-MAPS pointing accuracy. This optical system con-
sisted of a laser generator substituted for a feed horn, a tracking mirror for
an antenna, a corner cube reflector for an earth station and a two-dimensional
photo detector for an RF sensor.
137
The corner cube reflector was rotated with some eccentricity. In this
test system, the corner cube reflector rotation corresponded to the satellite
perturbation movement. In an actual situation, the earth station is fixed and
the remaining system components which are mounted on the satellite are moving.
The pointing closed loop, shown in Fig. Ii, consisted of PID controllers,
the magnetic suspension system described already, and the optical system.
This control loop simulated the tracking control for the RF beacon. The
deviation between the photo detector outputs and disturbances corresponded to
the pointing error. In order to obtain high pointing accuracy, an integral
compensator furnished an effective means to obtain the desired characteris-
tics. Ordinarily, integral compensator use not only stabilizes the system,
but also decreases the deviation. The disadvantage, however, is that pointing
response frequency would be low. However, the 2-ton class satellite con-
sidered has a low perturbation motion natural frequency, below 0.I Hz;
therefore integral compensation is sufficiently useful.
As a result, the pointing error, with integral compensation, was virtually
zero.
LASER TRACKING TEST
In this laser tracking system, when the tracking servo was not working, a
circle was drawn on the screen by a laser beam, in accordance with the corner
cube reflector rotation with constant eccentricity. The rotation frequency
was about 0.i Hz, as in the case of the satellite movement. For closed-loop
operation, a circle was drawn on a two-dimensional semiconductor photo
detector.
When the sensed signals from the detector were converted into 0y and 0z
commands, the tracking mirror tracked the corner cube reflector and the devi-
ation signals in the controller became virtually zero. At the same time, the
laser beam on the screen showed no observable motion.
Fig. 12 shows the x and y output signals for'the photo detector. In this
figure, tracking started at the time corresponding to maximum y direction
value. The pointing accuracy for the T-MAPS was confirmed to be as precise as
0.002 degrees.
Test results, including those from the functional test, are shown in
Table 2.
CONCLUSIONS
It has been clearly proved that the newly developed T-MAPS is well adapted
for multi-beam broadcasting satellite systems. The use of magnetic suspension
and a tetrahedral armature offers T-MAPS numerous advantages. These
advantages are realized in a concrete manner, as follows.
(a) High pointing accuracy, 0.002 degree with no wear, no friction, and no
lubrication required.
138
(b) LOw power consumption, less than 0.2 W in orbit except for power
consumption in electronics.
(c) Simple construction and easy manufacturing of electromagnet/displacement
sensor units and support members.
(d) Light weight with a reduction in the number of electromagnets.
(e) Sensor redundancy, with 9 displacement sensors. (Only 6 sensors are
needed.)
(f) Electromagnetic redundancy, with 9 electromagnets. (7 electromagnets are
needed.)
(g) Reliability, with contactless drive and the above mentioned redundancies.
(h) High resolution capability; the minimum sensed displacement was less than
0.5 _m in translation, and 5 x 10 -4 degrees in rotation.
(i) Possibility of changing the rotational center, by adjusting misalignments
between the satellite body and the antennas, in order to increase the
antenna gain.
(j) Flexible adaption to other applications; for example, jitter isolation
mounts, laser communication equipment and other drive mechanisms.
The identification of damaged electromagnets and displacement sensors has
been considered.
Improvement and development will be continued until the flight model is
completed.
REFERENCES
i. S. Yoshimoto, et al., A Trade-Off Study on 22 GHz-Band Multibeam Satellite
Broadcasting Systems, AIAA llth Communication Satellite Systems Conference
(1986)
2. H. Heimerdinger, AN ANTENNA POINTING MECHANISM FOR LARGE REFLECTOR
ANTENNAS, 15th Aerospace Mechanism Symposium, NASA CP-2181 (1981)
3. B. Hubert and P. Brunet, SOFA: SYSTEME D'ORIENTATION FINE D'ANTENNE, 15th
Aerospace Mechanism Symposium, NASA CP-2181 (1981)
4. W. Anderson and S. Joshi, The Annular Suspension and Pointing (ASP) System
for Space Experiments and Predicted Pointing Accuracies, NASA TR R-448
(1975)
BIBLIOGRAPHY
I. D. Cunningham, et al., Control System Design of the Annular Suspension and
Pointing System, J. GUIDANCE AND CONTROL, Vol. 3, No. 1 (1980)
2. S. Iwaki and R. Matsuda, Testing and Investigation of Magnetically
Suspended APM, Proceedings of 15th ISTS, Vol. 1 (1986)
139
Table i SPECIFICATIONS
ITEMS
DEGREES OF FREEDOM
PAYLOAD MOMENT OF INERTIA
PAYLOAD MASS
POINTING RANGE
CHARACTERISTICS
0.7 kg.m 2
2.0 kg
±2 mm
±1.5 deg.
ARMATURE MASS 2.1 kg
TOTAL MASS (WITH SUPPORT MEMBERS) 8.0 kg
TOTAL SIZE (WITHOUT PAYLOAD) []250 x 200 mm
Table 2 PERFORMANCE
(confirmed by laboratory tests)
ITEMS PERFORMANCE
NATURAL FREQUENCY 4 Hz
COIL WATTAGE
ON EARTH
IN ORBIT
(CALCULATION)
RES OLUT ION
TRANSLATION
ROTATION
i0 W
0.2W
0.5 _m
5 x10-4 deg.
POINTING ACCURACY 0.002 deg.
140
FREQUENCY
F1
F2
F3
BEAM
1,4
2,5
:3,6
!
/
I
\
/
/
Figure i Beam Allotment of Regional Broadcasting
for 6 Beams in the Future
RF BEACON
ANTE
POINTING
MECHANISM
(POINTING ACCURACY
+_.0.01 DEGREES )
SUB
SOLAR PADDLE
MAIN REFLECTOR
SATELLITE BODY
(ATTITUDE CONTROL
ACCURACY : + O. l
DEGREES)
Figure 2 Broadcasting Satellite Antenna System
141
F i g u r e  3 Magnet ica l ly  Suspended, Tetrahedron-  
Shaped Antenna P o i n t i n g  Mechanism 
F i g u r e  4 The Mechanism (T-MAPS) 
142 
COMMAND
TRANSFORMAT ION
MATRIX
IR
09
+
........
SATOR MAGNET
1 1
SATOR
2 2
I
: I :
COMPEN- ELECTRO-
SATOR MAGNET
9 9
POS ITIONTRANSFORMATION
MATRIX I
I
Oz, IP
09
DISP.
SENSOR
1
JDISP.
I SENSOR
I 2
I
I ID,sP.
I
I SE_ SORI
ARMATURE
I
I
I
I
I
I
\ ,
I
I
I
I
I
I
I
I
I
, I
I
Figure 5 Control Block Diagram for Magnetic Suspension System
143
40 - 1130
m
Z
<(.9
:30-
2O
I0
0
GAIN
90
"o
a.
i i i
10 100 I k 101(90-
FREQUENCY Hz
Figure 6 PD Compensator Transfer Function
5.0
m 0.0
z -5.0
I
-lO.O
-15-0_.1
|
I I
I 10
6,
W
CO
<
I
13.
-170 -
FREQUENCY Hz
'= " I
I I0
FREQUENCY Hz
Figure 7 Frequency Response with Antenna Attached
144
>E
c_
Z
<
_E
0
0
E
I--
Z
W
_E
W
0
._I
cO
c_
2.4
1.6
0
114
1130
I I I
10 20 30
TIME sec.
A.., AApv.... ,
Vv -
I I I
I0 20 30
TIME sec.
Figure 8 Resolution in z-axis with Antenna Attached
2.5
>
E
a
z
<
_E
_E
0
o
I I I
I0 20 30
TIME sec.
E 24.4
=L
I--
Z
W
_E
W
(.9
<
._I
0.
CO
o 21.20
I I I
I0 20 30
TIME sec.
Figure 9 Resolution in Rotation around x-axis with Antenna Attached
145
CORNER CUBE
REFLECTOR
Y
"_IV_VEMENT
Z
x,_Sz
/_ COORDINATE SYSTEM
y Oy
TRACKING MIRROR
ELECTROMAGNET
DISPLACEMENT
SENSOR
St
COIL'
/i/
TETRAHEDRAL
IMBER ARMATURE
BASE
OPTI CAL SYST
iiiiiini i
FIXED MIRROR
ANTENNA POINTING MECHANISM
SCREEN
LENS
PHOTO I
DETECTORJ = TO PID
Figure i0 Laser Tracking System
146
POINTING ERROR
DISTURBANCE, _ COMPENSATOR I
' SYSTEM
X
Y
OPTICAL
SYSTEM
Figure ii Pointing Closed Loop for Laser Tracking System
>
E
0
X
450
0
'_ _ STA RT TRAC KING
.
I I I
-45"0n 10 2O 3O
TIME sec.
450
I-
I.-
0
-45
L
Figure 12
10 20 30
TIME sec.
Tracking Characteristics
(Two-dimensional photo detector outputs)
147


Development of a magnetically suspended, tetrahedron-shaped antenna pointing system

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