The effects of different elevation and azimuth drive configurations on DSS-13 antenna performance are presented as well as a study of gearbox stiffness and motor inertia. Small motor inertia and rigid gearboxes would improve the pointing accuracy up to a certain limit. The limit is imposed by critical values of gearbox stiffness and motor inertia introduced in the article. The critical values depend on the lowest structural frequency of the rate-loop model. The tracking performance can be improved by raising gearbox stiffness to the critical stiffness and reducing motor inertia to the critical inertia. An azimuth drive configuration with four driven wheels was also investigated. For the four-wheel drive configuration in azimuth, the cross-coupling effects are reduced and wind disturbance rejection properties improved. Pointing is improved substantially in the cross-elevation but is relatively unaffected in the elevation direction. More significant improvements can be achieved through either structural redesign (stiffening the structure) or new control algorithms or control concepts, which would eliminate the effect of flexible deformations on the antenna pointing accuracy. Although the study is performed for the DSS-13 antenna, the results can be extended for other DSN antennas

Gawronski, W.

Mellstrom, J. A.

English

NASA Technical Reports Server

TDA ProgressReport 42-110 August15, 1992
N9 - C
J
Parameter and Configuration Study of the
DSS-13 Antenna Drives
W. Gawronski and J. A. Mellstrorn
GroundAntennasand FacilitiesEngineeringSection
The effects of different elevation and azimuth drive configurations on DSS-13
antenna performance are presented as well as a study of gearbox stiffness and mo-
tor inertia. Small motor inertia and rigid gearboxes would improve the pointing
accuracy up to a certain limit. The limit is imposed by critical values of gearbox
stiffness and motor inertia introduced in the article. The critical values depend
on the lowest structural frequency of the rate-loop model. The tracking perfor-
mance can be improved by raising gearbox stiffness to the critical stiffness and
reducing motor inertia to the critical inertia. An azimuth drive configuration with
four driven wheels was also investigated. For the four-wheel drive configuration
in azimuth, the cross-coupling effects are reduced and wind disturbance rejection
properties improved. Pointing is improved substantially in the cross-elevation but
is relatively unaffected in the elevation direction. More significant improvements
can be achieved through either structural redesign (stiffening the structure) or new
control algorithms or control concepts, which would eliminate the effect of flexible
deformations on the antenna pointing accuracy. Although the study is performed
for the DSS-13 antenna, the results can be extended for other DSN antennas.
I. Introduction
This article investigates the DSS-13 antenna drives and
their effect on antenna pointing accuracy. Each elevation
and azimuth drive consists of a pair of motors and gear-
boxes. The size of a motor and a gearbox is determined
from such criteria as static wind loads, which do not di-
rectly reflect pointing performance. The purpose of this
study was to determine criteria for sizing motors and gear-
boxes so that the pointing accuracy is accounted for. For
control system-design purposes, the motor size is given in
terms of motor inertia, while the gearbox size is given [n
terms of gearbox stiffness. Gearbox inertia is neglected
since it is less than 10 percent of motor inertia when the
gear ratio is taken into account. Different locations of
drives in azimuth and elevation are also investigated. One
drive in elevation and two drives in azimuth are compared
with two smaller drives in elevation and four smaller drives
in azimuth, each at a different location. The effect of this
drive configuration on antenna pointing accuracy is inves-
tigated.
II. Performance Criteria
Tracking performance and wind disturbance rejection
are used to evaluate the pointing performance of motors
and gearboxes in the elevation and azimuth drives. The
231
https://ntrs.nasa.gov/search.jsp?R=19930010243 2020-03-17T08:13:39+00:00Z
rate-loop bandwidth is used as a measure of tracking per-
for mance and rms pointing error due to wind gusts as a
measure of wind disturbance rejection. For the purpose
of this article, the rate-io0p bandwidth is defined as a fre-
quency range from zero up to the lowest lightly damped
mode in the rate-loop transfer function (rate command to
rate output). This definition is used for the PI controller
design, and the lowest lightly damped mode determines
the frequency range of the controller action. A lightly
damped mode is detected as a resonant peak in the plot of
magnitude of the transfer function (Fig. 1). The wider the
open-loop bandwidth is, the better the closed-loop track-
ing performance is. The wind disturbance rejection prop-
erties are evaluated through simulations using the antenna
model developed in [1] and the wind model described in
[21,
=
I
=_
III. Parameter Study
In this section, the effect of motor inertia and gear-
box stiffness on antenna performance is investigated, It
is obvious that a rigid drive would significantly improve a
rigid antenna performance. For a flexible antenna, even a
rigid drive cannot prevent its flexible deformations, thus
the performance improvement through gearbox stiffening
is limited, This is analyzed in detail below.
For the DSS-13 antenna performance evaluation(at a
60-deg elevationposition),the model developed in [I]is
used. The rate-loopmodel isshown in Fig.2, where for
clarityonly the elevationdrive ispresented. The model
consistsof the antenna structure model (21 modes, up
to 10 Hz, including two free-rotatingmodes), gearbox
model, motor armature, and amplifiers.The elevation
and azimuth drive configurationin the rate-loopmodel
isshown in Fig. 3. The nominal motor inertiaisJ,n,_=
0.14N m sec2,(1.236Ibin sec2),and the nonainalgearbox
stiffness is k#, = 1.65 x !0 s N m/tad (1.5x 10? lb in./rad).
The effectof the gearbox stiffnesson the antenna per-
formance isinvestigatedby observing the change of the
imaginary components of the rateloop-poleswith respect
to gearbox stiffness,ee Fig.4. The imaginary partsofthe
rootsrepresentthe structuralnaturalfrequencies.Natural
frequenciesofthe structureand the gearbox are shown in
thisfigure.The loweststructuralfrequency and the gear-
box frequency definethe bmadwidth as shown in Fig. 4.
The bandwidth grows with the gearbox stiffness,up to
the criticalvalue/¢g,= 1.!xI06 N m/rad (10r Ibin./rad).
For
k, > kg° (I)
the trackingperformance remains unchanged. Thus, the
criticalstiffnesskg¢ definesthe minimal stiffnessof a gear_
box, which assuresreasonable trackingproperties.
The bandwidth and the critical stiffness are also seen
in the transfer function plots, Fig. 5. For kg < kg_, the
gearbox resonant peak, which is smaller than the critical
bandwidth, defines the bandwidth (Fig. 5a). For kg >
kgc,the bandwidth changes insignificantly(Fig.5b),since
it isdetermined by the lowest natural frequency of the
structure,
The wind disturbance rejectionpropertieshave been
simulated forz-directionwind (along the elevationaxis),
and y-directionwind (horizontaldirectionorthogonal to
the elevationaxis). The resultsare summarized in Ta-
bles 1 and 2. The tablesshow that high gearbox stiffness
improves wind rejectionpropertiesfor y-directionwind,
while the z-directionwind pointing remains almost un-
changed.
The effect of motor inertia on antenna pointing perfor-
mance is investigated in a similar fashion. The variations
of the rate-loop poles due to motor inertia changes have
been evaluated, and their imaginary parts are plotted in
Fig. 6. The structural natural frequencies and the gearbox
frequency are distinguished in this plot, The lowest natu-
ral frequency of the structure and the gearbox frequency
determine the bandwidth. For
J., (2)
the bandwidth is constant, and decreases for J,n > Jm¢,
deteriorating the antenna tracking properties. Thus,
Jm_ _" 50 lb in sec 2 is the critical value of inertia. The
phenomenon can be observed in the transfer function plots
(elevation rate command to elevation rate), Fig. 7, where
for small inertia (small wizen compared with the critical
one) the bandwidth is constant and for large inertia the
bandwidth narrows.
Tables 1 and 2 summarize wind disturbance rejection
properties. They show that the properties do not improve
with motor inertia decrease below the critical value.
IV. Configuration Study
The existing drive configuration of the DSS-13 antenna
is shown in Fig. 3. It consists of one elevation and two
azimuth drives, A new configuration is compared. The
number of drives in this configuration is doubled, and they
are mounted at different structural locations. Motors are
232
sized so that their total power is the same as in the original
configuration.
Due to the high stiffness of the bullgear, two elevation
drives at different locations of the bullgear have the same
effect as two drives at the same location. Therefore, two
drives are equivalent to one drive with a properly sized
motor (the motor inertia of the two-drive configuration is
38 percent of the motor inertia of the one-drive config-
uration). Hence the two-elevation drive case reduces to
the one-drive parameter study presented previously. The
transfer function plots in Fig. 7 compare one- and two-
elevation drive cases. They show that the bandwidth in:
azimuth and elevation remains the same. Thus, no im-
provement in tracking accuracy is observed. Also, simula-
tions show no improvement in the x-direction wind distur-
bance rejection and moderate improvement in y-direction
wind disturbance rejection (assuming rigid enough gear-
boxes).
Since the stiffness of the alidade is comparable with
the stiffness of gearboxes, the problem of four-azimuth
drives cannot be reduced to an equivalent two-drive prob-
lem. In the four-azimuth-drive configuration, each drive is
mounted on a separate azimuth wheel. The same gear-
box stiffness is assumed, and the motor inertia is 2.6
times smaller than the motor inertia of the two-drive case.
The tracking performance is evaluated through bandwidth
comparison of two- and four-azimuth drives (Fig. 8), and
through step response simulations (Fig. 9). In Fig. 8(a)
the bandwidth in azimuth is slightly larger, and in eleva-
tion it remains the same in the four-drive case, w!file the
cross-transfer function (from elevation to azimuth rate and
from azimuth to elevation rate) shows significant change.
It is confirmed by the closed-loop unit step responses. The
responses to an azimuth step command differ slightly for
two- and four-azimuth drives, and the responses to an el-
evation step command overlap in both cases, while cross-
coupling responses show significant differences between the
four- and two-drive case.
Wind disturbance rejection for the two- and four-
azimuth-drive case is compared in Fig. 10 and Tables 3
and 4. The tables show improvement in z-direction wind
rejection properties in the four-drive case, but additional
stiffening of drives does not improve the wind disturbance
rejection properties.
V. Conclusions
The article has defined criteria for drive comparison
purposes and determines conditions imposed on gearbox
stiffness and motor inertia so that the tracking errors are
minimized and wind disturbance rejection properties are
improved. It showed the critical values of gearbox stiffness
and motor inertia limit tracking performance improve-
ment. The gearbox stiffness should be larger (but not
necessarily much larger) than the critical stiffness, and
the motor inertia should be smaller (but not necessarily
much smaller) than the critical inertia in order to pre-
serve tracking accuracy. The existing (nominal) param-
eters of the DSS-13 antenna satisfy these demands. An
overdesigned drive is a drive with a gearbox stiffness much
larger than the critical one and/or motor inertia much
smaller than the critical one. Overdesigned drives do not
significantly improve the tracking performance, although
an overdesigned gearbox improves wind disturbance rejec.
tion. Also, the four-azimuth-drive configuration does not
improve the tracking performance (bandwidth remains al-
most unchanged), but improves the cross-dynamic prop-
erties and wind disturbance rejection properties for winds
from y-direction.
Improvements due to stiffening gearboxes to downsiz-
ing drive motors, and to multiple drives are non-negligible,
but not dramatic. Thus, for moderate improvement of
performance it is advised to stiffen the gearboxes and
use four-azimuth drives. Significant improvement may be
achieved only through more innovative approaches, such
as antenna structure redesign (more rigid), application of
a new control algorithm (with vibration suppression prop-
erties), or implementation of either new or additional sen-
sors/actuators (e.g., active truss members for structural
vibration damping).
m
235
References
[I] W. Gawronski and J. A. Meltstrom, "Modeling and Simulations of the DSS-13
Antenna Control System," TDA Peog_ss Repor_ ._-106, vol. April-June 1991,
Jet Propulsion Laboratory, Pasadena, California, pp. 205-248, August 15, 1991.
[2] W. Gawronski, B. Bienkiewicz, and R. E. Hill, "Pointing-Error Simulations of
the DSS-13 Antenna Due to Wind Disturbances," TDA Prog_ss Repo_ .t,_-I08,
vol. October-December 1991, Jet Propulsion Laboratory, Pasadena, California,
pp. 109-134, February 15, 1092.
234
Table1.Pointingerrors due to x-direction wind.
Drlveparameters kgn, Jmn lOkgn, Jmn kgn, 0.5Jrnn
Elevation pointing error, mdeg 2.81 2.30 2.89
Cros_-elevstion pointing error, mdeg 1.64 2.01 1.69
X-band loss, dB 0.03 0.03 0.03
Ks-band loss, dB 0.44 0.39 0.46
Table 2. Pointing errors due lo),-dlrection wind.
Drive parameters kgn, J,'nn 10ken, Jrnn kgn, 0.5Jmn
Elevation pointing error, mdeg 3.7'7 2.09 4.10
Cross-elevation pointing error, mdeg 0.55 0.32 0.77
X-band loss, dB 0.04 0.01 0.05
K_band loss, dB 0.60 0.19 0.72
Table 3. Pointing errors due to x-direction wind disturbances for two- and four-azimuth drives.
Drive parametexs 2AZ, kgn 4AZ, kgn 2AZ, lOkgn 4AZ, 10kgn
Elevation pointing error, mdeg 2.81 2.43 2.51
Cross-elevatlon pointing error, mdeg 1.64 0.43 2.08
X-band lo_, dB 0.03 0.02 0.03
K_-baxtd loss, dB 0.44 0.25 0.44
2.40
0.36
0.02
0.24
Table 4. Pointing errors due to y-dlrection wind dlaturbances for two- and four-azimuth drives,
Drive parameters 2AZ, kgn 4AZ, kgn 2AZ, lOkgn 4AZ, lOkgn
Elevation pointing error, mdeg 3.77 3.77 3.51
Cross-elevation pointing error, mdeg 0.55 0.53 0.34
X-band loss, clB 0.04 0.04 0.04
Ka-band loss, dB 0.60 0.60 0.52
3.92
0.50
0.04
0.65
235
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a
z
101
0
tO
ILl
100
z
0
I11
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I 10_1
z
O
10-2
_1
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10 4
LOWEST LIGHTLY
DAMPED MODE -'-_
/
BANDWIDTH
10-2 10-1
i I 1 I i I li z _ 1 z i i i [ll i I l i i i _J
10 0 101 10 2
FREQUENCY, Hz
Fig. 1, Bandwidth of the antenna.
236
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237
ape
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DRIVE 2
epa2
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Fig. 3. Rate-loop modal of the antenna.
o
10 3
W
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101
0
10 0
< 10 -1
NOMINAL STIFFNESS--_,
]RAL FREQUENCIES
BANDWIDTH
RITICAL STIFFNESS
i i ! i : ! i t |
10 3 104 105 10 6 10_ ; 108 10 9 1010 1011
ELEVATION GEARBOX STIFFNESS, Ib in./rad
Fig. 4. Imaginary parts of the rata-loop poles versus elevation gearbox etiffneil.
1012
lO3]
102
(a)
101
100
10_1 .
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(b)
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i 1 1 •
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Fig. 5. Transfer functions: elevation rate output to elevation rate command.
239
ii
105
0
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c5
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0Q.
o.
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w
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 NOM,NAL,NERT,A
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CRIT
i i i i i! i i i
10--4 10-3 10-2 10-1 10 0 101 10 2 10 3 10 4 10 5
ELEVATION MOTOR INERTIA, Ib in. sec 2
Rg. 6. Imaginary parts of the rate-loop poles versus elevation motor inertia.
240
10 2
101
I0o
10-1
10-7
10-8
10 2
101
100
10-1
ELI
10_2
10_3
10-4
IJJ
(a)
BANDWIDTH
10--5
10-8
10-7
10-8
10-2
(b) 100 /
BANDWIDTH "'_' _"_ i/_,i',
BANDWIDTH
10 -1 100 101 10 2
FREQUENCY, Hz
FIg. 7. Trans_rfunctlona: elevation rateoutpullo eleva_on rate command.
241
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(a) - ! : BANDWlD'I;HS: . ; : i Z! i _ i !i _ : " " : :
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10 -6 , _ i i i iiii_ i __ i i iiiii _. i i _ i iii_ _ _ _ , i [
10-2 10-1 10 0 101 10 2
FREQUENCY,Hz
Rg. 8. Banclwldth for two- and four-wheel azimuth drives: (a) azimuth rate to azimuth rate
command and (b) elevation rate to elevation rate command.
nr"
LU
D
0
o
z
U.I
Z
_o
0
0.015
0.010
0.005
0
--,I
uJ -0.005
(a)
2-WHEELDRIVE
--- 4-WHEELDRIVE
-0.015 L _ _ , '
0 2 4 6 8 10 12 14 16 18 20
TIME, sec
Fig. 9. Step responses for two- and four-wheel azimuth drives: (e) azimuth encoder to azimuth
command; (b) elevation encoder to azimuth command; (c) elevation encoder to elevation
commend; and (d) azimuth encoder to elevation command.
243
rr
111
13
O
O
Z
Z
o_
W
..J
o
x
(c)
LU
n-
LU
0
0
(D
Z
ILl
2- AND4-WHEEL DRIVES
! :
i :
' _6 ' 1=80 2 4 6 8 I0 12 14 1 20
TIME, sec
Fig. 9 (contd).
244
3.0
2.5
2.0
£3
z
rn
1.505
09
S
en •
1.0
0
Z
05
o
_1
113
"o
0.5
0
5.0
4.5
4.0
3.5
3.0
2.5
2,0
1.5
1.0
0.5
0
0
(a)
2-WHEEL DRIVE
-- - 4-WHEEL DRIVE
I
2- AND 4-WHEEL
10 15 20 25 30 35
WIND SPEED. mph
4O 45 5O
Fig. 10. Ka-band decibel loss due to wind gusts: (a)x-direction wind end (b)y-direction wind.
245


Parameter and configuration study of the DSS-13 antenna drives

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