5
h
^r
IV. Spacecraft Control
GUIDANCE AND CONTROL DIVISION
A. Advanced Horizon Scon Platform, H. H. Horiuchi
1. Introduction
The horizon scanner, mounted on the servo-controlled
platform of a spacecraft, senses the local vertical of the
target planet in view. The angle between the optical axis
of the platform and the local veitical constitutes an error
signal to rotate the platform toward the local vertical
The scan platform consists of a planet sensor, actuator
electronics, a gear train and the spacecraft dynamics
(Fig. 1). The spacecraft dynamics includes the eflFect of
platform supporting boom and the motor mounting struc-
ture. The content of this study includes a survey of basic
performance requirements, system analysis, computer
simulation, breadboard design and testing. The advanced
planet sensor is being developer!, and should be available
in fiscal 1968. The planet sensor was simulated with ana-
log circuits.
2. Survey of Syttom Roquiromonts
The basic system requirements have been summarized
below from the past advanced studies, the technical re-
ports, and the requirements for the current project. The
following specifications have been assumed:
(1) The minimum slewing rate of the platform is
1 deg/sec.
N67-i9i^5
(2) The platform tracks the local vertical of the target
planet with an accuracy of ±0.5 deg.
(3) The platform follows the velocity input up to 0.2
deg/sec.
(4) The planet angular diameter varies from 4 to 60 deg.
SCAN PLATFORM
A'2 BOOM DYNAMICS
GEAR TRAIN
INPUT
MOTOR
MOTOR MOUNTING
STRUCTURE
DYNAMICS
SPACECRAFT
Fig. 1 . Scon ploff orm tysttm block di;igram
JPL SPACE PJtOGilAMS SUMMARY 37-44, VOL. IV
37
INPUT
O— -
SENSOR
/
/
i4r, 5
A'2 r-
5(5r^+i)
SENSOR COMPENSATION AMPLIFIER
DEAOBAND
FEEDBACK
MOTOR
GEAR
TRAIN
BACKLASH
Fig. 2. Platform functional block diagram
82 ^9
5^ + — 5+ —
^2 ^Z
BOOM DYNAMICS
— ^- OUTPUT
(5) The platform jitter \% below 500 ^rad in track modes
of operation,
3. System Description
The system functional block diagram i% shown in Fig. 2.
The planet sensor is shown as the summing point of the
feedback system. The pulse-width mc 'ulated error signal
from the sensor is integrated, amplified and drives the
servo system. The boom structural dynamics is shown as a
second-order resonance in the feedback loop.
The sensor consists of two halves of semicircular scan-
ning device, each of which has a view angle of 60 deg, and
is made of discrete thermopile elements. The maximum
sensor resolution then is determined by the angular sepa-
ration between the two consecutive elements. As an elec-
tronic sweep scans each element at 10 cps, the illuminated
element (planet in view) produces a pulse.
The first pulse produced in each sweep closes a sum-
ming gate, which in turn produces a step output This
step output remains constant until the end of each sweep.
The step outputs from the two sensors are summed in
the summing amplifier *o produce a pulse whose width is
proportional to the diff'Tence between the two step out-
puts. Hence the pulse width is proportional to the error
angle between the platform and the planet local vertical.
The sensor design approach with the discrete thermo-
pile elements seems to provide several advantages over
t!ie linear optical sensors. With this approach, the sensor
gain may be kept constant over the wide range of inpul
light intensity and also virtually eliminates the thermal
drift from the sensor.
4. System Analysis
The Bode diagram of the system shows two struc-
tural resonances (Fig. 3). The lower frequency resonance
(15 rad/sec, damping factor of 0.07) represents the boom
dynamics, and the higher frequency resonance (94 rad/sec,
damping fa'^tor of 0.01) represents the motor base struc-
tural dynamics.
The preliminary system stability analysis was per-
formed using a modified Bode diagram in which the
normal loop gain was adjusted to accommodate the gain
40
20-
a -20
t
2! -40
I
-60
-80
-KK)
-FILTER BREAK
I / FREQUENCY
MOTOR BREAK
FREQUENCY
MOTOR
MOUNT
RESONANCE
10'* I0-' 10®
FREQUENCY, cps
Fig. 3. Scon plotform iytt^m led« plot
lO*
38
»l SMCE PffOGtAMS IMIAIAMCi 37-44, VOL IV
variation as a function of signal level. The motor break
frequency was approximately 4 cps, and the filter break
frequency was set for 0.5 cps.
a. Initial simulation. The control system shown in Fig. 2
was simulated for dynamic response using the DSL-90
program on the IBM 7094 digital computer. In this simula-
tion, stiction was not included assuming that the motor
delivers sufficient torque to the load.
A permissible range of backlash was investigated to
meet the noise requirenients. The eflFect of the backlash
to the system noise is summarized in Table 1. The noise
level is proportional to the amount of backlash introduced
in the range of backlash considered, and the frequency of
oscillation is the boom resonant frequency.
Table 1 . Effect of backlash to scan system noise
Backlosh. rad
±0.0087
±0.0017
±0.00017
+ 0.000017
Noise, rod
±0.02
-+- 0.004
±0.00035
-+- 0.00004
Noise frequency,
rod/sec
15
15
15
}5
1
Base dynamics transfer function.
and T is the applied torque. The values of the constants,
i.e., the ^'s, ft\, ys and 8*s, are determined by the fs, Ks
and B*s in the diagram. Because of a comparatively large
assumed inertia of the spacecraft (170 slug-ft-), the effect
of the spacecraft motion was neglected in the analysis.
By using the RTL-90 program on the IBM 7094 digital
computer, the system root-locus plots were obtained to
study the transient and stability characteristics of the
system.
5. System Test
a. Initial breadboard test. The primary purpose of this
breadboard test was to determine the maximum jitter rate
during the slew a!)d null mode when the control system
is driven by a pulse-width modulated error signal. The test
circuit is shown in Fig. 5. It was found that the tachometer
feedback alone was not sufficient to smooth out the input
pulses through the motor due to a relatively small motor
time constant.
I
The tracking capability of the system was investigated
by applying a ramp input of 0.0034 rad/sec. The system
responds to the ramp input with the average error of
0.0024 rad and with the maximum oscillating amplitude
of ±:100 jLtrad. The frequency of oscillation is the boom
resonant frequency.
b. System analysis with structural dynamics. The struc-
tural dynamics was included in the scan platform control
system simulation. The modified section is shown in Fig. 4.
The stiction, rolling friction, and backlash are also in-
cluded in the diagram. The boom dynamics block is placed
in series with the feedback loop, while the base dynamics
block is placed in parallel with the loop.
The structural dynamics was investigated by using a
model which consists of three inertial wheels constrained
by springs and dash pots (Fig. 1). The transfer runctions
of the dynamics blocks were found as follows:
Boom dyruimicM tramfer function^
T \S^ + PtS + pj S»
A filter stage was provided for this purpose. The jitter
amplitude referred to the platform was approximately
±160 /Arad/sec at the motor threshold voltage. This indi-
cated that it might be possible to achieve a low jitter
operal-on using pulsewidth modulation.
b. Transient test on the breadboard. The characteristics
of the planet sensor were simulated using analog circuits
as shown in Fig. 6. The planet sensor consists of a saw-
tooth generator, two Schmitt triggers and a summing
amplifier.
The error signal is generated by manually rotating the
potentiometer shaft for a desired error angle. The unbal-
ance in the potentiometer position causes the Schmitt
triggers to trigger at a different input voltage level, thus
generating the error signal. The servo loop will move the
potentiometer shaft back to its original position. The
sensor characteristics as a function of potentiometer posi-
tion are shown in Fig. 7. In this model, the sensor gain
is approximately 10 V/deg within d:l deg range horn the
null. The transient error response of the system was ob-
served at test point 7T-1. The boom structural resonance
was simulate! by a second-order resonant circuit. The
general patterns of the transient response are shown in
Fig. 8.
jn sMCf nooMMs summahy 37-44, vol. fV
39
m.
AMPLIFIER
MOTOR
r
1
FRtCTION
BOOM
DYNAMICS
FEEDBACK
<x
BASE
DYNAMICS
DISTURBANCE
.rr
Fig. 4. Sean platform modd with dynamics
W
SCHMITT
TRIGGERS
ULTER DEAD9AN0
AMPLIFIER
Fig. 6. Scon platform system simulation
UJ
Q.
-2
/
A
MOTOR
SATURATION
LEVEL. 10 V
EXPANDED VIEW
OF DEADBAND
12 3
ERROR ANGLE, deg
PULSE
GENERATOR
400 cp« OSCILLATOR
• f REFERENCE
INTEGRATOR
MODULATOR
POWER
AMPUFIER
T\
W'NDING
TACHOMETER
OUTPUT
or*
MOTOR
Fig. 5. Puisowidth moduiotion tost circuit
40
/-
c "^
3U
O 9A
/
I
rt lA
A
/lOTOR S
LEVEL.
ATURATI
ON
"2 lU
/
tOv
/
/
t
-20
/
-5
5 K) 15 20 29 30
ERROR ANGLE, deg
Fig. 7. ChoroctorisNcs of simukitod oionot sonsor
40
in »ACB riOGIAAIS SUmUMMY 91-44, VOL IV
-
o
q:
tt:
UJ
.DEADBAND,
iO 25 deq
r
WITHOUT BOOM
RESONANCE
AMPLIFIER
SATURATION
LEVEL, -10 V
WITH SOOM
RL'.ONANCE
TIME
SYSTEM TRANSIENT RESPONSE
. ^
Z' -tif-ft:
ii. '
>
30
Uj" 20
Q
10
RESONANCE SIMULATOR
CHARACTERISTICS
Fig. 8. Platform breadboard test results
The major souice of error (other than stiction) in point-
ing accuracy comes Vom the planet sensor itself. The
selected deadband o* ±0.25 deg corresponds to ±2.5
volts at the ii^ut to the servo-amplifier. Therefore, all
drift and offset voltages referred to the amplifier input
(±8.5 mv maximum) becomes negligible. The circuit
design ivas considerably simplified by using integratet^
circuit amplifiers.
B. Calibration Procedure Us^d in the Attitude
Control Nozzle Thrust Measuring Technique,
J. 0. F^n^ra
The intent of this report is to update a previous report
entitletl "Attitude Control Thrust-Nozzle Measuring Tech-
niques" by J. C. Randall (SPS 37-39, Vol. IV, pp. 4(M2).
The cantilever beam and strain gage appkt)ach, as detailed
in Randall's report, has been attempted. A flattened rod
immersed in a pool of mercury has been added behind
the valve nozzle combination in order that the amount
of damping in the system can be easily varied (see Fig. 9).
In using the strain gage approadi, considerable damping
IS required to measure steady-state thrust levels; a mini-
mum ount uf damping is required in determining the
impulsi. bit as outlined in Randall's report.
Fig. 9. Micrometer mounted in front of thrust nozzle
The strain gage approach presented the following three
problems:
(1) The gages weve found to be very sensitive to 60-
cycle noise and vibrations from the mechanical
pump used in the vacuum station.
(2) The gages were found to be sensitive to various
temperature and pressure changes in and out of the
vacuum jar which resulted in a zero shift, making
any calibration procedure diiBcuIt.
(3) The gages were found to be slightly sensitive to the
flow of nitrogen gas in the cantilever beam feed
tube.
Because o' the problems encountered with the strain
gages, a photoelectric pickotf was installed. A square-
edged nlate was mounted to the thruster body such that
motion of *he beam results in a varying amount of light
passing thiMUgh a slot immediately above the photo-
sensitive cell. This technique appears to work very well
and is insensitive to the problems encountered with the
strain gage. The photoelectric pickoff that is currently
being used, however, is not shown in either Figs. 9 or 10.
We are presently calibr^^ting the system using the fol-
lowing method: By mounting a micrometer to the frame
immediately in f ont of the nozzle cone (see Fig. ^J) and
by advancing the micrometer in known increment's and
recording the ^'oltage output of the photocell, a curve of
thruster displaceirent versus output voltage can be gen-
erated. A stainless stc^I ball is then suspended in front
of the nozzle from a mici onieter attachment. This is shown
in Figs. 10, 11. 1 r ^hxm th^ microui^ier is moved a distance
X«, the beam, in equilibrium \\ith the applied r»rce, will
JH SMCf rtOOMMS SUMMAHY 37-44, VOi. tV
41
I *
^ \
■ ¥
^ % _ .^
rw
r^\
Fig. 10. Sf«el ball suspended in front of thrust nozzft
deflect an amount Xh\ Xj^ is determin(-d from the volt-
age output versus thn^ster displacement curve described
above. A study of Fig. 11 indicates that:
f = (m)itane)=-^p^ (1)
m ~ weight of ball, gm
x~ \Xm "Xt|, in.
I = length of wire plus one-half
the diame* T of the ball, in.
/ " applied force, gm.
Since / is from 2 to 3 in. and x is on the order of 0.001 to
0.003 in., / can be accurately determined by a simplifica-
tion of Eq. (1):
/-
M(x)
(0
NEW POSITION
ZFPO POSITION
THRUSTER
(2)
Fig. 11. B«c<n diftploc«m«nt calibration proccduro
for moasuring nozzle thrust
Using Eq. (2) and the curve mentioned above, a curve
can be plotted of the photocell voltage output versus the
applied force (//, which is equivalent to the force pro-
duced by a firing of the thruster. With this method, the
thrust level can be very accurately determined. The im-
pulse bit is determined a< outlined in Randall's report
(SPS 37-39, Vol. IV, pp. 40-42).
When this cahbration procedure is perfected, a test
program will begin using Mariner type thrusters to verif>
the results of a computer pro-am described in the SPS
report, "Parametric Analysis for Steady-State Performance
of AaituJ*? Control Thrusters," by J. D. Ferrer** and
P. M. McKown (SPS 37-42, Vol IV, pp. 47^8).
42
in SMCE mOGRAMS SUMMARY 37*44, VOL. IV
C. Generalized Cruise Gas Requirement Study,
G. Paine
1. Introduction
The aim of this study is to provide an estimate of the
cruise gas requirement for a general spacecraft as a func-
tion of spacecraft weiglit. If a setter estimate is required,
then the craft configuration must be specified since cruise
gas consumption depends heavily on botli the spacecraft
weight and configuration. This study can be used m an
evaluation of the tradeoffs between various gas systems
as well as of the tradeoffs between communication rates
and powers and antenna pointing accuracy.
The general spacecraft chosen has a cylindrical gf^om-
etry (Fig. 12), a uniform mass density, and no solar panels
The addition of solar panels can be allowed for easily;
however, their addition at this stage complicates the
design unnecessarily as their size depends on the power
requirements and the mission trajectory.
There are several types of gas attitude control cysi. ms
that can be considered: cold gas, warmed ^as, and hot
gas. The use of a dual thrust level system ran save con-
siderable gas in a large spacecraft by providing a low Igp
during cruise and a high I^^ during spacecraft maneuvers.
The use of heaters in a cold gas system fulfills these
requirements as the heaters may be turned on for space-
craft maneuvers and left off during cruise. Such a system
would be relatively simple and fail-safe.
The attitude control system analyzed is a cold gas sys-
tem in which the jets are sized for some angular accel-
eration constant. The constant is determined by the
maximum allowable initial acquisition time and the mid-
course maneuver times. A dual level system was not ana-
lyzed as they are not employed on current interplanetary
0' WEIGHT DENSITY
/? =
spaciXTift. Likewise the minimum on-time for a jet was
held at current levels, rather than being reduced to lower
the cruise gas rt^quirements in a large spacecraft.
The disturbance torques acting on the spacecraft have
been lumped into two classes: In the first are those result-
ing from valve leakage. The second includes all other
sources, such as imbalanced solar pressure and gravity
gradients. The second must be estimated for any particu-
lar spacecraft configuration and mission.
2. Conclusions
The cRiise gas consumption for a 200-day mission is
displayed in Fig. 13. These results include triple redun-
dancy but no tankage factor. The parameters not appear-
ing on the figure are from Mariner IV. The results can be
scaled directly for missions lasting other than 200 days.
The curve for zero disturbance torque limit cycie gas
consumption can be scaled inversely to the limit cycle
deadband. Less gas would be required with the addition
of solar panels and with the attitude control jets located
at their extremities since both the constant disturbance
torque and the zero disturbance torque gas consumptions
are inversely proportional to the jet lever arm.
It is apparent that for the spacecraft geometry and
other parameters assumed that cruise gas consumption
)02
10'
^. 6
I '
uj
6
4
2
I0-'
/
y
/
/
/
/
/
CONSTANT DISTURBANCE
SUM OF ALL THREE AXI
1 ...
TORQl
ES-^
JE.
/
/
^0
dyn
e-
en
1
/f
/
9
/
^^
^0
*-,
^d
/ /
/
/
,
-
"S
u
/
/ w
ORST-CASE
VALVE
LEAKAGE—!
..^^
^
-^
.^
./
/ ^
/
^
/
^
S^
y^
/
^
A
V
r
^
.. 6 cc/hr
L ' '
/
y
5 cc/hr J
/ /
\
^'
/
X
"^ ZERO DISTURBANCE
»/
»'4
>
mr
/
/
A
1 1 1
*— TORQUE, *=l TO >t«4
1
/
10* 2 4 6 10*
4 6 10^
4 6 10*
Fig* 12. Spoc^craft whost configuration
\% o hollow cylindor
SPACECRAFT WEIGHT, lb
Fig. 13. Cruiso gos consumption during
200-doy mitiion
in SMCf UtOQUAm SUMHHAItY 37-44, VOL IV
43
depends more on disturbance torque level than it does
on the zero disturbance torque situation for spacecraft
weighing less than about 2000 lb.
If the non-leakage disturbance torques are unspecified,
it is reasonable in the light of the disturbance torques
encountered on Manners II and IV to allow 2.0 lb of
gas for cruise purposes for spacecraft weighing less than
2000 lb. This is equivalent to about a 75 dyne-cm distur-
bance torque on a 500-^b craft without solar panels or
about 225 dyne-cm on a 500-lb cratt with them. On a
200-day mission, an additional 0.75 lb of gas will cover
the worst-case valve leakage.
For missions where either the spacecraft is heavy or
where the disturbance torques are expected to be small,
the zero disturbance torque gas -^onsumption will be the
dominating factor and the gas consumption will vary
according to spacecraft weight raised to the 4/3 power.
3. Ga$ Consumption
As the spacecraft studied is not equipped with solar
vanes which passively control the spacecraft, the gas con-
sumption will depend directly on the disturbing torque.
For a constant disturbing torque, Fig. 14 shows the rela-
tionship between the magnitude of the torque and the
weight of the gas consumed for a spacecraft which oscil-
lates inside a symmetrical deadband.
To the left of ro, the marginal torque in Fig. 14, the
spacecraft oscillates and touches both sides of the dead-
band. To the right, the spacecraft touches only one side
of the deadband.
If the maximum (worst-case) disturbance torque allowed
is greater than ri, then the gas consumption is determined
totally by the disturbance torque and the mission dura-
tion. If the maximum disturbance torque is less than tu
then the maximum gas consumption will occur with no
disturbance torque present, and the gas consumption
depends on a variety of vehicle parameters.
4. Disturbance Torques
A number of disturbances act on the spacecraft. They
include externally caused torques such as those arising
from solar pressure and gravity as well as internally gen-
erated ones from valve and piping gas leakage, as well as
other sources.
Each disturbance torque can be related to a wide range
of parameters. Here the parameters which depend on
vehicle weight are called out exphcitly while the others
are held constant. So, for instance, the solar torques will
be taken as proportional to vehicle area, or vehicle weight
raised to the 2/3 power, neglecting the many other factors
influencing solar torques. Valve leakage, which can pro-
duce a torque is taken as a worst-case constant, even
though it varies from valve firing to valve firing. The
same gas consumption will arise whether all twelve valves
are leaking or whether only six are leaking and the other
six must be fired to produce a restoring torque.
The gas weights required to counterbalance each of
these is shown in Fig. 15. The constant disturbing torque
^^
X
UJ
5
ZERO DISTURBANCE
TORQUE LIMIT CYCLE
DISTURBANCE TORQUE
PROPORTIONAL TO AREA
DISTURBANCE TORQUE
PROPORTIONAL TO
JET LEVER ARM
CONSTANT DISTURBANCE
TORQUE
DISTURBANCE TORQUE AMPLITUDE
Fig. 14. Mats of consumod got vorius
disturbonco torquos
SPACECRAFT WEIGHT
Fig. 15. Cruiso gos consumpHon vortus spococraft
wtiglit ond disturbonco torquo typ«
Jn SMCf FROGMMS SUMMAItY 97^44, VOL IV
r/
I"
and the special case of zero disturbing torque gas con-
sumptions are also included. In each case the counter-
balancing torque is proportional to the lever arm, or
spacecraft weight raised to the 1/3 power. Thus in the
example of an area-dependrnt torque, the gas required
increases only as the 1/3 power of the spacecraft weight
although the disturbance increases by the 2/3 power.
From Fig. 15 it can be seen that there are two distinct
regions: one where the disturbance torques control the
gas consumption, and another where the zero di^^turbance
torque gas consumption dominates. The weight of the gas
required depends in the former region on the predominant
disturbance and will vary with spacecraft weight accord-
ing to the nature of the largest disturbance. In the former
region, the worst worst-case valve leakage gas consump-
tion adds directly to the other gas weights.
5. Mathematics of Gas Consumption
As has been shown in many other places (Ee*^* 1 3
and 4)^ the weight of the gas consumed depends on :». . e.al
simple formulae,— making no allowances for either the
triple gas redundancy or tankage weight factors. The
formulae below give the gas consumption for each axis:
The terminology is listed in Table 2.
a. Zero disturbance torque gas consumption:
I(aAt)H„,
Table 2. Nomenclature
Wo =
4LI,,0oB
b. Marginal disturbance torque gas consumption: Mar-
ginal torque is the smallest torque for which the attitude
control system touches only one side of the deadband.
Wo =
_ I(<xAt)H„
c. Torque balance gas consumption:
Wo =
u
ep
d* Largest disturbatuse torque wUh gas consumption
equal to zero disturbance torque gas mnsumptiow
4$,
JDB
'Also by H. K. Bouvier: A Field Guide to LimU Cycles, and
Mariner TV Disturbance Torques, JPL-IOM 344*543.
jn SMCI nOOHAm summary 37*44, VOL. IV
Wo
gas weight
I
moment of inertia of spacecraft
L
gas jet lever arm
a
acceleration constant
M
minimum on time
tm
mission time
h.
specific impulse
OpB
deadband
To
marginal torque
Tl
unbalance torque resulting in the
sumption as no disturbing torque
same gas con-
P
spacecraft weight density
k
spacecraft length to radius ratio
g
gravity
We
spacecraft weight
R
spacecraft radius
I
spacecraft length
TD
disturbance torque
6. General Spacecraft Configuration
The general spacecraft was chosen to be a hollow cylin-
der (Fig. 12) with a uniform mass density. The gas jets
are placed so that the roll jets have a lever arm (L) equal
to the radius (R), and the pitch and yaw jets so that they
have a lever arm equal to the greater of the radius (R) or
half the vehicle length (/). In the following functions, k is
the ratio of spacecraft length to radius, and / is the inertia.
a. Pitch and yaw axis functior^.
ForaUJfc
3g U "^12/ 3g Vl6^12/
or
, Wc(4WcY'/S fc'X
^""4gV3W \4"^3;
45
Forfc^^2, L ^ i?, and
I Spkir
L" 16g
For it > 2, L = //2, and
L~ 8g Wfc-/ \4 3y 2% ^4"^ 3/
h. Roll axis function.
/-
2WrR' W,R' 5\V,R2
3g
24g
8g
For anv /c, L = R, and
I _ IS^fcTT / 4W^Y '^ ^ 5W,R
L ~ 32g VSiSfcTr/ "' 8g
These factors, which enter directly into the zero dis-
turbance torque gas consumption, are plotted in Fig. 16
for some typical parameters: k = 1 and /S ~ 15 Ih/iV On
Fig. 16, the actual (I/L) values are plotted for Mariner IV
and for a proposed Venus- Mercury 1973 craft. The diflFer-
ences are explained by the solar panels on these two craft.
While the solar panels increase the inertia per unit space-
craft weight significantly, they increase the jet moment
arm even more rapidly, giving rise to a net reduction
in i/L.
7. Gas Weights and Results
Even with the concepts stated earlier, more assump-
tions are necessary before the gas requirements can be
set down explicitly. Some of these concern the vehicle
geometry, others concern the jet size and minimum
on-time, while still others relate the disturbances and
deadbands of the three axes.
The gas weight shown is for three-axes stabilization
and includes the triple redtmdancy factor but does not
allow for tankage. The gas weights should be multiplied
by 2.6 to obtain gas weight plus variable tankage weight.
10*
6
4
105
s
4
10*
6
4
10'
6
4
lOO
,
^ A
r
/
/
roll/^
"^ITCH,
A
4-
YAW
/
//
k = 1
J
^
/
/
/
/
/
/
V
/
T
/ .
1
/ /
A
/
/
/
7
^ \ 1 1 1 1
^ VENUS -MERCURY '73
/
y^ROLL
/III
1 1 !
\ MARINER rST
/ /
1 1
^ 1
/
/
X Kl H-M, TAW J ^
/,
/
/
/
I02 2 4 6 10^ 2 4 6 10*
SPACECRAFT WEIGHT, lb
4 6 10'
Fig. 16. Ratio of inertia to lever arm length
versus spacecraft weight
The gas weight factor to account for half-system perfor-
mance is L5 rather than 3 in the case of valve leakage.
In Fig. 13, gas consumption is shown as a function of
spacecraft weight for A: = 1 to fc = 4, three levels of con-
stant disturbance torque, two levels of gas leakage, and
two deadband widths.
In Fig. 13 the following additional constants, taken from
Mariner IV (see Ref. 4), are assumed:
Odb = same for all three axes
a = 0.45 mr/sec*
M = 0.02 sec
hp " 60 sec
1.1 = 200 days
i8 = 15 lb/ft>
46
jn sPACff nooMm suiMAuir 97-44, vol iv
References
1. Project Report 4290, Barnes Engineering Co., 1966.
2. Nicklas, J. C, and Vivian, H. C, Derived-Rate Increment Stabilization, TR 32-69,
Jet Propulsion Laboratory, Pasadena, Calif., July 31, 1961.
3. Turk, W., Ranger Block III Attitude Control System, TR 32-663, Jet Propulsion
Laboratory, Pasadena, Calif., Nov. 15, 1964.
4. Mariner-Mars 1964 Project Report: Mission and Spacecraft Development, Vol. I,
TR 32-740, Jet Propulsion Laboratory, Pasadena, Calif., Mar. 1, 1965.
m SMCC PROORAMS SUMMAItY 37-44, VOL IV 47
