The elevation and azimuth servo rate loops at the 34-m High Efficiency Deep Space Station 15 (DSS 15) are described. Time and frequency response performance criteria were measured. The results are compared to theoretically deduced performance criteria. Unexpected anomalies in the frequency response are observed and identified

Ahlstrom, H. G.

Cox, D. G.

Engel, J. H.

Nickerson, J. A.

Smith, H. K.

English

NASA Technical Reports Server

TDA Progress Repm? 42-87 
Antenna Servo Control System Characterization: Rate Loop 
Analysis for 34-m Antenna at DSS 15 
J. A. Nickerson, D. G. Cox, H. K. Smith, J. H. Engel, and H. G. Ahlstrom 
G r o u n d  A n t e n n a  a n d  Faci l i t ies Engineer ing Sec t ion  
This report characterizes the elevation and azimuth servo rate loops at the 34-m High 
Efficiency Deep Space Station 15 (DSS IS). Time and frequency response perfonnance 
criteria were measured. The results are compared to theoretically deduced performance 
criteria. Unexpected anomdies in the frequency response are observed and identified. 
1. Introduction 
This report is the first in a series of reports aimed at study- 
ing and characterizing antenna drive control system compo- 
nents of the Deep Space Network antennas. Three types of 
antennas will be characterized: (a) the high efficiency 34-meter 
A i / E L  antenna at Deep Space Station 15 @SS 1 9 ,  (bj  the 
34-meter HA/DEC antenna at DSS 12, and (cj the 64/70-meter 
=/EL antenna at DSS 14. 
Two major control loops of the antenna control system are 
the position loop and rate loop. The position loop drives the 
antenna based on a desired angle command. Figure 1 is a func- 
tional block diagram of a typical position control loop. A 
major component of the position loop is the rate loop. The 
rate loop is a feedback control system designed to control 
motor angular velocity. It responds to  a motor rate command 
signal issued from the position loop. Characterization of an 
antenna’s motion control system requires operational knowl- 
edge of both the position and rate loops. 
Standard control system performance criteria include fre- 
quency and time domain characteristics. The frequency 
response of a system, typically displayed in a Bode plot, 
depicts system response in terms of gain and phase lag as a 
function of frequency. Control system bandwidth is deduced 
from Bode plots. Typical time domain characteristics describe 
system dynamics in response to a unit step command. Time 
domain measurements include rise time. percent overshoot, 
and settling time (see Ref. 1). 
This report presents a frequency response characterization 
of azimuth and elevation rate loops of the 34-meter antenna 
at DSS 15. Also, normalized rate loop step responses are pre- 
sented and discussed. Empirical results are compared to theo- 
retical responses derived from linear mathematical models. 
Sfihseqfient reperts vi!! ana!yze the pesitim !eep fer the same 
antenna and extend control system analysis to  other antennas 
in the Deep Space Network (DSN). 
II. Rate Loop Model 
A rate loop is closed around each drive motor using a 
tachometer as a feedback transducer. The simplified functional 
block diagram, using Laplace domain models, is presented in 
Fig. 2. The functional blocks around the simplified loop are: 
rate loop compensation, a current loop, motor load and 
165 
https://ntrs.nasa.gov/search.jsp?R=19870005914 2020-03-20T12:23:51+00:00Z
i ’  
f-  - 1  
r ?  
tachometer scaling. The K’s represent gain and conversion 
factors, T’S represent time constants of various components, 
and the J represents motor inertia. Elevation and azimuth 
models are identical in form but encompass different coeffi- 
cient values. 
The frequency response of elevation and azimuth rate loops 
is shown in Figs. 3 and 4. respectively. These frequency 
responses were generated from the model in Fig. 2 using con- 
stants supplied by the manufacturer. The frequency response 
of the elevation rate loop has a maximum gain of 1.2 dB at 
2.2 Hz. Beyond 2.2 Hz the gain rolls off with increasing nega- 
tive slope until near 20 Hz, the roll off is -40 dB per decade. 
The gain bandwidth is 9.1 Hz. The phase lag is small for low 
frequencies and monotonically decreases as a function of 
frequency. The azimuth rate loop frequency response is similar 
to the elevation rate loop and has a bandwidth of 9.4 Hz. 
The same mathematical models were used to simulate the 
rate loop time response to a unit step input. Figures 5 and 6 
show elevation and azimuth rate loop responses to a unit step. 
For each axis’s rate loop, the rise time and settling time are the 
same at 0.09 seconds and 0.30 seconds, respectively. The per- 
cent overshoot for the elevation loop was 4.0%, which is 
slightly different from 4.5% for the azimuth axis. Both the low 
percent overshoot and fast rise time, which the mathematical 
models suggest, are desirable qualities for a good pointing and 
tracking control system. 
111. Experimental Procedures 
At the DSS 15 antenna site each rate loop was disconnected 
from the position control computer and connected to the 
signal generator of a frequency response analyzer. A scaled 
tachometer feedback voltage was connected to the analyzer. 
The servo rate loop was driven with a sinusoidal voltage from 
the signal generator of the frequency analyzer at many fre- 
quencies selected to  cover the range desired (0.1 - 20 Hz). 
The amplitude of the tachometer voltage and its phase lag at 
each frequency were reported by the analyzer and recorded. 
In the first set of tests two types of input signals were used 
to measure the frequency response: (a) a biased sinusoidal 
input voltage, and (b) an unbiased sinusoidal input voltage. 
The sinusoidal voltage varied between k0.06 volts (correspond- 
ing to an antenna angular velocity of t5 mdeg/s). The bias 
was 0.12 volts (corresponding to an antenna angular velocity 
of 10 mdeg/s). Tests were conducted on the elevation rate 
loop centered around four elevation angles: 7, 45, 70, and 88 
degrees. Azimuth rate loop tests were conducted at three ele- 
vation angles: 7, 45. and 88 degrees. Only one azimuth angle 
was tested since the azimuth axis inertia changes only with 
elevation angle. The elevation angle was varied during azimuth 
tests to check for cross coupling and effects due to changing 
inertia. 
The second set of tests was performed which measured the 
step response of both rate loops. For these tests a portable, 
computer with digital-to-analog (D/A) and analog-to-digital 
(A/D) conversion capabilities was used. A voltage step was 
induced into the rate loop using the D/A converter, and the 
scaled tachometer voltage was recorded by the computer using 
the A/D converter. The rate loop response was sampled and 
digitized 50 times/second. 
IV. Results 
A total of eight frequency tests was made on both axes: 
four with biased input signals and four with no bias. A Bode 
plot was generated for each test as shown in Figs. 5 through 19. 
A. Biased Input Tests - Elevation Loop 
Figures 7, 8 , 9 ,  and 10 give the results of a biased sinusoidal 
input voltage for the elevation rate loop. Each was made at 
four different elevation angles. All four tests had similar results 
and indicate that the frequency response of the rate loop is 
not a function of elevation angle. Two abnormalities are seen 
in the frequency response of Figs. 7 through 10. The first is 
that a large anti-resonance (inverted resonance) appears in the 
neighborhood of 2.3 Hz. A second smaller anti-resonance 
appears near 3.4 Hz. These anti-resonances are seen in both 
magnitude and phase plots. 
The large anti-resonance is believed to be the first mode of 
torsional vibration between the motor’s rotor inertia and the 
antenna’s inertia. This two-degree of freedom system is ideal- 
ized as two inertias (or masses) connected by a spring. The 
antenna and the motor rotor are the two inertias while the 
gear reducer acts as the spring. The inertia of the antenna, as 
seen by each elevation motor, is reported to  be 0.01898 kg-m2 
(0.014 lb-ft-s2). The motor and gearbox inertia, as seen by the 
motor, is 0.141 kg-m2 (0.104 lb-ft-s2). The spring constant of 
the gear reducer is nonlinear and ranges between 3.96 N-m/rad 
(1.71 lb-ft/rad) and 5.33 N-m/rad (3.93 lb-ft/rad) for torque 
values less than 25% maximum motor torque. Equation (1) 
calculates the fundamental natural frequency, w,,, for a two 
mass torsional system connected by a spring, where K ,  is the 
torsional stiffness of the gear reducer, J1 is the inertia of the 
motor’s rotor, and J2 is the antennas’s inertia as seen by the 
motor (see Ref. 2 ) :  
166 
Using the above values for J , :  J 2 ;  and K ,  suggests the first 
mode of torsional oscillation is between 1.87 Hz and 2.84 Hz. 
The large 2.3-Hz anti-resonance frequency is centered between 
the two frequencies; therefore. it is reasonable to assume that 
the large anti-resonance is due to  this first torsional oscillatory 
mode. 
Note that during first torsional mode vibrations, a motion- 
less node exists on the flexible link between the two inertias. 
The greater the ratio of inertias the closer the node is to the 
larger inertia. This indicates that the motion of the larger 
inertia (which is the motor’s rotor) is attenuated. The second 
small anti-resonance located near 3.4 Hz is also believed to be 
due to a torsional mode of vibration. This has not, however, 
been verified. 
The frequency responses shown in Figs. 7, 8 , 9 ,  and 10 can 
also be compared with the theoretical frequency response 
shown in Fig. 3. The theoretical frequency response does not 
contain the anti-resonances found in the experimental data 
since these are not accounted for by the model. The actual 
frequency responses have slightly lower phase and gain margins 
compared to the theoretical frequency response shown in 
Fig. 3. The actual bandwidth is 8.8 Hz, which is 4% less than 
the theoretical bandwidth. 
6. Unbiased Input Tests - Elevation Loop 
Figures 11, 12, 13, and 14 show results from the elevation 
axis rate loop using an unbiased sinusoidal input voltage 
instead of a biased voltage. Three observations were made 
from these results: the frequency response is completely dif- 
ferent from biased tests yet the same large and small anti- 
resonances are still observed and the frequency response is not 
a function of elevation angle. The rate loop bandwidth is 
reduced from 3.8 Hz to 1 Hz. This is a 90% decrease in band- 
width. Greater phase lag also exists below 3 Hz. One cause of 
the bandwidth and phase lag behavior could be the suscepti- 
bility of the system to  friction; the friction occurring when the 
motors change direction. Changing motor direction reduces 
rate loop performance. 
C. Biased Input Tests - Azimuth Rate Loop 
The tests performed on the elevation axis were repeated on 
the azimuth axis. The results from biased input are plotted in 
Figs. 15. 16. and 17. The tests were performed at the three 
elevation angles of 7. 45. and 88 degrees. respectively. Again. 
the frequency response was found not to be a function of 
elevation angle. All three frequency responses are similar; but 
comparisons between the experimental results and theory 
show a significant difference. The measured rate loop band- 
width is greater than what theory predicts. A 27% increase is 
seen frorn 9.4 Hz to 12 Hz. Aca!yzicg phase margin yields 
similar comparisons. A small dip was observed in the gain at 
2 Hz in all three Bode plots; otherwise, no large anti-resonances 
were observed. The first mode is calculated from the azimuth 
axis inertias, J1 = 0.123 kg-m2 (0.0907 lbf-ft-s2) and J2 = 
0.0118 kg-m2 (0.0087 lbf-ft-s2). In the azimuth axis, four 
motors share the load instead of two as in the elevation axis. 
Assuming that each motor operates below 12.5% of maximum 
torque, the nonlinear spring constant ranges between 0.468 
N-m/rad (0.345 ft-lbf/rad) and 3.23 N-m/rad (2.38 ft-lbf/rad). 
This corresponds to a natural frequency between 1.12 and 
2.76 Hz. The small anti-resonance at 2.0 Hz is centered be- 
tween these calculated frequencies, The anti-resonance is not 
as significant, however, as in the elevation axis. This may be 
due to  cross coupling and structural damping between axes. 
An additional test using double the biased voltage and double 
the sinusoidal voltage amplitude was made to further investi- 
gate the anti-resonance reported above. Figure 18 presents the 
results of this test. The anti-resonance is pronounced during 
this test and validates prior observations. 
D. Unbiased Input Test - Azimuth Rate Loop 
Three additional tests were performed on the azimuth axis 
using an unbiased sinusoidal input voltage with the elevation 
axis at angles 7, 45. and 88 degrees. The empirical Bode plots 
shown in Figs. 19, 20, and 21 indicate dramatic gain attenua- 
tion and phase lag at low frequencies and that the frequency 
response is not a function of elevation angle. Gain attenuation 
and phase lag are attributed to friction, backlash, and drive- 
associated nonlinearities. The contributions of each type of 
nonlinearity to the frequency response have not been deter- 
mined. The frequency responses in Figs. 19, 20. and 21 are 
very different from the theoretical prediction shown in Fig. 4. 
E. Step Responses 
Step response tests were performed on both elevation and 
azimuth rate loops. Normalized tachometer voltage is pre- 
sented as a function of time in Figs. 22 and 23. The rise time 
and settling time of the elevation rate loop, 0.12 seconds and 
0.37 seconds, respectively, are more than 20% longer than the 
predicted values shown in Fig. 5. The measured rate loop 
response gave a 1% overshoot compared to the 4% predicted 
overshoot. 
The azimuth rate loop step response had similar character- 
istics to the elevation rate loop: rise time = 0.13 seconds; 
settling time = 0.34 seconds; percent overshoot = 0%. Again, 
the measured rise time and settling time are more than 20% 
longer than the predicted values in Fig. 6. Both the low 
percent overshoot and fast rise time exhibited by the rate 
loops are desirable performance characteristics. 
167 
V. Conclusions 
The frequency response of elevation and azimuth rate loops 
had several anomalies. Anti-resonances existed in both eleva- 
tion and azimuth rate loops. These resonances were deduced 
to be fundamental torsional modes of vibration between the 
antenna and motor inertias. The calculated elevation axis tor- 
sional natural frequency between 1.87 Hz and 2.84 Hz was in 
good agreement with the observed resonance at 2.3 Hz. The 
calculated azimuth axis natural frequency between 1.12 Hz 
and 2.76 Hz was also in good agreement with the observed 
resonance at 2.0 Hz. 
System bandwidth of elevation and azimuth rate loops, 
based on a biased input voltage, was 8.8 Hz and 12 Hz, respec- 
tively. These were similar to the predicted bandwidths of 9.1 
Hz and 9.4 Hz. Using an unbiased sinusoid voltage seriously 
degraded system bandwidth performance in the elevation axis 
by almost 90%. Unbiased voltage tests in the azimuth axis indi- 
cated that large nonlinearities exist such as friction, backlash. 
and other drive-associated nonlinearities. 
Step response characterization tests indicate elevation and 
azimuth rate loops have fast rise times (less than 0.13 seconds), 
low or no overshoot. and settling times less than 0.4 seconds. 
These performance characteristics indicate that the rate loops 
respond well to  command voltages. 
Both frequency and step response characterization indicate 
the linear mathematical model of the rate loop does not accu- 
rately describe system dynamics. 
References 
1. Dorf, R. C., Modern Control Systems, 3rd ed., Addison-Wesley, Reading. Mass., 1983. 
2. Baumeister. T., Avallone. E. A., and Baumeister 111. T., Mark’s Standard Handbook 
for Mechanical Engineers, 8th ed., McGraw-Hill; New York, 1978. 
168 
DIGITAL ANALOG 
POSITIONS + 
COMMAND -4 
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RATE LOOP CURRENT- MOTOR - I ~ GEAR - 
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Fig. 1. Position loop 
45 I 90 
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FREQUENCY, Hz 
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Fig. 3. Simulated frequency response of the elevation rate loop 
male!, DSS 15 entenna 
169 
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FREQUENCY, Hz 
Fig. 4. Simulated frequency response of the azimuth rate loop 10-1 1 00 101 102 
model, DSS 15 antenna 
FREQUENCY. Hz 
, I  I I l l  I I I I 180 
RISE TIME = 0.09 s 
PERCENT OVERSHOOT = 4.5% 
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TIME, s 
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Fig. 6. Simulated step response - azimuth rate loop model, 
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170 
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10-1 lo0 101 102 
FREQUENCY, Hz 
Fig. 10. Biased input test - elevation axis loop, EL = 88 deg 
-15 I 5 I 1 I I l l  I ,  
10-1 100 101 
FREQUENCY, Hz 
0 
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Fig. 11. Unbiased input test - elevation axis loop, EL = 7 deg 
m 
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10-1 1 00 101 102 
FREQUENCY, Hz 
Fig. 13. Unbiased input test - elevation axis loop, EL = 70 deg 
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10--1 100 101 102 
FREQUENCY, Hz 
3 
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Fig. 14. Unbiased input test - elevation axis loop, EL = 88 deg 
I 1 I I  I I I I I  I I I I 135 
10-1 1 00 101 102 
FREQUENCY. Hz 
Fig. 15. Biased input test - azimuth axis loop, EL = 7 deg 
Fig. 12. Unbiased input test - elevation axis loop, EL = 45 deg 
c - 3  
171 
- 45 
8: 
D 
-90 2 
2 
- 135 
-15 I 1 I I I I180 
10-1' 100 101 1 02 
FREQUENCY, Hz 
Fig. 16. Biased input test - azimuth axis loop, EL = 45 deg 
\ 
1135 
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10-1 1 00 101 102 
FREQUENCY, Hz 
Fig. 17. Biased input test - azimuth axis loop, EL = 88 deg 
8: 
u' 
n 
P 
v1 
4 
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10-1 1 00 101 1 0 2  
FREQUENCY, Hz 
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10-1 100 101 1 02 
FREQUENCY, Hz 
0 
45 
8 
u- 
135 CL 
90 
U 
ln 
4 
180 
225 
Fig. 19. Unbiased input test - azimuth axis loop, EL = 7 deg 
5 
0 
m 
n 
t 
;. -5 
2 -10 
3 
z u 
-15 
-20 
I I 1  0 
45 
90 z 
u' 
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135 ' 
P 
ln 
1 80 
225 
10-1 100 101 11 
FREQUENCY, Hz 
Fig. 20. Unbiased input test - azimuth axis loop, EL = 45 deg 
Fig. 18. Double input and double bias test - azimuth axis loop, 
EL = 45 deg 
172 
-20 * 
10-1 100 101 1C 
FREQUENCY, Hz 
0 
45 
90 
135 
180 
225 
Fig. 21. Unbiased input test - azimuth axis loop, EL = 88 deg 
v) 
3 
P 
E 
0 > 
N 
6 
0 z 
-1 
1.0 - 
= 0.12s 
= 0.37 s 
RISE TIME 
PERCENT OVERSHOOT = 1% 
TIME (STEADY STATE) 
0 0.1 0.2 0.3 0.4 0.5 
TIME. s 
Fig. 22. Actual step response - elevation axis loop, DSS 15 
1 .o 
ln 3 0.8 
0 > 
$ 0.6 
6 
n 
- 
-1 
0.4 ' 
0.2 ' 
RISE TIME = 0.13s 
PERCENT OVERSHOOT = 0% 
TIME (STEADY STATE) = 0.34 s 
0 I I I I I 
3 3.1 3.: 0.3 0.4 0.5 0 
TIME, s 
Fig. 23. Actual step response - azimuth axis loop, DSS 15 
1 73 


Antenna servo control system characterization: Rate loop analysis for 34-m antenna at DSS 15

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