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V1 0.323 0.542 0.217 1.20 6.36
V2 0.299 0.565 0.240 1.24 6.24
V3 0.335 0.595 0.215 1.33 6.13
V4 0.385 0.636 0.213 1.50 5.85
V10 0.795 0.725 0.000 3.10 4.27
10
-1
10
0
10
1
-20
-10
0
10
20
Magnitude, dB
V1
V2
V3
V4
V10
10
-1
10
0
10
1
-200
-150
-100
-50
0
Phase, deg
Frequency, rad/sec
Figure B3. Closed-loop vertical-velocity frequency responses.
If the changes in the closed-loop system roots are
examined for the above configurations, the effective heave
damping goes from –1.4 sec–1 for the full-motion case
(V1) to –1.1 sec–1 for the V4 configuration. The location
of this root accounts for much of the bandwidth difference.
This root is also the principal root of interest in the
pilot’s control of altitude. The corresponding effects on
the other roots are minimal. The heave damping
argument, however, does not hold for the no-motion case
(V10). In fact, although the bandwidth is less in this case,
the damping of the primary closed-loop roots is good.
The above model also predicts a degradation in closed-loop
performance from degradations in the motion filter alone.
78
Figure B4 illustrates how the closed-loop vertical-velocity
roots migrate as the motion filter changes. However, these
closed-loop poles are those that result when the model’s
gains are fixed at the full-motion (V1) condition for all the
remaining conditions (V2, V3, V4, V10). This situation
was examined to show the effect of the motion filter alone
without pilot adaptation. Only the region near the origin
is depicted, since the poles and zeros far from the origin
exhibit negligible change.
Two effects of the motion filter alone are noticed. First,
the effective heave damping is reduced as the motion
filter’s natural frequency increases. This result also occurs
when the adjustment rules of the model are followed.
Second, pole-zero dipoles form in which the separation
between the pole and zero become more prominent as the
motion filter is made more restrictive (going from V1 to
V4). As the filter natural frequency increases, these dipoles
encroach upon the pilot-vehicle crossover frequency. Thus,
a broad range of integrator-like characteristics in the
crossover region does not occur. So if the pilot wanted to
achieve a similar, but slower, closed-loop response, more
than just a simple gain change on his part would be
necessary. He would also have to adjust his dynamic
compensation, which would likely entail an increase in
workload or a reduction in his opinion of simulator
fidelity. As expected, the closed-loop bandwidth without
using the pilot adjustment rules becomes worse. The
bandwidth of the V10 configuration is 3.60 rad/sec
without the adjustment rules versus 4.27 rad/sec
with them.
Since this model was applied to Vertical Experiment I
(sec. 4), it is interesting to compare the phase-plane timehistories
from that experiment (figs. 40–43, 49) with the
phase-plane time-histories that the model predicts. The
model’s predictions for the five configurations analyzed
(V1, V2, V3, V4, and V10) are shown in figure B5.
Although the model shows degradations as the quality of
the platform motion becomes worse, the model poorly
represents the experimental results in two ways. First, the
model introduces a pronounced underdamped oscillatory
-2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Real axis
Imag axis
Decreasing heave damping
V1 V2 V3 V4
V1
V2
V3
V4
Figure B4. Closed-loop vertical-velocity spectrum versus motion filter changes.
79
mode for the V1-V4 configurations, which has a frequency
of 8 rad/sec. This mode is not present in the experimental
results, which show a reasonably smooth response during
the ascent. Second, the model does not predict the oscillatory
behavior that occurs experimentally at the terminal
altitude point (85 ft), which is especially prevalent in the
motionless (V10) configuration. The adjustment rules
need to be modified in the model in an attempt to match
the experimental results. This modification is left for
future work.
It should be clear that some key assumptions are made in
the development of this model, such as which parts of the
simulator system provide which cues, and the adjustment
　
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