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The vehicle vertical velocity and displacement are derived
from the visual system, which is represented by an
83-msec time delay. Hess and Malsbury point out in
reference 61 that the vertical velocity sensing assumption
affects the primary control loop, but that it is currently
not known how to select the appropriate division of the
vertical velocity estimation between the motion and visual
cues, which is a motivation for Vertical Experiment III
described in section 6.
The pilot gains shown in figure B2 are selected based on a
set of adjustment rules proposed by Hess and Malsbury.
For these tasks, only the high-pass filter was changed, and
using the adjustment rules results in the change of three
variables Kh˙˙, Kh ˙ , and Kh . The gain Kh˙˙ is determined so
that the lowest damping ratio of any oscillatory roots in
the ˙h˙(s) / ˙h˙c (s) transfer function is at least 0.15. This
value of damping ratio is selected to represent a trade-off
between stability and high-frequency phase-lag reduction
(ref. 70). In reference 70, Hess points out that requiring an
identical damping ratio of this loop for all configurations
reduces the sensitivity of the modeling procedure to the
particular value chosen.
Then, with the motion loop closed, Kh ˙ is determined so
as not to violate the combination of a phase margin of 45°
and a gain margin of 4 dB in the vertical velocity openloop
h˙ cue (s) / h˙ e (s) . These values are selected by Hess to
achieve adequate stability margins for the vertical-velocity
loop. Again, Hess states that requiring all configurations
to have the same level of relative stability (same phase
and gain margin) reduces the sensitivity of the model to
the particular values chosen.
76
Pilot
0.370
+
– –
0.434
0.218
+
–
+ hc
he dc
Kh hc h h hc h
hcue
hsim
Kh
Kh
(8)(26)
(s+8)(s+26)
hfilt
Ks2
Motion
system
Central nervous and
neuromuscular system Aircraft
Visual system
hardware
High-pass
motion filter
Motion servo
dynamics
s2+2zws+w2
187(s+0.2)e–0.15s
(s+0.05)(s2+2(0.35)(20)s+202)
9s
s+0.3
1
s
1
s
e
–0.083s
e
–0.083s
Figure B2. Structural pilot model for Vertical Experiment I (ref. 61).
Finally, the gain Kh is chosen to have adequate frequency
separation between the altitude and vertical-velocity loops
while maintaining good altitude-loop crossover characteristics.
A useful rule-of-thumb is to separate the altitude
and vertical-velocity crossover frequencies by a factor of 4
(ref. 71).
This pilot gain determination process was repeated for the
high-pass motion filter variations in Vertical
Experiment I. Although the motion filter gain, K, was
changed in that experiment, note that the adjustment rules
of the model do not account for an effect due to that gain
K. That is because any changes in K are offset by adjustments
in Kh˙˙ . So, the model only predicts performance
differences owing to changes in the motion-filter natural
frequency and not its gain.
For the five motion configurations that encompassed the
motion-filter natural frequency changes, the predictions
of the model are shown in table B1. The motion-filter
configurations, V1, V2, V3, V4, and V10 are fully
described in Vertical Experiment I; however, V1 essentially
represents a motion-filter transfer function of unity,
and V2 through V4 represent increasing break frequencies
of 0.245 to 0.885 rad/sec. The V10 configuration has no
motion at all.
The last two columns of table B1 are the altitude-rate
pilot-vehicle crossover frequency and the closed-loop
altitude-rate bandwidth, respectively. The definition of
bandwidth used in reference 61 was that of the –90° phase
point. The frequency responses along with the bandwidth
measure are shown in figure B3.
Note that the analytical model predicts a reduction in the
vertical-velocity closed-loop bandwidth, from 6.36 to
4.27 rad/sec, as the motion feedback degrades from near
full-motion to no motion. For the no-motion case, V10,
the pilot has to increase his visual velocity feedback,
which results in a higher crossover frequency than before,
but in a lower closed-loop bandwidth.
77
Table B1. Analytical pilot-vehicle characteristics.
Configuration Kh
(1/sec)
Kh ˙
(1/sec)
Kh˙˙
h˙ / h˙ cue e wc
(rad/sec)
h˙ / h˙ BW c
(rad/sec)
　
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