Civil Engineering Reference
In-Depth Information
For the velocity control system (k
s), the pilot equalization parameters can be zero or equal (t
I
¼
t
L
),
/
and the pilot can act like a proportional gain with a time delay:
K
p
e
jvt
e
H
p
¼
:
(12
:
20)
There is no need to “fix” the system dynamics through adaptation because the system dynamics itself
already mimics the integrator-like dynamics that are predicted by the COM.
For the proportional control system (k), the pilot must use the lag equalization (t
I
) to make the open-
loop an integrator:
1
jvt
I
)
e
jvt
e
H
p
¼
K
p
:
(12
:
21)
(1
þ
The lag parameter needs to be chosen such that it creates the integrator-like characteristic well before
the cross-over frequency, that is, 1
=t
I
v
c
. An intuitive interpretation for the lag is that the human inte-
grates or smoothers the input, responding to trends rather than to moment-to-moment variations. In
essence, the human is responding to the “averages” of error over moving windows of observations
rather than to the instantaneous error, values.
Finally, for the acceleration control system (k
s
2
), the pilot needs to use the lead equalization (t
L
)to
/
make the open-loop an integrator:
jvt
L
)e
jvt
e
H
p
¼
K
p
(1
þ
:
(12
:
22)
The lead parameter needs to be chosen such that it creates the integrator-like characteristic well before
the cross-over frequency, that is, 1
=t
L
v
c
. An intuitive interpretation for the lead is that the human
responds to both the position and velocity of the error signal. In essence, attending to velocity allows
the human to effectively anticipate future position errors.
12.4.5.3 Rule # 6: Choice of Cross-Over Frequency and Effective Time Delay
Based on the empirical results of McRuer's experiments, rule # 6 yields likely values for the cross-over
frequency and effective time delay for the three basic systems k, k
s
2
.
Experiments showed that t
e
decreases with v
i
with a slope, which is practically independent of
the controlled element, while the basic level of t
e
depends primarily on the controlled element and is
independent of v
i
:
s, and k
/
/
t
e
(H
c
; v
i
)
¼ t
0
(H
c
)
Dt(v
i
)
:
(12
:
23)
Similarly, the experiments showed that v
c
increases with v
i
with a slope that is also practically inde-
pendent of the controlled element, and again the basic level of v
c
depends primarily on the controlled
element and is independent of v
i
:
v
c
(H
c
; v
i
)
¼
v
c
0
(H
c
)
0
:
18 v
i
:
(12
:
24)
The values for t
0
, v
0
and Dtare summarized in Table 12.1.
Note that these qualitative models are based on the empirical results of McRuer's experiments, and
should be handled with care. An important phenomenon, for instance, is that for the double integrator
dynamics the cross-over frequency increases with forcing function bandwith upto a certain frequency.
For higher input signal bandwidths the cross-over frequency starts decreasing, a finding called cross-
over regression.
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