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Multimodal Pilot Control Behavior in
Combined Target-Following
Disturbance-Rejection Tasks
P.M.T. Zaal
∗
, D.M. Pool
†
, M. Mulder
‡
, and M.M. van Paassen
§
Delft University of Technology, Delft, The Netherlands
Investigating how humans utilize their perceptual modalities while con-
trolling a vehicle is important for the design of new control systems and the
optimization of simulator motion cueing. For the identification of separate
pilot response functions to the different p erc eived cues, multiple forcing
functions need to be inserted into the manual control loop. An example
of a task with multiple forcing functions is a combined target-following
disturbance-rejection task, where a target and disturbance signal are used
to separate the human visual a nd vestibular motion responses. The use of
multiple forcing functions, however, also affects the nature of the control
task and how the motion cues are utilized by the pilot to form a proper
control action. This paper presents the results of an experiment where
possible effects of using multiple forcing functions on pilot control behavior
in an aircraft pitch control task are investigated. The results indicate that
pilot performance and control activity are significantly lower when the rel-
ative power of the target forcing function is increased. This is caused by a
significant change in multimodal pilot control behavior. With an increase in
relative target power, the visual perception gain is reduced and the visual
time delay becomes higher. The motion perception gain reduces if both
∗
Ph.D. candidate, Control and Simulation Division, Faculty of Aerospace Engineering, P.O. Box 5058,
2600GB Delft, The Netherlands; p.m.t.zaal@tudelft.nl. Student member AIAA.
†
Ph.D. candidate, Control and Simulation Division, Faculty of Aerospace Engineering, P.O. Box 5058,
2600GB Delft, The Netherlands; d.m.pool@tudelft.nl. Student member AIAA.
‡
Professor, Control and Simulation Division, Faculty of Aerospace Engineering, P.O. Box 5058, 2600GB
Delft, The Netherlands; m.mulder@tudelft.nl. Member AIAA.
§
Associate Professor, Control and Simulation Division, Faculty of Aerospace Engineering, P.O. Box 5058,
2600GB Delft, The Netherlands; m.m.vanpaassen@tudelft.nl. Member AIAA.
1 of 28
Peter M. T. Zaal, Daan M. Pool, Max Mulder and Marinus M. van Paassen, Multimodal Pilot
Control Behavior in Combined Target-Following Disturbance-Rejection Tasks (2009), in:
Journal of Guidance, Control, and Dynamics, 32:5(1418-1428)
dx.doi.org/10.2514/1.4464
forcing functions have significant power. It is also found that multimodal
pilot control behavior in a pure target or disturbance task can be analyzed
by adding a small additional disturbance or target signal, respectively. In
this case, the effects on control behavior are found to be minimal, while
still being able to accurately estimate the parameters of the multi-channel
pilot model.
Nomenclature
A sinusoid amplitude deg
e tracking error signal deg
f forcing function signal deg
f
d
disturbance forcing function deg
f
t
target forcing function deg
H(s) transfer function -
H(jω) frequency response function -
J criterion function rad
2
K
m
motion-perception gain -
K
n
remnant intensity -
K
v
visual-perception gain -
N number of points -
n
d
disturbance forcing function frequency integer factor -
n
t
target forcing function frequency integer factor -
n pilot remnant signal deg
p relative forcing function power -
Q optimal control performance weighting factor -
R optimal control control effort weighting factor -
s Laplace variable -
T
lead
visual lead time constant s
T
lag
visual lag time constant s
T
sc1
, T
sc2
, T
sc3
semicircular canal time constants s
T
A1
, T
A2
forcing function filter time constants s
T
m
measurement time s
t time s
u pilot control signal deg
2 of 28
Symbols
δ
e
elevator deflection deg
θ pitch angle deg
σ standard deviation
ϕ
m
phase margin deg
φ sinusoid phase shift rad
τ
m
motion-perception time delay s
τ
v
visual-perception time delay s
ω frequency rad s
−1
ω
c
crossover frequency rad s
−1
ω
n
remnant filter break frequency rad s
−1
ω
nm
neuromuscular frequency rad s
−1
ζ
n
remnant filter damping -
ζ
nm
neuromuscular damping -
Subscripts
d disturbance
t target
I. Introduction
In most vehicular control tasks, human operators use multiple cues t o achieve a proper
control action. For example, in an aircraft pitch control task, pilots visually perceive the
pitch angle from their primary flight display and, due to the physical aircraft pitch rotation,
also sense changes in aircraft pitch with their vestibular system.
1
In a skill-based continuous
control task, these cues are processed by the central nervous system, where appropriate
weight is put on visual and vestibular responses. Modeling t his process can give insight into
the relative importance of the d ifferent motion cues and is important in, for example, flight
simulator fidelity research. As the simulation of motion cues is constrained by the limitations
of the simulator, such knowledge can be used to optimize simulator motion cueing.
2
When modeling the perceptual modalities of the pilot, a multi-channel model is often
used that takes the perceived cues as inputs. The output of this quasi-linear model is the
summation of pilots’ linear responses to each perceived cue, supplemented with a remnant
signal that accounts for the nonlinear behavior.
3, 4
The linear response functions consist of
sensor dynamics, gains, time constants, time delays, and n euromuscular dynamics. For ac-
curate estimation of these parameters, current identification techniques require the different
inputs of the model to be uncorrelated and sufficiently exciting. To achieve this, an inde-
3 of 28
pendent forcing function signal is inserted into the closed-loop system for every pilot model
input.
4–7
The location where the forcing functions are inserted into the closed-loop system,
and the intensity of the individual forcing functions, can affect the task of the pilot and how
the different motion cues are used in the control task.
Two classical types of manual control tasks that are frequently studied in literature
are disturbance-rejection and target-following tasks. Motion cues have been shown to have
different functions in these two types of tasks. In a disturbance-rejection task, the visual
and vestibular inputs to the pilot are driven by the same system output, yielding a task in
which the visual and vestibular modalities work in parallel. In a target-following task, the
physical motion cues are directly related to the control action of the pilot, as this action is
the only input to the controlled dynamics. Different effects of motion cues on pilot control
behavior in disturbance-rejection and target-following tasks have indeed been observed in
several experimental studies.
8–11
In these classical single forcing function tasks,
3, 9–14
the relation between t he visual and
vestibular cues and the pilot control action is evident. Reliable identification of pilots’ visual
and vestibular responses is, however, not possible for such tasks due to the use of only one
forcing function signal. A strategy that has been used in many experiments,
1, 4, 12, 15, 16
solely
to facilitate multi-channel pilot model identification, is to use both target and disturbance
forcing functions in a combined target-following and disturbance-rejection task. In such a
combined control task, the insertion of two forcing functions decreases the coherence between
both cues and may introduce a cue conflict. By limiting the magnitude of the additional
forcing function signal, the preferred target-following or disturbance-rejection portion of the
task can be made dominant, minimizing possible cue conflicts.
1, 4
However, a trade-off h as
to be made, as reducing the additional signal’s power below a certain level will again result
in unreliable identification results.
Although the concept of using an additional forcing function with relatively low power
for the modeling of multiple modalities has been used in many experiments, the minimum
power of this additional signal, required for accurate estimation results, has never been
determined. Additionally, it is crucial to know if adding an extra signal, even with low
power, significantly changes control behavior compared to the single forcing function tasks.
These topics are studied in this paper.
An experiment was performed in the SIMONA Research Simulator (SRS) of the Delft
University of Technology in which the influence of multiple forcing functions on pilot per-
formance and control behavior is investigated for an aircraft pitch control task. For this
purpose, the relative power of the target and disturbance forcing functions was systemat-
ically varied over the different experimental conditions. In a similar experiment studying
the same topics for a double-integrator roll control task, no significant effect on multimodal
4 of 28
pilot control behavior was found. Tracking performance and control activity, however, were
found to be significantly affected.
17
The use of more accurate identification techniques for
the estimation of the pilot model parameters
7
for the experiment discussed in the current
paper may yield new insights into how pilot control behavior is affected.
The paper is structured as follows. First, the multimodal pilot modeling procedure used
in this research will be discussed. Next, an optimal control analysis is presented, which
was performed to gain some insight into the theoretically optimal use of motion cues for a
systematic change in relative power of target and disturbance forcing functions. After this,
the experiment setup and results will be discussed. The paper ends with a discussion and
conclusions.
II. Multimodal Pilot Modeling
Pilot manual control behavior in skill-based continuous control tasks can be described
by relatively simple control-theoretic pilot models.
3
For vehicle control tasks in which pilots
use multiple perceptual modalities (for instance, visual and vestibular), modeling of control
behavior is, however, not straightforward and poses requirements on the forcing functions
that are u sed to induce control actions.
4–7
This section d escribes the control task, multi-
channel pilot model and forcing functions used in this paper for investigating how changes
in relative target and disturbance signal power affect multimodal pilot control behavior and
its identification from measurement data.
II.A. Control Task
The closed-loop compensatory aircraft pitch attitude control task studied in the experiment
described in this paper is depicted in Figure 1. This control task is similar to the task used in
a previous experiment, in which the influence of pitch and heave motion cues on multimodal
pilot control behavior was investigated.
1
H
θ,δ
e
f
t
u
−
e θ
f
d
θ
n
H
pe
H
pθ
δ
e
−
pilot
Figure 1. Schematic representation of a closed-loop compensatory aircraft pitch control task.
For the controlled aircraft pitch dynamics, indicated with H
θ,δ
e
in Figure 1, a linearized
model of the Cessna Citation I Ce500 – trimmed at an altitude of 10,000 ft and a true
5 of 28
airspeed of 160 kts – is used. The transfer function for these dynamics is given by:
H
θ,δ
e
(s) = −10.6189
s + 0.9906
s(s
2
+ 2.756s + 7.612)
(1)
A Bode plot of the controlled dynamics is given in Figure 2. As indicated in the figure
by the gray lines, the controlled aircraft dynamics resemble those of a single integrator for
frequencies below 1 rad/s and a double integrator for frequencies above 3 rad/s. Between 1
rad/s and the short period peak at ω
sp
= 2.76 rad/s the dynamics approximate a gain.
ω, rad s
−1
|H|, -
ω
sp
(a) magnitude
H
θ,δ
e
(jω)
K/(jω)
K/(jω)
2
10
-1
10
0
10
1
10
-2
10
-1
10
0
10
1
ω, rad s
−1
6
H, deg
ω
sp
(b) phase
10
-1
10
0
10
1
-45
0
45
90
135
Figure 2. Bode plot of controlled aircraft dynamics.
For identification of both pilot visual and vestibular responses (H
pe
and H
pθ
in Figure 1),
two forcing functions need t o be inserted into the closed-loop control task. A target forcing
function f
t
is inserted by displaying the error e between the target and the actual pitch angle
θ on a visual compensatory display. A disturbance forcing function f
d
is used as a physical
disturbance on the aircraft dynamics. Pitch rotational motion is generated by the simulator
motion base, and may be perceived by the pilot through his vestibular system. The heave
motion cues associated with a change in aircraft pitch attitude
1
were not provided by the
simulator.
If the power of the target is zero, the task is a pure disturbance task and the visual and
physical motion cues – that is, the two inputs of the pilot in Figure 1 – are similar. If the
power of the disturbance is zero, the task is a pure target task. In this case, the pilot control
signal is the only input to the controlled dynamics and the target signal induces a difference
between the information that is present in the visual and physical motion cues.
6 of 28
II.B. The Multimodal Pilot Model
The structure of an appropriate multimodal pilot model for the control task given in Figure 1
is given in Figure 3. The model contains a visual and a vestibular input (e and θ) and two
parallel channels (H
pe
and H
pθ
) to model the visual and vestibular modalities separately.
9
A
remnant signal n is added to the output of the linear channels to account for the nonlinear
behavior of the pilot.
u
θ
n
H
pe
e
sensor
dynamics
equalization limitations
K
v
(1 + jωT
lead
)
2
(1 + jωT
lag
)
H
sc
K
m
e
−jωτ
v
e
−jωτ
m
H
nm
(jω)
2
H
pθ
H
nm
Figure 3. Multi-channel pilot model structure.
Human operators adapt th eir control behavior to the controlled dynamics H
θ,δ
e
in such
a way that the open-loop dynamics in the crossover region can be described by a single
integrator and a time d elay.
3
With the aircraft pitch dynamics as depicted in Figure 2 and
typical crossover frequencies between 2 and 4 rad/s for this type of control task, the pilot
needs to generate lag to compensate for the gain dynamics around the short period frequency.
Subsequently, a quadratic lead term is needed to compensate the lag and to achieve the
required lead compensation for the double integrator dynamics at higher frequencies.
1
This
results in the pilot equalization given in Figure 3.
The visual perception channel H
pe
contains the visual perception gain K
v
, a visual lead
time constant T
lead
, a visual lag time constant T
lag
, and a visual perception time delay τ
v
. The
pitch motion perception channel H
pθ
includes the dynamics of the semicircular canals H
sc
,
the motion perception gain K
m
, and a motion perception time delay τ
m
. In both channels,
the control action of the pilot is affected by the neuromuscular dynamics H
nm
, given by:
H
nm
(jω) =
ω
2
nm
ω
2
nm
+ 2ζ
nm
ω
nm
jω + (jω)
2
, (2)
with ζ
nm
the neuromuscular damping and ω
nm
the neuromuscular frequency. The semicir-
cular canal dynamics in the pitch motion perception channel are given by:
H
sc
(jω) =
1 + jωT
sc1
(1 + jωT
sc2
)(1 + jωT
sc3
)
, (3)
with T
sc1
= 0.11 seconds, T
sc2
= 5.9 seconds and T
sc3
= 0.005 seconds the time constants
of the semicircular canal model. These values are taken from previous research
10
and are
7 of 28
fixed in the parameter estimation procedure. Note that due to the integrating action of
the semicircular-canal dynamics as defined by Eq. (3), the vestibular channel effectively
provides a second source of lead information in addition to the contribution of the visual
lead constant, T
lead
. A portion of the required lead generation may thus be taken over by a
pilot’s vestibular system if motion cues are available. A significant reduction in visual lead
time constant when physical motion cues were made available has been observed in previous
experiments where similar control tasks were considered.
1
With the time constants of the semicircular-canal model kept constant, a total of eight
pilot model parameters are left to be estimated (K
v
, T
lead
, T
lag
, τ
v
, K
m
, τ
m
, ζ
nm
, ω
nm
).
II.C. Forcing Functions
For the closed-loop pitch attitude control task as defin ed in Figure 1, the t arget and dis-
turbance signals are designed as quasi-random sum-of-sine signals with sines at multiple
frequencies. The random appearance of such multi-sine signals induces skill-based feedback
control behavior, while allowing the experiment designer to accurately define the forcing
function properties in the frequency domain. The forcing functions were generated accord-
ing to:
f
d,t
(t) =
√
p
d,t
N
d,t
X
k=1
A
d,t
(k) sin(ω
d,t
(k)t + φ
d,t
(k)), (4)
where the subscripts d and t indicate the disturbance or target forcing function, respectively.
In Eq. (4), A(k), ω(k) and φ(k) indicate the amplitude, frequency and phase of the k
th
sine
in f
d
or f
t
. N indicates the number of sines in the signals and p is the relative power fraction,
which is between 0 and 1. Both f
d
and f
t
consisted of 10 individual sinusoids, but each had
a different amplitude, frequency and phase distribution.
The measurement time of an individual experimental measur ement run is T
m
= 81.92
seconds. The sinusoid frequencies ω
d
(k) and ω
t
(k) were all integer multiples of the measure-
ment time base frequency, ω
m
= 2π/T
m
= 0.0767 rad/s. The selected sinusoid frequencies
and the corresponding integer factors of ω
m
, n
d
and n
t
, can be found in Table 1.
To determine the amplitudes of the individual sines for both the target and the distur-
bance forcing function, a second-order low-pass filter was used:
H
A
(jω) =
1 + T
A1
jω
1 + T
A2
jω
!
2
, (5)
with T
A1
= 0.1 sec and T
A2
= 0.8 sec. The absolute value of the filter at a sinusoid frequency
gives the corresponding sinusoid amplitude. The reduced magnitude of the amplitudes at
the higher frequencies yields a tracking task that is not overly difficult. The amplitude
8 of 28
Table 1. Experiment forcing function properties.
disturbance, f
d
target, f
t
n
d
, – ω
d
, rad s
−1
A
d
, deg φ
d
, rad n
t
, – ω
t
, rad s
−1
A
t
, deg φ
t
, rad
5 0.383 0.385 -0.269 6 0.460 1.562 1.288
11 0.844 0.505 4.016 13 0.997 1.092 6.089
23 1.764 0.308 -0.806 27 2.071 0.493 5.507
37 2.838 0.201 4.938 41 3.145 0.265 1.734
51 3.912 0.212 5.442 53 4.065 0.178 2.019
71 5.446 0.263 2.274 73 5.599 0.110 0.441
101 7.747 0.352 1.636 103 7.900 0.070 5.175
137 10.508 0.483 2.973 139 10.661 0.051 3.415
171 13.116 0.635 3.429 194 14.880 0.040 1.066
226 17.334 0.949 3.486 229 17.564 0.036 3.479
f(t), deg
t, s
disturbance f
d
target f
t
0 5 10 15 20 25 30
-4
-3
-2
-1
0
1
2
3
4
Figure 4. Time trace of the disturbance and target forcing function signals (p
d
= p
t
= 1).
distributions A
d
(k) and A
t
(k) were scaled to attain equal variances for f
d
and f
t
of 2.0 deg
2
.
To determine the forcing function phase distributions, a large number of random sets
of phases were generated. The two sets of phases that yielded signals with a probability
distribution closest to a Gaussian distribution, without leading to excessive peaks, were
selected for f
d
and f
t
.
18
The disturbance signal was inserted into the closed-loop control task before the controlled
aircraft dynamics by adding it to the pilot’s control signal u, as can be verified from Figure 1.
Therefore, the disturbance signal amplitudes and phases need to be prefiltered with the
inverse of t he aircraft model pitch response H
θ,δ
e
(jω). This ensured that f
d
had similar
properties as f
t
after passing the controlled dynamics.
In this research, the relative power of both forcing functions is varied between different
experimental conditions. The total power inserted by the forcing functions is always equal
to 2.0 deg
2
. This implies that the following relation for the relative power of the disturbance
and target holds: p
d
= 1−p
t
, where p
t
varies between zero an d one. For p
t
= 0, the target will
be zero and the control task will be a pure disturbance task. For p
t
= 1 all forcing function
power in the control loop will be provided by the target forcing function and the task will be
a pure target task. Because of this relation between relative target and disturb ance power,
9 of 28
it should be noted that when an increase in target power is mentioned in the paper without
any mention about t he disturbance power, the disturbance power consequently decreases.
Figure 4 d epicts a part of a time trace for both forcing function signals with p
d
and p
t
equal to 1. Note that the disturbance signal as depicted in the figure is the signal prefiltered
with the inverse of the controlled dynamics. The properties of the target and disturbance
signals are summarized in Table 1.
III. Optimal Control Analysis
An optimal control analysis was performed to determine the theoretically optimal pilot
model settings for a change in relative power of the forcing functions. For this analysis,
the target and disturbance forcing function power is systematically varied between 0 and
100%, that is, the task is changed from a pure disturbance task to a pure target task, with
combined target-following disturbance-rejection tasks in between. Due to the different role
motion cues play in target following and disturbance rejection, optimal weighting of pilot
visual and vestibular responses – for instance in the generation of pilot lead – may be different
for both tasks. This analysis will give some insight into the optimal use of visual and physical
motion cues for the different forcing function power settings.
III.A. Setup of the Optimal Control Analysis
In the optimal control analysis, the closed-loop control structure depicted in Figure 1 is used.
The pilot is represented by the full pilot model given in Figure 3. The control law for this
optimal control problem is given by:
u = H
pe
e − H
pθ
θ + H
n
n, (6)
with n a zero mean Gaussian white noise signal and H
n
the remnant filter given by:
H
n
(jω) =
K
n
ω
3
n
((jω)
2
+ 2ζ
n
ω
n
jω + ω
2
n
) (jω + ω
n
)
. (7)
The parameters in the remn ant filter are the remnant intensity K
n
, the remnant break
frequency ω
n
, and a damping coefficient ζ
n
. This remnant filter characteristic was found ex-
perimentally in p revious research.
7
The parameters in the optimal control law are computed
by minimizing the following criterion function:
J = Qσ
2
(e)
|
{z }
performance
+ Rσ
2
(u)
|
{z }
effort
. (8)
In the criterion function, the constant factors Q and R control the relative weighting of
10 of 28
the minimization of the variance of the error (tracking performance) and the variance of the
control signal (control effort), respectively.
As the optimization problem is highly overdetermined (the pilot model, including the
remnant filter consists of 11 parameters), some parameters need to be fixed. As t he change
in relative forcing function power will ch ange the relation between the d ifferent pilot model
inputs, it is expected that the equalization of the pilot model will be mostly affected. For
this reason the parameters of the pilot equalization are optimized, while the rest of the
parameters are fixed. The values of these fixed parameters can be found in Table 2 and are
taken from a previous human-in-the-loop experiment performed in the SRS, in which the
same aircraft pitch control task was performed.
1, 7
The forcing functions in this experiment
were identical to the ones defined in Sec. II.C, with p
t
= 0.2 and p
d
= 0.8. The remnant
intensity K
n
given in Table 2 ensures that 10% of the variance of the control signal is caused
by the remnant, as found in previous research.
1
Table 2. Values of the fixed parameters i n the optimal control analysis.
τ
v
, s τ
m
, s ζ
nm
, - ω
nm
, rad s
−1
K
n
, - ζ
n
, - ω
n
, rad s
−1
0.27 0.18 0.18 11.56 4.0 0.26 12.7
The optimal values for the visual perception gain K
v
, t he motion perception gain K
m
,
and the visual lead time constant T
lead
are determined by minimizing J as defined by Eq. (8).
The lag time constant T
lag
was set to 2.4T
lead
. This approximate relation was also found for
the experiment mentioned above
1
and further increases the probability of finding an optimal
solution of the optimization problem. The weighting factors Q and R of the cost function
were determined to provide values of K
v
, T
lead
, T
lag
, and K
m
that were very close to those
found for the experiment described in Ref. 1. The values for Q and R were set to 10 and 1,
respectively.
III.B. Results
The results of the optimal control analysis are depicted in Figures 5 and 6. Figure 5 gives the
optimal values of K
v
, T
lead
, and K
m
for a change in forcing function power given the assumed
control structure. The vertical line at p
t
= 0.2 indicates the condition of the experiment in
Ref. 1, of which the data is taken for the fixed parameters. From a pure disturbance to
a pure target task (p
t
from 0 to 1) the visual and motion perception gains decrease. As
lead information can result from either the integrating action of the semicircular canals, the
visual lead, or a combination of th ese, a consequence of the decrease of the motion gain is
an increase in the visual lead time constant, as is also observed in Figure 5.
Figure 6 gives the variance of the error signal and the variance of the control signal, the
pilot performance and control activity, respectively. It can be seen that tracking performance
11 of 28
K
v ,m
, -
p
t
, -
K
v
K
m
T
lead
T
lead
, s
p
d
, -
1 0.8
0.6 0.4 0.2 0
0 0.2 0.4 0.6 0.8 1
0.1
0.2
0.3
0.4
0.5
1.5
2.0
2.5
3.0
3.5
Figure 5. Visual and motion gains, and vi-
sual l ead time constant for change in rela-
tive forcing function power.
σ
2
(e, u), deg
2
p
t
, -
σ
2
(e)
σ
2
(u)
p
d
, -
1
0.8 0.6 0.4 0.2
0
0 0.2 0.4 0.6 0.8 1
0.3
0.4
0.5
0.6
0.7
Figure 6. Error and control signal vari-
ance for a change in relative forcing func-
tion power.
decreases (the variance of the error increases) and the control activity remains approximately
constant, as the control task is changed from pure disturbance-rejection to pure target-
following.
III.C. Discussion
For a pure disturbance task (p
t
= 0), the visual and physical motion cues are equal. Because
of this, and the fact that utilizing motion cues is a faster and more efficient way of generating
lead (due to the sm aller motion perception time delay, see Table 2), it can be expected that
the perception gains are relatively high and t he visual lead is minimized. For a target task
(p
t
= 1), the inputs to the p ilot model are not equal, that is, a cue conflict is introduced.
It can be expected that this results in a decrease of the perception gains and an increase in
visual lead, as lead information on the forcing function is only available visually. The results
found for the optimal parameters in Figure 5 support this.
Figure 6 indicates that the tracking performance is higher for a disturbance task than for
a target task. This is a result of the increased perception gains for the disturbance task. The
same result was found in previous research that investigated the effect of different motion
cues on target and disturbance tasks.
9
A logical consequence of the increase in performance
would be an increase in control activity. This result is, however, not found in the optimal
control analysis. Rather, a minimal increase in control activity can be observed.
IV. Experiment
To verify whether the differences in theoretically optimal control behavior for target-
following and disturbance-rejection as observed from the optimal control analysis indeed
represent typical tren ds for human manual control behavior, a human-in-the-loop experi-
12 of 28
ment was performed. This experiment was designed to reveal possible trends in manual
control behavior when varying forcing function settings from pure target to pure distur-
bance, and to compare control b ehavior for relative target and disturbance forcing function
power settings as used in some previous experiments
1, 2, 4, 6, 16, 19, 20
to control behavior for pure
target-following and disturbance-rejection tasks.
IV.A. Method
The experiment performed for this research was highly similar to the experiment described
in Ref. 1. As stated in Section II, the same controlled element dynamics and quasi-random
forcing function signals were used in both experiments. Further important details of the
current experiment are described below.
IV.A.1. Independent Variables
This experiment was designed to evaluate the effect of varying a single independent variable:
the proportion of target and disturb ance forcing function power in a compensatory control
task. The eight conditions of this experiment, numbered C1 to C8, are depicted in Figure 7.
The dark gray portion of the bars in this graph indicate the percentage of disturbance forcing
function power for each condition; the (upper) light gray portion indicates the percentage of
power accounted for by f
t
. The experimental conditions were selected to be very similar to
those evaluated in an earlier experiment.
17
f
d
f
t
experimental condition
p
d
, -
p
t
, -
C1 C2 C3 C4 C5 C6 C7 C8
0.0
0.1
0.2
0.4
0.5
0.6
0.8
1.00.0
0.2
0.4
0.5
0.6
0.8
0.9
1.0
Figure 7. Graphical representation of the eight experimental conditions.
As physical motion cues most significantly affect pilot control behavior in a pure disturbance-
rejection task, in many earlier piloted tracking experiments where different modalities were
modeled separately, a disturban ce-rejection task was used with an additional target signal
that had 20% of the total forcing function power.
1, 2, 4, 6, 16, 19, 20
This relative forcing function
power distribution is represented by condition C3 in Figure 7. To investigate if further reduc-
tion of the target forcing function power would yield a task for which multimodal pilot model
13 of 28
identification is still possible, condition C2 was added. For a pure disturbance-rejection task
the pilot model inputs are the same, yielding a highly overdetermined identification problem.
As this problem is less severe for a pure target task, where the pilot inputs are not similar,
no condition was added between C7 and C8.
IV.A.2. Apparatus
The experiment was performed in the SRS at Delft University of Technology (see Figure 8).
Rotational pitch motion cues were provided by the six degree-of-freedom hydraulic hexapod
motion system during all experiment runs. No washout filter was used and controlled element
pitch attitudes were presented 1-to-1. The center of rotation was located at the upper gimbal
point (UGP) of the simulator. The UGP is located 1.2075 meters below the design eye
reference point, that is, 1.2075 meters below the approximate location of the pilot’s head.
No heave motion cues were provided. The time delay associated with the response of t he
SRS motion system has been experimentally determined to be approximately 30 ms.
21
During the experiment, subjects were seated in the right pilot seat. They controlled the
Citation pitch dynamics using an electrical sidestick without breakout force and a m aximum
pitch deflection of 14 degrees. Stick stiffness was set to 1.1 N/degree for deflections below
9 degrees; at higher stick deflections the stiffness was increased to 2.6 N/deg. A simplified
artificial horizon image was projected on the right primary flight display in the SRS cockpit
to indicate the tracking error e, which subjects were to minimize during the experiment.
The primary flight display had an update rate of 60 Hz and a time delay (including the
projection) of no more than 25 ms.
Figure 8. The SIMONA Research Simulator.
e
Figure 9. Compensatory display.
IV.A.3. Participants and Instructions
Seven subjects were invited to perform this experiment. All participants were male and
their ages ranged from 23 to 47 years old. Four of the participants were university staff
members, who all had experience as pilots of single or multi-engine aircraft. Two of them
were active Citation II pilots. The remaining three participants were students at the Faculty
of Aerospace engineering. One of these students had 119 flight hours in single engine aircraft;
14 of 28
the others had experience with manual vehicle control tasks from previous human-in-the-loop
experiments.
Before the start of the experiment, the objective of the experiment was explained to the
participants. They were told that they would be performing a combined target-following
and disturbance-rejection task and that the relative power of the target and disturbance
signals would be varied over the eight different conditions depicted in Figure 7. The main
instruction the participants received was that they should attempt to minimize the pitch
tracking error, that is, the signal e presented on the visual display, within their capabilities.
IV.A.4. Experimental Procedure
An individual experiment run was defined to last 90 seconds, of which the final 81.92 seconds
were used as the measurement data. Data were logged at a frequency of 100 Hz. Data from
the first 8.08 second s of each run were logged, but discarded for analysis. From previous
experiments
1
it was known th at 8 seconds is more than enough time for participants to
stabilize the controlled aircraft dynamics after the start of a run.
During the experiment, the participants’ tracking performance – expressed in terms of the
root mean square of the error signal e – was recorded for each condition by the experimenter.
When a participant’s level of performance had clearly stabilized and six repetitions of each
condition had been collected at this stable performance level, the experiment was terminated.
No fixed number of training runs was defined prior to the experiment. On average, 9 to 10
repetitions of each experimental condition were sufficient to gather the measurement d ata
for each subject. Typically, each subject performed 24 runs, that is, three repetitions of
all conditions, in between breaks. This allowed each subject to complete the experiment in
approximately 4 hours.
The experiment had a balanced Latin square design: the eight conditions of the experi-
ment were presented in quasi-random ord er. Subjects were informed of their tracking score
after each run in order to motivate them to consistently perform the tracking task at their
maximum level of performance.
IV.A.5. Dependent Measures
To investigate the effects of a systematic variation in target and disturbance forcing function
power as depicted in Figure 7, a number of dependent measures were considered to be of
interest. First of all, the variances of the recorded error signal e and control signal u were
calculated as measures of tracking performance and control activity, respectively. In addition,
the contributions of the target and disturbance signal p ower to these overall signal variances
were determined using a spectral method as described in Ref. 8.
15 of 28
In addition to these signal properties, the multimodal pilot model given in Figure 3 was
fitted to the time-domain data using a genetic maximum likelihood (MLE) procedure.
7
The
MLE method requires the inputs of the pilot model to be sufficiently exciting and informative
to give accurate parameter estimates. To have sufficiently exciting model inputs depends
on the control task, the controlled dynamics and even the control strategy adopted by the
subjects. This requirement was not met for the pure disturbance and target task in the
current experiment, condition C1 and C8. To accurately estimate the model parameters
for these tasks, some parameters were fixed to values extrapolated from those found for
neighboring conditions with two forcing functions, for which accurate estimates could be
achieved, C2 and C3, and C6 and C7. Using this strategy, reliable estimation of the remaining
parameters was guaranteed.
To evaluate the accuracy of the pilot model in the time domain, the variance accounted
for (VAF) was calculated using the measur ed pilot control signal and the output of the linear
pilot model.
6
The VAF gives the percentage of the measured pilot control signal variance
that can be explained by the linear response functions. The remaining portion of the variance
can be attributed to the pilot remnant.
Changes in pilot model parameters were used to quantify changes in pilot control strategy.
In addition, the effect of these changes in control behavior on the attenuation of the target
and disturbance signals was evaluated from the target and disturbance open-loop responses,
respectively.
8
In the frequency domain, pilot performance is determined by the crossover
frequencies and phase margins of the different open-loop responses. Using the pilot response
functions given in Figures 1 and 3, the disturbance open-loop response is determined by:
H
ol,d
(jω) =
U (jω)
δ
e
(jω)
= [H
pe
(jω) + H
pθ
(jω)] H
θ,δ
e
(jω) , (9)
and the target open-loop response function is given by:
H
ol,t
(jω) =
θ (jω)
E (jω)
=
H
pe
(jω) H
θ,δ
e
(jω)
1 + H
pθ
(jω) H
θ,δ
e
(jω)
. (10)
For a pure target and disturbance task, only one of the open-loop frequency response
functions is defined, as there is only one forcing function present. The disturbance and
target crossover frequencies, ω
c,d
and ω
c,t
, are the frequencies where the magnitude of the
disturbance and target open-loop responses cross the line with a magnitude of one. The
corresponding phase margins, ϕ
m,d
and ϕ
m,t
, are the phase differences with −180 degrees at
the crossover frequencies.
16 of 28
IV.B. Hypotheses
Previous experiments have shown that when physical motion cues are available, significantly
better tracking performance and higher control activity are observed for a disturbance-
rejection task compared to the target-following task.
11, 17
The results of the optimal control
analysis of Sec. III also show the performance increase, but indicate slightly decreased con-
trol activity for higher disturbance forcing function p ower levels. This disagreement between
experimental and theoretical results is thought to be at least partly due to the assumptions
made in the opt imal control analysis. Therefore, as found in the previous experiments, track-
ing performance and control activity are expected to increase in the current experiment with
increasing disturbance forcing function power.
For changes in manual control behavior, the optimal control analysis suggests that for
increasing levels of target forcing function power, more pilot lead will be generated from
visual cues. For disturbance rejection, it is better to acquire the required lead from physical
motion cues instead. Therefore, an increase in the value of the visual lead constant T
lead
and
a decrease in the value of the motion gain K
m
(see Sec. II.B) is expected to be found from
pilot model identification results with increasing target forcing function power. Based on the
findings from the experiment described in Ref. 17, however, it is expected that the changes
in control behavior over the different conditions will be relatively small in magnitude.
V. Results
This section presents the combined results of all seven subjects who participated in the
experiment. A repeated-measures analysis of variance (ANOVA) was performed to iden-
tify significant trends in the data. Significant linear or quadratic trends, if present in the
presented data, are indicated with gray lines in all graph s.
V.A. Tracking Performance and Control Activity
The variances of the error and control signals are given in Figure 10. For every condition the
mean data over all runs of all subjects is shown. The variance is decomposed into the variance
components due to the input signals of the control loop.
8
The variance components due to the
target and disturbance signals can be calculated using the power spectral density functions
of the error and control signals at the input frequencies of the target and disturbance forcing
functions, respectively. The remnant component is the difference between the total variance
in the signal and the sum of the target and disturbance components.
In Figure 10a it can be seen that the variance of the error increases – that is, performance
degrades – when the variance of the target signal is increased. The ANOVA indicates that
17 of 28
σ
2
(e), deg
2
(a) error signal
disturbance
target
remnant
C1 C2 C3 C4 C5 C6 C7 C8
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
σ
2
(u), deg
2
(b) control signal
C1 C2 C3 C4 C5 C6 C7 C8
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Figure 10. Variance decomposition of the error and control signals for every condition averaged
over seven subjects. The gray lines indicate significant trends
this effect is highly significant (F(7, 42) = 83.401, p < 0.05). The figure indicates an al-
most perfect linear trend across the conditions, which is confirmed by polynomial contrasts
(F(1, 6) = 131.772, p < 0.05). When inspecting the variance components, it can be seen
that the variance due to the target signal increases much faster than the variance due to
the disturbance decreases, causing the increase in the total variance of the error signal. The
remnant variance in the error signal remains approximately constant.
1 − σ
2
(e
d,t
)/σ
2
(f
d,t
), %
disturbance
target
C1 C2 C3 C4 C5 C6 C7 C8
65
70
75
80
85
90
95
100
Figure 11. Percentage of the disturbance and target variance in the error signal compensated
for by the control action of the subjects.
To further investigate these trends in the variance of the error signal, the percentage of
the variances induced by the target and disturbance signals that are compensated for by the
subjects have been calculated and are given in Figure 11. The error bar plot gives the means
and 95% confidence intervals for all subjects. The data is adjusted using the subject means
to compensate for the between-subject variability. Note t hat, as explained in Sec. II.C, the
total variance inserted by the target and d isturban ce forcing function is 2.0 deg
2
for all
conditions.
Figure 11 shows that the percentage of the variance compensated for remains constant for
all conditions for both the disturbance and the target components. This result is supported
18 of 28
by the ANOVA (F(6, 36) = 1.390, p > 0.05 and F(6, 36) = 1.271, p > 0.05). Furthermore, it
can be seen that disturbance errors are attenuated much more effectively (87%) than errors
introduced by the target signal (72%), a significant effect (F(1, 6) = 122.915, p < 0.05).
In Figure 10b the variance of the control signal shows a significant decrease if the power
of the target signal is increased (F(7, 42) = 6.131, p < 0.05). The control signal variance
changes quadratically over the conditions (F(1, 6) = 13.337, p < 0.05). The d ecrease in con-
trol activity results in a decrease in tracking performance as seen in Figure 10a. This result
was also found in a similar experiment.
17
It can be seen that the disturbance component in
the control signal decreases much faster than the target component increases. The remnant
component in the control signal remains more or less constant and contributes 40-45% of the
total variance in the control signal, as also observed in previous experiments.
1, 6
V.B. Pilot Control Behavior
For every subject and every condition, the pilot model of Figure 3 was fit to the time-
domain data using MLE. MLE requires the pilot model to be converted to a state-space
representation. For this conversion the controller canonical form was used. The time delays
of the model were included using fifth order Pad´e approximations. To reduce the influence of
the remnant on the parameter estimates, the averaged time-domain data of five measurement
runs was used as inp ut to the MLE method.
As explained in Sec. IV.A.5, accurate parameter estimates could only be achieved for the
conditions with both forcing functions having power (C2-C7). For condition C1, the visual
and physical motion perception delays were fixed. For the pure target-following t ask (C8),
the delays and the neuromuscular frequency were fixed. The fixed parameters for the pure
disturbance and target task were extrapolated from the neighboring conditions C2 and C3,
and C6 and C7, respectively.
V.B.1. Pilot Model Parameters
The identified pilot frequency response functions, H
pe
and H
pθ
, for all conditions averaged
over all subjects are given in Figure 12. The observed changes in control behavior over the
experimental conditions were highly similar for all subjects. As indicated by the arrow in
Figure 12a, only a clear trend in the magnitude of the pilot visual response can be observed.
The means and 95% confidence intervals of the multimodal pilot model parameters esti-
mated with the MLE method are given in Figure 13. The data is adjusted for between-subject
variability. Significant trends are indicated by the gray lines.
Figure 13a shows a clear decrease in visual gain as the power of the target forcing function
is increased. The ANOVA shows that the effect is significant (F(7, 42) = 8.592, p < 0.05)
19 of 28
(a) visual magnitude
|H
pe
|, -
ω, rad s
−1
10
-1
10
0
10
1
10
-1
10
0
10
1
(b) motion magnitude
|H
pθ
|, -
ω, rad s
−1
C1
C2
C3
C4
C5
C6
C7
C8
10
-1
10
0
10
1
10
-2
10
-1
10
0
10
1
(c) visual phase
6
H
pe
, deg
ω, rad s
−1
10
-1
10
0
10
1
-360
-270
-180
-90
0
90
180
(d) motion phase
6
H
pθ
, deg
ω, rad s
−1
10
-1
10
0
10
1
-360
-270
-180
-90
0
90
180
Figure 12. Mean pilot visual and pitch motion frequency response functions.
and polynomial contrasts indicate the trend is linear (F(1, 6) = 15.134, p < 0.05). This
decreasing trend in the visual gain, which is also apparent from Figure 12a, can be explained
by the increasing cue conflict with the physical motion cues as the target power increases.
The pitch motion perception gain first decreases as more target power is inserted into
the control loop, bu t then increases again when the target becomes dominant, as can be
seen in Figure 13b. This effect is significant (F(7, 42) = 3.114, p < 0.05) and the trend is
indeed quadratic (F(1, 6) = 34.987, p < 0.05). The higher gain for the pure disturbance task
(C1) is caused by the fact that the visual and physical motion cues are identical. Next, as
the cue conflict increases due to the increasing target power (C2-C5), th e relation between
the two cues becomes less clear and the physical motion gain decreases. If the target power
becomes dominant (C6-C7), the relation of the physical motion cues with the pilot control
input becomes stronger, resulting in an increasing motion perception gain. Finally, for the
pure target-following task (C8), the motion cues are completely related to the pilot control
signal and the magnitude of the motion perception gain is almost equal to the magnitude for
the pure disturbance task. This experimental result was not anticipated for by the results
of the optimal control analysis.
Figure 13c reveals an opposite trend to the motion perception gain for the visual lead
20 of 28
K
v
, -
(a) visual gain
C1 C2 C3 C4 C5 C6 C7 C8
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
K
m
, -
(b) pitch motion gain
C1 C2 C3 C4 C5 C6 C7 C8
0.8
0.9
1.0
1.1
1.2
1.3
replacemen
T
lead
, s
(c) visual lead
C1 C2 C3 C4 C5 C6 C7 C8
0.24
0.26
0.28
0.30
0.32
0.34
0.36
0.38
0.40
T
lag
, s
(d) visual lag
C1 C2 C3 C4 C5 C6 C7 C8
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
τ
v
, s
(e) visual time delay
C1 C2 C3 C4 C5 C6 C7 C8
0.26
0.27
0.28
0.29
0.30
τ
m
, s
(f) pitch motion time delay
C1 C2 C3 C4 C5 C6 C7 C8
0.18
0.19
0.20
0.21
0.22
ζ
nm
, -
(g) neuromuscular damping
C1 C2 C3 C4 C5 C6 C7 C8
0.16
0.18
0.20
0.22
0.24
0.26
ω
nm
, rad s
−1
(h) neuromuscular frequency
C1 C2 C3 C4 C5 C6 C7 C8
11.2
11.4
11.6
11.8
12.0
12.2
12.4
Figure 13. Means and 95% confidence intervals of the multimodal pilot-model parameters.
The data is corrected for between-subject variability. Gray lines i ndicate significant trends.
21 of 28
time constant. However, this trend is not significant according to the ANOVA analysis
(F(7, 42) = 2.055, p > 0.05). This is probably caused by the increased variance in the
estimates for conditions C1 and C8. The opposite trend compared to the motion perception
gain is an obvious result, as visual lead and lead resulting from the integrating action of the
semicircular canals are interchangeable. In Figure 13d no trend is observed for the visual lag
time constant and this is also confirmed by the ANOVA analysis (F(7, 42) = 0.789, p > 0.05).
The visual perception time delay significantly increases when the target forcing function
power increases (F(7, 42) = 3.854, p < 0.05). As can be verified from Figure 13e this trend
is linear (F(1, 6) = 9.575, p < 0.05). As the conflict between the visual and physical motion
cues increases, it takes more time to process the visual cues. Figure 13f shows that the pitch
motion perception time delay remains constant (F(7, 42) = 0.631, p > 0.05).
According to F igure 13g, the n euromuscular damping shows a similar trend as the motion
perception gain when the target power is increased. However, this effect is not significant
(F(7, 42) = 2.292, p > 0.05). The neuromuscular frequency is significantly affected by the
change in forcing function power (F(7, 42) = 3.545, p < 0.05). There is a significant linear
increasing trend (F(1, 6) = 7.839, p < 0.05), as can be seen in Figure 13h.
V.B.2. Variance Accounted For
Figure 14 illustrates the means and 95% confidence intervals of the VAF for all conditions.
The data is adjusted using the subject means to compensate for the between-subject vari-
ability. Note that the VAF is between 85 and 90 percent for all conditions. This implies
that 85 to 90 percent of the variance of the measured control signals can be explained by
the linear pilot model, the remaining 10 to 15 percent is pilot remnant. This percentage of
pilot remnant in the control signal is lower compared to t he value found in Sec. V.A. This
is caused by averaging the time-domain data for the MLE method, reducing th e remnant
component in the signals. The VAFs for the pure target and disturbance tasks are equal to
the VAFs found for the remaining conditions, indicating that fixing some of the parameters
did not affect the accuracy of the model fit in the time domain.
V.B.3. Disturbance and Target Open-Loop Response Functions
Figure 15 gives the disturbance and target open-loop response functions, including the
crossover frequencies and phase margins for condition C5 of subject 2. The open-loop es-
timates are constructed using the estimated pilot frequency response functions and Eq. (9)
and Eq. (10). However, the open-loop frequency response functions can also be calculated
analytically using the Fourier coefficients (FC) of u, δ
e
, θ and e at the input frequencies of the
forcing functions. The analytically calculated disturbance and target open-loop responses
22 of 28
VAF, %
C1 C2 C3 C4 C5 C6 C7 C8
75
80
85
90
95
100
Figure 14. Means and 95% confidence intervals of the variance accounted for, corrected for
between-subject variability.
are also given in Figure 15 and indicate that the MLE estimates have a high accuracy in the
frequency domain.
The means and 95% confidence intervals of the disturbance and target crossover frequen-
cies and phase margins are given in Figure 16. The between-subject variability is removed by
adjusting the data with the subject means. The figure shows that increasing the target forc-
ing function power decreases the disturbance crossover frequency and consequently increases
the disturb ance phase margin. The ANOVA analysis indicates that the decrease in crossover
frequency is significant (F(6, 36) = 27.699, p < 0.05) with a linear trend (F(1, 6) = 39.476,
p < 0.05), but the increase in phase margin is not (F(6, 36) = 4.429, p > 0.05). The tar-
get crossover frequency and phase margin remain constant when the power of the forcing
functions is varied (F(6, 36) = 2.054, p > 0.05 and F(6, 36) = 1.149, p > 0.05).
Figure 16 shows that for the pure disturbance-rejection task, for which the physical
motion cues are fully correlated with the visual cues, the disturbance crossover frequency
is found to be the highest. When the power of the target forcing function increases, the
correlation between the cues becomes smaller and the disturbance crossover frequency is
reduced. The disturbance phase margin is found to increase, indicating increased stability
margins for the disturbance-rejection loop. The target crossover frequency and phase margin
are not affected by the forcing function power settings. These results were also found in a
previous experiment.
17
VI. Discussion
Seven subjects participated in an experiment that investigated the effects of forcing func-
tion power settings on pilot performance and control behavior in a combined target-following
disturbance-rejection pitch control task. The experiment was performed in the SIMONA Re-
search Simulator at Delft University of Technology. In eight experimental conditions, the
23 of 28
ω
c,d
= 4.21 rad s
−1
(a) disturbance magnitude
|H
ol,d
|, -
ω, rad s
−1
10
-1
10
0
10
1
10
-2
10
-1
10
0
10
1
10
2
ω
c,t
= 2.95 rad s
−1
(b) target magnitude
|H
ol,t
|, -
ω, rad s
−1
10
-1
10
0
10
1
10
-2
10
-1
10
0
10
1
10
2
ϕ
m,d
= 33.9
◦
(c) disturbance phase
6
H
ol,d
, deg
ω, rad s
−1
10
-1
10
0
10
1
-540
-450
-360
-270
-180
-90
0
ϕ
m,t
= 50.1
◦
(d) target phase
6
H
ol,t
, deg
ω, rad s
−1
FC
MLE
10
-1
10
0
10
1
-540
-450
-360
-270
-180
-90
0
Figure 15. Open-loop frequency response functions (subject 2, C5).
pitch control task was varied from a pure disturbance task to a pure target task, with com-
bined tasks in between.
Overall, pilot performance degraded significantly for tasks with higher power of the target
forcing function. This is a result of the higher performance in decreasing the disturbance
variance component in the error signal compared to the target variance component, and can
be explained by the fact that the disturbance signal directly influences the physical motion
cues. Physical motion cues provide faster lead information on the effect of the disturb ance
signal, as compared to visual lead, increasing performance. In addition to the decrease in
overall performance, pilot control activity is also found to decrease.
The results of the MLE parameter estimation procedure indicate that multimodal pilot
control behavior is significantly affected by the power settings of the target and disturbance
signals. When the power of the target forcing function becomes higher, the relation between
the visual and physical motion cues becomes less evident and an increasing cue confl ict arises.
The resulting effect is a decrease in visual percep tion gain and an increase in visual perception
time delay. The motion perception gain first decreases, but when the target power becomes
dominant, increases again. The opposite effect is seen for the visual lead time constant, as
the visual lead and the lead resulting from the integrating action of the semicircular canals
24 of 28
(a) crossover frequency
ω
c
, rad s
−1
disturbance
target
C1 C2 C3 C4 C5 C6 C7 C8
1.5
2.0
2.5
3.0
3.5
4.0
4.5
(b) phase margin
ϕ
m
, deg
C1 C2 C3 C4 C5 C6 C7 C8
20
30
40
50
60
70
80
Figure 16. Means and 95% confidence intervals of the cross-over frequencies and phase margins,
corrected for between-subject variability. Gray lines indicate significant trends.
are interchangeable. With an increase in target forcing function power, the performance in
the attenuation of the disturbance error decreases, as is seen by a decrease in disturbance
crossover frequency.
The optimal control analysis proved to be helpful in understanding the theoretically op-
timal use of the different motion cues for a change in relative power of the forcing functions,
giving the limitations of t he pilot. The decrease in tracking performance and visual percep-
tion gain were predicted correctly. Also, the initial response of the visual lead time constant
and the physical motion perception gain proved to be correct. The parabolic trend in the
motion perception gain and the visual lead was not predicted correctly, wh ich was most
likely caused by the fact that some of the parameters that were fixed in the optimal control
analysis (for example, the visual perception time delay) were seen to change significantly
in the experiment. The initial response that was predicted correctly is near the condition
that was used to fix some of the parameters in this analysis. In addition, the cost function
weighting factors were also fixed and optimized for one condition. It can be expected that
as the relation between the motion cues changes, also the internal weighting of the different
cues and the control signal changes. These two factors show that due to the many assump-
tions required to obtain a solvable optimization problem, the use of the results of such a
theoretical analysis is limited.
Although marked changes in pilot control strategy are found in the exp erimental results,
the variations in the multimodal pilot model parameters are only very small. For some
parameters the change in magnitude for d ifferent experimental conditions is just in the
order of one percent. This warrants the use of parameter estimation techniques that can
guarantee very accurate parameter estimates, such as the MLE procedure adopted here. In
an earlier experiment investigating the influence of forcing function power settings on pilot
control behavior, no significant change in control behavior was found.
17
This could have
been because of the less accurate parameter estimation techniques used in this research.
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No accurate parameter estimates could be achieved for the pure target and disturbance
tasks without reducing the number of free parameters in the optimization problem. This is
caused by the general requirement of the parameter estimation techniques that both inputs
to the pilot model should be sufficiently exciting. When calculating the pilot responses from
Fourier coefficients it is even required that the number of forcing functions that need to
be inserted into the control loop equal th e number of pilot model inputs. As neighboring
conditions for which an accurate fit was possible were available for this exper iment, the data
from these conditions was used to fix the visual and pitch motion perception time delays
and the neuromuscular frequency. This allowed for an accurate estimate of the remaining
parameters for the pure target and disturbance task with an equally high variance accounted
for as for the conditions with two forcing functions.
Experimental measurements of the effects of physical motion cues on pilot control be-
havior during target following and disturbance rejection are not straightforward, as for p ure
target-following and disturbance-rejection tasks, multimodal pilot control behavior can not
be accurately estimated. In many previous experiments, this was solved by adding a dis-
turbance or target signal with relatively low power in addition to the original target or
disturbance signal, respectively. The results of the experiment described in this paper indi-
cate that this strategy can indeed be used, as such an additional signal was found to have
only a relatively small effect on pilot performance and control behavior. The experiment also
revealed that the additional signal can have very little power, thereby minimizing the inter-
ference with the dominant task, while still allowing for accurate estimation of pilot model
parameters. Using a target signal with 10% of the total power in addition to a disturbance
with 90% of the total power r esults in multimodal pilot control behavior that is highly similar
to control behavior in a pure disturbance task.
VII. Conclusions
In a combined target-following disturbance-rejection aircraft pitch control task, multi-
modal pilot control behavior is significantly affected by the relative power settings of the
target and disturbance forcing functions. With an increase in relative target power, the cue
conflict between the visual and physical motion cues increases. This causes a reduction in the
visual perception gain, while the visual perception time delay becomes higher. The motion
perception gain decreases, but is found to increase again if the target power becomes domi-
nant. As the lead information is the result of the integrating action of the semicircular canals,
the change in physical motion gain is counteracted by an opposite trend in the visual lead
time constant. The result of this change in control strategy when increasing the target forc-
ing function power is a reduction in tracking performance and control activity. The reduced
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performance is also apparent from the decrease in distu rbance crossover frequency, indicating
a decreased attenuation of the disturbance errors in the frequency domain. Despite these
effects, multimodal pilot control behavior in a pure target-following or disturbance-rejection
task can be evaluated by using a combined target-following disturbance-rejection task with
an additional signal with relatively small magnitude. In this case, control behavior is highly
comparable to the single forcing function tasks, while still allowing for accurate estimation
of the multimodal pilot model parameters.
VIII. Acknowledgments
This research was supported by the Technology Foundation STW, the applied science
division of NWO, and the technology program of the Ministry of Economic Affairs.
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