Properties of several structural variations in the neuromotor interface portion of the optimal control model (OCM) are investigated. For example, it is known that commanding control-rate introduces an open-loop pole at S=O and will generate low frequency phase and magnitude characteristics similar to experimental data. However, this gives rise to unusually high sensitivities with respect to motor and sensor noise-ratios, thereby reducing the models' predictive capabilities. Relationships for different motor submodels are discussed to show sources of these sensitivities. The models investigated include both pseudo motor-noise and actual (system driving) motor-noise characterizations. The effects of explicit proprioceptive feedback in the OCM is also examined. To show graphically the effects of each submodel on system outputs, sensitivity studies are included, and compared to data obtained from other tests

Kleinman, D. L.

Lancraft, R. E.

English

NASA Technical Reports Server

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A COMPARISON OF MOTOR SUBMODELS IN THE
OPTIMAL CONTROL MODEL
L
byRoy E. Lancraft and David L. Klelnman
Department of Electrical Engineering & Computer Science -""_
University of Connecticut -
Storrs, Conn. 06268
ABSTRACT
Recent interest in the areas of modeling the effects of motion on human
Operators, and manual control of low bandwidth systems has led to the need
for accurate submodels of the low frequency characteristics of the Human
Operator (HO). Unfortunately, matching low frequency human response data
has been a problem with almost all HO models, the well known Optimal Control
Model (OCM) being no exception. This research is an attempt to better under-
stand and hopefully eliminate these problems.
In this paper, properties of several structural variations in the neuro-
motor interface portion of the OCM are investigated. For example, it is
known [I-2] that commanding control-rate introduces an open-loop pole at
SffiOand will generate low frequency phase and magnitude characteristics
similar to experimental data. However this gives rise to unusually high
sensitivities with respect to motor and sensor noise-ratlos, thereby reducing
the models' predictive capabilities. Relationships for different motor sub-
models are discussed to show sources of these sensitivities. The models in-
vestigated include both pseudo motor-noise and actual (system driving) motor-
noise characterizations. The effects of explicit priprioceptive feedback
in the OCM is also examined. To show graphically the effects of each sub-
model on system outputs, sensitivity studies are included, and compared to
data obtained from [1-2].
INTRODUCTION
Recently, motion studies [2,3] have shown the major effects of motion :
to be on low frequency (W < 1 rad/sec) HO magnitude and phase characteristics.
This means that low frequency modeling errors present in the baseline im- _;
' plementation of the OCM must be minimized if the effects of including motion d
variables are to be felt. It is known [1,2] that ohanging the structure of
the neuro-motor interface portion of the OCM will give the desired low fre-
quency effects. Specifically if the HO commands control rate rather than
control, the low frequency phase drooping occurs. However, in order to match
human response data over simple vehicle dynamics, large deviations in the
motor noise ratios were needod [2]. This clearly degrades the predictive
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power of the model. In this paper sub-models developed in [1,2] will be
compared from a sensitivity point of view, in an attempt to better under-
stand the limitations of each approach.
Problem Formulation
In this section structural changes will be made to the baseline OCM
(for a more detailed description see Levlson [2]). A general form will be
developed first,,with specific models introduced as special cases to it.
In the development which follows, the time delay will be ignored since it
has littie bearing on our discussion.
The system being controlled is described by the state-.space equation
= Ax + Bu + Ew (i)
where:
x = "true" system state
u = "true" control input
and where displayed system variables are given by
y = Cx + Du (2)
The system is assumed to be controlled to minimize (in steady-state)
a quadratic cost functional
J ffiE{y' Qy y + g _2} (3)
based on the (delayed and) noisy information perceived by the HO, This in-
formation is assumed to consist of both displayed and proprioceptiv e vari-ables, i.e.,
yp Cx + Du + v (4a)Y
U = U+V
P u (4b)
where:
coV{Vy} = V + p E{y2} (Sa)Y Y
+ E{u 2}
c°V{Vu)= Vu Pu (5b)
The control law that minimizes J is given by
r -j0,,,i:f00c (6)
where:
ffi human's best internal estimate of x
(_ " " " " " U
102
.... liLi_!
19-/900-/41-/-103
To model any actual noise at the motor end, a driving motor noise is
added to (6). Notice control rate is generated rather than control. Thus,
= 6 + v. (7)
C U
where: "'"_
cov{v.}= V, + E{6 2}
u u P6 c (8)
However the human's internal representation of the neuromotor interface,
Eq. (7), is: _
= + v (9) _:|6 _c p
where: "
coV{Vp}= Vp + pp E{6c2} (i0)
and typically cov{v } # coy {v.} .
p u
The pseudo motor noise Vp does not act as a driving noise to the system,
but instead degrades performance by making estimation sub-optimal [2].
_: Implementing these changes gives rise to the structure shown in Fig. I.
r
r W
. _ SYSTEM & _l Z
, DYNAMICS_| "7 DISPLAY '
!
_ "Visual
!t Channel"
:" Vp
J 1
. ,---,.
i I , ,_ L,E__r'_.._ ,. _'-_ KALMANFILTER- i_I,_
PRED{CTOR /
V_ Vy
"ProprioceptiveChannel" Vu
I I I ii i I i im i i i 1 i • i ill ,1
FIG.]REVISEDOPTIMALCONTROLMODEL.
, 103
1979007417-104
The particular submodels considered in this study are as follows:
Driving Noise Models:
i) cov_v } = cov{v.} , i.e., optimal estimation occurs, driving motor
noisePequal to _.
u
" proprioceptive information available
2) Same as model (i), except no proprloceptive information available
Pseudo noise models:
3) v. = 0, i.e., sub-optimal estimation occurs, only pseudo noiseu
present
• proprloceptlve information available
4) Same as model (3) except no proprioceptive information available
SENSITIVITY RESULTS
Data from [1,2] was matched using each of the aforementioned models.
Only K/S and K/S**2 dynamics were considered. The reader is referred to
the sensitivity studies included in [I] so a comparison can be made to the
baseline model.
K/S Dynamics
The following nominal parameters were found to give reasonable matches
to the data, and will be used as a basis for the K/S sensitivity work.
Notice that proprioceptlve feedback is not needed for K/S dynamics; this
agrees with findings in [1,2]. Therefore, for K/S dynamics we need only
consider two models, driving noise and pseudo noise.
A
Model SNR SNR-u MNR TD TN SNR = O
YA
........ SNR - u = O
u
1 & 3 -20 -_ -40 .17 .08
2 & 4 -20 -- -40 .17 .08 MNR = p_ or Op
-I
..... TD = z, TN = L
u
It was found that the trends discussed in [i] for SNR, TD and TN were
the same for all the models considered. The only exception to this was for
the driving noise models, where the low frequency remnant curves were slight- i
ly higher. _
l Effects of MNR
From Fig. 2 it is clear that motor noise mainly affects the low ire-
104
1979007417-105
EFFECTSOF MNR ON KIS DYNAMICS.
105
• " 1979007417-106
quency portion of the magnitude, phase and remnant curves. There are bas-
ically two reasons for this. First,the shape of the low frequency portion
is due to the integrator at the motor end (where in the baseline OCM,
I/(T_S+I) was present). Secondly, the sensitivity is due to the degradation
of e§tlmatlon performance as the motor noise is increased. Because the level
of the driving noise is so low, the linear part of the HO model (Bode plot)
is the same whether pseudo noises or driving noises are used. Notice that
the driving noise has a dominant affect only on the low frequency remnant. -'"
All scores increase with increasing motor noise. Scores using the
pseudo model are fairly insensitive to motor noise, since it is the degraded
estimation which causes them to change. Scores using the driving model are
much more sensitive to motor noise, since increasing the motor noise in-
creases the remnant in the system.
K/S**2 Dynamics
The following is the nominal parameter set found for K/S**2 dynamics.
Model SNR SNR-u MNR TD TN
I & 3 -20 -25 -40 .21 .I
2 & 4 -20 .... 54 .21 .!
Here, as in K/S dynamics, trends discussed in [1] for SNR, TD, and TN
also hold for our revised models. Below we discuss only the effects of MNR
& SNR on control, i
Effects of MNR
No Proprioceptive Information (models 2 & 4)
Looking at Figure 3 it is clear that the motor noise affects the low
frequency Bode plots in a manner similar to that found for K/S dynamics.
Again, more remnant power is shifted to the low frequencies for model 2 than
for model 4.
Notice that model 4 matches the low frequency remnant very poorly (this
could be improved slightly by increasing the noise on displayed error) and
may be interpreted as a major shortcoming of this model since we desire a
nominal set of parameters,
106
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1979007417-107

'.,
-I,+ ]" _,
,._(=)__ .... mvI,G,OXSE
(dB___ 5 - ' I PSEUD( NOISE
"450.1 0.5 1.0 5.0" 10.0 50.0
w (rad/sec)
:, FIG.4 EFFECTSOF MNRONK/S**2 DYNAMICS(MODELS1 & 3).
; 108
1979007417-109
With Propioceptive Tnformation (Models 2 b 4)
The effects of including proprioceptive feedback can be seen by compar-
ing Figs. 3 & 4, Again remnant is higher for driving motor noises, but iS
is spread out over a wider band of frequencies. This may be due to the
circulation of remnant in the feedback loop. Although not shown, the scores
for model 1 were always higher and more sensitive than those for model 3,
and seemed to match the data better.
Notice that the sensitivity of the model to changes in the motor noise
has been reduced dramatically by including proprioceptive feedback. Because 1
the model now has observations of control and control rate to use in forming
an estimate of control, estimation stabilizes and improves.
_, Effects of SNR (Models i & 3)
i Figure 5 shows the low frequency remnant for model 3 much closer to
that of model 1, Notice if the sensor noise is too large (>-15dB), the
_ model ignores this observation and models 1 & 3 effectively become models
2 & 4. Since knowledge of the control signal is important in this task,
it is clear that the model should be, and is, sensitive to the quality of
this information• The low frequency effects result primarily from the move-
i merit of the estimator poles•
Sensitivity of Scores
Relative RMS error is plotted in Fig. 6 as a function of MNR• Because
RHS error is the moat sensitive score, Fig. 6 shows that including proprio-
ceptive feedback reduces the sensitivity of all the scores,
Review _'
From the sensitivities studies it was seen that in general:
• All predicted scores were lower than measured ones for pseudo noise
• All system measures were more sensitive to driving motor noise than
to pseudo noise
• Thls sensitivity can be reduced by including an observation of con-
trol
• The level of sensor noise on control induces the low frequency
effects
• The integrator at the motor end confines the remnant power to the
low frequencies
1979007417-110
|30 ..........
h(=)20 "'. .. j" _ '(dB) ./r10 _
-.fib" '
-:S_"
• i I
50 • -_l_"_ ,_, __..._ _,
-50 .....
(deg) ---- THEOIETICAL
-150 ' " _ HEASIRED ..... _ "
-250
0.1 0.5 I .0 5.0 10.0 50.0
= (rad/sec)
i' .I- '¢ ¢1
,,,,,,(=) -," psEuDoN,iSE
(dB) _ ._Jr ---,,-'-" DRIVINGOISE
-40 ........
-5O
0.1 0.5 1.0 5.0 10.0 50.0
(rad/sec)
i FIG,_.__5_5EFFECTSOFSNR-UONWS**2 DYNAHICS(MODEL1 & 3). 0_' l_K)O_Q_E'I'J¢¢'z'
110
I|
1979007417-111
w ALITy
i Hi2.0
r /(2) 'e M0del- ( )
r
_.0 "'
_ -60 -50 -40 -30 -20
_ HNR
i FIG. 5: SENSITIVITYOF RMS ERROR (K/S**2TASK)
" It Is dlfflcult to match K/S**2 data, wlth a nomlnal set of para-
meters, using models 2 b 4
FINAL COMMENTS
i
Sensitivity studies have shown that Including observations on control
can reduce model sensitivity to driving motor noises. Also it was shown
that a sensor noise added to control does not greatly affect the uncorre-
lated part of the model. Nominal parameters were found that could match K/S
& K/S**2 dynamics, provided that observations on control are Included for
K/$*'2 but not for K/S. If the model is allowed to allocate attention free-
ly among all observed variables, this may provide a scheme for determining
the sensor noises. One hypothesis is that this essentiaUy forms a decision _,
step (perhaps as part of the learning process) tn the HOmodel, where It
must evaluate the benefits of all the cues it has available to it and then
decide on a subset which will be useful for control purposes.
_ More work needs to be done in order to find a good rule for picking the
i: sensor noises. Testing models 1 and 3 over a wider set of system dynamics
:: Is also important to see if our findings are true in general or Just a ..
special case.
III
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1979007417-112
REFERENCES
1. Klelnman, D.L, & Baron, S,: Manned Vehlcle Systems Analysls by Means of
Modern Control Theory. NASACR-1753, June 1971.
2. Levlson, W.H., Baron, S., Junker, A.M.: Modellng the Effects of Envi-
ronmental Factors on Human Control and Information Processing, AMRL-
TR-76-74, Aug, 1976.
3. Levlson, W.N. & Junker, A.M.: A Model for the Pilots Use of Motion Cues
in Ro11-Axls Tracking Tasks. AMRL-TR-77-40, June 1977.
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A comparison of motor submodels in the optimal control model

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