The effect of the spectrum of the forcing function on the human pilot dynamics in manual control was investigated. A simple compensatory tracking experiment was conducted, where the controlled element was of a second-order dynamics and the forcing function was a random noise having a dominant frequency. The dominant frequency and the power of the forcing function were two variable parameters during the experiment. The results show that the human pilot describing functions are dependent not only on the dynamics of the controlled element, but also on the characteristics of the forcing function. This suggests that the human pilot behavior should be expressed by the transfer function taking into consideration his ability to sense and predict the forcing function

Osawa, T.

Tanaka, K.

Washizu, K.

English

NASA Technical Reports Server

r' N79- I 90il ..
?
A STUDY 0F TIIT.';ETFECT O;' FORCING FUNCTION CHARACTERIST'2S
! ON HUMAN OPERATOR DYNN4ICS IN MANUAL CONTROL
by Kyuichiro Washizu*, Keiji Tanaka** and Tatsuo Osawa*
*Department of Aeronaut [cs, Univer:;i ty of Tokyo, Tokyo,
**instrumentation and Control Division, National Aerospace
Laboratory, Chofu, Toky¢,
SUMMARY
This paper deals with the effect of the upectrum of the forcing f_u_c-
tlon on the human pilot dynamics in manual control. A simple compensatory
tracking experiment was conducted, where the controlled element was of a
second-order dynamics and the forcing function waz a random noise having a
dominant frequency. The dominant frequency and the power of the forcing
function were two variable parameters during our expuriment.
The results show that the human pilot describing functions are dependent #
not only on the dynamics of the controlled element, but also on the charac-
teristics of the forcin E function. This suggests that the human pilot be-
havior should b_ expressed by the transfer function taking into consideration
his ability to sense and predict the forcing functic_n.
SYMBOLS
Aij(k) element of k-th autoregressive coefficient matrix
B backward shift operator
c(t), c(n) human pilot output
dB decibel
e(t), e(n) displayed el'for
i(t), i(n) forcing function
Kf static gain of forcing function filt,_r
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1979007417-025
https://ntrs.nasa.gov/search.jsp?R=19790007419 2020-03-20T18:15:36+00:00Z
M order of autoregressive model
m(t), m(n) controlled element output
s variable of Laplace transform
Y:(j_) controlled element
Yf(j_) forcing function filter
Yp(jm) human pilot describing function
A sampling interval
Cf damping of forcing function filter
_n damping of controlled element
o_ 2 power of forcing function
_f undamped natural frequency of forcing function
_n undamped natural frequency of controlled element
INTRODUCTIOn{
It is well known that when a human pilot controls the system, his
control behavior depends on the characteristics of the forcing function to
the system as well as of the controlled element itself. A great number of
papers have been published on this problem.
Concerning the effect of the characteristics of the controlled e] nent
on pilot behavior, Washizu and MiyaJima (reference i), and Goto and W_.tzu
(reference 2) pointed out in a series of study on manual control of a second-
order system that the human pilot takes notice of the periodicity in the
response of the controlled element, if any, and makes use of it to improve
his control performance.
On the other hand, concerning the effect of the forcing function on
pilot behavior, McRuer and Krendel (reference 3) pointed out that as the
bandwidth of the forcing function increases, the effective time delay re-
duces probably due to the muscular reaction characteristics uf the human
pilot.
The purpose of the present paper is to investigate the effect of the
forcing function spectrum on the human pilot dynamics in manual control. A
simple compensstory tracking experiment was conducted, where the controlled
element was of the second-order dynamics and the forcing function was a
random noise having a dominant frequency. The dominant frequency and the
power of the forcing function were two variable parameters during the experi-
2O
1979007417-026
. . . ....
! ment. Pilot describing functions were derived from the autoregressive model
_ coefficients identified using the Akaike's Final Prediction Error method.
h
_- EXPERIMENT ,i
The _ystem of our experiment was built up with an analogue computer, an
oscilloscope and a control stick with a restoring spr_ng. Its block diagram
: is as shown in figure i. The error e(t) was displayed on the oscilloscope
by a line segment moving vertically. The pilot was requested to minimize
the error to the best of his ability. The controlled element had a second- ._
order stable dynamics, and its transfer function was of the form;
2
_nYc(s) = (1)
,s2+2_n(_ns+L0n2
The damping Cn and undamped natural frequency aJn of the controlled element
w_.re held fixed throughout our experiment such as,
=0.i
to =_ = 4.47 (tad/see) .
n
The shaping filter of the forcing function also had a second-order stable
dynamics as,
2
Kfmf
Yf,sjt_ = 2+. 2
(2)
s 2_f_fs+tof
where the damping _f was held fixed to 0.i and the static gain Kf and the
undamped natural frequency tof were two variable parameters. Thus, the white
noise was transformed into a forcing function having a dominant frequency
after passing the filter. The dominant frequency was varied by selecting the
values of tof as,
tof = 3.16, 2.24, 1.58 (rad/sec) .
We chose fo,n" levels for the power of the forcing function oi 2 by ad_ustlng
K£ of the equation,
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1979007417-0P7
2 _t" Kf2 2
_i = 4 _f _w (3)
where Gw 2 is the power of the noise source.
The experiment was of 12eases, namely 3 kinds of frequencies and 4
power levels of the forcing function, _nd two runs of each ease were perform-
ed. After sufficient excercise, the analog data of the length of 90
seconds for each runs were recorded. The data, i(t), e(t), c(t) and m(t)
in figure i were transformed into digital data by use of the NOVA mini- ._
computer system. The FACOM 230-75 computer was employed for numerical calcu-
lations of the following time series analysis.
ANALYSIS
By the use of the experimental data thus obtained, the human pilot
describing f_mctions were identified utilizing a time domain technique; ti._t
is, an autoregressiw model was fitted to the data by using the Akaike's
MFPE (Multiple Final Prediction Error) method. (reference 4)
In the first place, the data were sampled from the analog data of the
pilot output c(t) and the error e(t) with the smllpling interval A, which was
set as 0.] sec. The sampled data are denoted by c(n) and e(n). Then, the
autoregressive model of the form;
Ic(nll _AII(B)AI2(B) 1 Ii(n)I I_ll'_!21 _l(n) I
= + (_)
e(n A21(B) A22(B) (n) _! J22 _2 (n)
A_j(B) = aij(1)B + aij(2)B2+ ...... + aij(M)B M (5)
_x(n): x(n-1) (6)
|
was fitted to the given data. B is the backward sh_ft operator as shown in I
equation (6), and Aij(B)'s in equation (4) are the power series in B that
are made up of the autoregressive model coefficients aij(k ) with k going
Crom 1 through M. The order of the model M is determined by the MFPE
m,,thod. _i(_1)'s in equation (h) are mutually independent white noises.
Once we have succeeded in fitting the model to the given data, namely,
d}2 = c_2] _ 0, we csn compute the pilot describing function using
22 _
1979007417-028
4A12(J _) (7)
p i - All(JOJ)
where All(J_) and Al2(Jm) are obtained from All(B) and AI2(B) in equation (h)
respectively, by replacing B with exp(-JmA).
This method has recently been put into practical use, and our experience
;._' in using it has proved that it is quite efficient and powerful (reference 5). i
Application of this method to our data was also successful, as the estimated
correlation coefficient of the noise sources, (_12/,/(_IIG22,was quite small.
RESULTS
Figures 2 and 3 are examples of the time histories of the records.
Note that in figure 2, namely when the frequency of the forcing function _f
was large, it is not evident that c(t) was affected by the forcing function
periodicity. The pilot seemed to suppress only the controlled element
periodicity.
On the other hand, figure 3 shows the time history of the case when mf
was relatively small. In this case, it is evident that c(t) was made up of
two main sinusoidals; one reflected the forcing function periodicity and the
other reflected the pilot behavior which seemed to suppress the controlled
element periodicity. This suggests that, when a_.was relatively small, the
haman pilot behavior was affected by the forcing function.
Above tendencies can be seen more obviously in the power spectrum
densities of the pilot output as shown in figure 4_ namely in the vicinty of
= mf, the power spectra were pulled up as ai2 increased, and thisphenome-
non became more conspicuous when mf was relatively small.
Typical pilot describing functions are shown in figures 5 and 6. From
these figures, the following tendencies have been observed;
i) If the power of the forcing function _i2 is increased, while keeping
the undamped natural frequency mf unchanged, the gain of the pilot des-
cribing function increases, but the phase lead becomes smaller in the
frequency region below the undamped natural frequency of the controlled
element ah. :_
2) If the frequency of the forcing function _f is decreased, while keeping
the power oi2 unchanged, the gain of the pilot describing function _
increases, but the phase lead becomes smaller in the low frequency range, _
especially in the neighbourhood of the undamped natural frequency of the
forcing function.
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1979007417-029
AFigure 7 shows the performance of the pilot control indicated by G2/G2.
It is evident that the smaller the undamped natural frequency mf was, the
b_:tter the performance became. This implies that when mf was small, the.
pilot could easily recongnize th,.forcing function periodicity, and his
t.ask became easier.
These results lead to the following consideration concerning the for-
cing function effects on human pilot control behavior.
The effect of the forcing function bandwidth on the pilot describing
function is reported in reference 3. It is pointed out in the report that
the effective time delay of the human pilot decreases as the bandwidth of the
forcing function ipcreases.
On the other hand, the preseht study put emphasis on the effect of the
frequency _f and Kf of the forcing function shaping filter. It has been
_uggested that the increase in the power of the forcing, function is likely
to work so as to make the pilot employ the control that takes into account
the dominant periodicity in the forcing function. The attempt to suppress
the dominant frequency component may lead to the reduction of the power of
the error. It has also been suggested from the present study that if the
response of the controlled element and the forcing function have periodici-
ties, the human pilot would try to augment the system stability by making
use of the periodicity in the response of the controlled element, and then,
try to make the performance as good as possible by making use of the periodi-
city of the forcing function. Especially, if the power of the forcing
function is large and the two natural frequencies are separated, it would
be easy for the pilot to notice these frequencies and to make use of these
frequencies in the control,
The present study has shown that the human pilot dascribing functions
are dependent not only on the natural frequency of the controlled element,
but also on the frequency and the power of the forcing function. These
results seem to suggest that the human pilot control behavior couldn't be
expressed by a simple transfer function compensating the controlled element
delay only, but should be expressed by ,the transfer _unction taking into
consideration his ability to sense and predict the forcing function.
CONCLUDING REMARKS
!
The results show the effects of the forcing function on the human pilot I
such as;
l) If the power of the forcin_ function Gi 2 increases, the gain of the
human describing function IYpl increases, but the phase lead of Yp
becomes smaller at _ < mn.
2) If the undamped natural frequency of the forcing function mf de-
the gain l_p[ increases but the ph_!se lead of Yp becomescreases,
smaller especially in the vicinity of _ = (_f.
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- 1979007417-030
2.' 3) The human pilot seems to try to augment the system stability and
: make the performance better by use of _n and _f, especially when 0i2
i is large, and _n and _f are separated.
!
ACI_O_fLEIXIFNENT
5 The authors are deeply indebted to Mr. M° Okabe, Chief of Human
Engineering Section of NAL, for his support on conducting the experiment.
REFERENCES
I. Washizu,K.; and MiyaJima,K.: Some Consideration on the Controllability
Limit of a Human Pilot. AIAA J., Vol.5, No.l, 1967, pp.151-155.
2. Goto,N.; and Wahizu,K.: On the Dynamics of Human Pilots in Marginally
Controllable Systmes. AIAA J., Vol.12, No.3, 197h, pp.310-315.
3. McRuer,D.T.; and Krendel,E.S.: Mathematical Models of Human Pilot
Behavior. AGARD-AG-188, 197h.
h. Akaike,H.: Statistical Predictor Identification. Ann. Inst. Statist.
Math., Voi.22, 1970, pp.203-217.
5. Tanaka,K.; Goto,N.; and Wahizu,K.: A Comparison of Techniques for
identifying Human Operator Dynamics Utilizing Time Series Analysis.
12th Ann. Conf. on Manual Control, NASA TM X-73,170, 1976, pp.
• •673-685.
25
.... 1979007417-031
26
1979007417-032
27 f,
Ig7go07417-033
28
1979007417-034
29
1979007417-035
J ,,
- /
-20 ............. 240
_.: .................• -12o
' ........... I ., • J
-- YC" sZ i(_I.47)S+(ti_(IT)Z"I
Kf(3.16)2
- ' KCI,_I ------ -240
"_'-'" Kf'0,50
lo" !6o "10 oj (_ots_o
Figure 5. Comparison or Pilot Frequency Responses when _f=3.16 rad/sec.
30
1979007417-03(
0 .... ,,r,,
--0
-20..................... 2/.,0
,4
......................................... 120
- " ,_.2_o.,(4._7)s.i_,.,i7)-__, -120
-- , _,-_.oo "240 "
llll Kf'0.71/
10-I 100 I01 ¢_ (l_/S[C)
Figure 6. Comparison of Pilot Frequency Responses vhen _f=1.58 rad/sec.
31
_L
1979007417-037
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I I I I I c,,I
_ <1 "_-
® J
OD<I "_ i
g
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- _0 '_
o
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o_,,4
n 0. i
rn _
ooO -_
rn 0 °
D,._ 0¢9 '::I <_I . :
- ,:ooi _. . . .
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32
1979007417-038


A study of the effect of forcing function characteristics on human operator dynamics in manual control

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