The internal model concept: An application to modeling human control of large ships

HUMAN FACTORS,1977,19(4),367-380

THE INTERNAL MODEL CONCEPT

Since the early days of human behavior

studies, it has been recognized that the be-havior of human beings is organized around goals. The action of man cannot be under-stood except in terms of goals and of the striv-ing toward them (Kelley, 1968). To achieve these goals, the human being should possess certain knowledge about his environment in order to be able to change this erivironmept according to his plans.

This basic concept can also be recognized in the human control of systems. The objec-tives or goals are more or less prescribed by the task the human controller has to perform. Of particular interest is the way the operator tries to achieve these goals. Studies of human behavior in relation to these tasks have been performed by many researchers in the past; such a research orientation still prevails. The concept that the human operator-needs cer-tain knowledge about the system to be

con-trolled originates from psychology, although presently it is often used in the control

engi-367

The Internal Model Concept: An Application

to Modeling Human Control of Large Ships

WIM VELDHUYZEN and HENK G. STASSEN, Department of Mechanical Engineering, De/It

University of Tec.'z nology, The t'Ietherla nds

Man)' human operator studies have used successfully the concept that the humanopera tor

performs his task on the basis of certain knowledge about the system to be controlled, cal/ed

the internal model. In this paper, the literature on manual control will be reviewed brief7v

with attention focused on the use of the internal model concept. To illustrate the applicability of the internal model concept in the field of man-machine systems, an application is given in the hwnan control of large ships. A model to describe the helmsman's behavior in steeringa supertanker, and the influence on his behavior of additional displays such as a rate of turn

indica tor ivi/I be described.

neering literature. In many publications,

knowledge of the human operator about the system under control is called the "internal

model" or the ''internal representation''

(Cooke, 1965; Kelle\', 1968; 5mallvood, 1967;

Veldhuyzen and Stassen, 1976). The "internal model" may be considered to consist of the following parts:

(I) knowledge about the system under control, that is about its structure, its parameter val-ues, or in general its overall behavior: about

the possibilities to control it: etc.

knowledge about the disturbances acting on the system and the way they will influence the system under control. Often, this knowledge

will be ofa statistical nature, that means that only certain statistical properties of the

dis-turbances and their effects on the system

un-der control are krv'n.

knowledge about the task to be performed.

This includes items such as task instructions.

signals to be displayed, experimental setup. and objectives or goals to be achieved. In controlling a system the human operator may use the internal model he has built about the system to be controlled for the following purposes:

ft

to obtain estimates of all the state variables necessary to control the system,

to develop and adopt control strategies suit-able to the control of the system.

to select the proper control actions after an optimal strategy has been defined,

to check whether the control actions already started will yield the desired results, to understand the phenomena occurring

dur-ing the execution of the task. Phenomena which cannot be explained by the internal

model may be stored in the human operator's

memory and may be used occasionally to

up-date the internal model.

The importance and practical value of the internal model concept can be best elucidated

by reviewing the manual control literature (NASA-University Conferences on Manual Control, 1966-1975). Many models have been

developed in order to describe the human operator in manual control tasks, such as the

describing function model (McRuer and

Krendel, 1974), the optimal control model (Kleinman, Baron, and Levison, 1971). the decision model (Elkind and Miller, 1968), and

the many non-linear and adaptive models

(Bekey and Angel, 1966; Young, 1969). In

go-ing through this huge number of papers

(NASA-University Conferences on Manual Control, 1966-1975; Stassen, 1975), one can recognize that the models clearly show the features of the internal model concept; they all are based on knowledge of the dynamics of the system to be controlled and the properties of the sys-tem inputs, including the disturbances, such as bandwidth and variance. For instance, the cross-over model indicates to what extent the human operator is able to adapt his control strategy to the dynamics of the controlled element. The optimal control model shows ver-y clearly the use of the internal model con-cept. For the construction of the Kalman filter,

predictor, and the optimal controller, the

system dynamics should be known as should the statistical properties of the disturbances. Also, the decision model, and often the many proposed non-linear models, as based on the knowledge of the controlled element

dynam-ics the human operator is assumed to possess. Similar trends can be recognized in super-visory control, as for instance was explained at the NATO Conference on Monitoring Be-havior and Supervisory Control (Johannsen, 1976; Sheridan. 1976).

From all control and psychological papers in the field of manual and supervisory control reviewed, it can be concluded that the inter-nal model concept is of great importance in understanding human performance

(Veld-huyzen and Stassen, 1976) because

monitor-ing, decision makmonitor-ing, predicting or extrap-olating, and planning activities of human

beings are all based in one way or another on the knowledge the human operator has about the system to be controlled.

APPLICATION OF THE INTERNAL MODEL CONCEPT TO THE CONTROL OF

LARGE SHIPS Description ol the Helmsman's Task

In order to understand the nonlinear helms-man's model to be developed in this section, some remarks about the task the helmsman has to perform should be made. In general, the helmsman's task may be considered to be a pursuit tracking task, where the input signal or test signal (the headings ordered) consists of a series of steps of randomly disthbuted amplitudes and durations. The ordered head-ing Jd(t) can be displayed by means of an aiphanumerical display; the actual heading t/J(t) is normally presented by means of a com-pass. To control the ship's rudder position 8(t) often a steering wheel is provided of which the position is denoted by 8d(t).

To analyze the helmsman's behavior, a model describing the d:.namics of the ship has to be chosen. A simple model, suitable for

this purpose is the following one (Norrbin, 1963):

The model consists of a nonlinear

first-order differential equation in the rate of turn is(t). The coefficient T1 is related to the ship's moment of inertia with respect to a vertical axis through the center of mass; the coeffi-cient K1 is related to the effective moment which can be exerted on the ship's hull by the rudder; and finally the coefficients a, and a2 are related to the damping. When a, is smaller than zero, the ship is directionally unstable, which means that it starts turning to either

starboard or port when the rudder is kept

centered.

To simulate the steering gear, a first-order differential equation can be used, where an-gular velocity is limited. In this way the fol-lowing equations are obtained:

Tb(t) + (t) = d(t) (2)

Ibd(t)I (3)

where T5 is a time constant and 6m is the

maximum rudder angular velocity.

To simulate the ship's yawing motions due to waves, a sum of a large but finite, number of sinusoids can be added to the output of the model (Equation I). The motions of a ship in a seaway can be calculated by methods as de-scribed in the ship hydrodynamics literature (Vugts, 1970).

A Nonlinear Model for tile Helntsntair's

Control Behavior

The model described in detail inVeldhuyzen (1976a; 1976b) is based directly on the inter-nal model concept, presented in the first

sec-tion. The model consists of the following

parts:

(I) an internal model equation to make it possible

to predict future ship states.

(2)-a decision making element in order to gener.

ate the helmsman's actions in controlling the ship including the use of the predictions of

the internal model,

(3) an estimator to estimate the State of the ship from the displayed heading disturbed with

noise due to waves.

The structure of the model is shown in Figure 1. For the construction of the decision making

element and the estimator, the statistical

properties of the input signals were assumed to be known, since those properties are part of the internal model.

The structure of the internal model equa-tion of the ship, that part of the internal mod-el which describes the dynamics of the ship, has been chosen as follows:

Tm1t) + tb(t) = Km3d(t) . (4)

Here the parameters Tm and Km are param-eters of the internal model and thus of the model itself, since the results of preliminary experiments indicated that the most dominat-ing factor of the ship dynamics on the helms-man's behavior was the ship's sluggishness, parameters T5 and K5, and that the nonlinear

term in Equation

I

was of less interest.

This implies that, indeed, the internal model. Equation I, can be simplified to Equation 4.

Will cstma or ,-,

'

ti, i ti p ft ernL mod ti dtc,sian making {_Litmcnt 1)

0-Figure 1. Structure of the non-linear ?nodef of the

helmsman, where the quantitY q(t) is the desired

heading; _{d(t) the desired rudder call; I,(t) tile actual}

disturbed heading: Ij(t) and «t) the estimates of rue undisturbed heading and rate of turn respeciivelv: and finally where «t: t. t + r) and «t: t. t + r)are tite

heading and rate of turn estimated at tite interval

(t, t + r) with a rudder call 3(t) and based on the ini-liai conditions «t) and ,i,(t).

The structure of the decision-making ele-ment has been based on an analysis of the records obtained during a series of simulator tests ¼'here the ship sailed in calm undis-turbed water. Figure 2 shows that by analyz-ing the records some general characteristics of the helmsman's output during the

execu-tion oía maneuver can be recognized. In most of these cases, the maneuver can be divided into four phases. During the first phase, the

helmsman generates an output in order to

start the ship rotating, then during the second phase, the rudder is kept centered. During the third phase, the helmsman stops the rotat-ing motion of the ship and when the desired heading is achieved with only a small rate of turn (the desired or ordered state), the fourth phase starts, with a rudder angle of zero. If the rate of turn is not small, there will be an overshoot, and then to achieve the desired state, the cycle has to be repeated, starting with the first phase again. The four phases can be indicated easily in the phase-plane, that is, the plot of the rate of turn lii as a

func-tion of the heading error 1/Je (Gibson, 1963). By

-20-- -u

1M

.111

600 l200

r°°

,

600

I

rJ

1200

J,U

modeling the helmsman's control behavior. it is assumed that this phase-plane can be di-vided into four areas corresponding to the four phases (Figure 3). Furthermore, it is

as-sumed that the boundaries between these

areas can be approximated by straight lines, given by the equations:

where /ie(t) = tb(t) - 1/Jd(t). During the second

and fourth phase, the rudder angle is kept at zero; during the other two phases a rudder angle must be selected in order to achieve the goals given by the Equations 5 (Phase I) and 8, where p = O, that is the origin of the

phase-plane (Phase III). At the beginning of a

partic-ular phase, and thus when one of the bound-aries is passed, a rudder angle 6d(t) is chosen, using the internal model, in such a way that after a time t(t), the goal will be achieved. After the rudder angle is chosen, the internal

L2 0 O t [s) 00 t [sj (t) + C1/(t) = O (5) 1/j(t) + C2qi(t) = O (6) 1/,(t) + C1r1'(t) = O (7)

Ie(t)I + C1 I(t)1 = P

(8) I, 1800 L J

0

-Figure 2. Example of the rime histories ofihe desired heading jJ(t), the actual heading 6(t), and the desired rudder angle d(t), recorded during a test with a supertanker.

phose phase ir phase r phase

TV

\ We (t)

C3(t)=O

phase L

Figure 3. The four control phases indicated in the phase-plane.

model is used to determine whether the ob-jectives will be satisfied during the following period, or whether a new rudder angle has to be chosen. A flow-chart of the decision mak-ing element is given in Figure 4. The criteria used to judge the result of the instantaneous rudder angle are given by the following

equa-tions:

Phase J: _{J iJi(t} + t9) + Cr,(t ± t I d(t) (9)

p, I

Phase III: I e(t + t9) [ + C1 (t + t9) d(t) (10)

where rji(t + t9) and t(t ± t9) are predicted using the internal model equation (Equation 4). The threshold value d(t) depends on the heading error rli(t). For large heading errors, the helmsman is mainly interested in reduc-ing the instantaneous error; whereas for small errors, he is particularly focused on the

dif-ference between the predicted state of the

ship and the objectives to be reached. For the

relation between threshold d(t) and error

I,e(t)the following equation is assumed:

d(t) = p(I +

q'j)

(li)

where p and q are also model parameters. It should be mentioned that during the first phase man\' different rudder angles d(t) may

result in the selected goal depending on the time t9(t). Therefore, it

is assumed that a

combination of rudder angle d(t) and dura-tion t9(t)

is chosen in such a way that the

following criterion will be minimized:

J = t9(t) +

'Id(t)I

(12) where W is a model parameter. Equation 12 implies a trade off between the value of the rudder angle &d(t)and the time t9(t)

(Veldhuv-zen, 1976b). start

rd headrrg

arid rate

end

Figure 4. Flou' chart of the decision-making element.

<phase ?>ri0 yes /c o rr ccl to

\rrcded ?/

yes calculate IP

o

< phascl? yes /'corrcc Iron "\rrcc did'? yes calcu la t e 6d p

where t2 = (t1 + t3)/2 and t4 = (t5 ± t5)/2.

Setting

(t5 - t1) = 2t,

(15)

and

(t5 - t3) = 2,t2 (16)

estimations of the undisturbed heading and heading rate at time t5 can be obtained:

5(t5) =

(t4) + 5(tt2

(17) (t5) (t4) (t4) - ,(t2) (18)

,ít1 + t2

Equations 17 and 18 can be rewritten as: i3(t5) = i5(t4) + 5(t5)t2 (19)

6(15) - Ii(t) ₍₂₀₎

t.5 - ti

where i(t4) can be estimated using Equation 14. In this way, at discrete times, estimates of the undisturbed heading and heading rate are obtained. lt is important to realize that for the estimation the known statistical proper-ties of the signals are used. However, between two successive peaks information about these

I me

T T T T T 1

234

5

Figure 5. Estimation oft/se undisturbed heading b(t) and rate of turn at linie t!, using successive peaks of the disturbed heading 11(t).

When a ship sails in waves, the helmsman has to neglect the effects of the disturbances to avoid useless rudder motions. Therefore, the estimator must yield estimates of the un-disturbed heading and heading rate. As the frequency ranges of the ship motions due to the helmsman's control actions and those due to waves are very close to each other, the

ap-plication of a linear filter may not lead to

acceptable results. A very useful filter could be based on the following hypothesis (Mag-daleno, Jex, and Johnson, 1969). Based on the fact that ship motions due to waves can be re-garded as narrow-band noise, and thus a time history of such a signal looks more or less like a sine wave with a slowly time-varying am-plitude, estimates of the undisturbed heading and heading rate, i5(t) and q(t), can be ob-tained in the manner shown in Figure 5.Based ori three successive peaks at times, t1, t, and t, the undisturbed headings at times t2 and t4 can be estimated according to:

11(t) + iji(t) (13)

2

and

quantities must be available too. Using the internal model, this information can be

ob-tained continuously as the helmsman has

knowledge about the ship's response to his rudder action. In terms of the nonlinear helms-man's model, it means that the differential Equation 4 has to be solved with the steering wheel position as forcing input and the last ectimates i(t) and 43(t) as initial conditions. Thus the estimated values of the undisturbed heading and rate of turn are supplied contin-uously by the internal model, driven by the steering wheel position signal, where at the times a peak of the heading signal occurs, the internal model is reset at the new estimates. In Figure 6, a block diagram of the complete model is given.

Application of the Nonlinear Model

The nonlinear helmsman's model has been

,

' (t),

It)

S t

St

decisio n

C £ mt n t

used in a number of situations to analyze the helmsman's behavior (Veldhuyzen, l976a; 1976b); an example will be discussed to show its usefulness. A more extensive description of the analysis described below can be found in Veldhuyzen (1976a; l976b).

The model has been used to study the influ-ence of additional information presentation systems on the performance of the helmsman

steering a directionally stable or unstable

ship by means of computer simulations. The influence of this auxiliary equipment on the helmsman's performance in relation to the dynamics of ships has also been investigated by Wagenaar, Payrnans, Brummer, van Wijk, and Glansdorp (1972) who performed a num-ber of simulator experiments. A comparison between the results of both these studies will be made. Therefore, the performance mea-sures, and the experimental variables in the

6dtt)

d s tur CS

ship

s

present study were chosen to be as similar as possible to those used by Wagenaar. The fol-lowing performance measures, analagous to the well-known RMS error scores, have been computed:

Rate of turn score:

i, =4

JT2(t)dt

(22) T

Heading error score:

=\/1JT

_{{d(t) -}

,(t)]2dt (23)

Wagenaar investigated three different

ships, viz, a stable, a slightly unstable, and a vary unstable one. In the present computer

simulation study, the model given by the

Equations 1, 2, and 3 was used, where the pa-rameters were varied systematically in such a way that the four ships used in the study ap-proximated the characteristics of the three ships used by Wagenaar. Table I summarizes the parameter values used. All the ships can be regarded as supertankers of about 250,000 tons, sailing in waves with a speed of about 10 knots. Th.e disturbances due to the waves were equal to those used by Wagenaar.

With each ship, the following maneuvers were simulated:

Maneuver 1: Course keeping.

Maneuver2: The execution of a heading order of 5

degrees.

TABLE t

Model Parameters Used to Stimulate the Different Types of Ships

Maneuver 3: The execution of a heading order of 25

degrees.

The heading orders were given at the begin-ning of the tests. The duration of each test was equal to 15 minutes. In addition to the displays normally used in ship steering, viz. a compass and a rudder angle indicator, a rate of turn indicator, and a predictive dis-play were used by Wagenaar. To avoid diffi-cult filtering problems, the undisturbed

head-ing and rate of turn,

'5(t) and ji,(t), which were known in the simulation, were used to present the additional information. The pre-dictive display described by Wagenaar shows a predicted value of the heading at time (t + r) with r = 100 s. This value was reset every four seconds. Here it should be noted that on-ly one value was presented and not a whole prediction of the heading during rs. Later on, the consequences of this will be discussed.

To predict the performance measures by means of computer simulations with the non-linear model, the structure of the model must be adapted to the displays used during a par-ticular test. The information supplied by the rate of turn indicator can be used as an initial condition to make predictions with the inter-nal model. However, estimates of the rate of turn can also be obtained from the estimator

(Figure 6). It has been assumed that the helms-man uses the displayed information; other-wise the display is more or less superfluous. When the rate of turn is presented, the values

Model Parameters Stable 250 0.03 1 50 1 3 li Marginally Stable 250 0.03 0 50 1 3 III Unstable 250 0.03

1

50 1 3 IV Very Unstable 250 0.03

2

50 1 3 Rudder score:

="!

1T52(t)dt (21) T T, K, a, a2 T

necessary to reset the internal model ici the prediction of future ship states are obtained from the estimator (the estimated heading) and from the rate of turn indicator (the actual rate of turn).

The information supplied by the predictive display consists of a prediction of the heading at time (t + r) withr= 100 s. To make the de-cisions the predicted values of the heading

and the rate of turn during the time span

(t, t +

r) are necessary. This means that the

decision-making element can not directly

make use of the predicted information. As it has been found that the internal model param-eters Tm and Km are mostly of the same order as the ship parameters T5 and K (Veldhuyzen. 1976a; 1976b), the displayed information can be transformed to an estimate of the instan-taneous rate of turn, and therefore the main effect of the predictive display used by Wage-naar will be the same as that of a rate of turn indicator according to the nonlinear model. Differences probably originate from the dif-ferences in workload due to the information processing within the helmsman. The predic-tions with the nonlinear model with tespect to the effect of the predictive display in rela-tion to that of the rate of turn indicator cor-respond \vïth the findings of Wagenaar. When predictions of the heading during the time span (t, t ± 1-) are presented, some impottant differences between the effect of a predictive

display and that of a rate of turn indicator

can be found (Veldhuvzen, 1976b). However, as experimental data with respect to such a display are missing in Wagertaar's report, on-ly the tests where the compass and the rate of turn indicator had been used were simulated.

Bésides the model structure, the parameter values need to become available; that is the internal model parameters, Tm and Km, and the decision making element parameters, W,

C1, C2, C3, p, and q. The internal model param-eters relate to the ship dynamics. The deci-sion making element parameters, W, C1, C3

and C3, influence mainly the way of steering,

that is the magnitude and duration of the

rudder deflections. The parameter p indicates the precision of ship control, whereas the pa-rameter q is related to the influence of the magnitude of the heading error on this preci-sion (Equation 11); hence, the parameters p and q can be considered as being indicators of the accuracy of information transmission. When a helmsman is extremely well-trained, it may be assumed that the knowledge he has about the dynamics of the ship, as vell as the manner of steering are not influenced bs' pre-senting additional information. That means that the parameters Tm. Km, W, C, C2, and C1 can be chosen on the basis of experience

gath-ered during experiments executed earlier

(Veldhuyzen, 1976b), taking into account the

dynamics of the ships used, as described

above. The selected parameter values are given

in Table 2, just as is the value of the param-eter q. The paramparam-eter q is kept constant, as a relation between the presented information and this parameter is difficult to obtain, con-trary to the parameter p. The value of q is also based on the data given in Veldhuvzen (1976b). The parameter p is chosen on the

ba-sis of the following points

(I) When the parameter p is chosen to be too

small, every new value of the estimator

out-put vill result in a new rudder angle. A very

noisy output of the model is then obtained.

The parameter p should have that value where

TABLE 2

Parameters of the Nonlinear Helmsman's Model Used in the Computer Simulations

Parameter Value Dimension

Tm 250 K,,, 0.03 W 3 sdeg' C1 50 s C2 35 s io q 0.3 deg'

errors in the reset values of the internal mod-el do not result in rudder calls.

(2) On the other hand, when p is chosen to be too large, the performance is again rather poor, since, then, rather large heading errors and large overshoots occur.

When no additional information is supplied, the errors in the reset values of the internal model are caused by errors of the estimator, which are denoted by 4'(t) and ¿i(t1). They

¡ 15-.- ₁₅ 250 s a ___._ 10 I f o 15

5-are defined by:

1i(t) = t7i(t) - b5(ttr) (24)

=

5(t) -

5(t) (25)

Based on the above, the following inequalities with respect to the parameter p can be for-malized: p (26) 25° 0

f

iiO

-2 -1 0 1 0.0% 0.06 j 0.0L 0.02 0.0% - 0.02--2 -1 0 1 25° ck 25° a -2 -i 0 1 01

Figure 7.Results of the computer si;nulations The computed scores are plotted as a function of the ship's parameter a1.

5-mcncuer

as a function of the ship's parameter a1,

which can be regarded as an indicator for the stability of the ship with respect to course

keeping. From these scores, the averaged

scores are computed which are comparable with the experimental data given by Wage-naar. To this end, only the ships I, III, and IV have been used. The results are given in Fig-ures 8, 9, and 10, as well as the experimental

values.

With a few exceptions, the experimental values of the performance measures given by Wagenaar can be reasonably predicted by the computer simulations (Figures 8, 9, 10). In general, the order of magnitude corresponds

very well, just as the influence of the test con-ditions on the performance. Only the pre-dicted heading error scores with respect to the large maneuver (25 degrees) with the rate

of turn indicator as an additional display

show some significant differences (Figure 10).

The data given by Wagenaar show a perform-ance level which is independent of the ship's stability, whereas the model predicts that a dependency should exist just as the experi-mental and computer simulation results with respect to the tests without a rate of turn in-dicator. t 12- 6- L-2 OL I I 250 _0° 5° 25° mortsu'ver

E

cxperimcrtts eomputer simutoticrts

Figure8 _{Comparison between the predicted and measured rudder and course scores} for three maneuvers, averaged over the ships and equipment.

p (27)

each time t, a peak value in the heading, oc-curs, that is for each time the internal model is reset.

As it has been found that the probability density function of the estimator error is

in-sensitive with respect to p, this parameter

can be found by simulating the test with an

arbitrary value for p. When a rate of turn

indicator is used, the errors in the rate of turn (Equation 25) do not influence performance because the internal model is reset using the displayed exact value of the rate of turn. In this case, only Equation 26 has to be used to estimate p.

When only the compass or rate of turn in-dicator is used, p should be chosen to be as

small as possible. This rule together with

Equations 26 and 27 provide the information to select proper p values in each test condi-tion. The values of the parameter, p, used in the prediction of the helmsman's performance are as follows:

p = I degrees when only the compass is used

p = 03 degrees when the rate of turn is

pre-sented.

t

I.-Tr

n.

n-rypt of ship

In general, when the scores are small, the predicted values are even smaller. This fact may be caused by the way the results are

ob-tained. Wagenaar estimated the averaged

scores, whereas in the computer simulation study the scores were estimated relative to the average helmsman. As the scores are in-tegrals of nonlinear functions of the heading error and the rudder angle, this fact can easily be understood. Ql - 8-Io '-

6-t

12- C Rfl 10- 2-o

rra

t'.

2 o

I

I n-Type of ship

fl

experiments computer

Figure 9. Comparison between the predicted and measured rudder and course scores averaged over the small maneuvers (course keepirigand S degree head-ing order).

CONCLUDING REMARKS

The example given in the foregoing section demonstrates how the internal model concept can contribute in building models to

under-stand the behavior of the human operator

and in the analysis of additional displays. In the future, it is intended to apply the same approach to analyze the behavior of the navi-gator in the control of ships during the

ap-12- C 12 C Rh cl 10

'-

8

--I I

16 6 L 2 o type of ship

proach to a harbor, the supervision of a much more complex system. lt is an excellent ex-ample of a task where many problems in the updating of the internal model (the estimator part) and in the decision-making element can be distinguished. However, the application of the internal model concept in the analysis of the navigator's behavior is only one

exam-ple.

Many important problems in human oper-ator activities can be directly related to the

internal model concepts, e.g., mental load

16-II. w O 8 6- 2-I typc of ship

problems and the problems involved in mon-itoring and decision making. It is the opinion of the authors that in many problems the ap-plication of the internal model concept may be expected to be fruitful. Therefore in the fu-ture more attention should be paid to the use of the internal model concept in studies of human behavior.

ACKNOWLEDGMENTS

The research reported in this paper has

been partially sponsored by the Netherlands

I

type of ship type of ship

txperrncrts

R

computer sirrtulotiorts

Figure 10. Comparison between the predicted and measured rudder and

course scores for the large maneuver (25 degrees heading order).

8

12. C

Organization for the Advancement of Pure Research (ZWO).

REFERENCES

Annual Conferences on Manual Control:

Second NASA University Conference. Cambridge (MIT).

NASA SP-126, 1966.

Third NASA University Conference, Los Angeles (USC). NASA SP-144, 1967.

Fourth NASA University Conference, Ann Arbor (UM),

NASA SP-192, 1968.

Fifth NASA University Conference, Cambridge, (MIT),

NASA SP-215, 1969.

Sixth Conference, Dayton (WPAFB), 1970.

Seventh NASA University Conference, Los Angeles

(USC). NASA SP-281. 1971.

Eighth Conference, Dayton (WPAFB), AFFDL-TR-72-92, l972.

Ninth Conference, Cambridge (MIT). 1973. Tenth Conference. Dayton (WPAFB), 1974.

Eleventh NASA University Conference. Moffett Field

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