Ship Maneuvering Under Human Control
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SHIP MANOEUVRING UNDER HUMAN CONTROL
analysis control
of
the
helmsman's
behaviour.
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SHIP MANOEUVRING UNDER HUMAN CONTROL ANALYSIS OF THE HELMAN'S CONTROL BEHAVIOUR
PROEFSCHRIFT TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAPPEN AAN DE TECHNISCHE HOGESCHOOL DELFT, OP GEZAG VAN DE RECTOR MAGNIFICUS PROF. DR. IR. H. VAN BEKKUM, VOOR EEN COMMISSIE, AANGEWEZEN DOOR HET COLLEGE VAN DEKANEN, TE VERDEDIGEN OP WOENSDAG 16 JUNI 1976 TE 14.00 UUR DOOR WILHELMUS VELDHUYZEN
, , , r / / J> è
scheepsbouwkundig ingenieur geboren te Oegstgeest
BIBLIOTHEEK TU Delft P 1138 1336
C
263888
Dit proefschrift is goedgekeurd door de promotoren: LECTOR DR. IR. H. G. ST ASSEN PROF. IR. J. GERRITSMA
1
Aan Hendrina
The research reported in this thesis has been executed v/ithin the Manr%chine Systems Group of the Laboratory for Measurement and Control, Department of Mechanical Enp*ineerini? of the Delft University of Technology. The research was sponsored by the Delft University Foundation and by the Netherlands Organization for the Advancement of Pure Research (ZWO). The sim.ulator experiments were nade possible financially by the Netherlands Ship Research Centre (TNO). In particular I will acknov/ledge the help of the sta^f members of the Institute TNO for Mechanical Constructions, who cooperated in running the experiments. The Royal Netherlands Naval College contributed in putting the training ship "Zeefakkel" at the disposal of the ManMachine Systems Group. Many collaborators of the Delft University of Technology contributed in one or another way to this thesis. In particular I like to acknowledge Ir. C.C. Glansdorp of the Shipbuilding Laboratory for his contribution in the setup of the experim^ents, Mr. J.F. Zegwaard of the Hybrid Computer Centre for his enthousiastic and valuable assistance in computer programming and data processing, and finally the students Mr. H.B.M. van Rooyen, Mr. P.O. van Holten, Mr. D.H.P. Snel, Mr. H.V/.J.M. van Gendt, and Mr. R.E. Schermerhorn, who each contributed with their Master of Science work partially to the total research program.
CONTENTS page CHAPTER I
GENERAL INTRODUCTION
1.1 1.2 1.3 1.4 1.5
Problem statement Modelling the helmsman: A review of literature System identification Outline of the thesis Definition of symbols
9 10 12 15 16
CHAPTER II: SHIP DYNAMICS 2.1 2.2 2.3 2.4 2.5
Introduction Models of ship manoeuvring The model selected Parameter values Ship motions due to waves
20 20 22 23 26
CHAPTER III: SHIP MANOEUVRING IN CALM WATER 3.1 3.2 3.2.1 3.2.2 3.2.3 3.2.4 3.2.5 3.2.6 3.2.7 3.3 5.3.1 3.3.2 3.3.3 3.4
Introduction Experimental set up The manoeuvring simulator Ship dynamics Displays and controls The ordered headings: The test signal Subjects Experimental programme Data collection Modelling the helmsman's control behaviour Preliminary analysis of the experiments Linear modelling •lonlinear modelling Parameter estimation
31 31 31 32 33 34 35 35 36 36 36 41 42 47
5
page 3.5 3.6
Results Discussion and conclusions
CHAPTER IV:
SHIP MANOEUVRING IN WAVES
4.1
Introduction Extension of the nonlinear helmsman's model Experimental set up Ship dynamics Displays and controls The ordered headings: The test signal
65 66 68 68 70 72
Subjects Experimental programme
72 72
Data collection
73
4.5 4.6
Prediction of scores Model structure Parameter values Results Discussion and conclusions
73 73 76 78 8I
CHAPTER V:
FULL SCALE EXPERIMENTS WITH A SMALL SHIP
5 1 5. 2 5. 2 . 5 2. 5 2. 5 .2. 5 .2 5 .2 5 .3 5 .4 5 .5
Introduction
4.2 4.3 4.3.1 4.3.2 4.3.3 4.3.4 4.3.5 4.3.6 4.4 4.4.1 4.4.2
6
1 2
3 4 5 6
Experimental set up Ship dynamics Displays and controls The ordered headings: The test signal Subjects Experimental programme Data collection The analysis of the experimental data Results Discussion and conclusions
49 56
85 85 86 86 87 87 87 87 88 '89 93
page CHAPTER VI:
CONCLUDING REMARKS AND FURTHER RESEARCH
6.1
Results achieved ,
6.2
Further research
97
100
SUMMARY
101
SAMENVATTING
103
CHAPTER I: GENERAL INTRODUCTION 1.1
Problem statement
Progressively larger ships have been built during the last twenty five years [l]; the modern crude carriers often possess a length of more than three or even four hundred metres. As a consequence, the manoeuvring properties of these ships may differ from the conventional freighters. For instance, the very slowly responding supertankers can be directionally unstable, which means that they tend to start turning to either starboard or port when the rudder is kept amidships. In particular this phenomenon was felt undesirable. Therefore, a lot of research has been devoted to the principle factors which influence mainly the handling quality of ships. One of the first papers with a more theoretical approach on this subject was written by Davidson and Schiff [2], since that time many other studies were published [3, 4, 5, 6j. In particular, much attention was paid to the manoeuvring properties of large tankers
[7, 8, 9]. In trying to describe the handling quality of a ship it is important to state that the dynamic behaviour of a ship is not only determined by the dynamics of the ship itself, but also by those of the controller, i.e. the helmsman or autopilot. The system ControllerShip is a closed loop system; in order to obtain an optimal performance the dynamics of the ship and the controller must be known. In many cases automatic controllers are applied to keep èhips on the desired course or the desired track. Many authors treated the design of autopilots for course keeping [lO, 11, 12, 13, l4] ; also the design of controllers to steer ships along a prespecified track got rather much attention [l5, l6, 17]. At this m.oment emphasis is laid on automatic steering of ships in those circumstances where the dynamical behaviour is not constant, but time varying, so that an adaptive autopilot has to be preferred [l8]. Apart from the design of autopilots it is desirable to focus the attention on the human controller, as in rather dangerous circumstances this controller is preferred to automatic steering. An example is a large tanker sailing in restricted water with an intensive traffic density. Not much is known about this manual control of slowly responding systems (which are often unstable too). In particular data about the abilities of man to control slowly responding systems are unknown. Wagenaar performed a series of experiments to investigate the influence of auxiliary equipment, e.g. a rate of turn indicator, on the performance of helmsmen controlling ships with different dynamical properties [l9]. However, this study does not yield information of the dynamical behaviour of helmsmen. Stuurman published the results of a study to model the helmsman's control behaviour; however, he only studied rather small and thus relatively fastly responding ships [.20, 21^. But as stated before, to design a ship, which is optimal with respect to handling quality, information of the helmsman's control behaviour must be available. The study reported in this thesis is therefore aimed to obtain at least a part of this information. To restrict this wide area of research, the scope of this study is mainly limited to the helmsmen's behaviour during the control of a ship along a prescribed heading. The manual control of the ship's position, where often more people are involved, e.g. an officer, has not been studied. The investigations reported may be considered as a first attempt and should be followed by more extensive studies.
9
For practical reasons a manoeuvring sim.ulator has been used. It could be adapted to well defined goals, because the ship dynamics and disturbances acting on the ship could be m.ade as desired in a relatively simple and cheap way. This is generally not the case with full scale trials, or tests with ship models [22, 23]. During the simulation the manoeuvring dynam.ics of the ships were represented by a mathematical m.odel. As the helmsman adapts his behaviour to the ship dynamics, the dynamic behaviour of ships, and the models describing this behaviour constitute an essential part of the study. Using the results of the simulator tests an attempt has been made to develop a m.athematical model of the control behaviour of the helm.sman. In literature many human operator models are given. The literature reviewed is given in Ch. 1.2. To model the helmsman's behaviour a m.odel has to be selected on the base of certain selection criteria. V/hen a model, suitable to analyze the helmsman's behaviour is chosen, the parameters of this model have to be estim.ated by means of param.eter estim.ation methods. In Ch. 1.3 an introduction is given to the identification of systems, as well as to the m.ethods, which can be used to estim.ate the model param.eters. 1.2
Modelling the helm.sman; A review of literature
Starting in the forties much attention has been paid to manual control problems. The function of the human operator therein v/as considered to be that of a controller; an element that has to close the loop in a certain optim.al v;ay. The manual control theory thus developed has resulted into a number of useful models, which will be shortly reviev;ed in this paragraph. Based on linear system, theory the output of the human operator can be divided into two parts, one part which corresponds v;ith the response of an equivalent linear system, the describing function, and another part, the remnant, which represents the difference between the response of the actual system, and the equivalent linear element. The model is called the describing function model. The hum.an operator adapts his control behaviour to the system under control in such a way that a stable and well dam.ped closed loop performance is achieved. McRuer has summarized many studies and recognized that the open loop describing function H^H,, near the crossover frequency can be approxim.ated by an integrator and a time delay; where Kp means the human operator describing function, H(, represents the controlled element dynam.ics, and where the crossover frequency is the frequency for which the open loop gain (HpH^,) eauals 1. In this way McRuer's wellknov/n crossover model has been obtained [24, 25]: HpHc = 3^ eJ'^^e,
(1.1)
with H = human operator describing function; H^ = controlled element transfer function; (jü(, = crossover frequency; Tg = effective time delay including neurom.uscular dynamics. Here it should be mentioned again that the describing function model is only based on stability considerations. It was developed to describe the human operator's behaviour in controlling relatively fastly responding systems, such as aircraft,space vehicles, cars and bicycles. Applications of the crossover theory in the field of slowly responding systems could not be found in literature. 10
Another model, also originating from linear system theory is the optimal control model [26], This model is based on the assumption that the human operator behaves in a certain optimal way within his inherent limitations: He cannot observe without introducinpnoise; he cannot position the controls infinitely precisely, and finally he also needs a certain tim.e for data processing. This model, consisting of a Kalman filter, a predictor to compensate for the human time delay, an optimal controller and observation and motor noises, is based on the assumed knowledpe the human operator has about the system dynamics. Though this model is mostly used to describe the human operator in controlling fastly responding systems, it may be expected to be useful in relation to slowly responding systems. No examples hereof are reported in literature as far as known. Besides these two im.portant models m.any other models have been developed such as the decision model [27, 28], and many nonlinear models, which are mostly extended linear models [29, 30, 31, 32]. The decision model, based on statistical decision theory, describes the behaviour of the human operator in a system with abruptly changing dynamics during the adaptation phase. When the human operator has adapted his behaviour to the changed system dynamics, his behaviour can be described again with the crossover m.odel. The nonlinear models were often developed to obtain model outputs, which correspond better with the actual human operator output than the output of a linear model. The nonlinear elem.ents were mostly chosen rather intuitively, the applicability of these nonlinear models is restricted to the situation for which the model was developed. All these models show one com.mon aspect: In order to provide a successful control behaviour the human operator needs some information of the dynam.ics of the system, to be controlled; this information should also include knowledge of the disturbances actinr on the system. This knov;ledge is called an Internal Model, that is an internal representation of the knov/ledge the human operator has [33]. The existence of such an internal model is implicitely true for the crossover model [24, 25], where the human operator adapts his control to the dynam.ics of the controlled element and to the band width of the system input; it is very clearly true for the optim.al control m.odel [26j and the decision model [27, 28], Some nonlinear models are based on the internal model concept too. Besides the many studies executed by control and system engineers as mentioned above, a number of studies have been reported by psychologists. Some of these papers are related to specific situations [33, 34J, other papers deal with the behaviour of the human operator in a more general way [35, 36]. The models are all more or less based on the internal model concept. kn important aspect of the behaviour of the human operator controlling a slowly responding system, is his monitoring behaviour [33]. The quantity to be observed is often changing so slowly that the human operator does not watch the indicators continuously, but in an interm.ittent way. Som.e studies on the human's monitoring behaviour can be mentioned [37, 38, 39] ; again these studies are based on the internal model concept. To summarize the literature the following remarks can be made;
11
•
•
•
With a few exceptions, less attention has been paid to the human operator as a controller of slovrly responding systems. However, an increasing interest in the field of human control of slow response systems exists [4o]. All models describing the human operator are more or less based on the internal m.odel concept. VJhen the internal model is an explicit part of a system engineering m.odel, m.ostly the internal model contains all the information with respect to the controlled system, whereas the human operator may have less knowledge of the system dynamics. The following criteria to use a particular type of model to describe the human operator's behaviour in a particular situation were found: • The usefulness of the model to predict the human operator's control behaviour in terms of stability and damping of the system for conditions different from the test conditions. • Measures indicating how well the model output fits the human operator output. • The applicability of the model in practical situations such as display design. As an example the optimal control m.odel can be mentioned [4l]. • The character of the model output compared with the character of the human operator output. Sometimes nonlinear elements are used in connection with a linear m.odel to obtain a more realistic model output [29, 30, 31, 32]. e The simplicity of the model: A simple model with only a few parameters describing the human operator's behaviour in a reasonable way often yields more consistent results than a multi parameter model [42]; moreover it is more convenient to apply in analyzing the human operator's behaviour.
1.3
System identification
An important part of this thesis is concerned with models describing the helmsman's control behaviour, where linear models as well as nonlinear models are applied. To explain the problem.s encountered in the developm.ent of the models som.e introductory remarks about the identification of systems should be made. As mentioned before the output of a nonlinear system can be divided into two parts, one part which corresponds with the response of an equivalent liner system, the describing function, and an additional noise, the remnant (Fig. 1.1).
FlGURE 1.1: Time domain representation and a remnant. 12
of
a system
consisting
of
a linear
model
The describing function is obtained by minimizing the variance of the error between system output and describing function output, the remaining error is then the remnant; it can be proven that the remnant and the input of the system or the describing function are uncorrelated in the case of an open loop system. To identify the describing function, several methods are available, which can be divided into two main groups [43]: • Methods without any apriori knowledge. • Methods with certain apriori knowledge. In the case that no apriori knov/ledge is available about the system to be identified, the identification should be achieved on the basis of general methods such as the determination of Bode or Nyquist plots from the analysis of deterministic test signals or spectral density functions of stochastic processes. For instance, in an open loop, the human operator describing function denoted by H(v) can be determined by the following wellknown relation: (1.2) S (v) H(v) Suu (v). ^''' • uy' In closed loop systems, however, the noise n(t) is correlated with the systems input e(t) due to the feed back loon (Fig. 1.2.a)
[^3, 45].
mv) U(V)
E{V)
Y(V) H^(VJ
N(l/)
•
Z(V) HjfV)
^
;
UHj(l/)H2(V)
N,(»/) H,(»/.
U(VI
1
UHj(V)H^(»/)j
FIGURE 1.2: Trans formation
of a closed
loop
Y(V)
f
^v.J
system
into
an open
loop
system.
Therefore the determination of the describing function by minimization of the variance of the error between system output and describing function output v;ill lead to a biased describing function. 13
However, by transforming the closed loop system, into an equivalent open loop system (Fig. 1.2.b), the method explained justbefore can be applied again, hence it follows: S
(v) (1.3)
ue In determining the describing function, estimated of the cross spectral densities S (v) and S (v) as well as of the auto spectral density Suu(v) ^Kould be^a\^lilable. Methods to determine these estimates S^y(v), Sue(^^) and S„^(v) of the spectra Suy(v), Sye(v) and Suu(v) abe given in the literature [44]. In the case that the structure of the linear system is known, parameter estimation methods can be used. These m.ethods are based on the concept of minimization of an error criterion E(e,T) v.'ith respect to the unknown parameters (Fig. 1.3). The general criterion to be minimized is: E(e,T) = /^e(t)1^ w(et) dt, (1.4) eT ;vhere e(t) difference between system output and model output; factor indicating the influence of the magnitude of q e(t); w = v;eighting function to take into account the time history of the error e(t).
r»
stem
u(t)
linear model
SL
y(t)
_1 linear model
T FIGURE 1.3: Block diagram estimation.
of
system
 y ( > ' ^ f ^ ' ^ minimizaiicn of E(5,T) porameters
identification
by means
of
parameter
The block diagram of Fig. 1.3 shows the method for an open loop system. In Fig. 1.4 a block diagram of a parameter estimation method, applied in a closed loop situation, is given; here the controlled elem.ent dynam.ics have to be known. It can be proven that this method results into consistent estimates in closed loop systems.
14
controlled system
FIGURE 1.4: Block diagram
of
a closed
loop
parameter
estimation
•itJ
method.
Analoguous to the methods of linear modelling,the output of an open loop nonlinear system can be divided into a part resulting from a nonlinear model, having the same input as the nonlinear system, and an additional noise. As the number of possible nonlinear elements, as well as the structures of a model built up with these elements, is unlimited, it is from the practical point of view not possible to conclude to a certain configuration by minimization of the variance of the error signal between m.odel output and actual system output. Therefore,this structure has to be chosen on the basis of apriori knowledge of the system dynamics. To estimate the parameters of the nonlinear model, a general theory is not available. The parameter estimation m.ethods developed with respect to linear models can also be used in the case of nonlinear models. However, an analytical derivation of the estimators of the parameters to be determined, is not possible in general. 1.4
Outline of the thesis
This thesis deals mainly with the manual control of large ships. After giving an introduction into and a definition of the problem, a review of human operator models and some introductory remarks on system identification, the outline of the thesis and the definition of the symbols used are given in Ch. 1. To study the helmsman's control behaviour in relation to the dynamics of ships, knowledge of the manoeuvring characteristics of ships should be obtained. Moreover the application of simulator tests requires the choice of a mathematical model, describing the dynamics of the ships to be simulated. To be able to analyze the test results, this model should be as simple as possible. In Ch. 2 some models will be discussed, a simple mathem.atical model will be selected, and for several ships, for which data could be found in literature, the parameters of the model chosen will be given. Ch. 3 summarises the results of a large number of tests with a manoeuvring simulator. To analyze the helmsm.an's control behaviour two types of models were used, viz. a linear model and a nonlinear model. This nonlinear model results from a prelim.inary analysis and from the literature reviewed in Ch. 1. 15
Ch. 4 deals with a study of the influence of additional displays on the behaviour of the helmsm.an steering a ship in waves. The nonlinear m.odel, described in Ch. 3, had to be extended to be able to interprete the results of this study. During the simulator studies (Ch. 3 and Ch. 4) attention vras focussed mainly on rather large ships. Fortunately, the Royal Netherlands Naval College m.ade it possible to conduct a series of full scale trials with a rather sm.all ship. In this way the results of simulator tests, viz. linear and nonlinear m.odelling results, could be evaluated with respect to a small ship. In Ch. 5 these tests and the results obtained are described. Some concluding rem.arks are made in Ch. 6; this chapter also gives some guidelines with respect to further research work in this field 1.5
Definition of symbols
In Fig. 1.5 a block diagram is given of a ship under hum.an control. disturbances
i
»
FIGURE 1.5: Block diagram
of
helmsman I —
the
ship
»
steered
steering

6(t)
gear
by a
V^(t)
ship
helmsman.
Using the steering v/heel, of which the position is denoted by 2 (deg)2/3 Meg' sec'
1 2 3
I
10 50 250
.05 .05 .05
1 1 1
5 5 5
0 0 0
4 5
II
10 50
.05 .05
0 0
5 5
0 0
6
III
10 50 250
.05 .05 .05
1
5 5 5
0 0 0
10 50
.025 .025
5 5
0 0
I 9" 10
IV
11 12 13
V
10 50 250
.1 .1 .1
1
5 5 5
1 1 1
14 15
VI
10 50
.05 .05
1
5 5
1 1
_^
To show the stationary characteristics of the ships Fig. 3.3 is given. Besides the parameters of the ship dynam.ics the parameters of the steering gear had to be chosen as well. Some indications about actual values of the maximum angular velocity 6^ and the tim.e constant Tg could be found in literature [2, 3] . Based on these data the follov/ing values were chosen: 6
= 3 deg/sec;
Tj. = 1 sec.
3.2.3
Displays and controls
The displays used were a com.pass and a rudder angle indicator. Moreover, the subject could obtain information from a projection screen, displaying the ship sailing in unrestricted water; that means the helmsman only perceived the sea, the sky and the front part of the ship. No coast line v;as displayed.
33
5 [deg/sec]
24 16 char. I
8 16 24 .4^^^Ö[deg]
2 8
6 peg/sec]
.6 [deg/sec]
24 16 8 / ..2 8 char.H ^
16 24 Ö[deg]
16 24
Öfleg]
24 16 Sr" char.nZ
.6 6 [deg/sec]
char.31
FIGURE The six
3.3: stationary
characteristics
used
in
the
ship
simulations.
In these first series of experiments , no additional displays like a rate of turn indicator v;ere used, as it vras the intention to study the influence of additional displays lateron. The remaining indicators of the simulator, such as v.'at er depth indicator and speedlog, which were not im.portant with respec t to the task to be executed by the helmsman, were out of use. The o rdered heading was displayed by means of a digital counter; when a new heading was ordered, an auditory signal was given. The helmsman controlled the ship's h eading by m.eans o,f a steering wheel, which could easy be turned wi th only a small am.ount of physical effort. 3.2.4
The ordered headings: The test signal
The helmismen were instructed to steer the sh ip along prescribed headings. The sequence of these headings, de noted by input signal or test signal, was a periodic signal. Each test consisted of just one period, v;ith a random.ly cho sen starting point. The duration of a test depended on the tim.e con stant Tg of t he ship: 10 min for a time constant T_ 10 sec, 20 m in for Tg = 5 0 sec and 40 miin for Tg = 250 sec, since in steering a slowly responding ship the helm.sm.an needs m.ore time to exe cute a manoeu vre than in steering a small and fastly responding ship. A tim.e h istory of the test signal for a test with a large ship is shown in Fir. 3.4.
34
[deg] 2
o 2 4 6
400
800
1200
1600
2000
2400
2800 I
FIGURE 3.4: Time history
of
the
test
signal
of a forty
minutes
[*«]
test.
Tests were performed using the test signal with am.plitudes as indicated in Fig. 3.4, and with am.plitudes twice as larrre. In the first case the test signal is indicated by TS S, in the last case by TS L. 3.2.5
Subjects
Four subjects, trainees of the School of Navigation at Amsterdam, were used to analyze the helmsmian's behaviour. None of them was experienced in steering ships larger than 10,000 tons. To become familiar with the dynam.ic behaviour of large ships, each subject controlled about one hour the large unstable ship (Ts=250 sec. Char. Ill) before starting the experim.ents. The subjects were instructed to steer the ships just as they normally did. To keep them motivated small rewards were paid, but in spite of this fact a decrease of their m.otivation during the experim.ents could be observed. The com.ments m.ade by the subjects supported this fact. To keep the num.ber of tests the subjects had to perform; as small as possible, each of them, steered only a certain num.ber of all the ships simulated. The subjects Al and A2 steered the ship with the stationary characteristics I, III and IV, the subjects Bl and B2 the ships with the characteristics I, II, V and VI. 3.2.6
Experimental programme
In Table 3.2 a survey of the tests to be executed with the TNO sim.ulator is given. It was intended to execute two tests v;ith each subject and each condition, hence the total number of experiments was 144.
35
TABLE 3.2:
Summary
o'" the
tests
with
the
TNO
simulator,
Ship data Subjects Charact. I II III IV V VI
3.2.7
Tg(sec) 50  250 50 50  250 50 10  50  250 10  50 10 10 10 10

S/L S/L S/L S/L S/L S/L
Al A2 El El Al A2 Al A2 Bl Bl
B2 B2
B2 B2
Data collection
;he following signals were recorded on miagnetic tape: o The desired headin, ijj.,(t); The heading ,!;(t) ; ^ 0 o The rate of turn i;(t); o The steering wheel position 6^(t) o The rudder angle 6(t).
3.3
Modelling the helmsrian's control behaviour
3.3.1
Preliminary analysis of the experim.ents
By the Figs. 3.5 and 3.6 some exam.ples are given of the tim.e histories of the desired ship heading lijd(t), the actual heading i)(t), and the position of the steering wheel ^^{t) as recorded durinrthe tests.
P«g] \
Öj{t)40.
[deg]20
FIGURE 3.5: Time histories of Subject A2, TS S,
36
the signals T^ ,(t), T = 250 sec. Char.
\lj(t), and^n(t). Ill (unstable char.).
ÓdCUO
feg]20 O
FIGURE 3.6: Time histories of Subject Al, TS S,
the signals ii^(t), ip (t), and T = 250 sec. Char. Ill (unstable
6j(t). char.).
s
The following remarks can be m.ade with respect to the records: • In all cases the records of the steering v.'heel position 6(j(t) show that the helmsman generates a steering wheel position which consists m.ore or less of discrete steps. In peneral the number of rudder calls a helmsman uses to change the heading of the ship decreases with the training. • A change of heading often consists of four phases. Durinp* the first phase the helmsm.an generates an output in order to start the ship rotating, then during the second phase, the rudder is kept am.idships. During the third phase, the helmsman stops the rotating motion of the ship and when the desired heading is achieved with only a small rate of turn (the desired state) the fourth phase starts (rudder angle zero). If the rate of turn is not small enough, there will be an overshoot and to achieve the desired state the cycle is repeated starting with the first phase again. This behaviour can be showed clarly by means of the phaseplane: the rate of turn of the ship lii(t) plotted against the heading error ^e{t)  ^{t)  ^(^{t) . An example of such a phaseplane plot is shown in Fig. 3.7.
FIGURE 3.7: Phaseplane recorded during a large unstable
trajectories a test with ship.
37
As the ship was unstable in this case, during the second phase the rate of turn increased with the rudder angle 6(t) equal to zero. During the first phase the output of a helmsman is often shaped like a rect angular pulse v;ith only a few rudder calls, v/hereas during the third phase the num.ber of rudder calls is much larger. In some cas es when there will be an overshoot, som.etim.es during a short per iod of tim.e a peak in the steering v/heel position is generated b y the helm.sman. It looks as if the man prefers it to stop the m.o tion by large rudder am.plitudes to avoid overshoots. In Fig. 3.8 a set of estimated squared spectral density functions
SV'dV^d'^'
[LOG]
'
[LOG]»^
I 2.1 3.
4. 4, 5.
.01
^2
V[HZ]
.01
V[HZ]'
'.OOj
RtlV^e'»" 0.50
aoo
.001
.01
V[HZ]
FIGURE 3.8. Estimated squared spectral density functions and squared spectra of a test with a stable ship; T  50 sec; Char. Subject A^, TS L.
V[HZ]
coherency I;
and estimated squared coherency spectra of a test with a stable ship (Char. I, Tg = 50 sec) are shown. From the estimated coherency rij^4jg(v) it can be concluded that the feedback loop does not contain components with frequencies higher than .01 Hz. 38
This corresponds with the fact that the estimated cross ^spectrum. Si(;^i^g(v) I and the estimated auto spectra Sm
I
1
5j(.l
time
6ml FIGURE 3.10: Schematic representation a: helmsman, b: banabana
J
of the execution of an order. control. 5 .• maximum rudder anale m
maximum rudder angle. Also the existence of the second phase, during which the rudder angle is kept zero, indicates that the helm.sman's control behaviour differs from bangbang control. During the first phase the num.ber of rudder calls is generally less than during the third phase. This phenomenon may be explained by the fact that during the first phase the heading error is large, and the helm.sman v.'ill be less interested in whether there is a difference between his predictions and the actual state of the ship. As the helmsman does not v.'atch the indicators continuously, this indifference m.ay lead to larger sampling intervals and a decrease of willingness to change the position of the rudder [8]. From the questionnary, which the subjects had to fill in after each test, some insight could be obtained about the ideas the subjects had about the dynamics of the ship just steered. From these data it was concluded that in particular in the case of large ships the subjects could hardly recognize whether the ship was stable or unstable. Table 3.3 summarizes some of the results obtained with this questionnaries. Likewise the ships with a deadzone could hardly be recognized [9].
40
TABLE 3.3:
Percentages incorrect the ship just steered
answers on the question was stable or unstable.
Ship data Characti I
II
Subjects
T^ (sec) 10 50 250
Group A
Groun E 31.2 18.8 14.4
6.7 7.2 8.3
10
62.3 62.3
50 III
10 50 250
21.6 43.2 71.5
IV
10 50
6.7 71.5
V
10 50 250
6.2 6.2
10 50
13.3 0.0
VI
whether

8.3
Ships with characteristic II (marginal stable) are assumed to be stable.
From these results and from conversations with the subjects the impression v;as established that the subjects had only some vague thoughts about the dynamic response of the ship. 3.3.2
Linear modelling
As spectral analyses of the recordings did not provide accurate information with respect to the structure of the helm.sm^an's describing function, the structure has been based on data given in literature [7, lo], sothat given a certain structure, the parameters could be determ.ined. Starting with the simplest human operator m.odel, given by McRuer [10] (T^JO) + 1) JWT^ (3.1) taking into account that slowly responding system.s are considered, Eq. (3.1) can be simplified to Eq. (3.2)
(j.) Hj^U
= K.^y'
^]
(3.2)
41
v;here the time delay has been neglected because of this slowly responding character of the ship. By assuming that the crossover model may be applied, it follov;s that: (T^jt^ + 1) K H^(ja)).H^(jü))=K^^^ .^ + 1) • jw(T jt^ + 1)  J^ c.
(3.3)
5
where the dynamic behaviour of the ship has been approxim.ated by Nomoto's first order m.odel(Eq. 2.4). Hence H^(jw) = K^(T^jw + 1)
(3.4)
Comparing this m.odel v/ith the linear m.odel used by Stuurman L7J (T jw + 1) (3.2)
it may be expected that the model based on the crossover model (Eq. 3.**) has a rather large part of its output at higher frequencies due to the lead time constant. To investigate the influence of the lag term both models have been used to analyze the helmsman's control behaviour. 3.3.3
Nonlinear modelling
The nonlinear model has been based on the following startingpoints: • An internal model of the ship dynamics was used to make predictions about future headings and rates of turn of the ship. A decision making element was used to base the actions to be taken on these predictions. To predict future states of the ship the actual heading and rate of turn must be known. These nuantities have to be estim.ated from the inform.ation presented by the compass, which may be disturbed with noise. The part of the model which estimates the heading and the rate of turn is called the estimator (Fig. 3.11). o The model was constructed in such a way that its output shows the same characteristics as the helmsman's output (Ch. 3.3.1). e The model had to be as simple as possible in order to be able to analyze and to interpret the results. The internal model is an im.portant part of the helmsman's m.odel. It is used to make predictions of the heading and the rate of turn during the time span (t,t+T). These predictions can be based on the actual steering wheel position to monitor and to judge the results of an action already started, but they can also be based on arbitrary steering v;heel positions to choose the action necessary to achieve a desired state of the ship. Therefore, the input of the internal model is denoted by '^ci'^(^) (^^ig. 3.11). The choice of the internal model structure has been based on the following considerations: 42
V^(t)
1
r ^ t i m n inr
'^(t),^{t)
\f internal model
V^(t:t.t+n
ö>)
^(t:i,i+r) V/j(ti
FIGURE 3.11: Block diagram
of
the

nonlinear
deciision maki ng elerrlent
6j(tl
model.
•
Nomoto pointed out that the responses of a ship on a rudder angle input show mainly the characteristics of second order system responses [ll] . This fact corresponds v;ith the bangbang like control strategy of the helmsm.en. • The comments of the subjects suggested that nonlinearities in the ship dynamics could hardly be observed. • The steering gear is a rather fastly responding system, in relation to the dynamics of the ship. Therefore, and also as a m.atter of simplicity, the steering gear dynamics have been neglected. The internal model, as part of the helmsman's model, has been written in the following mathem.atical form:
Tjit)
Ht)
(3.5)
Vd^^)
where T^ and K^ are the parameters of the internal model, and thus parameters of the complete nonlinear m.odel. The choice of the internal m.odel structure was based only on an analysis of the records and the comments of the subjects during the experiments. Therefore, it should be stated that a relation between the internal model of a helmsman exist.
and that
of
the
nonlinear
model
does
not
necessarily
To make predictions with the internal model t wo initial conditions are needed: the ship's heading and the rate o f turn. This information is provided by the estimator. In general the heading presented by means of the compass is corrupted with noi se and thus the quantities needed have to be estimated (Ch. 4 ). However, durinp" the simulator tests described in this chapter no disturbances were introduced and the disturbances resulting from the simulator, e.g. computer noise, were small. In this case the structure of the estimator can be very simple (Fig. 3.12). To obtain the rate of turn only a differentiator had to be applied.
43
v^(t)
r
1 V^ci
1
T 1
1 V'C)
_d_ dt
1
1 1 estimator
FIGURE 3. 12: Structure of the estimator have been introduced.
in
the
_J situation
where
no
disturbances
It may be noted that the term, estimator is probably rather confusing in this context. However, to obtain a direct link v;ith the more general situation described in Ch. 4, also in this chanter the term. estimator is used since in this way possibilities to extend the model and to include refinements, such as m.odels describing the helmsman's sam.pling behaviour, can be explained similarly. In steering a ship the helm.sm.an has to adopt a strategy to achieve the desired state [l2]. This stratery has been based on his experience, the internal m.odel. The strategy used by the helm.sm.an's m.odel is represented by the structure of the decision making ele
ment. As shown in Ch. 3.3.1 a m.anoeuvre can often be divided into four phases. First a rudder deflection is given to start the ship rotating. VJhen this objective has been achieved the rudder is kept amidships in order to keep the rate of turn more or less at a constant value. When the heading error is small in relation to the ship's rate of turn, a second rudder deflection is needed to stop the rotating motion. The objective during the third phase is to make both heading error and rate of turn equal to zero, the desired state of the ship. In the phaseplane the four phases can be indicated (Fig. 3.7), v;here the boundaries between the regions corresponding with the first and second phase represents the pursued objective during the first phase and the origin of the plane the objective durinr the third phase. To keep the model sim.ple, the boundaries between the areas in the phaseplane have been approximated by straight lines (see Fig. 3.13), given by the Eos.:
4'e(t) + C. il'(t) + C, li'(t) i^g(t) + Cj iKt)
Ue(t) + C^il.(t)
= 0 = 0 = 0
J
p ,
(3.6) (3.7) (3.8) (3.9)
where C,, C„, C, and p are parameters of the decision making element.
44
^
'^
:>
phoseE phase I
phase I Vj(t)*C,V^(tl = 0 V^^lD+C^V^ItJrO V^dl^CjV^dlsO
FIGURE 3.13: The four phases
of
control
in
the
vhaseplane.
During the second and fourth phase the rudder angle is kept zero; during the other two phases a rudder angle m.ust be selected in order to achieve the objectives given by Eos. 3.6 (phase I) and 3.9, where p = 0 (phase III). At the beginning of a particular phase, and thus when one of the boundaries is passed, a steering wheel position 6(j(t) is chosen based on the internal m.odel predictions, in such a way that after a tim.e t3(t) the goal will be achieved. This means that the steering v/heel position ^(^(t) has to be estimated, for which the solution of the internal model equation (3.5) yields the heading (ij(t+tp) and rate of turn il;(t+tp) which satisfy the objective and where the actual heading and heading rate are the initial conditions. After the rudder angle is chosen the internal model is used to check, whether the objectives will be satisfied at the time determined, or whether a new rudder angle has to be chosen. Fig. 3.l4 illustrates the working principle of the decision making element. In general the predicted state of the ship will differ from the objective during a particular phase, due to e.g. differences between the internal model and the actual ship dynamics. As the helmsman changes the steering wheel position in a discrete v;ay small differences are allowed obviously. The criteria to choose a new rudder angle are given by the following Ens.: Phase
I
:
Phase I I I :
it)g(t+t
)+C^ii)(t+t
)<
d(t);
\A)At^t £ d(t), e p ) +C 1 tp(t+t pT —
(3.10) (3.11)
45
(
start 3
read heading and rate < ( p h a s e l ? > no
1 1 / o h n s e lir'>\ no lyes
yes
/'correctionN ^ \ needed?/ yes
0 the NRC becomes very large.
In the case of the predictive display PDl, p cannot be estimated from the Eos. 4.15 and 4.l6, as exact values of the undisturbed heading and heading rate were displayed. As p m.ust be larger than zero and there for p = .1 a rather large num.ber of rudder calls was found, (about lO rudder calls per m.inute) p is set eaual .2 deg. In Fig. 4.11 the scores obtained by the computer simulations and the measured scores are given, where the nonlinear helm.sman's model is modified as described in Ch. 4.4.1. The model parameters used during the computer sim.ulations are given in Tables 4.5 and 4.7. 4 .6
Discussion and conclusions
VJhen additional information, based on the undisturbed rate of turn was supplied (RTIl), the performance of the subjects improved (Table 4.4). The predictive display (PDl) also shov/ed the same effect, whereas the rudder scores Ig were a little bit smaller than those related to the rate of turn indicator. Hov/ever, the number of rudder calls becomes rather large in using predictive display. In general, the use of additional inform.ation, based on the ton detection principle, led to a small improvement in the perfonrance, be it that the number of rudder calls increased. This fact may be caused by the reason that the display based on the top detection method provides not fully accurate information, which may result
81
IMJIM im nu
2.5
¥e
.08 .06 .Oi .02 NRC
c
C,RTI^ C,PD
QRTI^ QPD QPD
Tp=250
n FIGURE Measured
4.11: and predicted
measured
•
Tp=250 200
CiPD^
300
predicted
scores.
into the generation of superfluous rudder calls. Based on remarks made by the subjects during the experim.ents, it m.ay be supposed that the main effect of these displays is a reduction of m.ental workload. Because of the fact that no workload measurements were carried out, this statem.ent could not be proven. From the estimated parameter values, given in Table 4.5, it may be concluded that the average param.eter values obtained from the test v/here the ship sailed in calm water show only small differences from the average parameter values related to the test where disturbances were introduced. The most important difference is found between the values of the parameter C3 related to both test conditions. This fact can be elucidated as follows: V.'hen no disturbances act on the ship, the ship is rather easy to control. Hence, onlv small overshoots will occur, /^s discussed in Ch. 3, the optimization criterion is then insensitive to this param.eter. VJhen the ship sails in waves, it is more difficult to control, resulting into 82
•^
larger overshoots, that means that the criterion may become sensitive to the parameter C3. Hence, the values of the parameter C3 related to the ship sailine* in calm water are m.eaningless. Except the case v/ith the predictive displays based on the top detection principle (PD2) the predictions of the scores v/ith the nonlinear model were reasonable. The changes of the measured scores related to the different test conditions v/ere predicted rather v/ell. The differences between the m.easured scores and the predicted ones related to the predictive displays PD2, may be caused by the following reasons: o It m.ay be that the helm.sman did not notice the magnitudes of the errors in the displayed information, that is, the information was considered to be more accurate than it actually was. This m.eans that the value of the param.eter p in the computer sim.ulations was chosen too large. This explanation corresponds with the m.easured num.ber of rudder calls which are larger than predicted, and with the heading error scores which are smaller than predicted (Fig. 4.11). o Only the param.eter p was assum.ed to be influenced by presenting additional information. Plowever, an interaction m.ay exist between the helm.sm.an's experience, that is his internal model and the presented information v/hich is also based on knowledge of the ship dynamics. For instance, the helm.sm.an's selection of the rudder angle during the first phase may be based more on the helmsman's experience, that means on the way he normally chooses the rudder angle in a particular situation, than on the displayed information. This fact may explain the difference betv/een the measured and predicted rudder angles scores related to the predictive display v/ith a predictor model time constant Tp = 3OO sec, since the applied rudder angles are related to the helmsm.an's knowledge of the ship dynamics in such a way that an internal m.odel or predictor model with a larger time constant corresponds with larger rudder angles than an internal model or a predictor model with a smaller tim.e constant. Also the parameter q, indicating the influence of the heading error on the precision of ship control, may be influenced by the display, e.g. a relation may exist between this parameter and the parameter p. For instance, when p is large due to the errors in the displayed information, the influence of the heading error on the threshold value d(t) v/ill be much larger than for sm.all values of p (Eq. 3.12). In the case of the predictive display PD2 where p = 2.2 and a = .3, the resulting threshold d(t) is at least 2.2 deg v/ith an increase of .66 deg per degree heading error. This means that rather large threshold values can occur. In particular during the third phase, the m.ethod applied of steering the ship using a predictive display, consisted of generating a predicted heading on the display touching to the desired heading. This corresponded with threshold values d(t) m.uch smaller than given by Eq. 3.12 and the riven values of p and q. On the base of this fact it may be concluded that also the param.eter q is influenced by the display. It should be mentioned that the influence of the accuracy of information presentation, by means of a predictive display, should be studied more in detail as in practice the displayed inform.ation is certainly inaccurate. The following conclusions can be summarized:
83
J
A rate of turn indicator im.proves the performance of the helmsman. The predictive display also leads to a better perform.ance with respect to the heading error scores and the rudder anple scores, however, the number of rudder calls increases. The important profit of additional inform.ation may be rather a decrease in v/orkload than the imnrovem.ent of the perform.ance m.easures. The scores derived from the simulation v/ith the nonlinear model are a good prediction of the scores measured. The influence of inaccurate information presented by m.eans of a predictive display needs certainly further research.
REFERENCES 1.
REFERENCES 1. Veldhuyzen, W.; Stassen, H.G., Modelling the behaviour of the helmsman steerinp a ship. Proc. of the ninth Annual Conf. on Manual Control, Cambridge (USA), 1973, pp. 639658. 2. Veldhuyzen, W., Modelling the helm.sman of a supertanker. In: H.G. Stassen et.al. Progress Report January 1970 until January 197 3 of the ManMachine Systems Group. Dept. of Mech. Engineering, Delft, 1973, No."WTHD55, pp. l40l60. 3. Magdeleno, R.E.; Jex, H.R.; Johnson, W.A., Tracking quasipredictable displays, subjective predictability gradations, pilot models for periodic and narrowband inputs. Proc. of the fifth Annual Conf. on Manual Control, Cambridge (USA), 1969, NASA SP215, pp. 391428. 4 . Gerritsm.a, J ., Behaviour of a ship in a seaway. Report: Delft, Netherlands Shin Research Centre TNO, 1966, No. 84S, 20 p. 5. Wagenaar, VJ.A.; Paymans, P.J.; Brumm.er, G.M.A.; Wijk, vr.P. van; Glansdorp, C.C, Auxiliary equipment as a compensation for the effect of course instability on the performance of helm.sm.en. Communication Netherl. Ship Research Centre TNG, Delft, 1972, No. 28s, 21 p.
84
CHAPTER V: FULL SCALE EXPERIMENTS VJITH A SMALL SHIP 5.1
Introduction
In Ch. 3 the experiments with the manoeuvring simulator were described. During the experiments large as well as sm.all ships were simulated. The results of the tests ^^/ith the small ships were not very satisfying, due to the chosen steering gear dynamics. Fortunately, the Royal Netherlands Navy College gave an opportunity to perform a series of full scale experiments with a small ship, the "Zeefakkel". This trainingship was originally designed to be used for hydrographical purposes, hence it possesses very good handling aualities. The principal data of this ship are shown in Table 5.1
[l]. TABLE 5.1:
Principal
data
of the
training
ship
"Zeefakkel"
Length 42.00 m Breadth 7.50 m Mean draught 2.22 m Displacem.ent 383 in3 Tonnage 324 tons Steering equi pment 2 rudders Rudder area 2 X 1,04 m2 Propulsion 2 diesel engines 2 controlable pitch propellers Nominal RPM 300 turns/min. Speed max. 12 kn.
5. 2
Experimental set up
The tests described in this chapter, have been performed at the North Sea during the summer 1975. The weather conditions were good: A light swell and a windforce of about 2 or 3 Beaufort. During the test to be executed the helmsm.an had to execute a number of manoeuvres which were equal to those with the simulator experiments. However, due to the different social environment, for instance the fact that the other crew members were present on the bridge, the results of these tests can be compared with the sim.ulator results only with great cautions. The test conditions were chosen as similar as possible to the sim.ulator study. Nevertheless, som.e differences occured, which could not be avoided. During the previous tests only a small number of men were present in the wheelhouse, whereas during the full scale experiments a rather large group of people v/ere present, sometim.es causing a diversion of the helmsman's attention. Besides, the presence of other ships, birds and waves has probably influenced the helmsm.an's behaviour. Also the dynamics of the shin, with m.otions due to waves, which could be felt, and the dynamics of the controls differed; these points will be discussed below.
85
5.2.1
:hip dynamics
The Laboratory for Control of the Department of Electrical Engineering of the Delft University of Technolory performed many experim:ents to model the m.anoeuvrinr behaviour of the Zeefakkel. The parameters of the models of L'omoto, Norrbin, and Bech have been estimated for different ship speeds and rudder angle inputs [2]. These inputs^v/ere binary sirnals: A binary maximum lenrth seouence and a periodic block shaped sirnal. In the experiments reported here, the results with the Norrbin model have been used, just as during the previous tests. The investigations were performed with two ship speeds, viz. about 9 and 12 knots corresponding with 15 and 27 degrees pitch of the propellers respectively. The parameter values of the Norrbin model related to these two conditions, have been chosen according to the data given by Van Amerongen. These values on which the final analysis of the test results has been based, are given in Table 5.2. This table also gives the parameters of the m.odel of the steering gear, estimated from data given by Van Maanen [l]. TABLE 5.2: Ship speed knots 9 12
Parameters
of
Prop.pitch
the m
model
of
the
trainings
•'s
Ks
^1
deg
sec
sec"

15 27
20.
.25 .64
1
.14
1
.28
34.
^2 ,secv2
^de?*
shiv
T
"Zeefakkel" 1
m
1
sec
defT 1 sec 1
1 1
7. 1 7.
As can be seen, the maximum: rudder angular velocity 6^ is here m.uch l§:rger than the maximum velocity during the simulator tests, where ój^, r 3 deg/sec (Ch. 3.2.2 and Table 5.2). During the tests a light swell could be observed, resulting into small ship motions. However, in the analyses of the tests these disturbances were neglected, as these m.otions could not be measured easily. Moreover» the accuracy of the ship model is unknown, and can introduce a bias in the results of the same order as the v/ave disturbances. 5.2.2
Displays and controls
During the field trials, the instrum.ents used caused some troubles. The first m.orning the gyro norm.ally used was out of order. Steering had to be done on the basis of the magnetic compass, which reacts slower, and on the basis of a small gyro. Especiallv, one of the subjects had a lot of difficulties in beinr used to this unusual situation. In later experiments, the normal gyro could be used again. No additional information, e.r. the rate of turn, was provided. A rudder angle indicator was available. To steer the shin only the steering wheel had to be used; it was not allowed to use the pitch control of the propellers.
86
An important difference between the full scale tests and the sim.ulator experiments resulted from the controls. The steering v/heel of the Zeefakkel was much bigger than that of the simulator, hence it demanded much miore physical effort of the subjects. 5.2.3
The ordered headings: The Test si.pnal
During the tests the ship had to be steered alonr the sam.e seouence of headings as the previous tests. Both seauences of ordered headings, TS S and TS L, were used. The duration of the tests has been varied: 20, 10 and 5 min. The helmsm.an was informed in a verbal way about the headinr to be steered, in correspondance with the way they normally get the orders. 5.2.4
Subjects
The three subjects. A, B and C, were members of the crew of the Zeefakkel. Each had up to thirty years experience as a helm.sman, most of the time on the Zeefakkel. This m.eans that for the helmsman the task included more than just plainly following the orders; they actively engaged in steering, which m.eans that the manoeuvring was influenced rem.arkable by e.g. other ships in the neighbourhood. 5.2.5
Experimental programme
Table 5.3 summarizes the experiments executed with the Zeefakkel. TABLE 5.3:
Summary
of
the
tests
executed Ship speed
Testsignal
Duration
TS S TS S TS S
5 min. 10 min. 20 min.
9 A A A
TS L
10 min.
A , B ,C
knots , B , C'' , B*, C , B ,C
 12 knots A*, R , C A*, B , C A*, B , C
These tests have not been elaborated due to troubles such as the interaction v/ith other ships.
5.2.6
Data collection
The following signals were recorded on magnetic tape: • The heading iii(t) ; ^ • The rate of turn il'(t); • The steering wheel position ^(^(t); • The rudder angle 6(t); • The sv/itching times of the com.m.and signal \b(^(t) .
87
These switching tim.es v/ere recorded by m.eans of a pulse .r^enerated by the experim.entor by pushing a knob when a nev/ order v/as «^iven. 5.3
The analysis of the experimental data
In analyzing the tests, it turned out that due to som.e troubles, for instance the interaction v/ith other shins in the direct environm.ent of the Zeefakkel, a fev/ tests were not suitable to elaborate. Moreover, the recordings of the steering v/heel position showed a rather big offset, about fifty derrees, varying for each experim.ent. Therefore, the records were corrected in such a way that the m.ean value of the 6(j(t) signals were eaual to zero. Tn addition, some records shov/ed not only an offset in fid(t), but also a drift. Table 5.3 indicates which experiments have been analyzed; this analysis included the following items: o A study of the characteristics of the time histories, particularly in relation to the characteristics of the previous tests with the simulator. o The estimation of performance m.easures, such as the mean absolute values, variances, and the time on tarret, that is the time in terms of percents of the test duration during v/hich the absolute value of the heading error if^e(t) is sm.aller than a certain boundary value bv. VJith respect to the steering wheel position, the heading, the heading error, and the rate of turn, the variances and the m.ean absolute values have been estim.ated according to T 1 Iv2 [ ^(t)] ^ dt; (5.1) X' = li n/
and 
^l = ^ J
T
I x(t) dt,
(5.2)
where the ouantity x(t) can be either 6(5(t), \b(t), ^i^it) or il(t). The estim.ation of the parameters of the three parameter linear m.odel (Eq. 3.2), and those of the nonlinear model, described in Ch. 3.3.3. As m.entioned already before, the steering v/heel of the Zeefakkel was much bigger than that of the simulator, this fact may lead to inertial effects. VJhen the freauencies of the signals involved are lov/ or when the dampinr of the system including the steering v/heel is large, such an effect may be approxim.ated by a firstorder lag. To investigate the influence of inserting such a lag between the output of the nonlinear m.odel and the input of the ship m.odel, some tests have been analyzed using the nonlinear m.odel, where the output of the model is fed through a firstorder filter (Fig. 5.1) T^ 5d^(t) + 6d^(t) = 6^(t), where ^^(t) = output of the nonlinear model; '5df(t) = output of the firstorder filter; Tf = filter time constant.
88
(5.3)
V^j(t)
nonlinear '
FIGURE
Block man's
fi
helmsman's model
öjiM
first order filter
ödf«"
ship model
1 V'OI
J
5.1:
diagram of the ship model steered model, where the output 6^(t) is
Iter.
by the nonlinear fed through a first
helmsorder
To estim.ate the param.eters of the linear and nonlinear helm.sm.an's m.odels, a digital computer was used. The criterion function:
.'^[6^(t)  6^*(t)]^ dt . 100?S
E^2 =
(3.15)
^[6^(t)]^ dt where ödjft) = helmsman's output; 6(j (t) = model output, was minim.ized by m.eans of cyclic variation of the m.odel parameters; a m.ethod which is easy to program digitally. Analoguous to Eg2, also EJK2 and E^2e, v/ere computed, indicating how well the time histories of the actual heading ij;(t) and the sim.ulated heading ^ (t) corresponds. 5.4
Results
Fig. 5.2 shov/s an exam.ple of the tim.e histories of the heading i!)(t), the desired heading ^^{t), and the steering v/heel position 6ci(t). The following remarks can be derived from Fir. 5.2:
[deg]
FIGURE 5.2: Time histories TS S; Subject
of ^f^(t), ^(t) C; Ship speed:
and S^(t). 9 knots.
Test
duration 20 m.in.
89
•
All time histories shov/ a more or less smiooth activity pattern of the helm.sm.an. • Some records of the heading show an oscillatory motion pattern of the ship. • Sometim.es a rather large difference between the desired heading and the actual one occurs, without any action of the helmsman in order to m.inim.ize the heading error. The estimated variances and mean absolute values of the steerinr wheel position 6(j(t),^the heading error ii^it), the headinr ^(t) and the rate of turn i)(t) during the experiments are given in Table 5.4, the times on target as a function of the boundary value bv are shown in Fir. 5.3.
S,
(0
,
40
7« 
/
X
/
/T
20
E o
10
10
0
n
o
/
>
%
10
20
, .S K6 bv—.
«0
in
/
0/
0
FIGURE 5.3: The times on target + slow, TS S ; "o
.8 1.6 bv—*
f
0
0
bv—i
^
.8
K6
bv—.•
40
 X
20
%
^
20
10
10
^
i y^
10
%
20
/
20
^ 0/ 3 .8 1.6
.Jc^
"F
/
40
%
c
/
10
0 / 0
U
40 .
/
•
\ /
3 .8 l!6 bv—^
1.6
\
•
^ /
0
.8
40
7o
ë
10
bv—.•
^^
20
/
()
.8 1.6 bv—^
40
C
"
7o• 20
I.
1
40
•
20
c
[)
'3
^2
/
0^
3
as a function fast, TS S ;
. , .8

•
f
10
0
1.6
bv—i^
of m
0
.8
1.6
b v — 1
the boundary slow, TS L.'
value
bv.
In Table 5.5 the results of the param.eter optimization with the nonlinear model are given. Just as before, the internal model parameter Kf^ was kept eaual to the parameter of the ship Ks. Nine tests were analyzed using the linear model. 90
The results are given in Table 5.6. To investigate the influence of the firstorder lag, five tests were analyzed. To limit the amount of com.puter timie only the most sensitive parameters, viz. W and Ci, were estimated again. The remaining parameters v/ere kept equal to the values given in Table 5.5. The results of the analysis of the five tests are given in Table 5.7. To compare the output of the models with the actual helm.sm.an's output ^ig. 5.4 is given.
Nonlinear model
Linear model
Nonlinear model extended with a first order filter.
FIGURE 5.4. Time histories of the heading ^p(t), the desired heading \jjf^(t). and the steering wheel position 6^(t) recorded during test, and the signals from the computer simulations with the nonlinear model, the linear model and th& nonlinear model extended with a first order filter: \p (t), ijj^ (t) and 6 , (t) respectively.
91
TABLE 5.4:
Estimated variances and m.ean absolute values signals t (t) , \!)(t), \IJ (t) and ^j(t).
Ship Duration TS Suhj. speed
6,(t) ..^(t) li'(t) iit) deg
fit)
deg
deg
deg
3.9 4.2 3.7 3.6 3.9
.24 .36 .30
.24 .42
dee
min.
9
20
5
A E C
23.4 25.3 22.4
4.8 4.8 4.7
18.1 21.8 17.5
.11 .22 .15
3.4 3.5 3.6
1.5 1.1 1.4
12
20
S
B C
9.8 10.7
15.3 19.3
.09 .32
10
S
A C
26.6 51.5
17.3 14.8
12
10
S
E C
23.4 17.8
3.9 3.4
1.6 2.1
3.7 3.4 3.6 3.7
9
10
L
A 3 C
73.9 83.2 85.4
46.0 34.2 46.4
65.8 66.9 64.6
.12 .26 .67 .43 .53 .52 .47
2.4 2.5 4.0 5.8
1.3 1.6
9
4.8 5.7 9.4 5.1 7.0 11.1
6.8 7.4 7.6
4.4 3.6 4.4
7.2 7.0 7.0
.54 .56 .53
9
5
s
A B
64.4 134.1
14.3 20.9
15.8 39.0
.36 .71
6.7 9.8
2.7 3.5
3.4 5.3
.50 .70
12
5
s
B C
38.2 48.9
11.1 11.2
15.8 .34 14.1 1.07
5.1 5.6
2.1 2.4
3.4 3.1
.50 .92
Results mode I.
17.7 17.6
of the varameter
Ship data Duration
sec
2.0 1.5
ovtimization
with
Model parameters
SPC
.22 .48
.69 .54
the
nonlinear
Criteria
J
Subj . TS Speed Ts
min.
92
i(t)
^,(t) i'^(t)
knots
TABLE 5.5:
'^s
knots sec sec" A B C
s
20
B C
s
12
10
A C
s
10
B C
10
20
deg
the
"•'ean ab.ïclute values
Variances
cieg
of
1
m
V/
^1
^2
1:
34. .63
31. 1.0 11. 35. 1.0 10.
9
20. .25
17. 16.
s
12
A E C
L
5
A B
K
E C
20. .25
P
q
sec sec deg sec sec sec deg deg'20. .4 7. 20. .8 11. 19. 1.5 8.
9
^3
^62
E.2
<
of
^ ^ of /J
4.
2. 3. 1.
.5 .5 .8
.5 .7 .5
53.2 10.7 42.6 56.6 2.9 12.9 76.1 9.9 30.6
7. 7.
2. 3.
.5 .5
.5 .5
73.2 8.4 ?7.2 7°. 8 12.1 40.7
8. 9.
4. 7.
3. 3.
.6 .5
.6 .4
41.8 q.i 20.9 69.0 13.9 40.1
3''. .63
42. .7 10. 34. 1.9 12.
6. 9.
3. 3.
.5 .5
.5
68.0 10.3 25.9 77.9 9.6 15.2
9
20. .25
14. 20. 18.
.5 .4 .6
9. 9. 6.
5. 5. 4.
4. 3. 4.
.7 .7 .6
.5 .4 .5
48.7 55.0 47.1
s
9
20. .25
19. 16.
.5 .4
9 6.
2. 3.
.6 .8
.5 .5
42.5 12.5 13.8 45.1 20.0 36.2
s
12
34. .63
34. 36.
.4 13. .5 9.
3. 4.
.7 .4
.6 .5
75.9 15.5 22.2 62.1 23.8 29.8
.6 .4
6. 5.
4.5 6.4 5.8 11.4 4.6 6.4
TABLE 5.6:
Results of the parameter parameter linear model. Shi r data
Duration
with
Kode 1 param.
Subj . TS
min.
optimization
Speed
^s
'^s
knots
sec
sec"
\
the
three
Criteria
1
^1
^2
^6^
W
sec
sec
%
%
'%^ %
20 20
A B
S S
9 9
20. 20.
.25 .25
2.3 1.9
6.8 7.0
1.8 2.9
56.7 52.6
10.6 5.4
42.2 24.1
10 10
A C
S S
9 9
20. 20.
.25 .25
2.4 2.3
8.9 7.7
2.9 1.7
45.7 69.6
19.3 11.4
44.2 32.9
10 10 10
A B C
L L L
9 9 9
20. 20. 20.
.25 .25 .25
1.2 1.2 1.5
8.7 8.0 7.2
3.5 1.5 3.3
46.7 6l.9 51.3
5.7 7.6 8.9
8.1 14.9 12.2
5 5
A B
S S
9 9
20. 20.
.25 .25
2.3 2.1
8.9 3.7
2.9 1.3
42.1 39.7
11.0
12.2
TABLE 5. 7: Results of the parameter ovtimization with the nonlinear model, extended with a firstorder filter. The remaining parameters are kept eaual to the values given in Table 5.5. Parameters
Ship data Duration
Speed min.
5.5
Cr iteria
Subj . TS
\
W
S
^f
sec
knots
sec
sec"
sec def
10
C
S
9
20.
.25
.4
10 10 10
A B C
L L L
9 9 9
20. 20. 20.
.25 .25 •25
.4 .4 .4
5
A
S
9
20.
.25
.4
9.
^^^
E,2
E, ,
sec
%
%
%
1.
68.7
12.5
36.1
42.9 54.3 35.5
5.2 6.3 5.3
7.4 12.6 7.4
37.7
16.6
11.7
10. • 2. 9. 1. 7. 2. 9.
1.
Discussion and conclusions
As indicated in Ch. 5.4, the time histories show that the helm.smen turned the steering wheel more or less in a sm.ooth way to a new position in contrast with all simulator experim.ents, including those with the sm.all ships, where a discrete control was achieved (Ch. 3 ) . This difference m.ay be caused by the following reasons:
•
A difference in ship dynamics: The Zeefakkel is a very fastly responding ship, whereas the sm^all simulated ships reacted much slov/er. • The influence of the inertia of the steering wheel of the Zeefakkel on the steering dynamics of this ship. The linear m.odel as v/ell as the nonlinear model extended with a first order lag generate a sm.ooth output comparable v/ith the helmsm.an's output (Fig. 5.4). The best modelling results have been obtained with the extended nonlinear model. Kov/ever, this does not explain whether this lag was introduced by the helm.sm.an as a controller of a fastly respondinr ship, or by the dynamics of the steering wheel itselves. To investigate this fact further experiments should be perform.ed. The records also show that the steerinr wheel position is almost never kept constant but small oscillations v/ere made. The records of the simulator tests showed a helmisman's output consisting of steering v/heel positions which were kept constant durinr a certain duration. This phenomenon may be introduced by one of the following items: • The influence of the v/aves on the ship: During the tests a very light swell v/as observed, resulting probably into sm.all ship m.otions. As the ship responds rather fast, it might be that the helm.sman reacts on these disturbances which is certainly not the case with larger ships. • The nonlinear behaviour of the steering gear: The dynam.ics of this servo system have been sim.ulated by a first order differential equation with lim.ited rudder angular velocity. However, the actual dynam.ics are much m.ore com.plicated v/ith e.g. dead zones and hysteresis loops. This means, that the steering wheel position does not indicate the actual rudder angle exactly. Probably by introducing small changes of the steering wheel position the helmsm.an can obtain more accurate information about the position of the rudder angle. This phenom.enon v/here subjects introduce test signals is also described in literature several times [3]. Except the results of a few tests, the variety in most of the perform.ance measures related to a certain test condition is small. For small test periods the performance measures related to steerinpwheel position and headinr error are larger than v/ould be expected; the perform.ance m.easure related to the heading is more or less constant. All perform.ance measures increase v/hen test sirnal L was applied. The variances and mean absolute values in the steering wheel position were extremely large for the tests v/ith a duration of five m.inutes, compared v/ith the longer period tests, under the same ship speed and test signal condition. Probably the subjects had not enough tim.e during the shortest tests to steer the ship as they were used to do; a statement which is primarely based on com.ments of the subjects during the execution of the tests. The rather heavy steering wheel again m.ay play an im.portant role in this respect. In particular with respect to the longer tests, the estim.ated times on target (Fig. 5.2) indicate a better perform.ance for the slow ship speeds than for faster ship speeds. During the longest tests, it is more im.portant to keep the ship at the ordered heading. This seems to be easier to do at slov/ speed than at full speed. Also the estimated performance measures given in Table 5.6 indicate a better performance v/ith respect to the heading error under slow speed condition. This fact can be understood by taking into account the
94
nonlinear behaviour of the steering gear, becoming more important when the ship reacts faster. The results obtained with the nonlinear m.odel and the linear model are rather poor, in general. The criterion values obtained by usinr the nonlinear model extended with a firstorder filter are slightly better. This can be caused by the following reasons: • The influence of measurem.ent noise: In particular the recordings of the ordered headinr ^6(.t) caused some troubles, the orders v/ere given verbally and thus an exact time was difficult to define. • Environmental influences, such as other ships in the neightbourhood of the Zeefakkel. • The difference existing between the model describing the ship dynam.ics and the actual dynamics. • The influence of waves. e The difference between displays and controls of the Zeefakkel and those of the simulator used to develop the nonlinear model. e A difference in behaviour of the subjects durinr this study and the simulator study due to task definition, etc. In spite of the large values of the optimization criterion, the variances of the parameter values found with respect to the nonlinear m.odel are in general rather sm.all. Table 5.10 shows the averaged values and standard deviation of the parameters for each of the ship speeds. TABLE 5.10:
Averaged nonlinear
values model
(x\) and standard deviations parameters for each of the
Ship data Speed
n 0
n a
of
the speeds.
Fodel parameters m
m
s
W
^1
^2
'3
P
q
sec deg
sec
sec
sec
deg
deg"^
8.3 1.6
5.0 .9
2.8 .9
.63 .14
.51 .10
10.8 1.5
6.6 1.4
3.0 .6
.51 .10
.51 .01
^s
•^s
knots
sec
sec"
sec
9 9 .
20. 20.
.25 .25
17.9 2.1
.90 .11
.61 .34
34. 34.
.63 .63
35.3 1.04 3.7 .11
.91 .70
12 12
(a) ship
When the standard deviation is not small, for instance the values of the parameter VJ, this is often caused by one extreme data point. From this table, it can also be concluded that the influence of the ship speed on the parameter values is mostly sm.all. The param.eters W and Q\ increase a little with increasing speed, but in particular W shows a rather large variance so that this increase may not be regarded as being significant. Only the internal model parameter T is strongly influenced by the ship param.eters Tg and Kg (Km is kept equal to Kg) and therefore also the normalized values of n and a with respect to Ts are given. This normalized value is rather constant too. The values of the decision making element param.eters Ci, C2 and VJ are all rather smiall compared with the sim.ulator test results, but
as the Zeefakkel possesses very good handling oualities, this can be understood (Ch. 3 ) . The param.eters C3, p and o are arain less sensitive, but the values found correspond v/ith the previous results . The criteria values obtained with the linear m.odel do not differ m.uch from the nonlinear modelling results: The output of the linear model is continuous just as the output of the helmsman. Only tests with the ship sailing at low speed are analyzed, as the results with the nonlinear model are the best for this test condition. From; the parameter values found, it may be concluded, that in particular the gain factor Y.^. is strongly influenced by the test signal used (Table 5.8). The criteria values found with the nonlinear model extended v/ith a firstorder lag, are sometimes much sm.aller than with the basic nonlinear model or the linear model. The output of this extended model looks most like the output of the helmsmen. As only three parameters vrere optimized, viz. W, Ci and Tf, and the rem.aining parameters were kept enual to the values given in Table 5.5, the results are possibly not the most optimal ones. As it was only the intention to investigate the question whether a lag, added in the loop, would yield better results, not all the parameters were varied. However, it can be concluded that for the tests analyzed a firstorder filter added to the ship dynam.ics yield better results with respect to the optim.ization criterion than the basic nonlinear m.odel or the linear model. Finally the following conclusions can be summ.arized: • The tim.e histories obtained with full scale tests show some significant differences with the sim.ulator test results, due to different ship dynamics including the dynamics of the steering wheel. • The performance m.easures are better when the ship sails slowly than at full speed, possibly due to nonlinearities of the steering gear or due to the fact that the ship itself is easier to handle at low speed. o The obtained values of the criterion used to optim.ize the models are large, both with the nonlinear m.odel as v/ell as with the linear model. Adding a firstorder lag simulating the inertia effects of the steering v/heel, to the ship dynam.ics, yield better results. e The parameter values of the nonlinear model agree with the results of the simulator study. • The variances of the nonlinear m.odel parameters found are rather sm.all, just as those of the linear m.odel, except the gain Kji, which is strongly influenced by the am.plitudes of the test sirnal used. This fact indicates the nonlinear behaviour of the helmsm.an. REFERENCES 1. REFERENCES 1. Maanen, M.A. van, Simulatie van een m.et verstelbare spoedschroeven uitperust vaartuig. Report: Den Helder, Roval Netherlands Naval College, 1974, 38 p. 2. Amerongen, J. van; Haarnan, J.C.; Verhage, V.'., Mathem.atical modelling of ships. In: Proc. Fourth Ship Control Svstems Svmo., Roval Netherlands Naval College, Den Helder, 1975, Vol. 4, pp. 163178. 3. Lunteren, A. van; Stassen, H.G., Annual Report 1969 of the ran"achine Svstems Groun. Qf)Report: Delft, Dept. of Mech. Engineering, 1970, No. '•n'HD21,
CHAPTER VI: CONCLUDING REMARKS AND FURTHER RESEARCH 6 .1
Results achieved
The problem stated in Ch. 1 was to obtain knowledge about the human control of ships, so that the handling Quality of ships can be quantified. To limit this v/ide area of research only the helm.sman steering a ship along prescribed headings has been considered. The inform.ation obtained has been summarized into two models: • A linear model consisting of a gain, a lag and a lead term. This model describes the helmsm.an's behaviour in the control of a ship sailing in calm, water. • A nonlinear model describing the helm.sm.an's behaviour in the control of a ship sailing in disturbed as v/ell as undisturbed water. This m.odel is based on the internal model concept (Ch. 1.2); it consists of an internal model, an estimator and a decision m.aking element. To predict future headings a sim.ple differential enuation describing the dynamic behaviour of ships is used: The internal m.odel. To update this internal model an estimator is needed to generate estimates of the undisturbed heading and heading rate, as the heading displayed by .the compass m.ay be disturbed by noise, e.g. due to waves. The proper actions necessary to achieve the desired state are selected by the decision making elem.ent on the basis of predictions with the internal model. The parameters of this nonlinear helmsman's model can be divided into two groups: one group being the internal model parameters (Tm, Km) and another one being the decision making element parameters. This last group of param.eters can be divided again into a group related to the way of steering, that m.eans the magnitudes and durations of the rudder angles to be applied (Ci, C2, C3, VI) and a group of parameters related to the comparison between the internal model predictions and the actual ship states (p, q ) . VJhen the difference between the predicted state and the actual state becom.es too large, new actions have to be taken. The param.eters involved in the process of deciding whether an action should be perform.ed or not, indicate the helmsman's precision of steering. The two m.odels justmentioned have been based on the follov/ing experiments: • A series of sim.ulator experim.ents to study the helmsman's control behaviour in relation to the dynamical behaviour of ships sailing in calm, water (Ch. 3 ) . • A series of simulator experiments to study the influence of waves and the influence of presenting additional information such as the ship's rate of turn and predictions of the heading on the helmsm.an's behaviour (Ch. 4 ) . • A series of full scale experiments with a small ship to com.pare sim.ulator test results with those obtained from tests with an actual ship (Ch. 5 ) . From these experim.ents the following conclusions with respect to the optimization of the models could be drav/n:
97*
•
The linear model ps v/ell as the nonlinear m.odel yield on the basis of the error criterion used, an acceptable description of the helm.sm:an's control behaviour in the simulator experiments (Ch. 3 ) . The description of the helm.sm.an during the full scale tests v/as much poorer (Ch. 5) due to differences betv/een the test conditions. • The simulated heading of the ship always closely matches the heading of the ship steered by the helmsman (Ch. 3, 5 ) . 9 The optim.ization of the nonlinear m.odel param.eters by m.eans of m.inim.izing the m.ean absolute value of the difference betv/een model output and helm.sm.an output, does not always yield the desired results (Ch. 3 ) . o This optimization criterion is rather insensitive to some of the nonlinear m.odel parameters, in particular those parameters which indicate the precision of steering. Concerning the parameters of the linear m.odel and those of the nonlinear one the followinr conclusions can be summarized: • The rain factor of the linear m.odel is stronrly influenced by the am.plitudes of the headings ordered. This fact indicates the nonlinear behaviour of the helmsm.an (Ch. 3, 5 ) . • The internal model parameters Tm and Km have been found to be strongly coupled. Therefore, instead of the simple internal m.odel structure used, even a sim.pler structure can be adopted (Ch. 3 ) . • In the case of larre ships (Ch. 3) as v/ell as in the case of the small actual ship (Ch. 5) the internal m.odel time constant Tm v/as found to be of the same order as the ship's time constant Ts . 9 The decision making element param.eters related to the way of steering may be regarded as a rather good estimator of the helm.sm.an's subjective judgement of the handlinr qualities of the ship (Ch. 3, 5 ) . • The decision making elem.ent param.eters related to the precision of steering influence mainly the character of the nonlinear m.odel output, in particular the number of rudder calls (Ch. 3 ) . These parameters are very important with respect to the accuracy of the information presented, to the helm.sm.an (Ch. 4 ) . With respect to the perform.ance of the helm.sman the follov/ing conclusions were drawn: • The control of very large ships in calm water by the helm.sm.an does not cause problems fundamentally different from the control of sm.all ships. The detrimental effect of course instability is dependent not only upon the ship's stationary characteristic, that is the relation between rate of turn and rudder angle in steady state, but also upon the ship's time constant (Ch. 3) • • The nonlinear steering gear dynamics may have a detrimental effect on the helnsmian's performance in the control of fastly responding ships (Ch. 3, 5 ) . 9 Additional inform.ation presented to the helm.sman of a large ship leads to a better perform.ance of the helm.sman . Hov.'ever, the main profit of additional displays m.ay be rather a decrease in v/orkload than the im.orovement of the helm.sm.an's perform.ance (Ch. 4 ) . o The helm.sm.an's performance and the influence of rather accurate additional information presented to the helmsm.an on this perform.ance, can be predicted with the nonlinear m.odel rather v/ell.
98
However, the influence of additional inform.ation v/hich is inaccurate due to differences between predictor model and the actual ship dynam.ics, needs further research (Ch. 4 ) . To elucidate the m.eaning of the results listed above, som.e remarks should be made. As mentioned before, the optim.ization criterion was rather insensitive to the parameters indicating the precision of steering (Ch. 3 ) . However, these parameters are very im.portant in the prediction of the influence of additional displays on the helmsman's performance (Ch. 4 ) . They are also important with respect to the character of the helsman's output, e.g. the number of rudder calls. Hence, the optimization criterion to be used should be also sensitive to the model parameters related to the precision of steering. As an example an optimization criterion may be defined based on the differences between model output and helmsm.an output v/ith respect to the average number of rudder calls and v/ith respect to the m.agnitudes and durations of the applied rudder deflections. The nonlinear model has been based on a relatively simple internal m.odel. Due to the available tim.e for this study the sensitivity of the error criteria with respect to the structure of the internal model has not been studied. Hov/ever, the fact that the simple internal miodel used yields already acceptable results, is a very im.portant conclusion. As m.any important problem.s in human operator activities can be directly related to the internal model concept, this conclusion can probably contribute to other manmachine problems. For instance, the information needed to update the internal m.odel, that is the information which has to be presented, is related to the complexity of the internal model. From, literature on linear human operator models (Ch. 1 ) , it is known that the human operator adapts his control behaviour to the dynamics of the controlled element, in such a way that a stable and welldamped closed loop performance is obtained. Also with respect to the nonlinear m.odel this m.ay be the case as can be concluded from the results of the simulator study. This means that in predicting the handling quality of ships, the quality can be determined by means of computer simulations. On the basis of a sensitivity analysis, where the stability and damping are determined depending on the decision making element param.eters related to the way of steering, those parameters can be estimated which yield the best closed loop performance with, respect to stability and damping. As discussed in Ch. 3, these decision making element parameters can be considered as an indicator of the ship's handling quality. Finally, the meaning of the decision m.aking element parameters related to the precision of steering will be discussed. These parameters are mainly dependent on the helmsman's indifference with respect to sm.all errors and the accuracy of the observed information. Hence, a relation exists between the helmsm.an's sampling behaviour and the values of the parameters related to the precision of steering. The prediction of the influence of additional information presentation on the helmsman's performance was based on such a relation (Ch. 4 ) . Therefore, it is believed that a more detailed study of the helmsman's sam.pling behaviour in steering a ship in calm, water may contribute to a better understanding of the parameters related to the precision of steering, and thus to the overall performance of the helmsman. As mentioned in the literature review, much research has been executed in the field of manual control of fastly responding systems; less attention has been paid to the manual control of slowly
99
responding systems and only some incidental studies in the field of supervisory control are reported. However, scale enlarging and automation leads to the fact that hum.an operators have to control and supervise m.ore and more slowly respondinr systems, /^s a consequence, much more knowledre about the hum.an behaviour in the control of slowly responding system.s should be gathered. The study reported contributes in two ways. In the particular case of the manoeuvring of large ships it provides a nonlinear model, on the base of which predictions about the handling ouality of shins can be estimated. This result is im.portant with respect to shin handling properties, but due to the nonlinear properties of the m.odel, the use of the model is restricted to a lim.ited area; an extension to other test conditions is difficult to foresee. In this sense the results are rather poor. However, much more im.portant is the general use of the internal m.odel concept. This concept is a. very general one. In the past it has been used in optim.al control models to describe hum.an behaviour in the control of fastly responding system.s, it now is proven to be of great value in studies of hum.an control of slowly responding system.s, an exam.ple of a supervisory control with only one input and one output. 6.2
Further research
The results mentioned above indicate that a com.plete solution of the problem, stated in Ch. 1, has not been obtained; further investigations should be executed. The suggestions to be given with respect to further research can be classified into two areas, viz. the control of ships and the supervisory control. VJith respect to the first area the follov/ing items should be considered: • A detailed study of the problems which have been arisen in the developm.ent of the nonlinear m.odel, such as the sensitivity of the internal model structure on the output of the nonlinear model, the optimization criteria to be used, and the sampling behaviour of the helmsman. • An extension of the application area of the nonlinear model to more general test conditions, such as tim.e varying ship dynamics and the control of the ship's position. e The m.anoeuvring of ships in those conditions, where the complete crew on the bridge is involved, for instance the approach of a harbour, the navigation in restricted water or in areas with a high traffic density. With respect to supervisory control problem.s, it may be expected that the use of the internal m.odel concept can be a basis for new research in the almost unknown area of supervisory control behaviour; it also may contribute to the integration of cybernetics and experimental psychology. This integration then can be achieved by relating the many cybernetical concepts on the one side and the psychological functions on the other. It is therefore recommanded to base further research on the general internal model concept.
100
SUMMARY In order to obtain an optimal performance of a ship controlled by a helmsman, the dynamics of the ship, as well as those of the helm.sman should be known. A lot of research has been devoted to the dynamics of ships; however, the dynamical behaviour of the helmsm.an got less attention. The research described in this thesis is aimed to obtain inform.ation with respect to the helmsman's control behaviour. The information obtained has been summ.arized into two models: • A linear model consisting of a gain, a lag and a lead term.. This model describes the helmsman's behaviour in the control of a ship sailing in calm, water. • A nonlinear model describing the helm.sman's behaviour in the control of a ship sailing in disturbed as well as undisturbed water. This model has been based on the internal model concept, that is the assumed knowledge the helm.sman has about the dynamics of the ship under control, about the disturbances acting on the ship and about the task to be executed. The internal m.odel as part of the nonlinear helmsman's m.odel is a sim.ple differential equation which is used to predict future ship states. As the heading displayed by the compass may be disturbed by noise, e.g. due to waves, an estimator is needed to generate estim.ates of the undisturbed heading and heading rate, to update the internal model. The proper actions necessary to achieve the desired states are selected by the decision m.aking element on the basis of predictions with the internal model. The two m.odels have been based on the follov/ing experiments: • A series of sim.ulator experiments to study the helmsm.an's control behaviour in relation to the dynamical behaviour of ships sailing in calm v/ater. • A series of simulator experiments to study the influence of waves and the influence of presentinr additional information, e.g. the ship's rate of turn and predictions of the heading on the helmsman's behaviour. • A series of full scale experim.ents v/ith a small ship to compare simulator test results with those obtained from, tests v/ith an actual ship. The optimization of the m.odel parameters has been executed by means of a hybrid comiputer, on which the models of the helm.sman and a model of the ship dynam.ics have been programmed. Those param.eters have been determ.ined for which the mean absolute value of the difference between model output and helmsm.an output v/as minimal. The study reported here contributes to the field of ship manoeuvring, which is a part of the much larger field of the control of slov/ly responding systems. With regard to the first area, the following conclusions can be drawn: e The two helmsman's models provide an acceptable description of the helmsman's control behaviour. A very good description of the ship's heading is obtained. • The internal model parameters are often of the same order as the corresponding parameters of the ship. The decision making element parameters are very im.portant in the prediction of the ship's handling ouality and in the prediction of the influence of presentinr additional information to the helmsman.
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The presentation of additional information improves the helms man's performance. VJith reference to the control of slowly respondinr systems, it i shown that the application of the internal model concept is very valuable.
SAMENVATTING Teneinde een optimaal gedrag van een door een roerganger bestuurd schip te verkrijgen, m.oet de dynamika van het schip en het dynamisch gedrag van de roerganger bekend zijn. Veel onderzoek is verricht op het gebied van het dynamisch gedrag van schepen; echter aan het gedrag van de roerganger is veel m.inder aandacht besteed. Het onderzoek beschreven in dit proefschrift had tot doel informatie ten aanzien van het regelgedrag van de roerranger te verkrijgen. De verkregen inform.atie is samengevat in tv/ee modellen: • Een lineair m.odel, bestaande uit een versterkinrsfaktor, een differentiërende en een integrerende term.. Dit model beschrijft het gedrag van de roerganger bij het besturen van schepen, varend in vlak water. • Een niet lineair m.odel, dat het gedrag van de roerganrer beschrijft bij het besturen van schepen varend zowel in vlak v/ater als in golven. Dit model is gebaseerd op het interne miodel concept, d.w.z. de kennis die de roerganger verondersteld wordt te hebben over het dynamisch gedrag van het te besturen schip, over de verstoringen die op "4^et schip werken en over de uit te voeren taak. Het interne model v/aar het niet lineaire model op rebaseerd is, is een eenvoudige differentiaal vergelijking die gebruikt wordt om de toestand van het schip in de toekomst te voorspellen. Voor het doen van deze voorspellingen moet de deviatie en hoeksnelheid van het schip bekend zijn. Aangezien de deviatie, die wordt aangegeven door het kompas, verstoord kan zijn door ruis, b.v. ten gevolge van golven, is een schatter nodig om de ongestoorde deviatie en hoeksnelheid van het schip te schatten. De akties, die nodig zijn om het gestelde doel te bereiken, worden gekozen door een beslissingselem.ent op grond van de voorspellingen met het interne m.odel. Deze twee m.odellen zijn gebaseerd op de volgende experimenten: • Een reeks experim.enten met een manoeuvreer simulator om het regelgedrag van de roerganger in relatie tot het dynamisch gedrag van het schip te bestuderen. Hierbij zijn schepen varend in vlak water beschouv/d. • Een reeks experim.enten, eveneens uitgevoerd met een manoeuvreer simulator, om de invloed van golven en de invloed van het aanbieden van extra informatie b.v. de hoeksnelheid van het schip of voorspellingen van de koers van het schip, op het regelgedrag van de roerganger te bestuderen. • Een reeks experim.enten met een klein schip. Het doel van deze proeven was om. de resultaten verkregen m.et de sim.ulator proeven te kunnen vergelijken met de resultaten van proeven met een echt schip. Voor de optim.alisatie van de model parameters is gebruik gem.aakt van een hybriede rekenmachine, waarop de m.odellen van de roerganger en het m.odel van de dynamika van de schepen zijn geprogram.m.eerd. De parameters zijn geschat door m.inimalisering van de gem.iddelde absolute waarde van het verschil tussen de door de roerganger en het model gegenereerde signalen. De studie beschreven in het proefschrift is een bijdrage op het gebied van het besturen van schepen, v/at deel uitmaakt van het veel grotere gebied van de besturing en regeling van traag reagerende systemen. Met betrekking tot het eerste gebied kunnen de volgende . konklusies getrokken worden: ..
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De tv/ee opgestelde m:odellen voor het gedrag van de roerganger geven een acceptabele beschrijvinr van het regelgedrag van de roerganger. Een zeer goede beschrijving van de door de roerganger gevaren koers is verkregen. 9 De param.eters van het interne model zijn vaak van dezelfde orde van grootte als de overeenkom.stire param.eters van het schip. De parameters van het beslissingselement zijn erg belanrrijk bij het voorspellen van de manoeuvreereigenschappen van een schip. Zij zijn eveneens belangrijk bij de voorspelling van de invloed van het aanbieden van extra informatie op de prestaties van de roerganrer. • Het aanbieden van extra inform.atie verbetert de prestaties van de roerganrer. Met betrekking tot de rereling van langzaam, reagerende systemen is aangetoond, dat de toepassing van het interne model concept zeer v/aardevol is.
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STELLINGEN I.
Studies van het menselijk regelgedrag zouden bij voorkeur gebaseerd moeten zijn op het InternModelconcept. Lit.: Dit proefschrift.
II.
Om een mensmachinesysteem te optimaliseren is een gedegen kennis omtrent de informatieuitwisseling tussen mens en machine van groot belang. Hierbij dienen twee vragen beantwoord te worden, nl.: "Over welke informatie dient te mens te beschikken, teneinde een machine zo goed mogelijk te kunnen besturen?", en "Hoe dient deze informatie te worden gepresenteerd?" Het is te betreuren, dat het overgrote deel van het mensmachineonderzoek gericht is op het verkrijgen van een antwoord op de laatste vraag, terwijl juist de eerste vraag van veel groter belang geacht moet worden.
III.
Voor de beschrijving van het gedrag van de mens als regelaar van relatief trage systemen kan met vrucht gebruik gemaakt worden van de reeds ontwikkelde lineaire modeltheorie met betrekking tot de regeling van relatief snelle systemen. Lit.: McRuer, D.T.j Jex, H.R. A review of quasilineair pilot models. lEEEtrans. on Human Factors in Electronics, Vol. HFE8 (196T), No. 3(Sept.), pp. 231249.
IV.
Door Wagenaar et.al. is experimenteel de invloed van koersstabiliteit op de prestaties van roergangers bepaald, waarbij verschillende informatiepresentatie systemen zijn onderzocht. Het door hen uitgevoerde onderzoek zou sterk in waaorde hebben gewonnen indien de onderzoekers hun resxiltaten op basis van een model ter beschrijving van het gedrag van de roergsinger zouden hebben verklaard. Lit.: Wagenaar, W.A.; et.al., Auxiliary equipment as a compensation for the effect of course instability on the performance of helmsmen. Communication Netherl.. Ship Research Centre TNO, Delft, 1972, No. 28 S, 21 p.
V.
Door Johannsen is een methode aangegeven om systemen opgenomen in een gesloten keten m.b.v. nietlineaire modellen te identificeren. De door Johannsen gesuggereerde algemeenheid van deze methode is aanvechtbaar. Lit.: Johannsen, G., Development and Optimization of a Nonlinear Multiparameter Hiunan Operator Model. lEEEtrans. on Systems, Man, and Cybernetics, Vol. SMC2 (1972), No. 4 (Sept.) pp. 494504.
VI.
Bij fundamenteel onderzoek naar het gedrag van de mens als bewaker/ regelaar van een systeem is het gebruik van een door een digitale rekenmachine gestuurde simulator te verkiezen boven het gebruik van een door een analoge rekenmachine gestuurde simulator.
VII.
De aandacht die thans besteed wordt aan het mondeling en schriftelijk rapporteren tijdens de voorkandidaatsstudie voor werktuigkundig ingenie\ir is volstrekt onvoldoende.
VIII.
Met het ontbreken van de mogelijkheid tot doubleren op de door de Minister van Onderwijs en Wetenschappen voorgestelde middenschool ontbreekt ook een belangrijke mogelijkheid tot het opdoen van levenservaring voor de scholier.
IX.
Het verschil tussen de doelstelling van de systeemtheoretisch geschoolde ergonoom en de doelstelling van de experimenteel psychologisch geschoolde ergonoom ten aanzien van onderzoek op het gebied van de mensmachinesystemen resulteert in een totaal verschillende opzet van uit te voeren experimenten. Dit verschil in experimentele condities vormt een sterke belemmering voor de noodzakelijke samenwerking van beide disciplines.
X.
Een doelmatiger muziekonderricht bij het basis onderwijs en het voortgezette onderwijs kan een belangrijke bijdrage leveren tot een grotere belangstelling voor de serieuze muziek van deze eeuw.
XI.
Werd vroeger het onderwijs nadelig beïnvloed door de zekerheid van de juistheid van het bestaande onderwijssysteem, tegenwoordig is het juist de onzekerheid die het onderwijs nadelig beïnvloed.
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