ship maneuvering under human control
TRANSCRIPT
SHIP MANOEUVRING
UNDER
HUMAN CONTROL
analysis of the helmsman's
control behaviour.
wim veldhuyzen
//2>i9 / 53 ^
00 o 00 M CD 0>
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
"O
UI W O' 00
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 Man-r%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 Man-Machine 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 set-up 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 9
Modelling the helmsman: A review of literature 10
System identification 12
Outline of the thesis 15
Definition of symbols 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
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page
3.5
3.6
Results
Discussion and conclusions
49
56
CHAPTER IV: SHIP MANOEUVRING IN WAVES
4.1
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
4.5
4.6
Introduction 65
Extension of the nonlinear helmsman's model 66
Experimental set up 68
Ship dynamics 68
Displays and controls 70
The ordered headings: The test signal 72
Subjects 72
Experimental programme 72
Data collection 73
Prediction of scores 73
Model structure 73
Parameter values 76
Results 78
Discussion and conclusions 8I
CHAPTER V:
5 5. 5. 5 5 5 5 5 5 5 5
1
2
2 .
2 .
2 .
. 2 .
.2
.2
.3
.4
.5
1
2
3 4
5 6
FULL SCALE EXPERIMENTS WITH A SMALL SHIP
Introduction
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
85
85
86
86
87
87
87
87
88
'89
93
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page
CHAPTER VI: CONCLUDING REMARKS AND FURTHER RESEARCH
6.1 Results achieved , 97
6.2 Further research 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- Controller-Ship 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.
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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 well-knov/n crossover model has been obtained [24, 25]:
HpHc = 3^ e-J'^^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.
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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 introducinp-noise; 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;
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• 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 non-linear 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 non-linear 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 of a system consisting of a linear model and a remnant.
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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 un-correlated 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 a-priori knowledge. • Methods with certain a-priori knowledge. In the case that no a-priori 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 well-known relation:
S (v) uy'
H(v) S (v). uu ''' • (1.2)
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].
U(V) E{V)
mv)
H^(VJ ^
Y(V) Z(V) HjfV)
N(l/)
U(VI
• ; UHj(l/)H2(V)|
H,(»/. 1
UHj(V)H^(»/)j ^v.
N,(»/)
f
J
Y(V)
FIGURE 1.2:
Trans formation of a closed loop 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.
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However, by transforming the closed loop system, into an equivalent open loop system (Fig. 1.2.b), the method explained just-before can be applied again, hence it follows:
S (v)
ue (1.3)
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(e-t) dt, e-T
(1.4)
;vhere e(t) q
difference between system output and model output; factor indicating the influence of the magnitude of e(t);
w = v;eighting function to take into account the time history of the error e(t).
u(t)
r» stem linear
model
T
SL y(t)
_1
linear | y (> '^ f ^ ' ^
model
minimizaiicn
of E(-5,T)
porameters
FIGURE 1.3:
Block diagram of system identification by means of parameter estimation.
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.
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controlled
system
•itJ
FIGURE 1.4: Block diagram of a closed loop parameter estimation 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 a-priori 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.
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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 full scale trials with a rather sm.all ship. In this way of simulator tests, viz. linear and nonlinear m.odelling could be evaluated with respect to a small ship. In Ch. 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
series of the results results, 5 these
1.5 Definition of symbols
In Fig. 1.5 a block diagram is given of a ship under hum.an control.
disturbances
» helmsman I — » steering | 6 ( t )
gear
i ship
FIGURE 1.5: Block diagram of the ship steered by a helmsman.
V^(t)
Using the steering v/heel, of which the position is denoted by <Sd(t), the helmsman controls the rudder position fi(t), by v.'hich the heading angle of the ship i(j(t) can be controlled. The heading angle is the angle between the longitudinal axis of the ship and the xo-axis of a right handed, orthogonal system, of coordinates fixed relatively to the earth: Ox y^z^ (Pif. 1.6).
FIGURE 1.6: Definition of the quantities involved in the manoeuvring of a ship,
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The XQ direction can be the south-north direction for example . The ordered heading is denoted by i|)(j(t). The positive direction of the heading is clockwise, just as for the rudder angle and the course ijj(t). The rudder angle is the angle betv/een the longitudinal axes of the ship and the rudder; the course angle is the anp-le between the direction of the ship velocity vector V and the x^-axis. A second right handed and orthogonal system of coordinates Gyvz is defined, fixed relatively to the ship, having its origin at the ship's centre of gravity. The x-direction coincides with the ship's longitudinal axis. The components of the ship's velocity vector V in X- and y-direction are denoted by u and v respectively. In thTs study it is assum.ed that the ship's centre of gravity is constrained to the horizontal Oxoyo pla^^e, and that this plane coincides with the Gxy plane at all tim.es.
REFERENCES •" ' '
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2. Davidson, K.S.M.; Schiff, L.I., Turning and course keeping qualities. Trans, of the S.N.A.M.E., Vol. 5t (igl^ö), pp. 152-200.
3. Nomoto, K.; Taguchi, T.; Konda, K.; Hirano, S., On the steering qualities of ships. I.S.P. Vol. iJ (1957) No, 35, pp. 35')-370.
H. Abkowitz, M.A. , Lectures on hydrodynamics. Report: Lyngby (Denmark), Hydro og Aerodynamisk Laboratorium., 1964, 113 p. No. Hy-5.
5. Eda, H.; Crane, C.L., Steering characteristics of ships in calm water and waves. Trans, of the S.N.A.M.E. Vol. 73 (1965), pp. 135-177.
6. Norrbin, N.H., Theory and observations on the use of a m.athematical model for ship m.anoeuvring in deep and confined waters. Public: Gothenburp:, SSPA, 1971, No. 68, 117 p.
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24. McRuer, D.T.; Jex, H.R., A review of quasi-linear pilot models. IEEE-trans, on Human Factors in Electronics, Vol. HFE-8 (1967), No. 3 (Sept.), pp. 231-249.
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27. Elkind, J.I,; Miller, D.C., On the process of adaption by the human controller. Proc Third IFAC congress on automatic and remote control, London, June 1966, Vol, 1, book 2, paper 30A, 13 p.
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29. Diamantides, N.D,, A pilot analog for airplane pitch control, Journ, Aeronautical Sci, Vol. 25 (1958), pp. 361-370.
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31. Pitkin, E.T., A non-linear feedback m.odel for tracking studies. Proc. Eighth Conf. on Man. Contr., Ann Arbor, 1972, AFFDL-TR-72-92, pp. 11-22.
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32. Phatak, A,V.; Weir, D.H., On the dynamic response of the human operator to transient inputs. Proc Fourth Conf. on Man. Contr., Ann Arbor, 1968, NASA-SP-192, pp. 383-392.
33. Cooke, J.E., Human decisions in the control of a slow response system. Diss.: Oxford, 1965, 403 p.
34. Bainbridge, L., The nature of the mental model in process control. Paper presented at Symp. on Man-Machine Systems, Cambridge (U.K.), 1969, 10 p,
35. Kelley, C.R., A psychological approach to operator modelling in manual control. Proc, Third Annual Conf, on Manual Control, Los Angelos, 1967, NASA-SP-126, pp. 165-180.
36. Kelley, C.R., Manual and autom.atic c o n t r o l . New York, Vfiley, 1968.
37. Senders, J,W., The human operator as a monitor and controller of multidegree of freedom system.s, IEEE-trans, on Human Factors in Electronics, Vol. HFE-5 (1964), No, 1 (Sept.), pp. 2-5.
38. Smallwood, R,D,, Internal models and the human instrument r.onitor, IEEE-trans, on Human Factors in Electronics, Vol, HFE-8 (1967), No. 3 (Sept.)., pp. 181-I87.
39. Rouse, W.B., A model of the human in a cognitive prediction task, IEEE-trans, on Systems, Man and Cybernetics, Vol. SMC-3 (1973), No. 5 (Sept.), pp, 473-477,
40. Int, Symp. on Monitoring behaviour and supervisory control. Berchtesgaden, 1976. To be published.
41. Kleinman, D.L.; Baron, S., Analytic Evaluation of Display Requirements for Approach to handing, Report: Cambridge (U.S.A.)', Bolt Beranek and Newman, NASA CR-1952.
42. Johannsen, G., The design of a non-linear multi-parameter model for the human operator. In: Displays and Controls, Proc. Adv. Study Institute, Berchtesgaden. Amsterdam, Swets and Zeilinger, 1972, pp. 249-367.
43. Lunteren, A. van; Stassen, H.G., Annual Report 1969 of the Man-Machine Systems Group. Report: Delft, Dept. of Mech. Engineering, 1970, WTHD 21, 102 p.
44. Jenkins, G.M.; Watts, D.G., Spectral Analysis and its Applications, Holden Day, I969.
45. Lunteren, A. van, Systeem identifikatie en parameter schatting in open en gesloten ketens. Rapport: Delft, Lab. voor Werkt. Meet- en Regelt., 1976, N-114, 109 p.
CHAPTER II: SHIP DYNAMICS
2.1 Introduction
To perform, simulator experiments a mathematical model describinfr the behaviour of a ship had to be selected. Keeping in mind the objectives of this study, the following requirements viith respect to such a model should be form.ulated: • The responses of the model to any rudder angle inout must be
as realistic as possible. • To be able to analyze the test results the model should be as
simple as possible. As the study is only concerned with the behaviour of helmsm.en steering a ship alonr prescribed headings, only the relation between rudder angle and heading is iriportant. By a sim.ple model is meant, a model simple with respect to its structure and with a sm.all amount of parameters.
• The tests should provide information about the im.portance of different manoeuvring properties such as sluggishness and course instability.
• It should be possible to introduce also the influence of v:aves in the simulation.
Before the model used can be selected, a brief review of mathem.atical models describing the m.anoeuvring behaviour of ships will be given.
2.2 Models of ship manoeuvring
The steering of ships has been studied already for many years, but the more scientific approach started just in the forties. In 1946 Davidson and Shiff published a method to analyze the behaviour of ships, which can be regarded as the base of all later research on this subject [l] . From elem.entary mechanics the equations of Euler for a sym.metric ship moving in the horizontal plane are known:
X = m (Ü - vr) ; (2.1-a)
. Y = m (v + ur) ; (2.1-b)
N = 1^2^ , (2.1-c)
where X = hydrodynamic force in x-direction; Y = hydrodynamic force in y-direction; N = hydrodynamic moment; m = ship's mass; Izz = ship's m.om.ent of inertia about the z-axis; r = dij;(t)/dt = angular velocity.
Referring Un, r-n" » Vn = 0 and 6^=0 as the nominal conditions, the following linearized equations of motions can be derived:
(X -m)u + X^Au
( Y . - m ) v + Y v + Y*f + V v r
N'V + N V + (N'-I )f + V V r zz
= 0
^-m.u^)r = -Yg5
V = - 6^
( 2 . 2 - a )
( 2 . 2 - b )
( 2 . 2 - c )
-20-
In Eqs. (2.2) the subscript means the partial derivative with respect to the specific variable, and the quantity u^ denotes the constant forward speed. This model, consisting of three equations of which two equations are coupled, is based on the following assumptions: • The ship is a rigid and sym.metric body. • Only the motions in the horizontal plane are considered. • The centre of gravity is considered to be situated in the Ox y
plane, which is the water plane. ° ° • The X, y, and z-axes are the ship's principle axes of inertia. • The influence of external disturbances such as wind, v;aves or
current is neglected. • The ship is sailing in unrestricted viater. • The propeller is kept at a constant num.ber of revolutions. • The perturbations of the variables around the equilibrium, are
small. To include also larger variations of the variables the model has to be extended v;ith nonlinear term.s. In this v;ay many different models have been suggested [2, 3, 4]. However, these m.odels have a rather large number of param.eters. To study the behaviour of a helmsm.an a much siripler miodel is to be preferred.
By elim.inating the drift speed v from, the Eos. (2.2-b) and (2.2-c) a single differential equation is obtained, knov/n as Nom.oto's second order model [5]:
T^T2^(t) + (T^+T2)if(t)+iI^(t)=K[T^(5(t) + 6(t)], (2.3)
where the parameters T., Tpj and T, are called time constants and K is a gain factor. These parameters are functions of the partial derivatives in the Eqs. (2.2). If the rudder m.otions are low frequent, this equation can be replaced by a simple first-order differential equation in the rate of turn [5, 6]:
Ti|}(t) + ii)(t) = K6(t). (2.4)
Some authors extended these two miodels to obtain with full scale test results [6. 7, 8, 9]. They r i|i(t) by a nonlinear function H[i|i(t)], for which o polynomial is,used. Wellknown models in this resp of Bech [7] :
T T2'ii.'(t) + (T^+T2)i(}(t)+H[iI»(t)]=K[T^é(t) + 6(t
and of Nomoto - Norrbin [6, 8]:
T if(t) + il»(t) + a
a better agreemient eplaced the term ften a cubic ect are the model
)] (2.5)
[Ht)]^ = K6(t). No simple mathem.atical model describing the manoe in waves has been found. Mostly a sum of sine v;a noise, is added to the output of the model descri of the ship in calm, water, in such a way that the output of the model obtained m.eets the actual spe motions of a ship in waves (Fig. 2.1).
(2.6)
uvring of ships ves or a coloured bing the behaviour spectrum of the
ctrum. of the
ö(t) model of
shipdynamics
in calm water
V^l»)
ship motions due to waves
• u* mt)
FIGURE 2.1:
Model describing the behaviour of a ship in waves.
-21-
2 . 3 The m.odel selected
On the basis of the requirements Fiven in Ch. selected. Nomoto's first-order m.odel (2.4) ha and is one of the sim.plest models developed t m.anoeuvring properties. The stationary charac between the rudder angle and the rate of turn is linear. However, from full scale experimen this stationary characteristic often is nonli shape of this curve might influence strongly our, also ships with different characteristic This mioans that a nonlinear m.odel had to be u of Bech or Norrbin [7, 8]. As Norrbin's model cribes the behaviour of ships viith characteri Pig. 2.2 rather well, this model had to be ch
2.1 a model has been 5 only two param.eters o describe ship teristic - the relation in the steady state -
ts it is known that near [10] . As the the helmsman's behavi-s had to be simulated. sed, e.g. the models is simpler and des-
stics as shown in osen.
FIGURE 2.2:
Stationary characteristics of a directionally stable and an directionally unstable ship.
However, twin screw ships with one rudder situated at the ship's centerline can show a stationary characteristic different from Fig. 2.2, but one like Fig. 2.3.
Ö [deg]
FIGURE 2.3:
Stationary characteristic of a twin screw ship with one rudder situated at the shiv's center-line.
-22-
To be able to simulate also this type of ships the Norrbin model was extended with a second nonlinear term:
Tgi(;(t)+a^iJ^(t)+a2['l'(t)]^+a^[iKt)]^^^ = K^6 (2.8)
Model (2.8) was finally used during the simulator experiments. It has been chosen mainly because of its simplicity, although also the three remaining requirements were fulfilled. In paragraph 2.4 a review is given of ship data in terms of this model as found in literature. It was hoped that those data were sufficient to choose the model parameters in such a v;ay that realistic sim.ulations could be obtained.
To control the rudder position often a hydraulic servo-system is used. Som.e models describing such a system are given by Bech and Brummer et. al. [lO, ll] . Though the actual dynamics are much more complicated, the dynam.ic behaviour can be approxim.ated in a reasonable way by m.eans of a first-order differential equation. Because of the lim.ited capacity of the oil pumps, the angular velocity of the rudder is lim.ited. The following model is thus obtained:
Tj 6(t) + 6(t) = <S (t) ; (2.9-a)
|5(t)| < 6 , (2.9-b) •
v;here T5 is a time constant and 6^ is the maximum rudder angular velocity. In Fig. 2.4 the block diagram of the steering gear, applied during the experiments, is given.
öd(t)
FIGURE 2.4: Block diagram of the steering gear.
2.4 Parameter values
As mentioned before, the dynamics of the ships to be simulated should be as realistic as possible. In order to obtain data to imiprove such a sim.ulation, the literature on ship steering vms therefore reviewed. A technique used by many authors to model ship dynamics is based on special tests or zig-zag tests. These data, however, had to be transformed in terms of the nonlinear model. The results of the spiral tests were used to estim.ate the model parameters a^, 32, S-j, and Kg by means of a least sauared error method. The results of the zig-zag tests were used to estimate the param.eter T3. As only a rough estimation was needed, some approximations were introduced in estimating Tg (Fig. 2 . 5 ) : e The rudder engine dynamics were neglected. o The heading ^(t) was considered to be a sinusoidal signal. • The nonlinear elements were approxim.ated by their describing
functions.
I — » J 5(t)dt ö(t)
-23-
•%n «0
^ 0
1 1
öitJ
1
Ks 4
1
1
i *
tnoaei
shipdynamics
L
1
f J
V'\ 1
s
^^ "
1 V^f ' l
. J
FIGURE 2.5:
Block diagram of the model during a zig-zag test.
In this way the following formula could be obtained:
T 6 / ilJ, - 6 ^ T.^ s o ^1 o 1
7 TT^ ii^ (2.10)
where 6 = actual rudder amplitude; i)^ - am.plitude of the heading; T. = period of one oscillation.
The results of the parameter estimations are given in Table 2.1. VJith respect to this- table the following remarks can be made: 9 A relatively small amount of full scale tests has been performed
The larper part is related to larp-e ships. © Not any ship with stationary characteristic like Fig. 2.2 has
been found, except the railroad ferrv when sailing backwards [11].
o In accordance to Norrbin [8] and Bech [?] the coefficient a was kept equal to 1 or -1 depending on the fact that the ship was stable or unstable. Some m.arginally stable ships v/ere found where B.^ is equal to zero. In these cases the parameter values were__norm.alized v/ith respect to Kg which was kept eoual to -.05
sec -1 A large number of ships were examined by Nom.oto [25] . Based on zig-zag tests v.'ith about seventy ships, the parameters of Nomoto's first-order m.odel v/ere calculated. As this model approximates the stationary characteristic by a straight line, Nomoto's data do not provide inform.ation about the actual shape of the stationary characteristics of the ships. The literature reviewed does not provide enough information to choose the model param.eters of a range of ships to be sim.ulated.
-24-
TABLE 2.1: Summary of the manoeuvring properties of different ships, found in literature.
Kind of ship
Railroadferry
Passenger and Cargo Liner
Cargo Liner
Container ship
Tanker
Loaded
Ballasted
Tanker
Loaded
Undeep water
Ballasted
Undeep water
Bulkcarrier
Bulkcarrier
Tanker
Tanker
Unknown
Unknown
Cruise ship
Pilot boat
Trainingship
Deadweight
tons
42 900
200 000
193 000
69 250
3 200
80 000
50 000
SHIP
Length
m
139.6
134.0
135.6
273.0
310.0
304.9
242.8
62.8
221.0
313
307
106
59
41
DATA
Breadth
m
17.4
20.0
18.9
32.2
46.9
47.2
32.2
15.3
29.6
48.2
48.2
10.6
7.5
Draught
m
5.9
5.4
7.8
8.1
18.9
dj- 7.3
djj-11.0
18.1
dj- 7.8
d^-10.8
12.8
4.9
12.5
19.4
19.4
3.7
2.2
Displ.
m'
9 100
7 300
13 170
238 000
106 000
215 000
3 800
65 089
250 251
250 750
382
Speed
Knots
19.8
23
16.5
20
15
15.5
10.5
13.8
14
12
10
8
12
8.
PARAMETERS MODEL
^s
sec
51
28
25
33
264
46
135
89
—
234
--
207
76
208
185
28
20
18
25
•'s
sec-1
-.22
-.10
-.05
-.04
-.05
-.04
-.05
-.05
-.04
-.04
-.05
-.09
-,14
-.06
-.07
-.05
-.05
-.05
-.12
-.92
-.63
-.26
-.25
-.10
»1
-0.156
-1.
.125
-1.
-1 .
-0.046
-0.042
-0.23
"2
« ! • ) '
.72
.49
.47
4.12
16.5
24.3
3.6
4.9
20.0
20.0
26
39.
6.
63.
3.8
5.3
7.4
10.
,22
1.07
1.59
2.10
.13
.04
"3
c-i»)*"' .0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
1
REF.
11
12
13
14
15
15
9
15
9
16
17
18
19
20
21
21
22
23
24
2 .5 Ship m.otions due to waves
To study the control behaviour of a helmsm.an steering a ship in a sea-way, the behaviour of ships in waves had to be known. As this study was mainly based on fixed base sim.ulator experiments (Ch. 3 and 4), only the yawing motions had to be considered. To introduce the disturbances in the sim.ulations, a signal simulating these yawing motions had to be available.
In calculating the ship motions in irregular sea, often a linear model based on the potential theory is applied [26, 27]. The results hereof show a fair agreem.ent between predictions and measure-m.ents [28]. The random, sea surface, denoted by (XQ, VQ, t), is assumed to be composed of an infinite number of sinusoidal components with different am.plitudes, frequencies and phases. Formulas describing the spectral density of the sea waves as function of the circular frequency '^ are given by Neumann [29], and by Pierson and Moskowitz [30] . The dynam.ic of a ship can be described just as the sea surface, by statistical methods. V.'hen the spectral density of the sea surface is denoted by S?c('^p), and the ship's responses are given by the transfer function H,jj ( Wg)j the spectrum of the
can be calculated bv: ship's yawing m.otions S . C^p)
s (%) = iH^^(^e) ; (" ). ^C^ e^
(2.11)
It should be noted that the spectrum and the transfer function depend on the frequency of encounter ^ . The wave spectrum based on the wave frequency ^ has to be transform.ed to a v;ave spectrum based on the frequency of encounter Wg. The relation betvjeen oj and ü3g follovjs from, classical wave theory and is given by:
U) cj^V |(o -ülJi cos y| g
(2.12)
where V = ship speed; g = acceleration of gravity; y = angle between the ship's velocity vector V and the wave
velocity c (Fig. 2.6).
V ^ \ \
\
\ \ \ \ \ \ \ \ \ \
FIGURE 2.6:
A ship sailing in a regular sea; V - ship speed; c_ = wave velocity; y - direction of wave propagation,
-26-
The spectral density of the waves as function of wg can be computed from the spectral density based on u by means of the following formula:
==U<"e) - Sec'"' % • (2-">
where du/dcog can be computed using Eq. (2.12). However, the frequency ID is not a uniquely function of I>)Q. TO transform the wave spectrum S (OJ) into S ((Dg) the spectrum S (a)) should be divided into parts^for which the relation between u and Wg is unique. Each of these parts result in a part of the spectrum S55((jL)g), which m.ay coincide with the other parts. The spectral density S^^(ue) is obtained by adding for each Wg the densities resulting from, the transformation of each part.
The ship's responses to the wave exerted m.oments are given by the following differential equation:
where I = ship's moment of inertia; Nr = damping coefficient; NÏ = added mass; N^ = hydrodynamic mom.ent.
The transfer function can be written as:
H, (joj ) = -, rrf w \ • rr—r • (2.15)
The hydrodynamical coefficients N.. and N^ can be estimated using the so called strip theory [27, 31, 32]. Starting points are the known two-dimensional solutions for the cross-sections, which can be computed by means of conform.al mapping. By integrating the cross-sectional values the result for the three dimensional ship is found [28] .
The right hand side of Eq. 2.l4, the wave exerted mom.ent, can be approximated by the assumption that the presence of the ship does not influence the pressure in a wave. This pressure, known from wave theory, can be integrated over the ship's hull, where a correction is needed to take into account the relative motion of the ship. In this way the moment exerted by one wave component can be calculated. As a liner theory is used a linear transfer function Hj r(jü)g) can be defined, describing the moments acting on the ship in regular as well as irregular waves. The spectral density of the ship's yawing motions then can be estimated by the formula:
^^^'^e^ -- l%^>e) • "nS^J'^e^l^ h^^'^e?' ^^.16)
To perform the computations described above the Delft Shipbuilding Laboratory has completed a number of com.puter program.s. Using these programs the motions of a ship in regular waves, i.e. the transfer functions Hjor(ü3g), can be computed, and using the wave spectra as given by Pierson and Moskowitz [30] Sr^(we) can.be calculated as described above.
-27-
The calculation of the ship m.otions in waves is based on frequency domain methods. However, as stated before a signal to be added to the output of the model describing the ship's responses to rudder actions, v;as required. An approxim.ation of such a signal can be obtained by a sum of a large, but finite number of sine v.'aves, with properly chosen amplitude, phase and freauency. Therefore, the calculated spectrum S..(tüg) is divided in small bands with ; bandwidth Aw (Fig. 2.7).
a
>^^(We'
FIGURE 2.7: Approximation of the continuous spectrum by a discrete spectrum.
The sine waves are chosen in such a way that the frequencies eauals the central frequencies of each of the bands. The amplitude of each component is selected in such a way that the power of a particular component equals the power within the corresponding band. Finally the phases are chosen randomly.
REFERENCES
1. Davidson, K.S.M.; Schiff, L.I., Turning and course keeping qualities. Trans, of the S,N,A,M.E. Vol. S't (.19'iè), pp. 152-200.
2. Abkowitz, M.A., Lectures on hydrodynamics. Report: Lyngby (Denmark), Hydro og Aerodynamisk Laboratorium, 1964, 113 p., Hy-5.
3. Eda, H.; Crane, C.L., Steering characteristics of ships in calm water and waves. Trans, of the S.N.A.M.E., Vol. 73 (1965), pp. 135-177.
4. Norrbin, N.H., Theory and observations on the use of a m.athematical model for ship m.anoeuvrinp in deep and confined waters. Public. Gothenburg, SSPA, 1971, 117 p.. No, 68,
5. Nomoto, K,; Taguchi, T.; Honda, K.; Hirano, S,, On the steering Qualities of ships, I,S,P, Vol, 4 (1957) No, 35, pp. 354-370.
6. Nomoto, K., Problems and requirements of directional stability and control of surface ships. Proc. Int. Sym.p. on Directional Stability and Control of Bodies Moving in Water, Journ. N'ech. Engineering Science, Vol. l4 (1972) No. 7, pp. 1-5.
7. Bech, M.I.; Wagner Smitt, L., Analogue simulation of ship manoeuvres based on full scale trials or free-sailing model tests. Report: Lyngby (Denmark), Hydro og Aerodynamisk Laboratorium, 1969, 24 p. No. Hy-14.
-28-
8. Norrbin. N.H., On the design and analysis of the zig-zag test on base of quasi-linear freauency response. Proc. Tenth Int. Towing Tank Conf. 1963, pp. 355-374,
9. Glansdorp, C.C, Simulation of full scale results of manoeuvrinr trials with a 200,000 tons tanker with a simple mathematical model. Report: Delft, Shipbuilding Laboratory,' 1971, 24 v., No. 301,
10. Bech, M.I., Some guidelines to the optimum adjustment of autopilots in ships. Proc. Symp. fodelvorm.ing voor scheepsbesturing. Delft 1970, 32 p.
11. Brix, J.; Fritsch, M., Eisenbahnf"ahrschiff "Deutschland". Modellversuche und Bordmessungen. 372. Mitteilung der Ham.burgischen Schiffbau Versuchanstalt. Schiff und Hafen, Jahrg. 24 (1972) Heft 11, pp. 791-795.
12. Enkvist, E.; Saarikangar, K., "Finlandia" Finish-built Passenger and Car Liner Some Design Considerations. Shipping V.'orld and Shipbuilder Vol. 160 (1967) No. 3811 (Sept.) pp. 1500-1513.
13. Lindgren, H.; Norrbin, N.H., Model tests and ship correlation for a cargo-liner. Trans, of the Royal Inst, of Naval Architects. Vol. 104 (1962), pp. I4l-l8l.
14. Containerschiff "Bremen Express". HANSA Jrg. 109 (1972) STG-Sondernumm.er II (Nov.) pp. 2043-2076.
15. Glansdorp, C.C; Buitenhek, V., Manoeuvring trials with a 200,000 tons tanker. Report: Delft, Shipbuilding Laboratory, 1969, 31 p.. No. 248.
16. Clarke, D.; Patterson, D.R.; Wooderson, R.K., Manoeuvring trials with the 193,000 tonne deadweight tanker "Esso Bernicia". Paper presented at Spring meeting 1972 of the Royal Inst, of Naval Architects, No. 10, 14 p.
17. Chirila, J.V., Sea trials of the "Sighansa". Part I. Pronulsion and Manoeuvring tests. Shipping World and Shipbuilder. Vol. 156 (1965) No. 3773 (Dec.) pp. 533-541.
18. "Mini Luck" Japanese-built mini bulk carrier. Shipping World and Shipbuilder. Vol. 162 (1969) No. 3834 (June) pp. 817-Ö21.
19. Lehmkuhl, J.; Chirilia, J.V.; Gerbitz, U.; "arx, K.H., Turbinentankschiff "Altanin". Schiff und Hafen, Jrg. 16 (1964) Heft 11 (Nov.) pp. 1033-1061.
20. Clarke, D., Manoeuvring trials with the 50,000 tons deadweirht tanker "British Bom.bardier". Report:. BSRA, 1966, No. NS-142,
21. Fujino, M.; Motora, S., On the modified zig-zag manoeuvre and its anplication. In: Selected papers SNA Japan, Vol. 9 (1972) pp. 133-148.
22. Hebecker, 0., Das Manover "Mann über Bord". Schiff und Hafen, Jrg. 15 (1963) Heft 10, pp. 963-966.
23. V.'inkelman, J.E.V.'.; Am.erongen, J. van, Verslag van de metingen verricht aan boord van de loodsboot "Capella" van 040472 tot 180472. Report: Delft, Laboratorium voor Regeltechniek, nn. 1-10.
24. Verstoep, N.D.L., Verslag van de metingen verricht aan boord van de "Zeefakkel" van 221073 tot 241073. Report: Delft, Laboratorium, voor Pegeltechniek, pp. 1-8.
25. Nomoto, K., Analysis of Kempf's standard manoeuvre test and nronosed steering quality indices. Proc. First Symp. on Ship Manoeuverabilitv. Report: David Taylor Model Basin, I960, No. l46l, pp, 275-304,
26. St. Denis, M.; Pierson, K.J., On the motions of ships in confused seas. Trans, of the S.N.A.M.E., Vol. 6I (1953) pp. 280-357.
27. Gerritsma, J., Behaviour of a-ship in a sea-way. Report: Delft, Netherlands Ship Research Centre TNO, 1966 , No. 84s, 20 p.
28. Gerritsm.a, J.; Beukelman, W., Com.parison of calculated and measured heaving and pitching motions of a series 60, CK= 70 ship m.odel in regular longitudinal waves. Report: Delft, Shipbuilding Laboratory, 1966, l6 p. No. 139.
29. Neumann, G., On "Ocean wave spectra and a new method of forecasting wind-generator sea". Technical Memoranium: Beach Erosion Board, No. 43,
30. Pierson, V.'.J.; Moskowitz, L., Proposed spectral form for fully developed wind seas. Report: New York University, Geophysical Sciences Lab, 1963, No, 63-12.
31. Vugts, J.H., The hydrodynamic coefficients for swaying, heaving and rolling cylinders in a free surface. Report: Delft, Shipbuilding Laboratory, 1968, No. 194, 115 p.
32. Vugts, J.H., The hydrodynamic forces and ship motions in waves. Diss.: Delft, 1970.
30-
CHAPTER III: SHIP MANOEUVRING IN CALM V.'ATER
3.1 Introduction
To gather information about the helmsm.an's control behaviour in relation to the ship dynam.ics, a series of experiments were performed, To structure the information obtained in this way a model of human behaviour has been developed. On the basis of some preliminary experiments linear as well as nonlinear models were formulated; the usefulness of the different models, being an im.portant part of this study, was analyzed.
The test conditions were chosen in such a way that a simple, well defined experiment could be executed, so that the results obtained could be analyzed and interpreted in an understandable v/ay. It was assumed that: • Only the heading of the ship had to be controlled by the helms
man, the position of the ship had not been taken into account. • The helmsman steered the ship by means of the steering wheel
only. The engine telegraph was not used. o The ship dynamics were constant. o The disturbances v/ere as sm.all as possible; that is, the influ
ences of waves, current, wind, etc., and also the presence of other people on the bridge, partly engaginr the helmsm.an's attention could be neglected.
To achieve these goals the simulation on a manoeuvring simulator was preferred to the execution of full scale tests, because then the test conditions can be controlled as desired. Moreover, full scale tests are very expensive. However, it should be noted that a validation of the simulator test results by means of full scale tests will be necessary (see Ch. 5).
3.2 Experimental set up
3.2.1 The manoeuvring simulator
The simulator of the Institute TNO for Mechanical Constructions at Delft was used to perform the tests. This simulator has been described extensively by Brummer and Van V/ijk [l] . Therefore, only a brief description will be given. Fig. 3.1 shows a block diagram, of
desiied state
projecrion
environmemoili ' 2 " " " ^
display
I I I »
rp indicating
instruments!
instiuciions
I ^ helmsman I — ^ nF5^^
controls ship's
dynamics
[ wheel house analogue
I j computer
FIGURE 3.1: Block diagram of the TNO simulator.
-31-
the sim.ulator. The m.ain p a r t s a re the v.'heelhouse, the p ro j ec t i on system and the analojrue computer. F ig . 3.2 shows a photorraph of the sim.ulator during a s imulated harbour approach.
FIGURE 3.2: The ship research and manoeuvring simulator of the Institute TNO for Mechanical Constructions at Delft.
On the computer the dynamics of the ship to be simulated have been program.med. The com.puter generates the sirnals to control the environmiental display system and the indicating instruments, " he sim.ulator is a fixed base simulator, hence the helmsman obtains only inform.ation from, the environmental display and the indicati'nr-instrum.ents .
3.2.2 Ship dynam.ics
The tests should provide information about the importance o^ different mianoeuvring properties, such as sluggishness and course instability, in relation to manual steerin,--. As the results of the literature study shov.-ed a rap v/ith respect to certain types cf ships, the param.eters of the model chosen to simulate the ships, could not be selected on the base of Table 2.1. Therefore an other and systemiatic approach had to be follov.'ed.
Using the extended version of Norrbin's m.odel (En. 2.8):
T^lO(t)+a^ii-(t)+a2['Ht)]^ + a^[Mt)]^''^ = K^6(t), ( 2 . R )
-32-
tv/o im.portant aspects can be distinguished, viz. the shape of the stationary characteristic, in particular the slope of this curve at zero rudder angle, and the sluggishness. These nuantities vrere varied system.atically: Three values of T^ v.'ere chosen, viz. 10, 50 and 250 seconds, corresponding with small, normal and large ships respectively. For each of these values the shane of the stationary characteristic was varied: Stable v.'ith a more or less linear characteristic, unstable, and stable with the characteristic simulating a dead zone. The m.odel parameters used are given in Table 3.1
TABLE 3.1: The selected parameters of the model used to simulate the ships
Ship
Nr.
1 2 3
4 5
6
I 9" 10
11 12 13
14 15
Characteristic (see Fig. 3.3)
I
II
III
IV
V
VI
Parameters model
Ts
Sec
10 50 250
10 50
10 50 250
10 50
10 50 250
10 50
K s
Sec-^
-.05 -.05 -.05
-.05 -.05
-.05 -.05 -.05
-.025 -.025
-.1 -.1 -.1
-.05 -.05
H
1 1 1
0 0
-1
_^
-1
-1
^2
/sec>2 Meg'
5 5 5
5 5
5 5 5
5 5
5 5 5
5 5
^3
(deg)2/3 sec'
0 0 0
0 0
0 0 0
0 0
1 1 1
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
-24 -16 -8 / char.H
8 16 24 -.4^-^-^Ö[deg]
6 peg/sec]
..2 8 16 24 ^ Ö[deg]
-.6
-2 8 16 24 Öfleg]
-24 -16 -Sr" char.nZ
.6 [deg/sec]
char.31
6 [deg/sec]
FIGURE 3.3:
The six stationary characteristics used in the ship simulations.
In these first series of experiments rate of turn indicator v;ere used, as the influence of additional displays cators of the simulator, such as v.'at which were not im.portant with respec the helmsman, were out of use. The o by means of a digital counter; when auditory signal was given.
The helmsman controlled the ship's h wheel, which could easy be turned wi physical effort.
, no additional displays like a it vras the intention to study lateron. The remaining indi-
er depth indicator and speedlog, t to the task to be executed by rdered heading was displayed a new heading was ordered, an
eading by m.eans o,f a steering th only a small am.ount of
3.2.4 The ordered headings: The test signal
The helmismen were instructed to headings. The sequence of these or test signal, was a periodic one period, v;ith a random.ly cho a test depended on the tim.e con time constant T_ 10 sec, 20 m Tg = 250 sec, since in steering helm.sm.an needs m.ore time to exe a small and fastly responding s signal for a test with a large
steer the sh headings, de signal. Each sen starting stant Tg of t in for Tg = 5 a slowly res
cute a manoeu hip. A tim.e h ship is shown
ip along prescribed noted by input signal test consisted of just point. The duration of he ship: 10 min for a 0 sec and 40 miin for ponding ship the vre than in steering istory of the test 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
Charact.
I
II
III
IV
V
VI
data
Tg(sec)
10 - 50 -
10 - 50
10 - 50 -
10 - 50
10 - 50 -
10 - 50
250
250
250
S/L
S/L
S/L
S/L
S/L
S/L
Subjects
Al A2 El B2
El B2
Al A2
Al A2
Bl B2
Bl B2
3.2.7 Data collection
o 0 o o o
;he following signals were recorded on miagnetic tape: The desired headin,-- ijj.,(t); The heading ,!;(t) ; ^ The rate of turn i|;(t); The steering wheel position 6^(t) 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 durinr-the tests.
P«g] \
Öj{t)40.
[deg]20
FIGURE 3.5:
Time histories of the signals T^ ,(t), \lj(t), and^n(t). Subject A2, TS S, T = 250 sec. Char. Ill (unstable char.).
-36-
ÓdCUO feg]20
O
FIGURE 3.6:
Time histories of the signals ii^(t), ip (t), and 6j(t). Subject Al, TS S, T = 250 sec. Char. Ill (unstable 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 p-eneral 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 phase-plane: the rate of turn of the ship lii(t) plotted against the heading error ^e{t) - ^{t) - ^(^{t) . An example of such a phase-plane plot is shown in Fig. 3.7.
FIGURE 3.7:
Phase-plane trajectories recorded during a test with a large unstable ship.
-37-
As the ship the rate of zero. During the like a rect during the In some cas a short per generated b stop the m.o
In Fig. 3.8 a
was unstable in this case, during the second phase turn increased with the rudder angle 6(t) equal to
first phase the output of a helmsman is often shaped angular pulse v;ith only a few rudder calls, v/hereas third phase the num.ber of rudder calls is much larger. es when there will be an overshoot, som.etim.es during iod of tim.e a peak in the steering v/heel position is y the helm.sman. It looks as if the man prefers it to tion by large rudder am.plitudes to avoid overshoots.
set of estimated squared spectral density functions
SV'dV^d'^'
[LOG]-»-^
-2.1
-4,
[LOG] -'
-I
-3.
-4.
-5.
.01 V[HZ] .01 V[HZ]'
^2 '.OOj
RtlV^e'»"
0.50
aoo .001 .01 V[HZ] V[HZ]
FIGURE 3.8. Estimated squared spectral density functions and squared coherency spectra of a test with a stable ship; T - 50 sec; Char. I; Subject A^, TS L.
and estimated squared coherency spectra of a test with a stable ship (Char. I, Tg = 50 sec) are shown. From the estimated coherency ri|j 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 S<|;dijjd(v) and Sij e'Pe ) show only very slight differences from these frequencies. The estim.ated coherency spectra ri(jd6d(v) show that the coherency between the signals '{' (t) and ó jTt) is small (Figs. 3.8 and 3.9).
fv^död I V ) ,
0.5
.001 .01 l/[HZj
FIGURE 3.9:
Estimated squared coherency spectrum f\^^j^(v) of a test with a large ship; T = 250 sec; Char. I; Subject Al; TS S. s
It should be noted that the region of interest is only the low frequency range. However, only a few data points are estimated in this range, since the number of data points is determ.ined by the duration of a test, the observation time [4]. This means that the test durations were too short to obtain reliable estim.ates of the spectra and also of the helm.sman's describing functions at lov.' frequencies (see Ch. 1).
In view of the experience in the field of linear m.odels available within the Man-Machine Systems Croup [5, 6], as well as the large amount of literature,indicating the practical use of linear models, these models m.ay be useful in analyzing the helmsm.an's control behaviour. However the following reasons can be mentioned to elucidate that the helmsman's behaviour in the control of large ships should be described by nonlinear models: • in an earlier study Stuurman [7] concluded that in the case of
large ships a more or less bang-bang like control strategy was applied by the subjects, and that therefore a nonlinear model would probably fit the data better. ^2
e The estimated squared coherency spectra V IJJ(36(J(V) (Fig. 3.9) show a very sm.all coherency between the signals i|;d(t) and 6cl(t), indicating that a nonlinear model might yield better results.
It was decided to analyze the records by means of linear models, as well as by means of a nonlinear model. It was hoped that, depending on the test conditions,such as the ship's time constant, for each of the models a area could be defined for which a certain model is superior with respect to certain criteria.
To construct a nonlinear model the internal model concept was used (Ch. 1). The well-trained helmsman uses only a small number of rudder calls to execute an order to change the ship's heading. Using his experience with regard to the ship behaviour, the internal model, he chooses a rudder angle which corresponds vrith his expectation of the ship response.
-39-
When the actual ship dynamics differ from, the helmsm.an's internal model, after a while he v.dll detect a difference betv/een predicted and actual ship state, and com.e to a new decision. Tn this way the discrete character of the helmsman's output may be explained. The helmsman's control stratery looks very m.uch like banm-banp-control, as indicated by Stuurman [7], but one important dif.ference exists (Fig. 3.10). During all the tests no subject ever used the
time
>m
5j(.l
I 1
-6ml J
time
FIGURE 3.10:
Schematic representation of the execution of an order. a: helmsman, b: bana-bana 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 bang-bang 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 answers on the question whether the ship just steered was stable or unstable.
Ship data
Characti
I
II
III
IV
V
VI
T^ (sec)
10
50
250
10
50
10
50
250
10
50
10
50
250
10
50
Subjects
Group A
6.7
7.2
8.3
21.6
43.2
71.5
6.7
71.5
Groun E
31.2
18.8
14.4
62.3
62.3
-
6.2
6.2
8.3
13.3 0.0
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)
Hj U (j.) = 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. 5
(3.3)
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 starting-points: • An internal model of the ship dynamics was used to make predic
tions 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) r ^ t i m n inr 1
V^(t:t.t+n
^ ( t : i , i + r )
V/j(ti -
\
'^(t),^{t)
f
internal
model
decii maki elerr
sion ng lent
ö>)
6j(tl
FIGURE 3.11:
Block diagram of the nonlinear 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 bang-bang 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) Vd^^) (3.5)
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 and that of the nonlinear model does not necessarily exist.
To make predictions with the internal model t are needed: the ship's heading and the rate o tion is provided by the estimator. In general by means of the compass is corrupted with noi quantities needed have to be estimated (Ch. 4 simulator tests described in this chapter no troduced and the disturbances resulting from computer noise, were small. In this case the estimator can be very simple (Fig. 3.12). To turn only a differentiator had to be applied.
wo initial conditions f turn. This informa-the heading presented se and thus the ). However, durinp" the disturbances were in-the simulator, e.g. structure of the obtain the rate of
-43-
v (t) r 1 V^ci T
1
1
_d_ dt
1 estimator
1
1 V'C)
1
_J
FIGURE 3. 12:
Structure of the estimator in the situation where no disturbances have been introduced.
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 element. 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 phase-plane 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 phase-plane have been approximated by straight lines (see Fig. 3.13), given by the Eos.:
4'e(t) + C.
+ C,
il'(t)
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^dl^CjV^dlsO
V^^lD+C^V^ItJrO
FIGURE 3.13: The four phases of control in the vhase-plane.
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 t|3(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.:
P h a s e I : | i t )g ( t+ t )+C^i i ) ( t+t ) | < d ( t ) ;
Phase I I I : \A)At^t ) |+C |tp(t+t T |£ d ( t ) , e p 1 p —
( 3 . 1 0 )
( 3 . 1 1 )
- 4 5 -
( start 3
read heading and rate
< (phasel?>
yes
/'correctionN \ needed? /
yes
calculate
5d ' 'p
( -Id )
no 1 1
/ohnse lir'>\ lyes
^ < /correctionN \ n e e d e d ? /
yes
calculote
no
"n
öd=o
FIGURE 3.14:
Flow chart of the decision making element.
where ii'e(t+tp) and i|;(t+tp) are predicted using the internal model; and where d(t) is a threshold value. As the number of rudder calls during the third phase is generally larger than during the first phase the threshold value depends possibly on the heading error 4'e(t) (Ch. 3.3.1). This dependence has been put in the following simple mathematical form:
d(t) = p(l + q \^At) I ) (3.12)
where p and q are model parameters. As will be shov/n in Ch. 4 a relation between the param.eter p and the accuracy of the displayed information exists.
It should be mentioned that during the first phase many different rudder angles may result in the selected goal depending on the time tp(t). Therefore, in addition to the objective Eq. (3.6) a second equation is needed. From the recordings it can be concluded that the subjects never applied the m.axim.um rudder angle during the first phase. On the other hand to execute the manoeuvre v/ithin a reasonable time the rudder angle to be used, cannot be too sm.all. Probably the selection of the rudder angle is based on an optimum between the ship's speed loss, related to the applied rudder angle, and the time needed to execute the m.anoeuvre. A relatively sim.ple model structure can be obtained by putting the above in the following mathem.atical form: That combination of steering wheel position ^^(t) and duration tp(t) is chosen which minimizes the following criterion:
-46-
t p ( t ) + w I 6,(t) (3.13)
with the weighting factor V/ as an additional model parameter. En. (3.13) implies that the rudder angle is weighted inversely to the time tp(t). When the rudder angle, determined by minimizing J, is larger than the maximum rudder angle this maximum, angle is chosen.
3.4 Parameter estimation
The parameters of the two linear models (Eqs. 3.2 and 3.4) as well as those of the nonlinear model were estimated as shov/n in Fig. 3.15. The upper loop represents the experimental loop with the manoeuvring simulator, the lower loop is a sim.ulation of ghip and helm.sman on a hybrid computer. The output of the model 6 (t) was subtracted from the helmsman's output ^^(t) in order to calculate the following criterion:
E J |6.(t) - 6 *(t)|dt
J' |<S (t)| dt 100^, (3.14)
This criterion was preferred to a quadratic criterion
t,^ ip—
J [«H(t)]'dt (3.15)
model of the
helmsmen
computer simulation
öj'
Lt-
model of
the ship
y/'u),
FIGURE 3.15:
Estimation of the parameters of the helmsman's model.
-47
as the integrations were executed by means of analogue components. The calculation of the absolute value of the difference betv/een the actual steering wheel position and the model output was expected to be m.ore accurate than the squared value, yielding more consistent results. However, in literature mostly a quadratic criterion is used, which enables often a direct computation of the unknown parameters [5, 6]. To be able to compare the results to be obtained by minim.izing Ei^j (Eq. 3.l4) with data given in literature, also £-2 has been calculated.
To minimize the criterion Eq. (3.13) with respect to the nonlinear m.odel parameters a random search m.ethod has been applied. This method has some advantages compared v/ith other methods such as gradient methods [l3, l4, 15]: • Random search m.ethods are easy to program. 0 They are less sensitive for com.puter noise. © They are effective to optimize irregular criterion functions
which have sharp ridges and discontinuous first derivatives. o To optimize a function of many variables, random search m.ethods
are very effective. As all the optimization programs which were available for the optimization of the nonlinear model, were based on random, search methods, also during the estim.ation of the linear model parameters this method has been applied.
Some rem.arks should be m.ade with respect to the parameter estimation method used (Fig. 3.15). This method has been suggested by Johannsen [l6] and leads to unbiased estimates for linear models [6], As discussed in Ch. 1.3 this method can be used also to optimize the nonlinear model, but then an analytical derivation of the estimators of the parameters is not possible.
Besides the quantity Eiri and Er2, also the followinr quantities have been computed: ' '
I'^l ^(t) - ;f.*(t)]Mt E,,,' = 2—^ . 100^ , (3.16)
o j ' \ ti;(t)]'dt
and l'^\i>(t) - ii *(t)|dt
E| 1= 2 _ ^ . 100^. (3.17)
The last two quantities indicate the correspondence between the time histories of the actual heading of the ship i( (t} steered by the helmsman and those generated by the ship model ^ (t) steered by the model of the helm.sman.
-48-
3.5 Results
As mentioned in paragraph 3.2 a number of experim.ents v/ith different ships were executed. The dynamics of the ship were changed according to Table 3.1 ; the steering gear dynamics were kept constant, since in general the m.inimally reouired rudder angular velocity is undependent of the seize of the ship. Only for the very small ships, with a tim.e constant Tg = 10 sec, the steering gear dynamics were lim.iting the control properties of the ships, in particular this was true for the unstable ones. The interpretation of the result of these small shins is therefore rather complicated; the emphasis in this chapter v.'ill be laid mainly on the handling qualities of large ships. In Ch. 5 full scale trials with a sm.all ship v/ill be discussed, but a comparison betv/een simulator experim.ents and the full scale trials is difficult to make as the simulator results mainly relate to large ships.
In Table 3.4 the results obtained with the two proposed linear m.odels (Eos. 3.2 and 3.4) are shown; the Table 3.4 provides information about the very large ships in terms of the parameter values determ.ined and the criterion values related to these param.eters. In the Figs. 3.l6 and 3.17 some typical time histories are shown of the heading iiit) and the steering v/heel position as well as the output of the linear miOdel with three param.eters (Ea. 3.3) 6 (t) and that of the ship model ^ (t).
During the analyses of the tests with the nonlinear model it has been found that som.e of the parameters, in particular the internal model param.eters Tj„ and Kjrj, were strongly coupled. In Fig. 3.18
a b c d Q
f
Char.
I I V V III I
^s
250 250 250 250 50 50
^s
-.05 -.05 -.10 -.10 -.05 -.05
TS
L S S L S L
Subj .
Al A2 Bl B2 Al B2
[sec-]
FIGURE 3.18: The relation between the model parameters T and K .
m m
the results of six tests, where Kj has been varied and the value of T estimated with all other model parameters constant are
TABLE 3.4: Results of the parameter ovtimization with the two linear models; large ships with T - 250 sec.
1 TEST CONDITIONS
1 Char
1 I
1 ^
1
TS
s
L
S
L
S
L
Subj .
Al Al Bl B2
Al Al A2 HI Bl
Al Al A2 A2
Al , A2 A2
Bl Bl B2 B2
Bl B2
TWO PARAMETERS. MODEL: Eq, 3.4
• h ^1
sec
4.8 32.8 1.2 98.5 3.8 31.6 3.7 41.9
5.0 29.5 S.4 28.5 3.8 31.5 3.7 26.5 2.3 43.1
4.5 33.1 5.5 28.1 3.2 45.0 1.6 142.8
4.9 33.7 1.0 104.6 1.0 132.7
2.2 24.2 3.0 30,8 3.4 29,5 3.3 29.2
1.7 37.1 2.5 37.2
^|«| ^«2 ^Uj ^t*
% \ % %
83 60 19 4 88 81 49 26 86 73 — — 85 68 18 5
65 42 — — 77 58 19 5 73 51 25 8 77 60 33 13 75 57 23 6
69 52 22 6 81 56 32 14 84 72 23 8 95 87 42 21
73 56 — — 85 77 36 15 93 82 — —
76 61 18 4 81 63 13 2 87 66 17 4 92 65 14 3
76 60 21 10 79 55 12 2
THREE PARAMETERS MODEL: Eq. 3.2 |
' h ^^ ^2
sec sec
5.5 46.2 8,1 2.8 89.4 21,6 6,5 73.2 16.1 4,5 64.3 9,1
4.3 48.3 11,3 8.2 46.7 13.4 5.1 49,6 11.8 4.1 46,9 11,2 3,1 69,4 19.1
5.1 43,2 6,2 5.9 37,6 7,8 3.2 67,8 18.8 2.6 136.9 23.8
4.6 53,9 11,9 1,9 94,9 21,5 2.1 106.8 31.2
3.0 34,3 9.2 3.3 33,7 6,1 5,6 30.2 10.0 4.4 30.2 5,5
2.5 44.7 14.0 3.0 38,4 7,2
'1*1 ^«* l l ^ V j I t t t
74 46 19 4 1 75 61 32 1 1 1 76 61 — — 78 59 20 6
49 22 — — 55 30 16 4 56 30 13 2 67 46 14 3 64 43 14 3 j
60 38 18 4 1 71 43 30 13 62 42 21 6 81 67 37 15
59 35 — — 74 57 15 3 75 50 — —
69 49 16 3 1 71 44 12 2 74 42 14 3 86 48 12 2
63 40 20 10 69 38 10 2
V ft» 10
Vd"» 5
i UI
FIGURE 3.16:
Typical time histories of the actual signals ^d^'^^i it)(tj and ^^[(t) compared with the linear model output 6^ (t) and the output of the ship model i|) (t): Subject Al; Char. I; T = 250 sec; Test sianal S s ' ^
V^(tl20T
V^d'"lO:
[deg] 0
V^jltjlO
[deg] -10
-201
Öj(t)50
600 ^
/{2'oqV 1/ Ï80Ö 2A00 . [sec]
FIGURE 3.17: Typical time histories of the actual signals ^(^(t), ii(t) and ^^(t) ^ompared with the linear model output 6^ (t) and the output of the ship model ii (t): Subject Al; Char. I; T = 250 sec; Test signal L. s
plotted, as well as the criterion value Ei^i. As can be seen in the region of interest where the model parameters Tjr, and K^ are near the ship param.eters Tg and Kg, the value of the criterion function El. I are found to be more or less constant. Furthermore, Fig. 3.l8 shows that a m.ore or less linear relation betv/een T^ and K^ exists. An explanation of this phenomenon may be the fact that only small rates of turn were generated by the helmsm.an. The internal m.odel (Eq. 3.5) now, consists of three terms, viz. the angular acceleration m.ultiplied by the tim.e constant T^, the rate of turn and the rudder angle multiplied by the gain factor K n, hence v/hen the rate of turn is always small in relation to the other two terms, this damping term can be neglected. Then the EG. 3.5 v/ill becom.e:
'^J'(t) = K <5 (t). (3.18)
This equation shows very clearly the coupling between the parameters Tjyj and Kjr. As these two parameters are linearly dependent Kj was not varied the parameter optimization, but kept equal to the coefficient K of the ship.
In Table 3.5 the parameter optimization results with the nonlinear model are given for tests v/ith large ships, Tg = 250 sec, while the Tables 3.6 and 3.7 summarize the results of tests with smaller ships, Tg = 50 and 10 sec. The tables give the parameter valueg as well as the criteria values indicating how v/ell the signals 6, (t) and ^ (t) correspond v/ith the recorded signals <5 (t) and ij;(t). Some optim.al values of Tjp given in Tables 3.6 ana 3.7 were found to be on the boundary of'the parameter space; the conseauence hereof will be elucidated in the next paragraph. In addition to the parameters and the criterion values also the subject's judgement with respect to the manoeuvring properties of the ship is given. These judgem.ents roughly indicate whether a ship should be regarded as difficult or as easy to steer.
In the Figs. 3.19 and 3.20 some typical tim.e histories of the heading ^(t) and the steering v/heel position 6(j(t) as v/ell as the output generated by the nonlinear helmsm.an's m.odel 6^ (t) and the output of the ship model i) (t) are shown. Finally in Fig. 3.21 a representative set of sensitivity functions is given; the figure indicates in what way the criterion values Eiri and E^2 depend on the parameters.
TABLE 3.7: Results of the parameter optimization for a small ship, T = 10 sec.
TEST CONDITIONS
Char.
I I
TS
S S
Subj .
Al A2
MODEL PARAMETERS
m "1^ 1 S S P Q. sec j | ^ sec sec sec deg deg
3.5* 1.66 11 5 5 .38 ,30 3.5* 4.85 5 9 5 .70 .21
CRITERIA
E|«|E«2 E|^| E^2
63 43 20 5 60 47 16 3
SUBJ.JUDGEMENT
easy very easy
52-
Table S.S: Results of the nonlinear model parameter optimisation for ships with T - 250 sec.
TEST CONDITIONS
Char.
I I I I
I I I I I
III III III III
III III III
V V V V
V V
TS
S S S S
L L L L L
S S S S
L L L
S S S S
L L
Subj .
Al A2 Bl B2
Al Al A2 HI Bl
Al Al A2 A2
Al A2 A2
Bl Bl B2 B2
Bl B2
MODEL PARAMETERS
m 3^^ S S S P Q sec J— see sec sec deg deg
167 0.60 39 13 5 .25 .45 168 2.39 19 16 2 ,74 .07 195 1,42 19 37 10 .72 ,27 211 0,96 50 22 2 ,27 .25
254 1.00 47 28 1 .34 .38 324 1.34 29 28 2 .59 .25 295 1.13 59 26 1 ,62 .08 256 1.11 40 37 2 .48 ,33 215 1.33 51 38 0 .44 .17
258 1.30 42 48 10 .17 .24 290 1.07 43 25 6 .16 .40 216 2,55 57 30 4 ,30 .11 215 3.15 41 24 2 .24 .28
304 1.16 55 36 3 .57 .24 237 3.36 56 30 4 .48 .39 208 3.23 53 36 3 .36 .16
233 1.46 25 15 10 .19 .41 257 1.32 22 21 1 .51 .27 302 1.05 27 16 0 .51 .25 259 0.83 23 15 1 .74 ,34
173 1.20 26 31 10 .56 .31 277 1.00 30 29 5 .91 .36
CRITERIA
E|«| E«2 E,^, E^2
% % % %
70 45 15 3 69 48 14 3 74 55 — — 71 48 12 3
38 20 -- — 54 33 15 3 59 31 8 1 69 45 12 0 62 42 11 0
62 39 18 5 70 42 32 14 67 44 21 6 76 55 20 5
61 40 — — 64 44 12 0 73 50 — —
67 46 13 2 61 38 11 2 57 36 13 2 69 45 12 3
60 36 21 10 61 36 10 2
SUBJ.JUDGEMENT
very easy very easy difficult difficult
very easy very easy easy difficult not too difficult
very easy very easy very easy easy
very easy easy not too difficult
not too difficult not too difficult not too difficult not too difficult
not too difficult easy
TABLE 3.6: Results of the nonlinear model parameter optimization for ships with T = 5 0 sec. •' ' s
TEST
Char.
i i 1 ^ 1 1
y
II
In III T T T
IV IV IV
IV IV IV IV
V V V
V V V V • VI VI VI VI
VI VI VI VI
CONDITIONS
TS
S S S
s L L L L
S S S S
L L L L
S S S S
L L L L
S S S S S
L L L L
S S S
L L L L
"s" S S
L L L L
S S
s s L L L L
Subj .
Al Al A2 A2
Al Al A2 A2
Bl Bl B2 B2
Bl Bl B2 B2
Bl Bl B2 B2
Bl Bl B2 B2
Al Al A2 A2 A2
Al Al A2 A2
Al Al A2
Al Al A2 A2
Bl Bl B2
Bl Bl 32 B2
Bl Bl B2 B2
Bl Bl B2 B2
m sec
50.6 61.3 25.0* 25.0*
55.3 63.7 25.0* 28.1
60.1 80.1 39.7 89.6
25.0* 39.6 41.8 49.0
73,7 77.8 44.4 74.3
66.3 52.7 53.7 85.5
82.7 40.4 84.7 79.0 78.7
58.7 70.4 73.9
100.0*
82.8 63.3 100.0*
61.1 84.3 93.1
100.0*
74.8 70.0 76.9
62.6 25.0* 38.6 36.0
28.6 37.9 55.8 37.7
28.6 53.9 28.5 25,0*
MODEL
W sec deg
1 .75 1 .81 2.00 3.00
1 .57 .95
2.97 3.00
1.18 1 .56 .66
1.05
0.77 0.95 .81
1 .04
1.23 0,92 0,98 1.25
2.07 1,31 1,12 0.75
1.55 2.80 2.14 3.00 2.48
1.51 1.75 3.00 3.00
2.57 1.99 3.00
1.90 2.31 2.00 2.57
1.68 1 .00 0.97
1.31 0.50 0.75 0.50
0.50 0.85 0.99 0.70
0.88 1.23 0.72 1.01
sec
28 15 22 17
16 17 28 29
19 10 16 10
24 12 14 19
10 13 18 18
18 19 18 33
27 46 10 10 24
28 20 19 60
40 45 43
29 25 60 54
9 15 13
16 10 9 10
5 5 5 5
5 11 9 5
PARAMETERS
sec
31 10 15 25
14 15 10 18
18 10 13 10
25 26 13 21
19 10 28 16
26 32 25 18
16 49 19 21 21
23 29 24 38
24 57 45
55 58 40 54
8 10 10
10 10 16 10
19 16 6 11
18 20 5 16
sec
8 0 10 15
0 0 7 0
12 8 5 6
3 8 8 12
1 5 7 0
6 10 12 5
6 11 0 5 2
7 10 0 9
14 9 5
12 13 4 14
8 5 5
0 10 6 10
0 0 0 5
3 7 2 5
P
deg
.69
.41
.56
.93
.62
.53
.77
.98
.57
.77
.50
.95
t89 .78 .41
1.00
.31
.67
.51
.24
.75
.23
.77
.66
.36 ,10 .19 .18 ,14
.78
.99
.10
.23
.86
.66
.10
.31
.39
.20 1,00
.64 ,60 ,87
1.00 1.00 .56 .74
.94
.74
.68
.40
.96
.31
.95
.49
Q
deg'^
,10 .50 ,22 .06
.50
.27
.21
.16
.30
.50
.13
.15
.30
.46
.41
.28
.43
.49
.05
.48
.45
.35
.22
.33
.15
.05
.24
.17
.36
.21
.17
.06
.30
.05
.05
.40
.43
.16
.12
.05
,05 .10 .17
.05
.20
.20
.38
.29
.22
.32
.15
.17
.38
.33
.49
CRITERIA
E|«|^«2
71 67 68 69
55 71 55 54
77 71 68 62
62 60 55 66
82 73 68 80
65 65 60 74
79 70 63 86 75
66 85 68 84
72 75 72
48 62 74 76
60 67 69
49 66 73 56
59 53 57 S3
54 52 47 49
53 48 52 53
34 46 42 38
69 56 46 43
43 41 33 48
72 57 49 49
48 49 41 52
58 45 45 71 54
49 73 56 64
60 59 50
25 41 56 58
41 44 43
25 43 47 32
37 31 37 28
42 34 26 29
1*1
"77" 20 21 19
--13 --24
18 14 10 13
16 9 21 11
14 19 12 12 _-11 --10
29 49 19 33 23
21 41 14 18
34 63 19 --— 25 18
15 13 19
19 19 14 10
17 16 --10
17 12 13
5 7 5
--2
--6
4 3 1 3
3 1 7 2
3 4 3 2 --2
--2
11 28 5 16 9
5 21 3 5
14 41 5 ----9 4
4 3 5
9 9 3 2
5 4 --2
5 3 2
"
SUBJ.JUDGEMENT
easy very easy very easy very easy
very easy very easy very easy very easy
difficult very easy easy easy
easy not too difficult easy not too difficult
very difficult easy not too difficult easy
not too difficult easy difficult not too difficult
difficult not too difficult easy difficult easy
difficult not too difficult easy easy
difficult easy easy
easy difficult difficult very easy
very easy very easy easy
easy easy easy very easy
very easy easy easy easy
easy not too difficult not too difficult easy
_5H.
[deg]
50
25|
-25
-50
ï o y y -•2400 ^ t [sec]
MAVTTHTVLATJU t [secj
UI
I
FIGURE 3.19:
Typical time histories of the actual signals ii(i(t), ^(t) and 6^(t) compared with the nonlinear model output 6j (t) and the output of the ship model \\i (t): Subject Al; Char. I; r„ = 250 sec; Test sianal S
P«g] 0
-10
-20
\ / ( i ) 2 0
V/j(il ) 0 :
[deg]
7 \ ^
^ - ^
/ \
V s o o ^
/ l 1200
V v _ / / 180
\ o\
/ ^ ^ /
\J 2400
-10
-201
öjj(f) 50
I V \J 600 ^ ^ ^ 181
Tsw
2400
FIGURE 3.20: Typical time histories of the actual signals yii^^(t), i'(t) and ^^^(t) gompared with the nonlinear model output (5j (t) and the output of the ship model ^ (t): Subject Al; Char. I; T = 250 sec; Test signal L
280 300
C2 [«<0
60
20
O
.9 13 1.7 W (scc/deg]
- f ( 1 »—^ *•—^ f^—4 •
- O — O O O — o — o — e — ö — o — o
2 C, [sec]
|6| 0 E 5 2
FIGURE 3.21: A set of sensitivity functions; Subject Al ; Char. I ; = 250 sec ; TS L,
3.6 Discussion and conclusions
The criterion values related to the two parameter linear m.odel Ea. 3.4 and to the three param.eter linear m.odel Ea. 3.2 indicate that the first one yields a much poorer description of the helmsman's control behaviour than the latter. Therefore, only the results of the three parameter model will be discussed. The criterion values £{2 range from. 30 until SQ% , with an average of about 45^ with only a fev.' exceptions. This m.eans that the linear model with three param.eters provides a rather poor averaged description of the helm.sm.an's control behaviour. The criterion values Ex\,2 show, however, that the heading of the ship as steered by the model closely approxim.ates the heading of the ship steered by the helm.sman; the values with respect to these signals are generally less than 10^. Although the output of the m.odel of the helm.sm.an's behaviour sometimies differs from the actual output, the heading of the ship generated by the m.odel is invariably a good fit due to the very low pass filtering properties of the ship.
-56-
Reviewing the r mentioned that on the boundary solution for th ever, it can be suit. It seems helm.sman's nons tim.e histories responses to a
esults obtained with the nonlinear model, it was some of the optim.al values of T^ were found to be of the param.eter space. Superficially seen, the is problem is to enlarge the param.eter space, how-shown that this will not lead to the desired re-
that an explanation of the phenom.enon may be the tationary behaviour. Therefore, in Fig. 3.22 five of the steering wheel position are given, all being certain heading order.
«d'"
16 [deg]
U
12
10
8
6
2
0
-2+
-k
-6
-8
-10
-12
- U
-16
-18
average steering wheel position
I
FIGURE 3.22:
Influence of the nonstationary behaviour of the helm.sman on the average steering wheel position.
These records could be generated by the nonlinear m.odel executing a particular manoeuvre five times, one after each other, v.'ith a constant internal model parameter Ti equal to the ship parameter Tg, whereas the decision making element param.eters W, C , Cp and Cj5 have different values each tim.e the manoeuvre is executed.
-57-
In optim.izing the m.odel parameters on the basis of these five manoeuvres, those values will be found v/here the model output approxim.ates as closely as possible the average recorded output (Fig. 3.22). In this case this average output corresponds with an internal m.odel time constant very m.uch different from, the actual value, because of the larp-e num.ber of rudder calls. Hence, when the estim.ated internal m.odel param.eter Tjv, differs very m.uch from Tj5, that is, it is laying on the boundary of the parameter space, this fact m.ay be caused by tim.e-varying decison making element parameters. In the same way, it can be arrued that when the helmsm.an turns the steering wheel very slov;ly, the internal model parameter v/ill drift av/ay from the actual value, and the estim.ation m.ethod v;ill yield incorrect results. So the conclusion may be dravm that the m.ethod used to estim.ate the parameters yields incorrect values v/hen the helmsm.an's behaviour is nonstationary or, when the helm.sm.an turns the steering wheel very slov.'ly. It should be noted that extreme values of the tim.e constant Tyri vrere found mainly during the analyses of the tests with the smaller ships, Tg = 50 sec and Tg = 10 sec. The estimated values of the parameter Tm v/ith respect to the tests with the large shins are of the same order as the param.eter of the ship (Table 3.8); the mean values Tm approximate in most of the cases the actual ship tim.e constant within about 10%.
TABLE 3. 8: The mean values T]Tm inc? variances oTm of the internal model time constant Tj^, averaged over the subjects; larae ships, T = 250 sec. - s
Number of tests
4
5 4
3 4
2
Char.
I
I
III
III
V
V
TS
s L
S
L
S
L
riip m
sec
185
, 269
245
250
263
225
m
.74
1.08
.98
1.00
1.05
.90
^T m
sec
22
42
33
49 24
74
^T /^s m. 1
.09 1
.17 1
.13
.20 1
.10 1
.30
The resulting sensitivity functions show that the criterion function is rather sensitive to the parameters W and C^, that it is less sensitive with respect to C2 and T^, and that the parameters C3, p and q do not influence the criterion value very much. V. ith regard to the parameter C3 this easily can be understood, since this parameter determines the transition from phase III to phase 1 when an overshoot will occur, that is, in those cases where no overshoot occurs the param.eter C, is unimportant.
-58-
The parameters p and q have a rather great influence on the character of the output signal, however, they have almost no effect on the duration of a specific phase or on the magnitude of the rudder angle used during a phase.
The criteria values Ei.i and Eg2 given in Tables 3.5 through 3.7 show that the description of the helmsm.an's control behaviour by the nonlinear model m.ostly leads also here in certain way to rather poor m.atch in time domain. The criterion values Eg2 are m.ostly found to be within 25% and 55% with an average of about 40%. Just as in the case of the linear m.odel, the heading of the ship as steered by the nonlinear model closely approxim.ates the headinp- of the ship steered by the helmsman although also in this case the output of the nonlinear model sometim.es differs from the actual output. The criterion Eü)2 values are mostly smaller than 10%. The criterion values obtained with the three parameter linear model differ not m.uch from those found with the nonlinear model (Fig. 3.23).
50 60 70 80 90 20 30 i.0 50 60 nonlinear model l ö l nonlinear model 6
FIGURE 3.23:
Comparison between the criterion values E\s\ and Efi2 obtained with the nonlinear model and the linear three varameter model. Each + represents a particular test with one of the ships.
As the linear model is much simpler, and as consistent parameters can be estimated without difficulties, the linear model may be preferred superficially seen. However, also a number of criteria such as the number of rudder calls, can be m.entioned for v/hich the nonlinear model is far superior. As can be seen in the Figs. 3.19 and 3.20, the character of the output of the nonlinear model looks more like the helm.sman's output than the output of the linear model (Figs. 3.l6 and 3.17). This is particularly important when the influence of the ship dynamics or the disturbances on the number of rudder calls is studied. In Ch. 4 it will be shown that on the basis of the nonlinear model and extention to more real world conditions can be made.
In Fig. 3.24 histograms are presented of the judgem.ents of the different ships, as given by the subjects. It m.ay be noted that the ships with stationary characteristic I are judged differently by the groups of subjects A and B.
-59-
a
N a .c u
H
N a u
»
o u
§ i ^ wmm
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
1 2 3 4 5
Wi 1 2 3 4 5
Ts = 50
i 1 2 3 4 5
1 2 3 4 5
I 1 2 3 4 5
Ts=250
1 very easy 2 easy
3 not loo difficult
4 difficult
5 very difficult
n subj. A1,A2
M subj. Bl, B2
FIGURE 3.24:
Histogram,s of the subject's judgements of the manoeuvrability of the different ships.
-60-
An explanation may be that in judging the manoeuvrability of ships, the results are dependent on the helmsman's personal experience and the test sequence. When it is assumed that the scale used in Fig. 3.24 is a linear scale it is possible to com.pute the average judgements for each ship. In Table 3.9 the ships have been arranged according to these average judgem.ents.
TABLE 3.9: The different ships ranked according the average judgement.
Ship
Char.
V
VI
I
V
II
I
III
IV
III
•'s
50
50
50
250
50
250
250
50
50
Average judgement
Subjects A
1.1
1.2
1.6
2.7
2.9
Subjects B
1.6
2-1
2.l4
2,8
3,0
3.8
From Table 3.9 it can be concluded that the ships which the group of subjects B had to steer, are judged as being easier to manoeuvre than the ships steered by the group of subjects A. This may be a reason, that the ships with characteristic I v/ere judged differently. Furthermore, it may be concluded from Table 3.9 that the detrimental effect of course instability with respect to the helmsman's judgement is not only a m.atter of the stationary characteristic, but also of the constant Tg. The unstable characteristic III is qualified m.uch better in relation with the constant Tg = 250 sec than in relation with the smaller constant Tg = 50 sec.
In Fig. 3.25 the values of C^ are plotted as a function of the values of W. These parameters influence the duration as well as the magnitude of the rudder deflection during the first phase. V.'hen C\ and W are sm.all, large rudder angles will be used during a rather long period. On the other hand, v/hen the parameters are large, small rudder angles are generated so that only small rates of turn of the ship occur. From Fig. 3.25 it can be concluded that very stable ships with the characteristics V and VI, correspond with very small values of C^ and W. Vfhen the ship is unstable, Characteristics III and IV, the parameters C^ and W are large. As discussed before, the stable ships were easier to manoeuvre than the unstable ships, whereas the ships v/ith a dead zone in the stationary characteristic were superior in relation to the ships with a more or less linear characteristic. When the ship is unstable and qualified as being rather difficult to handle, the parameters C^ and VJ are large, on the other hand when the ship is easy to steer, Ci and W are smiall. The parameters Ci and V m.ay be regarded as a rather good estim.ator of the judgem.ents of the handling qualities of the ship by the helmsman. With respect to the other decision making element parameter C2 the sam.e effect may be exist.
-61-
'1 50
40
3 0 -
20
10
char.I ;T-s50 char.II;T5s50 50
40
30
20| ^ •
10
50-
40
30
20
10+
char.lEiTjsSO
-1 50
40
30
20
10
O l 2 3 w O l 2 3 w char.IZ;T5=50
50
40
30
201
10
char.ï:V50 (
50 40
30 20
10
) 1 2 3 w char.31: Ts=50
•
— 1 — 1 — 1
0 1 2 3 W 0 1 2 3 W 0 1 2 3 W
'1 60 50
40
30
20
10
char.I;T,=250
• •
60 50 40 3a 20
10-
char.I]I;Ts=250 char.ï; Ts=250
• • 60+
50
40
30
20
10
O 1 2 3 vv O 1 2 3 w [sec/d eg]
O 1 2 3 w
FIGURE 3.25:
The value of the parameter C plotted as a function of W.
However, as the criterion function E|^| is less sensitive to this parameter a relation between the ship's handling aualities and this param.eter is m.ore difficult to show.
Fig. 3.26 shov/s the criterion values E|6| and E52 averared over the subjects for the nine large ships, arranged again accordinp* to Table 3.9. From this diarram it may be concluded that a weak correlation exists between the criterion values and the helmsman's opinion about the ship's handling aualities. V.'hen the shin is more difficult to m.anoeuvre the criterion values show a tendency to increase.
Sum.marizing the follov/ing conclusions can be drawn: I ;ription of the helmsman's control
The three param.eter linear mod gives often an acceptable desc behaviour. The heading of the ship steere m.atches the heading of the shi The method used to estimate th result in the desired values o Although a relatively sim.ple i of only the linear part of the to account the dynam.ics of the
d by the tv/o m.odels closely p steered by the helm.sman. e parameters does not alv/ays f the nonlinear model param.eters. nternal m.odel is used, consisting ship enuation and not takinp- in-steering: gear J a. relatively good
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' |5 |80
60-40-20 O
TSS
'|5|80 60 401 20
O
TSL
Ö 80 60
40 20 O
V 80 60 40 20
O
TSS
1 TSL
a e I
50
sr
50
I z
50 250
n
50
1 M IS. IK
250 250 50 50
FIGURE 3.26:
Values of the criterion function averaged over the subjects, and arranged according the subject's judgements.
description of the helm.sm.an's behaviour is obtained. The internal m.odel time constant T^ is of the same order as the ship's time constant Tg in the case of large ships. The decision m.aking elem.ent parameters C^ and VJ may be rep-arded as rather good estimators of the judgements of the handling qualities of the ship by the helmsm.an. A weak correlation exists between the criterion values E i j. i and Er2 and the ship handling aualities. ' '
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REFERENCES
1. Brummer, G.M.A.; Wijk, W.R. van, The ship manoeuvring and research simulator of the Institute TNO for Mechanical Constructions, Delft. Report: Delft, Inst. TNO for Mech. Constr., 1970, No. 8133/1 32 p.
2. Bech, K.I., Some aspects of the stability of automatic course control of ships. Proc. Int. Sym.p. on Directional Stability and Control of Bodies Moving in V/ater, Journ. Mech. Enpineerinr Science, Vol. lit (1972), No. 77, pp. 123-131.
3. Brummer, G.M.A.; Voorde, C.B. van der; V/ijk, W.R. van; Glansdorp, C.C, Sim.ulation of the steerinr and manoeuvring characteristics of a second generation container ship. Report: Delft, Netherl. Ship Research Centre TNG, 1972, No. 170 S, 37 p.
k. Jenkins, G.M.; Watts, D.G., Spectral Analysis and its Applications. Holden Day, San Francisco, 1969.
5. Lunteren, A. van; Stassen, H.G., Annual Report 1969 of the Man-Machine Systems Group. Report: Delft, Dept. of Mech. Engineering, 1970, No. VJTHD 21, 102 p.
6. Stassen, H.G. et.al., Progress Report January 1970 until January 1973 of the Man-Machine Systems Group. Report: Delft, Dept. of Mech. Engineering, 1973, No. WTHD 55, 320 p.
7. Stuurman, A.M., Modelling the helmsman: A Study to Define a Mathematical Model Describing the Behaviour of a Helmsman Steering a Ship along a straight course. Report: Delft, Inst. TNO for Mech. Constr., 1969, No. 4701, 59 p.
8. Grossman, E.R.F.V/.; Cooke, J.E.; Beishon, P.J., Visual Attention and the Sam.pling of Displayed Inform.ation in Process Control. Proc. Second Int. Congress on Ergonomics, Dortm.und, 1961, Supplement to Ergonomics, Taylor and Francis, London, 230 p.
9 . Veldhuyzen, W., De beoordeling van de manoeuvreereigenschappen van verschillende gesimuleerde schepen door de roerganger. Rapport: Delft, Lab. voor Werkt. Meet- en Pegeltechniek, 197*1, No. N-98, 33 p.
10. McRuer, D.T.; Jex, H.R., A review of quasi-linear oilot models. . • lEEE-trans. on Human Factors in Electronics. Vol. HFE-8 (1967), No. 3 (Sept.), pp. 231-249.
11. Nomoto, K.; Taguchi, T.; Honda, K.; Hirano, S., On the steering qualities of ships. I.S.P. Vol. H (1957), No. 35 pp. 354-370.
12. Cooke, J.E., Human decisions in the control of a slow response system. Diss.: Oxford, 1965, 403 p.
13. White, R.C., A Survey of random methods for parameter optim.ization. Simulation, Vol. 17 (1971), Nov., pp. 197-205.
14. Karnopp, D.C., Random search techniaues for optim.ization problem.s. Automatica, Vol. 1 (1963), pp. 111-121.
15. Gurin, L.S.; Rastzigin, L.A., Convergence of the random search method in the presence of noise. Automation and Remote Control, Vol. 26 (1965 II), pp. 1505-1511.
16. Johannsen, G., A method for the development and optimization of controller-models for man-machine systems. In: Displays and Controls, Proc. Adv. Study Institute, Berchtesgaden. Amsterdam, Swets and Zeilinger, 1972, pp. 349-366.
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CHAPTER IV: SHIP f^ANOEUVRING IN WAVES
4.1 Introduction
During a series of preliminary sim.ulator experiments, tests v.fere performed with a large tanker sailing in open sea with very high waves £l, 2]. These tests showed that rather dangerous situations can occur when the helmsm.en are not well trained. The heading signal i|;(t) of a ship in waves consists of tv/o components: One component i|jg(t) resulting from the steering actions with the rudder, and another com.ponent originating from the disturbances due to v/ave exitations of the ship (Fig. 2.1). It is important to realize that this first com.ponent is a low frequent one, v/hereas the latter is relatively high frequent. In general the helmsman of a ship is instructed not to respond on these high-frequent disturbances, he only has to deal with the low-frequent components in the heading signal \\){t) . The m.ain reason for this instruction is the fact that rudder calls increase the ship's resistance, and thus decrease its speed. So the helmsman has to estimate the undisturbed heading and. heading rate. However, from the com.ments made by the subjects it can be derived that it is often difficult to estimate the rate of turn in particular when this rate of turn is small. This means, in terms of the nonlinear helm.sman's m.odel, that it is hard to make on the bases of the internal m.odel an estim.ation of the reouired rudder angle as the initial conditions needed to solve the differential equation are not known exactly.
From, the above, it follows that additional inform.ation, e.g. by means of a rate of turn indicator, may be expected to be a help for the helmsman steering a ship sailing in waves. Therefore a preliminary study has been started to investigate the control behaviour of a helmsm.an steering a ship in waves instrum.ented v/ith additional displays. Just as before, sim.ulator techniaues have been applied, but as it has been the intention to perform only a prelim.inary study, a very simple laboratory simulation was set UP. Also here, the subjects were instructed to steer a ship along a seouence of prescribed headings sim.ilar to the tests mentioned in Ch. 3.
To include the influence of waves, the nonlinear helmsman's m.odel had to be extended. Then, it has been tried to estimate the parameters of this extended m.odel, v/here the structure was adapted to the displays used during a particular test. The method to estimate the parameters v/as similar to the method used before (Ch. 3), v/here again hybrid simulation techniques have been applied.Hov/ever, due to the noise of the analogue com.ponents, such as amplifiers, integrators, etc., the estimation method used resulted into unreprodu-cable results.Due to the restricted time available for this preliminary study a switch to a totally digital computer simulation, v/as impossible. Therefore, the following procedure has been developed. It has been tried to predict the influence of additional displays on the helm.sman's performance by means of computer sim.ulations with the extended nonlinear model. Therefore the structure of the model was adapted to each of the test conditions, i.e. the displays used. However, to make the predictions, a set of model parameter values is needed, which can not be estimated in this case as m.entioned above. Therefore, the parameters of the basic nonlinear model have been estimated with respect to a fev/ tests, where the wave disturbances in the computer simulation have been omitted, based on the
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assumption, that the extension of the nonlinear model may be replaced by an ideal filter v/ithout influencing the remaininp- part of the m;Odel. Using these parameters all the tests have been sim.ulated v/ith the extended nonlinear m.odel, where the influence of the displays on the m.odel structure and on the parameter values has been taken into account. In this way predictions of the performance m.easures could be obtained, v/hich could be com.pared v/ith the values measured during the experim.ents.
4.2 Extension of the nonlinear helmsm.an's m.odel
The nonlinear m.odel given in Ch. 3 has to be extended in such a v/ay that the behaviour of a helmsm.an steering a shin in waves could be described. This extension should include a kind of filter v/hich generates estimations of the undisturbed heading 'l g(t) and heading rate 'J g(t) based on the disturbed headinp- ili(t) (' ir. 2.1). These estim.ates are denoted by i]Jg(t) and ^5(t). In view of the structure of the m.odel, existing of an estim.ator, an internal miodel and a decision miaking element (Ch. 3.3.3), the extension concerns in particular the estim.ator.
A very simple extension of the model v/ould be a linear filter. However, the freauencies of the m.otions of a large tanker due to rudder calls range up to about .1 rad/sec as can be concluded from the results given in Ch. 3. Calculations of the yawing spectra of a 200,000 tons tanker with a speed of 15 knots showed that the freauencies of the ship motions are mostly centered between .2 and 1.0 rad/sec (Pig. 4.1).
Vv/*^e' xlO
V»7.72 m/sec
windspeed =22 /sec
o
m,
.6 .8 .1 0/ [rad/sec]
FIGURE 4.1: Calculated spectra of the yawing motions of a 200,000 tons tanker for different directions of wave propagation.
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Both frequency ranges are so close to each other that by means of linear filtering large phase shifts in the estimated heading and heading rate will occur. Therefore, the application of a linear filter may not lead to acceptable results. Other filtering techniques had to be applied. A very useful filter could be based on a publication of Magdeleno, et.al. [3]. Based on the fact that ship motions due to waves can be regarded as narrow band noise [4j, and thus a time history of such a signal looks m.ore or less like a sine wave v/ith a slowly and in time varying amplitude, estimates of the undisturbed heading and heading rate, H's^^^ SLnh ^sit), can be obtained in the following manner (Fig. 4.2).
V/-(»)
01
c '•5 a
FIGURE 4.2:
Estimation of \pg(t) and Tpgft) at time ts using successive peaks of the \l)(t) signal.
Based on the three successive peaks at tim.es t^, tj, and tc^, the undisturbed headings at times t2 and ti^ can be estim.ated according to:
^^it^) il'(t ) + ip(t^)
(4.1)
and
ü;3(t^) ii)(t^) + ^i){t^)
(4.2)
v/here t 2 = (t^ + t ) /
Setting:
(t^ + t^) / 2.
and
(t^ - t^) = 2At^,
(t^ - t^) = 2At25
(4.3)
(4.4)-
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estimations of the undisturbed heading and heading rate at tim.e tj-can be m.ade:
' s 5 = ^s^n^ "• s^^4^ • *2 ' ^^-5)
t - Ijt.) - U- (t ) ^s(^5) = s(H) = ' At, . At^ • ( -6)
The Eqs. (4.5) and (4.6) can be rewritten as:
^^(t^) = ? 3(t4) + ^g(t5) . At2 ; (4.7)
%(S^ - I - t, » ^^-8) 5 1
where 'ï' (t^) can be calculated using Eq. (4.2).
In this way at discrete tim.es estimates of the undisturbed heading and rate of turn, are obtained. But between tv/o successive peaks information about these quantities must be available too. Using the internal model Eq. 3.5 this information can be obtained by solving the differential equation with the steering wheel position as forcing input and the last estim.ates i (t- ) and l'g(t-{ ) as initial conditions. Thus the estimated values of the undisturbed heading and rate of turn are supplied continuously by the internal model, driven by the steering wheel position signal, where at the times a peak of the heading signal occurs, the internal model is reset at the new estim.ates. In Fig. 4.3 a block diagram, of the extended model is given. It m.ay be noted that just as described in Ch. 3 three m.ain blocks can be recop^nized, viz. the estim.ator, the internal model and the decision making element.
4.3 Experimental set up
To evaluate the applicability of the extended nonlinear model a number of tests has been perform.ed, so that the influence of additional inform.ation on the helm.sm.an's performance could be investigated. Rem.inding that the intention v/as to perform only a preliminary study, a very simple manoeuvring sim.ulator has been used consisting of a steering wheel, a rotating compass, a rudder angle indicator, a predictive display, and a rate of turn indicator. Only one ship has been sim.ulated, viz. a directionally unstable 200.000 tdw. tanker.
4.3.1 Ship dynamics
In describing the dynamics of the ship, the simple Mom.oto-Norrbin m.odel Eq. 2.6 was used; the parameters were chosen eaual to the parameters of the large unstable ship used before (Table 4.1).
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Fr «op |_rL
detection
1
l top
averager
^^•V'?
estimator
5 " ^ S (t)
V^-(t:i,t*T)
V{,f'>
P 'int. mod. I l
equation I j
ï intenal rnodel
I ^ decision
making ^ clement
.J ö^(t)
6j(t)
disturbances
i ship — •
FIGURE 4.3: Block diagram of the extended model of the helmsman steering a ship in waves.
TABLE 4.1: The model parameters of the ship.
Parameter
^s
^s
^2
K
Value
250
- . 0 5 - 1
5
3
Dim.ension
sec
sec
2 ( sec /deg)
deg/sec
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Using the computer programs of the Shipbuilding Laboratory of,the Delft University of Technology, spectra of the yav/ing motions of a 200,000 tons tanker in a sea-way have been calculated using strip theory methods (Fig. 4.1). As the largest amplitudes are found v/hen the angle between wave direction and ship speed is eaual to about 60°, this spectrum was chosen to sim.ulate the behaviour of the ship in waves (Fip-. 4.4).
windspeed: 22 /sec
/i=60'*
.2 .3 .4 .5 .6 Wj [rad/sec]
FIGURE 4.4: Spectrum of the calculated yawing motions of a 200,000 tons tanker with a wave direction of propoagation equal to 60 degrees.
It should be noted that even in are relatively small; the ampli deg. To create a disturbance si simiUlation, the spectrum, v/as di signal consisted of the sum of quencies corresponding with the bands, and am.plitudes chosen in specific component was equal to band. The phase of each compone turbance signal was added to th the ship's manoeuvring behaviou
this situat tudes are of gnal, which vided into t twenty three central fre such a v/ay the power o
nt v/as chose e output of r as discuss
ion the yavring motions the order of only .5
can be used in the wenty three bands. The sinusoids with fre
auency of each of the that the pov/er of a f the corresponding n randomly. The dis-the model describing ed in Ch. 2 (Fif'. 2.1)
4.3.2 Displays and controls
In addition to the displays normally in use in ship steerino-^ viz, a com.pass and a rudder angle indicator, a rate of turn indicator and a predictive display have been used. T- oreover an indicator to display the ordered heading ^^{t) has been applied. In practice, the contribution of the disturbances acting on the ship in the
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rate of turn is much higher than the contribution due to rudder deflection, hence when the actual rate of turn is displayed, the rate of turn indicator shows a very noisy signal. Likewise, when the predicted headings are based on the actual heading and rate of turn, these predictions are very inaccurate and unreliable. Therefore, the heading and rate of turn should he filtered in such a way that useful additional information is presented to the helmsman. This problem is already discussed in Ch. 4.2: To filter the disturbances out, linear filtering techniaues cannot be used. Because a m.anoeuvring sim.ulator has been used, the ideally filtered signals ^^it), and ^g(t) were known. The use of these signals, however, is not a realistic situation, but due to the limited time available for that study, this solution v/as chosen. The rate of turn indicator and the predictive display based on these ideally filtered inputs are indicated in this thesis by RTIl and PDl respectively. Moreover, tests have been performed using the principle on v/hich the extended helm.sman's model is based to estimate 4;g(t) and lijg(t). To obtain the estimates continuously, a m.odel describing the ship dynam.ics should be available. This model was also used to predict the heading to be shown by the predictive displays. The following structure of the predictor m.odel was chosen:
Tpi^(t) + ilj(t) = Kp6^(t), (4.9)
which is comparable with the structure of the internal model of the helmsm.an's model. The displays based on this principle are indicated by RTI2 and PD2 respectively. The prediction of the heading as given by the predictive display was repeated every four seconds, the prediction time was 100 sec, which was about two tim.es the ship length taking into account the velocity of 15 knots. This tim.e span is based on simulations with the nonlinear model of the helmsm.an as given in Ch. 3, where the prediction tim.e tp never exceeded 100 sec. Also V-'arenaar used this prediction time in his study [5] to investigate the influence of predictive displays on the helmsman's performance. The repetition time was chosen after som.e prelim.inary tests, in such a v/ay that a rather sm.ooth picture was obtained. A RT-screen v/as applied to shov/ the predicted heading.
FIGURE 4.5: Screen of the predictive display; a: momentary heading; b: the desired heading relative to the momentary heading; o: predicted heading relative to the momentary heading.
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The Fig. 4.5 shows the display configuration, the straight line "a" indicates the mom.entary heading, and "b" the desired heading relatively to the m.omentary heading. The angle betv/een these two lines is the heading error. The curved line "c" is the prediction of the heading, also given relatively to the m.om.entary heading. The circles are indicating constant prediction tim.es. The timie constant of the predictor m.odel T^ was chosen equal to 250 sec, the gain factor Kp equal to -.05 sec*"!. To investigate the influence of different time constants on the helm.sman's behaviour, a number of tests was performed with the predictive display PD2, where Tp was varied at values of 200, 250, or 300 sec.
To steer the ship the helm.sman could use a rather light steering wheel, which required not much physical effort. No other controls were available.
4.3.3 The ordered headings: The test signal
The task designed v/as to steer a ship along prescribed headings, using the displays and controls just discussed. The seouence of headings was the same as during the previous tests, v/ith the smaller amplitudes (TS S; Ch. 3). The duration of a test was 40 min.
4.3.4 Subjects
For this prelim.inary study the number of subjects was kept as small as possible. The two subjects participating in this program.mie, were students of the Delft University of Technology. They were trained until the moment they showed a more or less stationary steering behaviour.
^•3.5 Experimental program.m.e
Each of the tv/o subjects, indicated by A and B respectively, performed the tests summ.arized in Table 4.2.
TABLE 4.2: Summary of the tests to investigate the behaviour of a helmsman steering a ship in waves with different displays.
Indicators
C C
C, RTIl C, PDl
C, RTI2 C, FD2 C, PD2 -C, PD2
T (sec) p
-
250
250 250 200 300
Disturbances
No Ye«
Yes Yes
Yes Yes Yes Yes
C .= compass; RTI = rate of turn indicator; PD = predictive display.
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4.3.6 Data collection
The following signals were recorded on magnetic tape: • The desired heading ip^(t); • The undisturbed heading ij g(t); • The disturbance signal; • The undisturbed rate of turn i|j5(t); • The steering wheel position fi^^Tt); • The rudder angle <5(t). From these signals the follov/ing performance measures were computed:
Rudderscore I^ = ^ i o^ 62(t)dt (4.10)
Rate of turn score I, = V i^ J il;g (t)dt (4.11)
Heading error score I. = V '^ r" [i|; (t )-ii;g(t)] dt . (4.12)
Moreover the average number of rudder calls per minute NRC was calculated. As the steering wheel position 6^(t) is an analogue signal, the estimation of NRC is not simple, due to noise in the simulation. For that reason the number of times that the angular speed of the rudder exceeded 10^ of its maxim.um speed, was counted.
4.4 Prediction of scores
4.4.1 Model structure
To predict the scores by means of computer sim.ulations with the nonlinear model, the structure of this model m.ust be adapted to the displays used during a particular test. As mentioned before four types of. additional displays were investigated: • A rate of turn indicator, displaying the undisturbed heading
rate (RTIl). • A predictive display, based on the undisturbed heading and
heading rate (PDl). • A rate of turn indicator, displaying the filtered rate of turn,
using successive peaks (RTI2). • Three predictive displays, with different time constants of the
predictor model, based on the filtered heading and rate of turn (PD2).
Block diagrams of each of the displays together with the helmsman's model are shown in the Figs. 4.6 through 4.9. A few remarks with respect to these figures should be made. The information supplied by the rate of turn indicator can be used as an initial condition to make predictions with the internal model. Hov/ever, also estimates of the rate of turn can be achieved from the estimator. / Iso the information supplied by the predictive display can be obtained from the helm.sman's own estimator and from internal model. It should be mentioned that the inform.ation obtained from the predictive displays also contains the momentary values of the heading and the heading rate or estimates of these auantities. This means that this information can be used to reset the internal model as well.
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Finally, it should be noted that the helmsman has the possibility to m.ake no use of the displayed information and instead, to base his decision on his own estimates. However, in the predictions of the scores it is assum.ed that the helm.sman uses the displays indeed, as otherwise the display is more or less superfluous.
r n estimator
%1\)%U,)
I V^s(t:t,i*r)
V^.l'»!
internal
mod
decision
making element
[M Imsman's model
¥4 111
iternal M
lodel I-*—I disturbances
ój(t) i ship V/-(t)
FIGURE 4.6:
Block diagram^ of the helmsman's model steering a ship with a rate of turn indicator (RTIj).
V^s"t''V^s"tl V^s(t),V^s(t)
II predictor L
model I
disturbances
ship V^lt)
FIGURE A.7: Block diagram of the helr^cmar's model steerir.g n phiv v>ith a vre-dictive display (PDj).
--ji^.
r "1 ^ estimator
v^,(.,),v;(v ^pf'i
I
^slt:t,t.»r)
V^s(t:t,t*T) %lx)
internal M 1
model L4—I
decision making element
helmsman's model öj(tl
V^s"tl
V^f't)
top d tor and averager
etec- 1 nd L«— ger I
predi
model el I
disturbances
i ship
V^(t)
FIGURE 4.8:
Block diagram of the helmsm.an's model steering a shiv with a. rate of turn indicator (RTI2). Note that the vredictor model is used only to estimate \b (t) continuously.
r estimator
^•t'.^sf't'
%\\:x,\*r)
V^(t:t,t+T)(
V^H"! ^d'" I
V='''*V w i ?p":'.
internal | . * —
model L^—I
decision -*.] making
element
helmsman's model Sjftl
top detector and averager
predictor
model h disturbances
ship V (1)
FIGURE 4.9: Block diagram, of the helmsman's model steering a phiv with a vre-dictive disvlay (PD2).
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4.4.2 Parameter values
In simulating the tests with the nonlinear model, the parameter values had to become available; that are the internal m.odel parameters Tjn and Kj, and the decision making element param.eters \'I, Ci, 02, C3, p and q. The internal model parameters relate to the ship dynam.ics. The decision m.aking elem.ent parameters VI, Ci, C2 and C3 influence m.ainly the way of steering, that is the magnitude and duration of the rudder deflections. The param.eter p indicate the precision of ship control, v/hereas the parameter a is related to the influence of the magnitude of the heading error on this precision (Eq. 3.12); hence the param.eters p and q can be considered as being indicators of the accuracy of information transmission. The parameter values used in the sim.ulation have been selected in the following way. The set of param.eters is divided into a sub set which will be influenced by presenting additional information, and another sub set which v/ill not be influenced. V. hen a helmsm.an is extremely well-trained, it may be assumed that the knowledge he has about the dynamics of the ship, as well as the v/ay of steerinp-are not influenced by presenting additional inform.ation. The only param.eters which m.ay be im.portant, are the parameters P and o. The threshold value p is directly related to the accuracy of the predictions necessary to make the decisions, and so to the accuracy of the displayed information. The parameter a indicatinr an increase in the helm.sman's indif f ierence threshold for large heading errors, may also be related to the accuracy of the displayed inform.ation. However, as a relation between a and the information accuracy is difficult to obtain, the parameter o is assumed to be undependent upon the displayed information. Conseauently, the threshold value p is the only param.eter v/hich certainly is influenced by giving the helmsman additional inform.ation.
Before the selection of the values of p in relation to the different displays will be discussed, the v/ay used to obtain a set of the remaining model parameters will be elucidated. In Table 4.3 a summary is given of the tests perform.ed; they can be divided into two groups, viz. one with and another without wave disturbances.
TABLE 4.3: Summary of possibilities to estir^ate the parameters in the nonlinear helmsm.an's m.odel.
Tests performed
Ship sailing in calm, v/ater; without additional displays.
Ship sailing in v/aves; v/ith and [without addi-Itional displays.
Model to be used
Nonextended helmsman's m.odel (Ch.3)
Extended helmsman's model (Ch. 3, 4).
Nonextended helm.sm.an' s model (Ch.3)•
Parameter estimation 1
The parameters can be esti- 1 mated as described in Ch.3. 1
The parameters cannot be 1 estimated due to computer 1 noise. 1
The param.eters can be esti- 1 m.ated v/hen the wave distur- 1 bances are omitted in the 1 computer simulation. 1
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v.'hen no wave disturbances act on the shin, the model to be used to describe the helmsm.an's control behaviour is the nonextended model (Ch. 3.3). The parameters of this nonextended m.odel can be estimated v;ithout having difficulties due to computer noise (Ch. 3.4). In this v/ay a set of parameter values is obtained related to the m.anoeuvring of ships in calm; v/ater. Hov/ever, the scone o** this chapter is the manoeuvring of ships in v/aves. As mentioned before the estim.ation of the param.eters of the extended model v/as impossible due to computer noise. Put, by assum.inr that the replacement of the estimator of the extended helmsman's model (Ch. 4.2) by an ideal estimator generating the exact values of the undisturbed heading and heading rate, does not influence the parameter values of the m;odel, except the parameter p, the remaining parameter values can be estimated. This ideal estimator can easily be applied in a com.puter sim.ulation, since the undisturbed values of the heading and the heading rate are already available. The disturbances then become unimportant in the computer sim.ulation, and so they can be om.itted. The model of the helmsman to be used in this configuration is again identical to the model described in Ch. 3.3. Both the methods to estim.ate the m.odel parameters (Table 4.3) are based on certain assum.ptions. The first one is based on the assum^n-tion that the presence of wave disturbances does not influence the parameter values obtained from a test v/ithout wave disturbances; the latter is based on the assumption that a replacem.ent of the estimator part of the m.odel by an ideal estimator does not influence the parameter values. The selection of one of" these m.ethods is arbitrary at this stae-e, therefore both the methods have been used in parameter estimation in order to judp-e the best solution. Based on the results of the second method a prediction of the performance measures has been achieved. It should be noted that the helm.sman behaves in a nonstationary way causinr a variance in the estim.ated parameter values. To diminish the influence of this variance on the scores to be predicted, the estimated param.eter values have been averared over both the subjects.
The parameter estim.ation method selected in this v/ay yields a set of parameter values which is assumed to be undependent of the displayed information, viz. T^, %,, V,', Ci, C2, C3 and a. Only the parameter p has to be chosen depending on the test conditions. Sensitivity analyses with the nonlinear m.odel adapted to the different test conditions with varying param.eters showed the follov/ing phenom.ena: • VJhen the parameter p is chosen too small, every new value of
the estimator output will result into a new rudder angle (Fig. 4.3). A very noisy output of the helm.sman's m.odel is then obtained. The performance with respect to the steerinp- quality is very poor. Thus the param.eter p should have that value where errors in the reset values of the internal m.odel do not result into rudder calls.
• On the other hand, v/hen p is chosen too large, the performance is rather poor too, since then rather large heading errors and large overshoots occur.
When no additional information is supplied, the errors in the reset values of the internal model, are caused by errors of the estimator, which are denoted by Ati/(tti) and Ail)(tti). They are defined by:
Al'(tti) = $g(tti) - 'J^gCtti), (4.13)
and A'i'(tti) = il'g(tti) - 'l s(tti). (4.14)
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Taking into account the structure of the nonlinear m.odel, the first phenomenon can be translated into the following ineoualities with respect to the param.eter p:
|Ai|.'(t..) I < p, (4.15)
and
jCi.Ail;(tt. ) I < p, (4.16)
for each tim.e tt^ a peak value in the headinp- occurs, v/hich means for each time the estimator resets the internal m.odel. In addition to the inequalities Eos. 4.15 and 4.l6, it can be concluded from the sensitivity analyses that P should be as small as possible. VJhen additional information is supplied, the internal model reset errors can be sm.aller. For instance, in the case that the actual rate of turn is displayed by m.eans of the rate of turn indicator RTIl, the helmsman is aware of the exact value of the rate of turn. The reset errors are caused only by errors in the estim.ated heading, and so only Eq. 4.15 is im.portant. The predictive display PDl supplies very accurate inform.ation v/ith respect to the headinp- and the heading rate, this means that the param.eter p can be very small. The parameter is mainly determined by the reading-accuracy of the display. The inform.ation displayed by the rate of turn indicator and the predictive displays based on the top detection principle (RTI2 and PD2) is less accurate than the other tv/o displays (RTIl and PDl). As the estimates of the undisturbed heading and the undisturbed heading rate are obtained from, the same estimating principle as the helmsm.an's own estim.ates, the display of this additional information will not influence the parameter p. Thus, the performance measures are only influenced by the structure of the model. Also when additional information is supplied p should be as small as possible to avoid unaccurate steerinr and large overshoots . Finally, the probability density functions of the estimator errors (Eqs. 4.13 and 4.l4)have to be determ.ined in order to choose the proper values of the param.eter p. As the m.odel is part of a closed loop system., these probability density functions m.ay be dependent upon p itself, which makes the estim.ation of this parameter difficult. However, sim.ulations v/ith the nonlinear model with various values of p learned that this dependence could be nerlected. Thus, in the case the remaining model param.eters are known, the parameter p can be estim.ated depending on the display considered, using the Eqs. 4.15 and 4,l6, and the estimated probability density functions of AiJ;(tti) and AiJ;(tti), keeping in mind that p should be chosen as small as possible.
4.5 Results
Table 4.4 gives the perform.ance m.easures Eas. 4.10, 4.11 and 4.12 and the average number of rudder calls NRC for each of the subjects as well as the average values of these scores. The averap-e scores v/ill be compared at the end of this paragraph with the m.odel predictions. To obtain the predictions of the scores by m.eans of computer sim.ulations, the m.odel parameters have been estim.ated for the tests without additional displays. The m.ethod applied to estimate the param.eters has been discussed already in Ch. 4.4.2. The results of the param.eter estimations are sum.marized in Table 4.5.
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TABLE 4.4. Measured scores and average values of these scores. Parameters model ship dynamics: T = 250 sec, K = .05 sec~^, aj = -1, a2 = 5 (sec/deg)2, C = compass; RTI = rate PD = predictive display.
of turn indicator;
Test conditions
Indicator
C C
C.RTIl C.FDl
C,RTI2 C,PD2 C,PD2 C,PD2
^P
sec
_
250
250 250 200 300
Dist.
no yes
yes yes
yes yes yes yes
Scores |
Subject A
l6
deg
9.69 12.14
10.62 9.52
11.59 11.13 10.76 9.95
^*e
dep
3.58 4.09
3.51 3.45
3.82 3.68 3.66 3.53
I^
dep sec
.0599
.0705
.0630
.0630
.0689
.0724
.0633
.0568
NRC
nin"
3.03 2.58
2.23 4.03
2.58 3.50 2.60 2.78
Subject B
^6
dep
10.97 12.06
9.64 9.52
11.67 9.91 11.19 10.23
^*e
deg
3.46 3.87
3.48 3.53
4.05 3.72 3.68 3.64
H dep sec
.0642
.0665
.0582
.0593
.0728
.0620
.0675
.0635
NRC
min"
3.05 2.80
2.83 3.50
3.15 4.23 3.98 3.58
Averape value
!«
dep
10.33 12.10
10.13 9.52
11.64 10.52 10.98 10.09
^*e
dep
3.52 3.98
3.50 3.49
3.94 3.70 3.67 3.59
H dep sec
.0621
.0685
.0610
.0611
.0709
.0622
.0654
.0601
NRC
min"
3.04 2.6P
2.53 3.77
2.87 3.87 3.29 3.18
TABLE 4.5: The averaged parameter values and the criterion values for each of the tests without additional displays. Parameters of the ship: T = 250 sec, K = -.05 sec~ , C = compass.
Test conditions
Indicators
C C
. C c
c c
Disturbances
no no
yes yes
no yes
Subj .
A B
A B
A/B A/B
Model parameters
m
sec
252 287
215 291
•m
sec-^
-.05 -.05
-.05 -.05
W
sec deg
1.9 2.3
2.6 2.2
^1
sec
41 35
26 44
C2
sec
32 29
30 30
H sec
0 3
15 13
P
dep
.51
.95
.90
.59
a
dep"^
.09
.08
.14
.06
Criteria
^161
%
58 43
66 68
^5^
%
38 24
64 56
Average values
270 253
-.05 -.05
2.1 2.4
38 35
31 30
2 14
.73
.75 .09 .10
51 67
31 60
To obtain an idea about the possibility to predict the scores by means of computer simulations the tests with the ship sailing in calm water are simulated using the nonextended helmsman's m.odel and the average m.odel parameter values related to the calm water condition (Table 4.5). During this com.puter simulation as well as those which will be discussed below, the value of the parameter q has been changed from the values given in Table 4.5, to avoid a very large number of rudder calls. This parameter change in a was allowed due to the fact that the optimization criterion Ei,i was
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was rather insensitive_ with respect to a for values sm.aller than .3 deg~l. Therefore q is set equal to .3 deg~l. From Table 4.6 it can be concluded that in spite of this increase in the param,eter value of a, the number of rudder calls is still rather larp-e compared with the value measured.
TABLE 4.6: Comparison between the performance measures resulting from the tests and those predicted by computer sim.ulations. The parameters of the model are chosen as given in Table 4.5 (average values) with an exception for q which was set equal to .3 deg~^. C = compass.
1 Test conditions
1 Indicators
1 C
Disturbances
no
no
Perf. measures obtained from
Tests (average values)
Model predictions
Performance measures 1
^6
deg
10.33
10.81
I*e
dep
3.52
3.64
H dep sec
.062
.065
NPC 1
min" 1
1.44 1
3.73
By using the average param.eter values with respect to the ship sailing in waves (Table 4.5), the probability density functions of the estimator errors b.-^{tt^) and h^it^i) have been determined (Fig. 4.10). ^
J l n m xn -.L .t,
[d«g] "
.12 -.0& -.Qi. .Qi .08 .12
^ [deg/sec]
FIGURE 4.10:
Estimated vrobability density functions of the estimator errors hii(t^) and h^(t^).
- 8 0 -
From these probability density functions it may be concluded that the absolute value of the estim.ator errors are m.ostly sm.aller than .6 deg with respect to the heading, and sm.aller than .06 deg/sec with respect to the heading rate. Rased on these data the parameter p has been estim.ated by means of the Eos. 4.15 and 4.16, depending upon the kind of additional inform.ation displayed (Table 4.7).
TABLE 4.7: The values of the parameter p used to predict the performance measures by means of computer simulations
1 Test conditions
Indicators
C C, RTIl C, PDl C, RTI2 C, PD2
Disturbances
yes yes yes yes yes
P
sec
2.2 1 -7
.2 2.2 2.2
Eas.
4.15, 4.16 4.15
4.15, 4.16 4.15, 4.16
The value of p with respect to the predictive display (PDl) should be sm.all, but larger than zero as for p •> 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
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2.5
¥e
.08 .06 .Oi .02
NRC
IMJIM im nu
c
n
C,RTI^ C,PD
Tp=250
measured •
QRTI^
predicted
QPD QPD
Tp=250 200
CiPD^
300
FIGURE 4.11:
Measured and 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
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•^
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:
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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 anp-le 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. 639-658.
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 Man-Machine Systems Group. Dept. of Mech. Engineering, Delft, 1973, No."WTHD-55, pp. l40-l60.
3. Magdeleno, R.E.; Jex, H.R.; Johnson, W.A., Tracking quasi-predictable displays, subjective predictability gradations, pilot models for periodic and narrowband inputs. Proc. of the fifth Annual Conf. on Manual Control, Cambridge (USA), 1969, NASA SP-215, pp. 391-428.
4 . Gerritsm.a, J ., Behaviour of a ship in a sea-way. 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.
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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 Breadth Mean draught Displacem.ent Tonnage Steering equi Rudder area Propulsion
Nominal RPM Speed max.
pme nt
42.00 m 7.50 m 2.22 m
383 in3 324 tons 2 rudders 2 X 1,04 m2 2 diesel engines 2 controlable pitch propellers
300 turns/min. 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, some-tim.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.
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5.2.1 :hip dynamics
The Laboratory for Control of the Department of Electrical Engineering of the Delft University of Technolory performed many expe-rim: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: Parameters of the model of the trainings shiv "Zeefakkel"
Ship speed
knots
9
12
Prop.pitch
deg
15
27
m •'s
sec
20.
34.
K s
sec"
-.25
-.64
^1
-
1
1
^2
,secv2 de?-*
.14
.28
T
sec
1
1
1
m 1
defT 1 sec 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.
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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.p-nal
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
Test-signal
TS S
TS S
TS S
TS L
Duration
5 min.
10 min.
20 min.
10 min.
Ship speed |
9 knots
A , B , C''
A , B*, C
A , B , C
A , 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) .
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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 en-vironm.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 off-set, 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 off-set 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, particu
larly 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
1 T
Iv2 = li n/ [ (t)] ^ dt; (5.1) X'
and - T
^l = -^ J 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 first-order 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 first-order filter (Fig. 5.1)
T^ 5d^(t) + 6d^(t) = 6^(t), (5.3)
where ^^(t) = output of the nonlinear model; '5df(t) = output of the first-order filter; Tf = filter time constant.
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V^j(t)
'
FIGURE 5.1:
nonlinear
helmsman's model
ö j iM first order filter
ödf«" ship model
1 V'OI
J
Block diagram of the ship model steered by the nonlinear helmsman's model, where the output 6^(t) fi Iter.
is fed through a first order
To estim.ate the param.eters of the linear and nonlinear helm.s-m.an's m.odels, a digital computer was used. The criterion function:
E^2 =
.'^[6^(t) - 6^*(t)]^ dt
|^[6^(t)]^ dt . 100?S (3.15)
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 of ^f^(t), ^(t) and S^(t). Test duration TS S; Subject C; Ship speed: 9 knots.
20 m.in.
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• 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.
c
E o
C
ë o
c "F i n
S,
(0
7«
20
10
0
40-
7o 20-
10
0
«0-
%
20
10
0
,
- /
/
[) .8 1.6 bv—^
^^
• / >
/ , 0 .S K6
bv—.-
.Jc^
/
/ 0 .8 1.6
bv—*-
^2
40
X 20
10
n (
40
\
20
10-
0
40-
%
20
10-
0
/T •
/ I. ) .8 1.6
b v — . •
/
• / /
/ ^ 3 .8 1.6
b v — i -
- X / . -
^ , 3 .8 1.6
b v — i ^
' 3 1
40
7o
20
10
0
40
%
20
10-
0
40-
%
20-
10-
0
" ^ \ • / /
U / ^
3 .8 l!6 bv—^
. ^
i y ^
f 0 .8 K6
b v — . •
^
• f
0 .8 1.6 b v — 1
FIGURE 5.3:
The times on target as a function of the boundary value bv. + slow, TS S ; "o fast, TS S ; m slow, TS L.'
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.
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The results are given in Table 5.6. To investigate the influence of the first-order 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.
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TABLE 5.4: Estimated variances and m.ean absolute values of the signals t (t) , \!)(t), \IJ (t) and ^j(t).
Ship speed
knots
9
12
9
12
9
9
12
Duration
min.
20
20
10
10
10
5
5
TS
5
S
S
S
L
s
s
Suhj.
A E C
B C
A C
E C
A 3 C
A B
B C
Variances
6,(t)
cieg
23.4 25.3 22.4
9.8 10.7
26.6 51.5
23.4 17.8
73.9 83.2 85.4
64.4 134.1
38.2 48.9
.. (t)
deg
4.8 4.8 4.7
4.8 5.7
9.4 5.1
7.0 11.1
46.0 34.2 46.4
14.3 20.9
11.1 11.2
li'(t)
deg
18.1 21.8 17.5
15.3 19.3
17.3 14.8
17.7 17.6
65.8 66.9 64.6
15.8 39.0
15.8 14.1
iit)
sec
.11
.22
.15
.09
.32
.12
.26
.67
.43
.53
.52
.47
.36
.71
.34 1.07
"•'ean ab.-ïclute values
^,(t)
deg
3.4 3.5 3.6
2.4 2.5
4.0 5.8
3.9 3.4
6.8 7.4 7.6
6.7 9.8
5.1 5.6
i'^(t)
deg
1.5 1.1 1.4
1.3 1.6
2.0 1.5
1.6 2.1
4.4 3.6 4.4
2.7 3.5
2.1 2.4
fit)
deg
3.9 4.2 3.7 3.6 3.9
3.7 3.4
3.6 3.7
7.2 7.0 7.0
3.4 5.3
3.4 3.1
i(t)
dee SPC
.24
.36
.30
.22
.48
.24
.42
.69
.54
.54
.56
.53
.50
.70
.50
.92
TABLE 5.5: Results of the varameter ovtimization with the nonlinear mode I.
Duration
min.
20
20
10
10
10
5
K
Subj .
A B C
B C
A C
B C
A E C
A B
E C
TS
s
s
s
s
L
s
s
Ship data
Speed
knots
9
12
9
12
9
9
12
Ts
sec
20.
34.
20.
3''.
20.
20.
34.
's
sec"
-.25
-.63
-.25
-.63
-.25
-.25
-.63
Model parameters
1 m
sec
20. 20. 19.
31. 35.
17. 16.
42. 34.
14. 20. 18.
19. 16.
34. 36.
V/
sec deg
.4
.8 1.5
1.0 1.0
.6
.4
.7 1.9
.5
.4
.6
.5
.4
.4
.5
^1
sec
7. 11. 8.
11. 10.
8. 9.
10. 12.
9. 9. 6.
9 6.
13. 9.
^2
sec
1: 4.
7. 7.
4. 7.
6. 9.
5. 5. 4.
6. 5.
^3
sec
2. 3. 1.
2. 3.
3. 3.
3. 3.
4. 3. 4.
2. 3.
3. 4.
P
deg
.5
.5
.8
.5
.5
.6
.5
.5
.5
.7
.7
.6
.6
.8
.7
.4
q
deg'-
.5
.7
.5
.5
.5
.6
.4
.5
.5
.4
.5
.5
.5
.6
.5
Criteria J
^62
<
53.2 56.6 76.1
73.2 7°. 8
41.8 69.0
68.0 77.9
48.7 55.0 47.1
42.5 45.1
75.9 62.1
E.2
of
10.7 2.9 9.9
8.4 12.1
q.i 13.9
10.3 9.6
4.5 5.8 4.6
12.5 20.0
15.5 23.8
^ ^ of /J
42.6 12.9 30.6
?7.2 40.7
20.9 40.1
25.9 15.2
6.4 11.4 6.4
13.8 36.2
22.2 29.8
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TABLE 5.6: Results of the parameter optimization with the three parameter linear model.
Duration
min.
20 20
10 10
10 10 10
5 5
Subj .
A B
A C
A B C
A B
TS
S S
S S
L L L
S S
Shi
Speed
knots
9 9
9 9
9 9 9
9 9
r dat
^s
sec
20. 20.
20. 20.
20. 20. 20.
20. 20.
a
's
sec"
-.25 -.25
-.25 -.25
-.25 -.25 -.25-
-.25 -.25
Kode
\
2.3 1.9
2.4 2.3
1.2 1.2 1.5
2.3 2.1
1 param.
^1
sec
6.8 7.0
8.9 7.7
8.7 8.0 7.2
8.9 3.7
^2
sec
1.8 2.9
2.9 1.7
3.5 1.5 3.3
2.9 1.3
Criteria 1
^6^
%
56.7 52.6
45.7 69.6
46.7 6l.9 51.3
42.1 39.7
W %
10.6 5.4
19.3 11.4
5.7 7.6 8.9
11.0
'%^ %
42.2 24.1
44.2 32.9
8.1 14.9 12.2
12.2
TABLE 5. 7: Results of the parameter ovtimization with the nonlinear model, extended with a first-order filter. The remaining parameters are kept eaual to the values given in Table 5.5.
Duration
min.
10
10 10 10
5
Subj .
C
A B C
A
TS
S
L L L
S
Shi
Speed
knots
9
9 9 9
9
p data
sec
20.
20. 20. 20.
20.
\
sec"
-.25
-.25 -.25 -•25
-.25
Parameters
W
sec def
.4
.4
.4
.4
.4
S sec
9.
10. 9. 7.
9.
^f
sec
1.
• 2. 1. 2.
1.
Cr
^^^
%
68.7
42.9 54.3 35.5
37.7
iteria
E,2
%
12.5
5.2 6.3 5.3
16.6
E, ,
%
36.1
7.4 12.6 7.4
11.7
5.5 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 steerinp-wheel 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
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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 first-order 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 neightbour-hood 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 values (x\) and standard deviations (a) of the nonlinear model parameters for each of the ship speeds.
n 0
n a
Ship data
Speed
knots
9 9 .
12 12
^s
sec
20. 20.
34. 34.
•s
sec"
-.25 -.25
-.63 -.63
Fodel parameters
m
sec
17.9 2.1
35.3 3.7
m s
.90
.11
1.04 .11
W
sec deg
.61
.34
.91
.70
^1
sec
8.3 1.6
10.8 1.5
^2
sec
5.0 .9
6.6 1.4
'3
sec
2.8 .9
3.0 .6
P
deg
.63
.14
.51
.10
q
deg"^
.51
.10
.51
.01
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 first-order 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 first-order 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 first-order 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 spoed-schroeven uitp-erust 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. 163-178.
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'HD-21,
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 just-mentioned 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:
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*
• 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.
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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 man-machine 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 well-damped 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
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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.
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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 Intern-Model-concept.
Lit.: Dit proefschrift.
II. Om een mens-machinesysteem 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 mens-machineonderzoek 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 quasi-lineair pilot models. lEEE-trans. on Human Factors in Electronics, Vol. HFE-8 (196T), No. 3(Sept.), pp. 231-249.
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. niet-lineaire 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. lEEE-trans. on Systems, Man, and Cybernetics, Vol. SMC-2 (1972), No. 4 (Sept.) pp. 494-504.
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 voor-kandidaatsstudie voor werktuigkundig inge-nie\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 mens-machinesystemen 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.