A Fuzzy Track-keeping Autopilot For

8/13/2019 A Fuzzy Track-keeping Autopilot For

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23No. A2 Journal of Marine Engineering and Technology

A fuzzy track-keeping autopilot for ship steering

A fuzzy track-keeping autopilot for

ship steering

E Omerdic and GN Roberts, University of Wales College, New-

port, UK,and Z Vukic, University of Zagreb, Faculty of Electrical

Engineering and Computing, Zagreb, Croatia

In this paper a non-linear fuzzy autopilot for ship track-keeping is presented. The proposed

autopilot has four inputs (actual and desired heading, rate of change of heading and offset

from the desired path) and one output (command rudder angle). The track-keepingproblem is decomposed into two subtasks: (i) follow the desired heading, and (ii) bring the

ship onto the desired path and keep tracking. Internally, the autopilot consists of two

autopilots that fulfil these tasks simultaneously. The proposed control scheme has beenverified using a non-linear model of a Mariner-class vessel and steering mechanism under

the influence of wave and current disturbances. Results presented show how such a controlstrategy enables improved tracking performance.

INTRODUCTION

The pioneering work of Sperry1and Minorski2is consid-ered as the important milestones in the development ofautomatic steering for ships. Although the early autopilots

were very simple devices, in which heading error pro-duced a corrective signal for the steering mechanism (ie propor-tional control), experience with such devices indicated that dueto the ships enhanced course-keeping qualities there was areduction in propulsion losses and a consequent saving in fuelcosts. Further developments included the addition of derivativeof heading error to improve transient response, and integral of

Zoran Vukic is Professor of Control Engineering at the University

of Zagreb, Faculty of Electrical Engineering and Computing.

Between 1992 and 1996 he was Head of the Department of

Control and Computer Engineering in Automation, University of

Zagreb. His specific interests have been adaptive control, robust

control, identification, non-linear control, fault tolerant control

and reconfigurable control. He is currently working in the area of

intelligent and fault tolerant control for marine and underwater

vehicles. He is a Chapter Chair of IEEE Control Systems/Robotics

and Automation Society in Croatia, a member of IEEE Control

Systems society and Oceanic engineering society, and a member

of several IFAC Technical Committees.

AUTHORS' BIOGRAPHIES

Edin Omerdic graduated from the University of Zagreb, Faculty

of Electrical Engineering and Computing, Croatia in 1997, and

received the MS degree in electrical engineering (automatic

control) from the same university in 2001. He is currently a full-

time research student in the Mechatronics Research Centre, at

the University of Wales College, Newport. UK. His thesis concerns

the development of fault detection and data handling systems for

underwater vehicles. This research programme is being undertaken

as part of the EPSRC IMPROVES project.

Geoff Roberts is Professor of Mechatronics and Head of theMechatronics Research Centre at the University of Wales College,

Newport. UK. He has been active in the area of marine control

systems for many years and has contributed to the development

of control strategies for ship steering, rudder roll stabilisation,

integrated rudder/fin roll stabilisation and guidance and control of

underwater vehicles. He is presently working on fault detection

and data handling for underwater vehicles, parallel multi mode

controllers for ship stabilisation, and applications of intelligent

control for guidance and control of land and marine vehicles. He

is immediate past chairman of the IFAC Technical Committee on

Marine Systems and a member of the IFAC Technical Committee

on Mechatronic Systems.


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24 Journal of Marine Engineering and Technology No. A2


heading error to counteract constant yaw disturbances such ascrosswinds and tide.

Because of their simplicity, reliability and low cost, PID(proportional, integral and derivative) autopilots of this type haveremained in use for many years. This is despite the widely held

view that the steering characteristics of a PID controller were

unsatisfactory, mainly due to the necessity for user adjustmentto accommodate changes in ship loading conditions and theoperating environment. The huge increase in world fuel costs inthe early 70s, however, led to the development and application ofmore advanced control methods to meet the urgent need tominimise transportation costs. The majority of researchers at thattime favoured an optimal control approach and a number ofsolutions were proposed, eg Broom and Lambert3, Clarke4, andKabeti and Byrne5. Although using these approaches it waspossible to optimise performance to meet specific objectives, theirmain failing was that like their PID counterparts they werelargely unable to cope with the significant non-linearities encoun-tered. Other approaches, which gained some limited popularityat the same time, were autopilots based upon adaptive methodssuch as model-reference6 and self-tuning.7 More recently, re-searchers have attempted to combine the attributes of adaptiveand optimal control, designing robust autopilots using the H

methodology.8However, despite the attractiveness of these morerigorous approaches very few designs have resulted in actualimplementation.

This lack of real success led many researchers to considerwhether the use of intelligent paradigms such as fuzzy logic andartificial neural networks would be suitable for design or as theimplemented technology for ships autopilots. In this respectfuzzy logic, with its origins in human reasoning, was consideredas a most suitable candidate having the potential to replicateexperienced helmsmen thereby producing a robust and non-

linear autopilot.The first autopilot designed with fuzzy set theory was pre-sented by Amerongen et al.9The proposed autopilot used twodifferent inputs with five linguistic variables and a fixed rule base.It was shown that compared to a PID controller, the proposedfuzzy autopilot gave a significantly enhanced performance in anoisy environment with fewer rudder calls. However, the tuningof the fuzzy controller parameters was based on an extended trialand error procedure. This pioneering work was quickly followed

by complementary investigations. A different application of fuzzyset theory was pursued by Sutton10where fuzzy logic was used todesign a cognitive model of a helmsman, and it was suggested thatthe fuzzy model so produced could be used in the design ofintelligent autopilots based on fuzzy set theory. However, in order

to guarantee acceptable performances in different operating con-ditions, the proposed controller needed further adjustment. Themanual setting of the controller parameters was enhanced withthe introduction of automatic adaptation and learning mecha-nisms. One of the first examples in this direction was the self-organising fuzzy autopilot proposed in Sutton and Jess.11The firstcommercially available fuzzy autopilot, designed with the latterapproach, was presented by Polkinghorne et al.12,13,14

One of the main advantages of fuzzy logic autopilots is that therules may be formulated without a precise definition of the shipsdynamics. The control actions are normally decided such that therequired rudder demand is determined from knowledge of theexpected ships response to the input. Although this process is

best achieved through consultation with the helmsman or by

observation of his/her actions, the fuzzy rules may be formulatedfrom an understanding of the systems dynamical behaviour. Thisprocess illustrates the fundamental difference of fuzzy controllerdesign compared with more traditional model-based controllerdesigns. Whereas the latter is concerned with designs to meetperformance specifications, ie damping, speed of response, steady-

state error, etc, fuzzy controller design is focused on predictingsystem behaviour in response to specific inputs, as postulated bySperry1and Minorski2following their observations of the helms-man. What this means is that, often, fuzzy approaches areapplication specific and the final fuzzy controller is often arrivedat after considerable trial and error where the distribution andshape of the fuzzy sets used are tuned in order to achieve thedesired performance. However it should be noted that fuzzycontrollers are intrinsically robust, in the sense that through thegeneralisation property they can accommodate new situations (iesmallchanges in system parameters). They are also non-linear, inthat they incorporate (map) the functional relationship betweeninput and output, which is a non-linear relationship.

It was this analysis, together with the increased activity inintelligent systems, which led to the work described in this paper

being undertaken. The remainder of the paper is organised asfollows: the evolution of the proposed autopilot from the initialresearch is briefly described before the mathematical model isintroduced. Then the course-keeping and track-keeping prob-lems are addressed. Finally, simulation results are presented,followed by some conclusions.

Evolution of the fuzzy autopilotInitially the research described herein concentrated on the designof a simple course-keeping system where a fuzzy autopilot withtwo inputs (heading error and rate of change of heading) was usedto find control action (command rudder angle). Every input had

seven membership functions and the total number of rules was 7

2

,ie 49. The control surface of the proposed fuzzy autopilot was anon-linear function of the two input variables, symmetrical to anon-principal diagonal of the rule table. The proposed controlscheme gave better performance compared to PID autopilot, andcommand signals generated by fuzzy autopilot were similar tocommands generated by an experience helmsman. This latterpoint is important because it demonstrated how the fuzzy control-lers encapsulate and replicate the actions of skilled operators,

which in this application is the helmsman.The next stage of the research used this system as a basic

building block for developing the track-keeping system. In Vukicet al15, the first version of fuzzy autopilot for track-keeping wasproposed. The track-keeping problem, defined as tracking the

path specified by way points, has been simplified to course-tracking problem using appropriate transformation. In this waythe track-keeping problem was solved using the fuzzy course-keeping autopilot. This solution had a good performance if seacurrent disturbance did not act on the ship during manoeuvres.It was found that, in the presence of the current disturbance, theship would follow the desired course with some offset from thedesired path, depending on the direction and intensity of current.

One of the possibilities for improving the performance sug-gested in Vukic et al15was introducing an additional input (offsetfrom the desired path) to enhance the information presented tothe autopilot. In Vukic et al16 an improved fuzzy autopilot fortrack-keeping was proposed, which uses three inputs (headingerror, rate of change of heading and offset from the desired path)


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and direction of sea current. The outputs are yaw angle, yawvelocity and position inxandydirections.

Steering MechanismThe steering mechanism considered is the two-loop electro-hydraulic steering subsystem, common on many ships. A concep-

tual and equivalent block diagram of the steering mechanism isshown in Fig 1. This type of steering mechanism consists of anelectro-hydraulic servo subsystem with a telemotor and a ruddersubsystem. It can be seen that the system has two feedback loops:one from the cylinders of the telemotor, and the other from thehydraulic amplifier. The first loop includes a non-linear elementof type relay with dead zone and hysteresis (to reduce rudderactivity in the presence of a high frequency component in thecommand signal). The second loop contains a non-linear elementof type speed limiter (to limit rapid changes of rudder motion).The presence of these non-linear elements makes the design of theautopilot more difficult (see Fig 1).

Typical values of parameters shown in Fig 1 (b) are:

DB= 1 , H= 0 8. , K= 4 /s , PB= 7 and N= 5 /s .

DisturbancesThere are several disturbances with various effects on the vesseldynamics to be taken into account.15,20Three classes of distur-

bances can be distinguished: Disturbances which affect the dynamics of the system, eg

the depth of water. Disturbances which cause additional signals in the sys-

tem, eg waves. Disturbances that corrupt the measurements, eg noise in

the position measurements.In this paper the disturbances considered are wind-generated

waves and sea currents.

Wind-generated wavesPierson and Moskowitz21developed the standard wave spectra(PM-spectrum) analysing the wave spectra in the North AtlanticOcean, (Fossen17, pages 63-65). In order to simulate wavedisturbance, it is necessary to approximate the PM-spectrum.Linear wave model approximations are usually preferred by shipcontrol system engineers, owing to their simplicity. Linear ap-proximation is obtained by passing of white noise through a linearfilter.

The second-order wave transfer function approximation of thePM-spectrum is used in this paper (Fossen17, pages 70-71). Thismodel is written as

h sK s

s s( ) =

+ +

2

0 0

22

. (1)A linear state-space model can be obtained by transformingthis expression to the time-domain by:

d y

dt

dy

dty K

d

dt

h

2

2 0 0

22+ + =

. (2)

Defining dx

dtx

1

2= and x y

2 = , the state-space model can

be written as:

dx

dt

dx

dt

x

x K h

1

2 0

2

0

1

2

0 1

2

0

=

+

, (3)

in order to find the appropriate command rudder angle. The mainidea was in shifting the control surface of the previously developedtwo-input fuzzy autopilot out of a non-principal diagonal depend-ing on the value and sign of the offset. This means that if the shipis already on the desired path, the offset is zero and there is noshifting, the standard control surface is optimal and the ship

would track the desired course specified by the way points. If theship is not on the desired path, the offset is not zero and thecontrol surface is shifted out of the non-principal diagonal,proportional to the size and sign of offset. The advantage of thisapproach was rejection of the influence of the current disturbanceon the tracking performance, whilst disadvantages were a loss ofthe transparency of the control decision process and an increasein the autopilots complexity (number of membership functionsper input was seven, seven and five, so total number of rules was245).

In order to decrease complexity and to make a decisionprocess more understandable, the track-keeping problem is de-composed into two subtasks: (i) following the desired heading,and (ii) bringing the ship onto desired path and tracking. There-fore, the autopilot for track-keeping, proposed in this paper,consists internally of two autopilots that fulfil these tasks simul-taneously. Each of these autopilots has a simple structure andoperates similar to human reasoning.

MATHEMATICAL MODELSExperimenting with a real ship is time-consuming and expensive,so a dynamic model is essential for simulation purposes and forinvestigation of different control algorithms. In order to investi-gate different approaches for design of track-keeping controlsystems it is necessary to use a realistic model of the vessel anddisturbances. In this paper the models of a Mariner-class vessel,steering mechanism, wave/current disturbances and Notch filter

as in Fossen

17

, Vukic et al

16

and Omerdic

18

are used.

Ship dynamicsThe hydro- and aerodynamics laboratory in Lyngby, Denmark,has performed both planar motion mechanism (PMM) tests andfull-scale steering and manoeuvring predictions for a Mariner-class vessel. The main data and dimensions of the Mariner-class

vessel are given in Table 1, Chislett and Strm-Tejsen.19

Table 1: The main data for the Mariner-class vessel .

Using results from PMM tests, Fossen has built a non-linearmathematical model for this vessel in MATLAB. The model isgiven in Fossen17, Appendix E.1.1, and describes the dynamicmotion of the ship in a horizontal plane. For the work describedin this paper, the original model was transformed to Simulink S-function and augmented with the ability to investigate the influ-ence of external disturbances, for example, sea currents. Theinputs to the model are commanded rudder angle, average speed

Length overall (Loa

) 171.80m

Length between perpendiculars (Lpp

) 160.93m

Maximum beam (B) 23.17m

Design draught (T) 8.23m

Design displacement () 18 541m3

Design speed (u0) 15 knots = 7.72m/s


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2. Actual heading .3. The rate of change of heading r d / dt = (measured by

gyro rate sensor).4. Offset from the desired path d(this input is important for

the track-keeping problem; for the course-keeping prob-

lem this input is equal to zero).

Generally, the command signal c , generated by the autopi-lot, consists of two components: dc

1, generated by two input controller Fuzzy Autopilot

(Course). dc

2, generated by one input controller Autopilot (Off-

set).

Signal dc1is intended for course-keeping. Signaldc

2is used for

returning the ship to the desired path for the track-keepingproblem.

Fuzzy autopilot (Course)

The preprocessor performs signal conditioning (scaling andsaturation) of inputs e and ronto standard interval [ ]3 3, .

After preprocessing, the signals e and rare internally markedas linguistic variables errorand errordotinside the autopilot,and the output is marked as a linguistic variable y . Forexample, signal e is scaled by gain Ke and then passedthrough the saturation block with limits [ ]3 3, . Hence, therelationship between error(output of the saturation block)and e is

error

e

e e

e

e

e e

e

=

>

<

3 3

3

3 3

,

,

,

K

K K

K

. (10)

The postprocessor performs denormalisation and PItransformation of output y . PI transformation is per-formed by generating proportional and (limited) integralcomponents inside the Postprocessing block. Summingthese components gives the signal dc

1, the command

signal for the rudder angle c in the course-keepingproblem.

Membership functions for inputs error and errordot andoutput y are shown in Fig 3(a) and (b), respectively. Fig 3(b)displays the control surface of the Fuzzy autopilot (Course),

while the properties are shown in Table 2.

Table 2: 'Fuzzy autopilot (Course)' properties.

The fuzzy autopilot for course-keeping uses 7 492

= rules.Table 3 shows these rules in a compact matrix form.

where h is a zero-mean white noise process. Due to its simplic-ity, this model is useful for control systems design.

The second order Notch filter is used to reject the wave-induced components from the heading signal. The transfer func-tion of the Notch filter has a form (Fossen17, pages 226-227):

h ss s

sNO

n n

n

( )( )

=+ +

+

2 22

2

,(4)

wheren is the natural frequency and is the relative dampingfactor of the filter. Since most of the energy in the wave spectrumis located around the modal frequency of the wave spectrum, thenatural frequency of the Notch filter should be chosen equal to theencounter frequency e , that is:

n e=

. (5)An estimate of the encounter frequency

e can be computed

from the relation

eg

U= 00

2

cos , (6)

where 0 is wave modal frequency, g is the acceleration ofgravity, Uis the total speed of ship and is the angle betweenthe heading and the direction of the wave. The modal frequency

0 of the PM-spectrum can be estimated from

wg

V

g

Hs0

= =0.88 0.40(7)

where Vis the speed of the wind at an elevation of 19.4m andHs is the significant wave height.

Sea currentA two-dimensional current model is used (Fossen17, page 88).The earth-fixed current components can be described by twoparameters:average current speedVc and direction of current c . The

body-fixed components can be computed from:

uc Vccos c

vc Vcsin c

=

=

( )

( )

.(8)

The average current velocity for computer simulations can begenerated by using the first-order Gauss-Markov process (Fossen17,page 89), described by the following differential equation:

dV t

dtV t t

c

c G

( )( ) ( )+ = 0 , (9)

where G t

( )is a zero mean Gaussian white noise sequence and

0

0 is a constant. This process must be limitedV V t V

cmin max ( )( ) in order to simulate realistic sea currents.

Course-keepingA closed-loop control system with fuzzy autopilot for ship course-keeping (Fig 2a) was successfully applied in Vukic et al16, andOmerdic.18This structure will serve as a basic scheme for buildingmore complex control algorithms.

Fuzzy autopilotA fuzzy autopilot has four inputs (see Fig 2(b)):1. Desired heading d(error signal e d= is gener-

ated internally).

FIS type Mamdani# Inputs 2

# Outputs 1

AND method min

OR method max

Implication min

Aggregation max

Defuzzification centroid


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Table 3: Rule base for the 'Fuzzy autopilot (Course)'

error

Track-keepingA closed-loop control system with a fuzzy autopilot for ship track-keeping is shown in Fig 4, which is the control scheme for course-keeping, shown in Fig 2, augmented by an additional control-loop

with position feedback.

Fuzzy autopilotThe fuzzy autopilot consists of two autopilots: one is responsible

for course-keeping (defined implicitly by way points) and theother for minimising the offset from the desired path, ie theautopilot is the same as in Fig 2(b), but in this case the fourthinput d(distance between ship and nominal path) is not equal tozero. This input plays an important role in control process.Generally, the ship trajectory consists of n way pointsWP P P P

n= { }1 2, ,..., with coordinates P x yi i i=( ), . It is assumed

that the ship should move along a straight line between adjacentway points. In this paper the simplest trajectory, with only twopoints P x y1 1 1=( ), and P x y2 2 2=( ), , is considered (see Fig5(a)). It is assumed that at time tthe ship is located at pointS x y=( )0 0, . The desired path is a straight line from P1to P2 .

Course-keeping problems

Problem formulation: Change ship course from 0to d2 30=

Control goal e d t= ( ) 2 0Fuzzy autopilot (Course): Status:Active

Inputs: e d= and r= Output: dc1

Fuzzy autopilot (Offset): Status: Not active

Input: d= 0

Output: dc2 0=Command signal: c dc= 1

Track-keeping problem

Problem formulation: Follow the desired path P P1 2 defined by way points P1 0 0=( ),and P

2 2000 1154 7=

( ), . .

d

PP1 1 2

30= =

( )arg

Control goal Tracking problem is decomposed in two subtasks:

e d t= ( ) 1 0, (i)d distance=

( , )Ship PP

t1 2 0 (ii)

Fuzzy autopilot (Course): Status:Active

Inputs: e d= and r= Output: dc1

Fuzzy autopilot (Offset): Status:Active

Input: d

Output: dc2Command signal: c dc dc= +1 2

The distance (offset) dof point Sfrom the desired path P P1 2

can be calculated from:

d sign x x y y x x y y

y y x x x y x y y x

y y x x

=

+ +

+

( ) ( ) ( ) ( )[ ]

( ) ( )

( ) ( )

2 1 0 1 0 1 2 1

2 1 0 2 1 0 1 2 1 2

2 1

2

2 1

2.

(11)

The sign of dis defined with an angle between vectors P S1 and

PP1 2

: if the ship is located on the left (right) side from PP1 2 , sign isa plus (minus). In (11) the sign is estimated with asignfunction.Inside the fuzzy autopilot offset dis normalised with the shiplength L :

=d

L.

(12)The goal is to bring the ship back from point Sand to track

the desired path.The difference between course-keeping and track-keeping is

visible from Fig 5(b). It is assumed that at t= 0 the ship is locatedat point P1 0 0=( ), (moving with a constant speed in the x-direction, ie initial heading is 0o) and the desired course isd2 30= for the course-keeping. The requirement is to changethe ship course from the initial value 0to the new value 30. Fortrack-keeping, it is assumed that the desired path is defined by

wa y po in ts P1

0 0= ( ), andP

2 3000 3 000 30 3000 1 732 1= ( ) = ( ), tan , . . In order to

compare course-keeping and track-keeping, the same anglearg P P

d d1 2 1 2= = was chosen. It is needed to bring the ship

back to the desired path, ie condition d 0 should be satisfied,

Table 4: Comparison between course-keeping and track-keeping

NB NM NS ZE PS PM PB

NB NB NB NB NB NM NS ZE

NM NB NB NB NM NS ZE PS

errordot NS NB NB NM NS ZE PS PMZE NB NM NS ZE PS PM PB

PS NM NS ZE PS PM PB PB

PM NS ZE PS PM PB PB PB

PB ZE PS PM PB PB PB PB


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and to track the desired path to point P2, following the desired

course d1 . Therefore, for the course-keeping problem, thedecision about the size of command rudder signal c is madeusing an error signal e

d= and a signal r= . However, for

the track-keeping problem, the decision process is more complex,because in addition to signals eand r, another signal d (offset

from the desired path) plays an important role. A comparison ofcourse-keeping and track-keeping problems is given in Table 4.

Therefore, for track-keeping, the goal is to track the desired course

d1 (Condition (i)) and to minimise dat the same time (Condition(ii)). In order to satisfy these conditions, signals dc1 (realisation ofCondition (i)) and dc

2(realisation of Condition (ii)) are added so that

the composite signal dc dc dc1 2= + should achieve both conditionssimultaneously. Signal dc1is already known from course-keepingproblem. Hence, the problem can be formulated as a question: Whatis the mathematical form of unknown relationship dc dc

2 2= ( ) ?

Autopilot (Offset)This section describes a structure of the Autopilot (Offset). Thisautopilot has input dand output dc2 . Analysing Fig 5(b) it can

be concluded that the sign of signal dc2 depends on the shipposition in relation to the desired path:

If the ship is located on the left side, then d 0> . It can beeasily verified that a positive command signal produces a positivecourse change. Hence, signal dc2 should have a positive sign,

because it will produce an increase of the command signal and theship will have a course greater than that desired for some time (forexample, at point A is A d> 1). In this way the ship willapproach the desired path and offset dwill decrease.

Because of symmetry, it is easy to draw the conclusionthat, if the ship is located on the right side, then signal dc

2should

have negative sign. If the ship is located on the desired track, ie if d 0 , then

signal dc

2 should be equal to zero, iedc

2 0

.Therefore, the unknown function dc dc2 2

= ( ) is a continuousodd function, defined in the first and third quadrant and whichsatisfies condition dc

2 0 0( )= .

The unknown odd function dc dc2 2

= ( ) is selected from thefamily of functions F

dc K sf 2 eta

= ( )tanh , (13)

where Keta >0 and sf>0are scaling factors. Function definedby equation (13) satisfies all required conditions. Family F ischosen because many different shapes of functions can be gener-ated with appropriate selection of scaling factors (Fig 6(a) and(b)). Optimal values for Keta and sf were obtained by undertak-

ing a number of simulations (Keta =

20 and sf=

4 3. ).

SIMULATION RESULTSThe proposed control architecture has been implemented inSIMULINK. Simulations were performed using the non-linearmodel of a Mariner-class vessel and the steering mechanism,described earlier. In order to demonstrate robustness of theproposed autopilot for course-keeping, two different desiredheadings were chosen one with a small deviation from the initialheading (d = 10 ) and the other with a large deviation (d = 30 ).

A course-changing manoeuvre, performed by an expert shipoperator (experienced helmsman), is shown in Fig 7 (Amerongen22)and can be used for comparison purposes. Later it wil l be shown

that the fuzzy autopilot generates signals similar to an experiencedhelmsman.

Fig 8 displays time response of heading and rudder signals fortwo different cases:

d = 10 (left) and

d = 30 (right). Fig 8 (1)

shows the time responses for the no-disturbances case. It can beseen that the performance of the proposed autopilot is very good,

heading response is without overshoot and command ruddersignals are very similar to those produced by an experiencedhelmsman. The influence of the waves with the modal frequency

0 1= rad s/ and the encounter angle = 30 is demonstrated in

Fig 8 (2). Here the heading signal, obtained by gyrocompass, iscontaminated with wave components and the Notch filter was notused to reject them. Control effort is much higher than in the no-disturbance case. Filtering of the heading signal Fig 8 (3) gives goodperformance with acceptable control effort. Although the Notchfilter introduces some delay into the control loop, demands onactuator are less than without filtering. Analysing responses in Fig8 and other cases (not shown here) it is concluded that theproposed fuzzy autopilot with fixed parameters has good perform-ance over all range of the possible heading demands, ie it is notneeded to tune any of its parameters if desired heading is changed.This is not case for the PID autopilot. Experiments similar to thoseshown in Fig 8 were conducted with PID autopilot. PID tuned forthe case d = 10 could not give good performance for the case

d = 30 and vice versa. Beside that, the best-tuned PID was

inferior to the fuzzy autopilot for the same input reference and thecommand signals generated by the PID controller were not similarto those produced by an experienced helmsman.

Fig 9(a) shows time responses for track-keeping withoutdisturbances. It is assumed that at t= 0 the ship is located at pointP

1 0 0=( ), and moves with a constant speed in x-direction. The

desired path is defined by way points P1

0 0=( ), andP

2 3000 3000 30 3000 1732 1= = ( ) ( ), tan , . . The ships trajec-

tory, way points and the desired path are shown on the same plot.At the beginning of the simulation the ship moves in x-directionand its distance from the desired path temporally increases. Thefuzzy autopilot (Offset) responds to this by generating high signaldc

2in order to return the ship back to the desired path. Soon the

distance achieves maximum and decreases rapidly. At the sametime, the fuzzy autopilot (Course) generates signal dc1trying toforce the ship to follow the desired heading. When the ship isreturned to the path, signal dc

2vanishes and signal dc

1begins

to dominate. Simulations with way points located in all fourquadrants were performed and good performance has beenachieved in all cases. Influence of the wave disturbances on theperformance of track-keeping is demonstrated in Fig 9(b). In thiscase the Notch filter was not used to reject wave components in

the heading signal and control demand on rudder is much higherthan in the no-disturbance case. Better performance and betterresponse is achieved by filtering the heading signal (Fig 9(c)).Control effort is lower and at the same time accuracy is better. Theinfluence of the sea currents is shown in Fig 10(a). In this case,after the ship reaches the desired path, there is a small offset onthe right side of the path, but soon the ship is returned to the pathand continues sailing with very small tracking error, despite thepresence of the strong sea currents. Fig 10 (b) presents timeresponses in the case of waves and sea currents. The headingsignal, contaminated by the wave components, is not filtered and,simultaneously, strong sea currents act on the ship as is indicatedon the plot. Similar to the previous case, there is a small overshoot


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on the right side of the path but, in this case, control demands onthe rudder are very high. Better performance and acceptablecontrol effort can be obtained by filtering the heading signal, as itis shown in Fig 10(c). In this case the same disturbances (wavesand currents) act on the ship during the manoeuvre, but the fuzzyautopilot performs its task in a satisfactory manner, command

signals are in the acceptable bounds and tracking error is small.

CONCLUSIONThis paper described a new fuzzy autopilot for ship track-keeping.The proposed autopilot has four inputs (actual and desiredheading, rate of change of heading and offset from the desiredpath) and one output (command rudder angle). Track-keepingproblem is decomposed into two subtasks: (i) follow the desiredheading, and (ii) bring the ship onto desired path and keeptracking. Internally, the autopilot consists of two autopilots thatfulfilled these tasks simultaneously. Each of the autopilots has asimple internal structure, designed by copying the reasoning and

behaviour of the experienced helmsman. The process of generat-ing the action signals is transparent and understandable. Satura-tion of the actuator (steering mechanism) is avoided and com-mand signals, produced by fuzzy autopilot and experiencedhelmsman, are very similar.

The proposed control scheme has been successfully verifiedusing a non-linear model of the Mariner-class vessel and steeringmechanism under the influence of wave and current distur-

bances. Performance of the proposed control scheme has beeninvestigated under different conditions. In the case when the

waves and sea currents act on the ship, the unavoidable loss incontrol performance and control effort was found to be acceptableif a Notch filter is used to reject wave components from theheading signal. Hence, in order to reduce the effects of the wavedisturbance on the tracking performance, the recommendation is

to use a Notch filter with a natural frequency equal to theencounter frequency according to equations (5)-(7).Further improvement of the proposed control scheme could

be achieved by replacing Autopilot (Offset) with an equivalentAdaptive Neuro-Fuzzy Inference System (ANFIS, Jang et al23)network. ANFIS belongs to the family of adaptive networks andhas ability and flexibility for on-line fine-tuning. The starting pointfor tuning could be the approximation of the function y= ( )tanh .The local shape of this function could be tuned using the on-linetraining capabilities of ANFIS.

REFERENCES1. Sperry, EA, (1922).Automatic Steering, Trans. Society of

Naval Architects and Marine Engineers pp 53-61.2. Minorski, N, (1922). Directional stability of automaticallysteered bodies, Journal of American Society of Naval Engineers,Vol.34 pp 280-309.

3. Broom, DR, and Lambert, TM, (1978). An optimisingfunction for adaptive ships autopilot. Fifth Ship Control Sympo-sium, Bethesda. Vol. 3.

4. Clarke, D, (1980). Development of a cost function for autopi-lot design, Ship steering and Automatic Control, Genoa. pp. 59-77.

5. Katebi, MR, and Byrne, JC, (1988). LQG adaptive shipautopilot, Institute of Measurement and Control Transactions,

Vol.10, No.4, pp 187-197.

6. Amerongen, JV, and Udink Ten Cate, AJ, (1975). Modelreference adaptive autopilots for ships, Automatica, Vol.11, pp. 441-449.

7. Mort, N, (1983). Autopilot design for surface ship steeringusing self-tuning controller algorithms. PhD Thesis, University ofSheffield, UK.

8. Grimble, MJ, Zhang, Y, and Katebi, MR, (1993).H-basedautopilot design. 10th Ship Control Systems Symposium, Ottawa.pp. 2.51-2.56.

9. Amerongen, JV, Naute Lenke, HR, and Veen der Van, JCT,(1977).An autopilot for ships designed by with fuzzy sets. Proc. IFACConference on Digital Computer Applications to Process Con-trol. The Hague. pp 479-487.

10. Sutton, R, (1987). Fuzzy set models of the helmsman steeringa ship in course-keeping and course-changing modes. PhD thesis,University of Wales Institute of Science and Technology.

11. Sutton, R, and Jess, IM, (1991).A design study of a self-organising fuzzy autopilot for ship control. Proceedings I, Institutionof Mechanical Engineers. 205, pp 35-47.

12.Polkinhorne, MN, Roberts, GN, Burns, RS, and Winwood,D, (1995). The implementation of fixed rulebase fuzzy logic to thecontrol of small surface ships. Control Engineering Practice, 3 (3),pp 321-328.

13.Polkinhorne, MN, Roberts, GN, and Burns, RS, (1997a).Consideration of performance assessment criteria required for a self-organising fuzzy-logic autopilot. Proc. 11th. Ship Control SystemsSymposium:, Southampton. Vol.1. pp. 151-159.

14.Polkinhorne, MN, Roberts, GN, and Burns, RS, (1997b).Intelligent ship control with online learning ability. Computing andControl Engineering Journal, 8 (5), pp 196-200.

15.Vukic, Z, Omerdic, E, and Kuljaca, LJ, (1997). FuzzyAutopilot for Ships Experiencing Shallow Water Effect in Maneuvering,4th IFAC (International Federation of Automatic Control) Con-

ference on Maneuvering and Control of Marine Craft, 10-12September, Brijuni, Croatia.16.Vukic, Z, Omerdic, E, and Kuljaca, LJ, (1998). Improved

Fuzzy Autopilot for Track-Keeping. IFAC Conference CAMS98,Fukuoka, Japan, 27-30 October 1998.

17.Fossen, TI, (1994). Guidance and Control of Ocean Vehicles,John Wiley&Sons, Chichester.

18.Omerdic, E, (2001). Reconfigurable control system for shiptrack-keeping. Master Thesis, University of Zagreb, Faculty ofElectrical Engineering and Computing, Croatia.

19.Chislett, S, and Strm-Tejsen, J, (1965). Planar MotionMechanism Tests and Full-Scale Steering and Manoeuvring Predic-tions for a Mariner Class Vessel, Hydro and aerodynamics Labora-tory, Lyngby, Denmark, Report No. Hy-6, April 1965.

20.Amerongen, JV, (1979). An adaptive autopilot for track-keeping. Ship Operation Automation, III. Proceedings of the 3thIFIP/IFAC Symp., Tokyo, pp. 105-114.

21 Pierson, JP, and Moskowitz, L. 1964.A proposed spectralform for fully-developed wind seas based on the Similarity Theory of SAKitaigorodskii. Journal of Geophysical Research, Vol 69 No 24.

22.Amerongen, JV, (1980). Model Reference Adaptive ControlApplied to Steering of Ships. Methods and Applications in AdaptiveControl, Proceedings of an Int. Symp., Bochum, Germany, March20-21, 1980, pp. 199-208.

23. Jang, J-SR, Sun, C-T, and Mizutani, E, (1997). Neuro-Fuzzyand Soft Computing: A Computational Approach to Learning and MachineIntelligence, Prentice Hall, Upper Saddle River, NJ 07458.


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NOMENCLATURE

L Loa,Length Overall DB Switch on point (steering mechanism)

Lpp Length between perpendiculars H Hysteresis width (steering mechanism)

K Gain in the telemotor-loop (steering

B Maximum beam mechanism)T Design draft PB Limit point in the amplifier-loop (steering

mechanism)

Design displacement N Limit value in the amplifier-loop (steeringmechanism)

u0 Design speed h zero-mean white noise processn Natural frequency of the Notch filter e Encounter frequency

Relative damping factor of the Notch Angle between the heading and the directionfilter of the wave

g Acceleration of gravity Hs Significant wave height0 Modal frequency of the PM- U Total speed of ship

spectrum

Vc Average current speed c Direction of current

u vc c, The body-fixed components of 0 constant( 0 )current

d Desired heading Actual heading

r= Rate of change of heading d Distance between ship and desired pathdc1 Output of the fuzzy autopilot dc2 Output of the fuzzy autopilot (Offset)

(Course)

c Command rudder angle Actual rudder angle

Normalised distance derror

errordot

y

,

, Internal normalised variables of the fuzzyautopilot (Course)

X Y,( ) Ship co-ordinates obtained from X Yi i,( ) Way pointsGPS

Keta Gain sf Scaling factor0 Modal frequency of the PM-

spectrum Hs Significant wave height

FIGURES (a)

(b)

Fig 1: (a) Steering mechanism; (b) Block diagram

}


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(a)

(b)

Fig 2: (a) Control system for course-

keeping; (b) Internal structure of the

fuzzy autopilot

Fig 3: (a) Membership functions for inputs (error

and errordot) and output (y); (b) Control surface

of the 'Fuzzy autopilot (Course)'.

Fig 4: Control system for track-keeping


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(a) (b)

Fig 5: (a) Definition of the offset from the desired path d, (b) Comparison between course-keeping and track-keeping

(a) (b)

Fig 6: Different shapes of functions in F: (a) fixed Keta , (b) fixed sf

Fig 7: Course changing manoeuvre, performed by an

experienced helmsman


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Fig 8: Course-changing for desired heading 10(LHS) and 30(RHS): (1) without waves and filter,

(2) with waves, (3) with waves and filter


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Fig 9: Track-keeping: (a) without disturbances, (b) with waves, (c) with

waves and filter


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Fig 10: Track-keeping: (a) with currents, (b) with waves and currents, (c) with waves, filter and currents

A Fuzzy Track-keeping Autopilot For

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