711
1 INTRODUCTION
The route of a ship is planned roughly from some
startingpoint(x
0,y0)totheterminalpoint(xk,y k).Itis
usuallyspecifiedintermsofsocalledway‐pointsthat
are defined using Cartesian coordinates (x
i ,yi) for
i=1,..,k‐1 [8]. Usually the successive points of the
plannedroute are joint by straight‐lines, form a
desiredtrajectorytobecoveredbytheship.Inorder
tocompletethejourneyalongtheplannedrouteone
may approach the problem in different ways:
trajectorytracking andmaneuvering control(Skjet
ne
&Fossen2002).
Sometimes during the journey the need arises to
changeapartofassumedpaththensomefragments
of the trajectory require updating or further
refinement. At such instance the exact trajectory
trackingisnotalwaysjustified.Thisisbecauseitwill
resultinsuchcontroloftheship,ta
kingintoaccount
eitherthedynamicfactororthestaticfactoronly,that
seeks to minimize the deviation e(t) from the
designatedpathThis obviouslyleadsto lengthening
therouteandincreasingthecostofthe shipcontrol.
Therefore,amuchmoreflexibleapproachistorefrain
from the tra
jectory tracking, if for some reason the
ship was outside it, and to abandon the desire to
returntoitsclosestpoint,andinsteadtosteertowards
thenearestway‐point.Itinvolvestheconstructionof
such control system of the ship motion that could
covertheplanned route along it
s designatedpoints,
whichcanbereachedeitheralongastraightlineora
curve of thedesignatedradius. In this approachthe
way‐pointsarepartofthe plannedroute buthavea
higher priority than the points situated in between,
theonescomplementingtheaggregateofpointsofthe
assignedroute.
The proposed method of tra
jectory planning
together with system proper to control nonlinear
processes provides maneuvers that the ship will be
abletoperformwithminordeviations.
Thiscanbeof
great importance for optimizing the desired path
especially in restricted sea areas.
.The paper is
Control System of Training Ship Keeping the Desired
Path Consisting of Straight-lines and Circular Arcs
K.Kula&M.Tomera
GdyniaMaritimeUniversity,Gdynia,Poland
ABSTRACT:Presentedinthispaperisanew,expandedapproachtosettingtheplannedroutewithinrestricted
seaareaswheretherearepermanentobstaclesorothervessels,andthentrackingitbytheship.Inthisproject
the desired path is represented using a combination of straight‐lines and arcs. For this purpose a cascade
control system of the ship motion has been designed. The task of the outer loop controller to prepare the
referencesignalisexecutedbythereferencesignalgenerator.Thecontrolofangularvelocitytakesplaceinan
innerloopusingIMCapproach. Numericalsimulationstudiesofcontrolalgorithmsthathavebeendeveloped
forlaketrialsofthetrainingshiparealsocarriedouttodemonstratetheeffectivenessoftheproposedtracking
controlsystem.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 11
Number 4
December 2017
DOI:10.12716/1001.11.04.19
712
organized as follows. In Chapter 2 is presented an
overviewoftheproposedsystem.Thesubsection2.1
includesthedescriptionoftheplantthatisatraining
ship “Blue Lady”. 2.2 shows the most important
assumptions of the new system, including a new
method of creating a trajectory using
straight‐lines
and arcs of a set turning radius connecting
predetermined way‐points. The control system of a
shipmovingalongsuchtrajectory,whichmustmeet
the requirements of quality in a wide range of
operating conditions (changes in vessel speed, load
condition)isdescribedinsubsection2.3.Thenext
part
3 contains the results of simulation trials.
Determination of the planned route with the small
time horizon and directing the ship along the
trajectorydesignatedinanewwayhasbeentestedby
means of a computer simulation. The last section
summarizes the results and also contains some
suggestions regarding
the use of this method of
controlinmaritimetransport.
2 SYSTEMOVERVIEW
Itisassumedthattheshipcannotgetpastthenodal
points and has to track desired trajectory using
forward thrust T for speed control and a single
ruddertominimizethecross‐trackerror.
Thedesired
pathcanbegeneratedbyspecifyingthedesiredroute
way‐points. Each way‐point is defined using
Cartesiancoordinates(Fig.5).Forsurface vesselonly
two coordinates (x
i, yi) are used. The selected way‐
points are stored in a WP database and used for
generation of trajectory or a path for the moving
vesseltofollow.
In this work were prepared some algorithms to
control the ship motion along the desired path
consisting of straight‐lines and circular arcs.
The
structure of the considered system is presented in
Figure1.
Ship
Steering
Gear
Control system of
turning velocity
Reference
signal generator
r
+
-
-
+
x
y
r
ref
d
Figure1.Schemaofthecontrolsystemoftheshipmotion.
Itresemblesacascadecontrolsysteminwhichthe
referencesignalgeneratoractsasamastercontroller
.
Thusthereisanadditionalloopforthecontrolofthe
turning rate whose function is keeping the desired
angular speed of the ship. During the course
maneuver changes the surge and sway velocity,
heelinganddriftangle,whichhaveaverysignificant
impactonthedynamicpropertiesofthe
ship.
2.1 Descriptionoftheplant
The plant is a small training shipʺBlue Ladyʺ,
belonging to the Foundation for Safety Navigation
andEnvironmentalProtectioninIława thatprovides
training for masters and merchant navy officers to
practice and progress their skills through trial
manoeuvres in a safe
environment. It has been
inspected very carefully with reference to testing of
the allocation system of the thrusters. The ship is
madein1:24scalefromtheoriginalmodelandfloats
on a small lake Silm, where the training center is
located(Fig.2).
Figure2.Trainingship“BlueLady”ontheSilmLake.
BlueLadyisequippedwithasetofthrusterswith
electricmotorspoweredbyrechargeablecells.Ithasa
double control stand for traffic control which is
locatedatthestern(Fig.3.).
Figure3.Longitudinalsectionof„BlueLady”.
Table1.Theprincipalparticularsoftankeranditsmodel‐
thetrainingship[12]
_______________________________________________
ship model
_______________________________________________
Lengthoverall LOA[m] 330.65 13.75
LengthL
pp[m] 324.00 13.50
Breadth[m] 47.00 2.38
MaxDisplacement T[m] 20.60 0.86
DraughtΔ[T] 315000 22.83
MaximumSpeedV[m/s] 7.82 1.59
_______________________________________________
Themathematicalmodeloftheobjectincludingall
types of thrusters installed on it, such as tubular
rudders, Voight‐Schneider thrusters, was presented
byGierusz&Tomera(2006).
2.2 ReferenceSignalGenerator(RSB)
InRSBisgeneratedareferencesignalfortheturning
rate. The objective of this device is to
designate the
desiredcourseoftheshiporasetturningradius.The
blockdiagramofthesetpointdeviceispresentedin
Figure 4. Control of the ship motion along the
straight‐lines and along the arc takes place through
different channels, so it requires switching between
them.
713
The signal of the set turning rate is determined
automaticallyonthebasisofthemeasuredvariables
of the state vector such as course, surge and sway
velocity, taking into account the parameters of a
specified maneuver which have been calculated in
ReferenceSignalBuilder(RSB).Theleadingsignalis
a
desired path that can be generated using a route
managementsystem.Thisroutecanbeperformedina
modeoffixedsetcourseorusingaline‐of‐sight(LOS)
guidance technique (McGookin & Murray‐Smith
2006).Certainpartsoftheroughlydesignedpathmay
beplannedentirelydifferently
afterenlargement.
Figure4.BlockschemaofReferenceSignalGenerator.
2.2.1 Pathgenerationusingstraight‐linesandcircular
arcs
Afterroughlyplanningaseavoyageitcanbeused
tochange, addorupdatein moredetail newnodes.
These adjustments may be introduced to regard to
changingweather conditionsforcollisionavoidance,
oroftheoccurrenceofdeviations fromthis
route or
simplybecause oftheneed toprovide detailsofthe
moreprecisemaneuvers.
Theoperatoronthebasisoftheelectronicmap,by
guidingthecursortothepoint,givesithigherpriority
among the points of representation of the planned
route. Such a point, in contrast to
the rough route
way‐points or 3D‐Decision Support System for
Navigators(Łebkowski,2015)shouldnotbeomitted.
Additionally,theoperatordefinesthewayofarriving
at the next set point and selects the algorithm to
determine the parameters of this maneuver. RSB on
the basis of the data uploaded
into the coordinate
system of way‐points pinned (i,x,y,f,s) (i‐point
number, x, y‐the coordinates in Cartesian
coordinates, f‐flag‐specifying the selected operating
mode, s‐ sagitta) and the measured signals such as
speed, the shipʹs course and previously declared
constantvalues
suchasa route ofovertakingwhich
can differ for different maneuvers calculates the
parametersoftheplannedmaneuvers.Ontheirbasis
the Ship Path Generator (SPG) displays a planned
routeon thebackgroundofthemap ofthisbody of
waterwhichallowstheoperatortoassessifthegiven
partoftheroutewasplannedwell.
The proposed system of ship control in the sea
journey is meant to operate in 4 working modes of
steering:
byaspecifiedfixedcourse
towardsaspecifiedpointalongthestraightline
towardsaspecifiedpointalongaspecifiedarc
along an arc with a limited turning radius with
embarkingontoaspecifiedcourse
One of above non mentioned working modes is
capableofensuringthe
movement oftheshipalong
an arc at a specified constant angular velocity. This
maneuver with its advantages, was presented in
(Kula2016).
The course‐keeping is usually situational in its
character and often stems from the spontaneous
pursuit of the visible object. However, if the ship
deviates from the
set route, for example due to the
impact of the sea current, and maintains a specified
course, then, before its correction comes into effect,
the distance to be covered by the ship will be
unnecessarily lengthened. Such a delay in the case
presentedabove,thecaseofdirectingtheshipto
the
next way‐point, can be avoided when the shipʹs
specified course towards the next way‐point will be
determinedonanongoingbasisasareferencecourse
refvaryingdependingonthepositionofthecenterof
gravityofthevesselinrelationtothenextway‐point.
Figure5.Cartesiancoordinatesystem.
Letusassumethatthecenterofgravityinafixed
coordinates system has the coordinates G(x,y,z) and
theoffsetfromthenextway‐pointisatthemomentt
in the meridian line
)()( txxtx
ii
and in the
parallel line
)()( tyyty
ii
. Then the reference
coursecanbedeterminedfromtherelationship:
180
( ) 180
i
ref
i
y
tarctgn
x
[deg] (1)
where:
x,y–coordinatesofthecenterofgravity oftheship
x
k+1 yk+1 – specified coordinates for the successive
turningpoint
–n=0ifx
i>0andyi>0,
–n=1ifx
i<0,
–n=2ifx
i>0andyi<0
The third of these operating modes, that is the
movementoftheshipinanarcwhichisa fragmentof
acircle,requiresamoredetaileddiscussion.Itcanbe
anelementoftheroughlyplannedrouteoftheship,
but it attains greater importance at the stage
of
refinement e.g. when planning the maneuver of
avoidingpermanentobstaclesoravoidingacollision
with other vessels (Lisowski & Lazarowska, 2013).
Preparation for its implementation requires
determinationof
the coordinates of the planned begin of the turn
wp
i(xi,yi)andtheendpointofthemaneuveratthe
exitfromanarc
thecourseangle
i+2onthenextstraight‐linesector
with wp
i+1 on wpi+2 according to (6),taking into
accountthatiincreasesby1
714
the angle , that is half of the so‐called central
angle corresponding to the change of the course
angleby
from
iinto
i+2
and the selection of a flag f denoting the mode of
moving between the setpoints (if f=0 the choice of
straight line, f=±1 the choice of circle arc, where the
negative sign means the change of the direction of
calculated rotation). Preparing amaneuveralong an
arc can be
made at the pass from one straight‐line
sector to a next straight‐line sector, to a turn of a
differentradiusorofadifferentspindirection.Other
kindofmaneuverisacrossfromaturnalonganarc
toaturnalongadifferentarc.
Thetaskof
RSGistodeterminetheparametersof
theselectedmaneuverandtodraft,accordingtothe
results of calculations, a parameterized path which
will lead to successive set point. The algorithm of
determining the radius of the arc, along which the
shipistomovefrompointwp
iandfinishinginway‐
point wp
i+1 stems from the relationships shown in
Figure6.
Figure6.Turningalongthesetarctofixedway‐point.
c‐chord,s‐sagitta,R‐radius,M‐middleofthecircle,
l‐advancesection
Assume that the turn is made by an angle of no
morethan 180degrees. Thereisonlyone arcwhose
slope of tangents in points common to neighboring
straight lines will coincide with the slope of these
sections.Theradiusofthisarccanbedeterminedas
follows:
0.5 / cosRc
(2)
wherecmeansthechord,it’sthelengthofastraight
line joining the ends of a desired arc and can be
developedfromtheequation
22
cxy
(3)
where:
22
11
() ()
ii ii
xx x yy y
xi,yi,xi+1,yi+1‐coordinatesofthebeginwpiandtheend
oftheplannedturnwp
i+1respectively
The angle
, that is half of the so‐called central
anglecorrespondingtothechangeofthecourseangle
from
iinto
i+2canbecalculatedfromfollowing
equations:
2
2 180
0.5 ( 180 ) 0
0.5 0
o
i
o
(4)
If the course
i+2leading the vessel to the way‐
pointwp
i+1isnotpreviouslyknownthentheangle
willbeevaluatedfromfollowingexpressions
i1
ii
90
o
(5)
where:
i
i+1isthecourseanglefromwpitowpi+1
Figure6.Turningalongtwoarcssequence
Bydeterminingthesequenceofmoreslightturns
itmaybemore convenienttogiveasagittas (Fig.6)
Thentheradiusofthearccanbecalculatedfromthe
expression:
0.5
R
sctg
(6)
After the rudder is turned a ship does not
immediately adopt a circular, due to the inertia
relatedtothemassofthevessel.Inordertoincrease
theaccuracyofpathkeepingitisnecessarytodefine
the point B constituting the beginning of the new
maneuver,the
rudderwillbedeflectedbyasetangle
whereastheshipwillstartturningwithitsbowtothe
insideoftheturn.
300 350 400 450
100
150
200
260
Y
[
m
]
[
m
]
l
X
X
350 400 450
100
150
200
260
X
[m]
X
Y
[m]
ab
Figure8. The routeof theship without (a) and with (b) a
shiftofthebeginningofthemaneuver.
Whenplanningamaneuver,alsoalongthedesired
arc, itshouldbe noted that the command of rudder
deflection must precede the way‐point by a certain
distancel. Itdependson theinertia of theship. The
715
control system estimates the length of this route
aheadofthemaneuverbeginlbasedontheformula
() ( )lutTu
(7)
where T
‐ the resultant time constant of the Nomoto
modelT=T
1+T2‐T3 thatdependsontheshipvelocity
andrudderdeflection.
ThecoordinatesofthepointofstartingturnB(x’
i,
y’
i) that goes beyond the way‐point wpi can be
estmatedas
x’
i=xi+l
.
cos
iy’i=yi+l
.
sin
i (8)
where:
i–coursetowpi
In Figures 8a,b are illustrated two maneuvers of
theshipthatwereplannedfromwp
i(100,400)towpi+1
(260,400). During the first one, the command of the
rudderwasgivenwhentheshipreachedwp
iandthe
otheronebylmetersearlier(l=11.9m),thatallowed
the vessel in absence of disturbances to pass the
plannedtrajectoryalongthearcofacirclewithradius
R=80m.Thetransitiontothenextway‐pointoccurs
whenoneofthefollowingconditions
ismet
2
() 2
o
i
t
or
22
t
x
yr
(9)
wherer
t‐theradiusofthecirclewithcenterinwpi+1
representingacceptabledeviationfromroutenode
2.3 Thecontrolsystemofturningrate
Mostoftheautohelmsystemsaremainlyformulated
to follow a desired course under constant speed
settings.Thisisduetothefactthateveryvesselisa
highly nonlinear object and its dynamic varies with
the
changeofthelongitudinalvelocity.Thereforewe
can use a control systems designed to control
nonlinearobjects,suchasslidingmodecontrol(SMC)
(Faqng & Luo, 2007), predictive control (Velasco &
Lopez 2000), fuzzy control (Yang & Ren, 2003).
Althoughtheproposedcontrolsystemmustperform
the task of course‐
keeping and control of the ship
motion along a predetermined arc, the basis for the
executionofmaneuvering,mentionedintheprevious
chapter is the control system of angular velocity,
which uses the IMC structure (Morari & Zafiriou
1998).TheadvantagesofIMCtocontrolthemotionof
the ship have
been presented in (Tzeng 1999, Kula
2015).Thediagramofthecontrolsystemisshownin
Figure6.
PROCESS
Gp
r (s)
Model
M(s)
IMC Controller
+
-
+
d(s)
+
d1(s)
+
+
+
+
O-L Controller
Goc(s)
ref
r(s)
Figure9.StructureofInternalModelControlIMC.
Thestartingpointforthesynthesisofthiscontrol
system is to design a controller of ship angular
velocity G
oc (s) having to work in an open‐loop
system. Let us assume that the dynamics of the
linearizedobjectis presented inthe form of transfer
functionG
p(s).Then,thetransferfunctionofanopen‐
loopsystemcanbeexpressedas:
()
() ()
()
oc p
ref
rs
GsGs
rs
(10)
The controller which should ensure the perfect
control in this system should have transfer function
equaltotheinverseoftheobject
1
() ()
()
oc inv
p
Gs G s
Gs
(11)
To make this controller feasible, the transfer
functionG
oc(s)shouldbeproper.Forthisreason,the
transferfunctionoftheobjectcannotcontainzerosin
therightplainandpotentialdelaysmustbeomitted
intheinversemodel.Itisalsonecessarytoaddtothe
formingfilterwiththetransferfunctionF(s).Thenit
willhave
thefollowingform
)()()( sMsFsG
invoc
(12)
where
M
inv(s)isinversemodeloftheprocessand
F(s)–thetransferfunctionofthefilter
n
f
sTsF
)1()(
(13)
n‐ integer number, can be obtained as a difference
betweentheorderofthenumeratorandtheorderof
thedenominatoroftheinversemodel
Therefore if we managed to get compliance
between the plantandthe model, than according to
(12)wecouldachieveinthesystema
setvaluewith
the speed, which can be shaped using the time
constant of the transfer function of the filter T
f. In
generalIMCisanopen‐loopcontrolsysteminwhich
the input signal is corrected according to the
differencebetweentheresponseoftheplantandthe
model
() ()
()
()
()1 ()() ()()
poc
ref oc p oc
GsG s
rs
Gs
r s MsGs GsGs
(14)
It can be seen (14) that in the absence of
uncertainties and plant modeling errors, the control
system is working as a open‐loop system. The error
signalisabletoadjustthesetpointinsuchawaythat
thevalue,adjustableinthesteadystatewasequalto
thedesiredvalue,evenwhenthemodeldiffers from
theobject.Theperformanceofthecontrolsystemwill
dependontheaccuracyofthemodel
,
The signal of mistuning of the model and the
objectmaybetheresultofinfluenceofdisturbances,
model uncertainty or model incorrectness. It should
be noted at this point that such approach as IMC
cause that the arbitrary determination of the
parameterT
fmaylimitthesystemʹsabilitytousethe
716
full power of actuators. However, it is extremely
useful in implementation of the harmonious control
ofnonlinearsystems.
2.3.1 Nonlinearmodeloftheship
Themotionofashipcanbedescribedbyusingsix
nonlinear differential equations. Hence, ship
maneuveringistreatedasahorizontalpla ne motion
and only
the surge, sway and yaw modes are
considered.
The following approximations (Saari & Djemai
2012)aresetup:
2
00 ( )
0
0
G
G
Gzz G
muXmvrxr
mmx v Y mur
mx I r N mx ur
r
(15)
wheremisthemassoftheship,I
zzistheinertiaalong
thezaxis,andx
Gisthexco‐ordinateofthecenterof
gravity.
X, Yand N denotethehydrodynamicforces and
the momentum. They result from the movement of
theshiponthesurfaceanddependonspeed,weight
and a profile of the hull and also on the effect of
waves.
Basedon(15)afterlinearizationaroundaselected
point of work and after elimination of the sway
velocity we have a following simplified linear
differentialequation
3
1 2 12 12
11 1
() ( ) () [ () ()]
k
rt rt r T t t
T T TT TT
(16)
wheretimeconstantsT
1,T2,T3andgainkdependon
derivatives of the hydrodynamic forces and
momentums with respect to the sway and surge
velocityandyawrater.
However, the change of longitudinal and lateral
velocities during the maneuver leads to changes in
the dynamics of the ship and thus increases the
incorrectnessof
thelinearmodel.
Topreventthis,intheproposedcontrolstructure
such a model was introduced which parameters
dependingonshaftvelocitynandtherudderangle
.
Thiswillensurebetterqualityofthemodelinawider
rangeofchangesofthestatevariables ofasystem.
The equation (16) after rearranging to the new
form
3
12
12 12
(, )
() [ ( , ) () ()]
(, )
11 1
()()
(, ) (, ) (, )
kn
rt T n t t
TT n
rt r
Tn T n TT n
(17)
canbedirectlyusedtocreateanonlinearmodelofthe
ship.
2.3.2 Nonlinearinversemodeloftheship
IMC controller includes in its structure an inverse
modeloftheplant.Thegreateristheaccuracyofthe
model and the inverse model, the better control
performancecanbe
achievedin this system.Forthe
purpose of steering of the ship it was prepared a
linear and nonlinear training model. Both models
have been created based on the Nomoto model
(Nomoto1981).Assumingconstantspeedoftheship,
thetransferfunctionofthemodelisequalto
3
12
(1 )
()
()
() ( 1)( 1)
kTs
rs
Ms
sTsTs
(18)
Rearranging(19)ittakestheform
312 12 1 0
22
1 2 12 12 1 0
//
()
()/1/
kT s T T k T T b s b
Ms
s
sT T TT TT s as a
(19)
Determination of the parameters of the transfer
functionenablestopredictofresponseoftheshipto
deflection of the ship rudder at a constant speed.
Then the transfer function of the controller of the
open‐loop system (12) using a filter (13) of the first
order(n=1)
willbeequal
12
3
(1)( 1)
()
(1 )( 1)
oc
f
Ts T s
Gs
kTsTs
(21)
The use of a linear model for the control of
nonlinearplantisacceptable,however,toimprovethe
qualityofthecontrolitcouldbeincludeda nonlinear
modelinthestructureoftheIMCcontroller,causing
the better reflection of the behavior of the actual
controlledobjectthan
asimplelinearmodel.Theuse
of such models of the ship have been presented in
(Kula2015).
Asimplifiednonlinearmodelofthetrainingship
ʺBlue Ladyʺ was constructed on the basis of the
transfer function model but its parameters, i.e. the
steady state gain k and time constants
T1, T2, T3 are
dependent on the deflection of the rudder and
indirectoftheshipvelocity.
Figure10.Schemaofnonlinearinversemodeloftheplant.
The simplified ship model was created for only
onefullloadingcondition.Theblockdiagramofthe
inversemodelisshowninFigure9.Inasimilarway
an inverse model is constructed, except that it has
beenadditionallyextendedbytakingintoaccountthe
zerosinfeedforward..Stepresponsesof
theplantand
717
modelr(t)=f(,n)fordifferentva luesofrudderangle
andpropellerrotationarepresentedinFigures11,12.
0 200 400
-0.05
0
0.1
0.2
0.3
0.4
r
[ rad/s ]
[ s ]
t
Figure11.Stepresponsesofshipandmodel,=12
o
,n=240
0 200 400 600
-0.05
0
0,1
0,2
0,3
0,4
r
t
Figure12.Stepresponsesofshipandmodel,
=8
o
,n=180ship,‐‐‐‐model
The nonlinear functions T1=f1(
,n), T2= f2(
,n), T3=
f
3(
,n), k= f4(
,n) are prepared in form of low order
polynomial of rudder angle. The coefficients of this
polynomialarecalculatedusingtheLSMethod.
3 SIMULATIONRESULTS
The test of presented control system of the ship
motionwasperformedintwostages.Inthefirststep,
we have defined in a proposed
form a desired rout
whichthe training shipwas supposedto sailon the
LakeSilmTwovariantsoftheroutehavebeentested
using Matlab/Simulink/C++. For the simulation we
assumed that the ship was fully loaded and for
control used only main rudder. The specified
propellerrevolutionnwas
equalto200rpm.
3.1 Example1
The ship from the starting point wp
0(380,160) was
going with the course
=170
0
and after 400 s it
changedthecourseintheLOSmodewiththeaverage
value
1=143
0
to way‐point wp1(90,320). It was
adopted radius tolerance r
t=2 m, so reaching wp1
endedatthepoint(92,318.2).
InthepointBthatislocatedfromaway‐pointata
distancelstartsthepath‐keepingalongthearcwhich
radiusisuptodatecalculatingonthebasisof(2).In
thisphaseuntiltheship adoptsa circularmotionin
predetermined direction the reaction of the rudder
deflectionispoor.Forfirstmomentatthebeginning
ofthe turnbecausex=39.6, y=110.6m,
1‐>2=70.3
0
,
ß= 72.7
0
, =17.3
0
and c= 117.5 m the radius will be
equal to 61.5 m. After reaching the way‐point wp
2
(130,430),theturningradiuswillbechangedtofixed
valueequal to90 m.The waythatthe shiptraveled
duringthismaneuver andtheheading, isplottedin
Figure 13 on the contour of the lake, where the
trainingofnavigatorstakesplace.
Figure13. The position and heading trace of the ship
maneuver.
Other time histories of surge velocity, drift and
rudderanglemeasuredduringthetestarepresented
inFigure14.
200 600 1000 1400 1800
0
0.4
0.8
200 600 1000 1400 1800
-10
0
10
20
0 200 400 600 800 1000 1200 1400 1600 1800
-10
0
10
u
t
[deg]
t
t
[
m/s
]
[deg]
Figure14.Timehistoriesofsurgevelosityu(t),drift
ß
(t)and
rudderangle
(t)duringthetestedmaneuver.
3.2 Example2
The starting point was situated in wp
0(100,420) and
thecourseinfirststraight‐linesection
=20.After500
s the training ship reached the point (286,493), and
thentheautopilotcontrolledintheLOSmodeinwp
i
(610,670),whichatfirstmeantthechangeofthegiven
courseat
i=28.6.Fromthispointtheshipreachedon
thearchthenextway‐point wp
i+2(720,515), andthen
sailedfurtherat(550,420).Thecoursewascalculated
as
i+2=192
0
.
2
=
i+2–
i–180
0
=192
0
–29
0
–180
0
=–17
0
TheforecastedplaceofstartingoftheturnBhad
coordinates
664'599.3'
11
ii
yx
. The way that
the ship traveled during this maneuver and the
heading,hasbeenmarkedinFigure15.
718
Figure15.Thepositionandheadingtrace
3.3 Maneuvering topreventcollisionsatsea
Modificationoftheroutemayalsoberequiredincase
of meeting other ships. Figure 16 shows the picture
taken by the anti‐collision system from the radar
screenintheseagoingshiptogetherwithahinthow
to avoid collisions (Mohamed‐Seghir,2016). After
scaling for the tested model, the passage of this
sectionoftheshiproutewasplannedonthebasisof
projection after the next steps of monitoring of the
anti‐collisionsystem.Aftersignaledcollisionsituation
andgettingsomehintsfromthesystemtoturntothe
right, it was
changed a given course with the
minimumrequiredvalue10
o
.
Figure15. Comparision between game trajectory of own
shipinasituationofpassing3encounteredshipsfromanti‐
collision system and the path planned using proposed
method
Afteritwasreachedthenextway‐pointwp1was
put the first cross and then it was determined a
maneuver withacurve 1 with an access tothenew
course 350
o
. After reaching wp1 the course was
maintained,tosignalthecrewoftheship3,thatitis
respecteditsrightofpriorityandaftergoing30mit
was started the maneuver at wp
2 with coordinates
(895,‐8).
Indeed,duringthesemaneuversresultingfromthe
necessity of overtaking ships which are met on the
route it was not required a large deflection of the
rudder, after planned new trajectory of passage, the
extensionoftheroutewas10%shorterandadropof
speed
was16%lessthanusingaoriginalvariant
a)b)
Figure16. Print screen during the visualization of
conductedmaneuvers.
Theeffectiveness ofthe presentedroute planning
method also depends on the interface between the
operator and the computational system. The next
way‐points the crew can apply to the e‐map from
wheretheyarescannedtotheway‐pointsdatabase.
In Figures 16a,b are presented print screens of
the
visualizationofmaneuveringandspecifyingofway‐
pointonthee‐map.
Theresultsobtainedbyacomputersimulationof
considered training ship compared with similar
maneuvers carried out by PID controller show that
the overshoot can be eliminated. In addition the
settlingtimecanbeshortened.Itis
worthremarkthat
by adjustingthe turn radius accordingtotheneeds,
the mean drift angle is smaller, which results to a
lowerdecreaseinthesurgevelocity.
4 SUMMARY
Themost importantcontribution ofthis study isthe
developmentofthenovelmethodthatallowsforfast
correctioninslight
advanceofpre‐definedrouteand
thanks a control system suitable for steering of a
nonlinear plants for relatively precise keeping such
determined path. The required conditions for the
control system meets nonlinear IMC controller that
wasdesignedforthistarget.Theconceptofextension
the Internal Model Control to
a nonlinear form
allowed to obtain a more accuracy model what also
improved the control performance, which is
expressedbyreducingtheovershootandsettlingtime
forawiderangeofoperatingpoints.Inthisstudythe
parametric model of the process was created by
means of identification based of an
open‐loop step
response by different rudder angle thereby the
different ship velocity. Introducing into desired
trajectoryofdefinedcirculararcsmakesitpossibleto
avoid oversized rudder deflection. Long turns have
some additionaladvantages. They may considerably
decrease the hydrodynamic resistance which occurs
during the maneuver and thus reduce
the velocity
decreases that result from it. realize. As a result,
deviations occurring the path keeping can be
significantly reduced. This can make it easier to
optimize the set route that is required to pass other
surface vessels. Simulation results indicate that the
considered system can be a useful tool for
quite
preciseavoidingofobstaclesontherouteoftheship.
Themethodofrouteplanningpresentedinthispaper
creates wider possibilities for implementation by
maritime collisions avoidance.
It can also be very
useful to carry out planned search operation during
SAR actions where thesearch area must be devised
719
and patrolled with great accuracy (L.Kasyk &
K.Pleskacz, 2015). The results of research justify
conducting further trials on the lake and extending
thecontrolbyotherthrusters,especiallyinthecontext
toreducedriftwhenmakingturnsalongcirculararcs
withasmallradius.
REFERENCES
Fang,M.C.&Luo,J.H. 2007.Onthetrackkeepingandroll
reduction of theship inrandom waves using different
sliding mode controllers. Ocean Engineering 34:479‐
488.14(5):511‐524.
Fossen, T.I. 2002. Marine Control Systems:Guidance,
Navigation andControl of Ships,Rigs and Underwater
Vehicles.MarineCybernetics.
Gierusz, W. & Tomera,
M. 2006. Logic thrust allocation
applied to multivariable control of the training ship.
ControlEngineeringPractice
Källström, C.G. 2000. Autopilot and track‐keeping
algorithms for high‐speed craft. Control Engineering
Practice8:185‐190.
Kasyk, L. & Pleskacz, K. 2015. An adaptation of an
algorithm of search and rescue operation
to ship
manoeuvrability.TransNav9(2):265‐268.
Kula,K.S.2015.AutopilotUsingtheNonlinearInverseShip
Model.MarineNavigationandSafetyofSeaTransportation
WeintritA.,ActivitiesinNavigation:101‐111.
Kula, K.S. 2016 . Heading Control System with limited
Turning Radius based on IMC Structure.IEEE
Conference: 21st
International Conference on Methods and
ModelsinAutomationandRobotics(MMAR):134‐139.
Lisowski, J., Lazarowska, A. 2013. The radar data
transmissiontocomputersupportsystemofshipsafety,
Solid State Phenomena Trans Tech Publications,
SwitzerlandVol.196(2013)pp95‐101,(2013).
doi:10.4028/www.scientific.net/SSP.196.95
Łebkowski, A. 2015. 3d Decision Support
System for
Navigators Using the Smartglasses Technology.
Technology.Information,Communication andEnvironment:
MarineNavigationAndSafety:117‐122.
McGookin,E.W.Murray‐Smith,D.J.Lin,Y. &Fossen,T.I.
2000.ShipSteeringControlSystemOptimisation,Using
GeneticAlgorithms.IFACJournalofControl,Engineering
Practise.CEP(8):429‐443.
Mohamed‐Seghir, M.
2016. Computational Intelligence
Method for Ship Trajectory Planning. 21 International
Conference On Methods And Models In Automation And
Robotics(MMAR):636‐640.
Morari,M.&Zafiriou,E.1998.Robustprocesscontrol,PRT
PrenticeHall,UpperSaddleRiver,NJ07458.
Nomoto,K.1981. On theCoupled Motion ofSteering
and
RollingofaHighSpeedContainerShip.NavalArchitect
ofOcean Engineering20J.S.N.A.,Japan,vol.150:pp73‐
83.
Saari,H.,Djemai,M.2012.Shipmoti oncontrolusingmulti‐
controllerstructure.OceanEngineering55:184‐190.
Skjetne,R.,FossenT.I.,KokotovicP.V.2004.RobustOutput
maneuvering for a class
of nonlinear systems.
Automatica40(3):373‐383.
Tzeng,C.‐Y.1999.AnInternalModelControlApproachto
the Design of Yaw‐Rate‐Control Ship‐Steering
Autopilot.IEEE Journal of Oceanic Engineering 24(4) :
507‐513.
Tzeng, C.Y. 2000. On the design and analysis of ship
stabilizing fin controller.
Journal of Marine Science and
Technology8No.2:117‐124.
Velasco, F.J. & Lopez, E. 2000. Predictive Control of Ship
Steering Autopilots. 2nd. International Congress on
MaritimeTechnologicalInnovationsandResearch,Spain:89‐
98.
Velasco, F.J. Rueda, T.M. Lopez, E. & Moyano, E. 2002.
Marine course‐changing manoeuvre :
a comparative
study of control algorithms. Proceedings of 2002
InternationalConferenceonControlApplications:1064‐1069.
Y.S. Yang, Y.S. & J.S. Ren, 2003. Adaptive Fuzzy Robust
Tracking Controller Design via Small Gain Approach
and Its Application, IEEE Transactions on Fuzzy
Systems:783‐795.
