405
1 INTRODUCTION
The first known PID controller, referred to as the
threetermcontroller,wasusedasanautopilotona
ship.The resultsof thework byMinorski (1922)on
the autopilot making use of the three‐function
mechanism of automatic control were applied in
other branches of economy, and at present these
controllerscontributeinab
out90%toatotalnumber
of controllers used in the industry. Since 1928
Minorski also worked upon control of active
stabilizationtanksusedforrollmotiondamping.His
works based mostly on intuition. It was Chadwick
(1955) who was the first to make use the tra
nsfer
function in designing control systems for ship
stabilization. The state of knowledge on the control
theory in the last century’s sixties was used by
Webster(1967)asthebasisforanalyzingtheproblem
ofactiverollmotionstabilization.
Nowadays some time delay is observed in
introducing new control techniques on ships. New
methods are used, in general, only when they have
undergonepositiveverifica
tionininlandconditions.
This tendency is quite understandable. In the past,
the autopilot only replaced a human operator in
tiresomeworkorientedonkeepingthecourseinthe
environmentinwhichpreservinggoodconcentration
for a long ti
me was extremely difficult. Possible
incorrect operation of the autopilot could be easily
detectedandcorrectedbythehumanwheelman.On
the contrary, the new control systems are mainly
expectedtoworkreliably,withhighefficiencybeing
slightlylessimportant.Atpresent,incaseofafailure
ofthecontrolsystem,theoperationofthema
jorityof
itscomponents cannotbesubstituted by the actions
performed by a human being. Moreover, obvious
difficulties in contacting the manufacturer’s service
centersandhighcostofservicingisareasonwhythe
solutions most preferred in marine applications are
those which have already underwent positive
verifica
tion for their high reliability and are trusted
bythecrew.Butthisdoesnotmeanstagnationinthe
activity of researchers in the field of marine
automatics. Like in case of the automatics (now
referred to as conventional) which had to find its
An Overview of Roll Stabilizers and Systems for Their
Control
K.S.Kula
GdyniaMaritimeUniversity,Poland
ABSTRACT:Shiprollmotioninwavescanbecharacterizedasastronglynon‐linearandmultivariabledynamic
processwhich is moreaffected by disturbances,in general,thanbythe maximal controllingparameter.The
articlepresentsmethodsofrollmotioncompensation,themajorityofwhichhavebeenusedonshipsforma
ny
years.Althoughtheyarenotcapableofreducingpermanentlytheerrortozero,theirpotentialhasstillnotbeen
usedtothefull.Theoperationalefficiencyofrollmotioncompensatorscanbeimprovedusingcontrolsystems.
Research activities are in progress to check the applicability of advanced control methods ma
king use of
moderncomputertechniques.Someofthemarementionedinthispaper.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 9
Number 3
September 2015
DOI:10.12716/1001.09.03.14
406
place next to manual control systems by separating
manual and automatic control modes, now the
devices improving the operation of the present
automatic systems can be disconnected, leaving the
control to the devices which have been positively
verified and are known to the operator. One of
marine automatics segments, although
not the most
importantoneisthestabilizationofshiprollmotion.
From among all oscillatory movements which the
shipdoesonaheavysea,therollmotionreachesthe
highest amplitudes and can make proper ship’s
operation much more difficult. Different types of
ships require different types of roll
stabilization
systems. On a cruise ship or ocean liner excessive
motionsinterferewiththerecreationalactivitiesand
comfort of passengers. They can affect the
effectiveness of the crew too. On Ro‐Ro ships for
instance many containers are stowed above deck
wheretheyaresubjectedtolargeaccelerationsdueto
the
rolling. Insome extremeconditions thelashings
canfailandcontainersmaybelostoverboard
The paper presents an overview of roll motion
stabilizers.Thefirstsection presentsa mathematical
model describing the ship movements, and the
simplifiedmodelconcerningtheoscillationsdoneby
theship along itslongitudinal axis.
Particulartypes
ofstabilizersaredescribedinthenextsections,with
attentionpaidtocontrolmethodswhichcanhelpto
improve their performance characteristics. The final
sectionpresentsthesummaryoftheoverview.
2 THEMATHEMATICALMODEL
The mathematical model of dynamic processes
facilitates their analysis and can be used for
preliminaryverificationofsystemsdesignedfortheir
control. At the same time the simplified model is a
useful and convenient tool in the synthesis of the
controlsystems.
The motion of a ship on moderate water can be
described using six nonlinear differential equations.
Forthedescriptionofthismathematical
modelthree
coordinate systems are needed, which are the
inertial‐, body‐ and horizontal body coordinate
system.
The coefficients in the above equations can be
determinedanalyticallyandthencorrectedinmodel
tests. In the process of introduction of ship control
systems to marine operation it is important for the
calculated
resultstobeverifiedinfullscaleseatrials.
The below presented model Hamamoto of 6 DOF
(2010)wasverifiedinturningcircleandzigzagtrials,
whichweredoneonmoderatesea.Therollmotionis
investigated using simplified models. The 4 DOF
surge‐sway‐yaw‐roll model was worked
out by
UmedaandHashimoto(2002).
Theexistingdifferencesareobviousastheyresult
from both model uncertainties and incorrectness,
whichisusuallytreatedratherlightly–themoreso
that the ship dynamics depends on the load
condition(cargo,fuelsandoils,water)andobtaining
identical conditions during regular operation
is
practically impossible. However, the correctness of
the mathematical model can be improved after sea
trials.Themethodofcorrectingthecoefficientsinthe
differential equations which describe the motion of
the ship on moderate sea in such a way that the
results of the sea trials are consistent with
the
simulationsdonewith theaidof theexistingmodel
were proposed by Casado and Ferreiro (2005). The
full model of the motion of a ship making use of
stabilization fins was developed by Fang and Luo
(2007).
()(()) ()()
() (1 )
ye xe ze
ze FK RF SF p
mu m X u m u m w
mwXXXTtR
(1)
( ) () ()
() ()
xe ye
FK e RF SF DF e
mu m um YY
YY Y Y
YYYY
(2)
() () () ()
() () ()
ze we e e
eFKeDFeSF
mw m w Z w Z Z
ZZZZmg
(3)
()()()()
()() ()
xx xx e xx xx e
H
FKe RFSFDFe
IJ IJ K
YYzK K K K
(4)
( )() ( )() ()
() () () ()
yy yy e xx xx e e
ewe FKeSFDFe
IJ IJ M
MMwMMM
(5)
22
( )() ( )()
()
(
)()
zz zz e xx xx e
DF e
H
FK e RF SF
IJ IJ N N
NN N N N
NNN N YY
YYxY N NN
(6)
where; m‐ship mass, I‐moment of inertia, X,Y,Z
external forces; K,M,N external moments to surge,
sway and heave, respectively; u,v,w – surge, sway
and heave velocities;
,,
roll, pitch and yaw
angles,R‐shipresistance,t
p‐thrustdeductionfactor.
The subscripts DF, FK, RF and SF represent the
Froude‐Krylov diffraction, the rudder and the
stabilizing forces,
H
x
– coordinate of the midship,
H
z
–coordinateofthepoint.
Theequationofthemainengine:
2( )
p
ppp F P
I
JnQQ
(7)
The energy passed by the waves to the ship is
distributed in a number of planes. As can be seen
from the through couplings, these movements
interact with each other. Their effect on the roll
motion mostly depends on the nature of the wave.
The roll motion can be
described using one
differentialequation.
407
2.1 1‐DOFEquation
The roll motion of the ship can be described
(Zborowski&Taylan)bytherelation:
()(,)()
x
x xx xx ext
IJ B GZ K
(8)
where: t‐ time,
roll angle,
‐ weight
displacement,(I
xx+Jxx)arethewatermassandadded
mass moments of inertia and B
xx is the damping
moment, which can be expressed in the linear
quadraticform:
3
3
(,) ,
LNL
BBBB
(9)
only in the linear form
,)(
eq
BB
with the
equivalentdampingcoefficient
3
3
(, ) ,
LNL
BBBB
(10)
where:
B
f–theskinfrictionaldampingcoefficient
B
e–theeddydampingcoefficient,
B
L–theliftdampingcoefficient
B
BK–thebilgekeeldampingcoefficient
B
Fin–thedampingcoefficientduetothepresenceof
fins
Itcanbesolvedusingaformula:
3
3
83
() ()
34
eq L NL A A
BB B B
(11)
where:ϕ
Aistherollamplitude.
GZ‐rightingarmisanonlinearfunctionoftheroll
angleandcanbeexpressedas:
35
13 5
GZ C C C
(12)
The coefficients C
1, C3 and C5 can be calculated
fromthestaticstabilitycurve
1
()dGZ
CGM
d
2
3
4
(3 )CAGM
2
5
6
3
(4 )CAGM
(13)
representsthevanishingangleofstability,A
φvisthe
areaundertheGZcurveuptothevanishingstability,
K
ext‐wave exciting moment, GM0‐metacentric
height
In the version simplified only to the Froude’‐
Krylow term (Cholodin & Shmyrev 1972), the
momentgeneratedbythesidewavecanbegivenby
therelation:
ext A m
Kt GZ t t
(14)
where:
A is the reduction coefficient taking into
accounttheeffectoftheshipdimensionswithrespect
to the wave length;α
m is the wave slope (wave
amplitude)
The course of the roll motion is affected by
various agents, including the equivalent damping
coefficient,the addedmasses rightingarm. Some of
them,suchas thoserelatedto theshipstructure for
instance, do not change, while the others, like load
conditions, mass
(including cargo) distribution, free
liquid surfaces, and most of all the nature of the
external excitations change in time. But of highest
importance is generating an additional stabilizing
moment.
3 ANTIROLLTANKS
Thefirsttypeofrollstabilizingtankwasbasedonthe
pioneering work of William Froude. In 1874
he
installed water chambers for the purpose of
achievingstabilizationagainstroll.
In 1877 the stability of a Victorian ironclad
battleship HMS Inflexible was questioned due to
addition of unconventional armor. In 1880 the ship
wasequippedwithwatertanksfordampingtheroll,
which turned out to be ineffective.
The next
stabilizingtankswereconstructedbyWatt(1883)as
free‐surface tanks. The improved version, so‐called
U‐tube,wasdesignedbyFrahm(1911).
These tanks belong to the class of stabilizers
bearing the name of the moving weights. They
played remarkable role in the development of
devices used for
roll motion damping. Most of all,
they presented in a natural way the physics of
stabilizingmomentgeneration.Liketheseeactingon
theshipandthetanksituatedinit,thetankactson
thewaterinsideit.
Generally,thesetankscanbedividedintopassive,
controlled–passive, and active
tanks. The passive
tanksincludefree‐surfacetanksandU‐tubes.
TheU‐tubetanks,whichtakethenameaftertheir
shape (Fig.1), are situated on both sides of the ship
andconnectedinthewaterline,whileintheairline
they are connected or not when the air pressure
is
compensated by the atmosphere. The U‐tube tank
hasthebestperformancewhenitsnaturalfrequency
isthesameasthenaturalfrequencyoftheshiproll
motion.Theresearch activities uponthesetanksare
orientedonensuringtheirgoodperformancewithin
awiderangeofexcitationfrequenciesThe
ideaofthe
useofpassive‐controlledfreesurfacetanksconsistin
the use of the relation between the period of water
flowinthetankandthedegreeofitsfilling.Thetank
has sensors installed on its bottom to measure the
pressure exerted on the bottom. Based on their
indications,the phase lag ofthe stabilizingmoment
withrespecttotheheeliscalculated,whichprovides
opportunitiesfortuningthetankinsuchawaythat
the maximal stabilizing moment is obtained.
Moreover,whenthenaturalfrequencyoftheshipis
known,thebestdampingcanbeobtainedwithin
the
rangeofmostvulnerablewavefrequencies.Optimal
tuning for the tank to generate the stabilizing
moment being in counter‐phase to the exciting
408
moment can be made possible with the aid of the
effective wave slope measured by the wave height
sensors.
3.1 Passivetanks
Aconfigurationofan U‐tubepassivetankisshown
inFigure1.Thetank consistsoftwo sidereservoirs
and a connecting duct of constant rectangular cross
section.
Figure1.Passivetanks
Todescriptionforapurelyrollmotionoftheship
with a passive tank can be the following simplified
linearequationused:
extxxxxxx
KcaCBJI ][)(
441
(15)
whereisthetankangledefinedinFigure1.
a
4
‐4
th
momentduetounitangleacceleration
c
4
roll moment applied by tank due to unit roll
displacement
drr
t
hhww
gh
2
2
(16)
Thepassivetanksdonotincreasehullresistance.
Theirefficiencydoesnotdependontheship’sspeed.
After some adaptation they can be used as anti
heeling tanks for example for ballasting the train
ferries.Theiroperationalcostsarelow.Ontheother
hand: they require remarkable space, thus
reducing
the space available for transport of cargo. The free
surfaceofthetankreducesthemetacentricheightof
theship.
Thepassivetankscanbetuned automatically.In
thosecasestheyarereferredtoaspassive‐controlled
tanks.Thisgroupincludespassive‐controlledU‐tube
tanks,tankswithenergyIn
phase1theshipreached
the maximal angle to recovery and free‐surfaces
tanks“Flume”.
The energy for water flow between the tanks is
delivered by the waves, while the control system
shapes the signal controlling the valves in time.
PairohandHuang(2007)formulatedaseriesofrules,
such as linear‐quadratic regulator (LQR), predictive
control and the dead beat predictive control, which
are valid when controlling these tanks. This last
controlsystemisanimprovedversionofthecontrol
of activated tanks, developed in the last century’s
eighties, inwhich the valves situated in the air line
were
closed in selected times. The mass difference
between two tanks which acted on the arm h=w/2
created a stabilizing moment. Opening of the valve
provokedfastwaterflowtotheoppositesideofthe
ship, whereit was “frozen” again inthe next cycle.
Thephasecycleofsuchtanks
isshowninFigure2.
Inphase1theshipreachedthemaximalangleto
portandstartstorighttostarboard.Atthispointthe
waterisflowingfromthestarboardsidetotheport
sideduetotheeffectofgravity.Insecondphasethe
water obtained the maximal
level in the port side
tank, the valves on the port side are closed by the
automatic control ( point A). The water is kept
blockedintheportsidetank,duetothelowpressure
createdintheupperpartofthetank,fromposition2
uptoposition
4wherethecontrolsignalisopening
thevalves(pointB)
Figure2. Phase cycle for roll periods longer than natural
periodofactivatedtanksINTERINGGmbH
3.2 Activetanks
Tanksinwhich thestabilizingmoment isgenerated
by forced action of the actuator which presses the
waterfromoneship’ssidetotheotherbearthename
ofactivetanks.Theperformanceofthepassivetanks
islimitedbytheirabilitytocreatethenaturalwater
flow
fromone ship’s side to the other. At the same
timetheactivetanksarecapableofgeneratinglarger
stabilizing moments from the same tank volumes.
Thecontrolprocessitselfrequiresalargeamountof
the delivered energy. The ability to pump large
volumesofwaterinashorttime
requiressufficiently
largepowersfortheactuators.
Figure3. Active tanks system (Source: www.hoppe‐
marine.com)
409
Theactive tankswere mainlyused bythe Navy,
wheretheeconomicaspectwasofminorimportance.
Based on the results of laboratory tests (Alarcin
2007a) carried out on small‐scale models, a fully
active system was installed on the American
destroyerUSSHamilton.Thesystemmadeuseofthe
pump in which the rotor had the blades with the
variable attack angle. The measurements performed
duringthetestsonstagnantwaterhaverevealedthat
theuseoftheactivetankmakesitpossibletoincline
USSHamiltonby18º.Thetestsalsorevealedthatthe
system has sufficient potential
to stabilize the
destroyerat open sea afterthe waves had rockedit
off to 30º from the perpendicular. Another
applicationofactivetankswasinstalledonaGerman
cruiser,whereaturbine‐drivenblowerprovidedthe
airintheductsobtaininginthiswaydifferentlevel
in the tanks (Moaleji
& Greig 2007). These same
authorsproposedintheirwork(2006)regulatingthe
pumpsusinganadaptiveinversecontroller.
3.3 Finstabilizers
So‐called active fins belong to the group of most
popularrollmotionstabilizers.Theyaresituatedon
two sides of the ship and are rotated in opposite
direction.
Likefor the rudderblade, when the water flows
roundthefinsthezonesofhighandlowpressureare
created on their surfaces, thus generating a force
perpendiculartothefinsurfaceS. Thisforcecanbe
divided into two components: the lift L directed
perpendiculartothe
horizonline
2
()
2
L
u
LC S
(17)
andthedrag
2
()
2
D
u
DC S
(18)
z
G
e
y
p
z
G
p
R
L
L
Figure4.Localisingactivefinsonshiphull
The increase of the lift is proportional to the fin
surface.However,thefinsurfacearea islimitednot
only for constructional reasons as it should not be
protrudingfromtheshipcontour,butalsobecauseof
the limitation of maximum stabilizing moment,
whichcannotcauseexcessiveheelangleof
theship
morethan5degrees.
Figure5.Finwithgear
Athigh shipspeeds and largerattack anglesthe
water flow separates from the fin surface. To avoid
this unfavourable phenomenon, the fins are
complemented by an additional flap which rotates
aroundapinsituatedattherearfinedge(Fig.6).Due
to this flap the maximum fin deflection can be
increased by some degrees, which provides
opportunities for obtaining a larger buoyancy force
fromthesamefinsurface.
p
V
p
Figure6.Sectionalfin
Theflaprotationmechanismiscoupledinanon‐
inertialwayviaagearwiththefinshankdrive.This
waytheflap inclinationangle isproportionalto the
mainfininclinationangle.
pprzp
K
(19)
where:
p – flap inclination angle, p – main fin
inclinationangleK
prz–finrotationanglegear
Thepresenceoftheflapincreasestheefficiencyof
theuseofthefinsurface,whichleadstotheincrease
oftheliftforce.
2
L
kL
CkC
(20)
k2–coefficientcalculatedfromthe Karafoliformula
(Cholodin&Shmyrev1972)
21
p
k
p
b
k
b
(21)
where:b
k–flapchord,b‐chordoftheentirefin
The ratio
p/p is usually equal to 1.5, while the
flap is approximately equal to one a quarter of the
mainfinwidth.Theattackangleofthewaterflowing
round the fin depends on the fin rotation angle
p
andthewaterflowdirection,whichistheresultantof
the ship speed, the rolling speed, and the heaving
velocityu.Finallytheformulaforthehydrodynamic
inclinationangleofthefintakestheform:
410
p
v
arctg arctg
uu
(22)
In the fin stabilization systems, the gyroscope
sensormeasurestherollvelocitysignalwhichisthen
passedtothePIDcontroller.Ifwetakeintoaccount
that the control input signal is heel angle then we
becameaPDD
2
controllawgivenby
2
() () () ()
pD
D
ut K t K t K t
(23)
Itisimportanttolimitthefindeflectionanglein
proportion to the ship speed, to avoid the
phenomenonof cavitation.Thepermissible angleof
the fins depends on so‐called fin ratio
F which
reflects the relationship between the length and its
width. The maximum fin deflection should not
exceed30degrees.
Since the fin stabilizer is adopted for the roll
reduction, the stabilizer fin‐induced force and
moment must be derived and the related formulas
aresummarizedasbelow(Fangetal.2010)
F
FRDLD
XFF
(24)
cos cos
F
FRL FLL F
YF F
(25)
FLLFRLFF
FFZ
sinsin
(26)
[cos cos)
(sin sin)]
FF F RL F Ll F
FRL FLL F
KzF F
yF F
(27)
FF F FF
M
zX
(28)
F
FFFF
N
xY
(29)
wherethesubscriptsRL,RD,LLandLDrepresentthe
fin‐inducedliftforce(L)anddragforce(D)onright‐
handside(R)andleft‐handside(L),respectively.x
F,
y
F,andzF,arethecoordinatesoftheactioncenterof
thefinforce,
Ftheanglebetweenfinandtheplumb
line.
Oneofthekeyissuesincontrolofstabilizersisthe
adaptation to the changes in the environmental
conditions.Aclassiccontrolsystemoffinstabilizers
using a PDD
2
controller is able to provide the
correction of the phase shift between the wave and
stabilizingmoment.
The control signal components of proportional,
derivativeanddoublederivativepartdependonthe
wave frequency what allows them to change the
phase lag in a limited interval according to the
varyingwave
frequency.
Figure7.Schemaofthecontrolsystemforfinstabilizers.
Classic control system of fin stabilizers used a
PDD
2
controller that was able to provide optimal
phase shift since the stabilization, so that it was in
oppositeuntilyourequire.
Alarçin (2007) designed for fin stabilization an
internal model control system. He used three‐layer
neural network with back propagation to build an
inversemodeloftheroll dynamic.
TheideaofIMC
implementation in fin stabilization realized also
TzengandWu (2000).Theyintroduced additionally
to the internal model the inverse of nonlinearities
such as saturation of fin angle. Generally the lift
generateswhen the flow passes the finbut Zhou et
al.(2008), that a different mode of fin
should be
appliedto generate onthefin enough lifttoreduce
shiprollatanchor.
The fin stabilizers can reach over 90 % roll
damping in regular waves. In irregular waves, it is
lower but it can be increased by using a cascade
control structure which task is
to adjust the fin
deflection to achieve the desired effective angle of
attackofthewaterflowonthefin.(Kula2014).
Jin et al. ( 2008) describe the property of fins at
zerospeedtogeneratetheliftwhichisnormaltothe
surface and is in direct proportion to
tonnage per
unittime.Thefinstabilizerisconsideredasaplane
foranalyzingthisproblemeasily.Suchuseofthefins
isdefinedasso‐calledfinstabilizersystematanchor.
3.4 Rudderrollstabilization
Theeffectofrudderinclinationonthegenerationof
heel has been recognized relatively
late, when the
crew of the vessel SS American Resolute started
complainingaboutdiscomfortduringshipsteering.
Whentherudderwassteered,theshipheeledin
inwarddirectionduetotherollingmomentactingon
therudder.
ThisphenomenonisillustratedinFigure8
411
Time (seconds)
0 10 20 30 40 50 60
-0.4
-0.2
0
0.2
0.4
0.6
yaw
yaw
roll
Figure8. Yaw and roll responses in reaction of rapid
rudderanglechange(U=18kn)
In order to find the reason for this effect, the
abovecasewasexaminedindetail.Theexamination
resulted in developing the RRS system which
extended the operation of the autopilot by
introducing the function which compensated the
effectofwavesonshiprollmotion.Therudderangle
requiredfor
thebothfunctionscanbeexpressedas
(30)
where
,
,areappliedforcoursestabilizationand
rolldamping,respectively
The use of one control signal for the purpose of
twooutputsispossibleduetothedifferenceinscale
between the dominating time constants, while
reachingtheexpected result requiredincreasing the
speedofthesteeringgearaction.The
standardspeed
ofrudderbladerotation wasfrom3
o
/son merchant
ships,upto5‐7
o
/sonNavyvessels.Therequirements
formulated for the actuators in this control system
amount to 12
o
/s, the minimum (Roberts 2008). The
fins are used only for roll stabilisation, and should
interfereverylittlewiththeheading.Onthecontrary,
rudders have a great influence on roll motions, but
areprimaryusedtocontroltheyaw,
AdesignofthissystemwaspresentedbyCowley
and Lambert (1972).
It’s positive that between the
heel caused by rudder and yaw there is the vast
separationoffrequencies.Fastandashortmovement
of the rudder in order to compensate heel has a
negligibleimpactonthechangeofcourse(Robertset
al.1997).
The RRS system was the subject
of numerous
publications.Moreover,thisprocess,veryinteresting
fromthepointofviewofthetheoryofcontrol,was
complementedbydesignsofcontrolsystemsmaking
use of H
norm, as well as the Model Reference
AdaptiveControlandtheModelPredictiveControl.
Thediscretemodelwhichmakesitpossibletopredict
coursechanges and/or rollmotion canbe presented
usingtheequation:
11
() ()() ()()()
MM
mm
x
namxnmbmYnmun
(31)
where x(n) –denotes a 2‐dimensional state vector
whose componentsareyaw and roll motion,Y(n) –
ruddermotionandu(n)denotesawhitenoisevector,
M‐theorderofthemodel/obtainedbytheprocedure
(Akaike&Nakagawa,1994)/,a(m),b(m)‐coefficients
Partofthesesystems
underwentseatrialsandwere
successfully implemented on ships. The success of
the rudder roll stabilization was the motivation for
making attempt to integrate the roll motion
stabilization systems which make use of the main
rudderandsidefins.Thissystemisreferredtoasthe
Integrated Fin and Rudder Roll
Stabilization
(INFRRS). Its advantage is that the requirements
formulatedforthespeedofoperationofthesteering
geararenotasrestrictiveasinthepreviouscase,as
evenatlowerrudderrevolutionstheRRSsystemcan
improvetheeffectofoperationofthestabilizingfins.
The results of this
cooperation, supported by sea
trials,werepresentedbyRobertsetal.(1997)
Figure9. The integrated fin and rudder roll stabilization
controlsystem
The block scheme of this system is shown in
Figure 9. Perez (2005) presented a concept of the
integratedfinsteeringwithrudderassistance which
madeuseofthemodelpredictivecontroller.Lawet
al. (2005) have made a comparison several
combinationsofcontrolstotheSlidingModeControl
(SMC), PID,
dual Loop Transfer Recovery (LTR)
controllers working in this system. It was possible
usingtheLTRcontrollertoreducetheshiprollin30
%. Crossland (2002) shows on example an ASW
frigate that an IFRRS system indicates an 3.8 %
improvement rather than a standard fin
arrangement. Agarwal (1997)
proposed a control
designforthissystemusingH∞approach.Odaetal.
(1996) discussed a possible compromise when
realizing two RRS goals in the statistical approach,
which was keeping the ship’s course as the main
goal, and additionally reducing the occurring roll
movements. To smooth the rudder movements, the
multivariable
auto‐regressive rudder roll control
system MARCS takes into account the operation of
thesteeringgearinthesteeringqualitycriterion.The
qualitycriterionJ
p(Odaetal.,1996)formulatedinthe
above way aims at limiting three undesired
quantities:thefirstisthedeflectionoftherollmotion
andship’s course fromthe setvalues,the second is
theamountofruddermotion,andthethirdtherate
ofchangeofthesteeringgear.
P
n
t
tt
p
nYnYTnYnY
nRYnYnQXnX
J
1
)2()1(()2()1(
)1()1()()(
(32))
whereT‐weightingmatrix
412
In this formulation the third term is the
penalization of inclinationrudder angle changes. In
this case the control rule is obtained from the
relation:
)1()()( nFYnGZnY
(33)
where:GandFaretheoptimalgainandsmoothing
coefficients.
If the weighting matrices T take the zero value,
thenthecriterionfunctionisreducedtothequadratic
criterion.Tomakeuseofthestructureoftheprimary
autopilot installed on the ship, the MARCS was
installedin
theemergencycircuitoftheautopilot,as
showninFigure10.
Figure10.Blockschemeoftherudder/rollcontrolsystem.
The processor unit comprises the computer, the
interface, and the roll motion speed sensors. The
operating unit provides opportunities for selecting
one out of three control gains, and setting the
selectedcourse.Thisway,byswitchingonthemode
switchintheoperatingunitwecaneasilychooseone
of two
available control methods: the primary
autopilot or MARCS. Moreover, in cases when
abnormalconditionsoccurintheMARCSsystem,we
caneasilyswitchitoffandcontinuethesteeringwith
theaidoftheautopilotormanually.Therollmotion
can be reduced in this system by 30‐50%. Linear‐
quadraticregulatorLQR itis thequadraticcriterion
androbustcontrolwereproposed(Sharifetal.1995)
toproviderollstabilizationwith30deg/sfinsanda6
deg/srudder.Themodelpredictivecontrolwiththe
effective attack angle constraint was used by Perez
andGoodwin (2008) toprevent dynamic stall
offin
stabilizers.Severalautomatedgaintuningalgorithms
weresuggestedinordertoimprovetheperformance
of rudder roll stabilization controllers in saturation,
including the automatic gain controller (AGC) (v.d.
Klugt1987),(v.d.Amerongen&v.d.Klugt1990)and
the time‐varying gain reduction (TGR) algorithm.
The model predictive control was
applied to the
rudder roll problem by Perez (2005). The internal
modelcontrol(IMC)makinguseofneuralnetworks
was investigated by Alarcin (2007) who used fin
stabilizers to obtain 94% roll angle reduction. A
third‐order controller for a fin stabilizer roll
reduction system was reported by Tzeng and Wu
(2000)asapplyingthemaximumof38dBfeedback.
Figure11.Azimuthingpropulsion.
Inthecaseofthetrackkeepingandrolldamping
Fang&Luo(2006)composedtheircontrolsystemof
sliding mode controller. Controlling the motion of
thesteeringbladewiththeaidoftherobustadaptive
fuzzycontrol(RAFC)anditsapplicationtoshiproll
stabilization were presented by Yang, Zhou
& Jia
(2002).Similar cooperation of two propellers to that
observed in INFRRS was proposed by Lee et al
(2011).TheuseofINFRRSimprovesthedamping if
theshipsailsatamoderatespeed,astheminimum.
At low maneuvering speeds their efficiency is low.
Thesituationisdifferentin
caseofapodpropulsion
systemwhichcansupporttheactionofstabilization
finsintherangewhentheirefficiencyisalreadyvery
low. A mathematical model of the force due to the
pod propeller build in (Stettler & Hover 2004). The
force components: the normal force
N
F
and the
thrust force
T
F
can be expressed as a function of
the propeller RPS, propeller diameter, thrust and
torquecoefficients:
),(
42
PodPodN
N
JKDnF
(34)
),(
42
PodPodT
T
JKDnF
(35)
where: n‐resolution per second, D‐propeller
diameterK
TKN–non‐dimensionalcoefficients
Thesurgeandswayforce,rollmomentandyaw
moment of the pod thruster should be added
accordingtotheequations1,2,4,6respectively.
)sin(sin)cos(cos
2121
NT
P
FFX
(36)
)cos(cos)sin(sin
2121
NT
P
FFY
(37)
PPP
rYK
(38)
PPP
xYN
(39)
where:
δ
1,δ2–theanglesofthepropeller
r
p,xp–theverticalandlongitudinaldistancebetween
thecenterofgravityoftheshipandthecenterofthe
propeller
413
Steeringactionstheazimuthingthrustersandfin
unit requires a two‐dimensional control system
(TITO). The nominal plant and the frequency‐
weightedlinear‐quadraticregulatorLQRareapplied
toreducetherollmotioninirregularwaves.Theroll
motion of ships is effectively reduced when the fin
andpodpropeller
areusedasthecontrolactuatorsat
lowspeeds.
Inregularwavesbyu=7knthefinscompensated
therollingmotionto25%,podpropellersto38%and
boththeyreached52%oftheamplitudeofthenon
stabilizedship
4 SUMMARY
The choice of stabilizer depends on
many ship and
missionconsiderations.Thelargenumberofexisting
stabilizers makes it possible to find a stabilizer for
virtuallyevery conceivablemission, beitlow speed
trawling to high speed pursuit. The question of
whetherornottohaveastabilizerdependsnotupon
the availability of stabilizers, but
rather on whether
ornotaparticularstabilizerwillbeuseful.Thiscan
bedeterminedbyfindingtheincreaseinoperability
relative tosomemotion criterionIt would seem that
inachangingenvironmentinwhichiscarriedoutthe
rollstabilizationfindswideapplicationtheadaptive
control. However, the phenomenon of
resonance
requiresthattheclassiclinearcontrolleraccordingto
Minorsky’stheoryistunedtoafrequencyclosetothe
naturalfrequencyoftheship.
Apotentialresearchactivityhasacontrolsystem
designoffreesurfacetanks,whichcouldrealizethe
adaptationtothechangesintheseaenvironmentbut
theeffectivenessofthesestabilizersindependentlyof
thecontrolisrelativelylow.
ThroughadaptationofPI/PIDcontrollersettingsit
maybepossiblethatthecurrentstabilizingmoment
by this wave frequency counteracts the excitation
moment.
For some vessels of varying over a wide range
dynamic,itmaybedesirabletoadapt
thecontroller
to the new natural frequency of the ship. This
requirestheidentification,whichundertheinfluence
of disturbances can cause significant number of
difficulties.
Researchersintheworksdevotedtothesynthesis
of stochastic stabilization systems despite the
charactersofthedominantdisturbancesrarelycome
across a probabilistic
approach control. It appears
that the use for example of minimum variance
strategy, which the objective is to minimize the
steady‐stateoutputvarianceswouldbejustified.
The adaptive minimum variance control can be
usedinpredictiveformtoo.
To control a ship motion for certain operating
conditions, a particular controller
may yield a most
suitable performance. Therefore, a set of different
types of controllers should be designed depending
onvariousspeeds,environmentalandseaconditions
so that appropriate controllers are selected in
correspondencetotheseconditions.Ifitisdifficultto
obtainsatisfactoryresultsusingonecontroller,itcan
turn
to switched control techniques what is
implemented for instance in some devices of an
integratedfinandrudderrollstabilization
As shown by test results presented in the cited
papersinthecontrolofstabilizerssystemsmayalso
besuccessfullyusedvariousmodel‐basedcontrollers
for instance the model predictive controllers,
fuzzy
logic and artificial neural networks controllers. In
recent years were tested Linear Quadratic Gaussian
(LQG), as well Loop Transfer Recovery (LTR)
procedure.
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