⎡cos

R( )  ⎢sin

sin

cos

0⎤

0⎥。

(2)

⎢ ⎥

⎣⎢ 0 0 1⎥⎦

Therelativevelocityvectorconsidering the effectofcurrentisdefined as:

vu u , v v , rT 。

(3)

Andthecurrentcomponentsarecalculated by

Fig。1Oilandgasdrilling operation

ucVc cos(c ),

vc Vc sin(c ),

(4)

2。ProblemStatementand Modeling

where andare the velocity and direction of

surface current。

 ∈  isthelow-frequencysystem inertia



2。1。vessel dynamics

matrix including added mass,   ∈ 



and

The floating vessel is usually considered as

   ∈ 

are the skew-symmetricCoriolis

and centripetal matrices of the rigid body and

⎡ cos1

。。。 cosN ⎤

 ⎢ ⎥

added mass。   ∈ 

is the dampingvector,

T () ⎢

sin 1

。。。 sin N ⎥,

which is a function of the relative velocity  。

The restoring vector  ∈  , caused by the

⎢⎣ x1 sin 1 y1 cos1

。。。

xNsin  N  yNcos N⎥⎦

(7)

buoyancyandgravitationjustaffectedbyheave, roll and pitch motion, is neglectedin horizontal motion。 In station keeping application, where the velocityofshipisassumed small,

       can be ignored and  

isassumedtobeconstant。,,and

 are second-order wave disturbance, wind, mooringandthrustervectors, respectively。

2。2multi-cablemooring system

The mooring lineattachedatoneendto the vessel viaawinchsystemandtheotherendis fixed to the sea-floor by anchor。 Commonly, the mooring line issubjectedtothreetypesof excitation: large amplitude LF motion, medium amplitude WFmotionandsmallamplitudevery highfrequencyvortex-inducedvibration5)。Inthe PM system design,itissimplifiedbyconsidering theinfluenceduetoLFmotion。Thusthemodel forthegeneralizedmooringforceis

where   , and  are moment arms andangle betweenmooringlineandxaxisofvesselas shown inFig。2。Thehorizontalforceproduced from each mooring line is the function ofthe horizontal distance between the top point and the anchorpointofthelineandthelinelength。 Several marine software packages that solve the nonlinearhorizontalforceofmooringline are readily available。

τmoorR() gmo (η) dmo (v)。

Whereis the additional damping and  is theEarth-fixedrestoringforceduetothe mooringsystem。TheEarth-fixedrestoringforceis a combination oftensionsproducedfromthe mooring lines。 It can be given by the following expression

Fig。 2 Mooring line configuration in vessel control system

3。ControllerDesignand Experiment

3。1controllerdesignandexperimental setup

Inthispaperthe authorapplyPID control

gmoT ()H ,

(6)

approachtothepositionkeepingexperiment。And