Control Performance of a Turret-Moored Vessel Assisted by Dynamic Positioning System

Copyright © IFAC Control Applications in Marine Systems, Fukuoka, Japan, 1998

CONTROL PERFORMANCE OF A TURRET-MOORED VESSEL ASSISTED BY DYNAMIC POSITIONING SYSTEM

Dong H. Lee*, Sung M. Joo*, Hang S. Choi*, Myung J. Song**, Yong S. Kim**

*Department of Naval Architecture and Ocean Engineering Seoul National University, Seoul 151-742, Korea **Daewoo Heavy Industry, Koje, 656-714, Korea

Abstract: This paper presents a nonlinear motion simulation and a controller design for a turret-moored vessel assisted by dynamic positioning system. For the simulation, the hydrodynamic forces are calculated by applying Green function method. A dynamic positioning controller, robust to uncertainties brought about by time-varying environmental loads, has been designed applying H control synthesis. A two degree
of freedom control system is adopted for tracking mode. Numerical simulations show that the controller works satisfactorily. Copyright © 1998 IFAC Keywords: hydrodynamic analysis, H control synthesis, control, motion simulation of moored vessels.
two degree of freedom

I . INTRODUCTION In this paper, a nonlinear simulator of a floating vessel has been developed, where hydrodynamic forces are calculated by using the Green function method. However, restoring forces of mooring lines are estimated by the catenary equation and regarded as quasi-static. In order to guarantee the robust stability and perfonnance for the DP system, the robust two degree of freedom (TDF) controller has been designed based on H optimization method. Several numerical simulations were carried out to investigate the perfonnance of the controller. It can be concluded that the perfonnance was quite acceptable.

As the development of subsea resources proceeds further into deeper ocean, floating offshore structures are more frequently employed. Under the action of external forces, floating structures are required to maintain their position within a certain limit with the help of conventional mooring system and/or Dynamic Positioning(DP) system.


The DP system is well-known to maintain the desired position and heading of the vessel by using thrusters in the presence of disturbances caused by wind, currents and waves(Morgan, 1978). There are two important problems in designing the DP system. One is the reduction of the excessive thruster modulation caused by wave induced motions and the other is the economic thrust allocation.

2. MATHEMATICAL MODELLING For simplicity, only the horizontal plane motions (surge, sway, and yaw) are included herein. To describe the motion of a vessel, both earth-fixed coordinates and body-fixed coordinates are introduced.

Meanwhile, the robustness has to be secured in the design of the controller, because the dynamics of the moored vessel contains nonlinearity and uncertainty due to the time-varying environmental loads.

99

space model can be written as:

,,=

The vessel's position and orientation [x,y,ljIf are viewed from the earth-fixed coordinates, while

(5)

the velocities v = [u, v, r f are referred to the bodyfixed coordinates.

[x, y,ljI, u, v,rf is the low-frequency state vector, 't is the thrust vector, and W L is the where

The nonlinear coupled equation of motion of a vessel is formulated in terms of the body-fixed coordinates (Fossen,1994).

low-frequency environmental load vector. The HF motions are caused by first-order wave loads. The linear HF state-space model can be obtained from the transfer function of the waveinduced motion or approximated by using the wave spectrum(Fossen, 1994).

Mv + C RB (v)v + CA (v r)V r =F(t)memory

+ F(t)viseous + F(tkilld + F(t)eurrent'

XL =

(l)

+ F(t)wave + F(t)mooring + F(t)'hros,er

F(t)memory

= i~(t

(6)

-

r) JA r)dr,

(2) where X H is the state vector of the high frequency motion component.

where M is the mass matrix including added mass and C RB (v)v and CA (v Jv r are the Coriolis and

Since the performance of a DP system is affected by the thruster dynamics in terms of phase lag, the thruster dynamics has to be taken into consideration in its design. However, the thruster dynamics is too complicated to model in detail, and thus it is simplified by the following model

centripetal forces respectively. V r is the relative velocity vector. External forces are composed of the wave radiation force, the viscous damping force, the wind force, the current force, the wave exciting force, the mooring force and the thruster force(Choi, et al., 1994). The wave radiation force contains memory effect and the time memory function L(t)

i=-A('t-'tJ.

(7)

can be obtained from the hydrodynamic damping. Here The velocities in the body-fixed coordinates are transformed to those in the earth-fixed coordinates by the following relation:

Xl

,,= [; = SI~1jI

cOSIjI

thrust command vector and

3. CONTROLLER DESIGN

(3)

In order to design the DP controller, an augmented state-space model is constructed as

o

The Green function method is used to estimate the first- and second-order wave exciting forces and hydrodynamic coefficients (Newman, 1977), while the mooring forces are evaluated quasi-statically. The governing equation of a mooring line is written as:

Tde = (D + weos e)ds, dT = (wsin e - F)ds,

is the

A = diag{l / I;,l / T2 ,1 / T3 ) IS the equivalent time constant matrix of thrusters.

- sin IjI

[COSIjI

't e

x=Ax+B't e , y=Cx ,

x=[x~,'tTf,

(8)

where x L is the low frequency state vector and y = [x,y,ljIf is the measured vector. The frequency characteristics of a nominal model Go normalized

(4)

by the Bis-system is presented in Fig. 1.

where D and F are the horizontal and vertical drag forces, respectively. T and ware the tension and effective weight of cable, respectively.

The standard H follows:


control problem is formulated as

Find K(s)

In order to design the DP controller, the above nonlinear equation of motion is to be separated into the low-frequency (LF) model and the highfrequency (HF) model (Fossen, 1994). It is assumed that the LF motions are caused by second-order mean and slowly varying wave loads. The linear LF state-

(9)

where T zw is the closed-loop transfer function between the exogenous inputs wand the regulated outputs z (Maciejowski, 1989; Shahian, and Hassul, 1993).

100

"

"

W = 0.2(s + 2) I) s(s + 15)

...

... - .... ". ,

"

50~~~ .. ::;~~

,..~

....

.,......

"".

The above problem is solved with the help of MATLAB. The achieved value of r is 8.411. Fig. 3 and Fig. 4 show the desired loop shape and the achieved loop shape, respectively. The designed controller has six inputs (measured variables and command signals), three outputs and 48 states .

·50 .100 ...

. 150 .

,, ..... "". . ... "". .... ".. ,. , .,,," "......... ... ",."" ' ...... , .,.... ..""""'"..... ,.,''' ... ... "". ... ".".... , . , ,,,,... .. , ... ..... .... .... ....... ." ,.," . .. ,.".". .." .","...., ..,.,,........... .. ,....... ". ..,,, ".". , .. .... " ..... , ' "" . .... ," ., ............... " ,,'''' ... ,," ,. .." ....,,'" , ... "",, . .....,'"." ,,, .. , , . , .. "" .. ,.,""" .... ''''''''

"

"

,

,

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"

"

"

"

(12)

,

..:- ~ :.:.;~:; --~ -; ..:..:~~:.::.. --:. -:..;; ~:;:;- -..:- ..:-:..:.;..;:;~ -.; - ~~..:; "." , ''' , , " ", . ,

·200 ""

4. NUMERICAL SIMULA nON

-25?OL ·, ................;..1~0·'~~1~0·.,-·-~107",--10~·~~1"-:0'~............Jl0' Frequency - radlsec

In order to exemplify the design method described above, we consider a turret-moored Floating Production Storage and Offloading(FPSO) in a water 375 m deep. Its length is 277 m and its dead weight is 220,840 tons. The equivalent time constant for thrusters is 2.5 sec. The ISSC spectrum with a significant wave height of 6.0 m and its peak period of 8.6 sec is used to simulate the real sea condition. The turret mooring system consisting of 12 anchor lines is located at 45 m toward bow. The submerged weight of a mooring line is 2943 N/m.

Fig. 1 Go singular values In this study, a TDF control system based on the H control synthesis is adopted to achieve both the robust stability and the robust performance(Limbeer et al., 1993). The block diagram is given in Fig.2. K I is the prefilter for following a model Mo' and 00

K

2

is the feedback controller. The transfer function

T zw for this formulation is as follows:

(I-G K 2

r IG

1

(I-K 2Gr 1 K 2 G .

(10)

--f-} i~~~~---~- +~~H~~f- -,

0

10

··., .. '.. ... .... , ..... .··.,... , .... '""'" , ,,'" ,".,," ,,'

.,

There are two design methods for the robust TDF controller. One is a single step optimization procedure. The other optimizes the feedback controller and prefilter in two separated design stages. In this study, the single step approach is taken, see (Limbeer, et al., 1993), for details.

" ,,'

" "" . .... ,," . " "........ .... .... ""." ...........,,, ..",."'" ".,.,., ,,,... .. ,,, ...,,,,, .., ,.......... .........,.".". , ........ ", ... , . ,." ... , , . " " . """" . ...... , . " ...

""'".

, , , .....

,',

..

,.,

.... "

"

"'"''

"

'

"

"

i ". ·'1 ,,'~ ·1!1~!:'·.·· mr:··iiiit!·· ~:"'.... H, 10

10.

--

i,.,,,.,, -~ ~ ~ ~ ~:~:-........ --:- -:- ~~:-:~:i" --~ -i.-:-:-;~:~:--~ -:- i~ ~:~~ --.:- -:-:-:-:~ r:.",,'"

.... .. ,,"". ..... .. ". ... .. .... ...... ·, ... ,,, ... ,, .. ... ........ .. ..... ..... ....... , .. ... ,.,,,,.,, . ... ' " "

"". ,,'"

"""

,," ," " " ,.,,"" " "".

,

",,'

"",,

,."" ,',,""

: :::::::: : :::::::: : ::::::::

"

,,,.,,' " '" ""

,

'""'" "".,,'

: ::: :::::

""" ,,,,,, ,,"" ""

.

: : : ::::::

::::: :::: ::::: :::: ::: : ::::: : ::: ::::: :: : :::::; 10'3 10.2 10" 100 10' 102 Frequency - radlsec

The reference model was determined to meet the time response specifications as follows:

Fig. 3 Go W singular values

-~I

0-

•

,.,,,, ''' , " "", ,,,

"."

10"~

M

11 . . . "

."".

.-:~~!~~- -~-~;~ ~:~~- -~- ~-~~~~~ --~ -~ ~ ~ :~::

s + 0.3 )

(11)

The loop shaping function below was selected in order to obtain an optimum solution of the trade-off problem between stability and performance.

10'

.. ,,,,,., " ...," :: ::::::: ' .: ::::: .. '''''". , "" ~ 10~ -·t-~i~~r~t~-·-:-+r~~H--~-H-H+--~-~;>" ~ ~ ll~~llil ~ ~~~~~lii ~ ~i~iiiii ~ jjl~iiii

G(s)

~ lO- --~-~~~~~~-·-~~-~~~t~·-~·J~~~~~~--~-~~H~~-·..,... ""... , " ...... ,, ., , . "". ,',,',," .. ,,". , ,,, ..... , " ..... ., ......., , .... " ' ' ' ' ,'"",,. ".".". , .... "" ·."",''''''". ., .... ... " .. ," . '"',, .. " ' .11 • • , " ..... "."",, ,.,,"." ' . " ..... 10. ~ ~~:~;:-- -~ ~- ~ ~~:::: -:~~~~~ --~ -~: ~ ;~~ , .. ., " " .... ."".,."" , ... "" . ,'" ...... ....,..... .,, ..... ".. ..... . , . ,," .... .,, ..,"",,, ....... ... ,.,,"'" .. ,,"," ., """. . , ... ,." . 10'2'0 :: ::::::: :: ::::::: :: ::::::: :: ::::::: tO

"",

""" "

"" "" ""'" " "",,.

'"''''

"

"" "

111

- -: -

"""

10,3

L-------------~1Jor_------~

10'2

,,"" "..," , ',

- -:-:

--

'"''''

"

"'"

"

"'"''''

10"

100 10' Frequency - radlsec

Fig. 4 Go WK singular values

Fig. 2 Block diagram ofTDF controller

101

," ,,,'" '''"."

10'

10'

1o,--------,

':~

5 - - -.. - ---. -.... , . . . ... - -

0.5 N N

-'

°v

-'

°v -05 0

20

40

o

bme(s.c )

tlme(sec )

1000

1500

2000

f':~

.SO:-----2;:;;0-----::40::------;!60

60

500

001.--------,

.050~-----;::SO:;;:0---':-::000~---I;-;:'SO;;;;0'-------:2dooo 04 .. -.... . ~ ....... ~ .. - .... M

~

·0 01 0~-2;:;;0-----::40::------;!60'

I':~

"

0 2 .•. -----:----- -- -~--.-----

.020

time!sec)

20

40

60

.050

The nonlinear response of the FPSO for the stationkeeping mode is shown in Fig. 7. It is found that the motions of the FPSO are considerably suppressed. It should be noted that Fig. 7 has an enlarged scale compared to that of Fig. 6. Fig. 8 represents the motion behavior of the FPSO for tracking mode. After 1000 seconds, the desired position and orientation are commanded. They show a good tracking performance. The oscillatory motion at the desired position results from the reaction of the mooring lines.

5. DISCUSSION AND CONCLUSION A nonlinear simulator for a thruster-assisted turretmoored vessel has been developed. Hydrodynamic forces and wave-induced motions have been predicted by the Green function method based on potential theory. The robust TDF controller for DP system has been designed with the help of H control synthesis to secure the robustness. 00

Computer simulations demonstrate that the nonlinear

I:~ 1500

20r---~---~_--~_------'

I 1~1f----------=~

2000

.100

10

f,:~ -200

500

1000

1500

1000

1500

1000

1500

2000

'==!

fA

.200~-----;::50:;;:0---;-;;'0;;;;00'-----':-;:SO;;;;0'-------:2:::!000

2000

1~~Ir-~.~C5~=1

I:~ 500

500

10r---~----~---_---~

40

.200

2000

In order to check the robustness to different environmental conditions, numerical experiments are carried out with a significant wave height of 15.5 m and its peak period of 13.5 sec. Fig. 9 shows the results in this harsh environmental condition. The watch circle is naturally much larger than that in the mild condition. However, the radius of the circle is found to be within 3 % of the water depth, which implies that the designed controller still works satisfactorily.

Fig. 6 shows the nonlinear motion behavior of the FPSO without control in irregular waves. In this case, the incident angles of wave, winds and currents are all 190 0 . The wind velocity is 20 mls and the current velocity 0.5 mls. The drift motions besides the wave-frequency motions are clearly observed.

1000

1500

Fig. 7 Motion response of station-keeping mode (significant wave height of 6.0 m)

702 panels are used to calculate the hydrodynamic quantities. Hydrodynamic forces are calculated for 0 0 heading angles ranging from 0 to 180 with an 0 interval of 15 . Time memory functions are given in Fig. 5.

500

1000 bme(sec)

Fig. 5 Time memory functions of FPSO

.50

500

time!s.c)

2000

.,00

bme{sec)

Fig. 6 Motion response of FPSO without control (significant wave height of 6.0 m)

Fig.

102

500

1000 bme(s.c)

1500

8 Motion response of tracking (significant wave height of 6.0 m)

2000

mode

,':~ -1 00~----;5O;;: OO:;--------:;10~00;---------:1C;:50"'"0---;:-} 20-0 0

J :~ -50

500

1000

1500

2000

i:~ -50

500

1000

1500

2000

tJme(sec)

Fig. 9 Motion response of station-keeping mode (significant wave height of 15.5 m) motion of FPSO can be predicted accurately and that the H TDF controller works satisfactorily even in 00

harsh environments.

ACKNOWLEGEMENTS This work has been performed at the Research Institute of Marine Systems Engineering (RIMSE) under the financial support of SNU Development Foundation.

REFERENCES Choi, Y.R. , Won, Y.S., and Choi, H.S. (1994), The Motion Behavior of a Shuttle Tanker Connected to Submerged Turret Loading System, In: Proc. of the 41h International Offshore and Polar Engineering Conference. Fossen, T.I. (1994), Guidance and Control of Ocean Vehicles, John Wiley & Sons Ltd. Limbeer, DJ.N., Kasenally, E.M., and Perkins, J.D . (1993), On the design of robust two degree of freedom controllers, Automatica, 29, No. 1, pp.157-168. Morgan, MJ. (1978), Dynamic Positioning of Offshore Vessels, Tulsa, Oklahoma:Petroleum. Maciejowski, J.M . (1989), Multivariable Feedback Design, Addison-Wesley Ltd. Nakamura, M., and Koterayama, W., et al. (1994), Application of Dynamic Positioning System to a Moored Floating Platform, In: Proc. of the 41h International Offshore and Polar Engineering Conference. Newman, J.N. (1994), Marine Hydrodynamics, The MIT press. Shahian, B. and Hassul, M. (1993), Control System Design Using MATLAB, Prentice-Hall.

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