Dynamic Positioning of a Semi-Submersible: Results of Scale Model Tests

and Computer Simulations

C . G . Kallstrom and L. Bystrom, SSPA Marltlrne Consulting AB, Goteborg, Sweden

ABSTRACT

Scale model tests with the semi-submersible GVA 4000 under posltlon and heading control m irregular waves and wmds are presented and discussed. The propeller rates and force directions of four azunuthmg thruster uruts were controlled by a dynamic positlorung system mplemented in a rmcro-computer Motorola 68000 at the tests. The data from the tests are useful for the development of a mathematical smulation model for further analysis of the n g with different dynamic posltlonmg systems as discussed m the chapter

INTRODUCTION

Much theoretical and expenmental work has been devoted to investigations of the behavlour of floatlng offshore structures in different wind, wave and current condltlons. The forces then actmg on the structures are usually divided mto two parts, one high-frequency wave mduced part and one slowly oscillatmg part. The aun of a moonng or Dynamc Positlorung (DP) system is to compensate for the slowly oscillatmg forces T h s chapter descnbes model tests of a s e m - submersible ng, which was positioned on-line by a DP-system.

T h s work is a continuation of sunulation studies of DP-systems at SSPA, see refs (I), (2), (3). In these sunulation studies the hgh-frequency wave induced motions and the measurement disturbances were filtered away usmg a Kalman

Advances tn Undenuater techno lo^, Ocean Science and Ojjshore Engtneertng, Volume 9 Stahontng and Stabtit@ ofSemt-submerstbles @ Soc~ety for Underwater Technology (Graham & Trotman. 1986)

250 ADVANCES IN UNDERWATER TECHNOLOGY

Filter The estunates of surge, sway and heading were then used m a regulator designed w t h linear-quadratic control theory.

The mean optlmal thruster settings for a certain gven weather condition w t h respect to total power were l~utially calculated w t h the SSPA program THRUST 2 4 , and the DP-system thereafter operated around these optunal settmgs

The results discussed m t h s chapter are the first steps m a research program for studies of DP-systems in connection w t h model tests. The selected n g is GVA 4000, whch dunng the tests was positioned using a sunpllfied DP-system under influence of Irregular waves and gusting wnds

Dunng several years SSPA has developed sunulatlon models based on seakeepmg tests using soft moonng in combmation w t h thrusterlthruster and thrusterhull mteraction tests See refs (1)-(4). Scale model tests under DP-control, as descnbed m t h s chapter, can be regarded as an alternative approach.

The charactenstics of GVA 4000 are summanzed m Section 2. The tests were camed out in the SSPA Mantune Dynamlcs Laboratory (MDL) w t h a model in the scale 1:25. The model was equipped w t h four thruster umts, one m each column, w t h a diameter of 2.8 m (full-scale)

The DP-system was implemented In a Motorola 68000. The positions of two mfra-red spots on the platform were measured and used as mput to the DP-system From these measurements surge, sway and yaw of the n g were calculated.

The DP-system m this case consists of PID-controllers, and the hgh-frequency wave mduced motions and measurement noise were filtered away by a low-pass filter The filtered signals were then used m the controllers and the thruster settmgs were calculated for the four thruster umts See Sectlon 4.

Some of the scale model tests are discussed m Sectlon 5. In Section 6 some mdications how the scale model tests data can be used for the development of mathematical sunulation models are gven Fmally, the chapter is summanzed m Section 7. Acknowledgements and references are gven m Section 8 and 9, respectively.

TEST RIG GVA 4000

The four-column sem-submersible n g GVA 4000 was designed and constructed by Gotaverken Arendal AB (GVA), Goteborg, Sweden. A co-ordinate system xyz fixed to the n g is defined in Fig. 1. O n g n is at the centre of the n g and 0.45 m below the calm water level at operational draught. The particulars of the ng are summanzed m Table 1.

The version of GVA 4000 used at the scale model tests is equlpped with four a z u n u t h g thrusters below each column. Each thruster has a m m u m power of 2 3 MW and a maxlrnum thrust of 380 kN The dameter is 2.8 m.

DYNAMIC POSITIONING OF A SEMI-SUBMERSIBLE

Fig. 1 Defhtlon of co-ordinate system futed to the ng. Translations along the co-ordinate axes are called surge, sway and heave and rotations about

these axes are called roll, pitch and yaw, respectively.

TABLE 1 GVA 4000 data

Length over all (L) Beam over all (B) He~ght from keel to maln deck Helght from keel to lower deck Length of pontoon Beam of pontoon Depth of pontoon Column diameter Operatlonal draught ('I? Operatlonal displacement (0) Metacentnc helght (GM) Radlus of gyratlon around x-axls (k,) Radlus of gyratlon around y-ax~s (k9) Rad~us of gyratlon around z-axls (k,)

252 ADVANCES IN UNDERWATER TECHNOLOGY

TEST SET-UP

A scale model 1 25 of GVA 4000 was manufactured The model was set up in the SSPA Maritime Dynamcs Laboratory (MDL) See Fig 2

The measurement slgnals used in the DP-system were the x- and y- co-ordinates of two infra-red spots on the platform The control s~gnals from the DP-system, implemented in a Motorola 68000 micro-computer, were the propeller rates and the force directions of each thruster unit Thus eight ~ndividual control signals were computed

At the tests roll and pitch angles were measured with a gyro and the wave heights with a probe Propeller rate, thrust and torque of each thruster unlt were also measured.

DP-tests m three different wave directions and two different Irregular wave spectra were camed out. Wind, consisting of a constant mean value and a Auctuat~ng part, was applied using fans See Fig 2 A wind gust spectrum accord~ng to Harns5 was used

Fig. 2 The test set-up In the Mantlrne Dynam~cs Laboratory (MDL).

DYNAMIC POSITIONING O F A SEMI-SUBMERSIBLE

DYNAMIC POSITIONING SYSTEM

The four measured co-ordmates obtained from the SEL-spot system are first filtered with a first-order d g t a l low-pass Butterworth filter. The filtered signals are then used in the DP-system to calculate the deviations m earth-futed co-ordmates Axo, Aye and heading Av from the desired set-pomts.

T h e requ~red forces F,, and F,, In the xo- and y ,- direct~ons a s well a s the required torque F v are computed w t h the following PID-regulators

(4.1) F, = kl a, + k2 D, + ks.l,

where Dx, Dy and DQ are difference approxunations of the velocities and I,, I , and I , are approxunations of the Integrated control errors The controller galns are denoted kl-kg. The samphng lnterval was chosen to 0 2 s at the model tests, which corresponds to 1 s at full scale

The forces Fd and Fvo are transformed to the required forces F, and F, along and transverse the ng, respectively:

(4.2) F, = F,. cosv + FYo . smv

where v is the heading of the rig A special thrust allocation algonthm is used to calculate propeller rates and

force directions from F,, F, and Fy, for the four thrusters. A dead zone is used In such a way that only changes of force directions larger

than about 5" are effectuated The DP-system descnbed is a very sunple approach A more advanced system

conta~rung a Kalman filter, a linear-quadratic regulator and an optunal thrust allocation algorithm'*2 will be used in already planned, new, scale model tests

SCALE MODEL TESTS

To form a basis for the mathematical modellmg three different types of tests were carried out-

* seakeeping tests with the n g positioned by a soft-moonng system seakeeping tests with the n g positioned by the DP-system w t h and without a wnd load. All three types of tests were carried out in the wave directions 180" (head

seas), 135" and 90" (beam seas on port side) w t h significant wave heights Hs = 4 and 7 m.Corresponding mean wave penods Tz were 7 and 9 s Dunng the tests with a wnd load gusts with mean speeds of 13 and 21 mls were chosen. The standard deviation of the wind speed was about 10% in both cases The test program is summanzed in Table 2

ADVANCES IN UNDERWATER TECHNOLOGY

TABLE 2 Test program

Wave Hezght Penod Wave headzng Tfie of test Hs T z Y (m) (set) (deg)

Soft moonng 4 0 7 0 180, 135 and 90 Soft moorlng 7 0 9 0 180, 135 and 90 Soft moonng 4 0 7 0 180, 135 and 90 DP - wlthout wmd 7 0 9 0 180, 135 and 90 DP - wthout wind 4 0 7 0 180, 135 and 90 DP - wlth wlnd 7 0 9 0 180, 135 and 90 DP - wlth wmd

A co-ordinate system xyz fixed to the ng is defined m Fig 1 Ongm is at the centre of gravlty of the ng in operation condltlons. The four thrusters in the columns are numbered clockwise starting w t h thruster No 1 at starboard bow. the maximum tumng rate of the thrusters was 12"/s Wave helght, surge, sway, yaw, No of revs of the thrusters as well as thrust and torque were measured at a samplmg penod Ts corresponding to 0 2 s m full scale.

Examples of results from the DP-tests converted to full scale are shown m Figs 3-7. Figure 3 shows the results of a test m head seas w t h significant wave height 4.0 m, Figs 4 and 5 the same test m wave headmgs 135" and 90" respectively Figure 6 shows a DP-test at 135" and the wave height 9 0 m and, finally, Fig 7 shows as a comparison the same test wthout wnd. All tests were carried out w t h the same parameter settings of the controller.

If the direction of a thruster is 0 deg and the No of revs IS positive, a positive thrust on the rig will be obtamed. See e.g. in Fig. 3, head seas, where the directions of all thrusters are varylng around 0 deg and the Nos of revs are all posit~ve to compensate for w d and wave dnft forces, whch are mainly negative

In Fig. 4, bow quartering seas, the thrusters have to compensate for both forces in the x- and y-du-ections as well as for a y a w g moment As the above water part is unsyrnrnetncal, a yawng w d moment is also obtamed m beam seas, whch of course must be counteracted by the thrusters

The first 100 s are omitted in the plots of Figs 3-7, smce the irutial phases are not very interesting Normally each test lasted for 1500 s (full scale uruts).

DYNAMIC POSITIONING OF A SEMI-SUBMERSIBLE

4 O, WIVE HEIGHT IMI 8 O, Y A M IOEGI

100 0 300 0 500 0 700 0 800 SEC 0 -2 ' 100 0 O m , 0 300 0 500 0 700 0 800 SEC 0

15 0, SURGE Ill) 1 8 , NO OF REVS THRUSTER 1 IRPSl

5 0 -

-5 0 1 100 0 300 0 500 0 700 0 800 0 100 0 300 0 500 0 700 0 800 0

SEC SEC

- 1 0 4 . . . . . . . . . . . . . . . . 100 0 300 0 500 0 700 0 800 0 100 0 300 0 500 0 700 0 800 0

SEC SEC

B, NO OF REVS THRUSTER 3 IRPSI 10 0, OIRECTION THRUSTER 2 [DELI

1 . , 1 . . , 1 i 0 0 0 900 0 500 0 700 0 800 0

5EC -'~I~oo+ 0 . 706 0 . sod 0

SEC

. . . . . . . . 101 . . . . . . . . I 0 0 0 900 0 500 0 700 0 800 0

- 4 0 0 1 LOO 0 300 0 5 M 0 7 M 0 g*) 0

SEC SEC

20 O, OIECTIOU W T E R 1 DEG) 5 a, DIRECTION TWSTER 4 IOEG1

Fig. 3 DP-test in wlnd and waves. Wave height H s = 4 0 m, period T z = 7.0 s and wave heading 180 deg (head seas)

0 -5 0.

-20 0 . . . . . . . . 1 0 0 0 3 W O m o 7 0 0 0 m o o

-15 0, 1 0 0 0 m a m o 7 m o m o o

Y C Y C

256 ADVANCES IN UNDERWATER TECHNOLOGY

Ol HEIGHT (HI O1 jqEGl

-4 0 1 ' : . . . . . . . 100 0 300 0 500 0 700 0 800 0

-4 0 1 r . , , , . , . 100 0 300 0 500 0 700 0 800 0

SEE SEC

O l SURGE IN]

- 1 0, 110 OF REVS TWUSTER I IRPSI

0 - -2 0

- 4 0 2 . . . . . . I , 100 0 300 0 500 0 700 0 800 0

-3 0 100 0 300 0 500 0 700 0 800 0

SEC SEC

4 0 A 1 IN1

OM -4 0 100 0 300 0 SO0 0 700 0 800 0 100 0 300 0 500 0 700 0 800 0

SEC SEC

5, NO OF REVS THRUSTER 3 IRPSI 0, DIRECTION THRUSTER 2 lOEGl -I&, 1: -2 5

I 0 0 0 300 0 500 0 700 0 800 0 100 0 300 0 SO0 0 700 0 800 0

SEC SEC

" 1 NO OF REVS THRUSTER 4 IRPS) OIRECTION THRUSTER 3 lOEGl

b ! . . . . . . . . 100 0 300 0 500 0 700 0 800 0

80 0 1 . , . . , . , I W 0 300 0 500 0 700 0 BOO 0

SEC SEC

(30 O I R E C T I I THRUSTER I IOEGl

SEC SEC

Fig. 4 DP-tests m wlnd and waves. Wave helght H s = 4.0 m, perlod T z = 7.0 s and wave headlng 135 deg

DYNAMIC POSITIONING O F A SEMI-SUBMERSIBLE

- 5 0 4 I , , , , . . , , LOO 0 300 0 500 0 700 0 900 0

- 4 O C r I I I I I - 100 0 300 0 500 0 700 0 800 0

SEC SEC

NO OF REVS THRUSTER 1 1RPSI

L O - -2 5

- 1 0 . I I I I I I I I

100 0 300 0 500 0 700 0 800 0 -3 5

100 0 300 0 500 0 700 0 900 0

SEC SEC

15 0, SWAY (HI 1 0, NO OF REVS THRUSTER 2 lRPSl

ol NO OF REVS THRUSTER 3 IRPSI 120 o1 OIRECTIOH THRUSTER 2 lOEGl

5EC SEC

2 I] NO OF REVS THRUSTER 4 IRPSI 100 ,l OlRECTION THRUSTER 3 10EGl

5 1 , . . , , , , , I 0 0 0 300 0 500 0 700 0 800 0

, , . , . , , , , 100 0 300 0 500 0 700 0 800 0

SEC SEC

100 0 300 0 500 0 700 0 800 0 LOO 0 300 0 500 0 700 0 800 0

SEC SEC

Fig. 5 DP-tests In w~nd and waves Wave height H s = 4.0 m, period T z = 7 0 s and wave heading 90 deg (beam seas)

258 ADVANCES IN UNDERWATER TECHNOLOGY

0 UAVE HE lGHl 111

lo O1

5 0

-5 0 100 D 300 0 500 0 700 0 BOO 0

-10 0 100 0 300 0 500 0 700 0

SEC SEC

l5 O1 In'

-2 ol NO OF REVS THRUSTER 1 IRPSI

SEC SEC

3 51 NO OF REVS THRUSTER 2 (UP51

5 0 -

-10 0 4 . . . . . . . . 100 0 300 0 500 0 700 0 BOO 0

1 5 1 , . . , , , , . 100 0 300 0 500 0 700 0 BOO 0

SEC SEC

-3 0

NO OF REVS THRUSTER 3 (UPS1 DIRECTION THRUSTER 2 lDEGl

- 5 0 , , I , , , , . , 100 0 300 0 500 0 700 0 BOO 0

- 4 0 100 0 300 0 500 0 700 0 BOO 0

3 0 -20 0

- 4 0 100 0 300 0 500 0 700 0 BOO 0

-30 0 100 0 300 0 500 0 700 0 BOO 0

SEC 5EC

3 O, NO OF REVS THRUSTER 4 (RPSI 120 DIRECllON THRUSTER 3 IDEGI

. . . . . . . - . . . . . . . . 100 0 300 0 500 0 700 0 BOO 0

0 0 0 4 100 0 300 0 500 0 700 0 800 0

SEC 5EC

120 O, DIUECllON THRUSTER I C G l DIRECTION T U 6 1 E R 4 [DEGl

100 0 4 . . . . . . . . -BOO4 . . . . . . . 100 0 300 0 500 0 700 0 BOO 0 100 0 300 0 600 0 700 0 BOO 0

SEC SEC

Fig. 6 DP-test in wind and waves Wave height H s = 7 0 m, period T z = 9.0 s and wave heading 135 deg.

DYNAMIC POSITIONING OF A SEMI-SUBMERSIBLE

lo W E HEIGHT IMI

lo O l "AM IDEG1

, . . . . , , I

0 300 0 500 0 700 0 800 0 - 1 0 0 4 . . . . . . . '

100 0 300 0 500 0 700 0 800 0

SEC SEC

15 0. SURGE IN1

100 0 300 0 500 0 700 0 800 0

SEC SEC

- 1 0 0 . . . . , ' , ' - 1 0 0 300 0 500 0 700 0 800 0 10: 0 ' 300 0 500 0 700 0 BOO 0

SEC SEC

-3 0 -10 oL-----------. 10: 0 ' 3W' 0 ' 5W' 0 700 0 000 0 100 0 300 0 500 0 7 W 0 800 0

SEC SEC

0 Ol NO OF REVS TKfUSTER 4 W 1 lW o, OIRECTION THRISTER 3 !DELI

1W OIRECTION T W T E A 1 !DE61

I 0 OIRECTION THRISER 4 IDES1

I 80 o-

w l o o o Ljmpo o Y c -10 lw O r o o o sEc

Fig. 7 DP-test In waves wthout wnd. Wave he~ght H s = 7.0 m, period T z = 9.0 s and wave headlng 135 deg

260 ADVANCES IN UNDERWATER TECHNOLOGY

MATHEMATICAL MODELLING

The results from the scale model tests described in Section 5 are very useful for the determination of mathematical smulatlon models A technique where system identification is applied direct to data from the model tests is discussed in refs (6) and (7) This approach makes an efficient use of the collected data and the accuracy In the simulation model can be controlled by the model order chosen

The seakeeping tests w t h soft moonng and the DP-tests with no wind are specially useful for t h s purpose. The advantage with the DP-tests IS that the thruster/thruster and the thrusterhull interaction effects are inherent m the collected data The DP-tests with wind included can be used for the calibration of the complete simulation model

The scale model expenments in Section 5 will be used for the determination of a simlation model Different advanced DP-systems will be Investigated by simulations, and comparisons will also be made wlth new scale model tests T h s work is In progress.

SUMMARY

The chapter summarizes the first part of a research program, where DP-systems are analysed by using a comblnatlon of scale model tests and computer simulations

The first round of scale model tests w t h a DP-system mplemented in the mcro-computer Motorola 68000 is reported in the chapter. The test rig chosen IS

GVA 4000 with four azlmuthng thruster units Both seakeeplng tests w t h soft moonng and DP-tests m different irregular waves and wlnds (mean w n d and turbulence) were carned out Some DP-tests \nth only irregular waves (no wnd) were also performed.

Computer simulations and new scale model tests w t h DP-systems c o n t a m g a Kalman filter, a hnear-quadratic controller and an optlmal thruster allocation algonthrn are planned m the next step of the research program.

ACKNOWLEDGEMENTS

T h s work has been supported by the Swedlsh Board for Technical Development. The scale model tests were performed with a n g model partly paid for by Gotaverken Arendal AB, Goteborg They are both gratehlly acknowledged.

REFERENCES

1 C G Kallstrorn, Moorlng and Dynarmc Posltlorung of a Serm-Submersible A Computer Slrnulation Study, 2nd Intern Symp on Ocean Engneer~ng and Shlp Handhg, Goteborg, Sweden, 1983,417-442

2 C G Kallstrorn, A Dynamic Pos~tiomg System for Serm-Submersibles, RINA Symp on 'Seml-Submersibles The New Generation', London, 1983

3 B Allenstrorn and C G Kallstrorn, Power Mlnirmzation m Dynarnlc Positioning Systems, Offshore Goteborg 85, Goteborg, Sweden, 1985

DYNAMIC POSITIONING OF A SEMI-SUBMERSIBLE 261

4 S Moberg and S A Hellstrom, Dynamlc Pos~tlonlng of a Four-Column Seml- Submersible, 2nd Intern Symp on Ocean Engmeer~ng and Shlp Handlmg, Goteborg, Sweden, 1983, 443480

5 R I, Hams, The Nature of the Wmd, Proc The Modem Deslgn of Wmd-Sensitive Structures, London, 1970, 29-55

6 C G Kallstrom and F A Ramzan, The Use of Hybnd Model Tests and Computer Slmulatlons for Offshore Installat~ons, IFIPJIFAC Symp ASSOPO '85, Trondheun, Norway, 1985

7 C G Kallstrom, System Ident~ficat~on Apphed to Data from Scale Model Tests w ~ t h a Moored Seml-Submersible, 7th IFACJIFORS Symp on 'Identlficatlon and System Parameter Estlmatlon', York, 1985