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RAPPORT

VIEWS: 18 PAGES: 43

									                      NTNU                              RAPPORT                Rapportnummer
                                                                               2001-13-T
                      Norges teknisk-
                      naturvitenskapelige universitet                          Gradering
                                                                               OPEN
                      Fakultet for informasjonsteknologi, matematikk og
                      elektroteknikk                                           ISBN
                      Institutt for teknisk kybernetikk

Postadresse:          NTNU                                                    Sentralbord:         73 59 40 00
                      Institutt for teknisk kybernetikk                       Instituttet:         73 59 43 76
                      O.S. Bragstads plass 2D                                 Telefax:             73 59 43 99
                      N 7491 TRONDHEIM

  Rapportens tittel                                                            Dato
                                                                               Revised 11 May 2002
  Observer and Controller Design for an Offshore Crane
  Moonpool System                                                              Antall sider og bilag
                                                                               43
                                                                               Ansv. sign.



  Saksbearbeider/forfatter                                                    Prosjektnummer
  Tor Arne Johansen and Thor Inge Fossen

  Oppdragsgiver                                                               Oppdr. givers ref.
  Norsk Hydro                                                                 Svein Ivar Sagatun


  Ekstrakt
  A control system for active wave synchronization and heave compensation in heavy-lift offshore
  crane operations is described. Wave synchronization reduces the hydrodynamic forces via
  minimization of the relative speed between payload and moonpool waves using a wave amplitude
  measurement. Experimental results using a scale model of a semi-submerged rig with a moonpool
  in the NTNU MC lab shows that wave synchronization leads to significant improvements in
  performance. Depending on the sea state and payload, experiments indicate that typical reduction
  in the wire tension standard deviation is between 0 and 50 %. Experiments with regular waves and
  irregular waves (JONSWAP spectrum) are described and analyzed in detail.


  Acknowledgements
  We are grateful to Marintek and NTNU for giving us access to the MCLab in Trondheim where
  the experiments were conducted. We are also grateful to Norsk Hydro AS for supporting this
  project.



  Stikkord

  Offshore Moonpool Cranes                Marine Operations               Wave feedforward
Contents
1   Background                                                                                                                                                                             3

2   Dynamics                                                                                                                                                                                3

3   Control system                                                                                                                                                                         6
    3.1 Control objectives . . . . .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .   6
    3.2 Frequencies . . . . . . . .    .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .   6
    3.3 Control strategy . . . . . .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .   7
    3.4 Active heave compensation      .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .   7
    3.5 Wave synchronization . . .     .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .   8

4   Observer and Filter Design                                                                                                                                                             8
    4.1 Heave position and velocity estimator . . . . . . . . . .                                      .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .   8
    4.2 Wave amplitude velocity estimator . . . . . . . . . . . .                                      .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .   9
    4.3 Combined Tension and Motor Speed Observer . . . . . .                                          .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .   9
    4.4 Motor Speed Observer (No Tension Measurements) . . .                                           .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    . 10
    4.5 Combined Payload Position and Velocity Observer . . .                                          .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    . 10
        4.5.1 Payload position measurement . . . . . . . . . .                                         .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    . 11
        4.5.2 Motor encoder measurement . . . . . . . . . . .                                          .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    . 11
    4.6 Payload position reconstruction in the frequency domain                                         .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    .    . 11

5   Experimental setup and instrumentation                                                                                                                                                 11

6   Experimental results                                                                                                                                                                   12
    6.1 Regular waves at Ì ½ ¾ s and    ¾ cm . . . . . . . . . . . . . . . . . . . . . . . .                                                                                               14
    6.2 Regular waves at Ì ½ ¼ s and    cm . . . . . . . . . . . . . . . . . . . . . . . . .                                                                                               15
    6.3 JONSWAP spectrum at Ì ½ ¼ s and     ¿ cm . . . . . . . . . . . . . . . . . . . . .                                                                                                 15

7   Simulations                                                                                                                                                                            34

8   Discussions                                                                                                                                                                            40

9   Full scale implementability                                                                                                                                                            41

10 Suggestions for future work                                                                                                                                                             42

11 Conclusions                                                                                                                                                                             42




                                                                   2
1 Background
Higher operability of installations offshore of underwater equipment will become increasingly more im-
portant in the years to come. Offshore oil and gas fields will be developed with all processing equipment
on the seabed and in the production well itself. The lower cost in using subsea equipment compared to
using a floating or fixed production platform is penalized with lower availability for maintenance, repair
and replacement of equipment. Production stops due to component failure are costly, hence a high op-
erability on subsea intervention is required to operate subsea fields. High operability implies that subsea
intervention must be carried out also during winter time, which in the North Sea and other exposed areas
implies underwater intervention in harsh weather conditions. The objective of the marine operation is to
safely install a product on the seabed. One of the critical phase of the installation is the water entry phase
on which this report focuses. We study active control of heave compensated cranes or module handling
systems (MHS) during the water entry phase of a subsea installation, where it is of interest to minimize
loads due to the hydrodynamic forces caused by interactions between payload and waves. The principal
idea is to utilize a wave amplitude measurement in order to compensate directly for the water motion due
to waves inside the moonpool.


2 Dynamics
We will only consider the vertical motion of a payload moving through the water entry zone. The payload
is handled from a floating vessel. The vessel is kept in a mean fixed position and heading relative to the
incoming wave only moving due to the first order wave forces. Effects from the vessel’s roll and pitch
motion are neglected.
    In this section we describe the dynamics of a laboratory scale model moonpool crane-rig (scale 1:30).
Figure 1 shows a setup consisting of an electric motor and a payload connected by a wire that runs over
a pulley suspended in a spring. We notice that this setup contains no passive heave compensation system
or damping device. Figure 2 shows the coordinate system definitions:

               Þ¼         rig position in heave (Ñ)
               Þ          payload position (Ñ)
               ÞÑ         motor position (Ñ)
                          moonpool wave amplitude, relative to mean sea level (Ñ)
                ¼         moonpool wave amplitude, relative to vessel-fixed position (Ñ)
               Ñ          payload mass ( )
                 Ø   =    wire tension (Æ )
   The coordinate systems of Þ and ÞÑ are positive downwards and fixed in the crane rig, while the
coordinate systems of and Þ¼ are positive upwards and Earth-fixed. All have the origin at the still water
                                                                           Ñ
mean sea level. In [2], the following transfer functions from motor speed Þ to payload position Þ and
wire tension Ø are derived

                             Þ
                               ´×µ            ¿
                                                  ¾
                                                      ½  ×¾ · ¾ ¾ ¾ × · ¾ ¾

                                                      × ×¾ · ¾ ¿ ¿ × · ¿
                                                                                                          (1)
                            ÞÑ                ¾
                                                                          ¾

                              Ø ´×µ                     ¾
                                                             ×¾ · ¾ ¾ ¾ × ·   ¾

                             ÞÑ
                                           Ñ          ¿
                                                          × ¾
                                                             × · ¾ ¿ ¿× ·
                                                                              ¾
                                                                              ¾                           (2)
                                                      ¾                       ¿

where the resonance frequencies satisfies the relationship ¿       ¾ . The value ¿         rad/s is the
experimentally determined wire resonance frequency with a nominal payload mass of 0.572 kg when the
payload is moving in air, [3]. When the payload is partly or fully submerged, the hydrodynamic force
must be taken into account. This leads to increased damping and contributions from added mass and its
time derivatives. Depending on the size, shape, mass, position and velocity of the payload, significant

                                                          3
Figure 1: Experimental 1:30 scale model of vessel with moonpool.




                               4
Figure 2: Definition of the coordinate systems.




                      5
reduction in the resonance frequencies ( ¾ ¿ ) and increase in the relative damping factors ( ¾ ¿ ) are
experienced. A typical value of ¿ with the payload in submerged condition is 31 rad/s to 46 rad/s,
[3]. Typical values for the damping factors are ¿       ¼ ¼¾ and ¾ slightly higher, when moving in air
[3]. Identified models of these factors under submerged conditions are also found in [3]. Theoretical
relationships between ¾ ¿ ¾ and ¿ can be found in [2].
     A first order model of the transfer function from the reference motor speed Þ to the motor speed ÞÑ
is found in [2]:
                                          ÞÑ             ¼ ¼½¼×
                                          Þ
                                             ´×µ    ½ · ¼ ¼¾¼×                                        (3)

The time-delay is mainly due to digital communication and control within the motor drive and control
units.


3 Control system
3.1 Control objectives
The performance measures of interest are the following:
   ¯   Wire tension; The minimum value must never be less than zero to avoid high snatch loads, and
       the maximum value and variability should be minimized.
   ¯   Payload acceleration; Peak values should be minimized as this gives an indication of impulsive
       forces on the payload.
   ¯   Payload impulse; The impulsive hydrodynamic forces on the payload should be minimized.

3.2 Frequencies
The following are the key frequencies in the system:
   ¯     ¿         rad/s is the experimentally determined wire resonance frequency with a nominal pay-
       load mass of 0.572 kg when the payload is moving in air, [3]. When the payload is submerged in
       water, the added mass may lead to a significant reduction of ¾ and ¿ . A typical value of ¿ with
       the payload in submerged condition is 31 rad/s to 46 rad/s, [3].
   ¯   The frequency-dependent ratio between wave amplitudes inside the moonpool and in the basin is
       shown in Figure 3. The data are experimental and based on a frequency-sweep using regular waves
       at 2 cm. We notice the characteristic resonance near the period ÌÑÓÓÒÔÓÓÐ ½ ¿ s, or ÑÓÓÒÔÓÓÐ
           ¿ rad/s. In [4] the moonpool resonance frequency is found to be 5.43 rad/s, Ô on WAMIT
                                                                                       based
       analysis. This is more accurate than the simple theoretical formula ÑÓÓÒÔÓÓÐ      ´ ѵ       ¾
       rad/s, where Ñ is the moonpool depth Ñ ¼ ¾ m.
   ¯   Typical vessel heave frequencies are in the range ¼             Ú      ¼ rad/s. In [4], the natural
       frequency of the heave motion of the vessel is found to be 4.55 rad/s, using WAMIT analysis.
       In [1], this frequency is found to be 4.22 rad/s. In the experiment where the moonpool resonance
       frequency was determined, the vessel heave acceleration was also measured. The natural frequency
       of the heave motion of the vessel was found to be approximately       Ú        rad/s.
It should be remarked that significant differences between the theoretical value and the WAMIT analysis
are expected, since the WAMIT analysis is based on the main dimension specifications of the rig, while
the experimental ballasting was significantly different in order to stabilize the rig.
     The sampling frequency is chosen at 200 Hz = 1256 rad/s. Although the main frequency components
compensated for are around 10 rad/s, such a high sampling frequency gives considerable flexibility for
digital filtering and data analysis.

                                                    6
                                            moonpool amplification (−)
           2.5




            2




           1.5




            1




           0.5




            0
            0.6      0.7      0.8     0.9         1         1.1          1.2   1.3   1.4   1.5
                                                 wave period (s)




 Figure 3: Ratio between wave amplitudes in moonpool and basin as a function of basin wave period.


3.3 Control strategy
The wire elasticity introduce resonances that give fundamental limitations to the achievable feedback
control bandwidth. Analysis and simulations indicate that highest performance and robustness is achieved
using a pure feed-forward strategy. This report describes a control system with the following main com-
ponents

   ¯   Payload speed tracking control. The objective of this low level controller is to make the payload
       track a time-varying speed reference. This reference signal is composed of three components:
       Constant speed signal from the crane operator, heave compensation and wave synchronization.

   ¯   Heave compensation. A component is added to the payload speed reference that compensates
       for the heave motion of the rig. Ideally, the payload then moves with specified speed relative to
       an Earth-fixed coordinate frame. This is based on a heave velocity estimate generated from an
       accelerometer in the vessel.

   ¯   Wave synchronization. A component is added to the payload speed reference in order to syn-
       chronize its motion through water entry in order to minimize the relative velocity of the water
       and payload, and thereby minimizing the hydrodynamic forces. This signal is generated by feed-
       forward from a wave amplitude sensor, and overrides the heave compensation during the water
       entry phase.

3.4 Active heave compensation
The objective of a heave compensator can be formulated as follows: Make the payload track a given
trajectory in an Earth-fixed vertical reference system. This means that the payload position will not be
influenced by the heave motion of the vessel. This is easily implemented using feed-forward where an
estimate Þ¼ of the vessel’s vertical speed (in an Earth-fixed reference system) is added to the motor speed
reference signal

                                             Þ           £
                                                        ÞÑ · Þ¼                                       (4)


                                                       7
       £
Here ÞÑ is the motor speed commanded by the operator or a higher level control system. The vessel
vertical speed Þ¼ can be estimated using a state estimator which essentially integrates an accelerometer
signal and removes bias using a high-pass filter, see Section 4.1.

3.5 Wave synchronization
Wave amplitude measurements can be used in a feed-forward compensator to ensure that the payload
motion is synchronized with the wave motion during the water entry phase. An objective is to minimize
variations in the dynamic forces on the payload, Þ ´ÞÖ µ , where
                                                                                       ¬ ¬
               Þ ´ÞÖ µ           Ç ´ÞÖ µ ÞÖ   Þ ´ÞÖ µÞ Ö   Þ Þ´ÞÖ µ Þ¾   ½
                                                                     Ö ¾    Ö
                                                                                ÔÞ Þ Ö ¬Þ Ö ¬       (5)
                                                       Ö
                                                              Ö
and the relative position is ÞÖ Þ  ´   Þ¼ µ Þ   ¼ . The first term of (5) is the Froude-Kriloff pressure
force. The second term represents the contribution of the added mass, while the third term contains the
slamming loads. The fourth term is the viscous drag on the payload.
    Rather than minimizing this expression explicitly, we observe that a close to optimal solution is
achieved by minimizing variations in ÞÖ . This is achieved by the feed-forward compensator

                             Þ           £
                                        ÞÑ     ¼   ÜÔ´  Þµ · Þ¼ ´½   ÜÔ´  Þµµ                                       (6)

where is the wave number and ¼ is an estimate of the derivative (speed) of the wave amplitude inside
the moonpool (in a vessel-fixed coordinate frame), see section 4.2. Since this control should only be
applied during the water entry phase, it is blended with the active heave compensator as follows:

                         Þ             £
                                      ÞÑ   «´Þ µ   ¼       ÜÔ´  Þµ · Þ¼ ´½   ÜÔ´  Þµµ                               (7)
The position-dependent factor «´Þ µ goes smoothly from zero to one when the payload is submerged:
                                               ¼            Þ  ¼ ½¼
                              «´Þ µ            ½¼´Þ · ¼ ½¼µ  ¼ ½¼ Þ ¼                                               (8)
                                               ½            Þ ¼
It is remarked that the factor ÜÔ´  Þ µ accounting for the dependence of the water vertical velocity on
water depth is based on assumptions that are not realistic in the moonpool, and might be replaced by a
more accurate expression. In particular, one might except that the water vertical velocity is approximately
constant from the wave surface to the bottom of the moonpool.


4 Observer and Filter Design
4.1 Heave position and velocity estimator
Since the wave motion has zero mean, the following filter removes the accelerometer bias and recon-
structs the heave position and velocity
                                       À Ô´×µ                                   À Ô´×µ
                             Þ¼ ´×µ           Þ ´×µ                Þ¼ ´×µ              Þ¼ ´×µ
                                        ×¾ ¼                                      ×
The high-pass filter À Ô ´×µ is a 2nd order filter with critical damping                          ¼   and cutoff frequency
     ¼ ¾ rad/s (full scale) or     ½ ¿ rad/s (model scale):
                                                                       ×¾
                                        À Ô´×µ                ¾   ·¾        × · ×¾
                                                                                                                    (9)

In addition there are analog and digital lowpass filters to remove high-frequency noise from the ac-
celerometer measurement.

                                                             8
4.2 Wave amplitude velocity estimator
The wave amplitude ¼ relative to a vessel-fixed position inside the moonpool is measured. The wave
amplitude velocity ¼ is estimated by filtering and numerical differentiation:

                                                ¼   ´×µ            ×ÀÐÔ´×µÀÒÓØ               ´×µ ¼´×µ                                     (10)
The low pass filter ÀÐÔ ´×µ is composed of a 2nd order critically damped filter at 60 rad/s and a 2nd order
critically damped filter at 200 rad/s. In order to avoid exciting the wire resonance, we have introduced a
notch filter
                                                                        ×¾ · ¾ ¡ ¼ ½ ¡ Ò · Ò
                                                                                           ¾
                                        ÀÒÓØ            ´×µ              ¾ ·¾¡¼ ¡
                                                                                       Ò· Ò
                                                                                                                                          (11)
                                                                        ×                  ¾

typically tuned at Ò           ¿ . In the experiments we used Ò      ¿ Ö ×. Notice that this tuning
would depend on the payload mass, hydrodynamic properties such as added mass and drag, in addition
to wire elasticity. Ideally, the notch frequency should be adapted online in order to match the observed
resonance. The factors ¼ ½ and ¼ in (11) are chosen empirically to give good performance, i.e. to give
sufficient damping without too much phase loss.

4.3 Combined Tension and Motor Speed Observer
Consider the transfer functions for tension and closed-loop motor speed:
                                 Ø ´×µ  Ñ                          ¿
                                                                           ¾
                                                                                    ×¾ · ¾      ¾ ¾×       ·    ¾
                                                                                                                ¾
                                                                               ×
                                                                                    ×¾ · ¾              ¿× ·
                                                                                                                                          (12)
                                ÞÑ                                 ¾                            ¿
                                                                                                                ¾
                                                                                                                ¿
                                                               ÞÑ                    ½
                                                              ÞÑÖ ´×µ              Ì× · ½
                                                                                                                                          (13)

Here ½ Ì represents the bandwidth of the closed-loop motor control system. Combining these two
expressions, yields:
                            Ñ                                       ¾
                                                                               ×            ×¾ · ¾       ¾ ¾×   ·   ¾
                           Ö ´×µ  Ñ
                                                               ¿                                                    ¾
                                                                        Ì× · ½              ×¾ · ¾           ¿× ·
                                                                                                                    ¾                     (14)
                          ÞÑ                                   ¾                                         ¿          ¿
A state-space model with tension measurement                            Ø and encoder measurement ÞÑ is:
                                                          Ü            Ü·           Ù·Û                                                   (15)
                                                          Ý            Ü·           Ù·Ú                                                   (16)
This implies:
            ¾        ¿ ¾ ¼                         ¼ ¼ ¾ ¿ ¾ ܽ ¿ ¾ ¼¾ ¿
                                                    ½                      ¾ ¿
                ܽ                                                          ۽
                ܾ              ¿¾           ¾ ¿ ¿ ¼   Ì¿    ܾ
                                                                 · Ì ÞÑ · Û¾
                                                                      ¿
                                                                         Ö
                Ü¿             ¼              ¼ ¼ ½          Ü¿     ¼       Û¿
                                                                                                                                          (17)
                Ü              ¼              ¼ßÞ ¼   ̽     Ü      Ì
                                                                     ½
                                                                    ßÞ
                                                                            Û


                      ¾                                                                                                     ¿¾   ܽ
                                                                                                                                      ¿
                                                                                                             ¼ Ñ ¿
                                            ¾                                       ¾                                   ¾
             Ø            Ñ          ¿
                                     ¾
                                                 ½             ¾Ñ              ¿
                                                                               ¾
                                                                                        ¿
                                                                                        ¿           ¾
                                                                                                    ¾          Ì ¾               ܾ
            ÞÑ                          ¼                                           ¼                        ½   ¼               Ü¿
                                                                               ßÞ                                                Ü

                        Ñ                   ¾
                     ·  Ì                             Ö       ·     Ú½
                                    ¿
                                    ¾                ÞÑ                                                                                   (18)
                               ¼
                               ßÞ
                                                                    Ú¾



                                                                           9
A linear fiixed-gain observer based on pole-placement or the algebraic Riccati equation (ARE)
                                         ·        Ì             ÌÊ        ·É        ¼                            (19)

becomes

                                         Ü        Ü·       Ù   · Ã´Ý   ݵ                                        (20)
                                         Ý        Ü·       Ù                                                     (21)

where
                                                  Ã
                                                                Ì Ê ½                                            (22)
is the steady-state Kalman filter gain.

Tension measurement If a force ring is used to measure the tension                       Ø   the measurement equation
     simply becomes:
                                                           ݽ         Ø                                          (23)

Payload acceleration measurement If the tension ݽ                        Ø   cannot be measured directly, ݽ can be
     computed from the payload acceleration Þ as
                                                      ݽ       ÑÞ · Û                                            (24)

4.4 Motor Speed Observer (No Tension Measurements)
If only encoder measurements ÞÑ are available the model becomes:
                                ܽ     ½ ¼                       ܽ
                                                                          · ¼        Ö
                                                                                    ÞÑ
                                ܾ     ¼  Ì½
                                                                 ܾ         ½
                                                                                Ì
                                                                                                                 (25)

                                     ¢     £               ܽ
                                  ÞÑ   ½ ¼                 ܾ
                                                                                                                 (26)

In this case a linear observer for motor speed ܾ using encoder ܽ                                               Ö
                                                                                         ÞÑ and speed reference ÞÑ
measurements can be constructed as:
                      ܽ        ¼ ½               ܽ
                                                           · ¼             Ö
                                                                          ÞÑ   ·    ý
                                                                                             ´Ý   ݵ
                      ܾ        ¼  Ì
                                   ½
                                                  ܾ         ½
                                                                  Ì                 þ
                                                                                                                 (27)

                           Ý   ½ ¼ ܽ
                                   ܾ
                                                                                                                 (28)

where ý and þ are two positive design gains.

4.5 Combined Payload Position and Velocity Observer
Define

                                ܽ       Þ (payload position)                                                    (29)
                                ܾ       Þ (payload speed)                                                       (30)
                                 Ù       Þ (measured payload acceleration)                                       (31)
The observer model then becomes:

                                             ܽ       ܾ                                                         (32)
                                             ܾ       Ü¿ · Ù ·        ·Û                                         (33)
                                              Ý       ܽ · Ú                                                     (34)


                                                           10
where Û and Ú are zero-mean Gaussian white noise processes. The bias is found apriori as:

                                         Ñ Ò´Ù´½      Æ µµ       ½ m/s¾                           (35)

where Æ     ¼   Hence, the observer becomes:

                      ܽ         ¼ ½        ܽ
                                                  · ¼ ´Ù · µ ·            ý
                                                                               ´Ý   ݵ
                      ܾ         ¼ ¼        ܾ      ½                     þ
                                                                                                  (36)

                           Ý    ½ ¼ ܽ
                                     ܾ
                                                                                                  (37)

where pole-placement of a double integrator suggest that the observer gains are chosen as:

                                                 ý    ¾                                          (38)
                                                           ¾
                                                 þ                                               (39)

4.5.1   Payload position measurement
If a camera or another position sensor used to measure the payload position Þ the measurement equation
simply becomes:
                                                 Ý Þ                                             (40)

4.5.2   Motor encoder measurement
If the payload position Ý Þ cannot be measured directly, Ý can be computed from the motor position
ÞÑ simply by setting Ý ÞÑ . The limitation of this is that the motor position signal only contains the
low-frequency part of the payload position. However, this is not a major problem since the acceleration
sensor contains information mainly on the high-frequency part of the payload position. Another problem
is that there will be an offset that depends on the payload mass due to the steady state wire tension.
     A reasonable tuning of the observer is           ½ and         ¿          Ö ×. The bandwidth of
the observer should be placed below the resonance frequency since the encoder signal does not contain
useful information at this frequency.

4.6 Payload position reconstruction in the frequency domain
The motor encoder measurement can be used to reconstruct the low-frequency part of the payload posi-
tion signal and the payload acceleration measurement can be used to reconstruct the high-frequency part
of the payload position signal. The following estimate combines these signals

                                 Þ ´×µ
                                                                   ½
                                          ÀÐÔ´×µÞÑ ´×µ · À Ô´×µ ¾ Þ ´×µ
                                                               ×
We choose ÀÐÔ ´×µ     ½ and À Ô´×µ equal to a 2nd order Butterworth high-pass filter with cut-off fre-
quency at ¿       Ö        ×.

5 Experimental setup and instrumentation
The winch is an AC servomotor with an internal speed control loop. There are vertical accelerometers
in both the payload and vessel, and a wire tension sensor. In the moonpool there are wave meters
measuring the wave amplitude in a vessel-fixed coordinate frame, i.e. ¼         Þ¼. The motor position
ÞÑ is measured using an encoder.
    The total scale model mass is 157   with a water plane area of 0.63 Ѿ .
    Two payloads where tested: a sphere and a pump inside a frame, see Figure 4

                                                      11
                                 Figure 4: Payloads used during experiments.


6 Experimental results
Experimental results for the scenaria summarized in Table 1 are described in this section. The notation
”Ws” is an acronym for ”Wave synchronization” while ”Hc” is an acronym for ”Heave compensation”.
Notice that the reported values of the wave period Ì and amplitude are values specified to the wave
generator, and will therefore deviate somewhat from the values measured (especially the amplitude).
Three sea states are considered:

       ¯   Regular waves with period Ì ½ ¾ s and amplitude              ¾ cm. This wave frequency is close
           to the moonpool resonance frequency, see Figure 3, and the wave amplitude inside the moonpool
           is about 2 times the basin wave amplitude. The wave height (full scale) is around À× ½ ½ m.
       ¯   Regular waves with period Ì       ½ ¼ s and amplitude            cm. At this frequency there is no
           resonance. The wave height (full scale) is around À×      ½ m.
       ¯   JONSWAP spectrum with Ì         ½ ¼ s and        ¿ cm. The significant wave height (full scale) is
           around À× ½ m.

    We present both raw and filtered data. The filtered data contains mainly components in the frequency
band between 0.5 and 1.5 Hz, where the significant wave motion is located1 . This filtering allows the
effects of the wave synchronization to be separated from other effects, since this is the frequency band
where the wave synchronization is effective. It is therefore natural to verify the performance of the
wave synchronization on the filtered data, neglecting low-frequency components due to buoyancy and
high-frequency components due to measurement noise and wire resonances. Still, it is also of interest to
evaluate the performance of the wave synchronization with respect to excitation of the wire resonance.
This evaluation is, however, not straightforward to carry out since the laboratory model does not contain
passive heave compensation or damping. Also, the excitation caused by signal noise and winch motor
drive is not directly scalable to full scale implementation and must be considered in the context of the
technology used for implementation. Thus, we will base our conclusions mainly on the filtered data.
   1
    The filtering is carried out using 4th order Butterworth highpass and lowpass filters using the MATLAB filtfilt
algorithm to ensure no phase shift.


                                                       12
Wave spectrum                  Payload   Controller   Tests
Regular, Ì ½ ¾ s,     ¾ cm     Sphere    Ws           A,B
Regular, Ì ½ ¾ s,     ¾ cm     Sphere    Hc           A,B
Regular, Ì ½ ¾ s,     ¾ cm     Sphere    Ws+Hc        A,B
Regular, Ì ½ ¾ s,     ¾ cm     Sphere    -            A,B
Regular, Ì ½ ¼¼ s,      cm     Sphere    Ws           A,B
Regular, Ì ½ ¼¼ s,      cm     Sphere    Hc           A,B
Regular, Ì ½ ¼¼ s,      cm     Sphere    Ws+Hc        A,B
Regular, Ì ½ ¼¼ s,      cm     Sphere    -            A,B
Jonswap, Ì ½ ¼¼ s,     ¿ cm    Sphere    Ws           A,B,C,D,E
Jonswap, Ì ½ ¼¼ s,     ¿ cm    Sphere    Hc           A,B,C,D,E
Jonswap, Ì ½ ¼¼ s,     ¿ cm    Sphere    Ws+Hc        A,B,C,D,E
Jonswap, Ì ½ ¼¼ s,     ¿ cm    Sphere    -            A,B,C,D,E
Regular, Ì ½ ¾ s,     ¾ cm     Pump      Ws           A,B
Regular, Ì ½ ¾ s,     ¾ cm     Pump      Hc           A,B
Regular, Ì ½ ¾ s,     ¾ cm     Pump      Ws+Hc        A,B
Regular, Ì ½ ¾ s,     ¾ cm     Pump      -            A,B
Regular, Ì ½ ¼¼ s,      cm     Pump      Ws           A,B
Regular, Ì ½ ¼¼ s,      cm     Pump      Hc           A,B
Regular, Ì ½ ¼¼ s,      cm     Pump      Ws+Hc        A,B
Regular, Ì ½ ¼¼ s,      cm     Pump      -            A,B
Jonswap, Ì ½ ¼¼ s,     ¿ cm    Pump      Ws+Hc        A,B,C,D,E
Jonswap, Ì ½ ¼¼ s,     ¿ cm    Pump      Ws           A,B,C,D,E
Jonswap, Ì ½ ¼¼ s,     ¿ cm    Pump      Hc           A,B,C,D,E
Jonswap, Ì ½ ¼¼ s,     ¿ cm    Pump      -            A,B,C,D,E

              Table 1: Overview of experiments.




                              13
     Time series from selected tests will be shown. In addition we show the following statistics for each
test:

   ¯ À× ´Ñµ - significant wave height (model scale) or wave height (if the waves are regular).
   ¯ ´Æ µ - standard deviation for tension signal Ø where signal components under 0.5 Hz are
         Ø

       removed.

   ¯ Ñ Ò´ Ø µ ´Æ µ - peak minimum value of tension.
   ¯ Ñ Ü´ Ø µ ´Æ µ - peak maximum value of tension.
   ¯ Þ ´Ñ ×¾ µ - standard deviation for payload acceleration signal Ø where signal components under
       0.5 Hz are removed.

   ¯ Ñ Ò´Þµ ´Ñ ×¾ µ - peak minimum value of payload acceleration.
   ¯ Ñ Ü´Þ µ ´Ñ ×¾ µ - peak maximum value of payload acceleration.
The statistics presented are corrected for variations in average speed and length of experiments, such that
the standard deviations presented are averages over a constant number of wave periods during the water
entry phase of each operation.
    Experimental data.
    The experimental data can be found in MAT-files. The files are named such as
    reg 1.25 2.0 paysphere a.mat
    where reg indicates regular waves, 1.25 is the wave period, 2.0 is the wave amplitude, paysphere
indicate the payload and the last letter a indicates test A. The results can be plotted in MATLAB using
the plot exp script.

6.1 Regular waves at Ì           ½¾   s and        ¾ cm
The results of tests A and B are summarized in Table 2. Figures 5 - 8 shows some relevant signals for
test B with the spherical payload. Figures 9 - 12 shows some relevant signals for test A with the pump
payload. The following observations and remarks can be made:

   ¯   For the spherical payload, the wave synchronization reduces the tension standard deviation by
       25.2 % in test A and 21.4 % in test B, compared to no control, when considering filtered data. Wave
       synchronization in combination with heave compensation reduces the tension standard deviation
       by 22.0 % in test A and 21.8 % in test B, compared to no control, when considering filtered data.

   ¯   For the spherical payload, the peak minimum tension is increased from 1.21 N to 1.58 N using
       wave synchronization in test A and from 1.36 N to 1.58 N in test B, compared to no control, when
       considering filtered data. This is beneficial as it reduces the possibility of wire snatch. The peak
       maximum tension is somewhat increased with the wave synchronization.

   ¯   The use of heave compensation does not give any significant reduction of tension variability in
       this sea state. However, it gives significant reduction of the standard deviation of the payload
       acceleration.

   ¯   The payload acceleration is significantly increased using wave synchronization.

   ¯   When considering the unfiltered data, similar qualitative conclusions can be made in most cases.




                                                   14
   ¯   For the pump-in-frame payload, the wave synchronization reduces the tension standard deviation
       by 7.2 % in test A and 12.8 % in test B, compared to no control, when considering filtered data.
       Wave synchronization in combination with heave compensation reduces the tension standard de-
       viation by 8.9 % in test A and 15.3 % in test B, compared to no control, when considering filtered
       data.


6.2 Regular waves at Ì           ½ ¼ s and          cm
The results of tests A and B are summarized in Table 3. Figures 13 - 16 shows the relevant signals for
test B with the spherical payload. Figures 17 - 20 shows the relevant signals for test A with the pump
payload. The following observations and remarks can be made:

   ¯   For the spherical payload, the wave synchronization reduces the tension standard deviation by 31.0
       % in test A and 33.1 % in test B, compared to no control, when considering filtered data. Wave
       synchronization in combination with heave compensation reduces the tension standard deviation
       by 48.1 % in test A and 54.2 % in test B, compared to no control, when considering filtered data.

   ¯   For the spherical payload, the minimum tension is reduced from 1.36 N to 1.23 N using wave
       synchronization in test A and from 1.59 N to 1.67 N in test B, compared to no control, when
       considering filtered data.

   ¯   For the spherical payload, the use of heave compensation alone gives significant reduction of ten-
       sion variability in this very rough sea state, namely 50.3 % in test A and 25.9 % in test B. This
       indicates that significant reduction in tension variance can be achieved by either heave compensa-
       tion or wave synchronization, but largest reduction is achieved by combining them.

   ¯   The payload acceleration is significantly reduced using any combination of heave compensation
       and wave synchronization.

   ¯   When considering the unfiltered data with the spherical payload, similar qualitative conclusions
       can be made in most cases. With the pump-in-frame payload the unfiltered data shows increased
       variance with wave synchronization and heave compensation.

   ¯   For the pump payload the wave synchronization reduces the tension standard deviation by 36.9
       % in test A and 34.5 % in test B. Wave synchronization in combination with heave compensation
       reduces the tension standard deviation by 61.4 % in test A and 53.2 % in test B, when considering
       filtered data. Hence, the pump and spherical payloads give similar results in this sea state.


6.3 JONSWAP spectrum at Ì               ½ ¼ s and        ¿ cm
The averaged results of tests A to E are summarized in Table 4. Figures 21 - 24 shows the relevant
signals for test B with the spherical payload, which is the test with poorest performance of the wave
synchronization. The following observations and remarks can be made:

   ¯   For the spherical payload, the wave synchronization reduces the tension standard deviation by
       27.6 % on average, compared to no control, when considering filtered data. Wave synchronization
       in combination with heave compensation increases the tension standard deviation by 1.2 % on
       average, compared to no control, when considering filtered data.

   ¯   For the spherical payload, the minimum tension is reduced from 1.61 N to 1.68 N using wave syn-
       chronization on average, compared to no control, when considering filtered data and the spherical
       payload.


                                                    15
Mode        À×            Ø
                                   Ñ Ò´ Ø µ        Ñ Ü´ Ø µ       Þ           Ñ Ò´Þµ      Ñ Ü´Þ µ
Sphere    Test A      Filtered   (0.5 - 1.5 Hz)
  Ws     0.037702    0.267813      1.456132        5.795719    0.311217   -0.602558       0.614468
  Hc     0.036499    0.401340      1.138118        5.582255    0.038327   -0.067921       0.071675
Ws+Hc    0.033925    0.279348      1.583275        6.034342    0.306320   -0.617523       0.617327
 none    0.038299    0.357952      1.213946        5.722934    0.089129   -0.127943       0.130912

Sphere    Test A    Unfiltered
  Ws     0.037702   0.432547       0.696337        6.684045    0.600266   -2.162592       1.903956
  Hc     0.036499   0.507332       0.822350        6.100927    0.406043   -1.064087       0.827034
Ws+Hc    0.033925   0.447314       0.827344        6.704614    0.611461   -1.832424       1.710669
 none    0.038299   0.528371       0.641684        5.848055    0.522571   -1.263501       1.120482

Sphere    Test B      Filtered   (0.5 - 1.5 Hz)
  Ws     0.037784    0.268407      1.592595        6.202517    0.280106   -0.593456       0.601818
  Hc     0.035806    0.372235      1.360973        5.841397    0.039713   -0.074419       0.069177
Ws+Hc    0.034092    0.267272      1.580037        5.915207    0.270912   -0.595244       0.600746
 none    0.037597    0.341721      1.366221        5.822916    0.085884   -0.126354       0.130272

Sphere    Test B    Unfiltered
  Ws     0.037784   0.433747       0.880140        6.821880    0.561937   -1.969048       1.801773
  Hc     0.035806   0.464373       0.978126        6.170447    0.356264   -0.985576       0.778424
Ws+Hc    0.034092   0.433610       0.680507        6.712235    0.568871   -2.037143       1.383322
 none    0.037597   0.492832       0.873798        5.989654    0.482955   -0.977351       1.038329

Pump      Test A      Filtered   (0.5 - 1.5 Hz)
  Ws     0.039584    0.167990      3.959354        6.040978    0.284068   -0.589020       0.624885
  Hc     0.038119    0.180205      3.718327        5.793527    0.048950   -0.075886       0.078593
Ws+Hc    0.033350    0.164843      3.916865        5.993941    0.272455   -0.603828       0.668273
 none    0.039988    0.180951      3.839583        6.026410    0.104844   -0.157119       0.149506

Pump      Test A    Unfiltered
  Ws     0.039584   0.336488       3.416551        7.039119    0.569014   -2.287737       2.299409
  Hc     0.038119   0.299483       3.289559        6.244836    0.389238   -1.083781       0.833700
Ws+Hc    0.033350   0.327978       3.269907        6.501920    0.547977   -2.050921       2.273515
 none    0.039988   0.247486       3.597863        6.241724    0.276047   -0.737595       0.568726

Pump      Test B      Filtered   (0.5 - 1.5 Hz)
  Ws     0.039982    0.158423      3.819313        5.812970    0.261576   -0.567374       0.597118
  Hc     0.038632    0.162784      3.573695        5.765090    0.033465   -0.052580       0.064725
Ws+Hc    0.035470    0.153891      3.840655        5.841607    0.253084   -0.595864       0.629548
 none    0.040687    0.181612      3.560337        5.572643    0.106293   -0.154130       0.153616

Pump      Test B    Unfiltered
  Ws     0.039982   0.314047       3.127796        6.422724    0.519078   -1.695554       1.982500
  Hc     0.038632   0.293130       3.156398        6.223716    0.401000   -1.172815       0.920834
Ws+Hc    0.035470   0.311899       3.246430        6.242517    0.520933   -2.172067       1.457749
 none    0.040687   0.243299       3.310918        5.913031    0.270390   -0.720871       0.667572

         Table 2: Summary of results with regular waves at Ì     ½¾   s and       ¾ cm.

                                              16
                                    Wave synchronization                                                      Heave compensation

                      0.2                                                                       0.2
motor speed (m/s)




                                                                          motor speed (m/s)
                      0.1                                                                       0.1


                       0                                                                         0


                     −0.1                                                                      −0.1


                     −0.2                                                                      −0.2
                              260     265      270     275    280                                       185      190      195      200
                                            time (s)                                                               time (s)

                       Wave sychronization and heave compensation                                                   No control

                      0.2                                                                       0.2
motor speed (m/s)




                                                                          motor speed (m/s)


                      0.1                                                                       0.1


                       0                                                                         0


                     −0.1                                                                      −0.1


                     −0.2                                                                      −0.2
                            95      100      105     110     115                                      345     350       355      360     365
                                            time (s)                                                                 time (s)
                                    Wave synchronization                                                      Heave compensation
                      0.8                                                                       0.8

                      0.6                                                                       0.6
motor position (m)




                                                                          motor position (m)




                      0.4                                                                       0.4

                      0.2                                                                       0.2

                       0                                                                         0

                     −0.2                                                                      −0.2

                              260     265      270     275    280                                       185      190      195      200
                                            time (s)                                                               time (s)

                        Wave sychronization and heave compensation                                                  No control
                      0.8                                                                       0.8

                      0.6                                                                       0.6
motor position (m)




                                                                          motor position (m)




                      0.4                                                                       0.4

                      0.2                                                                       0.2

                       0                                                                         0

                     −0.2                                                                      −0.2

                            95      100      105     110     115                                      345     350       355      360     365
                                            time (s)                                                                 time (s)




                                 Figure 5: Regular waves at Ì        ½¾   s and                         ¾ cm, Sphere, Test B




                                                                     17
                                                     Wave synchronization                                                                        Heave compensation
                                  8                                                                                                  8
tension (N) and LF (cyan)




                                                                                                         tension (N) and LF (cyan)
                                  6                                                                                                  6


                                  4                                                                                                  4


                                  2                                                                                                  2


                                  0                                                                                                  0
                                           260         265      270         275    280                                                     185      190      195      200
                                                             time (s)                                                                                 time (s)

                                  Wave sychronization and heave compensation                                                                           No control
                                  8                                                                                                  8
tension (N) and LF (cyan)




                                                                                                         tension (N) and LF (cyan)
                                  6                                                                                                  6


                                  4                                                                                                  4


                                  2                                                                                                  2


                                  0                                                                                                  0
                                          95         100      105     110         115                                                    345     350       355      360     365
                                                             time (s)                                                                                   time (s)
                                                      Wave synchronization                                                                       Heave compensation
                                      2                                                                                              2
acc payload (red) and LF (cyan)




                                                                                               acc payload (red) and LF (cyan)




                                      1                                                                                              1


                                      0                                                                                              0


                                  −1                                                                                             −1


                                  −2                                                                                             −2
                                               260         265      270     275     280                                                    185      190      195      200
                                                                 time (s)                                                                             time (s)

                                      Wave sychronization and heave compensation                                                                       No control
                                      2                                                                                              2
acc payload (red) and LF (cyan)




                                                                                               acc payload (red) and LF (cyan)




                                      1                                                                                              1


                                      0                                                                                              0


                                  −1                                                                                             −1


                                  −2                                                                                             −2
                                          95         100          105     110     115                                                    345     350       355      360     365
                                                                 time (s)                                                                               time (s)




                                                     Figure 6: Regular waves at Ì         ½¾   s and                                       ¾ cm, Sphere, Test B




                                                                                          18
                                  Wave synchronization                                                   Heave compensation
                  0.5                                                                    0.5
acc vessel




                                                                           acc vessel
                   0                                                                      0




                 −0.5                                                                   −0.5
                            260     265      270     275       280                               185        190      195       200
                                          time (s)                                                            time (s)

                    Wave sychronization and heave compensation                                                 No control
                  0.5                                                                    0.5
acc vessel




                                                                           acc vessel




                   0                                                                      0




                 −0.5                                                                   −0.5
                           95     100      105     110     115                                 345       350       355       360     365
                                          time (s)                                                              time (s)
                                                     Moonpool (green and blue) and basin (red)
                 0.7



                 0.6



                 0.5
Power spectrum




                 0.4



                 0.3



                 0.2



                 0.1



                  0
                       0                0.5                1             1.5                         2                 2.5            3
                                                                 Wave frequency (Hz)




                                Figure 7: Regular waves at Ì         ½¾    s and                 ¾ cm, Sphere, Test B




                                                                      19
                                      Wave synchronization                                                         Heave compensation


                        0.06                                                                        0.06
wave (m) moonpool




                                                                            wave (m) moonpool
                        0.04                                                                        0.04
                        0.02                                                                        0.02
                          0                                                                           0
                       −0.02                                                                       −0.02
                       −0.04                                                                       −0.04
                       −0.06                                                                       −0.06
                       −0.08                                                                       −0.08
                                260     265      270     275    280                                          185      190      195      200
                                              time (s)                                                                  time (s)

                          Wave sychronization and heave compensation                                                     No control


                        0.06                                                                        0.06
wave (m) moonpool




                                                                            wave (m) moonpool

                        0.04                                                                        0.04
                        0.02                                                                        0.02
                          0                                                                           0
                       −0.02                                                                       −0.02
                       −0.04                                                                       −0.04
                       −0.06                                                                       −0.06
                       −0.08                                                                       −0.08
                               95     100      105     110     115                                         345     350       355      360     365
                                              time (s)                                                                    time (s)
                                      Wave synchronization                                                         Heave compensation


                        0.06                                                                        0.06
wave (m) basin (red)




                                                                            wave (m) basin (red)




                        0.04                                                                        0.04
                        0.02                                                                        0.02
                          0                                                                           0
                       −0.02                                                                       −0.02
                       −0.04                                                                       −0.04
                       −0.06                                                                       −0.06
                       −0.08                                                                       −0.08
                                260     265      270     275    280                                          185      190      195      200
                                              time (s)                                                                  time (s)

                          Wave sychronization and heave compensation                                                     No control


                        0.06                                                                        0.06
wave (m) basin (red)




                                                                            wave (m) basin (red)




                        0.04                                                                        0.04
                        0.02                                                                        0.02
                          0                                                                           0
                       −0.02                                                                       −0.02
                       −0.04                                                                       −0.04
                       −0.06                                                                       −0.06
                       −0.08                                                                       −0.08
                               95     100      105     110     115                                         345     350       355      360     365
                                              time (s)                                                                    time (s)




                                    Figure 8: Regular waves at Ì       ½¾               s and                ¾ cm, Pump, Test B




                                                                       20
                                   Wave synchronization                                                            Heave compensation

                      0.2                                                                           0.2
motor speed (m/s)




                                                                              motor speed (m/s)
                      0.1                                                                           0.1


                       0                                                                             0


                     −0.1                                                                          −0.1


                     −0.2                                                                          −0.2
                            250    255    260    265       270     275                                       170     175        180   185     190
                                          time (s)                                                                         time (s)

                       Wave sychronization and heave compensation                                                      No control

                      0.2                                                                           0.2
motor speed (m/s)




                                                                              motor speed (m/s)


                      0.1                                                                           0.1


                       0                                                                             0


                     −0.1                                                                          −0.1


                     −0.2                                                                          −0.2
                             90      95     100      105         110                                   335     340     345     350      355
                                          time (s)                                                                      time (s)
                                   Wave synchronization                                                            Heave compensation
                      0.8                                                                           0.8

                      0.6                                                                           0.6
motor position (m)




                                                                              motor position (m)




                      0.4                                                                           0.4

                      0.2                                                                           0.2

                       0                                                                             0

                     −0.2                                                                          −0.2

                            250    255    260    265       270     275                                       170     175        180   185     190
                                          time (s)                                                                         time (s)

                        Wave sychronization and heave compensation                                                     No control
                      0.8                                                                           0.8

                      0.6                                                                           0.6
motor position (m)




                                                                              motor position (m)




                      0.4                                                                           0.4

                      0.2                                                                           0.2

                       0                                                                             0

                     −0.2                                                                          −0.2

                             90      95     100      105         110                                  335      340     345     350      355
                                          time (s)                                                                      time (s)




                                  Figure 9: Regular waves at Ì           ½¾    s and                         ¾ cm, Pump, Test A




                                                                         21
                                                 Wave synchronization                                                                               Heave compensation
                                  8                                                                                                    8
tension (N) and LF (cyan)




                                                                                                           tension (N) and LF (cyan)
                                  6                                                                                                    6


                                  4                                                                                                    4


                                  2                                                                                                    2


                                  0                                                                                                    0
                                          250    255    260    265        270     275                                                         170     175        180   185     190
                                                        time (s)                                                                                            time (s)

                                  Wave sychronization and heave compensation                                                                            No control
                                  8                                                                                                    8
tension (N) and LF (cyan)




                                                                                                           tension (N) and LF (cyan)
                                  6                                                                                                    6


                                  4                                                                                                    4


                                  2                                                                                                    2


                                  0                                                                                                    0
                                           90     95      100       105         110                                                     335    340      345     350      355
                                                        time (s)                                                                                         time (s)
                                                  Wave synchronization                                                                              Heave compensation
                                      2                                                                                                2
acc payload (red) and LF (cyan)




                                                                                                 acc payload (red) and LF (cyan)




                                      1                                                                                                1


                                      0                                                                                                0


                                  −1                                                                                               −1


                                  −2                                                                                               −2
                                          250    255    260    265         270        275                                                     170     175        180   185     190
                                                        time (s)                                                                                            time (s)

                                      Wave sychronization and heave compensation                                                                        No control
                                      2                                                                                                2
acc payload (red) and LF (cyan)




                                                                                                 acc payload (red) and LF (cyan)




                                      1                                                                                                1


                                      0                                                                                                0


                                  −1                                                                                               −1


                                  −2                                                                                               −2
                                            90     95      100       105         110                                                 335        340     345     350      355
                                                         time (s)                                                                                        time (s)




                                                 Figure 10: Regular waves at Ì              ½¾   s and                                         ¾ cm, Pump, Test A




                                                                                            22
                                   Wave synchronization                                                            Heave compensation
                  0.5                                                                               0.5
acc vessel




                                                                                      acc vessel
                   0                                                                                 0




                 −0.5                                                                              −0.5
                           250    255     260    265           270     275                                   170     175        180   185     190
                                          time (s)                                                                         time (s)

                    Wave sychronization and heave compensation                                                         No control
                  0.5                                                                               0.5
acc vessel




                                                                                      acc vessel




                   0                                                                                 0




                 −0.5                                                                              −0.5
                            90      95          100      105         110                               335    340      345     350      355
                                              time (s)                                                                  time (s)
                                                         Moonpool (green and blue) and basin (red)

                 0.8



                 0.7



                 0.6



                 0.5
Power spectrum




                 0.4



                 0.3



                 0.2



                 0.1



                  0
                       0                0.5                    1                   1.5                        2                 2.5            3
                                                                           Wave frequency (Hz)




                                 Figure 11: Regular waves at Ì                   ½¾       s and              ¾ cm, Pump, Test A




                                                                                23
                                        Wave synchronization                                                              Heave compensation


                        0.06                                                                              0.06
wave (m) moonpool




                                                                                  wave (m) moonpool
                        0.04                                                                              0.04
                        0.02                                                                              0.02
                          0                                                                                 0
                       −0.02                                                                             −0.02
                       −0.04                                                                             −0.04
                       −0.06                                                                             −0.06
                       −0.08                                                                             −0.08
                               250     255    260    265       270     275                                          170     175        180   185     190
                                              time (s)                                                                            time (s)

                          Wave sychronization and heave compensation                                                          No control


                        0.06                                                                              0.06
wave (m) moonpool




                                                                                  wave (m) moonpool

                        0.04                                                                              0.04
                        0.02                                                                              0.02
                          0                                                                                 0
                       −0.02                                                                             −0.02
                       −0.04                                                                             −0.04
                       −0.06                                                                             −0.06
                       −0.08                                                                             −0.08
                                90       95     100      105         110                                      335     340     345     350      355
                                              time (s)                                                                         time (s)
                                        Wave synchronization                                                              Heave compensation


                        0.06                                                                              0.06
wave (m) basin (red)




                                                                                  wave (m) basin (red)




                        0.04                                                                              0.04
                        0.02                                                                              0.02
                          0                                                                                 0
                       −0.02                                                                             −0.02
                       −0.04                                                                             −0.04
                       −0.06                                                                             −0.06
                       −0.08                                                                             −0.08
                               250     255    260    265       270     275                                          170     175        180   185     190
                                              time (s)                                                                            time (s)

                          Wave sychronization and heave compensation                                                          No control


                        0.06                                                                              0.06
wave (m) basin (red)




                                                                                  wave (m) basin (red)




                        0.04                                                                              0.04
                        0.02                                                                              0.02
                          0                                                                                 0
                       −0.02                                                                             −0.02
                       −0.04                                                                             −0.04
                       −0.06                                                                             −0.06
                       −0.08                                                                             −0.08
                                90       95     100      105         110                                      335     340     345     350      355
                                              time (s)                                                                         time (s)




                                     Figure 12: Regular waves at Ì           ½¾                 s and               ¾ cm, Pump, Test A




                                                                             24
Mode       À×             Ø
                                   Ñ Ò´ Ø µ        Ñ Ü´ Ø µ       Þ          Ñ Ò´Þµ      Ñ Ü´Þ µ
Sphere    Test A     Filtered   (0.5 - 1.5 Hz)
  Ws     0.140929   0.119137      1.233426         5.787420    0.137208      -0.323603   0.314699
  Hc     0.129563   0.085772      1.566849         5.849324    0.085160      -0.183688   0.177011
Ws+Hc    0.145822   0.089639      1.441192         5.672045    0.071665      -0.172134   0.196842
 none    0.133366   0.172708      1.363261         5.783954    0.197983      -0.357805   0.403569

Sphere    Test A    Unfiltered
  Ws     0.140929   0.270422      0.897056         6.123736    0.377981      -1.452998   1.232566
  Hc     0.129563   0.310364      0.825410         6.321483    0.434072      -1.166016   1.282921
Ws+Hc    0.145822   0.268914      0.885345         6.116791    0.369244      -1.260728   1.184828
 none    0.133366   0.359688      0.839921         6.020499    0.475496      -1.228008   1.104505

Sphere    Test B     Filtered   (0.5 - 1.5 Hz)
  Ws     0.146149   0.126486      1.676149         6.391967    0.146075      -0.330311   0.351247
  Hc     0.125508   0.140045      1.812155         5.955645    0.088839      -0.196299   0.210371
Ws+Hc    0.132829   0.086440      1.634072         5.786055    0.066158      -0.158606   0.150261
 none    0.147696   0.188946      1.591259         5.968182    0.209952      -0.422405   0.444642

Sphere    Test B    Unfiltered
  Ws     0.146149   0.322511      1.220800         6.985844    0.434190      -1.462208   1.062934
  Hc     0.125508   0.341766      1.077042         6.340165    0.452463      -1.205510   1.179610
Ws+Hc    0.132829   0.280850      1.041029         6.271269    0.394364      -1.072351   1.046822
 none    0.147696   0.407262      0.968331         6.211750    0.529311      -1.537896   1.348271

Pump      Test A     Filtered   (0.5 - 1.5 Hz)
  Ws     0.125626   0.083144      3.643843         5.728446    0.133995      -0.357737   0.366876
  Hc     0.147884   0.063287      3.698299         5.592405    0.086909      -0.191490   0.177141
Ws+Hc    0.155504   0.050923      3.765016         5.584578    0.061904      -0.141546   0.135270
 none    0.138238   0.131814      3.681908         5.791855    0.196529      -0.333658   0.357109

Pump      Test A    Unfiltered
  Ws     0.125626   0.233171      3.134766         5.947250    0.381145      -1.316349   1.178281
  Hc     0.147884   0.233697      3.258585         6.097025    0.380192      -1.126635   0.932620
Ws+Hc    0.155504   0.233955      3.210500         6.068031    0.383082      -1.066368   1.109607
 none    0.138238   0.202107      3.409899         6.188390    0.315419      -0.821098   0.874770

Pump      Test B     Filtered   (0.5 - 1.5 Hz)
  Ws     0.131482   0.093484      3.854790         5.875933    0.131105      -0.306519   0.300447
  Hc     0.170757   0.074580      3.914421         5.846177    0.091627      -0.203026   0.200025
Ws+Hc    0.159757   0.066779      3.892946         5.792726    0.061494      -0.132914   0.131479
 none    0.145883   0.142775      3.754977         5.916678    0.200955      -0.361894   0.374791

Pump      Test B    Unfiltered
  Ws     0.131482   0.240533      3.315567         6.244126    0.383532      -1.219221   1.336926
  Hc     0.170757   0.239702      3.471249         6.235620    0.373924      -1.394553   1.069778
Ws+Hc    0.159757   0.255866      3.354529         6.422333    0.413939      -1.317648   1.333159
 none    0.145883   0.211895      3.518764         6.449334    0.314398      -0.828859   0.807912

         Table 3: Summary of results with regular waves at Ì     ½ ¼ s and         cm.


                                              25
                                    Wave synchronization                                                       Heave compensation

                      0.2                                                                       0.2
motor speed (m/s)




                                                                          motor speed (m/s)
                      0.1                                                                       0.1


                       0                                                                         0


                     −0.1                                                                      −0.1


                     −0.2                                                                      −0.2
                            260      265       270     275   280                                   185     190      195      200      205
                                            time (s)                                                                time (s)

                       Wave sychronization and heave compensation                                                  No control

                      0.2                                                                       0.2
motor speed (m/s)




                                                                          motor speed (m/s)


                      0.1                                                                       0.1


                       0                                                                         0


                     −0.1                                                                      −0.1


                     −0.2                                                                      −0.2
                             110      115       120    125   130                                         335      340      345      350
                                            time (s)                                                                time (s)
                                    Wave synchronization                                                       Heave compensation
                      0.8                                                                       0.8

                      0.6                                                                       0.6
motor position (m)




                                                                          motor position (m)




                      0.4                                                                       0.4

                      0.2                                                                       0.2

                       0                                                                         0

                     −0.2                                                                      −0.2

                            260      265       270     275   280                                  185      190      195      200      205
                                            time (s)                                                                time (s)

                        Wave sychronization and heave compensation                                                 No control
                      0.8                                                                       0.8

                      0.6                                                                       0.6
motor position (m)




                                                                          motor position (m)




                      0.4                                                                       0.4

                      0.2                                                                       0.2

                       0                                                                         0

                     −0.2                                                                      −0.2

                             110      115       120    125   130                                         335      340      345      350
                                            time (s)                                                                time (s)




                                   Figure 13: Regular waves at Ì     ½ ¼ s and                           cm, Sphere, Test B




                                                                     26
                                                  Wave synchronization                                                                     Heave compensation
                                  8                                                                                           8
tension (N) and LF (cyan)




                                                                                                  tension (N) and LF (cyan)
                                  6                                                                                           6


                                  4                                                                                           4


                                  2                                                                                           2


                                  0                                                                                           0
                                          260     265        270      275    280                                               185     190      195         200     205
                                                          time (s)                                                                              time (s)

                                  Wave sychronization and heave compensation                                                                   No control
                                  8                                                                                           8
tension (N) and LF (cyan)




                                                                                                  tension (N) and LF (cyan)
                                  6                                                                                           6


                                  4                                                                                           4


                                  2                                                                                           2


                                  0                                                                                           0
                                           110     115        120     125    130                                                     335      340      345        350
                                                          time (s)                                                                              time (s)
                                                   Wave synchronization                                                                    Heave compensation
                                      2                                                                                       2
acc payload (red) and LF (cyan)




                                                                                        acc payload (red) and LF (cyan)




                                      1                                                                                       1


                                      0                                                                                       0


                                  −1                                                                                      −1


                                  −2                                                                                      −2
                                          260      265        270     275    280                                            185        190       195        200     205
                                                           time (s)                                                                              time (s)

                                      Wave sychronization and heave compensation                                                               No control
                                      2                                                                                       2
acc payload (red) and LF (cyan)




                                                                                        acc payload (red) and LF (cyan)




                                      1                                                                                       1


                                      0                                                                                       0


                                  −1                                                                                      −1


                                  −2                                                                                      −2
                                            110     115        120     125   130                                                     335      340      345        350
                                                           time (s)                                                                             time (s)




                                                  Figure 14: Regular waves at Ì    ½ ¼ s and                                          cm, Sphere, Test B




                                                                                   27
                                   Wave synchronization                                                   Heave compensation
                  0.5                                                                      0.5
acc vessel




                                                                             acc vessel
                   0                                                                        0




                 −0.5                                                                     −0.5
                           260      265         270      275      280                         185     190      195      200      205
                                             time (s)                                                          time (s)

                    Wave sychronization and heave compensation                                                No control
                  0.5                                                                      0.5
acc vessel




                                                                             acc vessel




                   0                                                                        0




                 −0.5                                                                     −0.5
                            110      115         120     125      130                               335      340      345      350
                                             time (s)                                                          time (s)
                                                        Moonpool (green and blue) and basin (red)




                  2




                 1.5
Power spectrum




                  1




                 0.5




                  0
                       0               0.5                 1              1.5                        2               2.5               3
                                                                  Wave frequency (Hz)




                                  Figure 15: Regular waves at Ì         ½ ¼ s and                   cm, Sphere, Test B




                                                                        28
                                        Wave synchronization                                                        Heave compensation


                        0.06                                                                        0.06
wave (m) moonpool




                                                                            wave (m) moonpool
                        0.04                                                                        0.04
                        0.02                                                                        0.02
                          0                                                                           0
                       −0.02                                                                       −0.02
                       −0.04                                                                       −0.04
                       −0.06                                                                       −0.06
                       −0.08                                                                       −0.08
                               260      265        270     275   280                                    185     190      195      200      205
                                                time (s)                                                                 time (s)

                          Wave sychronization and heave compensation                                                    No control


                        0.06                                                                        0.06
wave (m) moonpool




                                                                            wave (m) moonpool

                        0.04                                                                        0.04
                        0.02                                                                        0.02
                          0                                                                           0
                       −0.02                                                                       −0.02
                       −0.04                                                                       −0.04
                       −0.06                                                                       −0.06
                       −0.08                                                                       −0.08
                                110       115       120    125   130                                          335      340      345      350
                                                time (s)                                                                 time (s)
                                        Wave synchronization                                                        Heave compensation


                        0.06                                                                        0.06
wave (m) basin (red)




                                                                            wave (m) basin (red)




                        0.04                                                                        0.04
                        0.02                                                                        0.02
                          0                                                                           0
                       −0.02                                                                       −0.02
                       −0.04                                                                       −0.04
                       −0.06                                                                       −0.06
                       −0.08                                                                       −0.08
                               260      265        270     275   280                                    185     190      195      200      205
                                                time (s)                                                                 time (s)

                          Wave sychronization and heave compensation                                                    No control


                        0.06                                                                        0.06
wave (m) basin (red)




                                                                            wave (m) basin (red)




                        0.04                                                                        0.04
                        0.02                                                                        0.02
                          0                                                                           0
                       −0.02                                                                       −0.02
                       −0.04                                                                       −0.04
                       −0.06                                                                       −0.06
                       −0.08                                                                       −0.08
                                110       115       120    125   130                                          335      340      345      350
                                                time (s)                                                                 time (s)




                                      Figure 16: Regular waves at Ì    ½ ¼ s and                              cm, Pump, Test B




                                                                       29
                                        Wave synchronization                                                        Heave compensation

                      0.2                                                                             0.2
motor speed (m/s)




                                                                                motor speed (m/s)
                      0.1                                                                             0.1


                       0                                                                               0


                     −0.1                                                                            −0.1


                     −0.2                                                                            −0.2
                                 225        230       235     240    245                                    150     155        160      165     170
                                                  time (s)                                                                 time (s)

                       Wave sychronization and heave compensation                                                         No control

                      0.2                                                                             0.2
motor speed (m/s)




                                                                                motor speed (m/s)


                      0.1                                                                             0.1


                       0                                                                               0


                     −0.1                                                                            −0.1


                     −0.2                                                                            −0.2
                            75         80           85       90     95                                      300     305       310      315    320
                                                  time (s)                                                                 time (s)
                                        Wave synchronization                                                        Heave compensation
                      0.8                                                                             0.8

                      0.6                                                                             0.6
motor position (m)




                                                                                motor position (m)




                      0.4                                                                             0.4

                      0.2                                                                             0.2

                       0                                                                               0

                     −0.2                                                                            −0.2

                                 225        230       235     240    245                                    150     155        160      165     170
                                                  time (s)                                                                 time (s)

                        Wave sychronization and heave compensation                                                        No control
                      0.8                                                                             0.8

                      0.6                                                                             0.6
motor position (m)




                                                                                motor position (m)




                      0.4                                                                             0.4

                      0.2                                                                             0.2

                       0                                                                               0

                     −0.2                                                                            −0.2

                            75         80           85       90     95                                      300     305       310      315    320
                                                  time (s)                                                                 time (s)




                                       Figure 17: Regular waves at Ì       ½ ¼ s and                              cm, Pump, Test A




                                                                           30
                                                     Wave synchronization                                                                               Heave compensation
                                  8                                                                                                          8
tension (N) and LF (cyan)




                                                                                                                 tension (N) and LF (cyan)
                                  6                                                                                                          6


                                  4                                                                                                          4


                                  2                                                                                                          2


                                  0                                                                                                          0
                                               225        230       235      240        245                                                      150     155        160      165     170
                                                                time (s)                                                                                        time (s)

                                  Wave sychronization and heave compensation                                                                                   No control
                                  8                                                                                                          8
tension (N) and LF (cyan)




                                                                                                                 tension (N) and LF (cyan)

                                  6                                                                                                          6


                                  4                                                                                                          4


                                  2                                                                                                          2


                                  0                                                                                                          0
                                      75             80           85        90         95                                                        300    305        310      315    320
                                                                time (s)                                                                                        time (s)
                                                      Wave synchronization                                                                              Heave compensation
                                      2                                                                                                      2
acc payload (red) and LF (cyan)




                                                                                                       acc payload (red) and LF (cyan)




                                      1                                                                                                      1


                                      0                                                                                                      0


                                  −1                                                                                                     −1


                                  −2                                                                                                     −2
                                               225        230        235         240        245                                                  150     155        160      165     170
                                                                 time (s)                                                                                       time (s)

                                      Wave sychronization and heave compensation                                                                               No control
                                      2                                                                                                      2
acc payload (red) and LF (cyan)




                                                                                                       acc payload (red) and LF (cyan)




                                      1                                                                                                      1


                                      0                                                                                                      0


                                  −1                                                                                                     −1


                                  −2                                                                                                     −2
                                          75         80            85       90         95                                                        300     305       310      315    320
                                                                 time (s)                                                                                       time (s)




                                                      Figure 18: Regular waves at Ì               ½ ¼ s and                                            cm, Pump, Test A




                                                                                                  31
                                       Wave synchronization                                                    Heave compensation
                  0.5                                                                          0.5
acc vessel




                                                                                 acc vessel
                   0                                                                            0




                 −0.5                                                                         −0.5
                                225        230       235     240      245                            150       155        160       165     170
                                                 time (s)                                                             time (s)

                    Wave sychronization and heave compensation                                                       No control
                  0.5                                                                          0.5
acc vessel




                                                                                 acc vessel




                   0                                                                            0




                 −0.5                                                                         −0.5
                           75         80           85       90       95                              300       305       310       315    320
                                                 time (s)                                                             time (s)
                                                            Moonpool (green and blue) and basin (red)




                  2




                 1.5
Power spectrum




                  1




                 0.5




                  0
                       0                    0.5                  1            1.5                          2                 2.5                3
                                                                      Wave frequency (Hz)




                                      Figure 19: Regular waves at Ì          ½ ¼ s and                     cm, Pump, Test A




                                                                            32
                                          Wave synchronization                                                            Heave compensation


                        0.06                                                                               0.06
wave (m) moonpool




                                                                                   wave (m) moonpool
                        0.04                                                                               0.04
                        0.02                                                                               0.02
                          0                                                                                  0
                       −0.02                                                                              −0.02
                       −0.04                                                                              −0.04
                       −0.06                                                                              −0.06
                       −0.08                                                                              −0.08
                                    225        230       235     240    245                                       150      155        160      165     170
                                                     time (s)                                                                     time (s)

                          Wave sychronization and heave compensation                                                             No control


                        0.06                                                                               0.06
wave (m) moonpool




                                                                                   wave (m) moonpool


                        0.04                                                                               0.04
                        0.02                                                                               0.02
                          0                                                                                  0
                       −0.02                                                                              −0.02
                       −0.04                                                                              −0.04
                       −0.06                                                                              −0.06
                       −0.08                                                                              −0.08
                               75         80           85       90     95                                         300      305       310      315    320
                                                     time (s)                                                                     time (s)
                                          Wave synchronization                                                            Heave compensation


                        0.06                                                                               0.06
wave (m) basin (red)




                                                                                   wave (m) basin (red)




                        0.04                                                                               0.04
                        0.02                                                                               0.02
                          0                                                                                  0
                       −0.02                                                                              −0.02
                       −0.04                                                                              −0.04
                       −0.06                                                                              −0.06
                       −0.08                                                                              −0.08
                                    225        230       235     240    245                                       150      155        160      165     170
                                                     time (s)                                                                     time (s)

                          Wave sychronization and heave compensation                                                             No control


                        0.06                                                                               0.06
wave (m) basin (red)




                                                                                   wave (m) basin (red)




                        0.04                                                                               0.04
                        0.02                                                                               0.02
                          0                                                                                  0
                       −0.02                                                                              −0.02
                       −0.04                                                                              −0.04
                       −0.06                                                                              −0.06
                       −0.08                                                                              −0.08
                               75         80           85       90     95                                         300      305       310      315    320
                                                     time (s)                                                                     time (s)




                                      Figure 20: Regular waves at Ì           ½ ¼ s and                                 cm, Pump, Test A




                                                                              33
   ¯   The use of heave compensation does not give any significant reduction of tension variability.

   ¯   The payload acceleration is significantly reduced using heave compensation but wave synchro-
       nization gives some increase in acceleration.

   ¯   For the pump-in-frame payload, the wave synchronization reduces the tension standard deviation
       by 4.2 % on average. Wave synchronization in combination with heave compensation increases
       the tension standard deviation by 10.0 % on average, when considering filtered data.

   ¯   When considering the unfiltered data with the spherical payload, similar qualitative conclusions
       can be made in most cases. With the pump-in-frame payload the variance is somewhat increased.

   ¯   It should be remarked that averaging not very meaningful because there are only five tests.


 Mode             À×               Ø
                                            Ñ Ò´ Ø µ       Ñ Ü´ Ø µ          Þ      Ñ Ò´Þµ      Ñ Ü´Þ µ
 Sphere     Avg. Test A-E     Filtered    (0.5 - 1.5 Hz)
   Ws         0.056344       0.077631       1.678904       5.852417   0.103220     -0.223124    0.223629
   Hc         0.052885       0.120011       1.586839       5.779087   0.047672     -0.107292    0.111874
 Ws+Hc        0.058565       0.108441       1.693125       6.066377   0.119405     -0.316455    0.316524
  none        0.063855       0.107173       1.608691       6.055017   0.082840     -0.187113    0.183162

 Sphere     Avg. Test A-E    Unfiltered
   Ws         0.056344       0.314209       0.995342       6.298145   0.434457     -1.523909    1.116269
   Hc         0.052885       0.302401       1.030220       6.238224   0.391227     -1.326201    1.012649
 Ws+Hc        0.058565       0.348831       0.947103       6.593276   0.471319     -1.719319    1.393762
  none        0.063855       0.381432       0.940792       6.431565   0.506801     -1.258611    1.133136

 Pump       Avg. Test A-E     Filtered    (0.5 - 1.5 Hz)
   Ws         0.051406       0.058548       3.919543       5.787056   0.106257     -0.274711    0.260420
   Hc         0.050830       0.062965       3.887495       5.794023   0.043820     -0.112190    0.108023
 Ws+Hc        0.061632       0.054974       3.902177       5.664070   0.110833     -0.295802    0.297791
  none        0.061182       0.061126       3.864759       5.811901   0.087255     -0.203082    0.194729

 Pump       Avg. Test A-E    Unfiltered
   Ws         0.051406       0.241929       3.291288       6.137570   0.398284     -1.512659    1.356862
   Hc         0.050830       0.223636       3.394861       6.363680   0.350418     -1.126899    0.944196
 Ws+Hc        0.061632       0.240381       3.319888       6.076801   0.398873     -1.456790    1.101630
  none        0.061182       0.160626       3.548589       6.315000   0.247505     -0.679781    0.598222

Table 4: Summary of results with JONSWAP spectrum at Ì           ½ ¼ s and       ¿ cm, averaged over 5
tests.




7 Simulations
Some simulations are included, primarily because they include the hydrodynamic forces on the payload,
which cannot be measured directly. The simulation model is documented in [2].
    Figures 25, 26, and 27 show the payload acceleration Þ , wire tension Ø and hydrodynamic forces
 Þ during a lifting operation with irregular waves, typical moonpool wave amplitude 0.04 Ñ and wave
period 1.0 × (1.2 Ñ and 6.3 × in full scale), and a typical vessel heave amplitude 0.025 Ñ and period 1.6


                                                   34
                                       Wave synchronization                                                         Heave compensation

                      0.2                                                                              0.2
motor speed (m/s)




                                                                                 motor speed (m/s)
                      0.1                                                                              0.1


                       0                                                                                0


                     −0.1                                                                             −0.1


                     −0.2                                                                             −0.2
                                 235        240      245        250                                          155      160       165    170   175
                                               time (s)                                                                     time (s)

                       Wave sychronization and heave compensation                                                        No control

                      0.2                                                                              0.2
motor speed (m/s)




                                                                                 motor speed (m/s)


                      0.1                                                                              0.1


                       0                                                                                0


                     −0.1                                                                             −0.1


                     −0.2                                                                             −0.2
                            80         85         90       95         100                                    310      315       320    325   330
                                               time (s)                                                                     time (s)
                                       Wave synchronization                                                         Heave compensation
                      0.8                                                                              0.8

                      0.6                                                                              0.6
motor position (m)




                                                                                 motor position (m)




                      0.4                                                                              0.4

                      0.2                                                                              0.2

                       0                                                                                0

                     −0.2                                                                             −0.2

                                 235        240      245        250                                          155      160       165    170   175
                                               time (s)                                                                     time (s)

                        Wave sychronization and heave compensation                                                       No control
                      0.8                                                                              0.8

                      0.6                                                                              0.6
motor position (m)




                                                                                 motor position (m)




                      0.4                                                                              0.4

                      0.2                                                                              0.2

                       0                                                                                0

                     −0.2                                                                             −0.2

                            80         85         90       95         100                                    310      315       320    325   330
                                               time (s)                                                                     time (s)




                                 Figure 21: JONSWAP spectrum at Ì                ½ ¼ s and                         ¿ cm, Sphere, Test B




                                                                            35
                                                     Wave synchronization                                                                         Heave compensation
                                  8                                                                                                    8
tension (N) and LF (cyan)




                                                                                                           tension (N) and LF (cyan)
                                  6                                                                                                    6


                                  4                                                                                                    4


                                  2                                                                                                    2


                                  0                                                                                                    0
                                               235        240      245         250                                                         155     160        165    170   175
                                                             time (s)                                                                                     time (s)

                                  Wave sychronization and heave compensation                                                                          No control
                                  8                                                                                                    8
tension (N) and LF (cyan)




                                                                                                           tension (N) and LF (cyan)
                                  6                                                                                                    6


                                  4                                                                                                    4


                                  2                                                                                                    2


                                  0                                                                                                    0
                                          80         85         90        95         100                                                   310      315       320    325   330
                                                             time (s)                                                                                     time (s)
                                                      Wave synchronization                                                                        Heave compensation
                                      2                                                                                                2
acc payload (red) and LF (cyan)




                                                                                                 acc payload (red) and LF (cyan)




                                      1                                                                                                1


                                      0                                                                                                0


                                  −1                                                                                               −1


                                  −2                                                                                               −2
                                               235         240      245        250                                                         155      160       165    170   175
                                                              time (s)                                                                                    time (s)

                                      Wave sychronization and heave compensation                                                                       No control
                                      2                                                                                                2
acc payload (red) and LF (cyan)




                                                                                                 acc payload (red) and LF (cyan)




                                      1                                                                                                1


                                      0                                                                                                0


                                  −1                                                                                               −1


                                  −2                                                                                               −2
                                          80          85         90       95         100                                                   310      315       320    325   330
                                                              time (s)                                                                                    time (s)




                                                Figure 22: JONSWAP spectrum at Ì                ½ ¼ s and                                        ¿ cm, Sphere, Test B




                                                                                           36
                                       Wave synchronization                                                    Heave compensation
                  0.5                                                                          0.5
acc vessel




                                                                                 acc vessel
                   0                                                                            0




                 −0.5                                                                         −0.5
                                 235        240      245        250                                  155        160       165      170   175
                                               time (s)                                                               time (s)

                    Wave sychronization and heave compensation                                                     No control
                  0.5                                                                          0.5
acc vessel




                                                                                 acc vessel




                   0                                                                            0




                 −0.5                                                                         −0.5
                            80         85         90       95         100                            310        315       320      325   330
                                               time (s)                                                               time (s)
                                                           Moonpool (green and blue) and basin (red)


                 0.06




                 0.05




                 0.04
Power spectrum




                 0.03




                 0.02




                 0.01




                   0
                        0                    0.5                1              1.5                         2                 2.5           3
                                                                       Wave frequency (Hz)




                                 Figure 23: JONSWAP spectrum at Ì                ½ ¼ s and                 ¿ cm, Sphere, Test B




                                                                            37
                                          Wave synchronization                                                            Heave compensation


                        0.06                                                                                0.06
wave (m) moonpool




                                                                                    wave (m) moonpool
                        0.04                                                                                0.04
                        0.02                                                                                0.02
                          0                                                                                   0
                       −0.02                                                                               −0.02
                       −0.04                                                                               −0.04
                       −0.06                                                                               −0.06
                       −0.08                                                                               −0.08
                                    235        240      245        250                                             155      160       165    170   175
                                                  time (s)                                                                        time (s)

                          Wave sychronization and heave compensation                                                           No control


                        0.06                                                                                0.06
wave (m) moonpool




                                                                                    wave (m) moonpool


                        0.04                                                                                0.04
                        0.02                                                                                0.02
                          0                                                                                   0
                       −0.02                                                                               −0.02
                       −0.04                                                                               −0.04
                       −0.06                                                                               −0.06
                       −0.08                                                                               −0.08
                               80         85         90       95         100                                       310      315       320    325   330
                                                  time (s)                                                                        time (s)
                                          Wave synchronization                                                            Heave compensation


                        0.06                                                                                0.06
wave (m) basin (red)




                                                                                    wave (m) basin (red)




                        0.04                                                                                0.04
                        0.02                                                                                0.02
                          0                                                                                   0
                       −0.02                                                                               −0.02
                       −0.04                                                                               −0.04
                       −0.06                                                                               −0.06
                       −0.08                                                                               −0.08
                                    235        240      245        250                                             155      160       165    170   175
                                                  time (s)                                                                        time (s)

                          Wave sychronization and heave compensation                                                           No control


                        0.06                                                                                0.06
wave (m) basin (red)




                                                                                    wave (m) basin (red)




                        0.04                                                                                0.04
                        0.02                                                                                0.02
                          0                                                                                   0
                       −0.02                                                                               −0.02
                       −0.04                                                                               −0.04
                       −0.06                                                                               −0.06
                       −0.08                                                                               −0.08
                               80         85         90       95         100                                       310      315       320    325   330
                                                  time (s)                                                                        time (s)




                                Figure 24: JONSWAP spectrum at Ì                           ½ ¼ s and                     ¿ cm, Pump, Test B




                                                                               38
× (0.75 Ñ and 8.7 × in full scale). The figures also show the vertical payload, vessel and wave positions
during the water entry phase. The required motor speed (not shown) is within realistic limits. The
different strategies are simulated with the same external excitations (waves) and similar improvements
in performance are typically achieved for other realizations of the random waves. It can be seen that
payload acceleration is smallest with heave compensation, while the wave synchronization reduces the
hydrodynamic forces and wire tension during water entry. The remaining hydrodynamic forces and wire
tension variations are to a large degree high-frequency (at the wire resonance). They might be further
damped by a standard passive heave compensation system as the motor bandwidth does not allow active
control at such high frequencies.
               Position (payload(−), relative(−−−), heave(−), wave (−−−))                             Payload acceleration
                                                                                         1.5


           0.3                                                                            1


           0.2
                                                                                         0.5




                                                                             ap (m/s )
                                                                            2
  z (m)




           0.1
                                                                                          0

               0
                                                                                   −0.5

          −0.1
                                                                                         −1

          −0.2
                                                                                   −1.5
               30                35                  40                45             25        30    35       40       45   50   55
                                         time (s)                                                           time (s)
                                      Wire tension                                                   Hydrodynamic force fz
           7                                                                         7

           6                                                                         6

           5                                                                         5

           4                                                                         4
  Ft (N)




                                                                            fz (N)




           3                                                                         3


           2                                                                         2


           1                                                                         1


           0                                                                         0


          −1                                                                     −1
           25          30       35         40        45      50        55         25           30    35       40       45    50   55
                                        time (s)                                                           time (s)




                               Figure 25: Simulations without active control, i.e. constant speed.


               Position (payload(−), relative(−−−), heave(−), wave (−−−))                             Payload acceleration
                                                                                         1.5


           0.3                                                                            1


           0.2
                                                                                         0.5
                                                                             ap (m/s )
                                                                            2
  z (m)




           0.1
                                                                                          0

               0
                                                                                   −0.5

          −0.1
                                                                                         −1

          −0.2
                                                                                   −1.5
               30                35                  40                45             25        30    35       40       45   50   55
                                         time (s)                                                           time (s)
                                      Wire tension                                                   Hydrodynamic force f
                                                                                                                         z
           7                                                                         7

           6                                                                         6

           5                                                                         5

           4                                                                         4
  Ft (N)




                                                                            fz (N)




           3                                                                         3


           2                                                                         2


           1                                                                         1


           0                                                                         0


          −1                                                                     −1
           25          30       35         40        45      50        55         25           30    35       40       45    50   55
                                        time (s)                                                           time (s)




                                          Figure 26: Simulations with heave compensation.




                                                                        39
               Position (payload(−), relative(−−−), heave(−), wave (−−−))                             Payload acceleration
                                                                                         1.5


           0.3                                                                            1


           0.2
                                                                                         0.5




                                                                             ap (m/s )
                                                                            2
  z (m)




           0.1
                                                                                          0

               0
                                                                                   −0.5

          −0.1
                                                                                         −1

          −0.2
                                                                                   −1.5
               30                35                  40                45             25        30    35       40       45   50   55
                                         time (s)                                                           time (s)
                                      Wire tension                                                   Hydrodynamic force fz
           7                                                                         7

           6                                                                         6

           5                                                                         5

           4                                                                         4
  Ft (N)




                                                                            fz (N)
           3                                                                         3


           2                                                                         2


           1                                                                         1


           0                                                                         0


          −1                                                                     −1
           25          30       35         40        45      50        55         25           30    35       40       45    50   55
                                        time (s)                                                           time (s)




                                         Figure 27: Simulations with wave synchronization.



8 Discussions
Wave synchronization, either alone or in combination with heave compensation, significantly reduces
tension variability and peak values in a large majority of the tests. However, under some sea states,
in particular with the ”pump in the frame” payload, no or only small improvement was experienced.
Payload acceleration is sometimes increased simply because the payload need to move more quickly in
order to synchronize with the wave motion, while under some sea states the payload acceleration is also
reduced. The experiments with regular waves showed high repeatability, with small variations between
experiments under the same sea state.
    There are significant differences in performance when comparing the spherical and pump-in-frame
payload. The wave synchronization shows consistently greater improvements with the spherical payload
than with the pump-in-the frame. Reasons for this may be that the sphere is more sensitive to the waves
because it is a closed structure, while the pump is in an open frame. The pump-in-frame has significantly
less buoyancy and more irregular shape, which is also expected to play a role.
    Overall, the results are encouraging, showing that wave synchronization has a significant benefit in
terms of reduced tension variability and peaks at least under some sea states and with some payloads.
    The following limitations to performance has been identified:

   1. The feedforward approach leads to a phase error, due to the dynamics of the motor and signal
      filtering. In our experimental setup this error is significant, but not compensated for. For a wave
      period of 1.0 s, the phase loss in the motor is 15 degrees and the phase loss in the filtering of the
      wave amplitude measurement is about 25 deg. The total phase loss is around 40 deg, which is
      significant. It is therefore clear that the use of some model-based predictor of the wave amplitude
      may lead to significant improvement of performance.

   2. The wire resonance is being excited, also without the use of wave synchronization or heave com-
      pensation. The use of heave compensation or heave compensation reduces the excitations of the
      resonance in most cases with the spherical payload, while the excitations of the resonance seems
      to be typically increased with the pump-in-frame payload. There are several possible sources for
      these excitations:

                   (a) Even with constant speed reference the AC motor speed measurement exhibit oscillations


                                                                        40
           with significant frequency components in area where the resonance frequency is. This situa-
           tion may be improved by the use of a gear that will increase operating range of the motor and
           shift the frequencies. Notice that the AC motor control system is built into the motor drive
           and cannot be modified.
       (b) The water flow inside the moonpool may contain frequency components that give hydrody-
           namic forces that excite the resonance.
       (c) With heave compensation and wave feed-forward is it clear that measurement noise may
           excite the resonance frequency. Since there is very little damping in the suspension and the
           resonance frequency is less than a decade above from typical wave frequencies, any filtering
           will lead to phase loss as described above. A further complication is that the resonance
           frequency depend on payload mass and position-dependent hydrodynamic properties such
           as added mass. Improvements may be expected by adaptive notch filtering, in combination
           with wave prediction. Obviously, the technical solutions for wave measurements, signal
           transmission and electronics may be modified to reduce the overall noise level. Noise is
           amplified due to numerical differentiation when computing the wave surface speed from the
           wave amplitude measurements. This may be avoided via the use of position control of the
           AC motor rather than velocity control.

      It may be that the degree of damping in the scale model is too small compared to typical full scale
      cranes, and the effects of resonances will be much less in full scale.


9 Full scale implementability
A full scale implementation of wave synchronization requires essentially a wave feedforward signal to
be added to an existing active heave compensation system. The key requirement is the availability of a
measurement or estimate of the water vertical velocity within the moonpool. In the scale experiments
we utilized a standard laboratory-type wave amplitude measurement system from DHI (wave gauge
202/201), which relies on measurement of the water-level dependent conductivity between two parallel
electrodes. In order to determine the water vertical velocity the measured amplitude was differentiated
after low-pass and notch filtering. In full scale implementation the same measurement principle may
prove useful, but alternatives such as water pressure and optical/radar systems should be evaluated. If
the water vertical velocity can be measured directly, it would be an advantage since the noise-sensitive
differentiation of the amplitude measurement can be avoided. Very rough estimates indicate that moon-
pool wave amplitude measurements at 0.05 m accuracy or water vertical velocity measurements at 0.05
m/s accuracy is sufficient.
    A measurement or estimate of the payload position relative to the mean sea level is required. Since
this measurement is only used to gradually activate/deactivate the wave synchronization as the payload
moves through the water entry phase, high accuracy is not required (0.50 m accuracy is expected to be
sufficient).
    A model scale sampling frequency on 200 Hz was utilized, corresponding to a full scale sampling
frequency of 36 Hz. Such a high sampling frequency was chosen mainly to allow accurate analysis
of data (for presentation and performance evaluation) and digital signal processing (rather than analog
filtering). In order to implement the core functionality of the wave synchronization, a significantly lower
sampling frequency is expected to be sufficient. In any case, the computational requirements are very
small, essentially limited to a few filters.
    The motor time constant Ì       ¼ ¼¾¼ s corresponds to approximately Ì ¼ ½ s in full scale, and its
time-delay Ì      ¼ ¼½¼ corresponds to Ì ¼ ¼ s in full scale. It is assumed the motor is equipped with
a speed controller.
    Tuning of the controller involves the following aspects:


                                                  41
   ¯   Bandpass filters must be tuned to reduce sensor signal high-frequency noise and low-frequency
       drift. The cutoff frequencies depend on the wave spectrum and may be adapted online for optimal
       performance.

   ¯   The notch filter is tuned to avoid excitation of the wire resonance. Since these will depend on the
       payload position, mass and hydrodynamic parameters, in addition to the type of wire, it should
       be considered to implement an adaptive filter that estimates the resonance frequency in real time
       during operation. In order to get information for the adaptive filter, a tension or acceleration
       measurement on payload or wire is useful.

   ¯   An estimate of how the water vertical velocity reduces with the water depth must be made, based
       on the moonpool geometry.


10 Suggestions for future work
Below are some ideas for future work:
   1. Redesign of rig. In particular the deplacement (main dimensions) of the rig should be increased to
      simplify ballasting and to improve metacentric stability.

   2. The springs used for station-keeping should be mounted in the horizontal plane in order to avoid
      excitation of the heave mode. In addition the optimal stiffness of the springs should be computed
      according the P-gain in DP control system.

   3. Improved design and tuning of filters, including predictors to reduce phase error due to filtering
      and motor dynamics as well as to avoid exciting resonant wire elasticity. This may give significant
      performance improvements.

   4. Motor position control rather than speed control: avoid numerical differentiation of wave ampli-
      tude measurements. This improves phase margins and performance of the wave synchronization
      algorithm.

   5. Compensation of roll and pitch for acceleration measurements (VRU-functionality).

   6. Redesign of suspension (four wires instead of one) to improve horizontal stability and to get real-
      istic amounts of passive damping in the system.

   7. Gear to improve motor accuracy.

   8. Consider alternative sensor solutions for wave amplitude (such as pressure) or water vertical ve-
      locity.

   9. Test the method also for water exit.

 10. Evaluate alternative control strategies such as combination of feedback/feedforward and optimiza-
     tion of payload trajectories.


11 Conclusions
Wave synchronization has been suggested to improve the performance of heave compensated offshore
cranes during the water entry phase in moonpool marine operations. The method requires measurement
of the wave amplitude in the moonpool, and is implemented as a feedforward compensator. Experimental
results using a scale model shows that typical reduction of the wire tension standard deviation is between
0 to 50 % depending on the sea state and payload.

                                                   42
References
[1] M. P. Fard and F. G. Nielsen. Simulation of coupled vessel-load dynamics. Technical Report NH-
    00036960, Norsk Hydro, Exploration and Production, Bergen, Norway, 2001.

[2] T. I. Fossen and T. A. Johansen. Modelling and identification of offshore crane-rig system. Technical
    Report 2001-12-T, Department of Engineering Cybernetics, NTNU, Trondheim, Norway, 2001.

[3] T. A. Johansen and T. I. Fossen. Hydrolaunch free decay tests. Technical Report 2001-18-T, Depart-
    ment of Engineering Cybernetics, NTNU, Trondheim, Norway, 2001.

[4] F. G. Nielsen. Coupled hydrodynamics for the hydrolaunch vessel with load. Technical report, Norsk
    Hydro, Exploration and Production, Bergen, Norway, 2001.




                                                  43

								
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