IntroductionMathematical Model

SimulationsConclusions

Control-Oriented Modelling of anInterconnected Marine Structure

Mícheál Ó Catháin

1Department of Marine TechnologyNTNU

2Department of Electronic EngineeringNational University of Ireland, Maynooth (NUIM)

6/4-06

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

Outline

1 IntroductionThe DeviceExperimental Scale Model

2 Mathematical ModelDynamicsPower Take OffSimplifications

3 SimulationsBlock DiagramPlots

4 ConclusionsDiscussionThe Road Ahead

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

Outline

1 IntroductionThe DeviceExperimental Scale Model

2 Mathematical ModelDynamicsPower Take OffSimplifications

3 SimulationsBlock DiagramPlots

4 ConclusionsDiscussionThe Road Ahead

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

Outline

1 IntroductionThe DeviceExperimental Scale Model

2 Mathematical ModelDynamicsPower Take OffSimplifications

3 SimulationsBlock DiagramPlots

4 ConclusionsDiscussionThe Road Ahead

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

Outline

1 IntroductionThe DeviceExperimental Scale Model

2 Mathematical ModelDynamicsPower Take OffSimplifications

3 SimulationsBlock DiagramPlots

4 ConclusionsDiscussionThe Road Ahead

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

The real-world systemExpMod

Outline

1 IntroductionThe DeviceExperimental Scale Model

2 Mathematical ModelDynamicsPower Take OffSimplifications

3 SimulationsBlock DiagramPlots

4 ConclusionsDiscussionThe Road Ahead

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

The real-world systemExpMod

McCabe Wave Pump

Figure: The McCabe Wave Pump

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

The real-world systemExpMod

Experimental Scale ModelBarge Connected Rigidly to Bottom via 4 legs

Figure: Experimental Scale Modelof a 2 barge interconnected marinestructure

Figure: MCLab InhouseComponents used: Statoil Bargeand Hydrolaunch

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

The real-world systemExpMod

Experimental Scale ModelBarge Connected Rigidly to Bottom via 4 legs

Figure: Experimental Scale Modelof a 2 barge interconnected marinestructure

Figure: MCLab InhouseComponents used: Statoil Bargeand Hydrolaunch

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

The real-world systemExpMod

Experimental Scale ModelBarge Connected Rigidly to Bottom via 4 legs

Figure: Experimental Scale Modelof a 2 barge interconnected marinestructure

Figure: MCLab InhouseComponents used: Statoil Bargeand Hydrolaunch

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DynamicsPower Take OffSimplifications

Outline

1 IntroductionThe DeviceExperimental Scale Model

2 Mathematical ModelDynamicsPower Take OffSimplifications

3 SimulationsBlock DiagramPlots

4 ConclusionsDiscussionThe Road Ahead

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DynamicsPower Take OffSimplifications

Rigid Body Dynamics (1)

Figure: Two link manipulatorapproximating thekinematics of theexperimental apparatus

Rigid Body Equations of Motion

hI1z + I2z + m1L2

c1 + m2

�L2

c2 + L21 + 2L1Lc2 cos q2

�iq̈1+

hI2z + m2

�L2

c2 + L1Lc2 cos q2

�iq̈2−

m2L1Lc2 sin q2

�2q̇1q̇2 + q̇2

2�

= τ1

(1)hI2z + m2(L2

c2 + L1Lc2 cos q2)i

q̈1+

hI2z + m2L2

c2

iq̈2+

m2L1Lc2 sin�

q2q̇12�

= τ2

(2)

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DynamicsPower Take OffSimplifications

Rigid Body Dynamics (1)

Figure: Two link manipulatorapproximating thekinematics of theexperimental apparatus

Rigid Body Equations of Motion

hI1z + I2z + m1L2

c1 + m2

�L2

c2 + L21 + 2L1Lc2 cos q2

�iq̈1+

hI2z + m2

�L2

c2 + L1Lc2 cos q2

�iq̈2−

m2L1Lc2 sin q2

�2q̇1q̇2 + q̇2

2�

= τ1

(1)hI2z + m2(L2

c2 + L1Lc2 cos q2)i

q̈1+

hI2z + m2L2

c2

iq̈2+

m2L1Lc2 sin�

q2q̇12�

= τ2

(2)

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DynamicsPower Take OffSimplifications

Rigid Body Dynamics (1)

Figure: Two link manipulatorapproximating thekinematics of theexperimental apparatus

Rigid Body Equations of Motion

hI1z + I2z + m1L2

c1 + m2

�L2

c2 + L21 + 2L1Lc2 cos q2

�iq̈1+

hI2z + m2

�L2

c2 + L1Lc2 cos q2

�iq̈2−

m2L1Lc2 sin q2

�2q̇1q̇2 + q̇2

2�

= τ1

(1)hI2z + m2(L2

c2 + L1Lc2 cos q2)i

q̈1+

hI2z + m2L2

c2

iq̈2+

m2L1Lc2 sin�

q2q̇12�

= τ2

(2)

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DynamicsPower Take OffSimplifications

Rigid Body Dynamics (1)

Figure: Two link manipulatorapproximating thekinematics of theexperimental apparatus

Rigid Body Equations of Motion

hI1z + I2z + m1L2

c1 + m2

�L2

c2 + L21 + 2L1Lc2 cos q2

�iq̈1+

hI2z + m2

�L2

c2 + L1Lc2 cos q2

�iq̈2−

m2L1Lc2 sin q2

�2q̇1q̇2 + q̇2

2�

= τ1

(1)hI2z + m2(L2

c2 + L1Lc2 cos q2)i

q̈1+

hI2z + m2L2

c2

iq̈2+

m2L1Lc2 sin�

q2q̇12�

= τ2

(2)

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DynamicsPower Take OffSimplifications

Rigid Body Dynamics (2)

From the acceleration proportional terms in (1) and (2), we extract a rigid body mass matrix MRB (q). From thevelocity proportional terms we extract a rigid body coriolis centripetal matrix CRB (q, q̇). This gives the followingvector equation, (3)

MRB (q) q̈ + CRB (q, q̇) q̇ = τRB (3)

where

q = [q1, q2]T ∈ R2 is the vector, in joint space, of the angular displacements of the bodies about theirorigins, relative to the frame of the body to which they are respectively connected. q is termed the vector ofgeneralised coordinates

MRB (q) ∈ R2x2 is the rigid body mass matrix

CRB (q, q̇) ∈ R2x2 is the rigid body coriolis-centripetal matrix

and

τRB = τ

E + τR + τ

B + τPTO (4)

where

τE ∈ R2 is the hydrodynamic exitation vector resolved in joint space

τR ∈ R2 is the hydrodynamic radiation vector resolved in joint space

τB ∈ R2 is the hydrostatic buoyancy vector resolved in joint space

τPTO ∈ R2 is the power take-off vector resolved in joint space

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DynamicsPower Take OffSimplifications

Rigid Body Dynamics (2)

From the acceleration proportional terms in (1) and (2), we extract a rigid body mass matrix MRB (q). From thevelocity proportional terms we extract a rigid body coriolis centripetal matrix CRB (q, q̇). This gives the followingvector equation, (3)

MRB (q) q̈ + CRB (q, q̇) q̇ = τRB (3)

where

q = [q1, q2]T ∈ R2 is the vector, in joint space, of the angular displacements of the bodies about theirorigins, relative to the frame of the body to which they are respectively connected. q is termed the vector ofgeneralised coordinates

MRB (q) ∈ R2x2 is the rigid body mass matrix

CRB (q, q̇) ∈ R2x2 is the rigid body coriolis-centripetal matrix

and

τRB = τ

E + τR + τ

B + τPTO (4)

where

τE ∈ R2 is the hydrodynamic exitation vector resolved in joint space

τR ∈ R2 is the hydrodynamic radiation vector resolved in joint space

τB ∈ R2 is the hydrostatic buoyancy vector resolved in joint space

τPTO ∈ R2 is the power take-off vector resolved in joint space

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DynamicsPower Take OffSimplifications

Rigid Body Dynamics (2)

From the acceleration proportional terms in (1) and (2), we extract a rigid body mass matrix MRB (q). From thevelocity proportional terms we extract a rigid body coriolis centripetal matrix CRB (q, q̇). This gives the followingvector equation, (3)

MRB (q) q̈ + CRB (q, q̇) q̇ = τRB (3)

where

q = [q1, q2]T ∈ R2 is the vector, in joint space, of the angular displacements of the bodies about theirorigins, relative to the frame of the body to which they are respectively connected. q is termed the vector ofgeneralised coordinates

MRB (q) ∈ R2x2 is the rigid body mass matrix

CRB (q, q̇) ∈ R2x2 is the rigid body coriolis-centripetal matrix

and

τRB = τ

E + τR + τ

B + τPTO (4)

where

τE ∈ R2 is the hydrodynamic exitation vector resolved in joint space

τR ∈ R2 is the hydrodynamic radiation vector resolved in joint space

τB ∈ R2 is the hydrostatic buoyancy vector resolved in joint space

τPTO ∈ R2 is the power take-off vector resolved in joint space

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DynamicsPower Take OffSimplifications

Rigid Body Dynamics (2)

From the acceleration proportional terms in (1) and (2), we extract a rigid body mass matrix MRB (q). From thevelocity proportional terms we extract a rigid body coriolis centripetal matrix CRB (q, q̇). This gives the followingvector equation, (3)

MRB (q) q̈ + CRB (q, q̇) q̇ = τRB (3)

where

q = [q1, q2]T ∈ R2 is the vector, in joint space, of the angular displacements of the bodies about theirorigins, relative to the frame of the body to which they are respectively connected. q is termed the vector ofgeneralised coordinates

MRB (q) ∈ R2x2 is the rigid body mass matrix

CRB (q, q̇) ∈ R2x2 is the rigid body coriolis-centripetal matrix

and

τRB = τ

E + τR + τ

B + τPTO (4)

where

τE ∈ R2 is the hydrodynamic exitation vector resolved in joint space

τR ∈ R2 is the hydrodynamic radiation vector resolved in joint space

τB ∈ R2 is the hydrostatic buoyancy vector resolved in joint space

τPTO ∈ R2 is the power take-off vector resolved in joint space

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DynamicsPower Take OffSimplifications

Rigid Body Dynamics (2)

From the acceleration proportional terms in (1) and (2), we extract a rigid body mass matrix MRB (q). From thevelocity proportional terms we extract a rigid body coriolis centripetal matrix CRB (q, q̇). This gives the followingvector equation, (3)

MRB (q) q̈ + CRB (q, q̇) q̇ = τRB (3)

where

q = [q1, q2]T ∈ R2 is the vector, in joint space, of the angular displacements of the bodies about theirorigins, relative to the frame of the body to which they are respectively connected. q is termed the vector ofgeneralised coordinates

MRB (q) ∈ R2x2 is the rigid body mass matrix

CRB (q, q̇) ∈ R2x2 is the rigid body coriolis-centripetal matrix

and

τRB = τ

E + τR + τ

B + τPTO (4)

where

τE ∈ R2 is the hydrodynamic exitation vector resolved in joint space

τR ∈ R2 is the hydrodynamic radiation vector resolved in joint space

τB ∈ R2 is the hydrostatic buoyancy vector resolved in joint space

τPTO ∈ R2 is the power take-off vector resolved in joint space

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DynamicsPower Take OffSimplifications

Rigid Body Dynamics (2)

From the acceleration proportional terms in (1) and (2), we extract a rigid body mass matrix MRB (q). From thevelocity proportional terms we extract a rigid body coriolis centripetal matrix CRB (q, q̇). This gives the followingvector equation, (3)

MRB (q) q̈ + CRB (q, q̇) q̇ = τRB (3)

where

q = [q1, q2]T ∈ R2 is the vector, in joint space, of the angular displacements of the bodies about theirorigins, relative to the frame of the body to which they are respectively connected. q is termed the vector ofgeneralised coordinates

MRB (q) ∈ R2x2 is the rigid body mass matrix

CRB (q, q̇) ∈ R2x2 is the rigid body coriolis-centripetal matrix

and

τRB = τ

E + τR + τ

B + τPTO (4)

where

τE ∈ R2 is the hydrodynamic exitation vector resolved in joint space

τR ∈ R2 is the hydrodynamic radiation vector resolved in joint space

τB ∈ R2 is the hydrostatic buoyancy vector resolved in joint space

τPTO ∈ R2 is the power take-off vector resolved in joint space

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DynamicsPower Take OffSimplifications

Rigid Body Dynamics (2)

From the acceleration proportional terms in (1) and (2), we extract a rigid body mass matrix MRB (q). From thevelocity proportional terms we extract a rigid body coriolis centripetal matrix CRB (q, q̇). This gives the followingvector equation, (3)

MRB (q) q̈ + CRB (q, q̇) q̇ = τRB (3)

where

q = [q1, q2]T ∈ R2 is the vector, in joint space, of the angular displacements of the bodies about theirorigins, relative to the frame of the body to which they are respectively connected. q is termed the vector ofgeneralised coordinates

MRB (q) ∈ R2x2 is the rigid body mass matrix

CRB (q, q̇) ∈ R2x2 is the rigid body coriolis-centripetal matrix

and

τRB = τ

E + τR + τ

B + τPTO (4)

where

τE ∈ R2 is the hydrodynamic exitation vector resolved in joint space

τR ∈ R2 is the hydrodynamic radiation vector resolved in joint space

τB ∈ R2 is the hydrostatic buoyancy vector resolved in joint space

τPTO ∈ R2 is the power take-off vector resolved in joint space

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DynamicsPower Take OffSimplifications

Hydrodynamics (1)Wave Excitation

Excitation ForceA JONSWAP spectrum withHs = 0.075m and Tav = 1s,together with the forceresponse amplitudeoperators (RAOs) from the3-D linear potential theorycode WAMITTMwas used.

Figure: JONSWAP Spectrum together withthe force RAO in pitch of body 2 given byWAMIT

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DynamicsPower Take OffSimplifications

Hydrodynamics (1)Wave Excitation

Excitation ForceA JONSWAP spectrum withHs = 0.075m and Tav = 1s,together with the forceresponse amplitudeoperators (RAOs) from the3-D linear potential theorycode WAMITTMwas used.

Figure: JONSWAP Spectrum together withthe force RAO in pitch of body 2 given byWAMIT

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DynamicsPower Take OffSimplifications

Hydrodynamics (1)Wave Excitation

Excitation ForceA JONSWAP spectrum withHs = 0.075m and Tav = 1s,together with the forceresponse amplitudeoperators (RAOs) from the3-D linear potential theorycode WAMITTMwas used.

Figure: JONSWAP Spectrum together withthe force RAO in pitch of body 2 given byWAMIT

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DynamicsPower Take OffSimplifications

Hydrodynamics (1)Wave Excitation

Excitation ForceA JONSWAP spectrum withHs = 0.075m and Tav = 1s,together with the forceresponse amplitudeoperators (RAOs) from the3-D linear potential theorycode WAMITTMwas used.

Figure: JONSWAP Spectrum together withthe force RAO in pitch of body 2 given byWAMIT

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DynamicsPower Take OffSimplifications

Hydrodynamics (2)Radiation Damping

For the specific case of linear exitation and motions at a fixedfrequency ω, the radiation damping forces and moments onbody1 and body2 are defined as follows:

F(t) = B(ω)η̇(t)where

η = [η1...η6, η7...η12, ]T ∈ R12 are the displacements in the

h1-frame and h2-frame of body1 and body2 respectively.

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DynamicsPower Take OffSimplifications

Hydrodynamics (2)Radiation Damping

For the specific case of linear exitation and motions at a fixedfrequency ω, the radiation damping forces and moments onbody1 and body2 are defined as follows:

F(t) = B(ω)η̇(t)where

η = [η1...η6, η7...η12, ]T ∈ R12 are the displacements in the

h1-frame and h2-frame of body1 and body2 respectively.

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DynamicsPower Take OffSimplifications

Hydrodynamics (3)Radiation Damping

The radiation damping matrix B(ω) ∈ R12x12 has the followingcomponents:

B(ω) =

266666666666666666666666666666666666666666666664

b1,1 . . . . b1,6 b1,7 . . .. b1,12

. b2,2 . . . . . . . .

. .

. . b3,3 . . . . . . .

. .

. . . b4,4 . . . . . .

. .

. . . . b5,5 . . . . .

. .b6,1 . . . . b6,6 . . . .. b12,6

b7,1 . . . . . b7,7 . . .. b12,7

. . . . . . . b8,8 . .

. .

. . . . . . . . b9,9 .

. .

. . . . . . . . . b10,10

. .

. . . . . . . . . .b11,11 .b12,1 . . . . b12,6 b12,7 . . .

. b12,12

377777777777777777777777777777777777777777777775

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DynamicsPower Take OffSimplifications

Hydrodynamics (4)Radiation Damping

Figure: Diagonal Radiation Damping Coefficients plotted againstfrequency

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DynamicsPower Take OffSimplifications

Hydrodynamics (5)Radiation Damping

(Cummins,1962) showed how the radiation damping terms,together with added mass terms at infinite frequency, could givea formulation of the time-domain forces and moments due topotential damping. This formulation does not rely on anyassumptions of linear forces and motions

Fm(t) = −12∑

n=1

am,n(∞)η̈n −12∑

n=1

bm,n(∞)η̇n

−12∑

n=1

cm,nηn −12∑

n=1

∫ t

−∞Km,n(t − τ)η̇n(τ)dτ

m = 1...12

(5)

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DynamicsPower Take OffSimplifications

Hydrodynamics (6)Radiation Damping

Figure: Diagonal Retardation Funtions together with their state-spaceapproximations

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DynamicsPower Take OffSimplifications

Power Take-Off

PTO is a hydraulic system in realityScale model will utilise a pneumatic pump with mech.springMath. model currently uses linear damper and springelements at the hinges.

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DynamicsPower Take OffSimplifications

Power Take-Off

PTO is a hydraulic system in realityScale model will utilise a pneumatic pump with mech.springMath. model currently uses linear damper and springelements at the hinges.

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DynamicsPower Take OffSimplifications

Power Take-Off

PTO is a hydraulic system in realityScale model will utilise a pneumatic pump with mech.springMath. model currently uses linear damper and springelements at the hinges.

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DynamicsPower Take OffSimplifications

Model Reduction

non-planar degrees of freedom can be ignoredsome of the B-coefficients are negligibly small for allfrequencies

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DynamicsPower Take OffSimplifications

Model Reduction

non-planar degrees of freedom can be ignoredsome of the B-coefficients are negligibly small for allfrequencies

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

Block DiagramPlots

Outline

1 IntroductionThe DeviceExperimental Scale Model

2 Mathematical ModelDynamicsPower Take OffSimplifications

3 SimulationsBlock DiagramPlots

4 ConclusionsDiscussionThe Road Ahead

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

Block DiagramPlots

Simulink Block Diagram Model

Figure: Simulink Block Diagram

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

Block DiagramPlots

Barge1 and Barge 2 translational and rotationaldisplacents and velocoties for t=0-100s

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DiscussionThe Road Ahead

Outline

1 IntroductionThe DeviceExperimental Scale Model

2 Mathematical ModelDynamicsPower Take OffSimplifications

3 SimulationsBlock DiagramPlots

4 ConclusionsDiscussionThe Road Ahead

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DiscussionThe Road Ahead

Discussion

better hydrodynamic data needed: numerically (removeirregular frequencies, constrain bodies) and experimentally(validation)transformations from h-frame to generalised frame used inRB equationsgeneralise the rigid body dynamics to N bodies?

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DiscussionThe Road Ahead

Discussion

better hydrodynamic data needed: numerically (removeirregular frequencies, constrain bodies) and experimentally(validation)transformations from h-frame to generalised frame used inRB equationsgeneralise the rigid body dynamics to N bodies?

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DiscussionThe Road Ahead

Discussion

better hydrodynamic data needed: numerically (removeirregular frequencies, constrain bodies) and experimentally(validation)transformations from h-frame to generalised frame used inRB equationsgeneralise the rigid body dynamics to N bodies?

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DiscussionThe Road Ahead

The Road Ahead

MCLab Experiments 13-30 April 2006Control considerations have begunAccurate, validated processplant and control models arecrucial

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DiscussionThe Road Ahead

The Road Ahead

MCLab Experiments 13-30 April 2006Control considerations have begunAccurate, validated processplant and control models arecrucial

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006

IntroductionMathematical Model

SimulationsConclusions

DiscussionThe Road Ahead

The Road Ahead

MCLab Experiments 13-30 April 2006Control considerations have begunAccurate, validated processplant and control models arecrucial

Modelling of an Interconnected Marine Structure, NTNU 6/4-2006