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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
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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
![Page 3: Control-Oriented Modelling of an Interconnected Marine ... · PDF fileIntroduction Mathematical Model Simulations Conclusions Control-Oriented Modelling of an Interconnected Marine](https://reader031.vdocuments.us/reader031/viewer/2022030404/5a79e6e97f8b9ae67b8d1e6e/html5/thumbnails/3.jpg)
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
![Page 4: Control-Oriented Modelling of an Interconnected Marine ... · PDF fileIntroduction Mathematical Model Simulations Conclusions Control-Oriented Modelling of an Interconnected Marine](https://reader031.vdocuments.us/reader031/viewer/2022030404/5a79e6e97f8b9ae67b8d1e6e/html5/thumbnails/4.jpg)
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
![Page 5: Control-Oriented Modelling of an Interconnected Marine ... · PDF fileIntroduction Mathematical Model Simulations Conclusions Control-Oriented Modelling of an Interconnected Marine](https://reader031.vdocuments.us/reader031/viewer/2022030404/5a79e6e97f8b9ae67b8d1e6e/html5/thumbnails/5.jpg)
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
![Page 6: Control-Oriented Modelling of an Interconnected Marine ... · PDF fileIntroduction Mathematical Model Simulations Conclusions Control-Oriented Modelling of an Interconnected Marine](https://reader031.vdocuments.us/reader031/viewer/2022030404/5a79e6e97f8b9ae67b8d1e6e/html5/thumbnails/6.jpg)
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
![Page 7: Control-Oriented Modelling of an Interconnected Marine ... · PDF fileIntroduction Mathematical Model Simulations Conclusions Control-Oriented Modelling of an Interconnected Marine](https://reader031.vdocuments.us/reader031/viewer/2022030404/5a79e6e97f8b9ae67b8d1e6e/html5/thumbnails/7.jpg)
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
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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
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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
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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
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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
![Page 12: Control-Oriented Modelling of an Interconnected Marine ... · PDF fileIntroduction Mathematical Model Simulations Conclusions Control-Oriented Modelling of an Interconnected Marine](https://reader031.vdocuments.us/reader031/viewer/2022030404/5a79e6e97f8b9ae67b8d1e6e/html5/thumbnails/12.jpg)
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
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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
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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
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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
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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
![Page 17: Control-Oriented Modelling of an Interconnected Marine ... · PDF fileIntroduction Mathematical Model Simulations Conclusions Control-Oriented Modelling of an Interconnected Marine](https://reader031.vdocuments.us/reader031/viewer/2022030404/5a79e6e97f8b9ae67b8d1e6e/html5/thumbnails/17.jpg)
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
![Page 18: Control-Oriented Modelling of an Interconnected Marine ... · PDF fileIntroduction Mathematical Model Simulations Conclusions Control-Oriented Modelling of an Interconnected Marine](https://reader031.vdocuments.us/reader031/viewer/2022030404/5a79e6e97f8b9ae67b8d1e6e/html5/thumbnails/18.jpg)
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
![Page 19: Control-Oriented Modelling of an Interconnected Marine ... · PDF fileIntroduction Mathematical Model Simulations Conclusions Control-Oriented Modelling of an Interconnected Marine](https://reader031.vdocuments.us/reader031/viewer/2022030404/5a79e6e97f8b9ae67b8d1e6e/html5/thumbnails/19.jpg)
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
![Page 20: Control-Oriented Modelling of an Interconnected Marine ... · PDF fileIntroduction Mathematical Model Simulations Conclusions Control-Oriented Modelling of an Interconnected Marine](https://reader031.vdocuments.us/reader031/viewer/2022030404/5a79e6e97f8b9ae67b8d1e6e/html5/thumbnails/20.jpg)
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
![Page 21: Control-Oriented Modelling of an Interconnected Marine ... · PDF fileIntroduction Mathematical Model Simulations Conclusions Control-Oriented Modelling of an Interconnected Marine](https://reader031.vdocuments.us/reader031/viewer/2022030404/5a79e6e97f8b9ae67b8d1e6e/html5/thumbnails/21.jpg)
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
![Page 22: Control-Oriented Modelling of an Interconnected Marine ... · PDF fileIntroduction Mathematical Model Simulations Conclusions Control-Oriented Modelling of an Interconnected Marine](https://reader031.vdocuments.us/reader031/viewer/2022030404/5a79e6e97f8b9ae67b8d1e6e/html5/thumbnails/22.jpg)
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
![Page 23: Control-Oriented Modelling of an Interconnected Marine ... · PDF fileIntroduction Mathematical Model Simulations Conclusions Control-Oriented Modelling of an Interconnected Marine](https://reader031.vdocuments.us/reader031/viewer/2022030404/5a79e6e97f8b9ae67b8d1e6e/html5/thumbnails/23.jpg)
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
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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
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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
![Page 26: Control-Oriented Modelling of an Interconnected Marine ... · PDF fileIntroduction Mathematical Model Simulations Conclusions Control-Oriented Modelling of an Interconnected Marine](https://reader031.vdocuments.us/reader031/viewer/2022030404/5a79e6e97f8b9ae67b8d1e6e/html5/thumbnails/26.jpg)
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
![Page 27: Control-Oriented Modelling of an Interconnected Marine ... · PDF fileIntroduction Mathematical Model Simulations Conclusions Control-Oriented Modelling of an Interconnected Marine](https://reader031.vdocuments.us/reader031/viewer/2022030404/5a79e6e97f8b9ae67b8d1e6e/html5/thumbnails/27.jpg)
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.
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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
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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
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IntroductionMathematical Model
SimulationsConclusions
DynamicsPower Take OffSimplifications
Hydrodynamics (4)Radiation Damping
Figure: Diagonal Radiation Damping Coefficients plotted againstfrequency
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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)
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IntroductionMathematical Model
SimulationsConclusions
DynamicsPower Take OffSimplifications
Hydrodynamics (6)Radiation Damping
Figure: Diagonal Retardation Funtions together with their state-spaceapproximations
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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.
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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.
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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.
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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
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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
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IntroductionMathematical Model
SimulationsConclusions
Block DiagramPlots
Outline
1 IntroductionThe DeviceExperimental Scale Model
2 Mathematical ModelDynamicsPower Take OffSimplifications
3 SimulationsBlock DiagramPlots
4 ConclusionsDiscussionThe Road Ahead
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IntroductionMathematical Model
SimulationsConclusions
Block DiagramPlots
Simulink Block Diagram Model
Figure: Simulink Block Diagram
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SimulationsConclusions
Block DiagramPlots
Barge1 and Barge 2 translational and rotationaldisplacents and velocoties for t=0-100s
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IntroductionMathematical Model
SimulationsConclusions
DiscussionThe Road Ahead
Outline
1 IntroductionThe DeviceExperimental Scale Model
2 Mathematical ModelDynamicsPower Take OffSimplifications
3 SimulationsBlock DiagramPlots
4 ConclusionsDiscussionThe Road Ahead
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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?
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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?
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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?
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IntroductionMathematical Model
SimulationsConclusions
DiscussionThe Road Ahead
The Road Ahead
MCLab Experiments 13-30 April 2006Control considerations have begunAccurate, validated processplant and control models arecrucial
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IntroductionMathematical Model
SimulationsConclusions
DiscussionThe Road Ahead
The Road Ahead
MCLab Experiments 13-30 April 2006Control considerations have begunAccurate, validated processplant and control models arecrucial
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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