Modeling and Simulator AHT Vessel
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June 2009
Thor Inge Fossen, ITK
Master of Science in Engineering CyberneticsSubmission date:
Supervisor:
Norwegian University of Science and Technology
Department of Engineering Cybernetics
Modeling and Simulation of AnchorHandling Vessels
Lars Andreas Lien Wennersberg
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Problem DescriptionThe purpose of the thesis is to develop a simulator of an anchor handling vessel that is capable ofsimulating anchor handling operations under influence of environmental forces with realisticvessel motions. The following elements must be considered:
1. Give an overview of the best practice for anchor handling operations. Classification rules,regulations and operational procedures should be considered.
2. Based on a vessel model from the MSS Toolbox, develop and implement a simulator of ananchor handling vessel in MATLAB/Simulink. The simulator should contain the necessary modulesfor ballast tanks, roll reduction, cable systems and anchor handling equipment on deck.
3. Verify the simulator by simulating relevant anchor handling scenarios.
4. Present your findings and theoretical results in a report.
Assignment given: 12. January 2009Supervisor: Thor Inge Fossen, ITK
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x
x
X
x(t)
x(s)
x
a
w
2
i i
a
b
d
f
w
a
a
s
b
g
gp
d 3
p 3
d
d
w
s
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2
f 2
b 2
4
φ
g
B
C
f
P
S
s
m 2
w 2
d
g
i
p
s
pp
B
S
d
gm
gw
i
m
p
wd
b 3
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b
e
s
δ g ∇ 3 µα α
ω4 ωm ωw φ
φg ψ
ψc ψ
ρ
3
σ0 σ1
σ2 σ4 σα αθm θw ζ 4
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•
• •
•
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•
•
•
• • • •
•
•
•
•
• •
•
• •
•
• • • •
•
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SEABED
SURFACE
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SEABED
SEABED
WORK WIRE
TARGET
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50°
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300
SEABED
MAIN
VESSEL
SECONDARY
VESSEL
WORK WIRE
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L
l
h
l
sd
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s
s
s
p
p
O(0,0)
Q(l,h)
x
z
s
W
B
T
B
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H
Ws
L
V
T
Bs
L
B = ρgA
A
g
ρ
d
A = πd2/4
W e
W e = W − B
W
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T dx
dp
= H
T dz
dp = V − W s
L
T
H
V
H
T = EA
dp
ds − 1
E
dx
dp
2+
dz
dp
2= 1
T (s) =
H 2 +
V − W sL
21/2
s
x(s)
z(s)
dx/ds
dz/ds
s
dx
ds =
dx
dp
dp
ds
dz
ds =
dz
dp
dp
ds
dx/dp
dz/dp
dp/ds
dx/ds
dz/ds
dx
ds
= H
EA
+ H
[H 2
+ {V − Ws/L}2
]1/2
dz
ds =
1
EA
V − W s
L
+
V − Ws/L[H 2 + {V − Ws/L}2]1/2
x = 0
z = 0
p = 0 s = 0
x = l
z = h
p = Ls s = L
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Ls
s = 0
s
x
x(s) = Hs
EA +
H L
W
V
H
−
V − Ws/L
H
x
x
s = 0
s z
z(s) = W s
EA
V
W − s
2L
+
H L
W
1 + V
H
21/2−
1 +
V − Ws/L
H
21/2
H
V
l = HL
EA +
H L
W
V
H
−
V − W
H
h = W L
EA
V
W − 1
2
+
H L
W
1 + V
H
21/2−
1 +
V − W
H
21/2
H
V
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O
z
C
H
x
C A B L E
S A G
H
V V
Q
CABLE SPAN
h = 0
W l
2HL − W
2EA
=
W
2H
V = W/2
H
E = ∞
F P
F P
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O(0,0)
P(la,ha)
z
Q(lb,hb) x
FP
CABLE A CABLE B
A
B
s1 0 ≤ s < s1 s1 ≤ s ≤ L
0 ≤ s < s1 s1 ≤ s ≤ LA
LA ≤ s < s2 s2 ≤ s ≤ LA + LB
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F P
T dzdp
= V − W i sLi
0 ≤ s < s1 s1 ≤ s < s2
T dz
dp = V − F P − W i s
Li
s1 ≤ s ≤ LA s2 ≤ s ≤ LA + LB
i ∈ {A, B}
O
x = 0
z = 0
s = 0
P
x = lA z = hA s = LA
Q
x = lB z = hB s = LA + LB
s = LA
F P
x−A = x+A z
−
A = z+A p
−
A = p+A s = s1 = LA
x−B = x+B z
−
B = z+B p
−
B = p+B s = s2 = LA
T
T (s) =
H 2 +
V − W i s
Li
21/2
0 ≤ s < s1 s1 ≤ s < s2
T (s) =
H 2 +
V − F P − W i s
Li
21/2
s1 ≤ s ≤ LA s2 ≤ s ≤ LA + LB
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dx/ds
dz/ds
dx
ds = H
E iAi + H
[H 2 + {V − W is/Li}2]1/2
0 ≤ s < s1 s1 ≤ s < s2
dx
ds =
H
E iAi+
H
[H 2 + {V − F P − W is/Li}2]1/2
s1 ≤ s ≤ LA s2 ≤ s ≤ LA + LB
dz
ds =
1
E iAi
V − W is
Li
+
V − W is/Li[H 2 +
{V i
−W is/Li
}2]1/2
0 ≤ s < s1 s1 ≤ s < s2
dz
ds =
1
E iAi
V − F P − W is
Li
+
V − F P − W is/Li[H 2 + {V − F P − W is/Li}2]1/2
s1 ≤ s ≤ LA s2 ≤ s ≤ LA + LB
x
s
x
s1 s x1 x x1 s = s1 x x
x
x(s) = Hs
E AAA+
H LAW A
−1
V
H
−
−1
V − W As/LA
H
0 ≤ s < s1
x(s) = Hs
E AAA+
H LAW A
sinh−1
V
H
− −1
V − F P − W As/LAH
+
−1
V − F P − W As1/LA
H
− −1
V − W As1/LAH
s1 ≤ s < LA
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x(s) = H (s − s1)
E B
AB
+ Hs1E
AA
A
+ H LB
W B
−1
V − W Bs1/LB
H
− −1
V − W Bs/LBH
+ H LA
W A
−1
V
H
− −1
V − W As1/LAH
LA ≤ s < s2
x(s) = H (s − s1)
E BAB+
Hs1E AAA
+
HLBW B
−1
V − F P − W Bs2/LBH
− −1V − F P − W Bs/LBH
+
−1
V − W Bs1/LB
H
− −1
V − W Bs2/LBH
+ H LA
W A
−1
V
H
− −1
V − W As1/LAH
s2 ≤ s < LA + LB
−1(x) =
(x) = x
√ 1 + x2 z
z(s) = W As
E AAA
V
W A− s
2LA
+
H LAW A
1 +
V
H
21/2−
1 +
V − W As/LA
H
21/2
0 ≤ s < s1
z(s) = W As
E AAA
V
W A− s
2LA
+
H LAW A
1 +
V
H
21/2−
1 +
V − F P − W As/LA
H
21/2
+
1 +
V − F P − W As1/LA
H
21/2−
1 +
V − W As1/LA
H
21/2
+ F P
H
W AE AAA
s1LA
− sLA
s1 ≤ s < LA
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z(s) = W Bs
E BAB
V
W B− s
2LB
− W Bs1
E BAB
V
W B− s1
2LB
+
W As1E AAA
V
W A− s1
2LA
+ H LB
W B
1 +
V − W Bs1/LB
H
21/2−
1 +
V − W Bs/LB
H
21/2
+ H LA
W A
1 +
V
H
21/2−
1 +
V − W As1/LA
H
21/2
LA ≤ s < s2
z(s) = W BsE BAB
V W B
− s2LB
− W Bs1
E BAB
V W B
− s12LB
+ W As1
E AAA
V W A
− s12LA
+ H LB
W B
1 +
V − F P − W Bs2/LB
H
21/2−
1 +
V − F P − W Bs/LB
H
21/2
+
1 +
V − W Bs1/LB
H
21/2−
1 +
V − W Bs2/LB
H
21/2+
F P H
W bE BAB
s2LB
− sLB
+ H LA
W A
1 +
V
H
21/2 −
1 +
V − W As1/LA
H
21/2
s2 ≤ s < LA + LB
H
V
lA hA H V
s = LA + LB
lA lB H V
mA ≤ mB
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x = x0 z = z0 p = 0 s = 0
x = l
z = h
p = Ls s = L
O(0,0)
P(la,ha)
z
Q(lb,hb) x
Vs
SUBMERGED ANCHOR
SEABED
WORK-WIRE
MOORING
CHAIN
x(s) = Hs
EA0+
H L
W
V
H
−
V − Ws/L
H
+ x0
z(s) = W s
EA0
V
W − s
2L
+
H L
W
1 + V H
21/2
−
1 +
V − Ws/L
H
21/2+ z0
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p
s
p = s +
1
2EAW s +
(V s + W ss)(H 2
+ (V s + W ss)2
)1/2
+ H 2
V s + W ss
H +
(H 2 + (V s + W ss)2)1/2
H
W s V s
V s = V − W sL
s = L p = Ls
Ls = L + 1
2EAW s
V (H 2 + V 2)1/2 + H 2
V
H +
1 +
V
H
21/2
L = Ls s = p x = l z = h
H
V
H
V
l
L
H
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V
L
l
P 1(α, β ) = a00 + a10α + a01β
P 2(α, β ) = a00 + a10α + a01β + a20α2 + a11αβ + a02β
2
P 3(α, β ) = a00 + a10α + a01β + a20α2 + a11αβ + a02β
2
+ a30α3 + a21α
2β + a12αβ 2 + a03β
3
aii i ∈ {1, 3} α β
n p
N (n p)
N (n) = (n p + 1)(n p + 2)
2
α
α̂ = α − µα
σ2α
µα α σ
2α
β
α = L
β = l
H
V
H (L, l) = h00 + h10L + h01l + h20L2 + h11Ll + h02l
2
+ h30L3 + h21L
2l + h12Ll2 + h03l
3
V (L, l) = v00 + v10L + v01l + v20L2 + v11Ll + v02l
2
+ v30L3 + v21L
2l + v12Ll2 + v03l
3
hii vii i
∈ {1, 3
}
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l
α = LA β = l
LB
H 50(LA, l) V 50(LB, l)
H 60(LB, l) V 60(LB, l)
H 70(LB, l) V 70(LB, l)
H 990(LB, l) V 990(LB, l)
H 1000(LB, l) V 1000(LB, l)
LB
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m
ms d A m
2
F P
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LB = 1100 LA = 10 − 500
100
−1000
F P = 176.5
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F b
Rb
F b = F −
W ≥
Rb
tb
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ż = v − σ0