S - Marine Systems Simulator

Plenary Talk Presented at the 8th IFAC Conference on Control Applications in Marine Systems, Sept 15th-17th, Rostock, Germany Tristan Perez*, *** and Mogens Blanke**,***
* School of Engineering, The University of Newcastle, AUSTRALIA
** Dept. of Elec. Eng. Automation and Control, Danish Technical University, DENMARK
*** CeSOS, Norwegian University of Science and Technology (NTNU), Trondheim NORWAY
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Motivation
The effects of roll on ship performance became more
noticeable in the mid-19th century when:
  Sails were replaced by engines
  Broad arranges changed to turrets
Many devices have been proposed leading
to interesting control problems
W. Froude (1819-1879)
Performance can easily fall short of expectations because of
deficiencies in control system design due to
 
 
 
2
Fundamental limitations due to system dynamics
Limited actuator authority
Disturbances with large changes in spectral characteristics
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Outline
 
Ship Roll Control Devices
 
Working Principles,
 
Performance,
Historical aspects
 
 
Key aspects of ship roll dynamics for control design
 
Models,
 
Wave-induced motion
Simulation and control design models
 
 
Control System Design
 
Objectives,
Fundamental limitations,
 
Control strategies
 
 
Research Outlook
 
3
Unsolved problems, new devices
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany I - Ship Roll Control Devices
Performance,
Working Principles,
and Historical Aspects
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Ship Performance and Roll Motion
Ship roll motion
 
Affects crew performance
 
Can damage cargo
May prevent the use of on-board equipment
 
From a ship operability point of view is necessary to
reduce not only roll angle but also roll accelerations.
5
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Bilge Keels
  10to 20% roll reduction (RMS)
  Low maintenance
  No control
  No occupied space
  Low price easy to install
  Increase hull resistance when damping is not needed
  Not every vessel can be fitted with them (ice-breakers)
6
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany U-tanks
  40 to 50% roll reduction (RMS)
 Active/Passive
  Independent of the vessel speed
 Anti heeling
  Heavy
  Occupy large spaces
 Affects stability due free-surface
Intering Rolls-Royce
7
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Gyro-stabilisers
  60% to 90% roll reduction (RMS)
  Performance independent of the vessel speed
1906
Torpedo Boat
1914 to 1925
active control
1914,1924
Twin Gyros
Schlick
(Germany)
Sperry
(USA)
Fieux
(France)
Today
Time
Halcyon
Ferretti
Sea Gyro
Shipdynamics
Seakeeper
Japanese aircraft carrier ‘Hosho’ 95% RR with
Sperry Gyro
Conte di Savoia 1932
8
8th IFAC CAMS, Sept 15th-17th, Rostock,
Germany Fin-stabilisers
  60% to 90% roll reduction (RMS)
  Performance depends on speed
  Control is important for performance
  Easy to damage
  Most Expensive stabiliser
  Can produce noise affecting sonar
  Dynamic stall
9
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Rolls-Royce
Rudder Roll Stabilisers (RRS)
  40% to 70% roll reduction (RMS)
  Performance depends on speed
  Control is important for performance
  Special rudder machinery
  Fundamental limitations in control due to
non-minimum phase dynamics (NMP)
10
8th IFAC CAMS, Sept 15th-17th, Rostock,
Germany Historical Aspects
T. Perez (2005) Ship Motion Control, Springer
11
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany II - Key Aspects of Ship Roll Dynamics
for Control Design
Models
Ocean Environment
Wave-induced motion
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Dynamics of Roll Motion
General model form to describe ship motion:
! n "
pb/n
= [N, E, D, φ, θ, ψ]T .
η!
Θ
ν!
13
!
n b
ṗb/n
ω bb/n
"
= [u, v, w, p, q, r]T .
Kinematic model:
η̇ = J(η)ν
Kinetic model:
Mν̇ + C(ν)ν + D(ν)ν + g(η) = τ
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Models for Control Design
For control design, output disturbance models are usually adopted:
Motion Time
series
Control
Forces
1DOF, 4DOF
Force to motion
For roll motion control problems this model is simplified to
 
 
14
1DOF: roll
4DOF: surge, roll, sway, and yaw
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Dynamics of Roll Motion—1DOF Model
Consider only roll motion,
φ̇ = p,
Kinematic model:
Ixx ṗ = Kh + Kc + Kd
Kinetic model:
Hydrodynamic
moments
Control
moments
Disturbance
moments
Hydrodynamic Moments:
Kh ≈ Kṗ ṗ + Kp p + Kp|p| p|p| + K(φ)
Potential
Effects
15
Viscous
Effects
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Hydrostatic
Effects
Dynamics of Roll Motion—4DOF
Motion Variables:
η = [φ ψ] ,
T
ν = [u v p r]T ,
τ i = [Xi Yi Ki Ni ] ,
T
Kinematic model:
Kinetic model:
φ̇ = p,
ψ̇ = r cos φ ≈ r
MRB ν̇ + CRB (ν)ν = τ h + τ c + τ d
τ h ≈ −MA ν̇ − CA (ν)ν − D(ν)ν − K(φ)
16
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Ocean Environment
Usual assumptions for sea surface elevation
  Zero-mean
 
Gaussian (depth dependent)
Narrow banded
 
Stationary (20min to 3 hours)
 
ζ(t):
All necessary information is then in the wave elevation power spectral
density (Sea Spectrum):
Φζζ (ω, χ)
17
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Sailing Condition and Encounter Spectrum
Encounter Frequency
Sailing Condition
 
 
Speed
Encounter angle
ω2 U
ωe = ω −
cos(χ)
g
18
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Φζζ (ωe ) = !!
!1 −
Φζζ (ω)
2ωU
g
!
!
cos(χ)!
Wave-induced Motion Motion
Seakeeping Model
Motion spectrum
Sζζ (ω)
Wave spectrum
F(jω,χ,U)
G(jω,U)
Wave to force FRF
Force to motion FRF
F(jω, χ) = [F1 (jω, χ), . . . , F6 (jω, χ)]T

G11 (jω, U ) · · ·

..
G(jω, U ) = 
.
G61 (jω, U ) · · ·
Roll RAO:
Motion Time
series

G16 (jω)

..
2
−1
=
(−[M
+
A(ω)]
ω
+
jωB(ω)
+
G)

RB
.
G66 (jω, U )
H4 (jω, χ, U ) =
6
!
G4k (jω, U )Fk (jω, χ, U )
k=1
19
Sηη (ω)
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Example Roll RAOs Naval Vessel @15kt
H4 (jω, χ, U ) =
6
!
4.2 Seakeeping Theory Models
G4k (jω,
U )Fk (jω, χ, U )
73
k=1
|H4 (ω, U, χ)|
)
&!*+,
'#*+,
(!*+,
-#*+,
.!*+,
$!#*+,
$%!*+,
$&#*+,
$#!*+,
$(#*+,
(
'
%
&
!
%!!
%"#
%
$#!
$"#
$!!
χ
$
#!
ω
!"#
!
!
Fig. 4.6. motion RAO Roll of the naval vessel benchmark at 15 kt for different
angles.
RAO
are given
as a function of the wave frequency.
20 encounter
8th IFAC
CAMS,The
Septmotion
15th-17th,
Rostock,
Germany
III – Motion Control Design
Objectives,
Performance Limitations,
and Control Strategies
8th IFAC CAMS, Sept 15th-17th, Rostock,
Germany Control Design and Performance Limitations
From the ship performance point of view, the control objectives are
  Reduce roll angle
 
Reduce roll accelerations
Actuators
u
Output sensitivity
φcl (s)
S(s) !
φol (s)
22
Kc
φol
Ship
φcl
Control
Roll spectrum relations
Φcl (ω) = |S(jω)|2 Φol (ω)
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Control Design and Performance Limitations
If the closed-loop system is stable minimum phase and strictly proper,
the following Bode integral constraint applies
!
0
∞
log |S(jω)| dω = 0
Φcl (ω) = |S(jω)|2 Φol (ω)
|φol (jω)| −| φcl (jω)|
RR(ω) = 1 − |S(jω)| =
|φol (jω)|
23
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Example Performance Limitations
Gyrostabiliser (Perez & Steinmann, 2009)
24
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Non-minimum phase Dynamics
In some cases, the location of the actuators may result in NMP
dynamics (with a real zero at s=q.)
Then, we have a Poisson-integral constrain:
!
∞
−∞
log |S(jω)| W (q, ω)dω = 0
q = σq + j0
σq
W (q, ω) = 2
σq + ω 2
25
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Non-minimum phase Dynamics
::;*4+5.*8.,8323532<*=>?:@*!*AB%CDE+5FD$G#!
#&"
Example Blanke
et al (2000)
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!
26
!
"
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8th IFAC CAMS, Sept 15th-17th, Rostock, Germany $!
$"
%!
Energy of Wave Excitation
The energy of the wave excitation changes with the seastate and sailing conditions (speed and heading)
φ(t)
For example a change in encounter angle can shift
the energy significantly:
27
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany τ2rudder ≈
L
b
τ4rudder ≈ zCP
L
(8)
τ6rudder ≈ xbCP L,
Fin Stabilisers (minimum phase case)
b
are the coordinates of the cenwhere xbCP and zCP
ter of pressure of the rudder (CP ) with respect to
IDOF model including fin forces:the b-frame. The center of pressure is assumed to
be located at the rudder stock and half the rudder
span. The rudder data is shown in Table A.4.
φ̇ = p,
[Ixx + Kṗ ] ṗ + (Kp +
Control issues:
• 
• 
Parametric uncertainty
Sensitivity-integral constraints
Control strategies:
• 
For the stabilizer fins, the center of pressure is
2
halfway
along
the
span
of
the
The
2 rf Klocated
U
)
p
+
K
φ
=
K
−
2U
Kfin.
α
φ
w
αα
coordinates of the center of pressure with respect
to the b-frame are given by the vector rbCP —see
Figure 1.
PID, Hinf
28
ing
the
is a
•
•
•
The
with
and
bas
(Pe
for
CG
ob
zb
yb
rbCP
CP
y!
y !!
z !! z !
Fig. 1. Reference frames used to compute fin
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany
forces.
τ̄in
whe
and
%
ωn
For
Fin Stabilisers and NMP Dynamics
If the response from the fins is NMP, then the IDOF cannot be used, in
this case roll-sway-yaw interactions need to be considered to avoid
large roll amplifications at low frequencies.
Observations about fin NMP dynamics were made by Lloyd (1989).
29
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Fin Stabilisers – Dynamic Stall
CL [-]
CL [-]
Experimental results of Galliarde (2002) (MARIN, Ned)
αe [deg]
φ [deg]
αe [deg]
Time [s]
30
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Fin Stabilisers
Perez & Goodwin (2003): MPC constraints effective angle of attack.
31
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Rudder Roll Damping
 
Potential discovered from autopilot without wave filter (Taggart 1970)
 
Results reported by van Gunsteren in 1972 (the Netherlands)
 
Cowley & Lambert (1972) used roll fbk, reported yaw interference.
 
Carley & Duberley (1972) integrated rudder-fin control
 
Carley (1975) & Lloyd (1975) recognise limitations of NMP dynamics
 
Baitis et al.(1983) highlighted need of adaptation
 
Advent of Computers in 1980 resulted in several successful results
 
Netherlands, Denmark, Sweden, United Kingdom
 
Hearns & Blanke (1998) limitations using the Poisson Integral
 
Perez (2003) analysed min variance and RR vs yaw interference
32
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Performance Limitations (Hearns & Blanke, 1998)
!S(jω)!∞ ≥
If the controller does not
adapt, we can easily
have roll amplification
33
33
!
1
α1
"
Θσ (ω1 ,ω2 )
π−Θσ (ω1 ,ω2 )
Performance Limitations – Perez et al. (2003)
Limiting Optimal Control with full knowledge of wave spectrum:
J = E[λφ2 + (1 − λ)(ψ − ψd )2 ]
Minimum variance case (λ=1):
34
E[φ ] ≥ 2 q Φφφ (q)
2
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Actuator limitations on RRD
 
Actuator rate limits may affect performance
Maximum required here
Maximum attained
here
35
35
AGC – Van Amerongen et al (1982)
36
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Performance Limitations – Perez et al. (2003)
IVC OCP: Rudder angle RMS limited to 15deg
37
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Performance Limitations – Perez et al (2003)
IVC OCP: Rudder angle RMS limited to 15deg
38
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Performance Limitations
 
At low encounter frequencies,
 
 
 
RR vs yaw interference can be large
MNP dynamics limits RR achievable performance.
At high encounter frequencies,
 
39
Limitations of rudder machinery usually dominate RR
achievable performance.
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Performance Limitations (quatering seas RR 40%)
40
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Performance Limitations (beam seas RR 64%)
41
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Control Strategies
  PID,
  Hinf
  Loop
shaping
  Adaptive LQG
  Model Predictive Control
  Switched control
  Nonlinear control
42
42
Changes with Speed (Blanke & Christiansen 1993)
 
Rudder to Roll TF: Gφδ (s) =
cφδ (1 + sτz1 )(1 − qs )
(1 + sτp1 )(1 +
s2
sτp2 )( ω2
p
*+,-./01
+ 2ζp ωsp + 1)
;+,-./01
&'(
!&'(
&'%#
!&'(:
&'%!
Changes in dynamic
response due to speed
coupled with changes in
disturbance spectrum
results in a strong need
for adaptation.
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H2 – Optimal Design
Φφφ (ω) = Hd∗ (jω)Hd (jω)
E(φ2 ) = !Hd − QV !22
Cδφ (s) =
G−
φδ (s)
− −1
(Gδφ )
s+q
= Gφδ (s)
s−q
1
V = Hd Gδφ
−1 −
Hd Hd
s−q
−1 −
− s+q Hd Hd
s+q
Hd (s)
= Hd− (s) + Hd+ (s)
s−q
This shows the strong dependency on sea state, sailing conditions and
changes in the vessel model --- adaptation is required.
44
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Direct Sensitivity Specification (Blanke et al. 2000)
Targeted (Desired) Sensitivity:
Sd (s) =
s2
ωd2
(1 +
+ 2ζd ωsd + 1
s
βωd )(1
+
βs
ωd )
S(s) = (1 + Cδφ (s)Gφδ (s))−1
s
Cδφ
(s) = (Sd (s)−1 − 1)G−1
φδ(s)
45
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany 1−
1+
s
q
s
q
P (s)−1
Direct Sensitivity Specification (Blanke et al. 2000)
s
Cδφ
(s)
k1 s
=
cφδ ωd
s2
ωp2
s2
ωd2
+ 2ζp ωsp + 1 (1 + sτ )(1 + sτ )
p1
p2
s
+ 2ζd ωs + 1 (1 + sτz1 )(1 + q )
d
::;*4+5.*8.,8323532<*=>?:@*!*AB%CDE+5FD$G#!
#&"
Successful performance
was demonstrated for the
SF300 patrol boat of the
Danish Navy
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46
!
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8th IFAC CAMS, Sept 15th-17th, Rostock, Germany #!
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Gyro Stabilisation
!ωs
!τm
α
!˙
Spin angular momentum
Kg = Is ωs
!τp
−!τg
!τw , φ̇
l
n
I44 φ̈ + B44
φ̇ + B44
|φ̇|φ̇ + C44 φ = τw − Kg α̇ cos α,
! "# $
τg
Ig α̈ + Bg α̇ + Cg sin α = Kg φ̇ cos α +τp
! "# $
τm
47
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Gyro as a Damper
τp : α̇ ≈ q φ̇
I44 φ̈ +
e
(B44
n- number of gyros
q-constant
48
+ nKg q)φ̇ + C44 φ = τw
Increase of roll damping
due to the gyrostabiliser
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Gyro-control Design
Gyro full state control: τp = −Ka α − Kr α̇
Roll to precession Transfer function:
α(s)
α̇(s)
Kg s
G(s) =
=
=
,
2
!
!
φ(s)
Ig s + Bg s + Cg
φ̇(s)
Bg!
= Bg + Kr ,
Cg!
= Cg + Ka
The control design objective becomes:
τp : α̇ ≈ q φ̇ →
∀ω ∈ Ω
|G(ω)| ≈ q,
arg G(ω) ≈ 0
τg
α̇
Ship
gyro
φ̇
This can be achieved by forcing two real poles on G(s) (Perez Steinman, 2009)
49
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Irregular Sea Performance (Perez & Steinamnn 2009)
Roll Reduction in RMS: 82%
Vessel displacement: 360 ton
Gyro unit weight: 13 ton
50
MCMC Conference, Sept 2009
50
IV - Research Outlook
New Devices
Unsolved Problems
8th IFAC CAMS, Sept 15th-17th, Rostock,
Germany New Devices Flapping fins (Fang et al. 2009 Ocean Engineering 36)
Added mass
52
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Form and Vortex drag
New Devices Rotor Stabiliser (Quantumhydraulic.com)
53
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Parametric roll
Parametric roll is an auto-parametric resonance phenomenon
whose onset causes a sudden rise in roll oscillations.
54
Two-day Tutorial, Ancona, Italy, Sept 2010 Conditions for PR
The following conditions can trigger the effect:
 
 
 
 
 
Hull designs with significant bow flare and hanged stern
Sailing in longitudinal waves
Wave length close to the length of the vessel
Encounter frequency is twice the roll natural frequency
Low roll damping
Parametric roll is particular of modern container ships,
cruise ships, car ferries, and fishing vessels.
55
Two-day Tutorial, Ancona, Italy, Sept 2010 Restoring in Waves – Dynamic Stability
K(φ) = ρ g ∇ GZ(φ)
56
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Videos
57
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Conclusion
 
For over 100 years different devices have been proposed to control
roll motion (reduction)
 
Most of these devices require control systems to work
 
Control design is not trivial due to
58
 
Fundamental limitations
 
Widely-varying disturbance characteristics
 
Actuator limited authority
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Current State and Research Outlook
 
New developments are being put forward by yacht industry
 
Gyros, Flap fins, rotor stabilisers (need for zero speed performance)
 
Navies are still considering RRD
 
Submarines need roll control at low speeds when in the surface
Research outlook
 
 
 
 
Adaptation to sea state and sailing conditions still remains an issue
New devices with interesting hydrodynamics
Integrated vessel and roll control design (performance prediction)
Parametric roll
59
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany Thank You
Death Roll of Sailing Vessels
60
8th IFAC CAMS, Sept 15th-17th, Rostock, Germany