Control System Design for Dynamic Positioning Part I: Overview
TMR4240 Marine Control Systems Department of Marine Technology, Norwegian University of Science and Technology Technology, 1
Outline Part I: Overview Motivation Applications Control system architecture Functionality Position reference systems and sensors Class requirements Part II: Signal Processing Part III: DP Controller Design
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Guidance, Navigation and Control Positioning systems: •
• •
Guidance, navigation and control for automatic sailing and maneuvering Dynamic positioning Thruster assisted position mooring Main function: To keep a vessel exposed to • wave loads • wind loads • current loads on specified position and heading coordinates by means of proper action off the th thruster th t and/or d/ propulsion l i system
3
Dynamic Positioning - Applications Th three The h big bi marine i industries i d i ….:
Shipping & Cruise
Offshore Fisheries and Aquaculture q
4
Dynamic Positioning - Offshore Operations Pipe and cable laying
Vibration control of marine risers
Position mooring
ROV operations Geological survey
Heavy lift lif operations
5
Cable laying vessel
Pipe laying vessel
Functionality: Control Modes • • • •
Station St ti keeping k i models d l Marine operation models Slender structures Multibody y operations p
• • • •
Manoeuvring M i models d l Linearized about some Uo Sea keeping Motion damping p g
High speed tracking/Transit
Low speed tracking Marked position Station keeping 0 6
1
2
Speed [knots] 3
4
5
6
7 …..
Office N Network
Control Structure Business enterprise/ Fleet management
Office Systems
Ship 3: Ship 2: Ship 1:
Operational management Real-Time Control
Rea al-Time Netw work
Control layers
7
Plant control
High level (0.1-5 s)
Actuator control
Low level (0.001-1 s)
Fa ault-Tolerant Control
Local optimization (min-hour)
Example: Control Structure Office Systems
Business enterprise/ Fleet management
• Supply chain management • Fleet planner & turbo router
Ship 3:
• Plant diagnostics and condition monitoring
Ship 2: Ship 1:
Operational management Real Time Control
Local optimization (min-hour)
• Guidance systems • Optimal setpoint chasing • Energy management
Control layers
8
Plant control
High level (0.1-5 s)
• DP control • Power P managementt • Ballast control
Actuator control
Low level (0.001-1 s)
• Thruster control • Motor and drive control
Automation Plant
Cond dition M Monitorring
Office Plant Network
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Control Network
Fieldbus Network
Stand Alone Systems
CARGO
10
VMS
DP
PMS
Integrated Systems
CARGO
11
VMS
DP
PMS
Integration Aspects POSITIONING SYSTEM POWER MANAGEMENT VESSEL AUTOMATION
ESD FIRE&GAS
12
CARGO CONTROL BALLAST CONTROL
Safety y • reliability • redundancy Performance • efficiency • speed Standard, proprietary hardware and software infrastructure
Openness Open networks: • Ethernet • TCP/IP • Fieldbus Standard interfaces
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Electrical Power System Generators
Transformers
MV and d LV Switchboards
P Propulsion l i D Drives i
Propulsors Variable Speed p Drives and Motors 14
Dynamically Positioned Drilling Rig BACK-UP SYSTEM SAFETY SYSTEM EMERGENCY SHUTDOWN FIRE & GAS
PLANT NETWORK WIND SENSORS
PROCESS CONTROL STATION VRU
INFORMATION MANAGEMENT REMOTE DIAGNOSTIC
CONTROL NETWORK
GYRO INTEGRATED THRUSTER CONTROL SYSTEM - DYNAMIC POSITIONING - POSMOOR - AUTOSAIL - OPERATOR CONTROL SYSTEM INTEGRATED MONITORING & CONTROL SYSTEM - EXTENSION ALARM - PROCESS CONTROL
PROPULSION
AZIPOD
15
DRILLING DRIVE SYSTEM ENERGY MANAGEMENT SYSTEM POWER GENERATION & DISTRIBUTION
FIELDBUS NETWORK
Operational Management - Industrial IT architecture
Real Time Flow w of Plant a and Trans sactional D Data
Enterprise business:
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Business Systems
- Logistics chains (D2D, ..) - Fleet management/allocation - Corporate management
Operational management: Operational Systems
Automation Systems and Devices
-
Maintenance philosophies Enterprise resource planning Supply chain management Diagnostics Condition monitoring
Physical and functional Integration: -
Connectivity C ti it Modularity Openness Optimization
Positioning Control Functionality W IND S E NS O RS
HP R
DP C O N -A M TC
M RU’s
DP C O N -B
DG P S
DP C O N -C
DG P S
G Y RO ’s A R TE M IS
P RIN TE R CO N TR O L NE TW O RK
DP CA B -A DP CA B -B DP CA B - C DP TRA IN ING S IM U LA TO R
FIE L DB US NE TW ORK
DRA UG H T S E NS O RS HP R TRA NS DU CE R
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• • • •
Initial Mode Manual Mode S iA Semi Auto t Mode M d Auto Mode – Damping p g Control – Station Keeping – Marked Position – Way-point Tracking – Optimal Heading Control – Roll and Pitch Damping – Optimal Setpoint Chasing
DP Control System Features • Selectable Wind Feedforward individually in surge sway and yaw surge, yaw. • Selectable Low, Medium and High gain in all operational p modes. • Selectable reference velocities in tracking operations • Selection of arbitrarily rotation point. • Automatic or manual sea state selection for improved performance in varying environmental conditions. 18
Standard DP measurements Position reference systems: – DGPS – Hydroacoustic y – Artemis (Microwave) – Laser – Taut-wire – (Riser)
Heading and yaw rate: – Gyrocompass / GPS Roll and p pitch angle: g – Vertical reference units (accelerometers, gyros) Wind speed and direction: – Anemometers 19
Measurements - challenges Challenges: • Time delays, synchronization of multiple signals • Measurement resolution and update rate • Noise level and nature • Error handling g • Multiple measurements: • Weighting and voting
Inertial Navigation Systems (INS) More use of accurate instruments for roll / pitch, Vertical motion and horizontal acceleration. acceleration Can improve measurement availability, accuracy and total system integrity 20
Litton LN 200 IMU
Position reference systems SATELLITE NAVIGATION SYSTEM (DGPS / GLONAS)
SURFACE REFERENCE SYSTEM
TAUT WIRE
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HYDROACOUSTIC POSITIONING SYSTEM
Signal alignment and noise compensation
GPS ANTENNA
VRU
HPR TRANSDUCER
22
All p position measurements are transformed to one common reference point on the vessel center of gravity / midship
DP Class requirements IMO Equipment q p Class Not applicable Equipment Class 1 Equipment Class 2 Equipment Class 3
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DNV DYNPOS-AUTS DYNPOS-AUT DYNPOS-AUTR DYNPOS-AUTRO DYNPOS AUTRO
LR DP CM DP AM DP AA DP AAA
ABS DPS-0 DPS-1 DPS-2 DPS-3 DPS 3
DP Class 0 Configuration DYNAMIC POSITIONING SYSTEM
WIND SENSOR
MTC
MRU
GYRO
DGPS
PLANT NETWORK
CONTROL NETWORK
DP CONTROLLER UNIT
FIELDBUS NETWORK
MAIN PROPELLER w / RUDDERS
TUNNEL THRUSTER
AZIMUTH THRUSTER
AZIPOD
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DP Class 1 Configuration WIND SENSOR
DYNAMIC POSITIONING SYSTEM
MTC HPR
MRU
DGPS
GYRO
CONTROL NETWORK
DP CONTROLLER UNIT
FIELDBUS NETWORK
MAIN PROPELLER w / RUDDERS
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HPR TRANSDUCER TUNNEL THRUSTER
AZIMUTH THRUSTER AZIPOD
DP Class 2 Configuration WIND SENSORS
DPCON-A
MTC
DPCON-B
DP CQA/SIM
MRU’s
HPR DGPS
GYRO’ss GYRO PRINTER ARTEMIS
CONTROL NETWORK
DPCAB-A DPCAB-B
FIELDBUS NETWORK
HPR TRANSDUCER TC
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DRAUGHT SENSORS
DP Class 3 Configuration WIND SENSORS
HPR
DPCON A DPCON-A MTC
MRU’s
DPCON-B
DGPS
DPCON-C
DGPS
GYRO’s ARTEMIS
PRINTER CONTROL NETWORK
DPCAB-A DPCAB-B DPCAB-C DP TRAINING SIMULATOR
FIELDBUS NETWORK
DRAUGHT SENSORS
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HPR TRANSDUCER
Total Integration: Floating Production FPSO • • • •
MRUs
Process automation Marine automation Posmoor/DP Power
WIND SENSORS GYROs
POSITIONING AND MARINE AUTOMATION
DARPS
PROCESS AUTOMATION & SAFETY SYSTEMS
ALARM & EVENT PRINTERS
Electric Power Generation and Distribution System
HPR
ENGINE CONTROL ROOM
ENGINEERING STATIONS AND X-TERMINALS
Automation and Positioning System
GENERATORS
HV
PCS
WATER INJECTION REINJECTION
ESD PSD
F&G
GAS COMPRESSION AFT CONTROL ROOM
690V SWBs & MCCs
THRUSTER PCS
HVAC & UTILITIES
HV SW B HV SW B
THRUSTER
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THRUSTER BALLAST & CARGO CONTROL
TURRET AND WELLHEAD/SUBSEA CONTROL
POSMOOR System UHF LINK
MRU
ARTEMIS
WIND SENSORS DARPS
TURRET DYNAMIC POSITIONING POSITIONING/ MOORING
GYRO
PROPULSION AZIPOD MASTERBUS NETWORK
SAFETY SYSTEM
DRAUGHT SENSORS PROPULSION AZIPOD
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Thruster Assisted Position Mooring (POSMOOR) System: Thruster assistance for position and heading keeping of anchored vessels
Position Mooring Purpose: - Give Thruster Assistance in position and heading keeping - Damping Function - Keep fixed position and heading - Tailor-made Tailor made solutions for special applications Turret
Anchor lines
Seabed
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Petrojarl Varg FPSO
Turret
Anchor lines
Seabed
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POSMOOR ATA Configuration WIND SENSORS MRU’s
PMCON-A
MTC
PMCON-B
PMANA HPR
DGPS
GYRO’s PRINTER ARTEMIS
CONTROL NETWORK
TURRET
PMCAB-A
PMCAB B PMCAB-B
FIELDBUS NETWORK
HPR TRANSDUCER DRAUGHT SENSORS
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Positioning Control Architecture THRUSTER SETPOINTS
THRUST US ALLOCATION POWER MANAGEMENT SYSTEM
POWER LIMITS
MEASUREMENTS
Process Plant
ADAPTIVE LAW
SIGNAL PROCESSING
VESSEL OBSERVER
CONTROLLER VESSEL MOTIONS
COMMANDED THRUST S
OPTIMAL SETPOINT CHASING
REFERENCE MODEL OPERATOR
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Si Signal l Processing P i Part II
Professor Asgeir g J. Sørensen, ø , Department of Marine Technology, Norwegian University of Science and Technology, Otto Nielsens Vei 10, NO-7491 Trondheim, Norway E-mail:
[email protected] 34
Outline • Motivation/Background M ti ti /B k d • Elementary Signal Quality Checking – Test T off individual i di id l signals i l – Handling of redundant measurements
35
Computer-controlled systems SATELLITE
Important aspects to consider in computer-controlled systems: ─ Signal quality checking. Each sensor signal has to be checked for errors subject to certain criteria before processed by the control system. ─ Handling of multiple signals signals. If several sensors provide measurements of the same state variable, weighting and voting mechanism must be introduced introduced.
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THRUSTER SETPOINTS
MEASUREMENTS
SIGNAL PROCESSING THRUSTER ALLOCATION
REAL WORLD
VESSEL OBSERVER
CONTROLLER COMMAND THRUSTER FORCES
VESSEL SETPOINTS
VESSEL MOTIONS
Signal Processing HW Signal Communication already checked
Features: • Online Signal Quality Check Signal Processing Unit
• Online weighting of sensor signals • Multiple signal voting algorithms • Filtering and smoothing of signals
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Signal Processing - Example Examples of four different signal failures the signal QA module is detecting. 35
High derivative
30
Frozen signal 25
High variance
20
Wild point
15 10 5 0
38
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Signal quality checking Three level testing: 1. Tests on individual signals 1 Range check Variance check Wild point i t detection d t ti and d removall 2. Sensor voting Detection of sensor drift 3. Sensor weighting Unbiased minimum variance measurements
+ Observer test (Innovation/injection term) 39
Windowing Windowing Wi d i is i the th operation ti off taking t ki a signal i l x[k] [k] and d multiply lti l it with ith a finite duration window signal w[k]:
pk xkwk p Rectangular window: wk
pk
1,
−M ≤ k ≤ M
0
otherwise.
xk,
−M ≤ k ≤ M
0
otherwise,
Windowing is used in calculation of signal variance to provide unbiased minimum variance estimates.
40
Statistics Consider the sequence of n-1 historical values: xi : i k − n − 1,..., k − 1, 1 k Average value:
x̄ k
1 n
∑ikk− k n−11 xi
Variance: 2k
41
1 n−1
∑kik−n−1 xi2 − nx̄ 2k
Range check Most of the signals available have a defined range: Example: Gyro signal within 0-360 0 360 degrees degrees. Signal outside the range will indicate that the sensor is f lt faulty: signal will be rejected. Alarm issued to the operator.
xk ∈ x min,x max
42
Variance check The variance of each signal is calculated. calculated High variance limit
High variance may indicate sensor failure fail re or inaccurate measurement. Low variance may indicate a frozen signal. Alarm issued to the operator. 43
Calculated signal variance
Low variance limit
Wild point check The signal value is a wild point if it is outside a band around the estimated signal mean. The signal value will be rejected for one sample. Alarm issued to the operator.
xk ∈ x̄ k − a,x̄ k a
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W ild p o in t W ild p o in t lim it
M e a s u re m e n t
W ild p o in t lim it
Sensor voting Purpose To detect drift of a sensor or position reference system
north east
north
Actions Alert the operator If possible, automatically y ignore g the erroneous sensor
north east east
Value
Advantage Improved safety Better utilization of redundant sensor configurations 45
1
2
3
Sensor No
Sensor weighting • Manual weighting – Operator O decide d id weights i h wi – Advantages: • intuitive understanding of operation • operator experience and judgement is utilized
3 sensors: xw w1xw11ww2x22ww33x3
• Automatic weighting – System calculate unbiased minimum variance measurements – Advantages: • best possible measurements in most situations • automatic operation 46
x̂ ∑i1 sixi n
∑ni1 si 1
2j
si
j≠i ∑nk1 2j j≠k
Handling loss of signals • Filt Filtering i should h ld nott give i phase h tto th the measurement. t • Tf depends on difference of sensors. Maximum change [m/s] is specified. • A change in average value is inevitable.
average
47
Enabling of sensors • When enabling sensors, average remains smooth. • No filtering of the sensor signals => no phase added to the measurement. meas rement
average
48
DP Controller Design Part III
Lecture 7, Spring 2008 TMR4240 Marine Control Systems Department of Marine Technology Technology, Norwegian University of Science and Technology, 49
Outline • Control plant model – Linear low-frequency vessel model – Linear wave wave-frequency frequency model
• DP Observer • Reference model • Horizontal-plane controller – – – –
PD control law based on LQG synthesis Integral action Wind feedforward Model reference feedforward
• Pitch and roll motion damping controller • Controller analysis • Thrust allocation 50
Vessel model Superposition, LF + WF
Surge
LF Yaw Swayy
tot w
WF
time
51
Modelling The mathematical models may be formulated in two complexity levels: Control plant model: Simplified mathematical description containing only the main physical properties of the process. This model may constitute a part of the controller. Examples of model based output controllers are e.g. LQG, H2/H∞, nonlinear feedback linearization controllers controllers, back back-stepping stepping controllers, controllers etc. etc The control plant model is also used in analytical stability analysis, e.q Lyapunov Stabilty. Process plant model: Comprehensive description of the actual process. The main purpose of this model is to simulate the real plant dynamics including process disturbance, sensor outputs and control inputs. The process plant model may be used in numerical performance and robustness analysis of the control systems. Maneuvering Model Low-Speed Model Station Keeping Model U0 -3 3 m/s < U < 3 m/s U Uo 52
Nonlinear Low-frequency Vessel Model Nonlinear 6 DOF low-frequency model - surge, sway, heave, roll, pitch and yaw : Ṁ CRB CA r r D r G env moor thr
Relative velocityy vector is defined: r u u c
53
v vc
w p q r T
u c Vc cos c − , v c Vc sin c −
env wind wave2
Environmental loads: Wind and 2. Order wave loads
moor
Generalised mooring forces
thr
Generalised thruster forces
Low--frequency Control Plant Model Low Ṁ D G thr w
Hydrodynamic yd ody a c Coup Couplings: gs ⎡
⎢ M=⎢ ⎣
⎡
⎢ D = −⎢ ⎣
54
m − Xu ˙ 0 −Zw ˙ 0 mzG − Mu ˙ 0 Xu 0 Zu 0 Mu 0
0 Yv 0 Kv 0 Nv
0 m − Yv˙ 0 −mzG − K v˙ 0 mxG − Nv˙ Xw 0 Zw 0 Mw 0
0 Yp 0 Kp 0 Np
−X w ˙ 0 m − Zw ˙ 0 −mxG − Zq ˙ 0
Xq 0 Zq 0 Mq 0
0 Yr 0 Kr 0 Nr
⎤ ⎥ ⎥ ⎦
0 −mzG − Yp˙ 0 I x − K p˙ 0 −I zx − Np˙
G −
mzG − X q ˙ 0 −mxG − Zq˙ 0 I y − Mq ˙ 0
0 mxG − Yr˙ 0 −I xz − K r˙ 0 I z − Nr˙
0 0 0 0 0 0
0 0 Z 0 M 0
0 0 0 0 0 0
0 0 Zz 0 Mz 0
0 0 0 K 0 0
0 0 0 0 0 0
⎤ ⎥ ⎥ ⎦
Model reduction matrices Define: H56
1 0 0 0 0 0
1 0 0
0 1 0 0 0 0 0 0 0 1 0 0
0 1 0 0 0 0
H53
0 0 0 0 1 0
0 0 0
0 0 0 0 0 1
0 0 1
Model reduction: M i Hi6 MHTi6 Di Hi6 DL Dm HTi6
G i Hi6 G B G m HTi6
55
H36
1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1
H33 I33 , H66 I66
Low-frequency Control Plant Model Linearized low-frequency state-space formulation: i = 3: surge, sway, and yaw i = 5:surge, sway, roll, pitch and yaw
ẋ i Ai xi B i ic Ei wi yi C i xi vi x3 u,v,r,x,y, T
where:
Ai
56
−1 −M−1 i Di −Mi G i
Iii
0 ii
Bi
x5 u,v,q,p,r,x,y,,, T
M−1 i Hi3 0 ii Hi3
Ei
M−1 i 0 ii
Ci
0 ii Iii
Low-frequency Control Plant Model 3 DOF Vessel model (Low Speed)
Bias model (Markov model)
Tb may be set equal to 0 (Wiener model).
57
- (Wind) - Waves - Current - Thruster Losses - Other unopened slowly-varying slowly varying effects
Wave-frequency Control Plant Model Synthetic white-noise-driven wave-frequency state-space formulation for i = 3 DOF horizontal model: ̇ 3w A3w 3w E3w w 3w
3w C3w 3w
where: A3w
3w x w ,y w , w T 0 I − 2 −2
diag 1 , 2 , 3
C3w
3w ∈ R 6 0 I
diag 1 , 2 , 3
w 3w ∈ R 3 E3w 3
0 K3w
Kw diagKw1 ,Kw2 ,Kw3
This corresponds to three decoupled WF models on the form: wi w wi 58
s
Kwi s
s2 2 i i s 2i
Wave-frequency Control Plant Model Synthetic white-noise-driven wave-frequency state-space formulation for i = 3 DOF horizontal model and i = 5 DOF model: ̇ iw Aiw iw Eiw w iw
iw Ciw iw
where: xiw
59
Tiw , Tiw
T
Wave-frequency Control Plant Model WF model
Example: 2nd order WF model (notch-filter)
60
Resulting Control Plant Model Wave-frequency model:
Low-frequency Low frequency ship dynamics:
Mν Dν RT ( )b τ c
Bias model accounting for un-modeled dynamics and d slowly l l varying i disturbance: di t b
b Eb w b
Kinematics:
η R ( ) ν
Measurements:
61
ξ Aξ Eww w ηw Cξ
y η ηw v
Model Uncertainties Vessel Speed Wave response Coupling p g effects and p parameters in M and D Degree / linearization of model Thruster losses (direction / thrust) Wave period (peak frequency)
62
Note ! Error in measurement can often be a significant contributor to reduced system performance !
Nonlinear Observer Observer Detailed ship model
Weighted, quality checked position iti and d heading h di measurements
Model adaptation
Purpose: Noise filtering Wave filtering Estimates of vessel positions and velocities Dead reckoning 63
Filtered estimates used by the feedback controller
LF estimate Measurement 0
50
100
150
200
250
300
350
400
450
500
Nonlinear Observer (Basic version)
Observer
64
Loop Shaping 1st order wave loads 0
[dB]
-10 10
y ̂
-20 -30 -40 -3 10
10
-2
10
-1
10
0
10
1
10
2
Frequency [rad/s] 0
[dB]
-20
y ̂
-40 -60 -80 -3 10
10
-2
10
-1
10
0
10
Frequency [rad/s] 65
o 2 /T p
1
10
2
Adaptive Control Systems y Some kind of ’adaptiveness’ present in most hi-tech Marine systems today (observer / controller): • Gain Scheduling (robust) wrt. • Operation • External measurements • Operations
• Model-predictive control (MPC) • Online adaptive observers / controllers
Examples: Autopilots, DP systems 66
Adaptive Observer WF model WF model parametrization:
Assumed constant parameters in stability analysis
67
(of course not entirely true …)
Adaptive Observer Purpose: Compute online the WF model parameters that Matches a c es the e WF motion o o o of the e vessel. esse
Ad ti version Adaptive i off WF update d t law: l High-pass filtered 68
Experimental Tests – GNC Lab 1999 C b hi I Cybership
69
Experimental Tests – Adaptive Observer
70
Experimental Tests – Adaptive Observer
71
72
Reference trajectories If our controller also needs to follow a specified trajectory, things get more complex (and also complicated) Something that we need to consider to the generation of the trajectories:
η d (t ( ) There are different ways of doing this: 11. U Using i filters filt to t smooth th the th switching it hi between b t waypoints i t η d ( t ), η d ( t ), η d ( t ) 2. Using a vessel model 3 Using complex guidance systems that specify 3.
73
Guidance system Generates the desired trajectories (position (position, velocity and acceleration) acceleration).
The waypoint generator establishes the desired way points according to mission, operator decision, weather, fleet operations, amount of power available etc. The waypoint management system updates the active waypoint based on the current position of the ship. The reference computing algorithms generate a smooth feasible trajectory based on a reference model, the ship actual position, amount of power available, and the active way point.
74
Different approaches to path generation
There are different ways of specifying the path • • • •
Filtering step signals Using a simplified vessel model and simulation Polynomial curve fitting Numerical optimisation
75
Filtering step signals H n (s ( ) Swithicing way points
H e (s )
η d (t )
H (s ) This is also called a refernce model approach. In this case both the path and the speed are determined by the order and tunning of the filters. Typical filters are 2nd and 3rd order. The response off the Th th filters filt can be b simulted i lt d so the th reference f trajectory t j t is i known k in i advance. d All this is done in discrete time.
76
Using a vessel model The time derivatives of the desired position can be specified as
Then we can use simplified reference models based on the vessel model d l tto generate t the th speed d and dh heading: di
The input of these models can be generated via feedback using PI control:
77
Using a vessel model
PID
Reference Model Reference model of third order: aed ved Γxed Γxref
ẋ ref
−Af xref Af r
Γ diag 2i diag2 di 2 i i , i 1 ,22 , 3 Af diag1/t i , i 1 ,2 , 3.
Where the final Earth-fixed position and heading are given by:
ηr x r , y r , r T In reference parallel frame the desired position and heading are given by: ad RT d aed
78
vd RT d ved
xd RT d xed
Reference Model Reference model of third order:
( ηd , η d , η d ) f ( η r , ηd , η d , η d ; t ) Where the final Earth-fixed position and heading are given by:
ηr x r , y r , r T Optimal Earth-fixed Earth fixed position and heading are given by: * η*r ηr Δrvessel
* Δrvessel
79
is the optimal vessel increment subject to some criteria
Controller Design - LQG Feedback Performance index defined to compute Linear-Quadratic-Gaussian feedback controller in surge, sway and yaw accounting for i = 3 DOF horizontal model and i = 5 DOF model: J E lim T→
1 T
T e T Qe Tpd P pd dt
Q QT ≥ 0
0
Deviation vector is defined to be: e 2 RT d ̂ − d T
̂ x̂ , y, ̂
T
̂ d x d , y d , d
P PT 0
e e T1 ,e T2 T
T
e1 ė2
Ricatti equation:
Let:
Ṙ − A 3 R − A T3 R R B 3 P − 1 B T3 R − Q
0 −A3 R − AT3 R R B 3 P−1 B T3 R − Q
Ṙ → 0
LQG Feedback Control law is:
pd −G p e 2 − G d e 1 80
G P −1 B T3 R
Gd Gp
Controller Design - Resulting Control Law LQG feedback control law is: pd −G p e 2 − G d e 1
Integral action: ̇ i Awi i G i e 2
Wind feedforward control action: w −G w ̂ wind
Reference model feedforward control action: t M3 ad D3 vd d3 vd Cvd vd
Resulting feedback and feedforward control law is: 3c 3 w t i pd d 81
Positioning with Roll, Pitch Damping Hydrodynamic coupling between: Surge and pitch Sway, roll and yaw Geometrical coupling by thruster configuration: Thruster Th t induced i d d pitch it h momentt due to surge positioning Thruster induced roll moment due to sway and yaw positioning Resonance periods in roll and pitch in the range of 35-65 s: within bandwidth of positioning p g controller
82
Controller Design - Resulting Control Law Roll-pitch damping controller: rpd −G rpd
p̂ q̂
where G rpd
0 g xq g yp 0 g p 0
Resulting positioning controller with roll-pitch damping: 5c 3c rpd pd
83
Thrust allocation Ṁ D G G ic w Relation between 3 DOF control vector - surge, sway and yaw and r number of thruster/propellers p p is: ic T3r Kuc Thrust p produced by y each p propeller: p
Kuc T3r ic
uc K−1 T3 r ic
Real thrust acting on the vessel in 6 DOF:
thr T6r Kuc
84
Thrust allocation Aziumuthing thrusters
1. Bow azimuthing thruster
lba
i
2. Bow tunnel thruster
Surge
lbt
Yaw Sway
lst
3. Stern tunnel thruster
lp T 35
cos 1
0
0
cos 4
cos 5
sin 1
1
1
sin 4
sin 1
l ba sin 1 l bt −l st −l p cos 4 − b s sin 4 l p cos 5 − b s sin 5
bp bs 5. Port p pod 4. Starboard pod 85
High Level Plant Control Low F Frequency
•Current loads •Wind Wind loads •2nd 2nd order wave loads
Wave
1st order wave Frequency q y response
τenv
e Controller
86
xˆ LF xd
τc
xWF
Thruster setpoints
Thruster Allocation
Observer
Vessel
xLF
y Measurements
Reference Model Operator
Sensors
x Actual positions,, p velocities
Coupled Dynamics Surge-Pitch Dynamics:
m 11 u̇ m 15q̇ d 11 u d 15q g 11 x 5surge
m 51 u̇ m 55q̇ d 51 u d 55q g 55 0 Surge Control Law:
5surge −gg x x − g u u
m11 m51
g xq q
Closed-Loop pitch dynamics: m 55 − d 51 −
m51 m15 m11 m51 d 11 m11
q̇ d 55 − − gu
m51 m11
m51 d 15 m11
g xq q g 55 m
u − g 11 g x m51 x 0. 11 X, U -> 0 by control
m 55 − 87
m51 m15 m11
q̇ d 55 −
m51 d 15 m11
g xq q g 55 0
Pitch damping
DP with Roll and Pitch Damping - Time Series Surge [m] 0.2 0 -0.2 02 -0.4
0
200
400
600
800
1000
0.4 With roll-pitch damping No roll-pitch damping
0 -0.4 -0.8 0
200
400
600
time [sec] 88
800
1000
DP with Roll and Pitch Damping - Time Series Thrust in surge [kN] 600 400 200 0
0
x 10
200
400
600
800
1000
4
2.5 With roll-pitch damping No roll-pitch damping
2 15 1.5 1 0.5 0
0
200
400
600
time [sec] 89
800
1000
DP with Roll and Pitch Damping - Time Series Sway [m]
0.5 0 -0.5
Roll [deg]
-1 1 0.5 0 -0.5
Heading [deg]
With roll-pitch damping No roll-pitch damping
0.1 0 -0.1 0
200
400
600
time [sec] 90
800
1000
DP with Roll and Pitch Damping - Time Series Thrust in sway [kN] 2000
1000
0
Thruster induced moment in roll [kNm]
x 10
4
0 -2 -4 4
Thrust in Yaw [kNm] 8000 4000 With roll-pitch damping
0
No roll-pitch damping
0
200
400
600
time [sec] 91
800
1000
DP w/ Roll and Pitch Damping - Power Spectra
x 10
8
-3
6 4 2 0
8
0
0.005
x 10
0.015
0.025
0.035
0.045
-3 With roll-pitch damping No roll-pitch damping
6 4 2 0
0
0.005
0.015
0.025
Frequency [Hz] 92
0.035
0.045
Environmental Data Typical North Sea environmental data T p 1.0 18.0 s H s 0.5 0 5 12 12.0 0 m H s 2.7 m Vw 0.0 0 0 33.4 33 4 m s Vw 8.4 m s Vc 0.0 0 0 1.5 1 5 m s
93
Nonlinear Observer (Wiener process)
ξˆ A ξˆ K1y M ˆ Dν Mν D ˆ RT ( y )bˆ τ c RT ( y )K 4 y bˆ K 3 y ηˆ R ( y ) νˆ K 2 y 94
yˆ ηˆ C ξˆ
Conventional Controller design PID controller
τ PD K Pe2 K De1 τ I Awτ I G I e2 e 2 R y ηˆ LF ηd T
T
e1 e 2
Wind feed-forward controller τ w G wτˆ wind
Resulting Resulting controller τc τ PD τ I τ w
95
DP Control in Extreme Seas Observer equations (skip wave filtering) bˆ K 3T y Mνˆ Dνˆ RT bˆ τ RT K y T
T
ηˆ R νˆ K y
y
yˆ ηˆ T
T
y
c
y
4T
2T
Controller error equations reformulated e 2T R T y ηˆ T ηd
T
e1T e 2T
96
Case Study: DP of Shuttle Tanker
Main dimensions
97
DWT
119 909
Metric tons
Design DWT
M
143 000
Metric tons
Mass
Loa
265,50
Meters
Length overall
Lpp
256,00
Meters
Length between perpendiculars
B
42,50
Meters
Breadth
D
22,00
Meters
Depth
Draught
15,65
Meters
Design draught
Case Study: DP of Shuttle Tanker Propulsion configuration
98
2 Main diesel engines
9985
Power [kW]
2 Auxiliary diesel engines
3520
Power [kW]
2 Auxiliary diesel engines
2640
Power [kW]
Tunnel thruster forward forward
2200
Max input power [kW]
T Tunnel l thruster th t forward f d aft ft
2200
M input Max i t power [kW]
Tunnel thruster aft forward
736
Input power [kW]
Tunnel thruster aft aft
736
Input power [kW]
Case Study: DP of Shuttle Tanker Stationkeeping Capability: Waves, Wind, Wind Induced Current Rotating 0 330
30
300
60
270
0.0
0.5
1.0
1.5
240
2.0
2.5
120
150
210 180
Mean Environmental Forces Relative To Maximum Holding Power
99
90
DP capability plot illustrates from which sectors the vessel is capable bl off withstanding the environmental forces
Torsethaugen Wave Spectrum The spectral model gives a parametric description of four different types of spectral peaks: •Primary wind sea peak •Primary swell peak •Secondary wind sea peak •Secondary swell peak Tp= 40s (green), 20s (blue), 15s (red) - and Hs=6m
100
Wave Filtering Properties 1st order wave loads Transfer functions between measured total and estimated LF surge position using conventional observer design:
y ˆ
Tp= 40s (green), 20s (blue), 15s (red) - and Hs=6m 101
Simulation Example 1 Conventional controller t ll design d i LF estimate does not follow real signal due to the wave filtering notch effect
Tp= 40s and Hs= 6m 102
Simulation Example 2
Tp= 40s and Hs= 6m
Conventional DP controller (left) DP controller t ll omitting itti wave filtering filt i (right) ( i ht) 103
Conclusions In extreme seas,, nonlinearities become more notable Couplings between the various degrees of freedom increase Thruster losses become important DP observer and controller omitting conventional wave filtering property was proposed d - in i order d to expand d the h operational window 104
