a survey on marine control systems

Hội nghị toàn quốc về Điều khiển và Tự động hoá - VCCA-2011

VCCA-2011

A Survey on Marine Control Systems

Tổng quan về hệ thống điều khiển hàng hải

Hung Duc Nguyen

University of Tasmania / Australian Maritime College

e-Mail: [email protected]

Abstract In this paper, a survey is made on modelling,

simulation, control design, advances, achievements

and trends in marine control systems. An overview of

history of development of marine control systems is

outlined. Over a long history, many achievements on

marine control systems have been reached in both

theory and practice. With the aid of computers and

high performance software many complicated control

algorithms could be applied in modelling, simulation

and design of control systems for marine vehicles

including surface vessels and underwater vehicles.

The development of GNSSs (GPS, GLONASS and

GALILEO) and RTK/D-GNSSs stimulates design of

accurate, precise and high-performance control

systems for marine vehicles. Telecommunication

satellite-based broadband techniques are a trend of

remote control systems at seas. The paper discusses

challenging problems in design and simulation of

marine control systems. The paper also deals with

some potential research projects related to the marine

control engineering at AMC/UTAS.

Tóm tắt: Trong bài báo này tác giả trình bày tổng

quan về mô hình hóa, mô phỏng, thiết kế điều khiển,

những tiến bộ và thành tựu cùng các khuynh hướng

phát triển hệ thống điều khiển phương tiện trên biển.

Bài báo khái quát lịch sử phát triển hệ thống điều

khiển phương tiện trên biển. Qua lịch sử lâu dài cho

đến nay có nhiều thanh tựu trong hệ thống điều khiển

hàng hải. Bằng sự hỗ trợ của máy tính và phần mềm

tính năng cao người ta có thể áp dụng nhiều thuật toán

điều khiển phức tạp trong mô hình hóa, mô phỏng và

thiết kế hệ thống điều khiển cho phương tiện trên

biển. Sự phát triển của các hệ thống vệ tinh dẫn

đường toàn cầu (GPS, GLONASS, GALILEO) và hệ

thống định vị vệ tinh vi phân đã kích thích việc thiết

kế các hệ thống điều khiển chuẩn xác, chính xác và có

đặc tính tốt cho phương tiện trên biển. Các kỹ thuật

dải băng thông rộng thông qua vệ tinh viễn thông là

một trong những khuynh hướng phát triển hệ thống

điều khiển từ xa trên biển. Bài báo thảo luận về những

vấn đề thách thức trong thiết kế và mô phỏng hệ

thống điều khiển hàng hải. Bài báo cũng đề cập đến

một số đề tài nghiên cứu khả thi liên quan đến lĩnh

vực công nghiệ điều khiển hàng hải tại AMC/UTAS.

Nomenclature Symbol Unit Meaning

ν T

u,v,w,p,q, rν

η T

n,e,d, , , η

Abbreviation AMC Australian Maritime College

UTAS University of Tasmania

PID Proportional, Integral, Derivative

LQG Linear quadratic Gaussian

GPS Global Positioning System

GNSS Global Navigation Satellite Systems

DP Dynamic positioning

D-GPS Differential GPS

RTK-GPS Real-time Kinematic-GPS

IFAC International Federation of Automatic

Control

ECEF Earth-centred Earth-fixed frame

ECI Earth-centred inertial frame

NED North-East-Down frame

FPP Fixed pitch propeller

CPP Controllable pitch propeller

1. Introduction Marine control engineering is about applications of

control theories into marine and offshore systems. It

involves the research and development of new control

algorithms, hardware and software for control systems

in maritime engineering systems.

Marine transport is more cost-effective than other

transports. The world’s fleets carry the majority of

cargo. In many countries like EU, Australia, America,

Japan and Korea the number of seafarers is decreasing

because sailing at sea is a job in severe working

conditions. This requires a high-level automation on

board cargo carrying marine vehicles because the

shipboard high-level automation can reduce the

number of crew. Advances in computer and

information technology, data communication

technique and instrumentation engineering play a very

important role in development of new control

solutions for optimal and high-performance control

systems and fuel saving. The new control solutions

are based on modification of feedback control

algorithm and new configuration of hardware. The

building of new types of marine vehicle and craft

inspires new design of instrumentation and control

systems.

In recent decades, more and more ROVs/AUVs have

been applied in exploration of seabed, discovery and

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exploitation of marine resources. This requires new

solutions for data communication and control

algorithms. Control of ROVs/AUVs is a great

challenge because they are operating in 6-DOF.

This paper is organized as follows: Section 1

Introduction; Section 2 Current status of marine

control systems; Section 3 Kinematics and kinetics;

Section 4 Overview of marine control systems;

Section 5 Modelling and identification of marine

vehicles; Section 6 Experimental facilities; Section 7

Challenges, Section 8 Trend; Section 9 Potential

projects at AMC/UTAS; and Section 10 Conclusions.

2. Current Status 2.1 Overview of History

The invention of the gyroscope contributed much to

the development of a ship’s autopilot system. The

development of the electronically-driven gyroscope

was motivated by the need for more reliable

navigation systems in steel ships and underwater

warfare [3][4]. The successful design of the gyroscope

at the beginning of 20th

century was the key

breakthrough in automatic ship control since it led to

the development of autopilots and other control

systems (see Fig. 1).

Fig. 1 Diagram of history of marine control systems

2.2 Research Activities

The IFAC organizes every 3 year (triennial)

conferences on marine systems including CAMS

(Control Applications in Marine Systems), MCMC

(Manoeuvring and Control of Marine Crafts). The

scopes of these IFAC conferences on marine control

systems are broad ranges from autopilot to dynamic

positioning systems and various applications of

control theories in control, simulation and modelling

of marine vehicles. These IFAC conferences on

control of marine vehicles cover a wide range of

scopes, for example, ship manoeuvring, autopilots,

roll damping, dynamic positioning, automatic

mooring and anchoring, navigation, guidance and

control of autonomous surface and underwater

vehicles, operational safety etc.

2.3 Development of GPS/GNSS and IMU/INS

Since 1995 when the GPS became operational for

civil use, the accuracy of GPS/GNSS has been

improved significantly. The augmentation, integration

and availability of GPS, GLONASS and GALILEO

for civil use with high accuracy, precision and

reliability inspire engineers and researchers to design

new types of tracking and path-following control

system. Moreover, the development of IMU/INS and

integration of GNSS and IMU/INS allows more

accurate and precise navigation systems to be

designed and helps more complicated marine control

systems to be developed.

3. Kinematics and Kinetics of Marine

Vehicles 3.1 Reference Frames

In the design of marine control systems, some

reference frames for descriptions of kinematics and

kinetics of marine vehicles are often used. Fig. 2

shows Earth-centred reference frames (the Earth-

centred Ear-fixed frame xeyeze, and the Earth-centred

inertial frame xiyizi), and geographic reference frames

(the North-East-Down coordinate system xnynzn and

the body-fixed reference frame xbybzb) [3][4].

Fig. 2 The ECEF frame xeyeze is rotating with angular rate

with respect to an ECI frame xiyizi fixed in the space [3][4]

Fig. 3 shows the 6DOF velocities in the body-fixed

frame. Table 1 gives the notation for the 6DOF

motions, forces and moments, linear and angular

velocities, position and Euler angles for marine

vehicles.

zi, ze

ωe yn

xn

zn

BODY

y

x

z

NED

ECEF ωet

ye

xe

yi xi

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Fig. 3 The 6DOF velocities u, v, w, p, q and r in the body-

fixed reference frame xbybzb [3][4]

Table 1 The notation of SNAME (1950) for marine

vessels

3.2 Equations of Kinematics

Referring to Fig. 2 the 6-DOF kinematic equations in

the NED (north-east-down) reference frame in the

vector form are,

η J η ν (1)

where

n

b 3 3

3 3

R Θ 0J η

0 T Θ (2)

with 3 3S η and 3ν . The angle rotation

matrix n 3 3

b

R Θ is defined in terms of the

principal rotations,

x,

1 0 0

0 c s

0 s c

R , y,

c 0 s

0 1 0

s 0 c

R and

z,

c s 0

s c 0

0 0 1

R (3)

where s = sin(.), c = cos(.) using the zyx-convention,

n

b z, y, x,: R Θ R R R (4)

or

n

b

c c s c c s s s s c c s

s c c c s s s c s s s c

s c s c c

R Θ (5)

The inverse transformation satisfies,

1n b T T T

b n x, y, z,

R Θ R Θ R R R (6)

The Euler angle attitude transformation matrix is:

1 s t c t

0 c s

0 s / c c / c

T Θ

1

1 0 s

0 c c s

0 s c c

T Θ o90 (7)

It should be noted that T Θ is undefined for a

pitch angle of o90 and that 1 T

T Θ T Θ .

3.3 Equations of Kinetics

Referring to Fig. 3 the 6-DOF kinetic equations in the

body-fixed reference frame in the vector form are,

0 wind wave Mν C ν ν D ν ν g η g τ τ τ (8)

where

M = MRB+MA: system inertia matrix (including added

mass);

C ν = RB AC ν C ν : Coriolis-centripetal matrix

(including added mass);

D ν : damping matrix;

g η : vector of gravitational/buoyancy forces and

moments;

0g : vector used for pretrimming (ballast control);

τ : vector of control inputs;

windτ : vector of wind-induced forces and moments;

and

waveτ : vector of wave-induced forces and moments.

3.4 Equations for Manoeuvring of Surface Vessels

For surface vessels their motions are often limited to

4-DOF: surge, sway, yaw and roll. It is assumed that

the vessel is symmetric about the plane of XGZ and

the origin and the mass concentration at the centre of

gravity, four 4-DOF kinetic equations are expressed

as [13],

mv mur Y (9)

mu mvr X (10)

zzI r N (11)

xxI K (12)

where

m is the mass of the vessel;

Izz is the moment of inertia about z-axis; and

Ixx is the moment of inertia about x-axis.

X, Y, N and K are forces and moments acting on the

vessel, including propeller-generated forces and

moments, hydrodynamic forces and moments due to

interaction between the propeller and the hull, rudder-

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or control surface-induced forces and moments and

external disturbances.

Equation (1) is simplified as,

posx ucos vsin (12)

posy usin vcos (13)

3.5 Equations for Environmental Disturbances

Environmental disturbances include wind, waves and

currents. According to Fossen [3] for control system

design it is common to assume the principle of

superposition when considering wind and wave

disturbances. With effects of external disturbances

Equation (8) is rewritten as,

RB RB A r A r r r r

0

M ν C ν ν M ν C ν ν D ν ν

g η g τ w (13)

where wind wave w τ τ and

r c ν ν ν (where

6

c ν is the velocity of the ocean current expressed

in the NED). Further information on modeling

environmental disturbances can be found in [2][3][4].

3.6 Discrete-time Models for Marine Vehicles

The classical methods of designing control systems

are using continuous-time models including

differential equations, transfer functions and state-

space models. The computer-aided methods are using

discrete-time models, including difference equations,

pulse transfer functions and discrete-time state space

models. Auto-regressive models are often used for

stochastic control algorithms and model reference

control. Discretisation of the following continuous-

time state-space model

(14)

results in

(15)

or

(16)

where

(17)

(18)

For stochastic control systems the following auto-

regressive average moving exogenous model and

auto-regressive exogenous model are used:

(19)

(20)

4. Overview of Marine Control Systems –

Motion Control Motion control of marine vehicles involves the

guidance, navigation and control of:

surface vessels;

underwater vehicles including submersibles

and submarines; and

oil rigs, floating and subsea structures.

The motion control systems for marine vehicles

include ship autopilots, roll damping/stabilising

systems and dynamic positioning systems.

For surface vessels the desired motions are surge,

sway and yaw (turning) while undesired motions are

heave, roll and heel, pitch and trim. Surge, sway and

yaw motions are often controlled by a rudder or

control surface, FPP or CPP, side thrusters. The

undesired motions are reduced to an acceptable level

by some motion control strategies such as fins,

trimtabs, interceptors, T-foils, rudder-roll, lifting foil

and air cushion support.

4.1 Guidance, Navigation and Control of Marine

Vehicles

An entire modern control system for marine vehicles

has three subsystems as shown in Fig. 4 [3]:

guidance system;

sensor and navigation system; and

control system.

Fig. 4 The GNC signal flow [3]

The guidance system is used to generate desired

signals based on the prior information, predefined

trajectory and weather data from weather forecast

stations. Some techniques that are applied in the

guidance systems are target tracking, trajectory

tracking, path following for straight-line paths, and

path following for curved paths [3].

The sensor and navigation system consists of

necessary sensor and navigation devices such as

GPS/GNSS receivers, wind gauges, depth sounder,

speed log, IMU/INS and engine sensors. In order to

have “clean” data for control purposes observer, filter

and estimator techniques are applied.

The control system is where control algorithms are

synthesised and control signals are computed. Modern

control algorithms are applied.

Fig. 5 shows an example of recursive optimal

trajectory control system.

Fig. 5 The GNC signal flow of the recursive optimal

trajectory tracking control system [7]

k 1 h

kh(k 1) exp h k exp k 1 h k d

x A x A Bu

x Ax Bu

k 1 k k x Φx Δu

exp hΦ A

1 Δ A Φ I B

1 1 1z k z k z k A y B u C e

1 1z k z k k A y B u e

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As shown in Fig. 5 the control system consists of a

guidance system that generates desired course, speed

and course changing points based on the LOS,

waypoint and decay exponential techniques. The

sensor and navigation consists of GPS/IMU/INS,

gyrocompass, sensors and a recursive estimator. The

control system consists of a controller based on the

optimal control law.

4.2 Autopilots

Autopilots are used for course keeping and changing.

The common method for conventional vessels

equipped with a propeller and rudder is illustrated in

Fig. 6. As shown in Fig. 6 the course (yaw) angle and

yaw rate are measured by a compass and gyro. For a

waterjet-propelled vessel, the course is controlled by

the waterjet nozzle.

Fig. 6 Ship’s autopilot system [4]

Modern and intelligent control algorithms have been

applied in the autopilots. Fig. 7 shows an example of

a stochastic model based autopilot with a combination

of a recursive estimation algorithm and the self-tuning

control algorithm. Fig. 8 shows an example of the

neural networks-based autopilot.

Fig. 7 Ship’s recursive self-tuning autopilot system

Fig. 8 Ship’s neural networks-based autopilot system

4.3 Rudder-roll Stabilisation Systems

The roll motion of a marine vehicle has bad and

unexpected effects on crew and passenger heath and

cargo as well as the stability of the vehicle. The

effects of roll motion (especially the parametric roll

motion) are seasickness, damage of cargo and damage

of vessel. A rudder-roll reduction system is based on

the principle illustrated in Fig. 9 and Fig. 10. The

main requirements for this system are:

fast rudder slew rate;

accurate measurement of roll motion; and

low pass filters.

Fig. 9 Principle of a rudder-roll stabilisation system

Fig. 10 Autopilot system with rudder-roll reduction

Fig. 11 shows an example of responses of an autopilot

system with rudder-roll damping function.

Fig. 11 Responses of an autopilot system with rudder-roll

reduction

4.4 Dynamic Positioning Systems

Dynamic positioning systems are used to control

marine vehicles at very low speeds where the effect of

rudder or control surface is almost zero. A modern

DPS has many functions such as autopilot, dynamic

positioning, trajectory tracking and shifting anchor

alarm. To design a DPS the waypoint, LOS and decay

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exponential techniques are applied. Fig. 12 shows the

main forces and moments generated by actuators and

external disturbances on a vessel equipped with a

DPS.

Fig. 12 The main forces and moments for DPS design

(courtesy of Kongsberg)

In the DPSs there are more than two controls. DPSs

require network data communication buses. Modern

and intelligent control algorithms such as optimal

control, self-tuning control and fuzzy logic control

have been applied in the design of DPSs.

4.5 Networked Control Systems and Integrated

Bridge

Nowadays marine control systems are in forms of a

networked control system, distributed control system

and integrated bridge that allow the operator to

control many onboard systems. The networked

control systems have data communication buses such

as NEMA, CANOpen, and Profibus. Fig. 13 shows a

networked control system with NAMA data

communication devices.

Fig. 13 Concept of networked control system with data

communication bus (NEMA)

The centralised control systems are obsolete and

replaced with distributed and networked control

systems. For high-level automation marine vehicles a

networked control system has some main features:

integrated, distributed, supervisory, redundancy and

safety as shown in Fig. 14.

Fig. 14 Example of high-level automation control system on

a modern vessel (courtesy of Kongsberg)

4.6 Control Systems for ROVs/AUVs, Oil Rigs and

Floating Structures

Control of ROVs/AUVs, oil rigs and floating

structures is a greater challenge in comparison with

control of surface vehicles because of their

complexity, moving at low speeds and

underactuation.

Control algorithms and methods for ROVs/AUVs are

described in [3][4][11] and [12].

5. Manoeuvrability, Modeling and

System Identification of Marine

Vehicles (Hydrodynamics) To assess manoeuvrability of marine vehicles is

important for safe operation. The manoeuvrability of

ocean vehicles must meet IMO standards, including

interim standards for ship manoeuvrability IMO

Resolution A.751(18), 1993 and standards for ship

manoeuvrability IMO Resolution MSC137(76), 2002,

issued by the IMO Maritime Safety Committee. The

marine vehicles built with very poor manoeuvring

qualities will cause marine casualties and pollution.

The manoeuvrability is often related to the:

seakeeping: a measure of how well-suited a

marine vehicle is to conditions when

underway; and

seaworthiness: the ability of a marine vehicle

to operate effectively under severe sea

conditions, i.e. very good seakeeping ability.

To quantify the manoeuvrability is to identify

hydrodynamic coefficients of the manoeuvring

models. Its applications are:

manoeuvring characteristics (for various

manoeuvres);

stability assessment;

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computer and HIL simulation (full mission

manoeuvring simulators) for educational and

training purposes;

control design (stochastic control, model based

adaptive control);

fault detection and diagnostics; and

prediction of forces and moments due to the

interaction between many submersible bodies.

The quantitative representation of manoeuvring

characteristics of marine vehicles consists of straight-

line stability and directional stability. The methods to

assess the manoeuvring characteristics are the turning

circle test, Kempf’s zig-zag test, Dieudome’s pull-out

manoeuvre test, Bech’s reverse spiral manoeuve test

and stopping trial.

Many authors proposed manoeuvring mathematical

models, for examples, Abkowitz (USA: SNAME),

MMG model group in Japan (SNAJ, JTTC), Norrbin

(1970), Blanke (1981), Nomoto and Sons, etc. Further

information can be found in [3][4][5].

The most common and well-known model of

manoeuvring is the Nomotor’s first order model that

relates the rudder angle and yaw rate (turning rate):

Tr r K (21)

where T and K are manoeuvrability indices.

In order to quantify the manoeuvring characteristics

of marine vehicles and determine hydrodynamic

coefficients of the manoeuvring mathematical models,

it is necessary to conduct full-scaled or model-scaled

experiments as shown in Fig. 15.

Fig. 15 Experiments for prediction of hydrodynamic

coefficients

In order to estimate hydrodynamic coefficients of a

vehicle there are several methods among which the

following are widely used:

Recursive least squares algorithm; and

Recursive prediction error method

5.1 Recursive Least Squares Algorithm (RLSA)

The recursive least squares algorithm is based on the

least squares algorithm proposed by Gauss. This

method is illustrated by the flowchart in Fig. 16.

Fig. 16 Flowchart of RLSA

5.2 Recursive Prediction Error Method (RPEM)

The recursive prediction error algorithm was

proposed by Ljung based on the Kalman filter and is

illustrated by flowchart in Fig. 17.

Fig.17 Flowchart of RPEM

4.7 Fault Detection and Diagnosis Monitoring and

Supervision and Fault Tolerant Control

Recursive system identification methods are applied

in fault detection and diagnostic monitoring and

supervision of marine and offshore engineering

systems. They are also applied in fault-tolerant

control. The conceptual system of fault detection and

diagnostic monitoring and supervision is shown in

Fig. 18. The fault detection system requires prior

knowledge of the plant (theoretical data) and sensors

to collect actual data. The system compares actual

data with the theoretical data and thus detects any

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faults occurring in every component of the

engineering systems when there is a great difference

between two sets of data. The system provides

solutions to manage faults. Further information on

fault detection and diagnostic monitoring and

supervision can be found in [14] [15].

Fig.18 Concept of fault detection and diagnostic monitoring

and supervision for marine and offshore systems

6. Experimental Facilities In order to support control design and to realise

marine control systems it is necessary to utilise

experimental facilities for full-scaled and model-

scaled experiments. Experiments require the

following facilities:

physical models or prototypes of marine

vehicles;

model test basin with artificial wavemaker and

wind generators for free-running models;

towing tank with PMM for captive models;

full-scale vessels (expensive); and

control hardware (instrumentation electronics,

data communication) and software.

The AMC/UTAS possesses the world’s leading

maritime experimental facilities. The facilities include

the towing tank (see Fig. 19 and Fig. 20), model test

basin (see Fig. 21) cavitation tunnel (see Fig. 21), and

circulating water channel (see Fig. 22), full mission

ship manoeuvring simulator, dynamic positioning

simulator, and training vessel (Bluefin).

Fig.19 AMC Towing Tank

Fig.20 AMC Towing Tank with PMM and captive model

Fig.21 AMC Model Test Basin with wavemakers and models

Fig.21 Three dimensional view of the AMC Capvitation

Tunnel

Fig. 22 The CWC and its arrangement

Other institutes that also have the world’s leading

maritime experimental facilities are Norwegian

University of Science and Technology and

MARINTEK, Tokyo University of Marine Science

and Technology.

7. Challenging Problems In design and simulation of marine control systems

some challenging problems are:

underwater communication between the AUVs

and mother vessel;

energy for ROVs/ AUVs that operate

underwater for a long time;

fault detection and diagnostics and safety, this

leads to losses of expensive ROVs/AUVs

control and operation of ROVs/AUVs at very

deep waters;

watertight electronic components; and

in-door navigation techniques for experiments.

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8. Future Trend Recent trends show the following applications:

networked control systems with data

communication buses;

Internet-based control systems utilising

satellite broadband services;

applications of advanced and intelligent

control algorithms;

wireless network;

underwater acoustic navigation systems for

ROVs/AUVs; and

optical communication between ROVs/AUVs

and the carriage vessels.

Fig. 23 shows an example of remote control system

via satellite broadband services in Norwary. Fig. 24

shows another example of remote control system via

satellite broadband services in Japan.

Fig 23 Remote control system via satellite broadband

services (Norway)

Fig 23 Remote control system via satellite broadband

services at Tokyo University of Marine Science and

Technology, Japan

9. Potential Projects Related to Marine

Control Engineering at AMC/UTAS The AMC, possessing the world’s leading maritime

experimental facilities, is undergoing several potential

projects related to marine control engineering. These

projects are:

design and testing of ROV/AUVs;

modelling, simulation and control of

ROVs/AUVs;

modelling, simulation and control of AUVs

using a cyclic and collective pitch propeller;

modelling and control of surface vessels with

electrically-operated water-jet (GreenLiner)

development of ROVs/AUVs with a collective

and cyclic pitch propeller;

development of a (solar-wind-diesel) trybrid

trimaran and its control systems;

development of automatic manoeuvring

systems for surface vessels;

development of dynamic positioning systems

by applying advanced control algorithms; and

prediction, simulation of hydrodynamic

interaction between many submersible bodies.

10. Conclusions The paper has discussed the current status of marine

control systems and description of kinematics and

kinetics of marine vehicles for design and analysis of

their control systems. It has overviewed marine

control systems and modelling and identification of

marine vehicles. To design and analyse control

systems full-scaled and model-scaled experiments are

necessary and require maritime engineering

specialised experimental facilities such model test

basin, towing tank, circulating water channel. The

paper has also dealt with future trend of marine

control application and some potential projects at

AMC/UTAS.

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Underwater Vehicles – Design for

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Springer-Verlag. London, 2009.

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Keeping and Roll Stabilization Using Rudder

and Fins. Springer, 2005.

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Chapter 2 Mathematical Models of Ship

Manoeuvring Motion, The 12th Symposium on

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小林英一・影本浩・古川芳孝:第2章操縦運

動の数学モデル運動性能研究委員会・第12

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[14] Isermann, R.. Fault-Diagnosis Systems – An

Introduction from Fault Detection to Fault

Tolerance. Springer, 2006.

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Biography

Dr. Hung Nguyen is a lecturer

in Marine Control Engineering

at National Centre for

Maritime Engineering and

Hydrodynamics, Australian

Maritime College, Australia.

He obtained his BE degree in

Nautical Science at Vietnam

Maritime University in 1991,

then he worked as a lecturer

there until 1995. He

completed the MSc in Marine Systems Engineering in

1998 at Tokyo University of Marine Science and

Technology and then the PhD degree in Marine

Control Engineering at the same university in 2001.

During April 2001 to July 2002 he worked as a

research and development engineer at Fieldtech Co.

Ltd., a civil engineering related nuclear instrument

manufacturing company, in Japan. He moved to the

Australian Maritime College, Australia in August

2002. His research interests include guidance,

navigation and control of marine vehicles, self-tuning

and optimal control, recursive system identification,

real-time control and hardware-in-the-loop simulation

of marine vehicles and dynamics of marine vehicles.

Appendix Nonlinear Mathematical

Models of Marine Vehicles for Control

Design and Simulation Nonlinear mathematical models for design and

analysis of marine control systems are as follows:

Model of Cargo Mariner Class;

Model of Training Vessel Shoji Maru;

Model of Container Vessel;

Model of Tanker Esso; and

Models of Underwater Vehicles.

These nonlinear mathematical models are provided

upon request.

124

a survey on marine control systems

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