Marine navigation and safety of sea transportation : Navigational problems

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MARINE NAVIGATION AND SAFETY OF SEA TRANSPORTATION

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Marine Navigation and

Safety of Sea Transportation

Navigational Problems

Editor

Adam Weintrit

Gdynia Maritime University, Gdynia, Poland

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5

List of reviewers

Prof. Roland Akselsson, Lund University, Sweden

Prof. Yasuo Arai, Independent Administrative Institution Marine Technical Education Agency,

Prof. Michael Baldauf, Word Maritime University, Malmö, Sweden

Prof. Andrzej Banachowicz, West Pomeranian University of Technology, Szczecin, Poland

Prof. Marcin Barlik, Warsaw University of Technology, Poland

Prof. Michael Barnett, Southampton Solent University, United Kingdom

Prof. Eugen Barsan, Constanta Maritime University, Romania

Prof. Milan Batista, University of Ljubljana, Ljubljana, Slovenia

Prof. Angelica Baylon, Maritime Academy of Asia & the Pacific, Philippines

Prof. Christophe Berenguer, Grenoble Institute of Technology, Saint Martin d'Hères, France

Prof. Heinz Peter Berg, Bundesamt für Strahlenschutz, Salzgitter, Germany

Prof. Tor Einar Berg, Norwegian Marine Technology Research Institute, Trondheim, Norway

Prof. Jarosáaw Bosy, Wroclaw University of Environmental and Life Sciences, Wroclaw, Poland

Prof. Zbigniew Burciu, Gdynia Maritime University, Poland

Sr. Jesus Carbajosa Menendez, President of Spanish Institute of Navigation, Spain

Prof. Andrzej Chudzikiewicz, Warsaw University of Technology, Poland

Prof. Frank Coolen, Durham University, UK

Prof. Stephen J. Cross, Maritime Institute Willem Barentsz, Leeuwarden, The Netherlands

Prof. Jerzy Czajkowski, Gdynia Maritime University, Poland

Prof. Krzysztof Czaplewski, Polish Naval Academy, Gdynia, Poland

Prof. Daniel Duda, Naval University of Gdynia, Polish Nautological Society, Poland

Prof. Alfonso Farina, SELEX-Sistemi Integrati, Rome, Italy

Prof. Andrzej Fellner, Silesian University of Technology, Katowice, Poland

Prof. Andrzej Felski, Polish Naval Academy, Gdynia, Poland

Prof. Wáodzimierz Filipowicz, Gdynia Maritime University, Poland

Prof. Börje Forssell, Norwegian University of Science and Technology, Trondheim, Norway

Prof. Alberto Francescutto, University of Trieste, Trieste, Italy

Prof. Jens Froese, Jacobs University Bremen, Germany

Prof. Wiesáaw Galor, Maritime University of Szczecin, Poland

Prof. Jerzy GaĨdzicki, President of the Polish Association for Spatial Information; Warsaw, Poland

Prof. Witold Gierusz, Gdynia Maritime University, Poland

Prof. Dorota Grejner-Brzezinska, The Ohio State University, United States of America

Prof. Marek Grzegorzewski, Polish Air Force Academy, Deblin, Poland

Prof. Lucjan Gucma, Maritime University of Szczecin, Poland

Prof. Vladimir Hahanov, Kharkov National University of Radio Electronics, Kharkov, Ukraine

Prof. Jerzy Hajduk, Maritime University of Szczecin, Poland

Prof. Michaá Holec, Gdynia Maritime University, Poland

Prof. Stojce Dimov Ilcev, Durban University of Technology, South Africa

Prof. Toshio Iseki, Tokyo University of Marine Science and Technology, Japan,

Prof. Jacek Januszewski, Gdynia Maritime University, Poland

Prof. Tae-Gweon Jeong, Korean Maritime University, Pusan, Korea

Prof. Mirosáaw JurdziĔski, Gdynia Maritime University, Poland

Prof. John Kemp, Royal Institute of Navigation, London, UK

Prof. Andrzej Królikowski, Maritime Office in Gdynia; Gdynia Maritime University, Poland

Prof. Pentti Kujala, Helsinki University of Technology, Helsinki, Finland

Prof. Jan Kulczyk, Wroclaw University of Technology, Poland

Prof. Krzysztof Kulpa, Warsaw University of Technology, Warsaw, Poland

Prof. Shashi Kumar, U.S. Merchant Marine Academy, New York

Prof. Andrzej Lenart, Gdynia Maritime University, Poland

Prof. Nadav Levanon, Tel Aviv University, Tel Aviv, Israel

Prof. Andrzej LewiĔski, University of Technology and Humanities in Radom, Poland

Prof. Józef Lisowski, Gdynia Maritime University, Poland

Prof. Vladimir Loginovsky, Admiral Makarov State Maritime Academy, St. Petersburg, Russia

Prof. Mirosáaw Luft, University of Technology and Humanities in Radom, Poland

Prof. Evgeniy Lushnikov, Maritime University of Szczecin, Poland

Prof. Zbigniew àukasik, University of Technology and Humanities in Radom, Poland

Prof. Marek Malarski, Warsaw University of Technology, Poland

Prof. Boyan Mednikarov, Nikola Y. Vaptsarov Naval Academy,Varna, Bulgaria

Prof. Jerzy Mikulski, Silesian University of Technology, Katowice, Poland

Prof. Józef Modelski, Warsaw University of Technology, Poland

Prof. Wacáaw MorgaĞ, Polish Naval Academy, Gdynia, Poland

Prof. Janusz Narkiewicz, Warsaw University of Technology, Poland

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Prof. Nikitas Nikitakos, University of the Aegean, Chios, Greece

Prof. Gabriel Nowacki, Military University of Technology, Warsaw

Prof. Stanisáaw Oszczak, University of Warmia and Mazury in Olsztyn, Poland

Prof. Gyei-Kark Park, Mokpo National Maritime University, Mokpo, Korea

Prof. Vytautas Paulauskas, Maritime Institute College, Klaipeda University, Lithuania

Prof. Jan Pawelski, Gdynia Maritime University, Poland

Prof. Zbigniew Pietrzykowski, Maritime University of Szczecin, Poland

Prof. Francisco Piniella, University of Cadiz, Spain

Prof. Jerzy B. Rogowski, Warsaw University of Technology, Poland

Prof. Hermann Rohling, Hamburg University of Technology, Hamburg, Germany

Prof. Shigeaki Shiotani, Kobe University, Japan

Prof. Jacek Skorupski, Warsaw University of Technology, Poland

Prof. Leszek Smolarek, Gdynia Maritime University, Poland

Prof. Jac Spaans, Netherlands Institute of Navigation, The Netherlands

Prof. Cezary Specht, Polish Naval Academy, Gdynia, Poland

Prof. Andrzej Stateczny, Maritime University of Szczecin, Poland

Prof. Andrzej Stepnowski, GdaĔsk University of Technology, Poland

Prof. Janusz Szpytko, AGH University of Science and Technology, Kraków, Poland

Prof. ElĪbieta Szychta, University of Technology and Humanities in Radom, Poland

Prof. Wojciech ĝlączka, Maritime University of Szczecin, Poland

Prof. Roman ĝmierzchalski, GdaĔsk University of Technology, Poland

Prof. Henryk ĝniegocki, Gdynia Maritime University, Poland

Prof. Vladimir Torskiy, Odessa National Maritime Academy, Ukraine

Prof. Lysandros Tsoulos, National Technical University of Athens, Greece

Prof. Mykola Tsymbal, Odessa National Maritime Academy, Ukraine

Capt. Rein van Gooswilligen, Netherlands Institute of Navigation

Prof. František Vejražka, Czech Technical University in Prague, Czech

Prof. George Yesu Vedha Victor, International Seaport Dredging Limited, Chennai, India

Prof. Vladimir A. Volkogon, Baltic Fishing Fleet State Academy, Kaliningrad, Russian Federation

Prof. Ryszard Wawruch, Gdynia Maritime University, Poland

Prof. Adam Weintrit, Gdynia Maritime University, Poland

Prof. Bernard WiĞniewski, Maritime University of Szczecin, Poland

Prof. Jia-Jang Wu, National Kaohsiung Marine University, Kaohsiung, Taiwan (ROC)

Prof. Min Xie, National University of Singapore, Singapore

Prof. Lu Yilong, Nanyang Technological University, Singapore

Prof. Homayoun Yousefi, Chabahar Maritime University, Iran

Prof. Janusz ZieliĔski, Space Research Centre, Warsaw, Poland

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TABLE OF CONTENTS

Navigational Problems. Introduction .......................................................................................................................................... 9

A. Weintrit

1 Chapter 1. Ship Control ................................................................................................................................................................ 11

1.1. The Course-keeping Adaptive Control System for the Nonlinear MIMO Model of a Container Vessel ................................. 13

M. Brasel & P. Dworak

1.2. The Multi-step Matrix Game of Safe Ship Control with Different Amounts Admissible Strategies ....................................... 19

J. Lisowski

1.3. Catastrophe Theory in Intelligent Control System of Vessel Operational Strength ................................................................. 29

E.P. Burakovskiy, Yu.I. Nechaev, P.E. Burakovskiy & V.P. Prokhnich

1.4. Concept of Integrated INS/Visual System for Autonomous Mobile Robot Operation ............................................................. 35

P. Kicman & J. Narkiewicz

2 Chapter 2. Decision Support Systems ......................................................................................................................................... 41

2.1. Functionality of Navigation Decision Supporting System – NAVDEC ................................................................................... 43

P. Woáejsza

2.2. A Study on the Development of Navigation Visual Supporting System and its Sea Trial Test ............................................... 47

N. Im, E.K. Kim, S.H. Han & J.S. Jeong

2.3. Application of Ant Colony Optimization in Ship’s Navigational Decision Support System ................................................... 53

A. Lazarowska

2.4. Issue of Making Decisions with Regard to Ship Traffic Safety in Different Situations at Sea ................................................ 63

J. Girtler

2.5. Ship Handling in Wind and Current with Neuroevolutionary Decision Support System ......................................................... 71

M. àącki

3 Chapter 3. Marine Traffic ............................................................................................................................................................. 79

3.1. Development and Evaluation of Traffic Routing Measurements .............................................................................................. 81

R. Müller & M. Demuth

3.2. ĝwinoujĞcie – Szczecin Fairway Expert Safety Evaluation ...................................................................................................... 87

P. Górtowski & A. Bąk

3.3. Expert Indication of Dangerous Sections in ĝwinoujĞcie - Szczecin Fairway ......................................................................... 95

P. Górtowski & A. Bąk

3.4. Traffic Incidents Analysis as a Tool for Improvement of Transport Safety ........................................................................... 101

J. Skorupski

3.5. Vessel Traffic Stream Analysis in Vicinity of The Great Belt Bridge .................................................................................... 109

K. Marcjan, L. Gucma & A. Voskamp

4 Chapter 4. Search and Rescue ................................................................................................................................................... 115

4.1. Search and Rescue of Migrants at Sea .................................................................................................................................... 117

J. Coppens

4.2. Ergonomics-based Design of a Life-Saving Appliance for Search and Rescue Activities ..................................................... 125

H.J. Kang

4.3. The Signals of Marine Continuous Radar for Operation with SART ..................................................................................... 131

V.M. Koshevoy & D.O. Dolzhenko

4.4. Risk Analysis on Dutch Search and Rescue Capacity on the North Sea ................................................................................ 135

Y. Koldenhof & C. van der Tak

4.5. The Operational Black Sea Delta Regional Exercise on Oil Spill Preparedness and Search and Rescue –

GEODELTA 2011 .................................................................................................................................................................. 143

A. Gegenava & I. Sharabidze

5 Chapter 5. Meteorological Aspects and Weather Condition ................................................................................................. 151

5.1. Operational Enhancement of Numerical Weather Prediction with Data from Real-time Satellite Images ............................. 153

à. Markiewicz, A. Chybicki, K. Drypczewski, K. Bruniecki & J. Dąbrowski

5.2. Analysis of the Prevailing Weather Conditions Criteria to Evaluate the Adoption of a Future ECA

in the Mediterranean Sea ........................................................................................................................................................ 161

M. Castells, F.X. Martínez de Osés & J.J. Usabiaga

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5.3. Monitoring of Ice Conditions in the Gulf of Riga Using Micro Class Unmanned Aerial Systems ........................................ 167

I. Lešinskis & A. Pavloviþs

5.4. Global Warming and Its Impact on Arctic Navigation: The Northern Sea Route Shipping Season 2012 ............................. 173

E. Franckx

5.5. Unloading Operations on the Fast Ice in the Region of Yamal Peninsula as the Part of Transportation Operations

in the Russian Western Arctic ................................................................................................................................................. 181

A.A. Skutin, N.V. Kubyshkin, G.K. Zubakin & Yu.P. Gudoshnikov

6 Chapter 6. Inland, Sea-River, Personal and Car Navigation Systems ................................................................................. 187

6.1. The Method of the Navigation Data Fusion in Inland Navigation .......................................................................................... 189

A. Lisaj

6.2. PER Estimation of AIS in Inland Rivers based on Three Dimensional Ray Tracking ........................................................... 193

F. Ma, X.M. Chu & C.G. Liu

6.3. Analysis of River – Sea Transport in the Direction of the Danube – Black Sea and the Danube - Rhine River -

River Main .............................................................................................................................................................................. 199

S. Šoškiü, Z. Ĉekiü & M. Kresojeviü

6.4. Study of the Usage of Car Navigation System and Navigational Information to Assist Coastal Navigational Safety ........... 209

S. Shiotani, S. Ryu & X. Gao

6.5. Remote Spatial Database Access in the Navigation System for the Blind.............................................................................. 217

K. Drypczewski, à. KamiĔski, à. Markiewicz, B. WiĞniewski & A. Stepnowski

6.6. Integration of Inertial Sensors and GPS System Data for the Personal Navigation in Urban Area ........................................ 223

K. Bikonis & J. Demkowicz

7 Chapter 7. Air Navigation .......................................................................................................................................................... 229

7.1. Accuracy of GPS Receivers in Naval Aviation ...................................................................................................................... 231

W.Z. Kaleta

7.2. Comparative Analysis of the Two Polish Hyperbolic Systems AEGIR and JEMIOLUSZKA .............................................. 237

S. Ambroziak, R. Katulski, J. Sadowski, J. StefaĔski & W. Siwicki

7.3. The Analysis of Implementation Needs for Automatic Dependent Surveillance in Air Traffic in Poland ............................. 241

M. Siergiejczyk & K. Krzykowska

8 Chapter 8. Maritime Communications ..................................................................................................................................... 247

8.1. Multiple Access Technique Applicable for Maritime Satellite Communications ................................................................... 249

S.D. Ilcev

8.2. Classification and Characteristics of Mobile Satellite Antennas (MSA) for Maritime Applications ..................................... 261

S.D. Ilcev

8.3. Development of Cospas-Sarsat Satellite Distress and Safety Systems (SDSS) for Maritime and Other Mobile

Applications ............................................................................................................................................................................ 269

S.D. Ilcev

8.4. The Propagation Characteristic of DGPS Correction Data Signal at Inland Sea – Propagation Characteristic

on LF/MF Band Radio Wave .................................................................................................................................................. 279

S. Okuda, M. Toba & Y. Arai

8.5. Communication Automation in Maritime Transport .............................................................................................................. 287

Z. Pietrzykowski, P. BanaĞ, A. Wójcik & T. Szewczuk

8.6. Audio Watermarking in the Maritime VHF Radiotelephony .................................................................................................. 293

A.V. Shishkin & V.M. Koshevoy

8.7. Enhancement of VHF Radiotelephony in the Frame of Integrated VHF/DSC – ECDIS/AIS System ................................... 299

V.M. Koshevoy & A.V. Shishkin

8.8. Modernization of the GMDSS ................................................................................................................................................ 305

K. Korcz

8.9. A VHF Satellite Broadcast Channel as a Complement to the Emerging VHF Data Exchange (VDE) System ..................... 313

F. Zeppenfeldt

9 Chapter 9. Methods and Algorithms ......................................................................................................................................... 317

9.1. Overview of the Mathematical Theory of Evidence and its Application in Navigation ......................................................... 319

W. Filipowicz

9.2. A New Method for Determining the Attitude of a Moving Object ......................................................................................... 327

S.M. Yakushin

9.3. Simulation of Zermelo Navigation on Riemannian Manifolds for dim(R×M)=3 ................................................................... 333

P. Kopacz

Author index ............................................................................................................................................................................ 339

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The monograph is addressed to scientists and

professionals in order to share their expert

knowledge, experience and research results

concerning all aspects of navigation, safety at sea

and marine transportation.

The contents of the book are partitioned into nine

separate chapters: Ship control (covering the

chapters 1.1 through 1.4), Decision Support Systems

(covering the chapters 2.1 through 2.5), Marine

Traffic (covering the chapters 3.1 through 3.5),

Search and Rescue (covering the chapters 4.1

through 4.5), Meteorological aspect and weather

condition (covering the chapters 5.1 through 5.5),

Inland, sea-river, personal and car navigation

systems (covering the chapters 6.1 through 6.6), Air

navigation (covering the chapters 7.1 through 7.3),

Maritime communications (covering the chapters 8.1

through 8.9), and Methods and algorithms (covering

the chapters 9.1 through 9.3).

In each of them readers can find a few chapters.

Chapters collected in the first chapter, titled ‘Ship

control’, concerning the course-keeping adaptive

control system for the nonlinear MIMO model of a

container vessel, the multi-step matrix game of safe

ship control with different amounts admissible

strategies, catastrophe theory in intellectual control

system of vessel operational strength, and concept of

integrated INS/visual system for autonomous mobile

robot operation

In the second chapter there are described

problems related to decision support systems:

functionality of navigation decision supporting

system – NAVDEC, a study on the development of

navigation visual supporting system and its sea trial

test, application of ant colony optimization in ship’s

navigational decision support system, issue of

making decisions with regard to ship traffic safety in

different situations at sea, and ship handling in wind

and current with neuroevolutionary decision support

system.

Third chapter is about marine traffic. The readers

can find some information about development and

evaluation of traffic routeing measurements,

ĝwinoujĞcie– Szczecin fairway expert safety

evaluation, expert indication of dangerous sections

in ĝwinoujĞcie–Szczecin fairway, traffic incidents

analysis as a tool for improvement of transport

safety, and vessel traffic stream analysis in vicinity

of the Great Belt Bridge.

The fourth chapter deals with Search and Rescue

(SAR) problems. The contents of the fourth chapter

are partitioned into five subchapters: search and

rescue of migrants at sea, ergonomics-based design

of a life-saving appliance for search and rescue

activities, the signals of marine continuous radar for

operation with SART, risk analysis on dutch search

and rescue capacity on the North Sea, and the

operational Black sea delta regional exercise on oil

spill preparedness and search and rescue –

GEODELTA 2011.

The fifth chapter deals with meteorological aspect

and weather conditions. The contents of the fifth

chapter are partitioned into five: operational

enhancement of numerical weather prediction with

data from real-time satellite images, analysis of the

prevailing weather conditions criteria to evaluate the

adoption of a future ECA in the Mediterranean Sea,

monitoring of ice conditions in the Gulf of Riga

using micro class unmanned aerial systems, global

warming and its impact on Arctic navigation: the

Northern Sea Route shipping season 2012, and

unloading operations on the fast ice in the region of

Yamal Peninsula as the chapter of transportation

operations in the Western Arctic.

In the sixth chapter there are described problems

related to inland, sea-river, personal and car

navigation systems: the method of the navigation

data fusion in inland navigation, PER estimation of

AIS in inland rivers based on three dimensional ray

tracking, analysis of river – sea transport in the

direction of the Danube – Black Sea and the Danube

- Rhine River - River Main, study of the usage of car

navigation system and navigational information to

assist coastal navigational safety, remote spatial

Navigational Problems

Introduction

A. Weintrit

Gdynia Maritime University, Gdynia, Poland

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10

database access in the navigation system for the

blind, and integration of inertial sensors and GPS

system data for the personal navigation in urban

area.

Seventh chapter concerns air navigation. The

readers can find some information about accuracy of

GPS receivers in naval aviation, comparative

analysis of the two Polish hyperbolic systems

AEGIR and Jemioluszka, and the analysis of

implementation needs for automatic dependent

surveillance in air traffic in Poland.

The eighth chapter deals with maritime

communications. The contents of the eighth chapter

are partitioned into nine: Multiple access technique

applicable for maritime satellite communications,

Classification and characteristics of mobile satellite

antennas (MSA) for maritime applications,

Development of Cospas-Sarsat satellite distress and

safety systems (SDSS) for maritime and other

mobile applications, The propagation characteristic

of DGPS correction data signal at inland sea –

propagation characteristic on LF/MF band radio

wave, Communication automation in maritime

transport, Audio watermarking in the maritime VHF

radiotelephony, Enhancement of VHF

radiotelephony in the frame of integrated VHF/DSC

– ECDIS/AIS system, Modernization of the

GMDSS, and VHF satellite broadcast channel as a

complement to the emerging VHF Data Exchange

(VDE) system.

The ninth chapter deals with methods and

algorithms. The contents of the ninth chapter

concerns the overview of the mathematical theory of

evidence and its application in navigation, a new

method for determining the attitude of a moving

object, and simulation of Zermelo navigation on

Riemannian manifolds for dim(R×M)=3

Each subchapter was reviewed at least by three

independent reviewers. The Editor would like to

express his gratitude to distinguished authors and

reviewers of chapters for their great contribution for

expected success of the publication. He

congratulates the authors for their excellent work.

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Chapter 1

Ship Control

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13

Ship Control

Navigational Problems – Marine Navigation and Safety of Sea Transportation – Weintrit (ed.)

1 INTRODUCTION

Nonlinear control systems are commonly

encountered in many different areas of science and

technology. In particular, problems difficult to solve

arise in motion and/or position control of various

vessels, like drilling platforms and ships, sea ferries,

container ships etc. Complex motions and/or

complex-shaped bodies moving in the water, and in

case of ships also at the boundary between water and

air, give rise to resistance forces dependent in a

nonlinear way on velocities and positions, thus

causing the floating bodies to become strongly

nonlinear dynamic plants.

In general, there are two basic approaches to

solve the control problem for nonlinear plants. The

first one called “nonlinear” consists in synthesizing

a nonlinear controller that would meet certain

requirements over the entire range of control signals

variability (Fabri & Kadrikamanathan 2001; Huba et

al. 2011; Khalil 2001; Tzirkel-Hancock & Fallside

1992; Witkowska et al. 2007). Substantial

difficulties encountered in employing this approach

are due to the fact that control plants are

multivariable (MIMO). The second approach called

“linear” consists in designing an adaptive linear

controller with varying parameters to be

systematically tuned up in keeping with changing

plant operating conditions determined by system

nominal “operating points”. Here, linearization of

nonlinear MIMO plants is a prerequisite for the

methods to be employed. After linearization local

linear models are obtained valid for small deviations

from “operating points” of the plant.

Since properties exhibited by linear models at

different (distant) “operating points” of the plant

may substantially vary, therefore the controllers

used should be either robust (Ioannou & Sun 1996)

(usually of a very high order as has been observed

by (Gierusz 2005)) or adaptive with parameters

being tuned in the process of operation (Äström &

Wittenmark 1995).

If the description of the nonlinear plant is known,

then it is possible to make use of systems with linear

controllers prepared earlier for possibly all

“operating points” of the plant. Such controllers can

create either a set of controllers with switchable

outputs from among which one controller designed

for the given system “operating point” (BaĔka et al.

2010a; BaĔka et al. 2010b; Dworak & Pietrusewicz

2010) is chosen, or multi-controller structures the

control signal components of which are formed, for

example, as weighted means of outputs of a selected

controller group according to Takagi-Sugeno-Kang

(TSK) rules, i.e. with weights being proportional to

the degree of their membership of appropriately

The Course-keeping Adaptive Control System for the Nonlinear MIMO

Model of a Container Vessel

M. Brasel & P. Dworak

West Pomeranian University of Technology, Szczecin, Poland

ABSTRACT: In the paper an adaptive multi-controller control system for a MIMO nonlinear dynamic

process is presented. The problems under study are exemplified by synthesis of a surge velocity and yaw

angle control system for a 4-DOF nonlinear MIMO mathematical model of a single-screw high-speed

container vessel. The paper presents the complexity of the assumed model to be analyzed and the method of

synthesis of the course-keeping control system. In the proposed course-keeping control system use is made of

a set of (stable) linear modal controllers that create a multi-controller structure from which a controller

appropriate to given operation conditions is chosen on the basis of the measured auxiliary signals. The system

synthesis is carried out by means of system pole placement method after having linearized the model 4-DOF

motions of the vessel in steady states. The final part of the paper includes simulation results of system

operation with an adaptive controller of stepwise varying parameters along with conclusions and final

remarks.

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14

fuzzyfied areas of plant outputs or other auxiliary

signals (Tanaka & Sugeno 1992; Tatjewski 2007;

Dworak et al. 2012a; Dworak et al. 2012b).

What all the above-mentioned multi-controller

structures, where not all controllers at the moment

are utilized in a closed-loop system, have in

common is that all controllers employed in these

structures must be stable by themselves, in

distinction to a single adaptive controller with

varying (tuned) parameters. This means that system

strong stability conditions should be fulfilled

(Vidyasagar 1985).

In the presented paper an adaptive modal MIMO

controller with (stepwise) varying parameters in the

process of operation is studied. The controller can be

physically realized as a multi-controller structure of

modal controllers with switchable outputs. The

considered adaptive control system will be designed

for all possible “operating points” of the plant. In the

simulation studies a 4-DoF nonlinear model of a

single-screw high-speed container vessel has been

used as a nonlinear MIMO plant. The main goal of

the paper is a synthesis of the course-keeping

adaptive control system for a container vessel

assuming two controlled variables: yaw angle and

forward speed of the ship relative to water.

2 NONLINEAR MODEL OF A CONTAINER

SHIP

The considered course-keeping control system

structure is studied by means of a 4-DOF nonlinear

mathematical model of container vessel (Son &

Nomoto 1981, Fossen 1994), having L =175m in

length, B =25.4m in beam, with an average draught

of H =8.5m. The yaw angle and the ship’s position

are defined in an Earth-based fixed reference

system. In contrast, force and speed components

with respect to water are determined in a moving

system related with the ship’s body and the axes

directed to the front and the starboard of the ship

with the origin placed in its gravity center (G).

These are shown in Fig. 1.

Designations for the linear and angular speed of

the ship, in the considered degrees of freedom ship

motion are as follows: u (surge velocity), v (sway

velocity), p (roll rate) and r (yaw rate).

Corresponding designations of the position

coordinates of the ship are as follows: o x (ship

position in N-S), o y (ship position in W-E), I (roll

angle), \ (yaw angle).

Figure 1. Ship’s co-ordinate systems.

General nonlinear equations of motion in surge,

sway, roll and yaw (Son & Nomoto 1981, Fossen

1994) are as follows:

  .

x y

y x y y yy

x x yy xx

z z yy G

m m u m m vr X

m m v m m ur m r m l p Y

I J p m l v m l ur W GM K

I J r m v N Yx

D

I

D

 

   

  

  



 

 

 

(1)

Here m denotes the ship mass; mx , my , x J , z J

denote the added mass and added moment of inertia

in the x and y directions and about the x -axes and

z - axes, respectively. x I and z I denote moment of

inertia about the x -axes and z - axes, respectively.

Furthermore, D y denotes the x -coordinates of the

center of my , while xl and y l denote the z -

coordinates of the centers of mx and my ,

respectively. Gx is the location of the center of

gravity in the x -axes, GM is the metacentric height

and W is the ship displacement.

The hydrodynamic forces X , Y and moments K ,

N in above equations are given as:

2 2

2

1

sin ,

uu vr vv rr

RX N

X = X u u t T X vr X v X r

X cF III G

   

 

(2)

3 3

2 22 2

2 2 1 cos ,

v r p vvv rrr

vvr vrr vv v

rr r H N

Y=Y v Y r Y p Y Y v Y r

Y v r Y vr Y v Y v

Yr Yr a F

I

I II

I II

I

I I

I I G

   

 

  

(3)

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