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1 Introduction1

1.1 From the Invention of the Gyroscope to Model Based Ship Control3

1.1.1 The Gyroscope and its Contributions to Ship Control4

1.1.2 Autopilots5

1.1.3 Dynamic Positioning and Position Mooring Systems6

1.1.4 Way-Point Tracking Control Systems7

1.1.5 The Sea Launch System7

1.2 Model Representations for Marine Vessels9

1.2.1 The Classical Model in Naval Architecture9

1.2.2 The Vectorial Model Representation of Fossen （1991）10

1.3 The Principle of Guidance， Navigation and Control11

1.3.1 Definitions of Guidance， Navigation and Control11

1.3.2 Set-Point Regulation versus Trajectory Tracking Control12

1.4 Organization of Book12

Ⅰ Modeling of Marine Vessels15

2 Kinematics17

2.1 Reference Frames19

2.2 Transformations between BODY and NED21

2.2.1 Euler Angle Transformation23

2.2.2 Unit Quaternions29

2.2.3 Quaternions from Euler Angles33

2.2.4 Euler Angles from Quaternions35

2.2.5 QUEST Algorithm for Position and Attitude Determination36

2.3 Transformation between ECEF and NED38

2.3.1 Longitude and Latitude Transformations38

2.3.2 Longitude and Latitude from ECEF Coordinates41

2.3.3 ECEF Coordinates from Longitude and Latitude43

2.4 Transformations for Stability and Flow Axes44

2.5 Exercises47

3 Dynamics of Marine Vessels49

3.1 Rigid-Body Dynamics50

3.1.1 Translational Motion51

3.1.2 Rotational Motion （Attitude Dynamics）53

3.1.3 Rigid-Body Equations of Motion57

3.2 Hydrodynamic Forces and Moments62

3.2.1 Added Mass and Inertia64

3.2.2 Hydrodynamic Damping71

3.2.3 Restoring Forces and Moments75

3.2.4 Ballast Systems82

3.3 6 DOF Equations of Motion88

3.3.1 Nonlinear Equations of Motion88

3.3.2 Linearized Equations of Motion91

3.4 Model Transformations using Matlab94

3.4.1 System Transformation Matrix94

3.4.2 Computation of the System Inertia Matrix96

3.4.3 Computation of the Coriolis-Centrifugal Matrix100

3.4.4 Computation of the Damping Matrix100

3.4.5 Computation of the Restoring Forces and Moments102

3.5 Standard Models for Marine Vessels103

3.5.1 3 DOF Horizontal Model104

3.5.2 Decoupled Models for Forward Speed/Maneuvering107

3.5.3 Longitudinal and Lateral Models109

3.6 Exercises113

4 Models for Wind， Waves and Ocean Currents115

4.1 Wind Models116

4.1.1 Wind Forces and Moments116

4.1.2 Wind Resistance of Merchant Ships （Isherwood 1972）117

4.1.3 Wind Resistance of Very Large Crude Carriers （OCIMF 1977）120

4.1.4 Wind Resistance of Large Tankers and Medium Sized Ships123

4.1.5 Wind Resistance of Moored Ships and Floating Structures123

4.2 Models for Wind Generated Waves123

4.2.1 Nonlinear Models of Wave Spectra123

4.2.2 Linear Wave Response Models130

4.2.3 Frequency of Encounter136

4.2.4 Wave Forces and Moments137

4.3 Models for Ocean Currents138

4.3.1 3D Irrotational Current Model139

4.3.2 2D Irrotational Current Model （Horizontal-Plane Model）139

4.4 Exercises140

Ⅱ Guidance， Navigation and Control Fundamentals143

5 Maritime Guidance Systems145

5.1 Reference Models146

5.1.1 Velocity Reference Model147

5.1.2 Position and Attitude Reference Models147

5.1.3 Saturating Elements148

5.1.4 Nonlinear Damping148

5.2 Way-Point Guidance Systems149

5.2.1 Trajectory Tracking and Maneuvering Control149

5.2.2 Way-Point Representation152

5.2.3 Trajectory Generation using a Vessel Simulator154

5.2.4 Path and Trajectory Generation using Interpolation156

5.2.5 Weather Routing165

5.3 Line-of-Sight Guidance167

5.3.1 2-Dimensional LOS Guidance System for Surface Vessel168

5.3.2 3-Dimensional LOS Guidance System for Underwater Vehicles169

5.4 Exercises169

6 Estimator Based Navigation Systems171

6.1 Observers for Heading Autopilots172

6.1.1 Magnetic and Gyroscopic Compasses172

6.1.2 Low-Pass and Notch Filtering of Wave Frequency Motions173

6.1.3 Fixed Gain Observers using only Compass Measurements177

6.1.4 Kalman Filter Based Wave Filter Design using only Compass Mea-surements185

6.1.5 Observer and Wave Filter Design using both Compass and Rate Mea-surements189

6.2 Observers for Dynamic Positioning Systems191

6.2.1 Navigation Systems191

6.2.2 Inertial Measurement Systems194

6.2.3 Kalman Filter for Velocity and Wave Frequency Motion196

6.2.4 Passive Nonlinear Observer for Velocity and Wave Frequency Motion201

6.3 6 DOF Integration Filter for IMU and Satellite Navigation Systems213

6.3.1 Integration Filter for Position and Linear Velocity214

6.3.2 Attitude Observer217

6.4 Exercises221

7 Control Methods for Marine Vessels223

7.1 PID-Control and Acceleration Feedback224

7.1.1 Linear Mass-Damper-Spring Systems224

7.1.2 Acceleration Feedback228

7.1.3 Acceleration Feedback + PID Control230

7.1.4 MIMO Acceleration Feedback and Nonlinear PID Control233

7.1.5 Inertia Shaping Techniques using Acceleration Feedback235

7.2 Linear Quadratic Optimal Control237

7.2.1 Linear Quadratic Regulator239

7.2.2 Extensions to Trajectory Tracking and Integral Action240

7.2.3 General Solution of the LQ Trajectory Tracking Problem242

7.3 State Feedback Linearization250

7.3.1 Decoupling in the b-Frame （Velocity）250

7.3.2 Decoupling in the n-Frame （Position and Attitude）252

7.3.3 Adaptive Feedback Linearization254

7.4 Integrator Backstepping256

7.4.1 A Brief History of Backstepping257

7.4.2 The Main Idea of Integrator Backstepping257

7.4.3 Backstepping of SISO Mass-Damper-Spring Systems264

7.4.4 Integral Action by Constant Parameter Adaptation268

7.4.5 Integrator Augmentation Technique272

7.4.6 Backstepping of MIMO Mass-Damper-Spring Systems276

7.4.7 MIMO Backstepping of Ships280

7.4.8 MIMO Backstepping Design with Acceleration Feedback284

7.5 Control Allocation288

7.5.1 Actuator Models288

7.5.2 Unconstrained Control Allocation （Nonrotatable Actuators）291

7.5.3 Constrained Control Allocation （Nonrotatable Actuators）293

7.5.4 Constrained Control Allocation （Azimuthing Thrusters）295

7.6 Exercises298

Ⅲ Ship and Rig Applications301

8 Course Autopilots303

8.1 Autopilot Models304

8.1.1 Rigid-Body Ship Dynamics304

8.1.2 The Linear Ship Steering Equations307

8.1.3 Non-Dimensional Autopilot Models311

8.1.4 Nonlinear Models for Autopilot Design315

8.2 Open-Loop Stability Analysis of Ships320

8.2.1 Stability Considerations for Ship Steering and Positioning320

8.2.2 Criteria for Straight-Line Stability324

8.2.3 Criteria for Directional Stability327

8.3 Maneuverability328

8.3.1 Turning Circle330

8.3.2 Kempf’s Zig-Zag Maneuver334

8.3.3 Pull-Out Maneuver336

8.3.4 Dieudonne’s Spiral Maneuver338

8.3.5 Bech’s Reverse Spiral Maneuver338

8.4 Course-Keeping Autopilots and Turning Control340

8.4.1 Autopilot Reference Model340

8.4.2 Conventional PID-Control342

8.4.3 PID Control including Acceleration Feedback347

8.4.4 PID Control including Wind Feedforward349

8.4.5 Linear Quadratic Optimal Control350

8.4.6 State Feedback Linearization355

8.4.7 Adaptive Feedback Linearization and Optimality356

8.4.8 Nonlinear Backstepping358

8.4.9 SISO Sliding Mode Contiol359

8.4.10 Output Feedback363

8.5 Exercises365

9 Autopilots with Roll Damping367

9.1 Autopilot Models for Steering and Roll Damping368

9.1.1 The Linear Model of Van Amerongen and Van Cappelle （1981）368

9.1.2 The Nonlinear Model of Son and Nomoto （1981）373

9.1.3 The Nonlinear Model of Christensen and Blanke （1986）374

9.2 Rudder-Roll Damping （RRD） Control Systems374

9.2.1 Linear Quadratic Optimal RRD Control System375

9.2.2 Performance Criterion for RRD380

9.3 Fin Stabilization Control Systems and RRD380

9.3.1 Linear Quadratic Energy Optimal Autopilot with Roll Damping381

9.4 Operability and Motion Sickness Incidence Criteria384

9.4.1 Human Operability Limiting Criteria in Roll384

9.4.2 Criterion for Motion Sickness Incidence （MSI）384

9.5 Exercises387

10 Trajectory Tracking and Maneuvering Control389

10.1 Trajectory Tracking Control389

10.1.1 Conventional PID Cross-Tracking System390

10.1.2 Line of Sight Cross-Tracking System391

10.1.3 Linear Quadratic Optimal Cross-Tracking System392

10.1.4 Underactuated Trajectory Tracking Control394

10.2 Maneuvering Control394

10.2.1 Robust Output Maneuvering396

10.2.2 Adaptive Output Maneuvering404

10.2.3 Maneuvering Control of Underactuated Ships415

10.3 Exercises416

11 Positioning Systems417

11.1 Models for Station-Keeping417

11.1.1 Vessel Kinematics and Dynamics417

11.1.2 DP and PM Thrust Models418

11.1.3 Environmental Disturbances422

11.2 Dynamic Positioning （DP） Systems423

11.2.1 Thrust Allocation in DP Systems424

11.2.2 Linear Quadratic Optimal Control425

11.2.3 Nonlinear PID Control427

11.2.4 Nonlinear Separation Principle for PD-Control/Observer Design428

11.2.5 Nonlinear Observer Backstepping436

11.2.6 Nonlinear Inverse Optimal Control447

11.2.7 Underactuated Stabilization448

11.3 Position Mooring （PM） Systems449

11.4 Weather Optimal Positioning Control （WOPC）450

11.4.1 3 DOF Equations of Motion using Polar Coordinates451

11.4.2 Weather Optimal Control Objectives454

11.4.3 Nonlinear and Adaptive Control Design456

11.4.4 Experiments and Simulations462

11.5 Exercises467

Ⅳ Underwater Vehicle Applications469

12 Propeller Control System Design471

12.1 Models for Propeller Shaft Speed and Motors471

12.1.1 Propeller Shaft Speed Models471

12.1.2 Unified Representation of DC-Motor Controllers473

12.1.3 Propeller Losses475

12.2 Propeller Thrust and Torque Modelling475

12.2.1 Quasi-Steady Thrust and Torque476

12.3 Nonlinear Observer for Estimation of Propeller Axial Velocity479

12.3.1 Vehicle Speed and Propeller Axial Flow Dynamics479

12.3.2 Observer Equations480

12.3.3 Lyapunov Analysis481

12.4 Nonlinear Output Feedback Control Design484

12.4.1 Nonlinear Model for Propeller Shaft Speed Control485

12.4.2 Lyapunov Analysis485

12.4.3 Extensions to Integral Control487

13 Decoupled Autopilot Design489

13.1 Course Autopilot491

13.1.1 PID， Optimal Control and H∞-Control491

13.1.2 Nonlinear Control491

13.1.3 Sliding Mode Control using the Eigenvalue Decomposition492

13.2 Depth Autopilot495

13.2.1 Optimal Control497

13.2.2 Sliding Mode Control using the Eigenvalue Decomposition497

13.3 Speed Control System498

13.4 Exercises498

14 6 DOF Position and Attitude Control501

14.1 Nonlinear PID Control501

14.1.1 Set-Point Regulation503

14.1.2 Trajectory Tracking Control504

14.2 State Feedback Linearization507

14.2.1 Trajectory Tracking Control507

14.2.2 Adaptive Feedback Linearization509

14.3 Exercises511

Ⅴ Appendices513

A Nonlinear Stability Theory515

A.1 Lyapunov Stability for Autonomous Systems515

A.1.1 Stability and Convergence515

A.1.2 Lyapunov’s Direct Method517

A.1.3 Krasovskii—LaSalle’s Theorem518

A.1.4 Global Exponential Stability519

A.2 Lyapunov Stability of Nonautonomous Systems520

A.2.1 Barbalat’s Lemma520

A.2.2 LaSalle-Yoshizawa’s Theorem520

A.2.3 Matrosov’s Theorem521

A.2.4 UGAS when Backstepping with Integral Action522

B Numerical Methods525

B.1 Discretization of Continuous-Time Systems525

B.1.1 Linear State-Space Models525

B.1.2 Nonlinear State-Space Models527

B.2 Numerical Integration Methods529

B.2.1 Euler’s Method529

B.2.2 Adams-Bashforth’s 2nd-Order Method530

B.2.3 Runge-Kutta 2nd-Order Method （Heun’s Method）531

B.2.4 Runge-Kutta 4th-Order Method531

B.3 Numerical Differentiation531

C Matlab GNC Toolbox533

C.1 M-File Library534

C.2 Simulink Library535