Ship Motion Control : Course Keeping and Roll Stabilisation Using Rudder and Fins

Introduction to Ship Motion Control 1(16) The Fundamental Problem of Ship Motion Control 2(2) Ship Motion Control Problems and Control Designs Addressed in this Book 4(1) Mathematical Models for Control 5(1) State-space and Input-output Models Revisited 6(5) State-Space Models 8(2) Laplace-Transform Models 10(1) Computer-Controlled Systems 11(2) The Road Ahead 13(4) Part I Ship Modelling for Control Environmental Disturbances 17(28) Basic Hydrodynamic Assumptions 17(3) Fluid Flow and Continuity 17(1) Material Derivative 18(1) Navier-Stokes Equations 19(1) Potential Flows and The Bernoulli Equation 19(1) Regular Waves in Deep Water 20(3) Encounter Frequency 23(2) Ocean Waves and Wave Spectra 25(6) Statistics of Wave Period 27(1) Statistics of Maxima 27(3) A Note on the Units of the Spectral Density 30(1) Standard Spectrum Formulae 31(3) Linear Representation of Long-crested Irregular Seas 34(2) The Encounter Spectrum 36(1) Short-crested Irregular Seas 36(2) Long-term Statistics of Ocean Waves 38(1) Simulation of Wave Elevation 39(6) Kinematics of Ship Motion 45(14) Reference Frames 45(3) Vector Notation 48(1) Coordinates Used to Describe Ship Motion 48(5) Manoeuvring and Seakeeping 48(1) Manoeuvring Coordinates and Reference Frames 49(1) Seakeeping Coordinates and Reference Frames 50(2) Angles About the z-axis 52(1) Velocity Transformations 53(6) Rotation Matrices 53(1) Kinematic Transformation Between the b- and the n-frame 54(1) Kinematic Transformation Between the b- and the h-frame 55(4) Ship Kinetics 59(34) An Overview of Ship Modeling for Control 59(3) Seakeeping Theory Models 62(17) Equations of Motion and Hydrodynamic Forces in the h-frame 63(3) Wave Force Response Amplitude Operator (Force RAO) 66(1) Motion Response Amplitude Operator (Motion RAO) 67(4) Ship Motion Spectra and Statistics of Ship Motion 71(2) Time-series of Ship Motion using Seakeeping Models 73(6) Manoeuvring Theory Models 79(7) Rigid Body Dynamics in the b-frame 79(3) Manoeuvring Hydrodynamics 82(1) Nonlinear Manoeuvring State-space Models 83(2) Linear Manoeuvring State-space Models 85(1) A Force-superposition Model for Slow Manoeuvring in a Seaway 86(7) Time Domain Seakeeping Models in the h-frame 86(3) Seakeeping Model in the b-frame 89(2) A Unified Nonlinear State-pace Model 91(2) Control Surfaces (Actuators) 93(20) Geometry of Fin and Rudder Hydrofoils 93(1) Hydrodynamic Forces Acting on a Foil 93(4) Unsteady Hydrodynamics 97(4) Forces and Moments Acting on the Hull 101(3) Rudder 102(2) Rudder-Propeller Interaction 104(4) Fins 106(2) Hydraulic Machinery 108(1) Part I Summary and Discussion 109(4) Part II Introduction to Ship Roll Stabilisation Ship Roll Stabilisation 113(14) Effects of Roll Motion on Ship Performance 113(1) Damping or Stabilising Systems? 113(2) Ship Roll Stabilisation Techniques 115(7) Gyroscopes 116(1) Bilge Keels 116(1) Anti-rolling Tanks 117(2) Active Fin Stabilisers 119(1) Rudder Roll Stabilisation RRS 120(2) A Note on the Early Days of Ship Roll Stabilisation 122(5) Ship Motion Performance 127(18) Reduction of Roll at Resonance---RRR 127(1) Reduction of Statistics of Roll---RSR 128(1) Reduction of Probability of Roll Peak Occurrence---RRO 128(2) Increase in Percentage of Time Operable---IPTO 130(5) Seakeeping Indices Affected by Roll 135(6) Lateral Force Estimator---LFE 136(2) Motion-induced Interruptions---MII 138(2) Motion Sickness Incidence---MSI 140(1) Implications for Stabiliser Control System Design 141(1) Part II Summary and Discussion 142(3) Part III Performance Limitations in Feedback Control with Application to Ship Roll Stabilisers Linear Performance Limitations 145(32) Introduction to Fundamental Limitation in Feedback Control Systems 146(4) Non-minimum Phase Dynamics in Ship Response 150(4) Deterministic SISO Performance Limitations of RRS 154(7) Sensitivity Integrals-Frequency Domain Approach 155(4) Performance Trade-offs of Non-adaptive Feedback Controllers for RRS 159(2) Stochastic SISO Performance Limitations of RRS 161(4) Limiting Optimal Control Performance Limitations 161(3) Stochastic SISO Results and RRS 164(1) Optimal Roll Reduction vs. Yaw Interference Trade-off 165(6) SITO Control Problems in the Frequency Domain 165(2) Limiting Stochastic LQR 167(4) Comments on the Applicability of Rudder Stabilisers 171(4) NMP Dynamics in Fin Stabilizers 175(2) Constrained Performance Limitations 177(16) Input Constraints and Saturation Effects 177(1) Input Constraints and Performance at a Single Frequency 178(3) Magnitude Limitations 179(1) Rate Limitations 180(1) Application to Rudder-Based Stabilizers 181(1) Stochastic Approach: Variance Constraints 182(6) IVC Optical Control Problem Formulation 182(3) IVC Application to RRS 185(3) Part III Summary and Discussion 188(5) Part IV Control System Design for Autopilot with Rudder Roll Stabilisation and Fin Stabilisers Previous Research in Control of Rudder Roll Stabilisation and Fin Stabilisers 193(14) Rudder Roll Stabilisation in the 1970s 193(3) Rudder Roll Stabilisation in the 1980s 196(5) Rudder Roll Stabilisation in the 1990s 201(2) Rudder Roll Stabilisation from 2000 to 2004 203(1) Work on Fin and Combined Rudder and Fin Stabiliser Control 204(1) Main Issues Reported in Previous Work 204(3) Constrained Control via Optimisation 207(14) Constraint Classification 208(1) Different Approaches to Constrained Control Problems 208(1) Finite-horizon Sequential-decision Problems 209(1) Infinite Horizons and Receding-horizon Implementation 210(1) Model Predictive Control 211(2) Constrained Linear Systems 213(3) Explicit and Implicit Implementations of QP-MPC 216(1) Stability of Model Predictive Control 217(2) Constrained Control of Uncertain Systems 219(2) Control System Design for Autopilots with Rudder Roll Stabilisation 221(30) Overview of Autopilot Functions and their Influence on Control Design 221(2) RRS: A Challenging Control Problem 223(1) Control System Architecture 224(1) Control Design Models 225(4) Control to Motion Model 226(2) Wave-induced Motion Model 228(1) Disturbance Parameter Estimation and Forecasting 229(4) Observer Design: State Estimation and Wave Filtering 233(4) Autopilot Control System Design 237(1) Autopilot Control Problem and Assumptions for the Design 237(3) A Model Predictive Control Solution 240(2) Performance of Model Predictive RRS 242(9) Choosing the Prediction Horizon 243(1) Penalising Roll Acceleration in the Cost 243(1) Case A: Beam Seas at the Top of Sea State 4 244(1) Case B: Quartering Seas at the Top of Sea State 5 245(1) Case C: Bow Seas at the Top of Sea State 5 246(1) The Role of Adaptation 246(2) A Comment About the Simulation Results 248(3) Constrained Control of Fin Stabilisers 251(14) Performance and Control of Rudder and Fins 251(1) A Model for Fin Stabilizer Control Design 252(2) Output Constraints to avoid Dynamic Stall 254(2) A MPC Fin-Stabiliser Controller 256(2) Numerical Simulations 258(5) Integrated Control of Rudder and Fins 263(1) Summary and Discussion 263(2) A Observers and Kalman Filtering 265(8) A.1 State Estimation via Observers 265(1) A.2 Kalman Filtering 266(2) A.3 Optimality of Kalman Filters 268(1) A.4 Correlated Disturbances 269(1) A.5 Practical Kalman Filter: Tuning 270(1) A.6 Steady State Kalman filter 270(1) A.7 Implementation Issues 271(2) B A Benchmark Example: Naval Vessel 273(10) B.1 Hull Shape 274(1) B.2 Adopted Reference frames 275(1) B.3 Principal Hull Data and Loading Condition 276(1) B.4 Rudder, Fins and Bilge Keels 277(2) B.5 Manoeuvring Coefficients and Motion RAO 279(4) References 283(14) Index 297