Lecture Notes

Triantafyllou, Michael S., and Franz S. Hover. Maneuvering and Control of Marine Vehicles. (Full text available here ( PDF - 1.6 MB); also available by chapter below)

Contents

  1. Kinematics of Moving Frames ( PDF

    1.1 Rotation of Reference Frames 
    1.2 Differential Rotations 
    1.3 Rate of Change of Euler Angles 
    1.4 Dead Reckoning 
     

  2. Vessel Inertial Dynamics ( PDF

    2.1 Momentum of a Particle 
    2.2 Linear Momentum in a Moving Frame 
    2.3 Example: Mass on a String 
    2.3.1 Moving Frame Affixed to Mass 
    2.3.2 Rotating Frame Attached to Pivot Point 
    2.3.3 Stationary Frame 
    2.4 Angular Momentum 
    2.5 Example: Spinning Book 
    2.5.1 x-axis 
    2.5.2 y-axis 
    2.5.3 z-axis 
    2.6 Parallel Axis Theorem 
    2.7 Basics for Simulation

  3. Nonlinear Coefficients in Detail ( PDF

    3.1 Helpful Facts 
    3.2 Nonlinear Equations in the Horizontal Plane 
    3.2.1 Fluid Force X 
    3.2.2 Fluid Force Y 
    3.2.3 Fluid Moment N

  4. Vessel Dynamics: Linear Case ( PDF

    4.1 Surface Vessel Linear Model 
    4.2 Stability of the Sway/Yaw System 
    4.3 Basic Rudder Action in the Sway/Yaw Model 
    4.3.1 Adding Yaw Damping through Feedback 
    4.3.2 Heading Control in the Sway/Yaw Model 
    4.4 Response of the Vessel to Step Rudder Input 
    4.4.1 Phase 1: Accelerations Dominate 
    4.4.2 Phase 3: Steady State 
    4.5 Summary of the Linear Maneuvering Model 
    4.6 Stability in the Vertical Plane

  5. Similitude ( PDF

    5.1 Use of Nondimensional Groups 
    5.2 Common Groups in Marine Engineering 
    5.3 Similitude in Maneuvering 
    5.4 Roll Equation Similitude

  6. Captive Measurements ( PDF

    6.1 Towtank 
    6.2 Rotating Arm Device 
    6.3 Planar-Motion Mechanism

  7. Standard Maneuvering Tests ( PDF

    7.1 Dieudonné Spiral 
    7.2 Zig-Zag Maneuver 
    7.3 Circle Maneuver 
    7.3.1 Drift Angle 
    7.3.2 Speed Loss 
    7.3.3 Heel Angle 
    7.3.4 Heeling in Submarines with Sails

  8. Streamlined Bodies ( PDF

    8.1 Nominal Drag Force 
    8.2 Munk Moment 
    8.3 Separation Moment 
    8.4 Net Effects: Aerodynamic Center 
    8.5 Role of Fins in Moving the Aerodynamic Center 
    8.6 Aggregate Effects of Body and Fins 
    8.7 Coefficients Zw, Mw, Zq, and Mq for a Slender Body

  9. Slender-Body Theory ( PDF

    9.1 Introduction 
    9.2 Kinematics Following the Fluid 
    9.3 Derivative Following the Fluid 
    9.4 Differential Force on the Body 
    9.5 Total Force on a Vessel 
    9.6 Total Moment on a Vessel 
    9.7 Relation to Wing Lift 
    9.8 Convention: Hydrodynamic Mass Matrix A

  10. Practical Lift Calculations ( PDF

    10.1 Characteristics of Lift-Producing Mechanisms 
    10.2 Jorgensen’s Formulas 
    10.3 Hoerner’s Data: Notation 
    10.4 Slender-Body Theory vs. Experiment 
    10.5 Slender-Body Approximation for Fin Lift

  11. Fins and Lifting Surfaces ( PDF

    11.1 Origin of Lift 
    11.2 Three-Dimensional Effects: Finite Length 
    11.3 Ring Fins

  12. Propellers and Propulsion ( PDF

    12.1 Introduction 
    12.2 Steady Propulsion of Vessels 
    12.2.1 Basic Characteristics 
    12.2.2 Solution for Steady Conditions 
    12.2.3 Engine/Motor Models 
    12.3 Unsteady Propulsion Models 
    12.3.1 One-State Model: Yoerger et al 
    12.3.2 Two-State Model: Healey et al

  13. Electric Motors ( PDF

    13.1 Basic Relations 
    13.1.1 Concepts 
    13.1.2 Faraday’s Law 
    13.1.3 Ampere’s Law 
    13.1.4 Force 
    13.2 DC Motors 
    13.2.1 Permanent Field Magnets 
    13.2.2 Shunt or Independent Field Windings 
    13.2.3 Series Windings 
    13.3 Three-Phase Synchronous Motor 
    13.4 Three-Phase Induction Motor

  14. Towing of Vehicles ( PDF

    14.1 Statics 
    14.1.1 Force Balance 
    14.1.2 Critical Angle 
    14.2 Linearized Dynamics 
    14.2.1 Derivation 
    14.2.2 Damped Axial Motion 
    14.3 Cable Strumming 
    14.4 Vehicle Design

  15. Transfer Functions and Stability ( PDF

    15.1 Partial Fractions 
    15.2 Partial Fractions: Unique Poles 
    15.3 Example: Partial Fractions with Unique Real Poles 
    15.4 Partial Fractions: Complex-Conjugate Poles 
    15.5 Example: Partial Fractions with Complex Poles 
    15.6 Stability in Linear Systems 
    15.7 Stability ⇔ Poles in LHP 
    15.8 General Stability

  16. Control Fundamentals ( PDF

    16.1 Introduction 
    16.1.1 Plants, Inputs, and Outputs 
    16.1.2 The Need for Modeling 
    16.1.3 Nonlinear Control 
    16.2 Representing Linear Systems 
    16.2.1 Standard State-Space Form 
    16.2.2 Converting a State-Space Model into a Transfer Function 
    16.2.3 Converting a Transfer Function into a State-Space Model 
    16.3 PID Controllers 
    16.4 Example: PID Control 
    16.4.1 Proportional Only 
    16.4.2 Proportional-Derivative Only 
    16.4.3 Proportional-Integral-Derivative 
    16.5 Heuristic Tuning 
    16.6 Block Diagrams of Systems 
    16.6.1 Fundamental Feedback Loop 
    16.6.2 Block Diagrams: General Case 
    16.6.3 Primary Transfer Functions

  17. Modal Analysis ( PDF

    17.1 Introduction 
    17.2 Matrix Exponential 
    17.2.1 Definition 
    17.2.2 Modal Canonical Form 
    17.2.3 Modal Decomposition of Response 
    17.3 Forced Response and Controllability 
    17.4 Plant Output and Observability

  18. Control Systems - Loopshaping ( PDF

    18.1 Introduction 
    18.2 Roots of Stability - Nyquist Criterion 
    18.2.1 Mapping Theorem 
    18.2.2 Nyquist Criterion 
    18.2.3 Robustness on the Nyquist Plot 
    18.3 Design for Nominal Performance 
    18.4 Design for Robustness 
    18.5 Robust Performance 
    18.6 Implications of Bode’s Integral 
    18.7 The Recipe for Loopshaping

  19. Linear Quadratic Regulator ( PDF

    19.1 Introduction 
    19.2 Full-State Feedback 
    19.3 The Maximum Principle 
    19.4 Gradient Method Solution for the General Case 
    19.5 LQR Solution 
    19.6 Optimal Full-State Feedback 
    19.7 Properties and Use of the LQR 
    19.8 Proof of the Gain and Phase Margins

  20. Kalman Filter ( PDF

    20.1 Introduction 
    20.2 Problem Statement 
    20.3 Step 1: An Equation for ∑ 
    20.4 Step 2: H as a Function of ∑ 
    20.5 Properties of the Solution 
    20.6 Combination of LQR and KF 
    20.7 Proofs of the Intermediate Results

  21. Loop Transfer Recovery ( PDF

    21.1 Introduction 
    21.2 A Special Property of the LQR Solution 
    21.3 The Loop Transfer Recovery Result 
    21.4 Usage of the Loop Transfer Recovery 
    21.5 Three Lemmas

  22. Appendix 1: Math Facts ( PDF

    22.1 Vectors 
    22.1.1 Definition 
    22.1.2 Vector Magnitude 
    22.1.3 Vector Dot or Inner Product 
    22.1.4 Vector Cross Product 
    22.2 Matrices 
    22.2.1 Definition 
    22.2.2 Multiplying a Vector by a Matrix 
    22.2.3 Multiplying a Matrix by a Matrix 
    22.2.4 Common Matrices 
    22.2.5 Transpose 
    22.2.6 Determinant 
    22.2.7 Inverse 
    22.2.8 Trace 
    22.2.9 Eigen values and Eigen vectors 
    22.2.10 Modal Decomposition 
    22.2.11Singular Value 
    22.3 Laplace Transform 
    22.3.1 Definition 
    22.3.2 Convergence 
    22.3.3 Convolution Theorem 
    22.3.4 Solution of Differential Equations by Laplace Transform 
    22.4 Back ground for the Mapping Theorem

  23. Appendix 2: Added Mass via Lagrangian Dynamics ( PDF

    23.1 Kinetic Energy of the Fluid 
    23.2 Kirchhoff’s Relations 
    23.3 Fluid Inertia Terms 
    23.4 Derivation of Kirchhoff’s Relations 
    23.5 Nomenclature 
    23.5.1 Free versus Column Vector 
    23.5.2 Derivative of a Scalar with Respect to a Vector 
    23.5.3 Dot and Cross Product

  24. Appendix 3: LQR via Dynamic Programming ( PDF

    24.1 Example in the Case of Discrete States 
    24.2 Dynamic Programming and Full-State Feedback

  25. Further Robustness of the LQR ( PDF

    25.1 Tools 
    25.1.1 Lyapunov’s Second Method 
    25.1.2 Matrix Inequality Definition 
    25.1.3 Franklin Inequality 
    25.1.4 Schur Complement 
    25.1.5 Proof of Schur Complement Sign 
    25.1.6 Schur Complement of a Nine-Block Matrix 
    25.1.7 Quadratic Optimization with a Linear Constraint 
    25.2 Comments on Linear Matrix Inequalities (LMI’s) 
    25.3 Parametric Uncertainty in A and B Matrices 
    25.3.1 General Case 
    25.3.2 Uncertainty in B 
    25.3.3 Uncertainty in A 
    25.3.4 A and B Perturbations as an LMI 
    25.4 Input Nonlinearities

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