Maneuvering and Control of Surface and Underwater Vehicles (13.49)

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Complete textbook for this course: Triantafyllou, Michael S., and Franz S. Hover. Maneuvering and Control of Marine Vehicles. Individual chapters can be downloaded 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 Z_w, M_w, Z_q, and M_q 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