Lecture Notes

MANEUVERING AND CONTROL OF MARINE VEHICLES (Fulltext in PDF 738K, also available by chapter below)
by Michael S. Triantafyllou and Franz S. Hover

Department of Ocean Engineering
Massachusetts Institute of Technology
Cambridge, Massachusetts USA

These notes were developed in the instruction of the MIT graduate subject 13.49: Maneuvering and Control of Surface and Underwater Vehicles. We plan many enhancements; your comments are welcome!

Contents  (Chapter headings link to 100-500K PDF files)

1. MATH FACTS
   1.1 Vectors
   1.1.1 Definition
   1.1.2 Vector Magnitude
   1.1.3 Vector Dot Product
   1.1.4 Vector Cross Product
   1.2 Matrices
   1.2.1 Definition
   1.2.2 Multiplying a Vector by a Matrix
   1.2.3 Multiplying a Matrix by a Matrix
   1.2.4 Common Matrices
      Identity
      Diagonal Matrices
   1.2.5 Transpose
   1.2.6 Determinant
   1.2.7 Inverse
   1.2.8 Trace
   1.2.9 Eigenvalues and Eigenvectors
   1.2.10 Modal Decomposition
   1.2.11 Singular Value
   1.3 Laplace Transform
   1.3.1 Definition
   1.3.2 Convergence
   1.3.3 Convolution Theorem
   1.3.4 Solution of Differential Equations by Laplace Transform
   
2. KINEMATICS OF MOVING FRAMES
   2.1 Rotation of Reference Frames
   2.2 Differential Rotations
   2.3 Rate of Change of Euler Angles
   2.4 Dead Reckoning
   
3. VESSEL INERTIAL DYNAMICS
   3.1 Momentum of a Particle
   3.2 Linear Momentum in a Moving Frame
   3.3 Example: Mass on a String
   3.3.1 Moving Frame Affixed to Mass
   3.3.2 Rotating Frame Attached to Pivot Point
   3.3.3 Stationary Frame
   3.4 Angular Momentum
   3.5 Example: Spinning Book
   3.5.1 x-axis
   3.5.2 y-axis
   3.5.3 z-axis
   3.6 Parallel Axis Theorem
   3.7 Basis for Simulation
   
4. HYDRODYNAMICS: INTRODUCTION
   4.1 Taylor Series and Hydrodynamic Coefficients
   4.2 Surface Vessel Linear Model
   4.3 Stability of the Sway/Yaw System
   4.4 Basic Rudder Action in the Sway/Yaw Model
   4.4.1 Adding Yaw Damping through Feedback
   4.4.2 Heading Control in the Sway/Yaw Model
   4.5 Response of the Vessel to Step Rudder Input
   4.5.1 Phase 1: Accelerations Dominate
   4.5.2 Phase 3: Steady State
   4.6 Summary of the Linear Maneuvering Model
   4.7 Stability in the Vertical Plane
   
5. SIMILITUDE
   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
   6.1 Towtank
   6.2 Rotating Arm Device
   6.3 Planar-Motion Mechanism
   
7. STANDARD MANEUVERING TESTS
   7.1 Dieudonn?? 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
   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 Zomega;,Momega , Zq, andMq for a Slender Body
   
9. SLENDER-BODY THEORY
   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
    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
    11.1 Origin of Lift
    11.2 Three-Dimensional Effects: Finite Length
    11.3 Ring Fins
    
12. PROPELLERS AND PROPULSION
    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. TOWING OF VEHICLES
    13.1 Statics
    13.1.1 Force Balance
    13.1.2 Critical Angle
    13.2 Linearized Dynamics
    13.2.1 Derivation
    13.2.2 Damped Axial Motion
    13.3 Cable Strumming
    13.4 Vehicle Design
    
14. TRANSFER FUNCTIONS & STABILITY
    14.1 Partial Fractions
    14.2 Partial Fractions: Unique Poles
    14.3 Example: Partial Fractions with Unique Real Poles
    14.4 Partial Fractions: Complex-Conjugate Poles
    14.5 Example: Partial Fractions with Complex Poles
    14.6 Stability in Linear Systems
    14.7 Stability<==> Poles in LHP
    14.8 General Stability
    
15. CONTROL FUNDAMENTALS
    15.1 Introduction
    15.1.1 Plants, Inputs, and Outputs
    15.1.2 The Need for Modeling
    15.1.3 Nonlinear Control
    15.2 Representing Linear Systems
    15.2.1 Standard State-Space Form
    15.2.2 Converting a State-Space Model into a Transfer Function
    15.2.3 Converting a Transfer Function into a State-Space Model
    15.3 PID Controllers
    15.4 Example: PID Control
    15.4.1 Proportional Only
    15.4.2 Proportional-Derivative Only
    15.4.3 Proportional-Integral-Derivative
    15.5 Heuristic Tuning
    15.6 Block Diagrams of Systems
    15.6.1 Fundamental Feedback Loop
    15.6.2 Block Diagrams: General Case
    15.6.3 Primary Transfer Functions
    
16. MODAL ANALYSIS
    16.1 Introduction
    16.2 Matrix Exponential
    16.2.1 Definition
    16.2.2 Modal Canonical Form
    16.2.3 Modal Decomposition of Response
    16.3 Forced Response and Controllability
    16.4 Plant Output and Observability
    
17. CONTROL SYSTEMS - LOOPSHAPING
    17.1 Introduction
    17.2 Roots of Stability - Nyquist Criterion
    17.2.1 Mapping Theorem
    17.2.2 Nyquist Criterion
    17.2.3 Robustness on the Nyquist Plot
    17.3 Design for Nominal Performance
    17.4 Design for Robustness
    17.5 Robust Performance
    17.6 Implications of Bode's Integral
    17.7 The Recipe for Loopshaping
    
18. LINEAR QUADRATIC REGULATOR
    18.1 Introduction
    18.2 Full-State Feedback
    18.3 Dynamic Programming
    18.4 Dynamic Programming and Full-State Feedback
    18.5 Properties and Use of the LQR
    
19. KALMAN FILTER
    19.1 Introduction
    19.2 Problem Statement
    19.3 Step 1: An Equation for∑
    19.4 Step 2:H as a Function of∑
    19.5 Properties of the Solution
    19.6 Combination of LQR and KF
    19.7 Proofs of the Intermediate Results
    
20. LOOP TRANSFER RECOVERY
    20.1 Introduction
    20.2 A Special Property of the LQR Solution
    20.3 The Loop Transfer Recovery Result
    20.4 Usage of the Loop Transfer Recovery
    20.5 Three Lemmas
    
21. SYSTEM IDENTIFICATION
    21.1 Introduction
    21.2 Visual Output from a Simple Input
    21.3 Transfer Function Estimation - Sinusoidal Input
    21.4 Transfer Function Estimation - Broadband Input
    21.4.1 Fourier Transform of Sampled Data
    21.4.2 Estimating the Transfer Function
    21.5 Time-Domain Simulation
    
22. CARTESIAN NAVIGATION
    22.1 Acoustic Navigation
    (Ultra) Short-Baseline
    Long-Baseline
    22.2 Global Positioning System (GPS)
    
23. REFERENCES
    
24. PROBLEMS