Maneuvering and Control of Marine Vehicles
Series: Lecture Notes
Publisher: Massachusetts Institute of Technology
Published: 2003
Place of publication: Massachusetts USA
Number of pages: 152
Table of contents: title: 1. Kinematics of Moving Frames; title: 1.1 Rotation of Reference Frames; title: 1.2 Differential Rotations; title: 1.3 Rate of Change of Euler Angles; title: 1.4 Dead Reckoning; title: 2. Vessel Inertial Dynamics; title: 2.1 Momentum of a Particle; title: 2.2 Linear Momentum in a Moving Frame; title: 2.3 Example: Mass on a String; title: 2.3.1 Moving Frame Affixed to Mass; title: 2.3.2 Rotating Frame Attached to Pivot Point; title: 2.3.3 Stationary Frame; title: 2.4 Angular Momentum; title: 2.5 Example: Spinning Book; title: 2.5.1 x-axis; title: 2.5.2 y-axis; title: 2.5.3 z-axis; title: 2.6 Parallel Axis Theorem; title: 2.7 Basics for Simulation; title: 3.Nonlinear Coefficients in Detail; title: 3.1 Helpful Facts; title: 3.2 Nonlinear Equations in the Horizontal Plane; title: 3.2.1 Fluid Force X; title: 3.2.2 Fluid Force Y; title: 3.2.3 Fluid Moment N; title: 4.Vessel Dynamics: Linear Case; title: 4.1 Surface Vessel Linear Model; title: 4.2 Stability of the Sway/Yaw System; title: 4.3 Basic Rudder Action in the Sway/Yaw Model; title: 4.3.1 Adding Yaw Damping through Feedback; title: 4.3.2 Heading Control in the Sway/Yaw Model; title: 4.4 Response of the Vessel to Step Rudder Input; title: 4.4.1 Phase 1: Accelerations Dominate; title: 4.4.2 Phase 3: Steady State; title: 4.5 Summary of the Linear Maneuvering Model; title: 4.6 Stability in the Vertical Plane; title: 5.Similitude; title: 5.1 Use of Nondimensional Groups; title: 5.2 Common Groups in Marine Engineering; title: 5.3 Similitude in Maneuvering; title: 5.4 Roll Equation Similitude; title: 6.Captive Measurements; title: 6.1 Towtank; title: 6.2 Rotating Arm Device; title: 6.3 Planar-Motion Mechanism; title: 7.Standard Maneuvering Tests; title: 7.1 Dieudonné Spiral; title: 7.2 Zig-Zag Maneuver; title: 7.3 Circle Maneuver; title: 7.3.1 Drift Angle; title: 7.3.2 Speed Loss; title: 7.3.3 Heel Angle; title: 7.3.4 Heeling in Submarines with Sails; title: 8.Streamlined Bodies; title: 8.1 Nominal Drag Force; title: 8.2 Munk Moment; title: 8.3 Separation Moment; title: 8.4 Net Effects: Aerodynamic Center; title: 8.5 Role of Fins in Moving the Aerodynamic Center; title: 8.6 Aggregate Effects of Body and Fins; title: 8.7 Coefficients Zw, Mw, Zq, and Mq for a Slender Body; title: 9. Slender-Body Theory; title: 9.1 Introduction; title: 9.2 Kinematics Following the Fluid; title: 9.3 Derivative Following the Fluid; title: 9.4 Differential Force on the Body; title: 9.5 Total Force on a Vessel; title: 9.6 Total Moment on a Vessel; title: 9.7 Relation to Wing Lift; title: 9.8 Convention: Hydrodynamic Mass Matrix A; title: 10. Practical Lift Calculations; title: 10.1 Characteristics of Lift-Producing Mechanisms; title: 10.2 Jorgensen’s Formulas; title: 10.3 Hoerner’s Data: Notation; title: 10.4 Slender-Body Theory vs. Experiment; title: 10.5 Slender-Body Approximation for Fin Lift; title: 11.Fins and Lifting Surfaces; title: 11.1 Origin of Lift; title: 11.2 Three-Dimensional Effects: Finite Length; title: 11.3 Ring Fins; title: 12. Propellers and Propulsion; title: 12.1 Introduction; title: 12.2 Steady Propulsion of Vessels; title: 12.2.1 Basic Characteristics; title: 12.2.2 Solution for Steady Conditions; title: 12.2.3 Engine/Motor Models; title: 12.3 Unsteady Propulsion Models; title: 12.3.1 One-State Model: Yoerger et al; title: 12.3.2 Two-State Model: Healey et al; title: 13. Electric Motors; title: 13.1 Basic Relations; title: 13.1.1 Concepts; title: 13.1.2 Faraday’s Law; title: 13.1.3 Ampere’s Law; title: 13.1.4 Force; title: 13.2 DC Motors; title: 13.2.1 Permanent Field Magnets; title: 13.2.2 Shunt or Independent Field Windings; title: 13.2.3 Series Windings; title: 13.3 Three-Phase Synchronous Motor; title: 13.4 Three-Phase Induction Motor; title: 14.Towing of Vehicles; title: 14.1 Statics; title: 14.1.1 Force Balance; title: 14.1.2 Critical Angle; title: 14.2 Linearized Dynamics; title: 14.2.1 Derivation; title: 14.2.2 Damped Axial Motion; title: 14.3 Cable Strumming; title: 14.4 Vehicle Design; title: 15.Transfer Functions and Stability; title: 15.1 Partial Fractions; title: 15.2 Partial Fractions: Unique Poles; title: 15.3 Example: Partial Fractions with Unique Real Poles; title: 15.4 Partial Fractions: Complex-Conjugate Poles; title: 15.5 Example: Partial Fractions with Complex Poles; title: 15.6 Stability in Linear Systems; title: 15.7 Stability ⇔ Poles in LHP; title: 15.8 General Stability; title: 16.Control Fundamentals; title: 16.1 Introduction; title: 16.1.1 Plants, Inputs, and Outputs; title: 16.1.2 The Need for Modeling; title: 16.1.3 Nonlinear Control; title: 16.2 Representing Linear Systems; title: 16.2.1 Standard State-Space Form; title: 16.2.2 Converting a State-Space Model into a Transfer Function; title: 16.2.3 Converting a Transfer Function into a State-Space Model; title: 16.3 PID Controllers; title: 16.4 Example: PID Control; title: 16.4.1 Proportional Only; title: 16.4.2 Proportional-Derivative Only; title: 16.4.3 Proportional-Integral-Derivative; title: 16.5 Heuristic Tuning; title: 16.6 Block Diagrams of Systems; title: 16.6.1 Fundamental Feedback Loop; title: 16.6.2 Block Diagrams: General Case; title: 16.6.3 Primary Transfer Functions; title: 17.Modal Analysis; title: 17.1 Introduction; title: 17.2 Matrix Exponential; title: 17.2.1 Definition; title: 17.2.2 Modal Canonical Form; title: 17.2.3 Modal Decomposition of Response; title: 17.3 Forced Response and Controllability; title: 17.4 Plant Output and Observability; title: 18.Control Systems - Loopshaping; title: 18.1 Introduction; title: 18.2 Roots of Stability - Nyquist Criterion; title: 18.2.1 Mapping Theorem; title: 18.2.2 Nyquist Criterion; title: 18.2.3 Robustness on the Nyquist Plot; title: 18.3 Design for Nominal Performance; title: 18.4 Design for Robustness; title: 18.5 Robust Performance; title: 18.6 Implications of Bode’s Integral; title: 18.7 The Recipe for Loopshaping; title: 19.Linear Quadratic Regulator; title: 19.1 Introduction; title: 19.2 Full-State Feedback; title: 19.3 The Maximum Principle; title: 19.4 Gradient Method Solution for the General Case; title: 19.5 LQR Solution; title: 19.6 Optimal Full-State Feedback; title: 19.7 Properties and Use of the LQR; title: 19.8 Proof of the Gain and Phase Margins; title: 20.Kalman Filter; title: 20.1 Introduction; title: 20.2 Problem Statement; title: 20.3 Step 1: An Equation for ∑; title: 20.4 Step 2: H as a Function of ∑; title: 20.5 Properties of the Solution; title: 20.6 Combination of LQR and KF; title: 20.7 Proofs of the Intermediate Results; title: 21.Loop Transfer Recovery; title: 21.1 Introduction; title: 21.2 A Special Property of the LQR Solution; title: 21.3 The Loop Transfer Recovery Result; title: 21.4 Usage of the Loop Transfer Recovery; title: 21.5 Three Lemmas; title: 22. Appendix 1: Math Facts; title: 22.1 Vectors; title: 22.1.1 Definition; title: 22.1.2 Vector Magnitude; title: 22.1.3 Vector Dot or Inner Product; title: 22.1.4 Vector Cross Product; title: 22.2 Matrices; title: 22.2.1 Definition; title: 22.2.2 Multiplying a Vector by a Matrix; title: 22.2.3 Multiplying a Matrix by a Matrix; title: 22.2.4 Common Matrices; title: 22.2.5 Transpose; title: 22.2.6 Determinant; title: 22.2.7 Inverse; title: 22.2.8 Trace; title: 22.2.9 Eigen values and Eigen vectors; title: 22.2.10 Modal Decomposition; title: 22.2.11Singular Value; title: 22.3 Laplace Transform; title: 22.3.1 Definition; title: 22.3.2 Convergence; title: 22.3.3 Convolution Theorem; title: 22.3.4 Solution of Differential Equations by Laplace Transform; title: 22.4 Back ground for the Mapping Theorem; title: 23. Appendix 2: Added Mass via Lagrangian Dynamics; title: 23.1 Kinetic Energy of the Fluid; title: 23.2 Kirchhoff’s Relations; title: 23.3 Fluid Inertia Terms; title: 23.4 Derivation of Kirchhoff’s Relations; title: 23.5 Nomenclature; title: 23.5.1 Free versus Column Vector; title: 23.5.2 Derivative of a Scalar with Respect to a Vector; title: 23.5.3 Dot and Cross Product; title: 24. Appendix 3: LQR via Dynamic Programming; title: 24.1 Example in the Case of Discrete States; title: 24.2 Dynamic Programming and Full-State Feedback; title: 25. Further Robustness of the LQR; title: 25.1 Tools; title: 25.1.1 Lyapunov’s Second Method; title: 25.1.2 Matrix Inequality Definition; title: 25.1.3 Franklin Inequality; title: 25.1.4 Schur Complement; title: 25.1.5 Proof of Schur Complement Sign; title: 25.1.6 Schur Complement of a Nine-Block Matrix; title: 25.1.7 Quadratic Optimization with a Linear Constraint; title: 25.2 Comments on Linear Matrix Inequalities (LMI’s); title: 25.3 Parametric Uncertainty in A and B Matrices; title: 25.3.1 General Case; title: 25.3.2 Uncertainty in B; title: 25.3.3 Uncertainty in A; title: 25.3.4 A and B Perturbations as an LMI; title: 25.4 Input Nonlinearities