Control of Marine Vehicles

Preface
Contents
About the Author
1 Introduction
	1.1 Overview
	1.2 Automatic Control
	1.3 Background Ideas
	1.4 Typical Guidance, Navigation and Control Architectures of Marine Vehicles
		1.4.1 Multilayered Software Architectures for Unmanned Vehicles
		1.4.2 Inter-Process Communications Methods
	1.5 Dynamic Modeling of Marine Vehicles
		1.5.1 Kinematics of Marine Vehicles
		1.5.2 Kinetics of Marine Vehicles
	Problems
	References
Part I Linear Methods
2 Stability: Basic Concepts and Linear Stability
	2.1 The Stability of Marine Systems
	2.2 Basic Concepts in Stability
	2.3 Flow Along a Line
		2.3.1 Linear 1D Stability Analysis
	2.4 Phase Plane Analysis
		2.4.1 Linear 2D Stability Analysis
		2.4.2 Classification of Linear 2D Systems
	2.5 Lyapunov's Indirect (First) Method
	2.6 Stability of Linear Time Invariant Systems
		2.6.1 The Laplace Transform
		2.6.2 Routh's Stability Criterion
	References
3 Time Response and Basic Feedback Control
	3.1 Dynamic Response
		3.1.1 The Impulse Response of 1st and 2nd Order Systems
		3.1.2 The Step Response of 2nd Order Systems
		3.1.3 Effects of Additional Poles and Zeros
	3.2 Block Diagrams
	3.3 Feedback Control
		3.3.1 Proportional Feedback Control
		3.3.2 Derivative Feedback Control
		3.3.3 Integral Feedback Control
		3.3.4 PID Feedback Control
	3.4 Steady State Response
	3.5 Additional Performance Measures
	References
4 Root Locus Methods
	4.1 Introduction
	4.2 Root–Locus Diagrams
		4.2.1 Constructing a Root–Locus
		4.2.2 Properties of the Root Locus
	4.3 Root Locus Controller Design Methods
		4.3.1 Selecting Gain from the Root Locus
		4.3.2 Compensation by Adding or Moving Poles and Zeros
		4.3.3 Phase Lag Controllers
		4.3.4 Phase Lead Controllers
	4.4 General Guidelines for Root Locus Controller Design
	4.5 Matlab for Root Locus Analysis and Controller Design
		4.5.1 Constructing a Root Locus with Matlab
		4.5.2 Use of Matlab for Designing a Phase Lag Controller
		4.5.3 Use of Matlab for Designing a Phase Lead Controller
	References
5 Frequency Response Methods
	5.1 Frequency Domain Analysis
	5.2 The Nyquist Criterion
		5.2.1 Nyquist Plots
		5.2.2 General Nyquist Criterion
		5.2.3 Stability Margins
	5.3 Bode Diagrams
		5.3.1 Constructing A Bode Diagram
	5.4 Assessing Closed Loop Stability from the Bode Diagram
		5.4.1 Time Delays
	5.5 Dynamic Response from the Bode Diagram
		5.5.1 Closed Loop Frequency Response
	5.6 Steady-State Response from the Bode Diagram
	5.7 Controller Design in the Frequency Domain
		5.7.1 Phase Lag Controllers
		5.7.2 Phase Lead Controllers
		5.7.3 Lead-Lag or PID Controllers
		5.7.4 Summary of Compensator Design in the Frequency Domain
	5.8 Matlab for Frequency Response Analysis and Control Design
		5.8.1 Nyquist Plots
		5.8.2 Bode Plots
		5.8.3 Matlab for Constructing A PD Controller
	References
6 Linear State Space Control Methods
	6.1 Introduction
		6.1.1 State Variables
	6.2 Reachability/Controllability
		6.2.1 Reachable Canonical Form
	6.3 State Feedback
		6.3.1 Where Do I Place the Poles for State Feedback?
		6.3.2 Reachable Canonical Form for State Feedback
		6.3.3 Eigenvalue Assignment
		6.3.4 State Space Integral Control
		6.3.5 Linear Quadratic Regulators
	6.4 Observability
		6.4.1 Observable Canonical Form
	6.5 State Estimation
		6.5.1 Where Do I Place the Observer Poles?
	6.6 Separation Principle
	6.7 Two Degree of Freedom Controllers
	6.8 Linear Disturbance Observer Based Control
	6.9 Matlab for State Space Controller and Observer Design
	References
Part II Nonlinear Methods
7 Nonlinear Stability for Marine Vehicles
	7.1 Introduction
	7.2 Stability of Time–Invariant Nonlinear Systems
		7.2.1 Stability Definitions
		7.2.2 Lyapunov's Second (Direct) Method
	7.3 Invariant Set Theorem
	7.4 Stability of Time–Varying Nonlinear Systems
	7.5 Input-to-State Stability
	7.6 Ultimate Boundedness
	7.7 Practical Stability
	7.8 Barbalat's Lemma
	7.9 Summary
	References
8 Feedback Linearization
	8.1 Introduction
	8.2 Inverse Dynamics
		8.2.1 Body-Fixed Frame Inverse Dynamics
		8.2.2 NED Frame Inverse Dynamics
	8.3 Fundamental Concepts in Feedback Linearization
		8.3.1 Use of a Linearizing Control Law
		8.3.2 Coordinate Transformations for Feedback Linearization
	8.4 Structural Properties of Feedback-Linearizable Systems
		8.4.1 Manifolds, Lie Derivatives, Lie Brackets and Vector Fields
		8.4.2 Frobenius Theorem
	8.5 Input-State Linearization
	8.6 Input-Output Linearization
		8.6.1 Relative Degree
		8.6.2 The Normal Form and Zero Dynamics
		8.6.3 Stabilization
		8.6.4 Tracking
	References
9 Control of Underactuated Marine Vehicles
	9.1 Introduction
	9.2 The Terminology of Underactuated Vehicles
	9.3 Motion Constraints
	9.4 The Dynamics of Underactuated Marine Vehicles
		9.4.1 The Dynamics of Underactuated Surface Vessels
	9.5 Stabilization of Nonholonomic Vehicles
		9.5.1 The Controllability of Nonlinear Systems
		9.5.2 Stabilization of Nonholonomic Systems
		9.5.3 Chained Forms
	9.6 Path-Following Control for Surface Vessels
		9.6.1 Surge Speed Control
		9.6.2 Control of the Cross-Track Error
		9.6.3 Waypoint Switching
		9.6.4 Other Path Following Approaches
	9.7 Trajectory Tracking for Underactuated Surface Vessels
		9.7.1 Point-to-Point Motion Planning
		9.7.2 Desired Heading and Feedforward Control Inputs
	References
10 Integrator Backstepping and Related Techniques
	10.1 Introduction
	10.2 Integrator Backstepping
		10.2.1 A Simple 2-State SISO System
		10.2.2 More General 2-State and 3-State SISO Systems
		10.2.3 Generalized n-State SISO Systems: Recursive Backstepping
		10.2.4 Vectorial Backstepping for MIMO Systems
	10.3 Backstepping for Trajectory Tracking Marine Vehicles
		10.3.1 Straight-Forward Backstepping
		10.3.2 Passivity-Based Backstepping
		10.3.3 Backstepping Implementation Issues
	10.4 Augmented Integrator Backstepping
	10.5 Dynamic Surface Control
		10.5.1 DSC for Trajectory Tracking Marine Vehicles
	10.6 Actuator Constraints
	10.7 Nonlinear Disturbance Observer Based Control
	References
11 Adaptive Control
	11.1 Introduction
	11.2 Model Reference Adaptive Control
	11.3 Adaptive SISO Control via Feedback Linearization
	11.4 Adaptive MIMO Control via Feedback Linearization
	References
12 Sliding Mode Control
	12.1 Introduction
	12.2 Linear Feedback Control Under the Influence of Disturbances
	12.3 First Order Sliding Mode Control
	12.4 Chattering Mitigation
	12.5 Equivalent Control
	12.6 Summary of First Order Sliding Mode Control
	12.7 Stabilization Versus Tracking
	12.8 SISO Super–Twisting Sliding Mode Control
	12.9 MIMO Super-Twisting Sliding Modes
	12.10 Higher Order Sliding Mode Differentiation
	12.11 An HOSM Controller–Observer
	12.12 An HOSM Controller-Observer for Marine Vehicles
	References
Index