Chapter 1
Introduction to Part I

The subject of this book is motion control and hydrodynamics of marine craft. The term marine craft includes ships, high-speed craft, semi-submersibles, floating rigs, submarines, remotely operated and autonomous underwater vehicles, torpedoes, and other propelled and powered structures, for instance a floating air field. Offshore operations involve the use of many marine craft, as shown in Figure 1.1. Vehicles that do not travel on land (ocean and flight vehicles) are usually called craft, such as watercraft, sailcraft, aircraft, hovercraft and spacecraft. The term vessel can be defined as follows:

Vessel: "hollow structure made to float upon the water for purposes of transportation and navigation; especially, one that is larger than a rowboat."

The words vessel, ship and boat are often used interchangeably. In Encyclopedia Britannica, a ship and a boat are distinguished by their size through the following definition:

Ship: "any large floating vessel capable of crossing open waters, as opposed to a boat, which is generally a smaller craft. The term formerly was applied to sailing vessels having three or more masts; in modern times it usually denotes a vessel of more than of displacement. Submersible ships are generally called boats regardless of their size."

Similar definitions are given for submerged vehicles:

Submarine: "any naval vessel that is capable of propelling itself beneath the water as well as on the water's surface. This is a unique capability among warships, and submarines are quite different in design and appearance from surface ships."

Underwater vehicle: "small vehicle that is capable of propelling itself beneath the water surface as well as on the water's surface. This includes unmanned underwater vehicles (UUV), remotely operated vehicles (ROV), autonomous underwater vehicles (AUV) and underwater robotic vehicles (URV). Underwater vehicles are used both commercially and by the navy."

Figure 1.1 Marine craft in operation. Source: illustration by B. Stenberg.

From a hydrodynamic point of view, marine craft can be classified according to their maximum operating speed. For this purpose it is common to use the Froude number

where is the craft speed, is the overall submerged length of the craft and is the acceleration of gravity. The pressure carrying the craft can be divided into hydrostatic and hydrodynamic pressure. The corresponding forces are:

• Buoyancy force due to the hydrostatic pressure (proportional to the displacement of the ship).
• Hydrodynamic force due to the hydrodynamic pressure (approximately proportional to the square of the relative speed to the water).

For a marine craft sailing at constant speed , the following classifications can be made (Faltinsen 2005):

• Displacement vessels (): The buoyancy force (restoring terms) dominates relative to the hydrodynamic forces (added mass and damping).
• Semi-displacement vessel (0.4--1.2): The buoyancy force is not dominant at the maximum operating speed for a high-speed submerged hull type of craft.
• Planing vessel (-1.2): The hydrodynamic force mainly carries the weight. There will be strong flow separation and the aerodynamic lift and drag forces start playing a role.

Figure 1.2 Displacement vessel.

In this book only displacement vessels are covered; see Figure 1.2.

The Froude number has influence on the hydrodynamic analysis. For displacement vessels, the waves radiated by different parts of the hull do not influence other parts of the hull. For semi-displacement vessels, waves generated at the bow influence the hydrodynamic pressure along the hull towards the stern. These characteristics give rise to different modeling hypotheses, which lead to different hydrodynamic theories.

For displacement ships it is widely accepted that two- and three-dimensional potential theory programs are used to compute the potential coefficients and wave loads; see Section 5.1. For semi-displacement vessels and planing vessels it is important to include the lift and drag forces in the computations (Faltinsen 2005).

Degrees of Freedom and Motion of a Marine Craft

In maneuvering, a marine craft experiences motion in six degrees of freedom (DOFs). The DOFs are the set of independent displacements and rotations that specify completely the displaced position and orientation of the craft. The motion in the horizontal plane is referred to as surge (longitudinal motion, usually superimposed on the steady propulsive motion) and sway (sideways motion). Yaw (rotation about the vertical axis) describes the heading of the craft. The remaining three DOFs are roll (rotation about the longitudinal axis), pitch(rotation about the transverse axis) and heave (vertical motion); see Figure 1.3.

Roll motion is probably the most influential DOF with regards to human performance, since it produces the highest accelerations and, hence, is the principal villain in seasickness. Similarly, pitching and heaving feel uncomfortable to people. When designing ship autopilots, yaw is the primary mode for feedback control. Stationkeeping of a marine craft implies stabilization of the surge, sway and yaw motions.

When designing feedback control systems for marine craft, reduced-order models are often used since most craft do not have actuation in all DOFs. This is usually done by decoupling the motions of the craft according to:

Figure 1.3 Motion in six degrees of freedom (DOFs).

• 1-DOF models can be used to design forward speed controllers (surge), heading autopilots (yaw) and roll-damping systems (roll).
• 3-DOF models are usually:
  • Horizontal-plane models (surge, sway and yaw) for ships, semi-submersibles and underwater vehicles that are used in dynamic positioning systems, trajectory-tracking control systems and path-following systems. For slender bodies such as submarines, it is also common to assume that the motions can be decoupled into longitudinal and lateral motions.
  • Longitudinal models (surge, heave and pitch) for forward speed, diving and pitch control.
  • Lateral models (sway, roll and yaw) for turning and heading control.
• 4-DOF models (surge, sway, roll and yaw) are usually formed by adding the roll equation to the 3-DOF horizontal-plane model. These models are used in maneuvering situations where it is important to include the rolling motion, usually in order to reduce roll by active control of fins, rudders or stabilizing liquid tanks.
• 6-DOF models (surge, sway, heave, roll, pitch and yaw) are fully coupled equations of motion used for simulation and prediction of coupled vehicle motions. These models can also be used in advanced control systems for underwater vehicles that are actuated in all DOFs.

1.1 Classification of Models

The models in this book can be used for prediction, real-time simulation, decision-support systems, situational awareness as well as controller-observer design. The complexity and number of differential equations needed for the various purposes will vary. Consequently, one can distinguish between three types of models (see Figure 1.4):

Figure 1.4 Models used in guidance, navigation and control systems.

• Simulation model: This model is the most accurate description of a system, for instance a 6-DOF high-fidelity model for simulation of coupled motions in the time domain. It includes the marine craft dynamics, propulsion system, measurement system and the environmental forces due to wind, waves and ocean currents. It also includes other features not used for control and observer design that have a direct impact on model accuracy. The simulation model should be able to reconstruct the time responses of the real system and it should also be possible to trigger failure modes to simulate events such as accidents and erroneous signals. Simulation models where the fluid-memory effects are included due to frequency-dependent added mass and potential damping typically consist of 50-200 ordinary differential equations (ODEs) while a maneuvering model can be represented in 6 DOFs with 12 ODEs for generalized position and velocity. In addition, some states are needed to describe the environmental forces and actuators, but still the number of states will be less than 50 for a marine craft.
• Control design model: The motion control system is usually designed using a reduced-order or simplified version of the simulation model. In its simplest form, this model is used to compute a set of constant gains for a proportional, integral, derivative (PID) controller. More sophisticated control systems such as model-based control systems use a dynamic model to generate feedforward and feedback signals. The number of ODEs used in conventional model-based ship control systems is usually less than 20. A PID controller typically requires two states: one for the integrator and one for the low-pass filter used...