【Practical Exercise】MATLAB Simulink Ship Dynamic Positioning Simulator

# Introduction to MATLAB Simulink

MATLAB Simulink is a graphical modeling and simulation software developed by MathWorks, widely used in engineering, science, and education. It offers a rich library of modules and simulation environments, enabling engineers to quickly build and simulate complex systems.

The core concept of Simulink is block diagram modeling, where each module represents a specific function or component. Users can create system models by dragging and dropping modules and connecting them. Simulink provides a wide range of module libraries covering signal processing, control systems, dynamics, and communications, among other areas.

In addition, Simulink supports custom module development, allowing users to create their own modules to extend its functionality. This makes Simulink a highly flexible simulation platform capable of meeting various modeling and simulation needs.

# Theoretical Foundation of Marine Dynamic Positioning

### 2.1 Principle of Dynamic Positioning System

A Dynamic Positioning (DP) system is an advanced control system designed to keep a vessel at a specified position and heading, unaffected by external forces such as wind, waves, and currents. DP systems achieve this through the use of thrusters, rudders, and sensors.

**Thrusters and Rudders**

DP systems use thrusters and rudders to generate thrust and torque to control the vessel's movements. Thrusters are typically installed at the bow, stern, and sides of the vessel, while rudders are mounted at the stern.

**Sensors**

DP systems utilize various sensors to measure the vessel's position, heading, and speed. These sensors include:

- **GPS (Global Positioning System):** Used to measure the vessel's absolute position.
- **IMU (Inertial Measurement Unit):** Used to measure the vessel's motion and heading.
- **Anemometer and Wind Vane:** Used to measure wind force.
- **Wave Sensor:** Used to measure wave height and period.

### 2.2 Control Algorithm Design

The control algorithm of the DP system is responsible for calculating the required thrust and torque based on sensor data to keep the vessel at the specified position and heading. The control algorithm typically follows these steps:

1. **Reference Point Calculation:** Calculate the vessel's reference position and heading.
2. **Error Calculation:** Calculate the error between the vessel's current position and heading and the reference point.
3. **Control Law Design:** Design the control law to calculate the required thrust and torque based on the error.
4. **Thrust Allocation:** Allocate the required thrust and torque to the thrusters and rudders.

**Control Law Design**

***mon control laws include:

- **Proportional-Integral-Derivative (PID) Control:** The most commonly used control law, it calculates the control amount based on the error's proportion, integral, and derivative.
- **State Feedback Control:** This control law uses the vessel's state (position, speed, acceleration, etc.) to calculate the control amount.
- **Model Predictive Control:** This control law uses the vessel's mathematical model to predict future movements and calculates the control amount based on these predictions.

**Thrust Allocation**

Thrust allocation is the process of assigning the required thrust and torque to the thrusters and rudders. Thrust allocation algorithms typically consider the following factors:

- **Thruster Efficiency:** Different thrusters have different efficiencies, so it is necessary to consider thruster efficiency to optimize thrust allocation.
- **Vessel Dynamics:** The dynamic characteristics of the vessel (e.g., resistance, inertia) will affect thrust allocation.
- **Safety Constraints:** Thrust allocation must satisfy safety constraints, such as maximum thruster force and maximum rudder angle.

# Simulink Modeling Practices

### 3.1 Establishing a Marine Dynamics Model

**3.1.1 Marine Motion Equations**

The marine dynamics model describes the vessel's motion state under the action of external environmental forces. The motion equations are as follows:

m(u - v) = X_H + X_P + X_R
m(v + u) = Y_H + Y_P + Y_R
I_z(r - p) = N_H + N_P + N_R

Where:

- $m$ is the mass of the vessel
- $u$ is the vessel's longitudinal speed
- $v$ is the vessel's lateral speed
- $r$ is the vessel's heading angular velocity
- $p$ is the vessel's lateral angular velocity
- $X_H$、$Y_H$、$N_H$ are the hydrodynamic forces
- $X_P$、$Y_P$、$N_P$ are the propulsion forces
- $X_R$、$Y_R$、$N_R$ are the damping forces

**3.1.2 Simulink Model Construction**

Based on the marine motion equations, a marine dynamics model can be established in Simulink, as shown in the following figure:

[Image: Marine Dynamics Model Simulink Model]

In the model, the functions of each module are as follows:

- **Hull Dynamics:** Calculates the vessel's hydrodynamic forces
- **Propuls