Báo cáo nghiên cứu khoa học: Student research report submarine model and optimized control system

Linear control method for Autonomous Underwater Vehicle .... Chapter I: An overview of the Autonomous Underwater Vehicle: System and Control method Abstract - This research paper focuses

INTERNATIONAL SCHOOL

STUDENT RESEARCH REPORT

SUBMARINE MODEL AND OPTIMIZED

CONTROL SYSTEM

Team Leader: Tran The Bach

ID: 23070105 Class: AAI2023 Team Advisor: Ph.D Le Xuan Hai

Hanoi, 15 th April, 2024

TEAM LEADER INFORMATION

- Address: Nam Tu Liem, Hanoi

- Phone no./Email: 0981364668 / thebach25@gmail.com

II Project Name and Code:

Project Name: Submarine Model and Optimized Control System

Code: CN.NC.SV.23_54

Team Members (no more than 5 people):

1 Trần Thế Bách 23070105 AAI2023A 0981364668 23070105@vnu.edu.vn

2 Phạm Đức Hoàng 23070032 AAI2023A 0852291974 23070032@vnu.edu.vn

3 Nguyễn Minh Hiếu 23070059 AAI2023A 0855053155 23070059@vnu.edu.vn

4 Triệu Vy 23070130 AAI2023A 0345841844 23070130@vnu.edu.vn

5 Hoàng Gia Bảo 23070423 ISEL2023A 0987662473 23070423@vnu.edu.vn Advisors (fullname, academic rank, academic degree):

1 Ts Lê Xuân Hải Khoa Các Khoa học ứng dụng 035580888 hailx@vnu.edu.vn

Advisor

Lê Xuân Hải

Research group

Trần Thế Bách

Table of Contents

Chapter I: An overview of the Autonomous Underwater Vehicle: System and Control

method 3

1.1 Motivations 3

1.2 Objectives of research topic 4

1.3 Research methods 4

1.3.1 Optimized Control System 5

1.4 Conclusion 5

Chapter II: Modeling of the Autonomous Underwater Vehicle 6

2.1 Modeling Assumptions 6

2.1.1 Environmental Assumptions 6

2.1.2 Dynamics Assumptions 6

2.1.3 6-DOF Rigid-Body Equations of Motion 6

2.1.4 Coordinate Frames 7

2.2 Parameters and symbols in the AUV 8

2.2.1 Newtonian and Lagrangian Mechanics 9

2.2.2 Hydrostatic Forces and Moments 11

2.2.3 Gravitational Forces 12

2.2.4 Added Mass and Inertia 14

2.2.5 Propeller Effect 14

Chapter III: Control method for Autonomous Underwater Vehicle 15

3.1 Linear control method for Autonomous Underwater Vehicle 15

3.1.1 Theoretical basis of linear control 15

3.1.2 PID Control 17

3.2 Optimized Control 20

3.2.1 Heuristic Method 20

3.2.1 PSO Result and Simulation 21

4 Conclusion 23

REFERENCES 24

Chapter I: An overview of the Autonomous Underwater Vehicle: System and Control method

Abstract - This research paper focuses on the control of Autonomous Underwater Vehicles (AUVs) in challenging underwater environments AUVs are unmanned underwater vehicles designed to perform tasks autonomously, without human intervention The paper addresses the challenges associated with controlling the heave and pitch movements of AUVs Proportional-Integral-Derivative (PID) control, a widely used control technique, is employed

to regulate the AUV's motion To enhance the performance of the PID controller, the optimization of its parameters is conducted using heuristic methods, namely Particle Swarm Optimization (PSO) The MATLAB/Simulink software is utilized for simulations, demonstrating the effectiveness of the proposed Heuristic Control approach The results showcase improved control performance and highlight the potential of this approach for enhancing the maneuverability and stability of AUVs in real-life scenarios

Keywords - AUV(Autonomous Underwater Vehicles), Heuristic methods, PID controller, Optimize control system

Research on submarines plays a crucial and necessary role in various fields From deep-sea exploration to military and technology applications, understanding and studying submarines provide profound knowledge and wide-ranging applications With the ability to operate underwater and withstand extreme pressure, submarines represent the marvel of human capabilities in conquering the marine environment

With their ability to dive deep and transport nuclear weapons, military submarines have become an indispensable part of many countries' defense strategies Understanding the technology, tactics, and capabilities of submarines helps policymakers ensure safety and influence in a dangerous and competitive maritime environment

Furthermore, research on submarines also contributes significantly to the discovery of scientific knowledge at the bottom of the ocean With over two-thirds of Earth's surface covered by the ocean, only a small portion of it has been explored and understood Submarines provide the capability to access deep-sea regions where unique ecosystems exist Research

on submarines helps us explore and gain a better understanding of marine life, human impacts, and the role of the ocean in the global ecosystem

Moreover, submarine research contributes to technological development and progress From high-pressure-resistant materials to automated control systems, technologies related to submarines require continuous research and innovation Submarine research opens up opportunities for developing new technologies, improving performance and safety, and achieving significant advancements in this field

By combining elements of security, science, and technology, research on submarines not only provides vital knowledge but also creates significant achievements for humanity Understanding submarines is an engaging and crucial journey that contributes to our development and understanding of an essential part of our planet - the ocean

The linear control method is based on the assumption that the submarine system can

be modeled using linear differential equations, and the interactions between the system components are linear This allows the application of linear control methods such as PID (Proportional-Integral-Derivative) control

PID control is a widely used control technique known for its effectiveness in multiple control system applications By utilizing PID control, the researchers aim to regulate the motion of AUVs, ensuring stability and precise maneuverability in underwater environments The optimization of PID parameters using Heuristic methods, such as Particle Swarm Optimization (PSO), further enhances the performance of the PID controller The objective is

to improve the control accuracy and response of AUVs, ultimately contributing to the advancement of submarine research and the effectiveness of AUV operations in real-life scenarios

The linear control method is based on the assumption that the submarine system can

be modeled using linear differential equations, and the interactions between the system components are linear This allows the application of linear control methods such as PID (Proportional-Integral-Derivative) control

PID control is a widely used control technique known for its effectiveness in multiple control system applications By utilizing PID control, the researchers aim to regulate the motion of AUVs, ensuring stability and precise maneuverability in underwater environments The optimization of PID parameters using Heuristic methods, such as Particle Swarm Optimization (PSO) and Ant Colony Optimization (ACO), further enhances the performance

of the PID controller The objective is to improve the control accuracy and response of AUVs, ultimately contributing to the advancement of submarine research and the effectiveness of AUV operations in real-life scenarios

1.3.1 Optimized Control System

An optimized control system using heuristic methods is developed to enhance a submarine's performance in various conditions The focus is on maximizing maneuverability, stability, and efficiency through intelligent optimization techniques like Particle Swarm Optimization (PSO) These methods iteratively search for optimal control parameters, considering factors such as accurate positioning, stable motion, and energy efficiency Simulation results using MATLAB/Simulink show improved performance in terms of maneuverability, stability, and response time Heuristic methods offer advantages by exploring a wide range of parameter combinations and enabling real-time adaptation The research contributes to advancing submarine control systems and improving operational capabilities, safety, and effectiveness in complex maritime environments

In conclusion, this research paper has presented a heuristic control approach for Autonomous Underwater Vehicles (AUVs) with a focus on optimizing the PID parameters using Particle Swarm Optimization (PSO) techniques The utilization of PSO algorithms has successfully optimized the PID parameters, leading to enhanced maneuverability and stability

of AUVs in real-life scenarios The findings of this study contribute to the advancement of AUV control systems, offering insights into improving the autonomous operation of AUVs and their effectiveness in complex underwater environments Future research can explore further enhancements to the heuristic control approach and investigate its applicability to other control parameters and AUV motion dynamics

Chapter II: Modeling of the Autonomous Underwater Vehicle

 The AUV does not experience underwater currents

2.1.2 Dynamics Assumptions

In dynamic modeling of AUV, the following assumptions are used:

 The AUV behaves as a rigid body of a constant mass

 The earth’s rotation is negligible for acceleration components of the vehicle’s center

of mass

 The primary forces that act on the AUV are inertial and gravitational in the center of buoyancy and are derived from hydrostatic, propulsion, thruster, and hydrodynamic lift and drag forces

 The thruster assumption is that it uses an extremely simple propulsion model, which treats the vehicle propeller as a source of constant thrust and torque

2.1.3 6-DOF Rigid-Body Equations of Motion

 AUVs move in six degrees of freedom (6-DOF) since six independent coordinates are necessary to determine the position and orientation angle of a rigid body dynamics The first three coordinates and their time derivatives are based off of translational motion along the x, y and z-axes, while the last three coordinates (ϕ,θ,ψ) and their time derivatives are used to describe orientation angle and rotational motion

 Velocity and angular velocity components of the AUV relative to the body axes (x,y,z) are denoted by the velocity of surge, sway, heave motion, (u,v,w) and angular velocity

of roll, pitch, and yaw motion(p,q,r), respectively X, Y, Z, K, M and N represent the resultant forces and moments with respect to the x, y, and z axis For AUVs, it is common to use the SNAME notation In Table 1 below, the six different translational

and rotational motion components are defined as: surge, sway, heave, roll, pitch and yaw, respectively

of AUV can be seen on:

figure 1 6 DOF Navigation Frames

figure 2 6 DOF modeling of the submarine

Based Newton Law, the mathematical model of AUV can be constructed as follows:

2.2 Parameters and symbols in the AUV

The parameters and symbols of the AUV through Figure 1 and the meaning of those parameters and symbols are given in Table 1

Table 1 Parameters and symbols nomencalutures

Another modeling approach is the Newtonian-Euler formulation, which is based on Newton’s Second Law that relates mass (m), acceleration (a) and force (F) Euler

suggested expressing Newton's Second Law in terms of conservation of both linear and angular momentum The forces (F) and moments (M) refers to the body's center of gravity

In this study, the dynamic behavior of an AUV is described through Newton's laws of linear and angular momentum Newton’s Second Law is expressed as:

It is convenient to regard the sums of applied torque (M) and force (F) as consisting of

an equilibrium point and a perturbational component Thus, assuming constant AUV mass

Furthermore, since the axis system being used as an inertial reference system is the Earth fixed coordinate system, Equations and can be expressed as

( ) ( ) ( ) ( ) ( ( ) ( ))( ) ( ) ( ) ( ) ( ( ) (

where Iii denotes a moment of inertia, and Iij a product of inertia j ≠ i In this chapter,

we assume that the AUV is symmetrical along the XY and XZ planes, therefore cross inertia parameters become:

When an AUV is submerged in a fluid under the effect of gravity, two forces act on the vehicle: the gravitational force, which is mentioned in the previous sub-section and the buoyancy, which is called “hydrostatic effect”

The buoyant force acting on the center of buoyancy (CB) is represented in body-fixed frame (figure 1) It can be recognized that the difference between gravity and buoyancy (WB) only affects the linear force acting on the vehicle It is also clear that the restoring linear force is constant in the Earth-fixed frame On the other hand, the two vectors of the first moment of inertia W and B affect the momentum acting on the vehicle and are constant in the body-fixed frame A solid body submerged in a fluid will have upward buoyant force acting on it equivalent to the weight of displaced fluid, enabling it to float

or at least appear to become lighter If the buoyancy exceeds the weight, then the object floats; if the weight exceeds the buoyancy, the object sinks If the buoyancy equals the weight, the body has neutral buoyancy and may remain at its level Discovery of the principle of buoyancy, which is a result of the hydrostatic pressure in the fluid, is attributed to Archimedes

In pitch moment equation, consider equation:

( ) ( ) ( ) ( )( ( ) ( ))

Therefore, for the body axis system, gravity contributes only to the external force vector F Three components of the gravitational force in the body frame depend on the AUV’s attitude relative to an inertia frame The gravitational force acting upon an AUV is most obviously expressed in terms of the Earth’s axes With respect to these axes, the

gravity vector mg, is directed along the Ze axis The gravitational acceleration forces and moments are represented by the weight minus buoyancy (W−B) and weight moment terms respectively

The added ( z W zG  B) in right side and fin as control unit M then state equation

in pitch moment becomes:

By ignoring surge, sway, roll and yaw, the variables v = r = p = ϕ = ψ = y = 0

Heave force Z can be expanded as Z  Z q Z q Z w Z wq  q  w   w then heave force equation becomes:

2

With is added mass due to pitch rate, is added mass due to heave velocity, is coefficient

of heave force induced by pitch rate, is coefficient of heave force induced by heave velocity The added fin as control unit Z then state equation in heave force becomes:

2 ( Zq mx qG)   ( Zw  m w )    muq mz q  G  Z q Z w Zq  w   (1.22)

From equation (8) and (10), we obtain nonlinear system and the state space model of AUV is: