MINISTRY OF EDUCATION AND TRAINING MINISTRY OF NATIONAL DEFENSE

ACADEMY OF MILITARY SCIENCE AND TECHNOLOGY

PHAM VAN PHUC

DESIGN THE ALGORITHMS TO DETECT THE POSITION, STATUS AND

CONTROL THE MOVEMENT OF UNDERWATER VEHICLES

Major: Control Engineering and Automation

Code:

9 52 02 16

SUMMARY OF PhD THESIS IN ENGINEERING

HA NOI – 2019

The thesis was completed at

ACADEMY OF MILITARY SCIENCE AND TECHNOLOGY

Scientific Supervisors:

1. Assoc. Prof. Dr Tran Duc Thuan

2. Dr. Nguyen Quang Vinh

Review 1: Assoc. Prof. Dr. Pham Tuan Thanh

Military Technical Academy

Review 2: Assoc. Prof. Dr. Luu Kim Thanh

Vietnam Maritime University

Review 3: Assoc. Prof. Dr. Nguyen Quang Hung

Academy of Military Science and Technology

The thesis was defended in front of the Doctoral Evaluating Committee at Academy

level held at Academy of Military Science and Technology at ………/………, 2019

The thesis can be found at:

- The Library of Academy of Military Science and Technology

- Vietnam National Library

THE SCIENTIFIC PUBLICATIONS

1. Pham Van Phuc, Nguyen Quang Vinh, Nguyen Đuc Anh, (2015), “ A

system for positioning underwater vehivles based on combination of

IMU and Doppler speed measument enquipment”, The 3rd Vietnam

Conference on Control and Automation, pp. 37-42.

2. Pham Van Phuc, Truong Duy Trung, Nguyen Quang Vinh, (2016), “

Control of the motion orientation and the depth of underwater

vehicles by use of the neural network”, JMST, Academy of Military

Science and Technology, Special number of Rocket, pp.15-22.

3. Pham Van Phuc, Nguyen Quang Vinh, (2017), “The nonlinear

control of underwater vehicles using hedge algebras”, JMST,

Academy of Military Science and Technology, Vol 51, pp.40-45.

4. Pham Van Phuc, Tran Duc Thuan, Nguyen Viet Anh, Nguyen Quang

Vinh, (2018), “An algorithm for determination the location and

position for underwater vehicles”, JMST, Academy of Military

Science and Technology, Vol 56, pp.03-13.

5. Pham Van Phuc, Tran Duc Thuan, Nguyen Quang Vinh, (2018), “A

dynamics model of underwater vehicle”. JMST, Academy of Military

Science and Technology, Vol 58, pp. 14-20.

6. Nguyen Quang Vinh, Pham Van Phuc, (2018), “Control of the

motion orientation of autonomous underwater vehicle”. XIIIth

International Symposium «Intelligent Systems», INTELS’18, 22-24

October 2018, St. Petersburg, Russia. Procedia Computer Science

2018, pp.192-198.

7. Pham Van Phuc, Nguyen Quang Vinh (2019), “Construction of a

backstepping controller for controlling the depth motion of an

automatic underwater vehicle”. The 4th International Conference on

Research in Intelligent and Computing in Engineering, 8-9 August

2019, Hanoi, VietNam. ( Đã có xác nhận đăng)

1

INTRODUCTION

1. The necessity of the thesis

Vietnam is a country with long maritime border and the East Sea

region plays a strategic role especially in marine combat and defense,

as well as connecting with international maritime routes. Nowadays,

exploration and exploitation of marine resources is highly concerned

in many countries. That makes the maritime disputes among

countries becom complicated and consequently threatening the

sovereignty, country security and maritime safety of the region and

the world.

Therefore, it is an urgent requirement to develop combined

weapons that effectively counteract sea attacks in our marintime

territory. It is also nessesary to equip underwater vehicles that

effectively serve the reconnaissance and guard mission as well as,

the exploration, exploitation of our marine resources.

Underwater Vehicles (UV) in the official force of the Navy are

mainly submarines and anti-submarine weapons such as torpedoes,

anti-submarine missiles. There are also small underwater robots that

are used for search rescue and ocean exploration.

The essential components of the UV's control structure are the

navigation system and the control system. The navigation system

conducts the positioning and navigation functions to determine the

position and posture of the UV and then create desired trajectory for

the UV to follow. The control system sends instant control signals

that allow the UV to move in the desired trajectory.

Until now, there are many reports on the studying and developing

the Autonomous Underwater Vehicle (AUV) navigation and control

systems for both military and civilian purposes, as in [3], [16], [17].

These studies have solved some problems in dynamics, motion

control of AUV and Remotely Operated Underwater Vehilce (ROV)

using traditional control theory. The results of the study [17]

suggested the addition the inertial guidance equipment as well as

design an adaptive neuron controller to guide and control anti-

2

submarine weapons. However, in order to efficiently apply the above

results on solving the stability and control problems for AUV, it is

necessary to develop better appropriate controllers and algorithms.

Over the world, there are many countries interested in

developing AUVs with devices for navigation and control. However,

it is difficult for local researchers and system integrators to access

this resource, if any, it is in an improper form with implicit

algorithms.

The above analysis shows the complication of the AUV

navigation and control problem and the urgency to solve those

problem, especially for the military applications. The requirement of

having a modern People's Navy force demands, deep understaning

of the armed weapons and the ablity to repair, improve, upgrade and

manufacture new weapons and underground vehicles. Therefore, the

thesis:''Design the algorithms to detect the position, status and

control the movements of underwater vehicles '' is conducted in

order to contribute to solve the practical problems of the exploitation

and manufacture of underwater vehicles.

2. Research objectives of the thesis

Summarize the algorithms to determine position, status and the

algorithms to control motion trajectories for an underwater vehicle

category.

3. Subjects and scope of research

Research object of the thesis: Control system of an Autonomus

Underwater Vehicle (AUV) with basic specifications as follows: the

total weight of AUV is 20 kg; 1600mm length; 300mm width;

velocity 0.2m/s;100m diving depth; operation time is 10 hours.

4. Research methodology

Research methodology of the thesis: The research combines the

theoretical method and the numerical method.

5. Scientific significance and practical meaning of the thesis

- The research result of the thesis contributes to provide the

scientific knowledge for other research and education in the stability

3

system, controlling the movement trajectory of the underwater

vehicle and the related fields.

- The results of the thesis can be applied to improve and

modernize the existing underwater vehicles as well as design and

manufacture new underwater vehicles.

6. The structure of the thesis

The whole thesis is 109 pages divided in to 4 chapters along

with the Introduction, Conclusion, List of published scientific

works, References and Appendix.

CHAPTER 1: OVERVIEW OF THE UNDERWATER

DEVICES AND RESEARCH PROBLEMS ON

KINEMATICS, POSITIONING AND CONTROL

OF UNDERWATER DEVICES

1.1. Overview of the underwater vehicle

The underwater vehicles began to appear in the early 19th century

at the University of Washington and have made great achievements

during the past decades. Currently, the underwater vehicles are

widely used in many different civilian and military tasks such as

objective monitoring, exploration and exploitation of marine

resources, oceanographic survey, disaster warning, search and

rescue, handling landmines, cleaning contaminated water

environment [3].

Based on the degree of man involve menton the conduction of

underwater vehicles, the underwater vehicles are divided into two

catergories, unmanned underwater vehicles and the unmanned

underwater vehicles, in which the unmanned underwater vehicles

are divided into remotely underwater vehicle (ROV) and autonomous

underwater vehicle (AUV) [14]. The difference between AUV and

ROV is: ROV is connected to the control center with cable or an

audio link in the form of sound waves. Connecting cables ensure the

providing of information and control signals, in this way the operator

can continuously grip and control the vehicle using to the predictable

programs.

4

The underwater vehicle mentioned in this thesis is an AUV that

move three-dimensional space in the water by a pushing system. This

AUV can be used in

ocean research and exploration,

reconnaissance, guard mission in the defined sea region.

1.2. Kinetics and dynamics for underwater vehicles

1.2.1. Reference systems

1.2.1.1. N-frame system

N-frame system is a reference system associated with the earth;

the selected reference origin coincides with the starting point of the

underwater vehicle. Attached to this n-frame system, a Decartes

coordinate system deals with the origin of the coordinate with the

reference root, the axis xof the N-frame system to the geographic

Northern direction, the axis yof the N-frame system to the

geographic Eastern direction, axis xand axisy form a tangent plane to

the Earth's surface.

1.2.1.2. B-frame system

B-frame system is a reference system attached to the selected

reference object and the origin coincides with the center root of the

gravity of the underwater vehicle. Attached to the b-frame system,

the coordinate system with the origin of the coordinate coincides

with the reference origin, the vertical axis 0b X b is directed vertically

of the underwater vehicle, the axis 0b X b is directed downwards and

the axis 0b Yb is directed horizontally that forms the positive triangle.

1.2.1.3. Converting the coordinate system by Ơle corner method

Performing coordinate rotations to convert from the coordinate

system linked to the geographical coordinate system with the

direction Cbn of the Cosin matrix shown in the following form:

n

Cb

RZ , RY , RX ,

(1.5)

The corners , , are called the Ơle corners. Matrix Cbn is an

orthogonal matrix so it can convert a vector from a geographic

coordinate system to a linked coordinate system by a transfer matrix:

5

n 1

Cn (Cb ) (Cb )

b

n T

RTX , RYT , RZT , .

(1.6)

1.2.2. Kinetic model of AUV

The movement of AUV is 6-free-degree movement including 3

vertical movements along 3 orthogonal axes X , Y , Z and 3 rotational

movements around each axis.

(V T , T )T (u , v, w, p , q , r )T ; (1T , 2T )T ( x, y , z , , , )T

The relationship between the vector components in the linked

coordinate system and the geographic coordinate system for the

AUV is [6]:

(1.9)

J ( )

1.2.3. Dynamics of AUV

The nonlinear dynamical equation of AUV in 6-free-degree of the

coordinate system is described as follows [20], [32]:

(1.11)

M C ( ) D( ) g ( ) ,

in which: M M RB M A is an inertial matrix 6 6 consisting of

AUV mass M RB and additional mass M A ;

C ( ) CRB ( ) CA ( ) is the Coriolis matrix and the radial force for

moving the solid object and the additional mass;

D ( ) Dl ( ) Dq ( ) is a hydrodynamic damping matrix 6 6 ; Dl ( )

represents linear damping quantity; Dq ( ) is nonlinear damping

quantity; g ( ) is vector 6 1 of gravitational force; are forces and

floating moments. is the control force vector / torque of the input.

1.3. The positioning and status for moving vehicles

In water, the electromagnetic wave is absorbed; UV can not

receive the signal directly from the GPS to deal the drift of the

measuring elements for the INS device. Therefore, it is necessary to

use additional information from fixed or mobile buoys on the sea

surface to determine the exact position and status of AUV (in case of

using mobile buoys, a satellite navigation device must be attached on

6

the buoy to determine the location and information of coordinates

updated for UV).

1.4. Studies on control for underwwater vehicles

It had been known, designing control systems for AUV faces

many difficulties because it must be closely connected with dynamic

models. So far, there are many different control methods to design

precise motion control system for AUV such as PID control,

adaptive, sliding mode, neural network…

1.5. Conclusion of Chapter 1

Through the overview of UV, kinetic descriptions and studies of

determining position, status and control, some conclusions are shown

as follows:

1. UVs are increasingly used in economy, security and defense.

They are many types of in many types of Uvs with diverse functions.

Navigation and motion control are fundamental for UVs, however

this is issuesare new in Vietnam, especially in the military. In order

to efficiently exploit the existing UVs (mainly the imported) and

even manufacture and design new UV, it is necessary to investigate

the problems related to UV including. Navigation and movement

control of underwater vehicles.

2. Navigation of UV differs from that of others in space, on the

ground, and in water (rivers, lakes and ocean). Therefore, in-depth

research is required to provide the scientific infomation for futher the

exploitation and design as well as manufacture the navigation and

motion control systems for underwater vehicles.

3. In order to improve the quality of motion control for UV, it is

important to study the control nature of UV, new equipments in

Vietnam and to use the modern the oretical control tools to design

the control algorithms for UV. This will serve as basis infomation to

develop softwares for UV control system.

CHAPTER 2: DESIGN THE ALGORYTHM TO DETECT

THE POSITION AND STATUS FOR UV

7

2.1. Sound wave navigation methods

2.1.1. Long Base Line method (LBL)

The Long Base Line (LBL) method uses a set of sound

transceivers fixed known coordinates on the seabed surface. The

signaldata from the underwater vehicle to a defined transceivers with

3 or more distances is used calculate the position of the underwater

vehicle. At that time, the underwater vehicle emits sound signals and

receives feedback signals from these sonar (sound navigation and

ranging) floats.

2.1.2. Short Base Line method (SBL)

Short Base Line (SBL) system uses a sequence of at least 3

transceivers mounted on the underwater vehicle, the distance

between the receivers is about 10 to 50m, the fixed receiver transmitter on the seabed has a predetermined position. In addition to

identifying the distance from the object to the transceivers, the

system can also determine the direction based on the comparison of

the delay time of the signal sent to the transceivers.

2.1.3. Unlike Short Base Line method USBL(USBL)

Unlike Short Base Line system, transceivers are designed and

arranged in a single transceiver that allows easy and convenient

installation for small-sized underwater vehicel. The USBL uses a

series of small transceiver elements with different layout schemes to

determine the distance and azimuth of the response transmitter

mounted on objects need to locate.

2.2. Design the algorithm to detect the position for UV

The center of underground vehicle block coordinates (coordinate

point O ' -origin of coordinate system O ' x ' y ' z ' ) is called ( x, y, z ) ,

D1 is called the distance between the undergwater vehicle and buoy

No.1 (the origin of the coordinate system Oxyz ), D2 , D3 are the

distance measured between the center of mass vehicles and buoys

No.2 and 3, respectively.

8

x"

y3

P1

x3

0

x

x2

P2

P3

x'

y

y"

z

z"

i

i

0'

AUV

y'

z'

Figure 2.4.Navigation method for the underwater vehicle

From algorythm we have the following equations:

x y z D1

2

2

2

2

(2.1)

( x x2 ) 2 y 2 z 2 D22

(2.2)

( x x3 ) 2 ( y y3 ) 2 z 2 D32

(2.3)

Apply Newton-Raphson algorythm from three equations (2.1),

(2.2), (2.3) we setup new three equations:

f1 ( x, y, z ) x 2 y 2 z 2 D12

(2.8)

f 2 ( x, y, z ) ( x x2 ) 2 y 2 z 2 D22

(2.9)

f 3 ( x, y, z ) ( x x3 ) ( y y3 ) z D (2.10)

2

2

2

2

3

Deployment of partial derivatives for functions (2.8), (2.9), (2.10)

setup of the Jacobi matrix form (2.6) and replace (2.11),(2.12),(2.13)

into (2.14) we have the following equation:

2y

2z

2 x

J q 2( x x2 ) 2 y

2 o control the rotation of the steering wheel

and ensure the AUV follow the predetermined calibration trajectory.

A algorithms design for the movement control for the AUV is

classified into two cases: when the kinematic model parameters of

the AUV are clearly defined, the backstepping algorithm is applied

in order to synthesize the controller. When the dynamic model

parameters of the AUV are not determined correctly, the fuzzy

control algorithm and hedge algebra could be used to control the

movement of the AUV.

3.1. Backstepping control theory

The backstepping technique is a recursive design method to

build both feedback control rule and control function Lyapunov in a

systematic way. The backstepping technique divides the n nonlinear

system into the n subsystem, designing the backstepping control

rule and the Lyapunov control function for these subsystems [37].

Consider the non-linear transmission system SISO n steps as

follows:

x1 f1 ( x1 ) g1 ( x1 ) x2

x f ( x ) g ( x ) x

i

i

i

i

i

i 1

,

xn f n ( xn ) g n ( xn )u

y = x1

(3.1)

In which xn x1 , x2 ,...xn R n is the system state vector, u R is

T

the control input of the system, y R is the system output, f i (.) and

12

g i (.) with i 1,2...,n is the known nonlinear parameter functions of

the system. To ensure tight reverse transmission of the system

g i (.) 0. The goal of the problem is to find the control rule u so

that the system is stable, the output of the system as the desired

signal y = x1 xd .

3.2. Design the AUV backstepping movement controller.

From equation (1.11), do the transformation and we have the

following equation:

M 1 ( C( ) D( ) g ( ))

(3.2)

Combine (1.9) with (3.2) for a system of equations showing the

process of underwater vehicle control

J ( )

1

M ( C ( ) D( ) g ( ))

(3.3)

The nature of the underwater vehicle control here is to determine

the rule of changing the torque vector in the system (3.3) so that the

output parameter vector follows the desired value . The desired

d

set of values depends on the specific problem (such as the need to

stabilize the posture while moving in a predetermined trajectory,

etc.), ie it needs to change so that:

d

d or ( d ) 0

(3.4)

From system (3.3) shows that the output parameter vector is

not directly dependent on the input control parameter vector but

depends on the vector . This new vector depends directly on the

input control vector . From this property, the back-stepping

algorithm can be used to synthesize the control law so as to meet

the requirement (3.4). Call the deviation vector

1 d

(3.5)

Call the virtual control vector.The discrepancy between the virtual

control vector and the vector shall be:

13

2

(3.7)

Setup Lyapunov function for dynamical system (1.13) as follows:

1

V1 1T 1

2

(3.8)

The input control parameter vector needs to be defined so that the

following equation is satisfied:

c2 2 M 1 ( C ( ) D ( ) g ( )) 0,

(3.23)

to make this change (3.23) as follows:

M 1 ( C ( ) D( ) g ( )) c2 2 hoặc:

M 1 ( C ( ) D( ) g ( )) c2 2

(3.24)

multiply the two equations (3.32) with the matrix M received:

C ( ) D( ) g ( ) M (c2 2 )

(3.25)

From (3.25) we have:

M (c2 2 ) C ( ) D( ) g ( ),

(3.26)

It is the control rule required to satisfy equation (3.31).

From the expression (3.26), it is necessary to determine the

control law vector in addition to the information 2 , , , and

also need the coefficient c2 . To determine , it needs for a series of

data about vectors according to the expression (3.14) that is to

have information about 1 and must have a coefficient c2

Then determine c1 and c2 per the formula (3.51). Thus, only the

rule of c1 and c2 has been defined to satisfy the requirement under the

condition (3.37), ie, V2 0 . In this case, according to the theory of

dynamical stability Lyapunov (3.15), (3.22) will be asymptotic, ie:

1 0, 2 0

(3.54)

This shows that the posture and position of the underwater

vehicle block approach to the set values (desired values).

14

3.3. Design fuzzy controller and hedge algebra controller for

movement of underwater vehicle

3.3.1. Design fuzzy controller

3.3.1.1. Structure of fuzzy control system for the AUV

AUV control system consists of four modules:

- Speed control module is responsible for controlling the speed of

AUV by setting the motor speed.

- Direction control system isused to control direction and output

for vertical steering wheels.

- The depth control module performs AUV control in the vertical

plane.

- The waterflow module is used to calibrate AUV position when

the waterflow appears.

3.3.1.2. Design fuzzy controller for stable depth for AUV

-The deviation variable has the following forms: Noise Big (NB),

Negative Medium (NM), Negative Small (NS), Zero (Ze), Positive

Small (PS), Positive Medium (PM), Positive Big (PB ).

- Variable "deviation speed" has the following forms: Normal Big

(NB), Normal Medium (NM), Zero (Ze), Positive Medium (PM),

Positive Big (PB).

- It turns out that the control voltage has the following forms:

Noise Big (NB), Normal Medium (NM), Normal Sound (NS), zero

(ZE), Positive Small (PS), Positive Medium (PM), Positive Big (PB).

The control law consists of 35 format rules: if the deviation is NB

and the deviation rate is NB, the voltage is NB.

Select MIN-MAX rule, defuzzification by Wtaver method

(average value).

3.3.2. Design the controller for the underwater vehicle to apply

hedge algebra.

3.3.2.1 Hedge algebra and its application in control

3.3.2.2.Method of design the controller using hedge algebra

The steps to design controllers per hedge algebras as follows:

Step 1: Determine the input and output variables, their variation

domain and the control rule system with language elements in HA.

15

Step 2: Select the structure AX i (i 1 m) and Ay for the variables

and X i và y. Determine the fuzzy parameters of the and the hedge.

Step 3: Calculate quantitative semantic value for language labels in

m 1

the law system. Setup real super S real

.

m 1

Step 4: Select the interpolation method on the super S real

and

optimize the parameters of the controller.

3.2.2.2. Controller design using hedge algebra for movement of AUV

to the depth

The controller has two input variables and one variable as follows:

+ The first input variable of the controller is the difference

between the current depth and the set depth and is denoted E as the

range of variation of [-1, 1].

+ The second input variable is the rate of variation of the depth

(the derivative of the discrepancy) and is denoted IE as the variable

range IE of [-1, 1].

+ The output variable of the controller is the control unit u to

control the voltage of the power source and is denoted U as the

variable range in the range [-2, 2].

Select the element

G = 0,N,W,P,1 and the set of hedge

H - = L ; H + = V .

Select the degree of fuzzy measurement of elements and the degree

of fuzzy measurement of hedges as follows:

v(W) W 0,5; fm( N ) W 0,5; fm( P) 1 0,5 0,5

With the fuzzy parameters selected in Table 3.2 and the

relationship between the hedges, between the hedges with the

elements as shown in Table 3.3, using quantitative semantics, we

calculate the quantitative value of the term the meaning of language

elements in the law table.

(N) W . fm(N) 0,5 0, 45*0,5 0, 275

16

l

(VN) (N) sign(VN) fm(VN) 0.5 1 sign(VN ) sign(VVN)( ) fm(VN)

i 1

0, 275 (1) 0,55.0,5 0,5 1 (1).1.(1).(0,55 0, 45) 0,55.0,5 0, 261

l

(VVN) (V N) sign(VVN) fm(VVN) 0.5 1 sign(VN ) sign(VVVN)( ) fm(VVN)

i 1

1

0, 261 (1) 0,55.0,55.0,5 0.5 1 (1).(1).( 1)(0,55 0, 45).0,55.0,55.0,5 0,194

i1

1

( LN) (N) sign( LN) fm( LN) 0.5 1 sign( LN) sign(VLN)( ) fm( LN)

i

1

0, 275 1.0, 45.0,5 0,5 1 1.( 1).1.(0,55 0, 45) 0, 45.0,5 0, 298

(P) W . fm(P) 0,5 0,5*0, 45 0,725 ;

1

(VP) (P) sign(VP) fm(VP) 0.5 1 sign(VP) sign(VVP)( ) fm(VP)

i 1

0, 725 (1) 0,55.0,5 0,5 1 1.1.1.(0,55 0, 45) 0,55.0,5 0,849

1

(VVP) (VP) sign(VVP) fm(VVP) 0.5 1 sign(VVP) sign(VVVP)( ) fm(VVP)

i 1

0,849 (1) 0,55.0,55.0,5 0,5 1 1.1.1.(0,55 0,45).0,55.0,55.0,5 0,916

1

( LP) (P) sign( LP) fm( LP) 0.5 1 sign( LP) sign(VLP)( ) fm( LP)

i 1

0,849 0, 45.0,5 0,5 1 (1).(1).(1).(0,55 0, 45) 0, 45.0,5 0, 707

Design the quantitative semantic curve: from the values in table

3.7, using the connection AND = MIN

to the meaning

Es AND IEs MIN(Es , IEs ), that each point (Es , IEs Us ) of

table 3.7 brings a point from which the points MIN((Es , IEs ),Us ),

of the quantitative semantic curve above on the basic principles of

average point on table 3.8.

Solve semantic value control u s to get control value u .

Assuming the linguistic variable X belongs to the real range

[x0 x1 ] and its linguistic labels receive quantitative values in the

17

corresponding semantic quantitative range [s0 s1 ] , then the problem

of quantifying the real value and the quantitative solution is done

with defined intervals and the semantic interval of the variables

E, IE, U given by Figure 3.9 per the following formula [61].

3.4. Conclusion of Chapter 3

1. In case the parameters in the model which is used to describe

the underground vehicle are clearly defined, the control rules will

rely on the backstepping algorithm. By demonstrating the additional

clause, it has come up with an explicit formula for choosing the

c1 , c2 coefficients in the backstepping control law to ensure that

underground vehicles follow the desired trajectory and posture.

2. In case the controllers were design using hedge algebras, it

can create an algebraic structure in the form of functional relations

which allows the formation of a large arbitrarily set of linguistic

values to describe in and out relationships. Thus the quality of the

control system is better than the fuzzy control.

The content of chapter 3 is published in the work [02], [03],

[06], [07] and this is the new contribution of the thesis.

CHAPTER 4: THE SIMULATION OF ALGORITHMS FOR

DETECT THE POSITION STATUS AND CONTROL

UNDERWATER VEHICLES

4.1. The simulation determining the position and status for

underwater vehicles

4.1.1. Setup simulation parameters

In order to perform the simulation, it is necessary to create two

vectors, the acceleration vector and the velocity vector. Acceleration

is established with consideration of noise measurement with white

noise (Gauss noise). Suppose the correct initial corners are valid

(0) 500 ; (0) 400 ; (0) 200.

4.1.2. Results of simulation

18

Figure 4.1.Elements a11 , a12 , a13 of the directional Cosine matrix

4.2. The Simulation of the back-stepping motion control of AUV

4.2.1. Simulation of the input control signals

In order to verify the performance of the controller, the thesis

uses model parameters as in documents [21] and [25].

Scenario 1: The law of control is implemented under (3.106)

with c1 , c2 coefficients that are under (3.105).

Figure 4.4 and 4.5.Input force control signals by axis X , Y

Scenario 2: The law of control is implemented under (3.106)

but c1 , c2 coefficients are not under (3.105), we choose c2

3

.

cos

19

Figure 4.8 and 4.9. Input force control signals by axis X , Y

Between the two scenarios shows that the movement of

underground vehicles is still stable, but fluctuates with large

amplitude and time transits. Thus, when choosing the factors that do

not meet the condition (3,105), the control quality of the system

decreases significantly. This shows that proving additional clause

and giving the condition (3.105) is scholarly valid.

4.2.2. The simulation of motion control in depth

The simulation carried out during the period 80s with the inlet

angle of the rudder steering wheel controlled in a pre-set angle s so

that the output system is the angle changed to a lower angle of

inclination. Depth diagram is shown in Figure 4.12.

Figure 4.12.Response system to the control in depth

20

The results show that the pitch angle, in this case, oscillates

around the corner of 900 for 8 seconds and stabilizes at the angle of

900.

4.3. AUV control simulations applying fuzzy controller

The input data is shown as follows: the values of AUV are taken

from a category of underground vehicles (Appendix 1).

Figure 4.15. Result of AUV control in the direction of using FC

The fuzzy controller has the advantage of resisting external

influences as well as the changes in internal parameters which ensure

maintaining the reference trajectory, but time for AUV to stay in

orbit for 8.5s.

4.4. AUV control simulation applying the hedge algebra

With simulation data in cases where the value of AUV is taken

from a category of the underwater vehicles (Appendix 1), the

parameters of the hedge algebra controller are taken as item 3.2:

v(W) W 0,5; fm( N ) W 0,5;

fm( P) 1 0,5 0,5, 0, 45, 0,55

4.4.1 Simulation of AUV control in the direction of HA

Assuming that the moment of 50(s) has white noise impacting

the AUV, then the direction angle shall be deflected from the orbit

angle, since the system uses a hedge algebra controller so it quickly

adapts and after the time of 7.8s, it shall return to the reference

trajectory.

21

Figure 4.17. Response of AUV control in the direction of using HA

4.4.2. Simulation AUV control per the angle HA application

Figure 4.19. Response of AUV control per the angle using hedge

algebra

The simulation results shown in Figure 4.19 show that at the

start of the simulation, the AUV angle does not coincide with the

desired pitch angle, so there is an error of the trajectory, but the

trajectory of the system quickly resists the desired trajectory

response, especially when the moment 50(s) is affected by the noise

due to the HAC controller and the system quickly adheres to the

desired trajectory.

4.4.3. Control simulation shaking angle of hedge algebra

Figure 4.21. Result of AUV control per the angle using HAC

22

4.4.4. Control simulation of hedge algebra application for AUV

in the direction, angle and shaking angle

Figure 4.23.AUV control results applying hedge algebra per the

directional angle, angle and shaking angle

Figure 4.24 Angle deviation at AUV control applying hedge algebra

HA controller for AUV form 6-free-degree has done close

asymptoically to the predetermined trajectory. The proximity cability

23

based on the adaptation to the nonlinear model of AUV is very good,

from 28 seconds onwards; the system almost clings completely to

orbit. HA algorithm allows AUV to follow a continuous trajectory.

4.5. Comparing the simulation result of the motion control AUV

between fuzzy method and HA application

With the input data as Appendix 1, after many times of

experimenting with fuzzy control method and method of controlling

the use of hedge algebra on the same model, the same parameters get

the following results:

Figure 4.26. Simulation of HA/FLC control for AUV

4.6. Conclusion of Chapter 4

1. Backstepping control technique showed the efficiency of

controlling AUV motion according to the reference trajectory.

2. The fuzzy controller satisfied the kinematic requirements.

However, when the parameters of the subject change, the quality of

the system also changes.

3. The controller using hedge algebra to stabilize the motion angle

of AUV, responded effectively to the effects of the external noise,

maintained th orbital deviation and rapid convergence force.

24

CONCLUSION

- Navigation and control to operate underwater vehicles (in the

water environment) is different to navigation and control the vehicle

that operate in space, on land and on the water surface (sea surface,

the surface of rivers and lakes). Therefore, special solutions on both

equipment and scientific research are required for navigation and

control in underwater vehicles. In Vietnam, this field is relatively

new.

- In the case where the parameters of the underwater vehicle are

updated, the backstepping control solution has provided the

trajectory and the position of the vehicle is well set, when selecting a

reasonable coefficient in the control law. By proving additional

clauses, there sults suggested a solution; that helps to determine the

rational coefficients in the backstepping control law.

For cases where the model parameters of the underwater vehicles

are not fully updated, it is possible to use hedge algebra to develop

control algorithms for the movement of the underwater vehicle.

- The simulation results showed the efficiency of the proposed

algorithms: the algorithm to determine the position and status of

underwater vehicles based on negative buoys; the algorithm for

controlling the motion of the underwater vehicles by backstepping,

fuzzy control, and algebraic algebra control.

* New contributions of the thesis

- Had designed an algorithm to determine the position and status

of underwater vehicles using information from the hydroacoustic

navigation buoys.

- Had designed an algorithm to control the movement of

underwater vehicles using backstepping method and hedge algebras.

* Further direction

Deploying experimental algorithms for different types and

gradually develop the theoretical results of the thesis into

applications into implementation especially when improving and

modernizing underwater vehicles.

ACADEMY OF MILITARY SCIENCE AND TECHNOLOGY

PHAM VAN PHUC

DESIGN THE ALGORITHMS TO DETECT THE POSITION, STATUS AND

CONTROL THE MOVEMENT OF UNDERWATER VEHICLES

Major: Control Engineering and Automation

Code:

9 52 02 16

SUMMARY OF PhD THESIS IN ENGINEERING

HA NOI – 2019

The thesis was completed at

ACADEMY OF MILITARY SCIENCE AND TECHNOLOGY

Scientific Supervisors:

1. Assoc. Prof. Dr Tran Duc Thuan

2. Dr. Nguyen Quang Vinh

Review 1: Assoc. Prof. Dr. Pham Tuan Thanh

Military Technical Academy

Review 2: Assoc. Prof. Dr. Luu Kim Thanh

Vietnam Maritime University

Review 3: Assoc. Prof. Dr. Nguyen Quang Hung

Academy of Military Science and Technology

The thesis was defended in front of the Doctoral Evaluating Committee at Academy

level held at Academy of Military Science and Technology at ………/………, 2019

The thesis can be found at:

- The Library of Academy of Military Science and Technology

- Vietnam National Library

THE SCIENTIFIC PUBLICATIONS

1. Pham Van Phuc, Nguyen Quang Vinh, Nguyen Đuc Anh, (2015), “ A

system for positioning underwater vehivles based on combination of

IMU and Doppler speed measument enquipment”, The 3rd Vietnam

Conference on Control and Automation, pp. 37-42.

2. Pham Van Phuc, Truong Duy Trung, Nguyen Quang Vinh, (2016), “

Control of the motion orientation and the depth of underwater

vehicles by use of the neural network”, JMST, Academy of Military

Science and Technology, Special number of Rocket, pp.15-22.

3. Pham Van Phuc, Nguyen Quang Vinh, (2017), “The nonlinear

control of underwater vehicles using hedge algebras”, JMST,

Academy of Military Science and Technology, Vol 51, pp.40-45.

4. Pham Van Phuc, Tran Duc Thuan, Nguyen Viet Anh, Nguyen Quang

Vinh, (2018), “An algorithm for determination the location and

position for underwater vehicles”, JMST, Academy of Military

Science and Technology, Vol 56, pp.03-13.

5. Pham Van Phuc, Tran Duc Thuan, Nguyen Quang Vinh, (2018), “A

dynamics model of underwater vehicle”. JMST, Academy of Military

Science and Technology, Vol 58, pp. 14-20.

6. Nguyen Quang Vinh, Pham Van Phuc, (2018), “Control of the

motion orientation of autonomous underwater vehicle”. XIIIth

International Symposium «Intelligent Systems», INTELS’18, 22-24

October 2018, St. Petersburg, Russia. Procedia Computer Science

2018, pp.192-198.

7. Pham Van Phuc, Nguyen Quang Vinh (2019), “Construction of a

backstepping controller for controlling the depth motion of an

automatic underwater vehicle”. The 4th International Conference on

Research in Intelligent and Computing in Engineering, 8-9 August

2019, Hanoi, VietNam. ( Đã có xác nhận đăng)

1

INTRODUCTION

1. The necessity of the thesis

Vietnam is a country with long maritime border and the East Sea

region plays a strategic role especially in marine combat and defense,

as well as connecting with international maritime routes. Nowadays,

exploration and exploitation of marine resources is highly concerned

in many countries. That makes the maritime disputes among

countries becom complicated and consequently threatening the

sovereignty, country security and maritime safety of the region and

the world.

Therefore, it is an urgent requirement to develop combined

weapons that effectively counteract sea attacks in our marintime

territory. It is also nessesary to equip underwater vehicles that

effectively serve the reconnaissance and guard mission as well as,

the exploration, exploitation of our marine resources.

Underwater Vehicles (UV) in the official force of the Navy are

mainly submarines and anti-submarine weapons such as torpedoes,

anti-submarine missiles. There are also small underwater robots that

are used for search rescue and ocean exploration.

The essential components of the UV's control structure are the

navigation system and the control system. The navigation system

conducts the positioning and navigation functions to determine the

position and posture of the UV and then create desired trajectory for

the UV to follow. The control system sends instant control signals

that allow the UV to move in the desired trajectory.

Until now, there are many reports on the studying and developing

the Autonomous Underwater Vehicle (AUV) navigation and control

systems for both military and civilian purposes, as in [3], [16], [17].

These studies have solved some problems in dynamics, motion

control of AUV and Remotely Operated Underwater Vehilce (ROV)

using traditional control theory. The results of the study [17]

suggested the addition the inertial guidance equipment as well as

design an adaptive neuron controller to guide and control anti-

2

submarine weapons. However, in order to efficiently apply the above

results on solving the stability and control problems for AUV, it is

necessary to develop better appropriate controllers and algorithms.

Over the world, there are many countries interested in

developing AUVs with devices for navigation and control. However,

it is difficult for local researchers and system integrators to access

this resource, if any, it is in an improper form with implicit

algorithms.

The above analysis shows the complication of the AUV

navigation and control problem and the urgency to solve those

problem, especially for the military applications. The requirement of

having a modern People's Navy force demands, deep understaning

of the armed weapons and the ablity to repair, improve, upgrade and

manufacture new weapons and underground vehicles. Therefore, the

thesis:''Design the algorithms to detect the position, status and

control the movements of underwater vehicles '' is conducted in

order to contribute to solve the practical problems of the exploitation

and manufacture of underwater vehicles.

2. Research objectives of the thesis

Summarize the algorithms to determine position, status and the

algorithms to control motion trajectories for an underwater vehicle

category.

3. Subjects and scope of research

Research object of the thesis: Control system of an Autonomus

Underwater Vehicle (AUV) with basic specifications as follows: the

total weight of AUV is 20 kg; 1600mm length; 300mm width;

velocity 0.2m/s;100m diving depth; operation time is 10 hours.

4. Research methodology

Research methodology of the thesis: The research combines the

theoretical method and the numerical method.

5. Scientific significance and practical meaning of the thesis

- The research result of the thesis contributes to provide the

scientific knowledge for other research and education in the stability

3

system, controlling the movement trajectory of the underwater

vehicle and the related fields.

- The results of the thesis can be applied to improve and

modernize the existing underwater vehicles as well as design and

manufacture new underwater vehicles.

6. The structure of the thesis

The whole thesis is 109 pages divided in to 4 chapters along

with the Introduction, Conclusion, List of published scientific

works, References and Appendix.

CHAPTER 1: OVERVIEW OF THE UNDERWATER

DEVICES AND RESEARCH PROBLEMS ON

KINEMATICS, POSITIONING AND CONTROL

OF UNDERWATER DEVICES

1.1. Overview of the underwater vehicle

The underwater vehicles began to appear in the early 19th century

at the University of Washington and have made great achievements

during the past decades. Currently, the underwater vehicles are

widely used in many different civilian and military tasks such as

objective monitoring, exploration and exploitation of marine

resources, oceanographic survey, disaster warning, search and

rescue, handling landmines, cleaning contaminated water

environment [3].

Based on the degree of man involve menton the conduction of

underwater vehicles, the underwater vehicles are divided into two

catergories, unmanned underwater vehicles and the unmanned

underwater vehicles, in which the unmanned underwater vehicles

are divided into remotely underwater vehicle (ROV) and autonomous

underwater vehicle (AUV) [14]. The difference between AUV and

ROV is: ROV is connected to the control center with cable or an

audio link in the form of sound waves. Connecting cables ensure the

providing of information and control signals, in this way the operator

can continuously grip and control the vehicle using to the predictable

programs.

4

The underwater vehicle mentioned in this thesis is an AUV that

move three-dimensional space in the water by a pushing system. This

AUV can be used in

ocean research and exploration,

reconnaissance, guard mission in the defined sea region.

1.2. Kinetics and dynamics for underwater vehicles

1.2.1. Reference systems

1.2.1.1. N-frame system

N-frame system is a reference system associated with the earth;

the selected reference origin coincides with the starting point of the

underwater vehicle. Attached to this n-frame system, a Decartes

coordinate system deals with the origin of the coordinate with the

reference root, the axis xof the N-frame system to the geographic

Northern direction, the axis yof the N-frame system to the

geographic Eastern direction, axis xand axisy form a tangent plane to

the Earth's surface.

1.2.1.2. B-frame system

B-frame system is a reference system attached to the selected

reference object and the origin coincides with the center root of the

gravity of the underwater vehicle. Attached to the b-frame system,

the coordinate system with the origin of the coordinate coincides

with the reference origin, the vertical axis 0b X b is directed vertically

of the underwater vehicle, the axis 0b X b is directed downwards and

the axis 0b Yb is directed horizontally that forms the positive triangle.

1.2.1.3. Converting the coordinate system by Ơle corner method

Performing coordinate rotations to convert from the coordinate

system linked to the geographical coordinate system with the

direction Cbn of the Cosin matrix shown in the following form:

n

Cb

RZ , RY , RX ,

(1.5)

The corners , , are called the Ơle corners. Matrix Cbn is an

orthogonal matrix so it can convert a vector from a geographic

coordinate system to a linked coordinate system by a transfer matrix:

5

n 1

Cn (Cb ) (Cb )

b

n T

RTX , RYT , RZT , .

(1.6)

1.2.2. Kinetic model of AUV

The movement of AUV is 6-free-degree movement including 3

vertical movements along 3 orthogonal axes X , Y , Z and 3 rotational

movements around each axis.

(V T , T )T (u , v, w, p , q , r )T ; (1T , 2T )T ( x, y , z , , , )T

The relationship between the vector components in the linked

coordinate system and the geographic coordinate system for the

AUV is [6]:

(1.9)

J ( )

1.2.3. Dynamics of AUV

The nonlinear dynamical equation of AUV in 6-free-degree of the

coordinate system is described as follows [20], [32]:

(1.11)

M C ( ) D( ) g ( ) ,

in which: M M RB M A is an inertial matrix 6 6 consisting of

AUV mass M RB and additional mass M A ;

C ( ) CRB ( ) CA ( ) is the Coriolis matrix and the radial force for

moving the solid object and the additional mass;

D ( ) Dl ( ) Dq ( ) is a hydrodynamic damping matrix 6 6 ; Dl ( )

represents linear damping quantity; Dq ( ) is nonlinear damping

quantity; g ( ) is vector 6 1 of gravitational force; are forces and

floating moments. is the control force vector / torque of the input.

1.3. The positioning and status for moving vehicles

In water, the electromagnetic wave is absorbed; UV can not

receive the signal directly from the GPS to deal the drift of the

measuring elements for the INS device. Therefore, it is necessary to

use additional information from fixed or mobile buoys on the sea

surface to determine the exact position and status of AUV (in case of

using mobile buoys, a satellite navigation device must be attached on

6

the buoy to determine the location and information of coordinates

updated for UV).

1.4. Studies on control for underwwater vehicles

It had been known, designing control systems for AUV faces

many difficulties because it must be closely connected with dynamic

models. So far, there are many different control methods to design

precise motion control system for AUV such as PID control,

adaptive, sliding mode, neural network…

1.5. Conclusion of Chapter 1

Through the overview of UV, kinetic descriptions and studies of

determining position, status and control, some conclusions are shown

as follows:

1. UVs are increasingly used in economy, security and defense.

They are many types of in many types of Uvs with diverse functions.

Navigation and motion control are fundamental for UVs, however

this is issuesare new in Vietnam, especially in the military. In order

to efficiently exploit the existing UVs (mainly the imported) and

even manufacture and design new UV, it is necessary to investigate

the problems related to UV including. Navigation and movement

control of underwater vehicles.

2. Navigation of UV differs from that of others in space, on the

ground, and in water (rivers, lakes and ocean). Therefore, in-depth

research is required to provide the scientific infomation for futher the

exploitation and design as well as manufacture the navigation and

motion control systems for underwater vehicles.

3. In order to improve the quality of motion control for UV, it is

important to study the control nature of UV, new equipments in

Vietnam and to use the modern the oretical control tools to design

the control algorithms for UV. This will serve as basis infomation to

develop softwares for UV control system.

CHAPTER 2: DESIGN THE ALGORYTHM TO DETECT

THE POSITION AND STATUS FOR UV

7

2.1. Sound wave navigation methods

2.1.1. Long Base Line method (LBL)

The Long Base Line (LBL) method uses a set of sound

transceivers fixed known coordinates on the seabed surface. The

signaldata from the underwater vehicle to a defined transceivers with

3 or more distances is used calculate the position of the underwater

vehicle. At that time, the underwater vehicle emits sound signals and

receives feedback signals from these sonar (sound navigation and

ranging) floats.

2.1.2. Short Base Line method (SBL)

Short Base Line (SBL) system uses a sequence of at least 3

transceivers mounted on the underwater vehicle, the distance

between the receivers is about 10 to 50m, the fixed receiver transmitter on the seabed has a predetermined position. In addition to

identifying the distance from the object to the transceivers, the

system can also determine the direction based on the comparison of

the delay time of the signal sent to the transceivers.

2.1.3. Unlike Short Base Line method USBL(USBL)

Unlike Short Base Line system, transceivers are designed and

arranged in a single transceiver that allows easy and convenient

installation for small-sized underwater vehicel. The USBL uses a

series of small transceiver elements with different layout schemes to

determine the distance and azimuth of the response transmitter

mounted on objects need to locate.

2.2. Design the algorithm to detect the position for UV

The center of underground vehicle block coordinates (coordinate

point O ' -origin of coordinate system O ' x ' y ' z ' ) is called ( x, y, z ) ,

D1 is called the distance between the undergwater vehicle and buoy

No.1 (the origin of the coordinate system Oxyz ), D2 , D3 are the

distance measured between the center of mass vehicles and buoys

No.2 and 3, respectively.

8

x"

y3

P1

x3

0

x

x2

P2

P3

x'

y

y"

z

z"

i

i

0'

AUV

y'

z'

Figure 2.4.Navigation method for the underwater vehicle

From algorythm we have the following equations:

x y z D1

2

2

2

2

(2.1)

( x x2 ) 2 y 2 z 2 D22

(2.2)

( x x3 ) 2 ( y y3 ) 2 z 2 D32

(2.3)

Apply Newton-Raphson algorythm from three equations (2.1),

(2.2), (2.3) we setup new three equations:

f1 ( x, y, z ) x 2 y 2 z 2 D12

(2.8)

f 2 ( x, y, z ) ( x x2 ) 2 y 2 z 2 D22

(2.9)

f 3 ( x, y, z ) ( x x3 ) ( y y3 ) z D (2.10)

2

2

2

2

3

Deployment of partial derivatives for functions (2.8), (2.9), (2.10)

setup of the Jacobi matrix form (2.6) and replace (2.11),(2.12),(2.13)

into (2.14) we have the following equation:

2y

2z

2 x

J q 2( x x2 ) 2 y

2 o control the rotation of the steering wheel

and ensure the AUV follow the predetermined calibration trajectory.

A algorithms design for the movement control for the AUV is

classified into two cases: when the kinematic model parameters of

the AUV are clearly defined, the backstepping algorithm is applied

in order to synthesize the controller. When the dynamic model

parameters of the AUV are not determined correctly, the fuzzy

control algorithm and hedge algebra could be used to control the

movement of the AUV.

3.1. Backstepping control theory

The backstepping technique is a recursive design method to

build both feedback control rule and control function Lyapunov in a

systematic way. The backstepping technique divides the n nonlinear

system into the n subsystem, designing the backstepping control

rule and the Lyapunov control function for these subsystems [37].

Consider the non-linear transmission system SISO n steps as

follows:

x1 f1 ( x1 ) g1 ( x1 ) x2

x f ( x ) g ( x ) x

i

i

i

i

i

i 1

,

xn f n ( xn ) g n ( xn )u

y = x1

(3.1)

In which xn x1 , x2 ,...xn R n is the system state vector, u R is

T

the control input of the system, y R is the system output, f i (.) and

12

g i (.) with i 1,2...,n is the known nonlinear parameter functions of

the system. To ensure tight reverse transmission of the system

g i (.) 0. The goal of the problem is to find the control rule u so

that the system is stable, the output of the system as the desired

signal y = x1 xd .

3.2. Design the AUV backstepping movement controller.

From equation (1.11), do the transformation and we have the

following equation:

M 1 ( C( ) D( ) g ( ))

(3.2)

Combine (1.9) with (3.2) for a system of equations showing the

process of underwater vehicle control

J ( )

1

M ( C ( ) D( ) g ( ))

(3.3)

The nature of the underwater vehicle control here is to determine

the rule of changing the torque vector in the system (3.3) so that the

output parameter vector follows the desired value . The desired

d

set of values depends on the specific problem (such as the need to

stabilize the posture while moving in a predetermined trajectory,

etc.), ie it needs to change so that:

d

d or ( d ) 0

(3.4)

From system (3.3) shows that the output parameter vector is

not directly dependent on the input control parameter vector but

depends on the vector . This new vector depends directly on the

input control vector . From this property, the back-stepping

algorithm can be used to synthesize the control law so as to meet

the requirement (3.4). Call the deviation vector

1 d

(3.5)

Call the virtual control vector.The discrepancy between the virtual

control vector and the vector shall be:

13

2

(3.7)

Setup Lyapunov function for dynamical system (1.13) as follows:

1

V1 1T 1

2

(3.8)

The input control parameter vector needs to be defined so that the

following equation is satisfied:

c2 2 M 1 ( C ( ) D ( ) g ( )) 0,

(3.23)

to make this change (3.23) as follows:

M 1 ( C ( ) D( ) g ( )) c2 2 hoặc:

M 1 ( C ( ) D( ) g ( )) c2 2

(3.24)

multiply the two equations (3.32) with the matrix M received:

C ( ) D( ) g ( ) M (c2 2 )

(3.25)

From (3.25) we have:

M (c2 2 ) C ( ) D( ) g ( ),

(3.26)

It is the control rule required to satisfy equation (3.31).

From the expression (3.26), it is necessary to determine the

control law vector in addition to the information 2 , , , and

also need the coefficient c2 . To determine , it needs for a series of

data about vectors according to the expression (3.14) that is to

have information about 1 and must have a coefficient c2

Then determine c1 and c2 per the formula (3.51). Thus, only the

rule of c1 and c2 has been defined to satisfy the requirement under the

condition (3.37), ie, V2 0 . In this case, according to the theory of

dynamical stability Lyapunov (3.15), (3.22) will be asymptotic, ie:

1 0, 2 0

(3.54)

This shows that the posture and position of the underwater

vehicle block approach to the set values (desired values).

14

3.3. Design fuzzy controller and hedge algebra controller for

movement of underwater vehicle

3.3.1. Design fuzzy controller

3.3.1.1. Structure of fuzzy control system for the AUV

AUV control system consists of four modules:

- Speed control module is responsible for controlling the speed of

AUV by setting the motor speed.

- Direction control system isused to control direction and output

for vertical steering wheels.

- The depth control module performs AUV control in the vertical

plane.

- The waterflow module is used to calibrate AUV position when

the waterflow appears.

3.3.1.2. Design fuzzy controller for stable depth for AUV

-The deviation variable has the following forms: Noise Big (NB),

Negative Medium (NM), Negative Small (NS), Zero (Ze), Positive

Small (PS), Positive Medium (PM), Positive Big (PB ).

- Variable "deviation speed" has the following forms: Normal Big

(NB), Normal Medium (NM), Zero (Ze), Positive Medium (PM),

Positive Big (PB).

- It turns out that the control voltage has the following forms:

Noise Big (NB), Normal Medium (NM), Normal Sound (NS), zero

(ZE), Positive Small (PS), Positive Medium (PM), Positive Big (PB).

The control law consists of 35 format rules: if the deviation is NB

and the deviation rate is NB, the voltage is NB.

Select MIN-MAX rule, defuzzification by Wtaver method

(average value).

3.3.2. Design the controller for the underwater vehicle to apply

hedge algebra.

3.3.2.1 Hedge algebra and its application in control

3.3.2.2.Method of design the controller using hedge algebra

The steps to design controllers per hedge algebras as follows:

Step 1: Determine the input and output variables, their variation

domain and the control rule system with language elements in HA.

15

Step 2: Select the structure AX i (i 1 m) and Ay for the variables

and X i và y. Determine the fuzzy parameters of the and the hedge.

Step 3: Calculate quantitative semantic value for language labels in

m 1

the law system. Setup real super S real

.

m 1

Step 4: Select the interpolation method on the super S real

and

optimize the parameters of the controller.

3.2.2.2. Controller design using hedge algebra for movement of AUV

to the depth

The controller has two input variables and one variable as follows:

+ The first input variable of the controller is the difference

between the current depth and the set depth and is denoted E as the

range of variation of [-1, 1].

+ The second input variable is the rate of variation of the depth

(the derivative of the discrepancy) and is denoted IE as the variable

range IE of [-1, 1].

+ The output variable of the controller is the control unit u to

control the voltage of the power source and is denoted U as the

variable range in the range [-2, 2].

Select the element

G = 0,N,W,P,1 and the set of hedge

H - = L ; H + = V .

Select the degree of fuzzy measurement of elements and the degree

of fuzzy measurement of hedges as follows:

v(W) W 0,5; fm( N ) W 0,5; fm( P) 1 0,5 0,5

With the fuzzy parameters selected in Table 3.2 and the

relationship between the hedges, between the hedges with the

elements as shown in Table 3.3, using quantitative semantics, we

calculate the quantitative value of the term the meaning of language

elements in the law table.

(N) W . fm(N) 0,5 0, 45*0,5 0, 275

16

l

(VN) (N) sign(VN) fm(VN) 0.5 1 sign(VN ) sign(VVN)( ) fm(VN)

i 1

0, 275 (1) 0,55.0,5 0,5 1 (1).1.(1).(0,55 0, 45) 0,55.0,5 0, 261

l

(VVN) (V N) sign(VVN) fm(VVN) 0.5 1 sign(VN ) sign(VVVN)( ) fm(VVN)

i 1

1

0, 261 (1) 0,55.0,55.0,5 0.5 1 (1).(1).( 1)(0,55 0, 45).0,55.0,55.0,5 0,194

i1

1

( LN) (N) sign( LN) fm( LN) 0.5 1 sign( LN) sign(VLN)( ) fm( LN)

i

1

0, 275 1.0, 45.0,5 0,5 1 1.( 1).1.(0,55 0, 45) 0, 45.0,5 0, 298

(P) W . fm(P) 0,5 0,5*0, 45 0,725 ;

1

(VP) (P) sign(VP) fm(VP) 0.5 1 sign(VP) sign(VVP)( ) fm(VP)

i 1

0, 725 (1) 0,55.0,5 0,5 1 1.1.1.(0,55 0, 45) 0,55.0,5 0,849

1

(VVP) (VP) sign(VVP) fm(VVP) 0.5 1 sign(VVP) sign(VVVP)( ) fm(VVP)

i 1

0,849 (1) 0,55.0,55.0,5 0,5 1 1.1.1.(0,55 0,45).0,55.0,55.0,5 0,916

1

( LP) (P) sign( LP) fm( LP) 0.5 1 sign( LP) sign(VLP)( ) fm( LP)

i 1

0,849 0, 45.0,5 0,5 1 (1).(1).(1).(0,55 0, 45) 0, 45.0,5 0, 707

Design the quantitative semantic curve: from the values in table

3.7, using the connection AND = MIN

to the meaning

Es AND IEs MIN(Es , IEs ), that each point (Es , IEs Us ) of

table 3.7 brings a point from which the points MIN((Es , IEs ),Us ),

of the quantitative semantic curve above on the basic principles of

average point on table 3.8.

Solve semantic value control u s to get control value u .

Assuming the linguistic variable X belongs to the real range

[x0 x1 ] and its linguistic labels receive quantitative values in the

17

corresponding semantic quantitative range [s0 s1 ] , then the problem

of quantifying the real value and the quantitative solution is done

with defined intervals and the semantic interval of the variables

E, IE, U given by Figure 3.9 per the following formula [61].

3.4. Conclusion of Chapter 3

1. In case the parameters in the model which is used to describe

the underground vehicle are clearly defined, the control rules will

rely on the backstepping algorithm. By demonstrating the additional

clause, it has come up with an explicit formula for choosing the

c1 , c2 coefficients in the backstepping control law to ensure that

underground vehicles follow the desired trajectory and posture.

2. In case the controllers were design using hedge algebras, it

can create an algebraic structure in the form of functional relations

which allows the formation of a large arbitrarily set of linguistic

values to describe in and out relationships. Thus the quality of the

control system is better than the fuzzy control.

The content of chapter 3 is published in the work [02], [03],

[06], [07] and this is the new contribution of the thesis.

CHAPTER 4: THE SIMULATION OF ALGORITHMS FOR

DETECT THE POSITION STATUS AND CONTROL

UNDERWATER VEHICLES

4.1. The simulation determining the position and status for

underwater vehicles

4.1.1. Setup simulation parameters

In order to perform the simulation, it is necessary to create two

vectors, the acceleration vector and the velocity vector. Acceleration

is established with consideration of noise measurement with white

noise (Gauss noise). Suppose the correct initial corners are valid

(0) 500 ; (0) 400 ; (0) 200.

4.1.2. Results of simulation

18

Figure 4.1.Elements a11 , a12 , a13 of the directional Cosine matrix

4.2. The Simulation of the back-stepping motion control of AUV

4.2.1. Simulation of the input control signals

In order to verify the performance of the controller, the thesis

uses model parameters as in documents [21] and [25].

Scenario 1: The law of control is implemented under (3.106)

with c1 , c2 coefficients that are under (3.105).

Figure 4.4 and 4.5.Input force control signals by axis X , Y

Scenario 2: The law of control is implemented under (3.106)

but c1 , c2 coefficients are not under (3.105), we choose c2

3

.

cos

19

Figure 4.8 and 4.9. Input force control signals by axis X , Y

Between the two scenarios shows that the movement of

underground vehicles is still stable, but fluctuates with large

amplitude and time transits. Thus, when choosing the factors that do

not meet the condition (3,105), the control quality of the system

decreases significantly. This shows that proving additional clause

and giving the condition (3.105) is scholarly valid.

4.2.2. The simulation of motion control in depth

The simulation carried out during the period 80s with the inlet

angle of the rudder steering wheel controlled in a pre-set angle s so

that the output system is the angle changed to a lower angle of

inclination. Depth diagram is shown in Figure 4.12.

Figure 4.12.Response system to the control in depth

20

The results show that the pitch angle, in this case, oscillates

around the corner of 900 for 8 seconds and stabilizes at the angle of

900.

4.3. AUV control simulations applying fuzzy controller

The input data is shown as follows: the values of AUV are taken

from a category of underground vehicles (Appendix 1).

Figure 4.15. Result of AUV control in the direction of using FC

The fuzzy controller has the advantage of resisting external

influences as well as the changes in internal parameters which ensure

maintaining the reference trajectory, but time for AUV to stay in

orbit for 8.5s.

4.4. AUV control simulation applying the hedge algebra

With simulation data in cases where the value of AUV is taken

from a category of the underwater vehicles (Appendix 1), the

parameters of the hedge algebra controller are taken as item 3.2:

v(W) W 0,5; fm( N ) W 0,5;

fm( P) 1 0,5 0,5, 0, 45, 0,55

4.4.1 Simulation of AUV control in the direction of HA

Assuming that the moment of 50(s) has white noise impacting

the AUV, then the direction angle shall be deflected from the orbit

angle, since the system uses a hedge algebra controller so it quickly

adapts and after the time of 7.8s, it shall return to the reference

trajectory.

21

Figure 4.17. Response of AUV control in the direction of using HA

4.4.2. Simulation AUV control per the angle HA application

Figure 4.19. Response of AUV control per the angle using hedge

algebra

The simulation results shown in Figure 4.19 show that at the

start of the simulation, the AUV angle does not coincide with the

desired pitch angle, so there is an error of the trajectory, but the

trajectory of the system quickly resists the desired trajectory

response, especially when the moment 50(s) is affected by the noise

due to the HAC controller and the system quickly adheres to the

desired trajectory.

4.4.3. Control simulation shaking angle of hedge algebra

Figure 4.21. Result of AUV control per the angle using HAC

22

4.4.4. Control simulation of hedge algebra application for AUV

in the direction, angle and shaking angle

Figure 4.23.AUV control results applying hedge algebra per the

directional angle, angle and shaking angle

Figure 4.24 Angle deviation at AUV control applying hedge algebra

HA controller for AUV form 6-free-degree has done close

asymptoically to the predetermined trajectory. The proximity cability

23

based on the adaptation to the nonlinear model of AUV is very good,

from 28 seconds onwards; the system almost clings completely to

orbit. HA algorithm allows AUV to follow a continuous trajectory.

4.5. Comparing the simulation result of the motion control AUV

between fuzzy method and HA application

With the input data as Appendix 1, after many times of

experimenting with fuzzy control method and method of controlling

the use of hedge algebra on the same model, the same parameters get

the following results:

Figure 4.26. Simulation of HA/FLC control for AUV

4.6. Conclusion of Chapter 4

1. Backstepping control technique showed the efficiency of

controlling AUV motion according to the reference trajectory.

2. The fuzzy controller satisfied the kinematic requirements.

However, when the parameters of the subject change, the quality of

the system also changes.

3. The controller using hedge algebra to stabilize the motion angle

of AUV, responded effectively to the effects of the external noise,

maintained th orbital deviation and rapid convergence force.

24

CONCLUSION

- Navigation and control to operate underwater vehicles (in the

water environment) is different to navigation and control the vehicle

that operate in space, on land and on the water surface (sea surface,

the surface of rivers and lakes). Therefore, special solutions on both

equipment and scientific research are required for navigation and

control in underwater vehicles. In Vietnam, this field is relatively

new.

- In the case where the parameters of the underwater vehicle are

updated, the backstepping control solution has provided the

trajectory and the position of the vehicle is well set, when selecting a

reasonable coefficient in the control law. By proving additional

clauses, there sults suggested a solution; that helps to determine the

rational coefficients in the backstepping control law.

For cases where the model parameters of the underwater vehicles

are not fully updated, it is possible to use hedge algebra to develop

control algorithms for the movement of the underwater vehicle.

- The simulation results showed the efficiency of the proposed

algorithms: the algorithm to determine the position and status of

underwater vehicles based on negative buoys; the algorithm for

controlling the motion of the underwater vehicles by backstepping,

fuzzy control, and algebraic algebra control.

* New contributions of the thesis

- Had designed an algorithm to determine the position and status

of underwater vehicles using information from the hydroacoustic

navigation buoys.

- Had designed an algorithm to control the movement of

underwater vehicles using backstepping method and hedge algebras.

* Further direction

Deploying experimental algorithms for different types and

gradually develop the theoretical results of the thesis into

applications into implementation especially when improving and

modernizing underwater vehicles.

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