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Major: Control Engineering and Automation
9 52 02 16


HA NOI – 2019

The thesis was completed at

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

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. 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-

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
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
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

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.
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

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 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. 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. 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:


 RZ , RY , RX ,


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:

n 1

Cn  (Cb )  (Cb )

n T

 RTX , RYT , RZT , .


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]:
  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]:
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

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.

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.
















Figure 2.4.Navigation method for the underwater vehicle
From algorythm we have the following equations:
x  y  z  D1





( x  x2 ) 2  y 2  z 2  D22


( x  x3 ) 2  ( y  y3 ) 2  z 2  D32


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


f 2 ( x, y, z )  ( x  x2 ) 2  y 2  z 2  D22


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




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:

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

 x1  f1 ( x1 )  g1 ( x1 ) x2
 x  f ( x )  g ( x ) x
 i
i 1

 xn  f n ( xn )  g n ( xn )u
 y = x1


In which xn   x1 , x2 ,...xn   R n is the system state vector, u  R is

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

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 ( ))

Combine (1.9) with (3.2) for a system of equations showing the
process of underwater vehicle control

  J ( )

  M (  C ( )  D( )  g ( ))


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

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 or (  d )  0

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


Call  the virtual control vector.The discrepancy between the virtual
control vector and the vector  shall be:

2    


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

V1  1T 1


The input control parameter vector  needs to be defined so that the
following equation is satisfied:

c2 2  M 1 (  C ( )  D ( )  g ( ))    0,


to make this change (3.23) as follows:

M 1 (  C ( )  D( )  g ( ))    c2 2 hoặc:
M 1 (  C ( )  D( )  g ( ))  c2 2  
multiply the two equations (3.32) with the matrix M received:

  C ( )  D( )  g ( )  M (c2 2  )


From (3.25) we have:

  M (c2 2   )  C ( )  D( )  g ( ),


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, V2  0 . In this case, according to the theory of
dynamical stability Lyapunov (3.15), (3.22) will be asymptotic, ie:
1  0,  2  0
This shows that the posture and position of the underwater
vehicle block approach to the set values (desired values).

3.3. Design fuzzy controller and hedge algebra controller for
movement of underwater vehicle
3.3.1. Design fuzzy controller 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
- The waterflow module is used to calibrate AUV position when
the waterflow appears. 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. Hedge algebra and its application in control 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.

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

optimize the parameters of the controller. 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


 (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

 (VVN)   (V N)  sign(VVN)  fm(VVN)  0.5 1  sign(VN ) sign(VVVN)(    )  fm(VVN) 
 i 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
 i1

 1

 ( LN)   (N)  sign( LN)   fm( LN)  0.5 1  sign( LN) sign(VLN)(    )  fm( LN) 

 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 ;


 (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


 ( 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

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.
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


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 



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

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
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


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
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

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

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.

- 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
- 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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