Experimental Buoyancy Control for a Spherical Underwater ...
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Journal of Control, Robotics and Mechatronic Systems, Vol. 1 (1) 42-52, September, 2015
ISSN: 2379-7207, DOI: pending, Published online: www.unitedscholars.net/archive
Experimental Buoyancy Control for a Spherical
Underwater Robot Vehicle (URV)
Abdalla Eltigani Ibrahim
*1, Mohd Noh Karsiti
2, Irraivan Elamvazuthi
3
Department of Electrical and Electronic Engineering, Universiti Teknologi PETRONAS, Perak, Malaysia
*Corresponding author: [email protected]
ABSTRACT
Recently, position control of URVs has been a challenge
due to the buoyancy forces, and high current load of
ocean.
In this paper, the shape of a spherical URV was
presented. The mathematical modeling of variable ballast
tank system and the forces affecting to the controller and
causing some disturbances were discussed by involving
the physical laws.
The URV system was simulated using fuzzy logic
controller and PID controller under downward and
upward vertical motion conditions and the analysis
results shown that both controllers give a good
performance but in term of fast response, the fuzzy logic
controller has produced a better result compared to the
PID controller.
In experimental setup, the prototype was tested and
verified for downward and upward trajectories and an
experimental comparison was carried out. These
promising limitations can be participated in underwater
activities such as, oil exploration, pipelines maintenance
and research explorations.
Keywords: Spherical URV, Buoyancy control, Variable
Ballast system, fuzzy logic control (FLC).
INTRODUCTION
Underwater Robot Vehicles (URVs) have greater
speed, endurance and depth capability. Their
applications in the subsea environment in many
works that difficult for human to do such as
constructing and repairing of subsea systems,
essentially in crude oil, pipelines, cable networks
and data collection for research purposes [1] and
[2]. However, URVs are available in various
designs depending on its application. Slender
shaped design like “a torpedo” is suitable for higher
speed activities, while boxed designs used for
simple directional movement. Thus, spherical
design has benefits of providing a uniform drag in
all directions of maneuvers, when compared with
other designs [3]. On the other hand, The URV
depth position control is based on the analysis of
buoyancy forces. When the URV moves laterally,
zero buoyancy should be maintained. Zero
buoyancy is the condition when the weight force is
equalized by the buoyancy force. Due to the
variations of seawater parameters (e.g. density,
temperature, pressure), different calculations are
often needed for the URV motion, and also for the
zero buoyancy condition. Accordingly, the good
design of URV depth position mechanism is
imperative to provide the balance and stability of
URV against the buoyancy forces.
Variable ballast tank actuator is more efficient in
terms of energy consumption when compared with
a thruster mechanism [4]. In this work, a variable
ballast tank (VBT) mechanism was proposed to
control the buoyancy of spherical URV and to be
used as vertical motion actuator.
1.0 LITERATURE REVIEW
1.1 Variable Ballast Mechanism
From the proposed variable ballast modules, can be
conclude that, the volume of ballast tank is fixed
and some empty space should be left. In case of the
amount of water in the ballast tank is not the
maximum range then the changes in the position of
center of mass of URV will change the pitch or roll
angle of the URV and these changes will disturbs
the stability of the URV that can leads to the
additional internal dynamic changes. This problem
is commonly faced by researchers and caused
Abdalla Eltigani Ibrahim et al, Journal of Control, Robotics and Mechatronic Systems, ISSN: 2379-7207, Vol. 1 (1), 42-52, 09, 2015 DOI: Pending.
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technical effects in controlling system of the URV
[1].
1.1.1 Pump
Tube pumps based ballast tank mechanism is one of
the simpler and cheapest systems available. The
tube pumps are used to fill the ballast tank with
water or any liquid, in order to control the
buoyancy of the underwater vehicle.
Variable ballast for soft grounding of Autonomous
Underwater Vehicle (AUV) was developed in [4]
and [5]. In this designs, two tanks were used, one in
front and the other at the back of the URV. Then,
two pumps were used to deliver the sea water in or
out of the tanks. Since this mechanism used a fixed
volume of ballast system, the internal dynamic
occurs. Therefore, it is hard to create a controller in
order to stabilize this system.
In tube pump techniques the internal dynamic in
variable ballast tank changes the position of Centre
of mass and disturbs the stability of URV. In
addition to that, in this mechanism, the water flow
control is less accurate and flood time is longer.
1.1.2 Compressed Air
Systems using compressed air to control the water
flow in the ballast tanks are rare to find, because
equipment like magnetic valves and throttles are
complex and costly. Due to the difficulties in exact
valve and throttle control, this system is often used
for rough diving systems.
High pressure air compressor was used in [6], [7].
Compressed air is used to control the amount of
water in the ballast tank. To release the ballast tank,
the high pressure air from the compressor is used to
decrease the amount of water in the tank.
Alternatively, to increase the amount of water in the
tank, the air in the ballast tank will be released; so
water will enter the tank. If, at certain depth, the
water pressure is higher than air compressor, then
the buoyancy cannot be increased. If the URV does
not have vertical propeller, then it not be able to
move to surface. In this mechanism also, if the
water does not fully fill the ballast tank, then empty
space will exist. Hence, this condition causes
internal dynamic that is not easy to be controlled.
1.1.3 Movable Plate
Controlling the buoyancy of underwater vehicle by
movable plate was implemented in [1] and [8]. In
these techniques the piston tank driven by DC
motor contains a power screw attached to the
movable plate at one end and the other end of the
power screw is coupled with the gear mounted on
the DC motor. Therefore, when the DC motor
rotates in the clock-wise direction the power nut
moves outward which allows the blast tank to
create a suction pressure hence water enters inside
the ballast, by which the overall weight of the
system increase and the robot can submerge.
Similarly, when the DC motor rotates in the anti-
clock wise direction the power nut moves inward
which created injection pressure; therefore, the
water stored inside the ballast tank gets flushed out.
In this technique there is no an empty space to
cause internal dynamics when push water in or out
the ballast tank therefore, this system can easily be
controlled.
1.2 Spherical URV Design
There are many types of URVs that are proposed by
the designers and organizations around the world,
like; Dish Type Underwater Robot (DTUR) by
Harbin University in [9]. The control system
module mainly contains the host computer, the
interface driver board, the DC motor drives, stepper
motor drivers, wireless debug interface, depth
sensors, attitude sensors and image sensors. They
carried out some experiments on hydrodynamic
performances to validate the coefficients and make
sure the stability and performance.
A flat-shaped of Autonomous Underwater Vehicles
(AUV) was designed by University of Tokyo in
[10]. But AUV had some problems of an umbilical
cable that may become entangled with other
structures. A symmetric boxed shape underwater
robotic vehicle was designed in [11]. They used
6DOF technique to control the maneuvers in all
directions, but vehicle shape was slow with
underwater effects. A torpedo autonomous
underwater vehicle was designed in [12]. They used
propellers beside Variable ballast tank system to
control the buoyancy of the vehicle.
The sphere shape has many characteristics such as
small size, light weight, high maneuverability and
Abdalla Eltigani Ibrahim et al, Journal of Control, Robotics and Mechatronic Systems, ISSN: 2379-7207, Vol. 1 (1), 42-52, 09, 2015 DOI: Pending.
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noiselessness. The spherical underwater vehicle
using the movable plate ballast tank technique was
proposed in [1]. They used fixed volume tank
beside the ballast tank to control the buoyancy of
vehicle as shown in Figure 1.
Fig. 1: Shape of Spherical URV and Its Parts
The variable ballast is located at the top of the hull
with the top side open to the water environment.
This design will allow the volume of the water in
the variable ballast to be controlled by the movable
plate while keeping the tank full, whereby
eliminating the concern for water movement that
may affect the overall stability of the URV.
Another design of a spherical URV using movable
plate tank with three independent thrusters for
horizontal movement was developed in [8].
This work puts forward a URV design which
proposed in [1]. Movable plate tank plays as
vertical motion actuator and to fix the problem of
internal dynamic. The URV contains two
waterproof cylinders. One is for ballast tank and
another one is for storage of electrical components
such as, controller, batteries, inertial measurement
and pressure sensors. The mechanism involves a
DC-motor driven piston tank which converts the
rotational motion of the motor to the linear motion
of the piston shaft such that suction and injection of
water flow is created. A dynamic model of variable
ballast tank depth control system will be formulated
base on this prototype design.
1.3 URV Control
The control system of URVs has been reviewed in
several works but nonlinearity of the URV system
becomes a challenge for the researchers to develop
a good controller.
1.3.1 Input-output feedback control
A simple controller can be designed by linearizing
the model of URV by using Taylor series
expansion. This method linearizes the nonlinear
model about steady condition or the equilibrium
point and then if the linearized model is
controllable, a linear feedback controller law can be
designed based upon this linearized model. The
controller of underwater glider was designed in
[13]. In this controller, a nonlinear underwater
glider was modeled for a steady glide path.
Therefore, the linearized model was controllable
and then the linear controller was designed. A
Linear Quadratic Regulator (LQR) was applied by
way of a standard linear optimal control design
method to control an underwater glider based on
the linearized model. Input-output feedback
linearization control for buoyancy control of a
spherical URV which utilizes movable plate in
place of actuator was presented in [14] and [15].
They analyzed the stability of the equilibrium point
using Lyapunov Direct Method (LDM). Full-State
feedback control laws were developed by using the
linear Quadratic Regulator (LQR) and PP (pole
plate) techniques and the observer developed by the
Kalman-Bucy filtering theory.
1.3.2 Neural network
Neural network based-time sliding mode control
was designed in [16]. This controller used to
control a 6 Degree of Freedom (6DOF)
Autonomous Underwater Vehicle (AUV). This type
of control was used with an intelligent neural
network method to dive a variable mass underwater
vehicle in. They discovered that, this technique was
effective at particular region of system behavior
and control structure. An intelligent neural network
method for diving Sliding mode control (SMC) is a
type of variable complicated structure control
which is a combination of subsystem in which each
of it has a fixed control structure and effective at
Abdalla Eltigani Ibrahim et al, Journal of Control, Robotics and Mechatronic Systems, ISSN: 2379-7207, Vol. 1 (1), 42-52, 09, 2015 DOI: Pending.
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particular region of system behavior.
An intelligent neural network method for diving of
a variable mass underwater vehicle is presented in
[17] and [18]. However, in many cases, the
traditional controllers like PID, Feedback and
neural network controller can be implemented in
any application and perform tasks, but not able to
achieve high accurate buoyancy control for these
reasons; delay in system response, requires high
processing time, difficult to accurately determine
the hydrodynamics, and complex, and sometimes
not practical. In submarine headway control, the
depth and pitch dynamics are highly coupled.
Therefore, the modern controllers, like Fuzzy Logic
Controller (FLC) can be used.
1.3.3 Fuzzy Logic Controller (FLC)
Fuzzy logic control (FLC) is well suited and mainly
applied to nonlinear systems to avoid the local
minima which can cause a vehicle to become
immobilized behind obstacles [19]. Fuzzy logic
controller was applied to motion control of an
Autonomous Underwater Vehicle (AUV) to
command the pump to pump amount of water in the
ballast tank in order to control the buoyancy of the
URV in [20]. Fuzzy logic controller to control the
path following of underwater robotic vehicle was
implemented in [21]. Dynamics of the propulsion
system was regarded by using of both the affine
model of the propeller and the propellers
configuration matrix to determine of thrust
allocation. It makes the algorithms simple and
useful for practical usage.
3.0 SYSTEM MODELING
Knowing the properties of the system such as linear,
nonlinear and stable or not stable are very
necessary to design the controller. In this work the
final dynamic modeling was designed depending on
specified motions equations of URV [1].
V = �̇� (1)
a = V̇ = ΔW
(ms+ma+ΔW
g)
−signal(v)CD Afb ρw V2
2(ms+ma+ΔW
g)
(2)
∆W =ρw g Avb Pm
Km Kgc (Wbs + ∆W + ρw g Avb Z −∆W Avb Pa
ρw g Vin−∆W)
(3)
The prototype’s parameters used to control the
vehicle are listed in Table 1 below.
Table 1 System Parameters
Parameters Sym Value
Atmospheric pressure of
water surface
Pa 1 amt
Density of water Pw 998 kg/m³
Gravitational acceleration g 9.81 m/s²
Transmission ratio of worm
gear and power screw
Kgc 81.64×10³
Coefficient of worm gear
and power screw downward
Kml 0.046×10¯³
Coefficient of worm gear
and power screw upward
Kmu 0.1122×10¯³
Power by dc motor Pm_
max
48 watt
Diameter of variable ballast
tank (VBT)
Dvb 0.13 m
Volume of water inside
(VBT)
kg 0.266 kg
Added mass (ballast
weight) of URV
Ma 8.222 Kg
Diameter of URV Dfb 0.26 m
Projected area of URV Afb 0.053091 m²
Weight of electronic
devices
kg 0.17 kg
Weight of empty ballast
tank with DC motor
kg 0.774
4.0 SIMULATION SETUP
4.1 Fuzzy Logic Controller
In Simulation, Fuzzy Logic Controller is used to
control the depth position of URV as is shown in
figure 2.
Fig. 2: FLC to Control the Depth Position of the URV
4.1.1 Fuzzification
This unit transforms the non-fuzzy input variable
measurements into the fuzzy set variable that is a
clearly defined boundary, without a crisp. For the
fuzzy logic controller, two inputs were used to
Abdalla Eltigani Ibrahim et al, Journal of Control, Robotics and Mechatronic Systems, ISSN: 2379-7207, Vol. 1 (1), 42-52, 09, 2015 DOI: Pending.
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control the buoyancy of URV, water pressure
(URV’s pressure) and error (error reading).
The input water pressure is defined by linguistic
variables such as high (H), medium (M), normal
(N), medium low (ML), low (L). The input error is
defined by linguistic variables such as large
positive (LP), positive (P), zero (Z), negative (N),
large negative (LN), and characterized by
memberships.
The memberships are curves that define how each
point in the input space is mapped to a membership
value between 0 and 1. The membership functions
Gaussian is implemented for input variables. The
shape is generally less important than the number
of curves and their placement. Five curves are
mapped for each input and output variables in order
to cover the required range as are listed in Figure 3
and 4.
Fig. 3: Fuzzy membership functions of water input (pressure)
Fig. 4: Fuzzy Membership Functions of Input (Error)
The membership functions change gradually from
one state to the next. Table 2 shows the weights of
input membership functions.
Table 2 Weights of the Input Membership Functions
Input Range Function
𝒆
L [0 12.5 25] Gaussian
ML [0 25 50] Gaussian
M [25 50 75] Gaussian
MH [50 75 100] Gaussian
H [75 87.5 100] Gaussian
p
LN [-1 -0.7 -0.4] Gaussian
N [-1 -0.4 0.4] Gaussian
Z [-0.6 0 0.6] Gaussian
P [-0.4 0.4 1] Gaussian
LP [0.4 0.7 1] Gaussian
4.1.2 Decision Making
Fuzzy inference process is realized by the Mamdani
method which can be expressed as a highly non-
linear functional relation using small number of
fuzzy rules. It provides higher performance and
accuracy to non-linear dynamic systems under
various operating conditions.
The output variables of FLC are defined by
linguistic variables such as close fast (CF), close
slow (CS), no change (NC), open slow (OS), open
fast (OF), and characterized by memberships as is
shown in figure 5.
The FLC strategy can be defined from this
equation:
Y = 𝑝 − 𝑒 (4)
Y is output of FLC
p is FLC’s input (pressure)
e is the FLC’s input (error)
The memberships are curves that define how each
point in the output space is mapped to a
membership value between 0 and 1, and triangular
and trapezoidal memberships are used for output
variables.
Abdalla Eltigani Ibrahim et al, Journal of Control, Robotics and Mechatronic Systems, ISSN: 2379-7207, Vol. 1 (1), 42-52, 09, 2015 DOI: Pending.
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Fig. 5. Fuzzy membership function of output
Table 3 shows the weights of output membership
functions.
Table 3 The Weights of the Output Membership Functions
Output Range Function
Movable
Pump
(Y)
CF [-1 -1 -0.8 -0.4] Trapezoidal
CS [-0.8 -0.4 0] Triangular
NC [-0.4 0 0.4] Triangular
OS [0 0.4 0.8] Triangular
OF [0.4 0.8 1 1] Trapezoidal
In this application, the symmetry of the positive and
negative half-waves of the ac variables is used. The
task of this variable would be to switch between
two rule tables at every zero-axis crossing of the
reference.
Table 4 Decision Table for Fuzzy Logic Control Rules
p
LN N Z p LP
𝒆
L CF CF CS CS NC
ML CF CS CS NC NC
M CS CS NC NC OS
MH CS NC NC OS OF
H NC NC OS OF OF
Fig. 6. Control surface of fuzzy controllers
4.1.3 Defuzzification
Fuzzy system is used to control the depth position
of URV depending on the operator. Mamdani
method is used as the inference engine and the
output of the fuzzy system is then used as the time
reference for the DC motor to operate the pump.
When the variable ballast system receives the
buoyancy adjustment command from the operator,
the controller calculates the required ambient
pressure of the URV position and then sends the
pulse width modulation (PWM) signals to the
driver of the DC motor.
5.0 EXPERIMENTAL SETUP
In experimental studies the buoyancy control
technique was used to control the depth position of
the vehicle. The microcontroller, relays, DC motor,
variable ballast tank and pressure sensor were
installed inside URV as shown in Figure 7.
Fig. 7: Block diagram of Experimental Setup
Abdalla Eltigani Ibrahim et al, Journal of Control, Robotics and Mechatronic Systems, ISSN: 2379-7207, Vol. 1 (1), 42-52, 09, 2015 DOI: Pending.
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5.1 Controller
The Arduino board is an open source
microcontroller development platform based on the
Atmega 328 [22]. The Arduino microcontroller
board which is selected for this research has the
specifications as listed in Table 5.
Table 5 Specifications of Arduino Due Board
Microcontroller Arduino UNO
Operating Voltage 3.3V
Input Voltage
(recommended)
5-12V
Input Voltage (limits) 5-16V
Digital I/O Pins 12 (of which 6 provide
PWM output)
Analog Input Pins 12
DC Current for 3.3V Pin 800 mA
DC Current for 5V Pin 800 mA
Clock Speed 84 MHz
In this study, fuzzy logic controller was designed
and developed in an Arduino UNO board. The
software agent Arduino Due 32-bit open source
software and MATLAB 2013a were used to control
the non-linear buoyancy control of the URV.
Fuzzy rules which are downloaded in the Arduino,
adaptively determine the critical depth points for
ballast adjustment based on a key parameter of the
URV dynamic model.
5.2 Relays
Relays play an important role in the field of modern
electrical engineering and become an essential part
of modern power systems. Relay is an
electrically operated switch, which can be used to
control a circuit by a low-power signal (with
complete electrical isolation between control and
controlled circuits), or where several circuits must
be controlled by one signal. The relay’s
specifications are listed in Table 6.
Table 6 Specifications of the System’s Relay
Operating Voltage (vcc) 3 V
Max Working Current 35mA
Size 5*2.6cm
DC Output ( Max) 30 VDC / 10A
AC Output (Max) 250 VAC / 10A
Fig. 8: URV’s Relays Connections
In this system, the output of the Arduino board is
connected to three relays in order to control the
direction and time running of the DC motor as is
shown in Figure 8.
5.3 DC motor
DC motor is an electro-mechanic machine which is
used to convert electrical power to mechanical
torque and there are many types of DC motor it
depends on the function of each one. In this work a
DC motor is used as mechanical generator to fill or
empty the ballast tank in order to control the
buoyancy of the vehicle. The Specifications of the
DC motor are listed in table 7;
Table 7 DC motor Specifications
Operating Voltage 12 VDC
operating temperature (-40 to +85) °C.
consumption power 50 W
weight (0.23) kg
5.4 Variable Ballast Tank
The variable ballast tank plays as URV’s buoyancy
controller, hence when it filled by water the
buoyancy force will be less than weight force
therefore, the URV will move in downward vertical
motion. When the tank empty from water the
buoyancy force will be greater than weight force
Therefore, the URV will move in upward vertical
motion.
Abdalla Eltigani Ibrahim et al, Journal of Control, Robotics and Mechatronic Systems, ISSN: 2379-7207, Vol. 1 (1), 42-52, 09, 2015 DOI: Pending.
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5.5 Pressure Sensor
A high sensitive integrated digital pressure sensor
(MS5803-05BA) was used to measure the control
signals of URV as is shown in Figure 9. Table 8
contains the selected Pressure sensor’s
specifications.
Table 8 Pressure Sensor’s Specifications
Integrated digital pressure
sensor
MS5803-05BA
Operating Voltage (1.8 to 3.6) VDC
Operating current 1 μA
Standby current 0.15 μA
Operating range (0 - 6) bar
Clock 24 bit - 20 MHz
Operating temperature (-40 to +85) °C.
Underwater depth 100 m
Fig. 9: URV’s Pressure Sensor MS5803-05BA
In this study one pressure sensor was used to sense
the pressure inside variable ballast tank, and outside
URV. Digital signals (+3 volts) are sent to the
controller to make comparisons with its logical
program and sends signal to the specific relay to
connect the main power supply to the DC motor in
order to run the motor on clockwise to fill the
ballast tank or to run the DC motor on
anticlockwise to empty the ballast tank from water
as is depicted in Figure 10.
Fig. 10: Final Fabricated Prototype
Fig. 11: URV in Real-Time Experiment
6.0 RESULTS AND DISCUSSION
6.1 Simulation Results
Fuzzy Logic Controller is used to control the
buoyancy of URV. PID is involved to be compared
with FLC to examine the controller response.
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6.1.1 Open loop Response
A URV system without a controller has been
simulated using MATLAB Simulink as shown in
Figure 12 (a). The results show the simulated
response which is extremely stable but not
controllable. Therefore, a fuzzy logic control as a
feedback controller must be applied in order to
control the system.
(a)
(b)
Time (Secs) (c)
Fig. 12: A URV open loop response
6.1.2 Fuzzy logic control (FLC) Response
The system model in MATLAB/SIMULINK
platform is shown in Figure 13. The simulation
results show the capabilities of the proposed
controller scheme to maintain the output of the
URV in steady state operation conditions without
errors, as shown in Figure 13.
Fig. 13. Fuzzy logic control system response
6.1.3 FLC VS PID
Figure 14 shows the response of proposed
controller based fuzzy logic control and PID
controller. As seen FLC shows very fast response
with acceptable deviation from the reference
compared to PID controller.
Fig. 14: FLC Response Compare to PID Controller
6.3 Comparison Simulation with Experimental
Results
Fig. 15. Comparison between Simulation and experimental
Vertical Motion (Downward) of URV
Change in
weight
Velocity
FLC
Reference
Reference
Depth
Position
Experimental
Simulation
PID
FLC
Reference
Abdalla Eltigani Ibrahim et al, Journal of Control, Robotics and Mechatronic Systems, ISSN: 2379-7207, Vol. 1 (1), 42-52, 09, 2015 DOI: Pending.
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Fig. 16: Comparison between Simulation and experimental
Vertical Motion (Upward) of URV
Figure 15 and 16 show the comparisons between
real-time setup and simulation setup for downward
and upward vertical velocity. The test was
implemented 24 times in 1 meter underwater depth.
For downward trajectory, the origin position of
URV is at 0 meter from surface, then by applying
positive voltage to DC motor to fill the tank by
water the weight of URV can be increased and URV
can descended from surface by certain velocity.
When the voltage is reset to zero, the URV still
moves with a velocity.
For upward trajectory, by applying negative voltage
to the DC motor to empty the tank the weight can
be decreased and URV can moved up to surface of
a certain velocity.
In comparison results the horizontal effects caused
some difficulties in vertical control of URV and the
differences between experimental curve and
simulation curve clearly can be seen.
7.0 CONCLUSION & RECOMMENDATIONS
This research presents a new control scheme of
VBT system aims to find the solution for buoyancy
control of an underwater vehicle. The study
investigates previous research works in the same
field and adapts the essential elements to combat
the problem. It can be concluded that by using the
proposed spherical URV with variable ballast tank
system the problem can be solved.
The proposed method is based on experimentally
validated techniques, therefore, the URV system
was simulated under different operating conditions
based on fuzzy logic controller and PID controller
and analysis results show that both controllers
relatively gave good performance but in term of
fast response, the fuzzy logic controller produced a
better result as compared to the PID controller.
The performance of the system was tested and
verified in different conditions for downward and
upward trajectories and can be emphasis that, by
using the proposed URV with mentioned
specifications and variable ballast tank system the
studied problem can be solved. The design of the
URV’s hull can be affected by the water pressure
load, therefore, in this research the prototype was
designed well for 5 meter underwater depth.
Moreover, A 8.22 kg of weight can be move up and
down in full controllable motion by consumption
power 48 watt for 17 seconds only, without any
friction loss power or overheat in the DC motor.
These promising limitations can be participated in
underwater activities such as oil exploration,
pipelines maintenance and underwater research
explorations.
Simulation and experimental results are very close.
But there are small differences in the values. These
differences are caused by horizontal effects during
the URV’s task. Therefore, for the future work,
another modern controller could be involved.
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