Experimental Analysis on Sinking Time of Littoral Submarine .docx

Experimental Analysis on Sinking Time of Littoral Submarine
in Various Trim Angle
Luhut Tumpal Parulian SINAGA1,a*
1Senior Researcher at PTRIM, BPPT Laboratorium
Hydrodinamika Indonesia, Surabaya
[email protected]
*corresponding author
Keyword: Littoral submarine, dive, sink, experiment.
Abstract. A submarine must conform to Archimedes’ Principle,
which states that a body immersed
in a fluid has an upward force on it (buoyancy) equal to the
weight of the displaced fluid,
(displacement). Submarines are ships capable of being
submerged. The history of submarines and
their operation have largely revolved around being able to alter
the density of the vessel so that it
may dive below the surface, maintain a depth, and return to the
surface as needed. The way modern
submarines accomplish this task is to bring in and remove water
from tanks in the submarine called
ballast tanks. Ballast tanks fit into two categories: those used
for major adjustment of mass (main
ballast tanks); and those used for minor adjustments (trim
tanks). The effect of each tank is plotted
and this is compared with the changes in mass and trimming
moment possible during operations
using a trim polygon to determine whether the ballast tanks are
adequate. On the water surface,

metacentric height (GM) is important, whereas below the
surface it is the distance between the
centre of buoyancy and the centre of gravity (BG) which
governs the transverse stability of a
submarine.
Introduction
A submarine or a ship can float because the weight of water that
it displaces is equal to the
weight of the ship. This displacement of water creates an
upward force called the buoyant force and
acts opposite to gravity, which would pull the ship down.
Unlike a ship, a submarine can control its
buoyancy, thus allowing it to sink and surface at will [1].
As with any object in a fluid, a submarine must conform to
Archimedes’ Principle, which states
that a body immersed in a fluid has an upward force on it
(buoyancy) equal to the weight of the
displaced fluid, (displacement). This applies whether the
submarine is floating on the water surface,
or deeply submerged [2, 3].
To control its buoyancy, the submarine has ballast tanks and
auxiliary, or trim tanks, that can be
alternately filled with water or air (see Fig. 1). When the
submarine is on the surface, the ballast
tanks are filled with air and the submarine's overall density is
less than that of the surrounding
water. As the submarine dives, the ballast tanks are flooded
with water and the air in the ballast
tanks is vented from the submarine until its overall density is
greater than the surrounding water and
the submarine begins to sink (negative buoyancy) [4, 5].

A supply of compressed air is maintained aboard the submarine
in air flasks for life support and
for use with the ballast tanks. In addition, the submarine has
movable sets of short "wings" called
hydroplanes on the stern (back) that help to control the angle of
the dive. The hydroplanes are
angled so that water moves over the stern, which forces the
stern upward; therefore, the submarine
is angled downward [2].
Figure 2 shows the location of the MBT's in a submarine. The
bulk of the MBT's are located at
the bow and aft sections of the boat and a small MBT surrounds
the pressure hull in the center of
the boat. A large portion of the space between the pressure hull.
It is important to note that the MBT
is only used to change the buoyancy of the boat from very
positive to slightly positive.
Applied Mechanics and Materials Submitted: 2017-02-06
ISSN: 1662-7482, Vol. 874, pp 128-133 Revised: 2017-08-22
doi:10.4028/www.scientific.net/AMM.874.128 Accepted: 2017-
08-29
© 2018 Trans Tech Publications, Switzerland Online: 2018-01-
10
All rights reserved. No part of contents of this paper may be
reproduced or transmitted in any form or by any means without
the written permission of Trans
Tech Publications, www.scientific.net. (#113698139, ProQuest,
USA-29/03/19,15:02:51)
https://doi.org/10.4028/www.scientific.net/AMM.874.128

(a) Surface
(b) Dive
Figure 1. Submarine diving process.
Figure 2. Location ballast tank of submarine.
As the righting moment at an angle of heel must be the same for
these two definitions of
displacement, the relationship between the centres can be
obtained from Eq. 1.
BFGF x ΔF = BH x GH x ΔH (1)
Therefore,
��
��
= ��
∆��
(2)
where
�� = Total mass Hydrostatic displacement, other than free
flood water
∆�� = Total mass Form displacement, including free flood
water
�� = Centre of gravity Hydrostatic displacement
�� = Centre of gravity Hydrostatic displacement
�� = Centre of buoyancy Form displacement
�� = Centre of buoyancy Form displacement
The Main Ballast Tanks (MBTs), are usually ballast tanks

external to the pressure hull, which
are free flooding when the submarine is submerged, as shown in
Fig. 3.
The purpose of the MBTs is to allow major adjustment of the
submarine mass to enable it to
operate submerged as well as on the water surface. Water and
air enter and leave the MBTs through
flooding holes at the bottom and vents at the top of the tanks.
Applied Mechanics and Materials Vol. 874 129
Figure 3. Schematic of typical main ballast tank system.
During operations the mass and longitudinal centre of gravity of
a submarine will change due to
use of consumables including fuel, and weapons discharge. In
addition, changes in seawater
density, hull compressibility and surface suction when operating
close to the surface will all result
in the need to be able to make small changes to the submarine
mass and longitudinal centre of
gravity.
The trim and compensation ballast tanks are used to make these
small adjustments. A
schematic of such a typical system is shown in Fig. 4.
Figure 4. Schematic of typical trim and compensation ballast
tanks.

At the design stage it is necessary to determine whether the trim
and compensation ballast tanks
are adequate to cope with all possible changes in submarine
mass and longitudinal centre of gravity.
To do this, the effect of each tank is plotted as a function of
mass and trimming moment as shown
in Fig. 5 [6].
In this figure, the point with zero mass and zero trimming
moment is where all the tanks are
empty. The forward trim tank (FTT) is then filled. In this case,
the tank is a soft tank, not open to
the sea, so there is no change in mass, just a movement of the
centre of gravity forward from the
aft trim tank (ATT) to the forward trim tank. Thus, the effect is
a forward trimming moment with no
change in mass. This is shown by a horizontal line.
To perform a quick dive, the front ballast is filled with water
and then forms the angle required
to perform the dive, so the submarine has an effective range, see
Fig. 6. Once the boat is trimmed to
more or less neutral buoyancy, the depth of the boat is
controlled with the hydroplanes. To use the
hydroplanes the boat requires speed to create a force on the
tilted planes. At slow speeds, the fore
hydroplanes are exclusively used to keep the boat at the
required depth
The dive technology was shown that the bulk buoyancy of the
boat is changed with the MBT
followed by fine tuning with the MBT and finally the correct
depth is maintained using the
hydroplanes. Due to the application of the real submarine
technology is not always possible. In the
following, some of the available model diving technologies will

be treated [7].
This research focuses on the study of the influence of sloshing
against the coupling movement
heave the ship while the ship conducted a quick dive using
Physical Tests in Indonesia
Hydrodynamics Laboratory.
130 Marine Systems and Technologies
Figure 5. Polygon showing the effect of trim and compensation
ballast tanks.
Figure 6. Quick dive submarine.
Methodology
The investigation was carried out experimentally. The
experimental work was conducted using
towing tank and tested at various angle of trim. Physical models
of the submarine are shown in
Fig.7. The model is made from FRP (fibreglass reinforced
plastics) in order to obtain appropriate
displacement as scaled from full ship mode in accordance with
Froude law of similarity. Principal
particulars of the submarine given in Table 1.
Table 1. Main dimension submarines model.
Dimension SHIP (m) MODEL (mm)
LOA 22.00 700.00

B Total 4.29 136.30
D Total 5.13 163.30
T 2.60 82.70
dim. Press Hull 3.00 95.50
JR. FS 1.10 35.00
JR. WL 1.00 31.80
JR. BL 0.30 9.50
Scala 31.43
Figure 7. Design of submarine.
Results and Discussion
To get a angle dive effective when quick dive at model of litoral
submarine, has obtained the
water depth in Cavitation Tunnel = 0.6 m a summary of the test
results that can be seen from the
Table 2 below:
Table 2. Angle of Attack Pitch Ballast Water Depth.
Volume of ballast
in Fwd. Tank (gr.)
Angle of Trim Sinking time (sec.) Sinking velocity
(V m / sec)
150 5⁰ 3.2 0.188
300 7.5⁰ 3.0 0.200
400 10⁰ 2.8 0.214

500 12.5⁰ 2.7 0.220
550 15⁰ 2.5 0.240
In Table 2 was obtained dives fastest ship that is for 2.5
seconds at an angle of 150 trim. This is
due to the angle trim large enough so that the size of the area
aboard the front facing the water flow
becomes tighter. It is also their ballasts volume large enough to
add to the weight of the model
submarine. As shown in Fig. 8, the addition of ballast resulted
in a bigger angular change also.
However, the time it takes to sink even less.
Furthermore by addtion 150 gr ballast at forward ballast tank,
submarine can be have trim 50.
But, Litorral submarin have 3.2 sec in singking time. This is
due to wide cross section and blocking
into the water, causing longer sinking time.
The conditions of trim described apply of submarine operations
by flooding the forward ballast
tank. However, these buoyancy conditions always be considered
with respect to the law of the lever
on each side of the center of gravity of the boat. The trimming
of the submarine is accomplished by
varying, or adjusting, the amount of water in the variable ballast
tanks. The trim system is the
means by which this adjustment is made. However, the trim has
been so carefully adjusted that by
flooding the main ballast tanks and adding the required amount
of water to the special ballast tanks,
the submarine can be made to submerge at the desired rate [8].
132 Marine Systems and Technologies

Figure 8. Sinking time for submarine.
Conclusions
Ship model testing was conducted to determine the model to the
required time to dive to the
bottom. From the tests of models with angle of attack 150 has
the fastest time in the amount of
2.5 seconds or has a speed of 0.24 m/sec to reach the bottom of
the pool of test.
In general the vessel can sink due to a sharp angle so that the
area of the bow that is exposed to
water is smaller so that the resistance becomes small and the
weight gain due to the addition of the
front ballast. As the next stage should be calculated
comprehensively on navigation vessels arising
from the movement of the ship.
References
[1] Dmitri Kuzmin, Introduction to Computational Fluid
Dynamics, Institute of Applied
Mathematics University of Dortmund,
http://www.mathematik.uni-dortmund.de /_kuzmin/ cfdintro/
cfd.html (2000).
[2] M. Mackay, The Standard Submarine Model: a Survey of
Static Hydrodynamic Experiments
and Semi empirical Predictions, Defence R&D, TR 2003-079,
2003.
[3] Erwandi, T.S. Arief, C.S.J. Mintarso, The study on
hydrodynamic performances of ihl-mini-
submarine, In: Proc. The Second International Conference on
Port, Coastal, and Offshore

Engineering (2nd ICPCO), Bandung, 12-13 November 2012.
[4] S.W. Lee, H.S. Hwang, C.M. Ryu, H. I. Kim, S.M. Sin, A
Development of 3000-ton class
submarine and the study on its hydrodynamic performances, In:
Proc. the Thirteenth (2003)
International Offshore and Polar Engineering Con-Prosiding
InSINas 2012 HK-6 0026: Erwandi
dkk. ference Honolulu Hawaii, USA May 2003.
[5] L.T.P. Sinaga, Theoretical Analysis Of Sloshing Effect On
Pitch Angel To Optimize Quick
Dive On Litoral Submarine 22 M. In: The 8th International
Conference on Physics and Its
Applications (ICOPIA 2016), August 23, 2016, Denpasar,
Indonesia, 2016.
[6] A. F. Molland, S.R. Tunock, D.A. Hudson, 2011, Ship
Resistance and Propulsion, Cambridge
University Press, New York, 2001.
[7] A. Prisdianto, A. Sulisetyono, Perancangan ROV dengan
Hydrodinamic Performance yang
Baik untuk Misi Monitoring Bawah Laut, ITS, Surabaya, 2012.
[8] A. Sulisetyono, D. Purnomo, The Mini-Submarine Design
for Monitoring of the Pollutant and
Sewage Discharge in Coastal Area, In: Proc. 5th International
Conference on Asian and Pacific
Coasts, NTU, Singapore, 2009.
0
0,5
1
1,5
2

2,5
3
3,5
0
2
4
6
8
10
12
14
16
0 100 200 300 400 500 600
Tr
im
A
ng
le
(0
)

Forward Ballast (gr)
Trim
Sinking Time
Sinking tim
e (s)
Reproduced with permission of copyright owner. Further
reproduction
prohibited without permission.
Reproduced with permission of the copyright owner. Further
reproduction prohibited without permission.
TURTLE: David Bushnell's Revolutionary Vessel
Taylor, Blaine
Sea Classics; Nov 2010; 43, 11; ProQuest
pg. 66
Ocean Engineering 72 (2013) 441–447
Contents lists available at ScienceDirect
Ocean Engineering
0029-80

http://d
n Corr
E-m
jgpelaez
journal homepage: www.elsevier.com/locate/oceaneng
On a submarine hovering system based on blowing and venting
of ballast tanks
Roberto Font a,n, Javier García-Peláez b
a Departamento de Matemática Aplicada y Estadística, ETSI
Industriales, Universidad Politécnica de Cartagena, 30202
Cartagena, Spain
b Direction of Engineering, DICA, Navantia S. A., Cartagena
30205, Spain
a r t i c l e i n f o
Article history:
Received 27 July 2012
Accepted 27 July 2013
Available online 19 August 2013
Keywords:
Manned submarines
Underwater hovering
Variable buoyancy
Sliding control
18/$ - see front matter & 2013 Elsevier Ltd. A
x.doi.org/10.1016/j.oceaneng.2013.07.021
esponding author. Tel.: +34 968 338 947; fax:
ail addresses: [email protected], robertojav
@navantia.es (J. García-Peláez).
a b s t r a c t

A submarine hovering system based on the blowing and venting
of a set of dedicated tanks is
investigated. We review the mathematical models involved and
propose a sliding mode controller for
the input–output linearized system. Numerical simulation
results support the idea that this could be a
promising hovering strategy for manned submarines,
autonomous underwater vehicles or other plat-
forms.
& 2013 Elsevier Ltd. All rights reserved.
1. Introduction
Underwater hovering, the ability to statically keep a desired
depth, is at the same time a challenge, due to many uncertainties
associated with the underwater environment, and a very impor-
tant feature for both small size autonomous underwater vehicles
(AUVs) and large manned submarines. In the last years several
hovering AUVs have been developed (see Vasilescu et al., 2010
for
a survey on the subject). The hovering facility expands the
capabilities of AUVs allowing them to perform more complex
missions that previously could only be carried out through
Remotely Operated Vehicles (ROVs). For manned submarines,
accurate hovering can be an invaluable tool, for example, for
safe
swimmer delivery, cover supply replacement or the deployment
and recovery of AUVs, a subject that has recently raised an
extraordinary interest (see for example Hardy and Barlow,
2008;
Martínez-Conesa and Oakley, 2011).
From the technological point of view, AUVs usually hover by
using thrusters (Choi et al., 2003; Li et al., 2011). Due to the
large

energy requirements of this approach, however, buoyancy
control
by pumping seawater in or out of ballast tanks can be used to
save
energy (Vasilescu et al., 2010) or in larger designs (Tangirala
and
Dzielski, 2007). In manned submarines, hovering is
traditionally
performed using hydraulic pumps (Yang and Hao, 2010; Ying
and
Jian, 2010), although not very much information about hovering
ll rights reserved.
+34 968 338 916.
[email protected] (R. Font),
systems is available in the literature due to the military nature
of
these vehicles.
The aim of this work is to investigate the feasibility of a
hovering system in which dedicated tanks are blown and vented
similarly to the way the main ballast tanks are traditionally
operated in manned submarines.
In these vehicles, a variable number of main ballast tanks are
distributed along the hull. In case of emergency the main ballast
tanks can be emptied by blowing into them air from high
pressure
bottles. This way the water is expelled from the tanks, the
vehicle
gains buoyancy and can rise more quickly. To fill the tanks with
water, air is vented out of the ballast tanks. In the previous
works
(Font et al., to appear, 2013) we proposed mathematical models
for
the blowing and venting of ballast tanks and showed that the

implementation of a control system for these processes, usually
performed manually, can improve in a significant way the
perfor-
mance and stability in emergency rising manoeuvres. Our objec-
tive is to extend the approach used with the main ballast tanks
to a
set of dedicated hovering tanks (see Section 2 for details) in
order
to test the feasibility of a hovering system based on blowing and
venting of tanks. Although throughout this paper we will use a
manned submarine as test platform, it is worth noting that the
use
of blowing and venting of tanks as hovering control is not
limited
to these vehicles nor is our intention to carry out the discussion
of
conceptual designs for the compromise between efficiency and
stealth in a hovering system ready for military applications.
Indeed, this technology could be applicable to manned submar-
ines, AUVs, ROVs or any offshore platform requiring variable
buoyancy control.
The rest of the paper is organized as follows. In Section 2
we formulate the problem and describe the mathematical models
www.sciencedirect.com/science/journal/00298018
www.elsevier.com/locate/oceaneng
http://dx.doi.org/10.1016/j.oceaneng.2013.07.021
http://crossmark.dyndns.org/dialog/?doi=10.1016/j.oceaneng.20
13.07.021&domain=pdf

mailto:[email protected]
Table 1
Summary of symbols introduced in Section 2.1.
Av Vent pipe cross-section (m
2)
hwc(t) Height of water column in the tank (m)
mB(t) Mass of air in ballast tank (kg)
mF(t) Mass of air in pressure bottle (kg)
mF0 Initial mass of air in pressure bottle (kg)
_mFðtÞ Mass flow rate from pressure bottle (kg/s)
_m ðtÞ Mass flow rate through venting valve (kg/s)
R. Font, J. García-Peláez / Ocean Engineering 72 (2013) 441–
447442
for blowing and venting processes, vehicle motion and external
disturbances. In Section 3 we propose a feedback control
scheme
for the hovering submarine consisting of a sliding mode
controller
acting on a previously input–output exactly linearized system.
Section 4 is devoted to the results of numerical simulations
testing
the performance of the proposed hovering system. Finally, in
Section 5 we discuss the obtained results and present some
conclusions.
v
pB(t) Pressure in ballast tank (Pa)
pext(t) Pressure outside the venting valve (Pa)

pF(t) Pressure in bottle (Pa)
pF0 Initial pressure in bottle (Pa)
pSEA(t) Pressure outside the outlet hole (Pa)
qB(t) Water flow through outlet hole (m
3/s)
Rg Gas constant for air (J/kg K)
TB Water temperature (K)
VB0 Initial air volume in ballast tank (m
3)
VB(t) Volume of air in ballast tank (m
3)
VF Pressure bottle volume (m
3)
γ Isentropic constant
ρ Density of water (kg/m3)
2. Problem formulation. Mathematical models
As we said above, we will consider a manned submarine,
particularly the Navantia P-650 design, as the test platform for
our hovering system. Details about the hydrodynamic character-
istic and the blowing/venting system can be found in García et
al.
(2011) and Font et al. (to appear) respectively.
Our objective is to maintain a desired depth with no propulsion
(and thus without any help from the control surfaces) in the face
of external disturbances like changes in water density or forces
induced by the sea state. In the next sections we review the
mathematical models for the blowing/venting system, vehicle
motion and external disturbances.
2.1. Blowing/venting system

The blowing and venting system is composed of the tank, the
pressure bottle, the blowing and venting valves and the outlet/
inlet hole located at the bottom of the tank. When the blowing
valve is opened, air flows into the tank from the bottle
increasing
the pressure and forcing the water to flow out through the outlet
hole. When the venting valve is opened, air can flow out from
the
tank letting the water flow back into the tank. Fig. 1 shows
a schematic view of these processes. The subindex F denotes
conditions in the bottle, the subindex B denotes conditions in
the
tank, _mF and _mv are respectively the mass flow rates through
blowing and venting valves, qB is the water flow through the
tank
hole, hwc is the height of the water column in the tank and
pSEA,
pext are respectively the hydrostatic pressures outside the flood
port and venting outlet (they differ in the depth at which each
one
is evaluated). We will use 3 variables for each tank to
completely
describe its state: mass of air in the bottle, mF, mass of air in
the
tank, mB, and pressure in the tank, pB. We refer the reader to
Font
et al. (to appear) and Font and García (2011) for a more detailed
description of the model presented below. The symbols
introduced
in this section are summarized in Table 1.
Due to the high pressure difference between bottle and tank,
the flow from the bottle will usually be supersonic. As the
bottle
empties, however, this difference decreases and the flow can

become subsonic if the pressure ratio is below the critical
pressure
Fig. 1. Blowing and venting processes.
ratio Pc ¼ ððγ þ 1Þ=2Þγ=ðγ�1Þ, with γ the isentropic constant.
Let s
denote the variable aperture of the blowing valve, the equation
for
the mass of air in the bottle in both the supersonic and the
subsonic cases is
_mF tð Þ ¼ s tð ÞA
mFðtÞγþ1pF0
mγF0VF
!1=2
μ pB tð Þ; mF tð Þ
� �
ð1Þ
where A ¼ _mFmaxðð2=ðγ þ
1ÞÞ�ðγþ1Þ=ðγ�1ÞVF=γpF0mF0Þ1=2, with _mFmax
the maximum mass flow rate from the bottle, experimentally
measured, VF is the bottle volume, pF0, mF0 are respectively
the
initial pressure and mass of air in the bottle and
μ pB; mF
� �
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffiffiffiffiffiffiffiffiffiffiffiffiffi
γ

2
γ þ 1
� �ðγþ1Þ=ðγ�1Þs
; Pc r
pF
pBffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2γ
γ�1
pB
pF0
mF
mF0
� �γ
0
[email protected]
1
CCA
2=γ
� pB
pF0
mF
mF0

� �γ
0
[email protected]
1
CCA
ðγþ1Þ=γ0
[email protected]
1
CCA
vuuuuut ; 1opFpB oPc
0;
pF
pB
r1:
8>>>>>>>>>>>>>><
>>>>>>>>>>>>>>:
The mass flow through the venting valve is obtained similarly.
The variation in the mass of air in the tank is the difference
between the mass flow rate from the bottle and the mass flow
rate
through the venting valve. Let s denote the aperture of the
venting
valve. Then, the equation for the mass of air in the tank is
_mB tð Þ þ _mF tð Þ ¼ �μ
pextðtÞ
pBðtÞ
� �
sðtÞAvpBðtÞffiffiffiffiffiffiffiffiffiffi

RgTB
p ; ð2Þ
where Av is the venting pipe system cross-section, Rg is the gas
constant for air, TB is the temperature in the tank and
μðpextðtÞ=pBðtÞÞ
is a function of the tank and outside pressures obtained by curve
fitting from experimental measures.
Finally, the variation in the tank pressure is obtained from the
perfect gas equation as
mBðtÞ
pBðtÞ
_pB tð Þ� _mB tð Þ ¼ �
pBðtÞqBðtÞ
RgTB
; ð3Þ
where qB(t) is the water flow through the flood port.
We will consider two hovering tanks, bow and aft, with their
respective bottles and blowing and venting valves. The
geometric
characteristics of the blowing and venting system have been
adapted from the characteristics of the main ballast tanks
blowing
and venting system which can be found in Font et al. (to
appear).
Table 2

Hovering system characteristics.
Parameter Stern tank Bow tank
Flood port area, Ah ðm2Þ 0.1 0.1
Venting pipe system cross-section, Av ðm2Þ 9.62 � 10�4 9.62
� 10�4
Tank height, Htk (m) 1.5874 1.5874
Maximum mass flow rate, _mF;max ðkg=sÞ �2 �2
Initial bottle pressure, pF0 (Pa) 2.5 � 107 2.5 � 107
Initial bottle temperature, TF0 (K) 4 4
Tank volume, VBB ðm3Þ 293 293
Bottle volume, VF ðm3Þ 0.8 0.8
Tank location (m)
xb �28.6 23.7
yb 0 0
zb 0.595 0.595
447 443
However, since the size of the main ballast tanks is not
adequate
for the hovering system requirements, the size of the hovering
tanks has been considerably reduced with respect to the main
ballast tanks. Precisely, each hovering tank has a volume of 4
m3
and is initially filled up to half of its capacity. In the same way,
the
maximum mass flow rate from the bottle has been reduced to
2 kg/s. The main characteristics of the hovering system are
summarized in Table 2. We note that these are tentative values
in the context of this preliminary study. Of course, the
implemen-
tation in a real ship would require the careful selection of the

most
appropriate values.
2.2. Vehicle motion
Vehicle motion is given, as usual, by Feldman's (1979) 6 degree
of freedom equations of motion. The final form of these
equations
adapted to the particular vehicle we are considering can be
found
in García et al. (2011).
These equations assume the mass of the submarine to be
constant. In our case, however, water flowing in or out of the
hovering tanks will cause mass variations at several points of
the
vehicle. We will therefore need to write vehicle mass, weight,
moments and products of inertia and location of center of
gravity
as a function of the amount of water in the tanks.
Let m0 be the initial mass of the vehicle and Δmstern, Δmbow
the
mass variations in the stern and bow tanks respectively (positive
when mass is added). This mass variation can be obtained by
multiplying the increase in the volume occupied by water with
respect to the initial condition by the density of water, ρ. It is
easy
to see that this increase coincides with the decrease in the
volume
of air, i.e. the difference between the initial and momentary
volume of air in the tank. This way
Δmfstern;bowg tð Þ ¼ ρ VB0�VBfstern;bowg tð Þ
� �

¼ ρ VB0�
mBfstern;bowg ðtÞRgTB
pBfstern;bowg
!
;
and the momentary mass of the vehicle is given by
mðtÞ ¼ m0 þ ΔmsternðtÞ þ ΔmbowðtÞ:
The rest of parameters can be obtained analogously (Font et al.,
to
appear).
It is worth noting that coefficient based models can lead to
inaccurate results in certain situations. In movements at high
angles of incidence, like hovering, vortices generated by
crossflow
separation of the hull boundary layer and the trailing wakes
from appendages can produce significant loads (Watson et al.,
1993). We do think, however, that this standard model is
enough
for the purposes of this preliminary study. Up to our best
knowl-
edge, it is not easy to account for these phenomena without
using
computationally intensive techniques that are not suitable for
control system design (see for instance Bettle et al., 2009). Our
objective (see Section 3) is to design a robust controller that
can
maintain consistent performance in the presence of large
external
disturbances and/or modelling uncertainties. This approach has
been successfully used in the design of a variety of hovering
AUVs.

We refer the reader to, for example, Riedel et al. (2005) where a
sliding mode controller is used to address a similar problem.
2.3. Complete model in affine form
Let the state vector be
x ¼ ½x; y; z; ϕ; θ; ψ; u; v; w; p; q; r; …
mFstern ; mBstern ; pBstern ; mFbow ; mBbow ; pBbow � ð4Þ
composed of the state variables for the stern and bow tanks, the
vehicle position and orientation, x, y, z and ϕ (roll), θ (pitch)
and
ψ (yaw) respectively, and the linear and angular velocities, u, v,
w
and p, q, r. Let u ¼ ½sstern; sstern; sbow; sbow� be the control
vector. The
state law is composed of the equations of motion (see Section
2.2)
plus a set of Eqs. (1)–(3) for each of the two hovering tanks.
This
state law can be expressed in compact form as
AðxÞ _x ¼ Φðx; uÞ ð5Þ
where A (x) is the mass matrix of the system.
As we will see in Section 3, it is convenient, from the point of
view of control system design, to express (5) in the affine form
_x ¼ fðxÞ þ ∑
m
i
giðxÞui: ð6Þ

This expression can be obtained from (5) as follows. It is easy
to
see that the state law (5) can be expressed as
AEMðxÞ 012�6
06�12 ABV ðxÞ
" #
_x ¼
ΦEMðxÞ
ΦBV ðx; uÞ
" #
where AEM (x) and ΦEMðxÞ are respectively the mass matrix
and the
right hand side of the equations of motion, depending only on
the
state variable, ΦBV ðx; uÞ is the right hand side of Eqs. (1)–
(3), and
ABV xð Þ ¼
1 0 0 0 0 0
1 1 0 0 0 0
0 �1 mBstern
pBstern
0 0 0
0 0 0 1 0 0
0 0 0 1 1 0
0 0 0 0 �1 mBbow

pBbow
2
6666666666664
3
7777777777775
Since both AEM (x) and ABV (x) take non-singular values for
any
x (Font et al., to appear), the state law can be expressed in
explicit
form as
_x ¼
A�1EMΦEMðxÞ
A�1BV ΦBV ðx; uÞ
" #
It is immediate to separate the terms where the control input
appears to obtain the desired form (6) with
f xð Þ ¼ A�1EMΦEM; 0; 0;
pBstern qBstern
mBstern RgTB
; 0; 0;
pBbow qBbow
mBbow RgTB
T

447444
and gi; 1rmr4, the columns of the matrix
012�4
αstern 0 0 0
�αstern βstern 0 0
�pBstern
mBstern
αstern
pBstern
mBstern
βstern 0 0
0 0 αbow 0
0 0 �αbow βbow
0 0 �
pBbow
mBbow
αbow
pBbow
mBbow
βbow
2
6666666666666664
3
7777777777777775

with
αfstern;bowg ¼ μfstern;bowgA
mγþ1Ffstern;bowg pF0
mγF0VF
0
@
1
A
1=2
;
βfstern;bowg ¼ �μfstern;bowg
AvpBfstern;bowgffiffiffiffiffiffiffiffiffiffi
RgTB
p :
2.4. External disturbances
The main disturbances that a submerged submarine must face
are the wave induced forces and the changes in its buoyancy
caused by seawater density changes and hull compressibility.
2.4.1. Wave induced forces
The surface elevation of a long-crested irregular sea can be
modelled as a sum of N regular wave components. The
amplitude
of each regular wave is given by a wave energy spectrum, in
this
case the Pierson–Moskowitz spectrum. A detailed description of
this approach can be found in Fossen (1994).

To model the effect of an irregular sea over the vehicle it is
usual to consider 1st and 2nd order wave disturbances. Using
the
superposition principle the 1st order forces (in this work we
will
consider a heave force and a pitching moment) can be modelled
as
the sum of the forces caused by each individual regular compo-
nent, i.e. a wave with the same frequency and different
amplitudes
and phase angles.
For this work, the amplitude and phase angle of the vertical
force and pitching moment, Fi; Mi; ΦF;i; ΦM;i, have been
obtained
experimentally using captive tests on a scale model. The ampli-
tudes and phase angles under regular waves of different wave-
lengths were measured for several heading directions. These
data
were then adjusted using a least-squares fit. Fig. 2 shows the
results for the vertical force and pitching moment at 1801 wave
Fig. 2. Non-dimensional force (left) and moment (right) vs non-
dimensional wave leng
solid line.
heading. In this case the fitted curves are
F
ρgHL2
¼
0:01161
λ
L

λ
L
� �2
�3:898λ
L
þ 5:046
M
ρgHL3
¼
0:001932
λ
L
λ
L
� �2
�2:398λ
L
þ 1:917
where L is the vehicle length, λ the wave length, H the wave
height
and g the acceleration due to gravity. A similar methodology
was
used in Byström (1988).
The 2nd order force, or suction force, is an upward force,

usually small in comparison with 1st order forces. Under an
irregular sea, this is a slowly varying force (Booth, 1983). For
the
purpose of this work, however, it suffices to consider a mean
constant value. The series of captive tests mentioned above
provided a mean value for the suction force under Sea State 5 of
0.8 ton.
Both the 1st and 2nd order forces are assumed to decay
exponentially with depth in the form e�kiðzðtÞ�z0Þ where ki
is the
wave number of each component. For the suction force, k was
taken corresponding to the peak of the spectrum.
2.4.2. Compressibility and water density
Vehicle buoyancy can be expressed as B ¼ ρg∇ fd, where ρ is
the
water density and ∇ fd is the form displacement, i.e. the total
displaced volume in submerged condition. In trim condition the
vehicle buoyancy is equal to its weight. If the submarine moves
down from the equilibrium position, however, the outside pres-
sure will compress the hull and other materials reducing the
vehicle buoyancy, which will result in a downward acceleration.
In
the same way, moving the submarine up from its equilibrium
position will result in an upward acceleration (see, for instance,
Booth, 1983). The displacement variation caused by pressure
hull
compressibility can be considered linear with depth in the form
ΔVcðzÞ ¼ αðz�z0Þ, where α is a compression coefficient that
can be
easily determined for each particular vehicle.
Similarly, changes in seawater density will modify the vehicle
buoyancy also causing a destabilizing effect. The seawater
density

as a function of temperature and salinity can be obtained using
the
algorithms described in Fofonoff and Millard (1983). Let us
assume
that, for a certain temperature/salinity vertical profile, the water
density can be expressed as a function of depth. Let ρðzÞ
denote
this variable density (we will continue to denote the nominal
value by ρ). The vehicle buoyancy is given by
BðzÞ ¼ ρðzÞgð∇ fd�ΔVcðzÞÞ: ð7Þ
th for wave heading 1801. Measured values are shown as circles
and fitted curve as
447 445
3. Sliding mode controller
Sliding mode control (Slotine and Li, 1991) has been success-
fully applied in several AUV designs and has been identified as
one
of the most promising control strategies to account for large
disturbances or model uncertainties (Lea et al., 1999). Although
sliding mode control is often applied over a linearized model
(Demirci and Kerestecioğlu, 2004; Riedel et al., 2005), our
previous
experience with the dynamic model of the submarine leads us to
think that in this case, due to high coupling and severe
nonlinea-
rities, this could be inaccurate. Instead, we propose an exact
input–output feedback linearization (Isidori, 1995). The sliding
control of a nonlinear system using input–output linearization is
discussed more generally in Fossen and Foss (1991).

For the hovering control we will consider a single output, the
depth z, and 4 inputs, the apertures of the blowing and venting
valves. This way, the system can be expressed (see Section 2.3)
as
_x ¼ fðxÞ þ ∑
m
i
giðxÞui
y ¼ hðxÞ ¼ z: ð8Þ
Let Lfh, Lgi h denote the Lie derivatives of h with respect to f
and
gi respectively. The repeated Lie derivatives are recursively
defined
as Ljf h ¼ Lf ðL
j�1
f hÞ. In the same way, Lgi L
j
f h ¼ Lgi ðL
j
f hÞ. The computa-
tion of Lgi L
j
f h; j ¼ 1…r, shows that the system has a well defined
relative degree r¼3. We refer the reader to Isidori (1995) for
more
detail on this subject.

Define FðxÞ ¼ Lrf h and GðxÞ ¼ ½Lg1 L
r�1
f h ⋯ Lgm L
r�1
f h�. This way (8)
can be expressed as
yðrÞ ¼ FðxÞ þ GðxÞ
u1
⋮
um
2
64
3
75 ð9Þ
that can be reduced to
yð3Þ ¼ v ð10Þ
Fig. 3. Evolution of depth for Scenario 1.
Fig. 4. Flooded volume in stern (left) an
using the control law
u ¼ GnðxÞðv�FðxÞÞ ð11Þ
where GnðxÞ is a vector such that GðxÞGnðxÞ ¼ 1.
Once the input–output relation in system (8) has been reduced
to the linear form (10) it is easy to use linear control techniques
to
stabilize (10). The exact cancellation of the nonlinear terms,

however, relies on the perfect knowledge of fðxÞ and giðxÞ,
some-
thing that can hardly be achieved due to modelling errors or
unknown external disturbances. We propose the use of sliding
mode control to account for this issue.
Let y ¼ ½y _y ⋯ yðr�1Þ� be the output vector, yd ¼ ½yd _yd
⋯ yðr�1Þd � a
desired output vector and ~y ¼ y�yd ¼ ½~y _~y ⋯ ~yðr�1Þ�
the tracking
error vector. For r¼3 the sliding surface can be defined as
s ¼ €~y þ 2λ _~y þ λ2 ~y:
Taking the derivative with respect to time in the above equation
and taking into account that in our case yð3Þd ¼ 0 and in the
absence
of uncertainties yð3Þ ¼ v, the equivalent control is veq ¼ �2λ
€~y�λ2 _~y .
Let F̂ ðxÞ; ĜðxÞ be the estimates of FðxÞ and GðxÞ,
respectively. If
the signum function is linearly smoothed inside a boundary
layer
of thickness Φ (Slotine and Li, 1991), then the proposed control
law
is
u ¼ ĜnðxÞð�2λ €~y�λ2 _~y�k satðs=ΦÞ�F̂ ðxÞÞ ð12Þ
with satð�Þ the saturation function.
If we consider no errors in the modelling of the hovering
system, then ĜðxÞ ¼ GðxÞ. Let ΔZjFðxÞ�F̂ ðxÞj be an upper
bound of
the error in the estimation of FðxÞ, then it suffices to choose

k4Δ.
Considering extreme values for seawater density, the value of Δ
for changes in water density can be obtained. In the case of
wave
induced forces the value of Δ cannot be explicitly obtained due
to
the random nature of these forces. However, for a given sea
state,
upper bounds can be estimated. The choice of k¼0.001 is
enough
to account for both the density changes and the wave induced
forces in Sea State 5. For the rest of parameters we have taken
d bow (right) tanks for Scenario 1.
Fig. 5. Depth evolution for Scenario 2.
Fig. 6. Blowing valve aperture (top) and venting valve aperture
(bottom) for Scenario 2.
447446
λ ¼ 0:05, Φ ¼ 0:001. If modelling uncertainties, like those
discussed
in Section 2.2, were considered, an upper bound of the
associated
error should also be estimated and taken into account in the
choice of k.
4. Numerical simulations
The aim of this section is to test the performance of the
proposed hovering system against the disturbances treated in
Section 2.4. Two different scenarios are considered. In both
cases

the submarine starts at straight and level flight at 4 kn and at
t¼0
the propeller is stopped and the vehicle progressively loses
forward speed (it is around 0.4 kn at the end of simulation
time).
In the first scenario (Figs. 3 and 4) the submarine is at 50 m
depth
under the action of sea wave disturbances (Sea State 5, with
H1/3¼3.25 m, Tz¼6.2 s). Additionally, the hovering system has
to
compensate for sudden changes in water temperature. For
0rtr1250 s temperature varies with depth as TðzÞ ¼ 20�0:05z
1C.
At t¼1250 s, the temperature gradient is changed to TðzÞ ¼
5 þ 0:05z 1C. The vehicle buoyancy is affected by these
gradients
according to (7).
Flooded volume in stern and bow tanks is plotted in Fig. 4. We
can see how the buoyancy variation is rapidly compensated by
emptying the tanks. Depth evolution is plotted in Fig. 3.
Although
depth keeping is satisfactory for both temperature gradients, we
can see how, after the instability caused by the density jump,
the
second gradient, where the density increases with depth, is more
favourable. Indeed, density increasing with depth tends to com-
pensate the effect of hull compressibility while decreasing
density
adds up to …
Ocean Engineering 72 (2013) 441–447
Contents lists available at ScienceDirect

Ocean Engineering
0029-80
http://d
n Corr
E-m
jgpelaez
journal homepage: www.elsevier.com/locate/oceaneng
On a submarine hovering system based on blowing and venting
of ballast tanks
Roberto Font a,n, Javier García-Peláez b
a Departamento de Matemática Aplicada y Estadística, ETSI
Industriales, Universidad Politécnica de Cartagena, 30202
Cartagena, Spain
b Direction of Engineering, DICA, Navantia S. A., Cartagena
30205, Spain
a r t i c l e i n f o
Article history:
Received 27 July 2012
Accepted 27 July 2013
Available online 19 August 2013
Keywords:
Manned submarines
Underwater hovering
Variable buoyancy
Sliding control
18/$ - see front matter & 2013 Elsevier Ltd. A
x.doi.org/10.1016/j.oceaneng.2013.07.021
esponding author. Tel.: +34 968 338 947; fax:
ail addresses: [email protected], robertojav

@navantia.es (J. García-Peláez).
a b s t r a c t
A submarine hovering system based on the blowing and venting
of a set of dedicated tanks is
investigated. We review the mathematical models involved and
propose a sliding mode controller for
the input–output linearized system. Numerical simulation
results support the idea that this could be a
promising hovering strategy for manned submarines,
autonomous underwater vehicles or other plat-
forms.
& 2013 Elsevier Ltd. All rights reserved.
1. Introduction
Underwater hovering, the ability to statically keep a desired
depth, is at the same time a challenge, due to many uncertainties
associated with the underwater environment, and a very impor-
tant feature for both small size autonomous underwater vehicles
(AUVs) and large manned submarines. In the last years several
hovering AUVs have been developed (see Vasilescu et al., 2010
for
a survey on the subject). The hovering facility expands the
capabilities of AUVs allowing them to perform more complex
missions that previously could only be carried out through
Remotely Operated Vehicles (ROVs). For manned submarines,
accurate hovering can be an invaluable tool, for example, for
safe
swimmer delivery, cover supply replacement or the deployment
and recovery of AUVs, a subject that has recently raised an
extraordinary interest (see for example Hardy and Barlow,
2008;
Martínez-Conesa and Oakley, 2011).
From the technological point of view, AUVs usually hover by

using thrusters (Choi et al., 2003; Li et al., 2011). Due to the
large
energy requirements of this approach, however, buoyancy
control
by pumping seawater in or out of ballast tanks can be used to
save
energy (Vasilescu et al., 2010) or in larger designs (Tangirala
and
Dzielski, 2007). In manned submarines, hovering is
traditionally
performed using hydraulic pumps (Yang and Hao, 2010; Ying
and
Jian, 2010), although not very much information about hovering
ll rights reserved.
+34 968 338 916.
[email protected] (R. Font),
systems is available in the literature due to the military nature
of
these vehicles.
The aim of this work is to investigate the feasibility of a
hovering system in which dedicated tanks are blown and vented
similarly to the way the main ballast tanks are traditionally
operated in manned submarines.
In these vehicles, a variable number of main ballast tanks are
distributed along the hull. In case of emergency the main ballast
tanks can be emptied by blowing into them air from high
pressure
bottles. This way the water is expelled from the tanks, the
vehicle
gains buoyancy and can rise more quickly. To fill the tanks with
water, air is vented out of the ballast tanks. In the previous
works
(Font et al., to appear, 2013) we proposed mathematical models

for
the blowing and venting of ballast tanks and showed that the
implementation of a control system for these processes, usually
performed manually, can improve in a significant way the
perfor-
mance and stability in emergency rising manoeuvres. Our objec-
tive is to extend the approach used with the main ballast tanks
to a
set of dedicated hovering tanks (see Section 2 for details) in
order
to test the feasibility of a hovering system based on blowing and
venting of tanks. Although throughout this paper we will use a
manned submarine as test platform, it is worth noting that the
use
of blowing and venting of tanks as hovering control is not
limited
to these vehicles nor is our intention to carry out the discussion
of
conceptual designs for the compromise between efficiency and
stealth in a hovering system ready for military applications.
Indeed, this technology could be applicable to manned submar-
ines, AUVs, ROVs or any offshore platform requiring variable
buoyancy control.
The rest of the paper is organized as follows. In Section 2
we formulate the problem and describe the mathematical models
www.sciencedirect.com/science/journal/00298018
www.elsevier.com/locate/oceaneng

Table 1
Summary of symbols introduced in Section 2.1.
Av Vent pipe cross-section (m
2)
hwc(t) Height of water column in the tank (m)
mB(t) Mass of air in ballast tank (kg)
mF(t) Mass of air in pressure bottle (kg)
mF0 Initial mass of air in pressure bottle (kg)
_mFðtÞ Mass flow rate from pressure bottle (kg/s)
_m ðtÞ Mass flow rate through venting valve (kg/s)
447442
for blowing and venting processes, vehicle motion and external
disturbances. In Section 3 we propose a feedback control
scheme
for the hovering submarine consisting of a sliding mode
controller
acting on a previously input–output exactly linearized system.
Section 4 is devoted to the results of numerical simulations
testing
the performance of the proposed hovering system. Finally, in
Section 5 we discuss the obtained results and present some
conclusions.
v

pB(t) Pressure in ballast tank (Pa)
pext(t) Pressure outside the venting valve (Pa)
pF(t) Pressure in bottle (Pa)
pF0 Initial pressure in bottle (Pa)
pSEA(t) Pressure outside the outlet hole (Pa)
qB(t) Water flow through outlet hole (m
3/s)
Rg Gas constant for air (J/kg K)
TB Water temperature (K)
VB0 Initial air volume in ballast tank (m
3)
VB(t) Volume of air in ballast tank (m
3)
VF Pressure bottle volume (m
3)
γ Isentropic constant
ρ Density of water (kg/m3)
2. Problem formulation. Mathematical models
As we said above, we will consider a manned submarine,
particularly the Navantia P-650 design, as the test platform for
our hovering system. Details about the hydrodynamic character-
istic and the blowing/venting system can be found in García et
al.
(2011) and Font et al. (to appear) respectively.
Our objective is to maintain a desired depth with no propulsion
(and thus without any help from the control surfaces) in the face
of external disturbances like changes in water density or forces
induced by the sea state. In the next sections we review the
mathematical models for the blowing/venting system, vehicle
motion and external disturbances.

2.1. Blowing/venting system
The blowing and venting system is composed of the tank, the
pressure bottle, the blowing and venting valves and the outlet/
inlet hole located at the bottom of the tank. When the blowing
valve is opened, air flows into the tank from the bottle
increasing
the pressure and forcing the water to flow out through the outlet
hole. When the venting valve is opened, air can flow out from
the
tank letting the water flow back into the tank. Fig. 1 shows
a schematic view of these processes. The subindex F denotes
conditions in the bottle, the subindex B denotes conditions in
the
tank, _mF and _mv are respectively the mass flow rates through
blowing and venting valves, qB is the water flow through the
tank
hole, hwc is the height of the water column in the tank and
pSEA,
pext are respectively the hydrostatic pressures outside the flood
port and venting outlet (they differ in the depth at which each
one
is evaluated). We will use 3 variables for each tank to
completely
describe its state: mass of air in the bottle, mF, mass of air in
the
tank, mB, and pressure in the tank, pB. We refer the reader to
Font
et al. (to appear) and Font and García (2011) for a more detailed
description of the model presented below. The symbols
introduced
in this section are summarized in Table 1.
Due to the high pressure difference between bottle and tank,
the flow from the bottle will usually be supersonic. As the

bottle
empties, however, this difference decreases and the flow can
become subsonic if the pressure ratio is below the critical
pressure
Fig. 1. Blowing and venting processes.
ratio Pc ¼ ððγ þ 1Þ=2Þγ=ðγ�1Þ, with γ the isentropic constant.
Let s
denote the variable aperture of the blowing valve, the equation
for
the mass of air in the bottle in both the supersonic and the
subsonic cases is
_mF tð Þ ¼ s tð ÞA
mFðtÞγþ1pF0
mγF0VF
!1=2
μ pB tð Þ; mF tð Þ
� �
ð1Þ
where A ¼ _mFmaxðð2=ðγ þ
1ÞÞ�ðγþ1Þ=ðγ�1ÞVF=γpF0mF0Þ1=2, with _mFmax
the maximum mass flow rate from the bottle, experimentally
measured, VF is the bottle volume, pF0, mF0 are respectively
the
initial pressure and mass of air in the bottle and
μ pB; mF
� �
¼

ffiffiffiffiffiffiffiffiffiffiffiffiffi
γ
2
γ þ 1
� �ðγþ1Þ=ðγ�1Þs
; Pc r
pF
pBffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2γ
γ�1
pB
pF0
mF
mF0
� �γ
0
[email protected]
1
CCA
2=γ
� pB
pF0
mF

mF0
� �γ
0
[email protected]
1
CCA
ðγþ1Þ=γ0
[email protected]
1
CCA
vuuuuut ; 1opFpB oPc
0;
pF
pB
r1:
8>>>>>>>>>>>>>><
>>>>>>>>>>>>>>:
The mass flow through the venting valve is obtained similarly.
The variation in the mass of air in the tank is the difference
between the mass flow rate from the bottle and the mass flow
rate
through the venting valve. Let s denote the aperture of the
venting
valve. Then, the equation for the mass of air in the tank is
_mB tð Þ þ _mF tð Þ ¼ �μ
pextðtÞ
pBðtÞ

� �
sðtÞAvpBðtÞffiffiffiffiffiffiffiffiffiffi
RgTB
p ; ð2Þ
where Av is the venting pipe system cross-section, Rg is the gas
constant for air, TB is the temperature in the tank and
μðpextðtÞ=pBðtÞÞ
is a function of the tank and outside pressures obtained by curve
fitting from experimental measures.
Finally, the variation in the tank pressure is obtained from the
perfect gas equation as
mBðtÞ
pBðtÞ
_pB tð Þ� _mB tð Þ ¼ �
pBðtÞqBðtÞ
RgTB
; ð3Þ
where qB(t) is the water flow through the flood port.
We will consider two hovering tanks, bow and aft, with their
respective bottles and blowing and venting valves. The
geometric
characteristics of the blowing and venting system have been
adapted from the characteristics of the main ballast tanks
blowing
and venting system which can be found in Font et al. (to
appear).

Table 2
Hovering system characteristics.
Parameter Stern tank Bow tank
Flood port area, Ah ðm2Þ 0.1 0.1
Venting pipe system cross-section, Av ðm2Þ 9.62 � 10�4 9.62
� 10�4
Tank height, Htk (m) 1.5874 1.5874
Maximum mass flow rate, _mF;max ðkg=sÞ �2 �2
Initial bottle pressure, pF0 (Pa) 2.5 � 107 2.5 � 107
Initial bottle temperature, TF0 (K) 4 4
Tank volume, VBB ðm3Þ 293 293
Bottle volume, VF ðm3Þ 0.8 0.8
Tank location (m)
xb �28.6 23.7
yb 0 0
zb 0.595 0.595
447 443
However, since the size of the main ballast tanks is not
adequate
for the hovering system requirements, the size of the hovering
tanks has been considerably reduced with respect to the main
ballast tanks. Precisely, each hovering tank has a volume of 4
m3
and is initially filled up to half of its capacity. In the same way,
the
maximum mass flow rate from the bottle has been reduced to
2 kg/s. The main characteristics of the hovering system are
summarized in Table 2. We note that these are tentative values
in the context of this preliminary study. Of course, the

implemen-
tation in a real ship would require the careful selection of the
most
appropriate values.
2.2. Vehicle motion
Vehicle motion is given, as usual, by Feldman's (1979) 6 degree
of freedom equations of motion. The final form of these
equations
adapted to the particular vehicle we are considering can be
found
in García et al. (2011).
These equations assume the mass of the submarine to be
constant. In our case, however, water flowing in or out of the
hovering tanks will cause mass variations at several points of
the
vehicle. We will therefore need to write vehicle mass, weight,
moments and products of inertia and location of center of
gravity
as a function of the amount of water in the tanks.
Let m0 be the initial mass of the vehicle and Δmstern, Δmbow
the
mass variations in the stern and bow tanks respectively (positive
when mass is added). This mass variation can be obtained by
multiplying the increase in the volume occupied by water with
respect to the initial condition by the density of water, ρ. It is
easy
to see that this increase coincides with the decrease in the
volume
of air, i.e. the difference between the initial and momentary
volume of air in the tank. This way
Δmfstern;bowg tð Þ ¼ ρ VB0�VBfstern;bowg tð Þ

� �
¼ ρ VB0�
mBfstern;bowg ðtÞRgTB
pBfstern;bowg
!
;
and the momentary mass of the vehicle is given by
mðtÞ ¼ m0 þ ΔmsternðtÞ þ ΔmbowðtÞ:
The rest of parameters can be obtained analogously (Font et al.,
to
appear).
It is worth noting that coefficient based models can lead to
inaccurate results in certain situations. In movements at high
angles of incidence, like hovering, vortices generated by
crossflow
separation of the hull boundary layer and the trailing wakes
from appendages can produce significant loads (Watson et al.,
1993). We do think, however, that this standard model is
enough
for the purposes of this preliminary study. Up to our best
knowl-
edge, it is not easy to account for these phenomena without
using
computationally intensive techniques that are not suitable for
control system design (see for instance Bettle et al., 2009). Our
objective (see Section 3) is to design a robust controller that
can
maintain consistent performance in the presence of large
external
disturbances and/or modelling uncertainties. This approach has

been successfully used in the design of a variety of hovering
AUVs.
We refer the reader to, for example, Riedel et al. (2005) where a
sliding mode controller is used to address a similar problem.
2.3. Complete model in affine form
Let the state vector be
x ¼ ½x; y; z; ϕ; θ; ψ; u; v; w; p; q; r; …
mFstern ; mBstern ; pBstern ; mFbow ; mBbow ; pBbow � ð4Þ
composed of the state variables for the stern and bow tanks, the
vehicle position and orientation, x, y, z and ϕ (roll), θ (pitch)
and
ψ (yaw) respectively, and the linear and angular velocities, u, v,
w
and p, q, r. Let u ¼ ½sstern; sstern; sbow; sbow� be the control
vector. The
state law is composed of the equations of motion (see Section
2.2)
plus a set of Eqs. (1)–(3) for each of the two hovering tanks.
This
state law can be expressed in compact form as
AðxÞ _x ¼ Φðx; uÞ ð5Þ
where A (x) is the mass matrix of the system.
As we will see in Section 3, it is convenient, from the point of
view of control system design, to express (5) in the affine form
_x ¼ fðxÞ þ ∑
m
i

giðxÞui: ð6Þ
This expression can be obtained from (5) as follows. It is easy
to
see that the state law (5) can be expressed as
AEMðxÞ 012�6
06�12 ABV ðxÞ
" #
_x ¼
ΦEMðxÞ
ΦBV ðx; uÞ
" #
where AEM (x) and ΦEMðxÞ are respectively the mass matrix
and the
right hand side of the equations of motion, depending only on
the
state variable, ΦBV ðx; uÞ is the right hand side of Eqs. (1)–
(3), and
ABV xð Þ ¼
1 0 0 0 0 0
1 1 0 0 0 0
0 �1 mBstern
pBstern
0 0 0
0 0 0 1 0 0
0 0 0 1 1 0

0 0 0 0 �1 mBbow
pBbow
2
6666666666664
3
7777777777775
Since both AEM (x) and ABV (x) take non-singular values for
any
x (Font et al., to appear), the state law can be expressed in
explicit
form as
_x ¼
A�1EMΦEMðxÞ
A�1BV ΦBV ðx; uÞ
" #
It is immediate to separate the terms where the control input
appears to obtain the desired form (6) with
f xð Þ ¼ A�1EMΦEM; 0; 0;
pBstern qBstern
mBstern RgTB
; 0; 0;
pBbow qBbow
mBbow RgTB
T

447444
and gi; 1rmr4, the columns of the matrix
012�4
αstern 0 0 0
�αstern βstern 0 0
�pBstern
mBstern
αstern
pBstern
mBstern
βstern 0 0
0 0 αbow 0
0 0 �αbow βbow
0 0 �
pBbow
mBbow
αbow
pBbow
mBbow
βbow
2
6666666666666664
3

7777777777777775
with
αfstern;bowg ¼ μfstern;bowgA
mγþ1Ffstern;bowg pF0
mγF0VF
0
@
1
A
1=2
;
βfstern;bowg ¼ �μfstern;bowg
AvpBfstern;bowgffiffiffiffiffiffiffiffiffiffi
RgTB
p :
2.4. External disturbances
The main disturbances that a submerged submarine must face
are the wave induced forces and the changes in its buoyancy
caused by seawater density changes and hull compressibility.
2.4.1. Wave induced forces
The surface elevation of a long-crested irregular sea can be
modelled as a sum of N regular wave components. The
amplitude
of each regular wave is given by a wave energy spectrum, in
this

case the Pierson–Moskowitz spectrum. A detailed description of
this approach can be found in Fossen (1994).
To model the effect of an irregular sea over the vehicle it is
usual to consider 1st and 2nd order wave disturbances. Using
the
superposition principle the 1st order forces (in this work we
will
consider a heave force and a pitching moment) can be modelled
as
the sum of the forces caused by each individual regular compo-
nent, i.e. a wave with the same frequency and different
amplitudes
and phase angles.
For this work, the amplitude and phase angle of the vertical
force and pitching moment, Fi; Mi; ΦF;i; ΦM;i, have been
obtained
experimentally using captive tests on a scale model. The ampli-
tudes and phase angles under regular waves of different wave-
lengths were measured for several heading directions. These
data
were then adjusted using a least-squares fit. Fig. 2 shows the
results for the vertical force and pitching moment at 1801 wave
Fig. 2. Non-dimensional force (left) and moment (right) vs non-
dimensional wave leng
solid line.
heading. In this case the fitted curves are
F
ρgHL2
¼
0:01161
λ

L
λ
L
� �2
�3:898λ
L
þ 5:046
M
ρgHL3
¼
0:001932
λ
L
λ
L
� �2
�2:398λ
L
þ 1:917
where L is the vehicle length, λ the wave length, H the wave
height
and g the acceleration due to gravity. A similar methodology
was
used in Byström (1988).

The 2nd order force, or suction force, is an upward force,
usually small in comparison with 1st order forces. Under an
irregular sea, this is a slowly varying force (Booth, 1983). For
the
purpose of this work, however, it suffices to consider a mean
constant value. The series of captive tests mentioned above
provided a mean value for the suction force under Sea State 5 of
0.8 ton.
Both the 1st and 2nd order forces are assumed to decay
exponentially with depth in the form e�kiðzðtÞ�z0Þ where ki
is the
wave number of each component. For the suction force, k was
taken corresponding to the peak of the spectrum.
2.4.2. Compressibility and water density
Vehicle buoyancy can be expressed as B ¼ ρg∇ fd, where ρ is
the
water density and ∇ fd is the form displacement, i.e. the total
displaced volume in submerged condition. In trim condition the
vehicle buoyancy is equal to its weight. If the submarine moves
down from the equilibrium position, however, the outside pres-
sure will compress the hull and other materials reducing the
vehicle buoyancy, which will result in a downward acceleration.
In
the same way, moving the submarine up from its equilibrium
position will result in an upward acceleration (see, for instance,
Booth, 1983). The displacement variation caused by pressure
hull
compressibility can be considered linear with depth in the form
ΔVcðzÞ ¼ αðz�z0Þ, where α is a compression coefficient that
can be
easily determined for each particular vehicle.
Similarly, changes in seawater density will modify the vehicle

buoyancy also causing a destabilizing effect. The seawater
density
as a function of temperature and salinity can be obtained using
the
algorithms described in Fofonoff and Millard (1983). Let us
assume
that, for a certain temperature/salinity vertical profile, the water
density can be expressed as a function of depth. Let ρðzÞ
denote
this variable density (we will continue to denote the nominal
value by ρ). The vehicle buoyancy is given by
BðzÞ ¼ ρðzÞgð∇ fd�ΔVcðzÞÞ: ð7Þ
th for wave heading 1801. Measured values are shown as circles
and fitted curve as
447 445
3. Sliding mode controller
Sliding mode control (Slotine and Li, 1991) has been success-
fully applied in several AUV designs and has been identified as
one
of the most promising control strategies to account for large
disturbances or model uncertainties (Lea et al., 1999). Although
sliding mode control is often applied over a linearized model
(Demirci and Kerestecioğlu, 2004; Riedel et al., 2005), our
previous
experience with the dynamic model of the submarine leads us to
think that in this case, due to high coupling and severe
nonlinea-
rities, this could be inaccurate. Instead, we propose an exact
input–output feedback linearization (Isidori, 1995). The sliding
control of a nonlinear system using input–output linearization is

discussed more generally in Fossen and Foss (1991).
For the hovering control we will consider a single output, the
depth z, and 4 inputs, the apertures of the blowing and venting
valves. This way, the system can be expressed (see Section 2.3)
as
_x ¼ fðxÞ þ ∑
m
i
giðxÞui
y ¼ hðxÞ ¼ z: ð8Þ
Let Lfh, Lgi h denote the Lie derivatives of h with respect to f
and
gi respectively. The repeated Lie derivatives are recursively
defined
as Ljf h ¼ Lf ðL
j�1
f hÞ. In the same way, Lgi L
j
f h ¼ Lgi ðL
j
f hÞ. The computa-
tion of Lgi L
j
f h; j ¼ 1…r, shows that the system has a well defined
relative degree r¼3. We refer the reader to Isidori (1995) for
more

detail on this subject.
Define FðxÞ ¼ Lrf h and GðxÞ ¼ ½Lg1 L
r�1
f h ⋯ Lgm L
r�1
f h�. This way (8)
can be expressed as
yðrÞ ¼ FðxÞ þ GðxÞ
u1
⋮
um
2
64
3
75 ð9Þ
that can be reduced to
yð3Þ ¼ v ð10Þ
Fig. 3. Evolution of depth for Scenario 1.
Fig. 4. Flooded volume in stern (left) an
using the control law
u ¼ GnðxÞðv�FðxÞÞ ð11Þ
where GnðxÞ is a vector such that GðxÞGnðxÞ ¼ 1.
Once the input–output relation in system (8) has been reduced
to the linear form (10) it is easy to use linear control techniques

to
stabilize (10). The exact cancellation of the nonlinear terms,
however, relies on the perfect knowledge of fðxÞ and giðxÞ,
some-
thing that can hardly be achieved due to modelling errors or
unknown external disturbances. We propose the use of sliding
mode control to account for this issue.
Let y ¼ ½y _y ⋯ yðr�1Þ� be the output vector, yd ¼ ½yd _yd
⋯ yðr�1Þd � a
desired output vector and ~y ¼ y�yd ¼ ½~y _~y ⋯ ~yðr�1Þ�
the tracking
error vector. For r¼3 the sliding surface can be defined as
s ¼ €~y þ 2λ _~y þ λ2 ~y:
Taking the derivative with respect to time in the above equation
and taking into account that in our case yð3Þd ¼ 0 and in the
absence
of uncertainties yð3Þ ¼ v, the equivalent control is veq ¼ �2λ
€~y�λ2 _~y .
Let F̂ ðxÞ; ĜðxÞ be the estimates of FðxÞ and GðxÞ,
respectively. If
the signum function is linearly smoothed inside a boundary
layer
of thickness Φ (Slotine and Li, 1991), then the proposed control
law
is
u ¼ ĜnðxÞð�2λ €~y�λ2 _~y�k satðs=ΦÞ�F̂ ðxÞÞ ð12Þ
with satð�Þ the saturation function.
If we consider no errors in the modelling of the hovering
system, then ĜðxÞ ¼ GðxÞ. Let ΔZjFðxÞ�F̂ ðxÞj be an upper

bound of
the error in the estimation of FðxÞ, then it suffices to choose
k4Δ.
Considering extreme values for seawater density, the value of Δ
for changes in water density can be obtained. In the case of
wave
induced forces the value of Δ cannot be explicitly obtained due
to
the random nature of these forces. However, for a given sea
state,
upper bounds can be estimated. The choice of k¼0.001 is
enough
to account for both the density changes and the wave induced
forces in Sea State 5. For the rest of parameters we have taken
d bow (right) tanks for Scenario 1.
Fig. 5. Depth evolution for Scenario 2.
Fig. 6. Blowing valve aperture (top) and venting valve aperture
(bottom) for Scenario 2.
447446
λ ¼ 0:05, Φ ¼ 0:001. If modelling uncertainties, like those
discussed
in Section 2.2, were considered, an upper bound of the
associated
error should also be estimated and taken into account in the
choice of k.
4. Numerical simulations
The aim of this section is to test the performance of the
proposed hovering system against the disturbances treated in

Section 2.4. Two different scenarios are considered. In both
cases
the submarine starts at straight and level flight at 4 kn and at
t¼0
the propeller is stopped and the vehicle progressively loses
forward speed (it is around 0.4 kn at the end of simulation
time).
In the first scenario (Figs. 3 and 4) the submarine is at 50 m
depth
under the action of sea wave disturbances (Sea State 5, with
H1/3¼3.25 m, Tz¼6.2 s). Additionally, the hovering system has
to
compensate for sudden changes in water temperature. For
0rtr1250 s temperature varies with depth as TðzÞ ¼ 20�0:05z
1C.
At t¼1250 s, the temperature gradient is changed to TðzÞ ¼
5 þ 0:05z 1C. The vehicle buoyancy is affected by these
gradients
according to (7).
Flooded volume in stern and bow tanks is plotted in Fig. 4. We
can see how the buoyancy variation is rapidly compensated by
emptying the tanks. Depth evolution is plotted in Fig. 3.
Although
depth keeping is satisfactory for both temperature gradients, we
can see how, after the instability caused by the density jump,
the
second gradient, where the density increases with depth, is more
favourable. Indeed, density increasing with depth tends to com-
pensate the effect of hull compressibility while decreasing
density
adds up to this destabilizing effect (see Section 2.4).
For the second scenario we consider a more unfavourable
situation, with a depth of 35 m and Sea State 5. Fig. 5 shows the

evolution of vehicle depth. We can see how, again, the system
shows excellent performance with maximum error around 1.5 m.
The control inputs over a 250 s interval are shown in Fig. 6. In
all
cases there is no appreciable chattering and the oscillations are
smooth and compatible with the physical restrictions
considered.
The autonomy of the air bottles is around 30 min in this
operating condition and above 90 min at the same depth and
Sea State 4.
5. Conclusions
The performance of a hovering system based on blowing and
venting of ballast tanks has been investigated using a manned
submarine as test platform. Simulation results show that this
system has the ability to maintain a desired depth in the
presence
of significant external disturbances.
The blowing and venting of tanks, alone or in conjunction with
another control mechanism, like pumping, seems to be a promis-
ing hovering strategy to be used in manned submarines, AUVs
or
other submarine platforms.
Accuracy and fast response are the potential advantages of this
approach. On the other hand, the dependence on air bottles with
their associated payload and limited autonomy are the main
disadvantages for small platforms like AUVs. In the case of
manned
submarines, the main limitation is the noise generation
associated
with the blowing process. However, since the needed flow rates
are considerably lower than the flow rates used when blowing
the
main ballast tanks, we do believe that this problem could be

mitigated with an appropriate design of the blowing system.
This
will be the subject of our future work.
Acknowledgements
This work was supported by projects 2989/10MAE from
Navantia S.A. and 08720/PI/08 from Fundación Séneca,
Agencia
de Ciencia y Tecnología de la Región de Murcia (Programa de
Generación de Conocimiento Científico de Excelencia,
IIPCTRM
2007-10).
References
Bettle, M.C., Gerber, A.G., Watt, G.D., 2009. Unsteady analysis
of the six DOF motion
of a buoyantly rising submarine. Computers and Fluids 38,
1833–1849.
http://refhub.elsevier.com/S0029-8018(13)00320-X/sbref1
http://refhub.elsevier.com/S0029-8018(13)00320-X/sbref1
447 447
Booth, T.B., 1983. Optimal depth control of an underwater
vehicle under a seaway.
In: RINA International Symposium on Naval Submarines,
London, UK.
Byström, L., 1988. Adaptive control of a submarine in a
snorting condition in waves.
In: Warship 88, London.
Choi, H.T., Hanai, A., Choi, S.K., Yuh, J., 2003. Development

of an underwater robot,
ODIN-III. In: International Conference on Intelligent Robots
and Systems, Las
Vegas, USA.
Demirci, U., Kerestecioğlu, F., 2004. A re-configuring sliding-
mode controller with
adjustable robustness. Ocean Engineering 31, 1669–1682.
Feldman, J., 1979. Revised Standard Submarine Equations of
Motion. Report
DTNSRDC/SPD-0393-09. David W. Taylor Naval Ship
Research and Development
Center, Washington, DC.
Fofonoff, …
486 IETE TECHNICAL REVIEW | VOL 28 | ISSUE 6 |
NOV-DEC 2011
A Review Note for Position Control of an
Autonomous Underwater Vehicle
Ahmed Rhif
Department of Electronics, High Institute of Applied Sciences
and Technologies, Sousse, Tunisia
(Institut Supérieur des Sciences Appliquées et de Technologie
de Sousse)
Abstract
A new autonomous underwater vehicle (AUV) called H160 is
described in this article. The first prototype of

this AUV has been realized through collaboration between two
partners, which are the Laboratory of Data
processing, Robotics and Micro electronic of Montpellier
(LIRMM) and the ECA‑HYTEC (specialist in the de‑
sign and manufacture of remote controlled systems in “hostile”
environments). This paper shows a general
presentation of the vehicle, its hardware and software
architecture including the process modeling and the
control law used. Simulation results presented are based on the
AUV mathematical model.
Keywords
Autonomous underwater vehicle, Position control, Sliding mode
control, Underwater vehicle.
1. Introduction
The concept of underwater vehicle is not a recent idea.
The first proposal was designed by William Bourne
in 1578. In 1664, Cornelis Van Drebbel proposed the
first underwater vehicle advancing using 12 oarsmen
equipped with special oars that could be actuated in
order to carry out vertical movements. This ovoid boat
was built of wood and had been tested experimentally.
In 1776, David Bushnell and his brother introduced the
first submarine “Turtle” built out of steel. Its principle
operation was similar to that of the current submarines.
This mobile used a propeller for its propulsion. The
machine was immersed by actuating a valve, allowing
the water admission in a tank which was used as bal-
last. It went up thanks to a pump which expelled water.
Oxygen autonomy was of 30 min (Pararas‑Carayannis,
1976). Nowadays, the submarines have strongly evolved
from a technological point of view. A classification of the
underwater vehicles in two groups is proposed: Manned
vehicles and unmanned vehicles [1].

Under the manned vehicles, we can distinguish two
categories of underwater vehicles:
• The large‑sized submarines operated by a crew which
can reside on during long periods. This category
belongs to the military submarines.
• The small‑sized submarines intended for the great
depths’ exploration. The crew of this kind of machine
is reduced (two to three persons) and the oxygen quan-
tity is limited. For example, Nautile was conceived by
Ifremer 1 in 1984 and can immerse up to 6000 m with
three passengers. Its main missions were the search
for hydrothermal sources in the Pacific Ocean.
The unmanned vehicle was specially the interest of the
navy. In 1866, the Austrian navy asked Robert Whitehead
to develop a new weapon for the warships. He showed
the effectiveness of a system propelled at a speed of
3 m/s to a distance of 700 m transporting an explosive
load: The torpedo was born. However, this machine
did not have any monitoring system. Those underwater
vehicles exist in three different technology: those con-
nected to the surface by a cable, vehicle connected by
an acoustic bond, and finally completely autonomous
vehicles [2‑4].
Actually, the first autonomous underwater vehicles
(AUVs) developed during 1960s–1970s were as fol-
lows:
• The Self‑propelled Underwater Research Vehicle
(SPURV, USA, 1977): It weighed 480 kg and could
operate at a speed of 2.2 m/s during 5 hours until
a depth of 3000 m. The vehicle was acoustically

controlled from the surface. The researchers used it
to make conductivity and temperature measures to
perfect the theoretical wave modeling.
• Remotely Operated Vehicles (ROVs): Machines
equipped by a camera operated by an operator,
connected to surface via a cable, called umbilical,
by which the orders, energy and/or measurement
are provided. The principal disadvantage of these
robots is the presence of the umbilical which makes
their movements complicated and especially the
extent of their fields of application.
• Unmanned Underwater Vehicles (UUVs): Uninhabited
underwater machines which are equipped with
sophisticated systems for their navigation and their
work according to their degree of autonomy. The
487IETE TECHNICAL REVIEW | VOL 28 | ISSUE 6 |
NOV-DEC 2011
principal constraint lies in the energy necessary to
embark for mission realization. There exist two types
of UUVs:
• The AUV can be defined as a machine knowing
its position and which surfs toward an objective
[ Figure 1]. For this, we have to draw an operation list
to be carried out beforehand. The operators do not
intervene under nominal operation; the machine is
completely autonomous.[5]
• The Untethered Underwater Vehicle (UUV) func-
tions like the AUV, but there exists an acoustic bond

between the surface and the machine, allowing the
verification and the data exchange. In the event of
problems, the operator can order the system to be
in an emergency situation implying its return to the
surface. It is important to note that the redundancy
of term UUV poses a problem. In fact, UUVs are also
called AUVs.
2. Autonomous Underwater Vehicle Description
The AUVs can be classified into two types depending
on the immersion depth, i.e. AUVs coastal and AUVs
deep seas. From a few hundred meters of depth, the
dimensions, structure and the characteristics of the AUVs
change. This limit of depth makes difference between the
deep seas vehicles from the coastal one [2].
Today, the underwater robots are an integral part of
the scientific equipment for sea and ocean exploration.
Many examples show that ROVs and AUVs are used in
many fields and for various applications like the inspec-
tion, the cartography or bathymetry [1]. However, we
can distinguish a limiting depth for the various types
of existing autonomous underwater machines. Indeed,
starting from 300 m, the structure, dimensions and the
characteristics of these vehicles change. We have, on one
side, AUVs Hugin 3000 type of Kongsberg Simrad, the
Sea Oracle of Bluefin Robotics or Alistar 3000 of ECA,
which can reach depths of 3000 m, have a very great
autonomy, considerable dimensions and a weight which
requires important logistics. On the other side, AUVs
of Remus Hydroid or Gavia Hyfmind types, with much
less autonomy, but of reduced dimensions and logistics
and with good modularity capacities, seem to be the per-
fect tool for the exploration of not very deep water [2].

In this context, the Laboratory of Data processing,
Robotics and Micro electronic of Montpellie (LIRMM)
and the ECA‑HYTEC company became partners to
develop the first prototype of the AUV H160. This
prototype was developed to surf and position with the
using a global positioning system (GPS). On the surface,
the torpedo must be able to transmit the mission’s data.
The applications concerned are the inspection, bathym-
etry, the chemical data acquisition or sonar and video
images. The machine also has the possibility of surfing
between 1 and 2 m of depth with no angle of immersion.
H160 is a torpedo type vehicle of small size and low cost,
dedicated to the applications in not very deep water (up
to 160 m). The vehicle measures 1.80 m in length with a
diameter of 20 cm and a weight of 50 kg. Thanks to its
small size, the tests on the sea require a logistics reduced
to the minimum to two people and a motor boat. The
prototype is able to accomplish a mission of at least
3 hours, maintaining its speed of 3 knots. Its positive
floatability makes it possible for the torpedo to go back
to surface after the end of each mission. H160 is fed by
a battery 48 V/16 Ah of the NiMH type, has an actuator
with DC current 230 W and 430 N cm servo‑motors for
the riders control. The torpedo immersion capacity with
no angle of pitching is due to its pair of surface riders
that constitutes the main feature of this machine [2‑5].
The torpedo is a cylindrical vehicle form as shown in
Figure 2. Its structure is mainly made up of aluminum.
We can detail the prototype in seven parts:
1. The principal part is the electronic section, composed
of two stages. The first stage accommodates the
battery, while the second one is composed of all the

embarked charts (sensors, power, PC, etc.). This part
is obviously tight.
2. Section made by the antennas for GPS, Radio and
Wifi, also by the riders’ control of the front immersion.
3. The sensor Conductivity Temperature Depth (CTD)
and sidescan sonar are in a wet part.
4. The Doppler Log is located in a tight part.
5. The nose of the vehicle composed of a CCD camera
and two sounders.
6. Behind the principal part, we find the pressure
Figure 1: Schematic of an AUV.
Figure 2: Different components of the H160.
Rhif A: AUV Position Control
NOV-DEC 2011
pick‑ups and an emergency acoustic pinger in a wet
part.
7. Finally, the propeller and the riders constitute the
engine back part.
3. Autonomous Underwater Vehicle
Modeling and Control
3.1 Mathematical Model

For the modeling of this system, two referentials are
defined [Figure 3] [6]: One fixed referential related to
the vehicle which is defined in an origin point: R0(x0, y0,
z0) and the second one related to the Earth R(x, y, z) [1].
The referential related to the mobile R0 could be formu-
lated using the referential R as shown in Equation (1):
r r r
r r r
r r r
U U U
U U U
U U
x x z
y y x
z z
0
0
0
= +
= +

= +
cos sin
cos sin
cos sin
φ φ
θ θ
ψ ψUUx
(1)
The kinematic model is represented as follows (Equa-
tion (2)):

( )
( )
&
&
&
2
1
2
1 2 3 3
3 3 2 2
1
2
0
(2)

; ;
x
y
z
v
v
v
;; ;
;
v
u
v
w
v
p
q
r
X
Y
Z
1 2
1
2
1
=

; Γ2
K
M
N
(3)
z) reference, u represents the robot speed related to
R0(x0, y0, z0), and Γ is the forces vector applied to the
mobile.
The dynamic equation is represented by:
M C v D v gη η η η ηη η η η η η η τ( ) ( , ) (( , ) ( )&& & &+ +
+ =
(4)
and th is the input control vector.
In order to control the behavior of an underwater vehicle

in the immersion phase, we must be able to vary its
buoyancy. The buoyancy of a vehicle in immersion is
the difference between the Archimedes pressure and
the gravity. Buoyancy (denoted as Φ1) depends on the
vehicle mass (m), its volume (V) and the density of water
-m (5)
The AUV presents a strong nonlinear aspect that appears
when we describe the system in three dimensions (3D), so
the state function will present a new term of disturbances
as shown in Equation (6).
where | |j (X, u)| | ≤ MX, M > 0.
As we consider only the linear movement in immer-
sion phase, we need only four degrees of freedom. For
this, we describe the system only in two dimensions
(2D). With all the developments done, the result-
ing state space describing the system is given by
Equation (7):
X = AX + Bu (7)
where
&
&
&
&

,
. .
. . .
0 47 0 3 0 0
0 69 0 79 0 36 0
0 1 0 0
1 0 1 00
0 05
0 14
0
0
=

andB
.
.
where ω is the linear velocity, q the angular velocity, θ
the inclination and z is the depth.
Figure 3: AUV engine referentials.
u Xo
X
Y
Z

Origin referential
Yo
Zo
q r
v w
p
Fix referential
O
NOV-DEC 2011
3.2 Autonomous Underwater Vehicle Controller
Design
3.2.1 The Sliding Mode Control
The AUV position control is ensured by the sliding mode
approach. The choice of such a controller is imposed by
the strong nonlinear aspect of the AUV, thanks to the
robustness of this approach [7].
The development of the sliding mode approach
occurred in the Soviet Union in the sixties with the
discovery of the discontinuous control and its effect
on the system dynamics. This approach is classified in

the monitoring with Variable System Structure (VSS)
[8,9]. The sliding mode is strongly requested due to
its facility of establishment, its robustness against
the disturbances and model uncertainties [10]. The
principle of the sliding mode control is to force the
system to converge toward a selected surface and then
to evolve there in spite of the uncertainties and the
disturbances. The surface is defined by a set of rela-
tions between the state variables of the system. The
synthesis of a control law by sliding mode includes
two phases:
• The sliding surface is defined according to the control
objectives and to the wished performances in closed
loop.
• The synthesis of the discontinuous control is carried
out in order to force the trajectories of the system state
to reach the sliding surface, and then to evolve in spite
of uncertainties, of parametric variations, etc. The
sliding mode exists when commutations take place
in a continuous way between two extreme values
umax and umin [11]. To ensure a good commutation,
we choose a relay type control and get the desired
result when commutations are sufficiently high [12].
The sliding mode control [13] has largely proved its
effectiveness in the reported theoretical studies. Its
principal scopes of application are robotics [13‑17]
and the electrical motors [12,18,19].
For any control device which has imperfections such as
delay, hystereses, which impose a frequency of finished
commutation, the state trajectory oscillates in the vicinity
of the sliding surface. A phenomenon called chattering
appears [20].

3.2.2 The High Order Sliding Mode Control
The high order sliding mode consists of the sliding
variable system derivation [21,22]. This method allows
the total rejection of the chattering phenomenon while
maintaining the robustness of the approach. For this, two
algorithms could be used:
• The twisting algorithm: The system control is
increased by a nominal control ue; the system error,
on the phase plane, rotates around the origin until it
has been canceled. If we derive the sliding surface
(S) n times, we see that the convergence of S is even
more accurate when n is higher [23].
• The super twisting algorithm: The system control is
composed of two parts u1 and u2 with u1 being the
equivalent control and u2 the discontinuous control
used to reject disturbances. In this case, there is no
need to derive the sliding surface [6]. To obtain a
sliding mode of order n, in this method, we have to
derive the error of the system n times.
In [24], a comparison between the two algorithms was
achieved. In conclusion, we note that the super twisting
algorithm is more reliable than the twisting algorithm,
despite the approximate results, since it does not ensure
the same robustness to perturbations. Indeed, in his
arti cle [24], the author used the second‑order sliding
mode to improve the performances of a turbine torque.
Notice that the conventional control approaches of
double‑fed asynchronous generator is incapable to
make the torque convergence to the desired value, then,
the choice. Then, the choice of the high order sliding
mode approach was based on its robustness against

disturbances. On the other hand, the use of linear
surfaces in the control laws synthesis by sliding mode
was considered satisfactory by the author in terms of
stability. However, the dynamics imposed by this choice
is relatively slow. To overcome this problem, we may
use nonlinear sliding surfaces. In the same direction, to
work on the speed and position regulation or power of
asynchronous machines, we often limit the stator cur-
rent (torque) that can damage the system. In this case,
the author suggested the use of the high order sliding
mode approach considering a nonlinear switching law
that consists of two different sliding surfaces S1+ and
S1− using two switched positions. Thus, we get two
limits bands, a lower band and a higher one that reduces
the chattering phenomenon.
In the literature, different approaches have been pro-
posed for the synthesis of nonlinear surfaces [6,10,23‑
27]. In [25], the proposed area consists of two terms,
a linear term that is defined by the Herwitz stability
criteria and a nonlinear term used to improve transient
performance.
In [10], to measure the armature current of a DC motor,
Zhang Li used the high order sliding mode since it is
faster than the traditional methods such as vector control.
To eliminate the static error that appears when measur-
ing parameters, we use a Proportional Integrator (PI) con-
troller [23,28‑30]. Thus, the authors have chosen to write
the sliding surface in a transfer function of a proportional
integral form while respecting the convergence proper-
ties of the system to this surface. The same problem of

NOV-DEC 2011
the static error was treated by adding an integrator block
just after the sliding mode control [31‑34].
The tracking problem of an AUV is treated by using
sliding mode control [Figure 4] with nonlinear sliding
surface as shown in Equation (8).
s(t)=k1e(t)+k2e
.(t) (8)
where e(t) is the system error, k1 > 0 and k2 > 0.
To ensure the state convergence to the sliding hyper-
plane, we have to verify the Lyaponov stability criterion
(Equation (9)) [35‑37].
ss. ≤ ‑h|s| (9)
where h>0.
The control law can be then composed of two parts:
u=u0+u1 (10)
• u0 the nominal control
• u1 the discontinuous control allowing to reject the
disturbances.
4. Simulation Results and Discussion
Simulation results were accomplished using the MATLAB

software for both the first‑ and second‑order sliding modes
of the state function (Equation (7)) that represent the process
in the immersion phase using four degrees of freedom. In
2.5
2.0
1.5
1.0
0.5
0
-0.5
0.15
0.10
0.05
0
-0.05
-0.10
2.0
1.5

1.0
0.5
0
-0.5
-1.0
-1.5
-2.0
2.0
1.0
0
-1.0
-2.0
-3.0
-4.0
-5.0
-6.0
-7.0
0 5 10 15 20 25 30 35 40 45 50

0 5 10 15 20 25 30 35 40 45 50
0 2 4 6 8 10 12 14 16 18 20
0 5 10 15 20 25 30 35 40 45 50
Z(
m
)
ta
ta
(d
eg
)
w
(d
eg
/s
ec
)
U
t(s) t(s)
(a) (b)
(c) (d)
t(s) t(s)
Figure 4: Sliding mode control bloc representation.

Equivalent
control
∑
∑ Switching
control
Surface
Transducer
AUV
ueq
uc
xd e+
-
+
+S
u x
Figure 5: First‑order sliding mode control.
NOV-DEC 2011
this simulation, we need to study the system output evolu-

tion (the depth z), the linear control (u), the inclination θ
and the angular velocity q that ensures this output.
The sliding surface parameters used are k1=1 and k2=3.
The desired immersion point was fixed on 2m. For the
first‑order sliding mode, the simulation shows that the
system output [Figure 5a] reaches its desired value in a
short time (about 5 s) with good precision. But we notice
the presence of the chattering phenomenon (oscilla-
tions on the steady state). Moreover, the variations in
the inclination θ [Figure 5c] and in the angular velocity
q [Figure 5d] are due to this chattering phenomenon.
Other ways, the control level and the frequency of
switching of this control [Figure 5b] are not very sharp
that gives good operating conditions to actuators. By
using high order sliding mode control, the chattering
phenomenon has disappeared, the output evolution
[Figure 6a] is more stable and the tracking process is
more precise. The control level of the process is now less
than the first solution but its commutation frequency is
sharper [Figure 6b]. The inclination θ [Figure 6c] and
the angular velocity q [Figure 6d] are now very close to
0 which means that the system reaches the steady state.
5. Conclusion
An extensive review of the literature of AUVs and
tracking process by sliding mode has been carried out.
In this work, major components like actuators, sensors,
amplifier, etc. have been listed. AUVs’ controllers have
been presented, detailed and justified by the simulation
results. This paper could be a ready study for those who
want to start research with AUVs and sliding mode
control.

References
1. T. Fossen, and O. Fjellstad, “Non linear Modelling of Marine
Vehicules in 6 Degrees of Freedom”, International Journal of
Mathematical Modelling of Systems, JMMM‑1, pp. 17‑28, 1995.
2. T. Fossen, “Guidance and Control of Ocean Vehicules”, Jhon
Willey and Sons Ltd, 1994.
3. T. Salgado‑Jimenez, and B. Jouvencel, “Commande des
véhicules
autonomes sous‑marins”, LIRMM, France, 2002.
4. V. Creuze, and B. Jouvencel, “Perception et suivi de fond
pour
véhicules autonomes sous‑marins”, LIRMM, Traitement du
Signal,
Figure 6: Second‑order sliding mode control.
2.5
2.0
1.5
1.0
0.5
0
-0.5 0 5 10 15 20 25 30 35 40 45 50
Z(

m
)
2.0
1.5
1.0
0.5
0
-0.5
-1.0
-1.5
-2.0
0.12
0.10
0.08
0.06
0.04
0.02
0

-0.02
-0.04
-0.06
-0.08
U
0.1
0
-0.1
-0.2
-0.3
-0.4
-0.5
-0.6
-0.7
ta
ta
(d
eg
)

w
(d
eg
/s
ec
)
t(s)
(a)
0 5 10 15 20 25 30 35 40 45 50
t(s)
(c)
0 5 10 15 20 25 30 35 40 45 50
t(s)
(d)
0 2 4 6 8 10 12 14 16 18 20
t(s)
(b)
NOV-DEC 2011
Vol. 20, no. 4,pp.323‑336, 2003
5. S. Jean‑Mathias, J. Bruno, F. Philippe, and L. Lionel, “Un
véhicule sous‑marin autonome dédié à l’exploration des eaux
peu

profondes”, CMM’06, caractérisation du milieu marin, France,
Oct. 2006.
6. M. Rolink, T. Boukhobza, and D. Sauter, “High order sliding
mode
observer for fault actuator estimation and its application to the
three tanks benchmark”, Author manuscript, Vol.1, pp.1‑7,
2006.
7. A. Rhif, Z. Kardous, and N. Ben Hadj Braiek, “A high order
sliding
mode‑multimodel control of non linear system simulation on a
submarine mobile”, Eigth International Multi‑Conference on
Systems, Signals and Devices, Sousse, Tunisia, Mar. 2011.
8. D.S. Lee, and M. J. Youn, “Controller design of variable
structure
systems with nonlinear sliding surface,” Electronics Letters,
Vol.
25, no. 25, pp. 1715‑6, 1989.
9. V.I. Utkin, “Variable structure systems with sliding modes,”
IEEE
Transactions on Automatic Control, Vol. 22, no. 2, pp. 212‑22,
1977.
10. Z. Li, and Q. Shui‑sheng, “Analysis and Experimental Study
of Proportional‑Integral Sliding Mode Control for DC/DC
Converter”, Journal of Electronic Science and Technology of
China, Vol. 3, no. 2, 2005.
11. A. Kechich, and B. Mazari, “La commande par mode
glissant:
Application à la machine synchrone à aimants permanents
(approche linéaire)”, Afrique Science Vol. 04, pp. 21‑37, 2008.

12. A. Sellami, R. Andoulsi, R. Mhiri, and M. Ksouri, “Sliding
Mode
Control Approch for MPPT of a Photovoltaic Generator
Coupledto
a DC Water Pump”, JTEA, Sousse, 2002.
13. R. Ouiguini, R. Bouzid, and Y. Sellami, “Une commande
robuste
par mode glissant flou Appliquée à la poursuite de trajectoire
d’un
robot mobile non holonome”, CISTEMA, 2003.
14. H. Alaa, “Etude de la commande d’un dispositif de stockage
d’énergie par supercondensateurs”, JCGE’08, déc. 2008.
15. H. Brandtstädter, and M. Buss, “Control of
Electromechanical
Systems using Sliding Mode Techniques”, IEEE Conference on
Decision and Control, Spain, Dec. 2005.
16. M. Defoort, T. Floquet, and W. Perruquetti, “Commande
robuste
de robots mobiles par mode glissant, vers un ménage à
plusieurs”,
GT MOSAR, Nov. 2006.
17. Vadim, I. Utkin, and H. C. Chang, “Sliding Mode Control
on Electro‑Mechanical Systems”, Mathematical problems in
Engeneering, Vol. 8, pp. 451‑73, 2002.
18. İ. Eker, “Sliding mode control with PID sliding surface and
experimental application to an electromechanical plant”, ISA
Transaction, Turkey, Vol. 45, no. 1, pp. 109‑18, 2005.
19. V. I. Utkin, and K. D. Young, “Methods for constructing
discontinuity

planes in multidimensional variable structure systems,” Auto.
And
Remote Control, Vol.31, pp. 1466‑70, 1978.
20. R.N. Rodrigues, L.L. Luan, and V. Govindaraju,
“Robustness of
multimodel biometric fusion methods against spoof attacks”,
Journal of Visual Languages and Computing, Elsevier, Vol. 20,
pp.
169‑79, 2009.
21. N. Kemal Ure, and G. Inalhan “Design of Higher Order
Sliding
Mode Control Laws for a Multi Modal Agile Maneuvering
DCAV”,
IEEE, Turkey, 2008.
22. P. Alex, Y.B. Shtessel, and C.J. Gallegos, “Min‑max
sliding‑mode
control for multimodel linear time varying systems”, IEEE
Transaction On Automatic Control, Vol. 48, no. 12, pp.
2141‑50,
Dec. 2003.
23. T. Floquet, and W. Perruquetti, “Compte‑rendu
d’implantation
d’une commande par mode glissant d’ordre superieur sur la
plate‑forme de l’IRCCyN”, CIFA, Lille, avr. 2000.
24. B. Beltran, “Maximisation de la Puissance Produite par une
Génératrice Asynchrone Double Alimentation d’une Eolienne
par
Mode Glissant d’Ordre Supérieur”, JCGE’08, Lyon, déc. 2008.
25. A. Boubakir, F. Boudjema, C. Boubakir, and N. Ikhlef, “Loi

de Commande par Mode de Glissement avec Une Surface de
Glissement Non Linéaire Appliquée au Système Hydraulique à
Réservoirs Couplés”, 4th International Conference on Computer
Integrated Manufacturing CIP, Nov. 2007.
26. D. Boukhetala, F. Boudjema, T. Madani, M.S. Boucherit,
and N.
K. M’Sirdi, “A new decentralized variable structure control for
robot manipulators,” Int J of Robotics and Automation, Vol. 18,
pp. 28‑40, 2003.
27. Y. Feng, X. Yu, and X. Zhen, “Second‑Order terminal
sliding mode
control of input‑delay systems”, Asian Journal of Control, Vol.
8,
no. 1, pp. 12‑20, 2006.
28. B. Singh, and V. Rajagopal, “Decoupled Solid State
Controller for
Asynchronous Generator in Pico‑hydro Power Generation”,
IETE
Journal of Research, Vol. 56, pp. 139‑15, 2010.
29. B. Singh, and G. Kasal, “An improved electronic load
controller for
an isolated asynchronous generator feeding 3‑phase 4‑wire
loads”,
IETE Journal of Research, Vol.54, pp. 244‑54, 2008.
30. E.O. Hernandez‑Martinez, A. Medina, and D. Olguin‑
Salinas,
“Fast Time Domain Periodic Steady‑State

Solution
of Nonlinear
Electric Networks Containing DVRs”, IETE Journal of
Research,
Vol. 57, pp. 105‑10, 2011.
31. M. Hanmandlu, “An Al based Governing Technique for
Automatic
Control of small Hydro Power Plants”, IETE Journal of
Research,
Vol. 53, pp. …
The experiment research of high-pressure air blowing ballast
tanks
Liu Ruijie,Xiao Changrun,Liu Yihan
Naval University of Engineering,Wuhan 430033,China
Naval University of Engineering,Wuhan 430033,China

PetroChina Oil and Gas Pipeline Control Center,Beijing
100007,China
[email protected]
[email protected]
[email protected]
Key words: submarine self-propelled model;CFD;ballast
tanks;high-pressure gas
Abstract.In order to test and verify the accuracy and reasonable
of the mathematical model of the
high-pressure air blowing the main ballast tanks, the paper
design a submarine self-propelled model
with the system of high-pressure air blowing the ballast
tanks.Through the experiment without
propulsion, the paper obtains drainage performance and key
performance parameters of
motion.Through the comparing of CFD, the result shows the
ability to describe correctly the process

Experimental Analysis on Sinking Time of Littoral Submarine .docx

Experimental Analysis on Sinking Time of Littoral Submarine .docx

Recommended

Recommended

More Related Content

Similar to Experimental Analysis on Sinking Time of Littoral Submarine .docx

Similar to Experimental Analysis on Sinking Time of Littoral Submarine .docx (20)

More from rhetttrevannion

More from rhetttrevannion (20)

Recently uploaded

Recently uploaded (20)

Experimental Analysis on Sinking Time of Littoral Submarine .docx