Indonesian
J
our
nal
of
Electrical
Engineering
and
Computer
Science
V
ol.
17,
No.
3,
March
2020,
pp.
1150
1156
ISSN:
2502-4752,
DOI:
10.11591/ijeecs.v17i3.pp1150-1156
r
1150
Actuator
fault
detection
and
isolation
f
or
r
obot
manipulator
using
higher
order
sliding
mode
obser
v
ers
Khaoula
Oulidi
Omali,
Mohammed
Nabil
Kab
baj,
Mohammed
Benbrahim
USMB
A,
LIST
A
LIST
A,
Sidi
Mohamed
Ben
Abdellah
Uni
v
ersity
Fez,
Morocco
Article
Inf
o
Article
history:
Recei
v
ed
Jun
1,
2019
Re
vised
Aug
7,
2019
Accepted
Oct
3,
2019
K
eyw
ords:
F
ault
detection
and
isolation
Higher
order
sliding
mode
unkno
wn
input
observ
ers
Nonlinear
system
Robot
manipulators
ABSTRA
CT
F
ault
detection
and
isolation
(FDI)
method
for
actuator
f
aults
for
robot
manipulator
by
applying
a
model-based
FDI
f
ault,
which
may
happen
on
a
specific
component
of
the
system.
T
o
detect
and
isolate
actuator
f
aults,
higher
order
sliding
mode
Unkno
wn
Input
Observ
ers
(UIO)
are
proposed
to
mak
e
analyt
ical
redundanc
y
.
The
observ
ers
input
la
ws
are
designed
according
to
the
so-called
Super
-T
wisting
Second
Order
Sliding
Mode
Control
(SOSMC)
technique
and
the
y
are
pro
v
ed
to
be
able
to
guarantee
the
e
xponential
con
v
er
gence
of
the
f
ault
estimate
to
the
actual
f
ault
signal.
The
simulation
results
sho
w
the
ef
fecti
v
eness
and
rob
ustness
for
the
proposed
approach.
Copyright
c
2020
Insitute
of
Advanced
Engineeering
and
Science
.
All
rights
r
eserved.
Corresponding
A
uthor:
Khaoula
Oulidi
Omali,
USMB
A,
LIST
A,
LIST
A,
Sidi
Mohamed
Ben
Abdellah
Uni
v
ersity
Fez,
Morocco.
Email:
khaoula.oulidiomali@usmba.ac.ma
1.
INTR
ODUCTION
A
precise
dynamic
model
of
the
system
to
be
tested
must
be
formula
ted
to
design
a
high
performance
controller
.
Its
parameters
should
be
equally
precisely
identified.
Furthermore
applies
to
industrial
robots.
in
that
e
v
ent,
the
problem
of
identification
becomes
especially
comple
x
because
of
the
presence
of
nonlinearities
and
coupling
ef
fects,
typical
of
robotic
systems,
by
dint
of
the
inertial,
friction
torques,
gra
vity
,
centripetal
and
friction
torques
[4].
The
presence
of
a
f
ault
can
be
modeled
as
an
une
xpected
change
in
system
parameters
or
by
the
presence
of
unkno
wn
signals
in
the
industry
.
In
a
robot
manipulator
,
a
f
ault
be
able
to
occur
on
a
actuator
,
a
sensor
or
a
mechanical
component
of
the
system
.
specific
Actuator
and
sensor
f
aults
are
more
common
thanks
to
the
presence
of
electrical
de
vices,
which
possibly
be
subject
for
a
lot
of
possible
criticality
.
Diagnostic
de
vices
generate
on-line
diagnostic
signals
in
order
to
detect
and
isolate
the
presence
of
f
ault.
Specific
methods
considered
to
surmount
this
disadv
antage,
as
lik
e
the
use
of
Kalman
filters
[6],
or
gen-
eralized
moments,
see
[8].
These
approaches,
in
the
presence
of
typical
uncert
ainties
of
applied
applications,
can
not
ha
v
e
the
possibility
e
xactly
to
con
v
er
ge
from
the
state
of
the
system
to
the
s
tate
of
the
observ
er
.
T
o
minimize
this
dra
wback,
sliding
mode
techniques
are
also
frequently
adopted
to
perform
status
observ
ation
[10,
11]
o
wing
to
their
simplici
ty
of
design
and
rob
ustness.
Usually
,
the
FDI
can
be
treat
by
incorporating
v
arious
sliding
mode
observ
ers
[12,
13].
The
aim
of
this
paper
is
to
study
the
performance
in
terms
of
the
rob
ustness
and
diagnostic
capabil
ities
of
sliding-mode
input
la
w
for
the
observ
er
.
specifically
,
second-order
sliding
mode
(SOSM)
la
w
,
the
super
-
twisting
la
w
[17]
is
considered.
The
diagnostic
technique
proposed
in
this
w
ork
pro
v
es
t
o
be
capable
to
detect
non-simultaneous
sensor
and
actuator
f
aults,
specially
for
actuator
.
J
ournal
homepage:
http://ijeecs.iaescor
e
.com
Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian
J
Elec
Eng
&
Comp
Sci
ISSN:
2502-4752
r
1151
2.
THE
MANIPULA
T
OR
MODEL
The
equations
of
motion
of
an
n
De
gree
of
Fredeem
(DOF)
robot
manipulators
are
described
accord-
ing
to
the
Euler
-Lagrange
theory
,
as:
=
M
(
q
)
•
q
+
C
(
q
;
_
q
)
_
q
+
G
(
q
)
+
F
(
_
q
)
=
M
(
q
)
•
q
+
n
(
q
;
_
q
)
(1)
where
q
;
_
q
;
•
q
2
R
n
are
the
joint
position,
v
elocity
and
ac
celeration
v
ectors,
respecti
v
ely
,
M
(
q
)
2
R
(
n
n
)
is
the
inertia
matrix
(symmetrical
definite
positi
v
e,
thus,
M
(
q
)
1
al
w
ays
e
xists),
C
(
q
;
_
q
)
2
R
(
n
n
)
is
the
centrifug
al
and
Coriolis
matrix,
G
(
q
)
2
R
n
is
the
gra
vitational
v
ector
,
F
(
_
q
)
2
R
n
is
the
v
ector
of
viscous
friction
torque
at
the
joints.
No
w
,
introducing
the
v
ariables
x
1
(
t
)
=
q
(
t
)
,
x
2
(
t
)
=
_
q
(
t
)
,
model
1
can
be
re
written
in
state
space
representation
as:
8
>
<
>
:
_
x
1
(
t
)
=
x
2
(
t
)
_
x
2
(
t
)
=
f
(
(
t
)
;
x
1
(
t
)
;
x
2
(
t
))
h
(
t
)
=
x
1
(
t
)
(2)
Where
the
term
f
(
(
t
)
;
x
1
(
t
)
;
x
2
(
t
))
is
obtained
after
simple
algebric
manipulation
of
(1),
i.e.,
f
(
(
t
)
;
x
1
(
t
)
;
x
2
(
t
))
=
M
1
(
x
1
(
t
))(
(
t
)
n
(
x
1
(
t
)
;
x
2
(
t
)))
(3)
As
pre
viously
mentioned,
when
f
aults
af
fect
the
actua
tors,
the
input
torque
for
the
mechanical
system
i
s
dif
fer
-
ent
from
(
t
)
.
Then,
in
case
of
input
f
aults,
(1)
becomes:
(
t
)
+
(
t
)
=
M
(
x
1
(
t
))
_
x
2
(
t
)
+
n
(
x
1
(
t
)
;
x
2
(
t
))
(4)
and,
as
a
result,
the
state
space
representation
is:
8
>
<
>
:
_
x
1
(
t
)
=
x
2
(
t
)
_
x
2
(
t
)
=
f
(
(
t
)
+
(
t
)
;
x
1
(
t
)
;
x
2
(
t
))
q
(
t
)
=
x
1
(
t
)
(5)
where
f
(
(
t
)
+
(
t
)
;
x
1
(
t
)
;
x
2
(
t
))
is
analogous
to
(3).
In
practice,
model
(3)
is
not
e
xactly
kno
wn
and
must
be
identified.
Then,
in
case
of
f
aults,
the
follo
wing
relationship
holds.
(
f
(
(
t
)
;
x
1
(
t
)
;
x
2
(
t
))
=
M
1
(
x
1
(
t
))(
(
t
)+
(
t
)
^
n
(
x
1
(
t
)
;
x
2
(
t
))
(
t
))
(6)
(
t
)
=
n
(
x
1
(
t
)
;
x
2
(
t
))
^
n
(
x
1
(
t
)
;
x
2
(
t
))
(7)
When
(
t
)
is
uncertain
and
^
n
(
q
;
_
q
)
is
the
kno
wn
part
of
the
model.
Y
et,
by
virtue
of
the
particular
application
considered,
(
t
)
can
be
assumed
to
be
bounded.
Ob
viously
,
to
perform
f
ault
diagnosis,
one
has
to
rely
only
on
the
kno
wn
part
of
model
(3).
Indeed,
after
a
suitable
identification
procedure,
such
as
the
one
proposed
in
[19],
it
is
feasible
(in
absence
of
f
aults)
to
determine
only
an
approximated
representation
of
f
(
:
)
,
i.e.
f
(
(
t
)
;
x
1
(
t
)
;
x
2
(
t
))
=
M
1
(
x
1
(
t
))(
(
t
)
^
n
((
x
1
(
t
)
;
x
2
(
t
))
(8)
in
order
that
the
actually
usable
model
is:
8
>
<
>
:
_
x
1
(
t
)
=
x
2
(
t
)
_
x
2
(
t
)
=
^
f
(
(
t
)
;
x
1
(
t
)
;
x
2
(
t
))
q
(
t
)
=
x
1
(
t
)
(9)
3.
THE
PR
OPOSED
DIA
GNOSTIC
SCHEME
By
relying
on
the
so-called
Unkno
wn
Input
Observ
er
(UIO)
approach
[11],
ef
ficient
estimators
of
the
input
torques
can
be
designed
[21].
In
this
w
ork,
the
UIOs
of
sliding
mode
type
is
proposed
in
order
to
detect
the
actuator
f
aults.
The
proposed
UIOs
can
be
jointly
described
as
a
multi-input-multi-state
second
order
sliding
mode
observ
ers.
Actuator
fault
detection
and
isolation
for
r
obot
manipulator
...
(Khaoula
Oulidi
Omali)
Evaluation Warning : The document was created with Spire.PDF for Python.
1152
r
ISSN:
2502-4752
3.1.
Obser
v
er
Design
Let
us
consider
the
observ
er:
(
^
x
1
(
t
)
=
^
x
2
(
t
)
+
z
1
(
t
)
^
x
2
(
t
)
=
^
f
(
(
t
)
;
x
1
(
t
)
;
^
x
2
(
t
))
+
z
2
(
t
)
(10)
where
^
x
1
(
t
)
;
^
x
2
(
t
)
2
R
2
n
are
the
observ
er
states,
and
z
(
t
)
=
[
z
1
(
t
)
;
z
2
(
t
)]
T
is
an
auxiliary
input
signal,
which
is
designed
relying
on
the
sliding
mode
approach,
as
will
be
clarified.
This
signal
is
introduced
so
as
to
permit
and
guarantee
the
con
v
er
gence
of
the
observ
er
states
to
the
actual
state
of
the
system.
Each
component
of
z
(
t
)
is
an
input
la
w
of
the
observ
er
.
3.2.
Dynamics
of
the
Obser
v
er
Err
or
The
proposed
f
ault
diagnostic
scheme
requires
to
steer
to
zero
the
signal
e
(
t
)
=
[
e
1
(
t
)
;
e
2
(
t
)]
T
2
R
2
n
,
the
components
of
which
are
gi
v
en
by:
(
e
1
(
t
)
=
x
1
(
t
)
^
x
1
(
t
)
e
2
(
t
)
=
x
2
(
t
)
^
x
2
(
t
)
(11)
By
steering
to
zero
these
quantit
ies,
it
is
possible
to
guarantee
that
the
observ
er
(10)
gi
v
es
a
good
estimation
of
the
unkno
wn
input,
as
it
will
be
sho
wn
in
the
follo
wing.
The
dynamics
of
the
error
v
ariable
e
(
t
)
is
represented
by
a
second
order
dynamical
system:
8
>
<
>
:
_
e
1
(
t
)
=
e
2
(
t
)
z
1
(
t
)
_
e
2
(
t
)
=
f
(
(
t
)
;
x
1
(
t
)
;
x
2
(
t
))
^
f
(
(
t
)+
(
t
)
;
x
1
(
t
)
;
^
x
2
(
t
))
z
2
(
t
)
(12)
which
can
be
re
written
as:
(
_
e
1
(
t
)
=
e
2
(
t
)
z
1
(
t
)
_
e
2
(
t
)
=
M
1
(
x
1
(
t
))
(
(
t
)
(
t
))
z
2
(
t
)
(13)
No
w
,
Second
Order
Sliding
Mode
approach
is
studied
to
design
the
multi-input-multi-state
UIO
input
la
w
.
This
approach
is
the
so-called
Super
-T
wisting
[17].
The
proposal
will
be
depicted
in
the
ne
xt
subsections.
3.3.
Super
-T
wisting
based
Obser
v
er
The
design
of
the
observ
er
input
la
ws
which
are
the
components
of
z
(
t
)
=
[
z
1
(
t
)
;
z
2
(
t
)]
T
using
a
Super
-T
wisting
based
approach
(see
[17])
is
gi
v
en
by:
(
z
1
(
t
)
=
p
j
s
0j
sig
n
(
s
0
(
t
))
z
2
(
t
)
=
sing
(
s
0
(
t
))
(14)
Where
s
0
(
t
)
=
e
1
(
t
)
=
x
1
(
t
)
^
x
1
(
t
)
.
It
can
be
pro
v
ed
that
a
suitable
choice
of
and
e
xists
such
that,
starting
from
an
y
initial
condition
[
e
1
(0)
;
e
2
(0)]
T
,
the
condition:
(
e
1
(
t
)
=
0
e
2
(
t
)
=
0
(15)
is
guaranteed
in
finite
time
(the
proof
of
this
claim
can
be
de
v
eloped
as
in
[14]).
T
o
implement
the
proposed
method,
the
terms
and
ha
v
e
been
chosen
after
an
e
xperimental
tuning
procedure.
Note
that
the
term
z
2
(
t
)
is
a
discontinuous
signal
and,
by
virtue
of
the
filt
ering
action
considered
in
[22],
the
second
equation
of
the
system
(13)
can
be
re
written
as:
z
2
eq
(
t
)
=
M
1
(
x
2
(
t
))(
(
t
)
(
t
))
(16)
where
z
2
eq
(
t
)
is
the
equi
v
alent
input
signal
corresponding
to
the
discontinuous
signal
z
2
(
t
)
.
Thus,
theoret-
ically
,
the
equi
v
alent
input
signal
is
the
result
of
an
infinite
switching
frequenc
y
of
the
discontinuous
term
Indonesian
J
Elec
Eng
&
Comp
Sci,
V
ol.
17,
No.
3,
March
2020
:
1150
–
1156
Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian
J
Elec
Eng
&
Comp
Sci
ISSN:
2502-4752
r
1153
sing
(
s
0
(
t
))
.
In
f
act,
the
implementation
of
the
observ
er
produces
high
switching
frequenc
y
(since,
in
prac-
tice,
one
can
only
implement
z
2
(
t
)
as
in
(14)
and
not
z
2
eq
(
t
)
)
making
necessary
the
application
of
a
filter
to
obtain
useful
information
from
signal
z
2
(
t
)
.
The
filter
has
to
eliminate
the
high
frequenc
y
components
of
such
a
signal.
It
can
be
of
the
form:
p
_
z
eq
(
t
)
+
z
eq
(
t
)
=
z
2
(
t
)
:
(17)
Indeed,
in
[25],
it
w
as
sho
wn
that
:
lim
p
!
0
z
eq
(
t
)
=
z
2
eq
(
t
)
(18)
Then,
by
taking
a
small
p
it
is
possible
to
assume
that
the
equi
v
alent
input
l
a
w
(16)
is
similar
to
the
output
of
the
filter
.
4.
THE
CONSIDERED
F
A
UL
T
SCEN
ARIOS
In
this
w
ork,
the
occurrences
of
f
aults
on
inputs
of
a
robot
manipulator
is
considered.
In
this
sit
uation,
the
real
torque
applie
d
by
the
actuators
is
unkno
wn.
That
is,
2
R
n
being
the
nominal
torque
calculated
by
the
robot
controller
,
whil
e
2
R
n
being
the
input
f
ault,
the
actual
torque
v
ector
which
is
the
input
of
the
robotic
system,
can
be
written
as
(
t
)
=
(
t
)
+
(
t
)
as
sho
wn
in
Figure
1.
Figure
1.
The
proposed
FDI
scheme
for
actuator
f
aults
5.
RESIDU
AL
GENERA
TION
Error
of
the
state
estimation
r
(
t
)
can
be
calculated
as:
r
(
t
)
=
(
t
)
^
(
t
)
(19)
The
residuals
are
supposed
to
dif
fer
from
zero
in
the
present
of
f
aults
(
r
(
t
)
6
=
0
)
and
to
be
zero
when
there
are
no
f
aults
on
the
actuators
(
r
(
t
)
=
0
).
So
the
residuals
are
defined
as:
(
r
(
t
)
=
0
if
=
^
r
(
t
)
6
=
0
if
6
=
^
(20)
T
able
I
represents
the
f
ault
signatures
matrix
for
these
residuals.
W
e
find
that
the
signatures
for
each
of
the
f
ailures
are
quite
dif
ferent.
T
able
1.
Signature
T
able
for
Actuator
F
ault
Isolation
d
i
=r
i
r
1
r
2
r
3
r
4
r
5
d
1
1
0
0
0
0
d
2
0
1
0
0
0
d
3
0
0
1
0
0
d
4
0
0
0
1
0
d
5
0
0
0
0
1
6.
SIMULA
TION
RESUL
TS
In
this
section,
the
performances
of
the
proposed
FDI
scheme
for
robot
manipulators
are
v
erified,
by
simulating
actuator
f
aults.
T
o
carry
out
simulations,
the
model
(5)
has
been
simulated
together
with
the
Actuator
fault
detection
and
isolation
for
r
obot
manipulator
...
(Khaoula
Oulidi
Omali)
Evaluation Warning : The document was created with Spire.PDF for Python.
1154
r
ISSN:
2502-4752
observ
er
(10)
wi
th
the
input
la
ws
(14)
rele
v
ant
to
the
Super
-T
wisting
approach.
The
presence
of
actuator
f
aults
is
simulated
by
introducing
an
abrut
f
ault
signal
on
the
dif
ferent
articulation
of
the
robot
(joint
1,
2,
3,
4,
5,
respecti
v
ely).
The
simulation
sho
ws
f
ault
detection
and
isolation
for
the
fi
v
e
articulations
of
robot
manipulators.
Detection
and
isolation
of
the
f
ault
s
for
actuat
o
r
s
(
and
^
signals)
by
using
the
Super
-T
wisting
input
la
w
.
Figures
2,
3,
4,
5,
6
pres
ents
tw
o
signals,
one
for
the
actual
states
and
the
other
for
the
estimated
states.
Figures
are
simulated
during
the
time
of
T
=
10
s
.
The
kind
of
f
ault
is
”Abrut”.
the
dif
ference
between
the
tw
o
signals
gi
v
es
a
residual
for
each
joint
of
the
system.
Figure
(b)
in
figures
2,
3,
4,
5,
6
sho
ws
an
observ
ation
er
ror
between
the
actual
states
and
the
estimated
states.
Residuals
for
all
articulations
are
dif
ferent
from
each
other
and
react
according
to
signature
table
for
actuator
f
ault
isolation.
The
f
ault
is
appeared
at
the
time
t
=
3
s
.
This
methods
gi
v
es
a
good
results
in
comparison
between
the
original
state
and
the
state
es
timate,
therefore
the
state
estimate
con
v
er
ges
to
the
actual
state
rapidly
,
that’
s
wh
y
we
find
the
residuals
equal
to
zero.
So
this
proposed
technique
detect
and
isolate
the
actuator
f
aults
in
a
robot
manipulator
.
(a)
F
ault
signal
reconstruction
(b)
Residual
signal
for
the
first
actuator
Figure
2.
Simulation
of
FDI
on
the
first
actuator
(
and
^
signals).
Detection
and
isolation
of
the
f
aults
by
using
the
Super
-T
wisting
input
la
w
.
(a)
F
ault
signal
reconstruction
(b)
Residual
signal
for
the
second
actuator
Figure
3.
Simulation
of
FDI
on
the
second
actuator
(
and
^
signals).
Detection
and
isolation
of
the
f
aults
by
using
the
Super
-T
wisting
input
la
w
.
(a)
F
ault
signal
reconstruction
(b)
Residual
signal
for
the
third
actuator
Figure
4.
Simulation
of
FDI
on
the
third
actuator
(
and
^
signals).
Detection
and
isolation
of
the
f
aults
by
using
the
Super
-T
wisting
input
la
w
.
Indonesian
J
Elec
Eng
&
Comp
Sci,
V
ol.
17,
No.
3,
March
2020
:
1150
–
1156
Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian
J
Elec
Eng
&
Comp
Sci
ISSN:
2502-4752
r
1155
(a)
F
ault
signal
reconstruction
(b)
Residual
signal
for
the
fourth
actuator
Figure
5.
Simulation
of
FDI
on
the
fourth
actuator
(
and
^
signals).
Detection
and
isolation
of
the
f
aults
by
using
the
Super
-T
wisting
input
la
w
.
(a)
F
ault
signal
reconstruction
(b)
Residual
signal
for
the
fi
v
e
actuator
Figure
6.
Simulation
of
FDI
on
the
fi
v
e
actuator
(
and
^
signals).
Detection
and
isolation
of
the
f
aults
by
using
the
Super
-T
wisting
input
la
w
.
7.
CONCLUSION
The
problem
of
f
ault
detection
and
isolation
on
a
robot
manipulator
has
been
addressed.
The
pres
ence
of
f
ault
detection
is
performed
depending
on
higher
order
sliding
mode
Unkno
wn
Input
Observ
ers
(UIOs).
The
observ
er
input
la
ws
are
designed
by
the
so
called
Super
-T
wisting
Second
Order
Sliding
Mode
Control
(SOSMC).
The
proposed
scheme
allo
ws
one
to
detect
and
isolate
f
aults,
e
v
en
multiple
and
simultaneous,
on
the
actuators
of
the
robotic
system.
Simulations
are
presented
pro
v
es
The
ef
fecti
v
eness
and
the
performance
of
the
proposed
technique.
REFERENCES
[1]
L.
M.
Capisani,
A.
Ferrara,
and
L.
Magnani,
“Second
order
sliding
mode
motion
control
of
rigid
robot
manipulators,
”
Proc.
46th
IEEE
Conf.
Decision
Control,
Ne
w
Orleans
,
LA,
2007.
[2]
C.
Edw
ards,
S.
K.
Spur
geon,
and
R.
J.
P
atton,
“Sliding
mode
observ
ers
for
f
ault
detection
and
isolation,
”
Automatica
,
v
ol.
36,
no.
4,
pp.
541–553,
Apr
.
2000.
[3]
——,
“
An
identification
scheme
for
robot
actuator
f
ault
s,
”
Proc.
IEEE/RSJ
International
Conference
on
Intelligent
Robots
and
Systems
,
Canada,
Aug.
2005,
pp.
1127–1131.
[4]
P
.
Pisu
and
A.
Ferr
ara,
“
An
observ
er
-based
second
order
sliding
mode
v
ehicle
control
strate
gy
,
”
Proc.
IEEE
4th
Intelligent
V
ehicles
Symposium
,
USA,
pp.
180–185,
2000.
[5]
F
.
J.
J.
Hermans
and
M.
B.
Zarrop,
“Sliding
mode
observ
ers
for
rob
ust
sensor
monitoring,
”
Proc.
13th
IF
A
C
W
orld
Congress
,
California,
USA,
pp.
211–216,
1997.
[6]
C.
Edw
ards,
S.
K.
Spur
geon,
and
R.
J.
P
atton,
“Sliding
mode
observ
ers
for
f
ault
detection
and
isolation,
”
Automatica
,
v
ol.
36,
no.
4,
pp.
541–553,
Apr
.
2000.
[7]
C.
P
.
T
an
and
C.
Edw
ards,
“Sliding
mode
observ
ers
for
detection
a
n
d
reconstruction
of
sensor
f
aults,
”
Automatica
,
v
ol.
38,
no.
10,
pp.
1815–1821,
Oct.
2002.
[8]
J.
A.
Da
vila,
L.
M.
Fridman,
and
A.
Le
v
ant,
“Second-order
sliding-mode
observ
er
for
mechanical
sys-
tems,
”
IEEE
T
ransactions
on
Automatic
Control
,
v
ol.
50,
no.
11,
pp.
1785–1789,
2005.
Actuator
fault
detection
and
isolation
for
r
obot
manipulator
...
(Khaoula
Oulidi
Omali)
Evaluation Warning : The document was created with Spire.PDF for Python.
1156
r
ISSN:
2502-4752
[9]
L.
M.
Capisani,
A.
Ferrara,
and
L.
Magnani,
“MIMO
identification
with
optimal
e
xperiment
design
for
rigid
robot
manipulators,
”
Proc.
IEEE/ASME
International
Conference
on
Adv
anced
Intelligent
Mecha-
tronics
,
Zurich,
Switzerland,
pp.
1–6,
2007.
[10]
R.
Mattone
and
A.
De
Luca,
“F
ault
detection
and
isolation
in
mechanical
systems,
”
Italy
,
May
2004.
[11]
W
.
Chen
and
M.
Saif,
“Rob
ust
f
ault
detection
and
isola
tion
in
constrained
nonlinear
systems
via
a
second
order
sliding
mode
observ
er
,
”
Proc.
15th
IF
A
C
W
orld
Congress
,
Spain,,
pp.1498–1500,
2002.
[12]
J.
A.
Da
vila,
L.
M.
Fridman,
and
A.
S.
Pozn
yak,
“Observ
ation
and
identification
of
mechanical
systems
via
second
order
sliding
modes,
”
International
Journal
of
Control
,
v
ol.79,
no.10,
pp.
1251–1262,2006.
[13]
L.
M.
Fridman,
“The
problem
of
chattering:
an
a
v
eraging
approach,
”
V
ariable
Structure
,
Sliding
Mode
and
Nonlinear
Control
,
K.
Y
oung
and
U.
Ozguner
,
Eds.
London,
UK:
Springer
-V
erlag,
1999,
pp.
363–386.
[14]
khaoula.
Oulidi
Omali,
Mohammed.
Nabil
Kabbaj,
Mohammed.
Benbrahim,
Sensor
F
ault
Detection
and
Isolation
for
a
Robot
Manipulator
Based
on
High-Gain
Observ
ers.
Lecture
Notes
in
Real-T
ime
Intelligent
Systems,
Springer
International
Publishing
A
G,
part
of
Springer
Nature
2019
,
R
TIS
2017,
AISC
756,
pp.
426–435,
2019.
[15]
J.
F
.
Bejarano,
L.
M.
Fridman,
and
A.
S.
Pozn
yak,
“Exact
state
estimation
for
linear
systems
with
unkno
wn
inputs
based
on
hierarchical
supertwisting
algorithm,
”
International
Journal
of
Rob
ust
and
Nonlinear
Con-
trol
,
v
ol.
17,
no.
18,
pp.
1734–1753,
Mar
.
2007.
[16]
khaoula.
Oulidi
Omali,
Mohammed.
Nabil
Kabbaj,
Mohammed.
Benbrahim,
Nonlinear
Observ
er
-Based
F
ault
Detection
and
Isolation
for
a
Manipulator
Robot.
Ne
w
Bioprocessing
Strate
gies:
De
v
elopment
and
Manuf
acturing
of
Recombinant
Antibodies
and
Proteins
.
Springer
Nature
Sing
apore
Pte
Ltd,
163-185,
2019.
[17]
Antonella.
Ferrara,
F
ault
Detection
for
Robot
Manipulators
via
Second-Order
Sliding
Modes,
IEEE
T
ransactions
on
Industrial
Electronics
,
V
OL.
55,
NO.
11,
2008.
[18]
Raf
f
aella.
Mattone,
Alessandro.
De
Luca,
Relax
ed
f
ault
detection
and
isolation:
An
application
to
a
non-
linear
case
study
,
Automatica
,
42,
109-116,
2006.
[19]
khaoula.
Oulidi
Omali,
Mohammed.
Nabil
Kabbaj,
Mohammed.
Benbrahim,
F
ault
Detection
and
Isola-
tion
for
Manipulator
Robot,
International
Symposium
on
Adv
anced
Electrical
and
Communication
T
ech-
nologies
,
1-5,
IEEE,
2018.
[20]
T
rong-Thang
Nguyen,
Sliding
mode
control-based
system
for
the
tw
o-link
robot
arm,
International
Jour
-
nal
of
Electrical
and
Computer
Engineering
(IJECE)
,
V
ol.
9,
No.
4,
pp.
2771-2778,
August
2019.
[21]
S.
Nurmaini
and
B.
T
utuk
o,
Intelligent
Robotics
Na
vig
ation
System:
Problems,
Methods,
and
Algorithm,
International
Journal
of
Electrical
and
Computer
Engineering
(IJECE)
,
v
ol/issue:
7(6),
pp.
3711-3726,
2017.
[22]
Zhang,
X.,
Polycarpou,
M.
M.,
and
P
arisini,
T
.,
A
rob
ust
detection
and
isolation
scheme
for
abrupt
and
incipient
f
aults
in
nonlinear
systems,
IEEE
T
ransactions
on
Automatic
Control
,
47(4),
576–593,
2002.
[23]
Luca.
Massim
iliano
Capisani,
Antonella.
Ferrara,
Alejandra.
Ferreira
de
Loza,
and
Leonid
M.
Fridman,
Manipulator
F
ault
Diagnosis
via
Higher
Order
Sliding-Mode
Observ
ers,
IEEE
T
ransactions
on
Industrial
Electronics
,
V
OL.
59,
NO.
10,
2012.
[24]
Shahnaz.
T
ayebi-Haghighi,
F
arzin.
Piltan,
and
Jong-Myon.
Kim,
Rob
ust
Composite
High-Order
Super
-
T
wisting
Sliding
Mode
Control
of
Robot
Manipulators,
MDPI
Robotics
,
2018.
[25]
Fraguela,
L.;
Fridman,
L.;
Ale
xandro
v
,
V
.V
.
Position
stabilization
of
a
Ste
w
art
platform:
High-order
sliding
mode
Observ
ers-based
approach,
J.
Frankl.
Inst.
,
349,
441–455,
2012.
[26]
Kamal,
S.,
Bandyopadh
yay
,
B.,
Higher
Order
Sliding
Mode
Control:
A
Control
L
yapuno
v
Function
Based
Approach,
WSEAS
T
rans.
Syst.
Control
,
9,
38–46,
2014.
Indonesian
J
Elec
Eng
&
Comp
Sci,
V
ol.
17,
No.
3,
March
2020
:
1150
–
1156
Evaluation Warning : The document was created with Spire.PDF for Python.