IAES
Inter
national
J
our
nal
of
Robotics
and
A
utomation
(IJRA)
V
ol.
10,
No.
3,
September
2021,
pp.
261
∼
274
ISSN:
2089-4856,
DOI:
10.11591/ijra.v10i3.pp261-274
❒
261
P
erf
ormance
e
v
aluation
of
industrial
ether
net
pr
otocols
f
or
r
eal-time
fault
detection
based
adapti
v
e
obser
v
er
in
netw
ork
ed
contr
ol
systems
with
netw
ork
communication
constraints
Samba
Aim
´
e
Her
v
´
e
1
,
Y
er
emou
T
amtsia
A
ur
elien
2
,
Nneme
Nneme
Leandr
e
3
1,2
National
Adv
anced
School
of
Engineering
,
Uni
v
ersity
of
Douala,
Douala,
Cameroon
3
Adv
anced
T
eacher
is
T
raining
Colle
ge
for
T
echnical
Education,
Uni
v
ersity
of
Douala,
Douala,
Cameroon
Article
Inf
o
Article
history:
Recei
v
ed
Mar
20,
2020
Re
vised
May
16,
2021
Accepted
Jul
23,
2021
K
eyw
ords:
Adapti
v
e
sliding
mode
observ
er
F
ault
detection
Industrial
ethernet
P
ack
et
losses
Netw
ork
ed
control
systems
ABSTRA
CT
In
this
paper
,
the
performance
e
v
aluation
of
industrial
ethernet
(EtherNet/IP
,
Ether
-
CA
T
and
PR
OFINET
IR
T)
netw
orks
has
been
studi
ed
for
choosing
the
right
protocol
in
real-time
f
ault
detection
based
adapti
v
e
sliding
mode
observ
er
in
netw
ork
ed
control
systems
(NCSs)
under
time
netw
ork-induced
delays,
stochastic
pack
et
losses,
access
constraints
and
bounded
disturbances.
An
adapti
v
e
sliding-mode
observ
er
based
f
ault
detection
is
presented.
The
dynamic
h
ydroelectric
po
wer
plant
model
is
used
to
v
erify
the
ef
fecti
v
eness
of
the
proposed
method
based
on
T
rueT
ime
and
Matlab/
Simulink,
corroborated
our
predictions
that
an
ethernet
for
control
automation
technology
(Ether
-
CA
T)
protocol
w
ould
be
more
appropriate
to
reduce
the
f
alse
alarm
rate
and
increasing
the
ef
cienc
y
of
the
remote
control
of
industrial
h
ydroelectric
po
wer
plant.
This
is
an
open
access
article
under
the
CC
BY
-SA
license
.
Corresponding
A
uthor:
Samba
Aim
´
e
Herv
´
e
National
Adv
anced
School
of
Engineering
Uni
v
ersity
of
Douala,
Douala,
Cameroon
Email:
aimeherv
esamba@yahoo.fr
1.
INTR
ODUCTION
The
concept
of
netw
ork
ed
control
systems
(NCSs)
ha
v
e
been
mentioned
by
man
y
scientists
in
t
heir
w
orks
as
early
as
the
end
of
the
twentieth
century
.
Because
the
lo
w
maintenance
cost
and
con
v
enient
installa-
tion,
NCSs
ha
v
e
aroused
widely
concerned.
Due
to
the
introduction
of
shared
netw
ork,
ne
w
constraints
occur
when
the
plant
outputs
and
control
inputs
are
transmitted
through
communication
netw
orks:
quantization
errors
in
the
signals
transmitted
through
the
netw
ork,
pack
et
dropouts,
netw
ork-induced
delay
,
access
constraints
and
po
wer
consumption
mainly
in
wireless
netw
ork
ed
control
systems
[1]-[5],
thus
increasing
the
comple
xity
of
the
system.
These
f
actors
will
af
fect
the
reliability
of
the
system,
and
cause
the
system
performance
decline.
In
order
to
impro
v
e
the
reliability
and
security
of
the
NCSs,
f
ault
diagnosis
has
been
widely
used
in
engineer
-
ing
systems
such
as
aero
engines,
dynamic
v
ehicle
systems,
chemical
processes,
and
po
wer
systems
[6]-[8].
F
ault
detection
(FD)
has
recei
v
ed
widespread
attention
as
one
of
the
most
considerable
parts
of
f
ault
diagnosis.
F
ailure
is
the
phenomenon
that
the
state
of
the
system
de
viates
from
the
normal
w
orking
range
due
to
satura-
tion,
stuck
or
de
gradation
of
actuators,
sensors
and
other
components,
which
has
a
ne
g
ati
v
e
inuence
on
the
system
performance.
As
a
result,
it
is
v
ery
signicant
to
detect
the
system
f
aults
as
s
oon
as
possible
to
ensure
the
safety
of
systems.
There
are
man
y
researching
results
on
FD
for
kinds
of
systems
with
v
arious
methods
J
ournal
homepage:
http://ijr
a.iaescor
e
.com
Evaluation Warning : The document was created with Spire.PDF for Python.
262
❒
ISSN:
2089-4856
[9]-[12].
P
an
and
Y
ang
[11],
H
∞
FD
lter
is
proposed
for
NCS
with
lar
ge
transfer
del
ays.
An
adapti
v
e
Kalman
lter
for
NCSs
is
proposed
in
[12]
to
minimize
the
ef
fects
of
delay
on
the
residual
signal.
The
f
ault
detection
system
for
NCSs
with
pack
et
losses
w
as
been
designed
by
modelling
the
NC
Ss
as
a
Mark
o
v
jumping
linear
system
[13],
[14].
F
or
research
w
ork
of
FD
problem
of
NCSs,
construct
appropriat
e
lters
and
state
observ
ers
as
residual
generators
to
generate
residual
signals
[15]-[17].
The
problem
of
FD
of
a
NCSs
under
communica-
tion
constraints
limited
is
considered
[18].
The
practical
guideline
for
selecting
the
right
protocol
in
industrial
netw
ork
ed
control
systems
(NCSs)
is
pro
vided
in
[12],
[19].
The
e
v
aluated
the
performance
of
MPOLSR
pro-
tocol
and
MD
AR
T
protocol
using
NS-2
based
on
the
success
deli
v
ery
rate
and
pack
et
loss
bas
been
studied
in
[20].
Inspired
by
the
abo
v
e
discussions,
the
main
goal
of
this
paper
is
to
de
v
oted
to
FD
of
NCS
subject
to
both
random
communication
delays,
stochastic
pack
et
losses,
limited
communication
and
access
constraints.
The
main
contrib
utions
of
this
w
ork
can
be
highlighted
as
follo
ws:
-
The
f
ault
detection
problem
is
e
xtended
for
a
class
of
netw
ork
ed
control
systems
(NCSs)
with
random
pack
et
losses,
time-v
arying
delays
and
limited
communication
to
reect
more
realistic
en
vironment,
-
Adapti
v
e
Sliding
mode
observ
er
approach
is
utilized
to
deal
with
the
f
ault
detection,
-
Residuals
generator
is
designed,
reducing
the
f
alse
alarm
rate.
Then,
the
residual
signals
are
e
v
aluated
and
compared
with
a
threshold
to
detect
the
f
aults
occurrences.
-
Application
to
a
Hydro-turbine
go
v
erning
system
[21],
[22]
sho
ws
that
the
proposed
method
achie
v
es
better
f
ault
detection.
-
T
rue-T
ime
toolbox
is
used
to
reect
a
more
realistic
numerical
netw
ork
communication
and
v
alidity
of
the
proposed
design
method.
-
The
control
performance
of
the
proposed
method
is
e
v
aluated
for
se
v
eral
industrial
protocols:
EtherNet/IP
protocol,
PR
OFINET
IR
T
protocol
and
EtherCA
T
protocol
of
the
standard
IEEE
802.3,
the
right
protocol
for
a
NCS
is
pro
vided
.
The
remainder
of
this
paper
is
or
g
anized
as
follo
ws:
section
2
introduces
the
problem
statement
and
preliminaries,
our
step
of
adapti
v
e
observ
er
synthesis
is
gi
v
en
in
section
3.
The
simulation
results
based
on
T
rue-T
ime
toolbox
and
Matlab/Simulink
will
be
gi
v
en
in
section
4
to
v
erify
the
ef
cienc
y
of
proposed
method.
Finally
,
a
conclusion
is
pro
vided,
including
some
perspecti
v
es
of
this
w
ork.
2.
PR
OBLEM
FORMULA
TION
AND
PRELIMIN
ARIES
In
this
paper
,
the
discrete
linear
system
with
output
delay
is
structured
as
Figure
1;
the
st
ate-space
model
of
the
linear
plant
dynamics
(1).
x
(
k
+
1)
=
Ax
(
k
)
+
A
τ
k
x
(
k
−
τ
k
)
+
B
u
(
k
)
+
Γ
d
(
k
)
+
F
Υ(
k
)
y
(
k
)
=
C
x
(
k
)
(1)
Where
x
(
k
)
∈
R
n
denotes
the
state
v
ector
,
x
(
k
−
τ
k
)
∈
R
n
denotes
the
state
delay
v
ector
,
u
(
k
)
∈
R
m
denotes
the
control
input
v
ector
Υ(
k
)
∈
R
q
is
the
f
ault
v
ector
,
y
(
k
)
∈
R
p
denotes
the
measured
output
v
ector
and
d
(
k
)
∈
R
m
the
noise
v
ector
,
A
,
A
τ
k
,
B
,
C
and
F
are
matrices
of
appropriate
dimensions.
Assumption
1
[13]:
It
is
supposed
that
random
pack
et
losses
e
xists
in
output
channel.
It
is
modelled
in
the
system
as
Bernoulli
process.
W
e
dene
˜
y
(
k
)
the
output
of
the
system
(with
internal
noise)
and
y
(
k
)
the
data
used
with
a
probability
¯
β
(
ℑ
r
{
β
k
=
1
}
=
¯
β
)
.
If
the
data
is
not
a
v
ailable,
we
will
use
the
preceding
data
y
(
k
−
1)
with
probability
1
−
¯
β
(
ℑ
r
{
β
k
=
0
}
=
1
−
¯
β
)
.
The
follo
wing
equations
describe
this
phenomenon.
y
(
k
)
=
¯
β
˜
y
(
k
)
+
(1
−
¯
β
)
y
(
k
−
1)
(2)
Where
β
k
∈
{
0
,
1
}
obe
ys
the
Bernoulli
distrib
ution.
Assumption
2
[23]:
In
this
paper
we
will
consider
that
the
band-width
of
the
communication
netw
ork
connecting
the
sensors
and
the
f
ault
detection
module
which
generates
a
residue
is
limited
capacity
,
ϖ
ς
sensors
among
p
can
reach
these
channels
to
communicate
with
the
residues
generator
while
the
others
remain
on
standby
.
Similarly
,
ϖ
ϱ
from
p
actuators
recei
v
e
their
command
from
controller
at
each
sampling
period.
Int
J
Rob
&
Autom,
V
ol.
10,
No.
3,
September
2021
:
261
–
274
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Rob
&
Autom
ISSN:
2089-4856
❒
263
where
1
≤
ϖ
ϱ
≤
m
1
≤
ϖ
ς
≤
p
(3)
T
aking
the
phenomenon
of
sensor
and
actuator
saturation,
the
functions
of
saturation
ς
(
·
)
:
R
m
→
R
m
and
ϱ
(
·
)
:
R
m
→
R
m
are
dened
as
(4).
ς
(
k
)
=
ς
T
1
(
k
)
,
ς
T
2
(
k
)
,
·
·
·
,
ς
T
m
(
k
)
T
(4)
ϱ
(
k
)
=
ϱ
T
1
(
k
)
,
ϱ
T
2
(
k
)
,
·
·
·
,
ϱ
T
m
(
k
)
T
If
we
denote
by
¯
y
(
k
)
denotes
measurement
v
ector
a
v
ailable
to
controller
and
f
ault
detecti
on
module
and
¯
u
(
k
)
denote
the
control
signals
generated
by
controller
at
discrete
time
k
.
Based
on
the
abo
v
e
communi-
cation
sequence,
W
e
get
the
relations
in
(5).
¯
y
(
k
)
=
M
ς
(
k
)
.y
(
k
)
,
M
ς
≜
diag
(
ς
i
(
k
))
(5)
u
(
k
)
=
M
ϱ
(
k
)
.
¯
u
(
k
)
,
M
ϱ
≜
diag
(
ϱ
i
(
k
))
From
(1),
(2),
(3),
(4)
and
(5),
the
dynamics
of
the
netw
ork
ed
control
system
via
a
shared
communi-
cation
medium
can
be
described
as
(6).
x
(
k
+
1)
=
Ax
(
k
)
+
A
τ
k
x
(
k
−
τ
k
)
+
B
M
ϱ
(
t
)
¯
u
(
k
)
+
Γ
d
(
k
)
+
F
Υ(
k
)
,
y
(
k
)
=
¯
β
˜
y
(
k
)
+
(1
−
¯
β
)
y
(
k
−
1)
(6)
¯
y
(
k
)
=
M
ς
(
t
)
C
x
(
k
)
Lemma
1
[24]
(Schur
complement).
Gi
v
en
constant
matrices
of
appropriate
dimensions
B
11
,
B
12
and
B
22
∈
R
n
×
n
,
where
B
11
=
B
T
11
,
B
22
=
B
T
22
,
then
B
12
>
0
,
B
11
−
B
12
B
−
1
22
B
T
12
>
0
if
and
only
if
B
11
B
1
22
B
T
12
−
B
22
>
0
.
Lemma
2
[25]
Gi
v
en
matrices
of
appropriate
dimensions
Ξ
11
=
Ξ
T
11
,
Ξ
12
and
Ξ
22
.
F
a
function
which
s
atises
F
=
F
T
≤
I
,
where
is
an
identity
matrix.
Then
the
inequality
Ξ
11
+
Ξ
12
F
Ξ
22
+
Ξ
T
22
F
T
Ξ
T
12
<
0
.
Is
not
true
that,
if
and
only
if
there
e
xists
a
scalar
Z
such
as
the
inequality
is
check
ed:
Ξ
11
+
Z
Ξ
12
Ξ
T
12
+
Z
−
1
Ξ
22
Ξ
T
22
<
0
.
or
equi
v
alently
Ξ
11
Z
Ξ
12
Ξ
T
22
∗
−
Z
Ξ
12
0
∗
∗
−
Z
Ξ
12
<
0
.
where
the
symbols
(
∗
)
denote
the
symmetric
terms.
The
remote
FD
dynamic
beha
viour
of
NCSs
is
illustrated
in
Figure
1.
Notably
,
y
(
k
)
denotes
the
ac-
tual
output
signal
and
˜
y
(
k
)
denotes
the
output
signal
used
by
controller
,
u
(
k
)
is
the
control
signal
produced
by
controller
and
¯
u
(
k
)
is
the
actual
control
input.
In
this
structure
the
f
ault
information
is
not
af
fected
by
the
communication
delay
between
the
sensor
and
the
node
of
FD
unit
and
communication
delay
between
controller
and
the
node
of
FD
unit.
P
erformance
e
valuation
of
industrial
ethernet
pr
otocols
for
r
eal-time
fault
detection
...
(Samba
Aim
´
e
Herv
´
e
)
Evaluation Warning : The document was created with Spire.PDF for Python.
264
❒
ISSN:
2089-4856
Figure
1.
The
proposed
block
diagram
of
remote
FD
in
netw
ork
ed
control
systems
with
time
delays,
pack
et
losses
and
access
constraints
3.
RESIDU
AL
D
YN
AMIC
SYSTEMS
In
this
section,
we
aim
to
design
an
f
ault
observ
er
based
on
discrete-time
adapti
v
e
sliding
mode
for
considered
netw
ork
ed
system
with
pack
et
losses,
communication
delays
and
access
constraints.
The
structure
of
the
adapti
v
e
f
ault
observ
er
proposed
is
gi
v
en
by
(7).
ˆ
x
(
k
+
1)
=
A
ˆ
x
(
k
)
+
A
τ
k
ˆ
x
(
k
−
τ
k
)
+
B
M
ϱ
(
k
)
¯
u
(
k
)
+
L
[
y
(
k
)
−
ˆ
y
(
k
)]
ˆ
Υ
(
k
+
1)
=
Λ
1
ˆ
Υ(
k
)
+
Λ
2
(
y
(
k
)
−
ˆ
y
(
k
))
(7)
ˆ
y
(
k
)
=
(
1
−
¯
β
)
M
ς
(
k
)
C
ˆ
x
(
k
)
Where
ˆ
x
∈
R
n
and
ˆ
y
(
k
)
∈
R
p
denote
the
state
estimation
for
the
f
ault
observ
er
and
estimation
of
the
measurement
output
respecti
v
ely;
L
∈
R
n
×
p
is
the
the
observ
er
g
ain
matrix
and
ˆ
Υ(
k
)
is
the
estimation
o
f
the
f
ault
v
ector
.
This
adapti
v
e
sliding
mode
observ
er
allo
ws
to
generate
a
residue
which
will
be
analyzed
to
detect
the
f
aults.
It
is
signicant
to
note
that
in
the
conte
xt
considered
in
this
paper
,
Λ
1
,
Λ
2
are
the
f
ault
detection
parameters.
Let
ε
x
(
k
)
=
x
(
k
)
−
ˆ
x
(
k
)
and
ε
y
(
k
)
=
y
(
k
)
−
ˆ
y
(
k
)
.
According
to
(1)
and
(7),
we
get
the
estimaror
dynamics
by
(8).
ε
x
(
k
+
1)
=
A
−
(1
−
¯
β
)
M
ς
LC
ε
(
k
)
+
1
−
¯
β
LC
x
(
k
)
+
Γ
d
(
k
)
(8)
+
F
ˇ
Υ(
k
)
+
A
τ
k
ε
x
(
k
−
τ
k
)
ε
y
(
k
)
=
(1
−
¯
β
)
M
ς
(
k
)
C
ε
x
(
k
)
(9)
where
˘
Υ(
k
)
=
Υ(
k
)
−
ˆ
Υ(
k
)
F
or
the
f
ault
observ
er
,
the
logic
of
f
ault
detection
considered
in
this
w
ork
is
gi
v
en
by
(10).
∥
J
(
k
)
∥
>
J
th
Alarm,
f
ault
is
detected
(10)
∥
J
(
k
)
∥
≤
J
th
No
alarm,
f
ault
is
no
detected
Where
J
(
k
)
is
the
residual
e
v
aluation
function
of
the
residual
generator
and
J
th
is
the
threshold
are
selected
as
(11).
J
(
k
)
=
"
n
X
k
=1
r
(
k
)
T
r
(
k
)
#
1
2
J
th
=
sup
d
(
k
)
∈
I
2
Υ(
k
)=0
E
{
J
(
k
)
}
(11)
where
n
is
the
length
of
the
e
v
aluation
windo
w
and
r
(
k
))
=
ε
y
(
k
)
denotes
the
residual
signal
of
the
system.
Int
J
Rob
&
Autom,
V
ol.
10,
No.
3,
September
2021
:
261
–
274
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Rob
&
Autom
ISSN:
2089-4856
❒
265
4.
ST
ABILITY
AN
AL
YSIS
Theor
em
1.
Consider
the
system
(7)
with
the
gi
v
en
scalar
γ
>
0
,
if
there
e
xist
matrices
P
1
>
0
,
Λ
1
,
Λ
2
>
0
and
L
,
such
that
the
follo
wing
matrix
inequality
holds.
H
=
Σ
11
γ
Σ
12
Σ
T
22
∗
−
γ
Σ
12
0
∗
∗
−
γ
Σ
12
<
0
(12)
where
Σ
11
=
−
P
1
+
γ
I
0
0
−
I
+
γ
I
,
Σ
22
=
−
P
1
0
0
−
I
Σ
21
=
˜
Σ
11
˜
Σ
12
˜
Σ
21
˜
Σ
22
˜
Σ
12
=
Λ
2
(1
−
¯
β
)
M
ς
C
T
˜
Σ
21
=
F
T
P
1
˜
Σ
22
=
Λ
T
1
Then
the
residual
dynamic
system
(7)
is
asymptotically
stable.
Pr
oof
1.
Choose
a
L
yapuno
v
functional
candidate
as
(13).
V
(
k
)
=
ε
T
x
(
k
)
P
1
ε
x
(
k
)
+
˘
Υ
T
(
k
)
˘
Υ(
k
)
(13)
Then
,
it
can
be
obtained
as
(14).
E
{
V
(
k
+
1)
−
V
(
k
)
}
=
E
{
ε
x
(
k
)
T
A
−
(1
−
¯
β
)
M
ς
LC
T
P
1
A
−
(1
−
¯
β
)
M
ς
LC
ε
x
(
k
)
+
2
ε
x
(
k
)
A
−
(1
−
¯
β
)
M
ς
LC
T
P
1
F
˘
Υ(
k
)
+
˘
Υ
T
(
k
)
F
T
P
1
F
˘
Υ(
k
)
+
˘
Υ
T
(
k
+
1)
˘
Υ(
k
+
1)
ε
x
(
k
−
τ
k
)
T
A
T
τ
k
P
1
A
τ
k
ε
x
(
k
−
τ
k
)
+
2
e
x
(
k
)
T
(
A
−
(1
−
¯
β
)
M
ς
LC
)
T
P
1
A
τ
k
×
e
x
(
k
−
τ
k
)
(14)
+
2
ε
T
x
(
k
)(
A
−
(1
−
¯
β
)
M
ς
LC
)
T
(
A
−
(1
−
¯
β
)
M
ς
LC
)
T
P
1
×
Γ
d
(
k
)
+
2
e
(
k
−
τ
k
)
T
A
τ
k
P
1
Γ
d
(
k
)
+
[Γ
d
(
k
)]
T
P
1
[Γ
d
(
k
)]
+
Γ
d
(
k
)
−
ε
x
(
k
)
T
P
1
ε
x
(
k
)
−
˘
Υ
T
(
k
)
˘
Υ(
k
)
where
E
n
˘
Υ(
k
+
1)
o
=
−
Λ
1
˜
Υ(
k
)
−
Λ
2
ε
x
(
k
)
+
Φ
(
k
)
Φ
(
k
)
=
Λ
1
Υ(
k
)
+
Υ(
k
+
1)
(15)
T
aking
∥
d
(
k
)
∥
≤
¯
d
,
where
¯
d
is
kno
w
positi
v
e
constants,
it
is
deri
v
ed
that
[Γ
d
(
k
)]
T
P
1
[Γ
d
(
k
)]
≤
∥
Γ
d
(
k
)
∥
2
∥
P
1
∥
≤
∥
Γ
∥
¯
d
2
∥
P
1
∥
(16)
A
−
(1
−
¯
β
)
M
ς
LC
T
P
1
[Γ
d
(
k
)]
≤
A
−
(1
−
¯
β
)
M
ς
LC
T
P
1
∥
Γ
d
(
k
)
∥
(17)
2
ε
x
(
k
−
τ
k
)
T
A
T
τ
k
P
1
[Γ
d
(
k
)]
≤
2
ε
x
(
k
−
τ
k
)
T
A
T
τ
k
∥
P
1
∥
∥
Γ
∥
¯
d
(18)
P
erformance
e
valuation
of
industrial
ethernet
pr
otocols
for
r
eal-time
fault
detection
...
(Samba
Aim
´
e
Herv
´
e
)
Evaluation Warning : The document was created with Spire.PDF for Python.
266
❒
ISSN:
2089-4856
According
to
(15),
(16),
(17)
and
(18).
It
can
be
further
obtained
(19).
E
{
V
(
k
+
1)
−
V
(
k
)
}
≤
ε
x
(
k
)
T
(
A
−
(1
−
¯
β
)
M
ς
LC
)
T
P
1
(
A
−
(1
−
¯
β
)
M
ς
LC
)
−
P
1
×
ε
x
(
k
)
+
2
ε
x
(
k
)(
A
−
(1
−
¯
β
)
M
ς
LC
)
T
P
1
F
˘
Υ(
k
)
+
˘
Υ
T
(
k
)
×
(
F
T
P
1
Υ(
k
)
−
I
)
˘
Υ(
k
)
+
2
(
A
−
(1
−
¯
β
)
M
ς
LC
)
T
P
1
×
ε
x
(
k
)
T
∥
Γ
∥
¯
d
+
2
ε
x
(
k
−
τ
k
)
T
A
T
τ
k
∥
P
1
∥
(19)
×
∥
Γ
∥
¯
d
+
ε
x
(
k
)
T
(
A
−
(1
−
¯
β
)
M
ς
LC
)
T
P
1
×
(
A
−
(1
−
¯
β
)
M
ς
LC
)
ε
x
(
k
)
+
2
λ
2
ε
x
(
k
)
T
P
1
ε
x
(
k
)
+
M
T
Θ
T
+
Φ
(
k
)
M
T
Θ
+
Φ
(
k
)
∥
P
1
∥
+
∥
Γ
∥
¯
d
2
where,
M
T
=
ε
x
(
k
)
T
˘
Υ
T
(
k
)
Θ
T
=
−
Λ
2
(1
−
¯
β
)
M
ς
C
T
−
Λ
1
According
to
the
Lemma
2
and
(19),
it
easy
to
obtain
(20).
E
{
V
(
k
+
1)
−
V
(
k
)
}
≤
M
T
H
M
+
2
M
T
Θ
T
Φ
(
k
)
+
Φ
(
k
)
T
Φ
(
k
)
(20)
F
or
the
matrix
H
,
it
can
be
obtained
by
Lemma
1:
H
=
Σ
11
γ
Σ
12
Σ
T
22
∗
−
γ
Σ
12
0
∗
∗
−
γ
Σ
12
<
0
(21)
where
Σ
11
=
−
P
1
+
γ
I
0
0
−
I
+
γ
I
,
Σ
22
=
−
P
1
0
0
−
I
,
Σ
21
=
˜
Σ
11
˜
Σ
12
˜
Σ
21
˜
Σ
22
,
˜
Σ
11
=
A
−
(1
−
¯
β
)
M
ς
LC
T
P
1
,
˜
Σ
12
=
Λ
2
(1
−
¯
β
)
M
ς
C
T
,
˜
Σ
21
=
F
T
P
1
,
˜
Σ
22
=
Λ
T
1
,
The
proof
is
completed.
Theor
em
2.
Consider
the
dynamic
system
(8).
If
there
e
xist
matrices
L
∈
R
n
×
m
and
η
2
<
1
satisfying
the
condition.
¯
Ω
11
¯
Ω
12
∗
¯
Ω
22
<
0
(22)
Where
¯
Ω
11
=
−
η
2
(1
−
¯
β
)
M
ς
(
k
)
C
T
(1
−
¯
β
)
M
ς
(
k
)
C
,
¯
Ω
12
=
2
A
−
(1
−
¯
β
)
M
ς
LC
T
,
¯
Ω
22
=
−
1
2
(1
−
¯
β
)
M
ς
(
k
)
C
T
(1
−
¯
β
)
M
ς
(
k
)
C
,
then
system
motion
gets
into
the
sliding
surf
ace
in
nite
time.
Int
J
Rob
&
Autom,
V
ol.
10,
No.
3,
September
2021
:
261
–
274
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Rob
&
Autom
ISSN:
2089-4856
❒
267
Pr
oof
2.
According
to
[22],
the
system
motion
gets
into
the
sliding
surf
ace
in
ni
te
time,
then
s
(
k
)
satises.
∥
s
(
k
+
1)
∥
≤
∥
s
(
k
)
∥
(23)
the
condition
(23)
can
then
be
reformulated
in
(24).
s
(
k
+
1)
T
s
(
k
+
1)
−
η
2
s
(
k
)
T
s
(
k
)
=
ε
T
y
(
k
+
1)
ε
y
(
k
+
1)
−
η
2
ε
T
y
(
k
)
ε
y
(
k
)
(24)
According
to
(8),
then
we
ha
v
e
s
(
k
+
1)
T
s
(
k
+
1)
−
η
2
s
(
k
)
T
s
(
k
)
=
ε
T
x
(
k
+
1)((1
−
¯
β
)
M
ς
(
k
)
C
)
T
((1
−
¯
β
)
M
ς
(
k
)
C
)
×
ε
x
(
k
+
1)
−
η
2
ε
T
x
(
k
)((1
−
¯
β
)
M
ς
(
k
)
C
)
T
(25)
×
((1
−
¯
β
)
M
ς
(
k
)
C
)
ε
x
(
k
)
<
0
where
η
2
<
1
,
then
substituting
(8)
into
(26),
we
can
obtain
(26).
s
(
k
+
1)
T
s
(
k
+
1)
−
η
2
s
(
k
)
T
s
(
k
)
=
ε
T
x
(
k
)[(
A
−
(1
−
¯
β
)
M
ς
LC
)
T
((1
−
¯
β
)
M
ς
(
k
)
C
)
T
×
((1
−
¯
β
)
M
ς
(
k
)
C
)(
A
−
(1
−
¯
β
)
M
ς
LC
)
−
η
2
((1
−
¯
β
)
M
ς
(
k
)
C
)
T
((1
−
¯
β
)
M
ς
(
k
)
C
)]
×
ε
T
x
(
k
)
+
ε
x
(
k
−
τ
k
)
T
A
T
τ
k
((1
−
¯
β
)
M
ς
(
k
)
C
)
T
×
((1
−
¯
β
)
M
ς
(
k
)
C
)
ε
x
(
k
−
τ
k
)
+
[Γ
d
(
k
)]
T
(26)
×
((1
−
¯
β
)
M
ς
(
k
)
C
)
T
((1
−
¯
β
)
M
ς
(
k
)
C
)
×
Γ
d
(
k
)
+
2
ε
T
x
(
k
)
×
(
A
−
(1
−
¯
β
)
M
ς
LC
)
T
×
((1
−
¯
β
)
M
ς
(
k
)
C
)
T
((1
−
¯
β
)
M
ς
(
k
)
C
)
A
τ
k
×
ε
x
(
k
−
τ
k
)
+
2
ε
T
x
(
k
)
A
−
(1
−
¯
β
)
M
ς
LC
T
×
((1
−
¯
β
)
M
ς
(
k
)
C
)
T
((1
−
¯
β
)
M
ς
(
k
)
C
)Γ
d
(
k
)
+
2
ε
T
x
(
k
)
A
−
(1
−
¯
β
)
M
ς
LC
T
A
T
τ
k
×
((1
−
¯
β
)
M
ς
(
k
)
C
)
T
((1
−
¯
β
)
M
ς
(
k
)
C
)Γ
d
(
k
)
Simolarly
,
(24)
can
be
obtained
(27).
s
(
k
+
1)
T
s
(
k
+
1)
−
η
2
s
(
k
)
T
s
(
k
)
≤
ε
T
x
(
k
)[(
A
−
(1
−
¯
β
)
M
ς
LC
)
T
((1
−
¯
β
)
M
ς
(
k
)
C
)
T
−
η
2
((1
−
¯
β
)
M
ς
(
k
)
C
)
T
((1
−
¯
β
)
M
ς
(
k
)
C
×
(
A
−
(1
−
¯
β
)
M
ς
LC
)((1
−
¯
β
)
M
ς
(
k
)
C
)]
ε
x
(
k
))
+
2
ε
T
x
(
k
)(
A
−
(1
−
¯
β
)
M
ς
LC
)
T
((1
−
¯
β
)
M
ς
(
k
)
C
)
T
×
((1
−
¯
β
)
M
ς
(
k
)
C
)
A
τ
k
ε
x
(
k
−
τ
k
)
−
2
ε
T
x
(
k
)
×
(
A
−
(1
−
¯
β
)
M
ς
LC
)
T
((1
−
¯
β
)
M
ς
(
k
)
C
)
T
×
((1
−
¯
β
)
M
ς
(
k
)
C
)
Λ
2
(
k
)
−
2
ε
x
(
k
−
τ
k
)
T
(27)
×
((1
−
¯
β
)
M
ς
(
k
)
C
)
T
((1
−
¯
β
)
M
ς
(
k
)
C
)
Λ
(
k
)
One
can
further
get
(28).
s
(
k
+
1)
T
s
(
k
+
1)
−
η
2
s
(
k
)
T
s
(
k
)
≤
ε
T
x
(
k
)[2(
A
−
(1
−
¯
β
)
M
ς
LC
)
T
((1
−
¯
β
)
M
ς
(
k
)
C
)
T
×
((1
−
¯
β
)
M
ς
(
k
)
C
)(
A
−
(1
−
¯
β
)
M
ς
LC
)
(28)
−
η
2
((1
−
¯
β
)
M
ς
(
k
)
C
)
T
((1
−
¯
β
)
M
ς
(
k
)
C
)]
×
ε
x
(
k
)
<
0
P
erformance
e
valuation
of
industrial
ethernet
pr
otocols
for
r
eal-time
fault
detection
...
(Samba
Aim
´
e
Herv
´
e
)
Evaluation Warning : The document was created with Spire.PDF for Python.
268
❒
ISSN:
2089-4856
According
to
the
Lemma
2,
we
obtain
(29).
s
(
k
+
1)
T
s
(
k
+
1)
−
η
2
s
(
k
)
T
s
(
k
)
≤
ε
T
x
(
k
)
¯
Ξ
ε
x
(
k
)
<
0
(29)
Where
¯
Ξ
=
¯
¯
Ξ
11
¯
¯
Ξ
12
∗
¯
¯
Ξ
22
,
¯
¯
Ξ
11
=
−
η
2
((1
−
¯
β
)
M
ς
(
k
)
C
)
T
×
((1
−
¯
β
)
M
ς
(
k
)
C
)
¯
¯
Ξ
12
=
2(
A
−
(1
−
¯
β
)
M
ς
LC
)
T
¯
¯
Ξ
22
=
−
1
2
((1
−
¯
β
)
M
ς
(
k
)
C
)
T
((1
−
¯
β
)
M
ς
(
k
)
C
)
This
completes
the
proof.
5.
SIMULA
TION
RESUL
TS
In
this
section,
we
will
propose
a
numerical
e
xample
of
simulation
to
illustrate
the
ef
fecti
v
eness
of
the
methods
presented
in
this
w
ork.
Let
us
consider
the
model
of
netw
ork
ed
control
h
ydroelectric
po
wer
plant
[20].
The
o
wchart
of
the
winno
wing
de
vice
control
and
communication
netw
ork
is
represented
on
Figure
2.
Figure
2.
Schematic
diagram
of
netw
ork
ed
control
h
ydroelectric
po
wer
plant
This
s
y
s
tem
is
been
used
in
[21],
[25],
for
the
design
A
Netw
ork
ed
iterati
v
e
learning
f
ault
Diagnosis
algorithm
for
systems
with
sensor
random
pack
et
losses,
time-v
arying
delays,
limited
communication
and
actuator
f
ailure.
The
state
representation
of
dynamic
model
is
described
as
(30).
x
(
k
+
1)
=
1
.
1840
−
0
.
4046
0
0
.
5000
0
0
0
0
.
5000
0
x
(
k
)
+
1
0
0
u
(
k
)
y
(
k
)
=
h
0
.
2943
0
.
3382
0
.
0001
i
x
(
k
)
(30)
Dene
A
τ
k
=
0
.
034
0
−
0
.
01
0
.
031
0
.
03
0
0
.
04
0
.
05
−
0
.
01
According
to
the
time
scale,
we
dene
the
time-v
arying
communication
delays
as
τ
i
(
k
)(
i
=
0
,
1
,
2)
.
Int
J
Rob
&
Autom,
V
ol.
10,
No.
3,
September
2021
:
261
–
274
Evaluation Warning : The document was created with Spire.PDF for Python.
Int
J
Rob
&
Autom
ISSN:
2089-4856
❒
269
Let
the
f
ault
signal
Υ(
k
)
be
gi
v
en
as
(31).
Υ(
k
)
=
(
0
.
5
+
0
.
2
sin
(
k
)
122
≤
k
≤
142
0
,
others
(31)
And
F
=
1
1
1
T
The
communication
constraints
is
x
ed
to
one
channel
(
ϖ
ς
=
ϖ
ϱ
=
1)
so
the
follo
wing
3-periodic
sequence
can
be
proposed.
ς
(0)
,
ς
(1)
,
ς
(2)
,
·
·
·
=
1
0
0
,
0
1
0
,
0
0
1
,
1
0
0
,
·
·
·
ϱ
(0)
,
ϱ
(1)
,
ϱ
(2)
,
·
·
·
=
1
0
0
,
0
1
0
,
0
0
1
,
1
0
0
,
·
·
·
The
random
v
ariable
¯
β
satises
the
Bernoulli
distrib
ution,
let
¯
β
=
0
.
65
.
Applying
Theorem
1
and
2,
we
can
obtain
according
to
the
Matlab
LMI
toolbox,
the
desi
red
P
1
,
the
observ
er
g
ain
L
,
the
scalar
η
and
parameters
Λ
1
and
Λ
1
as
follo
ws:
P
1
=
0
.
231
−
0
.
005
0
.
002
0
0
.
0012
0
.
0021
0
0
.
0321
0
.
0063
,
L
=
−
0
.
0352
0
.
000011
−
0
.
0142
,
Λ
1
=
0
.
03621
,
Λ
2
=
0
.
0073
and
η
=
1
.
0173
e
−
3
.
W
e
obtain
the
Simulink/
true
time
models
of
netw
ork
ed
control
h
ydroelectric
po
wer
plant
Figure
3.
The
true-time
netw
ork
block
simulates
the
access
to
the
medium
and
allo
ws
the
transmission
and
the
reception
of
data
through
the
netw
ork.
T
able
1
sho
ws
the
simulation
parameter
for
wireless
netw
ork
block.
T
able
1.
Simulation
parameter
for
netw
ork
block
P
arameter
V
alues
Netw
ork
type
802.15
(LAN)
Data
rate
200
Mps
Minimum
frame
size
544
bits
T
ransmit
po
wer
200
dbm
Recei
v
er
signal
threshold
-48
dbm
P
ath
loss
e
xponent
33.5
In
order
to
sho
w
the
ef
fecti
v
eness
of
the
approach
proposed,
the
noise
signal
d
(
k
)
is
a
white
noise
Gaussian
of
an
amplitude
of
0.025
(sample
time
T
s
=
1
s
).
The
f
ault
signal
Υ(
k
)
occurs
between
the
moments
122
th
at
157
th
steps.
The
results
comprise
a
pack
ets
loss
at
the
moments:
steps
11
at
steps
19
steps,
steps
41
at
steps
52,
steps
63
at
steps
68,
steps
84
at
steps
86,
steps
89,
steps
101
at
steps
108,
steps
128,
steps
133
at
steps
139
and
steps
194
at
steps
196
Figure
4.
Figure
5
sho
w
the
e
v
olution
in
real
t
ime
of
the
actual
speed
of
h
ydroturbine
and
the
estimated
speed
by
adapti
v
e
sliding
mode
observ
er
with
EtherNet/IP
protocol,
PR
OFINET
IR
T
protocol
and
EtherCA
T
protocol.
The
generated
residue
is
illustrated
by
the
Figure
6,
which
sho
ws
that
the
residual
signal
con
v
er
ges
to
zero
without
f
aults
Figure
7
,
then
,
changes
rapidly
when
the
f
aults
occurre
d
this
for
the
three
communications
protocols.
Figure
8
illustrate
the
residual
e
v
aluation
function
J
(
k
)
.
Figure
9
sho
ws
that
the
same
f
aults
is
detected
at
steps
125
with
switched
ethernet
protocol.
Figure
10
sho
ws
the
occurrence
of
f
ault
can
detect
the
f
ault
at
steps
124
with
EtherCA
T
protocol.
P
erformance
e
valuation
of
industrial
ethernet
pr
otocols
for
r
eal-time
fault
detection
...
(Samba
Aim
´
e
Herv
´
e
)
Evaluation Warning : The document was created with Spire.PDF for Python.
270
❒
ISSN:
2089-4856
Figure
3.
Simulink/true-time
model
of
remote
FD
in
netw
ork
ed
control
h
ydroelectric
po
wer
plant
Figure
4.
The
distrib
ution
of
pack
et
losses
”1”
means
pack
et
recei
v
ed,
”0”
means
pack
et
lost
Figure
5.
Actual
and
estimated
speed
of
h
ydroturbine
Int
J
Rob
&
Autom,
V
ol.
10,
No.
3,
September
2021
:
261
–
274
Evaluation Warning : The document was created with Spire.PDF for Python.