Inter
national
J
our
nal
of
Electrical
and
Computer
Engineering
(IJECE)
V
ol.
7,
No.
5,
October
2017,
pp.
2605
ā
2613
ISSN:
2088-8708
2605
I
ns
t
it
u
t
e
o
f
A
d
v
a
nce
d
Eng
ine
e
r
i
ng
a
nd
S
cie
nce
w
w
w
.
i
a
e
s
j
o
u
r
n
a
l
.
c
o
m
Rob
ustness
and
Stability
Analysis
of
a
Pr
edicti
v
e
PI
Contr
oller
in
W
ir
elessHAR
T
Netw
ork
Characterised
by
Stochastic
Delay
Sabo
Miya
Hassan
1,2
,
Rosdiazli
Ibrahim
1
,
Nordin
Saad
1
,
V
ijanth
Sagayan
Asir
v
adam
1
,
Kishor
e
Bingi
1
,
and
T
ran
Duc
Chung
1
1
Department
of
Electrical
and
Electronic
Engineering,
Uni
v
ersiti
T
eknologi
PETR
ON
AS,
32610
Seri
Iskandar
,
Perak,
Malaysia
2
Department
of
Electrical
and
Electronic
Engineering,
Ab
ubakar
T
af
a
w
a
Bale
w
a
Uni
v
ersity
,
PMB
0248
Bauchi,
Nigeria
Article
Inf
o
Article
history:
Recei
v
ed:
Mar
11,
2017
Re
vised:
May
26,
2017
Accepted:
Jun
14,
2017
K
eyw
ord:
Rob
ustness
Stability
analysis
PPI
controller
Stochastic
delay
W
irelessHAR
T
control
Model
mismatch
ABSTRA
CT
As
control
o
v
er
wireless
netw
ork
in
the
industry
is
recei
v
es
increasing
attent
ion,
its
appli-
cation
comes
with
challenges
such
as
stochastic
netw
ork
delay
.
The
PIDs
are
ill
equipped
to
handle
such
challenges
while
the
model
based
controllers
are
comple
x.
A
settlement
be-
tween
the
tw
o
is
the
PPI
controller
.
Ho
we
v
er
,
there
is
no
certainty
on
its
ability
to
preserv
e
closed
loop
stability
under
such
challenges.
While
classical
rob
ustness
measures
do
not
re-
quire
e
xtensi
v
e
uncertainty
modelling,
the
y
do
not
guarantee
stability
under
simultaneous
process
and
netw
ork
delay
v
ariations.
On
the
other
ha
nd,
the
model
uncertainty
measures
tend
to
be
conserv
ati
v
e.
Thus,
this
w
ork
uses
e
xtended
complementary
sensiti
vity
function
method
which
ha
ndles
simultaneously
those
challenges.
Simulation
results
sho
ws
that
the
PPI
controller
can
guarantee
stability
e
v
en
under
model
and
delay
uncertainties.
Copyright
c
ī
2017
Institute
of
Advanced
Engineering
and
Science
.
All
rights
r
eserved.
Corresponding
A
uthor(s):
Sabo
Miya
Hassan,
Rosdiazli
Ibrahim
Department
of
Electrical
and
Electronic
Engineering
Uni
v
ersiti
T
eknologi
PETR
ON
AS,
32610
Seri
Iskandar
,
Perak,
Malaysia
Email:hsmiya2010@gmail.com,
rosdiazli@utp.edu.my
1.
INTR
ODUCTION
Emer
gence
of
W
irelessHAR
T
and
ISA100
W
ireless
as
the
only
industrial
wireless
standards
for
monitoring
and
automation
has
prompted
researchers
to
e
xplore
their
control
application
capabilities
[1,
2].
This
is
due
to
the
adv
antages
wireless
has
o
v
er
the
wired
system
of
ļ¬e
xibility
,
scalability
and
impro
v
ed
reliability
due
to
the
mesh
topology
the
tw
o
standards
support
[3,
4].
The
tw
o
standards
both
operate
on
the
2.5GHz
Industrial
scientiļ¬c
and
medical
(ISM)
radio
frequenc
y
band
and
are
based
on
the
IEEE802.14.4
ph
ysical
layer
[1].
W
irelessHAR
T
being
based
on
the
traditional
HAR
T
standard
and
the
ļ¬rst
to
hit
the
public
domain,
has
an
edge
o
v
er
the
ISA100
wireless
standard.
There
are
close
to
30
million
HAR
T
enabled
de
vices
already
installed
globally
in
the
industries
that
can
easily
be
con
v
erted
to
support
W
irelessHAR
T
[4].
Ho
we
v
er
,
application
of
the
standard
for
control
comes
with
problems
of
stochastic
netw
ork
delay
,
non
periodic
update
of
measurement
and
uncertainties
such
as
pack
et
loss
[5,
6].
T
o
curtail
this
problems,
especially
that
of
the
stochastic
netw
ork
delay
,
se
v
eral
control
strate
gies
ha
v
e
been
proposed,
among
which
is
the
use
of
Predicti
v
e
PI
controller
(PPI)
[7,
8].
The
controller
is
a
compromise
between
the
e
xpensi
v
e
and
comple
x
model
based
controllers
and
t
he
simple
b
ut
poorly
performing
PID.
The
controller
allo
ws
for
model
mismatch
hence
can
function
well
in
a
stochastic
delay
setting
[9].
It
is
w
orth
noting
that
a
k
e
y
task
of
an
y
control
system
is
to
ensure
close
loop
system
stability
e
v
en
in
the
presence
of
uncertainties
and
process
parameter
change.
This
is
not
an
e
xception
with
the
PPI
controller
.
Thus,
the
PPI
controller
if
used
in
the
W
ireles
sHAR
T
en
vironment
must
also
ensure
system
stability
under
changing
conditions
of
the
netw
ork
and
plant.
There
are
man
y
rob
ustness
measures
to
e
v
aluate
the
e
xtend
to
which
controll
ers
can
ef
fecti
v
ely
perform
while
maintaining
system
instability
[10,
11,
12,
13].
The
tw
o
most
commonly
used
measures
are
the
classical
and
model
uncertainty
methods
[14].
The
former
is
based
on
phase,
g
ain
and
deadtime
mar
gins
while
the
latter
is
based
on
sensiti
vity
and
its
compl
imentary
functions.
Ho
we
v
er
,
the
k
e
y
shortcomings
of
these
approach
is
that
the
y
too
conserv
ati
v
e.
F
or
e
xample,
the
classical
method
consider
v
ariation
in
the
process
separately
while
the
model
uncertainty
does
not
tak
e
into
account
v
ariation
in
delays.
J
ournal
Homepage:
http://iaesjournal.com/online/inde
x.php/IJECE
I
ns
t
it
u
t
e
o
f
A
d
v
a
nce
d
Eng
ine
e
r
i
ng
a
nd
S
cie
nce
w
w
w
.
i
a
e
s
j
o
u
r
n
a
l
.
c
o
m
,
DOI:
10.11591/ijece.v7i5.pp2605-2613
Evaluation Warning : The document was created with Spire.PDF for Python.
2606
ISSN:
2088-8708
In
this
w
ork,
a
rob
ustness
measure
using
complementary
sensiti
vity
function
[14,
15]
will
be
used
to
e
x-
amine
the
rob
ustness
of
the
PPI
controller
in
a
W
irelessHAR
T
en
vironment.
The
method
considers
simultaneously
v
ariation
in
process
parameters
such
as
g
ain,
phase,
deadtime
and
also
netw
ork
stochastic
delays.
The
rest
of
the
paper
is
or
g
anized
as
follo
ws:
the
methodology
is
gi
v
en
in
Section
2,
while
results
are
discussed
and
analysed
in
Section
3..
The
last
section
dra
ws
conclusion.
2.
METHODOLOGY
2.1.
The
Pr
edicti
v
e
PI
contr
oller
e
-
Ļ
ca
s
e
-
Ļ
sc
s
G
P
(
s
)
e
-
L
p
s
W
i
r
e
l
e
s
s
n
e
t
wo
r
k
Y
(
s
)
K
C
e
-
sL
/(
1+
sT
i
)
+
E
(
s
)
U
(
s
)
+
-
R
(
s
)
P
P
I
c
o
n
t
r
o
l
l
e
r
Figure
1.
PPI
controller
in
wireless
netw
ork
set-up
Consider
the
control
set-up
sho
wn
in
Fig.
1,
the
netw
ork
delay
ī
N
is
the
sum
of
the
controller
-to-actuator
delay
ī
ca
and
the
sensor
-to-controller
delay
ī
sc
gi
v
en
as
ī
N
=
ī
ca
+
ī
sc
(1)
Thus,
the
total
loop
delay
is
then
gi
v
en
as
L
=
ī
N
+
L
p
(2)
where
L
P
is
the
process
deadtime.
Consequently
,
the
PPI
controller
G
c
(
s
)
of
Fig.
1
for
the
wireless
systems
can
be
e
xpressed
as
(3).
U
(
s
)
=
K
c
E
(
s
)
+
1
1
+
T
s
e
ī
sL
U
(
s
)
(3)
Equation
(3)
can
be
e
xpressed
as
a
cascade
of
a
PI
controller
and
the
predictor
as
follo
ws
G
c
(
s
)
=
K
c
ī
1
+
1
T
i
s
ī
1
1
+
1
T
i
s
(1
ī
e
ī
sL
)
!
;
(4)
where,
C
P
I
(
s
)
=
K
c
(1
+
1
T
i
s
)
,
is
the
PI
controller
and
C
pr
ed
(
s
)
=
1
1+
1
T
i
s
(1
ī
e
ī
sL
)
is
the
predictor
.
2.2.
Extended
Complementary
Sensiti
vity
Function
Based
Rob
ustness
Rob
ust
stability
condition
of
the
PPI
controller
gi
v
en
in
(3)
and
(4)
will
be
established
based
on
the
e
xtended
sensiti
vity
function
method
proposed
by
[14].
The
method
is
adopted
here
to
include
alongside
model
parameter
v
ariations
the
wireless
stochastic
delay
.
The
rob
ustness
computation
is
established
on
the
open
loop
transfer
func-
tion.
If
the
controller
in
(4)
is
used
to
control
the
process
G
p
(
s
)
e
ī
L
p
s
of
Fig.
1,
assuming
commutati
vity
between
process
deadtime
L
p
and
total
netw
ork
dealy
ī
N
,
the
entire
proces
s
model
including
netw
ork
delays
under
nominal
conditions
can
be
e
xpressed
as
G
(
s
)
=
G
p
(
s
)
e
ī
sL
;
(5)
where,
G
p
(
s
)
is
the
delay
free
process.
Consider
some
de
viations
from
nominal
condition
where
there
is
v
ariation
in
both
process
deadtime
and
netw
ork
induced
delays,
assuming
that
the
delay
error
is
ī
L
2
[ī
L
min
;
ī
L
max
]
.
IJECE
V
ol.
7,
No.
5,
October
2017:
2605
ā
2613
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708
2607
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
G
c
G
A
Ļ
ā
L
G
c
G
e
ā
i
Ļ
ā
L
|
|
G
c
ā
G
|
|
ā
|
1
+
G
c
G
e
ā
i
Ļ
ā
L
|
Real Axis
Imaginary Axis
Figure
2.
Open
loop
transfer
function
Nyquist
plot
for
nominal
system
and
its
uncertainty
due
to
respecti
v
e
v
ariation
in
process
ī
G
and
total
netw
ork
delay
ī
L
.
Assume
also
that
the
multiplicati
v
e
uncertainty
between
the
nominal
process
G
p
(
s
)
and
the
real
process
G
(
s
)
is
ī
G
(
s
)
,
then
the
process
model
together
with
uncertainties
can
be
written
as
G
(
s
)
=
G
p
(
s
)
1
+
ī
G
(
s
)
G
p
(
s
)
!
e
ī
s
(
L
+ī
L
)
;
(6)
If
the
controller
of
the
system
is
considered
to
be
G
c
(
s
)
,
the
nominal
open
loop
in
the
frequenc
y
domain
gi
v
en
as
G
c
(
i!
)
G
(
i!
)
is
thus
assumed
to
be
stable
and
also
norm
bounded.
Consider
the
Nyquist
diagram
of
the
nominal
open
system
(
G
c
G
)
sho
wn
in
Fig.
2,
with
uncertainty
in
the
delay
ī
L
,
if
point
A
is
rotated
through
angle
ī
!
ī
L
and
mo
v
ed
slightly
to
an
y
direction
j
G
c
ī
G
(
i!
)
j
=
j
G
c
ī
G
(
i!
)
e
i!
(
L
+ī
L
)
j
,
it
will
stay
within
a
circle
deļ¬ned
by
centre
G
c
G
(
i!
)
e
i!
(ī
L
)
and
radius
jj
G
c
ī
G
(
i!
)
jj
1
.
The
distance
from
centre
G
c
G
(
i!
)
e
i!
(ī
L
)
to
the
critical
point
ī
1
is
j
1
+
G
c
ī
G
(
i!
)
e
i!
(ī
L
)
j
.
This
indicates
that
the
upset
G
c
ī
G
(
i!
)
e
i!
(
L
+ī
L
)
will
not
dri
v
e
the
system
unstable
as
long
as
j
G
c
ī
G
(
i!
)
j
<
j
1
+
G
c
G
(
i!
)
e
i!
(ī
L
)
j
;
8
!
;
ī
G;
ī
L
(7)
Di
viding
(7)
by
G
c
G
p
and
assuming
e
ī
i!
(
L
+ī
L
)
=
1
,
the
equation
can
be
written
as
ī
ī
ī
ī
1
+
Gc
(
i!
)
G
(
i!
)
e
ī
i!
(ī
L
)
Gc
(
i!
)
G
(
i!
)
e
ī
i!
(ī
L
)
ī
ī
ī
ī
>
ī
ī
ī
ī
ī
G
(
i!
)
G
p
(
i!
)
ī
ī
ī
ī
;
(8)
Deļ¬ning
the
e
xtended
complementary
sensiti
vity
function
as
the
in
v
erse
of
LHS
of
(8)
we
ha
v
e
T
(
s;
ī
L
)
=
G
c
(
s
)
G
(
s
)
e
ī
s
ī
L
1
+
G
c
(
s
)
G
(
s
)
e
ī
s
ī
L
;
(9)
Therefore,
the
condition
for
rob
ust
stability
can
be
gi
v
en
as
ī
ī
ī
ī
ī
G
(
s
)
G
p
(
s
)
T
(
s;
ī
L
)
ī
ī
ī
ī
1
<
1
;
ī
L
2
[ī
L
min
;
ī
L
max
]
:
(10)
where
ī
L
min
and
ī
L
max
are
the
lo
wer
and
upper
delay
v
ariation
bound,
ī
G
is
the
process
model
change.
If
for
ease
of
presentation
in
this
w
ork
ī
ī
ī
ī
G
(
s
)
G
p
(
s
)
T
(
s;
ī
L
)
ī
ī
ī
1
is
represented
as
ī
,
the
rob
ust
stability
condition
can
no
w
be
written
in
terms
of
ī
as
follo
ws
ī
<
1
;
ī
L
2
[ī
L
min
;
ī
L
max
]
:
(11)
Rob
ustness
and
Stability
Analysis
of
a
Pr
edictive
PI
Contr
oller
.....
(S.
M.
Hassan)
Evaluation Warning : The document was created with Spire.PDF for Python.
2608
ISSN:
2088-8708
3.
RESUL
T
AND
AN
AL
YSIS
F
or
the
purpose
of
this
analysis,
we
use
the
model
of
a
thermal
chamber
gi
v
en
in
(12)
[16].
The
measured
netw
ork
delay
as
obtained
from
the
netw
ork
is
sho
wn
in
Fig.
3,
while
the
statistics
of
the
delay
is
gi
v
en
in
T
able
1.
In
the
result
analysis,
rob
ustness
of
the
controller
to
changes
in
both
delay
and
process
v
ariable
for
the
W
irelessHAR
T
netw
ork
based
on
the
delay
information
obtained
from
the
netw
ork
will
be
e
v
aluated
in
both
time
and
frequenc
y
domains.
The
parameters
of
the
PPI
controller
used
for
this
plant
throughout
this
w
ork
are
K
c
=
0
:
125
and
T
i
=
9
:
13
s
.
The
simulation
results
in
this
w
ork
will
be
reported
in
tw
o
phases.
The
ļ¬rst
phase
will
report
on
rob
ustness
while
the
second
will
focus
on
stability
.
G
(
s
)
=
8
1
+
9
:
13
s
e
ī
10
s
(12)
0
500
1000
1500
2000
t
u
(s)
1
1.5
2
Time (s)
0
500
1000
1500
2000
t
d
(s)
1.26
1.28
1.3
Figure
3.
Netw
ork
delay
proļ¬le
T
able
1.
Netw
ork
Delay
Statistics
Delay
type
Max
Min
Mean
Std.
Upstream
(s)
2.084
1.214
1.573
0.217
Do
wnstream
(s)
1.280
1.280
1.280
0.000
3.1.
Rob
ustness
Analysis
This
section
ļ¬rst
analyses
the
rob
ustness
of
the
PPI
controller
to
stochastic
netw
ork
delay
,
then
further
analysis
is
pro
vided
to
its
rob
ustness
to
process
model
perturbation.
The
analysis
here
is
gi
v
en
in
the
time
domain.
3.1.1.
Rob
ustness
to
Delay
Mismatch
T
o
analyse
the
performance
of
the
PPI
controller
to
delay
mismatches,
the
plant
wit
h
the
controller
is
simulated
to
three
dif
ferent
conditions
of
delay
as
gi
v
en
in
T
able
1.
These
conditions
are
maxim
um,
minimum
and
a
v
erage
delays.
Ho
we
v
er
,
the
controller
design
is
based
on
the
a
v
erage
v
alue
of
the
delay
.
The
simulation
results
for
this
scenario
are
gi
v
en
in
Fig.
4,
while
the
re
gions
of
interest
from
this
table
are
zoomed
in
Fig.
5.
Numerical
ļ¬gures
of
the
ļ¬gures
are
gi
v
en
in
T
able
2.
From
both
the
ļ¬gures
and
the
table,
PPI
1,
PPI
2
and
PPI
3
represents
the
three
conditions
of
a
v
erage,
maximum
and
minimum
delays
re
specti
v
ely
.
Thus,
it
ca
n
be
observ
ed
that
for
all
cases
of
delay
,
the
performance
of
the
PPI
is
still
better
than
that
of
PI
controller
in
terms
of
both
setpoint
tracking
and
disturbance
re
gulation
ability
.
F
or
all
the
three
conditions,
the
o
v
ershoot
rise
time
and
both
settling
times
of
the
PPI
controller
are
less
than
those
of
the
PI
controller
compared.
T
able
2.
Rob
ustness
performance
of
the
PPI
controller
to
delay
change
P
arameters
PPI
1
PPI
2
PPI
3
PI
Rise
T
ime
(s)
19.7659
18.4454
21.4858
26.7562
Settling
T
ime
1
(s)
55.7688
51.4477
60.3851
99.4896
Settling
T
ime
2
(s)
269.0980
268.0324
272.1358
301.2938
Ov
ershoot
(%)
0.0000
0.0050
0.0000
5.8924
IAE
2309.3
2290.7
2341.1
3044.7
IJECE
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ā
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Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
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2609
0
50
100
150
200
250
300
350
400
450
500
Response
0
10
20
30
40
A
B
Setpoint
PI
PPI 3
PPI 2
PPI 1
Time(s)
0
50
100
150
200
250
300
350
400
450
500
Input
0
2
4
6
C
D
PI
PPI 3
PPI 2
PPI 1
Figure
4.
Rob
ustness
of
the
PPI
controller
to
change
in
netw
ork
delay
.
0
50
100
Response
20
25
30
A
220
240
260
280
300
320
15
20
25
30
B
Time(s)
0
50
100
Input
2.5
3
3.5
4
C
Time(s)
220
240
260
280
300
320
3.5
4
4.5
5
5.5
6
D
Figure
5.
Zoomed-in
vie
w
of
re
gions
of
interest
A,
B,
C
and
D
of
Fig.
4.
3.1.2.
Rob
ustness
to
Model
Mismatch
T
o
analyse
the
performance
of
the
PPI
controller
to
model
mismatches,
The
plant
with
the
controller
is
simulated
to
three
dif
ferent
conditions
of
model
parameters.
These
conditions
are
nominal
and
ī
10%
change
in
both
process
g
ain
K
and
time
constant
T
.
Ho
we
v
er
,
the
controller
design
is
based
on
the
a
v
erage
v
alue
of
the
delay
.
The
simulation
results
for
t
his
scenario
are
gi
v
en
in
Fig.
6
while
the
re
gions
of
interest
from
this
table
are
zoomed
in
Fig.
7.
Numerical
ļ¬gures
of
t
he
ļ¬gures
are
gi
v
en
in
T
able
3.
From
both
the
ļ¬gures
and
the
table,
PPI,
PPI
+10%
and
PPI
ī
10%
represents
the
three
conditions
of
nominal,
10%
increase
and
10%
decrease
in
plant
model
parameters
respect
i
v
ely
.
Therefore,
i
t
can
be
observ
ed
that
for
all
the
three
cases
of
nominal,
increase
and
decrease
in
parameters,
the
performance
of
the
PPI
outperformed
than
that
of
PI
controller
in
terms
of
both
setpoint
tracking
and
disturbance
re
gulation
capability
.
Numerical
assessment
of
settling
time
before
and
after
disturbance,
o
v
ershoot
and
IAE
also
conļ¬rmed
that
the
performance
of
PPI
controller
is
better
.
Ho
we
v
er
,
the
PI
controller
responds
f
aster
than
PPI-10%
with
a
rise
time
of
about
27s
as
ag
ainst
the
29s
of
the
latter
.
0
50
100
150
200
250
300
350
400
450
500
Response
0
10
20
30
40
A
B
Setpoint
PI
PPI+10%
PPI-10%
PPI
Time(s)
0
50
100
150
200
250
300
350
400
450
500
Input
0
2
4
6
8
C
D
PI
PPI+10%
PPI-10%
PPI
Figure
6.
Rob
ustness
of
t
he
PPI
control
ler
to
ī
10%
change
in
model
parameters.
0
50
100
Response
20
25
30
A
220
240
260
280
300
320
15
20
25
30
B
Time(s)
0
50
100
Input
2.5
3
3.5
4
C
Time(s)
220
240
260
280
300
320
4
5
6
D
Figure
7.
Zoomed-in
vie
w
of
re
gions
of
interest
A,
B,
C
and
D
of
Fig.
6.
3.2.
Stability
Analysis
This
section
analyses
the
stability
of
the
PPI
controller
in
the
frequenc
y
domain
through
Nyquist
plots
based
on
the
rob
ust
stability
conditions
gi
v
en
in
Section
2.2..
First,
ana
lysis
will
be
gi
v
en
based
on
the
delay
statistics
of
Rob
ustness
and
Stability
Analysis
of
a
Pr
edictive
PI
Contr
oller
.....
(S.
M.
Hassan)
Evaluation Warning : The document was created with Spire.PDF for Python.
2610
ISSN:
2088-8708
T
able
3.
Rob
ustness
performance
of
the
PPI
controller
to
model
mismatch
P
arameters
PPI
PPI
+10%
PPI
ī
10%
PI
Rise
T
ime
(s)
19.7698
15.4891
29.4930
26.7578
Settling
T
ime
1
(s)
55.7806
68.5160
78.6990
99.4898
Settling
T
ime
2
(s)
269.1218
261.5824
280.7254
301.3191
Ov
ershoot
(%)
0.0000
3.8335
0.0000
5.8919
IAE
2184.9
2169.6
2358.3
2920.2
T
able
1
and
ī
10%
change
in
model
parameters
as
discussed
in
S
ection
3.1.2.,
then
a
v
ariation
of
both
delay
and
model
parameters
of
up
to
ī
20%
will
be
analysed
for
stability
.
3.2.1.
Stability
of
PPI
Contr
oller
Under
W
ir
elessHAR
T
Netw
ork
Delay
and
Model
Mismatch
The
Nyquist
pl
ot
of
the
plant
for
mean,
maximum
and
minimum
W
irelessHAR
T
netw
ork
delays
in
T
able
1
is
gi
v
en
in
Fig.
8
while
the
plot
for
plant
with
ī
10%
model
misma
tch
is
gi
v
en
in
Fig.
9.
From
the
ļ¬rst
ļ¬gure,
it
can
be
seen
that
the
Nyquist
plots
for
all
the
three
delay
condition
satisfy
the
Nyquist
stability
criteria.
The
second
ļ¬gure
contains
the
Nyquist
plots
of
the
plant
with
both
delay
and
model
mism
atches.
T
o
further
conļ¬rm
the
stability
of
controller
at
these
conditions,
the
rob
ust
stability
condition
gi
v
en
in
Section
2.2.
is
tested
for
dif
ferent
frequencies
as
gi
v
en
in
the
results
of
T
able
4.
It
is
noted
as
gi
v
en
in
the
table
that
for
all
the
frequencies
considered,
the
rob
ust
stability
condition
is
met.
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
-1
-0.5
0
0.5
Average delay
Maximum delay
Minimum delay
Nyquist Diagram
Real Axis
Imaginary Axis
Figure
8.
Nyquist
plot
for
mean,
maximum
and
mini-
mum
netw
ork
delays.
-1
-0.5
0
0.5
-1
-0.5
0
0.5
Avg delay + Nominal
Max delay + 10% mismatch
Min delay - 10% mismatch
Nyquist Diagram
Real Axis
Imaginary Axis
Figure
9.
Nyquist
plot
for
nom
inal,
ī
10%
in
model
mismatch.
T
able
4.
Rob
ust
stability
test
of
PPI
controller
at
dif
ferent
frequencies
!
(
r
ad=s
)
ī
ī
<
1?
ī
max
ī
min
0.1
0.0269
0.0357
Y
es
1
6.41
ī
10
ī
4
9.12
ī
10
ī
4
Y
es
10
6.54
ī
10
ī
6
9.30
ī
10
ī
6
Y
es
100
6.55
ī
10
ī
8
9.31
ī
10
ī
8
Y
es
3.2.2.
Stability
of
PPI
Contr
oller
Under
ī
20%
Delay
and
Model
Mismatches
T
o
further
ensure
that
the
PPI
controller
will
maintain
stability
e
v
en
with
wider
range
of
paramet
er
v
aria-
tions,
ī
20%
mismatches
in
both
model
parameters
and
netw
ork
delay
are
considered.
The
corresponding
Nyquist
IJECE
V
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2611
plots
are
sho
wn
in
Fig.
10.
The
tw
o
rob
ust
stability
conditions
of
(7)
and
(11)
are
applied
at
frequenc
y
!
=
0
:
6
r
ad=s
.
The
result
of
this
stability
test
is
gi
v
en
in
T
able
5.
From
the
table,
it
is
sho
wn
that
the
PPI
controlled
plant
is
stable
at
that
frequenc
y
e
v
en
with
the
lar
ge
perturbation.
-1
-0.5
0
0.5
-1
-0.5
0
0.5
A
2
r
A
o
A
1
r
L
2
L
1
Nominal
20% mismatch
-20% mismatch
Nyquist Diagram
Real Axis
Imaginary Axis
Figure
10.
Nyquist
plot
for
ī
20%
mismatches
in
both
delay
and
model
parameters
!
=
0
:
6
r
ad=s
.
T
able
5.
Rob
ust
stability
test
of
PPI
to
model
and
delay
v
ariations
at
dif
ferent
frequencies
P
arameter
change
ī
Length
(
L
)
Radius
(
r
)
ī
<
1?
r
<
L
?
ī
max
0.5716
0.6450
0.1301
Y
es
Y
es
ī
min
0.3888
1.0080
0.1402
Y
es
Y
es
4.
CONCLUSION
This
paper
has
discussed
the
rob
ustness
and
stability
of
a
PPI
controller
when
used
in
a
wireless
netw
ork
ed
en
vironment.
The
rob
ust
stability
analysis
is
based
on
the
condition
deri
v
ed
from
the
e
xtended
complementary
sensiti
vity
function
which
handles
si
multaneously
both
process
parameter
changes
and
delay
v
ariations.
It
has
been
found
from
the
analysis
result
that
the
plant
controlled
with
the
PPI
controller
still
retains
stability
e
v
en
with
wide
v
ariation
of
model
parameters
and
delay
.
This
implies
that
the
PPI
control
though
s
imple
in
design,
can
handle
the
challenges
of
uncertainties
associated
with
wireless
netw
ork
ed
control.
A
CKNO
WLEDGEMENT
The
authors
of
this
paper
ackno
wledge
the
support
of
Uni
v
ersiti
T
eknologi
PETR
ON
AS
for
the
a
w
ard
of
Graduate
Assistantship
scheme.
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[11]
J.
Cv
ejn,
āPID
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plants
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dead
time
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modulus
optimum
criterion,
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c
hives
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ol
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[12]
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.
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esely
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v
a,
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ust
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v
e
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ol
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ences
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[13]
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ustness
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article
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arm
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[14]
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.-O.
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.
H
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agglund,
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.
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.
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agglund,
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ang,
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.
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.-H.
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BIOGRAPHIES
OF
A
UTHORS
Sabo
Miya
Hassan
is
a
graduate
assistant
at
Department
of
Electrical
and
Electronic
Engi
neering,
Uni
v
ersiti
T
eknologi
PETR
ON
AS,
Malaysia.
He
recei
v
ed
the
B.Eng.
(Hons.)
de
gree
in
electrical
and
electronic
engineering
from
Ab
ubakar
T
af
a
w
a
Bale
w
a
Uni
v
ersity
(A
TB
U),
Bauchi,
Nigeria,
in
2008,
and
the
M.Sc.Eng.
(Hons.)
de
gree
in
control
systems
from
the
Uni
v
ersity
of
Shef
ļ¬eld,
U.K.,
in
2011.
He
is
with
the
Depart
ment
of
Electrical
and
Electronic
Engineering,
A
TB
U.
He
is
currently
pursuing
the
Ph.D.
de
gree
with
the
Electrical
and
Electronic
Engineering
Department,
Uni
v
ersiti
T
eknologi
PETR
ON
AS,
Perak,
Malaysia.
His
current
research
interests
include
wireless
netw
ork
ed
control
systems,
intelligent
control,
and
optimization.
IJECE
V
ol.
7,
No.
5,
October
2017:
2605
ā
2613
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISSN:
2088-8708
2613
Rosdiazli
Ibrahim
recei
v
ed
the
B.Eng.
(Hons.)
de
gree
in
electrical
engineering
from
Uni
v
ersiti
Pu-
tra
Malaysia,
K
embang
an,
Malaysia,
in
1996,
the
M.Sc.
(Hons.)
de
gree
in
automation
and
control
from
Ne
wcastle
Uni
v
ersity
,
Ne
wcastle
upon
T
yne,
U.K.,
in
2000,
and
the
Ph.D.
de
gree
in
electrical
and
el
ectronic
engineering
from
the
Uni
v
ersity
of
Glasgo
w
,
Glasgo
w
,
U.K.,
in
2008.
He
is
currently
an
Associate
Professor
and
Head
of
the
Department
of
Electrical
and
Electronics
Engineering
Uni-
v
ersiti
T
eknologi
PETR
ON
AS,
Seri
Iskanar
,
Perak,
Malaysia.
His
current
research
i
nterests
include
intelligent
control
and
non-linear
multi-v
ariable
process
modelling
for
control
application.
Nordin
Saad
recei
v
ed
the
B.S.E.E.
de
gree
from
Kansas
State
Uni
v
ersity
,
Manhattan,
KS,
USA,
the
M.Sc.
de
gree
in
po
wer
electronics
engineering
from
Loughborough
Uni
v
ersity
,
Loughbor
-
ough,
U.K.,
and
the
Ph.D.
de
gree
in
automatic
control
systems
engineering
from
the
Uni
v
ersity
of
Shef
ļ¬eld,
Shef
ļ¬eld,
U.K.
He
is
currently
an
Associate
Professor
with
the
Department
of
Elec-
trical
and
Electronics
Engineering,
Uni
v
ers
iti
T
eknologi
Petronas,
Perak,
Malaysia.
His
current
research
interests
include
electrical
dri
v
es
control,
fuzzy
and
e
xpert
systems,
model
predict
i
v
e
con-
trol,
computer
control
of
industrial
processes,
f
ailure
analys
is
for
diagnostic
condition
monitoring
systems,
smart
sensors
and
ļ¬eld
intelligence,
smart
grid,
and
netw
ork
ed
and
wireless
control.
Dr
.
Saad
is
a
member
of
the
Institute
of
Measurement
and
Control,
U.K.
V
ijanth
Sagayan
Asir
v
adam
recei
v
ed
the
B.Sc.
(Hons.)
de
gree
in
statistic
from
Uni
v
ersiti
Putra
Malaysia,
K
embang
an,
Malaysia,
in
1997,
and
the
M
.Sc.
(Hons.)
de
gree
in
engineering
compu-
tation
and
the
Ph.D.
de
gree
with
a
focus
on
online
a
nd
constructi
v
e
neural
learning
methods
from
Queens
Uni
v
ersity
Belf
ast,
Belf
ast,
U.K.
He
joined
the
Intelligent
Systems
and
Control
Research
Group,
Queens
Uni
v
ersity
Belf
ast,
in
1999.
He
serv
es
as
an
Associate
Professor
with
the
Depart-
ment
of
Electrical
and
Electronics
Engineering,
Uni
v
ersiti
T
eknologi
Petronas,
Perak,
Malaysia,
where
he
is
the
Head
of
the
Health
Informatics
Modeling
Group
with
the
Ce
nter
of
Intelligent
Signal
and
Imaging
Research.
His
current
research
interest
includes
linear
and
nonlinear
system
identiļ¬cation
and
model
v
alidation
in
the
ļ¬eld
of
computational
intelligence,
control,
and
signal
and
image
processing.
Kishor
e
Bingi
recei
v
ed
the
B.T
ech.
(Hons.)
de
gre
e
in
Electrical
&
Electronics
Engineering
from
Bapatla
Engineering
Colle
ge
(BEC),
Bapatla,
Andhra
pradesh,
India,
in
2012,
and
the
M.T
ech
(Hons.)
de
gree
in
Instrumentation
and
Control
Systems
from
National
Insti
tute
of
T
echnology
(NIT)
Calicut,
Calicut,
K
erala,
India,
in
2014.
He
w
ork
ed
with
T
A
T
A
consultanc
y
service
as
an
Assistant
systems
Engineer
from
2015
to
2016.
He
is
currently
pursuing
the
Ph.D.
de
gree
with
the
Electrical
and
Electronic
Engineering
Departm
ent,
Uni
v
ersiti
T
eknologi
Petronas
(UTP),
Perak,
Malaysia.
His
current
research
interests
include
process
modeling,
control
and
optimization.
T
ran
Duc
Chung
w
as
born
in
H
Long,
V
ietnam,
in
1989.
He
recei
v
ed
the
B.E.E.E.
(Hons.)
de
gree
in
instrumentati
on
and
control
from
Uni
v
ersiti
T
eknologi
Petronas
(UTP),
Perak,
Malaysia,
in
2014,
where
he
is
currently
pursuing
the
Ph.D.
de
gree
with
a
focus
on
wireless
netw
ork
ed
control
system
for
industrial
applications.
His
current
research
interests
include
adv
anced
process
control
with
predicti
v
e
and
adapti
v
e
mechanisms,
big
data
processi
ng
and
analysis,
and
artiļ¬cial
intelligence.
Mr
.
Chung
recei
v
ed
the
V
ice
Chancellor
A
w
ard
and
the
Best
International
Student
A
w
ard
from
UTP
in
2014,
the
PETR
ON
AS
Full-T
ime
Scholarship
in
2009,
and
the
Third
Prize
in
the
National
Ph
ysics
Competition
from
the
Bureau
of
Educational
T
esting
and
Quality
Accreditation,
Ministry
of
Education,
V
ietnam,
in
2007.
Rob
ustness
and
Stability
Analysis
of
a
Pr
edictive
PI
Contr
oller
.....
(S.
M.
Hassan)
Evaluation Warning : The document was created with Spire.PDF for Python.