Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
Vol
.
4
,
No
. 5, Oct
o
ber
2
0
1
4
,
pp
. 70
3~
71
8
I
S
SN
: 208
8-8
7
0
8
7
03
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Desi
gn of Intelli
gent PID Contro
ll
er for AVR S
y
st
em Using an
Adaptive Neuro Fuzzy In
ference System
Kam
a
l
Yavarian, F
a
rid Ha
s
h
emi, Amir
Mohamm
adian
Department o
f
Electrical Engin
e
e
r
ing, Ard
a
bil
Br
anch,
Is
lam
i
c
Az
ad Univers
i
t
y
,
Ardabil
,
Ir
an
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
J
u
l 27, 2014
Rev
i
sed
Sep
16
, 20
14
Accepted
Sep 30, 2014
This paper presents a h
y
brid app
r
oach involv
i
ng signal to noise r
a
tio (SNR)
and parti
c
l
e
swarm
optim
ization
(PSO) for design the optim
al
an
d intel
ligen
t
proportional-integral-der
ivative (
P
ID)
controller
of an automatic voltag
e
regula
t
or (AVR) s
y
s
t
em
with us
e
s
an adaptive ne
uro fuzz
y
inf
e
re
nce s
y
s
t
em
(ANFIS). In this paper de
term
ine
d
optim
al par
a
m
e
ters of PID con
t
rolle
r with
S
N
R-PS
O approach for
s
o
m
e
eve
n
ts
and us
e
thes
e
optim
al p
a
ram
e
t
e
rs
of P
I
D
controll
er for d
e
sign the int
e
ll
i
g
ent PID controller for AVR s
y
stem
with
ANFIS. Trial and error method can be us
ed to find a suitable d
e
sign of anfis
bas
e
d an in
tel
l
i
g
ent con
t
roll
er.
However, th
ere
are m
a
n
y
option
s
includin
g
fuzz
y ru
les
,
M
e
m
b
ers
h
ip F
uncti
ons
(M
F
s
) and s
caling
fa
ctors
t
o
ach
iev
e
a
desired performance. An op
tim
izat
ion algorithm
facili
tat
e
s this process and
finds an optimal design to pr
ovide
a desir
e
d
performance.
This paper
presents a novel application
of the SNRPSO appr
oach to design an intelligen
t
controller for AVR. SNR-PSO i
s
a method
that combines the features of PSO
and SNR in order to improve th
e optim
ize op
er
ation
.
In order t
o
em
phas
i
ze
the adv
a
ntages o
f
the proposed S
N
R-PSO
PID controller, we
also
compared
with the CRPSO PID controller. The proposed
method was indeed more
efficient and ro
bust in improving the st
ep response of an AVR sy
stem and
nume
r
i
c
a
l
si
mula
t
i
ons a
r
e
provi
d
e
d
t
o
ve
ri
fy
t
h
e
e
ffe
ct
i
v
e
n
e
ss a
nd fe
a
s
i
b
i
lity
of PID contro
ller of AVR based
on SNRPSO algorithm.
Keyword:
Ada
p
t
i
v
e ne
ur
o fuzzy
Aut
o
m
a
ti
c vol
t
a
ge
reg
u
l
a
t
o
r
In
fere
nce sy
ste
m
Particle swarm op
ti
m
i
zatio
n
PID Con
r
t
o
ller
Si
gnal
t
o
noi
se
rat
i
o
Copyright ©
201
4 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Farid Has
h
em
i,
Depa
rtem
ent of Elect
ri
cal
E
n
gi
nee
r
i
n
g,
Islamic Azad
Uni
v
ersity,
Ar
da
bi
l
B
r
anc
h
,
Ar
da
bi
l
,
I
r
a
n
.
Em
a
il: farid
.
h
a
sh
em
i6
6
@
g
m
ail.co
m
1.
INTRODUCTION
No
wa
day
s
, ec
on
om
i
c
and en
vi
r
onm
ent
a
l
const
r
ai
nt
s ca
n l
e
ad t
o
hi
g
h
er
ut
i
l
i
zat
i
on of e
x
i
s
t
i
ng
pl
ant
,
defe
rre
d ex
pe
n
d
iture o
n
sy
stem
reinforcem
ent (an
d
lo
nger distance between powe
r pla
n
t and loa
d
center),
with conseque
nt erosi
on
of
stability
margins. Howeve
r,
it is
necessary
to ensure that
adequate stability
marg
in
s are main
tain
ed
fo
r t
h
e reliab
l
e power su
pp
ly. Mu
ltip
le g
e
n
e
rato
rs
in
a power statio
n
are co
nn
ect
ed
to
a com
m
on bu
s bar
an
d eac
h o
f
t
h
ese
gen
e
rat
o
r
s
ha
s an
aut
o
m
a
t
i
c
vol
t
a
ge re
gul
at
or
(A
VR
)
w
hose
m
a
i
n
o
b
j
ectiv
e is to
co
n
t
ro
l th
e primary v
o
ltag
e
. Du
e to
system d
i
stu
r
b
a
n
ces t
h
e electrical o
s
cillatio
n
s
m
a
y
o
ccur
for a long tim
e and m
i
ght result in system
instability.
Hence effective control algo
rith
m
s
are required to
alleviate these
issues.
The
aut
o
m
a
tic voltage
regulator
(AVR) system
s are use
d
e
x
tensi
v
ely in exciter c
ont
rol
sy
st
em
. The rol
e
of an
AV
R
i
s
hol
di
n
g
t
h
e ge
nerat
o
r t
e
rm
i
n
al
vol
t
a
ge const
a
nt
u
n
d
er n
o
r
m
a
l op
erat
i
n
g
co
nd
itio
ns at
variou
s l
o
ad levels. Th
e
AVR
lo
op
o
f
th
e excitatio
n
con
t
rol syste
m
e
m
p
l
o
y
s term
in
al vo
ltag
e
erro
r
fo
r adj
u
stin
g
th
e field
v
o
ltag
e
to
contro
l th
e term
in
al v
o
ltag
e
. Con
t
ro
l p
a
ram
e
te
rs
o
f
t
h
e au
tomatic
v
o
ltag
e
regu
lato
r
(AVR
) affect th
e
power syste
m
d
y
n
a
mic
s
and
stab
ility.
No
wad
a
ys, m
o
re th
an
9
0
%
co
n
t
ro
l
lo
op
s in
in
du
stry are PID co
n
t
ro
l. Th
is is
m
a
in
ly
due to the fact that PID
controller possesses robust
per
f
o
r
m
a
nce to m
eet t
h
e gl
obal
c
h
an
ge o
f
i
n
d
u
st
ry
p
r
o
cess, si
m
p
l
e
struct
ure t
o
be easi
l
y
unde
rst
o
o
d
b
y
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 4
,
N
o
. 5
,
O
c
tob
e
r
20
14
:
703
–
7
18
70
4
en
g
i
n
eers, and easin
ess to
desig
n
an
d
im
p
l
e
m
en
t. Th
e
PID an
d
its v
a
riatio
n
s
(P, PI, PD) still are wid
e
ly
appl
i
e
d
i
n
t
h
e
m
o
t
i
on co
nt
r
o
l
beca
use
o
f
i
t
s
sim
p
l
e
st
ru
ct
ure a
n
d r
o
bu
st
per
f
o
rm
ance i
n
a
wi
de
ra
n
g
e
of
o
p
e
rating
conditio
n
s
.
Unfortun
ately, it h
a
s been
qu
ite d
i
ffi
c
u
lt to
tu
ne pro
p
e
rly th
e g
a
i
n
s of PID con
t
ro
llers
because
m
a
ny indust
r
ial plants are ofte
n burdene
d
with
problem
s
such as high order, tim
e
delays, and
nonlinea
rities. There
f
ore,
when the sea
r
c
h
space c
o
m
p
le
xity increases the exact al
gorithm
s
can be slow t
o
fi
n
d
gl
obal
op
t
i
m
u
m
.
Li
near and
n
o
n
l
i
n
ear
pr
o
g
ram
m
i
ng, br
ut
e f
o
rce
o
r
exha
ust
i
v
e
se
arch a
n
d di
vi
d
e
an
d
con
q
u
er
m
e
t
hods a
r
e s
o
m
e
of
t
h
e e
x
act
o
p
t
i
m
i
zat
i
on m
e
t
hods
.
O
v
er
t
h
e
y
ears, se
ve
ral
heu
r
i
s
t
i
c
m
e
t
h
ods
hav
e
been
p
r
o
p
o
se
d
fo
r t
h
e t
uni
ng
of
PI
D c
ont
ro
l
l
e
rs. The
s
e m
e
t
h
o
d
s
have
se
veral
a
dva
nt
a
g
es com
p
ared t
o
ot
her
alg
o
rith
m
s
as
fo
llows: (a) Heu
r
istic alg
o
rith
m
s
are g
e
n
e
rally eas
y to
i
m
p
l
e
m
en
t; (b
) Th
ey can
b
e
u
s
ed
efficien
tly in
a m
u
lt
ip
ro
cessor env
i
ron
m
en
t;
(c)
Th
ey
d
o
n
o
t
requ
ire th
e p
r
ob
lem
d
e
finitio
n
fu
n
c
ti
o
n
to
b
e
co
n
tinuo
us; (d) Th
ey g
e
n
e
rally can
fin
d
op
ti
m
a
l o
r
n
ear-op
tim
a
l
so
lu
tio
n
s
. Particle swarm
o
p
t
i
m
iz
atio
n
(
P
SO
) is an
eff
i
cien
t and w
e
l
l
kn
ow
n stochastic alg
o
r
ith
m wh
ich h
a
s foun
d m
a
n
y
su
ccessf
u
l
app
licatio
n
s
in
engi
neeri
n
g
p
r
obl
em
s [1-
4
]
.
Si
gnal
t
o
noi
s
e
rat
i
o
al
g
o
r
i
t
h
m
doesn’t
req
u
i
r
e a
wi
de
so
l
u
t
i
on s
p
ace
, a
n
d
t
h
e
larg
e
nu
m
b
er o
f
search
ing
an
d iteratio
n
s
were su
scep
tib
le to
related
co
ntro
l
p
a
ram
e
ters. On
t
h
e
o
t
h
e
r
h
a
nd,
this
m
e
thod ha
s
an effective applianc
e
a
n
d better
re
su
lt for
unce
rtainties conditio
ns a
n
d differe
n
t
ope
ration
poi
nt
s. S
N
R
h
a
s a res
p
on
si
bl
e res
u
l
t
i
n
t
h
e
no
nl
i
n
ea
r
system
s o
p
t
i
m
iza
tio
n
.
Th
e in
tegral p
e
rfo
rm
an
ce criteria
i
n
f
r
eq
ue
ncy
d
o
m
a
i
n
were
oft
e
n
used
t
o
e
v
al
uat
e
t
h
e c
o
nt
ro
l
l
e
r per
f
o
r
m
a
nce, b
u
t
t
h
ese
cr
i
t
e
ri
a have t
h
ei
r
o
w
n
adva
nt
age
s
an
d
di
sad
v
a
n
t
a
ges
[5
-6]
.
In t
h
i
s
st
udy
a
no
vel
de
si
gn m
e
t
hod
fo
r det
e
rm
i
n
i
ng t
h
e o
p
t
i
m
al
si
gnal
t
o
noi
se rat
i
o
al
go
ri
t
h
m
and part
i
c
l
e
swar
m
opt
im
i
z
at
i
on (S
NR
-P
SO
)
param
e
t
e
rs for de
si
g
n
t
h
e
opt
i
m
a
l
p
r
op
ortio
n
a
l
-
integ
r
al-d
eri
v
ativ
e (PID) co
n
t
ro
ller of an
a
u
t
o
m
a
ti
c vol
t
a
ge
reg
u
l
a
t
o
r
(
A
V
R
) sy
st
em
usi
ng t
h
e
hy
b
r
i
d
S
N
R
P
S
O
a
p
p
r
oac
h
su
ch t
h
at
t
h
e c
o
n
t
rol
l
e
d sy
st
em
coul
d
obt
ai
n
a
go
o
d
st
ep
res
p
ons
e o
u
t
p
ut
fo
r
som
e
event and case
that
m
a
y be happe
n in the powe
r syste
m
.
After th
at we
u
s
e ANFIS for train
i
n
g
and
ob
tain
ed
th
e fu
zzy m
e
mb
ersh
ip
fun
c
tion
(MF)
for fu
zzy in
feren
ce sy
ste
m
with
result o
f
o
u
r op
ti
m
i
zatio
n
.
In
th
is p
a
p
e
r
a fuzzy i
n
fe
rence syste
m
m
odels whic
h takes
G
K
and
g
as in
pu
ts
an
d
p
K
,
i
K
and
d
K
as output. The
r
efore
after m
a
ke fuz
z
y
infere
nce s
y
stem
when o
u
r sy
stem
i
nputs change our
PID c
o
effi
cient controller change a
n
in
tellig
en
tly and
fed to
system and
always
our system
h
a
v
e
b
e
st
o
p
e
ration
.
2.
LINEA
R
IZ
ED
MO
DEL O
F
A
N
AUT
O
M
ATI
C
VOL
T
AGE REGULATOR
(AVR) SYSTEM
Exp
l
ain
i
ng
The aim
o
f
Au
tomatic Vo
ltag
e
regu
lato
r (AVR) co
n
t
ro
l is to m
a
in
tain
th
e syste
m
v
o
ltag
e
b
e
tween
li
m
i
ts b
y
ad
j
u
stin
g
th
e ex
citatio
n
o
f
th
e m
ach
in
es. Th
e au
t
o
matic v
o
ltag
e
reg
u
l
ator sen
s
es th
e
di
ffe
re
nce bet
w
een
a rect
i
f
i
e
d vol
t
a
ge der
i
ved
f
r
om
t
h
e st
at
or v
o
l
t
a
ge and
a refe
re
nc
e
v
o
l
t
a
ge.
T
h
i
s
er
ro
r
sig
n
a
l is am
p
lified
and
fed to th
e ex
citatio
n
circu
it.
Th
e chan
g
e
of ex
citatio
n
m
a
in
tain
s th
e
VAR
b
a
lance in
the network. T
h
is m
e
thod is also refe
rre
d a
s
Me
gawatt Volt Am
p Reactive (MVA
R) c
ont
rol or Reactive-
Vol
t
a
ge
(
Q
V) cont
rol
[7
-
14]
.
a.
PID Co
ntro
ller
The P
I
D
co
nt
r
o
l
l
e
r i
s
use
d
t
o
i
m
prove t
h
e
dy
nam
i
c
response as
well as
to re
duce
or elim
inate the
steady-state error. T
h
e
PID c
o
n
t
ro
ller t
r
ansfer fun
c
tio
n is:
S
K
S
K
K
s
G
d
i
p
PID
)
(
(1
)
Th
e fu
nctio
n
a
l
ities o
f
PID co
n
t
ro
ller in
cl
ud
e: (a) th
e
p
r
op
ortion
a
l term p
r
o
v
i
d
e
s an
ov
erall con
t
ro
l actio
n
p
r
op
ortio
n
a
l to th
e error signal th
rou
g
h
th
e all p
a
ss g
a
in
facto
r
(b) Th
e in
teg
r
al term
redu
ces stead
y
-
state
er
ro
r
s
thro
ugh lo
w
-
f
r
e
qu
en
cy co
m
p
en
sation
(
c
)
Th
e d
e
r
i
v
a
tiv
e ter
m
i
m
p
r
o
v
e
s tr
an
sien
t r
e
spon
se th
rough
high-fre
quency
com
p
ensation.
b.
M
o
del of
a
n
AV
R Sys
t
em
The
rol
e
of a
n
A
V
R
i
s
t
o
hol
d t
h
e t
e
rm
inal
v
o
l
t
a
ge m
a
gni
t
u
de
of
a
sy
nch
r
o
n
o
u
s
g
e
nerat
o
r at
a
sp
ecified
lev
e
l. A si
m
p
le
AVR system
co
m
p
rises four
m
a
in
co
m
p
o
n
e
n
t
s, nam
e
l
y
a
m
p
lifier, e
x
citer,
gene
rat
o
r, an
d
senso
r
. F
o
r
m
a
t
h
em
at
i
c
al
m
odel
i
ng an
d
t
r
ansfe
r
f
unct
i
on o
f
t
h
e f
o
ur c
o
m
pone
nt
s, t
h
ese
com
pone
nts m
u
st
be linea
rized,
which ta
ke
s into accoun
t
the m
a
jor tim
e constant a
n
d i
g
nores the
saturation
or
ot
her
nonl
inearities. T
h
e
reas
ona
ble t
r
ans
f
er fu
nction of the
s
e
com
pone
nts
m
a
y be re
pre
s
ented,
resp
ectiv
ely, as fo
llo
ws [14
-
19
].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Design
o
f
In
tellig
en
t PID C
ontro
ller fo
r AVR S
y
stem
Using
a
n
Ad
ap
tive N
e
u
r
o
Fu
zzy
In
feren
ce …
(Farid
H
)
70
5
2.
2.
1
Amplifier model
Th
e am
p
lifier
m
o
d
e
l is represen
ted
b
y
a
g
a
i
n
A
K
and a
A
ti
m
e
co
n
s
tan
t
. Th
e tran
sfer
fun
c
tion
i
s
A
A
A
K
G
1
(2
)
Whe
r
e t
h
e typi
cal value
of
A
K
is
in
th
e
ran
g
e
of
[10
,
400
] and
A
i
s
ve
ry
sm
all
ran
g
i
n
g
fr
om
0.0
2
t
o
0.
1 s
.
2.
2.
2
Exciter m
o
del
The t
r
a
n
s
f
er
f
unct
i
o
n
of
a
m
odern e
x
ci
t
e
r m
a
y
be repr
esent
e
d
by
a
gai
n
E
K
and a single tim
e
constant
E
.
E
E
E
K
G
1
(3
)
Whe
r
e the typi
cal value of
E
K
i
s
i
n
t
h
e ra
nge
of
[1
0,
40
0]
an
d t
h
e t
i
m
e
const
a
nt
E
r
a
ng
es fr
om 0
.
5
to
1.0
s.
2.
2.
3
Generator m
o
del
Th
e tran
sfer fun
c
tio
n
relatin
g th
e g
e
n
e
rator
termin
al
vol
t
a
ge t
o
i
t
s
fi
el
d
vol
t
a
ge ca
n
be
rep
r
esent
e
d
by
a
gai
n
G
K
an
d a
t
i
m
e
const
a
nt
G
G
G
G
K
G
1
(
4
)
These c
o
nst
a
nt
s are l
o
ad
s
dep
e
nde
nt
,
G
K
m
a
y
vary
bet
w
een
0
.
1
an
d
1.
0, a
n
d
G
is b
e
t
w
een 1.0
an
d 2.0 s.
2.
2.
4
Sensor
m
o
del
Th
e sen
s
o
r
circu
it, wh
ich
rectifies, filters, and
redu
ces th
e term
in
al vo
ltag
e
, is m
o
d
e
led
b
y
the
fo
llowing
sim
p
le first-o
r
d
e
r tran
sfer
fun
c
tion
S
S
S
K
G
1
(5
)
Whe
r
e
S
ra
nge
f
r
om
of
0.
0
0
1
t
o
0.
06
s.
c.
AVR Sys
t
em With
P
I
D
Contr
o
ller
Th
e ab
ov
e m
o
d
e
ls pr
ov
id
e an
AV
R
sy
st
em
co
m
p
ensat
e
d wi
t
h
a
PI
D
cont
rol
l
e
r
bl
o
c
k di
a
g
ram
,
whi
c
h i
s
s
h
ow
n i
n
Fi
g
u
r
e
1.
Fi
gu
re 1.
B
l
oc
k di
ag
ram
of
a
n
AVR
sy
st
em
wi
t
h
a PI
D
c
o
n
t
rol
l
e
r.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 4
,
N
o
. 5
,
O
c
tob
e
r
20
14
:
703
–
7
18
70
6
3.
HYBRID SIGNAL TO
NOISE
RATIO
&
PA
R
T
IC
LE
S
W
ARM
OP
T
I
M
I
ZA
T
I
O
N
Th
is p
a
p
e
r
p
r
esen
ts a SNR-PSO PID con
t
ro
ller for search
ing
th
e op
timal co
n
t
ro
ller param
e
ters o
f
AVR
.
I
n
t
h
i
s
sect
i
on, a
PI
D
cont
rol
l
e
r
usi
ng t
h
e S
N
R
P
S
O
al
g
o
ri
t
h
m
was
devel
ope
d
t
o
i
m
prove t
h
e st
ep
tran
sien
t
resp
on
se
o
f
an
AVR syste
m
. Si
g
n
a
l
-
to
-No
i
se
Ratio
(SNR
) alg
o
rith
m
are u
s
ed
in
t
h
is p
a
p
e
r
t
o
ev
alu
a
te ex
isten
ce
p
o
s
sib
ility
o
f
op
tim
al v
a
lu
e in
PID
p
a
ra
m
e
ters. Th
is
alg
o
rith
m
d
o
e
s no
t req
u
i
re a
wi
de
so
lu
tion
sp
ace, and
th
e larg
e nu
m
b
er of search
i
n
g
and
iteratio
n
s
were suscep
tib
l
e
to
related
co
n
t
ro
l
param
e
t
e
rs.
O
n
t
h
e ot
he
r ha
nd
,
t
h
i
s
m
e
t
hod has
an
ef
fec
t
i
v
e
ap
pl
i
a
nce
an
d bet
t
e
r re
sul
t
for
unce
r
t
a
i
n
t
i
e
s
co
nd
itio
ns and d
i
fferen
t
o
p
e
ratio
n
po
in
ts.
Sig
n
a
l-t
o
-No
i
se Ratio
alg
o
r
ithm h
a
s a respon
sib
l
e resu
lt in
th
e
n
o
n
lin
ear system
s o
p
t
i
m
iza
tio
n
.
Sign
al-to-No
ise Ratio
(SNR
) is a m
easu
r
e o
f
th
e
v
a
riatio
n with
i
n
a trial wh
en
n
o
i
se
factors
presen
t.
It loo
k
s lik
e a resp
on
se wh
ich
c
o
n
s
o
l
id
ates rep
e
titio
n
s
an
d
reflects
n
o
i
se lev
e
ls in
t
o
on
e
dat
a
p
o
i
n
t
.
SN
R
cons
ol
i
d
at
es
several
repet
i
t
i
ons i
n
t
o
one
v
a
l
u
e t
h
at
re
fl
ect
s t
h
e am
ount
of
vari
at
i
o
n
pr
esent
.
There
SNR
ar
e
defi
ne
d
depe
n
d
i
n
g o
n
t
h
e t
y
pe o
f
cha
r
act
er
i
s
t
i
c
desi
red,
h
i
ghe
r i
s
bet
t
e
r
(HB
)
, l
o
wer i
s
bet
t
e
r
(LB
)
a
n
d n
o
m
i
nal
i
s
best
(
N
B
)
. T
h
e e
q
uat
i
o
n
s
f
o
r cal
c
u
latin
g
S/
N ratio
s for HB
, LB
o
r
NB ch
aracteristics are
gi
ve
n as
f
o
l
l
o
ws
[1
9]
:
a.
Higher is
better
2
2
2
2
1
)
1
(
...
)
1
(
)
1
(
1
10
n
HB
y
y
y
n
Log
N
S
(6
)
Whe
r
e
n
y
y
y
,...,
2
,
1
refer t
o
th
e n ob
serv
ati
o
n
s
wit
h
in
an
ex
p
e
rim
e
n
t
al co
n
d
ition
o
f
th
e
c
ont
rol
l
a
bl
e fact
ors
.
b.
lower is better
2
)
1
(
10
i
LB
y
n
Log
N
S
(7
)
Wh
ere
n
is t
h
e
n
u
m
b
e
r
o
f
tests in
a trial (n
um
b
e
r o
f
rep
e
titio
n
s
reg
a
rd
le
ss of
n
o
i
se lev
e
ls).
c.
Nor
m
al is
bes
t
e
NB
LogV
N
S
10
1
(8
)
e
e
m
NB
nV
V
V
Log
N
S
)
(
10
2
(9
)
Th
e equ
i
p
m
en
t u
tilizat
io
n
in th
is stu
d
y
is a "Lo
w
er is better" ch
aracteristic, sin
ce the eq
u
i
p
m
en
t
u
tilizatio
n
is to
b
e
m
i
n
i
mize
d
.
So
we
u
s
ed th
e second
equ
a
tio
n
fo
r
ou
r
respon
se.
In gen
e
ral, t
w
o
arb
itrary
in
pu
t con
s
id
erate fo
r SNR alg
o
rith
m
,
o
n
e
is
fo
r sig
n
al an
d
the oth
e
r is f
o
r
noise
. This i
n
puts are selecte
d
from
[0, 1
]
i
n
terv
al, du
e to th
e
n
a
t
u
rally of SNR
alg
o
rith
m
.
Hence, if t
h
e signa
l
and noise a
r
e
stand in this
range
,
th
e resu
lts will b
e
h
a
v
i
ng
a same sig
n
e
d
and
co
m
p
ariso
n
fo
r th
e b
e
st select
in
g
will b
e
wit
h
ou
t m
i
stak
e. Sig
n
a
l
to
No
ise Ratio
(SNR
) algo
rithm is u
s
ed
to
g
e
n
e
rate th
e in
iti
al so
lu
tion
,
it actu
a
lly wid
e
n
s
th
e search
sp
ace of
PSO be
sides increasi
n
g the
efficiency
. The position
of the
ne
xt ge
ne
ra
tion
is
calculated according to PSO
alg
o
rith
m
an
d
it is
rep
eated
u
n
til
m
eetin
g
t
h
e end
con
d
itio
n. Th
e g
e
n
e
ratio
n
m
ech
an
ism o
f
so
lu
tion
ad
op
ts
p
r
ob
ab
ilistic d
i
strib
u
tion
fun
c
tio
n
,
an
d
on
e so
lu
tion
is d
e
ep
ly related
to
one an
o
t
h
e
r. Im
p
r
op
er
p
a
ram
e
te
rs are
v
e
ry lik
ely to
trap
PSO i
n
to
a
lo
cal o
p
tim
al s
o
lu
tion
,
o
r
m
a
k
e
it requ
ire mo
re tim
e
to
find
th
e g
l
o
b
a
l
o
p
ti
m
u
m
.
Th
e SNR
P
SO alg
o
r
ith
m
was
m
a
in
ly u
t
i
liz
ed
to
d
e
term
in
e th
ree op
ti
m
a
l co
n
t
ro
ller p
a
ram
e
ters
p
K
,
i
K
and
d
K
such t
h
at
t
h
e cont
rol
l
e
d sy
st
e
m
coul
d o
b
t
a
i
n
a goo
d st
ep re
spo
n
se
out
put
.
The desi
gn st
e
p
s o
f
SNR
-
PS
O
base
d P
I
D
co
nt
rol
l
e
r i
s
as
fol
l
ows
.
a)
In
itialize th
e al
g
o
rith
m
p
a
rameters lik
e
n
u
m
b
e
r of
g
e
n
e
ratio
n, p
opu
latio
n
,
in
ertia weigh
t
an
d
con
s
tan
t
s.
b)
In
itialize th
e
v
a
lu
es
o
f
th
e p
a
ram
e
ters
p
K
,
i
K
and
d
K
ra
nd
om
l
y
vi
a Si
gnal
-
t
o
-N
oi
se R
a
t
i
o
(S
NR
)
alg
o
rith
m
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Design
o
f
In
tellig
en
t PID C
ontro
ller fo
r AVR S
y
stem
Using
a
n
Ad
ap
tive N
e
u
r
o
Fu
zzy
In
feren
ce …
(Farid
H
)
70
7
c)
Calculate the fi
tness
function
of
each pa
rticle in eac
h
ge
neration.
d)
Calcu
l
ate th
e lo
cal b
e
st of each
p
a
rticle and
th
e g
l
o
b
a
l
b
e
st
o
f
th
e
p
a
rticles.
e)
Up
dat
e
t
h
e
p
o
s
i
t
i
on,
vel
o
ci
t
y
,
l
o
cal
best
a
n
d
gl
o
b
al
be
st
i
n
e
ach
gene
rat
i
o
n.
Rep
eat th
e steps 3
t
o
5
un
til th
e m
a
x
i
m
u
m
i
t
e
r
atio
n reach
e
d
o
r
th
e
b
e
st so
lutio
n
is
foun
d.
4.
AD
APTI
VE
NEU
R
O
-
FUZ
Z
Y
INFERE
N
C
E S
Y
STEM
(A
NFIS
)
Art
i
f
i
c
i
a
l
i
n
t
e
l
l
i
g
ence, i
n
cl
u
d
i
ng
neu
r
al
net
w
or
k, f
u
zzy
l
o
gi
c i
n
fere
nce,
ge
net
i
c
al
gori
t
hm
and e
xpe
rt
syste
m
s, has been use
d
to s
o
lve m
a
ny nonlinear classi
fi
ca
t
i
on p
r
o
b
l
e
m
s
[2
0-
2
3
]
.
The
m
a
i
n
adva
nt
ag
es of a
fu
zzy l
o
g
i
c sy
ste
m
(FLS) are th
e cap
a
b
ility to
expre
ss
n
o
n
lin
ear input-ou
t
pu
t relatio
n
s
h
i
p
s
b
y
a
set of
q
u
a
litativ
e if-th
e
n ru
les. Th
e
main
ad
v
a
n
t
age o
f
an artif
icial n
e
ural n
e
t
w
o
r
k
(ANN),
on th
e
o
t
h
e
r h
a
nd, is the
in
h
e
ren
t
learn
i
n
g
cap
a
b
ility,
wh
ich
en
ab
les
th
e n
e
two
r
k
s
t
o
ad
ap
tiv
ely im
p
r
o
v
e
th
eir
perfo
r
m
a
n
ce. Th
e k
e
y
p
r
op
erties of
neu
r
o
-fu
zzy n
e
t
w
ork are t
h
e accu
rate l
earn
i
ng
an
d
ad
ap
tiv
e cap
ab
ilities o
f
th
e neural n
e
t
w
orks,
to
g
e
th
er
with
th
e g
e
n
e
ralizati
o
n
and
fast learn
i
n
g
cap
a
b
iliti
es o
f
fu
zzy logic syste
m
s. A n
e
uro
-
fu
zzy (ANFIS)
syste
m
is a com
b
ination of
neural
ne
twork
and fuzzy syst
e
m
s in s
u
ch a
wa
y
t
h
at
ne
ura
l
net
w
or
k i
s
us
ed t
o
d
e
term
in
e th
e p
a
ram
e
ters o
f
fu
zzy system
.
A n
e
ural n
e
two
r
k
is u
s
ed
to
au
t
o
m
a
t
i
cally
tu
n
e
th
e syste
m
param
e
t
e
rs. T
h
e A
N
F
I
S i
s
a
very
p
o
we
rf
ul
app
r
oach
f
o
r
m
odel
i
ng
no
nl
i
n
ear a
n
d c
o
m
p
l
e
x
sy
st
em
s wi
t
h
l
e
ss
i
n
p
u
t
and
out
p
u
t
t
r
ai
ni
n
g
dat
a
wi
t
h
qui
c
k
er
l
earni
n
g
and
hi
g
h
pre
c
i
s
i
o
n
.
The neu
r
o fu
zzy
sy
st
em
wit
h
t
h
e
learn
i
ng
cap
a
bilit
y o
f
n
e
u
r
al
n
e
two
r
k
and
with
th
e adv
a
n
t
ag
es
o
f
th
e ru
le-b
ase
fu
zzy syste
m
can
im
p
r
ove th
e
perform
a
nce significa
ntly a
nd ca
n provi
d
e a
m
echan
is
m
to
in
co
rp
orate p
a
st ob
serv
ation
s
into
th
e
cl
assi
fi
cat
i
on
p
r
oces
s.
In
ne
u
r
al
net
w
or
k t
h
e
t
r
ai
ni
n
g
e
ssen
t
i
a
l
l
y
bui
l
d
s
t
h
e sy
st
em
. Ho
w
e
ver
,
usi
n
g a
n
e
ur
o
fu
zzy sch
e
m
e
, th
e system
is b
u
ilt b
y
fu
zzy l
o
g
i
c
d
e
fin
itio
ns and
is t
h
en
refin
e
d
u
s
ing
n
e
u
r
al
n
e
two
r
k train
i
ng
alg
o
rith
m
s
.
a.
ANF
IS Architecture
Th
e m
o
d
e
ling
ap
pro
ach
u
s
ed
b
y
ANFIS is si
milar to
m
a
n
y
syste
m
id
en
tificatio
n
techn
i
qu
es.
First,
a
p
a
ram
e
terized
m
o
d
e
l stru
ctu
r
e (relatin
g
i
n
pu
ts to
m
e
m
b
ersh
ip
fun
c
tion
s
to
ru
les to
ou
t
p
u
t
s t
o
m
e
m
b
e
r
sh
i
p
fun
c
tion
s
, and
so
o
n
) is h
y
p
o
th
esized
.
Nex
t
, in
pu
t/ou
t
pu
t data is co
llected
in
a
form
th
at will b
e
u
s
able b
y
AN
FIS
f
o
r t
r
ai
ni
n
g
.
A
N
F
I
S c
a
n t
h
en
be
u
s
e
d
t
o
t
r
ai
n t
h
e FIS m
o
d
e
l t
o
em
u
l
a
t
e th
e trai
n
i
ng
d
a
ta
p
r
esen
ted to
it by
m
odifying the m
e
m
b
ership func
tion param
e
ters according to a c
hos
en e
r
ror c
r
iterion.
Ope
r
at
ion
of
AN
FIS
l
o
oks
l
i
k
e fee
d
-
f
o
r
w
a
rd
bac
k
p
r
opa
gat
i
o
n
net
w
o
r
k. C
o
n
s
eq
ue
nt
param
e
t
e
rs ar
e cal
cul
a
t
e
d
f
o
r
w
ar
d
whi
l
e
p
r
em
i
s
e
param
e
t
e
rs are cal
cul
a
t
e
d bac
k
wa
r
d
. T
h
ere
are t
w
o l
ear
ni
ng m
e
t
hods i
n
neu
r
al
sect
i
o
n
of t
h
e
sy
st
em
: Hy
bri
d
l
earni
ng m
e
tho
d
an
d bac
k
-
p
r
o
pagat
i
o
n l
earni
ng m
e
t
hod
. In f
u
zzy
sect
i
on,
onl
y
zer
o or fi
rst
or
der
S
uge
n
o
i
n
fere
nce
sy
st
em
or Tsu
k
am
ot
o i
n
fe
renc
e
sy
st
em
can be
use
d
.
T
h
i
s
s
ect
i
on i
n
t
r
o
d
u
ces t
h
e
basi
cs
of
A
N
FI
S net
w
o
r
k
arc
h
i
t
ect
ure an
d i
t
s
hy
b
r
i
d
l
e
a
r
ni
n
g
r
u
l
e
.
The
Su
gen
o
fuz
z
y
m
o
del
was
p
r
op
os
ed
by
Taka
gi
, Su
ge
n
o
, an
d
Kan
g
i
n
an eff
o
rt
to
form
alize a syste
m
atic approac
h
to
g
e
n
e
ratin
g fu
zzy ru
les fro
m
an
in
pu
t-o
u
t
p
u
t
dataset.
To
p
r
esen
t
th
e ANFIS arch
itecture,
with
two inp
u
t
s,
o
n
e
ou
tpu
t
an
d two
ru
les is g
i
v
e
n in
Figure
2.
In t
h
is connected struct
ur
e, t
h
e in
pu
t and
o
u
tp
u
t
nod
es
r
e
pr
esent t
h
e trai
ning val
u
es a
nd t
h
e
pre
d
i
c
t
e
d
val
u
es, res
p
ect
i
v
el
y
,
and i
n
t
h
e hi
dde
n l
a
y
e
rs, t
h
ere are
no
des
f
unct
i
o
ni
n
g
as
m
e
m
b
ershi
p
fu
nct
i
o
n
s
(MFs) and
ru
les. Th
is arch
itectu
r
e
h
a
s th
e b
e
n
e
fit th
at
it elimin
ates th
e d
i
sad
v
a
n
t
ag
e
of a
norm
al feed forwa
r
d
m
u
l
tilayer n
e
twork,
wh
ere it is d
i
fficu
lt fo
r an
o
b
s
er
v
e
r t
o
und
erstand
or m
o
d
i
fy th
e
network. Here
x
,
y
are
in
pu
ts,
f
i
s
o
u
t
p
u
t
, t
h
e ci
rcl
e
s
re
prese
n
t
fi
xe
d
n
ode
f
u
nct
i
ons
a
n
d
sq
ua
res
rep
r
esent
a
d
apt
i
v
e
no
de
f
unct
i
o
ns
.
Figure
2. ANFIS a
r
chitecture
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 4
,
N
o
. 5
,
O
c
tob
e
r
20
14
:
703
–
7
18
70
8
C
onsi
d
er
a fi
rs
t
or
der
S
uge
n
o
fuzzy
i
n
fe
renc
e sy
st
em
whi
c
h c
ont
ai
n
s
t
w
o
rul
e
s:
1
1
1
1
1
1
f
then
,
B
is
Y
and
A
is
X
:
1
r
y
q
x
p
If
Rule
2
2
2
2
2
2
f
then
,
B
is
Y
and
A
is
X
:
2
r
y
q
x
p
If
Rule
Whe
r
e,
1
p
,
2
p
,
1
q
,
2
q
,
1
r
,
2
r
are linear
para
meters and
1
A
,
2
A
,
1
B
,
2
B
are
nonlinear param
e
ter. ANFIS
i
s
an im
pl
em
ent
a
t
i
on
of a f
u
zzy
l
ogi
c inference system with
the archite
cture of a fi
ve
-layer feed-forward
n
e
two
r
k
.
Th
e
syste
m
ar
ch
itectu
r
e con
s
ists
o
f
f
i
v
e
layer
s
, n
a
m
e
l
y
, f
u
zzy layer
,
p
r
oduct layer
,
n
o
r
m
alized
layer, d
e
-fu
zzy
layer an
d
to
tal o
u
t
pu
t layer. W
i
t
h
th
is
way ANFIS
u
s
es the ad
v
a
n
t
ag
es
of learn
i
n
g
cap
a
b
ility
of ne
u
r
al
net
w
or
ks an
d i
n
fe
re
nce m
echani
s
m
sim
i
l
a
r
t
o
hum
an brai
n p
r
ovi
ded
by
fuzz
y
l
ogi
c. The o
p
erat
i
o
n
of each layer is
as follows:
He
re the
output
node
i
in
layer
l
i
s
de
not
e
d
as
l
i
O
.
Layer 1 is fu
zzificatio
n
layer.
Ev
ery
no
d
e
i
in th
is layer is an ad
ap
tiv
e
n
o
d
e
with
n
o
d
e
fu
n
c
tio
n
4
,
3
),
(
2
,
1
),
(
,
1
,
1
i
for
x
B
O
i
for
x
A
O
i
i
i
i
(1
0)
Whe
r
e
x
is the in
pu
t t
o
th
i
nod
e,
l
i
O
is th
e m
e
m
b
ersh
ip
gra
d
e o
f
x
i
n
t
h
e
fuzzy set
Ai
.
G
e
neral
i
zed
bel
l
m
e
m
b
ershi
p
fu
nct
i
on
i
s
p
o
p
u
l
ar
m
e
t
hod f
o
r
specifying fuzzy sets becau
se of t
h
eir sm
oot
hne
ss and
c
onci
s
e
not
at
i
o
n, a
n
d
d
e
fi
ne
d as
i
b
i
i
i
A
a
c
x
x
2
1
1
)
(
(1
1)
Here {
i
a
,
i
b
,
i
c
} is
t
h
e p
a
ram
e
ter
set o
f
th
e m
e
m
b
ersh
ip
fu
n
c
tio
n
.
Th
e cen
t
er and
wid
t
h
o
f
th
e
me
m
b
ersh
ip
fun
c
tio
n
is
v
a
ried
b
y
adju
sting
i
c
and
i
a
. The
par
a
m
e
ter
i
b
is u
s
ed
to
con
t
ro
l th
e
slo
p
es at th
e
cro
s
sov
e
r po
in
t
s
. Th
is layer
form
s th
e an
teced
e
n
t
s of th
e fuzzy ru
les
(
IF
p
a
rt).
Layer
2 is th
e
r
u
les layer. Ever
y nod
e in
t
h
i
s
laye
r i
s
a
fi
x
e
d
no
de a
n
d c
o
nt
ai
n
s
one
f
u
zzy
rul
e
.
The
out
put
i
s
t
h
e
pr
od
uct
of
al
l
i
n
c
o
m
i
ng si
g
n
al
s
and
re
pre
s
ent
s
t
h
e fi
ri
ng
st
re
n
g
t
h
o
f
eac
h
r
u
l
e
.
2
,
1
),
(
)
(
2
i
y
x
w
O
i
B
i
A
i
i
(1
2)
Layer 3
is
no
rmalizat
io
n
layer. Ev
ery
n
o
d
e
in
th
is layer is a fix
e
d
n
o
d
e
an
d
t
h
e
th
i
no
de c
a
l
c
ul
at
es
th
e ratio
o
f
the
th
i
ru
le’s firing stren
g
t
h
to
the su
m o
f
all ru
les’ firi
n
g
stren
g
t
h
s
. Ou
tpu
t
s o
f
th
is layer are
called norm
alized
firing
stre
ngths
com
puted
as:
2
,
1
2
1
3
i
w
w
w
w
O
i
i
i
(1
3)
Layer
4 is co
nseq
u
e
n
t
layer
.
Ev
er
y
no
d
e
in
this la
yer is an a
d
aptive
node a
n
d com
putes t
h
e value
s
of
rule c
o
nseq
ue
n
t
(
THEN
part)
as:
)
(
4
i
i
i
i
i
i
i
r
y
q
x
p
w
f
w
O
(1
4)
Lay
e
r 5 is su
m
m
a
tion lay
e
r and c
o
n
s
ists of
single
fixe
d n
ode
whic
h calculates the ove
r
a
ll output as
the summation of all incom
i
n
g
si
gnals as:
i
i
i
i
i
i
i
i
i
w
f
w
f
w
O
5
(1
5)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN:
208
8-8
7
0
8
Design
of Intelligent PID C
ontro
ller for AVR System
Using
an Ad
aptive N
e
uro Fuzzy
Inference …
(Farid
H
)
70
9
It can
be
obse
rve
d
that t
h
ere
are two a
d
apt
i
ve la
yers in t
h
is ANFIS archit
ecture, nam
e
ly the first
lay
e
r an
d t
h
e
fo
urt
h
lay
e
r.
I
n
the
fi
rst lay
e
r, t
h
ere
are
three
m
odifiabl
e
pa
ram
e
ters {
ai
,
bi
,
ci
}, which are
related to the
input
m
e
m
b
er
ship functions.
These pa
ram
e
ters are th
e so-called prem
ise
param
e
ters. In the
fourt
h
layer, there are als
o
three m
odifiable
param
e
ters
{
pi
,
qi
,
ri
},
p
e
r
t
ain
i
ng
to
th
e
f
i
r
s
t o
r
der
p
o
l
ynomial.
These
pa
ram
e
ters a
r
e the
so
-c
alled co
nse
que
nt pa
ram
e
ters [
2
2
-
23]
.
b.
L
e
arni
n
g
al
g
o
r
i
t
hm of
A
N
F
I
S
The task
of the learni
ng algorith
m
for this architecture i
s
to t
une
all the m
odifiable
param
e
ters,
nam
e
ly
{
ai
,
bi
,
ci
} and {
pi
,
qi
,
ri
}, t
o
m
a
ke the
ANFIS output m
a
tch
the training
data.
W
h
en
th
e pre
m
is
e
param
e
ters
ai
,
bi
and
ci
of t
h
e m
e
m
b
ership function are fi
xed, t
h
e
output of
t
h
e ANFIS m
odel
can
be written
as:
2
2
1
2
1
2
1
1
f
w
w
w
f
w
w
w
f
(1
6)
Substituting
Eq. (4)
i
n
to Eq. (7)
yields:
2
2
1
1
f
w
f
w
f
(1
7)
Substituting the fuzzy if-t
hen
rule
s i
n
to
Eq. (8), it becom
e
s:
)
(
)
(
2
2
2
2
1
1
1
1
r
y
q
x
p
w
r
y
q
x
p
w
f
(1
8)
Af
ter r
e
ar
r
a
ng
emen
t, th
e
ou
tpu
t
can b
e
expr
essed
as:
2
2
2
2
2
2
1
1
1
1
1
1
)
(
)
(
)
(
)
(
)
(
)
(
r
w
q
y
w
p
x
w
r
w
q
y
w
p
x
w
f
(1
9)
Whic
h is a linear com
b
ination o
f
the m
odifiable conse
q
ue
nt param
e
ters
p
1,
q
1,
r
1,
p
2,
q
2 an
d
r
2. The least
squares m
e
thod can be
used to iden
tify the optim
al values of t
h
ese
pa
ram
e
ters easily.
W
h
e
n
t
h
e prem
is
e
param
e
ters are
not fi
xed, the
searc
h
s
p
ace
becom
e
s la
rge
r
a
nd t
h
e c
onverge
nce
of t
h
e training
bec
o
m
e
s
slowe
r
. A
hy
b
r
id algo
rithm
com
b
ining the l
east squa
re
s m
e
tho
d
an
d the
gra
d
ient de
sce
n
t m
e
thod is a
d
o
p
ted
to solve t
h
is problem
.
The hybrid al
go
rith
m
is co
m
pose
d
o
f
a f
o
r
w
ar
d
pass an
d a
ba
ckwa
r
d
pass
.
The least
sq
uar
e
s m
e
th
od
(f
orward
p
a
ss)
is u
s
e
d
to
o
p
tim
i
ze the conse
que
nt pa
ra
m
e
ters with the prem
ise parameters
fixe
d. O
n
ce th
e optim
al conseque
nt pa
ram
e
ters are f
o
un
d, t
h
e bac
k
ward pass starts im
m
e
diately. The gradient
desce
n
t m
e
thod
(bac
k
w
ar
d
p
a
ss) is
use
d
to
ad
just o
p
tim
ally
the p
r
em
ise pa
ram
e
te
rs cor
r
es
po
n
d
in
g t
o
th
e
fuzzy
sets i
n
the in
put
d
o
m
a
in. T
h
e
out
p
u
t o
f
the
A
N
F
IS is calc
u
la
ted by
em
plo
y
i
ng the c
o
ns
eque
nt
param
e
ters fo
u
n
d
in t
h
e f
o
rwa
r
d
pass
. T
h
e
o
u
tp
ut er
ro
r is
used t
o
adapt t
h
e prem
ise param
e
ters by m
e
a
n
s
of a
standa
rd
bac
k
pr
o
p
agatio
n al
go
rithm
.
It ha
s bee
n
pr
ove
n that this
hybrid
algorithm
is highly efficient in
training the ANFIS
[21-23].
5.
OBJ
E
CTIVE FUNCTION DEFINITION
In the
desig
n
of a PI
D co
ntr
o
ller, the pe
rf
orm
a
nce criterion or obj
ective function is first defined
base
d o
n
som
e
desired s
p
e
c
ifications an
d co
nstrai
nts
un
de
r inp
u
t testing si
g
n
al. Som
e
ty
pical
out
put
specifications in the ti
m
e
domain ar
e overshoot, rise tim
e
,
se
ttling ti
m
e
,
and steady
-
state error. In general
,
three ki
nds
of
per
f
o
r
m
a
nce criteria, th
e integrate
d
abs
o
lut
e
erro
r (I
AE
),
the integral o
f
squa
red
-
er
r
o
r
(IS
E),
and the i
n
tegr
a
t
ed of tim
e weighted
- sq
ua
re
d-e
r
r
o
r
(IT
SE
)
are us
ually
con
s
idere
d
in the
cont
rol de
sig
n
un
de
r
step input testing, as they
ca
n
be e
v
aluate
d analytically in the
fre
quen
cy
dom
a
in. It is
worthy t
o
noti
ce that
usin
g dif
f
e
r
ent
per
f
o
r
m
a
nce indices p
r
o
b
a
b
ly
m
a
kes diffe
re
n
t
solution
s
fo
r
PID c
o
nt
rollers. The three int
e
gral
per
f
o
r
m
a
nce criteria in the fr
eque
ncy
d
o
m
a
in have th
ei
r o
w
n a
dva
ntage
s
and disa
dva
nt
ages. F
o
r e
x
a
m
ple,
a
disad
v
a
n
tage o
f
the IAE
an
d
ISE criteria is that their m
i
ni
mization
can result in a response with
relatively
sm
a
ll overshoot but a long settling ti
me. Although th
e ITSE performance crite
rion can overcome the
disad
v
a
n
tage
o
f
the
IS
E c
r
iterio
n
, t
h
e
deri
v
a
tion
pr
oce
sse
s of the
a
n
alytical form
ula are com
p
lex a
n
d tim
e
-
con
s
um
ing [
4
]
.
The
I
A
E,
IS
E,
IT
AE a
n
d I
T
S
E
pe
rf
orm
a
nce
criteria f
o
rm
ulas are a
s
f
o
llo
ws:
Inte
gral of
abs
o
lu
te er
ro
r (I
AE)
:
dt
e
J
(2
0)
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S
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l. 4
,
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,
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e
r
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14
:
703
–
7
18
71
0
Inte
gral
of
sq
u
a
red
er
ro
r
(IS
E
)
:
dt
e
J
2
(2
1)
Integral
of ti
me weighted
abso
lu
te er
ro
r (I
TA
E)
:
dt
e
t
J
(2
2)
Inte
gral
of
tim
e
weig
hted
s
q
u
a
red
er
ro
r
(IT
S
E
):
dt
e
t
J
2
(2
3)
Each perform
a
nce
index has
its
own advantages and
di
sadvantages and
will
result in
different
syste
m
perform
a
nce. T
h
e ISE is a typi
cal perform
a
nce criterion used i
n
a
n
u
m
b
er of
cont
rol a
p
plications.
It
tends to
penalize all errors
with resp
ect to t
h
e gi
ven
weig
hting
facto
r
s.
The IT
AE is a
l
so widely
use
d
in
cont
rol applications and includes the ti
m
e
, t,
in orde
r to penalize the settl
ing ti
m
e
of the controlled syste
m
.
The m
i
ni
mizat
i
on
of
ISE and IAE can
result in a resp
onse with sm
all overshoot
but longer settling time and
is seen as
a
disadva
n
tage.
Henc
e
selection
o
f
a
pe
rf
o
r
m
a
nce inde
x
sh
oul
d
be
b
a
sed
on
the
desire
d
perform
a
nce aspects for t
h
e overall
system
.
The fitness function (obj
ectiv
e fu
nctio
n) f
o
r
SNR
-
PS
O is d
e
fine
d
as:
2
)
(max
001
.
0
2
2
)
1000
(
dv
st
t
sh
O
on
CostFuncti
(2
4)
In t
h
is pa
pe
r, t
h
e
desire
d pe
rf
orm
a
nce aspec
t
s are
to m
i
nim
i
zation of c
o
st fu
nctio
n wit
h
the
help
o
f
any
optim
ization tech
niq
u
e c
o
r
r
es
po
n
d
s to m
i
nim
u
m
over
s
ho
ot (
sh
O
), m
i
nim
u
m
settling tim
e
(
st
t
) an
d
dv
max
. The
r
efore, it
becom
e
s an
uncons
trained
opti
mization problem
to fi
nd a
set of
decisio
n
variabl
e
s
by
m
i
nim
i
zing the
ob
jective
fu
nctio
n. M
a
xim
u
m
popula
tion
size =
50
,
m
a
xim
u
m
allo
wed
iteration
c
y
cles =
10
0,
1
C
=
2
C
= 2.
05
. The pa
ram
e
ter
s
o
f
t
h
e bloc
k diag
ram
are
ch
ose
n
as
A
K
= 10,
e
K
=
s
K
=1
.0
,
a
= 0.
1 s
,
e
= 0.4 s,
S
= 0.
01
s,
g
= 1.
0 s.
O
n
ly
G
K
and
g
are loa
d
de
pendent.
6.
METHO
D
OL
OGY OF
TH
E PRO
P
OSE
D
ALGO
RIT
H
M
In this study,
we propose to
use a hybri
d
intelligent syste
m
ca
lled ANFIS for
design the optim
a
l
proportional
-
integral-deri
v
ative (P
I
D
) c
ont
roller
of a
n
a
u
tom
a
tic voltage re
gulat
or (
AVR
) sy
stem
.
We
com
b
ine the ability of a
neural net
w
ork (NN) to learn wi
th fuzzy
logic
(FL) to reason
in
order to form
a
hybrid i
n
telligent system
call
e
d
ANFIS.
The goal
of ANFIS is t
o
find a
m
odel or m
a
pping t
h
at
will correctly
associate the inputs with
t
h
e
target. The
fu
zzy
infere
nce sy
stem
(FIS) is a kn
owle
dg
e
repr
esentatio
n
whe
r
e
each f
u
zzy
rul
e
descri
bes a local be
havi
or
of the sy
stem
. The net
w
ork
structure that im
ple
m
ents FIS and
em
ploy
s hy
b
r
i
d
-lear
nin
g
rule
s to tr
ain is ca
lled AN
FI
S. T
h
e co
nce
p
t o
f
the p
r
o
p
o
se
d techni
que
is ba
sed
o
n
recognizing t
h
e patterns of t
h
e sensitivities of
som
e
indi
ces to prescribed
credible ev
ents since
every event
coul
d ha
ve a si
gnat
u
re
on t
h
e
patterns
of t
h
e
s
e indices.
Th
e f
o
llowing
indep
e
nd
en
t v
a
riables are
define
d with
respect t
o
thi
s
target l
o
cation. Table
2
has
been
com
puted to illustrate th
e com
p
arative
performance
characte
r
istics of SNRP
SO
PI
D
con
t
ro
ller
.
G
K
has bee
n
vari
ed fr
om
0.7 to
1.0 in ste
p
s o
f
0.
1.
g
has
been
va
ried
f
r
o
m
1.0
to
2.
0
in steps
of
0.
2
.
T
hus
, Ta
bl
e
2 incl
u
d
es
24
diffe
re
nt sets
of
in
put c
o
ndit
i
ons
o
f
AVR system
. Each i
n
put corresponds
to
nom
inal optim
al
PID
gai
n
as
o
u
t
put.
Fr
om
Table 2
it m
a
y be noted
that SNR
P
S
O
base
d o
p
tim
i
zation tech
niq
u
e of
fers
(a)
lesse
r overs
h
oot of
change
in term
inal voltage
(
sh
O
),
(b) lesser settling ti
m
e
of
cha
nge in term
inal voltage (
st
t
),
an
d
(c) m
o
re m
a
xim
u
m
derivative o
f
c
h
a
nge
i
n
terminal voltage (
dv
max
). T
h
e be
ha
vio
r
al
m
odel o
f
the p
r
o
p
o
sed
techniq
u
e ca
n be re
prese
n
ted
within th
e
fuzzy
i
n
fe
renc
e sy
stem
as fol
l
ows:
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I
J
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S
SN:
208
8-8
7
0
8
Design
of Intelligent PID C
ontro
ller for AVR System
Using
an Ad
aptive N
e
uro Fuzzy
Inference …
(Farid
H
)
71
1
]
[
S
M
1,2,...,
i
]
[
]
,
,
[
)
]
,
([
.
..........
..........
..........
.
..........
..........
..........
.
..........
..........
..........
)
]
,
([
)
]
,
([
]
,
[
......
..........
......
..........
......
..........
]
,
[
]
,
[
1
*
2
1
1
*
2
1
out
in
out
d
i
p
M
M
g
g
g
g
g
g
out
M
M
g
g
g
g
g
g
in
Data
Data
Data
K
K
K
T
K
Output
T
K
Output
T
K
Output
Data
T
K
T
K
T
K
Data
That:
g
K
:
U
nde
r t
h
e
th
i
event;
g
T
:
U
n
der
the
th
i
event;
:
M
T
h
e Num
b
er of pe
rf
orm
e
d tests
In t
h
is p
r
o
p
o
s
e
d m
e
thod
olo
g
y
,
e
x
tensive
presc
r
ibe
d
e
v
ents are sim
u
lated off-line
in
or
de
r to ca
pt
ure t
h
e
essential featu
r
es of
the sy
ste
m
behavior
tha
t
pr
od
uce
t
h
e
ANFIS. T
h
ese
presc
r
ibe
d
e
v
e
n
ts are
de
fine
d in the
event data
base fr
om
Table.2 (
2
4
di
ffe
rent
set
s
) whic
h the network sim
u
lato
r ex
ecutes t
h
e
requi
red eve
n
ts.
Table
2.
A
n
fis
rule
base ta
ble,
o
p
tim
i
zed PI
D
gain
s a
n
d
tran
sient res
p
onse
param
e
ters
MF
dv
max
st
t
sh
O
d
K
i
K
p
K
T
y
pe of
co
n
t
ro
ller
g
G
K
0.
3675
0.
1103
0.
5341
9.
7953e-
8
0.
2474
0.
5274
0.
7762
SNR-PSO
1
0.
7
0.
4292
0.
1131
0.
5922
1.
9037e-
6
0.
2750
0.
5102
0.
8430
SNR-PSO
1.
2
0.
5544
0.
1045
0.
6802
8.
7316e-
8
0.
2893
0.
4680
0.
8629
SNR-PSO
1.
4
0.
3511
0.
1205
0.
5312
1.
8994e-
8
0.
4003
0.
5284
1.
0964
SNR-PSO
1.
6
0.
3856
0.
1187
0.
5609
2.
5885e-
7
0.
4439
0.
5291
1.
1862
SNR-PSO
1.
8
0.
3790
0.
1171
0.
5532
4.
5202e-
7
0.
4852
0.
5184
1.
2800
SNR-PSO
2
0.
3628
0.
1130
0.
5333
3.
7172e-
7
0.
2167
0.
4616
0.
6795
SNR-PSO
1
0.
8
0.
5486
0.
0960
0.
6633
2.
3390e-
7
0.
2698
0.
4146
0.
6736
SNR-PSO
1.
2
0.
3562
0.
1197
0.
5353
1.
3507e-
7
0.
3052
0.
4619
0.
8655
SNR-PSO
1.
4
0.
3549
0.
1200
0.
5343
6.
9746e-
7
0.
3496
0.
4608
0.
9560
SNR-PSO
1.
6
0.
3909
0.
1146
0.
5616
2.
8920e-
7
0.
3666
0.
4490
1.
0127
SNR-PSO
1.
8
0.
7187
0.
0934
0.
7772
1.
5401e-
8
0.
3089
0.
3815
0.
9181
SNR-PSO
2
0.
4392
0.
1096
0.
5966
9.
1740e-
9
0.
1776
0.
3913
0.
5701
SNR-PSO
1
0.
9
0.
4795
0.
1037
0.
6217
1.
5431e-
9
0.
2048
0.
3887
0.
6382
SNR-PSO
1.
2
0.
3543
0.
1191
0.
5326
6.
6844e-
7
0.
2716
0.
4108
0.
7699
SNR-PSO
1.
4
0.
3967
0.
1169
0.
5688
5.
1328e-
8
0.
3017
0.
3986
0.
8269
SNR-PSO
1.
6
0.
4032
0.
1144
0.
5716
2.
2475e-
1
0
0.
3265
0.
3963
0.
8953
SNR-PSO
1.
8
0.
8295
0.
0920
0.
8434
1.
8179e-
7
0.
2579
0.
3202
0.
7700
SNR-PSO
2
0.
4931
0.
1053
0.
6330
4.
7599e-
6
0.
1407
0.
3278
0.
4938
SNR-PSO
1
1
0.
3760
0.
1123
0.
5435
8.
4153e-
8
0.
2066
0.
3681
0.
6147
SNR-PSO
1.
2
0.
4633
0.
1014
0.
6050
6.
2972e-
8
0.
2094
0.
3239
0.
6466
SNR-PSO
1.
4
0.
4054
0.
1125
0.
5713
8.
7420e-
8
0.
2579
0.
3577
0.
7342
SNR-PSO
1.
6
0.
3549
0.
1188
0.
5330
1.
6682e-
7
0.
3112
0.
3668
0.
8367
SNR-PSO
1.
8
0.
3989
0.
1152
0.
5689
2.
2754e-
7
0.
3308
0.
3586
0.
8829
SNR-PSO
2
7.
AR
CHITE
C
T
URE
OF T
H
E PR
OPOSE
D
ALGO
RITH
M
The architecture of t
h
e proposed
Intelligent-based for
design t
h
e
optimal PID
control
l
er of
AVR
sy
stem
is shown in
Fig
u
re
3
.
It is consists
of th
r
ee m
a
in
m
odules, nam
e
ly
the input m
o
d
u
le, f
u
zzy
in
fere
nce
sy
stem
, and t
h
e o
u
tp
ut m
odul
e. T
h
ese m
odul
es are
desc
ribe
d as
f
o
llow
s
:
a.
Inpu
t Module
The i
n
p
u
t to
th
is m
odule are
G
K
&
g
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN:
2
088
-87
08
I
J
ECE Vo
l. 4
,
No. 5
,
Octob
e
r
20
14
:
703
–
7
18
71
2
b.
Fuz
z
y
Infere
nce s
y
stem
(F
IS)
This m
odule is the fuzzy
in
fere
nce sy
stem
softwa
re m
o
d
e
l of desi
gn t
h
e o
p
tim
al PID co
ntr
o
ller o
f
A
V
R
sy
stem
. This m
o
d
u
le
has alre
a
d
y
bee
n
disc
us
sed i
n
Sectio
n
II.
c.
O
u
t
p
u
t
Mo
dule
This is an
output
un
it wh
ich in
clud
e
p
K
,
i
K
and
d
K
.
Figure 3.
Archi
t
ecture of
t
h
e propose
d
intelligent
-
based for design
t
h
e opt
i
m
al PID controller
of
AVR syste
m
This ap
pr
oac
h
use an
d fe
d to
the ANF
IS f
o
r trainin
g
an
d obtaine
d the f
u
zzy
m
e
m
b
ership f
u
nctio
n
(M
F)
witho
u
t need t
o
determ
ine of ty
pe a
n
d
num
ber o
f
m
e
m
b
ership f
unct
i
on.
In t
h
is pa
p
e
r a fuzzy
in
fe
rence
syste
m
m
odels which takes
G
K
and
g
as inputs and
p
K
,
i
K
and
d
K
as o
u
tp
ut. Fi
g
u
res
4-
6 s
h
ow
th
e
fuzzy m
e
m
b
ership function
for
p
K
,
i
K
and
d
K
obtain
e
d o
n
ly
from
dataset fo
r all conditional.
The result
obtaine
d t
o
i
n
dicate that ANF
I
S is e
ffective
m
e
thod
for
des
i
gn a
n
i
n
telligent P
I
D
controller.
(a)
(b
)
Fig
u
re
4
.
T
h
e
fuzzy
m
e
m
b
ership
f
unctio
n
o
b
t
ained
fr
om
ANFI
S
fo
r
p
K
: (a)
I
n
p
u
t
G
K
; (
b
) Inp
u
t
g
Fuzzy
In
fere
nc
e
Sy
stem
()
I
npu
t Mod
u
l
e
]
,
[
g
G
K
Out
put
Mo
du
le
]
,
,
[
d
i
p
K
K
K
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