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ller
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2088
-
8
694
A
F
u
z
z
y
P
I
D
C
o
n
tr
o
ller
fo
r
I
n
d
u
ctio
n
Hea
tin
g
S
ystems
w
ith
LL
C
V
o
lta
g
e
S
o
u
r
ce
....
(
A
r
iji
t
C
h
a
kra
b
a
r
ti)
1171
T
h
e
f
u
zz
y
t
u
n
i
n
g
u
n
it
w
ill
p
r
o
ce
s
s
t
w
o
in
p
u
t
v
ar
iab
les
an
d
w
i
ll
g
e
n
er
ate
t
h
r
ee
o
u
tp
u
t
v
a
r
iab
les
to
ac
h
iev
e
th
e
d
esire
d
lev
el
o
f
co
n
tr
o
l.
T
h
e
er
r
o
r
(
e
)
an
d
er
r
o
r
ch
an
g
e
r
ate
(
ec
=
d
e/d
t)
ar
e
th
e
t
w
o
i
n
p
u
t
v
ar
iab
les.
E
r
r
o
r
is
th
e
d
i
f
f
er
e
n
ce
b
et
w
ee
n
t
h
e
r
e
f
er
en
ce
s
et
p
o
in
t
a
n
d
t
h
e
o
u
tp
u
t,
w
h
er
ea
s
er
r
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r
ch
an
g
e
r
ate
(
ec
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is
th
e
d
i
f
f
er
en
ce
b
et
w
ee
n
th
e
er
r
o
r
at
ti
m
e
t
a
n
d
(
t
-
1
)
.
T
h
e
th
r
ee
o
u
tp
u
t
s
v
ar
iab
les
(
Δ
K
P
,
Δ
K
I
,
Δ
K
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)
w
ill
tu
n
e
th
e
p
r
o
p
o
r
tio
n
al,
in
teg
r
al
an
d
d
er
iv
ativ
e
g
ai
n
s
(
K
P
,
K
I
,
K
D
)
o
f
th
e
P
I
D
co
n
tr
o
ller
.
All
th
e
v
ar
iab
l
es
ar
e
d
iv
id
ed
in
to
f
u
zz
y
s
e
ts
[
9
]
.
T
r
ian
g
u
lar
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
h
a
s
b
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co
n
s
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ed
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o
r
t
h
is
r
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ch
w
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r
k
.
T
h
e
f
u
zz
y
P
I
D
co
n
tr
o
l c
an
b
e
ex
p
r
ess
ed
as E
q
u
atio
n
3
:
k
j
D
I
P
f
p
i
d
k
e
k
e
K
j
e
K
k
e
K
k
y
0
)
1
(
)
(
)
(
)
(
)
(
(
3
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A
l
s
o
,
P
P
P
K
K
K
0
(
4
)
I
I
I
K
K
K
0
(
5
)
D
D
D
K
K
K
0
(
6
)
ec
e
f
K
P
,
1
(
7
)
ec
e
f
K
I
,
2
(
8
)
ec
e
f
K
D
,
3
(
9
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K
P0
,
K
I0
,
K
D0
ar
e
t
h
e
i
n
itial
v
alu
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o
f
P
I
D
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n
tr
o
ller
a
n
d
(
Δ
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P
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Δ
K
I
,
Δ
K
D
)
ar
e
t
h
e
s
el
f
-
tu
n
ed
P
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D
p
ar
am
eter
s
ac
h
iev
ed
t
h
r
o
u
g
h
f
u
zz
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ea
s
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n
i
n
g
.
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h
e
u
n
i
v
er
s
e
o
f
d
is
co
u
r
s
e
o
f
ea
c
h
i
n
p
u
t
v
ar
i
ab
le
is
d
iv
id
ed
i
n
to
f
i
v
e
o
v
er
lap
p
in
g
f
u
zz
y
s
ets:
Neg
ati
v
e
B
ig
(
NB
)
,
Neg
ati
v
e
S
m
al
l
(
N
S),
Z
er
o
E
r
r
o
r
(
Z
E
)
,
P
o
s
itiv
e
S
m
all
(
P
S)
an
d
P
o
s
itiv
e
B
ig
(
P
B
)
.
T
h
e
f
u
zz
y
s
u
b
s
et
is
e
=
ec
=
{NB
,
NS,
Z
E
,
P
S,
PB
}.
T
h
e
g
r
ad
e
o
f
m
e
m
b
er
s
h
ip
d
is
tr
ib
u
tio
n
f
o
r
er
r
o
r
(
e
)
an
d
e
r
r
o
r
ch
an
g
e
r
ate
(
ec
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ar
e
g
iv
en
in
Fi
g
u
r
e
s
4
(
a)
&
4
(
b
)
.
(
a)
(
b
)
Fig
u
r
e
4
.
Me
m
b
er
s
h
ip
f
u
n
ctio
n
s
: (
a)
f
o
r
er
r
o
r
e
,
(
b
)
f
o
r
e
r
r
o
r
ch
an
g
e
r
ate
ec
Fig
u
r
e
5
.
Me
m
b
er
s
h
ip
f
u
n
ctio
n
f
o
r
Δ
K
P
,
Δ
K
I
,
Δ
K
D
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
IJ
PEDS
Vo
l.
8
,
No
.
3
,
Sep
te
m
b
er
201
7
:
1
1
6
8
–
1
1
7
5
1172
T
h
e
u
n
iv
er
s
e
o
f
d
is
co
u
r
s
e
o
f
ea
ch
o
u
tp
u
t
v
ar
iab
le
(
Δ
K
P
,
Δ
K
I
,
ΔK
D
)
is
d
iv
id
ed
in
to
f
iv
e
o
v
er
lap
p
in
g
f
u
zz
y
s
ets:
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m
all
(
S),
Me
d
i
u
m
S
m
a
ll
(
MS)
,
Me
d
iu
m
(
M)
,
Me
d
i
u
m
B
ig
(
MB
)
,
B
ig
(
B
)
as
s
h
o
w
n
i
n
Fig
u
r
e
5
w
it
h
th
e
f
u
zz
y
s
u
b
s
et
{S,
MS,
M,
MB
,
B
}
.
T
h
e
r
u
le
b
ase
is
b
ase
d
o
n
a
s
et
o
f
lin
g
u
i
s
tic
I
F
-
T
HE
N
r
u
les
h
a
v
in
g
t
w
o
an
tec
ed
en
ce
s
an
d
o
n
e
co
n
s
eq
u
en
ce
,
as e
x
p
r
es
s
ed
in
th
e
f
o
llo
w
i
n
g
f
o
r
m
:
R
i,
j,
k
: I
F e
=
A
i
an
d
Δ
e=
B
j
T
HE
N
u
=C
k
w
h
er
e
1
≤
i
≤
5
,
1
≤
j
≤
5
,
1
≤
k
≤
5
.
I
t
g
en
er
ates
2
5
I
F
-
T
HE
N
r
u
les
an
d
t
h
e
s
et
is
r
ep
r
esen
ted
as
a
m
a
tr
ix
,
ca
lled
a
f
u
zz
y
r
u
le
m
atr
ix
,
a
s
s
h
o
w
n
i
n
T
ab
le
2
.
T
ab
le
2
.
Fu
zz
y
R
u
les
e
c
e
NB
NS
ZE
PS
PB
NB
S
S
MS
MS
M
NS
S
MS
MS
M
MB
ZE
MS
MS
M
MB
MB
PS
MS
M
MB
MB
B
PB
M
MB
MB
B
B
T
h
e
d
ec
is
io
n
-
m
a
k
i
n
g
o
u
tp
u
t
ca
lcu
lated
b
y
th
e
ce
n
ter
o
f
g
r
av
it
y
(
C
OG)
m
et
h
o
d
o
f
d
ef
u
zz
i
f
icatio
n
.
I
n
t
h
is
m
et
h
o
d
th
e
w
ei
g
h
ted
av
er
a
g
e
o
f
t
h
e
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
o
r
th
e
ce
n
ter
o
f
g
r
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it
y
o
f
t
h
e
a
r
ea
b
o
u
n
d
ed
b
y
th
e
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
cu
r
v
e
i
s
co
m
p
u
ted
as t
h
e
m
o
s
t t
y
p
ical
cr
is
p
v
alu
e
o
f
th
e
u
n
io
n
o
f
all
o
u
tp
u
t
f
u
zz
y
s
et
s
:
dy
y
dy
y
y
y
A
A
c
)
(
)
(
H
er
e
y
i
s
t
h
e
o
u
tp
u
t
v
ar
iab
le
an
d
A
th
e
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
.
T
h
e
f
u
zz
y
to
o
lb
o
x
o
f
M
A
T
L
A
B
h
as
b
ee
n
u
s
ed
to
d
esi
g
n
th
e
f
u
zz
y
i
n
f
er
en
ce
.
T
h
e
p
r
o
p
o
s
ed
f
u
zz
y
lo
g
i
c
tu
n
er
u
s
es
Ma
m
d
an
i’
s
f
u
zz
y
in
f
er
en
ce
m
et
h
o
d
.
T
h
is
co
n
tr
o
ller
h
as
th
e
ad
v
a
n
tag
e
o
f
d
r
iv
in
g
th
e
lo
ad
at
it
s
r
eso
n
a
n
ce
f
r
eq
u
e
n
c
y
,
an
y
c
h
an
g
e
i
n
r
eso
n
an
ce
f
r
eq
u
en
c
y
w
ill
a
f
f
ec
t
o
u
tp
u
t
p
o
w
er
.
T
h
e
s
y
s
te
m
p
er
f
o
r
m
a
n
ce
is
in
d
icate
d
b
y
th
e
p
er
f
o
r
m
an
ce
i
n
d
ices
as
d
ef
in
ed
[
10
]:
a.
I
n
teg
r
al
Sq
u
ar
ed
E
r
r
o
r
(
I
SE)
0
2
)
(
dt
t
e
b.
I
n
teg
r
al
A
b
s
o
l
u
te
E
r
r
o
r
(
I
A
E
)
0
|
)
(
|
dt
t
e
c.
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n
teg
r
al
T
i
m
e
-
w
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g
h
ted
Sq
u
ar
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r
r
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r
(
I
T
SE)
0
2
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(
dt
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te
d.
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T
i
m
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ted
A
b
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r
r
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r
(
I
T
A
E
)
0
|
)
(
|
dt
t
e
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PEDS
I
SS
N:
2088
-
8
694
A
F
u
z
z
y
P
I
D
C
o
n
tr
o
ller
fo
r
I
n
d
u
ctio
n
Hea
tin
g
S
ystems
w
ith
LL
C
V
o
lta
g
e
S
o
u
r
ce
....
(
A
r
iji
t
C
h
a
kra
b
a
r
ti)
1173
4.
SI
M
UL
AT
I
O
N
R
E
S
UL
T
S
AND
DIS
CUSS
I
O
N
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
clo
s
e
d
lo
o
p
in
d
u
ctio
n
h
ea
ti
n
g
s
y
s
t
e
m
w
i
th
Fu
zz
y
P
I
D
co
n
tr
o
lle
r
h
as
b
ee
n
s
tu
d
ied
an
d
co
m
p
ar
ed
w
it
h
t
h
at
o
f
t
h
e
co
n
v
e
n
tio
n
al
P
I
D
co
n
tr
o
ller
.
Si
m
u
latio
n
h
a
s
b
ee
n
d
o
n
e
us
i
n
g
t
h
e
d
esig
n
s
p
ec
i
f
icatio
n
m
en
tio
n
e
d
in
T
ab
le
1
.
T
h
e
co
n
tr
o
ller
s
h
av
e
b
ee
n
d
esig
n
ed
u
s
i
n
g
M
AT
L
A
B
/
SIM
U
L
I
N
K
b
lo
ck
s
an
d
th
e
s
ets
o
f
g
ain
s
(
K
P
,
K
I
,
K
D
)
ar
e
d
eter
m
in
ed
th
r
o
u
g
h
s
i
m
u
lat
io
n
.
T
ab
le
3
p
r
o
v
id
es
th
e
co
n
tr
o
ller
g
ain
s
f
o
r
co
n
v
en
tio
n
al
P
I
D
an
d
Fu
zz
y
P
I
D
co
n
tr
o
ller
s
.
T
ab
le
3
.
C
o
n
tr
o
ller
g
ain
s
C
o
n
t
r
o
l
l
e
r
K
P
K
I
K
D
P
I
D
0
.
5
9
×
1
0
-
4
7
.
0
0
×
1
0
-
1
0
.
2
0
×
1
0
-
6
F
u
z
z
y
P
I
D
1
.
2
9
×
1
0
-
5
1
.
9
8
×
1
0
-
2
1
.
0
5
×
1
0
-
8
Fig
u
r
e
6
d
is
p
la
y
s
th
e
s
tep
r
e
s
p
o
n
s
e
f
o
r
th
e
g
i
v
en
i
n
d
u
c
ti
o
n
h
ea
ti
n
g
s
y
s
te
m
w
i
th
P
I
D
co
n
tr
o
ller
,
w
h
er
e
as
Fig
u
r
e
7
d
is
p
la
y
s
t
h
e
s
tep
r
esp
o
n
s
e
w
it
h
F
u
zz
y
P
I
D
co
n
tr
o
ller
i
m
p
le
m
e
n
tatio
n
.
Fig
u
r
e
6
.
Step
r
esp
o
n
s
e
o
f
th
e
in
d
u
ctio
n
h
ea
t
in
g
s
y
s
te
m
w
i
th
co
n
v
e
n
tio
n
al
P
I
D
co
n
tr
o
ller
im
p
le
m
e
n
tat
io
n
Fig
u
r
e
7
.
Step
r
esp
o
n
s
e
o
f
th
e
in
d
u
ctio
n
h
ea
t
in
g
s
y
s
te
m
w
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th
Fu
zz
y
P
I
D
co
n
tr
o
ller
im
p
le
m
e
n
tatio
n
T
h
e
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.
RE
F
E
R
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NC
E
S
[1
]
O.
L
u
c
ia,
e
t
a
l.
,
“
In
d
u
c
ti
o
n
He
a
ti
n
g
T
e
c
h
n
o
lo
g
y
a
n
d
it
s
A
p
p
li
c
a
ti
o
n
s: P
a
st
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v
e
lo
p
m
e
n
ts,
Cu
rre
n
t
Tec
h
n
o
l
o
g
y
,
a
n
d
F
u
tu
re
C
h
a
ll
e
n
g
e
s,
”
IEE
E
T
r
a
n
s
a
c
ti
o
n
s
o
n
I
n
d
u
stria
l
El
e
c
tro
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v
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l
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p
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0
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3
.
[2
]
A
.
Ch
a
k
r
a
b
o
rty
,
e
t
a
l.
,
“
Be
h
a
v
io
u
r
o
f
a
Hig
h
F
re
q
u
e
n
c
y
P
a
ra
ll
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l
Qu
a
si
Re
so
n
a
n
t
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v
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it
ted
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n
d
u
c
t
io
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He
a
ter
w
it
h
Di
ff
e
re
n
t
S
w
it
c
h
in
g
F
re
q
u
e
n
c
ies
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
mp
u
ter
En
g
i
n
e
e
rin
g
(
IJ
ECE
)
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v
o
l
/i
ss
u
e
:
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(
2
)
,
p
p
.
4
4
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5
7
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0
1
6
.
[3
]
A
.
Ch
a
k
ra
b
o
rty
,
e
t
a
l.
,
“
Ha
r
m
o
n
ics
Re
d
u
c
ti
o
n
in
a
Cu
rre
n
t
S
o
u
rc
e
F
e
d
Qu
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si
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so
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a
n
t
In
v
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rter
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a
se
d
In
d
u
c
ti
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He
a
ter,
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ter
n
a
ti
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n
a
l
J
o
u
r
n
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l
o
f
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we
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lec
tro
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d
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m
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)
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p
.
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3
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,
2
0
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6
.
[4
]
D.
L
e
n
in
e
,
e
t
a
l.
,
“
P
e
rf
o
rm
a
n
c
e
Ev
a
lu
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ti
o
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f
F
u
z
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y
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r
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st
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v
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rter
w
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h
Ac
ti
v
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ter
n
a
t
io
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a
l
J
o
u
rn
a
l
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f
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o
we
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tro
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n
d
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ive
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m (
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)
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/
issu
e
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,
p
p
.
4
4
5
-
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5
3
,
2
0
1
2
.
[5
]
V
.
A
rik
a
tl
a
a
n
d
A
.
Qa
h
o
u
q
,
“
Ad
a
p
ti
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e
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ig
it
a
l
p
ro
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ti
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a
l
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in
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ra
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d
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ti
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n
tro
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o
r
p
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r
c
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n
v
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rters
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tro
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I
ET
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p
p
.
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4
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0
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2
.
[6
]
M
.
P
o
p
e
sc
u
a
n
d
A
.
Bit
o
lea
n
u
,
“
P
o
w
e
r
Co
n
tro
l
S
y
ste
m
De
sig
n
in
In
d
u
c
t
io
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a
ti
n
g
w
it
h
Re
s
o
n
a
n
t
V
o
lt
a
g
e
In
v
e
rter,
”
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o
u
rn
a
l
o
f
Au
to
ma
t
io
n
a
n
d
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n
tro
l
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g
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r
in
g
,
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l
/i
ss
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e
:
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)
,
p
p
.
1
9
5
-
1
9
8
,
2
0
1
4
.
[7
]
O.
Ib
ra
h
im
,
e
t
a
l.
,
“
P
ID
Co
n
tro
l
ler
Re
sp
o
n
se
to
S
e
t
-
P
o
i
n
t
Ch
a
n
g
e
in
DC
-
DC
Co
n
v
e
rter
Co
n
tr
o
l,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
P
o
we
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n
d
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ste
m (
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J
PE
DS
)
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v
ol
/i
ss
u
e
:
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(
2
)
,
p
p
.
2
9
4
-
3
0
2
,
2
0
1
6
.
[8
]
X
.
Ya
n
g
,
e
t
a
l.
,
“
S
im
u
latio
n
a
n
d
I
m
p
le
m
e
n
tatio
n
o
f
A
d
a
p
ti
v
e
F
u
z
z
y
P
ID,”
J
o
u
rn
a
l
o
f
Ne
two
rk
s
,
v
o
l
/i
ss
u
e
:
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(
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)
,
p
p
.
2
5
7
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5
8
1
,
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0
1
4
.
[9
]
J.
M
.
E
.
Hu
e
rta,
e
t
a
l.
,
“
De
sig
n
o
f
th
e
L
-
L
C
re
so
n
a
n
t
in
v
e
rter
f
o
r
in
d
u
c
ti
o
n
h
e
a
ti
n
g
b
a
se
d
o
n
i
ts
e
q
u
iv
a
len
t
S
RI
,
”
IEE
E
T
ra
n
s.
o
n
I
n
d
u
stria
l
El
e
c
tro
n
ics
,
v
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l
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ss
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:
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p
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7
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8
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,
2
0
0
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.
[1
0
]
P
.
K.
M
o
h
a
n
ty
a
,
e
t
a
l.
,
“
T
u
n
in
g
a
n
d
A
ss
e
ss
m
e
n
t
o
f
P
r
o
p
o
rti
o
n
a
l
–
In
teg
ra
l
–
De
riv
a
ti
v
e
Co
n
tro
ll
e
r
f
o
r
a
n
A
u
to
m
a
ti
c
V
o
l
tag
e
Re
g
u
lato
r
S
y
ste
m
E
m
p
l
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g
L
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c
a
l
Un
i
m
o
d
a
l
S
a
m
p
li
n
g
A
lg
o
rit
h
m
,
”
El
e
c
tric
Po
we
r
C
o
mp
o
n
e
n
ts
a
n
d
S
y
ste
ms
,
v
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l
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ss
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e
:
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)
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p
p
.
9
5
9
-
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6
9
,
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0
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4
.
B
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RAP
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S
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F
AUTH
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RS
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iji
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Ch
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M
.
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h
.
d
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re
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in
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h
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s
&
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tro
n
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f
ro
m
th
e
In
stit
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te
o
f
Ra
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s
a
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d
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,
Un
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rsity
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lcu
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s.
Evaluation Warning : The document was created with Spire.PDF for Python.