Intern
ati
o
n
a
l
Jo
u
r
n
a
l
of
P
o
we
r El
ec
tr
on
i
c
s
an
d D
r
i
v
e
S
y
stem
(I
JPE
D
S)
V
o
l.
11
, N
o
. 2, Jun
e
20
20
, pp
. 73
5
~
74
2
I
SSN
:
208
8-8
6
9
4
, D
O
I:
10.
115
91
/i
jp
e
d
s.v
1
1
.i2
.
p
p73
5-7
42
7
35
Jo
urn
a
l
h
o
me
pa
ge
: h
t
t
p
:/
/ijpe
d
s.
i
a
e
s
c
o
re.
c
o
m
Relative stability enhancem
ent for brushed D
C
moto
r
using a PLL interfaced
with LabVIEW
Mo
stafa M
a
h
m
ou
d
,
Ah
me
d
E
l
-Bi
o
me
y
,
E
l
-S
ay
ed
S
o
l
i
m
an
Ah
me
d
De
p
a
rt
me
nt
o
f
Ele
ct
rica
l En
gi
ne
erin
g,
Al-Az
h
a
r
Uni
v
e
r
si
ty
,
E
gyp
t
A
r
ticle In
fo
A
B
S
T
RAC
T
A
r
tic
le
h
i
st
o
r
y:
Rec
e
i
v
ed
Ju
l
14
,
20
19
Re
vise
d N
o
v
8
,
20
19
Acc
e
pt
e
d
Fe
b 12
, 20
20
T
h
i
s
wo
rk
p
r
e
s
ent
s
a fa
st re
sp
onse
a
nd sta
b
le
c
o
m
p
ut
e
r
ba
se
d a
b
r
u
s
h
e
d DC
motor
s
p
eed
con
t
ro
ller.
Th
e
con
t
r
o
ller
con
f
igu
r
ed
o
f
g
a
te
d
r
iv
e
circ
uits
for
H-
Brid
ge
ac
comp
an
ied
with d
a
ta
a
c
quisition
uni
t
DA
Q-6
2
1
1
. The
s
e g
a
t
e
dr
ive
circu
i
ts in
c
l
u
d
e, ph
ase comp
arato
r
,
cu
rren
t
b
o
o
s
ter
an
d
wa
v
e
fo
rm
s
clean
in
g
circu
i
ts.
An
o
p
ti
cal
en
cod
e
r
is
us
ed
fo
r
motor
sp
e
e
d
to
frequ
en
cy
conv
ersion
.
Th
e CD40
46
P
L
L
ch
ip
co
mpar
es p
h
as
es of
th
e en
co
der
ou
tp
u
t
freq
u
e
ncy
(motor
sp
eed)
with
a
ref
e
ren
c
e
f
r
eq
uen
c
y
(d
e
s
ired sp
e
e
d).
Th
e
o
b
t
ain
e
d
ph
ase
d
i
ffer
e
n
c
e
(error
)
is
us
ed
to
a
l
loc
a
t
e
the
s
u
i
t
ab
le P
W
M
du
ty
cy
cles
. An
H-Bridg
e
BJT
s
w
itch
es
driv
en
by
P
W
M
i
s
int
e
rfa
ced
with t
h
e motor.
T
h
e
system h
a
rdware
is
provided
with a
simp
le
and
a
ccu
rate
d
a
ta
acquisit
ion
uni
t
DA
Q-
62
11
to
b
e
in
t
e
r
f
a
ced w
i
th
th
e L
a
bVI
E
W so
f
t
w
a
r
e
P
a
ck
age
.
T
h
is
al
lows
monit
o
ri
ng and
st
or
ing
the d
i
ffer
e
n
t
m
easure
d
dat
a
of t
h
i
s
p
l
a
t
form.
Th
e sys
t
em
relat
i
v
e
s
t
ab
ility
is
d
e
ter
m
in
ed
and
e
x
amin
ed bas
e
d
on
the Bo
d
e
plot anal
ysis and design.
T
h
en the re
lative st
abilit
y
cr
iteri
on (Ph
a
se
Margin)
is
measu
r
ed
the
c
l
os
ed-loo
p s
t
ab
ility
o
f
th
e sy
ste
m
. Th
is s
y
s
t
em
c
o
nsiders
th
e
fast feedback r
e
sponse wi
th
ind
i
cat
i
on of
i
t
s stabi
lity st
at
e as wel
l
as the
stable
w
i
d
e
dy
na
mic r
a
ng
e
.
It co
m
p
ens
a
tes
th
e c
h
anges
in sy
stem para
meters
du
e to
th
e en
v
i
ro
nmen
tal
effe
cts
an
d
oth
e
r d
i
sturb
a
nces.
Ke
yw
ords:
DA
Q-
621
1
DC
m
o
to
r
H-B
r
i
d
ge
LabVIE
W
P
h
ase ma
rg
i
n
PLL
PW
M
R
e
la
ti
v
e
sta
b
ili
ty
Th
is
is a
n
o
p
en
acces
s a
r
ticle
un
d
e
r the
C
C
B
Y
-SA
licens
e
.
Corres
p
o
n
din
g
A
u
t
h
or:
Mo
st
a
f
a M
a
hmou
d,
Depa
rt
me
nt o
f
Ele
c
t
r
i
c
a
l
Engi
ne
eri
n
g
,
F
a
c
u
lty
of
En
gi
n
e
e
r
ing
,
A
l
-Az
h
ar
U
n
i
v
e
r
si
ty
, Egyp
t.
Emai
l:
most
ph
emto@
g
mai
l
.
c
o
m
1.
IN
TR
O
DUCTION
The
DC
mot
o
r
s
have
bee
n
p
o
p
u
la
r i
n
t
h
e
i
n
d
u
st
ry
c
ont
ro
l
area
fo
r
a l
o
ng t
i
m
e
,
beca
u
s
e
t
h
ey
have
man
y
go
o
d
ch
a
r
ac
te
ri
sti
c
s, for e
x
a
m
pl
e:
hi
gh
st
art
t
o
rq
ue
, fast
re
sp
o
n
se
pe
rfo
r
ma
nce,
ea
sie
r
t
o
be
l
i
nea
r
cont
rol
[1
].
Th
e
di
ffe
r
e
n
t
c
ont
ro
l
a
p
p
r
oac
h
depe
nds
on th
e
di
ffe
r
e
n
t
pe
rfo
r
ma
nc
e of
m
o
to
rs. The
DC
mot
o
r
c
o
n
t
r
o
l is th
en ri
p
e
r
th
an
o
t
h
e
r
k
i
nd
s of
mo
t
o
r
s
n
o
matt
er
in
th
e th
eo
r
e
t
i
c
st
ud
y
o
r
in
th
e
r
e
sea
r
ch
a
n
d
deve
l
o
p
m
ent
o
f
t
h
e a
p
pl
i
cat
i
on
t
e
c
h
nol
og
y.
Ho
we
ver, t
h
e
t
e
c
hni
que
of i
n
st
rume
nt
desi
gn al
so
mo
ves
fo
rw
a
r
d
t
h
e
t
i
m
es of
"
v
i
r
t
u
al
i
n
st
rum
e
nt
”,
not
o
n
l
y
t
h
e desi
g
n
in
g t
i
m
e is sh
ort
e
n
e
d, b
u
t
a
l
so t
h
e
de
si
g
n
i
ng sp
ac
e is
more el
ast
i
c
e
x
te
nsi
o
n [2
].
U
s
ua
ll
y c
o
nt
ro
l syste
m
d
o
es
n
o
t
re
ma
i
n
c
onst
a
nt
t
h
ro
ug
ho
ut
i
t
s
l
i
fe c
y
cl
e,
so
t
h
e
r
e
a
r
e
al
wa
ys
cha
nge
s
in s
y
s
t
em pa
ra
me
t
e
rs bec
a
u
se
o
f
e
nvi
ro
nme
n
ta
l
e
ffe
ct
s a
n
d
ot
her pe
rtu
r
bat
i
ons a
nd
di
st
urb
a
nc
es.
Th
e
s
e
c
h
ang
e
s a
n
d
aff
e
ct
ion
s
a
r
e c
a
l
l
ed
p
a
ra
me
te
r v
a
r
i
a
tio
n
s
(
g
ain
a
n
d
st
a
b
ili
ty
, t
e
mp
era
t
u
r
e, supp
l
y
vo
lt
ag
e
varia
t
i
o
ns an
d
/
or ext
e
rna
l
d
i
sturba
nce
s
) w
h
e
r
e
c
a
n
be
studi
e
d
usi
n
g
mat
h
e
m
a
t
i
c
a
l
a
nd ph
ysi
c
al
t
e
rm
e
x
pr
ess
i
o
n
s
to
illu
s
t
r
a
te
e
n
tire
con
t
ro
l syst
em c
h
ang
e
.
The
mor
e
k
eep
ing
p
r
o
s
p
e
r
iti
es co
n
t
ro
l
sy
ste
m
w
ith
e
n
tir
e
ch
a
n
g
e
s
th
e
l
e
s
s
er sens
itiv
i
t
y
of co
n
t
r
o
l sy
ste
m
[1
,
3
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
Int
J
P
o
w
Ele
c
& D
r
i
S
y
st, V
o
l
.
1
1
,
N
o
.
2, Ju
ne
20
2
0
:
7
3
5
–
742
73
6
Thi
s
p
a
pe
r de
s
i
gns
a
c
ont
rol
ci
rcui
t
t
o
s
upe
rvi
s
e a
n
d
co
nt
rol t
h
e
spee
d
resp
onse
o
f
the
DC
mot
o
r
wi
th
t
h
e
vi
rt
ua
l
inst
rume
nt
g
r
ap
hi
c
mo
ni
to
r s
o
ft
wa
re
La
b
V
IE
W [4
]. T
o
co
nt
rol
t
h
e
s
p
ee
d
an
d
dis
p
l
a
y t
h
e
c
h
an
g
e
s of
r
o
t
a
tio
n
a
l sp
e
e
d
of t
h
e
mo
tor
w
i
th
a
sse
ssme
n
t
r
e
lat
i
v
e
sta
b
ilit
y
[1
7
]
by
in
stan
ta
n
e
o
u
s
mon
i
t
o
ri
n
g
pha
se
di
ffere
n
ce
a
ngle
(
Φ
)
a
s
t
h
e p
h
ase shi
f
t
bet
w
ee
n
de
s
i
re
d
an
d act
ua
l
signa
ls o
n
P
L
L out
pu
t
,
t
h
e
bet
t
e
r
re
sp
o
n
se
of
t
h
e syst
em ca
n b
e
a
c
hi
eve
d
by
usin
g the
N
I
USB
-
6
2
1
1
da
ta
ac
q
u
isi
t
i
on (DA
Q
)
[1, 5] t
h
a
t
wi
ll
r
e
a
d
t
h
e
d
a
ta
of t
h
e con
t
ro
l c
i
r
c
u
it for
tr
a
n
smitt
i
n
g
th
e
sig
n
a
l
u
s
i
n
g
in
r
eal
tim
e to
P
C
.
Th
is
d
o
e
s no
t
re
q
u
i
re
t
r
ans
f
e
r
func
ti
ons
, j
u
st
e
xpe
r
i
ment
al
f
r
eq
ue
nc
y
re
sp
o
n
se
d
a
ta
of t
h
e
(sta
b
l
e
)
o
p
e
n
-l
oo
p
s
y
st
em a
r
e
nec
e
ssary
to
ju
dg
e
t
h
e
c
l
o
s
e
d
-l
oo
p
st
a
b
i
lity
[
6
, 7].
B
e
c
a
u
se
th
e
D
A
Q
c
a
r
d
h
a
s t
h
e
ca
p
a
b
ilit
y
of
t
h
e
d
a
t
a
sto
r
ag
e,
ca
lc
ula
t
i
ng,
an
a
l
ysi
s
,
Anal
og
t
o
D
i
gi
t
a
l
C
o
n
v
ert
e
r
(A
DC) a
n
d
D
A
C
c
o
nve
rsio
n
[1
9]
2.
SY
ST
E
M
DE
SC
RIPT
ION
The
syst
em c
o
n
f
igu
r
e
d
of
a
pe
r
m
an
en
t magn
e
t
D
C
mo
tor
,
D
C
p
o
w
e
r
supp
ly
,
p
h
o
t
o e
l
e
c
t
r
ic
e
n
c
o
d
e
r
B83
6
0
9
,
m
o
t
o
r cont
rol
b
o
a
r
d
,
DA
Q c
a
rd
NI
US
B-
6
211 a
c
c
o
m
p
ani
e
d wi
t
h
t
h
e NI
-La
b
V
I
EW
packa
g
e [13
]
a
s
sh
own
in
Fig
u
re
1
.
It
is de
scri
bed a
nd
ex
pl
ai
n
e
d
bri
e
fl
y a
s
fol
l
ows:
Fi
gu
re
1. Bl
oc
k
di
ag
ram
of
t
h
e syst
e
m
2.1. Har
d
ware
i
m
pl
em
entati
on
Thi
s
c
i
rc
ui
t
c
ons
i
s
t
s
o
f
p
h
as
e
loc
k
e
d
lo
op
(P
LL - CD
404
6
)
,
pas
s
i
ve
l
o
w p
a
s
s
fi
l
t
e
r
(L
PF
)
[8
],
c
u
r
r
e
n
t
a
m
p
l
i
f
i
e
r,
(regu
l
a
to
r
LM
780
5)
an
d
(S
ch
mit
t
t
r
i
g
g
e
r
7
4
H
C
14
) a
s
sh
own
i
n
F
i
g
u
r
e
2
.
Fi
gu
re
2. V
o
l
t
a
g
e c
ont
rol
ci
rc
uit
o
f
pe
rma
n
e
n
t
ma
gne
t
b
r
us
hed
DC
mot
o
r
The
syst
em o
p
e
ra
ti
on i
n
cl
u
d
e
s
bo
t
h
ha
rdw
a
re
a
nd so
ftwa
re
mo
dul
es.
Usi
n
g
t
h
e
La
bV
IE
W p
r
o
g
r
am,
th
e
sy
st
em
a
llo
w
s
th
e
u
s
e
r
to
mo
n
i
tor
t
h
e
ac
tu
a
l
mo
t
o
r sp
e
e
d
in
a
d
d
i
tio
n
to
ta
k
e
d
i
r
e
ct
a
c
tion wh
e
n
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
o
w
Elec &
Dri Sy
st
I
SSN
: 2
0
8
8
-8
69
4
Re
la
t
i
v
e
stab
il
ity
e
n
han
c
e
m
e
nt
fo
r b
r
ush
e
d
D
C
m
o
to
r
u
s
i
n
g a
PL
L
i
n
te
rfa
c
e
d
…
(Mo
s
t
a
f
a
.
M
ah
mo
ud)
7
37
t
h
e
de
si
re
d
spe
e
d i
s
out
of
t
h
e
co
nt
r
o
l
ra
nge
.
T
h
i
s
i
s
acc
ompl
i
s
he
d
wi
th
sa
mpl
i
n
g
r
a
t
e
o
f
2.
5
k
H
z
f
o
r
ea
ch
o
f
t
h
e f
our
c
h
an
n
e
ls of
t
h
e de
v
e
l
ope
d s
y
ste
m
[
2
0]
. T
h
e
spe
e
d er
ro
r l
e
a
d
s t
o
t
h
e a
v
e
r
a
g
e
volt
a
ge
adj
u
st
ment
w
h
ich
w
i
ll b
e
ap
p
l
ie
d to
th
e
d
r
iv
er
o
f
t
h
e
mo
tor
af
ter
its f
i
l
t
er
in
g
and
amp
l
i
f
i
c
a
tio
n.
Th
e
D
C
mo
t
o
r
sp
e
e
d
i
s
mea
s
u
r
ed
usi
n
g (
D
A
S
) ki
t
f
o
r the
c
ont
r
o
l
syst
em.
The
s
y
st
e
m
mast
er cl
oc
k i
s
i
n
te
r
n
al
l
y
ge
ne
ra
te
d
i
n
t
h
e P
LL.
T
h
is
P
L
L (CD4
046
) re
c
e
iv
es
bo
th th
e a
c
t
u
al
and
th
e
r
e
fer
e
n
c
e sp
e
e
ds.
T
h
e PL
L av
e
r
a
g
e
vo
lta
g
e
e
r
r
o
r i
s
smoo
t
h
e
d
a
n
d
a
p
p
lie
d
to
mo
tor
dr
iv
e
c
i
r
c
u
its.
Fu
r
t
h
e
rmo
r
e,
th
e
o
p
timi
z
e
d
LP
F o
f
an
a
d
j
u
s
t
a
b
le
cu
t off
f
r
e
que
n
c
y t
h
a
t
is a
c
c
o
rdi
n
g
t
o
t
h
e
sel
ect
e
d
r
e
fe
re
nc
e
f
r
e
q
u
enc
y
ma
kes
t
w
o
in
di
vi
du
al
fu
nct
i
o
ns.
T
h
e
fi
r
s
t
fun
c
ti
on
i
s
r
e
qu
ir
e
d
fo
r no
ise
i
mmun
i
ty
and
t
h
e
se
con
d
is
wo
rk
ing
a
s
a le
a
d
/la
g
co
mp
en
sa
to
r
[2
3]
.
The
LP
F i
s
co
ns
id
e
r
ed
as
e
sse
n
tia
l sta
b
il
ity
issu
e
an
d
us
ed
fo
r
sy
s
t
em fi
n
a
l tu
n
i
ng
[1
1
]
.
For
goo
d
d
r
iv
ing
of t
h
e
mo
t
o
r,
sin
g
l
e (2
N22
2
2
)
c
u
rr
en
t booste
r
h
a
s b
e
en use
d
to re
info
r
ce th
e sig
n
a
l af
t
e
r
no
i
s
e
r
e
je
ct
io
n.
Qu
a
d
ch
opp
er
o
f
f
o
u
r
t
r
ansi
st
or
s
(2
N3
0
5
5
)
i
s
u
s
ed t
o
pr
ovi
de
the
ra
ti
n
g
c
u
r
r
e
nt
w
h
i
c
h is s
u
i
t
a
bl
e t
o
t
h
e
D
C
mot
o
r a
n
d
spe
e
d
redirecti
o
n. On the
ot
her
hand,
the
developed La
bVIE
W
modules
are use
d
for monitori
ng the
s
p
eed
, stability,
an
d ti
me r
e
sp
on
se
[
21]
.
2.
2.
S
o
f
t
w
a
re
Imp
l
eme
n
t
a
t
i
on
Th
e
so
ft
wa
r
e
of
th
i
s
wo
rk
is c
o
nf
igu
r
ed
of
the
fo
llo
w
i
n
g
mod
u
l
e
s
:
2.
2.
1.
L
a
b
V
IE
W
Pr
ogr
ams
The La
bV
IE
W i
s
the
most
d
o
mi
na
nt
pac
k
a
g
e
use
d
f
o
r
c
r
ea
t
i
ng,
te
sti
n
g
an
d mea
s
u
r
e
m
e
n
t
,
o
f
t
h
e
e
qui
d da
ta
ac
q
u
i
s
i
t
i
on s
y
st
em
s.
The
La
b
V
I
E
W syst
ems ar
e
br
oa
dl
y c
l
a
ssi
f
i
e
d
int
o
,
mo
ni
t
o
ri
n
g
, l
o
g
g
in
g
,
an
d
in
te
r
a
c
tiv
e
o
r
sma
r
t sy
ste
m
s [1
2]
. Th
e co
n
t
ro
l sy
ste
m
of t
h
i
s
w
o
rk
mon
i
t
o
rs
th
e
D
C
mo
tor
sp
eed
u
s
i
n
g th
e
LabV
I
E
W pr
og
r
a
m
v
i
rt
u
a
l ins
t
r
u
men
t
s
(
V
I
S
)
a
n
d
re
ad
s
t
h
e
act
ual
mot
o
r fee
dba
c
k
a
n
d
t
h
e
refe
re
nce s
p
eed
s
[
1
0
]
. Th
e re
a
d
i
ng
i
s
pe
rf
or
me
d as RP
M
an
d t
h
e a
n
a
l
o
gue
vol
t
a
ge
o
u
t
p
ut
of t
h
e s
y
st
e
m
i
n
f
our
te
st
poi
nts
(
r
e
f
ere
n
ce si
g
n
a
l
,
fe
ed
ba
c
k
signa
l,
PLL o
u
t
put,
c
u
r
r
e
nt
ampli
f
i
e
r
out
pu
t
)
a
s
sh
ow
n i
n
Fi
gu
re 2
.
The
fr
on
t
pa
nel
a
n
d bl
o
c
k
dia
g
ram
c
o
mpi
l
e
o
f
L
a
b
V
I
E
W o
n
P
C
un
de
r wi
n
d
o
w
s
8.
1
are
sh
o
w
i
ng in
Fi
g
u
r
e 3
a
n
d
Fig
u
re 4
.
F
i
gu
re
3.
Fr
o
n
t
pa
nel
o
f
t
h
e ac
t
u
al
an
d r
e
fe
re
nc
e
s
p
e
e
d
s wi
t
h
t
i
m
e
F
i
gu
r
e
4.
B
l
oc
k di
ag
r
a
m of
a
c
t
ua
l an
d
ref
e
r
e
nce s
p
ee
d
wi
th ti
me
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
Int
J
P
o
w
Ele
c
& D
r
i
S
y
st, V
o
l
.
1
1
,
N
o
.
2, Ju
ne
20
2
0
:
7
3
5
–
742
73
8
2.3. Fl
o
w
ch
art o
f
Th
e Pr
oce
ss
The
S
y
st
e
m
Al
gorit
hm
F
l
ow
c
h
art
of
T
h
e
P
r
o
c
e
s
si
s
sh
o
w
n
in Fi
gu
re
5.
Figu
re 5.
t
h
e syst
em al
go
ri
th
m
3. E
X
PE
RIM
E
NT
AL
RES
U
L
T
S
Th
e p
r
a
c
tic
al
sy
st
em
p
a
ra
me
t
e
rs
are
u
s
ed
fo
r th
e
s
y
ste
m
r
e
la
tiv
e
st
ab
il
ity
e
v
o
l
u
t
ion
[16
,
18
].
T
h
e
syst
em wa
s bu
il
t
and
te
st
ed
usi
ng a
DC
mot
o
r
wit
h
spee
d
of 1
2
0
0
rpm a
n
d
vo
l
t
a
ge
12
Vol
t
and cu
rre
n
t
0.8
Amp
e
re. T
h
e rot
a
ry enco
de
r
has 2
0
p
u
l
s
e
s
pe
r rev
o
l
u
ti
on (pp
r). The ra
ng
e of spee
d
c
ont
rol
i
s
from 40
rpm to
60
0 rpm Th
us, t
h
e syste
m
bl
ock
di
agra
m a
n
d
i
t
s
ga
in (K=
1
.1
) i
s
sh
ow
n
i
n
Fi
g
u
re
6, t
h
us trans
f
er
fu
nc
ti
on of
l
o
op trans
m
i
s
si
on wi
t
h
VI La
b
V
IEW prog
ra
m
c
o
d
e
a
s
in
Fi
gure
7
.
Fi
gu
re
6.
The
c
o
n
d
e
n
se
d mat
h
emat
ic
al
mo
del
of
t
h
e
syst
em
The l
o
o
p
t
r
ans
m
issi
on
sta
t
e
of
the
syst
em a
t
ce
rta
i
n
loa
d
:
G
ሺ
S
ሻ
H
ሺ
S
ሻ
ൌ
ଵ
.
ଵା
.
ଷ
ଵ
ଽୗ
.
ଵ
ହଽୗ
య
ା
.
ହ
ୗ
మ
ାୗ
(1)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
Rel
a
tiv
e
st
ab
ili
ty
e
n
han
ce
m
e
nt f
o
r
b
r
ush
e
d
DC m
o
t
o
r u
s
in
g
a
PLL
in
te
rfa
ced…
(Mo
s
t
a
f
a
.Mah
mo
ud)
7
39
Fi
gu
re
7. Lab
V
IEW
c
o
ntr
o
l s
y
st
em V
I
p
r
o
g
ra
m
c
o
de (Bo
d
e
P
l
ot
)
3.1.
Ex
p
eri
mental
r
e
sul
t
s of
the
PL
L.
Th
e co
r
e
o
f
th
e
sy
st
em
co
n
t
r
o
lle
r
is
th
e
PLL d
e
si
g
n
e
d
to
r
e
ce
iv
e
b
o
t
h
th
e
r
e
f
e
re
n
c
e
(d
e
s
i
r
e
d
)
fre
qu
e
n
cy
and t
h
e fe
edback
frequency t
h
at
correspon
di
ng
to t
h
e a
c
t
u
al
mot
o
r speed [24,
25
]. An enc
oder has
been
couple
d
wi
th t
h
e
mot
o
r shaft
in order t
o
c
o
n
v
e
r
ge
the
sp
e
e
d t
o
frequency. Th
e
P
LL
r
e
ce
iv
e
s
,
b
o
t
h
th
e
motor act
ua
l a
nd t
h
e refe
renc
e freque
nci
e
s [14]. Ac
cordi
ng t
o
t
h
e pha
se e
rror
of t
h
ese
tw
o
fre
quenci
e
s,
t
h
e
PLL
provi
des
a
sui
t
a
b
le
dut
y
c
y
cl
e for
dri
v
i
ng
t
h
e
DC
motor
[15].
T
h
e
va
ri
at
i
o
ns
in
the
P
LL
out
put
due t
o
t
h
e
PLL i
nput phase differenc
e
a
r
e di
spl
a
y
e
d
i
n
Fi
gure 8.
Fi
gu
re
8. Re
fe
renc
e fre
que
nc
y
,
Act
u
al
f
r
eq
ue
ncy
,
P
LL
out
p
u
t
o
n
Lab
V
I
E
W
s
o
ft
wa
re
de
si
gn p
r
o
g
r
a
m
(VI).
The
fol
l
owi
n
g fi
gures are t
h
e e
x
p
e
ri
me
nta
l
c
o
mpa
r
iso
n
ex
p
l
anat
i
on cases at
differe
n
t spee
ds
rel
a
t
e
d
t
o
t
h
e c
ontro
l
c
i
rc
uit
t
o
fol
l
ow up
or mo
ni
tori
ng i
t
usi
n
g
fou
r
me
asuri
n
g po
i
n
t
s
on c
i
rcuit
t
o
be sure
that
t
h
e
dynami
c
be
h
a
vior of the c
ont
rol
ci
rc
u
i
t
o
f
t
h
e
syste
m
i
s
in t
h
e
normal
c
a
se.
There
a
r
e four poi
nts pe
rt
ai
ning
t
o
fo
ur
chan
ne
l
s
on DA
Q (CH1, CH2, CH
3, CH
4)
a
s
de
monst
r
at
ed
i
n
Fi
gure
9
a
n
d
Fi
gure 10
. All
t
h
ese
channe
ls are rec
o
rded sim
u
l
t
a
n
e
ousl
y
on
D
AQ cha
nnel
s
(AI0,
AI1, A
I
2
,
A3). The
ch
annel
CH1 a
s
s
i
gn to
Re
fere
nce si
gn
al
(whi
te
color
)
, C
H
2 to
Feed
bac
k
si
g
n
al
(re
d colo
r), C
H
3
to c
o
m
p
ara
t
or
o
u
t
from
PLL
(g
reen
c
o
lo
r
)
,
CH4
to
P
W
M
in
pu
t
sig
n
al
(
b
lu
e
co
l
o
r
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
Int
J
P
o
w
Ele
c
& D
r
i
S
y
st, V
o
l
.
1
1
,
N
o
.
2, Ju
ne
20
2
0
:
7
3
5
–
742
74
0
Fi
gure
9. C
H
1,
CH2, C
H
3
,
C
H
4 si
mul
t
a
neo
u
sly
at
const
a
nt
speed
1
6
8
rpm
wit
h
fixe
d
l
o
a
d
of
1
5
0 gm for t
h
e DC mot
o
r.
Fi
gure.
10. C
H
1,
CH2
,
CH
3,
C
H
4 si
mul
t
a
n
eously
at
desi
re
d
spe
e
d
9
9
r
p
m
W
i
t
h
f
i
x
e
d
lo
ad
of
15
0g
fo
r
th
e
D
C
mo
to
r
.
3.2. Sy
stem
re
sponse for
di
ff
ere
nt
l
o
a
d
s
The
La
bV
IE
W soft
wa
re
m
o
d
u
l
e
s
are
t
h
e s
p
e
e
d c
o
ntr
o
l, st
abi
l
i
t
y
,
an
d t
i
m
e
res
p
o
n
se
o
n
t
h
e
s
y
st
em
moni
t
o
rs
[2
2]
. S
o
me
of the
P
LL
out
put
-c
o
n
t
r
o
l
l
e
d
pha
se
d
i
ffere
n
ce
an
gl
e
(
Φ
)
th
a
t
ar
e
co
rr
esp
o
n
d
i
ng
t
o
t
h
e
di
ffe
re
nt
l
o
a
d
s
are
l
i
s
t
e
d
i
n
Ta
bl
e
1
.
Ta
b
l
e
1
.
P
LL
ou
t
p
u
t
ph
as
e
ang
l
e vs
d
i
f
f
er
en
t
l
o
ad an
d
sp
e
e
d
s
53.
7 Hz
97.
5 H
z
126H
z
155H
z
202Hz
Wei
ght(gm
)
(
L
oa
d)
Phas
e angl
e (
D
e
g
r
e
e)
Φ
Pha
s
e a
ngle
(D
e
g
re
e
)
Φ
P
h
as
e
an
g
l
e
(D
eg
r
e
e
)
Φ
Ph
as
e a
n
g
l
e
(D
eg
r
e
e
)
Φ
Ph
a
s
e a
n
g
l
e
(
D
egr
ee)
Φ
0
L
o
ckout / unst
a
ble
syst
em
56.
2
ﹾ
72.
72
ﹾ
111.
6
ﹾ
145.
4
ﹾ
100
L
o
ckout / unst
a
ble
s
y
st
em
73.
8
ﹾ
90.
7
ﹾ
122.
8
ﹾ
159.
8
ﹾ
150
48.2
ﹾ
105.
1
ﹾ
127.
1
ﹾ
167.
4
ﹾ
L
o
ckout / unsta
ble
s
y
st
em
280
67.7
ﹾ
122.
8
ﹾ
176.
8
ﹾ
195.
5
ﹾ
L
o
ckout / unsta
ble
syst
em
535
91.8
ﹾ
140
ﹾ
222.
1
ﹾ
Loc
kout / unsta
ble
s
y
ste
m
L
o
ckout / unsta
ble
s
y
st
em
The mo
t
o
r
ope
ra
ti
on mo
des a
c
cordi
n
g
t
o
the
e
x
te
rnal
load
ca
n b
e
arra
n
g
e
d
throu
g
h
fi
v
e
d
i
ffere
n
t
m
o
t
o
r spee
d
[9],
whi
c
h
a
r
e:
16
1 R
P
M/
5
3
.7
Hz
F
o
r
no
l
o
ad
u
p
t
o
t
h
e
10
0g
m, t
h
e m
o
t
o
r i
s
s
t
i
l
l
lockout
an
d
n
o
effe
ct
ive
duty
cycl
e o
f
t
h
e
PLL
that
l
eads
t
h
e mo
t
o
r speed to
be lo
c
k
-in.
F
o
r
a
l
o
a
d
of
1
5
0
g
m
t
h
e
mot
o
r st
arts th
e l
o
ck-i
n
(st
a
bl
e opera
ti
onal
ra
nge)
and k
e
e
p
c
onst
a
nt
spee
d
u
p
to
arou
nd 53
5gm as show
n in Fi
gure
11.
One
c
a
n
se
e
t
h
at
the
duti
e
s (2.5
ms,
3
.
5ms
and
4.7
5
ms)
c
y
cl
es cha
nge a
ccordi
n
g t
o
t
h
e
gi
ven loads
15
0gm, 280
gm
a
nd
5
3
5gm
re
spe
c
t
i
ve
ly.
46
5 R
P
M/
1
5
5
H
z
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
Rel
a
tiv
e
st
ab
ili
ty
e
n
han
ce
m
e
nt f
o
r
b
r
ush
e
d
DC m
o
t
o
r u
s
in
g
a
PLL
in
te
rfa
ced…
(Mo
s
t
a
f
a
.Mah
mo
ud)
7
41
Loc
k
e
d
-i
n
mot
o
r spee
d ra
nge
is l
o
cat
ed start fro
m
t
h
e
no lo
a
d
con
d
it
i
o
n, u
p
to 2
8
0
g
m wi
t
h
consta
n
t
speed.
T
h
e
mo
t
o
r ha
d l
o
c
k
e
d
-out
a
t
l
o
ad
of 53
5gm result
i
n
g i
n
an
unsta
b
l
e ope
rat
i
on
as sho
w
n in
fi
g 1
2
.
Howe
ver, t
h
e
dut
ie
s
2ms, 2.
2ms,
3
m
s,
3.
5
m
s cyc
l
e
are
due t
o
the
giv
e
n n
o
l
o
a
d
,
100gm, 1
5
0
g
m,
28
0gm
respec
ti
vel
y
,
the
l
o
ad 5
3
5
g
m
resul
t
i
ng i
n
un
k
now
n
dut
y
out
goi
n
g
t
h
e
st
abl
e
operat
i
ona
l
z
one.
Fi
gu
re
11.
Dut
y
cyc
l
e
vs m
o
tor
L
o
ad (16
1
rpm)
Fi
gu
re
12.
Dut
y
Cyc
l
e
vs
Mot
o
r l
o
ad
(4
65
rp
m)
4. CO
N
C
LU
S
I
ON
D
i
gi
t
a
l
c
ont
rol
f
o
r t
h
e
DC
mot
o
r ba
sed
o
n
c
o
mp
ut
er
s
y
ste
m
has
be
e
n
de
si
g
n
ed
,
ex
p
e
ri
me
nta
l
l
y
im
p
l
e
m
en
te
d
an
d
el
abo
r
a
t
ed
. Th
e P
LL is u
s
ed
as ph
a
s
e a
n
d
f
r
eq
u
e
n
c
y
comp
ar
ato
r
for me
a
s
ur
ing
t
h
e
sp
e
e
d
dri
f
t
w
.
r.t
t
h
e
de
si
re
d re
fe
re
n
ce spe
e
d
.
Si
mpl
e
a
n
d
ea
s
y
to use
La
bV
IE
W we
re has
be
en use
d
t
o
ac
h
i
e
v
e
t
h
e
sug
g
este
d ap
proa
ch
of t
h
e D
C
mot
o
r spee
d
cont
rol
.
T
h
e s
y
st
em ha
s bee
n
de
vel
o
pe
d t
o
i
n
c
l
ude
t
h
e
gr
aphi
cal
user i
n
t
e
rfa
ce
usin
g La
b
V
IE
W
s
o
ft
ware as
we
l
l
as the
DA
Q-
6
2
1
1
m
odul
e
of
nat
i
o
n
a
l
i
n
st
rume
nt
s. T
h
e
sy
st
em
sh
ow
s
t
h
a
t
t
h
e
w
i
d
e
st sta
b
le
r
a
ng
e
i
s
l
o
ca
te
d
a
t
t
h
e me
as
ure
d
s
p
eed
r
a
n
g
e
of
(2
90
rp
m
to
37
8
rp
m)
fo
r
t
h
e al
l sel
e
ct
ed loa
d
s (10
0g
u
p
to
53
5
g
i
n
5 st
eps). The B
o
de
pl
ot
of
t
h
e s
y
ste
m
l
o
o
p
t
r
a
n
smi
ssi
on s
h
o
w
s
t
h
at
th
e
sy
ste
m
re
la
ti
v
e
sta
b
ili
ty
d
e
p
e
nd
s on
bo
t
h
t
h
e lo
ad
and
t
h
e
p
h
a
se
m
a
r
g
i
n
.
RE
FERE
NC
E
S
[1]
Ro
z
e
n
w
as
ser, E
.
an
d Y
u
s
upo
v,
R
.
, “S
en
sitiv
i
ty
o
f
autom
a
tic
co
ntro
l
sy
stems
,
” CRC
p
r
e
s
s, 19
99
.
[2]
LabVIEW Bas
i
c
s
, I.I
.
,
“Dev
elop
ment
cou
r
se
ma
nu
al,”
Na
tion
a
l
I
n
struments
Co
rp
o
r
at
ion,
Austin
, Texas, 2003.
[3]
S
o
m
e
rv
ille, J.
W.
and
M
acia, N.
F
.,
“A feed
b
ack
co
n
t
ro
l
sy
stem
for eng
i
n
e
ering
techn
o
l
o
g
y
labo
ratory
co
urs
e
s,”
2
001
.
[4]
Raj
Thu
mmar
,
Kalpes
h Chu
d
as
ama
,
Ra
j Ko
sh
iy
a
an
d Di
lp O
d
edara
,
“M
on
itor
ing o
f
E
l
ec
tri
c
i
n
d
u
s
t
rial pro
ces
s
pa
ra
me
te
rs using La
bVIE
W,
”
In
te
rna
t
i
o
n
a
l
J
o
u
r
na
l o
f
Cu
rrent
En
gi
nee
r
i
ng an
d
Te
c
h
nolog
y
,
v
o
l.
6
,
no.6,
p
p
. 212
6-2
1
2
9
,
D
ec
20
16
.
[5]
S
h
e
n
to
n, A.T
.
a
n
d
S
h
afi
e
i, Z., “Rel
a
t
iv
e
st
abili
ty for
con
t
ro
l
s
y
s
t
ems
w
i
th
ad
ju
stab
le
p
a
r
a
m
e
t
e
rs,”
Jour
na
l o
f
Gu
i
d
a
n
c
e
,
Con
t
r
o
l,
an
d
Dy
na
mics
,
v
o
l
.
17
,
n
o
. 2,
p
p
.
30
4-3
1
0
,
1994
.
[6]
Vi
k
h
e
,
P., Pu
njab
i,
N. a
nd Ka
du, C.,
“
R
ea
l
T
i
m
e
DC Mo
to
r Sp
e
e
d
Cont
rol
u
s
in
g PID Con
t
ro
lle
r in La
bVIEW,”
In
tern
atio
na
l Jo
ur
nal o
f
Adva
n
c
ed
Res
e
ar
ch
in
Ele
ct
rica
l, Ele
c
tr
on
ics
an
d Instru
men
t
atio
n
En
gin
eering
,
vol
. 3,
n
o
.
9,
pp.
12
16
2-1
216
7,
20
1
4
.
[7]
Sin
g
h
,
B
.
, Payasi, R.
P., Verma,
K.
S.,
Ku
mar
,
V
.
an
d
Gang
war
,
S
.
,
20
13
,
“D
esign
o
f
Co
ntro
llers
P
D
, P
I
&
P
I
D for
Spe
e
d
Con
t
rol
of DC Mo
to
r Usi
n
g
IGBT Ba
se
d
Ch
op
pe
r”
,
Ger
m
a
n
Jour
na
l of
R
e
n
e
wab
l
e
an
d
Sus
ta
in
ab
le
Ener
gy
Resear
ch (G
JRS
ER)
,
1
(
1), pp
. 29-49
.
[8]
Me
m
o
n,
A.
P.,
Kh
a
n
,
W.
A.
,
Me
m
o
n,
R.
H.
a
n
d
Akh
u
n
d
,
A.A.
,
“
L
a
b
o
r
a
t
ory
st
u
d
ie
s of spe
e
d
c
o
n
t
ro
l o
f
DC shunt
mo
tor an
d
th
e a
n
aly
s
is of par
a
meters
estim
a
tio
n
,
”
I
n
te
rn
at
io
n
a
l
J
o
u
r
na
l o
f
Eme
r
gi
ng
Tre
n
d
s
in
E
l
ec
t
r
i
c
a
l
a
nd
E
l
e
c
tr
on
ics
(
I
JE
T
E
E
)
,
vol. 9, n
o
. 1, pp
. 23
-29
,
2
013
.
[9]
A
ngalaesw
a
ri, S
.
, Ku
mar
,
A., K
u
mar, D. and
Bh
ado
r
iya
,
S
., “S
p
eed
contro
l of
p
e
rman
en
t magn
e
t
(P
M
)
DC mo
to
r
u
s
ing Ardu
in
o an
d LabV
IEW,
”
Comput
at
i
o
na
l
Intelligence a
n
d Comput
ing
R
e
search
(ICCI
C
)
,
20
16
IEE
E
In
tern
atio
na
l Co
nfer
enc
e
o
n
,
I
E
EE
, p
p
.
1-6
,
20
16
.
[10]
Bh
ara
t
iraja
,
C., M
und
a, J.L
., V
a
g
h
as
ia
, I., Val
i
v
e
ti,
R.
a
n
d
M
a
na
s
a
,
P.,
“L
ow
c
o
st
re
al
t
i
m
e
ce
nt
ral
i
ze
d
s
p
e
e
d
co
ntro
l of
DC
m
o
to
r us
in
g lab vi
ew-NI US
B
6
0
0
8
,”
Inte
rn
at
io
nal J
o
urna
l o
f
Po
we
r
E
l
ec
t
r
o
n
i
c
s
a
n
d
Driv
e
Sy
ste
m
s
(IJP
E
DS)
,
vo
l. 3, n
o
.
3
,
p
p
.
65
6-6
6
4
,
20
16.
[11]
Ba
ne
rj
ee
,
D.
,
2006
,
“
P
LL
pe
rfo
rm
a
n
c
e
,
sim
u
la
tion
a
n
d
de
sig
n
” Dog
E
a
r
Pu
bl
i
s
h
i
n
g
.
[12]
De
wa
n
g
a
n
, A.K.
,
Cha
k
ra
b
o
rt
y
,
N.
,
Sh
uk
la,
S.
and
Ya
d
u
,
V.
, “
P
W
M
b
a
se
d
a
u
tom
a
t
i
c
c
l
o
s
e
d
l
oop
sp
e
e
d
c
o
nt
rol
o
f
DC
m
o
to
r
,
”
In
te
r
natio
na
l
Jo
ur
nal o
f
Eng
i
n
e
er
in
g
T
r
end
s
a
n
d
T
ech
no
lo
gy
,
vo
l. 3
,
n
o
.
2
,
pp
.
11
0-1
1
2
,
20
12
.
[13]
Paras
k
evopoulos
,
P.
N
.
,
“Modern c
o
ntrol engi
ne
e
r
ing,
” CRC Press
,
2017.
[14]
Go
wt
ha
m
a
n
,
E
.
a
n
d
Ba
la
j
i
,
C.D.
, “
S
e
l
f-tu
ne
d P
I
D b
a
se
d
sp
ee
d con
t
rol
o
f
PMDC d
r
iv
e,
” Aut
o
m
a
ti
on
, Co
m
p
u
t
i
ng,
Co
m
m
u
n
ic
ation
,
Co
ntro
l
and
Co
mpres
s
ed S
e
ns
in
g (iM
ac4
s)
”,
Inte
rn
at
io
nal Mu
l
t
i
-
Confe
r
en
c
e
o
n
,
IEEE
,
pp
.
6
8
6
-6
92,
2
013
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
Int
J
P
o
w
Ele
c
& D
r
i
S
y
st, V
o
l
.
1
1
,
N
o
.
2, Ju
ne
20
2
0
:
7
3
5
–
742
74
2
[15]
S
a
hp
utro,
S
.
D.
,
F
a
dilah
,
F
.
,
Wicaks
ono
,
N
.
A.
and
Yu
siva
r,
F
.
, “D
esign
and
imp
l
em
ent
a
tion
of ad
apt
i
v
e
P
I
D
co
ntro
ll
er
for
sp
eed
co
nt
rol of
DC motor,
” In
20
1
7
1
5
th
In
tern
at
io
nal
Con
f
er
en
c
e
on
Qua
l
i
t
y
in
Res
e
ar
ch
(QiR):
I
n
tern
at
io
na
l
S
y
mpo
s
i
u
m
on
El
e
c
tr
ica
l
a
n
d
C
o
m
put
er
Eng
i
n
eeri
n
g
,
IEEE,
pp
.
17
9
-
18
3,
20
17
.
[16]
Sarhan, H
., “A
software-based
gai
n
sc
he
d
u
l
i
n
g
of PID
C
ontro
lle
r,
”
In
t
e
rna
t
i
onal
J
o
u
r
na
l o
f
Inst
ru
me
n
t
at
io
n
and
Co
ntr
o
l Sys
t
em
s
,
v
o
l
. 4, no
.
3
,
pp
.
1
-1
0,
20
14.
[17]
A
ngalaesw
a
ri, S
.
, Ku
mar
,
A., K
u
mar, D. and
Bh
ado
r
iya
,
S
., “S
p
eed
contro
l of
p
e
rman
en
t magn
e
t
(P
M
)
DC mo
to
r
u
s
ing Ard
u
ino
a
n
d LabV
IEW,
”
Comp
ut
at
io
na
l In
te
l
l
i
g
e
n
c
e
a
n
d
Compu
t
i
n
g Re
searc
h
(ICCIC),
IEE
E
In
t
e
rn
a
t
i
onal
Co
nfer
enc
e
o
n
,
I
EEE
, p
p
.
1-6
,
20
16
.
[18]
Patt
on,
J
.
L.
,
L
ee,
W.A.
and Pai,
Y.
C.
,
“Relative
s
t
ab
ili
ty
imp
r
ov
es
with
exp
e
ri
en
ce
in
a
,
d
y
n
a
mi
c
sta
n
ding
tas
k
,”
Experimen
t
al Brain Research,
v
o
l
.
13
5
,
no
. 1
,
pp
.
1
1
7
-1
26,
20
00
.
[19]
Ba
rt
h,
E
.
J., Zh
an
g,
J.
a
nd Gol
d
fa
rb
, M., “
C
o
n
trol
de
si
gn fo
r re
l
a
ti
ve sta
b
i
l
i
t
y
i
n
a
PWM-
c
o
n
t
ro
ll
e
d
pne
um
atic
sy
s
t
e
m
,
”
T
r
an
sac
t
io
ns-Ame
ric
a
n
So
cie
t
y o
f
Mech
an
i
c
al En
gin
e
ers J
o
urna
l
o
f
Dyna
mi
c
Sy
st
e
m
s
M
e
asu
r
e
m
e
n
t
a
n
d
Cont
r
o
l
,
vol. 1
2
5
,
n
o
.
3, p
p
.
50
4
-
50
8,
20
03.
[20]
Do
rf,
R.C. a
n
d Bi
sh
op
,
R
.
H.
, “M
od
e
r
n
c
o
nt
ro
l
sy
st
e
m
s,”
Pea
r
son,
20
11.
[21]
G
r
a
n
th
am
,
W.J.
and
Vinc
ent
,
T
.
L.,
“M
od
ern
Co
n
t
ro
l
Sy
st
ems A
n
alysis
and
Desi
gn
: A
n
alys
is
an
d
Des
i
gn
,”
J
o
h
n
Wiley
&
S
o
ns,
I
n
c.,
19
93
.
[22]
Fagiri
,
M.A. and Nerm
a, M.
H., “Effect of
propo
rt
ional i
n
t
e
gr
al
c
ontrolle
r
in
th
e s
t
ab
il
ity
of d
i
re
ct curr
en
t motor
,
”
Int
e
rnati
o
nal Jo
urnal in IT
&
Engi
neeri
n
g
,
vo
l.
3
,
n
o
.
3
,
pp
.
21
0-
2
20,
20
15
.
[23]
D
ubey
,
S
.
and
S
r
ivas
tav
a
, S
.
K.
, “A P
I
D co
nt
r
o
lled r
e
a
l
time
analysis o
f
DC
motor,”
In
te
rna
t
i
o
na
l J
o
urn
a
l of
In
nova
t
i
ve
Res
e
arch
in Co
mpu
t
e
r
an
d Co
mm
unic
a
tio
n
Eng
i
n
eer
in
g
,
v
o
l.
1,
no.
8,
pp
.
1
9
6
5
-1
9
73,
201
3
.
[24]
Tri
nh,
H.
H. a
nd Le
, T.D.
,
“
D
C Mo
de
l
-
ba
se
d IMC
Me
t
h
od
fo
r Bru
s
h
l
e
s
s DC Mot
o
r Sp
e
e
d
Co
nt
ro
l,”
Jo
ur
na
l o
f
Automa
tion
an
d
Co
ntrol Eng
i
n
e
e
r
in
g
,
vol
. 4
,
n
o
.
2
,
p
p
.
10
4-11
0
,
20
16.
[25]
Ther
aj
a, B.L.
an
d
Th
er
aja, A
.
K
.
,
“
Electr
i
ca
l te
chn
o
l
o
g
y
,”
S. c
h
a
nd Ne
w De
l
h
i
,
p
p
.9
26
,
2
0
02.
Evaluation Warning : The document was created with Spire.PDF for Python.