Int
ern
at
i
onal
Journ
al of Ele
ctrical
an
d
Co
mp
ut
er
En
gin
eeri
ng
(IJ
E
C
E)
Vo
l.
11
,
No.
1
,
Febr
uar
y
2021
, pp.
802
~
814
IS
S
N: 20
88
-
8708
,
DOI: 10
.11
591/
ijece
.
v11
i
1
.
pp
802
-
814
802
Journ
al h
om
e
page
:
http:
//
ij
ece.i
aesc
or
e.c
om
P
erform
ance
c
om
pariso
n
b
etween
variants PI
D
c
ontrolle
rs and
u
nity
fee
db
ac
k co
ntrol sys
tem
f
or th
e respo
nse of th
e angula
r
position
of
th
e D
C moto
r
Musta
fa A.
M
ha
w
esh
Al
-
Furat
Al
-
Aw
sat
T
ec
hni
cal
Un
ive
rsit
y
,
Ir
aq
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
Ma
y
11, 202
0
Re
vised
A
ug 7, 20
20
Accepte
d
Aug 17,
2020
Thi
s
pape
r
proposed
a
det
ai
l
ed
stud
y
for
the
resp
onse
of
angul
ar
posit
ion
of
the
ro
tor
of
a
DC
m
otor.
It
is
a
compara
t
ive
ana
l
y
sis
to
th
e
beha
vior
o
f
the
DC
m
otor
when
the
m
otor
is
al
one
an
d
when
it
is
with
cont
rollers.
Furthermore,
a
c
om
par
ison
bet
w
ee
n
the
r
esponse
s
of
cont
ro
ll
ers
t
hems
el
ves.
A
conve
nti
ona
l
PID
cont
roll
er
w
hic
h
was
tune
d
b
y
using
Ziegler
a
nd
Nichol
s
m
et
hod
was
proposed
in
th
is
pa
per
.
Also,
Modif
ic
a
ti
on
PID
controlle
rs
wer
e
proposed
in
thi
s
pape
r
.
The
m
odifi
c
at
ion
PID
co
ntrol
lers
are
PI
-
D
cont
roller
and
I
-
PD
cont
ro
ll
er
.
Math
emati
c
al
c
al
cu
lations
were
done
to
ge
t
the
tra
nsfer
func
ti
ons
for
th
e
DC
m
otor
and
the
controll
ers.
Ti
m
e
dom
ai
n
spec
if
ic
a
ti
ons
and
figure
s
we
re
obtained
f
or
ea
ch
ca
se
b
y
using
Matl
ab
progra
m
.
The
obt
ai
ned
r
esult
s
were
su
m
m
ari
ze
d
in
t
a
ble
s.
Th
is
paper
det
ermined
which
the
cont
r
oll
er
is
the
best
one
dep
endi
ng
on
the
ob
ta
in
ed
figure
s
an
d
the
ti
m
e
dom
ai
n
spec
ifica
t
ions.
Ke
yw
or
d
s
:
DC
m
oto
r
m
odel
ing
I
-
P
D
c
on
tr
oller
PI
D
co
ntr
oller
PI
-
D
c
on
tr
oller
Zie
gler
a
nd
Ni
cho
ls
m
et
ho
d
This
is an
open
acc
ess arti
cl
e
un
der
the
CC
B
Y
-
SA
l
ic
ense
.
Corres
pond
in
g
Aut
h
or
:
Mustafa
A. M
ha
wes
h
,
Al
-
F
ur
a
t
Al
-
A
wsat
Tec
hn
ic
al
Unive
rsity
,
Kufa,
N
a
j
af
, Ir
aq.
Em
a
il
:
m
us
ta
fa
azzam
@atu.edu.iq
1.
INTROD
U
CTION
DC
m
oto
rs
ar
e
com
m
on
ly
us
ed
in
m
any
u
ses
becau
s
e
it
has
si
m
plici
t
y
and
accu
rac
y
in
con
trol
char
act
e
risti
cs.
It
is
use
d
i
n
r
obotic
arm
s,
el
ect
ric
trai
ns
a
nd
car
s,
ste
el
rol
li
ng
m
i
ll
s,
dro
nes,
c
onvey
or
belts,
and
cra
nes
[1
-
7]
.
T
her
e
are
a
lot
of
resea
rc
hes
wer
e
ac
hieved
on
the
s
pe
ed
c
on
t
ro
l
of
DC
m
oto
rs.
M
os
t
of
them
us
ed
the
PID
c
on
t
ro
ll
er
to
set
the
DC
m
oto
r
s
pe
ed
[3,
8,
9]
.
PI
D
co
ntr
oller
is
com
bin
ed
from
pro
portion
al
(
P)
,
I
nteg
ral
(I)
,
and
der
i
vativ
e
(D
)
c
on
t
ro
ll
e
rs.
T
her
e
fore,
it
is
na
m
ed
three
te
r
m
s
con
tr
ollers.
Wh
e
n
PID
c
ontrolle
r
is
us
e
d,
the
res
ponse
will
be
go
od,
r
el
ia
ble,
an
d
r
obus
t
[
8,
10
-
12]
.
The
P
c
on
t
rol
le
r
of
P
ID
is
us
ed
to
dec
rease
the
disturba
nce
e
ffec
ts
on
the
syst
e
m
ou
tp
ut.
T
he
(
I
)
c
on
tr
oller
of
PID
is
use
d
t
o
rem
ov
e
ste
ady
-
sta
te
error.
T
he
D
c
on
t
ro
ll
er o
f
PID
is used to
wea
ke
n
the d
ynam
ic
resp
onse
m
akes
the syst
e
m
m
or
e stable
[
2]. P
I
D
t
ran
s
fe
r
f
un
ct
io
n
is
PI
D
=
(1+
1
+
)
The
a
uthors
of
[
2]
us
e
d
c
onve
ntio
nal
pro
portio
nal
integral
der
i
vative
,
ge
netic
al
gorithm
,
GA,
to
m
od
ify
the
PI
D
el
em
ents,
and
a
sel
f
-
t
un
i
ng
f
uzzy
PID
con
t
ro
ll
er
to
r
egu
la
te
the
spe
ed
of
BL
DC
m
oto
r
.
The
a
uthor
s
of
[
8]
us
e
d
c
on
ven
ti
onal
P
ID
an
d
PI
-
D
co
ntr
ol
to
c
on
tr
ol
a
fly
-
by
-
wir
e
fligh
t
.
Th
e
auth
ors
of
[
13]
us
ed
PID
co
ntro
ll
er
w
it
h
fr
ic
ti
on
co
m
pen
sat
or
to
fix
the
exactl
y
angular
posit
io
n
of
DC
gea
red
m
oto
r.
More
ov
e
r,
the
y
us
ed
the
U
N
O
Ard
uino
m
i
cro
c
ontrolle
r
t
o
co
ntr
ol
the
volt
age
of
the
brus
he
d
Nam
iki
direct
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N: 20
88
-
8708
Perf
orma
nce c
omp
ar
iso
n bet
we
en
v
ar
ia
nts
PID co
ntr
ollers a
nd
…
(
Must
afa
A. M
hawe
s
h
)
803
current
m
oto
r.
The
a
uthors
of
[14]
us
e
d
P
ID
con
t
ro
ll
er
t
o
gove
r
n
the
a
ngul
ar
posit
ion
of
DC
m
oto
r
at
ta
ch
e
d
to
a
hydr
a
ulic
pu
m
p
valve
.
The
auth
or
of
[
15
]
us
e
d
P
ID
and
F
LC
con
t
r
ollers
to
co
ntr
ol
shun
t
D
C
mo
tor.
The
a
uthors
of
[16]
pr
e
sente
d
a
com
par
iso
n
f
or
t
he
ways
of
tu
ning
th
e
PI
D
t
o
re
gula
te
the
sp
ee
d
of
direc
t
current
m
oto
r
.
The
a
uthor
s
of
[17]
use
d
the
PI
D
to
c
ontr
ol
DC
m
oto
r
wh
e
n
the
loa
d
is
va
riable.
T
he
a
ut
hors
of
[18]
us
e
d
a t
un
e
d
P
I
D
to se
t t
he
s
pee
d
of
PMDCM
. T
he a
uthors o
f
[
19]
us
e
d
dif
fe
ren
t
con
t
ro
ll
ers
t
o
gove
r
n
the
DC
m
oto
r.
The
PI
D
is
on
e
of
them
.
The
authors
of
[20
]
us
ed
the
Z
-
N
m
et
ho
d
to
tune
PI
/PI
D
con
t
r
ollers
for
inc
orp
orat
ing
f
racti
onal
-
orde
r
dynam
ic
s
in
an
e
xisti
ng
DC
m
oto
r
c
ontrol
sys
te
m
.
Va
riants
P
I
D
c
on
t
ro
ll
er
s
are
pr
opos
e
d
i
n
this
pa
per
to
co
ntro
l
t
he
a
ngula
r
posit
io
n
of
t
he
ro
t
or
of
a
DC
m
oto
r
.
Zie
gler
a
nd
Ni
cho
ls
seco
nd
m
et
ho
d
(Z
-
N
2
nd
m
e
tho
d
)
is
ap
plied
t
o
ad
just
the
el
e
m
ents
of
P
I
D
c
on
t
ro
ll
er
as
s
how
n
in
Table
1
and
Figure
1.
Table
1.
Z
-
N 2
nd
m
et
ho
d
tu
ning
ru
le
de
pendi
ng on c
riti
cal
gai
n
and crit
ic
al
p
eri
od
[18,
21]
Ty
p
e of
Co
n
troller
P
0
.5
∞
0
PI
0
.45
1
1
.
2
0
PID
0
.6
0
.5
0
.12
5
Figure
1
.
PID
con
t
ro
ll
er
[
21
]
Transfe
r
f
unct
ion o
f
it
=
(1+
1
+
)*
G
[
1
+
[
(
1
+
1
+
)
]
G
PI
-
D
c
o
n
t
r
o
l
l
e
r
i
s
r
e
a
r
r
a
n
g
e
m
e
n
t
t
h
e
c
o
n
n
e
c
t
i
o
n
o
f
P
I
D
e
l
e
m
e
n
t
s
.
T
h
e
D
p
a
r
t
o
f
t
h
e
P
I
D
i
s
c
o
n
n
e
c
t
e
d
with
the
fee
db
ack
path.
It
is
us
e
d
to
preve
nt
the
ef
fecti
ve
ness
of
t
he
set
-
point
kick
ph
eno
m
enon
[8,
21
]
as
sh
ow
n
in
Fi
gur
e 2
.
Figure
2
.
PI
-
D con
t
ro
ll
er
[
21
]
Transfe
r
f
unct
ion o
f
it
=
(1+
1
)*
G
[
1
+
[
(
1
+
1
+
)
]
G
I
-
P
D
co
ntr
oller
is
rearr
a
ng
em
ent
the
co
nn
ect
ion
of
PID
e
le
m
ents,
al
so
.
T
he
P
an
d
D
part
s
of
the
PID
are
co
nnect
ed
with
the
fee
dback
path
.
Th
e
influ
e
nce
of
these
pa
rts
w
il
l
be
on
fee
dback
path
only
[21]
.
As
s
how
n
i
n
Fi
gure
3.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
87
08
In
t J
Elec
&
C
om
p
En
g,
V
ol.
11
, No
.
1
,
Febr
uar
y
2021
:
802
-
814
804
Figure
3
.
I
-
P
D con
t
ro
ll
er
[
21
]
Transfe
r
f
unct
ion o
f
it
=
(
1
)*
G
[
1
+
[
(
1
+
1
+
)
]
G
In
the
sect
i
on
two
of
t
his
pa
pe
r,
m
od
el
in
g
of
DC
m
oto
r
will
be
prese
nted
.
T
he
re
spo
ns
e
of
the
D
C
m
oto
r
with
va
riant
c
on
t
ro
ll
er
s
an
d
u
nity
f
e
edb
ac
k
co
ntr
ol
s
yst
e
m
will
be
discusse
d
in
the
oth
er
se
ct
ion
s
.
Whe
n
it
is
wit
h
unit
y
feed
ba
ck
co
ntr
ol
syst
e
m
,
the
app
r
oa
ch
will
be
studi
ed
in
sect
ion
t
hr
ee
.
Wh
en
it
is
with
conve
ntion
al
P
ID
c
ontrolle
r
,
t
he
ap
proac
h
w
il
l
be
stud
ie
d
in
sect
io
n
f
our.
There
are
t
wo
par
ts
i
n
the
se
ct
ion
five.
Part
one
discusse
s
the
a
ppr
oach
o
f
us
i
ng
it
with
m
odific
at
ion
PID
c
on
t
ro
ll
er,
PI
-
D
con
t
ro
ll
er.
Par
t
tw
o
discusse
s
the
appr
oach
of
usi
ng
it
with
m
od
i
ficat
ion
P
I
D
co
ntr
oller,
I
-
PD
c
ontr
oller
.
The
sect
io
n
six
will
pr
ese
nt the
com
par
ison
.
The
sect
ion
s
e
ve
n
will
p
rese
nt t
he
conclusi
on.
2.
MO
DEL
IN
G
OF
DC M
OTOR
The
F
ig
ur
e
4
il
lustrate
s
the
cir
cuit o
f
direct c
urren
t
m
oto
r
, DC m
oto
r
[1]
.
Figure
4.
DC
m
oto
r
ci
rcu
it
[
1]
The
m
at
he
m
at
i
cal
eq
uati
on
s
of D
C
m
oto
r
ca
n be
wr
it
te
n
[1,
14, 1
8,
22
-
25]
:
V
=
+
+ E
(
1
)
E
∝
Φ
ω
E =
k
Φ
ω =
ω
ω =
E =
(
2
)
T
∝
Φ
=
1
Φ
T =
(3)
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N: 20
88
-
8708
Perf
orma
nce c
omp
ar
iso
n bet
we
en
v
ar
ia
nts
PID co
ntr
ollers a
nd
…
(
Must
afa
A. M
hawe
s
h
)
805
Me
chan
ic
al
to
r
qu
e
equati
on is
T= J
2
2
+ B
(4)
The param
et
ers
of the
D
C
m
oto
r
ca
n be
def
i
ned.
V,
,
, and
Vo
lt
age
(v),
r
esi
sta
nce
(Ω),
current
(
A),
and
in
duct
an
ce
(H)
are
th
e
arm
at
ur
e
el
e
m
ents
resp
e
ct
ively
.
ω and
The
a
ngula
r
s
peed
(
ra
d/sec)
an
d
t
he
a
ng
ular
posit
ion
(r
a
d)
of
t
he
r
otor
s
haf
t
resp
ect
ively
.
E
Ba
ck
el
ect
r
omoti
ve fo
rce
(e.
m
.f
.)
(v)
T
Torq
ue (N
.m
)
Ba
ck
-
em
f
co
nst
ant (v/rad/s
)
Torq
ue
c
onsta
nt (N.m
/A)
Φ
Flux (
wb)
J
Mom
ent o
f
ine
rtia
o
f
roto
r,
M
OI
,
(K
g.
2
)
B
Visco
us
-
Fr
ic
ti
on Coe
ff
ic
ie
nt
(N
.m
.s/rad)
The
La
pla
ce tr
ansfo
rm
s f
or
t
he
(
1
)
,
(
2
)
,
(
3
)
, a
nd
(
4
)
an
d
t
heir bloc
k diagr
a
m
s can
be ob
ta
ined:
V(
s
)
=
(
)
+
(
)
+ E
(
s)
V(
s
)
-
E
(s) =
(
)
+
(
)
E =
(s)
T(s)
=
(
)
T = J
2
(s)
+ B
(s)
T(s) =
S
(s)
(JS
+ B)
The
F
i
gure
5
il
lustrate
s the
di
rect cu
rr
e
nt
m
oto
r bloc
k diag
r
a
m
:
Figure
5
.
D
irec
t C
urren
t m
otor
blo
c
k diagr
a
m
[1
, 14]
G
=
=
3
+
(
+
)
2
+
(
+
)
G
is t
he DC m
otor tra
ns
fe
r funct
ion.
V
a
nd
are
the
in
pu
t a
nd outp
ut
rep
e
ct
ively
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
87
08
In
t J
Elec
&
C
om
p
En
g,
V
ol.
11
, No
.
1
,
Febr
uar
y
2021
:
802
-
814
806
3.
RESPO
NS
E
OF
ANGUL
A
R
P
OSITIO
N OF THE
ROT
OR OF TH
E DC M
OTO
R
WIT
H
UN
I
TY
FEE
DBA
CK
CONTR
OL S
YS
TE
M
To
stu
dy
the
resp
onse
of
the
DC
m
oto
r,
a
unit
y
feed
bac
k
con
t
ro
l
syst
em
is
us
ed
with
the
DC
m
oto
r.
The
in
put
is
a
unit
ste
p
f
un
ct
ion
wh
il
e
th
e
sco
pe
is
us
e
d
to
get
t
he
re
sp
onse
.
By
us
i
ng
Ma
tl
ab
pr
ogram
,
the
ti
m
e
do
m
ai
n
s
pecifica
ti
on
s
of
t
he
tr
ansient
res
ponse
an
d
t
he
r
esp
on
se
fi
gur
e
can
be
obt
ai
ned
.
The
F
ig
ur
e
6
il
lustrate
s
it
s
bl
oc
k diag
ram
.
Figure
6.
The
c
on
t
ro
l sy
ste
m
o
f
the
DC m
oto
r
The
syst
em
tran
sfe
r funct
io
n
i
s
TF =
1
+
=
3
+
(
+
)
2
+
(
+
)
+
The
pa
ram
et
ers
values
of
D
C
m
oto
r
we
re
ob
ta
ine
d
f
rom
the
pap
er
of
[
1].
T
hey
su
m
m
arized
the
pa
ram
et
ers
’
res
ult
s
for
th
r
ee
at
tem
pts
in
a
Table
2.
The
aver
a
ge
value
s
of
t
hese
rea
di
ng
s
a
re
use
d
i
n
this
pap
e
r
as
s
how
n
in
Ta
ble 3.
Table
2.
P
a
ram
et
ers
of
DC
mo
tor
[1]
Para
m
eters
1
st
case
2
nd
case
3
rd
case
B (N.
m
.s
)
0
.04
1
2
0
2
0
.04
3
9
2
6
0
.04
2
8
1
6
7
J (Kg.
2
)
0
.05
7
4
1
9
0
.04
4
0
4
2
0
.03
1
8
8
(V/r
ad
/s)
1
.83
5
1
.80
7
4
1
.86
7
4
(N.
m
/A)
1
.83
5
1
.80
7
4
1
.86
7
4
(H)
0
.10
4
1
9
0
.10
4
4
2
2
7
0
.10
4
3
0
5
(Ω)
3
.04
8
4
3
.04
3
2
5
3
.04
5
6
5
3
Table
3.
T
he
Avera
ge
values
of the
par
am
et
ers
Para
m
eters
Av
erage
B (N.
m
.s
)
0
.04
2
6
4
8
2
3
3
J (Kg.
2
)
0
.04
4
4
4
7
(V
/
r
ad
/s)
1
.83
6
6
(N
.
m
/
A)
1
.83
6
6
(H)
0
.10
4
3
0
5
9
(Ω
)
3
.04
5
7
6
7
6
6
7
TF
=
1
+
=
3
+
(
+
)
2
+
(
+
)
+
TF =
1
.
8366
0
.
004636
3
+
0
.
1398
2
+
3
.
503
+
1
.
8366
The
res
pons
e
was
got
by
us
ing
Ma
tl
ab
w
he
n
a
un
it
ste
p
fu
nctio
n
is
app
l
ie
d
as
sh
own
i
n
Fig
ur
e
7.
Th
e
tim
e
do
m
ai
n
val
ues of t
his case
w
e
re ac
qu
ire
d as
sh
ow
n
in
Ta
ble 4
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N: 20
88
-
8708
Perf
orma
nce c
omp
ar
iso
n bet
we
en
v
ar
ia
nts
PID co
ntr
ollers a
nd
…
(
Must
afa
A. M
hawe
s
h
)
807
Figure
7
.
Resp
on
s
e
of
t
he
a
ngular p
os
it
ion
D
C m
oto
r
with
unit
y feed
bac
k
c
o
nt
ro
l sy
ste
m
Table
4
. Tim
e
do
m
ai
n
sp
eci
ficat
ion
s
value
s
of the
DC
m
oto
r
w
it
h u
nity
fe
edb
ac
k
c
ontr
ol
syst
e
m
Ti
m
e
Do
m
a
in
Sp
e
cif
icatio
n
s
Valu
e
Ris
e ti
m
e
(
seco
n
d
s)
4
.10
3
4
Settlin
g
ti
m
e
(seco
n
d
s)
7
.34
5
1
Ov
ersh
o
o
t (
%)
0
Peak
(
A
m
p
litu
d
e un
it)
0
.99
9
3
Peak
t
i
m
e
(
seco
n
d
s)
1
3
.67
2
6
4.
RESPO
NS
E
OF
A
NGULAR
P
OSITI
ON
OF
TH
E
ROTOR
OF
D
C
M
OTOR
WI
T
H
CONVE
NTI
ONAL PI
D C
ONTROL
LE
R
By
ad
di
ng PID
contr
oller to
the syste
m
, th
e b
loc
k diag
ram
will
b
e
il
lustrat
ed
in
the
Fig
ure 8
.
Figure
8.
PID
con
t
ro
ll
er
with
D
C m
oto
r
Let
= P
ID =
(
1
+
1
+
)
(5)
TF
2
=
1
+
(6)
TF
2
:
Transfe
r
f
unct
ion o
f
t
he DC
m
oto
r
with
c
on
ven
ti
onal
P
I
D
con
t
ro
ll
er
TF
2
=
(1 +
1
+
)*
3
+
(
+
)
2
+
(
+
)
[
1
+
[
(
1
+
1
+
)
]
3
+
(
+
)
2
+
(
+
)
]
(7)
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
87
08
In
t J
Elec
&
C
om
p
En
g,
V
ol.
11
, No
.
1
,
Febr
uar
y
2021
:
802
-
814
808
TF
2
=
(1 +
1
+
) *
[
3
+
(
+
)
2
+
(
+
)
]
+
(
1
+
1
+
)
(8)
Using
t
he
Z
-
N
seco
nd m
et
ho
d i
n
th
e
pa
pe
r
is
to adj
us
t t
he
ele
m
ents o
f
P
ID
con
t
ro
ll
er.
Pu
t
= ∞ a
nd
= 0
a
nd s
u
bs
ti
tute
these
values
i
n
the
(8)
.
TF
ZN
=
3
+
(
+
)
2
+
(
+
)
+
(
9
)
TF
ZN
:
Transfe
r
f
unct
ion o
f
t
he DC
Motor wit
h C
onve
ntio
nal P
ID Co
ntro
ll
er
wh
en
Zie
gler Nic
ho
ls
Met
hod
is use
d
By
u
sin
g
R
ou
t
h Hurwitz
C
rite
rio
n
to
f
in
d
t
he
val
ue
3
(
+
)
2
(
+
)
S
(
+
)
-
(
+
)
0
0
0
(
+
)
-
(
+
)
=
0
=
(
+
)
(
+
)
(10)
By
su
bs
ti
tuti
ng
the
values
of
t
he
T
a
ble
3
in
the
(10)
,
= 57.
5247
By
exam
ining
the
c
oeffici
ents
of
t
he
first
c
olu
m
n
,
the
sus
ta
ined
os
ci
ll
at
ion
will
occur
wh
e
n
=
57.
5247.
Th
us
the
criti
cal
g
ai
n
will
be
57.524
7.
W
it
h gain
set
equ
al
=
57.52
47, th
e
ch
a
ract
erist
ic
eq
ua
ti
on of
TF
ZN
will
b
e
3
+
(
+
)
2
+
(
+
)
+
57
.
5247
= 0
The
f
re
qu
e
ncy o
f
t
he
sust
ai
ne
d
osc
il
la
ti
on
can
be
obta
ined
by
substi
tuti
ng
S
=
j
ω
in
the
c
har
act
erist
i
c
equ
at
io
n
.
(
)
3
+
(
+
)
(
)
2
+
(
+
)
+
57
.
5247
= 0
-
(
+
)
2
+
57
.
5247
=
0
2
=
57
.
52
47
(
+
)
= 755.5
937
= 27.
4
881 ra
d/sec
Ther
e
f
or
e,
the
crit
ic
al
p
erio
d (
)
can
be o
btained
.
=
2
= 0
.
2286
se
cond
,
, a
nd
can b
e
obtai
ned f
ro
m
Ziegler
Nich
ols
Seco
nd Met
ho
d
ta
ble,
T
a
b
le
1
.
= 0.6
= 34.
5148
= 0.5
=
0.114
3 sec
= 0.1
25
= 0
.
02
86 sec
The param
et
ers
of P
ID co
ntr
ol
le
r
are a
vaila
bl
e n
ow,
and it i
s goin
g
t
o be t
un
e
d by them
.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N: 20
88
-
8708
Perf
orma
nce c
omp
ar
iso
n bet
we
en
v
ar
ia
nts
PID co
ntr
ollers a
nd
…
(
Must
afa
A. M
hawe
s
h
)
809
Gett
ing
t
he
tra
ns
fe
r
f
unct
io
n
of
t
he
DC
m
oto
r
with
P
ID
c
on
t
ro
ll
er
ca
n
be
done
by
retu
rn
i
ng
bac
k
to
(8)
(
the
TF
2
eq
ua
ti
on
)
a
nd
s
ub
s
ti
tuti
ng
the
P
I
D
par
am
et
ers
a
nd
the
values
of
T
a
ble
3
.
T
he
respo
ns
e
ca
n
be
go
t
by
us
i
ng
Ma
tl
ab
wh
en
a
un
it
ste
p
func
ti
on
is
app
li
ed
as
sh
own
in
Fi
gure
9
.
Tim
e
d
om
ai
n
v
al
ues
of
this
case are a
cq
uir
ed
Ta
ble
5.
TF
2
=
(1+
1
+
) *
[
3
+
(
+
)
2
+
(
+
)
]
+
(
1
+
1
+
)
TF
2
=
2
+
+
4
+
(
+
)
3
+
(
+
+
)
2
+
+
(11)
TF
2
=
0
.
20
7
2
+
7
.
24
5
+
63
.
39
0
.
00
05
299
4
+
0
.
0
15
9
8
3
+
0
.
60
74
2
+
7
.
2
45
+
63
.
39
Figure
9
.
Resp
on
s
e
of
t
he
a
ngular p
os
it
ion
of
the
DC m
oto
r ro
t
or
with
PID
con
t
ro
ll
er
Table
5
. Tim
e
do
m
ai
n
sp
eci
ficat
ion
s
value
s
of the
DC
m
ot
or w
it
h
PID
c
ontr
oller
Ti
m
e
Do
m
a
in
Sp
e
cif
icatio
n
s
Valu
e
Ris
e ti
m
e
(
seco
n
d
s)
0
.05
5
9
Settlin
g
ti
m
e
(seco
n
d
s)
0
.55
7
4
Ov
ersh
o
o
t (
%)
4
8
.73
0
2
Peak
(
A
m
p
litu
d
e un
it)
1
.48
7
3
Peak
ti
m
e
(
seco
n
d
s)
0
.14
9
6
5.
RESPO
NS
E
OF
THE
ANGULA
R
PO
S
ITION
OF
THE
ROTO
R
OF
D
C
MOTO
R
WI
TH
MO
DIFI
CA
T
ION
S
PI
D C
ONTROL
LE
R
5.1.
Usin
g PI
-
D
c
on
t
rolle
r
By
ad
di
ng PI
-
D
c
on
t
ro
ll
er t
o t
he
syst
em
, th
e b
loc
k diag
ram
w
il
l be ill
us
t
ra
te
d
in t
he
Fi
gur
e 10
.
TF
3
=
(1+
1
)*
3
+
(
+
)
2
+
(
+
)
[
1
+
[
(
1
+
1
+
)
]
3
+
(
+
)
2
+
(
+
)
]
(12)
TF
3
=
(1+
1
)
*
[
3
+
(
+
)
2
+
(
+
)
]
+
(
1
+
1
+
)
(13)
TF
3
=
+
4
+
(
+
)
3
+
(
+
+
)
2
+
+
(14)
TF
3
:
Transfe
r
f
unct
ion o
f DC
m
oto
r
wit
h
m
od
ific
at
ion
PI
-
D
c
on
trolle
r
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
87
08
In
t J
Elec
&
C
om
p
En
g,
V
ol.
11
, No
.
1
,
Febr
uar
y
2021
:
802
-
814
810
TF
3
can
be
got
by
us
in
g
th
e
rea
di
ng
s
of
Ta
ble
and
t
he
sam
e
values
of
tu
ni
ng
pa
ram
et
ers,
wh
ic
h
is
us
e
d
in t
he
c
onven
ti
onal
P
I
D con
t
ro
ll
er
.
T
he
r
es
pons
e ca
n b
e got by
us
in
g M
at
la
b
w
he
n
a
unit
step
funct
ion
is
app
li
ed
as s
ho
wn in Fi
gure
11.
Tim
e
do
m
a
i
n v
al
ues
of this
case are
obtai
ned as s
how
n
i
n
Ta
ble
6.
TF
3
=
7
.
245
+
63
.
39
0
.
00
05
299
4
+
0
.
0
15
9
8
3
+
0
.
60
74
2
+
7
.
2
45
+
63
.
39
Figure
10
. PI
-
D
c
on
t
ro
ll
er
wi
th D
C
m
oto
r
Figure
11.
Re
s
pons
e
of the
angu
la
r po
sit
io
n of t
he DC m
oto
r
roto
r wit
h
P
I
-
D
c
on
t
ro
ll
er
Table
6
. Tim
e
do
m
ai
n
sp
eci
ficat
ion
s
va
lue
s
of the
DC M
oto
r
w
it
h PI
-
D
c
on
t
ro
ll
er
Ti
m
e
Do
m
a
in
Sp
e
cif
icatio
n
s
Valu
e
Ris
e ti
m
e
(
seco
n
d
s)
0
.06
0
3
Settlin
g
ti
m
e
(seco
n
d
s)
0
.59
8
7
Ov
ersh
o
o
t (
%)
6
1
.83
6
9
Peak
(
A
m
p
litu
d
e un
it)
1
.61
8
4
Peak
ti
m
e
(
seco
n
d
s)
0
.17
4
5
5.2.
Usin
g I
-
P
D
c
on
t
rolle
r
By
ad
di
ng
I
-
P
D
c
on
t
ro
ll
er t
o t
he
syst
em
, th
e b
loc
k diag
ram
w
il
l be ill
us
t
ra
te
d
in t
he
Fi
gur
e 12.
TF
4
=
(
1
)*
3
+
(
+
)
2
+
(
+
)
[
1
+
[
(
1
+
1
+
)
]
3
+
(
+
)
2
+
(
+
)
]
(15)
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
Elec
&
C
om
p
En
g
IS
S
N: 20
88
-
8708
Perf
orma
nce c
omp
ar
iso
n bet
we
en
v
ar
ia
nts
PID co
ntr
ollers a
nd
…
(
Must
afa
A. M
hawe
s
h
)
811
TF
4
=
(
1
) *
[
3
+
(
+
)
2
+
(
+
)
]
+
(
1
+
1
+
)
(
16
)
TF
4
=
4
+
(
+
)
3
+
(
+
+
)
2
+
+
(
17
)
TF
4
:
Transfe
r
f
unct
ion o
f DC M
ot
or w
it
h
Mo
dific
at
ion
I
-
P
D
C
on
trolle
r
TF
4
can
be
go
t
by
us
in
g
the
read
i
ng
s
of
T
able
3
and
t
he
sam
e
values
of
tun
i
ng
pa
ram
et
ers,
wh
ic
h
is
us
e
d
in t
he
c
onven
ti
onal
P
I
D con
t
ro
ll
er
.
T
he
r
es
pons
e ca
n b
e got by
us
in
g M
at
la
b
w
hen
a
unit
step
funct
ion
is
app
li
ed
as s
ho
wn in Fi
gure
13. Ti
m
e
do
m
a
i
n values
of this
case are
obtai
ned as s
how
n
i
n
Ta
ble
7.
TF
4
=
63
.
39
0
.
00
05
299
4
+
0
.
0
15
9
8
3
+
0
.
60
74
2
+
7
.
2
45
+
63
.
39
Figure
12.
I
-
P
D
c
on
t
ro
ll
er
wi
th D
C
m
ot
or
Figure
13
. Res
pons
e
of the
angu
la
r po
sit
io
n of t
he DC m
oto
r
roto
r wit
h
I
-
PD
c
ontr
oller
Table
7
. Tim
e
do
m
ai
n
sp
eci
ficat
ion
s
value
s
of the
DC
m
oto
r
w
it
h
I
-
P
D
c
on
t
ro
l
le
r
Ti
m
e
Do
m
a
in
Sp
e
cif
icatio
n
s
Valu
e
Ris
e ti
m
e
(
seco
n
d
s)
0
.11
3
3
Settlin
g
ti
m
e
(se
co
n
d
s)
0
.49
4
1
Ov
ersh
o
o
t (
%)
1
3
.70
5
9
Peak
(
A
m
p
litu
d
e un
it)
1
.13
7
1
Peak
ti
m
e
(
seco
n
d
s)
0
.28
0
5
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