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s
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o
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g
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esire
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r
o
ce
s
s
o
r
s
,
an
d
ar
e
o
f
v
ar
y
i
n
g
co
m
p
l
ex
it
y
.
T
h
e
ch
o
ice
o
f
co
n
tr
o
ller
o
f
te
n
d
ep
en
d
s
o
n
t
h
e
co
n
tr
o
l o
b
j
ec
tiv
es a
n
d
co
n
tr
o
ller
co
s
t.
DC
m
o
to
r
co
n
tr
o
ller
s
m
u
s
t b
e
ab
le
to
h
a
n
d
le
u
n
k
n
o
w
n
lo
ad
ch
ar
ac
ter
is
tic
s
a
n
d
p
ar
a
m
eter
v
ar
iatio
n
s
.
P
r
o
p
o
r
tio
n
al
-
in
te
g
r
al
-
d
er
iv
ati
v
e
(
P
I
D)
co
n
tr
o
ller
s
ar
e
m
o
s
t
co
m
m
o
n
l
y
u
s
ed
to
co
n
tr
o
l
D
C
m
o
to
r
s
.
T
h
ese
o
f
f
er
s
ev
er
al
i
m
p
o
r
ta
n
t
f
ea
t
u
r
es
a
n
d
ar
e
ea
s
y
to
i
m
p
le
m
e
n
t.
T
h
e
d
is
ad
v
an
ta
g
e
o
f
P
I
D
co
n
tr
o
ller
s
is
th
at
th
e
y
o
f
te
n
o
v
er
s
h
o
o
t
th
e
d
esire
d
o
b
j
ec
tiv
e
v
alu
e
f
o
llo
w
i
n
g
s
u
d
d
en
c
h
a
n
g
es
in
lo
ad
to
r
q
u
e.
A
d
d
itio
n
all
y
,
P
I
D
co
n
tr
o
ller
p
ar
am
eter
s
ar
e
v
er
y
d
if
f
ic
u
lt
to
co
n
tr
o
l,
m
a
k
i
n
g
it
h
ar
d
to
ac
h
i
ev
e
t
h
e
o
p
ti
m
al
s
tate.
T
o
o
v
er
co
m
e
t
h
i
s
d
is
ad
v
a
n
ta
g
e,
co
n
tr
o
l
m
et
h
o
d
s
s
u
c
h
as
lin
ea
r
q
u
ad
r
atic
r
eg
u
lato
r
s
(
L
Q
R
s
)
h
av
e
b
ee
n
d
e
v
elo
p
ed
[
2
,
1
3
]
.
L
QR
s
o
f
f
er
r
o
b
u
s
tn
es
s
in
ter
m
s
o
f
m
i
n
i
m
i
zi
n
g
a
g
iv
e
n
co
s
t
f
u
n
cti
o
n
[
3
]
.
T
h
e
s
i
m
p
licit
y
,
r
eliab
ilit
y
,
a
n
d
m
in
i
m
a
l
co
s
t
o
f
DC
m
o
to
r
s
m
ea
n
s
t
h
at
t
h
e
y
ar
e
o
f
te
n
p
r
ef
er
r
ed
o
v
er
o
th
er
m
o
to
r
s
[
4
]
.
T
h
e
b
est
s
tr
ateg
y
f
o
r
co
n
tr
o
llin
g
t
h
e
s
p
ee
d
o
f
a
DC
m
o
to
r
is
to
u
s
e
a
P
I
D
c
o
n
tr
o
ller
an
d
L
Q
R
,
w
h
ic
h
p
r
o
v
id
es
b
etter
t
r
an
s
ie
n
t
p
ar
a
m
eter
s
[
5
]
.
T
h
e
r
o
b
u
s
tn
e
s
s
o
f
L
QR
en
s
u
r
e
s
a
n
ac
cu
r
ate
d
y
n
a
m
ic
r
esp
o
n
s
e
[
6
]
.
I
n
ad
d
itio
n
,
L
Q
R
d
is
p
la
y
s
b
etter
h
ig
h
-
r
an
g
e
f
lex
ib
ilit
y
a
n
d
co
n
tr
o
l
w
h
en
c
o
m
p
ar
ed
w
i
th
o
th
er
co
n
tr
o
ller
s
[
7
,
1
3
]
.
T
h
er
ef
o
r
e,
L
Q
R
is
s
u
itab
le
f
o
r
r
o
b
o
ti
cs
ap
p
licatio
n
s
a
n
d
p
r
o
ce
s
s
co
n
tr
o
l,
b
ec
au
s
e
it
i
m
p
r
o
v
es s
y
s
te
m
s
tab
ilit
y
,
ef
f
e
ctiv
e
co
n
tr
o
l,
an
d
b
alan
ci
n
g
p
r
o
p
er
ties
[
8
]
.
2.
DE
S
I
G
N
AND
I
M
P
L
E
M
E
NT
AT
I
O
N
2
.
1
M
a
t
he
m
a
t
ica
l
m
o
del o
f
a
D
C
m
o
t
o
r
A
s
i
m
p
l
if
ied
m
at
h
e
m
atica
l
m
o
d
el
o
f
a
DC
m
o
to
r
ca
n
b
e
u
s
ed
to
b
u
ild
th
e
m
o
to
r
tr
an
s
f
e
r
f
u
n
ctio
n
.
T
h
e
s
ch
e
m
atic
d
iag
r
a
m
o
f
a
DC
m
o
to
r
i
n
Fi
g
u
r
e
1
s
h
o
w
s
th
e
elec
tr
ical
cir
c
u
it
o
f
t
h
e
ar
m
at
u
r
e
an
d
t
h
e
f
r
ee
b
o
d
y
d
iag
r
a
m
o
f
t
h
e
r
o
to
r
.
F
r
o
m
t
h
is
,
th
e
m
at
h
e
m
a
tical
m
o
d
el
ca
n
b
e
b
u
ilt
[
1
]
.
T
h
e
tr
an
s
f
er
f
u
n
ctio
n
is
d
er
iv
ed
f
r
o
m
t
h
e
DC
m
o
to
r
eq
u
atio
n
s
,
w
h
ic
h
ar
e
d
i
v
id
ed
in
to
a
m
ec
h
an
ical
p
ar
t,
elec
tr
ical
p
ar
t,
an
d
th
e
in
ter
co
n
n
ec
tio
n
b
et
w
ee
n
t
h
e
m
.
T
h
e
eq
u
atio
n
f
o
r
th
e
elec
tr
ic
a
l
p
ar
t
ca
n
b
e
d
er
iv
ed
as
s
h
o
w
n
i
n
eq
u
atio
n
s
(
1
)
an
d
(
2
)
:
Fig
u
r
e
1
.
DC
m
o
to
r
s
ch
e
m
atic
d
iag
r
a
m
(
)
(
1
)
(
)
(
2
)
V
:
m
o
to
r
ter
m
in
a
l v
o
lta
g
e
(
V)
W
:
m
o
t
o
r
s
p
ee
d
(
r
ad
/s
)
Ia
:
w
i
n
d
in
g
c
u
r
r
en
t (
A
)
KØ:
b
ac
k
elec
tr
o
m
o
ti
v
e
f
o
r
ce
(
E
MF)
co
n
s
tan
t (
V
s
/r
ad
)
Ra
: te
r
m
i
n
al
r
esis
ta
n
ce
(
Ω
)
La
: te
r
m
i
n
al
in
d
u
ctan
ce
(
H)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
IJ
RA
Vo
l.
6
,
No
.
4
,
Dec
em
b
er
201
7
:
2
5
2
–
2
68
254
T
h
e
eq
u
atio
n
f
o
r
th
e
m
ec
h
a
n
ical
p
ar
t
ca
n
b
e
d
er
iv
ed
u
s
in
g
Ne
w
to
n
’
s
la
w
,
w
h
ic
h
s
tate
s
th
at
t
h
e
s
u
m
m
atio
n
o
f
elec
tr
ical
an
d
lo
ad
to
r
q
u
es
is
eq
u
a
l
to
th
e
lo
ad
an
d
m
o
to
r
i
n
er
tia
m
u
ltip
lied
b
y
th
e
d
er
i
v
ati
v
e
o
f
th
e
an
g
u
lar
r
ate
as sh
o
w
n
i
n
eq
u
atio
n
s
(3
-
6)
.
(
3
)
–
(
4
)
–
(
)
–
(
5
)
(
)
(
)
(
6
)
w
h
er
e:
J
: lo
ad
an
d
m
o
to
r
in
er
tia
(
k
g
×
m
2
)
b
: d
am
p
i
n
g
f
r
ictio
n
(
N×
m
×s
/r
ad
)
T
L
: lo
ad
to
r
q
u
e
(
N×
m
)
T
e:
elec
tr
ical
to
r
q
u
e
(
N×
m
)
As
th
e
v
o
lta
g
e
is
t
h
e
in
p
u
t
to
t
h
e
s
y
s
te
m
a
n
d
th
e
s
p
ee
d
is
th
e
o
u
tp
u
t,
th
e
r
eq
u
ir
ed
tr
an
s
f
er
f
u
n
c
t
io
n
is
s
y
m
b
o
lized
b
y
w
(
s
)
/v
(
s
)
.
T
h
is
f
o
r
m
i
s
d
er
iv
ed
b
y
d
iv
id
i
n
g
eq
u
atio
n
(
8
)
b
y
eq
u
atio
n
(
3
)
.
I
t
ca
n
also
b
e
f
o
u
n
d
b
y
d
r
a
w
i
n
g
t
h
e
b
lo
ck
d
iag
r
a
m
o
f
a
DC
m
o
to
r
u
s
i
n
g
t
h
e
s
a
m
e
eq
u
atio
n
s
a
s
s
h
o
w
n
i
n
Fi
g
u
r
e
2
.
Fig
u
r
e
2
.
B
lo
ck
d
iag
r
a
m
o
f
a
DC
m
o
to
r
T
h
e
d
iag
r
a
m
ill
u
s
tr
ate
s
a
clo
s
ed
lo
o
p
an
d
R
o
o
t
lo
cu
s
a
n
al
y
s
i
s
f
o
r
D
C
m
o
to
r
s
y
s
te
m
as
s
h
o
w
n
i
n
Fig
u
r
e
3
.
T
h
er
ef
o
r
e,
it is
p
o
s
s
ib
le
to
u
s
e
th
e
r
o
o
t lo
cu
s
an
a
l
y
s
is
eq
u
atio
n
(
7
)
:
(
7
)
Fig
u
r
e
3
.
R
o
o
t lo
cu
s
an
al
y
s
i
s
f
o
r
DC
m
o
to
r
s
y
s
te
m
Fro
m
Fi
g
u
r
e
3
a
n
d
eq
u
atio
n
(
7
)
,
th
e
tr
an
s
f
er
f
u
n
ctio
n
f
o
r
a
DC
m
o
to
r
ca
n
b
e
d
er
iv
ed
as
s
h
o
w
n
in
eq
u
atio
n
s
(
8
)
an
d
(
9
)
:
(
)
(
)
(
)
(
)
(
)
(
)
(
8
)
Or
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
I
d
en
tify
in
g
th
e
O
p
tima
l Co
n
tr
o
ller
S
tr
a
teg
y
fo
r
DC
Mo
to
r
s
(
M.
R
.
Qa
d
er
)
255
(
)
(
)
(
)
(
)
(
)
(
9
)
2
.
2
Dy
na
m
ic
s
y
s
t
e
m
o
f
a
DC
m
o
t
o
r
Fro
m
Fi
g
u
r
e
1
,
ass
u
m
i
n
g
a
co
n
s
ta
n
t
e
x
citatio
n
f
ie
ld
ar
m
at
u
r
e,
th
e
v
o
lta
g
e
ca
n
b
e
r
ef
o
r
m
ed
as
s
h
o
wn
in
eq
u
atio
n
s
(
1
0
-
16)
:
(
1
0
)
(
1
1
)
Usi
n
g
Ne
w
to
n
’
s
s
ec
o
n
d
la
w
:
(
1
2
)
w
h
er
e
b
is
th
e
d
a
m
p
i
n
g
f
r
ictio
n
.
T
h
u
s
,
(
)
(
1
3
)
(
)
(
)
(
)
(
1
4
)
(
)
(
)
(
)
(
)
(
1
5
)
(
)
(
)
(
)
(
)
(
1
6
)
T
o
u
s
e
a
d
y
n
a
m
ic
s
y
s
te
m
m
et
h
o
d
,
w
e
s
h
o
u
ld
s
p
ec
if
y
t
h
e
s
ta
tes,
in
p
u
t,
an
d
o
u
tp
u
t
o
f
t
h
e
s
y
s
te
m
.
I
n
a
DC
m
o
to
r
s
y
s
te
m
,
t
h
e
cu
r
r
en
t
(
I
)
an
d
an
g
u
lar
r
ate
(
d
W
/d
t
)
a
r
e
th
e
s
tates,
th
e
ap
p
lied
v
o
ltag
e
(
V)
is
th
e
in
p
u
t,
an
d
th
e
an
g
u
lar
v
elo
cit
y
(
w
)
i
s
th
e
o
u
tp
u
t.
A
s
t
h
e
s
y
s
te
m
is
lin
ea
r
as
s
h
o
w
n
i
n
eq
u
atio
n
s
(
1
7
-
22)
,
th
e
s
tate
s
p
ac
e
ca
n
b
e
w
r
it
te
n
i
n
th
e
f
o
r
m
:
̇
(
)
[
]
(
)
[
]
(
)
(
1
7
)
̇
(
)
[
]
(
)
[
]
(
)
(
1
8
)
w
h
er
e:
x
(
t)
d
en
o
tes th
e
s
ta
te
v
ec
to
r
s
i a
n
d
w
y
(
t)
is
th
e
o
u
tp
u
t
w
u
(
t)
is
th
e
i
n
p
u
t V
̇
(
)
(
)
(
)
(
1
9
)
[
A
]
=
s
tate
m
at
r
ix
(
n
×n
)
[
B
]
=
in
p
u
t
m
atr
ix
(
n
×p
)
[
C
]
=
o
u
tp
u
t
m
a
tr
ix
(
q
×n
)
[
D]
=
f
ee
d
f
o
r
w
ar
d
(
ze
r
o
)
m
at
r
ix
(
q
×p
)
Fo
llo
w
i
n
g
th
e
m
et
h
o
d
ab
o
v
e,
an
d
f
r
o
m
eq
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s
(
1
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d
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1
3
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th
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s
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s
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es
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*
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[
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(
20
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W=
[
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2
1
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A=
[
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*
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[
]
(
2
2
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
IJ
RA
Vo
l.
6
,
No
.
4
,
Dec
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201
7
:
2
5
2
–
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68
256
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Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
RA
I
SS
N:
2089
-
4856
I
d
en
tify
in
g
th
e
O
p
tima
l Co
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tr
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S
tr
a
teg
y
fo
r
DC
Mo
to
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s
(
M.
R
.
Qa
d
er
)
257
2
.
4
Clo
s
ed
lo
o
p o
f
DC
m
o
t
o
r
a
ng
ula
r
v
elo
cit
y
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lo
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g
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C
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D
C
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Fig
u
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6
.
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lo
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lo
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2
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5
Co
ntr
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DC
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t
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t
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ec
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h
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m
ai
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j
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ap
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to
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ter
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ai
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s
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p
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co
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tr
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in
teg
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d
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tr
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r
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d
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t
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ase
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g
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m
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s
ato
r
,
lead
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g
r
al
co
m
p
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s
ato
r
,
an
d
lead
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co
m
p
en
s
ato
r
.
2
.
5
.
1
P
ro
po
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io
na
l c
o
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des
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Kn
o
w
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as
t
h
e
P
-
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o
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ates
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tl
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to
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r
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r
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al.
Ma
th
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atica
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is
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elatio
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s
h
ip
ca
n
b
e
in
ter
p
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as
s
h
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wn
in
eq
u
a
tio
n
(
2
4
)
:
(
)
(
2
4
)
W
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K1
is
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h
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p
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n
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Fi
g
u
r
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7
s
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P
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Fig
u
r
e
7
.
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tr
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lo
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d
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r
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m
2
.
5
.
2
I
nte
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ra
l c
o
ntr
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des
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A
l
s
o
k
n
o
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n
as
t
h
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n
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l,
th
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tr
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p
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T
h
e
co
r
r
esp
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n
d
in
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eq
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(
2
5
)
is
:
∫
(
)
(2
5
)
W
h
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K2
is
th
e
in
teg
r
al
co
n
tr
o
ller
g
ain
.
T
h
e
b
lo
ck
d
iag
r
a
m
f
o
r
th
is
co
n
tr
o
ller
is
s
h
o
w
n
i
n
Fig
u
r
e
8
.
Fig
u
r
e
8
.
In
teg
r
al
co
n
tr
o
ller
b
lo
ck
d
iag
r
a
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4856
IJ
RA
Vo
l.
6
,
No
.
4
,
Dec
em
b
er
201
7
:
2
5
2
–
2
68
258
2
.
5
.
3
Der
iv
a
t
iv
e
c
o
ntr
o
ller
d
esig
n
So
m
eti
m
es
ca
lled
t
h
e
r
ate
co
n
tr
o
ller
,
th
i
s
i
s
t
h
e
m
at
h
e
m
a
t
ical
o
p
p
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ite
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f
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te
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r
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co
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tr
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ller
,
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g
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ir
ec
tl
y
p
r
o
p
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r
tio
n
al
to
th
e
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er
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e
o
f
t
h
e
er
r
o
r
s
ig
n
al.
T
h
u
s
,
its
eq
u
atio
n
(
2
6
)
is
:
(
)
(
2
6
)
W
h
er
e
K3
is
th
e
d
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iv
ati
v
e
co
n
tr
o
ller
g
ai
n
.
T
h
e
b
lo
ck
d
iag
r
am
o
f
t
h
is
co
n
tr
o
ller
is
s
h
o
w
n
i
n
Fi
g
u
r
e
9
.
Fig
u
r
e
9
.
Der
i
v
ativ
e
co
n
tr
o
ller
b
lo
ck
d
iag
r
a
m
Usi
n
g
t
h
ese
t
h
r
ee
m
ai
n
co
n
tr
o
l
ler
s
,
th
e
f
o
llo
w
i
n
g
s
tr
ate
g
ies c
an
b
e
d
er
iv
ed
:
a.
P
r
o
p
o
r
tio
n
al
-
I
n
te
g
r
al
C
o
n
tr
o
ll
er
b.
P
r
o
p
o
r
tio
n
al
-
I
n
te
g
r
al
-
Der
i
v
ati
v
e
C
o
n
tr
o
ller
c.
P
h
ase
lag
co
m
p
e
n
s
ato
r
d.
L
ea
d
in
te
g
r
al
co
m
p
e
n
s
ato
r
e.
L
ea
d
lag
co
m
p
e
n
s
ato
r
2
.
5
.
4
P
ro
po
rt
io
na
l
-
inte
g
r
a
l (
P
I
)
co
ntr
o
ller
des
ig
n
P
I
co
n
tr
o
l
is
w
id
el
y
u
s
ed
i
n
i
n
d
u
s
tr
y
to
h
an
d
le
s
u
b
tle
v
ar
iat
i
o
n
s
i
n
co
n
d
itio
n
s
.
A
s
th
e
n
a
m
e
s
u
g
g
est
s
,
th
is
i
s
a
co
m
b
in
a
tio
n
o
f
t
h
e
p
r
o
p
o
r
tio
n
al
an
d
in
teg
r
al
co
n
tr
o
l
ler
s
,
an
d
h
as t
h
e
eq
u
atio
n
(
2
7
)
:
(
)
∫
(
)
(2
7
)
W
h
er
e
K1
an
d
K2
ar
e
t
h
e
p
r
o
p
o
r
tio
n
al
g
ai
n
a
n
d
in
teg
r
al
g
ai
n
,
r
esp
ec
ti
v
el
y
.
T
h
e
b
lo
ck
d
ia
g
r
a
m
o
f
a
P
I
co
n
tr
o
ller
is
s
h
o
w
n
in
Fig
u
r
e
1
0
.
Fig
u
r
e
1
0
.
P
I
co
n
tr
o
ller
b
lo
ck
d
iag
r
a
m
2
.
5
.
5
P
ro
po
rt
io
na
l
-
inte
g
r
a
l
-
deriv
a
t
iv
e
co
ntr
o
ller
des
ig
n
T
h
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IJ
RA
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2089
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4856
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