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tr
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M
C
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b
a
c
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BS
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a
n
d
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PI
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d
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ATLAB/
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ac
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EV
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Sli
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T
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ss
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rticle
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d
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CC B
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se
.
C
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s
p
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A
uth
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:
An
T
h
i H
o
ai
T
h
u
An
h
Dep
ar
tm
en
t o
f
E
lectr
ical
E
n
g
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Facu
lty
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-
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a
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s
p
o
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t a
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d
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o
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m
u
n
icatio
n
s
No
.
3
C
au
Giay
,
L
a
n
g
T
h
u
o
n
g
C
o
m
m
u
n
e,
Do
n
g
Da
Dis
tr
ict,
Han
o
i,
Vietn
am
E
m
ail:
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tan
h
.
k
td
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u
tc.
ed
u
.
v
n
1.
I
NT
RO
D
UCT
I
O
N
Dep
letin
g
f
o
s
s
il
f
u
els
an
d
en
v
ir
o
n
m
e
n
tal
p
o
llu
tio
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a
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b
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o
m
e
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ig
n
if
ican
t
is
s
u
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th
at
an
y
n
atio
n
wo
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ld
wid
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f
ac
es,
wh
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is
p
a
r
tially
attr
ib
u
tab
le
t
o
m
ea
n
s
o
f
tr
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s
p
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tatio
n
.
T
h
er
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r
e,
elec
tr
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v
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ar
e
cu
r
r
en
tly
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s
id
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a
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r
ess
th
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two
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s
u
es.
T
h
e
in
ter
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p
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m
an
en
t
m
ag
n
et
s
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ch
r
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to
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(
I
PMSM
)
p
o
s
s
ess
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s
ad
v
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tag
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s
u
ch
as
h
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h
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f
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ca
p
a
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o
f
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en
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am
p
le
to
r
q
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e,
wid
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s
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d
a
d
ju
s
tm
en
t
r
an
g
e,
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d
h
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n
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ity
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m
ak
in
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it
an
attr
ac
tiv
e
c
h
o
i
ce
in
v
ar
io
u
s
f
ield
s
s
u
ch
as
elec
tr
ic
v
eh
icle
m
an
u
f
ac
tu
r
in
g
,
win
d
p
o
wer
,
ae
r
o
s
p
ac
e,
an
d
wid
ely
a
p
p
lied
in
o
th
er
in
d
u
s
tr
ial
s
ec
to
r
s
[
1
]
.
W
h
en
th
e
m
o
t
o
r
o
p
er
ates
at
h
ig
h
s
p
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d
,
it
is
li
m
ited
b
y
v
o
ltag
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an
d
e
n
er
g
y
,
wh
ich
m
ay
ca
u
s
e
a
d
ec
r
ea
s
e
in
o
u
tp
u
t
to
r
q
u
e,
cu
r
r
en
t,
an
d
s
p
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d
;
th
e
I
PMSM
ca
n
wid
en
th
e
s
p
ee
d
ad
ju
s
tm
en
t
r
an
g
e
b
y
co
n
t
r
o
llin
g
th
e
to
r
q
u
e
in
th
e
wea
k
en
in
g
f
lu
x
r
eg
io
n
[
2
]
.
T
o
m
ax
im
ize
t
h
e
p
o
ten
tial
o
f
th
is
k
in
d
o
f
m
o
to
r
,
th
e
m
ax
im
u
m
to
r
q
u
e
p
er
am
p
e
r
e
(
MT
PA)
m
eth
o
d
is
p
r
ef
er
r
ed
[
3
]
,
[
4
]
.
W
id
ely
u
s
ed
m
eth
o
d
s
in
I
PMSM
d
r
iv
es
in
clu
d
e
d
ir
ec
t
to
r
q
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co
n
tr
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(
DT
C
)
an
d
f
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ld
-
o
r
ien
ted
co
n
t
r
o
l
(
FOC
)
[
5
]
-
[
8
]
,
wh
ich
a
r
e
ac
co
m
p
an
ied
b
y
v
a
r
io
u
s
co
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tr
o
l
m
eth
o
d
s
a
n
d
c
o
n
tr
o
ller
s
ap
p
li
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to
th
e
s
p
ee
d
lo
o
p
s
.
C
o
n
v
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n
tio
n
al
p
r
o
p
o
r
tio
n
al
in
teg
r
al
(
PI
)
co
n
tr
o
ller
s
ca
n
co
n
tr
o
l
th
e
m
o
to
r
[
9
]
,
[
1
0
]
,
b
u
t
d
is
tu
r
b
an
ce
s
an
d
ch
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in
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p
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am
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s
h
av
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ca
u
s
ed
s
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s
tab
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.
No
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co
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tr
o
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is
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o
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,
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d
v
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co
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tec
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iq
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wid
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tili
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u
ch
as
s
lid
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m
o
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co
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(
SMC
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,
b
ac
k
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tep
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c
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l,
s
li
d
in
g
m
o
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v
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s
tr
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r
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8
6
9
4
I
n
t J Po
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lec
&
Dr
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s
t
,
Vo
l.
1
6
,
No
.
2
,
J
u
n
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20
2
5
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1
9
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7
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co
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etwo
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k
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an
d
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tr
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,
wh
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ca
n
o
p
er
at
e
I
PMSM
with
h
ig
h
ef
f
icien
cy
[
1
1
]
-
[
2
0
]
.
Dian
o
v
et
a
l.
[
2
1
]
u
tili
ze
d
th
e
MT
PA
alg
o
r
ith
m
f
o
r
th
e
I
PMSM
d
r
iv
e
s
y
s
tem
w
ith
PI
c
o
n
tr
o
ller
s
.
Kir
ad
et
a
l.
[
2
2
]
ap
p
lie
d
s
en
s
o
r
less
b
ac
k
s
tep
p
in
g
tech
n
iq
u
e
with
Kalm
an
f
ilter
in
g
to
en
h
an
ce
m
o
to
r
p
er
f
o
r
m
an
ce
.
Fen
g
et
a
l.
[
2
3
]
d
ev
elo
p
ed
a
n
o
v
el
s
lid
in
g
m
o
d
e
co
n
tr
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tech
n
o
lo
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d
co
m
p
r
eh
en
s
iv
e
ev
alu
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n
m
eth
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d
f
o
r
s
p
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d
co
n
tr
o
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o
f
I
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to
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v
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e
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r
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ass
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m
en
t
o
f
s
p
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o
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n
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r
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n
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PMSMs
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v
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io
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s
o
p
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atin
g
s
tag
es
.
Z
h
an
g
et
a
l.
[
2
4
]
d
esig
n
ed
a
n
d
c
o
n
tr
o
lled
f
ield
wea
k
en
in
g
o
f
I
PMSM
f
o
r
el
ec
tr
ic
v
eh
icles
t
o
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o
n
s
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ate
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o
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d
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am
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ce
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d
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tab
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o
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with
th
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s
p
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p
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f
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u
r
tim
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.
B
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em
et
a
l.
[
2
5
]
co
m
p
ar
ed
b
ac
k
s
tep
p
in
g
s
lid
in
g
m
o
d
e
an
d
r
ev
er
s
e
co
n
tr
o
l
f
o
r
s
o
m
e
v
eh
icle
co
m
p
o
n
en
ts
to
d
em
o
n
s
tr
ate
ef
f
ec
tiv
en
ess
an
d
d
u
r
a
b
ilit
y
ag
ain
s
t
e
x
ter
n
al
d
is
tu
r
b
an
ce
s
an
d
d
if
f
er
e
n
t
r
o
ad
co
n
d
itio
n
s
.
Ho
s
s
ein
i
an
d
T
ab
atab
ae
i
[
2
6
]
co
n
tr
o
lled
c
u
r
r
en
t
a
n
d
s
p
ee
d
o
f
I
PMSM
u
s
in
g
s
eg
m
en
ted
a
d
a
p
tiv
e
s
lid
in
g
m
o
d
e
c
o
n
tr
o
l
b
a
s
ed
o
n
MT
PA
f
o
r
c
u
r
r
en
t
lo
o
p
.
T
u
n
g
et
a
l.
[2
7
]
ap
p
lied
s
lid
in
g
m
o
d
e
o
b
s
er
v
er
f
o
r
s
en
s
o
r
less
s
p
ee
d
-
co
n
tr
o
lle
d
I
PMSM
with
p
er
m
a
n
en
t
m
a
g
n
et
ex
citatio
n
al
o
n
g
th
e
ax
ial
m
ag
n
etic
f
ield
.
Fo
o
a
n
d
R
ah
m
an
[
2
8
]
co
n
tr
o
lled
M
T
PA in
s
en
s
o
r
less
s
lid
in
g
m
o
d
e
f
o
r
I
PMSM
d
r
iv
e
s
y
s
tem
u
s
in
g
s
lid
in
g
m
o
d
e
o
b
s
er
v
er
an
d
h
i
g
h
f
r
eq
u
en
cy
(
HF
)
s
ig
n
al
tr
an
s
m
is
s
io
n
.
Hash
em
i
et
a
l.
[
2
9
]
d
ev
elo
p
e
d
h
ig
h
-
p
er
f
o
r
m
a
n
ce
PI
-
b
ased
co
n
tr
o
ller
s
f
o
r
I
PM
m
o
to
r
d
r
iv
e
s
y
s
tem
.
Ho
wev
er
,
th
e
e
x
is
tin
g
s
tu
d
ies
h
av
e
y
et
t
o
p
r
o
p
o
s
e
an
d
im
p
le
m
en
t
v
ar
io
u
s
co
n
tr
o
l
m
eth
o
d
s
to
r
ep
lac
e
PI
an
d
p
r
o
p
o
r
tio
n
al
in
teg
r
al
d
er
iv
ativ
e
(
PID
)
co
n
tr
o
ller
s
f
o
r
I
PMSM
m
o
to
r
s
o
p
er
atin
g
in
t
h
e
f
ield
wea
k
en
in
g
r
eg
io
n
ap
p
licab
le
to
elec
tr
ic
v
eh
icles.
T
h
er
ef
o
r
e,
t
h
is
p
ap
er
will
p
r
o
p
o
s
e
t
h
r
ee
d
if
f
er
e
n
t
a
p
p
r
o
ac
h
es
to
d
esig
n
co
n
tr
o
ller
s
f
o
r
th
e
s
p
ee
d
lo
o
p
cir
cu
it
ap
p
licab
le
to
elec
tr
ic
c
ar
s
,
s
p
ec
if
ically
Vin
F
ast
elec
tr
ic
v
eh
icles.
Fin
ally
,
s
im
u
latio
n
r
esu
lts
o
n
MA
T
L
AB
/Si
m
u
lin
k
s
o
f
twar
e
v
er
if
ied
t
h
e
co
r
r
ec
t
n
ess
o
f
t
h
e
A
u
th
o
r
s
’
r
esear
ch
.
2.
M
O
DE
L
L
I
NG
DR
I
VE
S
YS
T
E
M
O
F
E
L
E
C
T
RI
C
VE
H
I
CL
E
S
2
.
1
.
M
a
t
hema
t
ica
l
m
o
del o
f
t
he
I
P
M
S
M
m
o
t
o
r
T
h
e
I
PMSM
m
o
d
el
is
r
ep
r
esen
ted
in
th
e
d
-
q
co
o
r
d
in
ate
s
y
s
t
em
as
(
1
)
[
3
0
]
-
[
3
3
]
.
W
h
er
e
U
sd
,
U
sq,
i
sd,
i
sq
R
s
,
L
sd
,
L
sq
ar
e
v
o
ltag
es,
cu
r
r
e
n
ts
,
r
esis
tan
ce
,
in
d
u
ctan
ce
s
o
f
th
e
s
tato
r
o
n
dq
-
ax
is
,
ω
s
is
th
e
an
g
u
lar
v
elo
city
o
f
th
e
m
o
to
r
,
ψ
p
is
th
e
r
o
to
r
f
lu
x
,
p
p
is
th
e
n
u
m
b
er
o
f
p
o
le
p
air
s
o
f
th
e
m
o
to
r
,
T
e
is
th
e
m
o
t
o
r
o
u
tp
u
t
to
r
q
u
e
,
ψ
sd
,
ψ
sq
ar
e
th
e
s
tato
r
f
lu
x
o
n
th
e
dq
-
ax
is
,
T
L
is
th
e
lo
ad
to
r
q
u
e,
J
is
th
e
m
o
m
en
t
o
f
in
er
tia
o
f
th
e
m
o
to
r
,
=
is
th
e
d
-
ax
is
tim
e
co
n
s
tan
t o
f
th
e
s
tato
r
cir
cu
it a
n
d
=
is
th
e
q
-
ax
i
s
tim
e
co
n
s
tan
t o
f
th
e
s
tato
r
ci
r
cu
it.
{
=
−
1
+
+
1
=
−
−
1
+
1
−
=
+
=
=
3
2
(
−
(
−
)
)
−
=
(
1
)
2
.
2
.
M
o
delin
g
t
he
f
o
rc
es a
ct
i
ng
o
n t
he
elec
t
ric
v
ehicle
As
th
e
v
eh
icle
m
o
v
es,
th
e
atm
o
s
p
h
er
e
will
im
p
ed
e
its
m
o
t
io
n
.
T
h
is
r
esis
tan
ce
f
o
r
ce
co
n
s
is
t
s
th
e
air
r
esis
tan
ce
an
d
th
e
v
eh
icle'
s
f
r
ictio
n
with
th
e
air
[
3
4
]
.
T
h
ese
tw
o
co
m
p
o
n
e
n
ts
co
m
b
in
e
d
f
o
r
m
th
e
win
d
r
esis
tan
ce
f
o
r
ce
,
wh
ic
h
is
ca
lcu
lated
b
y
(
2
)
.
=
1
2
(
ℎ
+
)
2
(
2
)
W
h
er
e
is
th
e
air
d
en
s
ity
,
C
d
i
s
th
e
co
ef
f
icien
t
o
f
air
r
esis
tan
ce
(
ty
p
ically
:
0
.
2
<
C
d
<
0
.
4
)
;
A
f
is
th
e
f
r
o
n
tal
ar
ea
o
f
th
e
v
eh
icle'
s
b
o
d
y
(
c
r
o
s
s
-
s
ec
tio
n
al
ar
ea
)
,
an
d
v
wind
is
th
e
win
d
s
p
ee
d
.
Fo
r
r
o
llin
g
r
esis
tan
ce
,
we
o
n
l
y
co
n
s
id
er
th
e
r
o
llin
g
f
r
ictio
n
o
n
a
r
ig
id
r
o
ad
s
u
r
f
ac
e,
an
d
i
n
th
e
id
ea
l
ca
s
e
wh
er
e
all
wh
ee
ls
h
av
e
th
e
s
am
e
co
n
d
itio
n
s
,
th
e
r
o
llin
g
f
r
ictio
n
f
o
r
ce
ca
n
b
e
ca
lcu
late
d
as
(
3
)
[
5
]
.
=
(
3
)
W
h
er
e
m
v
is
th
e
to
tal
m
ass
o
f
t
h
e
v
e
h
icle
an
d
p
ass
en
g
er
s
,
g
is
th
e
g
r
a
v
itatio
n
al
ac
ce
ler
atio
n
,
α
is
th
e
s
lo
p
e
a
n
g
le,
f
r
is
th
e
co
ef
f
icien
t o
f
r
o
llin
g
r
esis
tan
ce
ca
lcu
lated
b
y
(
4
)
.
W
ith
v
veh
b
ein
g
th
e
v
elo
city
o
f
th
e
v
eh
icle.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
C
o
mp
a
r
is
o
n
o
f sp
ee
d
lo
o
p
co
n
tr
o
l m
eth
o
d
s
fo
r
I
P
M mo
to
r
in
elec
tr
ic
ve
h
icles
(
A
n
Th
i H
o
a
i Th
u
A
n
h
)
721
=
0
.
01
(
1
+
3
.
6
100
ℎ
)
(
4
)
3.
SPEE
D
L
O
O
P
CO
NT
RO
L
DE
S
I
G
N
Fig
u
r
e
1
p
r
esen
ts
th
e
c
o
n
tr
o
l
s
tr
u
ctu
r
e
b
ased
o
n
th
e
p
r
in
cip
le
o
f
f
ield
-
o
r
ie
n
ted
co
n
tr
o
l
o
n
t
h
e
dq
-
a
x
is
s
y
s
tem
to
co
n
t
r
o
l
th
e
s
p
ee
d
ab
o
v
e
th
e
r
ated
s
p
ee
d
in
t
h
e
f
iel
d
wea
k
en
i
n
g
r
eg
io
n
.
At
t
h
e
s
a
m
e
tim
e,
th
e
to
r
q
u
e
r
ea
ch
es
th
e
m
ax
im
u
m
v
al
u
e.
T
h
e
s
p
ee
d
lo
o
p
c
o
n
tr
o
ller
s
a
r
e
PI,
b
ac
k
s
tep
p
in
g
,
a
n
d
s
lid
in
g
m
o
d
e
c
o
n
tr
o
l
to
co
m
p
ar
e
a
n
d
ev
al
u
ate
th
e
q
u
al
ity
o
f
s
p
ee
d
c
o
n
tr
o
l.
Fig
u
r
e
1
.
T
h
e
f
ield
-
o
r
ien
ted
c
o
n
tr
o
l stru
ctu
r
e
o
f
I
PM
3
.
1
.
T
he
s
lid
ing
m
o
de
co
ntr
o
l desig
n
Fig
u
r
e
2
s
h
o
ws
th
e
SMC
co
n
tr
o
ller
s
tr
u
ctu
r
e,
w
h
ich
d
e
f
in
es
t
h
e
er
r
o
r
b
etwe
en
th
e
d
esire
d
an
d
f
ee
d
b
ac
k
an
g
u
lar
v
elo
city
as
(
5
)
,
th
at
e
=−
.
T
ak
in
g
th
e
d
er
iv
ativ
e
o
f
th
e
er
r
o
r
as in
(
5
)
.
̇
=
̇
−
̇
∗
=
(
−
)
−
̇
∗
(
5
)
J
is
th
e
m
o
m
en
t
o
f
in
er
tia,
T
L
is
th
e
lo
ad
to
r
q
u
e,
p
p
is
t
h
e
n
u
m
b
er
o
f
p
o
le
p
air
s
.
C
h
o
o
s
in
g
th
e
L
y
ap
u
n
o
v
f
u
n
ctio
n
=
1
2
2
[
1
4
]
.
T
h
e
d
er
iv
ativ
e
o
f
V
is
w
r
itten
as (
6
)
.
̇
=
.
̇
(
6
)
T
o
en
s
u
r
e
s
tab
ilit
y
co
n
d
itio
n
s
̇
<
0
,
th
e
s
lid
in
g
s
u
r
f
ac
e
s
is
d
ef
in
ed
as
f
o
llo
ws:
=
⇒
̇
=
̇
.
Settin
g
̇
=
0
we
o
b
tain
th
e
r
o
b
u
s
t c
o
n
tr
o
l c
o
m
p
o
n
en
t
,
as in
(
7
)
.
=
−
(
−
−
̇
∗
)
(
7
)
T
h
e
s
y
s
tem
is
s
tab
le
wh
en
V
is
p
o
s
itiv
e
d
ef
in
ite,
c
o
n
t
in
u
o
u
s
ly
d
if
f
er
e
n
tiab
le
with
f
ir
s
t
-
o
r
d
e
r
d
er
iv
ativ
es,
an
d
n
e
g
ativ
e
d
ef
i
n
ite
[
3
5
]
.
T
o
en
s
u
r
e
.
̇
<
0
,
th
e
ex
p
o
n
en
tial
r
ea
ch
in
g
law
is
ch
o
s
en
to
h
av
e
th
e
f
o
llo
win
g
f
o
r
m
[
3
6
]
.
̇
=
−
(
)
−
,
>
0
,
>
0
(
8
)
T
h
er
ef
o
r
e,
th
e
c
o
n
tr
o
l sig
n
al
i
s
d
esig
n
ed
as
(
9
)
.
=
−
(
−
−
̇
∗
+
(
)
)
(
9
)
W
ith
k
= 1
0
0
,
ε
=
1
0
.
Pro
v
in
g
s
tab
ilit
y
as
(
1
0
)
.
̇
=
.
̇
=
̇
=
̇
−
̇
∗
=
[
(
−
)
−
̇
∗
]
=
[
(
−
(
−
−
̇
∗
+
(
)
)
−
)
−
̇
∗
]
=
(
−
−
(
)
)
=
−
(
|
|
+
2
)
≤
0
(
1
0
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
6
,
No
.
2
,
J
u
n
e
20
2
5
:
7
1
9
-
7
2
7
722
3
.
2
.
T
he
ba
ck
s
t
eppin
g
co
ntr
o
l desig
n
Fig
u
r
e
3
s
h
o
ws
th
e
B
SP
co
n
tr
o
ller
s
tr
u
ctu
r
e.
L
et'
s
d
ef
in
e
th
e
er
r
o
r
s
ig
n
al
as:
=
−
∗
,
tak
in
g
t
h
e
d
er
iv
ativ
e
o
f
b
o
t
h
s
id
es
as in
(
1
1
)
.
̇
=
̇
−
̇
∗
=
(
−
)
−
̇
∗
(
1
1
)
C
h
o
o
s
in
g
th
e
L
y
a
p
u
n
o
v
f
u
n
c
tio
n
=
1
2
2
.
T
ak
in
g
th
e
d
e
r
iv
ativ
e
o
f
V
[
1
]
:
̇
=
.
̇
.
C
h
o
o
s
in
g
th
e
c
o
n
tr
o
l
p
ar
am
eter
k
>
0
s
u
ch
as (
1
2
)
.
̇
=
−
⇒
̇
=
.
(
−
)
=
−
2
<
0
(
1
2
)
Su
b
s
titu
tin
g
̇
=
−
in
to
(
1
1
)
,
we
o
b
t
ain
(
1
3
)
.
W
ith
k
= 1
0
0
.
(
−
)
−
̇
∗
=
−
⇒
=
−
(
−
̇
∗
)
(
1
3
)
3
.
3
.
T
h
e
PI
co
n
tr
o
ller
d
esig
n
W
h
en
s
y
n
th
esizin
g
th
e
s
p
ee
d
lo
o
p
cir
cu
it
,
as
s
h
o
wn
in
Fig
u
r
e
4
,
we
co
n
s
id
er
th
e
en
tire
cu
r
r
en
t
lo
o
p
as
a
f
u
n
ctio
n
o
f
th
e
o
p
tim
al
m
o
d
u
le
s
tan
d
a
r
d
a
n
d
r
eg
ar
d
th
e
co
m
p
o
n
en
t
(
−
)
as
n
o
is
e
[
3
7
]
-
[
3
9
]
.
T
h
e
s
p
ee
d
co
n
tr
o
l lo
o
p
with
th
e
tr
an
s
f
er
f
u
n
ctio
n
,
as (
1
4
)
.
=
1
(
1
+
2
+
2
2
2
)
.
3
2
.
+
1
(
1
4
)
W
ith
T
si
= 2
T
i
.
Acc
o
r
d
in
g
to
t
h
e
o
p
tim
al
m
o
d
u
le
s
tan
d
a
r
d
,
s
elec
t th
e
n
o
r
m
alize
d
f
u
n
ctio
n
,
as (
1
5
)
.
=
1
2
2
2
+
2
+
1
(
1
5
)
Set
=
2
/
(
3
.
)
.
T
h
e
co
n
tr
o
ller
is
as (
1
6
)
.
=
(
1
−
)
=
(
1
+
2
+
2
2
2
)
.
.
(
1
+
)
.
2
(
1
+
)
(
1
6
)
Fig
u
r
e
2
.
SMC
co
n
tr
o
ller
s
tr
u
ctu
r
e
Fig
u
r
e
3
.
B
SP
co
n
tr
o
ller
s
tr
u
ct
u
r
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
C
o
mp
a
r
is
o
n
o
f sp
ee
d
lo
o
p
co
n
tr
o
l m
eth
o
d
s
fo
r
I
P
M mo
to
r
in
elec
tr
ic
ve
h
icles
(
A
n
Th
i H
o
a
i Th
u
A
n
h
)
723
E
lim
in
ate
h
ig
h
-
o
r
d
er
co
m
p
o
n
e
n
ts
,
as (
1
7
)
.
=
(
1
+
2
)
.
.
(
1
+
)
.
2
(
1
+
)
=
[
1
+
(
2
+
)
]
.
.
2
(
1
+
)
(
1
7
)
Deselec
t:
=
=
2
+
;
W
e
h
av
e
=
.
2
.
T
h
e
co
n
tr
o
ller
b
ec
o
m
es
a
s
im
p
le
s
tag
e
in
ca
p
ab
le
o
f
eli
m
in
atin
g
s
tatic
er
r
o
r
w
h
ile
th
er
e
is
lo
ad
d
is
tu
r
b
an
ce
.
T
h
e
s
y
m
m
etr
ic
o
p
tim
al
s
y
n
th
esis
m
eth
o
d
ca
n
o
v
er
co
m
e
th
is
d
r
awb
ac
k
.
C
h
o
o
s
in
g
th
e
s
tan
d
ar
d
f
u
n
ctio
n
ac
c
o
r
d
i
n
g
to
s
y
m
m
etr
ic
o
p
tim
izatio
n
as (
1
8
)
.
=
1
+
4
1
+
4
+
8
2
2
+
8
3
3
(
1
8
)
W
h
er
e
=
(
1
−
)
an
d
s
ettin
g
=
=
2
+
Fro
m
th
er
e,
we
o
b
tain
(
1
9
)
.
=
(
1
−
)
=
(
1
+
2
+
2
2
2
)
.
.
(
1
+
)
(
1
+
4
)
.
8
(
1
+
)
2
2
(
1
9
)
E
lim
in
atin
g
th
e
h
i
g
h
-
o
r
d
er
te
r
m
s
with
(
20
).
=
(
1
+
2
)
.
.
(
1
+
)
(
1
+
4
)
.
8
(
1
+
)
2
2
=
[
1
+
(
2
+
)
]
.
.
(
1
+
4
)
.
8
(
1
+
)
2
=
.
(
1
+
4
)
.
8
2
(
2
0
)
Ob
tain
in
g
th
e
s
p
ee
d
co
n
tr
o
ller
as
(
2
1
)
.
=
.
2
(
1
+
1
4
.
.
)
(
2
1
)
Fig
u
r
e
4
.
Sp
ee
d
lo
o
p
cir
cu
it
4.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
T
h
e
th
eo
r
etica
l
s
tu
d
ies
v
alid
at
ed
th
r
o
u
g
h
r
esp
o
n
s
es
s
im
u
lated
o
n
MA
T
L
AB
s
o
f
twar
e
in
c
lu
d
e
th
r
ee
co
n
tr
o
l
m
eth
o
d
s
f
o
r
th
e
s
p
ee
d
lo
o
p
o
f
th
e
FOC
s
tr
u
ctu
r
e
ap
p
lied
in
elec
tr
ic
v
eh
icles.
T
h
e
r
esp
o
n
s
es
ar
e
im
p
lem
en
ted
in
MA
T
L
AB
/
Si
m
u
lin
k
u
s
in
g
th
e
s
im
u
latio
n
p
ar
am
eter
s
f
r
o
m
T
ab
les
1
an
d
2
.
T
h
e
s
p
ee
d
p
r
o
f
ile
is
b
ased
o
n
E
u
r
o
p
e
E
C
E
'
s
s
ta
n
d
ar
d
u
r
b
an
cy
cle
[
4
0
]
.
T
h
e
s
p
ee
d
r
esp
o
n
s
e
o
f
t
h
e
elec
tr
ic
v
eh
icle
tr
an
s
m
is
s
io
n
co
n
tr
o
l
s
y
s
tem
u
s
in
g
PI,
B
SP
,
an
d
SMC
is
illu
s
tr
ated
in
Fig
u
r
e
5
.
Fig
u
r
e
5
co
m
p
ar
es
th
e
s
p
ee
d
r
esp
o
n
s
e
r
esu
lts
o
f
th
r
ee
m
eth
o
d
s
:
P
I
,
B
SP
,
an
d
SMC
.
SMC
an
d
B
SP
d
em
o
n
s
tr
ate
r
elativ
ely
s
h
o
r
t
tr
an
s
ie
n
t
r
esp
o
n
s
e
tim
es
o
f
ab
o
u
t
0
.
0
7
s
,
wh
er
ea
s
PI
r
esp
o
n
d
s
s
lo
wer
,
ar
o
u
n
d
0
.
2
s
.
M
o
r
eo
v
e
r
,
d
u
r
in
g
t
h
e
tr
a
n
s
itio
n
f
r
o
m
ac
ce
ler
atio
n
to
s
tead
y
-
s
tate,
an
o
v
er
s
h
o
o
t
o
c
cu
r
r
ed
.
Fro
m
Fig
u
r
e
5
,
we
ca
n
o
b
s
er
v
e
th
at
th
e
o
v
e
r
s
h
o
o
t
o
f
PI
is
th
e
lar
g
est,
lead
in
g
to
o
s
cillatio
n
an
d
a
m
o
r
e
ex
ten
d
ed
r
esp
o
n
s
e
tim
e,
f
o
llo
wed
b
y
B
SP
an
d
,
f
in
ally
,
SMC
.
T
h
e
th
r
ee
co
n
tr
o
l
m
eth
o
d
s
,
PI,
B
SP
,
an
d
SMC
,
h
av
e
b
ee
n
co
n
d
u
cted
wh
e
n
th
e
lo
a
d
ch
an
g
e
s
,
an
d
th
e
r
esu
lts
ar
e
p
r
esen
ted
in
Fig
u
r
e
6
.
Ov
er
all,
wh
e
n
o
p
er
atin
g
at
s
p
ee
d
s
h
ig
h
e
r
th
an
th
e
r
ate
d
s
p
ee
d
(
1
2
0
0
r
p
m
)
,
all
th
r
ee
m
eth
o
d
s
s
h
o
w
a
d
ec
r
ea
s
e
in
elec
tr
o
m
ag
n
eti
c
to
r
q
u
e
to
in
cr
ea
s
e
th
e
s
p
ee
d
.
T
h
is
lead
s
to
a
h
ig
h
er
p
ea
k
v
alu
e
o
f
th
e
to
r
q
u
e
o
s
cillatio
n
in
th
e
PI
m
et
h
o
d
an
d
a
lar
g
er
am
p
litu
d
e
o
f
o
s
cillatio
n
,
p
o
te
n
tially
af
f
ec
tin
g
th
e
s
y
s
tem
'
s
s
tab
ili
ty
.
C
o
n
v
er
s
ely
,
we
o
b
s
er
v
e
a
s
m
aller
p
ea
k
v
alu
e
o
f
th
e
elec
tr
o
m
ag
n
etic
t
o
r
q
u
e
o
s
cillatio
n
in
SMC
,
with
a
lo
wer
am
p
litu
d
e
o
f
o
s
cillatio
n
an
d
s
m
aller
to
r
q
u
e.
T
h
is
r
esu
lt
in
d
icate
s
th
at
th
e
s
y
s
tem
is
less
af
f
ec
ted
b
y
lo
ad
d
is
tu
r
b
an
ce
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
6
,
No
.
2
,
J
u
n
e
20
2
5
:
7
1
9
-
7
2
7
724
Fig
u
r
e
7
illu
s
tr
ates
th
e
wav
ef
o
r
m
s
o
f
i
sd
an
d
i
sq
.
L
o
o
k
in
g
at
Fig
u
r
e
7
(
a
)
,
we
ca
n
o
b
s
er
v
e
t
h
at
th
e
two
cu
r
r
en
ts
i
sd
an
d
i
sq
h
a
v
e
b
ee
n
d
ec
o
u
p
led
,
with
i
sd
b
ein
g
co
n
tr
o
lled
to
b
e
less
th
an
0
.
E
x
am
in
i
n
g
Fig
u
r
e
7
(
b
)
an
d
Fig
u
r
e
7
(
c
)
,
d
u
r
in
g
s
u
d
d
e
n
lo
a
d
ch
an
g
es
in
PI
an
d
B
SP
co
n
tr
o
l,
i
sd
an
d
i
sq
cu
r
r
en
ts
o
s
cillate
an
d
e
x
h
ib
it
m
o
r
e
g
ian
t
s
p
ik
es,
af
f
ec
tin
g
th
e
s
y
s
tem
'
s
s
tab
ilit
y
.
I
n
co
n
tr
ast,
SM
C
ex
h
ib
its
m
o
r
e
m
in
o
r
o
s
cillatio
n
s
,
p
r
o
v
id
in
g
b
etter
r
esp
o
n
s
e
an
d
b
ein
g
less
af
f
ec
t
ed
b
y
l
o
ad
ch
a
n
g
es.
T
ab
le
1
.
Par
am
eter
s
o
f
m
o
to
r
I
PM
P
a
r
a
me
t
e
r
s
S
y
mb
o
l
V
a
l
u
e
U
n
i
t
S
t
a
t
o
r
r
e
s
i
st
a
n
c
e
R
s
0
.
0
0
6
5
O
h
m
d
-
a
x
i
s
i
n
d
u
c
t
a
n
c
e
L
sd
0
.
0
0
1
5
9
7
H
q
-
a
x
i
s
i
n
d
u
c
t
a
n
c
e
L
sq
0
.
0
0
2
0
5
7
H
I
n
e
r
t
i
a
t
o
r
q
u
e
J
0
.
0
9
k
g
.
m
2
N
u
mb
e
r
o
f
p
o
l
e
p
a
i
r
s
p
p
3
D
C
v
o
l
t
a
g
e
V
dc
5
5
0
V
T
ab
le
2
.
Par
am
eter
s
o
f
an
elec
tr
ic
ca
r
P
a
r
a
me
t
e
r
s
V
a
l
u
e
U
n
i
t
V
e
h
i
c
l
e
w
e
i
g
h
t
+
l
o
a
d
2
0
1
8
kg
W
h
e
e
l
r
a
d
i
u
s
0
.
3
m
Tr
a
n
sm
i
ssi
o
n
r
a
t
i
o
9
.
7
3
M
a
x
i
m
u
m
sp
e
e
d
1
3
0
k
m/
h
Ef
f
e
c
t
i
v
e
a
r
e
a
2
.
3
m
2
A
i
r
d
e
n
s
i
t
y
1
.
2
5
k
g
/
m
3
R
o
a
d
g
r
a
d
i
e
n
t
0
R
o
l
l
i
n
g
r
e
si
s
t
a
n
c
e
c
o
e
f
f
i
c
i
e
n
t
0
.
0
2
Fig
u
r
e
5
.
T
h
e
s
p
ee
d
r
esp
o
n
s
e
Fig
u
r
e
6
.
T
o
r
q
u
e
r
esp
o
n
s
e
as lo
ad
ch
a
n
g
es
(
a)
(
b
)
(
c)
Fig
u
r
e
7
.
C
u
r
r
e
n
t r
esp
o
n
s
e
to
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