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20
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121
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3
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1
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5
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[
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[
7
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I
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C
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,
Vo
l.
1
6
,
No
.
1
,
Feb
r
u
ar
y
20
2
6
:
1
2
1
-
134
122
s
en
s
itiv
e
E
V
p
latf
o
r
m
s
.
Ho
wev
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,
th
e
c
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m
p
lex
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o
f
S
PIM
d
y
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am
ics
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itates
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DT
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MPC
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[
8
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–
[
1
1
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.
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2
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1
4
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ass
iv
e
co
n
t
r
o
l,
p
r
e
d
ictiv
e
co
n
tr
o
l
,
an
d
Ham
ilto
n
ian
co
n
tr
o
l
[
1
5
]
–
[
2
3
]
.
Ho
wev
e
r
,
th
ese
tec
h
n
iq
u
es
ty
p
ically
r
eq
u
ir
e
ac
c
u
r
ate
m
ath
em
atica
l
m
o
d
els
an
d
in
v
o
l
v
e
co
m
p
lex
co
m
p
u
tatio
n
.
W
h
en
ap
p
lied
i
n
d
ep
en
d
en
tly
,
th
e
y
m
ay
n
o
t
ac
h
iev
e
o
p
tim
al
r
esu
lts
,
esp
ec
ially
in
n
o
n
lin
ea
r
s
y
s
tem
s
.
Su
ch
as,
b
ac
k
s
tep
p
in
g
(
B
S)
an
d
s
lid
in
g
m
o
d
e
co
n
t
r
o
l
(
SMC
)
,
ea
ch
o
f
f
e
r
in
g
ad
v
an
tag
es
in
s
tab
ilit
y
an
aly
s
is
an
d
r
o
b
u
s
tn
ess
,
r
esp
ec
tiv
ely
.
Yet,
ea
ch
ap
p
r
o
a
ch
h
as
k
n
o
wn
d
r
awb
ac
k
s
:
B
S
is
s
en
s
itiv
e
to
u
n
ce
r
tain
ties
,
wh
ile
SMC
in
tr
o
d
u
ce
s
ch
atter
in
g
e
f
f
ec
ts
.
As
a
r
esu
lt,
in
teg
r
atin
g
m
u
ltip
le
c
o
n
tr
o
l
tech
n
i
q
u
es
to
lev
er
ag
e
th
eir
r
esp
ec
tiv
e
s
tr
en
g
th
s
h
as
b
ec
o
m
e
a
p
r
o
m
is
in
g
r
esear
ch
d
ir
ec
tio
n
f
o
r
im
p
r
o
v
in
g
th
e
p
er
f
o
r
m
an
ce
o
f
AC
m
o
to
r
d
r
iv
es
[
2
4
]
–
[
2
9
]
.
I
n
[
2
9
]
,
a
h
y
b
r
id
b
ac
k
s
tep
p
in
g
-
s
lid
in
g
m
o
d
e
(
B
S
-
SM)
co
n
tr
o
l
s
tr
u
ctu
r
e
was
p
r
o
p
o
s
ed
,
d
em
o
n
s
tr
atin
g
a
p
r
o
m
is
in
g
ap
p
r
o
ac
h
f
o
r
m
o
to
r
d
r
iv
es.
I
t
is
ea
s
y
to
s
ee
th
at,
wh
ile
b
ac
k
s
tep
p
in
g
p
r
o
v
id
es
a
s
y
s
tem
atic
f
r
am
ew
o
r
k
f
o
r
s
tab
ilit
y
an
aly
s
is
,
its
p
er
f
o
r
m
a
n
ce
d
e
g
r
ad
es
s
ig
n
if
ica
n
tly
in
th
e
p
r
esen
ce
o
f
p
ar
a
m
eter
u
n
ce
r
tain
ties
,
s
u
ch
as
v
ar
iatio
n
s
in
r
o
to
r
r
esis
tan
ce
an
d
v
eh
icle
in
e
r
tia,
an
d
alth
o
u
g
h
co
n
v
en
tio
n
al
s
lid
in
g
m
o
d
e
co
n
tr
o
l
o
f
f
e
r
s
ex
ce
llen
t
r
o
b
u
s
tn
e
s
s
ag
ain
s
t
s
u
ch
u
n
ce
r
tain
ties
,
it
in
h
er
en
tly
s
u
f
f
er
s
f
r
o
m
t
h
e
h
ig
h
-
f
r
eq
u
e
n
cy
c
h
atter
in
g
p
h
en
o
m
en
o
n
,
wh
ich
c
an
ex
cite
u
n
m
o
d
eled
d
y
n
am
i
cs
an
d
d
a
m
ag
e
th
e
ac
tu
ato
r
.
T
h
e
ch
allen
g
e
o
f
ch
atter
in
g
an
d
th
e
lac
k
o
f
ad
ap
t
iv
ity
u
n
d
er
tim
e
-
v
ar
y
in
g
lo
a
d
co
n
d
itio
n
s
r
em
ain
d
u
e
t
o
ex
is
tin
g
im
p
lem
e
n
tatio
n
s
o
f
ten
u
s
e
f
ix
ed
g
ain
s
o
r
n
e
g
lect
r
ea
l
-
tim
e
d
is
tu
r
b
an
ce
est
im
atio
n
,
lead
i
n
g
to
lim
itatio
n
s
in
ad
ap
tab
ilit
y
,
ex
c
ess
iv
e
co
n
tr
o
l e
f
f
o
r
t,
o
r
d
eg
r
a
d
ed
p
er
f
o
r
m
a
n
ce
in
p
r
ac
tical
E
V
s
ce
n
ar
io
s
.
T
o
ad
d
r
ess
th
ese
ch
allen
g
es,
t
h
is
p
ap
er
p
r
o
p
o
s
es
a
n
o
v
el
co
n
tr
o
l
s
tr
ateg
y
,
ter
m
e
d
im
p
r
o
v
e
d
ad
ap
tiv
e
b
ac
k
s
tep
p
in
g
–
s
ec
o
n
d
-
o
r
d
e
r
s
lid
in
g
m
o
d
e
(
I
AB
SS
OS
M)
,
w
h
ich
in
co
r
p
o
r
ates
a
v
ar
iab
le
g
ain
s
u
p
er
-
twis
tin
g
alg
o
r
ith
m
(
VGST
A)
in
b
o
t
h
s
p
ee
d
an
d
c
u
r
r
en
t
lo
o
p
s
.
T
h
is
VGST
A
p
r
o
p
o
s
ed
s
tr
u
ctu
r
e
d
y
n
am
ically
ad
ju
s
ts
th
e
co
n
tr
o
l
g
ain
s
b
ased
o
n
d
is
tu
r
b
an
ce
esti
m
ates,
th
er
eb
y
m
a
in
tain
in
g
f
in
ite
-
tim
e
co
n
v
e
r
g
e
n
ce
an
d
r
o
b
u
s
tn
ess
wh
ile
ef
f
ec
tiv
ely
r
ed
u
ci
n
g
c
h
atter
in
g
with
o
u
t
r
eq
u
ir
in
g
p
r
i
o
r
k
n
o
wled
g
e
o
f
d
is
tu
r
b
a
n
ce
b
o
u
n
d
s
.
Mo
r
e
o
v
er
,
a
p
r
ed
ictiv
e
t
o
r
q
u
e
esti
m
ato
r
b
ased
o
n
th
e
f
o
r
war
d
E
u
ler
d
is
cr
etiza
tio
n
o
f
t
h
e
SP
I
M
m
o
d
el
to
p
r
o
ac
tiv
ely
h
an
d
le
ex
ter
n
al
lo
ad
v
ar
iatio
n
s
also
is
p
r
o
p
o
s
ed
.
T
h
is
esti
m
ato
r
en
h
an
ce
s
s
y
s
tem
r
esp
o
n
s
e
b
y
an
ticip
atin
g
to
r
q
u
e
d
em
an
d
s
a
n
d
d
is
tu
r
b
an
ce
ef
f
ec
ts
,
im
p
r
o
v
in
g
tr
a
n
s
ien
t p
er
f
o
r
m
an
ce
a
n
d
o
v
er
all
s
y
s
tem
r
o
b
u
s
tn
ess
.
T
h
e
p
er
f
o
r
m
an
ce
a
n
d
r
o
b
u
s
tn
ess
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l
s
ch
em
e
f
o
r
a
SP
I
M
d
r
i
v
e
in
E
V
ap
p
licatio
n
s
,
p
ar
ticu
lar
ly
in
t
er
m
s
o
f
s
tab
ilit
y
,
r
esp
o
n
s
e
s
p
ee
d
,
an
d
d
is
tu
r
b
a
n
ce
r
ejec
tio
n
,
ar
e
v
alid
ated
v
ia
ex
ten
s
iv
e
s
im
u
latio
n
s
u
n
d
er
s
tan
d
ar
d
ized
E
V
d
r
iv
in
g
cy
cle
s
(
E
C
E
-
4
0
,
E
C
E
-
1
5
)
,
s
tep
s
p
e
ed
co
m
m
a
n
d
s
,
a
n
d
lo
ad
d
is
tu
r
b
an
ce
s
.
R
esu
lts
co
n
f
ir
m
its
s
u
p
er
io
r
ity
o
v
er
co
n
v
e
n
tio
n
al
tech
n
iq
u
es
in
ter
m
s
o
f
tr
ac
k
in
g
ac
cu
r
ac
y
,
r
o
b
u
s
tn
ess
,
an
d
d
y
n
am
ic
r
esp
o
n
s
e.
T
h
e
p
a
p
er
is
o
r
g
a
n
ized
as
f
o
llo
ws:
s
ec
tio
n
2
p
r
esen
ts
th
e
SP
I
M
d
r
iv
e
s
y
s
tem
m
o
d
el.
Sectio
n
3
in
tr
o
d
u
ce
s
th
e
p
r
o
p
o
s
ed
STABS
_
PC
H
co
n
tr
o
ller
an
d
r
esis
tan
ce
/f
lu
x
esti
m
ato
r
s
.
Sectio
n
4
d
is
cu
s
s
es th
e
s
im
u
latio
n
r
esu
lts
.
Fin
ally
,
co
n
clu
s
io
n
s
ar
e
d
r
awn
i
n
s
ec
tio
n
5.
2.
M
O
DE
L
I
NG
O
F
SPI
M
DR
I
VE
AND
E
V
P
RO
P
UL
SI
O
N
SYST
E
M
2
.
1
.
SPIM
driv
e
s
y
s
t
em
m
o
delin
g
T
h
e
d
r
iv
e
s
y
s
tem
co
n
s
id
er
ed
in
th
is
s
tu
d
y
in
clu
d
es
a
SP
I
M
p
o
wer
ed
b
y
a
s
ix
-
p
h
ase
v
o
lt
ag
e
s
o
u
r
ce
in
v
er
ter
(
SP
VSI
)
.
T
h
e
o
v
er
all
s
tr
u
ctu
r
e
o
f
t
h
e
SP
I
M
d
r
iv
e
s
y
s
tem
is
illu
s
tr
ated
in
Fig
u
r
e
1
.
T
h
e
v
ec
to
r
s
p
ac
e
d
ec
o
m
p
o
s
itio
n
(
VSD)
tec
h
n
iq
u
e
is
u
s
ed
to
tr
an
s
f
o
r
m
t
h
e
s
i
x
-
d
im
en
s
io
n
al
s
p
ac
e
i
n
to
t
h
r
e
e
two
-
d
im
e
n
s
io
n
al
s
u
b
s
p
ac
es
in
th
e
s
tatio
n
ar
y
r
ef
er
en
ce
f
r
am
e.
T
h
e
tr
an
s
f
o
r
m
atio
n
is
p
er
f
o
r
m
ed
u
s
in
g
a
6
×6
tr
an
s
f
o
r
m
atio
n
m
atr
ix
as d
ev
elo
p
ed
in
p
r
ev
io
u
s
liter
atu
r
e
[
1
]
.
6
=
1
3
[
1
−
1
2
−
1
2
√
3
2
−
√
3
2
0
0
√
3
2
−
√
3
2
1
2
1
2
−
1
1
−
1
2
−
1
2
−
√
3
2
√
3
2
0
0
−
√
3
2
√
3
2
1
2
1
2
−
1
1
1
1
0
0
0
0
0
0
1
1
1
]
(
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
A
n
en
h
a
n
ce
d
imp
r
o
ve
d
a
d
a
p
t
ive
b
a
ck
s
tep
p
in
g
–
s
ec
o
n
d
-
o
r
d
e
r
s
lid
in
g
mo
d
e
…
(
Ho
a
n
g
Da
t
P
h
a
m
)
123
T
h
e
m
ath
em
atica
l e
q
u
atio
n
s
o
f
th
e
SP
I
M
in
th
e
s
tatio
n
ar
y
r
e
f
er
en
ce
f
r
am
e
ar
e
wr
itten
as
(
2
)
:
[
]
=
[
]
[
]
+
(
[
]
[
]
+
[
]
[
]
)
[
0
]
=
[
]
[
]
+
(
[
]
[
]
+
[
]
[
]
)
(
2
)
wh
er
e
[
]
,
[
]
,
[
]
,
[
]
,
an
d
[
]
r
ep
r
esen
t
th
e
v
o
ltag
e,
c
u
r
r
en
t,
r
esis
tan
ce
,
s
elf
-
in
d
u
ctan
ce
,
an
d
m
u
tu
al
in
d
u
ctan
ce
v
ec
to
r
s
,
r
esp
ec
tiv
ely
.
P
is
th
e
d
if
f
er
en
tial
o
p
er
ato
r
.
Su
b
s
cr
ip
ts
r
an
d
s
d
en
o
te
r
o
to
r
an
d
s
tato
r
co
m
p
o
n
en
ts
,
r
esp
ec
tiv
ely
.
Sin
ce
th
e
r
o
to
r
is
s
q
u
ir
r
el
-
ca
g
e
ty
p
e,
[
]
eq
u
als
ze
r
o
.
T
h
e
ele
ctr
o
m
ec
h
an
ical
en
er
g
y
c
o
n
v
e
r
s
io
n
o
n
ly
o
cc
u
r
s
in
th
e
D
–
Q
s
u
b
s
p
ac
e:
[
0
0
]
=
[
+
0
0
0
+
0
+
−
−
+
]
[
]
(
3
)
am
o
n
g
th
e
th
r
ee
s
u
b
s
p
ac
es,
o
n
ly
th
e
D
–
Q
s
u
b
s
p
ac
e
c
o
n
tr
ib
u
tes
to
to
r
q
u
e
p
r
o
d
u
ctio
n
[
1
]
.
T
h
e
r
e
m
ain
in
g
x
–
y
an
d
z
1
–
z2
s
u
b
s
p
ac
es
ca
u
s
e
p
o
wer
lo
s
s
an
d
d
o
n
o
t
p
ar
ticip
at
e
in
e
n
er
g
y
c
o
n
v
e
r
s
io
n
,
h
en
ce
th
ey
ar
e
ex
clu
d
ed
f
r
o
m
th
e
c
o
n
tr
o
l
d
esig
n
.
T
h
er
ef
o
r
e,
th
e
SP
I
M
co
n
tr
o
l
s
y
s
tem
ca
n
b
e
r
ed
u
ce
d
to
a
f
o
r
m
s
im
ilar
to
th
e
D
–
Q
m
o
d
el
o
f
a
co
n
v
en
tio
n
al
in
d
u
c
tio
n
m
o
to
r
.
Ho
wev
er
,
d
esig
n
i
n
g
co
n
t
r
o
ller
s
in
th
e
s
tatio
n
ar
y
r
ef
er
e
n
ce
f
r
am
e
is
ch
allen
g
in
g
.
T
o
o
v
er
co
m
e
th
i
s
,
th
e
SP
I
M
m
o
d
el
is
tr
an
s
f
o
r
m
ed
in
to
a
s
y
n
ch
r
o
n
o
u
s
r
o
tatin
g
r
ef
e
r
en
ce
f
r
am
e
(
d
q
-
f
r
am
e)
,
wh
ic
h
co
n
v
e
r
ts
cu
r
r
en
t
s
ig
n
als
in
to
DC
co
m
p
o
n
en
ts
,
th
er
eb
y
s
im
p
lify
i
n
g
co
n
tr
o
l
an
d
e
n
h
an
cin
g
s
p
ee
d
an
d
to
r
q
u
e
tr
ac
k
in
g
ac
c
u
r
ac
y
.
T
h
e
tr
an
s
f
o
r
m
atio
n
f
r
o
m
t
h
e
DQ
to
d
q
f
r
am
e
is
p
er
f
o
r
m
ed
u
s
in
g
th
e
tr
an
s
f
o
r
m
atio
n
m
atr
ix
T
2
d
ef
in
ed
as
(
4
)
:
2
=
[
c
os
(
)
−
(
)
(
)
c
os
(
)
]
(
4
)
wh
er
e
is
th
e
r
o
to
r
an
g
u
lar
p
o
s
itio
n
with
r
esp
ec
t to
th
e
s
tato
r
,
as sh
o
wn
in
Fig
u
r
e
1.
Fig
u
r
e
1
.
Ov
e
r
all
s
tr
u
ctu
r
e
o
f
t
h
e
SP
I
M
d
r
iv
e
s
y
s
tem
2
.
2
.
Vehicle
pro
pu
ls
io
n m
o
delin
g
Un
d
er
FOC
co
n
tr
o
l,
ѱ
rq
=
0
,
ѱ
rd
=
ѱ
rd
.
T
h
e
u
p
d
ated
d
y
n
am
ic
m
o
d
el
o
f
th
e
m
o
t
o
r
is
d
escr
ib
e
d
u
s
in
g
th
e
f
o
llo
win
g
s
p
ac
e
v
ec
to
r
d
i
f
f
er
e
n
tial e
q
u
atio
n
s
:
x
b
y
c
z
a
O
V
d
+
_
V
as
+
_
V
ds
+
_
V
bs
+
_
V
es
+
_
V
cs
+
_
V
fs
D
C
L
i
n
k
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
1
,
Feb
r
u
ar
y
20
2
6
:
1
2
1
-
134
124
{
=
−
+
+
+
=
−
+
+
+
=
3
2
(
)
−
−
=
−
1
(
5
)
wh
er
e:
=
1
−
2
;
=
;
=
2
+
2
2
;
=
2
2
;
=
1
;
=
=
3
2
(
6
)
=
(
7
)
Alter
n
ativ
ely
,
to
r
q
u
e
ca
n
also
b
e
ex
p
r
ess
ed
th
r
o
u
g
h
th
e
d
y
n
a
m
ic
eq
u
atio
n
:
=
+
+
(
8
)
T
o
p
r
o
p
el
t
h
e
E
V,
th
e
SP
I
M
m
u
s
t
g
en
er
ate
to
r
q
u
e
f
o
r
th
e
wh
ee
ls
as
p
er
f
o
r
m
in
g
in
Fig
u
r
e
2
.
T
h
is
illu
s
tr
ates
th
e
p
r
o
p
o
s
ed
tr
an
s
m
is
s
io
n
d
i
ag
r
am
in
elec
tr
ic
v
e
h
icle.
Ke
y
f
ac
to
r
s
i
n
f
lu
en
ci
n
g
t
h
e
E
V
’
s
d
y
n
am
ic
m
o
d
el
in
clu
d
e
r
o
ad
co
n
d
itio
n
s
,
in
cli
n
es,
ac
ce
ler
atio
n
ab
ilit
y
,
ae
r
o
d
y
n
a
m
ic
r
esis
tan
ce
,
etc.
T
h
e
p
r
o
p
o
s
ed
co
n
tr
o
l
s
tr
ateg
y
tak
es
th
ese
d
y
n
am
ic
s
in
to
ac
co
u
n
t.
T
h
e
m
o
d
el
is
b
ased
o
n
v
e
h
icle
m
ec
h
a
n
ics
an
d
ae
r
o
d
y
n
am
ics
p
r
in
cip
les [
1
8
]
.
T
h
e
to
tal
tr
ac
tiv
e
f
o
r
ce
is
g
iv
en
b
y
:
=
+
ℎ
+
+
+
≈
+
+
1
2
2
+
+
(
9
)
wh
er
e
:
tr
ac
tiv
e
f
o
r
ce
;
:
r
o
llin
g
r
esis
tan
ce
;
ℎ
:
h
ill
clim
b
in
g
f
o
r
ce
;
:
lin
ea
r
ac
ce
ler
atio
n
f
o
r
ce
;
:
an
g
u
lar
ac
ce
ler
atio
n
f
o
r
ce
;
m
: E
V
m
ass
;
g
:
g
r
av
itatio
n
al
ac
ce
ler
atio
n
;
v
:
v
eh
icle
s
p
ee
d
;
µ
:
r
o
l
lin
g
r
esis
tan
c
e
co
ef
f
icien
t;
ρ
:
air
d
en
s
ity
;
A:
f
r
o
n
tal
ar
ea
;
C
d
:
d
r
ag
co
ef
f
i
cien
t;
f
:
s
lo
p
e
a
n
g
le;
FL:
ex
te
r
n
al
d
is
tu
r
b
a
n
ce
;
r
:
wh
ee
l
r
ad
iu
s
;
G:
g
ea
r
r
atio
;
T
:
r
eq
u
ir
e
d
to
r
q
u
e;
v
r
:
m
o
to
r
s
p
ee
d
.
I
n
Fig
u
r
e
3
,
u
n
d
er
FOC
,
th
e
elec
tr
o
m
ag
n
etic
to
r
q
u
e
is
ex
p
r
ess
ed
s
im
p
ly
as
(
1
0
)
:
=
(
1
0
)
Fig
u
r
e
2
.
Pro
p
o
s
ed
tr
a
n
s
m
is
s
i
o
n
d
iag
r
am
in
elec
tr
ic
v
eh
icle
S
P
IM
1
S
P
IM
2
V
d
c
FO
C
u
s
i
n
g
IA
B
S
S
M
c
o
n
t
r
o
l
s
t
a
t
e
g
y
i
s
d1,
i
s
q1
i
s
d2,
i
s
q2
+
-
+
-
ω
r
δ
ω
r
e
f
_l
e
f
t
ω
r
e
f
_r
i
ght
S
t
r
e
e
r
i
n
g
w
h
e
e
l
ω
r
En
c
o
d
e
r
E
n
c
o
d
e
r
S
P
V
S
I
S
P
V
S
I
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
A
n
en
h
a
n
ce
d
imp
r
o
ve
d
a
d
a
p
t
ive
b
a
ck
s
tep
p
in
g
–
s
ec
o
n
d
-
o
r
d
e
r
s
lid
in
g
mo
d
e
…
(
Ho
a
n
g
Da
t
P
h
a
m
)
125
Fig
u
r
e
3
.
Me
ch
a
n
ical
f
o
r
ce
s
ac
tin
g
o
n
E
V
[
1
8
]
T
h
e
p
o
wer
r
eq
u
i
r
ed
to
d
r
iv
e
th
e
E
V
at
s
p
ee
d
v
m
u
s
t c
o
m
p
en
s
ate
f
o
r
th
e
r
esis
tiv
e
f
o
r
ce
s
:
=
=
(
+
+
1
2
2
+
+
)
(
1
1
)
Un
d
er
th
e
FOC
s
tr
ateg
y
,
th
e
el
ec
tr
o
m
ag
n
etic
to
r
q
u
e
ca
n
b
e
s
i
m
p
lifie
d
as
(
1
2
)
:
=
(
1
2
)
wh
er
e
is
th
e
to
r
q
u
e
co
n
s
tan
t;
is
th
e
s
tato
r
cu
r
r
en
t c
o
m
p
o
n
en
t in
th
e
d
q
f
r
am
e.
Fro
m
th
e
v
eh
icle
d
y
n
am
ic
m
o
d
el
(
1
)
–
(
3
)
,
th
e
r
eq
u
ir
e
d
to
r
q
u
e
o
f
th
e
in
-
wh
ee
l
m
o
to
r
ca
n
b
e
ex
p
r
ess
ed
as
(
1
3
)
:
=
=
(
1
3
)
wh
er
e
is
th
e
s
tato
r
cu
r
r
en
t
c
o
m
m
an
d
c
o
r
r
esp
o
n
d
in
g
to
th
e
d
esire
d
to
r
q
u
e;
n
is
th
e
n
u
m
b
er
o
f
tr
ac
tio
n
m
o
to
r
s
in
th
e
E
V.
T
h
e
to
r
q
u
e
eq
u
atio
n
f
o
r
th
e
in
-
wh
ee
l SPI
M
is
g
iv
en
b
y
(
1
4
)
:
=
+
+
=
+
+
(
1
4
)
wh
er
e
is
th
e
m
o
m
en
t
o
f
in
er
tia
o
f
th
e
in
-
wh
ee
l
SP
I
M
in
clu
d
in
g
t
h
e
tire
;
B
is
th
e
v
is
co
u
s
co
ef
f
icien
t.
Ass
u
m
in
g
co
n
s
tan
t
SP
I
M
p
ar
am
eter
s
,
th
e
o
v
er
all
E
V
d
y
n
a
m
ic
m
o
d
el
i
n
clu
d
in
g
th
e
SP
I
M
to
r
q
u
e
eq
u
atio
n
is
wr
itten
as
(
1
5
a)
:
=
(
+
2
2
)
+
+
(
+
1
2
2
+
+
)
(
1
5
a)
Simp
lify
in
g
g
iv
es:
=
(
+
2
2
)
+
+
(
1
5
b
)
w
h
er
e
T
L
is
th
e
lo
ad
t
o
r
q
u
e
in
clu
d
in
g
e
f
f
ec
ts
f
r
o
m
r
o
llin
g
r
esis
tan
ce
,
ae
r
o
d
y
n
a
m
ic
d
r
a
g
,
r
o
a
d
s
lo
p
e,
an
d
ex
ter
n
al
d
is
tu
r
b
a
n
ce
s
.
3.
T
H
E
S
T
A
B
S_
P
CH
CO
NT
R
O
L
ST
R
UCT
URE F
O
R
F
O
C
-
B
AS
E
D
SPI
M
DR
I
VE
S
3
.
1
.
Desig
n o
f
t
he
ST
AB
S
co
ntr
o
ller
f
o
r
o
ute
r
s
peed
a
nd
f
lux
lo
o
ps
I
n
th
is
s
tu
d
y
,
an
ad
ap
tiv
e
VGST
AB
S
ap
p
r
o
ac
h
is
d
ev
elo
p
e
d
f
o
r
th
e
v
ec
to
r
co
n
tr
o
l
o
f
SP
I
M
d
r
iv
es.
T
h
e
s
tab
ilit
y
an
d
d
y
n
a
m
ic
b
eh
av
io
r
o
f
th
e
p
r
o
p
o
s
ed
c
o
n
tr
o
l
s
y
s
tem
ar
e
an
aly
ze
d
wit
h
in
th
e
L
y
ap
u
n
o
v
f
r
am
ewo
r
k
[
1
4
]
.
B
S
co
n
tr
o
l
p
r
o
v
id
es
a
r
ec
u
r
s
iv
e
p
r
o
ce
d
u
r
e
f
o
r
co
n
s
tr
u
ctin
g
n
o
n
lin
ea
r
co
n
tr
o
l
laws,
wh
er
e
a
v
ir
tu
al
co
n
tr
o
l
s
ig
n
al
is
in
tr
o
d
u
ce
d
t
o
g
u
a
r
an
tee
s
y
s
tem
co
n
v
er
g
en
ce
to
war
d
eq
u
ilib
r
iu
m
.
T
h
is
s
tr
ateg
y
en
ab
les
th
e
d
esig
n
o
f
r
o
b
u
s
t
c
o
n
tr
o
ller
s
ca
p
a
b
le
o
f
h
a
n
d
lin
g
v
ar
io
u
s
d
is
tu
r
b
an
ce
s
an
d
p
ar
a
m
eter
u
n
ce
r
tain
ties
.
T
o
f
u
r
th
er
en
h
an
ce
r
o
b
u
s
tn
ess
,
in
teg
r
al
ter
m
s
o
f
th
e
tr
ac
k
in
g
er
r
o
r
s
ar
e
in
co
r
p
o
r
ated
in
to
th
e
B
S
d
esig
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
1
,
Feb
r
u
ar
y
20
2
6
:
1
2
1
-
134
126
Mo
r
eo
v
er
,
th
e
m
o
d
if
ied
B
S
s
ch
em
e
is
co
m
b
in
ed
with
th
e
VGST
A
m
eth
o
d
,
wh
ich
s
tr
en
g
th
en
s
its
ab
ilit
y
to
co
p
e
with
p
ar
am
eter
v
a
r
iatio
n
s
an
d
lo
ad
d
is
tu
r
b
an
ce
s
wh
i
le
ef
f
ec
tiv
ely
r
ed
u
cin
g
th
e
c
h
atter
in
g
co
m
m
o
n
l
y
o
b
s
er
v
ed
in
co
n
v
en
tio
n
al
s
lid
i
n
g
-
m
o
d
e
co
n
tr
o
l m
eth
o
d
s
.
=
(
∗
−
)
+
∫
(
∗
−
)
0
=
(
∗
−
)
+
∫
(
∗
−
)
0
(
1
6
)
T
h
e
er
r
o
r
d
y
n
am
ical
eq
u
atio
n
s
ar
e
.
=
∗
.
−
3
2
∗
+
+
+
′
(
∗
−
)
.
=
∗
.
−
∗
+
1
+
′
(
∗
−
)
(
1
7
)
T
o
o
b
tain
th
e
v
ir
tu
al
co
n
tr
o
ller
o
f
s
p
ee
d
a
n
d
r
o
to
r
f
lu
x
lo
o
p
,
th
e
f
o
llo
win
g
L
y
a
p
u
n
o
v
f
u
n
ctio
n
ca
n
d
id
ate
is
co
n
s
id
er
ed
:
(
,
)
=
1
2
(
2
+
2
)
(
1
8
)
Dif
f
er
en
tiatin
g
V
an
d
c
o
m
b
in
i
n
g
f
o
r
m
u
la
(
5
)
,
we
g
et:
(
,
)
.
=
.
+
.
=
[
∗
.
−
+
+
+
′
(
∗
−
)
+
{
∗
.
−
∗
+
1
+
′
(
∗
−
)
}
(
1
9
)
wh
er
e:
kω
,
kѰ
ar
e
p
o
s
itiv
e
co
n
s
tan
ts
=
3
2
δσ
L
;
T
o
V'
<0
,
th
e
s
tab
ilizin
g
v
ir
tu
al
co
n
tr
o
ls
ar
e
ch
o
s
en
as (
2
0
)
.
∗
=
1
{
+
∗
.
+
+
+
′
(
∗
−
)
}
+
∗
=
{
+
∗
.
+
1
+
′
(
∗
−
)
}
+
(
2
0
)
wh
er
e,
,
ar
e
th
e
co
n
tr
o
l
s
ig
n
als
in
jecte
d
in
o
r
d
er
to
im
p
r
o
v
e
d
th
e
p
er
f
o
r
m
a
n
ce
o
f
B
S
co
n
tr
o
ller
.
T
h
e
lo
a
d
to
r
q
u
e
T
L
is
esti
m
ated
:
=
1
1
+
0
[
(
3
2
^
)
−
]
;
(
2
1
)
wh
er
e:
τ
0
: is tim
e
g
ain
; p
: d
if
f
er
en
tial.
T
h
e
v
a
r
iab
le
-
g
ain
s
ec
o
n
d
-
o
r
d
er
s
lid
in
g
m
o
d
e
s
tr
ateg
y
a
d
ju
s
ts
its
g
ain
b
ased
o
n
th
e
r
ea
l
d
is
tu
r
b
an
ce
b
o
u
n
d
,
th
er
e
b
y
m
itig
atin
g
t
h
e
in
ten
s
ity
o
f
ch
atter
in
g
.
I
n
th
is
f
r
am
ewo
r
k
,
th
e
s
u
p
er
-
tw
is
tin
g
alg
o
r
ith
m
is
en
h
an
ce
d
with
a
v
ar
iab
le
-
g
ain
m
ec
h
an
is
m
to
co
m
p
en
s
ate
f
o
r
d
is
tu
r
b
an
ce
s
w
h
o
s
e
g
r
a
d
ien
t
b
o
u
n
d
s
d
e
p
en
d
o
n
th
e
s
y
s
tem
s
tates.
Acc
o
r
d
in
g
to
[
3
0
]
–
[
3
2
]
,
th
e
p
r
o
p
o
s
ed
v
ar
iab
le
-
g
ai
n
s
u
p
er
-
twis
tin
g
alg
o
r
ith
m
(
V
GSTA
)
is
f
o
r
m
u
lated
as
(
2
2
)
:
{
1
(
)
=
(
,
)
[
1
1
(
1
)
+
1
∫
2
(
1
)
0
]
2
(
)
=
(
,
)
[
2
1
(
2
)
+
2
∫
2
(
2
)
0
]
(
2
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
A
n
en
h
a
n
ce
d
imp
r
o
ve
d
a
d
a
p
t
ive
b
a
ck
s
tep
p
in
g
–
s
ec
o
n
d
-
o
r
d
e
r
s
lid
in
g
mo
d
e
…
(
Ho
a
n
g
Da
t
P
h
a
m
)
127
wh
er
e,
{
(
,
)
=
1
(
1
)
(
,
)
=
2
(
2
)
1
(
)
=
|
|
1
2
(
)
+
3
2
(
)
=
1
2
(
)
+
3
2
3
|
|
1
2
(
)
+
3
2
(
23)
Fro
m
(
1
9
)
-
(
2
0
)
a
n
d
(
2
2
)
-
(
2
3
)
,
we
o
b
tain
:
(
,
)
=
−
2
−
2
−
−
<
0
(
2
4
)
T
h
e
v
ir
t
u
al
co
n
tr
o
ls
in
(
2
0
)
a
r
e
ch
o
s
en
to
s
atis
f
y
th
e
c
o
n
tr
o
l
o
b
jectiv
es
a
n
d
also
p
r
o
v
id
e
r
ef
er
e
n
ce
s
f
o
r
th
e
n
ex
t step
o
f
t
h
e
VGST
A
SM
co
n
tr
o
ller
d
esig
n
.
3
.
2
.
SM
C
des
ig
n
wit
h t
he
v
a
ria
ble
-
g
a
in s
up
er
-
t
wis
t
ing
a
l
g
o
rit
hm
f
o
r
in t
he
inn
er
curr
ent
lo
o
ps
I
n
th
is
p
ar
t,
a
h
ig
h
-
o
r
d
er
n
o
n
lin
ea
r
s
lid
in
g
co
n
tr
o
l
alg
o
r
ith
m
b
ased
o
n
L
y
a
p
u
n
o
v
s
tab
ilit
y
th
eo
r
y
u
s
in
g
th
e
v
ar
iab
le
-
g
ain
s
u
p
er
-
t
wis
tin
g
alg
o
r
ith
m
is
p
r
o
p
o
s
ed
f
o
r
th
e
in
n
e
r
c
u
r
r
en
t
lo
o
p
s
to
i
n
cr
ea
s
e
r
o
b
u
s
tn
ess
o
f
o
v
er
all
s
y
s
tem
,
m
in
im
izin
g
th
e
ef
f
ec
ts
o
f
p
ar
am
eter
v
ar
ia
tio
n
s
an
d
u
n
f
o
r
eseen
d
is
tu
r
b
a
n
ce
s
in
th
e
co
n
tr
o
l
p
r
o
ce
s
s
.
T
h
e
cu
r
r
en
t e
r
r
o
r
t
r
ac
k
in
g
f
u
n
ctio
n
d
ef
in
e
d
:
=
∗
−
;
=
∗
−
(
2
5
)
T
h
e
co
r
r
esp
o
n
d
i
n
g
n
o
n
lin
ea
r
s
lip
s
u
r
f
ac
e
ac
co
r
d
in
g
t
o
th
e
cu
r
r
en
t c
o
m
p
o
n
e
n
ts
is
d
ef
in
ed
as
(
2
6
)
:
{
3
=
is
+
4
|
∫
is
|
1
2
(
∫
is
)
4
=
isq
+
5
|
∫
isq
|
1
2
(
∫
isq
)
(
2
6
)
C
o
m
b
in
in
g
f
o
r
m
u
la
(
5
)
,
tak
in
g
th
e
tim
e
d
if
f
er
en
tial o
n
b
o
t
h
s
id
es o
f
(
2
6
)
,
we
g
et:
3
=
is
+
[
4
|
∫
is
|
1
2
(
∫
is
)
]
=
∗
−
1
[
-
a
i
sd
+
L
sq
+
b
R
rd
+
c
u
sd
]
+
[
4
|
∫
is
|
1
2
(
∫
is
)
]
=
−
3
(
2
7
)
4
=
isq
+
5
|
∫
isq
|
1
2
(
∫
isq
)
=
∗
−
1
[
-
a
i
sq
-
L
sd
-
b
rd
+
c
u
sq
]
+
[
5
|
∫
isq
|
1
2
(
∫
isq
)
]
=
−
4
I
n
th
e
p
r
o
p
o
s
ed
m
eth
o
d
,
we
s
elec
t
th
e
ν
₃
an
d
ν
₄
s
witch
in
g
co
n
tr
o
l
f
u
n
ctio
n
s
,
b
ased
o
n
th
e
d
esig
n
p
r
in
cip
les
p
r
esen
ted
in
{
3
(
)
=
1
(
,
is
)
[
1
1
(
3
)
+
1
∫
2
(
3
)
0
]
4
(
)
=
2
(
,
isq
)
[
2
1
(
4
)
+
2
∫
2
(
4
)
0
]
(
2
8
)
wh
er
e,
{
1
(
,
is
)
=
3
(
3
)
2
(
,
isq
)
=
4
(
4
)
1
(
)
=
|
|
1
2
(
)
+
6
2
(
)
=
1
2
(
)
+
3
2
6
|
|
1
2
(
)
+
6
2
(
2
9
)
W
ith
x
=
1
:
2
,
k4
,
k5
,
k6
,
δ
1
,
δ
2
,
μ
1
,
μ2
a
r
e
p
o
s
itiv
e
co
ef
f
icie
n
ts
.
Fro
m
(
2
7
)
t
h
e
v
ir
t
u
al
co
n
t
r
o
l
f
u
n
ctio
n
s
o
f
th
e
cu
r
r
en
t c
o
n
tr
o
l lo
o
p
a
r
e
d
eter
m
in
ed
as f
o
llo
ws:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
1
,
Feb
r
u
ar
y
20
2
6
:
1
2
1
-
134
128
{
∗
=
{
3
(
)
+
∗
+
[
4
|
∫
is
|
1
2
(
∫
is
)
]
}
+
1
[
a
i
sd
-
L
sq
-
b
R
rd
]
∗
=
{
4
(
)
+
∗
+
[
5
|
∫
isq
|
1
2
(
∫
isq
)
]
}
+
1
[
a
i
sq
+
L
sd
+
b
rd
]
(
3
0
)
W
e
s
elec
t th
e
L
y
ap
u
n
o
v
f
u
n
cti
o
n
:
=
1
2
[
3
2
+
4
2
]
(
3
1
)
Dif
f
er
en
tiate
b
o
th
s
id
es o
f
(
3
1
)
,
co
m
b
i
n
e
with
f
o
r
m
u
las (
2
7
)
an
d
(
2
8
)
to
g
et:
=
3
3
+
4
4
=
−
1
(
,
is
)
1
[
1
(
3
)
+
∫
2
(
3
)
0
]
−
2
(
,
isq
)
4
[
1
(
4
)
+
∫
2
(
4
)
0
]
(
3
2
)
Fro
m
(
3
2
)
,
we
s
ee
th
at
th
e
d
i
f
f
er
en
tial
o
f
th
e
L
y
ap
u
n
o
v
f
u
n
ctio
n
is
alwa
y
s
n
eg
ativ
e.
T
h
er
ef
o
r
e,
th
e
s
y
s
tem
is
alwa
y
s
s
tab
le.
4.
SI
M
UL
A
T
I
O
N
A
ND
DI
SC
USSI
O
N
T
o
v
alid
ate
th
e
ef
f
ec
tiv
en
ess
an
d
r
o
b
u
s
tn
ess
o
f
th
e
p
r
o
p
o
s
e
d
I
AB
SS
OSM
co
n
tr
o
l
s
tr
ateg
y
,
d
etailed
s
im
u
latio
n
s
wer
e
co
n
d
u
cted
u
s
in
g
MA
T
L
AB
/Si
m
u
lin
k
o
n
a
n
elec
tr
ic
v
eh
icle
(
E
V)
p
r
o
p
u
ls
io
n
s
y
s
tem
d
r
iv
e
n
b
y
a
s
ix
-
p
h
ase
in
d
u
ctio
n
m
o
to
r
(
SP
I
M)
.
T
h
e
p
r
im
ar
y
o
b
j
ec
tiv
e
o
f
th
is
s
im
u
latio
n
s
tu
d
y
is
to
ass
e
s
s
th
e
d
y
n
am
ic
p
er
f
o
r
m
a
n
ce
,
r
ef
er
e
n
ce
s
p
ee
d
tr
ac
k
in
g
ac
c
u
r
ac
y
,
to
r
q
u
e
r
esp
o
n
s
e
q
u
ality
,
an
d
r
o
b
u
s
tn
ess
ag
ain
s
t
d
is
tu
r
b
an
ce
s
an
d
p
a
r
am
eter
v
ar
iatio
n
s
.
Fig
u
r
e
4
illu
s
tr
ates
th
e
co
m
p
lete
FOC
-
b
ased
v
ec
to
r
co
n
tr
o
l
s
y
s
tem
u
tili
zin
g
th
e
p
r
o
p
o
s
ed
h
y
b
r
id
s
tr
u
ctu
r
e.
Fig
u
r
e
4
.
FOC
v
ec
to
r
c
o
n
tr
o
l
o
f
SP
I
M
d
r
iv
e
u
s
in
g
n
o
v
el
im
p
r
o
v
e
d
B
S_
SM
co
n
tr
o
l stru
ctu
r
e
T
h
e
test
p
r
o
f
iles
in
clu
d
e
a
m
o
d
if
ied
E
C
E
-
4
0
u
r
b
an
d
r
i
v
in
g
cy
cle,
an
en
h
a
n
ce
d
E
C
E
-
1
5
c
y
cle,
an
d
a
s
tep
s
p
ee
d
r
ef
er
en
ce
p
r
o
f
ile,
b
ased
o
n
s
tan
d
ar
d
d
r
iv
e
p
atter
n
s
f
r
o
m
[
2
]
,
[
1
1
]
,
[
1
8
]
,
an
d
[
2
5
]
.
T
h
e
SP
I
M
m
o
to
r
Po
w
er
c
irc
uit
A
C
S
up
pl
y 3
~
D
C
l
i
n
k
S
P
V
S
I
V
G
S
T
A
B
S
C
ont
r
ol
l
e
r
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I
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