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sm
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t
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e
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re
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e
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targ
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b
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t
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e
p
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v
e
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ti
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n
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l
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m
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ra
c
ti
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sm
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x
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.
K
ey
w
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d
s
:
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n
h
an
ce
d
r
ea
ch
in
g
law
FOC
Fu
zz
y
lo
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ic
alg
o
r
ith
m
Mo
to
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s
p
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PMSM
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s
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CC B
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SA
li
c
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n
se
.
C
o
r
r
e
s
p
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ing
A
uth
o
r
:
Min
h
Du
c
Ph
am
Po
wer
E
lectr
o
n
ics R
esear
ch
L
ab
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ato
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y
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Facu
lty
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n
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in
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f
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HC
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2
6
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n
g
Kiet
Stre
et,
Dis
tr
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1
0
,
Ho
C
h
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h
C
ity
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V
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c@
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cm
u
t.e
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u
.
v
n
1.
I
NT
RO
D
UCT
I
O
N
Per
m
an
en
t
m
ag
n
et
s
y
n
ch
r
o
n
o
u
s
m
o
to
r
s
(
PMSMs)
ar
e
n
o
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s
ed
in
m
an
y
a
p
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licatio
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to
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ig
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-
p
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d
en
s
ity
,
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f
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c
y
,
a
n
d
t
o
r
q
u
e
-
to
-
c
u
r
r
en
t
r
atio
.
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h
eir
s
p
ee
d
p
er
f
o
r
m
an
ce
is
s
ig
n
if
ican
t,
an
d
th
ey
ar
e
cr
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in
ap
p
li
ca
tio
n
s
s
u
ch
as
r
o
b
o
tics
,
elec
tr
ic
v
eh
icles,
an
d
m
ac
h
in
e
to
o
ls
[
1
]
,
[
2
]
.
I
n
an
ex
ca
v
ato
r
,
f
o
r
in
s
tan
ce
,
s
u
ita
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le
s
p
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r
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u
latio
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n
ab
les
th
e
m
ac
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e
to
m
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p
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is
ely
an
d
e
f
f
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tiv
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m
ex
ca
v
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n
o
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er
atio
n
s
.
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t
en
s
u
r
es
th
at
liftin
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a
n
d
lo
wer
in
g
h
ea
v
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lo
ad
s
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e
d
o
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e
s
m
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th
ly
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n
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s
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o
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n
al
s
af
ety
wh
en
u
s
e
d
b
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cr
a
n
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n
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elev
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s
.
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o
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t
r
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l
l
i
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g
t
h
e
s
p
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e
d
o
f
a
P
MS
M
is
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l
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t
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v
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(
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V
s
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f
o
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ac
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e
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at
i
o
n
,
m
a
i
n
t
a
i
n
i
n
g
c
o
n
s
t
a
n
t
v
el
o
c
i
t
y
,
a
n
d
e
f
f
e
c
t
i
v
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l
y
o
p
e
r
a
ti
n
g
r
e
g
en
e
r
a
t
i
v
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b
r
a
k
i
n
g
.
I
n
c
o
n
t
r
a
s
t
,
t
o
r
q
u
e
c
o
n
t
r
o
l
i
s
c
o
m
m
o
n
i
n
h
e
a
v
y
i
n
d
u
s
t
r
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a
p
p
l
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c
a
t
i
o
n
s
s
u
c
h
a
s
e
x
c
a
v
at
o
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s
a
n
d
p
r
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d
u
c
t
c
o
n
v
e
y
o
r
b
e
l
t
s
.
T
h
e
i
m
p
o
r
t
a
n
c
e
o
f
s
p
e
e
d
c
o
n
tr
o
l
v
e
r
s
u
s
t
o
r
q
u
e
c
o
n
t
r
o
l
v
a
r
ie
s
s
i
g
n
i
f
i
c
a
n
t
l
y
d
e
p
e
n
d
i
n
g
o
n
a
p
p
l
i
c
a
ti
o
n
.
I
n
t
h
is
r
e
s
e
a
r
c
h
,
we
a
r
e
p
a
r
ti
c
u
l
a
r
l
y
f
o
c
u
s
e
d
o
n
d
e
s
i
g
n
i
n
g
a
s
p
e
e
d
c
o
n
tr
o
l
l
e
r
f
o
r
P
MS
M
m
o
t
o
r
i
n
E
V
ac
c
e
l
e
r
a
ti
o
n
s
y
s
t
e
m
s
.
PMSMs
ar
e
ch
ar
ac
ter
ized
b
y
n
o
n
lin
ea
r
a
n
d
m
u
lti
-
v
ar
iab
le
d
y
n
am
ics
in
f
lu
en
ce
d
b
y
f
lu
x
lin
k
ag
e
a
n
d
d
ir
ec
t
-
q
u
a
d
r
atu
r
e
o
r
DQ
-
a
x
es in
d
u
ctan
ce
s
,
wh
ich
ca
n
v
ar
y
d
u
r
in
g
m
o
to
r
o
p
er
ati
o
n
d
u
e
to
m
ag
n
etic
s
atu
r
atio
n
.
I
t
is
also
d
if
f
icu
lt
to
p
r
o
d
u
ce
b
o
th
h
ig
h
ac
cu
r
ac
y
an
d
s
p
ee
d
,
as
PMSMs
ex
h
ib
it
s
tr
o
n
g
n
o
n
lin
ea
r
ity
d
u
e
to
th
e
s
tr
o
n
g
co
u
p
lin
g
b
etwe
en
to
r
q
u
e
an
d
s
p
ee
d
i
n
a
m
ec
h
an
ical
m
o
d
el.
T
o
ad
d
r
ess
th
e
co
m
p
lex
i
s
s
u
es a
r
is
in
g
f
r
o
m
th
e
m
ec
h
an
ical
eq
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n
o
f
P
MSM
s
,
th
e
f
ield
-
o
r
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ted
c
o
n
t
r
o
l
(
FOC
)
tech
n
iq
u
e
em
e
r
g
ed
[
3
]
-
[5
].
In
th
e
FOC
tech
n
iq
u
e,
th
e
m
o
t
o
r
co
n
tr
o
l
s
y
s
tem
is
tr
an
s
f
o
r
m
ed
in
to
a
s
y
n
ch
r
o
n
o
u
s
r
ef
er
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f
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s
im
p
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in
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th
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co
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task
b
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p
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th
e
to
r
q
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e
an
d
f
lu
x
co
m
p
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n
e
n
ts
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
Dr
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N:
2088
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(
K
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)
419
T
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th
e
PMSM
m
o
to
r
s
p
ee
d
,
th
e
lin
ea
r
PI
co
n
tr
o
ller
is
em
p
lo
y
ed
to
ad
ju
s
t
th
e
q
cu
r
r
e
n
t
r
ef
er
en
ce
o
f
t
h
e
in
n
e
r
co
n
tr
o
l
lo
o
p
f
o
r
t
r
ac
k
in
g
m
o
to
r
s
p
e
ed
[
6
]
-
[
8
]
.
Alth
o
u
g
h
PI
s
p
ee
d
co
n
tr
o
l
o
f
f
er
s
ad
eq
u
a
te
co
n
tr
o
l
p
r
ec
is
io
n
a
n
d
r
o
b
u
s
tn
ess
,
it
o
f
ten
f
alls
s
h
o
r
t
in
ter
m
s
o
f
s
lo
w
r
esp
o
n
s
e
an
d
s
tab
ilit
y
wh
en
c
o
n
f
r
o
n
te
d
with
d
is
tu
r
b
an
ce
s
s
u
c
h
as
lo
ad
ch
an
g
es
an
d
v
ar
iatio
n
s
in
s
p
ee
d
[
9
]
,
[
1
0
]
.
C
o
n
v
en
tio
n
al
s
tu
d
ies
o
n
PMSM
s
p
ee
d
co
n
tr
o
l
u
s
in
g
th
e
PI
co
n
tr
o
ller
s
p
ec
if
ically
h
i
g
h
lig
h
t
s
ig
n
if
ican
t
ch
allen
g
es
r
elate
d
to
s
p
ee
d
r
e
s
p
o
n
s
e
an
d
s
tab
ilit
y
[
1
1
]
-
[
1
3
]
.
T
h
at
is
b
ec
au
s
e
s
p
ee
d
r
eg
u
latio
n
ten
d
s
to
b
e
a
lin
ea
r
ca
lcu
latio
n
,
b
u
t
PMSM
d
y
n
am
ics
ar
e
n
o
n
-
lin
ea
r
.
Fo
r
th
is
r
ea
s
o
n
,
m
o
r
e
im
p
r
o
v
ed
c
o
n
tr
o
l
m
eth
o
d
s
ar
e
n
ee
d
ed
to
im
p
r
o
v
e
th
e
s
lo
w
r
e
s
p
o
n
s
e
p
r
o
b
lem
an
d
s
y
s
tem
s
tab
ilit
y
.
No
n
lin
ea
r
co
n
tr
o
l
tech
n
iq
u
es
h
av
e
em
er
g
ed
as
p
o
ten
tial
alter
n
ativ
es
th
at
ca
n
ad
d
r
ess
th
e
lim
itatio
n
s
o
f
lin
ea
r
c
o
n
tr
o
ller
s
[
1
4
]
-
[
1
6
]
.
No
n
lin
ea
r
co
n
tr
o
l
tech
n
iq
u
es
s
u
ch
as
ad
ap
tiv
e
c
o
n
tr
o
l,
p
r
e
d
ictiv
e
co
n
tr
o
l,
an
d
s
lid
in
g
m
o
d
e
co
n
tr
o
l
h
av
e
d
e
m
o
n
s
tr
ated
th
e
p
o
ten
tial
to
im
p
r
o
v
e
th
e
s
tab
ilit
y
,
p
r
ec
is
io
n
,
an
d
r
o
b
u
s
tn
ess
o
f
PMSM
m
o
to
r
co
n
tr
o
l.
Ad
ap
ti
v
e
co
n
tr
o
l
ca
n
h
an
d
le
u
n
ce
r
tai
n
ties
b
y
ad
ju
s
tin
g
c
o
n
tr
o
l
p
ar
a
m
eter
s
in
r
ea
l
-
tim
e
,
but
it
n
ee
d
s
ac
cu
r
ate
s
y
s
tem
p
ar
am
eter
s
an
d
m
ay
ca
u
s
e
s
y
s
tem
in
s
tab
ilit
y
[
1
7
]
-
[
1
9
]
.
Ho
wev
er
,
o
n
th
e
o
t
h
er
h
an
d
,
p
r
ed
ictiv
e
c
o
n
tr
o
l
i
n
v
o
lv
es
p
r
ed
ictin
g
f
u
tu
r
e
s
y
s
tem
b
eh
av
io
r
wh
ich
is
ab
le
to
a
ch
iev
e
s
atis
f
ac
to
r
y
p
er
f
o
r
m
an
ce
b
u
t
at
h
ig
h
co
m
p
u
tatio
n
al
co
s
ts
an
d
s
en
s
itiv
ity
d
u
e
to
s
y
s
tem
m
is
m
atch
es
[
2
0
]
-
[
2
2
]
.
Sli
d
in
g
m
o
d
e
co
n
tr
o
l
p
r
o
v
id
es
r
o
b
u
s
tn
ess
in
th
e
p
r
esen
ce
o
f
u
n
ce
r
tain
tie
s
an
d
d
is
tu
r
b
an
ce
s
u
s
in
g
d
is
co
n
tin
u
o
u
s
co
n
tr
o
ls
;
h
o
wev
er
,
it
m
ay
i
n
tr
o
d
u
ce
ch
atter
in
g
p
r
o
b
lem
s
[
2
3
]
-
[
2
5
]
.
T
h
e
u
s
e
o
f
s
lid
in
g
m
o
d
e
co
n
t
r
o
l
is
im
p
o
r
ta
n
t
f
o
r
s
tab
ilit
y
r
ea
s
o
n
s
in
th
e
p
r
esen
c
e
o
f
d
is
tu
r
b
a
n
ce
s
an
d
u
n
ce
r
tai
n
ties
.
Giv
en
th
e
d
r
awb
ac
k
s
o
f
p
r
ev
i
o
u
s
wo
r
k
s
,
it r
eq
u
ir
es a
n
im
p
r
o
v
ed
co
n
tr
o
l
law
an
d
r
ea
ch
i
n
g
co
n
d
itio
n
s
f
o
r
ch
atter
in
g
atten
u
atio
n
al
o
n
g
with
s
p
ee
d
r
esp
o
n
s
e
im
p
r
o
v
em
en
ts
.
An
e
n
h
an
ce
d
s
lid
i
n
g
m
o
d
e
c
o
n
tr
o
l
is
p
r
esen
ted
in
th
is
p
ap
er
t
o
im
p
r
o
v
e
c
o
n
tr
o
l
r
esp
o
n
s
e
an
d
s
t
ab
ilit
y
with
r
ed
u
ce
d
c
h
atter
in
g
.
A
s
lid
in
g
s
u
r
f
ac
e
with
th
e
im
p
r
o
v
ed
r
ea
ch
in
g
la
w
is
ad
d
ed
in
th
is
p
r
o
p
o
s
ed
c
o
n
tr
o
l
a
p
p
r
o
ac
h
,
w
h
ich
also
i
n
clu
d
es
f
u
zz
y
lo
g
ic
co
n
tr
o
l
in
te
g
r
atio
n
.
T
h
ese
m
o
d
if
icatio
n
s
will
allo
w
th
e
s
y
s
tem
s
tate
to
ar
r
iv
e
at
th
e
s
lid
in
g
s
u
r
f
ac
e
as
f
ast
as
p
o
s
s
ib
le
an
d
r
ed
u
ce
ch
atter
in
g
o
f
co
n
tr
o
l
ac
tio
n
s
th
an
k
s
to
th
e
ad
ju
s
tab
le
s
lid
in
g
g
ain
.
Fu
r
th
er
m
o
r
e,
th
e
s
y
s
tem
is
alwa
y
s
s
tab
le
wi
th
th
is
d
ef
in
ed
r
ea
ch
i
n
g
law
.
T
h
is
co
n
tr
o
l
ap
p
r
o
ac
h
n
o
t
o
n
ly
p
r
o
v
id
es
s
m
o
o
th
er
d
y
n
am
ics
b
u
t
also
o
b
tain
a
s
h
o
r
ter
r
esp
o
n
s
e
tim
e
th
an
th
e
c
o
n
v
e
n
tio
n
al
s
lid
in
g
m
o
d
e
c
o
n
tr
o
l.
T
h
e
co
n
tr
o
l
th
eo
r
y
is
v
er
if
ied
b
y
m
ea
n
s
o
f
ex
p
er
im
en
tal
r
esu
lts
with
a
s
m
all
-
s
ca
le
P
MSM
s
y
s
tem
.
2.
F
O
C
AND
M
A
T
H
E
M
AT
I
C
AL
M
O
D
E
L
O
F
P
M
SM
2
.
1
.
P
rinciple o
f
F
O
C
a
lg
o
rit
hm
I
n
p
er
m
a
n
en
t
m
ag
n
et
s
y
n
ch
r
o
n
o
u
s
m
o
to
r
s
,
th
e
s
tato
r
cu
r
r
en
t
af
f
ec
ts
b
o
th
th
e
m
ag
n
etic
f
l
u
x
an
d
th
e
g
en
er
ated
to
r
q
u
e.
Hen
ce
,
f
ield
-
o
r
ien
ted
co
n
tr
o
l
was
p
r
o
p
o
s
e
d
to
d
ec
o
u
p
le
f
lu
x
an
d
to
r
q
u
e
ca
n
b
e
a
ch
iev
ed
b
y
an
aly
zin
g
th
e
in
s
tan
tan
eo
u
s
c
u
r
r
en
t
in
to
two
co
m
p
o
n
en
ts
:
On
e
co
m
p
o
n
e
n
t
alig
n
ed
with
th
e
r
o
to
r
m
ag
n
etic
f
ield
,
ca
lled
th
e
d
ir
ec
t
ax
is
(
d
)
,
an
d
th
e
o
th
er
p
er
p
en
d
ic
u
lar
to
th
e
r
o
to
r
m
ag
n
etic
f
ield
,
ca
lled
th
e
q
u
ad
r
atu
r
e
ax
is
(
q
)
[
2
6
]
.
Field
-
o
r
ien
ted
c
o
n
tr
o
l
is
th
e
b
asic
id
ea
o
f
s
y
n
th
esizin
g
s
in
u
s
o
id
al
in
v
e
r
t
er
v
o
ltag
e
to
p
r
o
v
id
e
p
r
o
g
r
ess
iv
e
s
p
ee
d
co
n
tr
o
l
with
o
p
tim
al
to
r
q
u
e
o
u
tp
u
t.
Ma
x
im
u
m
to
r
q
u
e
is
r
ea
ch
ed
wh
en
th
e
an
g
le
b
etwe
en
th
e
m
ag
n
etic
f
ield
s
o
f
th
e
s
tato
r
a
n
d
r
o
t
o
r
b
ec
o
m
es
9
0
d
eg
r
ee
s
.
T
h
e
s
tato
r
m
ag
n
etic
f
lu
x
is
ali
g
n
ed
o
r
th
o
g
o
n
ally
to
th
e
r
o
to
r
b
y
f
o
r
cin
g
th
e
d
-
ax
is
cu
r
r
en
t to
0
an
d
p
r
o
p
er
l
y
ad
ju
s
tin
g
th
e
q
-
ax
is
.
2
.
2
.
Co
o
rdina
t
io
n bet
wee
n
s
peed
co
ntr
o
ller
a
nd
F
O
C
T
h
e
b
lo
c
k
d
ia
g
r
am
o
f
a
co
n
v
en
tio
n
al
s
p
ee
d
co
n
tr
o
ller
with
FOC
with
s
p
ee
d
co
n
tr
o
ller
is
s
h
o
wn
in
Fig
u
r
e
1
.
I
n
th
e
f
ig
u
r
e
,
t
h
e
co
n
tr
o
l
p
r
o
ce
s
s
b
eg
in
s
with
m
ea
s
u
r
in
g
th
e
m
o
to
r
th
r
ee
-
p
h
ase
cu
r
r
en
ts
,
wh
ich
ar
e
th
en
tr
an
s
f
o
r
m
e
d
th
r
o
u
g
h
C
lar
k
an
d
Par
k
tr
a
n
s
f
o
r
m
atio
n
s
to
o
b
tain
cu
r
r
en
ts
alo
n
g
th
e
i
n
d
ep
en
d
e
n
t
d
an
d
q
ax
es.
T
h
en
,
th
e
c
u
r
r
e
n
t r
o
to
r
s
p
ee
d
is
co
m
p
ar
ed
with
th
e
r
ef
er
en
ce
s
p
ee
d
(
∗
)
to
g
e
n
er
ate
a
s
p
ee
d
er
r
o
r
s
ig
n
al
(
1
=
(
∗
−
)
)
,
wh
ich
is
f
ed
in
to
an
o
u
ter
s
p
ee
d
co
n
tr
o
ller
to
p
r
o
d
u
ce
a
r
e
f
er
en
ce
cu
r
r
en
t a
l
o
n
g
th
e
q
-
ax
i
s
(
∗
)
.
In
th
e
in
n
er
co
n
tr
o
l
lo
o
p
,
t
wo
PI
co
n
tr
o
ller
s
ar
e
u
tili
ze
d
to
r
eg
u
late
th
e
cu
r
r
en
ts
alo
n
g
th
e
d
an
d
q
a
x
es,
g
en
er
atin
g
r
ef
er
e
n
ce
v
o
lta
g
e
s
ig
n
als
alo
n
g
t
h
ese
ax
es
in
d
ep
e
n
d
en
tly
(
,
)
.
Fo
llo
win
g
th
is
,
in
v
er
s
e
C
lar
k
an
d
Par
k
tr
an
s
f
o
r
m
atio
n
s
ar
e
ap
p
li
ed
to
co
n
v
er
t
th
e
v
o
ltag
e
s
ig
n
a
ls
f
r
o
m
th
e
d
q
ax
es
to
th
r
ee
-
p
h
ase
v
o
ltag
e
s
ig
n
als
f
o
r
th
e
s
p
ac
e
v
ec
to
r
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
SVPW
M
)
b
lo
ck
.
T
h
e
SVPW
M
is
a
m
o
d
u
latio
n
tech
n
iq
u
e
u
s
ed
to
g
en
er
ate
PW
M
s
ig
n
als f
o
r
co
n
tr
o
llin
g
th
e
s
witch
in
g
d
ev
ices in
an
in
v
e
r
ter
[
2
7
]
-
[
2
9
]
.
2
.
3
.
M
a
t
hem
a
t
ica
l
m
o
del o
f
P
M
SM
T
o
im
p
lem
e
n
t
th
e
FOC
alg
o
r
ith
m
o
n
a
d
ig
ital
p
r
o
ce
s
s
o
r
,
a
m
at
h
em
atica
l
m
o
d
el
o
f
th
e
m
o
to
r
is
ess
en
tial.
T
h
r
o
u
g
h
th
e
C
lar
k
a
n
d
Par
k
tr
an
s
f
o
r
m
atio
n
,
th
e
m
ath
em
atica
l
m
o
d
el
o
f
th
e
PMSM
is
tr
an
s
f
o
r
m
ed
in
to
th
e
f
o
llo
win
g
m
ath
em
atic
al
r
ep
r
esen
tatio
n
in
th
e
DQ
f
r
a
m
e.
W
h
er
e
,
ar
e
d
-
ax
is
an
d
q
-
a
x
is
v
o
ltag
es,
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
.
1
,
Ma
r
c
h
20
2
5
:
418
-
430
420
,
ar
e
d
-
ax
is
an
d
q
-
a
x
is
cu
r
r
en
t
s
,
,
ar
e
d
-
ax
is
an
d
q
-
ax
is
in
d
u
ctan
ce
,
is
co
il
r
esis
tan
ce
,
is
th
e
elec
tr
ical
s
p
ee
d
o
f
th
e
r
o
to
r
,
is
th
e
m
ec
h
an
ical
an
g
u
lar
s
p
ee
d
o
f
th
e
r
o
to
r
,
an
d
is
p
er
m
an
en
t
m
ag
n
et
f
lu
x
lin
k
ag
e.
Fo
r
t
h
e
s
tead
y
s
tate,
t
h
e
d
if
f
er
en
tial te
r
m
s
ca
n
b
e
d
i
s
r
eg
ar
d
ed
s
in
ce
th
e
r
e
ar
e
n
o
v
ar
iatio
n
s
in
cu
r
r
e
n
ts
,
th
e
(
1
)
ca
n
b
e
s
im
p
lifie
d
as
(
2
)
.
{
=
−
+
=
+
(
+
)
+
(
1
)
{
=
−
=
+
(
+
)
(
2
)
T
h
e
r
elatio
n
s
h
ip
b
etwe
en
elec
tr
o
m
ag
n
etic
to
r
q
u
e
a
n
d
th
e
d
an
d
q
-
a
x
is
cu
r
r
en
ts
in
th
e
DQ
r
ef
er
en
ce
f
r
am
e
is
g
iv
en
b
y
th
e
(
3
)
:
{
=
3
2
[
+
(
−
)
]
−
=
(
3
)
w
h
er
e
is
elec
tr
o
m
ag
n
eti
c
to
r
q
u
e,
is
lo
ad
to
r
q
u
e,
is
n
u
m
b
er
o
f
th
e
p
o
le
p
air
s
,
is
in
er
tia
m
o
m
en
t.
I
n
th
e
FOC
alg
o
r
ith
m
,
ass
u
m
in
g
th
e
an
g
le
is
ac
cu
r
ately
m
ea
s
u
r
ed
f
r
o
m
th
e
m
o
to
r
,
to
ac
h
iev
e
th
e
o
p
tim
al
to
r
q
u
e,
co
n
tr
o
llin
g
th
e
cu
r
r
en
t
=
0
is
n
ec
e
s
s
ar
y
.
T
h
e
n
,
t
h
e
d
y
n
a
m
i
c
e
q
u
a
t
i
o
n
o
f
t
h
e
P
M
S
M
m
o
t
o
r
i
s
s
i
m
p
l
i
f
i
e
d
a
s
(
4
)
.
{
=
3
2
3
2
−
=
(
4
)
I
n
(
4
)
,
th
e
r
elatio
n
s
h
ip
b
etwe
e
n
th
e
m
ec
h
an
ical
an
g
u
lar
s
p
ee
d
o
f
th
e
r
o
to
r
an
d
th
e
co
n
t
r
o
ll
ed
cu
r
r
en
t
o
n
th
e
q
u
ad
r
atu
r
e
ax
is
(
)
is
d
eter
m
in
ed
.
T
h
is
r
elatio
n
s
h
ip
f
o
r
m
s
th
e
f
u
n
d
am
en
tal
e
q
u
atio
n
f
o
r
co
n
tr
o
llin
g
th
e
m
ec
h
an
ical
an
g
u
lar
s
p
ee
d
t
o
g
en
er
ate
th
e
r
ef
e
r
en
ce
c
u
r
r
en
t
∗
.
Fig
u
r
e
1
.
B
lo
ck
d
iag
r
am
o
f
F
OC
with
s
p
ee
d
co
n
tr
o
ller
3.
ST
A
T
E
V
ARIA
B
L
E
S
O
F
T
H
E
P
M
SM
SP
E
E
D
C
O
NT
RO
L
L
E
R
AND
CO
N
VE
N
T
I
O
NA
L
SL
I
DING
M
O
DE
CO
N
T
RO
L
Sli
d
in
g
m
o
d
e
co
n
tr
o
l
en
s
u
r
es
s
tab
ilit
y
in
u
n
ce
r
tain
an
d
n
o
is
y
co
n
d
itio
n
s
th
r
o
u
g
h
d
is
co
n
tin
u
o
u
s
co
n
tr
o
l
laws.
Ho
wev
er
,
s
elec
tin
g
an
in
ap
p
r
o
p
r
iate
s
lid
in
g
s
u
r
f
ac
e
c
an
lead
to
ch
atter
in
g
p
r
o
b
le
m
s
,
wh
ich
ar
e
co
m
m
o
n
is
s
u
es
in
s
lid
in
g
co
n
tr
o
l
s
y
s
tem
s
.
T
h
u
s
,
d
esig
n
in
g
a
s
lid
in
g
m
o
d
e
co
n
tr
o
l
s
y
s
tem
with
r
ed
u
ce
d
ch
atter
in
g
is
cr
u
cial.
T
h
is
d
r
iv
es
th
e
r
esea
r
ch
to
d
ev
el
o
p
an
e
n
h
an
ce
d
ap
p
r
o
ac
h
b
ased
o
n
t
h
e
ch
alle
n
g
es
ar
is
in
g
f
r
o
m
co
n
v
en
tio
n
al
ap
p
r
o
ac
h
es.
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
E
n
h
a
n
ce
d
r
ea
ch
in
g
la
w
fo
r
imp
r
o
ve
d
r
esp
o
n
s
e
in
s
lid
in
g
mo
d
e
co
n
tr
o
l o
f P
MS
M
…
(
K
h
a
n
h
Qu
o
c
Tr
u
o
n
g
)
421
3
.
1
.
F
o
rm
ula
t
ing
t
he
s
t
a
t
e
v
a
ri
a
bles
o
f
t
he
P
M
SM
s
peed
co
ntr
o
ller
T
h
e
s
y
s
tem
s
tate
v
ar
iab
les
o
f
th
e
s
p
ee
d
co
n
tr
o
ller
ar
e
d
ef
in
ed
as
(
5
)
.
W
h
er
e
∗
an
d
ar
e
s
p
ee
d
r
ef
er
en
ce
s
an
d
th
e
in
s
tan
t sp
ee
d
o
f
th
e
PMSM
m
o
to
r
.
Der
iv
e
d
f
r
o
m
(
5
)
,
̇
2
is
d
er
iv
ed
as
(
6
)
.
{
1
=
=
∗
−
2
=
̇
=
1
=
−
=
−
(
3
2
−
)
(
5
)
̇
2
=
̈
=
−
2
2
=
−
3
2
2
(
6
)
Fo
r
s
im
p
licity
,
we
ass
ig
n
3
2
2
an
d
in
(
6
)
as
(
7
)
.
=
3
2
2
;
=
(
7
)
Fro
m
(
5
)
an
d
(
6
)
,
th
e
s
tate
eq
u
atio
n
o
f
th
e
s
y
s
tem
ca
n
b
e
e
x
p
r
ess
ed
as
(
8
)
.
[
̇
1
̇
2
]
=
[
0
1
0
0
]
[
1
2
]
+
[
0
−
]
(
8
)
On
ce
th
e
s
y
s
tem
s
tate
v
ar
iab
les ar
e
id
en
tifie
d
,
th
e
s
u
b
s
eq
u
e
n
t step
in
v
o
lv
es selectin
g
a
r
ep
r
esen
tativ
e
s
lid
in
g
s
u
r
f
ac
e,
ty
p
ically
as
in
(
9
)
.
=
2
+
1
(
9
)
W
ith
th
e
ex
p
r
ess
io
n
o
f
th
e
s
l
id
in
g
s
u
r
f
ac
e
,
th
e
v
alu
e
o
f
th
e
co
ef
f
icien
t
is
co
r
r
elate
d
wi
th
th
e
asy
m
p
to
tic
s
tab
ilit
y
o
f
th
e
s
lid
in
g
m
o
d
e
a
n
d
th
e
co
n
v
er
g
en
ce
r
ate
t
o
war
d
s
th
e
s
lid
in
g
s
u
r
f
a
ce
.
Giv
e
n
t
h
e
d
e
f
in
ed
s
lid
in
g
s
u
r
f
ac
e,
th
e
r
e
f
er
en
ce
c
u
r
r
e
n
t
alo
n
g
th
e
q
-
ax
is
(
∗
)
ca
n
b
e
d
eter
m
in
ed
f
r
o
m
its
ex
p
r
ess
io
n
(
9
)
as
in
(
1
0
)
.
̇
=
̇
2
+
̇
1
=
̇
2
+
2
→
̇
2
=
̇
−
2
=
−
∗
→
∗
=
1
(
−
̇
+
2
)
(
1
0
)
T
ak
in
g
th
e
i
n
teg
r
al
o
f
b
o
t
h
s
id
es
o
f
(
1
0
)
,
we
o
b
tain
(
1
1
)
.
∗
=
1
∫
(
−
̇
+
2
)
(
1
1
)
T
h
e
ex
p
r
ess
io
n
f
o
r
t
h
e
r
ef
e
r
en
ce
cu
r
r
en
t
∗
in
(
1
1
)
f
o
r
m
s
th
e
b
a
s
is
f
o
r
d
ev
elo
p
i
n
g
th
e
co
n
tr
o
l
a
lg
o
r
ith
m
f
o
r
th
e
s
p
ee
d
c
o
n
tr
o
ller
.
T
h
r
o
u
g
h
th
is
ex
p
r
ess
io
n
,
th
e
d
ep
en
d
en
cy
o
f
th
e
s
lid
in
g
s
u
r
f
ac
e
co
n
v
er
g
en
ce
r
ate
̇
on
g
en
er
atin
g
th
e
r
ef
er
en
ce
cu
r
r
e
n
t
∗
ca
n
b
e
o
b
s
er
v
e
d
,
an
d
d
esig
n
in
g
th
e
eq
u
atio
n
f
o
r
̇
is
cr
u
cial
an
d
d
ir
ec
tly
im
p
ac
ts
co
n
tr
o
l
p
er
f
o
r
m
a
n
ce
.
Ass
u
m
in
g
th
at
th
e
PMSM
an
g
le
is
ac
cu
r
ately
m
ea
s
u
r
ed
f
r
o
m
th
e
m
o
to
r
e
n
co
d
e
r
,
th
e
m
o
to
r
s
p
ee
d
is
ca
lcu
lated
,
an
d
th
is
v
alu
e
is
u
s
ed
to
d
eter
m
in
e
1
an
d
2
.
T
h
en
,
th
ese
s
tate
v
ar
iab
les
ar
e
u
s
ed
to
d
eter
m
i
n
e
th
e
r
e
f
er
en
c
e
cu
r
r
en
t
∗
,
as sh
o
wn
in
(
1
1
)
.
3
.
2
.
T
he
co
nv
ent
io
na
l r
ea
ching
l
a
w
m
et
ho
d
T
h
e
co
n
v
en
tio
n
al
r
ea
c
h
in
g
law
m
eth
o
d
aim
s
to
en
s
u
r
e
f
ast
co
n
v
er
g
en
ce
o
f
th
e
s
y
s
tem
to
th
e
s
lid
in
g
s
u
r
f
ac
e
wh
ile
m
itig
atin
g
ch
at
ter
in
g
an
d
o
v
er
s
h
o
o
t.
T
h
e
li
n
ea
r
r
ea
ch
in
g
law
o
f
f
e
r
s
s
im
p
licity
an
d
ea
s
e
o
f
im
p
lem
en
tatio
n
.
T
h
e
c
o
n
v
e
n
tio
n
al
r
ea
ch
i
n
g
law
is
d
esig
n
is
g
iv
en
b
y
(
1
2
)
.
I
n
th
e
co
n
v
en
t
io
n
al
r
ea
ch
in
g
law
m
eth
o
d
,
th
e
r
ea
c
h
in
g
tim
e
1
is
d
ef
in
ed
as
th
e
tim
e
r
eq
u
ir
e
d
f
o
r
th
e
s
tates
to
ap
p
r
o
ac
h
th
e
s
lid
in
g
s
u
r
f
ac
e
,
an
d
it
ca
n
b
e
u
s
ed
to
ev
alu
ate
th
e
co
n
tr
o
ller
p
er
f
o
r
m
a
n
ce
.
T
h
e
r
ea
ch
in
g
tim
e
1
ca
n
b
e
ca
lcu
lated
a
cc
o
r
d
in
g
to
(
1
2
)
as
in
(
1
3
)
.
̇
=
−
(
)
(
1
2
)
̇
=
=
−
(
)
→
∫
1
0
=
∫
1
−
(
)
→
1
=
(
0
)
0
(
0
)
(
1
3
)
B
ased
o
n
th
e
ab
o
v
e
ex
p
r
ess
io
n
,
it
ca
n
b
e
s
ee
n
th
at
th
e
r
ea
ch
in
g
tim
e
1
d
ep
en
d
s
o
n
th
e
co
n
s
tan
t
,
an
d
th
e
in
itial
s
tate
p
o
s
itio
n
o
f
(
0
)
.
T
o
im
p
r
o
v
e
th
e
tim
e
to
r
ea
ch
th
e
s
lid
in
g
s
u
r
f
ac
e
1
,
th
e
co
n
s
tan
t
is
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
.
1
,
Ma
r
c
h
20
2
5
:
418
-
430
422
in
tr
o
d
u
ce
d
.
T
h
e
l
i
n
e
a
r
r
e
a
c
h
i
n
g
l
a
w
i
n
t
h
e
c
o
n
v
e
n
t
i
o
n
a
l
m
e
t
h
o
d
i
n
[
2
4
]
o
f
f
e
r
s
i
m
p
r
o
v
e
m
e
n
t
i
n
r
e
a
c
h
i
n
g
t
i
m
e
1
,
m
a
k
i
n
g
i
t
a
p
o
p
u
l
a
r
c
h
o
i
c
e
i
n
m
a
n
y
c
o
n
t
r
o
l
a
p
p
l
i
c
a
t
i
o
n
s
.
T
h
e
c
o
n
v
e
n
t
i
o
n
a
l
r
e
a
c
h
i
n
g
l
a
w
i
s
d
e
s
i
g
n
e
d
a
s
i
n
(
1
4
)
:
̇
=
−
(
)
−
(
1
4
)
wh
er
e
,
ar
e
p
o
s
itiv
e
c
o
n
s
tan
t
s
.
Su
b
s
titu
tin
g
(
14
)
in
to
(
1
1
)
,
w
e
h
a
v
e
t
h
e
f
o
l
l
o
w
i
n
g
c
u
r
r
e
n
t
r
e
f
e
r
e
n
c
e
a
s
i
n
(
1
5
)
.
∗
=
1
∫
(
(
)
+
+
2
)
(
1
5
)
Fro
m
(
1
5
)
,
it
is
n
ec
ess
ar
y
to
c
o
n
s
id
er
th
e
in
f
lu
e
n
ce
s
o
f
co
n
s
tan
ts
an
d
in
c
o
n
tr
o
llin
g
th
e
s
p
ee
d
o
f
PMSM.
I
n
p
ar
ticu
lar
,
a
lar
g
er
v
alu
e
o
f
co
n
s
tan
ts
an
d
r
esu
lts
in
a
s
h
o
r
ter
ap
p
r
o
ac
h
tim
e.
H
o
wev
er
,
th
is
also
lead
s
to
a
s
u
d
d
en
in
cr
ea
s
e
in
m
o
to
r
s
p
ee
d
,
p
o
ten
tially
ca
u
s
in
g
it
to
s
lid
e
o
u
t
o
f
th
e
s
u
r
f
a
ce
an
d
r
esu
ltin
g
i
n
ch
atter
in
g
.
Fu
r
th
er
m
o
r
e,
if
t
h
e
in
itial
p
o
s
itio
n
(
0
)
is
f
u
r
th
e
r
f
r
o
m
th
e
s
lid
in
g
s
u
r
f
ac
e,
t
h
e
a
p
p
r
o
ac
h
tim
e
will
s
ig
n
if
ican
tly
in
cr
ea
s
e.
I
n
s
lid
in
g
m
o
d
e
co
n
tr
o
l,
th
e
c
h
atter
in
g
is
s
u
e
o
f
te
n
o
cc
u
r
s
w
h
en
th
e
co
n
tr
o
l
s
y
s
tem
is
o
p
er
atin
g
n
ea
r
th
e
b
o
u
n
d
ar
y
o
f
th
e
s
lid
in
g
s
u
r
f
ac
e,
wh
er
e
s
m
all
p
er
tu
r
b
atio
n
s
o
r
u
n
ce
r
tain
ties
ca
n
ca
u
s
e
t
h
e
co
n
tr
o
l
s
ig
n
al
to
f
lu
ctu
ate
r
ap
id
l
y
b
etwe
en
d
if
f
er
en
t
v
alu
es.
T
h
is
is
s
u
e
m
ay
lead
to
in
s
tab
ilit
y
,
d
eg
r
a
d
e
d
p
er
f
o
r
m
an
ce
,
an
d
in
cr
ea
s
ed
en
e
r
g
y
co
n
s
u
m
p
tio
n
.
T
o
an
aly
ze
th
e
ch
atter
in
g
is
s
u
e,
̇
in
th
e
c
o
n
tin
u
o
u
s
d
o
m
ain
is
co
n
v
er
ted
to
th
e
d
is
cr
ete
d
o
m
ain
.
As
r
ea
l
-
tim
e
co
n
tr
o
l
is
in
d
is
p
en
s
ab
le
in
p
r
ac
tical
co
n
tr
o
l
s
y
s
tem
im
p
lem
en
tatio
n
s
,
co
n
tr
o
l
o
p
er
atio
n
s
m
u
s
t
b
e
ca
r
r
ied
o
u
t
with
in
a
d
is
cr
ete
d
o
m
ain
.
Fro
m
(
1
4
)
,
t
h
e
d
is
cr
ete
e
x
p
r
ess
io
n
o
f
t
h
e
co
n
v
en
tio
n
al
r
ea
ch
in
g
law
m
eth
o
d
as
ap
p
r
o
ac
h
es 0
is
r
ep
r
esen
ted
as
in
(
1
6
)
:
(
+
1
)
−
(
)
=
−
(
(
)
)
(
1
6
)
wh
er
e
is
th
e
s
am
p
lin
g
tim
e.
U
n
d
er
th
e
ass
u
m
p
tio
n
th
at
th
e
s
y
s
tem
tr
ajec
to
r
y
r
ea
ch
es
th
e
s
lid
in
g
-
m
o
d
e
s
u
r
f
ac
e
with
in
a
f
in
ite
s
tep
,
wh
ich
im
p
lies
th
at
(
)
=
0
+
an
d
(
)
=
0
−
,
th
e
e
q
u
atio
n
f
o
r
th
e
s
u
b
s
eq
u
en
t
p
er
i
o
d
ca
n
b
e
d
er
iv
e
d
with
(
)
=
0
+
an
d
(
)
=
0
−
as
in
(
1
7
)
.
(
+
1
)
=
−
(
ℎ
(
)
=
0
+
)
;
(
+
1
)
=
(
ℎ
(
)
=
0
−
)
(
1
7
)
T
h
e
wid
th
o
f
th
e
d
is
cr
ete
s
lid
in
g
-
m
o
d
e
b
an
d
1
is
ca
lcu
lated
b
etwe
en
th
e
b
o
u
n
d
ar
y
(
)
=
0
+
an
d
(
)
=
0
−
.
Fig
u
r
e
2
s
h
o
ws
th
e
s
tate
tr
ajec
to
r
y
o
f
th
e
co
n
v
en
tio
n
al
r
ea
ch
in
g
law.
I
t
ca
n
b
e
s
ee
n
in
Fig
u
r
e
2
th
at
th
e
wid
t
h
o
f
th
e
d
is
cr
ete
s
lid
in
g
-
m
o
d
e
b
an
d
1
in
(
1
8
)
ca
u
s
es
th
e
s
y
s
tem
to
f
ail
to
r
ea
ch
th
e
e
q
u
ilib
r
iu
m
p
o
in
t
O
an
d
th
e
s
tate
tr
ajec
to
r
y
o
s
cillatin
g
ar
o
u
n
d
t
h
e
p
o
i
n
t
O.
T
h
is
r
esu
lt
lead
s
to
a
s
ig
n
if
ican
t
ch
atter
in
g
p
r
o
b
lem
wh
e
n
in
cr
ea
s
in
g
p
ar
am
ete
r
to
r
ed
u
c
e
th
e
r
ea
ch
in
g
tim
e
to
th
e
s
lid
in
g
s
u
r
f
ac
e.
1
=
2
(
1
8
)
Fig
u
r
e
2
.
State
tr
ajec
to
r
y
o
f
t
h
e
co
n
v
e
n
tio
n
al
r
ea
ch
i
n
g
law
4.
P
RO
P
O
SE
D
E
NH
A
NCE
D
RE
ACH
I
NG
L
AW
D
E
S
I
G
N
WI
T
H
F
U
Z
Z
Y
L
O
G
I
C
CO
NT
RO
L
L
E
R
4
.
1
.
T
he
ba
s
ic
i
dea
o
f
enha
nced
re
a
ching
la
w
inte
g
ra
t
ed
wit
h f
uzzy
lo
g
ic
co
ntr
o
ller
T
o
ef
f
ec
tiv
ely
ad
d
r
ess
th
e
ch
atter
in
g
is
s
u
e
an
d
im
p
r
o
v
e
th
e
s
y
s
tem
r
esp
o
n
s
e,
it
is
es
s
en
tial
t
o
estab
lis
h
two
co
ef
f
icien
ts
an
d
as
v
ar
ia
b
les
th
at
ca
n
ch
an
g
e
ac
c
o
r
d
in
g
to
th
e
s
tate
v
a
r
iab
le
1
an
d
th
e
s
lid
in
g
s
u
r
f
ac
e
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I
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8
6
9
4
E
n
h
a
n
ce
d
r
ea
ch
in
g
la
w
fo
r
imp
r
o
ve
d
r
esp
o
n
s
e
in
s
lid
in
g
mo
d
e
co
n
tr
o
l o
f P
MS
M
…
(
K
h
a
n
h
Qu
o
c
Tr
u
o
n
g
)
423
p
o
s
itio
n
.
T
h
is
f
o
r
m
s
th
e
b
asis
f
o
r
p
r
o
p
o
s
in
g
e
n
h
an
ce
d
r
ea
ch
in
g
law
d
esig
n
with
f
u
zz
y
l
o
g
ic
co
n
tr
o
ller
f
o
r
ad
ap
tiv
e
a
d
ju
s
tin
g
o
f
c
o
ef
f
ici
en
ts
an
d
.
Ad
d
itio
n
ally
,
th
e
g
ain
(
)
is
ad
ap
tiv
ely
a
d
ju
s
ted
u
s
in
g
th
e
p
r
o
p
o
s
ed
f
u
zz
y
lo
g
ic
c
o
n
tr
o
lle
r
.
Hen
ce
th
e
p
r
o
p
o
s
ed
r
ea
c
h
in
g
law
is
g
iv
en
b
y
th
e
(
1
9
)
:
̇
=
−
|
1
|
|
1
|
+
−
|
|
(
)
−
(
)
(
1
9
)
w
h
er
e
,
,
,
,
ar
e
p
o
s
itiv
e
co
n
s
tan
ts
an
d
0
<
<
1
,
(
)
is
th
e
o
u
tp
u
t
o
f
th
e
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
ac
co
r
d
in
g
t
o
th
e
in
p
u
t
an
d
̇
.
T
h
e
p
r
o
p
o
s
ed
r
ea
ch
in
g
law
is
an
aly
ze
d
in
two
s
tates:
r
ea
ch
in
g
th
e
s
lid
in
g
m
o
d
e
s
u
r
f
ac
e
an
d
o
p
er
atin
g
n
ea
r
t
h
e
b
o
u
n
d
ar
y
o
f
th
e
s
lid
in
g
s
u
r
f
ac
e
.
Fo
r
s
im
p
licity
,
th
e
s
y
s
tem
is
an
aly
ze
d
wh
e
n
th
e
s
y
s
tem
s
tate
v
ar
iab
le
is
p
o
s
itiv
e.
I
n
th
e
r
ea
c
h
in
g
s
lid
in
g
m
o
d
e
s
u
r
f
ac
e
s
tate,
th
e
s
y
s
tem
s
tat
e
v
ar
iab
le
is
lo
ca
ted
f
ar
awa
y
f
r
o
m
t
h
e
s
lid
in
g
s
u
r
f
ac
e,
s
o
th
at
−
|
|
≈
0
.
Hen
c
e
th
e
(
1
9
)
will c
o
n
v
e
r
g
e
to
t
h
e
(
2
0
)
.
̇
≈
−
(
)
−
(
)
(
2
0
)
C
o
m
p
ar
ed
to
th
e
co
n
v
e
n
tio
n
al
r
ea
ch
in
g
law
in
(
1
4
)
,
wh
ich
t
h
e
co
ef
f
icien
t
is
a
f
ix
ed
n
u
m
b
er
,
th
e
p
r
o
p
o
s
ed
r
ea
ch
in
g
law
h
as
th
e
ad
ap
tiv
e
r
ea
ch
in
g
g
ain
(
)
.
T
h
is
f
u
zz
y
o
u
t
p
u
t
is
ad
ap
tiv
ely
ad
ju
s
ted
ac
co
r
d
in
g
to
th
e
in
p
u
t
an
d
̇
.
T
h
an
k
s
to
th
e
a
d
ap
tiv
e
ad
j
u
s
tm
en
t
o
f
f
u
zz
y
o
u
tp
u
t,
th
e
r
ea
ch
in
g
tim
e
is
im
p
r
o
v
ed
with
a
h
i
g
h
g
ain
(
)
,
an
d
th
is
v
ar
iab
le
is
r
e
d
u
ce
d
wh
en
a
p
p
r
o
ac
h
in
g
t
h
e
s
lid
in
g
m
o
d
e
s
u
r
f
ac
e.
I
n
th
e
b
o
u
n
d
a
r
y
o
p
e
r
atio
n
o
f
th
e
s
lid
in
g
s
u
r
f
ac
e
s
tate,
th
e
f
o
llo
win
g
co
n
d
itio
n
is
s
atis
f
ied
→
0
,
an
d
th
e
(
1
9
)
will
co
n
v
er
g
e
to
th
e
(
2
1
)
.
T
h
e
(
2
1
)
d
e
p
en
d
o
n
1
,
an
d
its
v
alu
e
is
g
r
ad
u
ally
r
ed
u
ce
d
to
0
as
1
m
o
v
es
to
th
e
o
r
ig
i
n
.
T
h
e
p
r
o
p
o
s
ed
c
o
n
tr
o
l
law
co
n
t
r
ib
u
tes
to
a
s
m
o
o
th
r
esp
o
n
s
e
wh
en
th
e
s
y
s
te
m
s
tate
1
n
ea
r
th
e
s
lid
in
g
s
u
r
f
ac
e,
wh
ich
co
n
t
r
ib
u
te
to
elim
in
ate
ch
atter
i
n
g
is
s
u
es
.
T
h
e
co
m
b
in
atio
n
o
f
ad
ap
t
iv
e
g
ain
s
(
)
in
th
e
r
ea
ch
in
g
s
lid
in
g
m
o
d
e
s
u
r
f
ac
e
s
tate
an
d
|
1
|
|
1
|
+
in
th
e
b
o
u
n
d
ar
y
o
p
er
atio
n
o
f
th
e
s
lid
in
g
s
u
r
f
ac
e
,
th
e
s
tate
co
n
tr
ib
u
tes to
th
e
im
p
r
o
v
ed
s
y
s
tem
r
esp
o
n
s
e
an
d
c
h
atter
in
g
r
ed
u
ctio
n
.
Fig
u
r
e
3
s
h
o
ws th
e
b
lo
ck
d
iag
r
am
o
f
th
e
p
r
o
p
o
s
ed
en
h
a
n
ce
d
s
lid
i
n
g
m
o
d
e
co
n
tr
o
l
.
̇
≈
−
|
1
|
|
1
|
+
(
)
(
2
1
)
Fig
u
r
e
3
.
B
lo
ck
d
iag
r
am
o
f
th
e
p
r
o
p
o
s
ed
en
h
a
n
ce
d
s
lid
in
g
m
o
d
e
co
n
tr
o
l
4
.
2
.
T
he
de
s
ig
n o
f
f
uzzy
(
q)
in
f
uzzy
lo
g
ic
co
ntr
o
ller
T
h
e
co
n
t
r
o
l
v
a
r
iab
le
(
)
is
th
e
o
u
tp
u
t
o
f
th
e
f
u
zz
y
l
o
g
ic
co
n
tr
o
l
ler
,
allo
win
g
a
n
ad
a
p
tiv
e
tu
n
e
ac
co
r
d
in
g
to
th
e
s
tate
v
a
r
iab
le
s
1
an
d
2
.
B
ased
o
n
th
e
ex
p
e
r
ien
ce
,
th
e
in
p
u
t
c
o
ef
f
icien
t
o
f
th
e
s
tate
v
ar
iab
les
1
an
d
2
r
an
g
e
f
r
o
m
[
-
1
0
;
1
0
]
,
an
d
th
e
o
u
tp
u
t
(
)
with
g
ain
r
an
g
es
f
r
o
m
0
t
o
2
0
0
0
.
T
h
e
f
u
zz
y
s
et
is
d
ef
in
ed
as
f
o
llo
ws:
=
{
,
,
,
,
,
,
}
;
̇
=
{
,
,
,
,
,
,
}
,
wh
er
e
n
eg
ativ
e
b
ig
(
NB
)
,
n
eg
ativ
e
m
ed
iu
m
(
NM
)
,
n
eg
ativ
e
s
m
all
(
NS
)
,
ze
r
o
(
ZE
)
,
p
o
s
itiv
e
s
m
all
(
PS
)
,
p
o
s
i
tiv
e
m
ed
iu
m
(
PM
)
,
an
d
p
o
s
itiv
e
b
ig
(
PB
)
r
ep
r
esen
t
d
if
f
er
en
t
lev
els
o
f
in
p
u
t
v
ar
i
ab
les.
T
h
e
o
u
tp
u
t
(
)
=
{
,
,
,
,
}
,
w
h
er
e
s
m
all
(
S
)
,
m
ed
iu
m
s
m
all
(
MS
)
,
m
ed
iu
m
(
M
)
,
m
ed
iu
m
b
ig
(
MB
)
,
an
d
b
ig
(
B
)
r
ep
r
esen
t
d
if
f
er
en
t
lev
els
o
f
o
u
t
p
u
t.
T
h
e
f
u
z
zy
r
u
le
tab
le
is
p
r
o
v
id
ed
in
T
ab
le
1
a
n
d
th
e
r
elatio
n
s
h
ip
b
etwe
en
,
̇
,
an
d
th
e
o
u
tp
u
t
(
)
is
s
h
o
wn
in
Fig
u
r
e
s
4
(
a)
-
4
(
c)
.
B
y
u
s
in
g
th
e
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
an
d
f
u
zz
y
r
u
le
tab
le,
t
h
e
co
ef
f
icien
t
is
ad
ap
tiv
ely
a
d
ju
s
ted
ac
co
r
d
in
g
to
th
e
v
alu
e
o
f
an
d
its
d
er
i
v
ativ
es.
T
h
e
3
D
p
lo
t
o
f
,
,
/
,
an
d
th
eir
r
elatio
n
s
h
ip
is
s
h
o
wn
in
Fig
u
r
e
5
.
W
h
en
an
d
its
d
e
r
iv
ati
v
e
h
a
v
e
h
i
g
h
v
alu
es,
w
h
ich
i
n
d
icate
s
th
e
s
tate
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
.
1
,
Ma
r
c
h
20
2
5
:
418
-
430
424
tr
ajac
to
r
y
is
lo
ca
ted
f
ar
f
r
o
m
th
e
s
lid
in
g
s
u
r
f
ac
e,
th
e
co
ef
f
icien
t
is
in
cr
ea
s
ed
to
en
h
an
ce
th
e
r
ea
ch
in
g
s
p
ee
d
to
th
e
s
lid
in
g
s
u
r
f
ac
e.
On
th
e
o
th
er
h
an
d
,
wh
en
th
e
v
al
u
e
an
d
its
d
er
iv
ativ
e
ar
e
s
m
all,
wh
en
m
ea
n
s
th
e
s
tate
tr
ajac
to
r
y
is
n
ea
r
th
e
s
lid
in
g
s
u
r
f
ac
e,
th
e
co
ef
f
icien
t
is
m
in
im
ized
to
en
s
u
r
e
th
at
th
e
s
tate
tr
ajec
to
r
y
r
ea
ch
es
th
e
s
lid
in
g
s
u
r
f
ac
e
with
o
u
t o
v
er
s
h
o
o
t.
T
ab
le
1
.
T
h
e
r
u
le
b
ase
o
f
th
e
f
u
zz
y
co
n
tr
o
ller
̇
NB
NM
NS
ZE
PS
PM
PB
NB
B
MB
M
MS
M
MB
B
NM
MB
M
M
M
M
M
MB
NS
MB
M
MS
S
MS
M
MB
ZE
M
MS
S
S
S
MS
M
PS
MB
M
MS
S
MS
M
MB
PM
MB
M
M
M
M
M
MB
PB
B
MB
M
MS
M
MB
B
(
a)
(
b
)
(
c)
Fig
u
r
e
4
.
T
h
e
m
em
b
er
s
h
ip
f
u
n
ctio
n
o
f
th
e
f
u
zz
y
co
n
tr
o
ller
f
o
r
in
p
u
t
,
̇
,
an
d
(
)
:
(
a)
in
p
u
t
,
(
b
)
in
p
u
t
̇
,
an
d
(
c)
o
u
tp
u
t
(
)
Fig
u
r
e
5
.
T
h
e
f
u
zz
y
lo
g
ic
c
o
n
t
r
o
l
s
u
r
f
ac
e
Su
b
s
titu
tin
g
(
1
9
)
in
to
(
1
1
)
,
r
ef
er
en
ce
cu
r
r
en
t
∗
is
o
b
tain
ed
as (
2
2
)
.
∗
=
1
∫
(
|
1
|
|
1
|
+
−
|
|
(
)
+
(
)
+
2
)
(
2
2
)
I
n
th
e
b
o
u
n
d
ar
y
o
p
er
atio
n
o
f
th
e
s
lid
in
g
s
u
r
f
ac
e
s
tate,
t
h
e
s
lid
in
g
m
o
d
e
s
u
r
f
ac
e
s
ap
p
r
o
ac
h
es
0
,
an
d
th
e
p
r
o
p
o
s
ed
en
h
a
n
ce
d
r
ea
c
h
in
g
l
aw
in
(
1
9
)
ca
n
b
e
co
n
v
er
ted
to
th
e
d
is
cr
ete
-
tim
e
d
o
m
ain
as
(
2
3
)
:
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
E
n
h
a
n
ce
d
r
ea
ch
in
g
la
w
fo
r
imp
r
o
ve
d
r
esp
o
n
s
e
in
s
lid
in
g
mo
d
e
co
n
tr
o
l o
f P
MS
M
…
(
K
h
a
n
h
Qu
o
c
Tr
u
o
n
g
)
425
(
+
1
)
−
(
)
=
−
|
1
|
|
1
|
+
(
(
)
)
(
2
3
)
w
h
er
e
r
ep
r
esen
ts
th
e
s
am
p
lin
g
p
er
i
o
d
.
Un
d
er
th
e
ass
u
m
p
tio
n
th
at
t
h
e
s
y
s
tem
'
s
tr
ajec
to
r
y
r
ea
ch
es th
e
s
lid
in
g
-
m
o
d
e
s
u
r
f
ac
e
with
in
a
f
in
ite
s
tep
,
wh
ich
im
p
lies
th
at
(
)
=
0
+
,
(
)
=
0
−
,
th
e
eq
u
atio
n
f
o
r
th
e
s
u
b
s
eq
u
en
t
p
er
io
d
ca
n
b
e
d
er
iv
ed
with
(
)
=
0
+
an
d
(
)
=
0
−
as
in
(
2
4
)
.
(
+
1
)
=
−
|
1
|
|
1
|
+
(
ℎ
(
)
=
0
+
)
;
(
+
1
)
=
|
1
|
|
1
|
+
(
ℎ
(
)
=
0
−
)
(
2
4
)
T
h
e
wid
th
o
f
t
h
e
d
is
cr
ete
s
lid
in
g
-
m
o
d
e
b
a
n
d
2
is
ca
lcu
lated
b
etwe
en
th
e
b
o
u
n
d
ar
y
(
)
=
0
+
an
d
(
)
=
0
−
.
C
o
m
p
ar
ed
to
th
e
co
n
v
en
ti
o
n
al
r
ea
ch
in
g
law,
in
wh
ich
t
h
e
wid
th
o
f
th
e
d
is
cr
ete
s
lid
in
g
-
m
o
d
e
b
an
d
1
in
(
1
8
)
is
a
co
n
s
tan
t
v
alu
e,
t
h
e
p
r
o
p
o
s
e
d
m
eth
o
d
h
as
an
a
d
ap
tiv
e
wi
d
th
o
f
t
h
e
d
is
cr
ete
s
lid
in
g
-
m
o
d
e
b
an
d
2
in
(
2
5
)
,
wh
ich
r
ed
u
ce
s
th
e
ch
atter
in
g
i
s
s
u
e.
T
o
illu
s
tr
ate
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
p
r
o
p
o
s
ed
m
eth
o
d
,
th
e
s
lid
in
g
-
m
o
d
e
b
an
d
is
s
h
o
wn
in
Fig
u
r
e
6
.
I
n
Fig
u
r
e
6
,
th
e
s
lid
in
g
s
u
r
f
ac
e
tr
ajec
to
r
y
g
r
ad
u
ally
a
p
p
r
o
ac
h
e
s
0
,
1
an
d
2
also
ap
p
r
o
ac
h
es
0
.
I
t
ca
n
b
e
s
ee
n
th
at
d
is
cr
ete
s
lid
in
g
-
m
o
d
e
b
a
n
d
2
r
ed
u
ce
s
to
0
,
r
ath
er
th
an
o
s
cillatin
g
ar
o
u
n
d
th
e
o
r
ig
in
0
o
f
t
h
e
co
n
v
en
tio
n
al
m
eth
o
d
in
Fig
u
r
e
2
.
2
=
2
|
1
|
|
1
|
+
(
2
5
)
Fig
u
r
e
6
.
State
tr
ajec
to
r
y
o
f
t
h
e
p
r
o
p
o
s
ed
en
h
a
n
ce
d
r
ea
ch
in
g
law
4
.
3
.
Sta
bil
it
y
a
na
ly
s
is
T
o
ass
ess
th
e
s
tab
ilit
y
o
f
th
e
PMSM
s
y
s
tem
s
,
th
e
L
y
ap
u
n
o
v
s
tab
ilit
y
cr
iter
io
n
an
d
s
tab
ilit
y
an
aly
s
is
ar
e
em
p
lo
y
ed
[
3
0
]
.
I
n
th
e
L
y
a
p
u
n
o
v
th
eo
r
y
,
th
e
co
n
d
itio
n
f
o
r
th
e
s
tate
v
ar
iab
les
to
r
ea
ch
th
e
s
lid
in
g
s
u
r
f
ac
e
=
2
+
1
is
th
at
th
e
co
n
d
itio
n
̇
<
0
m
u
s
t b
e
s
atis
f
ied
.
I
n
th
is
s
tu
d
y
,
we
ch
o
o
s
e
th
e
L
y
ap
u
n
o
v
f
u
n
cti
o
n
as
a
q
u
ad
r
atic
f
u
n
ctio
n
as in
(
2
6
)
.
T
ak
in
g
th
e
d
er
iv
ativ
e
o
f
t
h
e
(
2
6
)
,
we
o
b
tain
(
2
7
)
.
=
1
2
2
(
2
6
)
̇
=
̇
(
2
7
)
Su
b
s
titu
tin
g
(
1
9
)
to
(
2
7
)
,
we
g
et
(
2
8
)
:
̇
=
[
−
|
1
|
|
1
|
+
−
|
|
(
)
−
(
)
]
→
̇
=
−
|
1
|
|
1
|
+
−
|
|
|
|
−
(
)
2
<
0
(
2
8
)
wh
er
e
0
<
<
1
,
>
0
,
>
0
,
>
0
,
an
d
(
)
2
>
0
.
T
h
e
(
2
8
)
g
u
ar
an
tees
th
e
L
y
ap
u
n
o
v
s
tab
ilit
y
cr
iter
ia
̇
<
0
.
T
h
er
ef
o
r
e,
th
e
p
r
o
p
o
s
ed
r
ea
ch
in
g
law
is
well
-
s
u
ited
f
o
r
th
e
PMSM
m
o
to
r
s
p
ee
d
co
n
tr
o
l
s
y
s
tem
,
en
s
u
r
in
g
b
o
th
s
tab
ilit
y
an
d
en
h
an
ce
d
r
esp
o
n
s
e.
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
.
1
,
Ma
r
c
h
20
2
5
:
418
-
430
426
5.
E
XP
E
R
I
M
E
N
T
A
L
RE
SUL
T
S
T
o
v
er
if
y
th
e
ef
f
ec
tiv
e
n
ess
o
f
th
e
p
r
o
p
o
s
ed
co
n
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o
l
s
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an
ex
p
er
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en
tal
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ar
d
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e
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l
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o
r
m
f
o
r
th
e
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is
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et
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p
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ex
as
I
n
s
tr
u
m
en
ts
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ic
r
o
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o
n
tr
o
ller
T
MS2
8
0
S2
8
3
7
9
D
is
ad
ap
ted
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o
a
p
p
ly
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n
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o
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o
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ith
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d
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te
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ig
n
als
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o
r
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n
tr
o
llin
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e
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Fig
u
r
e
7
s
h
o
ws
th
e
ex
p
er
im
en
tal
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ar
d
war
e
p
latf
o
r
m
,
an
d
th
e
PMSM
m
o
to
r
p
ar
a
m
eter
s
ar
e
lis
ted
in
T
ab
le
2
.
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h
e
co
n
tr
o
l
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ar
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eter
s
o
f
th
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en
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3
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r
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a
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e
ad
o
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ted
[
3
1
]
,
[
3
2
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.
Fig
u
r
e
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.
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x
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im
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tal
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eter
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o
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042
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Fig
u
r
es 8
(
a)
-
8
(
d
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illu
s
tr
ate
th
e
o
b
s
er
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s
p
ee
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r
esp
o
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s
e
as th
e
PMSM
s
p
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in
cr
ea
s
ed
f
r
o
m
5
0
0
r
p
m
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0
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p
m
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s
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g
a
co
n
v
e
n
tio
n
al
PI
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n
tr
o
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,
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
,
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n
v
en
tio
n
al
s
lid
in
g
m
o
d
e,
an
d
p
r
o
p
o
s
ed
s
lid
in
g
m
o
d
e
co
n
tr
o
ller
.
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h
e
c
o
n
v
en
tio
n
al
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tr
o
ller
(
=
0
.
008
,
=
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,
as
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o
wn
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Fig
u
r
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8
(
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,
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ad
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r
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e
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o
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li
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i
n
Fig
u
r
e
8
(
b
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,
th
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zz
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tr
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tp
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d
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o
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o
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m
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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&
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2088
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8
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o
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Fig
u
r
e
9
.
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Fig
u
r
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,
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th
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ar
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ter
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o
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9
(
b
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r
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e
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0
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7
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ay
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ip
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Fig
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e
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(
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.
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th
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n
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wn
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Fig
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e
9
(
d
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e
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e
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r
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r
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o
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ly
0
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4
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o
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ly
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ller
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Fig
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8
.
E
x
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as th
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es f
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5
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(
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(
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law,
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d
(
d
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p
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s
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co
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o
ller
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