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s.
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p
a
p
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p
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h
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t
t
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:
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(
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twe
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a
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s
in
v
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in
c
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n
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rg
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g
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ti
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terfe
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,
a
n
d
sm
o
o
th
e
r
to
r
q
u
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p
ro
d
u
c
ti
o
n
.
K
ey
w
o
r
d
s
:
Ad
alin
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co
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tr
o
ller
Har
m
o
n
ic
co
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tr
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Ph
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co
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p
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R
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o
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tr
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ller
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s
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h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
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ing
A
uth
o
r
:
T
h
an
h
L
ic
h
Ng
u
y
en
Dep
ar
tm
en
t o
f
Me
ch
atr
o
n
ics,
Facu
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o
f
Me
ch
a
n
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E
n
g
in
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in
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Un
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s
ity
o
f
T
r
a
n
s
p
o
r
t a
n
d
C
o
m
m
u
n
icatio
n
s
No
.
3
C
au
Giay
Stre
et,
Han
o
i,
Vietn
am
E
m
ail:
lich
n
t@
u
tc.
ed
u
.
v
n
1.
I
NT
RO
D
UCT
I
O
N
T
o
ad
d
r
ess
th
e
g
lo
b
al
ch
allen
g
e
o
f
r
ed
u
cin
g
ca
r
b
o
n
d
io
x
id
e
e
m
is
s
io
n
s
,
elec
tr
ical
m
ac
h
in
es
ar
e
wid
ely
u
s
ed
in
im
p
o
r
ta
n
t
in
d
u
s
tr
ial
s
ec
to
r
s
,
p
ar
ticu
lar
l
y
in
tr
an
s
p
o
r
tatio
n
ap
p
licatio
n
s
s
u
ch
as
a
er
o
s
p
ac
e,
r
o
b
o
tics
,
cr
an
e
s
y
s
tem
s
,
an
d
elec
tr
ic
v
eh
icles
[
1
]
.
E
lectr
ical
d
r
iv
es
ar
e
a
p
r
ef
er
r
ed
c
h
o
ice
d
u
e
to
th
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h
ig
h
p
o
wer
d
e
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s
ity
,
lo
w
m
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ten
an
ce
co
s
ts
,
h
ig
h
to
r
q
u
e
d
en
s
ity
,
a
n
d
h
ig
h
ef
f
icien
cy
[
2
]
.
Desp
ite
th
e
n
u
m
er
o
u
s
b
en
ef
its
o
f
elec
tr
ica
l
d
r
iv
es,
th
er
e
ar
e
s
o
m
e
u
n
wan
ted
p
h
en
o
m
en
a
th
at
lead
t
o
to
r
q
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e/sp
ee
d
r
ip
p
les
d
u
r
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th
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co
m
m
is
s
io
n
in
g
o
f
elec
tr
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m
ac
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in
es,
af
f
ec
tin
g
th
eir
p
er
f
o
r
m
an
ce
an
d
r
eliab
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y
[
3
]
.
T
h
e
m
o
s
t
well
-
k
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o
wn
f
ac
to
r
s
co
n
tr
ib
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g
to
to
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q
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r
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p
les
ar
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th
e
cu
r
r
en
t
m
ea
s
u
r
em
en
t
er
r
o
r
[
4
]
,
[
5
]
,
d
ea
d
-
tim
e
ef
f
ec
ts
[
6
]
,
[
7
]
,
co
g
g
in
g
to
r
q
u
e
h
ar
m
o
n
ics
[
8
]
,
[
9
]
,
a
n
d
f
l
u
x
h
a
r
m
o
n
ics
[
1
0
]
.
Am
o
n
g
th
e
a
b
o
v
e
p
h
en
o
m
en
a,
th
e
cu
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r
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n
t
m
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s
u
r
em
en
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r
o
r
is
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ajo
r
s
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th
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p
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d
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tu
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b
an
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s
in
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tr
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d
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T
h
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DC
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f
f
s
et
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r
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r
s
in
t
h
e
cu
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r
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p
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r
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s
in
th
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co
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p
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f
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ase
cu
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t
in
th
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f
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en
ce
ca
u
s
in
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p
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io
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ic
to
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q
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r
ip
p
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[
1
1
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Dea
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p
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to
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d
q
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c
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t c
o
m
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[
6
]
,
[
1
2
]
,
[
1
3
]
.
T
h
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u
n
d
esira
b
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h
a
r
m
o
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th
e
m
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d
u
lated
v
o
ltag
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d
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t
o
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tp
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v
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lead
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to
co
r
r
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in
g
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8
8
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6
9
4
I
n
t J Po
w
E
lec
&
Dr
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s
t
,
Vo
l.
16
,
No
.
2
,
J
u
n
e
20
25
:
8
2
7
-
8
3
9
828
h
ar
m
o
n
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i
n
th
e
p
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ase
cu
r
r
en
ts
an
d
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b
s
eq
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en
tly
ca
u
s
in
g
r
i
p
p
les
in
t
h
e
elec
tr
o
m
ag
n
etic
to
r
q
u
e.
Ad
d
itio
n
ally
,
f
lu
x
h
a
r
m
o
n
ics
ar
e
d
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o
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in
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lu
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b
y
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e
m
ac
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tr
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p
r
o
p
e
r
ties
o
f
th
e
p
e
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m
an
en
t
m
ag
n
ets
[
1
4
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.
I
n
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d
itio
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to
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c
u
r
r
e
n
t
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i
p
p
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p
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s
ca
n
also
b
e
o
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s
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v
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in
elec
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d
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v
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T
h
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p
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en
o
m
e
n
o
n
is
p
ar
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lar
ly
p
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ev
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t
in
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n
s
p
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s
s
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ch
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co
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v
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o
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b
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g
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b
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wh
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r
ep
etitiv
e
p
h
en
o
m
en
a.
A
ch
ar
ac
ter
is
tic
f
ea
tu
r
e
o
f
s
u
ch
s
y
s
t
em
s
is
th
e
p
er
io
d
ic
lo
ad
to
r
q
u
e,
wh
ich
ev
en
t
u
ally
ca
u
s
es
s
p
ee
d
o
s
cillatio
n
s
.
T
h
e
s
e
o
s
cillatio
n
s
in
tr
o
d
u
ce
u
n
d
esire
d
h
ar
m
o
n
ics
in
t
o
th
e
c
o
n
tr
o
l
s
ig
n
als,
n
eg
ativ
ely
im
p
ac
tin
g
th
e
o
v
er
all
p
er
f
o
r
m
an
ce
.
Sp
ec
if
ically
,
t
h
ey
ca
n
r
ed
u
ce
th
e
p
r
ec
is
io
n
o
f
th
e
p
o
s
itio
n
co
n
tr
o
l
l
o
o
p
,
d
ec
r
ea
s
e
th
e
to
r
q
u
e
p
er
am
p
er
e
r
atio
o
f
th
e
elec
tr
ical
m
ac
h
i
n
e,
an
d
i
n
cr
ea
s
e
th
e
o
h
m
ic
lo
s
s
es
d
u
e
to
th
e
s
k
in
ef
f
ec
t a
s
s
o
ciate
d
with
h
ig
h
-
f
r
e
q
u
en
cy
co
m
p
o
n
en
ts
in
th
e
f
lu
x
an
d
s
tato
r
c
u
r
r
e
n
t sp
ec
tr
a.
T
o
m
itig
ate
th
e
n
eg
ativ
e
ef
f
ec
ts
o
f
u
n
d
esira
b
le
h
ar
m
o
n
ics,
th
e
im
p
lem
en
tatio
n
o
f
h
ar
m
o
n
ic
co
n
tr
o
ller
s
in
in
d
u
s
tr
ial
elec
tr
ical
d
r
iv
es
is
cr
u
cial
[
4
]
,
[
1
5
]
,
[
1
6
]
.
Var
io
u
s
h
ar
m
o
n
ic
co
n
tr
o
ller
to
p
o
lo
g
ies
h
av
e
b
ee
n
d
ev
elo
p
e
d
,
in
clu
d
in
g
th
e
r
eso
n
an
t
co
n
tr
o
ller
(
R
C
)
[
1
7
]
,
[
1
8
]
,
h
ar
m
o
n
ic
co
n
tr
o
ller
(
HC
)
[
1
9
]
,
an
d
ad
ap
tiv
e
lin
ea
r
n
eu
r
al
(
Ad
alin
e)
[
1
5
]
,
[
2
0
]
,
[
2
1
]
.
T
h
e
t
h
r
ee
af
o
r
e
m
en
tio
n
e
d
to
p
o
lo
g
ies
s
h
a
r
e
a
co
m
m
o
n
w
o
r
k
in
g
p
r
in
cip
le
o
f
d
ea
lin
g
with
th
e
s
p
ec
if
ic
h
a
r
m
o
n
ic
in
p
h
y
s
ical
q
u
an
titi
e
s
.
Ho
wev
er
,
a
co
m
p
r
e
h
en
s
iv
e
an
aly
s
is
o
f
th
eir
s
im
ilar
ities
an
d
d
if
f
er
en
ce
s
,
p
ar
ticu
lar
ly
with
r
esp
ec
t
to
m
ath
em
atica
l
d
escr
ip
t
io
n
an
d
ex
p
er
im
en
tal
im
p
lem
en
tatio
n
,
is
s
till
lack
in
g
.
T
h
is
r
esear
ch
w
o
r
k
f
o
c
u
s
es
o
n
f
illi
n
g
th
is
r
esear
ch
g
a
p
b
y
h
ig
h
lig
h
tin
g
th
e
s
am
e
m
ath
em
atica
l
d
escr
ip
tio
n
o
f
th
ese
to
p
o
l
o
g
ies
an
d
also
in
v
esti
g
atin
g
th
e
d
if
f
er
e
n
ce
s
r
eg
ar
d
in
g
t
h
e
d
is
cr
etize
d
im
p
lem
en
ta
tio
n
a
n
d
p
h
ase
co
m
p
en
s
atio
n
tech
n
iq
u
es.
T
h
e
m
ain
co
n
tr
ib
u
tio
n
s
o
f
th
is
wo
r
k
ar
e
as f
o
llo
ws.
First,
it
d
em
o
n
s
tr
ates th
at
wh
ile
t
h
e
m
at
h
em
atica
l
d
escr
ip
tio
n
s
o
f
th
e
th
r
ee
co
n
s
id
er
ed
to
p
o
l
o
g
ies
ar
e
eq
u
i
v
alen
t,
th
eir
d
is
cr
etize
d
i
m
p
lem
en
tatio
n
s
d
if
f
er
d
u
e
to
v
ar
iatio
n
s
in
d
is
cr
etiza
tio
n
m
et
h
o
d
s
.
Sec
o
n
d
,
a
n
o
v
el
p
h
ase
co
m
p
en
s
atio
n
a
p
p
r
o
ac
h
is
p
r
o
p
o
s
ed
f
o
r
th
e
Ad
alin
e
an
d
HC
to
p
o
lo
g
ies,
f
illi
n
g
a
g
ap
in
th
e
e
x
is
tin
g
liter
atu
r
e.
T
h
ir
d
,
t
h
e
ef
f
ec
tiv
en
ess
o
f
th
e
h
ar
m
o
n
ic
c
o
n
tr
o
ller
s
is
v
alid
ated
th
r
o
u
g
h
b
o
t
h
s
im
u
latio
n
an
d
ex
p
er
im
en
tal
r
esu
lts
,
s
p
ec
if
ical
ly
in
th
e
co
n
tex
t
o
f
h
ar
m
o
n
ic
ca
n
ce
llatio
n
in
s
p
ee
d
a
n
d
c
u
r
r
en
t c
o
n
tr
o
l l
o
o
p
s
.
T
h
e
r
em
ain
d
er
o
f
th
e
p
a
p
er
is
o
r
g
an
ized
as
s
ec
tio
n
2
is
d
e
d
icate
d
to
th
e
co
n
tr
o
l
to
p
o
lo
g
ies
o
f
Ad
alin
e,
RC
,
an
d
HC
,
f
o
llo
wed
b
y
th
e
s
im
u
latio
n
an
d
ex
p
er
im
en
tal
v
al
id
atio
n
g
iv
e
n
in
s
ec
tio
n
3
.
Fin
a
lly
,
th
e
co
n
clu
s
io
n
s
ar
e
s
u
m
m
ar
ized
in
s
ec
tio
n
4
.
2.
CO
M
P
ARI
SO
N
AND
I
M
P
L
E
M
E
N
T
AT
I
O
N
O
F
H
ARM
O
NIC CO
NT
RO
L
L
E
R
S
2
.
1
.
Co
m
pa
riso
n bet
wee
n Ada
lin
e,
RC,
a
nd
H
C
T
o
illu
s
tr
ate
th
e
s
im
ilar
itie
s
b
etwe
en
th
e
Ad
alin
e,
h
ar
m
o
n
ic
co
n
tr
o
ller
,
an
d
th
e
r
eso
n
an
t
co
n
tr
o
ller
,
let’
s
co
n
s
id
er
an
ex
am
p
le
o
f
p
h
ase
cu
r
r
en
t
h
ar
m
o
n
ic
co
n
tr
o
l
in
th
e
r
o
to
r
f
l
u
x
-
o
r
ien
ted
r
ef
er
en
ce
f
r
am
e
(
-
r
ef
er
en
ce
f
r
am
e)
.
First,
th
e
tr
an
s
f
er
f
u
n
ctio
n
o
f
th
e
R
C
will
b
e
p
r
esen
ted
.
T
h
e
n
th
e
co
m
p
ar
is
o
n
am
o
n
g
th
e
Ad
alin
e,
HC
,
an
d
R
C
will
b
e
ad
d
r
ess
ed
as
f
o
llo
ws:
i)
th
e
HC
an
d
R
C
ar
e
co
m
p
a
r
ed
in
ter
m
s
o
f
m
ath
em
atica
l
r
ep
r
esen
tatio
n
an
d
ii)
th
e
HC
an
d
Ad
alin
e
ar
e
c
o
m
p
ar
e
d
with
r
eg
ar
d
to
w
o
r
k
in
g
p
r
in
ci
p
le
a
n
d
im
p
lem
en
tatio
n
.
Fig
u
r
e
1
(
a)
s
h
o
ws
th
e
s
tr
u
ctu
r
e
o
f
th
e
h
ar
m
o
n
ic
co
n
tr
o
ller
,
c
o
m
p
o
s
ed
o
f
a
r
eso
n
an
t
c
o
m
p
o
n
en
t
(
R
C
)
wo
r
k
in
g
in
p
ar
allel
with
a
co
n
v
en
tio
n
al
p
r
o
p
o
r
tio
n
al
-
in
teg
r
al
(
PI)
co
n
tr
o
ller
[
4
]
.
T
h
e
tr
an
s
f
er
f
u
n
ctio
n
o
f
th
e
r
eso
n
an
t c
o
n
tr
o
ller
with
o
u
t p
h
ase
co
m
p
en
s
atio
n
is
g
iv
en
b
y
(
1
)
.
RC
(
)
=
i
∙
2
+
2
(
1
)
W
h
er
e
=
2
π
with
is
th
e
f
r
eq
u
en
cy
o
f
th
e
x
th
h
ar
m
o
n
ic
to
b
e
co
n
s
i
d
er
ed
;
i
is
th
e
g
ain
o
f
th
e
R
C
;
an
d
(
)
=
1
(
+
)
⁄
is
th
e
eq
u
iv
alen
t
tr
an
s
f
er
f
u
n
c
tio
n
th
at
co
m
b
i
n
es
th
e
tr
an
s
f
er
f
u
n
ctio
n
s
o
f
th
e
m
ac
h
i
n
e,
th
e
in
v
er
ter
a
n
d
th
e
lo
w
-
p
ass
f
ilter
u
s
ed
f
o
r
t
h
e
cu
r
r
en
t m
ea
s
u
r
em
en
t.
T
h
e
p
r
im
a
r
y
id
ea
o
f
th
e
R
C
is
to
p
r
o
v
id
e
in
f
in
ite
g
ain
o
f
th
e
o
p
en
l
o
o
p
at
th
e
r
eso
n
an
t f
r
eq
u
en
cy
,
an
d
h
en
ce
it
en
s
u
r
es
a
ze
r
o
er
r
o
r
f
o
r
th
e
clo
s
ed
co
n
tr
o
l
lo
o
p
.
Ho
wev
er
,
th
e
R
C
co
n
tr
o
ller
g
iv
en
in
(
1
)
ca
n
n
o
t
m
an
ip
u
late
a
r
eso
n
an
t
f
r
eq
u
e
n
cy
th
at
is
r
elativ
ely
h
ig
h
co
m
p
ar
ed
to
th
e
s
am
p
lin
g
f
r
e
q
u
en
cy
o
f
th
e
co
n
tr
o
l
alg
o
r
ith
m
.
T
h
is
is
d
u
e
to
th
e
ti
m
e
d
elay
o
r
ig
in
ated
f
r
o
m
th
e
c
o
n
tr
o
l
alg
o
r
ith
m
.
T
h
e
tim
e
d
elay
r
ed
u
ce
s
th
e
p
h
ase
m
ar
g
in
o
f
th
e
clo
s
ed
co
n
tr
o
l
lo
o
p
,
wh
ich
is
th
en
p
r
o
n
e
to
in
s
tab
ilit
y
.
T
o
ad
d
r
ess
th
is
is
s
u
e,
p
h
ase
co
m
p
en
s
atio
n
is
co
m
m
o
n
ly
ap
p
lied
to
th
e
R
C
to
in
cr
ea
s
e
th
e
p
h
ase
m
ar
g
i
n
.
T
h
e
tr
an
s
f
e
r
f
u
n
ctio
n
o
f
t
h
e
m
o
d
if
ied
r
eso
n
an
t
co
n
tr
o
ller
with
p
h
ase
co
m
p
e
n
s
atio
n
is
g
iv
en
in
(
2
)
[
1
8
]
,
[
2
2
]
.
RC
(
)
=
i
∙
∙
co
s
m
−
∙
s
i
n
m
2
+
2
(
2
)
W
h
er
e
m
is
th
e
co
m
p
en
s
ated
p
h
ase.
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
Ha
r
mo
n
ic
co
n
tr
o
l in
elec
tr
ica
l d
r
ives fo
r
tr
a
n
s
p
o
r
t sys
tems
(
Th
a
n
h
Lich
N
g
u
ye
n
)
829
Fig
u
r
e
1
(
b
)
d
ep
icts
th
e
clo
s
ed
-
lo
o
p
cu
r
r
en
t
co
n
tr
o
l
in
co
r
p
o
r
at
in
g
th
e
m
o
d
if
ied
r
eso
n
a
n
t
co
n
t
r
o
ller
.
As
ex
p
r
ess
ed
in
(
2
)
,
t
h
e
tr
an
s
f
er
f
u
n
ctio
n
RC
(
)
in
v
o
lv
es two
k
ey
d
esi
g
n
p
ar
am
eter
s
,
n
a
m
ely
th
e
g
ai
n
i
an
d
th
e
p
h
ase
m
.
Ph
ase
co
m
p
en
s
atio
n
is
ex
clu
d
ed
in
th
e
s
co
p
e
o
f
th
i
s
s
tu
d
y
an
d
will
b
e
p
r
esen
ted
in
d
etail
in
th
e
o
n
g
o
in
g
wo
r
k
.
R
eg
ar
d
in
g
th
e
d
esig
n
o
f
g
ain
i
,
th
er
e
a
r
e
s
o
m
e
r
em
ar
k
s
.
Firstl
y
,
i
d
ec
id
es
th
e
d
y
n
am
ics
o
f
th
e
clo
s
ed
lo
o
p
p
er
tain
in
g
to
r
e
f
e
r
en
ce
tr
ac
k
in
g
ca
p
a
b
ilit
y
.
T
h
e
h
ig
h
er
th
e
v
al
u
e
o
f
i
,
th
e
f
aster
o
f
t
h
e
o
u
t
p
u
t
r
esp
o
n
s
e
,
b
u
t
th
e
co
n
tr
o
ller
r
ea
ch
es
s
atu
r
atio
n
ea
r
lier
.
Se
co
n
d
ly
,
t
h
e
h
ig
h
er
th
e
v
alu
e
o
f
th
e
am
p
litu
d
e
ass
o
ciate
d
with
th
e
r
eso
n
a
n
t
h
a
r
m
o
n
ic,
th
e
h
i
g
h
er
th
e
g
ain
i
.
T
h
ir
d
ly
,
if
th
er
e
ar
e
s
ev
er
al
r
eso
n
an
t
co
m
p
o
n
e
n
ts
,
th
e
g
ain
s
m
u
s
t
b
e
o
p
tim
ized
s
eq
u
en
tially
to
en
s
u
r
e
t
h
at
th
e
in
ter
ac
tio
n
b
etwe
en
th
e
h
ar
m
o
n
ic
co
m
p
o
n
en
ts
is
u
n
d
er
f
u
lly
tak
e
n
in
to
ac
c
o
u
n
t.
(
a)
(
b
)
Fig
u
r
e
1
.
R
eso
n
an
t c
o
n
tr
o
ller
f
o
r
th
e
c
u
r
r
e
n
t c
o
n
tr
o
l lo
o
p
:
(
a
)
with
o
u
t p
h
ase
co
m
p
e
n
s
atio
n
an
d
(
b
)
with
p
h
ase
co
m
p
e
n
s
atio
n
2
.
1
.
1
.
Co
m
pa
riso
n o
f
H
C
a
n
d RC
T
h
is
s
ec
tio
n
p
r
esen
ts
a
d
etail
ed
m
ath
em
atica
l
an
aly
s
is
d
em
o
n
s
tr
atin
g
th
e
eq
u
iv
alen
ce
b
etwe
en
th
e
r
eso
n
an
t
co
n
tr
o
ller
an
d
th
e
h
a
r
m
o
n
ic
c
o
n
tr
o
ller
in
ter
m
s
o
f
th
eir
m
ath
em
atica
l
f
o
r
m
u
latio
n
.
I
t
is
well
k
n
o
w
n
th
at
as (
3
)
-
(
5
)
.
co
s
(
)
=
(
)
∙
c
os
(
+
m
)
=
(
)
∙
e
j
(
+
m
)
+
e
−
j
(
+
m
)
2
(
3
)
s
i
n
(
)
=
(
)
∙
s
in
(
+
m
)
=
(
)
∙
e
j
(
+
m
)
−
e
−
j
(
+
m
)
2
j
(
4
)
ℒ
{
e
(
)
}
→
(
−
)
(
5
)
W
h
er
e
ℒ
is
th
e
L
ap
lace
tr
an
s
f
o
r
m
an
d
is
th
e
an
g
u
lar
v
elo
city
o
f
th
e
x
th
h
ar
m
o
n
ic.
T
ak
i
n
g
th
e
L
ap
lace
tr
an
s
f
o
r
m
atio
n
,
we
h
av
e
(
6
)
a
n
d
(
7
)
.
co
s
(
)
=
1
2
[
(
−
0
)
∙
e
j
m
+
(
+
0
)
∙
e
−
j
m
]
(
6
)
s
i
n
(
)
=
j
2
[
(
−
0
)
∙
e
j
m
−
(
+
0
)
∙
e
−
j
m
]
(
7
)
W
e
d
en
o
te
∗
as th
e
co
n
v
o
lu
tio
n
m
u
ltip
licatio
n
,
th
en
as (
8
)
.
x
H
ar
(
)
=
{
[
∆
(
)
∙
c
os
(
)
∗
ℎ
(
)
]
}
∙
c
os
(
+
m
)
+
{
[
∆
(
)
∙
s
in
(
)
∗
ℎ
(
)
]
}
∙
s
in
(
+
m
)
(
8
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
2
,
J
u
n
e
20
25
:
8
2
7
-
8
3
9
830
W
e
d
en
o
te
as (
9
)
a
n
d
(
1
0
)
.
1
(
)
=
∆
(
)
∙
c
os
(
)
∗
ℎ
(
)
(
9
)
2
(
)
=
∆
(
)
∙
(
)
∗
ℎ
(
)
(
1
0
)
T
h
en
th
e
L
a
p
lace
tr
an
s
f
o
r
m
atio
n
o
f
1
(
)
an
d
2
(
)
ar
e
as (
1
1
)
a
n
d
(
1
2
)
.
1
(
)
=
ℒ
{
∆
(
)
∙
c
os
(
)
∗
ℎ
(
)
}
=
ℒ
{
∆
(
)
∙
c
os
(
)
}
∙
(
)
=
1
2
[
∆
(
+
j
)
+
∆
(
−
j
)
]
∙
(
)
(
1
1
)
2
(
)
=
ℒ
{
∆
(
)
∙
s
in
(
)
∗
ℎ
(
)
}
=
ℒ
{
∆
(
)
∙
s
in
(
)
}
∙
(
)
=
j
2
[
∆
(
+
j
)
−
∆
(
−
j
)
]
∙
(
)
(
1
2
)
Acc
o
r
d
in
g
t
o
(
6
)
an
d
(
1
1
)
,
we
h
av
e
(
1
3
)
.
=
ℒ
{
[
∆
(
)
∙
c
os
(
)
∗
ℎ
(
)
]
∙
c
os
(
+
m
)
}
=
ℒ
{
1
(
)
∙
c
os
(
+
m
)
}
=
1
2
{
1
(
−
j
)
∙
e
j
m
+
1
(
+
j
)
∙
e
−
j
m
}
=
1
4
{
[
[
∆
(
)
+
∆
(
−
2
j
)
]
∙
(
−
j
)
]
∙
e
j
m
+
[
∆
(
+
2
j
)
+
∆
(
)
]
∙
(
+
j
)
∙
e
−
j
m
}
(
1
3
)
Acc
o
r
d
in
g
t
o
(
7
)
an
d
(
1
2
)
,
we
h
av
e
(
1
4
)
.
=
ℒ
{
[
∆
(
)
∙
s
in
(
)
∗
ℎ
(
)
]
∙
s
in
(
+
m
)
}
=
ℒ
{
2
(
)
∙
s
in
(
+
m
)
}
=
j
2
{
2
(
−
j
)
∙
e
j
m
−
1
(
+
j
)
∙
e
−
j
m
}
=
1
4
{
[
[
∆
(
)
−
∆
(
−
2
j
)
]
∙
(
−
j
)
]
∙
e
j
m
−
[
∆
(
+
2
j
)
−
∆
(
)
]
∙
(
+
j
)
∙
e
−
j
m
}
(
1
4
)
Su
b
s
titu
te
(
1
3
)
an
d
(
1
4
)
in
t
o
(
8
)
we
h
av
e
(
1
5
)
.
ℒ
(
Ha
r
)
=
+
=
1
2
{
(
−
j
)
∙
e
j
m
+
(
+
j
)
∙
e
−
j
m
}
∆
(
)
(
1
5
)
Fro
m
(
1
5
)
with
(
)
=
i
/
,
th
e
tr
an
s
f
er
f
u
n
ctio
n
o
f
th
e
h
ar
m
o
n
ic
co
n
tr
o
ller
is
(
1
6
)
.
HC
(
)
=
1
2
[
(
−
j
)
∙
e
j
m
+
(
+
j
)
∙
e
−
j
m
]
=
1
2
i
−
j
∙
e
j
m
+
1
2
i
+
j
∙
e
−
j
m
=
i
(
∙
co
s
m
−
∙
s
i
n
m
)
2
+
2
(
1
6
)
Fro
m
(
2
)
an
d
(
1
6
)
it is
o
b
v
io
u
s
th
at
th
e
tr
an
s
f
er
f
u
n
ctio
n
s
o
f
th
e
HC
an
d
o
f
th
e
R
C
ar
e
id
en
tical.
2
.
1
.
2
.
Co
m
pa
riso
n o
f
H
C
a
n
d Ada
lin
e
T
h
e
g
r
a
p
h
ical
d
ep
ictio
n
o
f
th
e
HC
is
s
h
o
wn
in
Fig
u
r
e
2
,
wit
h
(
1
7
)
.
=
∫
d
(
17
)
W
h
er
e:
is
th
e
elec
tr
ical
an
g
le
o
f
th
e
x
th
h
ar
m
o
n
ic.
T
h
e
r
elatio
n
s
h
ip
b
etwe
en
th
e
Ad
alin
e
a
n
d
th
e
h
ar
m
o
n
ic
co
n
tr
o
ller
to
p
o
lo
g
ies,
as
s
h
o
wn
in
Fig
u
r
es
3
(
a)
an
d
3
(
b
)
,
is
n
o
w
d
is
cu
s
s
ed
.
T
h
e
Ad
alin
e
to
p
o
lo
g
y
with
p
h
ase
co
m
p
en
s
atio
n
,
as
d
ep
icted
i
n
Fig
u
r
e
3
(
a)
,
is
a
co
n
tr
ib
u
tio
n
to
th
is
wo
r
k
.
I
n
th
e
s
am
e
m
a
n
n
er
as
th
e
R
C
,
th
e
Ad
alin
e
with
p
h
ase
co
m
p
e
n
s
atio
n
en
h
a
n
ce
s
th
e
s
y
s
tem
s
tab
ilit
y
an
d
im
p
r
o
v
es
th
e
d
y
n
am
ic
p
er
f
o
r
m
an
ce
o
f
th
e
r
ef
er
en
ce
tr
ac
k
in
g
.
T
h
e
(
1
8
)
an
d
(
1
9
)
d
escr
ib
e
th
e
weig
h
t u
p
d
ate
law
in
t
h
e
Ad
a
lin
e
m
o
d
el,
wh
er
e
,
A
d
a
co
s
an
d
,
A
d
a
s
i
n
ar
e
weig
h
t
p
ar
am
ete
r
s
ass
o
ciate
d
with
th
e
x
th
h
ar
m
o
n
ic
at
an
g
l
e
.
Sp
ec
if
ically
,
th
ese
weig
h
ts
ar
e
u
p
d
ated
b
y
ad
d
in
g
a
ter
m
p
r
o
p
o
r
tio
n
al
to
th
e
lear
n
in
g
r
ate
,
cu
r
r
en
t
e
r
r
o
r
∆
,
an
d
s
in
e/co
s
in
e
v
alu
es
o
f
d
ef
in
ed
in
(
1
7
)
.
,
A
d
a
co
s
=
,
A
d
a
co
s
+
∙
∆
∙
c
os
(
)
(
1
8
)
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
Ha
r
mo
n
ic
co
n
tr
o
l in
elec
tr
ica
l d
r
ives fo
r
tr
a
n
s
p
o
r
t sys
tems
(
Th
a
n
h
Lich
N
g
u
ye
n
)
831
,
A
d
a
s
i
n
=
,
A
d
a
s
i
n
+
∙
∆
∙
s
in
(
)
(
1
9
)
I
t
is
n
ec
ess
ar
y
to
m
en
tio
n
ag
ain
th
at
f
o
r
d
if
f
er
en
t
h
ar
m
o
n
ics
co
r
r
esp
o
n
d
in
g
to
d
is
tin
ct
r
eso
n
an
t
f
r
eq
u
en
cies
th
e
ap
p
r
o
p
r
iate
lear
n
in
g
r
ate
m
u
s
t
b
e
ch
o
s
en
s
eq
u
en
tially
t
o
en
s
u
r
e
s
tab
ilit
y
an
d
o
p
tim
al
p
er
f
o
r
m
an
ce
.
T
h
e
f
in
al
esti
m
ated
h
ar
m
o
n
ic
v
o
ltag
e
A
d
a
is
th
en
in
c
o
r
p
o
r
ated
in
to
th
e
cu
r
r
e
n
t
c
o
n
tr
o
l
lo
o
p
t
o
e
n
h
a
n
ce
h
a
r
m
o
n
ic
co
m
p
en
s
atio
n
.
On
th
e
o
th
er
h
a
n
d
,
(
2
0
)
a
n
d
(
2
1
)
d
e
f
in
e
th
e
u
p
d
ate
law
f
o
r
th
e
HC
,
wh
er
e
x
,
Har
co
s
an
d
x
,
Har
s
i
n
ar
e
o
b
tain
ed
th
r
o
u
g
h
in
teg
r
al
o
p
e
r
atio
n
s
in
v
o
lv
in
g
i
∙
∆
,
an
d
th
e
c
o
r
r
esp
o
n
d
in
g
tr
ig
o
n
o
m
etr
ic
ter
m
s
.
x
,
Har
co
s
=
∫
i
∙
∆
∙
c
os
(
)
∙
d
(
2
0
)
x
,
Har
s
i
n
=
∫
i
∙
∆
∙
s
in
(
)
∙
d
(
2
1
)
W
h
er
e
i
is
th
e
g
ain
o
f
th
e
h
ar
m
o
n
ic
co
n
t
r
o
ller
.
T
h
e
s
elec
tio
n
o
f
i
ca
n
b
e
d
o
n
e
b
y
th
e
r
o
o
t
-
lo
c
u
s
m
eth
o
d
a
n
d
is
co
n
d
u
cted
o
n
e
-
by
-
o
n
e
to
co
n
s
id
er
th
e
in
ter
ac
tio
n
b
et
wee
n
d
if
f
er
e
n
t
HC
s
co
r
r
esp
o
n
d
in
g
to
d
if
f
er
en
t
h
ar
m
o
n
ics
[
2
3
]
.
B
y
co
m
p
a
r
in
g
(
1
8
)
with
(
2
0
)
an
d
(
1
9
)
with
(
2
1
)
,
we
o
b
s
er
v
e
th
at
i
f
we
s
et
=
i
∙
Δ
,
wh
er
e
Δ
is
th
e
s
am
p
lin
g
tim
e
o
f
th
e
in
teg
r
al
,
an
d
if
th
e
ap
p
r
o
x
im
ati
o
n
o
f
th
e
in
teg
r
als
in
(
2
0
)
an
d
(
2
1
)
ad
o
p
ts
th
e
f
o
r
war
d
E
u
ler
m
eth
o
d
,
t
h
en
w
e
o
b
tain
(
2
2
)
a
n
d
(
2
3
)
.
x
,
Har
co
s
=
x
,
Har
co
s
+
i
∙
∆
∙
c
os
(
)
∙
Δ
(
2
2
)
x
,
Har
s
i
n
=
x
,
Har
s
i
n
+
i
∙
∆
∙
s
in
(
)
∙
Δ
(
2
3
)
I
t
is
o
b
s
er
v
ed
th
at
th
e
u
p
d
ate
r
u
les
f
o
r
th
e
Ad
alin
e
an
d
th
e
HC
b
ec
o
m
e
m
ath
em
atica
lly
i
d
e
n
tical.
T
h
is
co
n
f
ir
m
s
th
at
th
e
two
m
eth
o
d
s
ar
e
f
u
n
d
am
en
tally
eq
u
iv
ale
n
t.
Fig
u
r
e
2
.
Stru
ctu
r
e
o
f
th
e
h
a
r
m
o
n
ic
co
n
tr
o
ller
(
a)
(
b
)
Fig
u
r
e
3
.
Stru
ctu
r
es o
f
th
e
(
a)
Ad
alin
e
an
d
(
b
)
h
ar
m
o
n
ic
co
n
t
r
o
ller
s
eq
u
ip
p
e
d
with
a
PI
c
o
n
tr
o
ller
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
2
,
J
u
n
e
20
25
:
8
2
7
-
8
3
9
832
T
h
e
r
e
a
r
e
s
e
v
e
r
a
l
i
m
p
o
r
t
a
n
t
r
em
a
r
k
s
t
h
a
t
c
a
n
b
e
d
r
a
w
n
f
r
o
m
A
d
a
l
i
n
e
a
n
d
HC
.
Fi
r
s
t
,
b
o
t
h
o
f
th
e
m
o
p
e
r
a
t
e
b
a
s
e
d
o
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i
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l
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p
h
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r
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r
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t
i
o
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il
a
r
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o
Pa
r
k
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n
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i
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l
d
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o
r
i
e
n
t
e
d
c
o
n
t
r
o
l
(
F
OC
)
.
T
h
is
t
r
a
n
s
f
o
r
m
a
t
i
o
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al
lo
w
s
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h
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p
d
a
t
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k
d
i
r
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l
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t
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t
h
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o
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p
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o
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r
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l
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n
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l
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m
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v
i
n
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b
o
t
h
t
h
e
d
y
n
a
m
i
c
s
a
n
d
a
c
c
u
r
a
c
y
o
f
t
h
e
c
o
n
tr
o
l
a
l
g
o
r
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t
h
m
.
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o
t
h
A
d
a
l
i
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C
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s
u
r
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e
p
o
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e
p
l
a
c
e
m
e
n
t
at
t
h
e
r
es
o
n
a
n
t
f
r
e
q
u
e
n
c
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w
h
e
n
d
i
s
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r
e
t
iz
i
n
g
t
h
e
c
o
n
t
r
o
l
a
l
g
o
r
i
t
h
m
wi
t
h
a
n
y
m
e
t
h
o
d
.
2
.
2
.
I
m
ple
m
ent
a
t
io
n o
f
t
he
ha
rm
o
nic
co
ntr
o
ller
As
p
r
esen
ted
in
s
ec
tio
n
2
.
1
.
,
th
e
Ad
alin
e,
th
e
R
C
,
an
d
t
h
e
HC
ar
e
m
ath
em
atica
lly
eq
u
iv
alen
t.
T
h
e
d
if
f
er
en
ce
s
am
o
n
g
th
ese
to
p
o
lo
g
ies
lie
in
th
eir
d
is
cr
etiza
tio
n
m
eth
o
d
s
.
T
h
e
d
is
cr
etize
d
p
o
les
o
f
th
e
r
eso
n
an
t
co
n
tr
o
ller
,
wh
o
s
e
to
p
o
lo
g
y
is
s
h
o
wn
in
Fig
u
r
e
1
(
a
)
,
s
tr
o
n
g
l
y
d
ep
en
d
o
n
th
e
d
is
cr
etiza
tio
n
m
eth
o
d
[
1
7
]
.
I
d
ea
lly
,
th
e
r
eso
n
an
t
c
o
n
tr
o
ller
p
r
o
v
id
e
s
in
f
in
ite
g
ain
at
1
,
2
=
±
j
h
.
C
o
n
s
eq
u
en
tl
y
,
th
e
d
is
cr
etize
d
d
en
o
m
in
ato
r
o
f
th
e
r
eso
n
an
t c
o
n
tr
o
ller
s
h
o
u
ld
b
e
i
n
th
e
f
o
r
m
o
f
(
2
4
)
.
D
e
nom
ina
t
or
=
(
−
1
)
(
−
2
)
→
(
−
e
−
j
s
)
(
−
e
j
s
)
=
2
−
2
cos
(
s
)
+
1
(
2
4
)
W
h
er
e
s
is
th
e
s
am
p
lin
g
tim
e
o
f
th
e
h
ar
m
o
n
ic
co
n
tr
o
ller
.
T
ab
le
1
s
u
m
m
ar
izes
th
e
d
en
o
m
in
ato
r
f
o
r
m
s
o
f
th
e
r
eso
n
an
t
co
n
tr
o
ller
ac
co
r
d
in
g
to
d
if
f
e
r
en
t
d
is
cr
etiza
tio
n
m
et
h
o
d
s
.
I
t
is
o
b
v
i
o
u
s
th
at
o
n
ly
t
h
e
m
eth
o
d
in
g
r
o
u
p
E
,
co
n
s
is
tin
g
o
f
t
h
e
ze
r
o
-
o
r
d
e
r
h
o
ld
(
Z
OH)
,
f
ir
s
t
-
o
r
d
er
h
o
l
d
(
FOH)
,
T
u
s
tin
with
p
r
e
-
war
p
in
g
(
T
P),
im
p
u
ls
e
r
esp
o
n
s
e
(
I
PM)
,
a
n
d
ze
r
o
-
p
o
le
m
atch
in
g
(
Z
PM)
,
en
s
u
r
es
p
r
ec
is
e
p
o
les
o
f
th
e
r
eso
n
an
t
co
n
tr
o
ller
af
te
r
th
e
d
is
cr
etiza
tio
n
p
r
o
ce
s
s
.
I
n
co
n
tr
ast,
o
th
er
d
is
cr
etiza
tio
n
m
et
h
o
d
s
in
tr
o
d
u
ce
p
o
le
s
h
if
ts
ar
o
u
n
d
t
h
e
r
eso
n
an
t
f
r
eq
u
e
n
cy
.
T
h
is
s
h
if
t
r
ed
u
ce
s
th
e
g
ain
o
f
th
e
r
eso
n
a
n
t
co
m
p
o
n
en
t
at
th
e
r
eso
n
an
t
f
r
eq
u
en
cy
,
r
esu
ltin
g
in
a
n
o
n
-
ze
r
o
s
tead
y
-
s
tate
er
r
o
r
in
th
e
c
lo
s
ed
lo
o
p
c
o
n
tr
o
l sy
s
tem
.
T
h
e
d
eter
m
i
n
atio
n
o
f
th
e
p
h
as
e
co
m
p
e
n
s
atio
n
p
lay
s
a
cr
u
cial
r
o
le
in
f
ac
ilit
atin
g
th
e
im
p
lem
en
tatio
n
o
f
h
ar
m
o
n
ic
c
o
n
tr
o
ller
s
.
I
n
p
r
in
ci
p
le,
th
e
co
m
p
en
s
ated
p
h
ase
f
o
r
ea
ch
h
ar
m
o
n
ic
ca
n
b
e
d
e
f
in
ed
b
y
a
lo
o
k
-
u
p
tab
le.
T
o
b
u
ild
u
p
th
e
lo
o
k
-
u
p
tab
le,
a
p
r
o
ce
d
u
r
e
as
d
ep
icted
in
Fi
g
u
r
e
4
ca
n
b
e
em
p
lo
y
ed
.
T
h
e
m
ac
h
in
e
o
p
er
ates
at
d
if
f
er
en
t
o
p
er
atin
g
p
o
in
ts
d
e
f
in
ed
b
y
d
if
f
er
e
n
t
lo
ad
to
r
q
u
es
an
d
s
p
ee
d
s
u
s
in
g
a
co
n
v
en
tio
n
al
PI
cu
r
r
en
t
co
n
tr
o
ller
,
with
o
u
t
im
p
lem
en
t
in
g
R
C
,
HC
,
o
r
Ad
alin
e
c
o
n
tr
o
ller
s
.
At
ea
ch
o
p
er
atin
g
p
o
in
t,
th
e
r
ef
e
r
en
ce
a
n
d
m
ea
s
u
r
ed
cu
r
r
en
t
i
n
th
e
d
-
a
n
d
q
-
ax
es
ar
e
r
ec
o
r
d
ed
an
d
p
r
o
ce
s
s
ed
u
s
in
g
an
o
n
lin
e
f
ast
Fo
u
r
i
er
tr
an
s
f
o
r
m
(
FF
T
)
alg
o
r
ith
m
.
T
h
e
m
ain
f
u
n
ctio
n
o
f
th
e
o
n
lin
e
FF
T
alg
o
r
ith
m
is
to
ex
tr
ac
t
t
h
e
p
h
ase
in
f
o
r
m
atio
n
o
f
th
e
co
n
s
id
er
e
d
h
ar
m
o
n
ics
em
b
e
d
d
ed
in
t
h
e
r
ef
er
en
ce
an
d
m
ea
s
u
r
ed
cu
r
r
e
n
ts
.
T
h
e
p
h
ase
d
if
f
er
e
n
ce
b
et
wee
n
th
ese
s
ig
n
als
d
eter
m
in
es
th
e
r
eq
u
ir
ed
p
h
ase
co
m
p
en
s
atio
n
at
ea
c
h
o
p
e
r
atin
g
p
o
i
n
t.
B
y
co
m
b
i
n
in
g
th
e
p
h
ase
co
m
p
en
s
atio
n
d
ata
f
r
o
m
m
u
lt
ip
le
o
p
er
atin
g
p
o
in
ts
,
th
e
f
in
al
lo
o
k
-
u
p
tab
le
f
o
r
th
e
p
h
ase
co
m
p
en
s
atio
n
i
s
b
u
ilt.
Fo
r
s
im
p
le
im
p
lem
en
tatio
n
,
lin
ea
r
in
ter
p
o
latio
n
ca
n
b
e
u
s
ed
f
o
r
th
e
lo
o
k
-
u
p
tab
le.
T
ab
le
1
.
Dis
cr
etiza
tio
n
o
f
th
e
r
eso
n
an
t c
o
n
tr
o
ller
G
r
o
u
p
Ex
p
r
e
ssi
o
n
D
e
n
o
mi
n
a
t
o
r
A
f
(
)
-
F
o
r
w
a
r
d
E
u
l
e
r
1
−
2
−
1
+
−
2
(
2
s
2
+
1
)
B
b
(
)
-
B
a
c
k
w
a
r
d
Eu
l
e
r
(
2
s
2
+
1
)
−
2
−
1
+
−
2
C
t
(
)
-
Tu
s
t
i
n
(
2
s
2
+
4
)
+
(
2
2
s
2
−
8
)
−
1
+
−
2
(
2
s
2
+
4
)
D
f
&
b
(
)
-
F
o
r
w
a
r
d
&
B
a
c
k
w
a
r
d
1
+
(
2
s
2
−
2
)
−
1
+
−
2
E
z
o
h
(
)
,
f
o
h
(
)
,
tp
(
)
,
ip
m
(
)
,
zpm
(
)
1
−
2
cos
(
s
)
−
1
+
−
2
Fig
u
r
e
4
.
Pro
ce
d
u
r
e
f
o
r
b
u
ild
i
n
g
th
e
lo
o
k
-
u
p
tab
le
T
h
e
th
r
ee
ty
p
es o
f
co
n
tr
o
ller
s
ar
e
th
en
co
m
p
ar
e
d
in
ter
m
s
o
f
m
em
o
r
y
r
e
q
u
ir
em
e
n
t a
n
d
co
m
p
u
tatio
n
al
co
m
p
lex
ity
.
As
alr
ea
d
y
m
en
ti
o
n
ed
in
s
ec
tio
n
2
.
2
,
th
e
d
is
cr
etiza
tio
n
m
eth
o
d
s
b
elo
n
g
i
n
g
to
g
r
o
u
p
E
en
s
u
r
e
an
in
f
in
ite
g
ain
o
f
th
e
r
eso
n
an
t
co
n
tr
o
ller
,
as
g
iv
en
in
(
2
)
,
at
t
h
e
r
eso
n
an
t f
r
eq
u
e
n
cy
,
m
ak
in
g
th
em
s
u
itab
le
f
o
r
th
e
R
C
im
p
lem
en
tatio
n
.
Fo
r
ev
al
u
atio
n
p
u
r
p
o
s
es,
th
e
T
u
s
tin
m
eth
o
d
with
p
r
e
-
wr
ap
p
in
g
is
s
e
lecte
d
to
ass
ess
th
e
r
u
n
tim
e
p
er
f
o
r
m
a
n
ce
an
d
m
e
m
o
r
y
r
e
q
u
ir
em
e
n
ts
.
T
h
e
d
is
cr
e
tized
tr
an
s
f
er
f
u
n
ctio
n
o
f
th
e
r
eso
n
an
t c
o
n
tr
o
ller
is
ex
p
r
ess
ed
as (
2
5
)
[
2
4
]
.
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
Ha
r
mo
n
ic
co
n
tr
o
l in
elec
tr
ica
l d
r
ives fo
r
tr
a
n
s
p
o
r
t sys
tems
(
Th
a
n
h
Lich
N
g
u
ye
n
)
833
G
RC
(
)
=
i
∙
∙
co
s
m
−
∙
s
i
n
m
2
+
2
→
G
RC
(
)
=
i
∙
1
2
(
1
−
−
2
)
co
s
m
s
i
n
(
s
)
−
(
1
+
2
−
1
+
−
2
)
s
i
n
m
s
i
n
2
(
s
2
)
m
(
1
−
2
co
s
(
s
)
−
1
+
−
2
)
(
2
5
)
W
h
er
e
s
is
th
e
s
am
p
lin
g
tim
e
o
f
th
e
R
C
.
Fo
r
th
e
ca
s
e
o
f
Ad
alin
e
an
d
HC
,
th
e
f
o
r
war
d
E
u
ler
d
is
cr
etiza
tio
n
m
eth
o
d
is
ad
o
p
ted
d
u
e
to
its
s
im
p
licity
,
wh
ile
s
till
en
s
u
r
in
g
g
o
o
d
b
e
h
av
io
r
o
f
th
e
co
n
tr
o
ller
s
.
I
t
is
n
ec
ess
ar
y
to
m
en
tio
n
th
at
th
e
s
in
g
le
p
r
ec
is
io
n
f
lo
atin
g
-
p
o
i
n
t
v
ar
ia
b
le
is
p
r
ef
er
r
e
d
in
th
e
a
u
to
m
o
tiv
e
in
d
u
s
tr
y
d
u
e
to
t
h
e
co
m
p
r
o
m
is
e
b
etwe
en
th
e
p
r
ec
is
io
n
an
d
m
em
o
r
y
/r
u
n
tim
e
o
p
tim
izatio
n
.
T
ab
le
2
s
h
o
ws
a
co
m
p
a
r
ativ
e
ev
alu
at
io
n
o
f
th
e
m
em
o
r
y
r
eq
u
ir
em
e
n
t
an
d
co
m
p
u
tatio
n
a
l
lo
ad
o
f
th
e
R
C
,
HC
,
an
d
Ad
a
lin
e
co
n
tr
o
ller
s
.
I
t
is
o
b
s
er
v
e
d
th
at
th
e
e
x
ec
u
tio
n
o
f
HC
an
d
Ad
alin
e
is
id
en
t
ical
an
d
less
co
m
p
licated
c
o
m
p
ar
ed
to
th
e
R
C
.
I
n
a
d
d
i
tio
n
,
an
o
p
tim
ized
tr
ig
o
n
o
m
et
r
ic
f
u
n
ctio
n
ev
alu
at
io
n
m
eth
o
d
,
s
u
ch
as
th
o
s
e
p
r
e
s
en
ted
in
[
2
5
]
,
ca
n
b
e
u
s
ed
to
r
ed
u
ce
t
h
e
r
u
n
tim
e
o
f
th
e
0
4
tr
ig
o
n
o
m
etr
ic
f
u
n
cti
o
n
s
,
m
ak
in
g
th
e
th
r
ee
p
r
o
p
o
s
e
d
co
n
tr
o
ller
s
f
ea
s
ib
le
in
r
ea
lity
.
T
ab
le
2.
Me
m
o
r
y
r
eq
u
ir
em
e
n
t
an
d
co
m
p
u
tatio
n
al
b
u
r
d
en
o
f
th
e
R
C
,
HC
,
an
d
Ad
alin
e
M
e
t
h
o
d
RC
HC
A
d
a
l
i
n
e
M
e
m
o
r
y
r
e
q
u
i
r
e
me
n
t
5
s
i
n
g
l
e
s
3
s
i
n
g
l
e
s
3
s
i
n
g
l
e
s
Lo
a
d
b
u
r
d
e
n
+
0
4
t
r
i
g
o
n
o
me
t
r
i
c
f
u
n
c
t
i
o
n
s:
cos
m
,
si
n
m
,
si
n
(
s
)
,
cos
(
s
)
.
+
1
6
mu
l
t
i
p
l
i
c
a
t
i
o
n
s
+
0
6
a
d
d
i
t
i
o
n
s
o
r
s
u
b
t
r
a
c
t
i
o
n
s
+
0
1
d
i
v
i
si
o
n
+
0
4
t
r
i
g
o
n
o
me
t
r
i
c
f
u
n
c
t
i
o
n
s:
cos
,
si
n
,
cos
(
+
m
)
,
si
n
(
+
m
)
+
0
8
mu
l
t
i
p
l
i
c
a
t
i
o
n
s
+
0
4
a
d
d
i
t
i
o
n
s
o
r
s
u
b
t
r
a
c
t
i
o
n
s
+
0
4
t
r
i
g
o
n
o
me
t
r
i
c
f
u
n
c
t
i
o
n
s:
cos
θ
x
,
si
n
θ
x
,
cos
(
+
m
)
,
si
n
(
+
m
)
+
0
8
mu
l
t
i
p
l
i
c
a
t
i
o
n
s
+
0
4
a
d
d
i
t
i
o
n
s
o
r
s
u
b
t
r
a
c
t
i
o
n
s
3.
SI
M
UL
A
T
I
O
N
A
ND
E
XP
E
RIM
E
N
T
AL
V
AL
I
DA
T
I
O
N
I
n
th
is
s
ec
tio
n
,
s
im
u
latio
n
an
d
ex
p
er
im
en
tal
r
esu
lts
ar
e
u
s
ed
to
v
er
if
y
t
h
e
ef
f
ec
tiv
e
n
ess
o
f
th
e
cu
r
r
e
n
t
an
d
h
ar
m
o
n
ic
c
o
n
tr
o
ller
s
in
a
n
elec
tr
ical
d
r
iv
e.
3
.
1
.
Sim
ula
t
i
o
n v
a
lid
a
t
io
n f
o
r
ha
rm
o
nic c
urre
nt
co
ntr
o
ll
er
T
h
e
p
a
r
am
eter
s
o
f
th
e
cu
r
r
en
t
co
n
tr
o
l
lo
o
p
ar
e
d
e
f
in
ed
as
f
o
llo
ws:
=
90
m
Ω
,
=
1
mH
,
s
=
10
k
Hz
,
=
600
Hz
,
m
=
1
.
5
r
a
d
.
T
h
e
am
p
litu
d
e
o
f
th
e
cu
r
r
en
t r
ef
er
en
ce
is
s
et
to
4
A.
T
h
e
s
im
u
latio
n
s
ar
e
co
n
d
u
cte
d
u
s
in
g
t
h
e
HC
,
Ad
alin
e,
an
d
R
C
co
n
tr
o
ller
s
,
b
o
th
wi
th
an
d
with
o
u
t
p
h
ase
co
m
p
e
n
s
atio
n
.
Ad
d
itio
n
all
y
,
th
e
o
p
er
atio
n
p
er
f
o
r
m
a
n
ce
o
f
th
e
R
C
co
n
tr
o
ller
is
ev
alu
ated
u
n
d
er
d
if
f
er
e
n
t d
is
cr
etiza
tio
n
m
eth
o
d
s
.
Fig
u
r
es
5
(
a)
-
5
(
c
)
illu
s
tr
ate
th
e
cu
r
r
en
t
r
esp
o
n
s
e
b
eh
a
v
io
r
o
f
th
e
HC
,
Ad
alin
e,
an
d
R
C
c
o
n
tr
o
ller
s
,
r
esp
ec
tiv
ely
,
d
em
o
n
s
tr
atin
g
th
eir
ab
ilit
y
to
ef
f
ec
tiv
ely
tr
ac
k
th
e
r
ef
er
e
n
ce
cu
r
r
en
t
with
in
a
p
p
r
o
x
im
ately
0
.
1
s
.
T
h
e
m
ag
n
if
ied
v
iew
o
f
th
ese
th
r
ee
co
n
tr
o
ller
s
,
as
s
h
o
wn
in
F
ig
u
r
es
6
(
a)
-
6
(
c)
,
h
i
g
h
lig
h
ts
a
ze
r
o
cu
r
r
e
n
t
tr
ac
k
in
g
er
r
o
r
,
illu
s
tr
atin
g
t
h
e
ex
ce
llen
t
r
ef
er
en
ce
t
r
ac
k
in
g
p
er
f
o
r
m
an
ce
o
f
th
e
h
ar
m
o
n
ic
co
n
tr
o
ller
.
Fig
u
r
e
5
.
(
Simu
latio
n
)
o
f
cu
r
r
e
n
t r
esp
o
n
s
es o
f
(
a
)
HC
,
(
b
)
A
d
alin
e,
(
c)
R
C
,
an
d
(
d
)
R
C
-
b
a
ck
war
d
with
p
h
ase
co
m
p
e
n
s
atio
n
(
a)
(
b
)
(
c)
(
d
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
2
,
J
u
n
e
20
25
:
8
2
7
-
8
3
9
834
I
n
co
n
tr
ast,
Fig
u
r
e
5
(
d
)
a
n
d
its
en
lar
g
ed
v
iew
in
Fig
u
r
e
6
(
d
)
s
h
o
w
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
R
C
co
n
tr
o
ller
wh
en
a
d
is
cr
etiza
tio
n
m
eth
o
d
f
r
o
m
Gr
o
u
p
B
in
T
a
b
le
1
is
e
m
p
lo
y
ed
.
I
n
t
h
is
s
ce
n
ar
io
,
th
e
cu
r
r
en
t e
r
r
o
r
p
er
s
is
ts
o
v
er
tim
e,
i
n
d
icatin
g
t
h
at
th
e
R
C
co
n
tr
o
l
ler
ca
n
n
o
t
ac
h
iev
e
ac
cu
r
ate
cu
r
r
en
t
r
e
g
u
latio
n
u
n
d
er
th
is
d
is
cr
etiza
tio
n
ap
p
r
o
ac
h
.
No
tab
ly
,
as
d
ep
icted
in
Fig
u
r
e
5
(
c)
,
th
e
R
C
co
n
tr
o
ller
m
ain
tain
s
p
r
o
p
er
f
u
n
cti
o
n
ality
o
n
ly
wh
en
d
is
cr
etiza
tio
n
m
eth
o
d
s
ca
teg
o
r
ized
u
n
d
er
Gr
o
u
p
E
ar
e
e
m
p
lo
y
ed
.
T
h
ese
r
esu
lts
ar
e
co
n
s
is
ten
t
with
th
e
th
eo
r
etica
l
an
aly
s
is
o
u
tlin
e
d
i
n
s
ec
tio
n
2
.
1
,
r
ein
f
o
r
cin
g
th
e
cr
itical
r
o
le
o
f
d
is
cr
etiza
tio
n
s
elec
tio
n
in
e
n
s
u
r
in
g
o
p
tim
al
co
n
tr
o
ller
p
er
f
o
r
m
a
n
c
e.
F
i
g
u
r
e
s
7
(
a
)
-
7
(
d
)
a
n
d
i
ts
m
a
g
n
i
f
i
e
d
v
i
e
w
i
n
F
i
g
u
r
es
8
(
a
)
-
8
(
d
)
s
h
o
w
t
h
e
c
u
r
r
e
n
t
r
es
p
o
n
s
es
wi
t
h
o
u
t
t
h
e
p
h
a
s
e
c
o
m
p
e
n
s
a
t
i
o
n
f
o
r
t
h
e
h
a
r
m
o
n
i
c
c
o
m
p
o
n
e
n
t
.
I
n
t
h
i
s
c
a
s
e
,
t
h
e
c
u
r
r
e
n
t
r
e
s
p
o
n
s
e
b
e
c
o
m
e
s
u
n
s
t
a
b
l
e
as
i
t
g
o
e
s
t
o
i
n
f
i
n
i
t
y
w
i
t
h
i
n
a
s
h
o
r
t t
i
m
e
.
T
h
i
s
p
h
e
n
o
m
e
n
o
n
p
r
o
v
e
s
t
h
a
t
p
h
a
s
e
c
o
m
p
e
n
s
at
i
o
n
is
m
a
n
d
a
to
r
y
f
o
r
t
h
e
h
a
r
m
o
n
i
c
c
o
n
t
r
o
l
l
e
r
,
es
p
e
c
i
al
l
y
w
h
e
n
t
h
e
c
o
n
t
r
o
l
l
e
d
s
i
g
n
a
l
f
r
e
q
u
e
n
c
y
is
r
e
l
a
t
i
v
el
y
h
i
g
h
c
o
m
p
a
r
e
d
t
o
t
h
e
s
a
m
p
l
i
n
g
f
r
e
q
u
e
n
c
y
.
Fig
u
r
e
6
.
Z
o
o
m
-
i
n
o
f
(
s
im
u
latio
n
)
cu
r
r
en
t
r
esp
o
n
s
es o
f
(
a
)
H
C
,
(
b
)
Ad
alin
e,
(
c)
R
C
,
an
d
(
d
)
R
C
-
b
ac
k
war
d
with
p
h
ase
co
m
p
e
n
s
atio
n
Fig
u
r
e
7
. (
S
im
u
latio
n
)
cu
r
r
en
t
r
esp
o
n
s
es o
f
(
a)
HC
,
(
b
)
Ad
ali
n
e,
(
c)
R
C
,
an
d
(
d
)
R
C
-
b
ac
k
w
ar
d
with
o
u
t
p
h
ase
co
m
p
en
s
atio
n
3
.
2
.
E
x
perim
ent
a
l
v
a
lid
a
t
io
n o
f
ha
rm
o
nic sp
ee
d c
o
ntr
o
ller
f
o
r
t
he
P
M
SM
I
n
th
is
s
ec
tio
n
,
ex
p
er
im
en
tal
r
e
s
u
lts
ar
e
p
r
esen
ted
to
v
er
if
y
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
p
r
o
p
o
s
ed
h
ar
m
o
n
ic
s
p
ee
d
co
n
tr
o
l
f
o
r
a
p
er
m
an
en
t
m
ag
n
et
s
y
n
ch
r
o
n
o
u
s
m
ac
h
in
e
(
PMSM)
.
T
h
e
co
n
tr
o
l
s
ch
em
e
f
o
r
th
e
PMSM,
as
s
h
o
wn
in
Fig
u
r
es
9
(
a)
a
n
d
9
(
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ip
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ical
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ig
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f
o
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n
d
in
[
2
6
]
.
T
h
e
(
a)
(
b
)
(
c)
(
d
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(
a)
(
b
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(
c)
(
d
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
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&
Dr
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s
t
I
SS
N:
2088
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8
6
9
4
Ha
r
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l in
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ives fo
r
tr
a
n
s
p
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tems
(
Th
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835
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ch
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ith
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atin
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itio
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s
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Fig
u
r
e
8
.
Z
o
o
m
-
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o
f
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s
im
u
latio
n
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c
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r
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en
t
r
esp
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s
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f
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a
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with
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ase
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a)
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b
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Fig
u
r
e
9
.
T
h
e
PMSM
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i
n
s
t
all
ed
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n
a
s
li
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r
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cr
a
n
k
m
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m
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(
a)
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n
d
(
b
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t
r
o
l s
c
h
e
m
e
(
a)
(
b
)
(
c)
(
d
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
2
,
J
u
n
e
20
25
:
8
2
7
-
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3
9
836
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u
r
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1
2
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