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Fawza
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Po
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e
d
am
p
ed
if
th
e
AVR
is
p
r
o
p
er
ly
ad
ju
s
ted
.
Fo
r
s
y
s
tem
o
s
cillatio
n
s
r
ed
u
c
tio
n
,
th
e
ex
citatio
n
ch
an
n
el
c
o
u
ld
b
e
s
u
p
p
lem
e
n
ted
with
a
n
o
th
er
s
tab
ilizin
g
s
i
g
n
al,
th
r
o
u
g
h
a
p
o
wer
s
y
s
tem
s
tab
ilizer
PS
S
[
1
]
,
[
3
]
.
Nu
m
er
o
u
s
r
esear
ch
ac
tiv
ities
h
av
e
b
ee
n
co
n
d
u
cted
to
d
eter
m
in
e
th
e
ex
ten
t
to
wh
ich
th
e
PS
S
an
d
AV
R
ca
n
co
n
tr
ib
u
te
s
ig
n
if
ican
tly
t
o
p
o
wer
s
y
s
tem
s
tab
ilit
y
.
T
h
e
PS
S
an
d
AVR
es
s
en
tially
co
m
p
ete
with
o
n
e
an
o
th
er
.
T
h
e
f
ast r
esp
o
n
s
e
an
d
h
ig
h
g
ain
o
f
th
e
AVR
r
ed
u
ce
o
s
cillatio
n
s
tab
ilit
y
o
f
a
p
o
wer
s
y
s
tem
an
d
,
at
th
e
s
am
e
tim
e
,
in
cr
ea
s
e
tr
an
s
ien
t
s
tab
ilit
y
,
an
d
v
ice
v
er
s
a.
I
n
c
o
n
tr
ast,
th
e
PS
S
d
im
in
is
h
es
tr
an
s
ien
t
s
tab
ilit
y
b
y
o
v
er
r
id
i
n
g
th
e
v
o
ltag
e
s
ig
n
al
to
th
e
ex
citer
wh
ile
im
p
r
o
v
in
g
o
s
cillatio
n
s
tab
ilit
y
[
4
]
.
AV
R
an
d
PS
S
d
esig
n
s
(
b
o
th
d
y
n
am
ically
lin
k
ed
)
ca
n
,
h
o
wev
er
,
b
e
c
o
u
p
led
to
d
eli
v
er
m
ax
im
u
m
p
o
wer
s
tab
ilit
y
f
o
r
o
s
cillatio
n
an
d
tr
an
s
ien
t stab
ilit
y
s
tu
d
ies [
4
]
.
Sy
s
tem
u
n
ce
r
tain
ty
m
ig
h
t
b
e
eith
er
s
to
ch
asti
c
o
r
d
eter
m
in
is
tic.
T
h
e
f
o
llo
win
g
ar
e
tech
n
iq
u
es
f
o
r
PS
S/A
VR
s
y
s
tem
s
with
d
eter
m
in
is
tic
u
n
ce
r
tain
ty
d
esig
n
:
i)
PS
S
is
wid
ely
u
tili
ze
d
n
o
wad
ay
s
.
I
ts
ar
ch
itectu
r
e
co
u
ld
b
e
a
p
r
o
p
o
r
tio
n
al
-
in
teg
r
al
-
d
er
iv
ativ
e
(
PID
)
[
5
]
,
a
m
u
l
ti
-
b
an
d
[
6
]
,
o
r
a
s
in
g
le
-
o
r
d
o
u
b
le
-
s
tag
e
lead
-
lag
with
o
n
e
o
r
two
in
p
u
ts
;
ii)
Am
o
n
g
r
esil
ien
cy
tech
n
iq
u
es
em
p
lo
y
ed
in
cl
u
d
e
Kh
a
r
ito
n
o
v
T
h
e
o
r
y
[
7
]
,
q
u
alitativ
e
f
ee
d
b
ac
k
th
eo
r
y
(
QFT)
[
8
]
,
s
lid
in
g
m
o
d
e
co
n
tr
o
l
(
SMC
)
[
9
]
,
an
d
H∞
f
o
r
d
is
tu
r
b
a
n
c
e
atten
u
atio
n
[
1
0
]
;
iii)
PS
S
with
ad
ap
tiv
e
ca
p
ab
ilit
ies
[
1
1
]
;
an
d
iv
)
I
n
tellig
en
t
-
b
ased
PS
S
em
p
lo
y
s
a
v
a
r
iety
o
f
e
v
o
lu
tio
n
a
r
y
tech
n
iq
u
es,
in
clu
d
i
n
g
p
a
r
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
,
tab
u
s
ea
r
ch
,
g
e
n
etic
alg
o
r
ith
m
(
GA)
,
s
im
u
lated
an
n
ea
lin
g
[
1
2
]
,
n
eu
r
al
n
etwo
r
k
s
[
1
3
]
,
f
u
zz
y
lo
g
ic
[
1
4
]
,
an
d
ad
ap
tiv
e
f
u
zz
y
SMC
[
1
5
]
.
Am
o
n
g
th
e
v
ar
io
u
s
s
tr
ateg
ies
m
en
tio
n
ed
ab
o
v
e,
SMC
is
o
n
e
of
th
e
m
o
s
t
s
u
cc
ess
f
u
l
n
o
n
lin
ea
r
co
n
tr
o
l
m
eth
o
d
s
f
o
r
s
tab
ilizin
g
n
o
n
li
n
ea
r
p
o
wer
s
y
s
tem
s
b
ec
au
s
e
o
f
its
ex
ce
p
tio
n
al
r
esis
tan
ce
t
o
u
n
ce
r
tain
ty
.
T
h
e
p
r
ec
ed
in
g
p
ar
ag
r
ap
h
co
n
ce
r
n
s
p
o
wer
s
y
s
tem
s
with
d
eter
m
in
is
tic
u
n
ce
r
tain
ties
.
I
n
wh
at
f
o
llo
ws,
we
s
h
all
p
r
esen
t
th
e
r
esear
ch
ef
f
o
r
ts
in
s
tab
ilizatio
n
o
f
p
o
wer
s
y
s
tem
s
s
u
b
ject
to
s
to
ch
asti
c
(
o
r
p
r
o
b
ab
ilis
tic)
u
n
ce
r
tain
ties
.
B
ec
au
s
e
o
f
th
e
ex
ter
n
al
s
to
ch
asti
c
d
is
tu
r
b
a
n
ce
,
ab
r
u
p
t
an
d
s
h
a
r
p
s
lo
p
e
ch
an
g
es,
o
r
d
in
ar
y
d
if
f
er
en
tial
eq
u
atio
n
s
(
ODE
s
)
ca
n
n
o
t
b
e
u
s
ed
to
m
o
d
el
p
o
wer
s
y
s
tem
s
to
ch
asti
c
s
tab
ilit
y
.
Sto
ch
asti
c
d
if
f
er
en
tial
eq
u
atio
n
s
ar
e
u
s
ed
to
r
ep
r
esen
t
s
y
s
tem
d
y
n
a
m
ics
in
th
e
p
r
esen
ce
o
f
r
an
d
o
m
s
win
g
s
.
T
h
er
e
h
as
b
ee
n
litt
le
r
esear
ch
ac
tiv
ity
s
tu
d
y
in
g
s
to
ch
asti
c
s
tab
ilit
y
in
p
o
wer
s
y
s
tem
s
[
1
6
]
,
[
1
7
]
.
T
h
e
f
o
llo
win
g
ar
e
ex
am
p
les o
f
s
to
ch
asti
c
d
is
tu
r
b
an
ce
s
o
cc
u
r
r
in
g
in
a
p
o
wer
s
y
s
tem
:
a)
L
ig
h
tn
in
g
s
tr
ik
es
h
itti
n
g
a
tr
an
s
m
is
s
io
n
lin
e
ca
n
ca
u
s
e
r
an
d
o
m
to
p
o
lo
g
ical
ch
an
g
es
in
th
e
s
y
s
tem
(
lead
in
g
to
th
e
o
p
e
n
in
g
a
n
d
clo
s
in
g
o
f
cir
cu
it b
r
ea
k
er
s
in
p
o
wer
s
y
s
te
m
s
)
.
b)
R
an
d
o
m
win
d
s
p
ee
d
f
lu
ctu
at
io
n
s
af
f
ec
t
lin
e
r
ea
ctan
ce
,
as
it
is
b
ased
o
n
p
h
ase
co
n
d
u
cto
r
s
p
ac
in
g
is
m
o
d
elled
as a
s
to
ch
asti
c
ex
ter
n
al
d
is
tu
r
b
an
ce
.
c
)
T
h
e
lin
e
r
esis
tan
ce
is
a
f
u
n
c
tio
n
o
f
e
n
v
ir
o
n
m
en
tal
tem
p
e
r
a
tu
r
e
ch
an
g
es/flu
ctu
atio
n
s
.
Ma
r
k
o
v
ju
m
p
ca
n
b
e
u
s
ed
to
s
im
u
late
s
u
ch
s
to
ch
asti
c
d
is
t
u
r
b
an
ce
s
an
d
r
a
n
d
o
m
to
p
o
lo
g
ical
ch
an
g
es.
T
h
e
o
b
s
er
v
er
-
b
ased
o
r
s
tate
ex
cita
tio
n
f
ee
d
b
ac
k
c
o
n
tr
o
l
u
tili
zin
g
an
i
n
v
ar
ian
t
ellip
s
o
id
ap
p
r
o
ac
h
is
d
escr
ib
ed
in
[
1
8
]
,
[
1
9
]
.
Po
zn
y
ak
et
a
l.
[
2
0
]
in
v
esti
g
ate
p
o
wer
s
y
s
tem
s
'
s
to
ch
asti
c
s
tab
ilit
y
with
tim
e
d
elay
.
Po
wer
n
etwo
r
k
s
ca
n
b
e
s
tab
ili
ze
d
b
y
ce
n
tr
alize
d
o
r
d
ec
e
n
tr
a
lized
co
n
tr
o
l.
Alth
o
u
g
h
r
eg
u
la
tin
g
lar
g
e
p
o
wer
n
etwo
r
k
s
with
a
s
in
g
le
h
u
b
co
m
p
u
ter
(
ce
n
tr
alize
d
co
n
tr
o
l)
g
iv
es
g
o
o
d
co
n
tr
o
l
g
r
ip
,
th
e
f
o
llo
win
g
lim
itatio
n
s
ap
p
ly
:
i)
I
n
ca
s
e
th
e
h
u
b
f
ails
,
th
er
e
will
b
e
a
co
m
p
lete
lo
s
s
o
f
co
n
tr
o
l
;
ii)
T
r
an
s
m
itti
n
g
th
e
s
tates
to
th
e
h
u
b
r
e
q
u
ir
es
a
co
s
tly
co
m
m
u
n
icatio
n
n
etwo
r
k
;
iii)
Data
p
ac
k
et
l
o
s
s
an
d
tim
e
d
e
lay
s
im
p
air
s
y
s
tem
p
er
f
o
r
m
an
ce
a
n
d
m
ig
h
t
lea
d
to
in
s
tab
ilit
y
:
an
d
iv
)
T
o
a
d
d
r
ess
th
ese
r
estrictio
n
s
,
th
is
s
tu
d
y
p
r
o
p
o
s
es
th
e
f
o
llo
win
g
tak
in
g
in
to
ac
c
o
u
n
t
th
e
ch
allen
g
es
en
co
u
n
ter
e
d
wh
en
im
p
lem
e
n
tin
g
d
ec
e
n
tr
aliz
ed
s
tab
ilizatio
n
in
a
p
o
wer
s
y
s
tem
with
m
u
ltip
le
m
ac
h
in
es.
-
C
o
n
tr
ib
u
tio
n
s
i)
C
o
n
tr
o
l
d
ec
e
n
tr
aliza
tio
n
is
a
cc
o
m
p
lis
h
ed
b
y
s
eg
m
en
tin
g
th
e
m
u
lti
-
m
ac
h
in
e
s
y
s
tem
i
n
to
s
m
aller
s
u
b
s
y
s
tem
s
.
A
co
n
tr
o
ller
th
at
o
n
ly
m
ak
es
u
s
e
o
f
th
e
lo
ca
l
s
t
ates
is
in
clu
d
ed
with
e
v
er
y
m
a
ch
in
e.
T
h
e
r
est o
f
th
e
s
y
s
tem
’
s
ef
f
ec
t is
s
ee
n
b
y
a
s
p
ec
if
ic
m
ac
h
in
e
as a
n
ex
o
g
en
o
u
s
d
is
tu
r
b
an
ce
th
at
n
ee
d
s
to
b
e
less
en
ed
.
ii)
Fo
r
ex
citatio
n
co
n
t
r
o
l
o
f
t
h
e
p
o
wer
s
y
s
tem
,
th
e
SMC
d
esig
n
f
o
llo
ws
th
e
p
r
o
ce
d
u
r
e
o
u
tlin
e
d
in
[
9
]
.
I
t
is
b
ased
o
n
em
p
l
o
y
in
g
th
e
in
v
ar
ian
t e
llip
s
o
id
ap
p
r
o
ac
h
t
o
ac
cu
r
ately
s
elec
t
th
e
s
lid
in
g
s
u
r
f
ac
e.
iii)
Me
th
o
d
o
lo
g
y
in
[
9
]
is
ex
te
n
d
e
d
,
in
th
is
p
ap
e
r
,
to
tac
k
le
th
e
c
o
n
tr
o
l d
ec
e
n
tr
aliza
tio
n
.
iv
)
T
h
e
p
r
o
p
o
s
ed
SMC
g
u
ar
an
t
ee
s
m
in
im
izin
g
th
e
im
p
ac
t
o
f
u
n
m
atch
ed
d
is
tu
r
b
an
ce
s
o
n
s
y
s
tem
p
er
f
o
r
m
an
ce
.
T
h
is
is
u
n
lik
e
tr
ad
itio
n
al
SMC
s
,
wh
ich
ca
n
n
o
t
d
ea
l
with
u
n
m
atc
h
ed
d
is
tu
r
b
a
n
ce
s
.
v)
A
s
tr
aig
h
tf
o
r
war
d
d
esig
n
p
r
o
c
ed
u
r
e
th
at
r
eq
u
ir
es n
o
co
s
tly
c
o
m
p
u
tatio
n
al
m
eth
o
d
s
.
v
i)
L
y
ap
u
n
o
v
f
u
n
ctio
n
s
ar
e
u
s
ed
t
o
ass
u
r
e
clo
s
ed
-
lo
o
p
s
tab
ilit
y
.
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
.
4
,
Dec
em
b
er
20
25
:
2332
-
2
3
4
1
2334
v
ii)
T
h
e
p
r
o
p
o
s
ed
c
o
n
tr
o
ller
is
test
ed
u
s
in
g
a
m
u
lti
-
m
ac
h
in
e
s
y
s
tem
.
T
h
e
s
im
u
latio
n
s
tu
d
ies
co
n
d
u
cte
d
o
n
th
at
s
y
s
tem
co
n
f
ir
m
th
e
t
h
e
o
r
etica
l w
o
r
k
p
r
esen
ted
in
t
h
is
p
ap
er
.
-
No
tatio
n
s
T
h
is
wo
r
k
u
tili
ze
d
th
e
co
n
v
en
tio
n
al
n
o
tatio
n
as
f
o
llo
ws:
(
.
)
′
r
ep
r
esen
ts
a
m
atr
ix
o
r
a
v
ec
to
r
tr
an
s
p
o
s
e
.
Def
in
ite
p
o
s
itiv
e
an
d
n
eg
ativ
e
s
y
m
m
etr
ic
m
a
tr
ices
ar
e
s
y
m
b
o
lized
b
y
P
>
0
an
d
P
<
0
,
r
esp
ec
tiv
ely
.
(
M
+
N
+M
'
+N
'
)
n
o
tatio
n
is
r
ep
r
esen
ted
b
y
(
M
+
N+
∗
)
.
A
s
y
m
b
o
l
(
*
)
in
an
y
m
atr
ix
m
ea
n
s
th
e
s
y
m
m
etr
ic
p
ar
t;
f
o
r
ex
am
p
l
e
[
M
N
∗
Z
]
in
dic
a
te
s
[
M
N
N′
Z
]
.
I
a
n
d
0
s
y
m
b
o
ls
s
tan
d
f
o
r
id
en
tity
an
d
ze
r
o
m
atr
ices
,
r
esp
ec
tiv
ely
,
is
th
e
x
tim
e
d
er
iv
ativ
e.
T
h
e
p
ap
e
r
is
o
r
g
an
ized
as
f
o
llo
ws:
i)
Sectio
n
1
d
is
cu
s
s
es
p
r
ev
io
u
s
s
tu
d
ies
o
n
p
o
w
er
s
y
s
tem
s
tab
ilizatio
n
;
ii)
Sectio
n
2
p
r
e
s
en
ts
a
m
u
lti
-
m
ac
h
in
e
s
y
s
tem
m
o
d
ellin
g
a
n
d
p
r
o
b
lem
d
escr
ip
tio
n
;
iii)
Sectio
n
3
d
em
o
n
s
tr
ates
th
e
in
v
ar
ian
t
ellip
s
o
id
m
eth
o
d
f
o
r
s
tate
f
ee
d
b
a
ck
s
lid
in
g
m
o
d
e
co
n
tr
o
l
d
esig
n
;
iv
)
T
h
e
r
esu
lts
o
f
a
b
en
ch
m
a
r
k
ex
a
m
p
le
s
im
u
latio
n
ar
e
d
etailed
in
s
ec
tio
n
4
; a
n
d
v
)
C
o
n
clu
s
io
n
s
ar
e
s
u
m
m
ar
i
ze
d
in
s
ec
tio
n
5
.
2.
M
UL
T
I
-
M
ACH
I
NE
M
O
DE
L
I
NG
AND
P
RO
B
L
E
M
ST
AT
E
M
E
NT
C
o
n
s
id
er
th
e
f
o
llo
win
g
p
o
wer
s
y
s
tem
,
wh
ich
co
n
s
is
ts
o
f
N+
1
m
ac
h
in
es.
T
h
e
m
ac
h
in
e
n
u
m
b
er
N+
1
is
u
s
ed
as a
r
ef
er
en
ce
.
A
t
h
ir
d
-
o
r
d
er
d
y
n
a
m
ic
m
o
d
el
is
u
s
ed
t
o
r
ep
r
esen
t e
ac
h
m
ac
h
in
e
[
1
]
:
δ
i
̇
=
w
0
∆
w
i
,
∆
w
i
=
(
w
i
−
w
0
)
w
i
̇
=
1
2
H
i
(
P
mi
−
P
ei
)
E
̇
qi
′
=
1
T
d0
′
(
E
fi
−
E
qi
)
(
1
)
wh
er
e
E
qi
=
E
qi
′
+
(
x
di
−
x
di
′
)
I
di
E
fi
=
u
i
P
ei
=
∑
E
qi
′
n
j
=
1
E
qj
′
B
ij
s
in
(
δ
i
−
δ
j
)
Q
ei
=
−
∑
E
qi
′
n
j
=
1
E
qj
′
B
ij
cos
(
δ
i
−
δ
j
)
I
di
=
−
∑
E
qj
′
B
ij
cos
(
δ
i
−
δ
j
)
n
j
=
1
I
qi
=
∑
E
qj
′
B
ij
s
in
(
δ
i
−
δ
j
)
n
j
=
1
E
qi
=
V
ti
+
Q
ei
x
di
V
ti
(
2
)
T
h
e
m
u
lti
-
m
ac
h
in
e
p
o
wer
s
y
s
tem
m
o
d
el
n
o
tatio
n
s
ar
e
p
r
o
v
id
e
d
in
th
e
ab
o
v
e
lis
t
o
f
s
y
m
b
o
ls
.
Ass
u
m
e
th
at
m
ac
h
in
e
#
i
is
wo
r
k
in
g
at
an
o
p
er
atin
g
p
o
in
t
δ
i0
,
w
i0
,
P
ei
0
.
Ass
u
m
e
P
mi
=
c
on
s
ta
n
t
,
∆
δ
i
=
δ
i
−
δ
i0
a
n
d
∆
w
i
=
w
i
−
w
i0
.
T
h
e
d
y
n
am
ics
o
f
th
e
r
est
o
f
th
e
N
m
ac
h
in
es
f
o
r
s
m
all
o
s
cillatio
n
s
ar
o
u
n
d
th
e
o
p
er
atin
g
p
o
in
t c
a
n
b
e
r
ep
r
ese
n
ted
b
y
th
e
lin
ea
r
ized
s
tate
eq
u
atio
n
.
x
̇
̂
=
A
̂
x
̂
+
B
̂
u
̂
(
3
)
T
h
e
s
elec
ted
test
s
y
s
tem
is
th
e
th
r
ee
-
m
ac
h
i
n
e
p
o
wer
s
y
s
tem
[
1
]
s
h
o
wn
in
Fig
u
r
e
1
.
E
ac
h
m
ac
h
in
e'
s
s
tate
v
ec
to
r
(
x
)
an
d
co
n
tr
o
l
i
n
p
u
t
(
u
)
a
r
e
[
∆
δ
∆
w
∆
E
q
′
]
,
an
d
E
f
r
e
s
pe
c
tive
l
y
.
Usi
n
g
m
ac
h
in
e
#
3
as
a
r
ef
er
e
n
ce
f
o
r
th
e
b
e
n
ch
m
a
r
k
s
y
s
tem
N+
1
=3
,
th
e
d
y
n
am
ics
o
f
th
e
o
th
er
two
m
ac
h
in
es,
th
e
(
3
)
b
ec
o
m
es
x
̂
=
[
x
1
′
x
2
′
]
′
,
s
imil
a
r
l
y
for
u
̂
=
[
u
1
u
2
]
′
.
The
m
atr
ices
A
̂
=
[
A
1
A
12
A
21
A
2
]
,
B
̂
=
b
l
oc
k
dia
g
[
B
1
B
2
]
.
T
h
e
ab
o
v
e
m
at
r
ices'
n
u
m
er
ical
v
alu
es
ar
e
p
r
o
v
id
e
d
in
th
e
A
p
p
en
d
i
x
.
Sy
s
tem
(
3
)
is
d
iv
id
e
d
in
to
th
r
ee
s
u
b
s
y
s
tem
s
to
ac
h
iev
e
co
n
tr
o
l
d
ec
en
tr
aliza
tio
n
,
with
th
e
d
y
n
am
ics f
o
r
ea
ch
m
ac
h
in
e
b
ein
g
:
x
̇
=
Ax
+
Bu
+
Dw
,
x
(
0
)
=
x
0
,
w
=
x
̂
,
(
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
N
o
n
lin
ea
r
ex
cita
tio
n
co
n
tr
o
l o
f m
u
ltima
ch
in
e
s
ystems
via
th
e
in
va
r
ia
n
t
-
s
et
d
esig
n
(
His
h
a
m
M.
S
o
lima
n
)
2335
I
t
is
im
p
o
r
ta
n
t
to
n
o
te
th
at
th
e
in
f
lu
e
n
ce
o
f
th
e
r
est
o
n
a
s
p
ec
if
ic
s
u
b
s
y
s
tem
is
tr
e
ated
as
an
ex
ter
n
al
d
is
tu
r
b
an
ce
.
I
ts
im
p
ac
t
s
h
o
u
l
d
b
e
less
en
ed
.
R
eg
ar
d
in
g
a
n
y
g
en
er
ato
r
i,
wh
e
r
e
i=1
,
2
,
…N,
an
d
N=
2
f
o
r
o
u
r
s
y
s
tem
.
A
=
A
i
,
B
=
B
i
,
D
=
D
i
=
[
A
i1
A
i2
…
0
ii
…
.
A
iN
]
,
w
=
x
̂
Fo
r
ev
er
y
g
en
er
ato
r
,
x
(
t)
is
th
e
s
tate
o
f
n
d
im
en
s
io
n
s
,
u
(
t
)
r
ep
r
esen
ts
th
e
co
n
tr
o
l
in
p
u
t
o
f
d
im
en
s
io
n
m
,
an
d
w(
t
)
d
en
o
tes
th
e
ex
ter
n
al
d
is
tu
r
b
an
ce
o
f
d
i
m
en
s
io
n
k
(
k
=n
.
N)
.
T
h
e
(
A,
B
)
p
air
is
co
n
tr
o
llab
le.
T
h
e
ex
ter
n
al
d
is
tu
r
b
a
n
ce
is
n
o
t k
n
o
wn
b
u
t b
o
u
n
d
as
:
w
′
Q
w
w
≤
w
0
+
x′
Q
x
x
(
5
)
Q
w
, Q
x
,
th
e
p
o
s
itiv
e
d
ef
in
ite
m
atr
ices,
as we
ll a
s
th
e
p
o
s
itiv
e
s
ca
lar
w
0
ar
e
g
iv
en
.
Po
wer
s
y
s
tem
s
ex
ter
n
al
d
is
tu
r
b
an
ce
is
m
is
m
atch
ed
as
th
e
D
m
atr
ix
is
n
o
t
in
th
e
r
an
g
e
o
f
m
atr
ix
B
,
wh
ich
m
ea
n
s
th
at
D
≠
B
Φ
,
wh
er
e
Φ
=
an
y
m
atr
ix
.
E
ac
h
m
ac
h
in
e’
s
d
ec
e
n
tr
alize
d
s
tate
f
ee
d
b
ac
k
c
o
n
tr
o
l
u
tili
ze
s
its
o
wn
lo
ca
l states
i
s
:
u
=
Kx
(
6
)
I
n
o
r
d
e
r
to
m
ain
tain
th
e
s
tab
ilit
y
o
f
th
e
b
en
ch
m
a
r
k
s
y
s
tem
wh
ile
ad
h
er
in
g
to
co
n
s
tr
ain
t
(
5
)
,
th
e
co
n
tr
o
ller
g
ain
K
s
h
o
u
l
d
b
e
ac
co
r
d
in
g
l
y
d
esig
n
ed
.
Fo
r
th
e
co
n
tr
o
ller
(
6
)
,
th
e
SMC
is
s
elec
ted
d
u
e
to
its
r
em
ar
k
ab
le
r
esil
ien
ce
to
th
e
s
y
s
tem
’s
u
n
ce
r
tain
ties
.
Fig
u
r
e
1
.
Mu
lti
-
m
ac
h
in
e
6
-
b
u
s
test
p
o
wer
s
y
s
tem
3.
T
H
E
I
N
VARI
ANT
E
L
L
I
P
S
O
I
D
AP
P
RO
ACH
I
N
S
M
C
T
h
e
in
v
ar
ian
t
ellip
s
o
id
a
p
p
r
o
ac
h
is
a
n
ew
an
d
e
f
f
ec
tiv
e
co
n
tr
o
l
m
ec
h
an
is
m
[
9
]
.
T
h
e
ap
p
r
o
ac
h
s
tab
ilizes
lin
ea
r
an
d
n
o
n
lin
e
ar
s
y
s
tem
s
ag
ain
s
t
p
lan
t
u
n
ce
r
tain
ty
an
d
m
itig
ates
th
e
i
m
p
ac
t
o
f
ex
ter
n
al
d
is
tu
r
b
an
ce
s
.
T
h
is
ap
p
r
o
ac
h
h
as
v
ar
io
u
s
ap
p
licatio
n
s
,
in
clu
d
in
g
m
icr
o
g
r
i
d
co
n
tr
o
l
[
2
1
]
.
T
h
e
SMC
s
tr
u
ctu
r
e
to
s
tab
ilize
d
is
tu
r
b
ed
s
y
s
tem
s
is
[
2
2
]
:
u
(
t
)
=
−
(
C
̃
B
)
−
1
C
̃
Ax
(
t
)
−
M
(
x
(
t
)
)
.
s
ign
[
C
̃
x
(
t
)
]
,
M
(
x
(
t
)
)
>
0
(
7
)
T
h
e
m
atr
ix
C
̃
∈
R
m×
n
r
ep
r
esen
ts
a
s
lid
in
g
s
u
r
f
ac
e
with
d
et
(
C
̃
B
)
≠
0
.
M(
x
)
,
th
e
p
o
s
itiv
e
co
n
tr
o
l
g
ain
f
u
n
ctio
n
,
tak
es th
e
f
o
r
m
:
M
(
x
)
=
√
(
α
+
x
′
Rx
)
,
(
8
)
T
h
e
p
o
s
itiv
e
d
ef
in
ite
m
atr
i
x
R
an
d
th
e
s
ca
lar
α
ar
e
b
o
u
n
d
ed
p
ar
am
ete
r
s
b
ec
au
s
e
α
<
α
max
,
‖
R
‖
≤
β,
α
,
β
ar
e
s
ca
lar
s
>
0
.
I
f
th
e
d
is
tu
r
b
an
c
e
is
in
s
id
e
th
e
r
an
g
e
(
B
)
,
als
o
k
n
o
wn
as
t
h
e
m
atch
e
d
co
n
d
itio
n
,
th
is
c
o
n
tr
o
l
can
er
ad
icate
it.
T
h
e
m
atch
i
n
g
c
o
n
d
itio
n
in
p
o
wer
s
y
s
tem
s
d
o
es
n
o
t
h
o
ld
.
No
te
th
at
th
e
p
o
wer
s
y
s
tem
d
y
n
am
ics
(
2
)
h
av
e
"
u
n
m
atch
e
d
d
is
tu
r
b
an
c
es"
th
at
ca
n
n
o
t
b
e
s
u
p
p
r
ess
ed
b
y
a
n
y
co
n
v
en
tio
n
al
s
lid
in
g
-
m
o
d
e
co
n
tr
o
l.
T
h
er
ef
o
r
e,
th
e
g
r
ea
test
o
b
s
tac
le
is
to
d
e
v
elo
p
a
s
lid
in
g
-
m
o
d
e
co
n
tr
o
l
w
h
ich
em
p
lo
y
s
t
h
e
in
v
ar
ia
n
t
-
ellip
s
o
id
tech
n
iq
u
e
to
m
itig
ate,
in
s
o
m
e
s
en
s
e
,
m
is
m
atch
ed
d
is
tu
r
b
an
c
e
ef
f
ec
ts
[
9
]
.
3
.
1
.
I
nv
a
ria
nt
ellips
o
id t
ec
hn
iqu
e
[
9
]
Def
in
itio
n
1
: E
llip
s
o
id
E
(
P)
is
as f
o
llo
ws:
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
.
4
,
Dec
em
b
er
20
25
:
2332
-
2
3
4
1
2336
E
(
P
)
=
{
x
′
P
−
1
x
<
1
}
,
P
>
0
,
(
9
)
T
h
is
ellip
s
o
id
,
ce
n
ter
ed
at
th
e
o
r
ig
in
with
a
co
n
f
ig
u
r
atio
n
m
atr
ix
P,
is
s
tate
in
v
ar
ian
t
f
o
r
th
e
s
y
s
tem
(
4
)
co
n
ce
r
n
in
g
d
is
tu
r
b
a
n
ce
(
5
)
i
f
a
n
y
s
y
s
tem
s
tate
tr
ajec
to
r
y
s
tar
tin
g
in
s
id
e
th
e
ellip
s
o
id
s
tay
s
in
s
id
e
it f
o
r
all
tim
e
in
s
tan
ts
t
>
0
.
T
h
is
p
r
o
p
e
r
ty
g
u
ar
an
tees
th
at
t
h
e
s
y
s
tem
'
s
s
ta
te
r
em
ain
s
b
o
u
n
d
with
in
a
s
p
e
cif
ic
r
eg
io
n
d
esp
ite
th
e
p
r
esen
ce
o
f
ex
ter
n
al
d
is
tu
r
b
an
ce
s
.
Ho
we
v
er
,
if
a
tr
aje
cto
r
y
b
e
g
in
s
o
u
ts
id
e
th
e
ellip
s
o
id
an
d
b
ec
o
m
es
attr
ac
ted
to
it o
v
er
tim
e,
th
e
el
lip
s
o
id
is
also
k
n
o
wn
as a
ttra
c
tiv
e.
T
h
e
in
v
ar
ian
t
ellip
s
o
id
ca
n
b
e
th
o
u
g
h
t
o
f
as
a
n
e
x
am
p
le
o
f
h
o
w
m
is
m
atch
ed
p
er
tu
r
b
atio
n
s
(
5
)
im
p
ac
t
th
e
s
y
s
tem
(
4
)
.
I
n
th
e
SMC
ap
p
licatio
n
,
th
e
s
m
allest
,
in
a
s
e
n
s
e,
in
v
ar
ian
t
ellip
s
o
id
(
9
)
p
r
o
v
id
es
a
"m
in
im
u
m
d
ev
iatio
n
o
f
an
y
p
o
s
s
ib
le
tr
ajec
to
r
y
f
r
o
m
th
e
o
r
ig
in
i
n
a
s
lid
in
g
m
o
d
e"
.
T
h
e
m
ain
c
h
allen
g
e
is
to
d
ev
el
o
p
a
co
n
tr
o
l
co
n
f
ig
u
r
atio
n
th
at
allo
ws
an
y
s
y
s
tem
(
4
)
tr
ajec
t
o
r
y
to
co
n
v
er
g
e
in
to
th
e
b
e
f
o
r
eh
a
n
d
s
p
ec
if
ied
"m
in
im
u
m
in
v
ar
ia
n
t
ellip
s
o
id
".
Fo
r
s
u
ch
o
p
tim
izatio
n
is
s
u
es,
th
e
ty
p
ical
cr
iter
io
n
is
m
i
n
im
al
s
tr
(
P
−1
)
.
T
h
e
m
atr
ix
P
−
1
tr
ac
e
r
ep
r
esen
ts
th
e
s
u
m
o
f
th
e
s
q
u
ar
es
o
f
th
e
ellip
s
o
id
’
s
s
em
i
-
ax
es.
U
s
in
g
lin
ea
r
m
atr
ix
in
eq
u
alities
o
p
tim
izatio
n
,
th
e
in
v
ar
ian
t
ellip
s
o
id
o
f
t
h
e
lin
e
ar
d
is
tu
r
b
ed
co
n
tr
o
l
s
y
s
tem
is
u
tili
ze
d
to
d
ev
elo
p
an
ap
p
r
o
p
r
iate
s
lid
in
g
s
u
r
f
ac
e
C
̃
x
=
0
,
[
9
]
.
3
.
2
.
Sy
s
t
e
m
deco
m
po
s
it
io
n a
nd
m
a
in re
s
ults
Giv
en
r
an
k
(
B
)
=
m
,
m
atr
ix
B
ca
n
b
e
d
ec
o
m
p
o
s
ed
as f
o
llo
ws:
B
=
[
B
1
B
2
]
B
1
,
an
d
B
2
h
av
e
d
im
en
s
io
n
s
o
f
(
n
-
m
)
,
m
a
n
d
m
,
m
r
esp
ec
tiv
ely
an
d
d
et
(
B
2
)
≠
0
.
T
h
e
n
o
n
s
in
g
u
la
r
tr
an
s
f
o
r
m
atio
n
is
p
r
esen
t in
th
i
s
s
itu
atio
n
[
2
3
]
.
[
x
1
x
2
]
=
Gx
,
whe
r
e
G
=
[
I
n
−
m
−
B
1
B
2
−
1
0
B
2
−
1
]
Sy
s
tem
(
4
)
ca
n
th
e
n
b
e
r
ed
u
ce
d
to
th
e
f
o
r
m
:
x
̇
1
=
A
11
x
1
+
A
12
x
2
+
D
1
w
x
̇
2
=
A
21
x
2
+
A
22
x
2
+
u
+
D
2
w
(
1
0
)
wh
er
e
n
-
m
,
an
d
m
ar
e
th
e
d
i
m
en
s
io
n
s
o
f
x
1
,
x
2
,
r
esp
ec
tiv
ely
.
Ma
tr
ices
A1
1
.
A2
2
h
av
e
p
r
o
p
er
d
im
en
s
io
n
s
an
d
s
h
o
u
ld
n
o
t b
e
co
n
f
u
s
ed
with
t
h
o
s
e
lis
ted
in
th
e
Ap
p
e
n
d
ix
.
T
h
er
ef
o
r
e
,
[
A
11
A
12
A
21
A
22
]
=
GA
G
−
1
a
n
d
[
D
1
D
2
]
=
GD
w
h
er
e
(
n
-
m
)
.
k
,
an
d
m
.
k
ar
e
t
h
e
d
im
en
s
io
n
s
o
f
D
1
,
D
2
,
r
esp
e
ctiv
ely
.
I
t
m
u
s
t
b
e
n
o
ted
th
at
if
th
e
s
y
s
tem
(
4
)
is
co
n
tr
o
llab
le,
th
e
n
{A
11
, A
12
}
i
s
co
n
tr
o
llab
le
as we
ll [
2
3
]
.
T
h
e
f
o
llo
win
g
th
e
o
r
em
is
d
e
r
iv
ed
in
[
9
]
.
T
h
eo
r
em
:
th
e
s
o
lu
tio
n
(
α
,
τ
,
δ
,
L
,
Y
,
Z
,
Z
)
o
f
th
e
m
in
im
izatio
n
p
r
o
b
lem
min
i
mize
tr
a
c
e
(
Z
)
Su
b
ject
to
th
e
f
o
llo
win
g
in
eq
u
ality
co
n
s
tr
ain
ts
:
[
β
2
I
n
∗
R
I
n
]
≥
0
,
R
≥
α
w
0
Q
x
,
0
<
α
≤
α
m
ax
,
[
(
A
11
X
−
A
12
Y
+
∗
)
+
τ
X
∗
∗
D
1
′
−
τ
w
0
Q
w
∗
[
X
−
Y
]
0
−
w
0
τ
Q
x
−
1
]
<
0
,
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
N
o
n
lin
ea
r
ex
cita
tio
n
co
n
tr
o
l o
f m
u
ltima
ch
in
e
s
ystems
via
th
e
in
va
r
ia
n
t
-
s
et
d
esig
n
(
His
h
a
m
M.
S
o
lima
n
)
2337
[
X
∗
[
X
−
Y
]
GZG′
]
≥
0
,
[
α
w
0
Q
w
∗
GD
[
δ
X
∗
0
L
]
]
>
0
,
[
1
δ
X
∗
Y
I
m
−
L
]
≥
0
g
iv
es
th
e
m
in
i
m
al
in
v
a
r
ian
t
e
llip
s
o
id
o
f
t
h
e
s
y
s
tem
(
4
)
.
Fu
r
th
er
m
o
r
e
,
th
e
SMC
as
p
r
o
v
i
d
ed
b
y
(
7
)
a
n
d
(
8
)
,
with
th
e
s
lid
in
g
s
u
r
f
ac
e
,
is
C
̃
=
(
Y
X
−
1
,
I
m
)
G
.
Usi
n
g
an
y
g
r
a
d
ien
t
-
f
r
ee
a
p
p
r
o
ac
h
s
u
c
h
as
p
ar
ticle
s
war
m
o
p
tim
izatio
n
tech
n
i
q
u
e,
th
e
af
o
r
em
en
tio
n
e
d
m
in
im
izatio
n
p
r
o
b
lem
ca
n
b
e
h
a
n
d
led
.
Pr
o
o
f
:
s
ee
[
9
]
.
So
lv
in
g
th
e
af
o
r
em
en
tio
n
ed
th
eo
r
e
m
u
n
d
er
ass
u
m
p
tio
n
s
(
α
m
ax
=
100
,
β
m
ax
=
7
,
Q
w0
=
I
,
Q
x
=
I
,
w
0
=
0
.
1
)
y
ield
s
a
d
ec
en
tr
alize
d
ex
ci
tatio
n
co
n
tr
o
l
s
y
s
tem
.
T
h
is
s
y
s
tem
is
d
esig
n
ed
u
s
in
g
th
e
s
lid
in
g
s
u
r
f
ac
es
p
r
esen
ted
in
T
ab
le
1
,
an
d
th
e
s
ca
lar
s
lid
in
g
m
o
d
e
co
n
tr
o
ller
,
u
(
t)
,
f
o
r
ea
ch
m
ac
h
in
e
tak
es
th
e
f
o
r
m
s
p
ec
if
ied
in
(
7
)
.
T
h
e
p
ar
am
ete
r
s
,
in
clu
d
in
g
th
e
c
o
n
s
tan
ts
α
,
R
an
d
th
e
Sli
d
in
g
s
u
r
f
ac
e
C
̃
,
ar
e
c
o
m
p
r
eh
e
n
s
iv
ely
illu
s
tr
ated
in
T
ab
le
1
to
p
r
o
v
id
e
all
n
ec
ess
ar
y
im
p
lem
en
tatio
n
d
etails.
T
ab
le
1
.
Pro
p
o
s
ed
SMC
M
a
c
h
i
n
e
#
α
R
S
l
i
d
i
n
g
S
u
r
f
a
c
e
C
̃
1
0
.
6
9
8
4
5
[
6
.
9
9
2
2
,
1
.
5
2
8
1
e
-
1
4
,
-
6
.
1
3
9
8
e
-
1
4
;
1
.
5
2
8
1
e
-
1
4
,
6
.
9
9
2
2
,
-
2
.
1
0
9
7
e
-
13;
-
6
.
1
3
9
8
e
-
1
4
,
-
2
.
1
0
9
7
e
-
13
,
6
.
9
9
2
2
]
[
-
2
.
5
3
9
,
-
1
9
6
.
6
4
,
5
.
8
0
0
5
]
2
0
.
6
9
9
3
6
[
6
.
9
9
6
8
,
-
1
.
5
5
7
2
e
-
1
4
,
2
.
6
9
8
3
e
-
1
4
;
-
1
.
5
5
7
2
e
-
1
4
,
6
.
9
9
6
8
,
1
.
4
5
9
4
e
-
1
4
;
2
.
6
9
8
3
e
-
1
4
,
1
.
4
5
9
4
e
-
1
4
,
6
.
9
9
6
8
]
[
-
2
.
4
7
5
7
,
-
2
7
0
.
3
3
,
5
.
9
9
8
8
]
4.
SI
M
UL
A
T
I
O
N
V
E
R
I
F
I
CA
T
I
O
N
T
h
e
s
im
u
latio
n
f
in
d
in
g
s
d
e
m
o
n
s
tr
ate
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
'
s
r
o
b
u
s
tn
ess
an
d
p
er
f
o
r
m
an
ce
in
co
m
p
ar
is
o
n
with
a
class
ical
s
lid
in
g
m
o
d
e
ex
citatio
n
co
n
t
r
o
l.
Simu
latio
n
r
esu
lts
wer
e
im
p
lem
en
ted
u
s
in
g
MA
T
L
AB
L
MI
T
o
o
lb
o
x
[
2
4
]
,
Yalm
ip
I
n
ter
f
ac
e
[
2
5
]
,
a
n
d
S
ed
u
m
i
So
lv
er
s
[
2
6
]
.
T
h
e
Od
e
2
3
s
o
lv
er
was
u
s
ed
b
y
a
to
ler
a
n
ce
o
f
1
0
−
3
.
T
o
elim
in
ate
th
e
ch
atter
in
g
p
r
o
b
lem
,
th
e
s
ig
n
f
u
n
ctio
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n
(
7
)
is
r
ep
lace
d
b
y
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s
atu
r
atio
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f
u
n
ctio
n
[
2
3
]
.
4
.
1
.
T
he
m
ulti
-
ma
chine
t
est
po
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s
y
s
t
em
s
im
ula
t
io
n
A
th
r
ee
-
p
h
ase
f
au
lt
is
ap
p
lie
d
at
Gen
er
ato
r
1
t
o
co
n
f
ir
m
s
ta
b
ilit
y
en
h
an
ce
m
en
t
d
u
e
to
th
e
p
r
o
p
o
s
ed
s
tab
ilizer
.
T
h
is
lead
s
to
r
o
to
r
a
n
g
le
d
ev
iatio
n
x
0
=
[
0
.
3
,
0
,
0
,
0
.
1
,
0
,
0
]
′
.
T
h
r
ee
d
if
f
er
en
t o
p
e
r
atin
g
s
ce
n
ar
i
o
s
wer
e
in
v
esti
g
ated
:
n
o
m
i
n
al,
lig
h
t,
a
n
d
h
ea
v
y
lo
ad
s
.
Af
ter
clea
r
in
g
th
e
f
au
lt.
T
h
e
co
n
tr
o
ller
s
u
p
p
o
r
ts
th
e
s
y
s
tem
in
q
u
ick
ly
r
ec
o
v
e
r
in
g
to
a
s
tead
y
o
p
er
atio
n
al
c
o
n
d
itio
n
.
Fig
u
r
e
2
illu
s
tr
ates
th
at,
r
eg
ar
d
in
g
th
e
d
am
p
in
g
ef
f
ec
t
an
d
s
ettlin
g
tim
e
at
n
o
m
in
al
l
o
ad
,
th
e
s
u
g
g
ested
tech
n
iq
u
e
o
u
tp
er
f
o
r
m
s
th
e
t
r
ad
itio
n
al
S
MC.
Mo
r
eo
v
er
,
wh
en
co
m
p
ar
ed
t
o
th
e
s
tan
d
ar
d
SMC
,
th
e
s
u
g
g
ested
SMC
g
e
n
er
ates
o
s
cillatio
n
s
with
s
m
a
ller
m
ag
n
itu
d
es
an
d
f
r
eq
u
e
n
cies.
As a
r
esu
lt,
th
e
g
en
er
ato
r
r
o
to
r
'
s
u
s
ef
u
l lif
e
is
ex
ten
d
ed
a
n
d
f
atig
u
e
is
r
ed
u
ce
d
.
Fig
u
r
e
2
.
R
o
to
r
-
an
g
le
v
ar
iatio
n
s
an
d
co
n
tr
o
l
-
in
p
u
t u
n
d
er
n
o
m
in
al
lo
ad
co
n
d
itio
n
:
(
a)
d
elta
1
(
r
ad
)
,
(
b
)
co
n
tr
o
l sig
n
al
1
(
u
1
(
t)
)
,
(
c)
d
elta
2
(
r
a
d
)
,
a
n
d
(
d
)
co
n
tr
o
l s
ig
n
al
2
(
u
2
(
t)
)
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
.
4
,
Dec
em
b
er
20
25
:
2332
-
2
3
4
1
2338
4
.
2
.
Ro
bu
s
t
nes
s
a
s
s
e
s
s
m
ent
T
h
e
p
r
o
p
o
s
ed
s
tab
ilizer
'
s
r
esi
lien
cy
is
f
u
r
t
h
er
ev
al
u
ated
b
y
test
in
g
th
e
p
o
wer
s
y
s
tem
u
n
d
er
b
o
th
h
ea
v
y
an
d
lig
h
t
lo
ad
co
n
d
iti
o
n
s
,
as
s
h
o
wn
in
Fig
u
r
es
3
an
d
4
.
T
h
ese
test
s
ar
e
cr
u
cial
f
o
r
ass
ess
in
g
th
e
co
n
tr
o
ller
'
s
r
o
b
u
s
tn
ess
ac
r
o
s
s
a
wid
e
r
an
g
e
o
f
o
p
er
atio
n
al
s
ce
n
ar
io
s
.
T
h
e
r
esu
lts
co
n
s
is
ten
tly
d
em
o
n
s
tr
ate
th
at
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
o
u
tp
er
f
o
r
m
s
its
tr
ad
itio
n
al
co
u
n
ter
p
a
r
t in
th
e
m
u
lti
-
m
ac
h
in
e
p
o
wer
s
y
s
tem
.
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
3
.
R
o
to
r
-
an
g
le
v
ar
iatio
n
s
an
d
co
n
tr
o
l
-
in
p
u
t u
n
d
er
h
ig
h
lo
ad
c
o
n
d
itio
n
:
(
a)
d
elta
1
(
r
ad
)
,
(
b
)
co
n
tr
o
l sig
n
al
1
(
u
1
(
t)
)
,
(
c)
d
elta
2
(
r
a
d
)
,
a
n
d
(
d
)
co
n
tr
o
l s
ig
n
al
2
(
u
2
(
t)
)
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
4
.
R
o
to
r
-
an
g
le
v
ar
iatio
n
s
an
d
co
n
tr
o
l in
p
u
t
u
n
d
er
lig
h
t lo
ad
co
n
d
itio
n
s
: (
a)
d
elta
1
(
r
ad
)
,
(
b
)
co
n
tr
o
l sig
n
al
1
(
u
1
(
t)
)
,
(
c)
d
elta
2
(
r
a
d
)
,
a
n
d
(
d
)
co
n
tr
o
l s
ig
n
al
2
(
u
2
(
t)
)
I
n
th
is
s
tu
d
y
,
we
em
p
lo
y
a
d
iv
er
s
e
r
an
g
e
o
f
o
p
er
atin
g
p
o
in
ts
to
illu
s
tr
ate
th
e
ef
f
icie
n
cy
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l
f
o
r
o
s
cillatio
n
d
am
p
in
g
f
o
llo
win
g
a
lar
g
e
d
is
tu
r
b
an
ce
o
n
a
p
o
wer
s
y
s
tem
.
T
h
is
co
m
p
r
eh
e
n
s
iv
e
ap
p
r
o
ac
h
e
n
s
u
r
es
th
at
th
e
co
n
tr
o
ller
'
s
p
er
f
o
r
m
an
ce
is
r
o
b
u
s
tly
ev
al
u
ated
u
n
d
er
v
a
r
io
u
s
r
ea
l
-
wo
r
ld
co
n
d
itio
n
s
.
T
h
e
r
esu
lts
co
n
s
is
ten
tly
s
h
o
w
th
at
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
p
r
o
v
id
es
e
n
h
an
ce
d
tr
a
n
s
ien
t
r
esp
o
n
s
iv
en
ess
an
d
g
r
ea
ter
r
o
b
u
s
tn
ess
co
m
p
ar
ed
to
co
n
v
en
t
io
n
al
SMC
.
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
N
o
n
lin
ea
r
ex
cita
tio
n
co
n
tr
o
l o
f m
u
ltima
ch
in
e
s
ystems
via
th
e
in
va
r
ia
n
t
-
s
et
d
esig
n
(
His
h
a
m
M.
S
o
lima
n
)
2339
5.
CO
NCLU
SI
O
N
T
h
is
p
ap
er
in
tr
o
d
u
ce
s
a
n
e
w
tech
n
iq
u
e
f
o
r
p
o
wer
s
y
s
tem
d
ec
en
tr
alize
d
ex
citatio
n
co
n
tr
o
l.
Dec
en
tr
aliza
tio
n
o
f
ex
citatio
n
co
n
tr
o
l
is
p
er
f
o
r
m
e
d
b
y
d
iv
i
d
in
g
th
e
en
tire
s
y
s
tem
in
to
s
m
aller
s
y
s
tem
s
an
d
p
lacin
g
a
co
n
tr
o
ller
on
ea
ch
g
en
er
ato
r
t
h
at
u
tili
ze
s
its
lo
c
al
s
tates.
T
h
e
r
est
o
f
th
e
s
y
s
tem
’
s
im
p
ac
t
o
n
a
s
p
ec
if
ic
g
en
er
ato
r
is
r
eg
ar
d
ed
as
ex
ter
n
al
d
is
tu
r
b
an
ce
s
th
at
s
h
o
u
ld
b
e
m
itig
ated
.
T
o
r
ed
u
ce
th
e
m
is
m
atch
ed
ex
ter
n
al
d
is
tu
r
b
an
ce
s
,
th
e
p
r
o
p
o
s
ed
d
esig
n
is
b
ased
o
n
SMC
an
d
em
p
lo
y
s
th
e
in
v
ar
ian
t
ellip
s
o
id
tech
n
iq
u
e.
Simu
latio
n
s
o
f
a
m
u
lti
-
m
ac
h
in
e
test
s
y
s
tem
illu
s
tr
ate
th
e
ef
f
icac
y
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l
m
eth
o
d
.
Var
io
u
s
lo
ad
in
g
s
ce
n
ar
io
s
ar
e
u
s
ed
to
ass
ess
th
e
p
r
o
p
o
s
ed
d
ec
en
t
r
alize
d
ex
citatio
n
SMC
ef
f
icien
cy
.
T
h
is
clea
r
ly
in
d
icate
s
th
e
s
u
p
er
io
r
p
er
f
o
r
m
an
ce
o
f
th
e
p
r
o
p
o
s
ed
tech
n
iq
u
e
o
v
er
c
o
n
v
e
n
tio
n
al
SMC
.
F
UNDING
I
NF
O
R
M
A
T
I
O
N
Au
th
o
r
s
s
tate
th
at
th
er
e
is
n
o
f
u
n
d
in
g
in
v
o
l
v
ed
.
AUTHO
R
CO
NT
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B
UT
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NS ST
A
T
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M
E
N
T
T
h
is
jo
u
r
n
al
u
s
es
th
e
C
o
n
t
r
ib
u
to
r
R
o
les
T
a
x
o
n
o
m
y
(
C
R
ed
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to
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ec
o
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n
ize
in
d
iv
i
d
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al
au
th
o
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tio
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,
r
ed
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th
o
r
s
h
ip
d
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p
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tes,
an
d
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ac
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co
llab
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r
atio
n
.
Na
m
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o
f
Aut
ho
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C
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So
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Vi
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Fu
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h
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ay
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Far
ag
Ali
El
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i
✓
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Fawza
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Salem
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C
:
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p
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Au
th
o
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s
s
tate
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co
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f
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f
in
t
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th
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p
a
p
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n
o
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p
u
b
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s
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ed
o
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s
u
b
m
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y
wh
e
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e.
DATA
AV
AI
L
AB
I
L
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Y
Data
av
ailab
ilit
y
is
n
o
t a
p
p
lica
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le
to
th
is
p
ap
er
as d
ata
u
s
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o
r
an
aly
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d
a
r
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g
iv
e
n
in
th
is
p
a
p
er
.
RE
F
E
R
E
NC
E
S
[
1
]
H
.
S
a
a
d
a
t
,
Po
w
e
r
S
y
st
e
m
A
n
a
l
y
s
i
s
,
3
r
d
e
d
.
P
S
A
P
u
b
l
i
s
h
i
n
g
,
2
0
1
0
.
[
2
]
E.
M
u
d
a
h
e
r
a
n
w
a
,
H
.
B
.
S
o
n
d
e
r
,
Y
.
-
O
.
U
d
o
a
k
a
h
,
L.
C
i
p
c
i
g
a
n
,
a
n
d
C
.
E.
U
g
a
l
d
e
-
Lo
o
,
“
P
a
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c
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p
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l
o
a
d
a
g
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g
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r
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r
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q
u
e
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c
y
st
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b
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z
a
t
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o
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w
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t
h
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o
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s
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d
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o
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w
a
b
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g
y
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c
a
n
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tac
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ra
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lsh
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c
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tac
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:
fa
wz
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sc
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g
.
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