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y
P
r
o
f
ess
o
r
Neil
Mu
n
r
o
.
He
g
at
h
er
ed
m
a
n
y
v
alu
ab
le
ap
p
licatio
n
s
o
f
s
y
m
b
o
lic
alg
eb
r
a
to
co
n
tr
o
l
th
eo
r
y
[
4
]
,
w
h
ic
h
d
r
e
w
in
te
n
s
e
at
ten
tio
n
to
t
h
e
u
s
e
o
f
s
y
m
b
o
lic
tech
n
iq
u
es
a
s
a
n
e
w
p
o
w
er
f
u
l
to
o
l
f
o
r
s
o
lv
in
g
m
a
n
y
p
r
o
b
le
m
s
i
n
co
n
tr
o
l
s
y
s
te
m
s
e
n
g
in
ee
r
i
n
g
.
T
h
is
led
to
th
e
d
ev
elo
p
m
en
t
o
f
m
an
y
s
y
m
b
o
lic
to
o
lb
o
x
es
in
co
n
tr
o
l
s
y
s
te
m
d
esig
n
[
5
,
6
]
.
I
n
r
ec
en
t
y
ea
r
s
,
as
th
e
c
y
b
er
-
p
h
y
s
ical
s
y
s
te
m
s
i
n
cr
ea
s
e,
r
esear
ch
er
s
r
et
u
r
n
a
g
ain
to
f
o
cu
s
o
n
s
y
m
b
o
lic
alg
eb
r
a
i
n
co
n
tr
o
l
ap
p
li
ca
tio
n
s
in
c
lu
d
i
n
g
f
ield
s
lik
e
s
y
s
te
m
m
o
d
elli
n
g
,
a
n
al
y
s
is
a
n
d
co
n
tr
o
ller
d
esig
n
[
7
]
.
R
e
g
ar
d
in
g
t
h
e
s
y
s
t
e
m
m
o
d
elli
n
g
,
P
o
la
et
a
l
.
[
8
]
d
er
iv
ed
a
s
y
m
b
o
lic
m
o
d
el
as
an
ap
p
r
o
x
i
m
atio
n
f
o
r
th
e
p
lan
t
an
d
t
h
e
n
ex
p
lo
ited
t
o
o
b
tain
th
e
co
n
tr
o
l
p
r
o
b
lem
s
o
lu
tio
n
.
T
h
e
r
e
s
u
lts
w
er
e
u
t
ili
ze
d
in
t
h
e
s
y
m
b
o
lic
co
n
tr
o
l
o
f
a
ca
r
-
lik
e
r
o
b
o
t.
Fak
h
r
o
lesl
a
m
e
t
a
l
.
[
9
]
co
n
s
tr
u
ct
ed
ap
p
r
o
x
im
ate
l
y
b
i
s
i
m
ilar
s
y
m
b
o
lic
m
o
d
els
f
o
r
n
o
n
li
n
ea
r
co
n
tr
o
l
s
y
s
te
m
s
.
I
t
s
h
o
w
s
h
o
w
t
h
e
ch
e
m
ical
p
r
o
ce
s
s
co
n
tr
o
l
ca
n
b
e
m
a
n
a
g
ed
v
ia
th
e
u
s
a
g
e
of
m
et
h
o
d
s
th
at
is
b
ased
o
n
s
y
m
b
o
lic
m
o
d
els.
Gir
ar
d
et
a
l
.
[
1
0
]
p
r
o
p
o
s
ed
m
u
lti
s
ca
l
e
s
y
m
b
o
lic
m
o
d
els
co
n
s
tr
u
ct
io
n
f
o
r
s
w
itc
h
ed
s
y
s
te
m
s
.
I
t
w
a
s
d
e
m
o
n
s
tr
ated
th
at
th
e
s
e
m
o
d
els
ar
e
ap
p
r
o
x
im
atel
y
b
i
s
i
m
ilar
t
o
th
e
g
e
n
u
in
e
s
y
s
te
m
s
.
T
h
en
,
it
w
a
s
u
s
ed
f
o
r
co
n
tr
o
ller
c
o
m
p
u
tatio
n
an
d
ap
p
lied
to
t
h
e
s
a
f
et
y
a
u
to
m
a
ta.
R
ad
a
y
d
eh
an
d
Mo
t
h
af
ar
[
1
1
]
d
ev
elo
p
ed
a
s
y
m
b
o
lic
s
tate
-
s
p
ac
e
-
b
ased
m
o
d
el
f
o
r
c
u
r
r
en
t
-
m
o
d
e
co
n
tr
o
lled
m
o
d
u
lar
DC
-
D
C
co
n
v
er
ter
s
.
T
h
en
th
e
co
n
tr
o
l
-
to
-
o
u
tp
u
t
v
o
ltag
e
tr
an
s
f
er
f
u
n
ctio
n
s
ar
e
d
e
r
iv
ed
in
a
s
y
m
b
o
lic
f
o
r
m
.
R
eg
ar
d
in
g
co
n
tr
o
ller
d
esi
g
n
,
Miz
o
g
u
c
h
i
a
n
d
U
s
h
io
[
1
2
]
d
esig
n
ed
a
d
ea
d
lo
ck
-
f
r
ee
s
y
m
b
o
lic
o
u
tp
u
t
f
ee
d
b
ac
k
co
n
tr
o
ller
.
B
o
r
r
i
et
a
l
.
[
1
3
]
p
r
o
p
o
s
ed
a
s
y
m
b
o
lic
m
et
h
o
d
to
th
e
co
n
tr
o
l
d
esi
g
n
o
f
NC
S,
ta
k
i
n
g
in
to
ac
co
u
n
t
th
e
m
o
s
t
s
ig
n
i
f
ica
n
t
n
o
n
-
id
ea
liti
e
s
i
n
t
h
e
co
m
m
u
n
ic
atio
n
c
h
an
n
el
w
it
h
ap
p
licati
o
n
to
r
o
b
o
t
m
o
tio
n
p
lan
n
i
n
g
.
Sh
a
m
g
ah
et
a
l
.
[
1
4
]
d
ev
elo
p
ed
a
n
o
v
el
s
y
m
b
o
lic
tech
n
iq
u
e
f
o
r
co
n
tr
o
llin
g
au
t
o
n
o
m
o
u
s
attac
k
i
n
g
v
eh
ic
les
in
f
eu
d
i
n
g
e
n
v
ir
o
n
m
e
n
ts
.
Do
r
r
ah
et
a
l
.
[
1
5
]
p
r
o
p
o
s
e
d
a
n
e
w
g
en
er
ic
m
eth
o
d
o
lo
g
y
f
o
r
d
er
iv
atio
n
an
d
r
ea
lizatio
n
o
f
f
ee
d
b
ac
k
g
ai
n
s
f
o
r
au
to
m
atic
co
n
tr
o
l
s
y
s
te
m
s
b
ased
o
n
s
y
m
b
o
lic
r
ep
r
esen
tatio
n
o
f
f
ee
d
b
ac
k
s
tab
ilizatio
n
f
u
n
ct
io
n
s
.
R
eg
ar
d
in
g
t
h
e
s
y
s
te
m
a
n
al
y
s
is
,
Mla
d
e
n
o
v
ić
et
a
l
.
[
1
6
]
an
al
y
ze
d
t
h
e
e
x
p
ec
tatio
n
-
m
a
x
i
m
izatio
n
alg
o
r
ith
m
v
ia
s
y
m
b
o
lic
p
r
o
ce
s
s
i
n
g
a
n
d
co
m
p
u
ter
al
g
eb
r
a
t
o
o
ls
.
T
h
en
,
t
h
e
o
b
tain
ed
r
esu
l
ts
ar
e
e
m
p
lo
y
ed
f
o
r
f
u
r
t
h
er
o
p
ti
m
izat
io
n
.
Setia
w
a
n
et
a
l
.
[
1
7
]
p
r
o
p
o
s
ed
a
s
tead
y
s
tate
s
y
m
b
o
lic
a
n
al
y
s
i
s
f
o
r
b
u
ck
co
n
v
er
ter
w
h
ic
h
g
iv
e
s
th
e
ex
ac
t
ca
lc
u
latio
n
o
f
s
tead
y
s
tate
o
u
tp
u
t
w
i
th
n
o
n
ee
d
f
o
r
tr
an
s
ien
t
r
esp
o
n
s
e
e
v
al
u
atio
n
.
A
b
d
-
Alr
ah
e
m
e
t
a
l
.
[
2
]
ex
a
m
in
e
d
th
e
p
r
o
b
lem
o
f
f
u
ll
y
s
y
m
b
o
lic
r
ep
r
esen
tatio
n
an
d
an
al
y
s
i
s
f
o
r
p
a
r
a
m
eter
v
ar
y
i
n
g
s
y
s
te
m
s
(
P
VS)
.
T
h
e
s
i
m
u
latio
n
r
es
u
lt
s
w
er
e
c
ar
r
ied
o
u
t
o
n
th
e
d
r
u
g
co
n
ce
n
tr
atio
n
p
h
ar
m
ac
o
k
i
n
etics
an
d
p
r
o
p
o
r
tio
n
al
-
d
er
iv
ativ
e
ac
tio
n
i
n
t
h
e
r
etin
a.
T
h
e
g
en
er
at
ed
o
u
tp
u
t
w
as
r
ep
o
r
ted
to
b
e
n
ea
ter
th
a
n
a
n
d
a
s
clo
s
e
as
al
g
eb
r
aic,
an
d
t
h
e
e
f
f
ec
t
o
f
p
ar
a
m
eter
v
ar
iatio
n
o
n
s
tate
v
ar
iab
les
w
as
an
al
y
z
ed
.
Ne
v
er
th
ele
s
s
,
it is
in
co
n
v
e
n
ie
n
t
f
o
r
h
ig
h
o
r
d
er
s
tate
s
p
ac
e
m
o
d
els,
as it s
u
f
f
er
s
f
r
o
m
h
i
g
h
co
m
p
u
tatio
n
al
co
m
p
le
x
it
y
.
T
h
er
ef
o
r
e,
in
th
i
s
p
ap
er
,
a
f
u
ll
y
s
y
m
b
o
lic
-
b
a
s
ed
tech
n
iq
u
e
is
p
r
o
p
o
s
ed
f
o
r
s
o
lv
i
n
g
n
th
o
r
d
er
s
tate
-
s
p
ac
e
m
o
d
els
a
n
d
t
h
u
s
u
tili
ze
d
in
t
h
e
a
n
al
y
s
is
o
f
p
ar
a
m
e
ter
v
ar
iatio
n
s
.
T
h
e
p
r
o
p
o
s
ed
tech
n
iq
u
e
h
as
th
e
ab
ilit
y
to
d
ea
l
w
i
th
lar
g
e
co
m
p
lex
s
y
s
te
m
s
th
r
o
u
g
h
p
ar
titi
o
n
i
n
g
t
h
e
o
r
ig
in
al
m
a
tr
ices,
th
e
n
ea
ch
s
u
b
-
m
atr
i
x
is
tr
ea
ted
s
ep
ar
atel
y
w
i
th
t
h
e
ap
p
r
o
p
r
iate
m
et
h
o
d
s
a
n
d
as
s
e
m
b
led
ev
e
n
tu
a
ll
y
alto
g
eth
e
r
.
Hen
ce
,
s
p
e
ed
in
g
u
p
th
e
p
r
o
ce
s
s
an
d
r
ed
u
ce
th
e
co
m
p
u
tatio
n
al
co
m
p
le
x
it
y
p
r
o
b
le
m
f
o
u
n
d
in
[
2
].
T
h
e
r
est
o
f
th
is
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
w
s
:
T
h
e
co
n
v
e
n
tio
n
al
cr
iter
io
n
f
o
r
s
o
lv
in
g
s
tate
s
p
ac
e
m
o
d
el
i
s
f
o
r
m
u
lated
in
Sec
ti
o
n
2
.
T
h
e
p
r
o
p
o
s
ed
s
y
m
b
o
lic
-
b
ased
tech
n
iq
u
e
v
ia
p
ar
titi
o
n
m
a
tr
ix
t
h
eo
r
y
f
o
r
s
o
lv
i
n
g
s
tate
m
o
d
els
is
d
escr
i
b
ed
in
Sectio
n
3
.
T
h
e
s
i
m
u
la
tio
n
r
es
u
lt
s
ar
e
p
r
esen
ted
in
Sectio
n
4
.
F
in
al
l
y
,
th
e
p
ap
er
is
co
n
clu
d
ed
in
Sect
i
o
n
5.
2.
P
RO
B
L
E
M
ST
AT
E
M
E
NT
As
m
o
d
er
n
s
y
s
te
m
s
b
ec
o
m
e
i
n
h
er
e
n
tl
y
co
m
p
lex
,
t
h
e
s
tate
s
p
ac
e
r
ep
r
esen
tatio
n
o
f
a
d
y
n
a
m
ic
s
y
s
te
m
r
ep
lace
s
an
n
th
o
r
d
er
d
if
f
er
en
t
i
al
eq
u
atio
n
w
it
h
a
s
i
n
g
le
f
ir
s
t
o
r
d
er
m
atr
ix
d
i
f
f
er
e
n
tial e
q
u
a
t
io
n
as f
o
llo
w
s
[1
8
]
:
̇
= A
x
+ B
u
(
1
)
y
= C x
+ D
u
(
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
1
,
No
.
1
,
Feb
r
u
ar
y
2
0
2
1
:
27
2
-
28
3
274
w
h
er
e
(
1
)
is
ca
lled
th
e
s
tate
e
q
u
atio
n
a
n
d
(
2
)
is
ca
lled
th
e
o
u
tp
u
t
eq
u
at
io
n
.
u
is
t
h
e
i
n
p
u
t
f
u
n
ct
io
n
a
n
d
y
is
th
e
o
u
tp
u
t
f
u
n
c
tio
n
.
A
(n
×
n)
,
B
(n
×
p)
,
C
(q
×
)
,
D
(
q
×
)
r
ep
r
esen
ts
th
e
s
tate
m
atr
ix
,
t
h
e
i
n
p
u
t
m
atr
ix
,
th
e
o
u
tp
u
t
m
atr
i
x
a
n
d
th
e
f
ee
d
th
r
o
u
g
h
m
atr
i
x
r
esp
ec
tiv
el
y
.
T
h
e
co
m
p
lete
s
y
s
te
m
s
ta
te
r
esp
o
n
s
e
x
(
t)
co
n
s
is
ts
o
f
t
w
o
p
ar
ts
:
a
ze
r
o
-
in
p
u
t
r
esp
o
n
s
e
th
at
r
ep
r
esen
ts
t
h
e
r
esp
o
n
s
e
d
u
e
to
ar
b
itra
r
y
i
n
itial
co
n
d
itio
n
s
x
(
0
)
w
it
h
n
o
i
n
p
u
ts
at
al
l,
an
d
a
ze
r
o
s
tate
r
esp
o
n
s
e
th
at
r
ep
r
esen
ts
t
h
e
r
esp
o
n
s
e
d
u
e
to
ar
b
itra
r
y
in
p
u
t
w
it
h
ze
r
o
in
itial
co
n
d
itio
n
s
.
T
h
e
t
w
o
p
ar
ts
ar
e
th
en
j
o
in
ed
to
p
r
o
d
u
ce
th
e
co
m
p
let
e
r
esp
o
n
s
e
as f
o
llo
w
s
,
=
Φ(
t
)
.
x(
0
)
(
3
)
=
∫
(
−
)
(
)
0
(
4
)
X
(
t
)
= Φ
(
t
)
.
x(
0
)
+
∫
(
−
)
(
)
0
(
5
)
w
h
er
e
Φ
(
t)
is
id
en
ti
f
ied
to
b
e
th
e
s
tate
tr
a
n
s
it
io
n
m
atr
ix
,
w
h
i
ch
is
co
m
p
u
ted
b
y
:
Φ(
t
)
=
−
1
[
S
I
−
A
]
-
1
(
6
)
A
cc
o
r
d
in
g
to
[
2
]
,
a
s
tr
aig
h
t
f
o
r
w
ar
d
s
y
s
te
m
atic
m
et
h
o
d
f
o
r
s
y
m
b
o
lic
d
er
iv
atio
n
o
f
s
tate
s
p
ac
e
s
o
lu
tio
n
is
p
r
esen
ted
.
A
n
atte
m
p
t
to
ex
p
lo
it
th
e
m
eth
o
d
f
o
r
s
o
lv
in
g
lar
g
e
s
tate
s
p
ac
e
m
o
d
els
u
n
f
o
r
tu
n
atel
y
s
h
o
w
s
s
e
v
er
e
s
h
o
r
tco
m
in
g
s
in
s
p
ee
d
an
d
r
eso
u
r
ce
s
u
s
a
g
e
d
u
e
to
h
ig
h
d
i
m
en
s
io
n
m
atr
i
x
m
a
n
ip
u
lat
io
n
s
w
it
h
its
r
elate
d
p
r
o
s
p
ec
ts
o
f
r
u
n
n
in
g
o
u
t
o
f
av
ai
lab
le
m
e
m
o
r
y
[
1
9
]
.
S
y
m
b
o
lic
s
o
lu
tio
n
s
o
f
h
ig
h
er
d
i
m
en
s
io
n
m
atr
ice
s
ar
e
in
ev
i
tab
l
y
lar
g
e.
Fo
r
in
s
ta
n
ce
,
co
m
p
u
tin
g
t
h
e
i
n
v
er
s
e
m
atr
ix
i
n
s
y
m
b
o
lic
f
o
r
m
is
a
c
u
m
b
er
s
o
m
e
p
r
o
ce
s
s
.
5
×
5
in
v
er
s
e
m
atr
ix
e
x
ce
ed
s
2
0
0
0
0
0
ch
ar
ac
ter
s
lo
n
g
,
6
x
6
in
v
er
s
e
m
atr
i
x
e
x
ce
ed
s
2
0
0
0
0
0
0
,
th
e
in
v
er
s
e
b
ec
o
m
e
s
1
0
ti
m
es
lar
g
er
i
n
len
g
t
h
f
o
r
ea
ch
ad
d
itio
n
al
in
cr
ea
s
e
o
f
m
atr
i
x
d
i
m
en
s
io
n
.
I
n
g
e
n
er
al,
f
o
r
a
s
y
m
b
o
lic
in
v
er
s
e
o
f
n
×
n
m
at
r
ix
,
th
e
o
u
tp
u
t
s
ize
i
s
ab
o
u
t
2
.
2
x
10
.
So
,
m
u
ltip
le
g
ig
ab
y
tes
ar
e
n
ee
d
ed
to
ca
lcu
late
th
e
i
n
v
er
s
e
o
th
er
t
h
an
t
h
e
o
th
er
p
r
o
ce
s
s
es.
Als
o
,
th
e
c
u
r
r
en
t
s
o
f
t
w
ar
e
o
f
te
n
g
en
er
ate
s
h
i
g
h
l
y
co
m
p
le
x
r
a
w
ex
p
r
es
s
io
n
s
w
h
i
ch
ar
e
to
o
d
if
f
ic
u
lt to
b
e
d
ir
ec
tl
y
u
s
ed
[
2
0
]
.
I
n
r
esp
o
n
s
e
to
t
h
ese
p
r
o
b
le
m
s
,
a
f
u
ll
y
s
y
m
b
o
lic
b
ased
tec
h
n
iq
u
e
f
o
r
s
o
l
v
in
g
co
m
p
lex
s
tate
s
p
ac
e
m
o
d
el
s
is
p
r
o
p
o
s
ed
.
T
h
e
p
r
o
p
o
s
ed
tech
n
iq
u
e
tr
ie
s
to
o
v
er
co
m
e
t
h
e
b
ar
r
ier
s
o
f
h
i
g
h
r
eso
u
r
ce
s
,
ti
m
e
co
n
s
u
m
p
tio
n
an
d
co
m
p
u
ta
tio
n
al
co
m
p
le
x
it
y
u
s
in
g
t
h
e
p
ar
titi
o
n
ed
m
atr
i
x
t
h
eo
r
y
.
All
t
h
e
s
tate,
i
n
p
u
t
a
n
d
o
u
tp
u
t
m
a
tr
ices
o
f
th
e
o
r
ig
i
n
al
s
y
s
te
m
ar
e
b
r
o
k
en
u
p
in
to
b
lo
ck
s
an
d
all
th
e
s
u
b
s
eq
u
en
t
p
r
o
ce
s
s
i
n
g
i
s
m
ad
e
o
n
th
ese
b
lo
c
k
s
,
t
h
e
n
to
b
e
as
s
e
m
b
led
at
th
e
e
n
d
.
A
lt
h
o
u
g
h
th
e
s
tate
s
p
ac
e
m
o
d
el
m
a
y
b
e
o
f
an
y
d
i
m
en
s
io
n
e
ith
e
r
o
d
d
o
r
ev
en
,
th
e
p
ar
titi
o
n
p
r
o
ce
s
s
m
a
y
lead
to
r
ec
tan
g
u
la
r
b
lo
ck
s
w
h
ic
h
w
ill
b
e
co
n
s
i
d
er
ed
a
p
r
o
b
lem
as
th
e
p
r
o
ce
s
s
i
n
g
i
n
cl
u
d
es
i
n
v
er
s
e
m
atr
ix
o
p
er
atio
n
s
.
T
h
is
b
ar
r
ier
is
o
v
er
co
m
e
b
y
b
lo
ck
w
i
s
e
in
v
er
s
io
n
f
o
r
m
u
la
w
h
ic
h
in
s
u
r
e
s
th
at
o
n
l
y
ei
th
er
th
e
to
p
-
le
f
t o
r
b
o
tto
m
-
r
i
g
h
t
m
a
tr
ices sh
o
u
ld
o
n
l
y
b
e
s
q
u
ar
e
b
lo
ck
s
.
3.
T
H
E
P
RO
P
O
SE
D
T
E
CH
NI
Q
U
E
I
n
o
r
d
er
to
o
v
er
co
m
e
t
h
e
a
f
o
r
e
m
en
tio
n
ed
d
r
a
w
b
ac
k
s
,
a
p
r
o
ce
d
u
r
e
th
at
is
b
ased
o
n
p
ar
titi
o
n
m
atr
ix
th
eo
r
y
a
lo
n
g
w
it
h
b
lo
ck
w
is
e
i
n
v
er
s
es
is
p
r
o
p
o
s
ed
.
P
ar
titi
o
n
m
atr
i
x
t
h
eo
r
y
is
co
n
s
id
er
ed
to
b
e
th
e
b
est
m
et
h
o
d
to
d
ea
l
w
it
h
h
i
g
h
d
i
m
en
s
io
n
m
atr
ices.
I
t
r
elies
o
n
p
ar
titi
o
n
i
n
g
a
lar
g
e
m
atr
i
x
in
to
co
m
p
ati
b
le
s
m
aller
s
ec
tio
n
s
r
ef
er
r
ed
to
as
s
u
b
-
m
a
tr
ices
o
r
b
lo
ck
s
.
Hen
ce
,
m
a
n
ip
u
lat
io
n
s
ca
n
b
e
p
er
f
o
r
m
ed
o
n
t
h
e
s
m
all
er
b
lo
ck
s
w
h
ic
h
i
n
tu
r
n
lead
s
to
s
ig
n
i
f
ica
n
t
co
m
p
u
tatio
n
al
b
e
n
ef
i
ts
[
2
1
]
.
T
h
e
co
m
p
lete
f
lo
w
c
h
ar
t
o
f
t
h
e
p
r
o
p
o
s
ed
s
y
m
b
o
lic
-
b
ased
tech
n
iq
u
e
f
o
r
s
o
lv
i
n
g
c
o
m
p
le
x
s
tate
s
p
ac
e
m
o
d
el
s
is
d
ep
icted
in
Fig
u
r
e
1
.
Fo
r
lo
w
d
i
m
en
s
io
n
s
y
s
te
m
s
,
it
is
co
n
v
e
n
ie
n
t
to
u
s
e
th
e
s
t
r
aig
h
t
f
o
r
w
ar
d
s
y
s
te
m
a
tic
p
r
o
ce
d
u
r
e
f
o
r
s
o
lv
i
n
g
s
tate
s
p
ac
e
m
o
d
el
d
ir
ec
tly
o
n
th
e
o
r
ig
i
n
al
m
atr
ice
s
w
it
h
o
u
t
an
y
ad
d
itio
n
al
p
r
o
ce
s
s
i
n
g
.
Me
an
w
h
ile
f
o
r
h
i
g
h
d
i
m
e
n
s
io
n
s
y
s
t
e
m
s
,
i
t
i
s
d
e
s
i
r
a
b
l
e
t
o
p
a
r
t
i
t
i
o
n
t
h
e
o
r
i
g
i
n
a
l
s
y
s
t
e
m
i
n
t
o
l
o
w
e
r
d
i
m
e
n
s
i
o
n
a
l
b
l
o
c
k
s
.
S
o
t
h
a
t
a
n
y
f
u
r
t
h
e
r
p
r
o
c
e
s
s
i
n
g
i
s
m
a
d
e
o
n
t
h
e
s
e
b
l
o
c
k
s
i
n
s
t
e
a
d
,
w
h
i
c
h
m
a
k
e
s
t
h
e
p
r
o
c
e
s
s
i
n
g
m
u
c
h
p
o
w
e
r
f
u
l
a
n
d
e
a
s
i
e
r
t
o
b
e
a
p
p
l
i
e
d
.
T
h
e
p
r
o
p
o
s
ed
tech
n
iq
u
e
b
eg
i
n
s
w
it
h
d
ec
id
in
g
w
h
et
h
er
tec
h
n
iq
u
e
to
b
e
u
s
ed
ac
co
r
d
in
g
to
t
h
e
o
r
ig
i
n
al
m
o
d
el
d
i
m
e
n
s
io
n
.
I
f
t
h
e
m
at
r
ix
d
i
m
e
n
s
io
n
s
e
x
ce
ed
a
p
r
ed
ef
in
ed
li
m
it,
al
l
s
u
b
s
eq
u
e
n
t
o
p
er
atio
n
s
w
ill
b
e
p
er
f
o
r
m
ed
o
n
s
u
b
-
m
atr
ix
le
v
e
l,
o
th
er
w
i
s
e
o
n
f
u
ll
m
atr
ix
le
v
el.
T
h
e
v
alu
e
o
f
t
h
e
d
i
m
e
n
s
io
n
li
m
it
i
s
s
et
to
7
as
it
w
as
f
o
u
n
d
e
m
p
ir
icall
y
b
y
o
u
r
ex
p
er
i
m
e
n
ts
.
As
th
e
d
i
m
e
n
s
io
n
s
g
e
t
lar
g
er
,
th
e
d
if
f
er
en
c
e
b
et
w
ee
n
th
e
t
w
o
m
et
h
o
d
s
g
ets
f
u
r
th
er
e
n
tire
l
y
i
n
f
a
v
o
u
r
s
o
f
th
e
p
ar
titi
o
n
ed
m
atr
ix
tech
n
iq
u
e.
P
ar
titi
o
n
in
g
o
cc
u
r
s
ac
co
r
d
in
g
to
a
ce
r
tai
n
cr
iter
io
n
as
s
h
o
w
n
i
n
Fi
g
u
r
e
2
.
If
n
(
th
e
s
ta
te
m
a
tr
i
x
d
i
m
en
s
io
n
)
i
s
an
e
v
e
n
n
u
m
b
er
,
th
e
s
ta
te
m
a
tr
ix
i
s
d
iv
id
ed
in
t
o
f
o
u
r
eq
u
al
q
u
ar
ter
s
o
f
s
ize
n
/2
.
I
n
ca
s
e
t
h
at
n
is
an
o
d
d
n
u
m
b
er
,
th
e
p
ar
titi
o
n
p
r
o
ce
s
s
en
s
u
r
es
th
a
t
o
n
l
y
11
an
d
22
ar
e
s
q
u
ar
e
b
lo
ck
s
s
o
th
at
t
h
e
y
ca
n
b
e
in
v
er
ted
b
lo
c
k
w
is
e
w
h
ile
12
an
d
21
ar
e
m
ai
n
tai
n
ed
as
r
ec
tan
g
u
lar
b
lo
ck
m
atr
ice
s
.
I
n
ca
s
e
o
f
v
er
y
h
i
g
h
d
i
m
en
s
io
n
m
atr
i
x
,
th
e
s
o
-
ca
lle
d
n
ested
p
ar
titi
o
n
s
ca
n
b
e
ex
p
lo
ited
if
n
ee
d
ed
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
F
u
lly
s
ymb
o
lic
-
b
a
s
ed
tech
n
iq
u
e
fo
r
s
o
lvin
g
co
mp
lex
s
ta
te
-
s
p
a
ce
co
n
tr
o
l sys
tems
(
A
me
r
a
M
.
A
b
d
-
A
lr
a
h
em
)
275
Fig
u
r
e
1
.
T
h
e
p
r
o
p
o
s
ed
s
y
m
b
o
lic
b
ased
tech
n
iq
u
e
f
lo
w
c
h
ar
t
(
a)
(
b
)
(
c)
Fig
u
r
e
2
.
P
ar
titi
o
n
ed
m
atr
i
x
p
r
o
ce
s
s
in
ca
s
e
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f
(
a)
n
is
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en
,
(
b
)
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is
o
d
d
,
an
d
(
c)
n
ested
p
ar
titi
o
n
s
T
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e
m
ai
n
p
ar
t
o
f
t
h
e
al
g
o
r
ith
m
i
s
r
esp
o
n
s
ib
le
f
o
r
t
h
e
ac
t
u
a
l
p
r
o
ce
s
s
es
th
at
f
o
r
m
t
h
e
ze
r
o
s
tate
an
d
ze
r
o
in
p
u
t
r
esp
o
n
s
es
o
f
th
e
co
m
p
lete
f
i
n
al
s
o
lu
ti
o
n
.
I
f
th
e
m
atr
ix
w
a
s
d
etec
ted
to
b
e
a
lo
w
d
im
e
n
s
io
n
m
o
d
el,
(
3
)
th
r
o
u
g
h
(
6
)
ar
e
em
p
lo
y
ed
d
ir
ec
tly
o
n
t
h
e
f
u
ll
m
a
tr
ix
o
f
th
e
o
r
ig
i
n
al
s
y
s
te
m
m
o
d
el.
Ho
w
e
v
er
,
if
a
h
i
g
h
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
1
,
No
.
1
,
Feb
r
u
ar
y
2
0
2
1
:
27
2
-
28
3
276
d
i
m
en
s
io
n
m
o
d
el
i
s
d
etec
ted
a
n
d
p
ar
titi
o
n
w
a
s
m
ad
e
to
all
m
o
d
el
m
atr
ices,
all
p
r
o
ce
s
s
es
s
h
o
u
ld
b
e
ap
p
lie
d
o
n
a
s
u
b
-
m
atr
i
x
b
asis
.
B
eg
i
n
n
in
g
f
r
o
m
t
h
e
s
tate
tr
a
n
s
i
tio
n
m
atr
ix
ca
lcu
la
tio
n
ac
co
r
d
in
g
to
(
6
)
,
b
lo
ck
m
atr
i
x
in
v
er
s
io
n
s
h
o
u
ld
b
e
ca
r
r
ied
o
u
t.
T
h
e
b
lo
ck
w
is
e
i
n
v
er
s
io
n
f
o
r
m
u
la
f
o
r
ca
lcu
lat
in
g
th
e
n
o
n
s
i
n
g
u
lar
p
ar
titi
o
n
ed
m
atr
i
x
in
v
er
s
e
s
ta
tes t
h
at:
f
o
r
an
y
g
i
v
en
m
atr
i
x
A
th
a
t is p
ar
titi
o
n
ed
in
to
4
b
lo
ck
s
as
f
o
llo
ws,
A
=
[
11
12
13
14
15
21
22
23
24
25
31
32
33
34
35
41
42
43
44
45
51
52
53
54
55
]
=
[
11
12
21
22
]
(
7
)
T
h
e
in
v
er
s
e
m
atr
ix
−
1
ca
n
b
e
ex
p
r
ess
ed
as f
o
llo
w
s
,
−
1
=
[
11
̃
12
̃
21
̃
22
̃
]
(
8
)
No
w
t
h
er
e
ar
e
t
w
o
s
et
s
o
f
f
o
r
m
u
las to
ca
lcu
late
11
̃
,
12
̃
,
21
̃
an
d
22
̃
[
22
]:
I
f
b
o
th
11
an
d
its
s
c
h
u
r
co
m
p
le
m
en
t (
22
-
21
11
−
1
12
)
ar
e
n
o
n
s
in
g
u
lar
; th
e
m
atr
i
x
is
i
n
v
er
tib
le
u
s
i
n
g
,
11
̃
=
11
−
1
+
11
−
1
12
(
22
−
21
11
−
1
12
)
−
1
21
11
−
1
(
9
)
12
̃
=
−
11
−
1
12
(
22
−
21
11
−
1
12
)
−
1
(
1
0
)
21
̃
=
−
(
22
−
21
11
−
1
12
)
−
1
21
11
−
1
(
1
1
)
22
̃
=
(
22
−
21
11
−
1
12
)
−
1
(
1
2
)
I
f
b
o
th
22
an
d
its
s
c
h
u
r
co
m
p
le
m
en
t (
11
-
12
22
−
1
21
)
ar
e
n
o
n
s
in
g
u
lar
; th
e
m
atr
i
x
is
i
n
v
er
tib
le
u
s
i
n
g
,
11
̃
=
(
11
−
12
22
−
1
21
)
−
1
(
1
3
)
12
̃
=
−
(
11
−
12
22
−
1
21
)
−
1
12
22
−
1
(
1
4
)
21
̃
=
−
22
−
1
(
11
−
12
22
−
1
21
)
−
1
(
1
5
)
22
̃
=
22
−
1
+
22
−
1
21
(
11
−
12
22
−
1
21
)
−
1
12
22
−
1
(
1
6
)
A
l
s
o
t
h
e
p
s
e
u
d
o
in
v
er
s
e
[
2
3
]
w
a
s
tes
ted
in
th
e
s
tate
tr
an
s
iti
o
n
m
a
tr
ix
ca
lcu
la
tio
n
,
b
u
t
it
y
ield
s
p
o
o
r
r
esu
lt
s
i
n
ter
m
s
o
f
ti
m
e
a
n
d
m
e
m
o
r
y
co
m
p
ar
ed
to
t
h
e
b
lo
ck
w
i
s
e
i
n
v
er
s
io
n
f
o
r
m
u
la.
T
h
en
,
all
t
h
e
s
u
b
s
eq
u
e
n
t
o
p
er
atio
n
s
ca
n
b
e
ea
s
il
y
e
m
p
lo
y
ed
u
s
in
g
t
h
e
co
r
r
esp
o
n
d
in
g
b
lo
ck
s
as
eq
u
atio
n
s
(
3
)
to
(
6
)
s
tates.
As
th
e
i
n
v
er
s
io
n
o
f
h
i
g
h
o
r
d
er
m
a
tr
ices
h
a
s
al
w
a
y
s
b
ee
n
a
ch
allen
g
e
d
u
e
to
th
e
li
m
i
t
ed
p
r
o
ce
s
s
in
g
an
d
m
e
m
o
r
y
ca
p
ac
it
y
o
f
tr
ad
itio
n
al
co
m
p
u
ter
s
[
2
4
]
.
T
h
er
ef
o
r
e,
co
m
b
i
n
in
g
t
h
e
p
ar
titi
o
n
-
m
atr
i
x
th
eo
r
y
a
n
d
b
lo
ck
w
i
s
e
in
v
er
s
e
y
ie
ld
s
a
n
in
ter
e
s
ti
n
g
m
eth
o
d
o
lo
g
y
w
i
th
at
tr
ac
tiv
e
s
o
l
u
tio
n
o
f
n
o
m
atr
i
x
o
p
er
atio
n
s
o
v
er
h
ea
d
f
o
r
t
h
e
p
r
o
b
le
m
o
f
h
ig
h
d
i
m
e
n
s
io
n
alit
y
.
Fi
n
all
y
,
th
e
co
r
r
esp
o
n
d
in
g
s
u
b
-
m
atr
ic
es
o
f
ze
r
o
i
n
p
u
t
a
n
d
ze
r
o
s
tate
r
esp
o
n
s
es
ar
e
ad
d
ed
,
th
en
,
ass
e
m
b
le
t
h
e
b
lo
ck
s
ag
ain
al
to
g
et
h
er
to
f
o
r
m
t
h
e
co
m
p
lete
s
tate
p
ac
e
s
o
lu
tio
n
.
4.
I
M
P
L
E
M
E
NT
AT
I
O
N
A
ND
CASE
S
T
UD
I
E
S
Sev
er
al
e
x
p
er
i
m
e
n
ts
h
a
v
e
b
ee
n
p
er
f
o
r
m
ed
to
p
r
o
v
e
t
h
e
ap
p
li
ca
b
ilit
y
o
f
t
h
e
p
r
o
p
o
s
ed
tech
n
i
q
u
e
u
s
in
g
MA
T
L
A
B
M
u
P
A
D
S
y
m
b
o
li
c
Ma
th
T
o
o
lb
o
x
[
2
5
]
w
it
h
d
if
f
er
e
n
t
s
ta
te
s
p
ac
e
s
y
s
te
m
m
o
d
el
o
f
v
ar
io
u
s
d
i
m
en
s
io
n
s
.
I
n
t
h
e
n
e
x
t
s
u
b
s
ec
tio
n
s
,
ea
ch
ca
s
e
s
t
u
d
y
is
b
r
ief
l
y
d
escr
ib
ed
,
s
y
m
b
o
l
icall
y
s
o
l
v
ed
,
th
e
n
th
e
p
ar
a
m
eter
v
ar
y
i
n
g
b
eh
a
v
io
r
is
an
al
y
ze
d
a
n
d
f
i
n
all
y
th
e
r
e
s
u
lt
s
ar
e
co
m
p
ar
ed
w
it
h
n
u
m
e
r
ical
s
o
lu
tio
n
s
.
4
.
1
.
Ca
s
e
s
t
ud
y
#
1
(
s
hip
m
o
t
io
n
m
o
de
l
)
T
o
f
u
ll
y
r
ep
r
ese
n
t
t
h
e
m
o
tio
n
o
f
a
r
i
g
id
b
o
d
y
i
n
s
p
ac
e,
s
ix
d
eg
r
ee
s
o
f
f
r
ee
d
o
m
(
DO
F)
ar
e
r
eq
u
ir
ed
.
T
h
e
Stan
d
ar
d
No
tatio
n
f
o
r
s
h
ip
m
o
tio
n
is
d
ep
icted
in
Fig
u
r
e
3
[
2
6
]
an
d
it
s
p
ar
a
m
eter
s
ar
e
g
iv
e
n
i
n
T
ab
le
1
[
2
6
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
F
u
lly
s
ymb
o
lic
-
b
a
s
ed
tech
n
iq
u
e
fo
r
s
o
lvin
g
co
mp
lex
s
ta
te
-
s
p
a
ce
co
n
tr
o
l sys
tems
(
A
me
r
a
M
.
A
b
d
-
A
lr
a
h
em
)
277
Fig
u
r
e
3
.
Stan
d
ar
d
n
o
tatio
n
f
o
r
s
h
ip
m
o
tio
n
d
escr
ip
tio
n
T
ab
le
1
.
Sh
ip
Mo
tio
n
s
i
m
u
lati
o
n
p
ar
am
e
ter
s
d
ef
i
n
itio
n
s
P
a
r
a
me
t
e
r
s
D
e
f
i
n
i
t
i
o
n
P
a
r
a
me
t
e
r
s
D
e
f
i
n
i
t
i
o
n
x
,
y
,
z
D
i
st
a
n
c
e
a
l
o
n
g
b
o
d
y
-
f
i
x
e
d
sy
st
e
m a
x
e
s [
m
]
Y
a
w
a
n
g
l
e
[
r
a
d
]
0
,
v
,
w
T
r
a
n
sl
a
t
i
o
n
a
l
v
e
l
o
c
i
t
y
i
n
b
o
d
y
-
f
i
x
e
d
f
r
a
me
[
m
/
s
]
θ
P
i
t
c
h
a
n
g
l
e
[
r
a
d
]
,
,
F
o
r
c
e
c
o
mp
o
n
e
n
t
s
a
l
o
n
g
b
o
d
y
a
x
e
s [
k
g
]
R
o
l
l
a
n
g
l
e
[
r
a
d
]
,
,
R
o
t
a
t
i
o
n
a
l
v
e
l
o
c
i
t
y
i
n
b
o
d
y
-
f
i
x
e
d
f
r
a
me
[
r
a
d
/
s
]
δ
R
u
d
d
e
r
A
n
g
l
e
[
r
a
d
]
K
,
M,
N
M
o
me
n
t
c
o
mp
o
n
e
n
t
s
a
l
o
n
g
b
o
d
y
a
x
e
s
[
k
g
.
m
]
Ho
w
e
v
er
,
f
o
r
s
h
ip
m
a
n
o
eu
v
r
i
n
g
,
a
4
DO
F
d
escr
ip
tio
n
t
h
at
i
n
v
o
l
v
es
s
u
r
g
e,
s
w
a
y
,
y
a
w
an
d
r
o
ll
m
o
d
es
is
t
y
p
icall
y
r
e
g
ar
d
ed
ad
eq
u
ate
[
2
7
]
.
C
o
n
s
eq
u
en
t
l
y
,
a
f
o
u
r
t
h
o
r
d
er
s
tate
s
p
ac
e
m
o
d
el
f
o
r
th
e
s
h
ip
m
o
tio
n
u
n
d
er
co
n
s
id
er
atio
n
b
ased
o
n
th
e
No
m
o
to
m
o
d
el
is
g
iv
e
n
i
n
a
s
y
m
b
o
lic
f
o
r
m
a
s
f
o
llo
w
s
[
2
6
]
,
[
̇
̇
̇
̇
̇
]
=
[
11
12
0
0
0
21
22
0
0
0
0
1
0
0
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45
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1
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]
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1
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A
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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n
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a)
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Ca
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T
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l
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(
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(
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ated
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ize
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d
s
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o
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n
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n
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er
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en
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test
i
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g
[
2
9
]
.
Nu
m
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ical
v
alu
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f
o
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h
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liq
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i
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le
3
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Fig
u
r
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6
s
h
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m
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eter
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d
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
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8
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I
n
t J
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lec
&
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p
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n
g
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Vo
l.
1
1
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1
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r
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1
:
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2
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t is n
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(
a)
(
b
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Fig
u
r
e
6
.
T
h
e
ef
f
ec
t o
f
c
h
an
g
i
n
g
m
o
n
s
tate
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ar
iab
le
s
(
a)
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v
er
s
u
s
ti
m
e
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b
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̇
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er
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u
s
ti
m
e
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.
3
.
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s
e
s
t
ud
y
#
3
(
Wind
t
urbin
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m
o
del)
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n
th
i
s
ca
s
e
s
tu
d
y
,
t
h
e
w
i
n
d
t
u
r
b
in
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te
s
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m
o
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ated
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a
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h
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b
lad
e
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ar
iab
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d
h
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izo
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ax
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s
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in
d
t
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b
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e
[
3
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]
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v
er
all
s
tate
s
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1
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I
n
t J
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p
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N:
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w
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1
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t
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a
f
t
4
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.
6
To
f
ac
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ate
t
h
e
p
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ce
s
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g
,
t
h
e
co
m
p
le
x
m
atr
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s
(
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0
)
ar
e
r
ep
r
esen
ted
i
n
t
h
e
p
ar
a
m
etr
i
c
co
m
p
ac
t
.
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y
ap
p
l
y
i
n
g
th
e
p
r
o
p
o
s
ed
s
y
m
b
o
lic
b
ased
tech
n
iq
u
e
o
n
th
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n
o
n
h
o
m
o
g
e
n
eo
u
s
w
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n
d
tu
r
b
in
e
s
tate
s
p
ac
e
m
o
d
el,
th
e
m
a
tr
ix
le
v
el
d
ec
is
io
n
in
d
i
ca
tes
a
h
i
g
h
d
i
m
e
n
s
io
n
s
y
s
te
m
n=
1
0
i.e
.
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en
n
u
m
b
er
.
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h
u
s
,
t
h
e
s
y
s
te
m
m
o
d
el
is
p
ar
titi
o
n
ed
in
to
lo
w
er
d
i
m
en
s
io
n
al
s
u
b
s
y
s
te
m
s
.
T
h
en
al
l
th
e
s
u
cc
ee
d
in
g
p
r
o
ce
s
s
es
i
n
tu
r
n
ar
e
m
ad
e
o
n
th
e
s
u
b
m
atr
i
x
b
asis
.
First
co
m
p
u
ti
n
g
th
e
ter
m
[
SI
−
A
]
−
1
,
w
h
er
e
b
o
t
h
11
an
d
its
s
ch
u
r
co
m
p
le
m
e
n
t
ar
e
n
o
n
s
in
g
u
lar
;
s
o
it
is
in
v
er
ti
b
le
u
s
i
n
g
eq
u
atio
n
s
f
r
o
m
(
9
)
to
(
1
2
)
.
Sy
m
b
o
lic
ca
lcu
la
t
io
n
s
ar
e
p
r
o
ce
ed
ed
co
n
s
is
ten
tl
y
,
t
h
e
s
tate
tr
an
s
iti
o
n
m
atr
i
x
is
ca
lc
u
lated
as
f
o
u
r
s
ep
ar
ate
b
lo
ck
s
d
en
o
ted
o
f
s
ize
(
5
×
5
)
f
o
r
ea
ch
b
lo
ck
.
T
h
en
t
h
e
ze
r
o
-
i
n
p
u
t
r
esp
o
n
s
e
is
g
en
er
ated
i
n
t
wo
s
ep
ar
ate
p
ar
titi
o
n
s
o
f
s
ize
(
5
×
1
)
.
T
h
e
ze
r
o
-
s
tate
r
esp
o
n
s
e
is
also
co
m
p
u
ted
o
n
a
b
lo
ck
-
b
asis
ac
co
r
d
in
g
to
(
4
)
th
at
y
ield
s
t
w
o
s
ep
ar
ate
ze
r
o
s
tate
b
lo
ck
s
o
f
s
ize
(5
×
1
)
.
Fin
all
y
,
th
e
ze
r
o
s
tate
an
d
ze
r
o
in
p
u
t
r
esp
o
n
s
e
b
lo
ck
s
ar
e
a
d
d
ed
an
d
s
im
p
li
f
ied
to
f
o
r
m
t
h
e
co
m
p
lete
s
y
m
b
o
lic
s
o
lu
t
io
n
o
f
t
h
e
w
i
n
d
tu
r
b
in
e
s
ta
te
s
p
ac
e
m
o
d
el.
Si
m
u
lat
io
n
r
es
u
lt
s
u
s
i
n
g
r
ea
l
m
o
d
el
p
ar
a
m
eter
s
h
a
v
e
b
ee
n
u
n
d
er
ta
k
en
f
o
r
te
s
ti
n
g
[
30
]
.
Nu
m
er
ical
v
alu
e
s
f
o
r
w
i
n
d
tu
r
b
i
n
e
m
o
d
el
p
ar
am
eter
s
ar
e
s
u
m
m
ar
ize
d
in
T
ab
le
4
.
Fo
r
illu
s
tr
atio
n
,
Fi
g
u
r
e
7
s
h
o
w
s
th
e
i
m
p
ac
t
o
f
v
ar
y
i
n
g
t
h
e
v
al
u
e
o
f
p
ar
a
m
eter
1
o
n
l
y
o
v
er
t
h
e
r
an
g
e
f
r
o
m
0
.
0
0
1
to
0
.
0
2
,
w
h
er
ea
s
all
o
t
h
er
p
ar
am
eter
s
v
alu
e
s
ar
e
k
ep
t
u
n
v
ar
y
i
n
g
.
I
t
is
n
o
ted
th
at
ch
an
g
i
n
g
1
h
as
a
n
o
ticea
b
le
im
p
ac
t
o
n
r
o
to
r
an
d
g
en
er
ato
r
s
p
ee
d
an
d
to
r
s
io
n
an
g
le
o
f
d
r
iv
e
tr
ai
n
(
,
,
∆
),
w
h
ile
i
n
th
e
m
ea
n
ti
m
e
h
as
n
o
e
f
f
ec
t
o
n
th
e
o
th
er
s
tate
p
ar
a
m
eter
s
at
all
.
He
n
c
e,
th
ese
eq
u
atio
n
s
ca
n
b
e
u
s
ed
to
an
al
y
ze
th
e
e
f
f
ec
t
o
f
a
n
y
o
f
th
e
i
n
ter
n
al
p
ar
am
eter
ch
a
n
g
es
w
it
h
in
a
n
y
r
an
g
e
o
f
v
ar
iatio
n
.
Mo
r
eo
v
er
,
it
i
s
n
o
ted
f
r
o
m
th
e
p
lo
t
t
h
at
s
o
m
e
r
e
s
p
o
n
s
es
ar
e
u
n
s
tab
le
an
d
i
n
n
ee
d
f
o
r
a
co
n
t
r
o
llin
g
cr
iter
io
n
.
Fo
r
all
t
h
e
p
r
ev
io
u
s
ca
s
e
s
tu
d
i
es,
t
h
e
p
er
f
o
r
m
a
n
ce
o
f
t
h
e
p
r
o
p
o
s
ed
s
y
m
b
o
lic
-
b
ased
tec
h
n
iq
u
e
h
as
b
ee
n
co
m
p
ar
ed
to
t
h
e
co
r
r
esp
o
n
d
in
g
Si
m
u
lin
k
m
o
d
el.
Up
to
n
o
w
,
Si
m
u
li
n
k
is
to
tall
y
n
u
m
er
ical.
T
o
v
er
if
y
th
e
co
r
r
ec
tn
es
s
o
f
t
h
e
r
es
u
lted
s
y
m
b
o
lic
s
o
l
u
tio
n
,
a
Si
m
u
li
n
k
m
o
d
el
f
o
r
ea
ch
ca
s
e
s
t
u
d
y
h
as
b
ee
n
d
e
v
elo
p
ed
an
d
th
e
n
u
m
er
ical
v
al
u
es
f
o
r
th
e
p
ar
a
m
eter
s
h
a
ve
b
ee
n
f
ed
in
to
t
h
e
s
tate
s
p
ac
e
b
lo
ck
.
T
h
e
r
es
u
lted
o
u
tp
u
ts
f
r
o
m
th
e
s
co
p
e
b
lo
ck
s
s
h
o
w
t
h
e
s
a
m
e
b
eh
a
v
io
u
r
id
e
n
ticall
y
to
th
at
g
e
n
er
ated
f
r
o
m
th
e
s
y
m
b
o
lic
eq
u
atio
n
s
in
all
ca
s
e
s
t
u
d
ies
.
A
t
la
s
t
it
ca
n
b
e
co
n
clu
d
ed
f
r
o
m
all
ca
s
e
s
t
u
d
ies
i
m
p
le
m
e
n
tat
io
n
s
t
h
at
t
h
e
s
y
m
b
o
lic
s
o
lu
tio
n
g
iv
e
s
id
en
tical
r
es
u
lts
as
t
h
e
n
u
m
er
ica
l
co
r
r
esp
o
n
d
in
g
s
o
lu
ti
o
n
.
So
,
t
h
e
s
y
m
b
o
lic
b
a
s
ed
m
o
d
el
ca
n
b
e
a
b
etter
alter
n
ati
v
e
to
th
e
n
u
m
er
ical
m
et
h
o
d
s
w
h
ic
h
h
as
th
e
ad
v
an
tag
e
o
f
g
e
n
er
alit
y
a
n
d
f
le
x
ib
ilit
y
.
Mo
r
eo
v
er
,
th
e
p
ar
titi
o
n
ed
m
atr
i
x
tec
h
n
i
q
u
e
i
m
p
r
o
v
es
t
h
e
m
e
m
o
r
y
u
s
e
an
d
ti
m
e
co
n
s
u
m
p
tio
n
t
h
a
n
th
e
d
ir
ec
t
m
eth
o
d
w
h
er
e
t
h
e
ti
m
e
i
s
d
ec
r
ea
s
e
d
b
y
2
0
%
an
d
m
e
m
o
r
y
u
s
e
b
y
ab
o
u
t
5
%
as
ca
lcu
lated
f
r
o
m
t
h
e
p
r
ev
io
u
s
ca
s
e
s
tu
d
ie
s
ex
p
er
i
m
e
n
tat
io
n
s
.
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