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n
a
m
ics.
T
h
e
y
a
ls
o
a
llo
w
f
o
r
m
o
r
e
f
le
x
ib
ilit
y
to
a
ll
ev
iate
th
e
p
r
o
b
lem
s
ass
o
ciate
d
to
th
e
u
n
ce
r
tai
n
tie
s
p
er
tain
in
g
to
th
e
c
h
o
ice
o
f
th
e
s
y
s
te
m
’
s
f
u
zz
y
r
u
les
a
n
d
f
u
zz
y
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
s
[
12
]
.
R
ec
en
tl
y
,
m
an
y
r
e
s
ea
r
ch
es
h
av
e
b
ee
n
d
o
n
e
o
n
s
y
s
te
m
co
n
tr
o
l
an
d
s
tab
ilit
y
a
n
al
y
s
i
s
b
ased
o
n
t
y
p
e
-
2
f
u
zz
y
s
y
s
te
m
s
s
u
c
h
i
n
[
1
3
-
1
5
]
b
ec
au
s
e
t
h
ese
r
e
s
ea
r
ch
er
s
s
h
o
w
n
t
h
at
t
y
p
e
-
1
f
u
zz
y
lo
g
ic
co
n
tr
o
l
h
av
e
d
if
f
ic
u
lt
y
i
n
m
o
d
eli
n
g
a
n
d
m
i
n
i
m
izi
n
g
th
e
e
f
f
ec
t o
f
u
n
ce
r
tai
n
ties
[
1
6
,
1
7
]
.
I
n
o
th
er
w
o
r
d
,
o
n
e
o
f
ad
ap
tiv
e
an
d
r
o
b
u
s
t
s
c
h
e
m
es
t
h
at
ar
e
u
s
ed
to
co
n
tr
o
l
t
h
e
n
o
n
li
n
ea
r
s
y
s
te
m
i
s
th
e
m
o
d
el
r
ef
er
e
n
ce
co
n
tr
o
l
(
MRC
)
w
h
ic
h
p
o
p
u
lar
in
th
e
a
r
ea
o
f
s
elf
-
t
u
n
in
g
co
n
tr
o
l,
I
n
t
h
e
MR
C
,
th
e
er
r
o
r
b
et
w
ee
n
t
h
e
r
e
f
er
en
ce
m
o
d
el
o
u
tp
u
t
a
n
d
t
h
e
r
ea
l
p
la
n
t
o
u
tp
u
t
i
s
u
s
ed
to
ad
j
u
s
t
i
ts
p
ar
a
m
eter
s
in
o
r
d
er
to
co
n
tr
o
l th
e
p
lan
t to
f
o
llo
w
t
h
e
d
esire
d
o
u
tp
u
t f
r
o
m
t
h
e
r
ef
er
e
n
ce
m
o
d
el
[
1
8
].
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
MR
C
ca
n
b
e
i
m
p
r
o
v
ed
b
y
ad
d
itio
n
al
co
n
tr
o
ller
s
li
k
e
i
n
[
1
9
]
w
h
ic
h
s
u
g
g
est
a
f
u
zz
y
m
o
d
el
r
ef
er
e
n
ce
lear
n
i
n
g
co
n
tr
o
l
(
FMR
L
C
)
to
i
m
p
r
o
v
e
th
e
ex
i
s
ti
n
g
lear
n
in
g
c
o
n
tr
o
l
ap
p
r
o
ac
h
es
o
r
in
tr
o
d
u
ci
n
g
n
e
w
o
n
es
b
ec
a
u
s
e
t
h
e
f
u
zz
y
co
n
tr
o
ller
co
n
s
tr
u
cted
f
o
r
t
h
e
n
o
m
i
n
al
p
lan
t
m
a
y
p
er
f
o
r
m
in
ad
eq
u
atel
y
i
f
s
i
g
n
i
f
ica
n
t
a
n
d
u
n
p
r
ed
ictab
le
p
lan
t
p
ar
a
m
eter
v
ar
iatio
n
s
.
W
h
ile
i
n
[
2
0
]
,
th
e
f
ee
d
b
ac
k
lin
ea
r
izatio
n
,
t
h
e
co
n
v
en
t
io
n
al
m
o
d
el
r
ef
er
en
ce
co
n
tr
o
l,
in
te
r
v
al
t
y
p
e
-
2
f
u
zz
y
s
c
h
e
m
e
(
I
T
2
FL
S)
an
d
t
h
e
id
ea
o
f
th
e
s
lid
i
n
g
m
o
d
e
co
n
tr
o
l
m
eth
o
d
ar
e
co
m
b
in
ed
to
p
r
o
p
o
s
e
a
h
y
b
r
id
co
n
tr
o
l
s
y
s
te
m
to
ad
d
r
ess
th
e
p
r
o
b
lem
o
f
th
e
co
n
v
e
n
tio
n
al
m
o
d
el
r
ef
e
r
en
ce
co
n
tr
o
l a
n
d
r
eso
lv
e
t
h
e
u
n
ce
r
tai
n
h
y
p
er
ch
ao
tic
s
y
s
te
m
tr
ac
k
in
g
p
r
o
b
lem
.
I
n
t
h
is
p
ap
er
,
a
m
o
d
el
r
e
f
er
e
n
ce
co
n
tr
o
ller
co
m
b
i
n
ed
w
it
h
ad
ap
tiv
e
(
t
y
p
e
-
1
a
n
d
i
n
ter
v
al
t
y
p
e
-
2
)
f
u
zz
y
co
n
tr
o
l
s
ch
e
m
e,
is
d
esi
g
n
ed
f
o
r
s
tab
ilizatio
n
o
f
SISO
n
o
n
li
n
ea
r
s
ec
o
n
d
o
r
d
er
s
y
s
t
e
m
s
,
w
o
r
k
i
n
g
i
n
th
e
p
r
esen
ce
o
f
u
n
ce
r
tain
tie
s
a
n
d
ex
ter
n
al
d
is
tu
r
b
an
ce
s
.
T
h
e
u
p
d
ates
f
o
r
th
e
MR
C
ar
e
p
er
f
o
r
m
ed
u
s
i
n
g
ad
ap
tatio
n
la
w
s
d
er
iv
ed
f
r
o
m
t
h
e
s
tab
ilit
y
s
tu
d
y
i
n
th
e
L
y
ap
u
n
o
v
s
e
n
s
e.
T
h
e
ad
ap
tiv
e
(
t
y
p
e
-
1
,
i
n
te
r
v
al
t
y
p
e
-
2
)
f
u
zz
y
co
n
tr
o
l
s
ch
e
m
e
is
u
s
ed
to
i
m
p
r
o
v
e
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
MRC
b
y
r
ed
u
ce
er
r
o
r
s
tead
y
s
tate
f
r
o
m
p
en
d
u
l
u
m
r
esp
o
n
s
e.
T
h
e
o
r
g
an
izatio
n
o
f
th
is
p
ap
er
is
as
f
o
llo
w
s
.
I
n
s
ec
tio
n
2
,
th
e
p
r
o
b
lem
f
o
r
m
u
la
tio
n
an
d
th
e
d
etails
f
o
r
th
e
ad
ap
tiv
e
m
o
d
el
r
ef
er
en
ce
co
n
tr
o
ller
d
esig
n
ar
e
ex
p
lain
ed
.
A
b
r
ief
l
y
i
n
tr
o
d
u
cti
o
n
f
o
r
t
y
p
e
-
1
an
d
in
ter
v
a
l
t
y
p
e
-
2
f
u
zz
y
is
g
i
v
e
n
in
s
ec
tio
n
3
.
T
h
e
co
m
b
i
n
atio
n
o
f
M
R
C
w
it
h
f
u
zz
y
co
n
tr
o
l
s
ch
e
m
e
d
esi
g
n
is
ad
d
r
ess
ed
in
s
ec
tio
n
4
.
Sectio
n
5
d
e
m
o
n
s
tr
ate
t
h
e
ef
f
icie
n
tl
y
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
b
y
s
i
m
u
lat
io
n
r
es
u
lts
.
Fin
all
y
,
t
h
e
s
u
m
m
ar
y
a
n
d
co
n
clu
s
io
n
s
ar
e
g
i
v
e
n
in
s
ec
tio
n
6
.
2.
P
RO
B
L
E
M
F
O
R
M
UL
AT
I
O
N
AND
M
O
DE
L
-
RE
F
E
R
E
NC
E
CO
NT
RO
L
L
E
R
D
E
SI
G
N
T
h
e
g
en
er
al
clas
s
o
f
s
in
g
le
-
i
n
p
u
t
a
n
d
s
i
n
g
le
-
o
u
tp
u
t
(
SIS
O)
u
n
ce
r
tai
n
d
y
n
a
m
ic
n
o
n
li
n
ea
r
s
y
s
te
m
s
ca
n
b
e
d
escr
ib
ed
b
y
t
h
e
f
o
llo
w
i
n
g
m
at
h
e
m
a
tical
eq
u
atio
n
[
2
1
,
2
2
]
:
(
)
=
(
)
+
(
)
(
)
+
(
)
=
(
1
)
w
h
er
e
R
x
x
x
x
T
n
)
,
,
,
(
)
1
(
is
t
h
e
s
tate
v
ec
to
r
o
f
t
h
e
s
y
s
te
m
,
f
(
x
)
is
u
n
k
n
o
wn
co
n
t
in
u
o
u
s
n
o
n
li
n
ea
r
u
n
ce
r
tai
n
f
u
n
ct
io
n
,
g
(
x
)
is
t
h
e
co
n
tr
o
l
g
ai
n
f
u
n
ctio
n
,
R
t
u
)
(
is
t
h
e
i
n
p
u
t
o
f
t
h
e
s
y
s
te
m
a
n
d
R
t
y
)
(
is
s
y
s
te
m
o
u
tp
u
t,
u
n
k
n
o
w
n
n
o
n
li
n
ea
r
u
n
ce
r
tai
n
f
u
n
ctio
n
o
f
th
e
s
y
s
te
m
,
an
d
d
(
t
)
is
th
e
ex
ter
n
al
u
n
k
n
o
w
n
d
is
tu
r
b
an
ce
.
T
h
e
p
r
o
b
lem
o
f
co
n
tr
o
ller
d
esi
g
n
i
s
s
ta
te
as
f
o
llo
w
s
.
I
f
t
h
e
d
e
s
ir
ed
tr
aj
ec
to
r
ies
d
d
d
x
x
x
,
,
(
n
d
R
x
is
b
o
u
n
d
ed
)
ar
e
g
iv
en
w
it
h
all
(
o
r
s
o
m
e)
s
y
s
te
m
s
ta
tes
b
ein
g
u
n
k
n
o
w
n
,
t
h
en
d
er
iv
e
a
lo
w
o
f
co
n
tr
o
ller
f
o
r
th
e
f
o
r
ce
(
o
r
to
r
q
u
e)
in
p
u
t
to
m
a
k
e
th
e
s
tate
s
o
f
t
h
e
s
y
s
te
m
to
f
l
o
w
a
d
esire
d
s
tate
s
T
n
d
d
d
x
x
x
x
)
,
,
,
(
)
1
(
in
th
e
p
r
esen
ce
o
f
ex
ter
n
al
d
is
t
u
r
b
an
ce
s
an
d
m
o
d
el
u
n
ce
r
tain
ties
,
c
lo
s
el
y
i
f
n
o
t
v
er
y
e
x
ac
tl
y
.
A
r
o
b
u
s
t
a
n
d
ad
ap
tiv
e
co
n
tr
o
l
la
w
i
s
n
ee
d
ed
to
d
ea
l
w
i
th
s
y
s
te
m
u
n
ce
r
t
ai
n
tie
s
,
e
x
ter
n
al
d
is
tu
r
b
an
ce
s
an
d
th
e
r
o
u
n
d
in
g
er
r
o
r
s
.
T
o
a
ch
iv
e
th
i
s
o
b
j
ec
tiv
e,
w
e
s
u
g
g
est
to
u
s
e
m
o
d
el
r
ef
er
e
n
ce
co
n
tr
o
ller
(
MRC
)
f
o
r
n
o
n
li
n
ea
r
s
ec
o
n
d
o
r
d
er
s
y
s
te
m
s
(
n
=2
)
.
T
h
e
m
o
d
el
-
r
ef
er
e
n
c
e
co
n
tr
o
ller
ca
n
b
e
co
n
s
id
er
ed
as
o
n
e
o
f
th
e
m
o
s
t
u
s
e
f
u
l
m
e
th
o
d
s
to
s
p
ec
i
f
ic
p
er
f
o
r
m
a
n
ce
s
y
s
te
m
w
h
er
e
th
e
d
esire
d
o
u
tp
u
t
is
p
r
o
d
u
ce
d
f
o
r
a
g
iv
e
n
i
n
p
u
t.
T
h
is
co
n
tr
o
ller
ca
n
b
e
s
im
u
lated
as
m
at
h
e
m
atica
l
m
o
d
el
o
n
a
co
m
p
u
ter
w
it
h
o
u
t
n
ee
d
i
n
g
o
f
p
r
ac
tical
h
ar
d
w
ar
e
an
d
th
e
co
n
tr
o
ller
u
s
ed
t
h
e
d
if
f
er
en
ce
b
et
w
ee
n
th
e
o
u
tp
u
t
s
o
f
th
e
p
lan
t
an
d
t
h
e
m
o
d
el
b
y
co
m
p
ar
i
n
g
th
e
m
to
p
r
o
d
u
ce
th
e
s
i
g
n
a
ls
o
f
th
e
co
n
tr
o
l
[
23
].
T
h
e
m
o
d
el
o
f
t
h
e
n
o
n
li
n
ea
r
s
y
s
te
m
i
n
(
1
)
w
ith
(
n
=
2
)
ca
n
b
e
w
r
i
tte
n
a
s
th
e
s
tate
eq
u
atio
n
:
̇
=
(
,
,
)
(
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
Desig
n
n
o
n
lin
ea
r
mo
d
el
r
eferen
ce
w
ith
fu
z
z
y
co
n
tr
o
ller
fo
r
n
o
n
lin
ea
r
S
I
S
O
s
ec
o
n
d
...
(
E
k
h
la
s
H.
K
a
r
a
m)
2493
o
r
ca
n
b
e
w
r
it
ten
a
s
:
[
̇
1
̇
2
]
=
[
0
1
0
0
]
[
1
2
]
+
[
0
1
]
(
+
+
)
,
=
[
1
0
]
[
1
2
]
(
3
)
w
h
er
e
x
=state
v
ec
to
r
(
2
-
s
tate)
,
u
is
s
in
g
le
co
n
tr
o
l
s
i
g
n
a
l,
f
is
n
o
n
li
n
ea
r
f
u
n
ctio
n
,
d
is
th
e
s
y
s
t
e
m
p
er
tu
r
b
atio
n
.
T
h
e
p
r
o
ce
d
u
r
e
f
o
r
d
esig
n
i
n
g
MRC
i
s
g
i
v
e
n
b
y
t
h
e
f
o
llo
w
i
n
g
s
tep
s
:
Step
1
:
d
ef
in
e
t
h
e
d
esire
d
m
o
d
el
eq
u
atio
n
b
y
:
̇
=
+
(
4
)
w
h
er
e
x
d
i
s
t
h
e
s
tate
v
ec
to
r
o
f
th
e
d
esire
d
m
o
d
el,
v
is
t
h
e
d
e
s
ir
ed
in
p
u
t
s
ig
n
al,
A
is
2
×2
co
n
s
ta
n
t
m
atr
i
x
,
an
d
B
is
2
×1
co
n
s
ta
n
t
m
a
tr
ix
.
T
h
e
s
y
s
te
m
o
f
m
o
d
el
-
r
ef
er
e
n
c
e
h
as
a
n
as
y
m
p
to
ticall
y
s
tab
l
e
eq
u
ilib
r
iu
m
s
ta
te,
w
h
e
n
th
e
ei
g
e
n
v
a
lu
e
s
o
f
(
A
)
h
av
e
n
e
g
ati
v
e
r
ea
l
p
ar
ts
.
"
I
n
th
is
p
ap
er
th
e
eq
u
a
tio
n
o
f
th
e
d
esire
d
r
ef
er
en
ce
m
o
d
el
c
h
o
s
e
n
as:
[
̇
1
̇
2
]
=
[
0
1
−
2
−
2
]
[
1
2
]
+
[
0
2
]
(
5
)
w
h
er
e
is
d
esire
d
n
at
u
r
al
f
r
eq
u
en
c
y
,
a
n
d
is
d
a
m
p
i
n
g
r
atio
.
Step
2
:
d
ef
in
e
t
h
e
er
r
o
r
v
ec
to
r
(
e
)
b
y
:
=
−
(
6
)
I
f
th
e
er
r
o
r
v
ec
to
r
w
as r
ed
u
ce
d
to
ze
r
o
w
it
h
a
s
u
i
tab
le
v
al
u
e
o
f
(
u
):
"
̇
=
̇
−
̇
=
+
−
(
,
,
)
=
+
−
(
,
,
)
+
(
7
)
T
h
e
ab
o
v
e
eq
u
atio
n
r
ep
r
esen
ts
th
e
d
if
f
er
en
t
ial
eq
u
atio
n
f
o
r
th
e
er
r
o
r
v
ec
to
r
.
Step
3
:
ass
u
m
e
t
h
at
th
e
f
u
n
c
ti
o
n
o
f
L
y
ap
u
n
o
v
ca
n
b
e
w
r
it
te
n
as:
(
)
=
(
8
)
w
h
er
e
P
=
a
p
o
s
itiv
e
-
d
e
f
i
n
ite
r
ea
l,
s
y
m
m
etr
ic
m
atr
i
x
.
B
y
ta
k
en
th
e
d
er
iv
a
tiv
e
o
f
V
(
e
)
w
it
h
t
i
m
e
r
esp
ec
t:
̇
(
)
=
̇
+
̇
=
[
+
−
(
,
,
)
+
]
+
[
+
−
(
,
,
)
+
]
=
(
+
)
+
2
(
9
)
w
h
er
e
=
[
−
(
,
,
)
+
]
(
1
0
)
Sin
ce
,
s
o
E
q
u
atio
n
(
9
)
ca
n
b
e
w
r
itte
n
as:
̇
(
)
=
−
+
2
(
1
1
)
T
h
e
V
(
e
)
is
a
s
s
u
m
ed
L
y
ap
u
n
o
v
f
u
n
ctio
n
i
f
(
-
Q
)
i
s
a
n
e
g
ati
v
e
d
ef
in
i
te
m
atr
i
x
a
n
d
t
h
e
co
n
tr
o
l
s
ig
n
a
l
u
(
t
)
s
h
o
u
ld
b
e
ch
o
s
en
s
u
ch
th
at
t
h
e
s
ca
lar
M
is
n
e
g
ati
v
e
[
2
0
]
.
W
h
en
as
,
th
en
t
h
e
eq
u
ilib
r
iu
m
s
t
ate
(
e
1
,
e
2
)
=(
0
,
0
)
is
a
s
y
m
p
ticall
y
s
tab
le
i
n
lar
g
e.
I
n
o
r
d
er
to
s
atis
f
y
E
q
u
at
io
n
(
1
1
)
,
T
h
e
Q
m
atr
i
x
is
c
h
o
s
e
n
as
d
iag
o
n
al
m
atr
ix
:
=
[
11
0
0
22
]
=
p
o
s
itiv
e
d
ef
i
n
ite
T
h
e
r
ate
o
f
co
n
v
er
g
e
n
ce
o
f
tr
an
s
ie
n
t
r
esp
o
n
s
e
d
ep
en
d
s
o
n
m
atr
ix
P
,
w
h
ich
i
n
tu
r
n
d
ep
en
d
s
o
n
m
atr
i
x
Q
,
s
o
V
b
ec
o
m
e
s
;
̇
(
)
=
−
(
11
1
2
+
22
2
2
)
+
2
(
1
2
)
n
Q
PA
P
A
T
)
(
e
V
e
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.
9
,
No
.
4
,
A
u
g
u
s
t 2
0
1
9
:
2
4
9
1
-
2502
2494
A
cc
o
r
d
in
g
to
s
ec
o
n
d
o
r
d
er
m
o
d
el
(
E
q
u
atio
n
(
3
)
)
an
d
th
e
d
esire
d
m
o
d
el
(
E
q
u
atio
n
(
5
)
)
,
th
e
s
ca
lar
M
is
:
(
=
[
1
2
]
[
11
12
21
22
]
(
[
0
1
−
2
−
2
]
[
1
2
]
−
[
0
1
0
0
]
−
[
0
]
+
[
0
2
]
−
[
0
]
)
=
(
1
12
+
2
22
)
[
−
2
1
−
2
2
+
2
−
−
]
(
1
3
)
Her
e,
if
w
e
ch
o
s
e
u
f
o
r
o
u
r
d
esig
n
as:
=
[
−
2
1
−
2
2
+
(
ℎ
(
12
+
2
22
)
)
+
2
−
]
/
(
1
4
)
w
h
er
e
tan
h
(
.
)
(
h
y
b
er
b
o
lic
tan
g
en
t)
a
n
d
k
is
s
u
itab
le
co
n
s
ta
n
t.
W
ith
E
q
u
atio
n
(
1
4
)
th
e
s
ca
la
r
M
is
b
ec
o
m
e
s
:
=
(
12
+
2
22
)
[
−
ta
n
h
(
12
+
2
22
)
]
=
(
1
5
)
3.
TY
PE
-
1
AND
T
YP
E
-
2
F
U
Z
Z
Y
SYS
T
E
M
S
T
y
p
e
-
1
f
u
zz
y
lo
g
ic
s
y
s
te
m
s
(
FLSs
)
ar
e
k
n
o
w
n
"
as
t
h
e
u
n
i
v
er
s
al
ap
p
r
o
x
i
m
a
tes
a
n
d
w
id
e
l
y
u
s
ed
to
s
o
lv
e
th
e
r
ea
l
p
r
o
b
lem
s
b
ec
a
u
s
e
it
is
ca
p
ab
le
o
f
co
m
p
en
s
ate
th
e
s
tr
u
ct
u
r
e
an
d
"
u
n
s
tr
u
c
tu
r
ed
u
n
ce
r
tai
n
tie
s
,
b
u
t
o
n
l
y
"
to
a
ce
r
tain
d
e
g
r
ee
,
"
b
ec
au
s
e
s
o
m
e
o
f
th
e
d
esi
g
n
ed
ap
p
r
o
ac
h
es
f
ac
e
h
i
g
h
lev
el
o
f
u
n
ce
r
tain
t
ies
w
h
ic
h
ef
f
ec
t
o
n
s
y
s
te
m
s
p
er
f
o
r
m
an
ce
s
an
d
s
i
n
ce
t
y
p
e
-
1
f
u
zz
y
s
y
s
te
m
u
s
e
cr
is
p
t
y
p
e
-
1
f
u
zz
y
s
et
s
i
n
r
ep
r
esen
tatio
n
o
f
f
u
zz
y
r
u
le
s
,
s
o
its
ca
n
n
o
t
p
r
o
ce
s
s
t
h
e
h
i
g
h
lev
el
o
f
u
n
ce
r
ta
i
n
tie
s
w
h
i
ch
as
s
o
ciate
d
w
ith
k
n
o
w
led
g
e
b
ases
d
ata
o
r
in
f
o
r
m
atio
n
.
"
T
h
e
s
y
s
te
m
o
f
t
y
p
e
-
2
f
u
zz
y
th
at
s
u
g
g
e
s
ted
b
y
Z
ad
e
h
a
n
d
d
ev
elo
p
ed
f
r
o
m
Me
n
d
el
w
it
h
h
is
co
au
th
o
r
s
[
24
-
26
]
co
u
ld
m
ak
e
ad
d
itio
n
al
p
r
o
f
icien
t
o
v
er
c
o
m
p
e
n
s
at
in
g
t
h
at
h
ig
h
er
lev
e
l
f
o
r
u
n
ce
r
tain
t
i
e
s
b
ec
au
s
e
th
e
m
e
m
b
er
s
h
ip
f
u
n
ct
io
n
s
o
f
th
is
s
y
s
te
m
ar
e
th
e
m
s
e
lv
es
f
u
zz
y
.
T
h
is
t
y
p
e
o
f
f
u
zz
y
co
n
s
id
er
ed
as
o
n
e
o
f
m
o
r
e
s
u
itab
le
s
y
s
te
m
s
t
h
at
h
as
u
n
k
n
o
w
n
ti
m
e
-
v
ar
y
i
n
g
d
y
n
a
m
ics
[
27
].
I
n
ter
v
al
t
y
p
e
-
2
f
u
zz
y
s
y
s
te
m
s
(
I
T
2
FS
s
)
is
co
n
s
id
er
as
o
n
e
a
s
p
ec
ial
s
tate
o
f
T
2
FS
s
.
b
ec
a
u
s
e
o
f
t
h
e
r
ed
u
ctio
n
lo
ad
o
f
co
m
p
u
tatio
n
al
[
28
]
,
I
T
2
FS
s
ar
e
u
s
ed
ac
tu
al
l
y
at
d
i
f
f
er
en
t e
n
g
in
ee
r
i
n
g
ar
ea
s
[
2
9
]
,
[
3
0
].
T
h
e
I
T
2
FS
s
s
tr
u
ct
u
r
e
is
c
o
n
s
i
s
ts
o
f
a
s
s
h
o
w
n
in
Fi
g
u
r
e
1
(
f
u
zz
if
ier
,
r
u
le
b
ase,
in
f
er
en
ce
e
n
g
in
e,
t
y
p
e
r
ed
u
ce
r
,
an
d
d
ef
u
zz
i
f
ier
)
.
I
t
is
s
i
m
i
lar
it
y
o
f
T
1
FL
S,
o
n
l
y
t
h
e
m
ain
d
i
f
f
er
en
ce
b
et
w
ee
n
t
h
e
m
w
as
h
ap
p
en
ed
in
th
e
o
u
tp
u
t
p
r
o
ce
s
s
in
g
w
h
ic
h
c
o
n
tain
s
a
r
ed
u
ce
r
f
o
r
m
a
n
d
a
d
ef
u
zz
i
f
ier
to
p
r
o
d
u
ce
t
h
e
o
u
t
p
u
t
s
i
g
n
al
f
r
o
m
t
h
e
t
y
p
e
r
ed
u
ce
r
o
r
a
cr
is
p
v
alu
e
f
r
o
m
th
e
d
ef
u
zz
i
f
ier
[
28
]
.
So
,
th
e
r
ed
u
ctio
n
t
y
p
e
ca
n
tak
e
in
f
o
r
m
at
io
n
o
n
t
h
e
r
u
l
e
o
f
u
n
ce
r
tai
n
tie
s
m
o
r
e
t
h
an
t
h
e
v
al
u
e
o
f
d
e
f
u
zz
i
f
ied
.
T
h
er
e
ar
e
t
w
o
m
a
in
s
tr
u
ct
u
r
es
f
o
r
a
n
I
T
2
FLC
a
s
f
o
r
a
(
T
1
FL
C
)
,
Ma
m
d
a
n
i a
n
d
T
ak
a
g
i
-
S
u
g
e
n
o
-
Kan
g
(
T
SK)
.
T
SK is co
v
er
ed
in
th
is
Sect
io
n
.
Fig
u
r
e
1
.
T
y
p
e
2
f
u
zz
y
s
y
s
te
m
[
31
]
T
h
e
o
u
tp
u
ts
d
e
f
i
n
itio
n
w
it
h
t
h
e
co
n
s
eq
u
e
n
t
p
ar
t
o
f
r
u
les
is
th
e
m
ai
n
d
i
f
f
er
e
n
ce
b
et
w
ee
n
th
e
t
y
p
e
-
1
T
SK
f
u
zz
y
lo
g
ic
co
n
tr
o
ller
[
32
]
an
d
a
Ma
m
d
a
n
i
t
y
p
e
-
1
f
u
z
z
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I
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
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&
C
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g
,
Vo
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4
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1
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2502
2496
4.
M
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f
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e
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zz
y
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t
r
o
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n
p
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s
(
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r
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g
r
al
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r
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r
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d
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tp
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t
as
s
h
o
w
n
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n
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u
r
e
2
,
w
h
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e
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K
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r
al
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n
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u
r
e
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r
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e
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h
e
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o
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f
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4
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1
.
F
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s
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r
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er
r
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r
)
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d
o
n
e
o
u
tp
u
t
u
f
,
th
e
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
s
f
o
r
th
e
in
p
u
t
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d
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tp
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le
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ig
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3
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d
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NU
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t
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g
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r
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3
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ip
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n
o
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tp
u
t
f
o
r
b
o
th
f
u
zz
y
t
y
p
e
s
as s
h
o
w
n
in
Fi
g
u
r
e
3
(
c
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.
(
a)
(
b
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Fig
u
r
e
3
.
Me
m
b
er
s
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ip
f
u
n
ctio
n
f
o
r
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(
a)
in
p
u
t
v
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le
f
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r
t
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u
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b
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in
p
u
t
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ar
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le
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r
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ter
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al
t
y
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P
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uzz
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C
ontr
oller
K
i
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e
)
(
K
f
e
(
t
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u
f
(
t
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
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&
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p
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n
g
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N:
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n
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n
d
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k
h
la
s
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a
r
a
m)
2497
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u
zz
y
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u
r
e
3
.
Me
m
b
er
s
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ip
f
u
n
ctio
n
f
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r
,
(
c)
o
u
tp
u
t v
ar
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le
4
.
2
.
T
he
rule
s
o
f
f
uzzy
co
ntr
o
l
Utilizi
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g
th
e
p
r
ev
io
u
s
l
y
m
en
ti
o
n
ed
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ar
ticip
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f
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n
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n
s
,
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m
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g
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n
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l
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le
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e
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u
il
t
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p
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o
r
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u
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n
tr
o
ller
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i
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I
F
(
i/p
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is
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A
N
D
(
i/p
2
)
is
---
,
THEN fu
z
z
y
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I
o
u
tp
u
t is
---
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w
h
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e
i/p
1
is
t
h
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er
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o
r
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n
al,
i/p
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te
g
r
al
o
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er
r
o
r
s
ig
n
al.
T
h
e
lo
g
ical
“A
N
D”
tak
e
s
th
e
m
i
n
i
m
u
m
.
T
ab
le
3
[
35
]
-
[
37
]
,
s
h
o
w
s
th
e
r
u
les tab
u
lar
.
I
f
th
e
n
u
m
b
er
o
f
o
u
tp
u
t
m
e
m
b
er
s
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ip
is
r
ed
u
ce
to
t
h
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ee
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l
y
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en
t
h
e
ab
o
v
e
tab
le
ca
n
b
e
m
o
d
if
ied
to
T
ab
le
4
.
T
ab
le
3
.
R
u
les o
f
P
I
f
u
zz
y
co
n
tr
o
ller
Δ e
e
P
Z
N
P
PB
PM
Z
Z
PM
Z
NM
N
Z
NM
NB
T
ab
le
4
.
R
ed
u
ctio
n
r
u
les o
f
P
I
f
u
zz
y
co
n
tr
o
ller
Δ
e
e
N
Z
P
N
N
N
Z
Z
N
N
P
P
Z
P
P
4
.
3
.
Reduct
io
n
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nd
def
uzzf
ica
t
io
n
T
o
co
m
p
u
te
t
h
e
o
u
tp
u
t
v
al
u
e
,
it’
s
n
ee
d
ed
to
ca
lcu
late
th
e
m
ain
f
u
zz
y
t
y
p
e
-
2
b
y
(
1
8
)
an
d
(
1
9
)
.
5.
SI
M
UL
AT
I
O
N
R
E
S
UL
T
S
ANALY
SI
S A
ND
CO
M
P
ARIS
O
N
I
n
th
is
s
ec
tio
n
,
th
e
s
ec
o
n
d
o
r
d
er
in
v
er
ted
p
e
n
d
u
l
u
m
s
y
s
te
m
w
h
ic
h
is
s
h
o
w
n
in
Fi
g
u
r
e
4
i
s
co
n
s
id
er
ed
to
s
h
o
w
t
h
e
ef
f
icie
n
c
y
o
f
t
h
e
p
r
o
p
o
s
ed
c
o
n
tr
o
ller
s
ch
e
m
.
I
n
v
er
ted
p
en
d
u
lu
m
is
a
tr
ad
itio
n
al
p
r
o
b
lem
i
n
d
y
n
a
m
ics
s
y
s
te
m
s
a
n
d
co
n
tr
o
l
th
eo
r
y
,
it
is
u
s
ed
m
ai
n
l
y
to
test
co
n
tr
o
l
alg
o
r
it
h
m
s
.
T
h
e
m
ai
n
f
ea
t
u
r
e
o
f
t
h
i
s
s
y
s
te
m
is
ch
ar
ac
ter
ized
b
y
:
u
n
s
tab
le,
n
o
n
l
in
ea
r
a
n
d
t
h
e
p
h
ase
is
n
o
n
-
m
i
n
i
m
u
m
,
w
h
ich
i
s
lead
to
m
ak
e
t
h
e
s
y
s
te
m
m
o
r
e
r
o
b
u
s
tl
y
a
n
d
s
ta
b
ilit
y
ed
g
e,
m
ad
e
it
th
e
f
o
c
u
s
o
f
atte
n
tio
n
o
f
m
a
n
y
r
esear
c
h
er
s
.
So
,
m
o
s
t
o
f
t
h
e
co
m
p
le
x
s
y
s
te
m
s
ar
e
u
s
ed
t
h
e
i
n
v
er
ted
p
en
d
u
l
u
m
as
a
b
en
ch
m
ar
k
to
co
n
tr
o
l
th
e
s
y
s
te
m
w
it
h
d
if
f
er
e
n
t
co
n
tr
o
ller
tech
n
iq
u
es [
38
].
Fig
u
r
e
4
.
T
h
e
Sy
s
te
m
o
f
t
h
e
in
v
er
ted
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
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&
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o
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p
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Vo
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9
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4
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u
g
u
s
t 2
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1
9
:
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4
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2502
2498
T
h
e
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g
le
o
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ted
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l
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eg
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e
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er
tical
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,
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e
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atio
n
s
f
o
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th
is
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v
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ted
p
en
d
u
lu
m
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y
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te
m
ca
n
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e
w
r
it
ten
a
s
[
39
-
44
]:
1
2
2
1
,
x
y
d
gu
f
x
x
x
(
2
3
)
w
he
re
)
c
o
s
3
4
(
)
s
i
n
c
o
s
(
s
i
n
1
2
1
1
2
2
1
m
m
x
m
l
m
m
x
x
m
l
x
x
g
f
c
v
c
v
,
0
.
)
c
o
s
3
4
(
c
o
s
1
2
1
m
m
x
m
l
m
m
x
g
c
c
(
24
)
I
n
th
i
s
p
ap
er
,
d
is
d
e
fi
n
e
b
y
[
43
]:
d
= 7
s
in
(
10
x
1
)
+
co
s
x
2
(
25
)
T
h
e
p
ar
am
eter
s
o
f
i
n
v
er
ted
p
en
d
u
l
u
m
ar
e
g
i
v
en
b
y
T
ab
le
5
[
43
,
45
].
T
ab
le
5
.
P
ar
am
eter
s
i
n
v
er
ted
p
en
d
u
lu
m
S
y
mb
o
l
D
e
scri
p
t
i
o
n
V
a
l
u
e
s
g
v
a
c
c
e
l
e
r
a
t
i
o
n
d
u
e
t
o
g
r
a
v
i
t
y
9
.
8
m
/
se
c
2
m
c
mass
o
f
t
h
e
c
a
r
t
1
K
g
l
"
t
h
e
h
a
l
f
-
l
e
n
g
t
h
o
f
t
h
e
p
o
l
e
"
0
.
5
m
u
c
o
n
t
r
o
l
i
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t
…….
.
m
"
t
h
e
mass
o
f
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e
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0
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1
K
g
B
y
u
s
i
n
g
th
e
f
ac
ilit
y
a
v
ailab
le
in
th
e
Ma
tlab
s
o
f
t
w
ar
e
v
er
s
i
o
n
(
R
2
0
1
5
)
,
d
if
f
er
en
t
s
i
m
u
lat
i
o
n
s
o
f
t
h
e
in
v
er
ted
p
e
n
d
u
l
u
m
m
o
d
el
ar
e
ca
r
r
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o
u
t
f
o
r
li
n
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r
a
n
d
n
o
n
lin
ea
r
tr
aj
ec
to
r
ies
ar
e
co
n
s
id
er
ed
to
illu
s
tr
ate
t
h
e
ef
f
icien
c
y
o
f
t
h
e
p
r
o
p
o
s
ed
co
n
tr
o
l
s
ch
e
m
e.
Fig
u
r
e
5
s
h
o
w
th
e
Ma
tlab
Si
m
u
li
n
k
co
n
n
ec
t
i
o
n
f
o
r
th
e
in
v
er
ted
p
en
d
u
lu
m
w
i
th
t
h
e
p
r
o
p
o
s
ed
c
o
n
tr
o
ller
s
(
MRC
,
M
R
C
+T
I
F,
an
d
MRC
+T
2
F).
Fig
u
r
e
5
.
C
o
m
p
lete
m
a
tlab
s
i
m
u
lin
k
co
n
n
ec
tio
n
f
o
r
th
e
n
o
n
lin
ea
r
in
v
er
ted
p
en
d
u
l
u
m
w
it
h
t
h
e
s
u
g
g
e
s
ted
co
n
tr
o
ller
T
h
e
co
n
tr
o
ller
'
s
p
ar
a
m
eter
s
ar
e
g
iv
e
n
b
y
T
ab
le
6
.
W
h
er
e
d
esig
n
ed
p
ar
a
m
ter
s
K
f
=2
f
o
r
lin
ea
r
tr
aj
ec
to
r
y
an
d
K
f
=2
0
f
o
r
n
o
n
li
n
ea
r
tr
aj
ec
to
r
y
.
T
ab
le
6
.
T
h
e
C
o
n
tr
o
ller
'
s
P
ar
am
eter
s
P
12
P
22
K
K
f
K
i
n
14
2
100
2
o
r
2
0
10
10
0.5
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
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&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
Desig
n
n
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n
lin
ea
r
mo
d
el
r
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ce
w
ith
fu
z
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co
n
tr
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r
n
o
n
lin
ea
r
S
I
S
O
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ec
o
n
d
...
(
E
k
h
la
s
H.
K
a
r
a
m)
2499
T
h
e
d
if
f
er
en
t
s
i
m
u
la
tio
n
s
ar
e
p
r
esen
ted
as f
o
llo
w
s
:
5
.
1
.
Si
m
ula
t
io
n a
nd
a
na
ly
s
i
s
w
it
h linea
r
t
ra
j
ec
t
o
ry
(
s
t
ep
s
ig
na
l)
a
nd
un
ce
rt
a
inty
I
n
th
e
f
ir
s
t
s
i
m
u
latio
n
,
a
li
n
ea
r
u
n
it
s
tep
i
n
p
u
t
s
i
g
n
al
is
u
s
e
d
to
test
th
e
o
v
er
all
i
n
v
er
ted
co
n
tr
o
lled
s
y
s
te
m
w
it
h
th
e
n
o
n
li
n
ea
r
d
i
s
tu
r
b
an
ce
o
f
(
2
5
)
an
d
r
u
le
s
o
f
T
ab
les
3
an
d
5
f
o
r
t
h
e
f
u
zz
y
co
n
tr
o
ller
p
ar
t.
T
h
e
r
esu
lts
f
o
r
th
i
s
s
i
m
u
latio
n
w
it
h
r
u
le
o
f
T
ab
le
4
ar
e
s
h
o
w
n
i
n
F
ig
u
r
e
6
,
w
h
ic
h
s
h
o
w
t
h
at
t
h
e
a
n
g
u
lar
p
o
s
itio
n
t
r
ac
k
in
g
f
air
l
y
g
o
o
d
th
e
d
es
ir
ed
in
p
u
t
w
i
th
n
o
o
v
e
r
s
h
o
o
t
an
d
n
ea
r
l
y
ze
r
o
s
tead
y
s
tate
er
r
o
r
f
o
r
th
e
m
o
d
el
r
e
f
er
en
ce
co
n
tr
o
ller
s
e
s
p
atiall
y
w
it
h
t
y
p
e
-
1
f
u
zz
y
s
c
h
e
m
e.
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
6
.
Si
m
u
latio
n
r
esu
l
ts
f
o
r
in
v
er
ted
p
en
d
u
l
u
m
co
n
tr
o
lle
d
b
y
(
MR
C
,
MR
C
+T
1
F,
MRC
+T
2
F)
w
it
h
s
tep
in
p
u
t (
a)
an
g
ler
p
o
s
itio
n
; (
b
)
zo
o
m
u
p
th
e
an
g
u
lar
p
o
s
itio
n
; (
c)
er
r
o
r
s
ig
n
al
; (
d
)
co
n
tr
o
l sig
n
al
Fo
r
th
is
s
i
m
u
latio
n
,
t
h
e
p
er
f
o
r
m
an
ce
o
f
th
e
i
n
v
er
ted
p
en
d
u
l
u
m
w
i
th
(
MR
C
,
MR
C
+T
1
F,
MRC
+T
2
F)
is
e
v
al
u
ate
b
y
m
ea
s
u
r
e
t
h
e
i
n
d
ices
s
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y
s
tate
er
r
o
r
(
e
s
.
s
)
,
s
ettlin
g
ti
m
e
(
t
s
)
,
t
h
e
s
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lar
M
(
t
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at
t
h
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s
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ad
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in
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e
m
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ip
lied
b
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u
ar
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er
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r
(
I
T
SE)
as
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s
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ated
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y
T
ab
le
7
w
h
ich
i
s
s
h
o
w
t
h
at
th
e
n
o
n
p
o
s
i
tiv
e
co
n
d
itio
n
o
f
M
(
E
q
u
atio
n
(
2
2
)
)
is
s
atis
f
y
f
o
r
(
MRC
+T
1
F,
MRC
+T
2
F)
an
d
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
(
MRC
+T
1
F)
is
m
o
r
e
ef
f
icie
n
t
t
h
an
(
M
R
C
)
a
n
d
(
MRC
+T
2
F)
esp
ec
ially
w
it
h
r
u
le
s
o
f
T
ab
le
4
b
ec
au
s
e
it
m
a
k
es
th
e
p
en
d
u
l
u
m
s
y
s
te
m
f
lo
w
th
e
d
esire
d
in
p
u
t
s
i
g
n
al
v
er
y
f
as
t
(
t
s
is
s
m
al
l)
an
d
w
it
h
a
s
m
all
IT
S
E
as
a
co
m
p
ar
is
o
n
w
it
h
(
MRC
)
a
n
d
(
MRC
+T
2
F).
T
ab
le
7
.
T
h
e
p
en
d
u
lu
m
p
er
f
o
r
m
an
ce
co
m
p
ar
i
s
o
n
b
et
w
ee
n
t
h
e
(
M
R
C
,
M
R
C
+T
1
F,
a
n
d
MRC
+T
2
F)
C
o
n
t
r
o
l
l
e
r
t
s
e
s
.
s
M
I
TSE
M
R
C
0
.
2
4
0
3
0
.
0
0
0
2
0
.
0
1
8
1
0
.
0
0
2
4
8
M
R
C
+
T
1
F
w
i
t
h
T
a
b
l
e
5
0
.
2
3
8
6
0
.
0
0
0
8
-
0
.
0
5
0
7
0
.
0
0
2
4
7
M
R
C
+
T
2
F
w
i
t
h
T
a
b
l
e
5
0
.
2
3
8
0
0
.
0
0
0
9
-
0
.
0
3
9
7
0
.
0
0
2
4
9
M
R
C
+
T
1
F
w
i
t
h
T
a
b
l
e
4
0
.
2
3
8
1
0
.
0
0
0
3
-
0
.
0
1
9
3
0
.
0
0
2
4
6
3
M
R
C
+
T
2
F
w
i
t
h
T
a
b
l
e
4
0
.
2
3
8
8
0
.
0
0
0
4
-
0
.
0
1
5
2
0
.
0
0
2
4
7
8
5
.
2
.
Si
m
ula
t
io
n a
nd
a
na
ly
s
i
s
w
it
h no
nli
nea
r
t
ra
j
ec
t
o
ry
(
s
inu
s
o
ida
l
s
ig
na
l)
a
nd
un
ce
rt
a
inty
I
n
th
e
s
ec
o
n
d
s
i
m
u
latio
n
s
ee
Fig
u
r
e
7
th
e
n
o
n
li
n
ea
r
s
i
n
u
s
o
i
d
al
s
ig
n
al
is
u
s
ed
to
test
th
e
co
n
tr
o
lled
in
v
er
ted
s
y
s
te
m
w
ith
n
o
n
li
n
ea
r
s
i
n
u
s
o
id
al
d
is
t
u
r
b
an
ce
(
2
5
)
,
r
esu
lt
s
o
f
th
i
s
c
ase
ar
e
ill
u
s
tr
ate
i
n
Fig
u
r
e
7
,
th
e
s
e
f
i
g
u
r
es
s
h
o
w
t
h
at
t
h
e
i
n
v
er
ted
p
en
d
u
l
u
m
is
r
e
m
ai
n
s
tab
le
w
it
h
s
u
itab
le
co
n
tr
o
l
s
ig
n
al
a
n
d
v
er
y
s
m
al
l
er
r
o
r
s
ee
in
Fi
g
u
r
e
7
(
c
)
an
d
7
(
d
)
an
d
th
e
d
is
tu
r
b
a
n
ce
is
r
e
m
o
v
e
f
r
o
m
t
h
e
r
esp
o
n
s
e
o
f
th
e
a
n
g
u
lar
p
o
s
itio
n
w
it
h
all
co
n
tr
o
ller
s
s
p
atiall
y
(
M
R
C
+T
2
F).
)
5
.
0
s
i
n
(
t
r
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.
9
,
No
.
4
,
A
u
g
u
s
t 2
0
1
9
:
2
4
9
1
-
2502
2500
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
7
.
Si
m
u
latio
n
r
esu
l
ts
f
o
r
in
v
er
ted
p
en
d
u
l
u
m
co
n
tr
o
lle
d
b
y
(
MR
C
,
MR
C
+T
1
F,
MRC
+T
2
F)
w
it
h
n
o
n
li
n
ea
r
in
p
u
t si
g
n
al,
(
a)
an
g
u
l
a
r
p
o
s
itio
n
; (
b
)
zo
o
m
u
p
th
e
an
g
u
lar
p
o
s
itio
n
;
(
c)
er
r
o
r
s
ig
n
al;
(
d
)
co
n
tr
o
l sig
n
al
T
ab
le
8
s
h
o
w
th
e
M
(
t
)
an
d
I
T
SE
af
ter
i
m
p
le
m
en
t
th
is
s
i
m
u
l
atio
n
,
it
ca
n
b
e
n
o
ted
f
r
o
m
t
h
i
s
tab
le
th
a
t
s
ca
lar
M
is
s
atis
f
y
t
h
e
n
e
g
a
tiv
e
co
n
d
itio
n
w
it
h
all
co
n
t
r
o
ller
s
(
MRC
,
MR
C
+T
1
F,
MRC
+T
2
F)
an
d
th
e
(
MRC
+T
2
F)
is
m
o
r
e
e
f
f
ic
ien
t
th
a
n
(
MR
C
)
an
d
(
M
R
C
+T
2
F)
esp
ec
iall
y
w
i
th
r
u
les
o
f
T
ab
le
5
b
ec
au
s
e
it
m
ak
e
s
t
h
e
p
en
d
u
l
u
m
s
y
s
te
m
f
lo
w
t
he
d
esire
d
in
p
u
t
s
i
g
n
al
w
it
h
s
m
all
M
(
t
)
an
d
IT
S
E
as
a
co
m
p
ar
is
o
n
w
i
th
(
MRC
)
an
d
(
MR
C
+T
1
F).
T
ab
le
8
.
T
h
e
P
en
d
u
lu
m
p
er
f
o
r
m
an
ce
co
m
p
ar
i
s
o
n
w
it
h
(
MR
C
,
MR
C
+T
1
F,
an
d
MRC
+T
2
F)
C
o
n
t
r
o
l
l
e
r
M
I
TSE
M
R
C
-
2
.
6
5
0
.
0
0
1
4
4
M
R
C
+
T
1
F
w
i
t
h
T
a
b
l
e
5
-
1
.
9
4
3
8
0
.
0
0
0
8
6
1
9
M
R
C
+
T
2F
w
i
t
h
T
a
b
l
e
5
-
1
.
8
7
8
6
0
.
0
0
0
8
1
2
8
M
R
C
+
T
1
F
w
i
t
h
T
a
b
l
e
4
-
2
.
1
8
6
2
0
.
0
0
1
0
9
2
M
R
C
+
T
2
F
w
i
t
h
T
a
b
l
e
4
-
2
.
1
5
4
1
0
.
0
0
1
0
6
3
5
.
3
.
Co
m
pa
re
t
he
re
s
ults o
f
t
he
p
ro
po
s
ed
co
ntr
o
ller
w
it
h r
esu
lt
s
o
f
Ref
.
[
4
4
]
T
h
e
r
esu
lts
o
f
s
ec
o
n
d
s
i
m
u
lat
io
n
f
o
r
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
s
as
s
h
o
w
n
i
n
Fi
g
u
r
e
7
ar
e
co
m
p
ar
ed
w
it
h
t
h
e
r
esu
lt
s
o
f
th
e
ad
ap
tiv
e
in
te
g
r
al
s
ec
o
n
d
o
r
d
er
s
li
d
in
g
m
o
d
e
co
n
tr
o
ller
[
44
]
w
h
ich
ar
e
s
h
o
w
n
in
Fig
u
r
e
8
.
I
t
is
clea
r
f
r
o
m
t
h
ese
r
esu
lts
t
h
at,
r
e
g
ar
d
less
o
f
t
h
e
p
er
f
o
r
m
a
n
c
e
o
f
th
e
r
eq
u
ir
ed
tr
ac
ea
b
ilit
y
,
th
e
co
n
tr
o
l
s
i
g
n
al
u
(
t
)
s
u
f
f
er
s
f
r
o
m
u
n
w
a
n
ted
ch
atter
i
n
g
an
d
its
r
an
g
e
tr
ac
ea
b
ilit
y
,
t
h
e
co
n
tr
o
l
s
ig
n
al
u
(
t
)
s
u
f
f
er
s
f
r
o
m
u
n
w
a
n
ted
ch
a
tter
in
g
an
d
its
r
an
g
e
is
b
o
u
n
d
ed
f
r
o
m
(
-
2
0
to
2
0
)
w
h
ile
w
i
th
p
r
o
p
o
s
ed
co
n
tr
o
ller
s
,
th
er
e
is
n
o
ch
at
ter
in
g
i
n
co
n
t
r
o
l
s
ig
n
al
an
d
t
h
e
r
an
g
e
o
f
it
is
s
et
b
et
w
ee
n
(
-
5
to
5
)
an
d
th
is
i
n
d
icate
s
th
e
ef
f
icien
c
y
o
f
t
h
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.