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C
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p
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A
uth
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r
:
Om
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Ma
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i,
Dep
ar
tm
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lectr
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E
n
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B
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0
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Alg
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m
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m
ar
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ah
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
L
in
ea
r
in
d
u
ctio
n
m
o
to
r
s
(
L
I
Ms)
ar
e
wid
ely
u
s
ed
in
i
n
d
u
s
tr
ial
p
r
o
ce
s
s
es
an
d
tr
an
s
p
o
r
tatio
n
ap
p
licatio
n
s
[
1
,
2
]
.
T
h
e
m
ain
ad
v
an
tag
e
o
f
t
h
e
L
I
M
is
its
ab
ilit
y
to
p
er
f
o
r
m
a
d
ir
ec
t
lin
ea
r
m
o
tio
n
with
o
u
t
th
e
n
ee
d
o
f
an
y
g
ea
r
b
o
x
o
r
m
ec
h
an
ical
r
o
tar
y
t
o
lin
ea
r
m
o
tio
n
t
r
an
s
f
o
r
m
atio
n
[
3
]
.
T
h
e
d
r
iv
in
g
p
r
i
n
cip
le
o
f
t
h
e
L
I
M
is
s
im
ilar
to
th
at
o
f
a
r
o
tar
y
in
d
u
ctio
n
m
o
to
r
(
R
I
M)
,
h
o
wev
er
,
th
e
co
n
tr
o
l
c
h
ar
ac
ter
is
tics
ar
e
m
o
r
e
c
o
m
p
licated
a
n
d
t
h
e
p
ar
am
e
ter
s
ar
e
tim
e
v
ar
y
i
n
g
d
u
e
to
c
h
an
g
e
o
f
o
p
er
atin
g
co
n
d
itio
n
s
,
s
u
ch
as sp
ee
d
o
f
m
o
v
er
,
tem
p
er
atu
r
e
a
n
d
c
o
n
f
ig
u
r
atio
n
o
f
r
ail.
[
4
,
5]
Field
o
r
ien
ted
co
n
t
r
o
l
(
FOC
)
is
co
n
s
id
er
ed
as
th
e
m
o
s
t
p
o
p
u
lar
h
ig
h
p
e
r
f
o
r
m
an
ce
co
n
tr
o
l m
eth
o
d
f
o
r
in
d
u
ctio
n
m
ac
h
in
es.
T
h
e
m
ai
n
id
ea
o
f
th
e
FOC
is
to
d
ec
o
u
p
le
th
e
d
y
n
am
ics
o
f
th
r
u
s
t
f
o
r
ce
an
d
r
o
to
r
f
lu
x
to
m
ak
e
th
e
co
n
tr
o
l
as
s
im
p
le
as
in
a
s
ep
ar
ately
ex
cited
DC
m
ac
h
in
e
[
6
-
8
]
.
Un
f
o
r
tu
n
ately
,
a
g
o
o
d
p
er
f
o
r
m
a
n
ce
o
f
FOC
ca
n
o
n
ly
b
e
ac
h
iev
ed
b
y
a
p
r
ec
is
e
p
lan
t
m
o
d
el
an
d
i
t
ca
n
b
e
d
is
tu
r
b
ed
b
y
p
ar
am
et
er
v
ar
iatio
n
s
,
wh
ich
p
r
esen
ts
a
b
i
g
is
s
u
e,
b
ec
au
s
e
u
n
lik
e
R
I
M
t
h
e
m
o
d
el
o
f
L
I
M
p
r
esen
ts
m
o
r
e
c
o
m
p
lex
ity
.
Mo
r
eo
v
er
,
th
er
e
ar
e
s
ig
n
if
ican
t
p
ar
a
m
eter
v
ar
iatio
n
s
in
th
e
r
ea
ctio
n
r
ail
r
esis
tiv
ity
,
th
e
d
y
n
a
m
ics
o
f
th
e
ai
r
g
ap
,
s
lip
f
r
eq
u
e
n
cy
,
p
h
ase
u
n
b
alan
ce
,
s
atu
r
atio
n
o
f
th
e
m
ag
n
etizin
g
in
d
u
ctan
ce
,
an
d
en
d
-
ef
f
ec
ts
p
h
en
o
m
e
n
o
n
[
9
-
1
2
]
,
ca
u
s
in
g
a
d
if
f
icu
lty
in
ac
h
iev
i
n
g
a
g
o
o
d
co
n
tr
o
l
p
er
f
o
r
m
a
n
ce
.
Ma
n
y
r
esear
ch
es
h
av
e
b
ee
n
d
o
n
e
in
m
o
d
elin
g
th
e
L
I
M
p
er
f
o
r
m
an
ce
tak
en
in
t
o
co
n
s
id
er
atio
n
tim
e
v
ar
y
i
n
g
p
ar
a
m
ete
r
s
an
d
en
d
ef
f
ec
t
p
h
e
n
o
m
en
o
n
[
3
,
8
-
1
0
,
1
3
]
.
Ho
wev
er
,
th
er
e
ar
e
alwa
y
s
s
o
m
e
m
o
d
elin
g
u
n
ce
r
tain
ties
d
u
e
to
u
n
d
esira
b
le
b
eh
a
v
io
r
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
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8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
10
,
No
.
2
,
J
u
n
e
2
0
1
9
:
709
–
719
710
T
h
e
ad
v
an
ce
m
e
n
t
in
n
o
n
lin
ea
r
co
n
tr
o
l
f
ield
g
a
v
e
a
v
ar
iety
o
f
s
o
lu
tio
n
s
in
d
ea
lin
g
with
p
ar
am
eter
v
ar
iatio
n
s
an
d
lo
a
d
d
is
tu
r
b
an
c
e.
On
e
o
f
th
ese
s
o
lu
tio
n
s
is
b
ac
k
s
tep
p
in
g
co
n
tr
o
l,
th
is
last
is
a
n
o
n
lin
ea
r
c
o
n
tr
o
l
tech
n
iq
u
e
t
h
at
h
as
b
ee
n
wid
el
y
ap
p
lied
in
c
o
n
tr
o
llin
g
L
I
Ms
[
1
2
,
1
4
]
.
T
h
e
b
asic
id
ea
o
f
b
ac
k
s
tep
p
in
g
is
th
e
d
ec
o
m
p
o
s
itio
n
o
f
a
h
ig
h
o
r
d
er
n
o
n
l
in
ea
r
co
n
tr
o
l
d
esig
n
p
r
o
b
lem
in
to
s
m
aller
s
tep
s
,
in
wh
ich
ev
er
y
s
tep
in
tr
o
d
u
ce
s
a
r
ef
e
r
en
ce
to
s
tab
i
lize
th
e
n
ex
t
o
n
e
u
s
in
g
th
e
s
o
ca
lled
“v
ir
tu
al
co
n
tr
o
l”
v
ar
iab
les,
u
n
til
we
r
ea
ch
th
e
r
ea
l
co
n
tr
o
l
in
p
u
t
t
h
at
in
s
u
r
es
th
e
g
lo
b
al
s
tab
ilit
y
b
ased
o
n
ly
ap
u
n
o
v
f
u
n
ctio
n
[
1
2
,
1
4
,
1
5
]
.
I
n
ad
d
itio
n
,
th
e
ad
ap
tiv
e
v
er
s
io
n
o
f
b
ac
k
s
tep
p
in
g
co
n
tr
o
l
g
u
ar
a
n
tees
th
e
g
l
o
b
al
s
tab
ilit
y
o
f
th
e
s
y
s
tem
d
esp
ite
o
f
p
ar
am
eter
u
n
ce
r
tain
ties
an
d
v
ar
iatio
n
s
th
an
k
s
to
p
ar
a
m
eter
u
p
d
ate
laws [
1
5
]
.
I
n
th
is
p
ap
e
r
we
p
r
o
p
o
s
e
an
a
d
ap
tiv
e
b
ac
k
s
tep
p
in
g
c
o
n
tr
o
l
d
esig
n
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ased
o
n
f
ield
o
r
ien
ted
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n
tr
o
l
t
o
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h
iev
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d
esire
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p
o
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itio
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aj
ec
to
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y
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n
d
e
r
t
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e
ass
u
m
p
tio
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f
u
n
k
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m
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er
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ass
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f
r
ic
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co
e
f
f
icien
t
a
n
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is
tu
r
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ce
.
T
h
e
r
est
o
f
th
e
p
ap
er
is
o
r
g
a
n
ized
as
f
o
llo
ws:
in
s
ec
tio
n
2,
we
in
tr
o
d
u
ce
th
e
b
asics
o
f
in
d
ir
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t
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ield
o
r
ien
ted
co
n
tr
o
l.
Sectio
n
3
p
r
esen
ts
th
e
p
r
o
p
o
s
ed
ad
ap
tiv
e
b
ac
k
s
tep
p
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n
g
c
o
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t
r
o
l
ler
.
I
n
s
ec
tio
n
4,
we
s
h
o
w
th
e
s
im
u
latio
n
r
esu
lt
s
f
o
llo
wed
b
y
d
is
cu
s
s
io
n
.
Fin
ally
,
a
co
n
clu
s
io
n
is
d
r
awn
in
s
ec
tio
n
5
.
2.
I
NDIR
E
C
T
F
I
E
L
D
O
R
I
E
N
T
E
D
CO
N
T
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L
Fig
u
r
e
1
s
h
o
ws
th
e
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n
s
tr
u
cti
o
n
o
f
a
L
I
M.
T
h
e
p
r
im
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y
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im
p
ly
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t
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o
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n
d
r
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f
lat
r
o
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p
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ar
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,
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th
e
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ec
o
n
d
ar
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s
u
ally
co
n
s
is
ts
o
f
a
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h
ee
t
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d
u
cto
r
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s
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g
alu
m
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u
m
w
ith
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ir
o
n
b
ac
k
f
o
r
th
e
r
etu
r
n
p
ath
o
f
th
e
m
ag
n
et
ic
f
lu
x
.
Fo
r
a
ze
r
o
r
elativ
e
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e
lo
city
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th
e
L
I
M
ca
n
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e
co
n
s
i
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ed
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h
a
v
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n
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ite
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r
im
ar
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in
wh
ic
h
ca
s
e
th
e
en
d
e
f
f
ec
ts
m
ay
b
e
ig
n
o
r
e
d
[
1
2
]
.
Fig
u
r
e
1
.
C
o
n
s
tr
iu
ctio
n
o
f
a
L
I
M
T
h
e
f
if
th
o
r
d
er
m
o
d
el
o
f
th
e
L
I
M
in
th
e
d
-
q
ax
is
r
ef
er
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n
ce
f
r
am
e
m
o
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if
ied
f
r
o
m
a
th
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ase
Y
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co
n
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ec
ted
r
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tar
y
in
d
u
ctio
n
m
o
to
r
m
o
d
el
is
g
i
v
en
as [
1
2
,
1
6
]
:
ds
V
s
σL
.v
qr
.
h
r
L
π
m
PL
dr
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r
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r
R
m
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qs
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e
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h
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r
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r
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m
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s
R
s
σL
dt
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s
s
σL
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1
2
2
1
+
+
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=
(
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V
s
σL
qr
.
r
L
r
R
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L
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dr
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h
r
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r
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qs
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s
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1
2
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1
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(
2
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(
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v
P
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V
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.
r
L
r
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r
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r
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)
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h
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L
c
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e
F
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f
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M
i
i
K
F
+
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=
−
=
.
)
(
(
5
)
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:
2
0
8
8
-
8
694
A
d
a
p
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teg
r
a
l
b
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ck
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tep
p
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o
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r
in
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cti
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s
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Oma
r
Ma
h
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d
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711
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s
R
is
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tato
r
r
esis
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r
p
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ase,
r
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itch
,
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s
m
L
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is
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co
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icien
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e
V
is
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ch
r
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m
o
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d
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d
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n
d
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u
r
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ts
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s
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o
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2
/(
3
h
L
L
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r
m
f
=
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f
o
r
ce
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n
s
tan
t,
e
F
is
th
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elec
tr
o
m
ag
n
etic
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o
r
ce
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F
is
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e
ex
ter
n
al
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ad
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r
b
a
n
ce
,
M
is
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ass
o
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th
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m
o
v
in
g
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ar
t a
n
d
c
f
is
th
e
v
is
co
u
s
f
r
ictio
n
a
n
d
ir
o
n
-
lo
s
s
co
ef
f
icien
t.
T
h
e
m
ain
i
d
ea
o
f
th
e
f
ield
o
r
i
en
ted
co
n
tr
o
l
is
to
r
en
d
er
th
e
b
eh
av
io
u
r
o
f
th
e
L
I
M
s
im
ilar
to
th
at
o
f
a
s
ep
ar
ately
ex
cited
DC
m
ac
h
in
e,
th
is
las
t
g
iv
es
th
e
ab
ilit
y
to
co
n
tr
o
l
th
e
elec
tr
o
m
ag
n
etic
f
o
r
ce
an
d
r
o
to
r
f
lu
x
in
d
ep
en
d
en
tly
[
7
]
,
[
1
7
]
.
T
h
e
d
ec
o
u
p
lin
g
is
r
ea
lized
b
y
f
o
r
ci
n
g
th
e
s
ec
o
n
d
ar
y
f
lu
x
lin
k
a
g
e
to
alig
n
with
th
e
d
-
ax
is
.
As a
r
esu
lt we
g
et,
0
=
qr
,
0
=
dt
d
qr
(
6
)
Usi
n
g
(
6
)
an
d
r
ep
laci
n
g
in
t
h
e
r
o
to
r
f
l
u
x
eq
u
atio
n
s
(
3
)
an
d
(
4
)
we
g
et,
ds
r
m
dr
i
s
L
+
=
1
(
7
)
wh
er
e
s
is
th
e
L
ap
lace
o
p
er
ato
r
,
an
d
r
r
r
R
L
/
=
is
th
e
s
ec
o
n
d
ar
y
tim
e
co
n
s
tan
t.
R
ep
lacin
g
(
6
)
in
elec
tr
o
m
ag
n
e
tic
f
o
r
ce
eq
u
atio
n
(
5
)
g
i
v
es,
qs
dr
f
e
i
K
F
=
(
8
)
Viewin
g
eq
u
atio
n
s
(
7
)
a
n
d
(
8
)
we
ca
n
s
ee
t
h
at
th
e
r
o
t
o
r
f
lu
x
an
d
th
e
elec
tr
o
m
a
g
n
etic
f
o
r
ce
ca
n
n
o
w
b
e
co
n
tr
o
lled
s
ep
ar
ately
u
s
in
g
s
tato
r
cu
r
r
en
ts
ds
i
an
d
qs
i
.
Usi
n
g
(
6
)
an
d
(
4
)
th
e
s
lip
v
elo
city
ca
n
b
e
wr
itten
as
i
q
s
L
hL
Pv
V
V
dr
r
r
m
e
sl
=
−
=
(
9
)
3.
A
DAP
T
I
VE
B
ACK
S
T
E
P
P
I
NG
CO
NT
RO
L
W
I
T
H
I
NT
E
G
RAL A
CT
I
O
N
T
h
e
b
asic
id
ea
o
f
th
e
b
ac
k
s
te
p
p
in
g
d
esig
n
is
th
e
d
ec
o
m
p
o
s
itio
n
o
f
a
co
m
p
le
x
n
o
n
lin
ea
r
s
y
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tem
in
to
m
u
ltip
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in
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le
in
p
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t
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o
u
tp
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t
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ir
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er
s
u
b
s
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tem
s
,
u
s
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g
t
h
e
s
o
-
ca
lled
“v
ir
t
u
al
c
o
n
tr
o
l”
v
ar
iab
les
[
1
8
]
,
in
wh
ich
ev
er
y
co
n
tr
o
l
v
ar
iab
le
is
f
o
r
ce
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to
s
tab
ilize
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e
p
r
ev
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u
s
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u
b
s
y
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tem
g
en
er
atin
g
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r
r
esp
o
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d
in
g
er
r
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r
wh
ich
ca
n
b
e
s
tab
ilized
b
y
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n
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en
ie
n
t
in
p
u
t
s
elec
tio
n
v
ia
ly
ap
u
n
o
v
s
tab
ilit
y
[
1
4
,
1
6
,
1
8
,
1
9
]
,
T
h
e
s
tep
s
to
d
esig
n
s
u
ch
c
o
n
tr
o
ller
f
o
r
L
I
M
p
o
s
itio
n
tr
ac
k
in
g
ar
e
as f
o
llo
ws:
Def
in
e
th
e
p
o
s
itio
n
tr
ac
k
in
g
e
r
r
o
r
d
d
e
r
e
f
−
=
1
(
1
0
)
I
ts
d
y
n
am
ic
ca
n
b
e
wr
itten
as
v
d
d
d
e
r
e
f
r
e
f
−
=
−
=
1
(
1
1
)
C
o
n
s
id
er
th
e
ly
ap
u
n
o
v
f
u
n
ctio
n
ca
n
d
id
ate
2
1
1
2
1
e
V
=
(
1
2
)
Der
iv
in
g
V
1
an
d
u
s
in
g
t
h
e
er
r
o
r
d
y
n
am
ic
e
q
u
atio
n
(
1
1
)
we
o
b
t
ain
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
10
,
No
.
2
,
J
u
n
e
2
0
1
9
:
709
–
719
712
)
(
1
1
1
1
v
d
e
e
e
V
r
e
f
−
=
=
(
1
3
)
C
h
o
o
s
in
g
th
e
v
el
o
city
s
tab
ilis
i
n
g
f
u
n
ctio
n
as
r
e
f
r
e
f
d
e
k
v
+
=
1
1
(
1
4
)
wh
er
e
1
k
is
a
p
o
s
itiv
e
d
esig
n
co
n
s
tan
t to
b
e
d
eter
m
in
e
d
later
,
g
iv
es
0
2
1
1
1
−
=
e
k
V
(
1
5
)
witch
g
u
ar
an
tees th
e
s
tab
ilis
atio
n
o
f
o
u
r
cl
o
s
ed
-
lo
o
p
co
n
t
r
o
l.
Ho
wev
er
th
e
v
elo
city
v
is
n
o
t
a
r
ea
l
in
p
u
t,
it’s
a
“
v
ir
tu
al
c
o
n
tr
o
l”
in
p
u
t
[
1
9
,
2
0
]
,
s
o
we
d
ef
in
e
th
e
f
o
llo
win
g
v
el
o
city
tr
ac
k
in
g
er
r
o
r
:
v
v
e
r
e
f
−
=
2
(
1
6
)
T
o
en
s
u
r
e
th
e
co
n
v
e
r
g
en
ce
o
f
th
e
p
o
s
itio
n
tr
ac
k
in
g
er
r
o
r
to
ze
r
o
at
th
e
s
tead
y
s
tate
d
esp
ite
th
e
p
r
esen
ce
o
f
d
is
tu
r
b
a
n
ce
an
d
m
o
d
elin
g
i
n
ac
cu
r
ac
y
o
f
th
e
s
y
s
t
em
we
in
tr
o
d
u
ce
a
n
in
teg
r
al
a
ctio
n
to
th
e
d
esire
d
v
elo
city
as f
o
llo
ws [
1
5
]
'
'
1
1
1
1
e
k
d
e
k
v
r
e
f
r
e
f
+
+
=
(
1
7
)
wh
er
e
=
dt
t
e
e
)
(
'
1
1
is
th
e
in
teg
r
al
ac
tio
n
o
f
th
e
p
o
s
itio
n
tr
ac
k
in
g
er
r
o
r
an
d
'
1
k
is
a
p
o
s
itiv
e
d
esig
n
co
n
s
tan
t.
T
h
e
d
y
n
am
ics o
f
th
e
v
elo
city
t
r
ac
k
in
g
e
r
r
o
r
g
iv
e,
M
F
v
M
f
M
F
e
k
v
d
k
d
v
v
e
L
c
e
r
e
f
r
e
f
r
e
f
+
+
−
+
−
+
=
−
=
1
1
1
2
'
)
(
(
1
8
)
T
h
en
th
e
d
y
n
am
ics o
f
1
e
ca
n
b
e
r
ewr
itten
as
2
1
1
1
1
1
'
'
e
e
k
e
k
e
+
+
−
=
(
1
9
)
Def
in
e
an
o
th
e
r
ly
ap
u
n
o
v
f
u
n
ctio
n
2
1
1
2
2
2
1
2
'
2
'
2
1
2
1
e
k
e
e
V
+
+
=
(
2
0
)
I
ts
tim
e
d
er
iv
ativ
e
is
1
1
1
2
2
1
1
2
'
'
e
e
k
e
e
e
e
V
+
+
=
(
2
1
)
Usi
n
g
(
1
9
)
,
(
2
0
)
an
d
(
2
1
)
we
g
et,
+
+
−
+
+
+
+
+
−
+
−
−
=
L
v
D
M
F
d
k
k
e
e
k
k
k
k
e
e
e
k
e
k
V
e
r
e
f
.
)
(
'
'
)
'
1
(
2
1
2
1
1
1
1
2
1
1
2
2
2
2
2
1
1
2
(
2
2
)
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:
2
0
8
8
-
8
694
A
d
a
p
tive
in
teg
r
a
l
b
a
ck
s
tep
p
in
g
co
n
tr
o
ller
fo
r
lin
ea
r
in
d
u
cti
o
n
mo
to
r
s
(
Oma
r
Ma
h
mo
u
d
i
)
713
wh
er
e
2
k
is
a
p
o
s
itiv
e
d
esig
n
p
ar
am
eter
,
M
f
D
c
/
=
is
th
e
n
o
r
m
alize
d
f
r
ict
io
n
co
ef
f
icien
t a
n
d
M
F
L
L
/
=
is
th
e
n
o
r
m
alize
d
L
o
ad
d
is
tu
r
b
an
ce
.
No
w
we
ca
n
ch
o
o
s
e
o
u
r
f
o
r
ce
co
n
tr
o
l
in
p
u
t
r
e
f
e
F
_
to
ca
n
ce
l
th
e
u
n
d
esira
b
le
b
eh
a
v
io
u
r
s
an
d
g
u
ar
an
tee
ac
h
iev
in
g
t
h
e
d
esire
d
p
o
s
itio
n
tr
ajec
to
r
y
.
I
f
we
ch
o
o
s
e
L
v
D
d
k
k
e
e
k
k
k
k
e
M
F
r
e
f
r
e
f
e
+
+
+
+
+
+
+
−
=
.
)
(
'
'
)
'
1
(
2
1
2
1
1
1
1
2
1
1
_
(
2
3
)
we
g
et
0
2
2
2
2
1
1
2
−
−
=
e
k
e
k
V
(
2
4
)
witch
g
u
ar
an
tees th
e
s
tab
ilizatio
n
o
f
o
u
r
c
o
n
tr
o
l in
th
e
clo
s
e
d
-
lo
o
p
.
Ho
wev
er
,
th
e
r
ea
l
v
al
u
es
o
f
p
ar
am
eter
s
M
,
D
an
d
L
ar
e
u
n
k
n
o
wn
an
d
ca
n
’
t
b
e
u
s
ed
,
s
o
we
u
s
e
th
eir
esti
m
ates
M
ˆ
,
D
ˆ
an
d
L
ˆ
in
s
tead
:
L
v
D
d
k
k
e
e
k
k
k
k
e
M
F
r
e
f
r
e
f
e
ˆ
.
ˆ
)
(
'
'
)
'
1
(
ˆ
ˆ
2
1
2
1
1
1
1
2
1
1
_
+
+
+
+
+
+
+
−
=
(
2
5
)
T
h
e
n
ex
t
s
tep
is
to
ex
tr
ac
t
th
e
u
p
d
ate
laws
o
f
esti
m
ated
p
ar
am
eter
s
,
f
o
r
th
at
p
u
r
p
o
s
e
we
d
ef
in
e
th
e
f
o
llo
win
g
p
a
r
am
eter
esti
m
atio
n
er
r
o
r
s
:
M
M
M
ˆ
~
−
=
(
2
6
)
D
D
D
ˆ
~
−
=
(
2
7
)
L
L
L
ˆ
~
−
=
(
2
8
)
Usi
n
g
th
ese
d
ef
in
itio
n
s
an
d
s
u
b
s
titu
tin
g
th
e
f
o
r
ce
co
n
tr
o
l in
(
2
5
)
to
th
e
v
elo
city
tr
ac
k
i
n
g
er
r
o
r
in
(
1
8
)
th
e
d
y
n
a
m
ics o
f
2
e
b
ec
o
m
e,
L
v
D
M
M
M
e
k
e
e
k
e
k
k
d
e
r
e
f
+
+
−
−
+
+
−
−
+
=
.
~
'
)
'
'
(
1
1
2
1
1
1
1
1
2
(
2
9
)
wh
er
e
L
v
D
d
k
k
e
e
k
k
k
k
e
r
e
f
ˆ
.
ˆ
)
(
'
'
)
'
1
(
2
1
2
1
1
1
1
2
1
1
+
+
+
+
+
+
+
−
=
Af
ter
f
ew
ca
lcu
latio
n
s
we
g
et,
M
M
L
v
D
e
k
e
e
ˆ
ˆ
.
ˆ
2
2
1
2
+
+
+
−
−
=
(
3
0
)
Fin
ally
,
we
co
n
s
tr
u
ct
t
h
e
f
in
al
ly
ap
u
n
o
v
f
u
n
ctio
n
th
at
i
n
clu
d
es
all
th
e
s
y
s
tem
’
s
er
r
o
r
s
ig
n
al
s
in
o
r
d
e
r
to
d
er
iv
e
th
e
esti
m
ates u
p
d
ate
laws,
2
3
2
2
2
1
2
1
1
2
2
2
1
3
~
2
1
~
2
1
~
2
1
'
2
'
2
1
2
1
L
D
M
M
e
k
e
e
V
+
+
+
+
+
=
(
3
1
)
wh
er
e
1
,
2
an
d
3
ar
e
p
o
s
itiv
e
d
esi
g
n
co
n
s
tan
ts
.
Ass
u
m
in
g
th
at
M
,
D
an
d
L
ar
e
co
n
s
tan
t p
ar
am
eter
s
,
we
ca
n
w
r
ite,
M
M
ˆ
~
−
=
(
3
2
)
D
D
ˆ
~
−
=
(
3
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
10
,
No
.
2
,
J
u
n
e
2
0
1
9
:
709
–
719
714
L
L
ˆ
~
−
=
(
3
4
)
Usi
n
g
(
3
2
)
,
(
3
3
)
,
(
3
4
)
an
d
th
e
er
r
o
r
d
y
n
am
ics
in
(
1
9
)
a
n
d
(
3
0
)
we
ca
lcu
late
th
e
tim
e
d
e
r
iv
ativ
e
o
f
(
3
1
)
)
'
'
(
ˆ
~
1
ˆ
~
1
ˆ
~
1
ˆ
.
ˆ
~
'
'
ˆ
~
1
ˆ
~
1
ˆ
~
1
'
'
2
1
1
1
3
2
1
1
2
1
1
1
2
2
2
2
1
1
3
2
1
1
1
1
2
2
1
1
3
e
e
k
e
L
L
D
D
M
M
M
L
v
D
M
M
e
e
e
e
k
e
k
e
k
L
L
D
D
M
M
M
e
e
k
e
e
e
e
V
+
−
+
−
−
−
+
+
+
−
+
+
−
−
=
−
−
−
+
+
=
(
3
5
)
W
e
f
in
ally
g
et
−
+
−
+
−
+
−
−
=
L
e
L
D
v
e
D
M
e
M
M
e
k
e
k
V
ˆ
1
~
ˆ
1
~
ˆ
1
~
3
2
2
2
1
2
2
2
2
2
1
1
3
(
3
6
)
I
n
o
r
d
er
to
r
en
d
e
r
th
e
g
lo
b
al
l
y
ap
u
n
o
v
f
u
n
ctio
n
n
eg
ativ
e
we
ch
o
o
s
e
th
e
u
p
d
ate
laws
o
f
th
e
p
ar
am
eter
esti
m
ates a
s
:
2
1
ˆ
e
M
=
(
3
7
)
v
e
D
2
2
ˆ
=
(
3
8
)
2
3
ˆ
e
L
=
(
3
9
)
T
h
e
r
esu
ltin
g
ly
a
p
u
n
o
v
f
u
n
cti
o
n
d
y
n
am
ics g
iv
e
0
2
2
2
2
1
1
3
−
−
=
e
k
e
k
V
wh
ich
g
u
ar
an
tees
th
e
s
tab
ilit
y
o
f
th
e
g
lo
b
al
s
y
s
tem
an
d
t
h
e
ac
h
iev
e
m
en
t
o
f
t
h
e
d
esire
d
p
o
s
itio
n
tr
ajec
to
r
y
.
d
esp
ite
o
f
lo
ad
d
is
tu
r
b
an
ce
an
d
u
n
d
esira
b
le
b
e
h
av
i
o
u
r
s
.
T
h
e
p
r
e
v
ieu
s
co
n
tr
o
ll
er
d
esig
n
in
g
s
tep
s
ar
e
s
u
m
m
ed
u
p
in
th
e
d
iag
r
am
in
Fig
u
r
e
2
:
Fig
u
r
e
2
.
Ad
a
p
tiv
e
b
ac
k
s
tep
p
i
n
g
co
n
t
r
o
ller
s
ch
em
e
4.
SI
M
UL
A
T
I
O
N
A
ND
DI
SC
USSI
O
N
T
o
in
v
esti
g
ate
th
e
p
er
f
o
r
m
an
c
e
o
f
th
e
p
r
o
p
o
s
ed
ad
ap
tiv
e
b
ac
k
s
tep
p
in
g
co
n
tr
o
ller
with
in
te
g
r
al
ac
tio
n
f
o
r
th
e
L
I
M
p
o
s
itio
n
tr
ac
k
i
n
g
,
we
r
u
n
n
u
m
er
ical
s
im
u
latio
n
in
wh
ich
th
e
ef
f
ec
tiv
en
e
s
s
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
ller
u
n
d
e
r
d
if
f
er
en
t
o
p
e
r
atin
g
co
n
d
itio
n
s
is
test
ed
(
ex
ter
n
al
lo
ad
d
is
tu
r
b
an
ce
,
f
r
icti
o
n
an
d
m
o
v
er
m
ass
v
ar
iatio
n
)
.
T
h
e
o
b
tain
e
d
r
esu
lts
ar
e
co
m
p
ar
ed
to
th
o
s
e
o
f
c
o
n
v
e
n
tio
n
al
b
ac
k
s
tep
p
in
g
c
o
n
tr
o
l
tec
h
n
iq
u
e.
T
h
e
L
I
M
p
ar
am
eter
s
u
s
ed
f
o
r
s
im
u
latio
n
ar
e
s
h
o
wn
i
n
T
ab
le.
1
.
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:
2
0
8
8
-
8
694
A
d
a
p
tive
in
teg
r
a
l
b
a
ck
s
tep
p
in
g
co
n
tr
o
ller
fo
r
lin
ea
r
in
d
u
cti
o
n
mo
to
r
s
(
Oma
r
Ma
h
mo
u
d
i
)
715
T
ab
le
1
.
L
I
M
p
ar
am
eter
s
P
a
r
a
me
t
e
r
V
a
l
u
e
Rs
3
.
4
(
Ω
)
Rr
1
.
9
5
(
Ω
)
Ls
0
.
1
0
7
8
(H)
Lr
0
.
1
0
7
8
(H)
Lm
0
.
1
0
4
2
(
H
)
P
2
M
5
.
4
7
(
K
g
)
Fc
2
6
.
3
6
(
N
m.s
/
r
d
)
4
.
1
.
Ca
s
e
1
(
k
no
wn pa
ra
m
et
er
s
)
First,
we
p
r
esen
t
th
e
s
im
u
late
d
r
esu
lts
f
o
r
a
p
er
i
o
d
ic
s
tep
r
ef
er
en
ce
with
k
n
o
wn
p
ar
am
et
er
s
an
d
n
o
lo
ad
d
is
tu
r
b
a
n
ce
.
T
h
e
c
o
n
tr
o
ll
er
d
esig
n
p
ar
am
eter
s
a
n
d
u
p
d
a
te
laws
ar
e
ch
o
s
en
as
f
o
llo
ws:
10
1
=
k
,
1
.
0
'
1
=
k
,
80
2
=
k
001
.
0
1
=
,
8
.
0
2
=
,
500
3
=
.
T
h
e
p
o
s
itio
n
tr
ac
k
in
g
r
es
p
o
n
s
e
is
s
h
o
wn
i
n
Fig
u
r
e
3
a.
T
h
e
ap
p
lied
elec
tr
o
m
ag
n
etic
f
o
r
ce
is
s
h
o
w
n
in
Fig
u
r
e
3
b
.
T
h
e
s
tato
r
cu
r
r
en
t
I
q
s
is
s
h
o
wn
in
Fig
u
r
e
3
c.
An
d
Fig
u
r
e
3
d
.
s
h
o
ws th
e
r
o
to
r
f
lu
x
es.
T
h
e
o
b
tain
ed
r
esu
lts
s
h
o
w
g
o
o
d
p
er
f
o
r
m
an
ce
f
o
r
b
o
th
c
o
n
v
en
tio
n
al
an
d
ad
a
p
tiv
e
b
a
ck
s
tep
p
in
g
co
n
tr
o
ller
s
wh
en
th
e
p
ar
am
ete
r
s
ar
e
k
n
o
wn
an
d
in
v
ar
ia
n
t.
T
h
e
p
o
s
itio
n
tr
ac
k
in
g
er
r
o
r
co
n
v
er
g
es
to
ze
r
o
with
fa
s
t
r
esp
o
n
s
e
tim
e
ab
o
u
t
0
.
5
s
,
th
e
d
ec
o
u
p
lin
g
b
etwe
en
elec
tr
o
m
ag
n
etic
f
o
r
ce
an
d
r
o
t
o
r
f
l
u
x
is
r
ea
lized
,
an
d
we
ca
n
s
ee
th
at
th
e
r
o
t
o
r
f
lu
x
is
k
ep
t
co
n
s
tan
t
in
th
e
s
tead
y
s
tate
(
Fig
u
r
e
3
d
)
wh
ile
th
e
ele
ctr
o
m
ag
n
etic
f
o
r
ce
is
b
ein
g
co
n
tr
o
lled
b
y
th
e
v
a
r
iatio
n
o
f
q
u
ad
r
atic
s
tato
r
cu
r
r
e
n
t
I
q
s
(
Fig
u
r
e
3
b
.
Fig
u
r
e
3
c
.
)
.
Nex
t,
we
test
th
e
r
o
b
u
s
tn
ess
o
f
th
e
p
r
o
p
o
s
ed
c
o
n
tr
o
l
s
ch
em
e
u
n
d
er
t
h
e
ex
is
ten
ce
o
f
p
ar
am
eter
u
n
ce
r
tain
ties
.
Fo
r
th
at
p
u
r
p
o
s
e
we
d
ev
i
d
e
th
e
n
ex
t
s
im
u
latio
n
in
to
th
r
ee
s
tep
s
,
ea
ch
s
tep
p
r
esen
ts
a
p
o
s
s
ib
le
p
ar
am
eter
v
a
r
iatio
n
as
C
ase
2
,
3
,
4
.
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
3
.
Ad
a
p
tiv
e
b
ac
k
s
tep
p
i
n
g
p
o
s
itio
n
c
o
n
tr
o
l o
f
L
I
M
with
k
n
o
w
n
p
ar
a
m
eter
s
,
(
a)
p
o
s
itio
n
tr
ac
k
in
g
r
esp
o
n
s
e,
(
b
)
elec
tr
o
m
ag
n
etic
f
o
r
ce
,
(
c)
s
tato
r
cu
r
r
en
t I
q
s
,
(
d
)
r
o
to
r
f
lu
x
es
4
.
2
.
Ca
s
e
2
(
lo
a
d dis
t
urba
nce)
C
ase
2
:
a
co
n
s
tan
t
f
o
r
ce
d
is
tu
r
b
an
ce
o
f
1
0
N
is
in
jecte
d
at
t
=5
s
an
d
r
em
o
v
ed
at
t=7
s
.
T
h
e
o
b
tain
ed
r
esu
lts
ar
e
p
r
esen
ted
in
Fig
u
r
e
4
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
10
,
No
.
2
,
J
u
n
e
2
0
1
9
:
709
–
719
716
(
a)
(
b
)
(
c)
(
d
)
(
e)
(f)
Fig
u
r
e
4
.
Ad
a
p
tiv
e
b
ac
k
s
tep
p
i
n
g
p
o
s
itio
n
c
o
n
tr
o
l o
f
L
I
M
with
ap
p
lied
l
o
ad
f
o
r
ce
o
f
1
0
N
,
(
a)
p
o
s
itio
n
tr
ac
k
in
g
r
esp
o
n
s
e,
(
b
)
zo
o
m
in
p
o
s
itio
n
,
(
c)
elec
t
r
o
m
ag
n
etic
f
o
r
ce
,
(
d
)
z
o
o
m
i
n
elec
tr
o
m
ag
n
etic
f
o
r
ce
,
(
e
)
s
tato
r
cu
r
r
en
t I
q
s
,
(
f
)
r
o
to
r
f
lu
x
es
.
4
.
3
.
Ca
s
e
3
(
1
.
5
×
D
)
C
ase
3
: f
r
ictio
n
co
ef
f
icien
t
v
ar
iatio
n
eq
u
als to
1
.
5
×D
.
T
h
e
o
b
tain
ed
r
esu
lts
ar
e
p
r
ese
n
ted
i
n
Fig
u
r
e
5
.
(
a)
(
b
)
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:
2
0
8
8
-
8
694
A
d
a
p
tive
in
teg
r
a
l
b
a
ck
s
tep
p
in
g
co
n
tr
o
ller
fo
r
lin
ea
r
in
d
u
cti
o
n
mo
to
r
s
(
Oma
r
Ma
h
mo
u
d
i
)
717
(
c)
(
d
)
(
e)
Fig
u
r
e
5
.
Ad
a
p
tiv
e
b
ac
k
s
tep
p
i
n
g
p
o
s
itio
n
c
o
n
tr
o
l o
f
L
I
M
with
1
.
5
×D
,
(
a)
p
o
s
itio
n
tr
ac
k
in
g
r
esp
o
n
s
e,
(
b
)
zo
o
m
in
p
o
s
itio
n
,
(
c
)
elec
tr
o
m
ag
n
etic
f
o
r
ce
,
(
d
)
s
tato
r
c
u
r
r
en
t I
q
s
,
(
e
)
r
o
to
r
f
lu
x
es
.
4
.
4
.
Ca
s
e
4
(
2
×M
)
C
ase
4
: m
o
v
er
m
ass
v
ar
iatio
n
eq
u
als to
2
×M
.
T
h
e
r
esu
lts
ar
e
p
r
esen
ted
in
Fig
u
r
e
6
.
(
a)
(
b
)
(
c)
(
d
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
10
,
No
.
2
,
J
u
n
e
2
0
1
9
:
709
–
719
718
(
e)
Fig
u
r
e
6
.
Ad
a
p
tiv
e
b
ac
k
s
tep
p
i
n
g
p
o
s
itio
n
c
o
n
tr
o
l o
f
L
I
M
with
2
×M
,
(
a
)
p
o
s
itio
n
tr
ac
k
in
g
r
esp
o
n
s
e,
(
b
)
z
o
o
m
in
p
o
s
itio
n
,
(
c
)
elec
tr
o
m
ag
n
etic
f
o
r
ce
,
(
d
)
s
tato
r
c
u
r
r
en
t I
q
s
,
(
e
)
r
o
to
r
f
lu
x
es.
T
h
e
s
im
u
lated
r
esu
lts
p
r
o
v
e
th
at
ad
ap
tiv
e
b
ac
k
s
tep
p
in
g
co
n
tr
o
lle
r
is
in
s
en
s
itiv
e
ag
ain
s
t
lo
ad
d
is
tu
r
b
an
ce
an
d
ca
n
r
ejec
t
it
with
n
ea
r
ly
n
o
o
v
er
s
h
o
o
t,
in
co
n
tr
ar
y
o
f
co
n
v
en
tio
n
al
b
ac
k
s
tep
p
in
g
wh
er
e
th
e
co
n
tr
o
l
is
s
en
s
itiv
e
ca
u
s
in
g
a
f
ailu
r
e
in
p
o
s
itio
n
tr
ac
k
in
g
wi
th
a
n
o
n
-
n
u
ll
s
tatic
er
r
o
r
(
Fig
u
r
e
4
a.
Fig
u
r
e
4
b
.
)
.
T
h
e
el
ec
tr
o
m
ag
n
etiq
u
e
f
o
r
ce
g
en
er
ated
b
y
th
e
ad
ap
tiv
e
co
n
tr
o
ller
h
as
r
is
en
b
y
1
0
N
af
te
r
ap
p
ly
in
g
th
e
lo
ad
f
o
r
ce
in
o
r
d
e
r
to
ca
n
ce
l t
h
e
d
is
tu
r
b
an
ce
(
Fig
u
r
e
4
c
.
Fig
u
r
e
4
d
.
)
.
I
n
ca
s
e
3
,
wh
er
e
th
e
f
r
ictio
n
co
ef
f
icien
t
h
as
r
is
en
b
y
5
0
%,
we
ca
n
s
ee
th
at
th
e
r
esp
o
n
s
e
tim
e
f
o
r
co
n
v
en
tio
n
al
b
ac
k
s
tep
p
in
g
h
a
s
r
is
en
s
lig
h
tly
t
o
0
.
7
s
,
w
h
ile
f
o
r
t
h
e
a
d
ap
tiv
e
co
n
tr
o
ller
it
h
asn
’
t
b
ee
n
af
f
ec
te
d
(
Fig
u
r
e
5
a.
Fig
u
r
e
5
b
.
)
,
th
a
t
s
h
o
ws
th
at
th
e
p
r
o
p
o
s
ed
tech
n
iq
u
e
is
in
s
en
s
itiv
e
ag
ai
n
s
t
f
r
ictio
n
f
o
r
ce
v
ar
iatio
n
to
o
.
I
n
th
e
ca
s
e
o
f
m
o
v
er
m
ass
ch
an
g
e
to
d
o
u
b
le
v
alu
e
,
we
ca
n
o
b
s
er
v
e
th
at
th
e
ad
a
p
tiv
e
b
a
ck
s
tep
p
in
g
co
n
tr
o
ller
is
alwa
y
s
in
s
en
s
itiv
e
an
d
ca
n
ac
h
iev
e
th
e
d
esire
d
p
o
s
itio
n
tr
ajec
to
r
y
with
f
ast
r
e
s
p
o
n
s
e
tim
e
an
d
n
o
o
v
er
s
h
o
o
t,
wh
ile
th
e
co
n
v
en
ti
o
n
al
b
ac
k
s
tep
p
in
g
co
n
tr
o
ller
r
esp
o
n
s
e
h
as
o
v
er
s
h
o
t
b
ef
o
r
e
it
co
u
ld
ac
h
iev
e
th
e
d
esire
d
tr
ajec
to
r
y
ca
u
s
in
g
a
d
e
lay
in
r
esp
o
n
s
e
tim
e
as we
ll (
Fig
u
r
e
6
a.
Fig
u
r
e
6
b
.
)
.
T
h
e
p
r
e
v
io
u
s
n
u
m
er
ical
v
al
id
atio
n
s
s
h
o
w
g
o
o
d
p
er
f
o
r
m
an
ce
an
d
p
r
o
v
e
th
e
r
o
b
u
s
tn
ess
o
f
th
e
ad
ap
tiv
e
b
ac
k
s
tep
p
in
g
co
n
t
r
o
ller
ag
a
in
s
t
s
u
d
d
en
c
h
an
g
e
s
th
an
k
s
to
p
ar
am
eter
u
p
d
a
te
lo
ws
b
ased
o
n
L
y
ap
u
n
o
v
s
tab
ilit
y
,
wh
ich
g
u
ar
an
tees
th
e
s
tab
ilit
y
o
f
t
h
e
g
lo
b
al
s
y
s
tem
d
esp
ite
o
f
lo
ad
d
is
tu
r
b
a
n
ce
an
d
p
ar
am
eter
v
ar
iatio
n
s
.
T
h
e
esti
m
ated
p
a
r
am
eter
s
ar
e
s
h
o
wn
i
n
Fig
u
r
e
7
.
W
e
ca
n
o
b
s
er
v
e
f
r
o
m
t
h
e
f
i
g
u
r
e
th
at
th
e
esti
m
ated
p
ar
a
m
eter
s
co
n
v
er
g
e
to
th
e
r
ea
l
v
alu
es
with
ac
ce
p
tab
le
r
esp
o
n
s
e
tim
e
a
n
d
e
r
r
o
r
r
an
g
e
allo
win
g
th
e
co
n
tr
o
ller
to
tr
ac
k
th
e
d
esi
r
ed
tr
ajec
to
r
y
d
esp
ite
o
f
p
ar
am
eter
ch
an
g
es.
(
a)
(
b
)
(
c)
Fig
u
r
e
7
.
E
s
tim
ated
p
a
r
am
eter
s
,
(
a)
lo
ad
f
o
r
ce
d
is
tu
r
b
an
ce
,
(
b
)
v
is
co
u
s
f
r
ictio
n
co
ef
f
icien
t,
(
c)
m
o
v
er
m
ass
Evaluation Warning : The document was created with Spire.PDF for Python.