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p
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n
tr
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r
P
MSM
d
r
i
v
es
[1
]
,
[
2
]
.
A
v
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y
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f
f
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ti
v
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co
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tr
o
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[3
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5
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T
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[
5
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.
T
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an
tee
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C
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[
6
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8
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.
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s
[
9
]
.
I
n
th
i
s
p
ap
er
,
s
p
ee
d
o
f
P
MSM
is
co
n
tr
o
lled
w
it
h
th
e
h
elp
o
f
a
P
I
D
s
p
ee
d
co
n
tr
o
ller
u
s
i
n
g
A
I
tech
n
iq
u
es.
T
h
e
d
e
s
ig
n
i
n
g
o
f
t
h
e
P
I
D
s
p
ee
d
co
n
tr
o
ller
is
tr
ea
ted
as
an
o
p
ti
m
izatio
n
p
r
o
b
lem
,
e
m
p
lo
y
i
n
g
MP
SO
[
1
0
]
-
[
1
7
]
an
d
A
n
t
C
o
lo
n
y
Op
ti
m
izatio
n
(
A
C
O)
[1
8
]
-
[
23]
f
o
r
its
s
o
l
u
tio
n
.
I
n
t
h
is
w
o
r
k
tu
n
in
g
o
f
P
I
D
co
n
tr
o
ller
b
y
u
s
in
g
MP
SO a
n
d
A
C
O
tec
h
n
iq
u
e
is
i
m
p
le
m
e
n
ted
to
co
n
tr
o
l sp
ee
d
o
f
P
MSM
.
T
h
is
ch
ap
ter
is
ar
r
an
g
ed
in
s
i
x
s
ec
tio
n
s
i
n
cl
u
d
in
g
t
h
e
cu
r
r
e
n
t
i
n
tr
o
d
u
cto
r
y
Sectio
n
1
.
T
h
e
tu
n
in
g
o
f
P
I
D
s
p
ee
d
co
n
tr
o
ller
u
s
in
g
M
P
SO
m
e
th
o
d
is
d
is
cu
s
s
ed
i
n
S
ec
tio
n
2
.
P
r
o
b
lem
f
o
r
m
u
la
tio
n
o
f
P
I
D
c
o
n
tr
o
ller
th
at
h
a
s
b
ee
n
u
s
ed
in
P
MSM
d
r
iv
e
is
d
is
cu
s
s
ed
in
Sec
tio
n
3
.
T
h
e
tu
n
i
n
g
o
f
P
I
D
s
p
ee
d
c
o
n
tr
o
ller
u
s
i
n
g
AC
O
m
et
h
o
d
is
d
is
cu
s
s
ed
in
Sect
io
n
4
.
P
MSM
s
i
m
u
latio
n
m
o
d
el
an
d
an
al
y
t
ical
r
esu
lts
ar
e
v
ali
d
ated
in
Sectio
n
5
.
Fin
all
y
,
a
s
u
m
m
ar
y
o
f
t
h
e
p
ap
er
is
co
n
clu
d
ed
in
Sect
io
n
6
.
2.
M
E
T
H
O
DO
L
O
G
Y
O
F
P
RO
P
O
SE
D
M
O
DIFIE
D
P
SO
T
h
e
Mo
d
if
ied
P
SO
tech
n
iq
u
e
o
v
er
co
m
e
t
h
e
d
e
m
er
it
s
o
f
P
SO
tech
n
iq
u
e
[
2
4
]
,
it
im
p
r
o
v
e
th
e
co
n
v
er
g
e
n
ce
r
ate
a
n
d
p
r
ev
en
t
th
e
p
r
e
m
at
u
r
el
y
co
n
d
itio
n
.
W
h
en
ea
c
h
g
r
o
u
p
is
d
i
v
id
ed
,
th
e
g
r
o
u
p
w
h
ich
h
as
m
ax
i
m
u
m
p
o
p
u
latio
n
at
t
h
e
c
en
ter
is
p
r
e
f
er
r
ed
.
I
t
s
h
o
w
s
a
p
ar
ticle
s
u
b
g
r
o
u
p
a
s
a
ce
n
tr
al
s
u
b
g
r
o
u
p
,
an
d
th
e
o
th
er
s
u
b
g
r
o
u
p
s
ar
e
n
e
ig
h
b
o
r
h
o
o
d
s
to
th
e
ce
n
tr
al
s
u
b
g
r
o
u
p
s
,
it
ca
n
co
m
m
u
n
icate
w
i
th
o
t
h
e
r
s
u
b
g
r
o
u
p
n
ea
r
to
it
an
d
o
t
h
er
s
u
b
g
r
o
u
p
s
ca
n
n
o
t
s
h
ar
e
t
h
e
in
f
o
r
m
at
io
n
w
i
t
h
ea
c
h
o
th
er
.
B
y
u
s
i
n
g
MP
SO
tec
h
n
iq
u
e
t
h
e
in
f
o
r
m
atio
n
ca
n
tr
an
s
m
it
f
aste
r
an
d
im
p
r
o
v
i
n
g
e
f
f
ic
ien
c
y
o
f
th
e
alg
o
r
ith
m
.
A
cc
o
r
d
in
g
l
y
,
th
e
d
is
tan
ce
o
f
t
w
o
v
ec
to
r
s
w
as
o
b
tain
ed
b
y
t
h
e
s
p
ac
e
p
o
s
i
-
tio
n
o
f
ea
c
h
p
ar
ticle.
T
h
e
L
m
ax
d
en
o
ted
as
t
h
e
m
ax
i
m
u
m
d
is
ta
n
ce
o
f
an
y
t
w
o
p
ar
ticles.
Me
a
n
w
h
ile
|
|
X
i
(
k
)
-
X
j
(
k
)
|
|
/
L
m
ax
w
a
s
al
s
o
ca
lcu
lated
.
I
f
th
e
r
atio
is
s
m
aller
t
h
a
n
a
ce
r
tai
n
v
alu
e
t
h
en
t
w
o
p
ar
ticle
s
m
er
g
e
in
to
o
n
e
g
r
o
u
p
,
i
f
th
e
r
atio
i
s
g
r
ea
ter
th
a
n
a
ce
r
tai
n
v
al
u
e
t
h
en
t
h
e
y
s
h
o
u
ld
b
e
d
iv
id
ed
f
r
o
m
th
e
g
r
o
u
p
.
E
ac
h
p
ar
ticle
u
p
d
ates its
s
tat
u
s
ac
co
r
d
in
g
to
eq
u
atio
n
(
1
)
,
(
2
)
as f
o
llo
w
s
[
2
5
]
:
V
i
(
k+1
)
=w
(
k
)
V
i
(
k
)
+c
1
(
k
)
r
1
(P
i
-
X
i
(
k)
)
+ c
2
(
k
)
r
2
(P
g
-
X
i
(
k
)
)
(
1
)
X
i
(
k+1
)
= X
i
(
k
)
+ V
i
(
k+1
)
(
2
)
Fit
n
e
s
s
f
u
n
ctio
n
is
u
s
ed
to
e
v
alu
ate
e
v
er
y
n
e
w
p
o
s
itio
n
.
I
n
MP
SO
tech
n
iq
u
e,
t
h
e
v
al
u
e
o
f
w
ei
g
h
t
w
ad
j
u
s
t
th
e
p
r
o
p
er
ly
,
w
h
ic
h
p
r
ev
en
t
al
g
o
r
ith
m
f
r
o
m
g
etti
n
g
in
to
a
lo
ca
l o
p
tim
izatio
n
.
I
n
th
e
f
u
r
t
h
er
s
ta
g
e,
s
m
al
l
o
n
e
is
p
r
o
p
itio
u
s
to
ac
ce
ler
ate
alg
o
r
ith
m
co
n
v
er
g
e.
T
h
is
w
a
y
u
s
ed
is
ill
u
s
tr
ated
as f
o
llo
w
s
:
w
(
k
)
=
w
initi
al
+(
w
initial
-
w
final
)(1
-
k
/K)
(
3
)
c
1
(
k
)
=c
1initial
+(
c
1initial
–
c
1final
)(1
-
k
/K)
(
4
)
c
2
(
k
)
=c
2initial
+(
c
2initial
–
c
2final
)(1
-
k
/K)
(
5
)
k
d
en
o
te
s
c
u
r
r
en
t iter
ate
ti
m
e;
K
d
en
o
tes
m
a
x
iter
ate
ti
m
e.
T
h
e
o
p
tim
ized
v
al
u
es
o
f
P
I
D
co
n
tr
o
ller
g
ain
s
ar
e
s
h
o
wn
in
T
ab
le
1
.
I
m
p
le
m
e
n
ted
MP
SO
-
P
I
D
co
n
tr
o
ller
is
d
escr
ib
ed
in
f
lo
wch
ar
t a
s
s
h
o
w
n
i
n
Fi
g
u
r
e
1
.
T
ab
le
1
.
Valu
es o
f
P
I
D
g
ain
s
o
b
tain
ed
f
r
o
m
MP
SO
m
et
h
o
d
Z
-
N
Te
c
h
n
i
q
u
e
M
P
S
O
T
e
c
h
n
i
q
u
e
K
p
:
0
.
3
4
5
8
4
K
p
:
2
K
i
:
3
.
4
6
0
1
6
5
K
i
:
3
K
d
:
0
.
0
0
8
6
4
1
5
9
1
K
d
:
0
.
0
0
8
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
4
,
Dec
em
b
er
2
0
1
8
:
1510
–
1
5
2
2
1512
Fig
u
r
e
1
.
Flo
w
c
h
ar
t o
f
Mo
d
if
i
ed
P
SO PI
D
C
o
n
tr
o
ller
3.
P
RO
B
L
E
M
F
O
R
M
UL
AT
I
O
N
I
n
t
h
is
s
ec
tio
n
,
t
h
e
b
asic
co
n
c
ep
t
o
f
t
h
e
P
I
D
co
n
tr
o
ller
is
e
x
p
lain
ed
.
T
h
e
b
lo
ck
d
ia
g
r
a
m
o
f
t
h
e
P
I
D
s
p
ee
d
co
n
tr
o
ller
em
p
lo
y
ed
i
n
t
h
e
w
o
r
k
is
ill
u
s
tr
ated
in
Fi
g
u
r
e
2
.
Fig
u
r
e
2
.
B
lo
ck
d
iag
r
a
m
r
ep
r
esen
tat
io
n
o
f
P
I
D
s
p
ee
d
co
n
tr
o
ller
T
h
e
tr
an
s
f
er
f
u
n
c
tio
n
o
f
th
e
P
I
D
s
p
ee
d
co
n
tr
o
ller
f
o
r
a
co
n
tin
u
o
u
s
s
y
s
te
m
is
d
escr
ib
ed
b
y
th
e
eq
u
atio
n
(
6
)
G
PID
(
s
)
=
K
p
+
K
i
s
+
K
d
N
1
+
N
.
1
s
(
6
)
w
h
er
e
K
p
,
K
i
,
K
d
ar
e
p
r
o
p
o
r
ti
o
n
al,
i
n
teg
r
al
an
d
d
er
i
v
ati
v
e
g
ain
s
r
esp
ec
tiv
e
l
y
o
f
th
e
P
I
D
s
p
ee
d
co
n
tr
o
ller
an
d
N
is
co
n
s
tan
t
f
ilter
co
ef
f
icie
n
t.
T
h
e
g
ain
s
K
p
,
K
i
,
an
d
K
d
a
r
e
g
en
er
ated
b
y
A
C
O
alg
o
r
it
h
m
.
T
h
e
s
ch
e
m
ati
c
b
lo
ck
d
iag
r
a
m
o
f
P
MSM
d
r
iv
e
w
it
h
P
I
D
s
p
ee
d
co
n
tr
o
l
s
y
s
te
m
u
s
ed
in
tr
a
n
s
ie
n
t
r
esp
o
n
s
e
an
al
y
s
is
a
n
d
p
ar
am
eter
e
x
tr
ac
tio
n
i
s
s
h
o
w
n
in
Fi
g
u
r
e
3
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
C
o
mp
era
tive
P
erfo
r
ma
n
ce
A
n
a
lysi
s
o
f P
MS
M Drive
U
s
in
g
MPS
O
a
n
d
A
C
O
Tech
n
iq
u
es (
Dee
p
ti Ya
d
a
v)
1513
Fig
u
r
e
3
.
B
lo
ck
Diag
r
a
m
o
f
P
MSM
w
it
h
P
I
D
C
o
n
tr
o
l S
y
s
te
m
As
s
h
o
w
n
i
n
t
h
e
F
i
g
u
r
e
3
,
th
e
r
ef
er
en
ce
s
p
ee
d
ω
ref
is
co
m
p
a
r
ed
w
it
h
t
h
e
m
ea
s
u
r
ed
s
p
ee
d
ω
r
an
d
t
h
e
er
r
o
r
s
ig
n
al
is
f
ed
to
th
e
P
I
D
s
p
ee
d
co
n
tr
o
ller
.
T
h
is
co
m
p
ar
es
th
e
ac
t
u
al
an
d
r
ef
er
e
n
ce
s
p
ee
d
.
T
h
e
o
u
tp
u
t
o
f
th
e
co
n
tr
o
ller
is
tr
a
n
s
f
o
r
m
ed
d
q
to
ab
c
tr
an
s
f
o
r
m
atio
n
.
T
h
en
,
th
at
r
ef
er
e
n
ce
cu
r
r
e
n
t
i
s
f
ed
to
t
h
e
P
W
M
in
v
er
ter
to
g
e
n
er
ate
th
e
i
n
v
er
t
er
’
s
co
m
m
a
n
d
s
ig
n
als.
Her
e
t
h
e
p
h
ase
cu
r
r
e
n
t
I
abc
an
d
I
ref
ar
e
g
iv
e
n
as
in
p
u
t.
T
h
ese
ar
e
co
m
p
ar
ed
b
y
u
s
i
n
g
t
h
e
co
m
p
ar
ato
r
s
.
T
h
e
o
u
tp
u
t o
f
th
e
co
m
p
ar
ato
r
s
is
f
ed
to
th
e
m
o
to
r
.
T
o
ac
h
iev
e
d
esire
d
r
esp
o
n
s
e
t
h
r
o
u
g
h
co
n
tr
o
l
s
y
s
te
m
a
co
s
t
f
u
n
ctio
n
i
s
i
m
p
le
m
en
ted
th
at
d
escr
ib
es
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
s
y
s
te
m
q
u
a
n
tita
tiv
e
l
y
.
T
h
e
tr
an
s
ie
n
t
r
esp
o
n
s
e
s
p
ec
i
f
icatio
n
s
a
n
d
p
er
f
o
r
m
a
n
ce
i
n
d
ices
tak
en
i
n
to
co
n
s
id
er
atio
n
ar
e
as
f
o
llo
w
s
.
3
.
1
.
M
a
x
i
m
u
m
O
v
er
s
ho
o
t
(
M
p)
I
t
is
t
h
e
n
o
r
m
alize
d
d
i
f
f
er
e
n
c
e
b
et
w
ee
n
t
h
e
m
a
x
i
m
u
m
s
p
ee
d
(
ω
m
ax
)
attai
n
ed
b
y
t
h
e
P
MS
M
an
d
t
h
e
d
esire
d
r
ef
er
en
ce
s
p
ee
d
(
ω
ref
)
o
f
th
e
m
o
to
r
i.e
.
f
m
=
M
p
=
ω
m
ax
−
ω
r
ef
ω
m
ax
×
100
%
(
7
)
3
.
2
.
P
ea
k
T
i
m
e
(
t
p
)
I
t is th
e
ti
m
e
ta
k
en
b
y
P
MSM
to
r
ea
ch
th
e
m
a
x
i
m
u
m
s
p
ee
d
(
ω
m
ax
).
f
p
=
t
p
(
8
)
3
.
3
.
Ris
e
T
i
m
e
(
t
r
)
I
t is th
e
ti
m
e
ta
k
en
b
y
t
h
e
P
MSM
to
r
aise its
s
p
ee
d
f
r
o
m
1
0
% to
9
0
% o
f
th
e
d
esire
d
r
ef
er
en
ce
s
p
ee
d
.
f
r
=
t
r
(
9
)
3
.
4
.
Set
t
lin
g
T
i
m
e
(
t
s
)
I
t
is
th
e
ti
m
e
r
eq
u
ir
ed
b
y
P
MSM
s
p
ee
d
to
r
ea
ch
an
d
s
t
a
y
w
ith
in
a
p
er
m
is
s
ib
le
to
ler
an
ce
b
an
d
(
s
elec
ted
as 0
.
0
2
%)
o
f
th
e
r
ef
er
en
ce
s
p
ee
d
.
f
s
=
t
s
(
1
0
)
3
.
5
.
I
nte
g
ra
l A
bs
o
lute
E
rr
o
r
I
t is th
e
i
n
teg
r
al
o
f
th
e
ab
s
o
l
u
t
e
m
ag
n
it
u
d
e
o
f
t
h
e
er
r
o
r
w
h
ic
h
is
g
iv
e
n
as:
f
IA
E
=
IA
E
=
∫
|
e
(
t
)
|
dt
∞
0
(
1
1
)
T
h
u
s
s
u
m
m
ar
izi
n
g
,
th
e
co
s
t
f
u
n
ctio
n
(
f
)
is
g
i
v
e
n
as:
f
=
f
m
+
f
p
+
f
r
+
f
s
+
f
IA
E
(
1
2
)
T
h
e
o
b
j
ec
tiv
e
is
to
m
in
i
m
ize
t
h
is
f
u
n
ctio
n
f
,
to
ac
h
iev
e
f
ast
an
d
ef
f
ec
ti
v
e
s
p
ee
d
co
n
tr
o
l o
f
P
MSM
.
4.
ANT CO
L
O
N
Y
O
P
T
I
M
I
Z
A
T
I
O
N
A
L
G
O
R
I
T
H
M
AC
O
is
d
e
f
i
n
ed
as
a
m
eta
-
h
e
u
r
is
tic
al
g
o
r
ith
m
d
er
iv
ed
f
r
o
m
t
h
e
co
-
o
p
er
ativ
e
f
o
r
ag
in
g
b
eh
av
io
u
r
o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
,
Vo
l.
9
,
No
.
4
,
Dec
em
b
er
2
0
1
8
:
1510
–
1
5
2
2
1514
r
ea
l
an
t
s
[
1
8
]
.
T
h
e
o
p
tim
iza
t
io
n
p
r
o
b
le
m
to
b
e
s
o
lv
ed
u
s
i
n
g
AC
O
al
g
o
r
ith
m
is
m
o
d
e
led
as
a
g
r
ap
h
ical
p
r
o
b
lem
.
Vir
tu
al
a
n
t
s
tr
av
er
s
e
th
e
n
o
d
es o
f
t
h
i
s
g
r
ap
h
i
n
s
ea
r
ch
o
f
a
m
in
i
m
u
m
co
s
t p
ath
.
E
a
ch
an
t i
n
d
i
v
id
u
all
y
ch
o
o
s
es
a
r
ath
er
p
o
o
r
-
q
u
alit
y
p
ath
.
B
etter
p
ath
s
ar
e
f
o
u
n
d
b
y
co
-
o
p
er
atio
n
a
m
o
n
g
t
h
e
e
n
tire
an
t
p
o
p
u
la
tio
n
[
1
9
]
,
[
2
0
]
.
T
h
e
p
r
o
b
lem
o
f
f
in
d
in
g
o
p
ti
m
ized
v
al
u
es
o
f
K
p
,
K
i
,
K
d
o
f
th
e
P
I
D
s
p
ee
d
co
n
tr
o
ller
is
r
ep
r
esen
ted
as
a
g
r
ap
h
ical
p
r
o
b
lem
a
s
s
h
o
w
n
in
Fi
g
u
r
e
4
.
Fig
u
r
e
4
.
Gr
ap
h
ical
R
ep
r
esen
t
atio
n
o
f
AC
O
f
o
r
tu
n
i
n
g
P
I
D
Sp
ee
d
C
o
n
tr
o
ller
I
n
th
i
s
g
r
ap
h
K
p
,
K
i
,
K
d
ar
e
r
ep
r
esen
ted
as
th
r
ee
d
if
f
er
e
n
t
v
ec
to
r
s
in
w
h
ich
ea
c
h
v
al
u
e
o
f
th
e
v
ec
to
r
ac
ts
as
a
n
o
d
e
o
f
t
h
e
g
r
ap
h
.
An
a
n
t
w
h
i
le
tr
a
v
er
s
i
n
g
t
h
e
g
r
ap
h
m
u
s
t
ch
o
o
s
e
th
r
ee
n
o
d
es,
o
n
e
f
r
o
m
ea
c
h
v
ec
to
r
.
T
h
e
ch
o
ice
f
o
r
a
n
o
d
e
is
m
ad
e
b
y
t
h
e
an
t b
ased
o
n
a
p
r
o
b
ab
ili
s
tic
f
u
n
ctio
n
[
1
7
]
,
[
1
8
]
g
iv
en
i
n
eq
u
atio
n
(
1
3
)
:
ρ
ij
=
[
h
ij
]
α
[
p
ij
]
β
∑
[
h
ij
]
α
[
p
ij
]
β
i
ϵ
S
(
1
3
)
h
ij
: h
eu
r
i
s
tic
f
ac
to
r
d
ep
en
d
en
t o
n
p
r
o
b
lem
p
ar
a
m
eter
s
p
ij
: p
h
er
o
m
o
n
e
f
ac
to
r
d
eter
m
i
n
i
n
g
th
e
a
m
o
u
n
t o
f
p
h
er
o
m
o
n
e
d
e
p
o
s
ited
at
a
n
o
d
e
α
: c
o
n
s
ta
n
t d
eter
m
i
n
i
n
g
r
elati
v
e
i
m
p
o
r
tan
ce
o
f
p
h
er
o
m
o
n
e
v
al
u
e
at
a
n
o
d
e
β
: c
o
n
s
ta
n
t d
eter
m
i
n
i
n
g
r
elati
v
e
i
m
p
o
r
tan
ce
o
f
h
e
u
r
is
tic
f
ac
to
r
at
a
n
o
d
e
S
: set o
f
n
o
d
es
n
o
t
y
et
v
is
ited
b
y
th
e
a
n
t
On
e
iter
atio
n
o
r
to
u
r
is
co
m
p
l
e
ted
w
h
en
a
ll
t
h
e
an
ts
h
av
e
c
h
o
s
en
t
h
r
ee
n
o
d
es,
o
n
e
f
r
o
m
ea
ch
v
ec
to
r
.
An
a
n
t
w
h
ile
tr
av
elli
n
g
m
ar
k
s
its
p
r
ese
n
ce
o
n
a
n
o
d
e
b
y
d
e
p
o
s
itin
g
p
h
er
o
m
o
n
es.
P
h
er
o
m
o
n
e
d
ep
o
s
itio
n
i
s
a
w
a
y
o
f
co
m
m
u
n
icat
io
n
b
et
w
e
en
th
e
an
t
s
.
T
h
e
p
h
er
o
m
o
n
e
le
v
els
at
a
n
o
d
e
ar
e
u
p
d
ated
af
ter
ea
ch
to
u
r
s
o
as
to
d
if
f
er
e
n
tiate
b
et
w
ee
n
g
o
o
d
an
d
b
ad
p
ath
s
i.e
.
p
ath
s
w
i
th
lo
w
an
d
h
ig
h
co
s
t
r
esp
ec
ti
v
e
l
y
.
I
n
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
,
t
w
o
f
o
ld
u
p
d
ati
n
g
o
f
p
h
er
o
m
o
n
e
i
s
i
m
p
le
m
e
n
te
d
.
T
h
ese
ar
e
ca
lled
lo
ca
l
an
d
g
lo
b
al
p
h
er
o
m
o
n
e
u
p
d
atin
g
r
u
le.
L
o
ca
l
p
h
e
r
o
m
o
n
e
u
p
d
atin
g
is
ca
r
r
ied
af
ter
ea
ch
an
t
h
as
co
m
p
leted
o
n
e
to
u
r
ac
co
r
d
in
g
to
eq
u
atio
n
(
1
4
)
:
p
(
k
)
ij
=
p
(
k
−
1
)
ij
+
p
.
p
po
s
f
(
1
4
)
p
(
k
)
ij
: p
h
er
o
m
o
n
e
d
ep
o
s
ited
o
n
p
ath
co
n
n
ec
tin
g
t
h
e
n
o
d
es i
a
n
d
j
at
th
e
k
th
to
u
r
p
: c
o
n
s
ta
n
t
p
h
er
o
m
o
n
e
v
al
u
e
p
pos
: p
o
s
itiv
e
p
h
er
o
m
o
n
e
u
p
d
atin
g
co
ef
f
icie
n
t
C
: c
o
s
t f
u
n
ctio
n
o
f
t
h
e
to
u
r
tr
av
er
s
ed
b
y
t
h
e
an
t
Glo
b
al
p
h
er
o
m
o
n
e
u
p
d
ati
n
g
i
s
i
m
p
le
m
e
n
ted
af
ter
co
m
p
letio
n
o
f
a
to
u
r
b
y
all
th
e
an
t
s
o
f
th
e
co
lo
n
y
.
A
cc
o
r
d
in
g
to
th
i
s
r
u
le
t
h
e
p
h
er
o
m
o
n
e
o
f
t
h
e
b
est an
d
w
o
r
s
t t
o
u
r
s
p
ath
s
ar
e
u
p
d
ated
as f
o
llo
w
s
:
p
(
k
)
ij
=
p
(
k
)
ij
γ
+
[
p
(
k
)
ij
b
es
t
+
p
(
k
)
ij
w
o
r
s
t
]
(
1
5
)
p
(
k
)
ij
=
p
(
k
)
ij
+
p
(
1
6
)
p
(
k
)
ij
=
p
(
k
)
ij
−
p
.
p
neg
(
1
7
)
p
(
k
)
ij
best
:
p
h
er
o
m
o
n
e
o
f
n
o
d
es c
h
o
s
e
n
in
b
est to
u
r
i.e
.
to
u
r
r
esu
lti
n
g
i
n
lo
w
es
t c
o
s
t f
bes
t
p
(
k
)
ij
worst
:
p
h
er
o
m
o
n
e
o
f
n
o
d
es c
h
o
s
e
n
in
w
o
r
s
t to
u
r
i.e
.
to
u
r
w
it
h
h
ig
h
e
s
t c
o
s
t f
wo
rst
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
P
o
w
E
lec
&
Dr
i
S
y
s
t
I
SS
N:
2
0
8
8
-
8
694
C
o
mp
era
tive
P
erfo
r
ma
n
ce
A
n
a
lysi
s
o
f P
MS
M Drive
U
s
in
g
MPS
O
a
n
d
A
C
O
Tech
n
iq
u
es (
Dee
p
ti Ya
d
a
v)
1515
γ
:
p
h
er
o
m
o
n
e
ev
ap
o
r
ati
o
n
f
ac
to
r
to
d
eg
r
ad
e
p
h
er
o
m
o
n
e
v
a
lu
e
w
it
h
ti
m
e,
allo
w
i
n
g
a
n
t
s
to
f
o
r
g
et
p
ast h
is
to
r
y
o
f
t
h
e
to
u
r
s
tr
av
e
ll
ed
.
Glo
b
al
p
h
er
o
m
o
n
e
u
p
d
atin
g
i
s
ca
r
r
ied
o
u
t
to
av
o
id
ea
r
l
y
c
o
n
v
er
g
e
n
ce
d
u
e
to
an
ts
b
ei
n
g
tr
ap
p
ed
in
lo
ca
l
m
i
n
i
m
a,
a
n
d
allo
w
i
n
g
an
ts
to
co
n
ti
n
u
e
s
ea
r
c
h
i
n
g
in
n
e
w
d
ir
ec
tio
n
s
.
T
h
e
AC
O
a
lg
o
r
ith
m
ap
p
lied
to
d
esig
n
an
o
p
ti
m
a
l P
I
D
s
p
ee
d
c
o
n
tr
o
ller
f
o
r
P
MSM
is
as f
o
llo
w
s
(
Fig
u
r
e
5
)
:
Ste
p 1
:
I
nitia
liza
t
io
n
Nu
m
b
er
o
f
an
ts
k
i
n
t
h
e
co
lo
n
y
ar
e
in
itialized
at
t
h
e
s
tar
t
n
o
d
e.
Nu
m
b
er
o
f
to
u
r
s
m
a
n
d
v
a
lu
es
o
f
p
,
p
pos
,
p
neg
an
d
λ
ar
e
al
s
o
s
et.
A
g
a
in
m
a
t
r
ix
w
it
h
t
h
r
ee
co
l
u
m
n
s
o
n
e
f
o
r
ea
ch
o
f
t
h
e
g
ain
p
ar
a
m
eter
K
p
,
K
i
an
d
K
d
is
also
co
n
s
tr
u
cted
.
Fo
r
: n
u
m
b
er
o
f
to
u
r
s
=
1
to
m
Fo
r
: n
u
m
b
er
o
f
an
t
s
=
1
to
k
Ste
p 2
:
Cho
ice
o
f
no
des
An
ts
tr
av
er
s
e
t
h
e
g
ain
m
atr
i
x
an
d
c
h
o
o
s
e
t
h
e
v
al
u
es
o
f
K
p
,
K
i
an
d
K
d
w
it
h
m
ax
i
m
u
m
p
h
er
o
m
o
n
e
lev
e
l
ac
co
r
d
in
g
to
eq
u
atio
n
(
1
3
)
.
Ste
p 3
:
Ca
lcula
t
io
n o
f
c
o
s
t
o
f
t
o
ur
C
o
s
t o
f
t
h
e
to
u
r
tr
av
er
s
ed
b
y
a
n
an
t i
s
ca
lcu
lated
ac
co
r
d
in
g
t
o
th
e
co
s
t f
u
n
ct
io
n
g
iv
e
n
i
n
eq
u
atio
n
(
1
2
)
.
Ste
p 4
:
L
o
ca
l phero
m
o
ne
u
p
da
t
ing
L
o
ca
l
p
h
er
o
m
o
n
e
u
p
d
ati
n
g
is
ca
r
r
ied
o
u
t
ac
co
r
d
in
g
to
eq
u
atio
n
(
1
4
)
u
n
til
m
a
x
i
m
u
m
a
n
t
co
u
n
t
h
as
b
ee
n
r
ea
ch
ed
.
Step
s
2
to
4
ar
e
r
ep
ea
ted
o
u
t u
n
t
il
m
a
x
i
m
u
m
a
n
t c
o
u
n
t i
s
r
ea
ch
ed
.
Ste
p 5
:
G
lo
ba
l phero
m
o
ne
u
pd
a
t
ing
On
ce
m
a
x
i
m
u
m
a
n
t
co
u
n
t
is
r
ea
ch
ed
,
b
est
to
u
r
h
a
v
in
g
lo
w
e
s
t
co
s
t
a
n
d
w
o
r
s
t
to
u
r
h
a
v
in
g
h
ig
h
est
co
s
t
i
s
ch
o
s
en
.
P
h
er
o
m
o
n
e
o
f
b
est
to
u
r
n
o
d
es
is
i
n
cr
ea
s
ed
w
h
ile
th
at
o
f
w
o
r
s
t
to
u
r
n
o
d
es
is
d
ec
r
ea
s
ed
ac
co
r
d
in
g
to
eq
u
atio
n
s
(
1
5
)
-
(
1
7
)
.
Step
s
2
to
5
ar
e
r
e
p
ea
ted
u
n
til
m
a
x
i
m
u
m
to
u
r
co
u
n
t is r
ea
c
h
ed
.
Fig
u
r
e
5
.
Flo
w
c
h
ar
t f
o
r
A
C
O
A
l
g
o
r
ith
m
5.
M
O
DE
L
O
F P
M
S
M
A
ND
R
E
SU
L
T
S
T
h
e
r
ef
er
en
ce
s
p
ee
d
o
f
th
e
PMSM
is
ch
o
s
e
n
as
1
0
0
0
r
p
m
an
d
s
tep
f
u
n
ctio
n
ap
p
lied
f
o
r
lo
ad
to
r
q
u
e
w
it
h
s
i
m
u
lat
io
n
ti
m
e
o
f
0
.
5
s
ec
o
n
d
s
.
T
h
e
v
alu
e
s
o
f
g
a
in
p
ar
a
m
eter
s
o
b
tain
ed
f
r
o
m
clas
s
ical
Z
-
N
m
et
h
o
d
,
MP
SO
an
d
AC
O
m
e
th
o
d
ar
e
t
ab
u
lated
i
n
T
ab
le
1
an
d
2
.
T
h
e
m
o
d
el
f
o
r
s
p
ee
d
co
n
tr
o
l
o
f
P
MSM
is
a
s
s
h
o
w
n
in
Fi
g
u
r
e
6
.
Ma
tlab
R
2
0
1
3
a
is
u
s
ed
f
o
r
s
i
m
u
latio
n
o
f
th
e
m
o
d
el.
T
ab
le
2
.
Valu
es o
f
P
I
D
g
ain
s
o
b
tain
ed
f
r
o
m
A
C
O
m
et
h
o
d
Z
-
N
me
t
h
o
d
A
C
O
me
t
h
o
d
K
p
:
0
.
3
4
5
8
4
K
p
:
9
.
6
0
K
i
:
3
.
4
6
0
1
6
5
K
i
:
0
.
4
0
5
K
d
:
0
.
0
0
8
6
4
1
5
9
1
K
d
:
0
.
0
0
0
1
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4
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em
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er
2
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8
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–
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2
2
1516
Fig
u
r
e
6
.
Mo
d
el
o
f
P
MSM
T
h
e
m
o
to
r
s
p
ee
d
is
co
m
p
ar
ed
w
it
h
r
ef
er
en
ce
s
p
ee
d
b
y
th
e
co
m
p
ar
ato
r
an
d
th
e
o
u
tp
u
t
is
f
ed
to
th
e
P
I
D
co
n
tr
o
ller
.
T
h
ese
co
n
tr
o
ller
s
i
m
p
r
o
v
e
th
e
tr
an
s
ien
t
r
esp
o
n
s
e.
T
h
e
o
u
tp
u
t
o
f
co
n
tr
o
ller
is
f
ed
to
th
e
d
q
to
ab
c
tr
an
s
f
o
r
m
at
io
n
b
y
u
s
i
n
g
in
v
er
s
e
p
ar
k
’
s
tr
a
n
s
f
o
r
m
atio
n
.
T
h
e
in
v
er
ter
cir
cu
it
is
f
ed
b
y
t
h
e
d
q
to
a
b
c
tr
an
s
f
o
r
m
atio
n
.
T
h
e
o
u
tp
u
t
o
f
in
v
er
ter
cir
cu
it
is
f
ed
to
P
MS
M.
T
h
e
o
u
tp
u
t
o
f
P
MSM
i
s
ta
k
en
w
it
h
th
e
h
elp
o
f
b
u
s
-
s
elec
to
r
.
T
h
e
R
o
to
r
s
p
ee
d
is
f
ed
b
ac
k
to
th
e
co
m
p
ar
ato
r
to
ac
h
iev
e
th
e
d
esire
d
s
p
ee
d
w
h
ic
h
i
s
r
eq
u
ir
ed
.
T
h
e
s
i
m
u
la
tio
n
is
ca
r
r
ied
o
u
t
u
n
d
er
th
e
d
if
f
er
en
t
o
p
er
atin
g
co
n
d
itio
n
s
s
u
c
h
as
s
tar
ti
n
g
,
b
r
ak
in
g
an
d
lo
ad
ap
p
licatio
n
an
d
r
e
m
o
v
al.
Fig
u
r
es
7
-
9
illu
s
tr
ates
t
h
e
tr
an
s
ien
t
s
p
ee
d
r
esp
o
n
s
e,
s
tato
r
cu
r
r
en
t
an
d
elec
tr
o
m
a
g
n
et
ic
to
r
q
u
e
o
f
th
e
P
MSM
in
co
r
p
o
r
atin
g
a
Z
-
N
tu
n
ed
P
I
D
s
p
ee
d
co
n
tr
o
ller
u
n
d
er
s
tar
tin
g
,
s
p
ee
d
r
ev
er
s
al
an
d
lo
ad
d
is
tu
r
b
an
ce
co
n
d
itio
n
s
.
Fig
u
r
e
7
.
Star
tin
g
d
y
n
a
m
ic
s
o
f
P
MSM
d
r
iv
e
u
s
i
n
g
Z
-
N
m
eth
o
d
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8
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Sp
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ter
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f
P
SMM
d
r
iv
e
u
s
i
n
g
Z
-
N
Fig
u
r
e
9
.
L
o
ad
ap
p
licatio
n
an
d
L
o
ad
r
em
o
v
a
l c
h
ar
ac
ter
is
t
ic
s
o
f
P
SMM
d
r
iv
e
u
s
in
g
Z
-
N
Fig
u
r
es
1
0
-
1
2
ill
u
s
tr
ates
t
h
e
t
r
an
s
ie
n
t
s
p
ee
d
r
esp
o
n
s
e,
s
ta
to
r
cu
r
r
en
t
a
n
d
elec
tr
o
m
a
g
n
etic
to
r
q
u
e
o
f
th
e
P
MSM
in
co
r
p
o
r
atin
g
a
MP
SO
tu
n
ed
P
I
D
s
p
ee
d
co
n
tr
o
ller
u
n
d
er
s
tar
tin
g
,
s
p
ee
d
r
ev
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s
al
an
d
lo
ad
d
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tu
r
b
an
ce
co
n
d
itio
n
s
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I
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N
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0
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l.
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4
,
Dec
em
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2
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5
2
2
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Fig
u
r
e
1
0
.
Star
tin
g
d
y
n
a
m
ic
s
o
f
P
MSM
d
r
iv
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u
s
i
n
g
MP
SO m
et
h
o
d
Fig
u
r
e
1
1
.
Sp
ee
d
r
ev
er
s
al
ch
ar
ac
ter
is
tics
o
f
P
SMM
d
r
iv
e
u
s
i
n
g
MP
SO
Fig
u
r
e
1
2
.
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licatio
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e
m
o
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c
h
ar
ac
ter
is
ti
cs o
f
P
SMM
d
r
iv
e
u
s
in
g
MP
S
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u
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1
3
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5
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ep
ict
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ien
t
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ee
d
r
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e,
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r
r
en
t
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n
d
elec
tr
o
m
ag
n
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to
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q
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e
o
f
th
e
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MSM
em
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lo
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g
an
AC
O
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ed
P
I
D
s
p
ee
d
co
n
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ller
u
n
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g
,
s
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ee
d
r
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an
d
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ad
d
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r
b
an
ce
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n
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itio
n
s
.
Fig
u
r
e
1
3
.
P
MSM
Step
R
esp
o
n
s
e
w
it
h
AC
O
T
u
n
i
n
g
u
n
d
er
Star
tin
g
C
o
n
d
itio
n
Fig
u
r
e
1
4
.
P
MSM
Step
R
esp
o
n
s
e
w
it
h
AC
O
T
u
n
i
n
g
u
n
d
er
Sp
ee
d
R
ev
er
s
al
C
o
n
d
it
io
n
Evaluation Warning : The document was created with Spire.PDF for Python.