Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 2
,
A
p
r
il
201
6, p
p
.
62
1
~
62
9
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
2.8
123
6
21
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Speed Control of a Single Taip
ei Mass Rapid Transit System
Train by Using a Single In
put Fuzzy L
ogi
c Cont
roll
er
Hari Ma
gh
fir
o
h
1
, O
yas
W
a
hyu
n
g
g
o
ro
1
,
A
d
ha
Ima
m
Ca
hy
ad
i
1
, K
u
o
Lung Li
an
2
, B
w
o Re
n Ke
3
1
Dept. of
Electrical Engin
eer
ing
a
nd Information
Techno
log
y
, Universita
s Gad
j
ah
Mada, Yog
y
akar
ta, Indonesia
2
Dept. of
Electrical Engin
eer
ing,
Nationa
l T
a
iwan
Universit
y
of Sc
ienc
e
and T
echn
o
log
y
,
Taip
ei
,
T
a
iwan
3
Dept. of
Electrical Engin
eer
ing,
National Penghu
Un
iversity
of Science
and Techn
o
log
y
, Penghu
,
Taiwan
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
J
u
l 13, 2015
Rev
i
sed
D
ec 19
, 20
15
Accepte
d
Ja
n 12, 2016
The purpose of this stud
y
was to design a speed controller for mass rapid
transit (MRT) tr
ain b
y
using a single i
nput fuzzy logic controller
(SIFLC). A
com
p
lete tr
ain
m
odel, which was
des
i
gned according to the
des
i
gn of a
Taip
ei M
R
T tra
i
n, was
us
ed for anal
yz
ing bot
h m
echanic
al a
nd ele
c
tri
c
a
l
parts. Th
e SIFLC was used for improvi
ng a fuzz
y log
i
c con
t
roll
e
r
(F
LC) b
y
reducing
its nu
mber of control rules.
The r
e
su
lts indi
cat
ed th
a
t
the
SIFLC
exhibited more
favorable perfor
m
ance
than
the FLC did and a substantial
reduction in
the
number of fuzzy rules an
d
processing time.
Ther
efore,
tuning
the S
I
F
L
C was
eas
ier
com
p
ared with tuning
the F
L
C; furt
herm
ore, t
h
e
sim
u
lation tim
e
of the SIFLC was shorter
than that of the FLC
,
exhibiting
reductions of up to 17.3% in a constant
tra
c
k (track withou
t gradien
t
and
curvatur
e)
and
up to 12
.27%
i
n
a v
a
ri
able
tr
a
c
k (tr
ack
with
gradien
t
and
curvatur
e).
Keyword:
Fuzzy logic c
o
ntroller
M
a
ss ra
pi
d t
r
a
n
si
t
Railway
Single i
n
put
fuzzy
Copyright ©
201
6 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
H. M
a
gh
fi
r
o
h,
Depa
rtem
ent of Electrical E
n
ginee
r
ing a
n
d
In
fo
rm
ation Te
chn
o
lo
gy
,
Uni
v
ersitas Ga
dja
h
M
a
da,
Yo
gy
aka
r
t
a
, In
do
nesi
a.
Em
a
il: h
a
ri.m
a
g
hfiro
h
@g
m
a
i
l
.co
m
1.
INTRODUCTION
Mass rapi
d tra
n
sit (MRT) sy
ste
m
s play a crucial role
in public
tra
n
s
p
ortation because
of
t
h
eir high
efficien
cy and
rid
e
rsh
i
p
,
esp
e
cially
in
h
i
g
h
p
opu
lati
o
n
d
e
nsity areas su
ch as
m
e
tro
p
o
litan
areas. Th
e Taip
ei
R
a
pi
d Tra
n
si
t
Sy
st
em
(TR
T
S), al
so cal
l
e
d T
a
i
p
ei
M
e
t
r
o, w
a
s est
a
bl
i
s
hed
by
t
h
e Depa
rt
m
e
nt
of R
a
pi
d
Tran
si
t
Sy
st
em
s and
o
p
erat
e
d
by
Tai
p
ei
R
a
pi
d
Tra
n
si
t
C
o
rp
o
r
at
i
o
n
.
The
TR
TS c
o
m
p
ri
ses 10
9 st
at
i
ons a
n
d
1
1
l
i
nes,
wi
t
h
a t
o
t
a
l
of
12
1.
3
km
of
re
ven
u
e t
r
ack
, a
n
d
i
t
t
r
ans
p
ort
e
d,
o
n
a
v
era
g
e
,
m
o
re t
h
an
1
.
96
m
i
l
l
i
on pas
s
en
gers
p
e
r d
a
y i
n
May 20
15
[1
].
Au
t
o
m
a
t
i
c trai
n
op
eration
(ATO) is an
in
tegrated
aut
o
m
a
t
i
on t
r
ai
n co
nt
r
o
l
sy
st
em
whi
c
h
has a di
rect
im
pact in the devel
opm
ent of train
operation
syste
m
. Therefore
,
the st
udy
of
AT
O has attraced significant
at
t
e
nt
i
on i
n
t
h
e rece
nt
deca
d
e
s. C
h
i
u
[2]
pr
op
ose
d
a Taipei MRT m
o
d
e
l th
at using
a
propo
rtion
a
l-in
t
e
g
r
al-
deri
vat
i
v
e (
P
I
D
) c
o
nt
rol
l
e
r
m
e
t
hod.
The
P
I
D
gai
n
s a
r
e
u
s
ual
l
y
det
e
rm
ined t
h
r
o
ug
h t
r
i
a
l
and er
r
o
r,
and t
h
i
s
m
e
thod m
a
y not return optim
al gains. A
fuz
z
y logic c
ontroller (FLC) is a
widely
use
d
de
vice
for controlling
t
r
ai
n spee
d. Y
a
su
no
b
u
et al.
[3] designed
a fuzzy AT
O cont
roller th
at
can control a train autom
a
tically.
Ch
ang
et al
.
[4] also applie
d fuzzy logic rules to a
n
AT
O
co
nt
r
o
l
l
e
r t
o
p
r
ovi
de m
u
lt
i
object
i
v
e co
n
t
rol
f
o
r
satisfyin
g
v
a
rio
u
s
railway op
eration
a
l requ
irem
en
ts.
Both of these fuzzy ATO
co
n
t
rollers can
p
e
rf
orm
effectively a
n
d are s
u
peri
or t
o
PID c
ont
rollers.
C
h
an
g a
nd
X
u
[5]
use
d
di
f
f
e
r
ent
i
a
l
ev
ol
ut
i
on
(D
E) al
go
ri
t
h
m
based t
u
n
i
ng t
o
i
m
pl
em
ent
a f
u
zzy
ATO.
DE is
u
s
ed
for op
tim
iz
i
n
g fu
zzy m
e
mb
ersh
ip fu
n
c
ti
on
s.
Tao
et al.
[6
] propo
sed a
m
u
l
ti
m
o
d
e
in
tellifen
t
cont
rol
usi
n
g B
a
ng
-ba
n
g-
Fu
zzy
-PI
s
w
i
t
c
hi
ng
c
o
nt
r
o
l
fo
r spee
d
co
nt
r
o
l
of hi
g
h
s
p
eed r
a
i
l
w
ay
.
The pu
rp
ose of
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 2, A
p
ri
l
20
16
:
62
1 – 6
2
9
62
2
m
i
xed co
nt
r
o
l
l
e
rs i
s
t
h
at
t
h
e
ban
g
-
ba
n
g
c
o
n
t
rol
i
s
used
wh
en th
e erro
r is to
o larg
e, t
h
en
to g
e
t t
h
e smaller
er
ro
r,
th
e fu
zzy co
n
t
ro
l is u
s
ed
.
Wh
en
th
e erro
r is v
e
y sm
a
ll, PID con
t
ro
ller is u
s
ed. Ke
et al.
[
7
] pr
oposed
a
fuzzy
-
P
I
D
gai
n
sche
d
u
l
e
r f
o
r t
r
acki
ng t
h
e
spee
d o
f
M
R
T t
r
ai
ns, an
d t
h
e pr
op
ose
d
sc
h
e
dul
e
r
ex
hi
bi
t
e
d hi
gh
perform
a
nce unde
r acceleration restri
ctions
. Howe
ve
r, they used co
m
p
lex and tim
e
consum
ing three
d
i
m
e
n
s
io
n
a
l win
d
o
w
s
for fu
zzy ru
les. FLC
s
requ
ire a lo
ng
co
m
p
u
t
atio
nal ti
me
th
at is
p
r
opo
rtion
a
l to
th
e
num
ber o
f
f
u
z
z
y
rul
e
s. The c
u
r
r
ent
st
u
d
y
pr
op
oses a si
m
p
le si
ngl
e i
n
p
u
t
fuzzy
l
o
gi
c co
nt
r
o
l
l
e
r (SI
F
L
C
) fo
r
repl
aci
n
g
FLC
s
i
n
s
p
ee
d c
ont
rol
of
m
a
ss rap
i
d t
r
a
n
si
t
(M
R
T
) t
r
ai
n.
The
SIFLC es
sentially has t
h
e sam
e
conc
ept as
th
at
o
f
FLCs;
h
o
wever, it
u
s
es ju
st
on
e i
n
pu
t.
There
f
ore, it offe
rs a c
onsi
d
e
r
able
redu
ction in
fu
zzy ru
les. Cho
i
et al.
[
8
]
pro
p
o
se
d t
h
e
SIFLC
a
n
d p
r
ove
d
th
at it o
p
e
rates effectiv
ely in
regu
latio
n and
track
ing
p
r
ob
le
m
s
. Lon
d
h
e
et a
l
.
[
9
]
use
d
a
n
S
I
FLC
t
o
pe
rf
orm
spatial control of a
n
a
dva
nc
ed
heavy
wate
r react
or, a
n
d
their results s
h
owe
d
t
h
at the
SIFLC
ha
d s
u
peri
or
per
f
o
r
m
a
nce and a s
h
o
r
t
e
r co
m
put
at
i
on t
i
m
e
com
p
ared with a conv
en
tional FLC. I
s
h
a
que
et al.
[10]
us
ed an
SIFLC t
o
co
n
t
ro
l an un
m
a
n
n
e
d
u
n
d
e
rwater veh
i
cle; th
ey
con
c
lud
e
d th
at the SIFLC exh
i
bited
h
i
gh
er tenab
ility
and a s
h
orter c
o
m
putation time co
m
p
ared
with an FLC.
There
f
ore, t
h
e SIFLC ca
n be
im
ple
m
ented in sl
ow
process
o
rs at a
low cost. C
h
iang
et al.
[11
]
u
s
ed
an
SIFLC as a reg
u
l
atio
n
co
n
t
ro
l fo
r
in
tellig
en
t v
e
hicles
because
of its si
m
p
licit
y com
p
ared with conventional
FLCs.
Th
e r
e
st of
this p
a
p
e
r
is o
r
g
a
n
i
zed
as fo
llo
w
s
.
Sectio
n
I
I
pr
esen
ts th
e MRT
m
o
d
e
l.
Sectio
n
III
prese
n
t
s
t
h
e
fo
rm
ul
at
i
on of t
h
e pr
op
ose
d
S
I
F
L
C
C
ont
r
o
ller. The res
u
lts and case study a
n
alysis are des
c
ribe
d
in
Section
IV.
Fin
a
lly, th
e con
c
lu
si
o
n
is prov
id
ed
in Section
V.
2.
MASS RAPID
TRANSIT MODEL
A t
r
ai
n m
odel
of t
h
e B
a
n
n
a
n
Li
ne of t
h
e T
a
i
p
ei
M
R
T was const
r
uct
e
d usi
n
g M
A
TL
A
B
-Si
m
ul
i
nk.
Th
e m
o
d
e
led
train
is an
electrical
m
u
ltip
le
u
n
it (EM
U
) that co
m
p
rises two
m
o
to
r cars an
d
a trailer car. For
sim
u
lating spe
e
d control, the
train
propulsi
on system
and track profiles
were m
odeled. Because the
train
d
e
ri
v
e
s
po
wer fro
m
th
ird rails, a th
ird
rai
l
m
o
d
e
l
was
also
in
cl
u
d
e
d
.
Data
on
th
e
Taip
ei MRT syste
m
reg
a
rd
i
n
g th
e t
r
ain
,
track, and th
ird
rail
were u
s
ed
i
n
th
e m
o
d
e
l.
The p
r
o
p
u
l
s
i
o
n sy
st
em
of t
h
e B
a
nna
n Li
ne
of t
h
e Tai
p
ei
M
R
T com
p
ri
ses an AC
i
n
du
ct
i
on m
o
t
o
r
cont
rol
l
e
d
by
a vari
a
b
l
e
-v
ol
t
a
ge va
ri
abl
e
-
f
r
e
que
ncy
(
V
V
V
F) c
o
nt
r
o
l
l
e
r
by
m
eans of
V/
f t
ech
ni
q
u
e[
2]
. The
three
phase
voltage are
m
eas
ure
d
a
n
d
c
o
mpare
d
with the
re
fere
nce
val
u
e
of
vol
t
a
ge
req
u
i
r
e
d
a
n
d t
h
en
t
h
e
req
u
i
r
e
d
fre
q
u
e
ncy
of p
u
l
s
e are gene
rat
e
d
by
t
h
e P
W
M
g
e
nerat
o
r so as
t
o
m
a
i
n
t
a
i
n
a const
a
nt
t
o
r
que
even at
lowe
r spee
d [12]. The Taipei
MRT uses thre
e switching
m
e
thods accordi
n
g to the tr
ain s
p
eed; SPWM is used
at 0
–22
k
m
/h
, a qu
asi-
si
x
-
step
m
e
th
o
d
is used
at
22
–42
km/h
, and
a six-
step
m
e
th
od
i
s
u
s
ed
at
42–
80
k
m
/h
[1
3]
.
Taip
ei MRT tr
ain
s
d
e
r
i
v
e
pow
er
fr
o
m
a tr
a
c
tio
n
sub
s
tation
(
T
SS)
th
rough
a th
ir
d
r
a
il w
ith
a 7
5
0
V
dc sy
st
em
. Thi
s
st
udy
e
x
am
i
n
ed t
h
e s
p
ee
d c
ont
rol
of a
single train t
h
at operates
bet
w
ee
n t
w
o TS
Ss.
Fi
gu
re
1
sh
ow
s th
e cur
r
en
t f
l
o
w
th
roug
h
the t
r
ain a
n
d its re
sistance
s.
Fig
u
r
e
1
.
Cur
r
e
n
t
f
l
o
w
fr
o
m
tw
o TSS thr
ough
a t
r
ain
The electrical resistances ca
n
be
form
ulated as follows:
(
1
)
(
2
)
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I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Spee
d
C
o
nt
rol
of
a
Si
ngl
e
Tai
p
ei
M
a
ss R
a
pi
d Tr
a
n
si
t
Sy
st
em Tr
ai
n
b
y
U
s
i
n
g
a
Si
ngl
e …
(
H
ari
M
a
g
h
f
i
r
oh)
62
3
(
3
)
(4)
whe
r
e
is th
e th
ird
rail resistan
ce fro
m
TSS
1
(
Ω
),
is th
e th
ird
rail resistan
ce fro
m
TSS
2
(
Ω
),
is th
e
runn
ing
rail
resistan
ce conn
ected
to TSS 1 (
Ω
),
is th
e ru
nnin
g
rail resistan
ce co
nn
ected
to
TSS
2
(
Ω
),
is
th
e
t
h
ird rail resistan
ce p
e
r k
ilo
m
e
ter
(
Ω
/ k
m
),
is
th
e
ru
nn
ing
rail resistan
ce p
e
r k
ilo
m
e
ter
(
Ω
/ k
m
)
,
is t
h
e
train s
p
eed (km/h), a
n
d
is the distance
bet
w
een two T
S
Ss (km
)
.
There
are
f
o
ur
t
y
pes
of
f
o
rce
resi
st
ance
,
which are
starting
resistance
(
R
S
,
kN
), r
unn
ing
r
e
sistance
(
R
R
, kN), gra
d
ient resistance
(
R
G
, kN
), a
nd c
u
r
v
e resi
st
a
n
ce
(
R
C
, kN
). Runn
ing
r
e
sistan
ce is ad
op
ted
fr
om th
e
Davi
s
eq
uat
i
o
n
as (
5
):
(
5
)
whe
r
e
A
is the
coefficient in
N,
B
is the coe
fficient in
Ns/
m
, and
C
is the coefficient in Ns
2
/m
2
. Furth
e
rm
ore,
R
G
occ
u
rs
beca
use
of the t
r
ack gradie
nt, a
n
d its value
is relat
e
d
to th
e t
r
ain
mass as exp
r
essed
i
n
(6):
(6)
whe
r
e
is th
e
mass o
f
t
h
e train
(ton),
is g
r
av
itatio
n
a
l acceleratio
n
(m
/s
2
), a
n
d
is the angle
of gradie
nt
.
Curve
resistance, as e
x
presse
d in (7), is
ca
us
ed
by the e
ffe
c
t
of track curve
[14].
0
.
0
1
(7)
Here
,
k
i
s
a dim
e
nsi
onl
ess p
a
ram
e
t
e
r (depen
di
n
g
o
n
t
h
e t
r
ai
n desi
g
n
, a
nd
v
a
ri
es fr
om
500 t
o
12
0
0
wi
t
h
8
00 as
the ave
r
age
)
a
n
d
r
is the
cu
rv
e
radi
us (m
) o
n
a h
o
rizo
ntal pl
an
e.
As e
x
pres
sed in (8), the t
o
tal resistance
(
R
) is
the s
u
m
of all
of the a
f
orem
e
n
tione
d
resista
n
ces.
(8)
There
f
ore,
t
h
e
m
o
ti
on e
q
u
a
t
i
o
n
becom
e
s
(
9
)
whe
r
e
F
is trac
tion
force
(kN) and
a
is t
h
e tra
i
n acceleration
(m
/s
2
).
3.
CONTROLLER DE
SIGN
3.
1.
Fuz
z
y
L
o
gi
c C
o
n
t
r
o
l
l
er
Zade
h i
n
t
r
od
u
ced t
h
e
fuzzy
l
ogi
c sy
st
em
(
F
LS) i
n
1
9
6
5
,
and M
a
m
d
ani
devel
ope
d t
h
e
fi
rst
f
u
zzy
co
n
t
ro
l m
o
d
e
l in
19
81
[15
]
. In
a con
t
ro
l syste
m
, th
e FLS is called
as Fu
zzy Lo
g
i
c Con
t
ro
ller (FLC).
An
FLC
req
u
i
r
es si
m
p
l
e
r m
a
t
h
em
at
i
c
s and
o
ffe
rs
a hi
g
h
er
de
gr
ee of
free
d
om
i
n
t
uni
ng i
t
s
cont
rol
p
a
ra
m
e
t
e
rs
com
p
ared wi
t
h
ot
her
n
onl
i
n
ea
r co
nt
r
o
l
l
e
rs [
1
0]
. A
n
FLC
co
m
p
ri
ses fou
r
c
o
m
pone
nt
s, w
h
i
c
h are f
u
zzi
fi
c
a
t
i
on,
a ru
le b
a
se, an
inferen
c
e mech
an
ism
,
and d
e
ffu
z
ifi
cation
.
Figu
r
e
2 sh
ow
s th
e c
o
mpone
n
ts
of a
fuzzy
co
n
t
ro
ller
with two inp
u
t
s (erro
r
(
e
) a
n
d
cha
n
ge
of
er
ro
r
(
)
)
an
d on
e
ou
tpu
t
(
c
o
n
t
ro
ller
si
gn
al (
u
))
.
Fi
gu
re 2.
FLC
st
ruct
u
r
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 2, A
p
ri
l
20
16
:
62
1 – 6
2
9
62
4
3.
2.
Si
n
g
l
e
In
put
Fuz
z
y
L
o
gi
c C
o
n
t
r
o
l
l
er
The m
a
i
n
i
npu
t
s
of a
n
FLC
a
r
e err
o
r an
d ch
ange
of e
r
r
o
r,
rega
rdl
e
ss
of t
h
e com
p
l
e
xi
t
y
of
pl
ant
s
.
A
two
d
i
m
e
n
s
io
nal (2D) ru
le tab
l
e is th
en
constr
u
c
ted on
a ph
ase
p
l
an
e (
e
,
). Th
e
ou
tpu
t
o
f
th
e FLC is
applied
to
th
e p
l
an
t as th
e con
t
ro
ller sig
n
a
l
u
. M
o
st
r
u
l
e
t
a
bl
es o
f
F
L
C
s
have a
skew-symm
e
try
p
r
op
erty [8
].
In
th
is
stru
cture, th
e sa
m
e
o
u
t
p
u
t
m
e
m
b
ersh
ip
s are arran
g
ed in
a d
i
ag
onal d
i
rectio
n
,
co
nstitu
tin
g
the
m
a
in
ch
aracteristic o
f
th
e stru
ct
u
r
e (Tab
le 1). In th
is cas
e, fiv
e
m
e
m
b
ersh
ip
s
are u
s
ed
,
n
a
mely p
o
s
itiv
e b
i
g
(PB
)
,
positive sm
all
(PS), zero (Z), negativ
e sm
all
(NS), and ne
gative big (NB
)
. The
m
a
gnitude of each point
on a
part
i
c
ul
a
r
di
a
g
onal
l
i
n
e i
s
pr
op
o
r
t
i
onal
t
o
t
h
e di
st
a
n
ce
fro
m
i
t
s
m
a
in
d
i
ag
on
al lin
e. Th
is prop
erty en
ab
les
usi
n
g
sign
ed
dista
n
ce,
wh
ich is th
e d
i
stan
ce fro
m
th
e
m
a
i
n
d
i
ag
on
al line
to an actual st
ate [8]. The
de
rive
d
si
gne
d di
st
a
n
c
e
i
s
t
h
en use
d
as t
h
e fuzzy
i
n
put
. T
h
e i
n
put
of t
h
e F
L
C
i
s
thus
o
n
l
y
one v
a
ri
abl
e
. T
h
ere
f
ore
,
t
h
e
rule
base is
conside
r
ably
reduced com
p
ared with
t
h
at of con
v
e
n
tion
a
l FLCs.
As s
h
ow
n i
n
Tabl
e
1, t
h
e b
o
u
n
d
ari
e
s
of
e
and
in
th
e sa
m
e
co
n
t
ro
l
ou
tpu
t
are
sh
aped
lik
e a
staircase. If the q
u
a
n
tizatio
n
lev
e
l o
f
th
e ind
e
p
e
nd
en
t v
a
ri
ab
les b
e
co
m
e
s
in
fin
itesi
m
a
l,
th
en
th
e bou
nd
aries
b
eco
m
e
straigh
t
lin
es
(Figu
r
e 3
)
. Th
e ab
solu
te m
a
g
n
itu
d
e
o
f
th
e con
t
ro
l
in
pu
t is
p
r
o
portio
n
a
l t
o
th
e
sig
n
e
d
distance
(
d
)
fro
m
th
e m
a
in
diag
on
al. To
d
e
termin
e
d,
as
su
me
,
is an in
t
e
rsectio
n
po
in
t
of th
e m
a
in
di
ag
onal
l
i
ne a
n
d
t
h
e l
i
n
e
per
p
en
di
cul
a
r t
o
i
t
fr
om
a kn
o
w
n
ope
rat
i
n
g
poi
nt
,
(Fi
g
ure
4
)
.
Tabl
e 1. FLC
r
u
l
e
t
a
bl
e
\
PB PS
Z
NS
NB
NB
Z
NS
NS
NB
NB
NS
PS
Z
NS
NS
NB
Z
PS
PS Z
NS
NS
PS
PB
PS
PS Z
NS
PB
PB
PB
PS
PS Z
Fig
u
re 3
.
Ru
le Tab
l
e with
Infin
itesi
m
a
l
Qu
antizatio
n
Levels
Fi
gu
re 4.
Si
g
n
e
d
Di
st
ance
The m
a
in diagonal is
a s
w
itching line
or sli
d
in
g s
u
rface t
h
at can
be
repre
s
ented as
follows:
:
0
(
1
0
)
whe
r
e
λ
is th
e slo
p
e
of th
e
main
d
i
ag
on
al lin
e L
Z
(Fi
g
ure
3). T
h
e di
st
a
n
ce bet
w
ee
n p
o
i
nt
s A an
d B
can be
calcu
lated
as
fo
llo
ws:
|
|
(11)
In g
e
n
e
ral, th
is equ
a
tio
n
can
be rewritten
as fo
llo
ws:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Spee
d
C
o
nt
rol
of
a
Si
ngl
e
Tai
p
ei
M
a
ss R
a
pi
d Tr
a
n
si
t
Sy
st
em Tr
ai
n
b
y
U
s
i
n
g
a
Si
ngl
e …
(
H
ari
M
a
g
h
f
i
r
oh)
62
5
|
|
(
1
2
)
Fo
r an
y arb
itrary po
in
t,
,
, t
h
e s
i
gne
d
di
st
ance
(
) i
s
de
fi
ne
d as
f
o
l
l
o
ws:
|
|
(
1
3
)
w
h
er
e
1,
0
1,
0
(
9
)
Because the si
gn
of the c
o
ntrol input is ne
gative whe
n
s >
0
and posi
tive whe
n
s < 0
and beca
us
e its
mag
n
itu
d
e
is
propo
rtion
a
l to th
e
d
i
stan
ce
from
s = 0
,
th
en [9
]
∝
(15)
Since t
h
e c
o
ntrol action ca
n be dete
rm
ined by only
, it is app
r
op
riate to cal
l th
e con
t
ro
ller a
SIFLC. Th
e
2
D
rul
e
t
a
bl
e ca
n be co
n
v
ert
e
d i
n
t
o
a
one
di
m
e
nsi
o
nal
r
u
l
e
t
a
bl
e (Ta
b
l
e
2)
,
whe
r
e L
NB
is the signed
dista
n
ce of
NB to the m
a
in diagonal (L
Z
) (re
fer to Fi
g
u
re
3). T
h
e
r
ef
ore
,
the n
u
m
b
er of
rules is con
s
idera
b
ly
r
e
duce
d
com
p
ared
with that of t
h
e
F
L
C
.
Fu
rt
he
rm
ore, t
h
e
r
u
l
e
s ca
n
be a
d
ded
o
r
m
odi
fi
ed t
o
ac
hi
eve
fi
ne c
o
nt
r
o
l
.
Tabl
e 2.
R
u
l
e
Tabl
e of SI
FL
C
L
NB
L
NS
L
Z
L
PS
L
PB
u
PB PS
Z
NS
NB
Depe
n
d
i
n
g
on
t
h
e
fuzzy
i
n
f
e
rence
an
d
de
fuzzi
fi
cat
i
o
n
m
e
t
hod
use
d
,
t
h
e FLC
p
r
o
v
i
d
es ei
t
h
e
r
a
l
i
n
ear
o
r
n
o
n
lin
ear in
terp
o
l
ation
.
Th
e SIFLC
u
s
es lin
ear in
te
rpolation; therefore, t
h
e cont
rol
si
gnal
becom
e
s
(16)
whe
r
e
0
is a co
nstan
t
.
Fi
gu
re
5 s
h
ows
t
h
e S
I
FLC
st
r
u
ct
u
r
e.
Wh
en
t
h
e si
gne
d
di
st
ance m
e
t
hod i
s
use
d
, t
h
e t
w
o i
n
p
u
t
s
(
e
and
) bec
o
m
e
one i
n
p
u
t
(
). T
h
e
di
ffe
rence
bet
w
e
e
n t
h
e F
L
C
an
d SI
FLC
ca
n b
e
cl
earl
y
obse
r
ved
by
com
p
ar
i
n
g
Fi
gu
res
2 a
nd
5. T
h
e S
I
FLC
has
num
erou
s
adva
nt
age
s
i
n
com
p
ari
s
on
wi
t
h
FLC
s
[
1
6]
:
It
req
u
i
r
es
o
n
l
y
one
i
n
p
u
t
va
ri
abl
e
(i
.e.,
si
g
n
e
d
di
st
ance)
,
rega
rdl
e
ss
o
f
t
h
e
com
p
l
e
xi
t
y
of
t
h
e
pl
ant
s
. T
h
e
num
ber
of
t
uni
n
g
param
e
ters is consi
d
era
b
ly de
creased. T
h
ere
f
ore, t
uni
ng
the ru
les, m
e
m
b
ersh
i
p
fu
nct
i
o
n
s
, an
d sc
al
i
ng
f
act
or
s
is m
u
ch
easier
in
th
e
SIFLC t
h
an in
an
FLC. It is eq
u
i
val
e
n
t
t
o
a sl
i
d
i
n
g
m
ode
co
nt
r
o
l
(
S
M
C
) wi
t
h
a
bo
un
da
ry
layer. Th
is fact
ev
id
en
ces th
e
cl
o
s
e-loop
stabilit
y o
f
t
h
e SIFLC.
Figure
5.
SIFL
C Struct
ure
4.
SIMULATION RESULT
AN
D D
I
SCU
SSION
The di
st
a
n
ce b
e
t
w
een t
w
o st
at
i
ons was
1
2
76 m
,
and t
h
e
speed l
i
m
i
t
and s
p
ee
d refe
r
e
nce we
re 8
0
km
/h. Acceleration a
nd
je
rk
restrictions
we
re set to
within 1 m
/
s
2
and ±1 m
/
s
3
, respe
c
tively, in accorda
n
c
e
with
th
e Tai
p
ei MRT regu
latio
n
s
. In
th
is case, th
e grad
ie
nt
and c
u
rve
resis
t
ances we
re conside
r
ed a
s
shown i
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 2, A
p
ri
l
20
16
:
62
1 – 6
2
9
62
6
Tabl
e 3 a
nd
4,
respect
i
v
el
y
.
C
onst
a
nt
t
r
ack a
nd
vari
a
b
l
e
t
r
a
c
k we
re use
d
f
o
r
val
i
d
at
i
n
g t
h
e per
f
o
r
m
a
nce of t
h
e
pr
o
pose
d
c
ont
r
o
l
l
e
r. C
o
nst
a
nt
t
r
ack re
fers t
o
t
r
ack
w
itho
u
t g
r
ad
ien
t
and cu
rv
atur
e, whereas
va
riable trac
k
refers to track
with
g
r
ad
ien
t
an
d curv
atu
r
e.
The si
m
u
l
a
t
i
on wa
s pe
rf
or
m
e
d i
n
t
h
e M
A
TL
AB
-Si
m
ul
i
nk e
nvi
ro
nm
ent
.
Tri
a
n
gul
ar
m
e
m
b
ershi
p
fu
nct
i
o
ns, M
a
m
d
ani
i
n
ferenc
e, and cent
e
r o
f
gra
v
i
t
y
defu
zzificatio
n
were u
s
ed
in
bo
th
th
e FLC an
d
SIFLC
.
Fi
ve m
e
m
b
ershi
p
f
unct
i
o
ns
were
use
d
:
NB
, N
S
, Z
,
P
S
, a
n
d PB
.
Tabl
e 3.
T
r
ac
k Gra
d
i
e
nt
S
t
ar
t
P
o
in
t
(m
)
En
d
P
o
in
t (m
)
G
r
ad
ie
n
t
(%
)
0
160
0
160
561
-
2
.
11
561
928
2.
43
928
1143
0.
3
1143
1276
0
Tabl
e 4.
T
r
ac
k C
u
r
v
at
u
r
e
S
t
ar
t
P
o
in
t
(m
)
En
d
P
o
in
t (m
)
R
a
d
i
u
s
(m
)
0
201
0
201
287
280
287
428
0
428
514
280
514
870
0
870
999
1000
999
1276
0
4.
1. C
o
ns
ta
nt T
r
ack
Fig
u
re
6
illu
strates th
e sp
eed
v
e
rsu
s
ti
m
e
cu
rv
e,
ind
i
catin
g
th
at, co
m
p
ared with
t
h
e
FLC, th
e SIFLC
h
a
d a
faster resp
on
se at th
e same startin
g
time and
b
r
ak
i
n
g
p
o
i
n
t
. Th
e SIFLC exh
i
b
ited a sho
r
ter settling
time
an
d sim
u
latio
n
ti
m
e
. In
t
h
is case, th
e SIFLC
was
faster th
an
th
e FLC
b
y
1
7
.3%. Th
is
p
r
o
v
e
s th
at t
h
e SIFLC
has a sh
ort
e
r com
put
at
i
on t
i
m
e t
h
an t
h
e FL
C
does,
beca
us
e it contains fe
wer fuzzy ru
les. Bo
th
th
e SIFLC an
d
FLC
di
d not
sh
ow
o
v
e
r
sh
o
o
t
or
u
n
d
ers
h
oot
.
Fi
gu
re 6.
S
p
ee
d
vs
.
Ti
m
e
for
C
onst
a
nt
Tra
c
k
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8-8
7
0
8
Spee
d
C
o
nt
rol
of
a
Si
ngl
e
Tai
p
ei
M
a
ss R
a
pi
d Tr
a
n
si
t
Sy
st
em Tr
ai
n
b
y
U
s
i
n
g
a
Si
ngl
e …
(
H
ari
M
a
g
h
f
i
r
oh)
62
7
Fi
gu
re
7.
C
o
ns
t
a
nt
Trac
k:
(a
)
Spee
d
vs
.
distance (b) Accele
r
ation, jerk, and gra
d
ient
vs
.
distance
(c)
Vo
ltag
e
and
cu
rren
t
vs
.
di
stance (d) Power
vs.
di
st
a
n
ce
Fi
gu
re
7 s
h
o
w
s a spee
d
ver
s
us
di
st
ance c
u
rve a
s
we
ll as
an electrical c
u
rve
(voltage, current,
and
powe
r) whic
h depicted
the
s
p
eed res
p
on
se
, acceleration a
nd
je
rk
restrict
ions
, re
gene
rat
i
ve braki
n
g, and also
m
odel’s efficiency. Figure
7(a) de
pi
cts the
speed c
u
rve,
indicating that
the
speed res
p
onse was
consistent
with the spee
d
command and
the train was st
op at target
distance. The acc
eleration curve
ascende
d whe
n
the
spee
d com
m
and
was i
n
c
r
ease
d
a
nd i
t
desce
nde
d
w
h
en t
h
e
spee
d c
o
m
m
a
nd
was
dec
r
ea
sed.
The
je
rk
cur
v
e,
whic
h is the de
rivative
of the
acceleration, e
xhi
bite
d the sa
me phenom
e
non. The
highes
t acceleration occure
d
whe
n
t
h
e train
started to run,
while
negative
value
of accel
eration m
eans th
at braki
ng
was activated. Both t
h
e
acceleration a
n
d
jerk
were stil
l below the li
mit of ±1 m
/
s
2
for acceleration a
nd
±1 m
/
s
3
fo
r jer
k
, Fig
u
r
e
7(
b
)
.
The
gra
d
ient
in this
case
wa
s zero.
Figure
7(c
)
s
h
ows
th
e vo
lta
g
e
an
d cu
rr
e
n
t cur
v
es
of contact
shoes.
T
h
e
v
o
ltag
e
and
curren
t
were inv
e
rsely p
r
op
ortion
a
l; th
at is,
when the
voltage
was at a m
i
nimum
,
curre
nt wa
s at a
maxim
u
m
and
vice ve
rsa.
Howeve
r, t
h
e current was
propo
rtio
n
a
l
to
p
o
wer. Wh
en
th
e trai
n cons
um
ed energy,
the power consum
ption c
u
rve increas
ed
.
Whe
n
t
h
e t
r
ai
n
obt
ai
ne
d
en
ergy
fr
om
t
h
e t
h
i
r
d rai
l
,
i
t
s
ene
r
gy
decrease
d
(
r
e
p
resent
e
d
by
t
h
e vol
t
a
ge
of t
h
e co
nt
act
sh
o
e
s).
Whe
n
t
h
e
t
r
ai
n st
op
pe
d,
t
h
e vol
t
a
ge
o
f
t
h
e
co
n
t
act sho
e
s
was equ
a
l to
th
at o
f
th
e t
h
ird rail (i.e., 75
0
V d
c
). A
v
o
ltag
e
v
a
l
u
e th
at was lower th
an
75
0
V
indicated t
h
at the train a
b
s
o
rbed th
e e
n
er
gy
.
On t
h
e ot
her
h
a
nd
, a v
o
l
t
a
ge
val
u
e
hi
g
h
er t
h
an 7
5
0
V i
ndi
c
a
t
e
d
that the trai
n released e
n
ergy thro
ugh rege
nerative bra
k
ing.
Because
of
t
h
e acceleration and
jerk lim
itation,
the
m
a
xim
u
m
voltage
was lower tha
n
900
V, indicati
ng that it did not exceed th
e limit of the third rail
vol
t
a
ge
,
whi
c
h
was
9
0
0
V
.
Fi
gu
re
7(
d
)
d
e
pi
c
t
s t
h
e
po
wer
curve;
both t
h
e el
ectrical
and m
e
chanical c
u
rve
s
are
also
sho
w
n
in
th
is fig
u
re. These tw
o curves
are nearly the sa
m
e
, indicat
ing that the syste
m
efficiency wa
s
fav
o
ra
ble.
4.
2. V
a
ri
abl
e
T
r
ack
After th
e
p
r
o
p
o
s
ed
co
n
t
ro
ller was p
r
o
v
e
d
to o
p
e
rate effectiv
ely in
th
e co
nstan
t
track
case, th
is stu
d
y
tested its perform
a
nce in a va
riable
trac
k ca
se. Figure
8
shows
the s
p
ee
d
vers
us tim
e curve
for the
va
riable
track, i
ndicating that the SIFL
C had a fa
ster
response
com
p
ared
with the FLC. Th
e S
I
FL
C
exhi
bi
t
e
d a s
h
o
r
t
e
r
settlin
g
ti
m
e
a
n
d
sim
u
latio
n
ti
m
e
. In
th
is case, th
e sim
u
l
a
tio
n
ti
m
e
o
f
b
o
t
h
th
e SIFLC an
d
FLC increased
com
p
ared
with the case of th
e consta
nt track beca
use
of the
gra
d
ient
and c
u
rve e
ffe
cts. In t
h
is cas
e, the
SIFLC
was still faster t
h
an the FLC
b
y
1
2
.27
%
. Th
is
proved
th
at
th
e
SIFLC h
a
s a sho
r
t
e
r co
m
p
u
t
atio
n ti
m
e
.
Th
e track
g
r
adien
t
cau
sed
a little o
v
e
r-shoo
t an
d
un
d
e
r-s
hoo
t in
th
e
resp
on
se sp
eed. Howev
e
r, t
h
is v
a
l
u
e was
l
o
w (l
o
w
er
t
h
a
n
0.
5 km
/
h
)
an
d,
t
h
u
s
,
ca
n be t
o
l
e
rat
e
d.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
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:
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088
-87
08
IJEC
E V
o
l
.
6, No
. 2, A
p
ri
l
20
16
:
62
1 – 6
2
9
62
8
Fi
gu
re 8.
S
p
ee
d
vs
.
Tim
e
for
Varia
b
le Trac
k
Figure
9(a) shows
the
s
p
eed
curve
ve
rsu
s
di
st
ance. Al
t
h
ou
gh
t
h
e
r
e were
som
e
gra
d
i
e
nt
chan
ges
,
t
h
e
spee
d re
sponse
was
consistent with the s
p
ee
d c
o
mmand.
Figure
9(b) shows accelera
tion,
je
rk, a
n
d gradient
cu
rv
es, ind
i
catin
g th
at th
e acceleratio
n
curv
e was
b
e
l
o
w th
e li
m
i
t o
f
±1
m
/
s
2
and
th
e j
e
rk
was i
n
th
e li
m
i
t o
f
±
1 m
/
s
3
, d
e
sp
ite th
e ex
isten
ce
o
f
g
r
ad
ien
t
ch
an
g
e
s. Neg
a
tiv
e g
r
ad
ien
t
s
o
r
do
wnh
ill track
s
co
nsu
m
e less e
n
erg
y
t
h
an zer
o
gra
d
i
e
nt
s do
beca
u
s
e t
h
e rege
ne
r
a
t
i
v
e bra
k
i
n
g
was activ
ated
to
m
a
in
tain
th
e sp
eed
at th
e
d
e
sired
lev
e
l, as
shown
at t
h
e
4
00-m
d
i
stan
ce. Ho
wev
e
r,
po
sitiv
e
g
r
ad
ien
t
s or
u
p
h
ill tracks con
s
u
m
e
m
o
re po
wer
com
p
ared with zero and ne
ga
tive gradie
nt
s,
for exam
ple, Figure
9(
d) cl
ea
rl
y
depi
ct
s t
h
i
s
effect at the 800-
m
distance.
Fi
gu
re 9.
Va
ri
abl
e
Trac
k:
(a)
Spee
d
vs
.
distance (b) Accele
r
ation, jerk, and gra
d
ient
vs
.
distance
(c)
Vo
ltag
e
and
cu
rren
t
vs
.
di
stance (d) Power
vs.
di
st
a
n
ce
5.
CO
NCL
USI
O
N
Thi
s
st
u
d
y
i
n
vol
ved m
odel
i
ng a
n
d co
nt
r
o
l
l
i
ng Tai
p
ei
M
R
T t
r
ai
ns.
C
a
se st
udi
es
wi
t
h
di
f
f
ere
n
t
schem
e
s were
per
f
o
r
m
e
d. Th
e resul
t
s
i
n
di
c
a
t
e
d t
h
at
t
h
e
S
I
FLC
e
xhi
bi
t
e
d m
o
re fa
vo
ra
bl
e pe
rf
orm
a
nce t
h
an
th
e FLC d
i
d
and
a sub
s
tan
tial redu
ction
in
the n
u
m
b
e
r of
fuzzy rules. The
r
efore,
tun
i
ng
th
e SIFLC was
easier
co
m
p
ared
with tu
n
i
n
g
t
h
e FLC; fu
rt
h
e
rm
o
r
e, th
e sim
u
latio
n
tim
e o
f
th
e
SIFLC
was sho
r
ter th
an
th
at
o
f
t
h
e
FLC. Th
e SIFLC ad
op
ts th
e SMC
met
h
o
d
; th
erefore, its stab
ility
is
g
u
aran
teed
. It can
b
e
con
c
lud
e
d
th
at
SIFLC
can
be
use
d
t
o
re
pl
ace
FLC
i
n
s
p
eed
cont
rol
of
m
a
ss ra
pi
d t
r
ansi
t
(
M
R
T
) t
r
ai
n
.
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I
J
ECE
I
S
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:
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8-8
7
0
8
Spee
d
C
o
nt
rol
of
a
Si
ngl
e
Tai
p
ei
M
a
ss R
a
pi
d Tr
a
n
si
t
Sy
st
em Tr
ai
n
b
y
U
s
i
n
g
a
Si
ngl
e …
(
H
ari
M
a
g
h
f
i
r
oh)
62
9
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