Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
Vol.
4, No. 6, Decem
ber
2014, pp. 952~
961
I
S
SN
: 208
8-8
7
0
8
9
52
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
A Neural Network Based Speed
Control of
a Dual Star
Induction Motor
Meliani B
o
uz
iane,
Mer
o
u
f
el
Ab
delkader
F
acult
y of Engin
eer
S
c
ien
c
e
,
Dep
a
rtem
ent
of Ele
c
t
ric
a
l Engin
eerin
g,
Dji
l
al
i Liab
es
Univers
i
t
y
,
Alge
ria
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
J
u
n 12, 2014
Rev
i
sed
Au
g
20
, 20
14
Accepted Aug 26, 2014
This paper propose the use of
artificial neural networ
ks to control the speed
of a Double Star
Induction
Moto
r drives fed
b
y
a two matrix
con
v
erter
using
Venturini modulation
algor
ithm, The
a
dvent o
f
the field oriented with
modern speed control techniqu
e has pa
rtially
solved DSIM control problems
because i
t
is sensitive to driv
e
para
m
e
ter v
a
ri
at
ions and perfor
m
ance m
a
y
deter
i
orate if convention
a
l con
t
rolle
rs are used. Neural network based
controll
er
is
co
ns
idered
as
pote
n
tial
c
a
ndida
tes
for s
u
ch an
ap
plic
ation
.
In
this work the si
m
u
lations result
s are
provided
to
evalu
a
te p
e
rfor
m
ance of the
proposed contro
l strateg
y
.
Keyword:
Dual Star
Fi
el
d O
r
i
e
nt
e
d
C
ont
r
o
l
I
ndu
ctio
n Mach
in
e
Matrix
Conv
erter
Neu
r
al Netw
or
k
Copyright ©
201
4 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
:
M
e
l
i
a
ni
B
ouzi
a
ne,
Faculty of E
n
gineer
Science,
Depa
rt
m
e
nt
of
El
ect
ri
cal
Engi
neeri
n
g
,
Dj
ilali
Liab
es Un
i
v
ersity, 2
2
0
0
, Alg
e
ria,
Em
a
il: melfat0
6
@
yah
o
o
.
fr.
1.
INTRODUCTION
The
use
of si
x-phase induct
ion m
o
t
o
r
f
o
r
i
n
d
u
st
ri
al
dri
v
es
pre
s
ent
s
s
e
veral
a
d
vant
a
g
es
o
v
er
t
h
e
co
nv
en
tio
n
a
l
th
ree-ph
ase dri
v
e su
ch
as i
m
p
r
o
v
e
d
reliab
ility,
m
a
g
n
e
tic flux h
a
rm
o
n
i
c redu
ction
,
to
rqu
e
pul
sat
i
o
ns m
i
nim
i
zati
on, a
n
d
red
u
ct
i
o
n
on
t
h
e
po
we
r rat
i
n
gs
fo
r t
h
e
st
at
i
c
co
nve
rt
er.
F
o
r t
h
ese
reas
o
n
s,
si
x-
pha
se induction m
o
tors are begi
nni
ng to
be a widely
acceptable alternative in
high power applications.
D
u
r
i
ng
t
h
e last year
s, t
h
e mo
d
e
ling
and
co
n
t
r
o
l
o
f
d
ouble star
indu
ctio
n m
ach
in
e h
a
s b
e
en
t
h
e subj
ect
o
f
in
v
e
stig
ation
s
[1,
2
]
, it is d
e
sirab
l
e to co
n
t
ro
l t
h
e fl
u
x
an
d torqu
e
separately in
order to h
a
v
e
t
h
e same
per
f
o
r
m
a
nces as t
hose o
f
D
C
m
o
t
o
rs. O
n
e way
of d
o
i
n
g t
h
i
s
i
s
by
usi
ng t
h
e fi
el
d
ori
e
nt
ed co
nt
r
o
l
.
Thi
s
m
e
t
hod a
ssu
re
s t
h
e
dec
o
u
p
l
i
n
g
of
fl
u
x
a
n
d t
o
r
q
ue. T
h
e
vec
t
or-c
o
n
t
r
ol
l
e
d
DSIM
wi
t
h
a c
o
n
v
e
n
t
i
onal
PI
spee
d
cont
roller is used e
x
tensi
v
el
y in industry, beca
use
has
easily im
ple
m
ented. Al
ongsi
d
e this
succes
s, the
p
r
ob
lem
o
f
tu
nin
g
PI-con
tro
llers h
a
s
rem
a
in
ed
an
activ
e
re
search a
r
ea.
Furtherm
ore,
with cha
n
ges in s
y
ste
m
dy
nam
i
cs and vari
at
i
o
ns i
n
o
p
erat
i
n
g
poi
nt
s PI-C
ont
rol
l
e
rs
sh
ou
ld
b
e
r
e
t
u
r
n
ed
on
a r
e
gular
b
a
sis.
O
n
e
o
f
the
m
o
st noticeable control t
h
eories is the m
e
thod
us
ing
t
h
e
Ada
p
tive Ne
ural Ne
twork .Recently,
the neural
net
w
or
k (
N
N
)
i
s
wi
del
y
use
d
as a u
n
i
v
e
r
s
a
l
appr
o
x
i
m
ator i
n
t
h
e area
of
no
nl
i
n
ea
r m
a
ppi
n
g
an
d
unce
r
t
a
i
n
no
nl
i
n
ea
r c
ont
rol
pr
o
b
l
e
m
s
[3]
,
T
h
e
NN
st
r
u
ct
u
r
e i
s
t
o
be
im
pl
em
ent
e
d by
i
n
put
o
u
t
p
u
t
no
nl
i
n
ea
r m
a
ppi
ng
m
odels and is constructe
d wi
th input, out
p
ut and hi
dd
en la
yers of activati
on
functions.
Because the
NN can
be
used
f
o
r
a
uni
versal
a
p
pr
oxi
m
a
t
o
r l
i
k
e
fuzzy
a
n
d
ne
u
r
al
sy
st
em
s, i
t
has
bee
n
i
n
t
r
od
uce
d
as a
p
o
ssi
b
l
e
so
lu
tion
t
o
th
e
real m
u
ltiv
ariat
e
in
terp
o
l
ation
p
r
ob
lem.
Th
e i
n
du
ction m
o
to
r driv
e fed
b
y
a m
a
trix
co
nv
erter is sup
e
ri
o
r
to
t
h
e co
nv
en
tional PW
M-VS
inve
rter
becaus
e
of the lack of bulk
y
DC-link ca
pacitors
wi
th lim
ited lif
e tim
e, the bi-directional power flow
capability, the
sinusoidal
input/
output c
u
rrents, and
adjustable input pow
e
r
fa
ctor. Furthe
rm
ore, because
of a
high integration ca
pa
bility
and a
hi
gher
reliability of the sem
i
conduct
or de
vice struct
ures
, the
m
a
trix
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJECE Vol. 4, No. 6, D
ecem
ber 2014
:
952 – 961
9
53
con
v
e
r
t
e
r t
o
p
o
l
ogy
i
s
recom
m
e
nded f
o
r extrem
e te
m
p
er
atures and cri
ti
cal
vol
um
e/wei
g
ht
appl
i
c
at
i
ons.
Ho
we
ver
,
onl
y
a fe
w
of
t
h
e
pract
i
cal
m
a
t
r
ix c
o
n
v
e
r
t
e
rs
h
a
ve
been
ap
pl
i
e
d t
o
i
n
duct
i
o
n
m
o
t
o
r
dri
v
e
sy
st
e
m
because the im
plem
entation of the switc
h de
vices in
the m
a
trix converter is
diffi
c
ult and m
odulation
technique
and
comm
utation c
ont
rol a
r
e m
o
re com
p
li
cated than the c
o
nve
ntional PWM inverter [4, 5].
2.
DOUBLE ST
AR IND
UCTION MODELING
Ex
pl
ai
ni
n
g
r
e
s
earch
ch
ro
n
o
l
o
gi
cal
, i
n
cl
udi
n
g
r
e
searc
h
des
i
gn,
resea
r
c
h
pr
oce
d
u
r
e
(i
n
t
h
e f
o
rm
of
alg
o
rith
m
s
, Pseu
do
co
d
e
or o
t
h
e
r),
h
o
w t
o
test an
d
d
a
ta
acq
u
i
sition
[1
]-[3
]. Th
e d
e
scri
p
tio
n
of th
e cou
r
se
of
researc
h
s
h
oul
d
be s
u
pporte
d
refe
rences
, s
o
t
h
e e
xpl
a
n
ation can be
acce
pte
d
sc
ie
ntifically
[2], [4].
Th
e m
ach
in
e styd
ied
is rep
r
esen
ted
b
y
with
two
stators wind
ing
s
:
1
,
1
1
sc
sb
,
sa
and
2
,
2
2
sc
sb
,
sa
whic
h
a
r
e displaced by
0
30
α
and
the rotorical phases:
rc
rb,
,
ra
, this is a m
o
st r
ugg
ed
an
d m
a
in
te
n
a
n
c
e
free m
achine
Figu
re
1.
Do
u
b
le stator
wi
nd
ing
re
prese
n
tation
The following assum
p
tions have been m
a
de in deriving the m
achine m
odel
- Machine windings are si
nusoidally
distributed
- M
achine m
a
gnetic saturation and the m
u
tu
al leakage inductances are neglected
- The two stars have sam
e
param
e
ters
The
m
a
them
atical m
odel of the m
ach
ine is
written as a set of state
e
quations, both for th
e electrical and
m
echanical parts, the voltage equation is[2]
:
qdr
r
s
dqr
dqr
r
dqr
qds
s
dq
dqs
s
dqs
qds
s
dq
dqs
s
dqs
Φ
).
ω
(
ω
Φ
dt
d
I
.
R
V
Φ
.
ω
Φ
dt
d
I
.
R
V
Φ
.
ω
Φ
dt
d
I
.
R
V
2
2
2
2
2
1
1
1
1
1
(1
)
with:
dqr
dqs
dqs
m
dqr
s
dqr
dqr
dqs
dqs
m
dqs
s
dqs
I
I
I
L
I
L
I
I
I
L
I
L
2
1
12
2
1
12
12
12
]
[
]
[
]
[
]
[
(2
)
the electrical state varia
b
les in the “
dq”
syst
em
are the flux
represe
n
ted
by
vector [
Φ
], while the input
variable
in the “
d
q”syste
m
are expressed
by vect
or [V].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN:
208
8-8
7
0
8
A N
e
ur
al N
e
tw
ork B
a
se
d
S
p
e
e
d C
ontr
o
l of
a
D
ual
Sta
r
I
n
d
u
ction
M
o
tor
(
M
eliani B
o
uzia
ne)
95
4
V
B
A
dt
d
.
.
(3
)
with:
T
dqr
dqs
dqs
T
dqr
dqs
dqs
V
V
V
V
2
1
2
1
,
the equation of the electrom
a
gnetic torque is:
qr
ds
ds
dr
qs
qs
r
m
m
e
I
I
I
I
L
L
L
p
T
).
(
).
(
2
1
2
1
(4
)
the equation of flux is:
)
(
]
[
2
1
dqr
dqs
dqs
m
dqm
I
I
I
L
(5
)
or:
r
dqr
s
dqs
s
dqs
a
dqm
L
L
L
L
2
2
1
1
.
]
[
(6
)
W
h
ere
r
s
s
m
a
L
L
L
L
L
1
1
1
1
1
2
1
(7
)
the state m
a
trix
A a
n
d vect
or B in t
h
e
d-q a
x
is are:
66
65
64
63
56
55
52
51
46
44
43
42
36
34
33
31
25
24
22
21
15
13
12
11
0
0
0
0
0
0
0
0
0
0
0
0
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
a
A
(8
)
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
B
(9
)
whe
r
e:
1
1
1
33
11
1
s
s
s
a
T
L
T
L
a
a
2
2
2
44
22
1
2
43
21
1
35
15
42
31
24
12
1
,
,
s
s
s
a
s
s
a
r
s
a
s
T
L
T
L
a
a
L
T
L
a
a
L
T
L
a
a
a
a
a
a
Evaluation Warning : The document was created with Spire.PDF for Python.
ISS
N
:
20
8
8
-
8
70
8
IJECE Vol. 4, No. 6, Decem
ber 2014
:
952 – 961
9
55
r
s
a
r
s
a
L
T
L
a
a
L
T
L
a
a
1
63
51
2
46
25
,
r
r
r
s
s
s
r
r
r
r
a
r
s
a
R
L
T
R
L
T
a
a
T
L
T
L
a
a
L
T
L
a
a
,
,
1
,
65
56
66
55
2
64
52
and
m
s
r
3.
MAT
R
I
X
CO
NVE
RTER M
O
DELIN
G
In this section, it is explained the resul
t
s of
resea
r
ch
and at the sam
e
tim
e
is given th
e
com
p
rehe
nsive
discus
sio
n. R
e
sults can
be
pr
esented i
n
fi
gu
res,
gra
p
hs, ta
bles and ot
hers t
h
at m
a
ke the reade
r
un
de
rstan
d
eas
ily
[2]
,
[
5
]
.
A m
a
trix converter is a variable a
m
plitude and fr
e
que
ncy
po
we
r su
pply
that con
v
e
r
ts the three pha
se
line voltage di
rectly. It is very si
m
p
le
in structure
and has powerful cont
rollability
. The
real developm
ent of
the m
a
trix converter st
arts wi
th the
work of
Vent
uri
n
i and
Alesin
a
who
propose
d
a m
a
the
m
atical analysis and
intro
d
u
ced t
h
e
low
fre
q
u
enc
y
m
odulatio
n
m
a
trix con
cep
t to desc
ribe t
h
e lo
w
fre
que
ncy
be
ha
vior
of t
h
e
m
a
trix conve
r
ter [1]. In th
is
,
the output voltages a
r
e obtained
by
m
u
ltiplication of the
m
odulation m
a
trix
or
transfer m
a
trix with
the inpu
t voltages. T
h
e basic diagra
m
of a
m
a
trix converter ca
n be repre
s
ente
d by
Figu
re 2.
Figu
re
2.
B
a
si
c struct
ure
o
f
m
a
trix co
nve
rt
er
The existence
function provides a
m
a
the
m
atical
expressi
on f
o
r descri
bi
ng s
w
itchin
g
p
a
tterns. Th
e
existence
funct
i
on
for a
single switch a
ssum
e
s a value
of
unity whe
n
the switch is cl
osed a
n
d zero
when the
switch is
ope
n. For the m
a
trix conve
r
ter shown i
n
Fi
gure
2, the existence
function fo
r ea
ch of the
switc
hes is
exp
r
esse
d by
t
h
e follo
win
g
e
quatio
ns:
open
S
switch
closed
S
switch
S
kj
kj
kj
,
0
,
1
(1
0)
where k= {A, B
,
C
}
is input phase
and j={a, b, c} is output phase.
The above constraint can be e
xpressed in the following form
:
1
Cj
Bj
Aj
S
S
S
(1
1)
with the above restrictions a 3 X 3 m
a
trix
converter has 27 possi
ble switching states.
the m
a
them
atical
expression that
represents the
operati
on of
a three
phase ac to
ac M
a
trix
C
onverter can be
expressed as follows:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN:
208
8-8
7
0
8
A N
e
ur
al N
e
tw
ork B
a
se
d
S
p
e
e
d C
ontr
o
l of
a
D
ual
Sta
r
I
n
d
u
ction
M
o
tor
(
M
eliani B
o
uzia
ne)
95
6
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
t
v
t
v
t
v
t
S
t
S
t
S
t
S
t
S
t
S
t
S
t
S
t
S
t
v
t
v
t
v
C
B
A
Cc
Bc
Ac
Cb
Bb
Ab
Ca
Ba
Aa
c
b
a
(1
2)
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
t
i
t
i
t
i
t
S
t
S
t
S
t
S
t
S
t
S
t
S
t
S
t
S
t
i
t
i
t
i
c
b
a
T
Cc
Bc
Ac
Cb
Bb
Ab
Ca
Ba
Aa
C
B
A
(1
3)
where va, vb
and vc
and iA,
iB
and
iC
are
the output
voltages and
input currents
re
spectively
.
To
determ
ine
the behavior of the
M
C
at output frequencies
well
below the switching
frequency
,
a m
odulation duty
cy
cle
can
be defined for
each switch. The
m
odulation duty cycle
MKj for the
switc
h SKj in
Figure.2 is defined as
in equation (14) below.
s
kj
kj
T
t
M
(1
4)
where
kj
t
is the
one tim
e for
the switch
kj
S
between input phase k={A,
B
,
C
}
and
j={a, b, c}
and
s
T
is the
period of the PWM
switching signal or
sam
p
ling period. In term
s
of the m
odulation duty
sy
cle,
equations
12,
and 13 can be rewritten as given below.
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
t
v
t
v
t
v
t
M
t
M
t
M
t
M
t
M
t
M
t
M
t
M
t
M
t
v
t
v
t
v
C
B
A
Cc
Bc
Ac
Cb
Bb
Ab
Ca
Ba
Aa
c
b
a
(1
5)
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
t
i
t
i
t
i
t
M
t
M
t
M
t
M
t
M
t
M
t
M
t
M
t
M
t
i
t
i
t
i
c
b
a
T
Cc
Bc
Ac
Cb
Bb
Ab
Ca
Ba
Aa
C
B
A
1
Cj
Bj
Aj
M
M
M
(1
6)
j={a, b,
c}
the
high-frequency
sy
nthesis t
echnique introduced by
Venturini and Ales
ina in [4-5]
allows the use of low
frequency
continuous
functions
, referred to as the m
odulation m
a
trix
m
(
t), to calculate the existence
functions for each
switch of the
m
a
trix converter.
T
hus, the aim
when using the
Alesina and
Venturini
m
odulation m
e
thod is to find a m
odulation m
a
trix which satisfies
the following set of equations.
)
(
.
)
(
)
(
t
v
t
m
t
v
i
o
(1
7)
)
(
.
)
(
)
(
t
i
t
m
t
i
o
T
i
(1
8)
where the input voltages
(t)
v
i
are given by
the following set of functions
)
3
2
cos(
)
3
2
cos(
)
cos(
)
(
t
t
t
V
t
v
i
i
i
in
i
(1
9)
an
d th
e
d
e
sir
e
d ou
tpu
t
vo
ltag
e
s
(t)
v
o
are
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S
SN:
2
088
-87
08
IJECE Vol. 4, No. 6, D
ecem
ber 2014
:
952 – 961
9
57
)
3
2
cos(
)
3
2
cos(
)
cos(
)
(
t
t
t
V
t
v
o
o
o
o
o
(2
0)
output currents
)
(
t
i
o
can be expressed as:
)
3
2
cos(
)
3
2
cos(
)
cos(
)
(
o
o
à
o
o
o
o
o
t
t
t
I
t
i
(2
1)
where
o
is the phase angle of the linear load.
fi
nal
l
y
,
t
h
e desi
red i
nput
current
has an arbi
t
r
ary
phase
i
. Thi
s
angl
e can be set
t
o
0 t
o
obt
ai
n uni
t
y
i
nput
power fact
or of t
h
e m
a
t
r
i
x
convert
er.
)
3
2
cos(
)
3
2
cos(
)
cos(
)
(
i
i
i
i
i
i
i
i
t
t
t
I
t
i
(2
2)
The el
em
ent
s
of m
a
t
r
i
x
m
(
t
)
t
h
at
sat
i
s
fy
equat
i
ons 17 and 18 are gi
ven by
)
2
(
3
2
)
(
cos
1
3
1
)
(
3
2
)
(
cos
1
3
1
)
(
2
1
j
i
q
j
i
q
t
m
i
o
i
o
ij
(2
3)
where
)
tan(
)
tan(
1
2
1
1
1
o
,
1
2
1
,
i
o
V
V
q
W
ith the following restrictions
0
1
,
0
2
,
2
1
0
q
4.
SPEED
CO
N
T
ROL O
F
T
H
E DS
IM
WI
TH NE
UR
AL
NETWO
R
K
Feed
fo
rwa
r
d artificial neural
netw
or
ks (
A
N
N
’s
) are
uni
ve
rsal ap
pr
oxim
a
tors o
f
n
o
n
line
a
r f
unctio
ns
[7]
.
As s
u
ch
, t
h
e A
N
N
’s
use
a de
nse interc
on
nectio
n
of
n
e
ur
o
n
s that c
o
r
r
esp
o
nd t
o
c
o
m
puting n
o
d
es
. Each
node
perform
s
the m
u
ltiplicati
on
of
its
input signals by constant weights,
sum
s
up the results, and m
a
p
y
s the
sum
to a nonlinear functi
on (activation
function); t
h
e
result
is
then transferred to its
output. T
h
e m
a
them
atical
m
odel of a
ne
u
r
o
n
is
give
n
by
)
.
(
b
x
w
y
i
i
(2
4)
whe
r
e (
x
1, x2,
..., xN) are inputs fr
om
the previ
o
us
layer neur
ons, (
w
1,
w2, .
.., w
N
)
are the cor
r
es
pondi
ng
weig
hts, a
n
d
b
is the
bias o
f
t
h
e ne
ur
o
n
.
fo
r a l
oga
rithm
i
c sigm
oidal activation
fu
nctio
n, t
h
e
out
put is
give
n
by
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN:
208
8-8
7
0
8
A N
e
ur
al N
e
tw
ork B
a
se
d
S
p
e
e
d C
ontr
o
l of
a
D
ual
Sta
r
I
n
d
u
ction
M
o
tor
(
M
eliani B
o
uzia
ne)
95
8
N
i
i
i
b
x
w
e
y
1
]
.
[
1
1
(25)
A fee
d
f
o
r
w
a
r
d
neu
r
al netw
o
r
k is or
ga
nized
in lay
e
rs
: an in
put lay
e
r,
one
or m
o
re hi
dde
n lay
e
rs, a
n
d
an o
u
tp
ut lay
e
r. No c
o
m
putation is
pe
rf
o
r
m
e
d in the in
put l
a
y
e
r: the signa
ls are directly supplied to the first
h
i
dd
en
layer.
Hidd
en
and
outp
u
t
n
e
ur
on
s
gen
e
r
a
lly h
a
ve
a sigm
oidal activation f
u
nction
.
T
h
e k
n
o
wl
edge i
n
an ANN is acquire
d through a learning
algo
rithm
,
which p
e
rf
orm
s
the adaptation o
f
wei
ghts o
f
the net
w
o
r
k
iteratively unti
l
the error bet
w
een the
target vect
ors
and
output
of the
net
w
ork falls
bel
o
w a certain error goal.
The m
o
st popular learni
ng algorithm
for m
u
l
tilayer
net
w
orks is the backprop
agation algorithm
,
which
con
s
ists of a f
o
r
w
ar
d a
nd
ba
ckwa
r
d
action.
In the fi
rst, th
e signals are
p
r
o
p
a
g
ated th
ro
ug
h the
netw
or
k lay
e
r
by
lay
e
r.
A
n
o
u
tp
ut v
ector
is
thus
ge
ner
a
ted
and
s
ubtra
cted
fr
om
the de
sire
d out
put
vect
or
.
T
h
e resulta
nt err
o
r
vecto
r
is
pr
op
a
g
ated
bac
k
wa
r
d
in
the
netw
or
k a
n
d
ser
v
es
t
o
ad
just t
h
e
weights i
n
or
der
to
m
i
nim
i
ze the out
put
err
o
r
.
T
h
e
bac
k
p
r
opa
gatio
n t
r
ainin
g
al
go
rithm
and its
va
riants a
r
e im
plem
ented
by
m
a
ny
ge
ne
ral-
pu
rp
ose
soft
ware
pac
k
ages s
u
c
h
as t
h
e
neural-network to
o
l
bo
x
f
r
o
m
MATLAB, Th
e
str
u
ctur
e of
NN contr
o
ller
selected in this paper is shown in
Fi
gu
re 2
.
The N
N
c
ont
r
o
ller co
nsists
of three
neurons in the i
n
put
layer
,
seve
n
neu
r
o
n
s
in the
hid
d
e
n
l
a
y
e
r an
d a
ne
ur
on
in t
h
e
out
pu
t lay
e
r.
The three inputs signals e(k), e(k-1)
,
isq1
(k
-1
),
and
th
e to
rq
u
e
(
T
em
*
(
k)
) o
u
t
pu
t ar
e expo
r
t
ed
to
the
MATLAB
Wo
rks
p
ace
(e(k) i
s
the speed e
r
ror a
n
d e(k-1)
pre
v
ious s
p
ee
d error
). T
h
e
followi
ng M
A
T
L
AB
code trai
ns the
Neural Network. The
fi
rst section of code generates the
‘c
ell array’. The
cell array com
b
ines
the
3
diffe
re
nt in
puts
into
1
in
put
vecto
r
.
The acti
v
a
tio
n fu
n
c
tion
s
of
th
e
h
i
dd
en
an
d ou
tpu
t
n
e
uron
s are
Hy
pe
rb
olic tange
nt sigm
oid
and linea
r,
r
e
spectively
.
T
h
e lear
nin
g
o
f
NN c
o
ntrolle
r is d
one
usi
ng t
h
e
Leve
nbe
rg
-M
a
r
q
u
ar
dt bac
k
-p
ro
pa
gation al
g
o
rithm
[7]
.
Th
e trainin
g
pa
ra
m
e
ters for t
h
e
Leve
nbe
rg
-M
a
r
q
u
ar
dt
algorithm
( trainlm
)
are:
M
a
xim
u
m
num
ber of e
p
ochs to trai
n
(
n
et.trainP
a
r
a
m
.
epoc
hs=
4
00)
Perform
a
nce goal(net.trainPa
ram
.
goal =
1e-5;)
E
p
och
s
betwee
n
displa
y
s
(net.t
rainPa
r
a
m
.
sho
w
=
5;)
Figu
re
2.
M
u
lt
ilay
e
r Feedf
o
r
w
ar
d
Ne
ural
N
e
two
r
k
The o
f
f
-
line le
arni
ng
pr
ocess
of
NN c
o
ntroll
er is sh
ow
n in
Figu
re 3
.
Th
e data traini
ng is taken from
the input
and
out
put val
u
es of the PI cont
roller by sim
u
lati
ng it under norm
a
l and disturba
nce
conditions, (the fuzzy
logic sy
stem
is used o
n
-
line to ge
nera
te the
PI controller param
e
ters), the
learning rate were taken equal to
0.
2. T
h
e electr
o
m
a
gnetic tor
que
fr
om
PI cont
roller
a
n
d the electrom
a
gnetic tor
que
fr
om
NN co
ntr
o
ller are
com
p
ared
t
o
obtain desi
r
e
d
er
ro
r go
al [8
,9
].
ta
n
s
i
g
1
ta
n
s
i
g
pu
r
e
l
i
n
ne
t
s
um
2
ne
t
s
um
1
ne
t
s
um
do
t
p
rod
9
w
p
z
do
t
p
rod
8
w
p
z
do
t
p
rod
7
w
p
z
do
t
p
rod
6
w
p
z
do
t
p
rod
5
w
p
z
do
t
p
rod
4
w
p
z
dot
p
r
od
3
w
p
z
dot
p
r
od
2
w
p
z
dot
pr
o
d
1
1
w
p
z
do
t
p
rod
1
0
w
p
z
dot
p
r
od
1
w
p
z
b{
3}
bi
as
b{
2}
bi
a
s
b{
1}
bi
as
Uni
t
Del
a
y
2
z
1
Uni
t
Del
a
y
1
z
1
Mu
x
1
Mu
x
Mu
x
Mu
x
I
W
{
3
,2
}
(
1
,:)
'
wei
g
h
t
s
I
W
{2
,
1
}(7
,
:
)
'
wei
g
ht
s
I
W
{2
,
1
}(6
,
:
)
'
wei
g
ht
s
I
W
{2
,
1
}(5
,
:
)
'
wei
g
ht
s
I
W
{2
,
1
}(4
,
:
)
'
wei
g
ht
s
I
W
{2
,
1
}(3
,
:
)
'
wei
g
ht
s
I
W
{2
,
1
}(2
,
:
)
'
wei
g
ht
s
I
W
{2
,
1
}(1
,
:
)
'
wei
g
ht
s
I
W
{
1
,1
}
(
3
,:)
'
w
ei
g
h
t
s
I
W
{
1
,1
}
(
2
,:)
'
w
ei
gh
t
s
I
W
{
1
,1
}
(
1
,:)
'
w
ei
gh
t
s
[T
e
m
]
[
Wr
e
f
]
[W
m
]
[
i
s
q1]
Ad
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN:
2
088
-87
08
IJECE Vol. 4, No. 6, D
ecem
ber 2014
:
952 – 961
9
59
Figu
re
3.
Lear
nin
g
pr
ocess
o
f
N
N
c
ont
roller
5.
SIMULATION RESULTS
The S
I
M
U
LI
N
K
m
odel f
o
r i
ndi
rect FOC
o
f
the
4.
5
Kw
c
a
ge r
o
tor
DS
I
M
a
ssociated with
a
d
aptive
FLC
-
P
I
co
ntr
o
ller is show
n in Fig
u
re
4. T
h
e
m
achine is fed by a m
a
trix
converte
r. The param
e
ters of the
induction m
o
tor
are
s
u
m
m
a
rized in Appendi
x
.
The fi
rst test conce
r
ns a
no
-load
startin
g of
the m
o
tor with a refe
rence speed
ref
ω
= 28
8
rad/
sec. a
n
d
a n
o
m
i
nal load distu
r
ba
nce t
o
rq
ue
(1
4
N
.m
) is su
d
d
enly
a
p
p
lied betwee
n
1
s
ec an
d
2sec,
f
o
llowe
d
by
a c
onsi
g
n
inve
rsio
n
(-
28
8ra
d
/sec)
at 2
.
5sec.
At
4.
5s,
a
-1
4
N
m
load
di
stur
bance
is a
p
plied
du
rin
g
a
peri
od
o
f
2 s.
t
h
is test
has
fo
r
o
b
ject t
h
e st
udy
of
co
n
t
roller
beh
a
vi
o
r
s in
p
u
r
suit a
n
d in
re
g
u
lation.
The test result
s obtaine
d are
shown in fi
gure 5. The s
p
ee
d of the m
o
tor reaches
ω
ref
at 0.2 s
with
al
m
o
st no
overshoot. It t
h
en begins t
o
oscillate inside a
0.4% error stri
p around
ω
ref
,
The ne
ural netwo
r
k
cont
roller re
jec
t
s
the
loa
d
dist
ur
ba
nce very
q
u
ickly
with
n
o
ove
rs
ho
ot
a
n
d
with
a ne
g
ligible steady state
error.
In
o
r
de
r to tes
t
the r
o
b
u
stn
e
ss o
f
the
use
d
m
e
t
hod
we
h
a
ve stu
d
ied
th
e effect
of
the
param
e
ters
uncertainties on the perform
ances
of the spe
e
d control. To
show the effect
of the pa
ram
e
t
e
rs uncertainties, we
have sim
u
lated the system
wi
th diff
ere
n
t
values
of t
h
e pa
ra
m
e
ter consi
d
er
ed a
nd c
o
m
p
ar
ed to
n
o
m
i
nal
value
(real
value
)
. T
h
e Fi
gu
re
6 a
n
d
Fig
u
r
e
7
s
h
o
w
res
p
ectiv
ely
the be
havi
or
o
f
the
D
S
I
M
whe
n
R
r
is 10%
increased of its nom
inal value and
J
is inc
r
ea
sed and
decrea
sed 10%
of its
nom
inal value. An inc
r
ease
of the
m
o
m
e
nt of ine
r
tia gives
best
per
f
o
r
m
a
nces, but it p
r
es
ents
a slow
dynam
i
c response. T
h
e figures s
h
ow that
the
p
r
op
ose
d
c
ont
roller ga
ve satisfactory
per
f
o
r
m
a
n
ces thus
judges
that th
e controller is
robust
.
Figu
re
5.
Sim
u
lated res
u
lts o
f
neu
r
al
netw
or
k
co
ntr
o
ller f
o
r
DSIM
0
1
2
3
4
5
6
-30
0
-20
0
-10
0
0
10
0
20
0
30
0
Ti
m
e
(
s
)
Wm
(
r
a
d
/
s
)
R
e
f
S
p
eed
D
S
I
M
S
p
eed
0
1
2
3
4
5
6
-4
0
-2
0
0
20
40
60
80
Ti
m
e
(
s
)
To
r
q
ue[
N
.
m
]
0
1
2
3
4
5
6
-2
0
-1
5
-1
0
-5
0
5
10
15
20
i
s
q1(
A
)
Ti
m
e
(
s
)
0
1
2
3
4
5
6
0
1
2
d-
ax
i
s
Ti
m
e
(
s
)
Fl
u
x
[
w
e
b
]
0
1
2
3
4
5
6
-1
0
1
Ti
m
e
(
s
)
q-
a
x
i
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN:
208
8-8
7
0
8
A N
e
ur
al N
e
tw
ork B
a
se
d
S
p
e
e
d C
ontr
o
l of
a
D
ual
Sta
r
I
n
d
u
ction
M
o
tor
(
M
eliani B
o
uzia
ne)
96
0
Figu
re 6.
Sim
u
lated results o
f
ne
u
r
al net
w
o
r
k c
ont
roller
f
o
r
DS
IM
with
va
riation
of
the
r
o
to
r re
sistance
at t=2s
Figu
re
7.
Sim
u
lated res
u
lts o
f
neu
r
al
netw
or
k
co
nt
roller for
DSIM
with variation of t
h
e
rotor i
n
ertia
(+10
%J
)
Figu
re
4.
Sim
u
link
dia
g
ram
fo
r
DSIM
co
nt
rol sy
stem
s
6.
CO
NCL
USI
O
N
In this
paper
a contr
o
l strat
e
gy
whic
h inc
o
r
p
orates the
neu
r
al netw
o
r
k f
o
r c
ont
rol
of
no
n linear
sy
stem
is described an
d use
d
to dem
onstrate the effec
tive
n
e
ss of the ne
ura
l
networ
k f
o
r c
ont
rol o
f
no
n linea
r
sy
stem
is describe
d an
d use
d
to dem
onstrate the effec
tive
n
ess o
f
the
neu
r
al netw
or
k f
o
r
contr
o
l the s
p
eed
o
f
dual star i
n
duc
tion m
o
tor ba
s
e
d o
n
the
in
dir
ect FOC
.
T
h
e
m
achine is fe
d by a m
a
tr
ix c
o
nverter. Sim
u
lation
results sh
o
w
that the designe
d
neural
co
ntr
o
l
l
er realizes a goo
d dy
nam
i
c behavi
or o
f
the m
o
tor, with a rapid
settling ti
m
e
, no overshoot, al
m
o
st
instan
taneous rej
ection
of load dist
urba
nce, a perfect
speed tracki
ng
and it
deals
well with param
e
ter variations
of
the m
o
to
r.
It seem
s to
be a
hig
h
-
pe
rf
orm
a
nce r
o
b
u
st c
ontr
o
ller.
0
1
2
3
4
-5
0
5
10
15
20
Ti
m
e
(
s
)
i
s
q1(A
)
0
1
2
3
4
0
1
2
Ti
m
e
(
s
)
d-
ax
i
s
Flu
x
(
w
e
b
)
0
1
2
3
4
-1
0
1
Ti
m
e
(
s
)
q-
ax
i
s
0
1
2
3
4
-5
0
0
50
100
150
200
250
300
Ti
m
e
(
s
)
W
m
(
r
ad/
s
)
-1
0
%
J
+
10%
J
0
1
2
3
4
-1
0
0
10
20
30
40
50
60
Ti
m
e
(
s
)
T
o
r
que[
N
.
m]
-1
0
%
J
+1
0
%
J
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I
S
SN:
2
088
-87
08
IJECE Vol. 4, No. 6, D
ecem
ber 2014
:
952 – 961
9
61
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