TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.7, July 201
4, pp
. 5268 ~ 52
7
4
DOI: 10.115
9
1
/telkomni
ka.
v
12i7.436
7
5268
Re
cei
v
ed Se
ptem
ber 10, 2013; Revi
se
d F
ebruary 1
4
, 2014; Acce
pted March 5,
2014
A New Anti-Windup PI Controller for Direct Torque
Control System
MIAO Jing-L
i
*, LI Qi-meng
Heb
e
i Un
iversit
y
of Eng
i
ne
eri
n
g, Chin
a
*Corres
p
o
n
id
n
g
author, e-ma
i
l
: 8716
66
238
@
qq.com
A
b
st
r
a
ct
Spee
d c
ontrol
l
e
r i
n
i
nducti
o
n
motor
dir
e
ct torqu
e
c
ontro
l (DTC) syste
m
usu
a
lly
ad
o
p
ts th
e
traditio
nal PI c
ontrol
l
er. But the trad
itio
nal P
I
controll
er h
a
s
character
i
st
ic
of non
lin
ear s
a
turation, w
hat
w
ill
m
a
k
e
the control perfor
m
ance of actual s
ystem
be
com
e
worse. In or
der to
improv
e system
control
perfor
m
a
n
ce, this p
aper
ad
op
ts a new
type
Anti-W
ind
up PI
control
l
er, T
h
i
s
meth
od s
e
p
a
rately co
ntrol t
h
e
integr
al state
b
y
feed
back
i
n
g
the
outp
u
t of
the i
n
tegrat
or t
o
the
in
put
por
t of the
inte
gra
t
or accor
d
in
g t
o
whether the contro
ller output is saturated or
not, which can m
a
k
e
the system
leaving satur
a
tion as soon as
possible. As
a result, the
oversh
oot and settling tim
e
of the syst
em
ar
e reduced. Simulation
and
exper
imenta
l
r
e
sults s
how
th
at this
metho
d
can s
i
gn
ifica
n
tl
y sup
p
ress
the
inte
gral
w
i
nd
u
p
p
h
e
n
o
m
e
n
o
n
as
w
e
ll as re
duc
e
the overs
h
o
o
t and s
horte
n th
e settlin
g ti
me.
T
he new
Anti-
W
indu
p PI con
t
roller
has
a b
e
tter
perfor
m
a
n
ce th
an the traditi
on
al PI controll
er.
Key wo
rd
s:
induction motor; direct to
rque control; PI controller;
Anti-Windup; simulation
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Dire
ct torq
ue
control (DT
C
) te
chnol
og
y is
a high-perfo
rman
ce
AC spe
ed regulatin
g
techni
que. It
appe
ars later than the vector co
ntrol
technolo
g
y. But
comp
ared wit
h
vector cont
rol
techn
o
logy,
DTC technol
ogy will
not b
e
re
stri
cted
b
y
curre
n
t re
g
u
lator
ban
dwi
d
th. So the to
rque
dynamic resp
onse is faster and not
sen
s
itive to
the change of the
param
eters of motor [1-5]. But
a typical spe
ed cont
rolle
r of DTC syst
em usu
a
lly
use
s
PI controller. Whil
e the tradition
al
PI
controlle
r doe
s not
con
s
id
e
r
the up
pe
r li
mit of ac
tual t
o
rqu
e
. Wh
en
the mutation i
n
the spee
d i
s
happ
ened, PI
co
ntrolle
r
wil
l
output a
big
torqu
e
. Bu
t
actually the
motor
ca
n’t o
u
tput such a
big
torque. It will
make the p
e
rform
a
n
c
e o
f
the
system
become
worse. We call this phe
nom
en
on
Wind
up
[6-10]
.
To solve this
probl
em, this pape
r ado
pts a new type Anti-Win
dup
PI controlle
r. The ne
w
controlle
r can
qui
ckly exit
the saturated zon
e
,
So
a
s
to reali
z
e
the
red
u
ci
ng
of
overshoot
an
d
faster respon
se spee
d
[11-14].
2. Ne
w
Anti-Windup PI Controller
In the inducti
on motor, the
relation
ship
betwe
en spe
ed and torqu
e
is:
*
()
EL
TT
d
dt
J
J
B
(1)
Usi
ng s-fun
c
tion ca
n be ex
pre
s
sed a
s
:
*
()
E
L
TT
Js
B
(2)
In the
equ
ation,
is angu
lar vel
o
city of
the m
e
chani
cal
roto
r,
J
i
s
the mom
ent
of ine
r
tia
of the m
o
tor,
B
is th
e Viscous fri
c
tion
coefficient,
T
E
*
is th
e give
n
torque
of th
e
motor,
T
L
i
s
t
he
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A New Anti-Wind
up PI Controlle
r for Direct To
rqu
e
Control Syste
m
(MIAO Jing-Li)
5269
load torq
ue,
J
/
B
is
c
a
lled th
e
me
c
h
anic
a
l time
c
ons
ta
n
t. L
e
t
k
m
=
J
/
B
, that is
to s
a
y
k
m
is
mech
ani
cal t
i
me con
s
t
ant
.
Traditio
nal PI controller i
s
affected by
the Wi
ndup
p
henom
eno
n, its equivale
nt on the
output sid
e
joined a limiti
ng functio
n
T
E
*
(
u
). Equation (3
) is the
ex
pressio
n
. Figure 1 is the
function of th
e
corre
s
po
nd
ing cu
rve. Fig
u
re 2 is the P
I
controlle
r st
ructure with a
saturation lim
it.
max
m
ax
*
max
sgn(
)
,
,
E
Tu
u
T
Tu
uu
T
(3)
In this equati
on,
u
is the o
u
tput of traditional PI controller, sg
n(
u
) is
the s
i
gn func
tion.
Figure 1.
The
Function
Cu
rve of
T
E
*
(
u
)
u
*
E
T
*
e
B
Js
1
L
T
p
K
i
K
s
1
Figure 2.
T
r
a
d
itional PI Co
ntrolle
r Struct
ure with a Sat
u
ration Li
mit
To inhi
bition
the saturation ph
eno
me
non, this arti
cle int
r
od
uce
d
a n
e
w typ
e
Anti -
Wind
up PI co
ntrolle
r, figure
3 sho
w
s the control
blo
c
k diagram. Accordin
g to the Figure 3, Wh
en
u
=
T
E
*
,
swi
t
ch S
1
will be closed, S
2
will be opened. The
cont
roller
turns into the typical
PI
controlle
r. When
u
>
T
E
*
,
swit
ch S
2
will
be closed, S
1
will be opened. The out
put multiplied
by
a
coeffici
ent an
d then n
egati
v
e feedba
ck to the inp
u
t.
So that the inte
gral o
u
tput ca
n co
nverg
e
s t
o
zero ra
pidly.
p
K
i
K
s
1
C
B
Js
1
1
S
*
L
T
e
i
*
E
uT
*
E
uT
*
E
T
u
1
k
2
S
Figure 3.
The
New
Anti
-Wi
ndup PI Cont
rolle
r Structu
r
e
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ISSN: 23
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046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5268 – 52
74
5270
The
i
in the Figure 3 i
s
inte
gral state. Its
expre
ssi
on is:
,
1
,
i
s
n
s
n
K
eu
u
s
i
iu
u
k
(4)
In Equation (4),
K
i
is integral con
s
tant.
k
is the integra
l
feedba
ck g
a
i
n coeffici
ents. And
k
,
K
i
<<
k
m
.
3. Stabilit
y
Anal
y
s
is
If the system
is
stable, th
e sy
stem mu
st m
e
e
t
tw
o
c
o
nd
itio
ns
. F
i
r
s
t th
e s
y
s
t
em in
th
e
linear
regio
n
is stable. Seco
nd the system coul
d conve
r
ge
nce
to the linear are
a
from
the
saturated zone. If
two conditions are sati
sfied at
the same time, the system will be stable.
3.1. First Co
ndition
In the linea
r, the ne
w Anti-Wind
up PI co
ntrolle
r is the
same
as tra
d
itional PI co
ntrolle
r.
At this time th
e error
can b
e
expre
s
sed
as:
*
()
1
()
p
L
mm
K
iT
ee
kJ
k
J
(5)
Lyapun
ov function is d
e
fine
d as follo
w:
2
2
0
1
()
1
(,
)
2
i
ii
Le
i
J
e
K
(6)
In the Equation (6
),
i
0
is
i
’s stable value,
so:
*2
10
(,
)
(
)
(
)
p
L
K
Le
i
e
B
T
i
B
e
J
(7)
*
0
L
iB
T
(8)
In the linear, it always meet
s:
2
0m
a
x
(,
)
0
Ve
q
iT
(9)
To sum u
p
, the controlle
r’s
stable
con
d
ition in the line
a
r is:
*
ma
x
L
TB
T
(10)
3.2. Second Conditio
n
In the saturated zo
ne, we
can g
e
t the ex
pressio
n
of error fro
m
Equation (1
).
*
*
()
EL
mm
TT
e
e
kJ
k
(11)
From e
quatio
n (4)
we can
get:
i
i
k
(12)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A New Anti-Wind
up PI Controlle
r for Direct To
rqu
e
Control Syste
m
(MIAO Jing-Li)
5271
Be
c
a
us
e o
f
k
<<
k
m
, the d
y
namic
sp
ee
d erro
r i
s
far slo
w
e
r
tha
n
the integ
r
al
dynamic
state. That is
to sa
y, the integral
state
i
wa
s immedi
ately set to zero whe
n
the controlle
r is in
the
s
a
turated zone. So:
p
p
uK
e
i
K
e
(13)
If
E
b
=
T
max
/
K
p
. From E
quati
on (13),
we
can find that,
whe
n
|
e
|<=
E
b
the co
ntroll
er is in th
e
linear, when |
e
|>
E
b
the con
t
roller i
s
in the saturated zone.
Lyapun
ov function is d
e
fine
d as follo
w:
2
2
()
2
e
Le
(14)
After the deri
v
ation:
2
*
2*
()
()
EL
mm
Le
e
e
TT
e
e
kk
J
(15)
Take Eq
uatio
n (2) a
nd Equ
a
tion (13
)
into
Equation (1
5
)
2*
ma
x
2
*
2
ma
x
()
(
)
()
L
mm
L
mm
Te
T
e
Le
e
kJ
J
k
TT
e
e
kk
J
(16)
Becau
s
e of
1
()
0
Le
, only need to meet:
*
ma
x
1
{(
)
}
mL
ek
T
T
J
(17)
So we ca
n ge
t the conditio
n
:
*
ma
x
m
ax
L
p
B
TB
T
T
K
(18)
Comp
ared E
quation
(10
)
and Equ
a
tion
(18
)
, we
ca
n se
e that a
s
lon
g
a
s
th
e syste
m
meet Equatio
n (10
)
must
meet Equatio
n (18
)
. So Equation (1
0) i
s
the stable
co
ndition.
To sum u
p
we can g
e
t the stable
con
d
ition as follo
w:
*
ma
x
L
TB
T
(19)
4. Modeling and Simulation
Matlab/Simuli
nk is u
s
ed t
o
carry out the modeli
n
g
and simul
a
tion. Figure 4
is the
stru
cture ch
a
r
t of the DTC system
with
the new Anti
-Wind
up PI co
ntrolle
r. First
of all, accordi
ng
to Figu
re
4
the mod
e
l o
f
indu
ction
motor
DT
C
system
with
tradition
al
PI controller wa
s
establi
s
h
ed.
And then
the
model
of the
new Anti-Win
dup PI
cont
ro
ller
wa
s e
s
tab
lishe
d, sho
w
n
in
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ISSN: 23
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046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5268 – 52
74
5272
the Figu
re 5.
Finally the n
e
w Anti-win
d
up PI co
ntro
ll
er repla
c
e
d
the tra
d
itional
PI controller,
so
that we ca
n g
e
t two differe
nt simulation
diagram
s of speed respon
se.
c
b
a
s
s
s
,
,
a
i
b
i
d
c
U
s
i
s
e
T
s
U
*
e
T
*
IM
a
u
b
u
T
d
d
s
Figure 4.
The
Structure
Ch
art of the System
Figure 5.
The
New
Anti
-Wi
ndup PI Cont
rolle
r Simulati
on Dia
g
ra
m
5. Simulation and Experi
ment
5.1. The Simulation Re
su
lts
Motor
param
eters a
r
e li
sted a
s
follo
ws: th
e stat
or
re
sistan
ce
R
s
=2.5
, the rotor
resi
st
an
ce
R
r
=2.
7
, the
st
ator in
du
ctan
ce
L
s
=0.3
325
mH, the
roto
r indu
ctan
ce
L
r
=
L
s
= 0.33
25
mH,
the mutual
inducta
nce
L
m
= 0.319
4mH, the l
ogarith
m
ic
P
=2, the moment of inertia
J
=0.008
6kg.m
2
. PI para
m
eters is
sa
me in the t
w
o
cont
rolle
rs,
K
p
=1
，
K
i
=10. The i
n
te
gral
feedba
ck gai
n co
efficient
s in the n
e
w Anti-Win
dup
PI cont
rolle
r i
s
k
=0.95. Th
e
maximum o
u
tput
torque
of the motor is
T
ma
x
=10N.m, discrete
sam
p
lin
g peri
od is 5
0
s
. The stator flux linka
g
e
given value is
*
=
0
.8Wb.
Inductio
n
mo
tor is sta
r
ting
with no load
, but the load torque
will become 4
N
.m at 1s.
Speed i
s
0 at
the begin
n
in
g, then step t
o
400
rad/
s at
0.1s. Figu
re
6 is the resul
t
s of simul
a
tion
grap
hs. Fig
u
re 7 and Figu
re 8 are the p
a
rtial enla
r
ge
d figure
s
.
From
Figu
re
7 we
can
se
e that, tra
d
itional
PI
co
ntroller’
s ove
r
sh
oot am
ount
o
f
spe
e
d
respon
se
re
a
c
he
d 17.5%
and a
d
ju
stme
nt time is
0.6
s
, but the
ne
w Anti-Wind
u
p
PI cont
rolle
r is
almost
no ov
ershoot
amo
unt of spee
d
re
spo
n
se
an
d adju
s
tme
n
t time is
only
0.25s. F
r
om
the
simulatio
n
re
sults
can be see
n
,
the ne
w
Anti-Win
du
p PI controll
er’s
control p
e
rform
a
n
c
e
h
a
s
very obvious
advantag
e.
From
Figu
re
8 we can
se
e that, wh
en
the loa
d
tu
rns i
n
to 4
N
.m
, the two
cu
rves a
r
e
simila
r. Two t
y
pes of co
ntroller’
s ability to
resi
st load
disturban
ce i
s
almo
st the same.
q
TE
*
1
u
Su
m
P
P
r
o
por
t
i
on
al
1
s
I
n
t
egr
al
Ac
t
i
o
n
q&
q
If
A
c
t
i
o
n
Su
bs
y
s
tem
1
Ac
t
i
o
n
e&
q
If
A
c
t
i
o
n
S
ubs
y
s
t
e
m
u1
i
f
(
u1 ~
=
0)
el
s
e
If
2
1
e
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A New Anti-Wind
up PI Controlle
r for Direct To
rqu
e
Control Syste
m
(MIAO Jing-Li)
5273
Figure 6. Simulation Result
Figure 7. Partial Enlarg
ed
Grap
h of Spe
ed Step Re
sp
onse
Figure 8. Partial Enlarg
ed
Grap
h of Join
ing the Loa
d
5.2. Experimental Result
On
the ba
sis of
theoretical
analysi
s
a
nd digi
tal si
mulat
i
on, this
arti
cl
e ha
s
ca
rrie
d
on the
corre
s
p
ondin
g
expe
riment
al re
se
arch.
Experiment
system ad
opt
s the
spe
c
ial
motor control
digital sign
al pro
c
e
s
sor T
M
S320F2
812
as the co
ntroller. Pro
c
e
s
sor T
M
S320
F2812
with RS -
232 serial
co
mmuni
cation
ports
will be collecte
d
expe
rimental d
a
ta transmitted to the PC.
The motor p
a
ram
e
ters are the same.
The
stator flux linkage a
m
plitude to 0.8 Wb.
Speed given
value for 50 rad/s = 4
77.5
r/min. The loa
d
is abo
ut 1 N.m.
Figure 9 to
1
0
are the
experim
ental
re
sults.
T
he
experim
ental
re
sults and
si
mulation
results a
r
e co
nsi
s
tent. It validates
the
correctn
ess of th
is method.
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
7
0.
8
0.
9
1
1.1
1.2
1.
3
1.4
1.5
0
50
100
150
200
250
300
350
400
450
500
t/
s
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Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5268 – 52
74
5274
Figure 9. Experime
n
tal Re
sults of
Conve
n
tional
PI Controlle
r with Saturatio
n
Limits
Figure10. Experim
ental Result
s of Ne
w Anti-
Wind
up PI Controlle
r
6. Conclusio
n
The traditio
n
a
l PI controlle
r ha
s integ
r
al
saturation p
r
oblem, so this pap
er a
dop
ts a ne
w
type Anti-Wi
ndup PI con
t
roller. And the co
ndition
for the sta
b
ility of the
system i
s
given.
Simulation
an
d expe
rime
ntal re
sult
s
sho
w
that, th
e
ne
w Anti-Win
du
p PI controll
e
r
can
re
du
ce
or
even eliminat
e oversho
o
t amount of
sp
eed respon
se
, and sh
orten
s
adju
s
ting ti
me. At the sa
me
time, the co
ntrolle
r also
has the a
d
vantage
s o
f
simple structure and
easy to project
impleme
n
tation.
Referen
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hao F
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4.
0
1
2
3
4
5
0
10
20
30
40
50
60
S
p
e
e
d
/ra
d
/s
0
1
2
3
4
5
0
10
20
30
40
50
60
S
peed
/
r
ad/
s
Evaluation Warning : The document was created with Spire.PDF for Python.