TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 9, September
2014, pp. 65
7
3
~ 657
8
DOI: 10.115
9
1
/telkomni
ka.
v
12i9.461
5
6573
Re
cei
v
ed O
c
t
ober 3, 20
13;
Revi
se
d May 18, 2014; Accepte
d
Ju
ne
10, 2014
The Research on Control Method of Variable Speed
System of Permanent Magnet Synchronous Motor
Li Qian-Yu*
，
Zhang Rui-Ping
，
Xiong Jian
Sch
o
o
l
of A
u
to
mati
on & E
l
e
c
trica
l
En
gi
n
eer
in
g, La
nz
ho
u Ji
a
o
to
ng
Un
iver
sit
y
, L
a
n
zh
o
u
,Ch
i
na
*C
orre
sp
on
di
n
g
aut
hor,
e-m
a
i
l
:
lq
yzit
on
g@
16
3.com
Abstrac
t
In ord
e
r to so
lv
e the pr
o
b
l
e
m that th
e trad
iti
o
na
l
PI contr
o
l
l
e
r
can n
o
t meet
the h
i
g
h
p
e
rfor
manc
e
spe
e
d
c
ontr
o
l
r
e
q
u
ir
e
m
ent of per
ma
ne
nt ma
gn
et
sy
nc
hr
on
ou
s
mo
to
r, the
fu
z
z
y
con
t
rol
the
o
r
y i
s
app
li
ed
to
the speed loop of speed
control system
of per
m
anent
magnet sy
nchr
onous mo
tor,
and reali
z
ed t
h
e
par
a
m
eters
tu
n
i
n
g
in
re
al
ti
me
of PI
co
ntro
ll
er.
F
i
n
a
l
l
y,
by
me
ans
of
th
e s
i
mu
lati
o
n
exp
e
r
i
me
nt, th
e s
o
l
u
ti
o
n
verif
i
e
d
th
e n
e
w
fu
zz
y
PI c
ont
rol sy
ste
m
h
a
s
go
od r
o
b
u
st
nes
s to the sy
ste
m
loa
d
an
d d
i
stur
ba
nc
e.
Key
w
ords
:
p
e
rma
n
e
n
t
ma
gnet syn
ch
ron
o
u
s
mo
to
r,
p
a
r
am
e
t
e
r
s sel
f
reg
u
la
tin
g
,
fu
zz
y PI, rob
u
s
tn
ess
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.
Introduction
Sine-wave pe
rmanent mag
net synchron
ous mo
tor (P
MSM for short)has many features
like high po
wer factor, sim
p
le structure, high e
fficien
cy, small size, high powe
r
den
sity, hig
h
torque curre
nt, the moment of ine
r
tia is lo
w,
easy for h
e
a
t dissipatio
n
and
plann
ing
maintenance. In recent years, with the dev
elopment of microelectronic tech
nology, power
electronics, micro-comput
er technolog
y, s
ensor technology, rare earth permanent magnet
materials and
motor control theory, scholars begun
to
pay attention
to research a
nd application
of permanent
magnet synchronou
s moto
r control
sy
st
em [1-2]. Meanwhile, in th
e PMSM cont
rol
system, the conventional PI cont
rol can
not meet the requirement
s,
and it can
no
t achieve goo
d
control effect
desired.
According to the fuzzy the
o
ry, we use fuzzy
PI controller as a speed loop controller in
the whole sy
stem. And based on
the
simulation
experiments to
the system, we verified the
effective
and
feasible of th
is methoed.
2.
Vector Contr
o
l Theor
y
of
Permanent Magnet Sy
nc
hronous Motor
Esse
ntially, vector
control aimed at
the
motor
stator
curre
n
t
vector pha
se an
d
amplitude
co
ntrol. Thi
s
re
quire
s esta
bli
s
hme
n
t
of
dq
axis
mathe
m
atical
mod
e
l
of pe
rma
n
e
n
t
magnet syn
c
hron
ou
s moto
r [3]:
As can b
e
seen f
r
om th
e
mathe
m
ati
c
al mod
e
l, if the ex
citati
on
flux of perman
ent
mag
net
an
d
dire
ct-axis in
du
cta
n
ce,
cro
s
s-axi
s
i
ndu
ct
an
ce
i
s
d
e
te
rmine
d
, th
e m
o
tor to
rq
ue
ca
n
be d
e
te
rmi
n
e
d
by sp
a
c
e v
e
ct
or of
stato
r
curre
n
t is,
and th
e ma
g
n
itud
e a
nd p
h
a
s
e of i
s
a
r
e
dete
r
mi
ne
d b
y
id and iq, then it can b
e
said th
e mot
o
r to
rq
ue can
be co
ntroll
e
d
by co
ntrolli
ng
id an
d iq. An
y spe
ed
an
d torq
ue
corre
s
pon
d
s
to a
set of id*
and
iq*, by
co
ntro
lling t
h
e
s
e t
w
o
cu
rre
n
ts, t
h
e
act
ual
valu
e i
d
a
n
d
iq
woul
d tra
c
kin
g
th
e
in
stru
ctio
n v
a
lu
e id
*
an
d i
q
*, i
n
thi
s
wa
y,
we
re
ali
z
e
d
t
he m
o
to
r to
rq
ue a
nd
sp
ee
d
co
ntrol.
In thi
s
pa
pe
r,
we
use id
=0
co
ntrol
strate
gy. Co
ntrol
system i
s
sh
o
w
n i
n
Fi
gu
re
1 [4].
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 9, September 20
14: 65
73 – 657
8
6574
PI
Sp
ee
d
Co
nt
ro
ll
er
PI
Cu
rr
en
t
co
nt
ro
ll
er
In
ve
rs
e
Pa
rk
SV
PW
M
Th
re
e
-
ph
as
e
in
ve
rt
er
M
3~
Cl
ar
ke
Pa
rk
Po
si
ti
on
se
ns
or
Sp
ee
d
ca
lc
ul
at
i
o
n
Figure 1. PMSM Vector Control Structure
3. Design of
Fuzz
y
PI Controller
3.1. Th
e Bas
i
c Principl
e
of F
u
zzy
PI
Co
ntroller
Curre
n
tly, PI
regul
ator i
s
o
ne of the mo
st
widely u
s
ed
controlle
r, if the fun
c
tion of
input
error i
s
e
，
out
put function i
s
u
，
then th
e
time-dom
ain
expre
ssi
on
of the relatio
n
shi
p
betwe
en
e
and
u
can be written as [5]:
u
e
e
Where:
is pr
oportional coefficient,
is
in
tegral c
oeffic
i
ent,
1
/
,
is in
tegration
time c
ons
tant.
However, the
r
e are
some
thing wrong
with the con
t
rol quality o
f
PI control, in a
condition, the
PI paramete
r
s may be optimal, bu
t it may not be go
od in another condition. So
the traditional PI controller is not able to
meet
the d
y
namic require
m
ents of effe
ctive control.
Fuzzy PI controller is a combination of
conventional PI controller
and fuzzy co
ntrol
theory. In
this
paper, we de
signed a ‘2-in
put(input erro
r is e and error rate is
e
), 2-output(
and
)’ fuzzy PI controller as a speed regu
lator,
the
principle is shown in Figure 2 [6-7].
co
nv
en
tio
na
l
PI
c
on
tro
ll
e
r
PMS
M
D
riv
e
con
t
rol
sys
t
e
m
F
U
Z
Z
Y
q
u
a
n
t
i
z
a
t
i
o
n
FU
ZZ
Y
r
eas
o
nin
g
FU
ZZ
Y
d
eci
s
ion
Figure 2. Schematics of Fuzzy PI Controller
Through the
real-time detection and calculat
ion of speed of out
put data, we can
obtain the speed error
e
and change rat
e
of speed error
. We fuz
z
y
up
and
, a
n
d then
inputting
them into
fuzzy controller, by fu
zzy in
ference and de
fuzzification we can get
incremental o
f
PI controller
,
.
Self-tunin
g
controller p
a
rameters in
real time can be
realized throu
gh formula (1).
∆
K
∆
K
(1)
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TELKOM
NIKA
ISSN:
2302-4
046
The Re
se
arch on Co
ntrol
Method of Va
riabl
e Sp
eed
System
of Perm
anent… (L
i
Q
i
a
n
-
Y
u
)
6575
Where:
and
are original set parameters of PI controller, which
1
1
.
7
，
140
.
3.2. Th
e Cho
i
ce o
f
Univ
erse, Sc
aling
Fac
t
o
r
an
d
Qua
n
ti
zatio
n
Fac
t
o
r
The actual range of inputs
(error, erro
r
change rate)
and outputs (control variable) of
fuzzy controller is called basic universe o
f
variable.
We suppose the basic universe of error is
x
x
, the
basic universe of ch
ange rate of
error is
x
x
,
th
e basic universe of control volume
and
are
y
y
and
y
y
separately.
Let the basic universe of
fuzzy subset that error take is
，
, the
basic universe of fuzzy subset t
hat change rate of error take is
，
, the basic universe o
f
fuzzy subset that control vo
lume
and
tak
e
are
and
separately.
For fuzzy processing, input variables
need to be multiplied by the corresp
onding
quantization
factor, so th
e input variables fr
om th
e basi
c
universe
are
co
nverted to the
corre
spon
din
g
fuzzy universe. K
represents quantiza
t
ion factor ge
nerally, quantization factor
of
error is
, the
quantization factor of error
change rate is
, the
calculation
formula
is shown
as (2):
/
/
(2)
Similarly, control variable derived by fuzzy
control al
gorithm shoul
d operate wit
h
scale
factor, and th
en, they can
be converted
to a basi
c
uni
verse that a
control object
can a
cce
pt. The
scale factor of output control variable (
and
) are
and
.
the calculation formula is
shown a
s
(3):
/
/
(3)
Design
of fuzzy controlle
r, not only need
to have a good fuzzy control rul
e
, but a
reason
able choice of qua
ntization factor of fuzzy
controller inpu
t variable and scale facto
r
of
output control quantization
is also
very important. Th
ere are exper
iment conclusions shows that
the control e
ffect of fuzzy controller is influenc
ed
greatly by the size
of scale factor a
nd
quantization factor, and relative relationships of
size between different quantization factors.
3.3, Desi
gn
of F
u
zzy
Contr
o
l Rules
Fuzzy
control
rules are
ba
sed on lo
ng-st
anding experi
ence
and p
r
o
f
essional
kno
w
ledge
of operator, it is a langu
age rep
r
ese
n
tation wh
ich
reaso
n
ing i
n
accordan
ce with peopl
e's
perception. Fuzzy rules are usually connec
ted by a series of relative words.
The article ch
ooses
seven conventional word
s to describe input and out put
variables,
namely {positive big, positiv
e median,
positive small, zero
, negative small, negative median,
negative big}, abbreviated as {PB, PM,
PS, ZO, NS
, NM, NB}. If
the vocabulary is too small, it
will make the variable description be
comes
rough
, which led
to poor perf
ormance
of the
controller. But too much
vocabulary will make cont
rol
rules becom
e
so complex that brings rule
explosion pro
b
lem [10].
In the choice
of membership functions, in or
der to simplify
the calculation, the
article
uses triangle
as membe
r
sh
ip functions o
f
input
and ou
tput variables. Control rule
s are
sho
w
n i
n
Table 1, and
Table 2.
Table 1. Fu
zzy Control Rul
e
s of
∆
K
e
ec
NB
NM
NS
ZO
PS
PM
PB
NB
PB
PB
PM
PM
PS
ZO
ZO
NM
PB
PB
PM
PS
PS
ZO
NS
NS
PM
PM
PM
PS
ZO
NS
NS
ZO
PM
PM
PS
ZO
NS
NM
NM
PS
PS
PS
ZO
NS
NS
NM
NM
PM
PS
ZO
NS
NM
NM
NM
NB
PB
ZO
ZO
NM
NM
NM
NB
NB
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 9, September 20
14: 65
73 – 657
8
6576
Table 2. Fu
zzy Control Rul
e
s of
∆
K
e
ec
NB
NM
NS
ZO
PS
PM
PB
NB
NB
NB
NB
NB
NB
NB
NB
NM
NB
NB
NB
NB
NB
NB
NB
NS
NB
NB
NB
NB
NB
NM
NM
ZO
NB
NB
NB
NB
NM
NS
NS
PS
NB
NB
NB
NM
NM
NS
ZO
PM
NB
NB
NM
NM
NS
ZO
ZO
PB
NB
NB
NM
NS
NS
ZO
ZO
4
.
Simu
lat
i
o
n
Re
sea
rc
h
In the environ
ment of Matlab / Simulink,
the simul
a
tion
model of permanent ma
gn
et
synchro
nou
s motor
vecto
r
system
i
s
est
ablished, sho
w
n in Figu
re
3.
Figure 3. Vector Control Simulati
on Model of
PMSM
Based on Fuzzy
PI
Motor model
parameters shown in Table 3
：
Table 3.
P
a
ra
m
e
t
e
rs of PMSM
Mot
o
r p
a
r
am
et
ers
stat
or resist
anc
e Rs
2.8
75
Ώ
stat
or d
-
a
x
is in
du
ctanc
e
Ld
0.0
08
5H
m
o
me
nt
of
in
er
t
i
a J
0.0
08
Kg
·m
2
Exci
tati
on
fl
u
x
0.1
75W
b
stat
or q
-
a
x
is in
du
ctanc
e
Lq
0.0
08
5H
num
be
r
of
p
o
le
p
a
irs
p
1
In order to verify the performance
of t
he designed
system, the
article compa
r
ed the
fuzzy PI control with co
nventional PI con
t
rol. Simu
latio
n
time is
set to be 0.2
s
, the motor no
-loa
d
startup, the g
i
ven speed i
s
2000r/min,
when time
co
mes to 0.1s l
oaded 4
N • m. Simulation
waveforms sh
own in Figure 4-9.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
The Re
se
arch on Co
ntrol
Method of Va
riabl
e Sp
eed
System
of Perm
anent… (L
i
Q
i
a
n
-
Y
u
)
6577
Figure 4. Spe
ed Curve under the Fuzzy PI
Control
Figure 5. Spe
ed Curve under Conventional PI
Control
From the speed test results shown in Fi
gure 4 and Figure 5, we can see that the
regulating time of Fuzzy PI cont
roller system is shorter than the
traditional PI
control syste
m
obviously, an
d in the case of sudden load when the
time is 0.02s, the speed of fuzzy PI syste
m
almost have no disturban
ce and can
qu
ickly return
to
equilibrium. It follows that, the fuzzy PI
controller that
we
design
is much
better
than t
he conv
entional PI controller in re
sponse spee
d
and capacity of disturbance rejection.
Figure 6. stator 3-phase Current Waveforms
under the con
t
rol of
fuzzy PI controller
Figure 7. stator 3-phase Current Waveform
under the con
t
rol of conven
tional PI contr
o
lle
r
From the simulation results of three-phase st
ator cu
rrent waveform that F
i
gure 6 and
Figure 7 sho
w
s we can
see that under the contro
l o
f
the
fuzzy PI controller, th
e three-phase
stator cu
rrent
s is la
rge
after starting the
moto
r and
su
dden loading,
but soon
ach
i
eving stability,
and stability e
ffect is be
tter
than t
he
traditional PI control system.
Figure 8. Torque Waveform under the control
of fuz
z
y
P
i
c
ontroller
Figure 9. Torque Waveform under the
Control
of Convention
al PI Controller
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.1
8
0.2
0
50
0
100
0
150
0
200
0
250
0
t/s
n/
(
r
/
m
i
n
)
0
0.02
0.04
0.06
0.08
0.
1
0.12
0.14
0.16
0.
1
8
0.2
0
500
1
000
1
500
2
000
2
500
n/
(
r
/
m
i
n
)
t/
s
0
0.02
0.
0
4
0.06
0.08
0.1
0.
1
2
0.14
0.16
0.18
0.
2
-60
-40
-20
0
20
40
60
t/
s
i
sa
i
sb
i
sc
/A
0
0.
02
0.
04
0.
06
0.
08
0.
1
0.
12
0.
14
0.
16
0.
18
0.
2
-6
0
-4
0
-2
0
0
20
40
60
t/
s
i
sa
i
sb
i
sc
/A
0
0.02
0.04
0.06
0.
08
0.1
0.12
0.14
0.
16
0.18
0.2
-10
-5
0
5
10
15
t/
s
N
m
gq
(
)
0
0.0
2
0.0
4
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
-1
0
-5
0
5
10
15
t/
s
N
m
El
e
c
t
r
o
m
a
g
n
e
t
i
c
to
r
q
u
e
Te
(N
m
)
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 9, September 20
14: 65
73 – 657
8
6578
From the loa
d
torque waveform that F
i
gure
8 and Figure 9 shows we can see that both
the two syste
m
s have fluctuations
when starting, bu
t load torque
of fuzzy
PI control
system
back to 0 N • m quickly, wh
ile the load torque of c
onventional PI control sy
stem fluctuates ne
a
r
0 N • m, and
the pulse amplitude is greater; when
0.1s loaded 4 N • m,
the loa
d
torque of fu
zzy
PI control system restored
to 4 N • m qui
ckly, t
he traditional PI control sy
stem fluctuates near 4
N • m, and th
e pulse amplitude is greater.
5. Conclusio
n
Replace
spe
ed loop PI co
ntroller in the
permanent
magnet synchronou
s
mot
o
r vector
cont
rol sy
st
e
m
wit
h
f
u
zzy
P
I
cont
roller
，
there are outstanding advantages in making full use of
fuzzy control
in dealing wit
h
impreci
s
e a
nd comp
lex sys
tems
with
unc
ertain
c
o
ntrol objec
ts
. In
improving the speed control performan
ce of per
man
ent magnet synchronou
s
motor, the fu
zzy
PI control shows stro
nger
advantages
than PI control. Finally, simu
lation results sho
w
that, the
control syste
m
combined
with fuzzy co
ntrol t
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