SICE Annual Conference in Fukui, August 4-62003
Fukui University, Japan
MRAS Based Sensorless Control of Permanent Magnet
Synchronous Motor
Young Sam Kim, Sang Kyoon Kim and Young Ahn Kwon
Department of Electrical Engineering, Pusan National University, Pusan 609-735, Korea
yakwon@pusan.ac.!u
Abstract - Speed and torque controls of permanent magnet
saliency effects, artificial intelligence, direct control of
synchronous motors are usually attained by the application
torque and flux, and so on[l-4]. This paper proposes the
of position and speed sensors. However, speed and position
control strategy based on the MRAS(Mode1 Reference
sensors require the additional mounting space, reduce the
Adaptive System) in the sensorless control of a permanent
reliability in harsh environments and increase the cost of a
magnet synchronous motor. The MRAS algorithm is well-
motor. Therefore, many studies have been performed for the
known in the sensorless control of an induction motor, and
elimination of speed and position sensors. This paper
has been proved to be effective and physically clear[5-7].
investigates a novel speed sensorless control of a permanent
The MRAS algorithm is based on the comparison between
magnet synchronous motor. The proposed control strategy is
the outputs of two estimators. The error between the
based on the MRAS(Mode1 Reference Adaptive System)
estimated quantities obtained by the two models is used to
using the state observer model with the current error
drive a suitable adaptation mechanism which generates the
feedback and the magnet flux model as two models for the
estimated rotor speed. The MRAS proposed in this paper is
back-EMF estimation. The proposed algorithm is verified
using the state observer model with the current error
feedback and the magnet flux model as two models for the
through the simulation and experiment.
back-EMF estimation. The proposed algorithm is verified
Keywords : Permanent Magnet Synchronous Motor,
through the simulation and experiment.
Sensorless Control, Model Reference Adaptive System.
II.Mathematical Modeling of
I .Introduction
PMSM
The vector control in the speed and torque controlled ac
Fig. I shows the equivalent model of a permanent magnet
drive is widely used for a high performance application. The
synchronous motor. R, and L, in Fig. 1 indicate the
vector control of a permanent magnet synchronous motor is
equivalent resistance and inductance. Flux reference axes are
usually implemented through measuring the speed and
also shown in Fig. 1.
position. However, speed and position sensors require the
The stator voltage equations in the real axes may be
additional mounting space, reduce the reliability in harsh
expressed as
environments and increase the cost of a motor. Various
va =
control algorithms have been proposed for the elimination of
speed and position sensors: estimators using state equations,
= &i,
Luenberger or Kalman-filter observers, sliding mode control,
1632
Downloaded from http://www.elearnica.ir
i,
hv,
+d:
3 di,
+-La+e,
2 df
PR0001/03/0000-0132 F400 0 2003 SICE
3
and L, = - L , .
2
where R,=R,
e =--h&-- 0,K, sine,
dr
hw - U, K, case,
eb =-
dr
From ( I )
-
(3), d - and q - axis voltage equations in the
rotor reference frame with the rotating speed of m, may be
expressed as
vd, = &ids
did,
+ Ls ~ m Ls,iqs
Fig. 1 The Equivalent model of 3-phase PMSM
= 4 jh.r +
"bs
*
-
vq, =
vn
= & i,
4.C.+ L,-diqr +o,L3idv+ w, K,
bs
dt
(2)
3 dibs
= ,g ibx+ -&+eb3
2 dt
(12)
be expressed as
T = PKeiqs
dl
3
2
df
(11)
The electromagnetic torque in the rotor reference frame may
+-@er
=&iu+-&-
dr
(13)
(3)
di,
+e,
dt
where P is the number of poles.
The mechanical equation of a PMSM may be expressed as
where the back-EMFs of the phase windings induced from
T = JdY,
-+h+G
dt
the flux of the permanent magnet are as follows.
where J is the inertia coefficient andD is the friction
ea/
e =---w,KEsine,
df
(4)
coefficient, m m is the mechanical speed of the rotor, and
T, is the load torque.
(5)
@Cf
-
4
eh,=---m,KEsin(e,-n)
3
df
HI. MRAS Based Sensorless
Control
(6)
This paper proposes a novel sensorless control algorithm
de
where m7 = 2and K , is the back-EMF constant.
dt
From (1)
- (31,
a - and
P-
based on the M U S . In general the MRAS algorithm is
axis voltage equations in the
based on the comparison between the outputs of two
stationary reference frame fixed to the Stator may be
estimators. The error between the estimated quantities
expressed as
obtained by the two models is used to drive a suitable
adaptation mechanism which generates the estimated rotor
"m
= && + Ls-drh, +%
vB = &ib
df
speed. The MRAS algorithm is well-known in the sensorless
(7)
control of an induction motor, and has been proved to be
di
+ ~~2
+eb
dr
effective and physically clear[5-7]. The MRAS proposed in
(8)
1633
chis paper is using the state observer model with the current
error feedback and the magnet flux model as two models for
the back-EMF estimation.
A. State observer configuration
From (7) and (8). the state equations of the full order
observer in the stationw reference frame may be expressed
Fig. 2 Block diagram of the reduced order state observer
as
i = ~ i v +J + L
~ (is-is)
(15)
B. MRAS configuration
&=Ci
(16)
This paper proposes a novel sensorless control algorithm
where A means the estimated value, L is the observer gain
based on the M U S for the speed sensorless control of a
PMSM. The proposed MRAS is using the state observer
model of (17) and (18) and the magnet flux model of (9) and
( I O ) as two models for the back-EMF estimation. The rotor
speed is generated from the adaptation mechanism using the
error between the estimated quantities obtained by the two
models as follows:
where K , and K , are the gain constants,
i, and ips
are
the estimated values of back-EMFs in the state observer
model, and
Here, the estimated currents may be replaced by the
r,
and
5.are the estimated values of back-
EMFs in the magnet flux model.
measured currents, and the order of the observed states may
Fig. 3 shows the block diagram of the proposed M U S .
be reduced. This paper uses the reduced order observer
The proposed MRAS algorithm has a robust performance
which may be expressed as follows:
through combining the state observer model and the magnet
flux model.
w =I%-+ +DQ+GV,
(17)
i = l t +Lis
(18)
where
Model
;=[;,
F
d p , r , I?=[&,
3
G2y,
A,, -LA,, ,
Model
DsFL+A,,-LA,,,
ea,
GaB,-LB,.
Adaptive
Mechanism
Fig. 2 shows the block diagram of the reduced order state
Fig. 3 Block diagram of the proposed MRAS
observer for the back-EMF estimation.
1634
The overall system of the proposed sensorless control
algorithm is shown in Fig. 4.
-,~
B
....\.____..;
.........1....._;
...
i 1
......
.....
L"
i"I/.-...i
.........................
r.
~
.....
~
,_
__
E
_em
4
L
Fig. 4 Configuration of the overall system
...r...r......
Yam
...................L............
-
Iv.Simulation
~
E.flmntBp speed
TIMElrecl
The simulation has been performed for the verification of
the proposed control algorithm. Table 1 shows the
Fig. 5 Speed responses in the speed command of
specification of the permanent magnet synchronous motor
(a) 50 rpm (b) 200 rpm (c) I000 rpm
used in the simulation and experiment.
Fig. 6 and Fig. 7 show the speed responses in case of
Table 1 Motor specification
considering the parameter variations where the stator
Number ofpole
winding resistance is increased by 50% of the nominal value
Nominal eurrenl
Nominal p o r a
4.17mH
750 W
and the hack EMF constant is decreased by 20% of the
nominal value. The parameter vanations are applied in the
middle of the operation of 20"
Fig. 5 (a), (h) and (c) show the speed responses in the
and no-load. For the
comparison with the conventional state observer sensorless
speed commands of 50rpm, 200rpm and IOOOrpm and in the
conh-ol algorithm, the simulation is also performed under the
no load As shown in Fig. 5, the proposed sensorless control
same conditions. The simulation result shows an improved
algorithm has good speed responses in the low and high
and robust performance in the proposed sensorless control
speeds.
algorithm.
1635
algorithm has good speed responses in the low and high
speeds same as the simulation result.
Fig. 6 Speed responses in a stator resistance variation
( k , = I . 5 R s , 200 rpm)
(a) Proposed M U S (b) State observer
Fig. 7 Speed responses in a back-EMF constant
OM,, 200 rpm
variation (ie=
Fig. 8 Experimental speed responses in the speed
command of (a) 50 rpm (b) 200 rpm (c) 1000 rpm
(a) Proposed MRAS (b) State observer
.
V Experiments and Discussions
Fig. 9 and Fig. IO show the experimental speed responses
in case of considering the parameter variations where the
stator winding resistance is increased by 50% of the nominal
The experiments have been performed for the verification
of the proposed control algorithm. The microprocessor
value and the back EMF constant is decreased by 20% of the
system(80586/150MHz) is used for the digital processing of
nominal value. The parameter variations are applied in the
the proposed algorithm.
middle of the operation of 200rpm and no-load. For the
Fig. 8 (a), (b) and (c) show the experimental speed
comparison with the conventional state observer sensorless
responses in the speed commands of 50rpm, 200rpm and
control algorithm, the experiment is also performed under
IOOOrpm and in the no load. The proposed sensorless control
the same conditions. The experimental result shows an
1636
VI. Conclusions
improved and robust performance in the proposed sensorless
control algorithm.
This paper proposed a novel speed sensorless control
244
I
algorithm of a permanent magnet synchronous motor. The
proposed control algorithm is based on the MRAS using the
state observer model and the magnet flux model as two
models for the back-EMF estimation. The rotor speed is
generated from the adaptation mechanism using the error
between the estimated quantities obtained by the two models.
The simulation and experimental results indicate that the
proposed algorithm shows good speed responses in the low
and high speeds, and shows robust speed responses in the
stator resistance and back-EMF variations. Especially, the
proposed algorithm shows a better performance in the
parameter variation compared to the conventional algorithm.
W. References
(b)
Fig. 9 Experimental speed responses in a stator resistance
[I] Edited by K. Rajashekara, A. Kawamura and K. Matsuse,
variation(Ei, = I . s R , , ~ o o ~ ~ )
Sensorless Control of AC Motor Drives, IEEE Press,
(a) Proposed MRAS (b) State observer
1996.
[Z] J. Hole, "State of the Art of Controlled AC Drives
without Speed Sensors," Int. J. Electronics, Vol. 80,No.
2 , pp. 249-263, 1996.
[3] C. Ilas, A. Bettini, L. Ferraris, and F. Profumo,
"Comparison of Different Schemes without Shaft
Sensors for Field Oriented Control Drives," IEEE Proc.
IECON,pp. 1579-1588, 1994.
[4] P. Vas, Sensorless Vector and Direct Torque Confro/,
Oxford Univ. Press, 1998.
[SI C. Schauder, "Adaptive Speed Identification for Vector
Control of Induction Motors without Rotational
Transducers," IEEE Trans Ind Appl, Vol. 28, No. 5 , pp.
1054-106 I , 1992.
[6] F. 2. Peng and T. Fukao, "Robust Speed Identification
for Speed-Sensorless Vector Control of lnduction
Motors," IEEE Trans Ind Appl, Vol. 30, NOS, pp.
(b)
1234-1240, 1994.
Fig. I O Experimental speed responses in a hack-EMF
[7] Y. A. Kwon and D. W. Jin, "A Novel MRAS Based
constant variation (K#=o.sK,,ZOO y m
Speed Sensorless Control of lnduction Motor,"
(a) Proposed MRAS (b) State observer
IEEE Proc IECON, Vol.
1637
,pp. 933-938,1999.